Subgroups — #20261139

Order 6208.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15690809	C₂	1	2	yes	maximal
2	#15690744	C₂	1	1	yes	maximal, characteristic
3	#15690743	C₂	1	2	yes	maximal
4	C₈×Dic₉₇	C₂	1	1	yes	maximal, characteristic
5	#107×C₉₇	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₁₉₄	—	2	2	no	—
7	C₂×#11715895	C₂²	1	1	yes	characteristic
8	C₄⋊Dic₉₇	C₂²	1	2	yes	—
9	#13095490	—	2	2	no	—
10	C₄×Dic₉₇	C₂²	1	1	yes	characteristic
11	C₂×C₈×C₉₇	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×C₉₇	C₂²	1	2	yes	—
13	C₂×C₄×C₉₇	—	2	2	no	—
14	C₂×C₄×C₉₇	C₂³	1	1	yes	characteristic
15	C₂×Dic₉₇	—	2	2	no	—
16	C₂×Dic₉₇	D₄	1	1	yes	characteristic
17	C₂×Dic₉₇	D₄	1	1	yes	characteristic
18	Dic₁₉₄	—	4	4	no	—
19	C₈×C₉₇	Q₈	1	2	yes	complemented
20	#11715895	Q₈	1	2	yes	complemented
21	C₂²×C₉₇	C₂×D₄	1	1	yes	characteristic
22	C₄×C₉₇	—	4	2	no	—
23	C₄×C₉₇	C₂×Q₈	1	1	yes	characteristic
24	C₄×C₉₇	C₂×Q₈	1	1	yes	characteristic
25	Dic₉₇	—	4	2	no	—
26	Dic₉₇	D₈	1	2	yes	—
27	Dic₉₇	Q₁₆	1	2	yes	—
28	C₂×C₉₇	C₄⋊Q₈	1	1	yes	characteristic
29	C₂×C₉₇	C₂×D₈	1	1	yes	characteristic
30	C₂×C₉₇	C₂×Q₁₆	1	1	yes	characteristic
31	C₉₇	#500	1	1	yes	characteristic, complemented, Sylow
32	#500	—	97	1	no	maximal, Sylow
33	C₄⋊Q₈	—	97	2	no	—
34	#107	—	97	1	no	—
35	#107	—	97	2	no	—
36	#107	D₉₇	1	1	yes	characteristic
37	C₄×C₈	—	97	1	no	—
38	C₂×Q₈	—	194	2	no	—
39	C₂×C₈	—	97	1	no	—
40	C₂×C₈	C₂×D₉₇	1	1	yes	characteristic
41	C₄⋊C₄	—	97	2	no	—
42	C₄⋊C₄	—	194	2	no	—
43	C₄⋊C₄	C₂×D₉₇	1	2	yes	—
44	C₄²	—	97	1	no	—
45	Q₈	—	388	4	no	—
46	C₂×C₄	—	2	2	no	—
47	C₂×C₄	—	97	1	no	—
48	C₂×C₄	—	97	1	no	—
49	C₂×C₄	—	194	2	no	—
50	C₂×C₄	C₂²×D₉₇	1	1	yes	characteristic
51	C₈	—	97	2	no	—
52	C₈	Dic₁₉₄	1	2	yes	complemented
53	C₂²	D₄×D₉₇	1	1	yes	characteristic
54	C₄	—	4	2	no	—
55	C₄	—	97	2	no	—
56	C₄	—	97	2	no	—
57	C₄	—	388	2	no	—
58	C₄	Q₈×D₉₇	1	1	yes	characteristic
59	C₄	C₂×Dic₁₉₄	1	1	yes	characteristic
60	C₂	#15690809	1	1	yes	characteristic
61	C₂	D₈×D₉₇	1	1	yes	characteristic
62	C₂	Q₁₆×D₉₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₉₇
commutator	C₂×C₄×C₉₇	C₂³
Frattini	C₂×C₄	C₂²×D₉₇
Fitting	#107×C₉₇	C₂
socle	C₂²×C₉₇	C₂×D₄
hypercenter	#107	D₉₇
hypocenter	C₉₇	#500
LCS	G ▷ C₂×C₄×C₉₇ ▷ C₂×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

Complements

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

N	H ≅ G/N	type
19. C₈×C₉₇	Q₈	semidirect
20. #11715895	Q₈	semidirect
31. C₉₇	#500	semidirect
52. C₈	Dic₁₉₄	semidirect