Subgroups — #38763438

Order 25408.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27163171	C₂	1	1	yes	maximal, characteristic, complemented
2	#27163164	C₂	1	1	yes	maximal, characteristic, complemented
3	#27163115	C₂	1	1	yes	maximal, characteristic
4	C₄⋊#13097544	—	2	1	no	—
5	#20263734	—	2	1	no	—
6	#20263730	—	2	1	no	—
7	Dic₁₅₈₈	C₄	1	1	yes	characteristic, complemented
8	#20263719	—	2	1	no	—
9	C₈×D₃₉₇	C₂²	1	1	yes	characteristic
10	D₈×C₃₉₇	C₄	1	1	yes	characteristic, complemented
11	C₂×#13097544	—	4	1	no	—
12	Dic₇₉₄	—	2	1	no	—
13	C₂²⋊D₃₉₇	—	4	1	no	—
14	C₂×Dic₃₉₇	—	4	1	no	—
15	C₄×D₃₉₇	D₄	1	1	yes	characteristic
16	#15691787	D₄	1	1	yes	characteristic
17	D₄×C₃₉₇	—	2	1	no	—
18	C₈×C₃₉₇	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₃₉₇	—	4	1	no	—
20	C₂×D₃₉₇	D₈	1	1	yes	characteristic
21	#13097544	—	8	1	no	—
22	C₄×C₃₉₇	C₂²⋊C₄	1	1	yes	characteristic
23	Dic₃₉₇	—	4	1	no	—
24	Dic₃₉₇	SD₁₆	1	1	yes	characteristic
25	C₂×C₃₉₇	—	8	1	no	—
26	C₂×C₃₉₇	#102	1	1	yes	characteristic
27	D₃₉₇	—	2	1	no	—
28	C₃₉₇	#360	1	1	yes	characteristic, complemented, Sylow
29	#360	—	397	1	no	maximal, Sylow
30	#135	—	397	1	no	—
31	M₃₂	—	397	1	no	—
32	#106	—	397	1	no	—
33	#41	—	794	1	no	—
34	Q₁₆	—	397	1	no	—
35	SD₁₆	—	794	1	no	—
36	D₈	#13097544	1	1	yes	characteristic, complemented
37	C₂×C₈	—	397	1	no	—
38	C₄⋊C₄	—	794	1	no	—
39	C₁₆	—	794	1	no	—
40	Q₈	—	794	1	no	—
41	D₄	—	2	1	no	—
42	D₄	—	1588	1	no	—
43	C₂×C₄	—	1588	1	no	—
44	C₂×C₄	—	1588	1	no	—
45	C₂×C₄	—	397	1	no	—
46	C₈	—	397	1	no	—
47	C₈	C₂×#13097544	1	1	yes	characteristic
48	C₂²	—	4	1	no	—
49	C₂²	—	397	1	no	—
50	C₄	—	1588	1	no	—
51	C₄	—	3176	1	no	—
52	C₄	—	397	1	no	—
53	C₄	C₂²⋊#13097544	1	1	yes	characteristic
54	C₂	—	8	1	no	—
55	C₂	—	794	1	no	—
56	C₂	#27163158	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#27163158
commutator	C₈×C₃₉₇	C₂×C₄
Frattini	C₈	C₂×#13097544
Fitting	D₈×C₃₉₇	C₄
socle	C₂×C₃₉₇	#102
prime radical	#27163115	C₂
cosocle	C₈×D₃₉₇	C₂²
hypercenter	D₈	#13097544
hypocenter	C₃₉₇	#360
LCS	G ▷ C₈×C₃₉₇ ▷ C₄×C₃₉₇ ▷ C₂×C₃₉₇ ▷ C₃₉₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ D₈

Complements

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

N	H ≅ G/N	type
1. #27163171	C₂	semidirect
2. #27163164	C₂	semidirect
7. Dic₁₅₈₈	C₄	semidirect
10. D₈×C₃₉₇	C₄	semidirect
28. C₃₉₇	#360	semidirect
36. D₈	#13097544	semidirect

Maximal subgroups

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

subgroup	index
#27163171	2
#27163164	2
#27163115	2
#360	397