Subgroups — #89294

Order 448.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₇⋊C₃₂	C₂	1	2	yes	maximal, complemented
3	C₂×C₇×C₈	C₄	1	1	yes	characteristic
4	C₇×C₁₆	C₄	1	1	yes	characteristic
5	C₇×C₁₆	C₂²	1	1	yes	characteristic
6	M₆₄	—	7	1	no	maximal, Sylow
7	C₂×C₄×C₇	C₈	1	1	yes	characteristic
8	C₇×C₈	C₈	1	1	yes	characteristic
9	C₇×C₈	C₂×C₄	1	1	yes	characteristic
10	C₂×C₁₆	D₇	1	1	yes	characteristic
11	C₃₂	—	7	2	no	—
12	C₂²×C₇	C₁₆	1	1	yes	characteristic
13	C₄×C₇	C₁₆	1	1	yes	characteristic
14	C₄×C₇	C₂×C₈	1	1	yes	characteristic
15	C₂×C₈	Dic₇	1	1	yes	characteristic
16	C₁₆	Dic₇	1	1	yes	characteristic
17	C₁₆	C₂×D₇	1	1	yes	characteristic
18	C₂×C₇	—	2	1	no	—
19	C₂×C₇	C₂×C₁₆	1	1	yes	characteristic
20	C₂×C₄	C₇⋊C₈	1	1	yes	characteristic
21	C₈	C₇⋊C₈	1	1	yes	characteristic
22	C₈	C₂×Dic₇	1	1	yes	characteristic
23	C₇	M₆₄	1	1	yes	characteristic, complemented, Sylow
24	C₂²	C₇⋊C₁₆	1	1	yes	characteristic
25	C₄	C₇⋊C₁₆	1	1	yes	characteristic
26	C₄	C₂×C₇⋊C₈	1	1	yes	characteristic
27	C₂	—	2	1	no	—
28	C₂	C₂×C₇⋊C₁₆	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. C₇⋊C₃₂	C₂	semidirect
23. C₇	M₆₄	semidirect

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