Subgroups — #38762334

Order 25408.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃₁₇₆	C₂	1	1	yes	maximal, characteristic
2	#27163036	C₂	1	1	yes	maximal, characteristic, complemented
3	#108×C₃₉₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₅₈₈	—	2	1	no	—
5	D₃₁₇₆	—	2	1	no	—
6	D₃₁₇₆	C₄	1	2	yes	—
7	#20263706	—	2	1	no	—
8	M₁₆×C₃₉₇	—	2	1	no	—
9	C₂×C₈×C₃₉₇	C₂²	1	1	yes	characteristic
10	C₂²×D₃₉₇	—	4	1	no	—
11	D₁₅₈₈	—	2	2	no	—
12	D₁₅₈₈	—	4	1	no	—
13	C₂×C₄×C₃₉₇	D₄	1	1	yes	characteristic
14	C₈×C₃₉₇	—	4	1	no	—
15	C₈×C₃₉₇	C₂×C₄	1	1	yes	characteristic
16	C₈×C₃₉₇	D₄	1	1	yes	characteristic
17	C₂²×C₃₉₇	SD₁₆	1	1	yes	characteristic
18	C₂×D₃₉₇	—	4	2	no	—
19	C₂×D₃₉₇	—	8	2	no	—
20	C₄×C₃₉₇	C₂²⋊C₄	1	1	yes	characteristic
21	C₄×C₃₉₇	D₈	1	1	yes	characteristic
22	C₂×C₃₉₇	—	2	1	no	—
23	C₂×C₃₉₇	#102	1	1	yes	characteristic
24	D₃₉₇	—	8	2	no	—
25	C₃₉₇	#361	1	1	yes	characteristic, complemented, Sylow
26	#361	—	397	1	no	maximal, Sylow
27	C₂×D₈	—	397	1	no	—
28	M₃₂	—	397	1	no	—
29	#108	D₃₉₇	1	1	yes	characteristic, complemented
30	C₂×D₄	—	794	1	no	—
31	D₈	—	794	1	no	—
32	D₈	—	397	2	no	—
33	M₁₆	—	2	1	no	—
34	C₂×C₈	C₂×D₃₉₇	1	1	yes	characteristic
35	C₁₆	—	794	1	no	—
36	C₂³	—	1588	1	no	—
37	D₄	—	794	2	no	—
38	D₄	—	1588	1	no	—
39	C₂×C₄	C₂²⋊D₃₉₇	1	1	yes	characteristic
40	C₈	—	4	1	no	—
41	C₈	C₄×D₃₉₇	1	1	yes	characteristic
42	C₈	D₁₅₈₈	1	1	yes	characteristic
43	C₂²	—	1588	2	no	—
44	C₂²	—	3176	2	no	—
45	C₂²	#20263718	1	1	yes	characteristic
46	C₄	#20263708	1	1	yes	characteristic
47	C₄	#20263716	1	1	yes	characteristic
48	C₂	—	2	1	no	—
49	C₂	—	3176	2	no	—
50	C₂	#27163016	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#27163016
commutator	C₈×C₃₉₇	C₂×C₄
Frattini	C₂×C₈	C₂×D₃₉₇
Fitting	#108×C₃₉₇	C₂
socle	C₂×C₃₉₇	#102
prime radical	C₂×D₃₁₇₆	C₂
cosocle	C₂×C₈×C₃₉₇	C₂²
hypercenter	#108	D₃₉₇
hypocenter	C₃₉₇	#361
LCS	G ▷ C₈×C₃₉₇ ▷ C₄×C₃₉₇ ▷ C₂×C₃₉₇ ▷ C₃₉₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #108

Complements

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

N	H ≅ G/N	type
2. #27163036	C₂	semidirect
3. #108×C₃₉₇	C₂	semidirect
25. C₃₉₇	#361	semidirect
29. #108	D₃₉₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₃₁₇₆	2
#27163036	2
#108×C₃₉₇	2
#361	397