Subgroups — #38762886

Order 25408.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27163088	C₂	1	1	yes	maximal, characteristic, complemented
2	#27163017	C₂	1	4	yes	maximal, complemented
3	#27163007	C₂	1	1	yes	maximal, characteristic, complemented
4	#127×C₃₉₇	C₂	1	1	yes	maximal, characteristic
5	C₂×#15691787	C₂²	1	2	yes	—
6	C₄⋊Dic₃₉₇	C₂²	1	2	yes	—
7	#20263710	—	2	2	no	—
8	C₂×D₄×C₃₉₇	—	2	2	no	—
9	C₂×D₄×C₃₉₇	C₂²	1	2	yes	—
10	C₄²×C₃₉₇	C₂²	1	1	yes	characteristic
11	C₂×Dic₃₉₇	—	2	2	no	—
12	#15691787	—	2	2	no	—
13	C₂³×C₃₉₇	—	2	2	no	—
14	D₄×C₃₉₇	—	2	4	no	—
15	D₄×C₃₉₇	—	4	4	no	—
16	C₂×C₄×C₃₉₇	D₄	1	2	yes	—
17	C₂×C₄×C₃₉₇	C₂³	1	1	yes	characteristic
18	C₂²×C₃₉₇	—	4	2	no	—
19	C₂²×C₃₉₇	—	4	4	no	—
20	C₂²×C₃₉₇	C₂×D₄	1	1	yes	characteristic
21	C₄×C₃₉₇	—	2	2	no	—
22	C₄×C₃₉₇	#41	1	2	yes	—
23	Dic₃₉₇	—	4	2	no	—
24	C₂×C₃₉₇	—	8	2	no	—
25	C₂×C₃₉₇	#124	1	1	yes	characteristic
26	C₂×C₃₉₇	AGL(1,ℤ/8)	1	2	yes	—
27	C₃₉₇	#490	1	1	yes	characteristic, complemented, Sylow
28	#490	—	397	1	no	maximal, Sylow
29	#127	D₃₉₇	1	1	yes	characteristic
30	#125	—	397	1	no	—
31	#102	—	397	4	no	—
32	#97	—	397	1	no	—
33	C₂×D₄	—	2	2	no	—
34	C₂×D₄	C₂×D₃₉₇	1	2	yes	—
35	C₂×C₈	—	397	2	no	—
36	C₄⋊C₄	—	794	2	no	—
37	C₄⋊C₄	—	397	2	no	—
38	C₄²	C₂×D₃₉₇	1	1	yes	characteristic
39	C₂³	—	2	2	no	—
40	D₄	—	2	4	no	—
41	D₄	—	4	4	no	—
42	C₂×C₄	—	794	2	no	—
43	C₂×C₄	C₂²⋊D₃₉₇	1	2	yes	—
44	C₂×C₄	C₂²×D₃₉₇	1	1	yes	characteristic
45	C₈	—	794	2	no	—
46	C₂²	—	4	2	no	—
47	C₂²	—	4	4	no	—
48	C₂²	C₂×C₂²⋊D₃₉₇	1	1	yes	characteristic
49	C₄	—	2	2	no	—
50	C₄	—	1588	2	no	—
51	C₄	#20263730	1	2	yes	—
52	C₂	—	8	2	no	—
53	C₂	#27163083	1	1	yes	characteristic
54	C₂	#27163122	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₃₉₇
commutator, cosocle	C₂×C₄×C₃₉₇	C₂³
Frattini	C₂×C₄	C₂²×D₃₉₇
Fitting, prime radical	#127×C₃₉₇	C₂
socle	C₂²×C₃₉₇	C₂×D₄
hypercenter	#127	D₃₉₇
hypocenter	C₃₉₇	#490
LCS	G ▷ C₂×C₄×C₃₉₇ ▷ C₂×C₃₉₇ ▷ C₃₉₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #127

Complements

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

N	H ≅ G/N	type
1. #27163088	C₂	semidirect
2. #27163017	C₂	semidirect
3. #27163007	C₂	semidirect
27. C₃₉₇	#490	semidirect

Maximal subgroups

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

subgroup	index
#27163088	2
#27163017	2
#27163007	2
#127×C₃₉₇	2
#490	397