Subgroups — #38744991

Order 25216.

116 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27161481	C₂	1	2	yes	maximal
2	#27160907	C₂	1	2	yes	maximal
3	#27160905	C₂	1	2	yes	maximal
4	C₄×C₁₆×C₁₉₇	C₂	1	1	yes	maximal, characteristic
5	#20263318	—	2	2	no	—
6	#20263260	C₂²	1	4	yes	—
7	#20263258	—	2	2	no	—
8	C₂×C₁₆×C₁₉₇	C₂²	1	1	yes	characteristic
9	C₂×C₁₆×C₁₉₇	C₂²	1	1	yes	characteristic
10	C₄×C₈×C₁₉₇	C₂²	1	1	yes	characteristic
11	C₄⋊Dic₁₉₇	—	2	4	no	—
12	#15691337	—	4	4	no	—
13	C₂×C₈×C₁₉₇	D₄	1	1	yes	characteristic
14	C₂×C₈×C₁₉₇	C₂³	1	1	yes	characteristic
15	C₄²×C₁₉₇	D₄	1	1	yes	characteristic
16	C₁₆×C₁₉₇	Q₈	1	2	yes	—
17	C₁₆×C₁₉₇	Q₈	1	2	yes	—
18	C₂×Dic₁₉₇	—	4	4	no	—
19	C₂×C₄×C₁₉₇	D₈	1	2	yes	—
20	C₂×C₄×C₁₉₇	C₂×D₄	1	1	yes	characteristic
21	C₈×C₁₉₇	Q₁₆	1	2	yes	—
22	C₈×C₁₉₇	C₂×Q₈	1	1	yes	characteristic
23	C₈×C₁₉₇	C₂×Q₈	1	1	yes	characteristic
24	C₂²×C₁₉₇	C₂×D₈	1	1	yes	characteristic
25	C₄×C₁₉₇	—	2	2	no	—
26	C₄×C₁₉₇	C₄⋊Q₈	1	1	yes	characteristic
27	C₄×C₁₉₇	C₂×Q₁₆	1	1	yes	characteristic
28	Dic₁₉₇	—	8	4	no	—
29	C₂×C₁₉₇	#500	1	1	yes	characteristic
30	C₂×C₁₉₇	#508	1	2	yes	—
31	C₁₉₇	#2253	1	1	yes	characteristic, complemented, Sylow
32	#2253	—	197	1	no	maximal, Sylow
33	#499	—	197	2	no	—
34	#367	—	197	2	no	—
35	#366	—	197	2	no	—
36	C₄×C₁₆	D₁₉₇	1	1	yes	characteristic
37	#125	—	394	2	no	—
38	C₂×C₁₆	C₂×D₁₉₇	1	1	yes	characteristic
39	C₂×C₁₆	C₂×D₁₉₇	1	1	yes	characteristic
40	#107	—	197	4	no	—
41	#106	—	394	2	no	—
42	C₄×C₈	C₂×D₁₉₇	1	1	yes	characteristic
43	C₂×C₈	D₇₈₈	1	1	yes	characteristic
44	C₂×C₈	C₂²×D₁₉₇	1	1	yes	characteristic
45	C₄⋊C₄	—	788	4	no	—
46	C₄⋊C₄	—	394	4	no	—
47	C₄²	D₇₈₈	1	1	yes	characteristic
48	C₁₆	Dic₃₉₄	1	2	yes	—
49	C₁₆	Dic₃₉₄	1	2	yes	—
50	C₂×C₄	—	788	4	no	—
51	C₂×C₄	D₁₅₇₆	1	2	yes	—
52	C₂×C₄	C₂×D₇₈₈	1	1	yes	characteristic
53	C₈	Dic₇₈₈	1	2	yes	—
54	C₈	C₂×Dic₃₉₄	1	1	yes	characteristic
55	C₈	C₂×Dic₃₉₄	1	1	yes	characteristic
56	C₂²	C₂×D₁₅₇₆	1	1	yes	characteristic
57	C₄	—	2	2	no	—
58	C₄	—	1576	4	no	—
59	C₄	#20263326	1	1	yes	characteristic
60	C₄	C₂×Dic₇₈₈	1	1	yes	characteristic
61	C₂	#27161484	1	1	yes	characteristic
62	C₂	#27161511	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₁₅₇₆
commutator, cosocle	C₂×C₈×C₁₉₇	C₂³
Frattini	C₂×C₈	C₂²×D₁₉₇
Fitting	C₄×C₁₆×C₁₉₇	C₂
socle, prime radical	C₂²×C₁₉₇	C₂×D₈
hypercenter	C₄×C₁₆	D₁₉₇
hypocenter	C₁₉₇	#2253
LCS	G ▷ C₂×C₈×C₁₉₇ ▷ C₄×C₁₉₇ ▷ C₂×C₁₉₇ ▷ C₁₉₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
31. C₁₉₇	#2253	semidirect

Maximal subgroups

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

subgroup	index
#27161481	2
#27160907	2
#27160905	2
C₄×C₁₆×C₁₉₇	2
#2253	197