Subgroups — #38762927

Order 25408.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27163096	C₂	1	2	yes	maximal
2	#27163030	C₂	1	4	yes	maximal
3	C₄×C₈×C₃₉₇	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₇₉₄	—	2	2	no	—
5	C₄⋊Dic₃₉₇	—	2	2	no	—
6	C₄⋊Dic₃₉₇	C₂²	1	4	yes	—
7	C₂×C₈×C₃₉₇	C₂²	1	2	yes	—
8	C₄²×C₃₉₇	C₂²	1	1	yes	characteristic
9	Dic₇₉₄	—	4	4	no	—
10	C₂×Dic₃₉₇	—	2	4	no	—
11	C₂×C₄×C₃₉₇	D₄	1	1	yes	characteristic
12	C₂×C₄×C₃₉₇	D₄	1	1	yes	characteristic
13	C₂×C₄×C₃₉₇	C₂³	1	1	yes	characteristic
14	C₈×C₃₉₇	Q₈	1	4	yes	complemented
15	C₂²×C₃₉₇	C₂×D₄	1	1	yes	characteristic
16	C₄×C₃₉₇	D₈	1	2	yes	—
17	C₄×C₃₉₇	Q₁₆	1	2	yes	—
18	C₄×C₃₉₇	C₂×Q₈	1	2	yes	—
19	Dic₃₉₇	—	4	4	no	—
20	C₂×C₃₉₇	C₄⋊Q₈	1	1	yes	characteristic
21	C₂×C₃₉₇	C₂×D₈	1	1	yes	characteristic
22	C₂×C₃₉₇	C₂×Q₁₆	1	1	yes	characteristic
23	C₃₉₇	#500	1	1	yes	characteristic, complemented, Sylow
24	#500	—	397	1	no	maximal, Sylow
25	C₄⋊Q₈	—	397	2	no	—
26	#107	—	397	4	no	—
27	C₄×C₈	D₃₉₇	1	1	yes	characteristic
28	C₂×Q₈	—	794	2	no	—
29	C₂×C₈	C₂×D₃₉₇	1	2	yes	—
30	C₄⋊C₄	—	794	2	no	—
31	C₄⋊C₄	—	397	4	no	—
32	C₄²	C₂×D₃₉₇	1	1	yes	characteristic
33	Q₈	—	1588	4	no	—
34	C₂×C₄	—	794	4	no	—
35	C₂×C₄	D₁₅₈₈	1	1	yes	characteristic
36	C₂×C₄	D₁₅₈₈	1	1	yes	characteristic
37	C₂×C₄	C₂²×D₃₉₇	1	1	yes	characteristic
38	C₈	Dic₇₉₄	1	4	yes	complemented
39	C₂²	C₂×D₁₅₈₈	1	1	yes	characteristic
40	C₄	—	1588	4	no	—
41	C₄	D₃₁₇₆	1	2	yes	—
42	C₄	Dic₁₅₈₈	1	2	yes	—
43	C₄	C₂×Dic₇₉₄	1	2	yes	—
44	C₂	#27163096	1	1	yes	characteristic
45	C₂	C₂×D₃₁₇₆	1	1	yes	characteristic
46	C₂	C₂×Dic₁₅₈₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₁₅₈₈
commutator, cosocle	C₂×C₄×C₃₉₇	C₂³
Frattini	C₂×C₄	C₂²×D₃₉₇
Fitting	C₄×C₈×C₃₉₇	C₂
socle, prime radical	C₂²×C₃₉₇	C₂×D₄
hypercenter	C₄×C₈	D₃₉₇
hypocenter	C₃₉₇	#500
LCS	G ▷ C₂×C₄×C₃₉₇ ▷ C₂×C₃₉₇ ▷ C₃₉₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
14. C₈×C₃₉₇	Q₈	semidirect
23. C₃₉₇	#500	semidirect
38. C₈	Dic₇₉₄	semidirect

Maximal subgroups

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

subgroup	index
#27163096	2
#27163030	2
C₄×C₈×C₃₉₇	2
#500	397