Subgroups — #38762891

Order 25408.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27163096	C₂	1	1	yes	maximal, characteristic
2	#27163088	C₂	1	1	yes	maximal, characteristic
3	#27163021	C₂	1	4	yes	maximal
4	#97×C₃₉₇	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₇₉₄	C₂²	1	2	yes	—
6	C₄⋊Dic₃₉₇	—	2	2	no	—
7	C₄⋊Dic₃₉₇	C₂²	1	2	yes	—
8	#20263710	—	2	2	no	—
9	C₂×C₈×C₃₉₇	C₂²	1	2	yes	—
10	C₄²×C₃₉₇	C₂²	1	1	yes	characteristic
11	Dic₇₉₄	—	2	4	no	—
12	C₂×Dic₃₉₇	—	2	2	no	—
13	C₂×Dic₃₉₇	—	2	2	no	—
14	C₂×C₄×C₃₉₇	D₄	1	2	yes	—
15	C₂×C₄×C₃₉₇	C₂³	1	1	yes	characteristic
16	C₈×C₃₉₇	—	2	2	no	—
17	C₂²×C₃₉₇	C₂×D₄	1	1	yes	characteristic
18	C₄×C₃₉₇	—	2	2	no	—
19	C₄×C₃₉₇	#41	1	2	yes	—
20	Dic₃₉₇	—	4	2	no	—
21	Dic₃₉₇	—	4	2	no	—
22	C₂×C₃₉₇	#124	1	1	yes	characteristic
23	C₂×C₃₉₇	#137	1	2	yes	—
24	C₃₉₇	#491	1	1	yes	characteristic, complemented, Sylow
25	#491	—	397	1	no	maximal, Sylow
26	C₄⋊Q₈	—	397	1	no	—
27	#125	—	397	1	no	—
28	#103	—	397	4	no	—
29	#97	D₃₉₇	1	1	yes	characteristic
30	C₂×Q₈	—	397	2	no	—
31	C₂×C₈	C₂×D₃₉₇	1	2	yes	—
32	C₄⋊C₄	—	794	2	no	—
33	C₄⋊C₄	—	794	2	no	—
34	C₄⋊C₄	—	397	2	no	—
35	C₄²	C₂×D₃₉₇	1	1	yes	characteristic
36	Q₈	—	794	4	no	—
37	C₂×C₄	—	794	2	no	—
38	C₂×C₄	—	794	2	no	—
39	C₂×C₄	D₁₅₈₈	1	2	yes	—
40	C₂×C₄	C₂²×D₃₉₇	1	1	yes	characteristic
41	C₈	—	2	2	no	—
42	C₂²	C₂×D₁₅₈₈	1	1	yes	characteristic
43	C₄	—	2	2	no	—
44	C₄	—	1588	2	no	—
45	C₄	—	1588	2	no	—
46	C₄	#20263731	1	2	yes	—
47	C₂	#27163084	1	1	yes	characteristic
48	C₂	#27163129	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₁₅₈₈
commutator, cosocle	C₂×C₄×C₃₉₇	C₂³
Frattini	C₂×C₄	C₂²×D₃₉₇
Fitting	#97×C₃₉₇	C₂
socle, prime radical	C₂²×C₃₉₇	C₂×D₄
hypercenter	#97	D₃₉₇
hypocenter	C₃₉₇	#491
LCS	G ▷ C₂×C₄×C₃₉₇ ▷ C₂×C₃₉₇ ▷ C₃₉₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

Complements

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

N	H ≅ G/N	type
24. C₃₉₇	#491	semidirect

Maximal subgroups

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

subgroup	index
#27163096	2
#27163088	2
#27163021	2
#97×C₃₉₇	2
#491	397