Input Pilih dan tombol pada baris yang sama

<div class="form-inline">
    <div class="form-group">
        <div class="input-group">
            <input type="text" class="form-control" v-model="ClienteBusca.value" placeholder="Buscar cliente">
            <span class="input-group-btn">
                <button type="button" v-on:click.prevent="buscarCliente" class="btn btn-primary">Buscar</button>
            </span>
        </div>
    </div>
    <div class="form-group">
        <select class="form-control" id="selectedCliente">
            <option v-for="cliente in Clientes" v-bind:value="cliente">{{cliente.nome}}</option>
        </select>
    </div>
</div>
Cruel Capybara