Subgroups — #89338

Order 448.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#125	C₂	1	1	yes	maximal, characteristic
2	#6377	C₂	1	2	yes	maximal
3	C₇×C₄⋊C₄	—	2	2	no	—
4	C₇×C₄⋊C₄	C₄	1	2	yes	—
5	C₄²×C₇	C₂²	1	1	yes	characteristic
6	C₂×C₇⋊C₈	—	2	2	no	—
7	#330	—	7	1	no	maximal, Sylow
8	C₂×C₄×C₇	—	2	2	no	—
9	C₂×C₄×C₇	C₂×C₄	1	1	yes	characteristic
10	C₂×C₄×C₇	D₄	1	2	yes	—
11	C₇⋊C₈	—	2	4	no	—
12	#125	D₇	1	1	yes	characteristic
13	#97	—	7	2	no	—
14	C₂²×C₇	C₂²⋊C₄	1	1	yes	characteristic
15	C₄×C₇	—	2	1	no	—
16	C₄×C₇	—	2	2	no	—
17	C₄×C₇	—	4	2	no	—
18	C₂×C₈	—	14	2	no	—
19	C₄⋊C₄	—	2	2	no	—
20	C₄⋊C₄	Dic₇	1	2	yes	—
21	C₄²	C₂×D₇	1	1	yes	characteristic
22	C₂×C₇	#101	1	1	yes	characteristic
23	C₂×C₇	#104	1	2	yes	—
24	C₂×C₄	—	2	2	no	—
25	C₂×C₄	C₂×Dic₇	1	1	yes	characteristic
26	C₂×C₄	C₂²⋊D₇	1	2	yes	—
27	C₈	—	14	4	no	—
28	C₇	#330	1	1	yes	characteristic, complemented, Sylow
29	C₂²	C₂²⋊Dic₇	1	1	yes	characteristic
30	C₄	—	2	1	no	—
31	C₄	—	2	2	no	—
32	C₄	—	4	2	no	—
33	C₂	#6410	1	1	yes	characteristic
34	C₂	#6411	1	2	yes	—

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

N	H ≅ G/N	type
28. C₇	#330	semidirect

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