Subgroups — #38762347

Order 25408.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20263706	C₂	1	1	yes	maximal, characteristic
2	#27163030	C₂	1	1	yes	maximal, characteristic
3	#107×C₃₉₇	C₂	1	1	yes	maximal, characteristic
4	C₄⋊Dic₃₉₇	—	2	1	no	—
5	#20263706	C₄	1	2	yes	complemented
6	C₂×C₈×C₃₉₇	C₂²	1	1	yes	characteristic
7	C₄⋊C₄×C₃₉₇	—	2	1	no	—
8	C₂×Dic₃₉₇	—	4	1	no	—
9	C₂×C₄×C₃₉₇	—	4	1	no	—
10	C₂×C₄×C₃₉₇	D₄	1	1	yes	characteristic
11	C₈×C₃₉₇	C₂×C₄	1	1	yes	characteristic
12	C₈×C₃₉₇	Q₈	1	1	yes	characteristic
13	C₂²×C₃₉₇	D₈	1	1	yes	characteristic
14	C₄×C₃₉₇	—	8	1	no	—
15	C₄×C₃₉₇	C₄⋊C₄	1	1	yes	characteristic
16	C₄×C₃₉₇	Q₁₆	1	1	yes	characteristic
17	Dic₃₉₇	—	8	1	no	—
18	C₂×C₃₉₇	#107	1	1	yes	characteristic
19	C₂×C₃₉₇	D₁₆	1	1	yes	characteristic
20	C₂×C₃₉₇	Q₃₂	1	1	yes	characteristic
21	C₃₉₇	#366	1	1	yes	characteristic, complemented, Sylow
22	#366	—	397	1	no	maximal, Sylow
23	C₂×C₁₆	—	397	1	no	—
24	#107	—	397	1	no	—
25	#107	D₃₉₇	1	1	yes	characteristic
26	C₂×C₈	C₂×D₃₉₇	1	1	yes	characteristic
27	C₄⋊C₄	—	2	1	no	—
28	C₄⋊C₄	—	794	1	no	—
29	C₁₆	—	397	2	no	—
30	C₂×C₄	—	4	1	no	—
31	C₂×C₄	—	1588	1	no	—
32	C₂×C₄	C₂²⋊D₃₉₇	1	1	yes	characteristic
33	C₈	C₄×D₃₉₇	1	1	yes	characteristic
34	C₈	Dic₇₉₄	1	1	yes	characteristic
35	C₂²	#20263716	1	1	yes	characteristic
36	C₄	—	8	1	no	—
37	C₄	—	3176	1	no	—
38	C₄	#20263710	1	1	yes	characteristic
39	C₄	#20263721	1	1	yes	characteristic
40	C₂	#27163029	1	1	yes	characteristic
41	C₂	#27163037	1	1	yes	characteristic
42	C₂	#27163042	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#20263716
commutator	C₈×C₃₉₇	C₂×C₄
Frattini	C₂×C₈	C₂×D₃₉₇
Fitting	#107×C₃₉₇	C₂
socle, prime radical	C₂²×C₃₉₇	D₈
cosocle	C₂×C₈×C₃₉₇	C₂²
hypercenter	#107	D₃₉₇
hypocenter	C₃₉₇	#366
LCS	G ▷ C₈×C₃₉₇ ▷ C₄×C₃₉₇ ▷ C₂×C₃₉₇ ▷ C₃₉₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #107

Complements

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

N	H ≅ G/N	type
5. #20263706	C₄	semidirect
21. C₃₉₇	#366	semidirect

Maximal subgroups

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

subgroup	index
C₂×#20263706	2
#27163030	2
#107×C₃₉₇	2
#366	397