Subgroups — #89261

Order 448.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#97	C₂	1	1	yes	maximal, characteristic
2	#6386	C₂	1	2	yes	maximal
3	C₂×C₇×C₈	C₄	1	1	yes	characteristic
4	C₂×C₇×C₈	C₂²	1	1	yes	characteristic
5	C₄²×C₇	C₄	1	1	yes	characteristic
6	C₇⋊C₁₆	C₄	1	4	yes	complemented
7	#347	—	7	1	no	maximal, Sylow
8	C₂×C₄×C₇	—	2	1	no	—
9	C₂×C₄×C₇	C₂×C₄	1	1	yes	characteristic
10	C₇×C₈	—	2	1	no	—
11	C₇×C₈	C₂×C₄	1	2	yes	—
12	M₃₂	—	7	2	no	—
13	#97	D₇	1	1	yes	characteristic
14	C₂²×C₇	M₁₆	1	1	yes	characteristic
15	C₄×C₇	—	4	1	no	—
16	C₄×C₇	C₄²	1	1	yes	characteristic
17	C₄×C₇	M₁₆	1	1	yes	characteristic
18	C₂×C₈	Dic₇	1	1	yes	characteristic
19	C₂×C₈	C₂×D₇	1	1	yes	characteristic
20	C₄²	Dic₇	1	1	yes	characteristic
21	C₁₆	—	7	4	no	—
22	C₂×C₇	—	2	1	no	—
23	C₂×C₇	#97	1	1	yes	characteristic
24	C₂×C₄	—	2	1	no	—
25	C₂×C₄	C₂×Dic₇	1	1	yes	characteristic
26	C₈	—	2	1	no	—
27	C₈	C₄×D₇	1	2	yes	—
28	C₇	#347	1	1	yes	characteristic, complemented, Sylow
29	C₂²	#1136	1	1	yes	characteristic
30	C₄	—	4	1	no	—
31	C₄	#1136	1	1	yes	characteristic
32	C₄	C₄×Dic₇	1	1	yes	characteristic
33	C₂	—	2	1	no	—
34	C₂	#6377	1	1	yes	characteristic

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

N	H ≅ G/N	type
6. C₇⋊C₁₆	C₄	semidirect
28. C₇	#347	semidirect

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