Subgroups — #38763569

Order 25408.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27163183	C₂	1	2	yes	maximal, complemented
2	#27163166	C₂	1	1	yes	maximal, characteristic, complemented
3	#27163160	C₂	1	2	yes	maximal, complemented
4	#27163150	C₂	1	1	yes	maximal, characteristic, complemented
5	#27163115	C₂	1	1	yes	maximal, characteristic
6	#20263741	C₂²	1	2	yes	—
7	#20263740	—	2	2	no	—
8	D₃₉₇⋊C₈	C₂²	1	1	yes	characteristic
9	C₂×#15691794	—	2	2	no	—
10	C₄×#13097544	C₂²	1	1	yes	characteristic
11	#20263730	C₂²	1	2	yes	—
12	Dic₁₅₈₈	C₄	1	1	yes	characteristic, complemented
13	#20263719	C₄	1	2	yes	complemented
14	C₈×D₃₉₇	C₂²	1	1	yes	characteristic
15	D₈×C₃₉₇	C₄	1	1	yes	characteristic, complemented
16	C₂×#13097544	—	2	1	no	—
17	#15691794	—	2	2	no	—
18	#15691794	D₄	1	2	yes	—
19	Dic₇₉₄	C₂×C₄	1	2	yes	—
20	C₂²⋊D₃₉₇	—	2	2	no	—
21	C₂×Dic₃₉₇	—	2	2	no	—
22	C₄×D₃₉₇	C₂³	1	1	yes	characteristic
23	#15691787	C₂×C₄	1	1	yes	characteristic
24	D₄×C₃₉₇	C₂×C₄	1	2	yes	—
25	C₈×C₃₉₇	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₃₉₇	—	2	2	no	—
27	C₂×D₃₉₇	#41	1	1	yes	characteristic
28	#13097544	—	4	1	no	—
29	C₄×C₃₉₇	C₂²×C₄	1	1	yes	characteristic
30	Dic₃₉₇	—	2	2	no	—
31	Dic₃₉₇	C₂×D₄	1	1	yes	characteristic
32	C₂×C₃₉₇	—	4	2	no	—
33	C₂×C₃₉₇	C₄×D₄	1	1	yes	characteristic
34	D₃₉₇	—	2	1	no	—
35	C₃₉₇	#444	1	1	yes	characteristic, complemented, Sylow
36	#444	—	397	1	no	maximal, Sylow
37	#135	—	397	1	no	—
38	#131	—	397	2	no	—
39	#108	—	397	1	no	—
40	#104	—	397	2	no	—
41	#97	—	397	1	no	—
42	#41	—	397	2	no	—
43	Q₁₆	—	397	1	no	—
44	SD₁₆	—	397	2	no	—
45	D₈	#13097544	1	1	yes	characteristic, complemented
46	M₁₆	—	794	2	no	—
47	M₁₆	—	397	2	no	—
48	C₂×C₈	—	794	2	no	—
49	C₂×C₈	—	397	1	no	—
50	C₂×C₈	—	397	1	no	—
51	C₄²	—	397	1	no	—
52	Q₈	—	397	2	no	—
53	D₄	—	794	2	no	—
54	D₄	C₂×#13097544	1	2	yes	—
55	C₂×C₄	—	794	2	no	—
56	C₂×C₄	—	794	1	no	—
57	C₂×C₄	—	397	1	no	—
58	C₈	—	794	2	no	—
59	C₈	—	397	2	no	—
60	C₈	—	397	1	no	—
61	C₈	C₂×#13097544	1	1	yes	characteristic
62	C₂²	—	2	2	no	—
63	C₂²	—	397	1	no	—
64	C₄	—	794	2	no	—
65	C₄	—	1588	1	no	—
66	C₄	—	397	1	no	—
67	C₄	C₂²×#13097544	1	1	yes	characteristic
68	C₂	—	4	2	no	—
69	C₂	—	794	1	no	—
70	C₂	D₄×#13097544	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×#13097544
commutator	C₄×C₃₉₇	C₂²×C₄
Frattini	C₄	C₂²×#13097544
Fitting	D₈×C₃₉₇	C₄
socle	C₂×C₃₉₇	C₄×D₄
prime radical	#27163115	C₂
cosocle	C₄×D₃₉₇	C₂³
hypercenter	D₈	#13097544
hypocenter	C₃₉₇	#444
LCS	G ▷ C₄×C₃₉₇ ▷ C₂×C₃₉₇ ▷ C₃₉₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ D₈

Complements

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

N	H ≅ G/N	type
1. #27163183	C₂	semidirect
2. #27163166	C₂	semidirect
3. #27163160	C₂	semidirect
4. #27163150	C₂	semidirect
12. Dic₁₅₈₈	C₄	semidirect
13. #20263719	C₄	semidirect
15. D₈×C₃₉₇	C₄	semidirect
35. C₃₉₇	#444	semidirect
45. D₈	#13097544	semidirect

Maximal subgroups

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

subgroup	index
#27163183	2
#27163166	2
#27163160	2
#27163150	2
#27163115	2
#444	397