Subgroups — C₄×C₇×A₄ #66699

Order 336.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×A₄	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×C₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇×A₄	C₄	1	1	yes	characteristic, direct product factor
4	C₃×C₄×C₇	—	4	1	no	maximal
5	C₂³×C₇	C₂×C₃	1	1	yes	characteristic
6	C₂×C₄×C₇	—	3	1	no	—
7	C₂×C₄×C₇	—	3	1	no	—
8	C₄×A₄	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₇	—	4	1	no	—
10	C₂²×C₇	—	3	1	no	—
11	C₂²×C₇	—	3	1	no	—
12	C₂²×C₇	C₃×C₄	1	1	yes	characteristic, complemented
13	C₄×C₇	—	3	1	no	—
14	C₄×C₇	A₄	1	1	yes	characteristic, direct product factor
15	C₂×A₄	C₂×C₇	1	1	yes	characteristic
16	C₃×C₇	—	4	1	no	Hall
17	C₂²×C₄	C₃×C₇	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₇	—	3	1	no	—
19	C₂×C₇	—	3	1	no	—
20	C₂×C₇	C₂×A₄	1	1	yes	characteristic
21	A₄	C₄×C₇	1	1	yes	characteristic, direct product factor
22	C₃×C₄	—	4	1	no	—
23	C₂³	C₂×C₃×C₇	1	1	yes	characteristic
24	C₂×C₄	—	3	1	no	—
25	C₂×C₄	—	3	1	no	—
26	C₇	C₄×A₄	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₃	—	4	1	no	—
28	C₂²	—	3	1	no	—
29	C₂²	—	3	1	no	—
30	C₂²	C₃×C₄×C₇	1	1	yes	characteristic, complemented
31	C₄	—	3	1	no	—
32	C₄	C₇×A₄	1	1	yes	characteristic, direct product factor
33	C₃	—	4	1	no	Sylow
34	C₂	—	3	1	no	—
35	C₂	—	3	1	no	—
36	C₂	C₂×C₇×A₄	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.