Subgroups — #20261143

Order 6208.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15690809	C₂	1	1	yes	maximal, characteristic
2	#15690801	C₂	1	1	yes	maximal, characteristic
3	#15690743	C₂	1	1	yes	maximal, characteristic
4	#15690742	C₂	1	1	yes	maximal, characteristic
5	#15690741	C₂	1	1	yes	maximal, characteristic
6	#15690720	C₂	1	1	yes	maximal, characteristic
7	#107×C₉₇	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₁₉₄	—	2	1	no	—
9	C₂×#11715895	C₂²	1	1	yes	characteristic
10	C₄⋊Dic₉₇	—	2	1	no	—
11	C₄⋊Dic₉₇	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₉₇	C₂²	1	1	yes	characteristic
13	#13095490	—	2	1	no	—
14	#13095490	—	2	1	no	—
15	C₄×Dic₉₇	C₂²	1	1	yes	characteristic
16	C₂×C₈×C₉₇	C₂²	1	1	yes	characteristic
17	C₄⋊C₄×C₉₇	C₂²	1	1	yes	characteristic
18	C₄⋊C₄×C₉₇	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₉₇	—	2	1	no	—
20	C₂×C₄×C₉₇	—	2	1	no	—
21	C₂×C₄×C₉₇	C₂³	1	1	yes	characteristic
22	C₂×Dic₉₇	—	2	1	no	—
23	C₂×Dic₉₇	—	2	1	no	—
24	C₂×Dic₉₇	D₄	1	1	yes	characteristic
25	C₂×Dic₉₇	D₄	1	1	yes	characteristic
26	Dic₁₉₄	—	4	2	no	—
27	C₈×C₉₇	Q₈	1	2	yes	complemented
28	#11715895	Q₈	1	2	yes	complemented
29	C₂²×C₉₇	C₂×D₄	1	1	yes	characteristic
30	C₄×C₉₇	—	4	1	no	—
31	C₄×C₉₇	—	4	1	no	—
32	C₄×C₉₇	C₂×Q₈	1	1	yes	characteristic
33	C₄×C₉₇	C₂×Q₈	1	1	yes	characteristic
34	Dic₉₇	—	2	1	no	—
35	Dic₉₇	—	2	1	no	—
36	Dic₉₇	—	4	1	no	—
37	Dic₉₇	—	4	1	no	—
38	C₂×C₉₇	C₄⋊Q₈	1	1	yes	characteristic
39	C₂×C₉₇	AGL(1,ℤ/8)	1	1	yes	characteristic
40	C₂×C₉₇	#137	1	1	yes	characteristic
41	C₉₇	#501	1	1	yes	characteristic, complemented, Sylow
42	#501	—	97	1	no	maximal, Sylow
43	C₄⋊Q₈	—	97	1	no	—
44	#125	—	97	1	no	—
45	#107	—	97	1	no	—
46	#107	D₉₇	1	1	yes	characteristic
47	#106	—	97	1	no	—
48	#106	—	97	1	no	—
49	#97	—	97	1	no	—
50	C₂×Q₈	—	194	1	no	—
51	C₂×C₈	—	97	1	no	—
52	C₂×C₈	C₂×D₉₇	1	1	yes	characteristic
53	C₄⋊C₄	—	97	1	no	—
54	C₄⋊C₄	—	97	1	no	—
55	C₄⋊C₄	—	194	1	no	—
56	C₄⋊C₄	—	194	1	no	—
57	C₄⋊C₄	—	194	1	no	—
58	C₄⋊C₄	C₂×D₉₇	1	1	yes	characteristic
59	C₄⋊C₄	C₂×D₉₇	1	1	yes	characteristic
60	C₄²	—	97	1	no	—
61	Q₈	—	388	2	no	—
62	C₂×C₄	—	2	1	no	—
63	C₂×C₄	—	2	1	no	—
64	C₂×C₄	—	97	1	no	—
65	C₂×C₄	—	97	1	no	—
66	C₂×C₄	—	194	1	no	—
67	C₂×C₄	—	194	1	no	—
68	C₂×C₄	C₂²×D₉₇	1	1	yes	characteristic
69	C₈	—	97	2	no	—
70	C₈	Dic₁₉₄	1	2	yes	complemented
71	C₂²	D₄×D₉₇	1	1	yes	characteristic
72	C₄	—	4	1	no	—
73	C₄	—	4	1	no	—
74	C₄	—	388	1	no	—
75	C₄	—	388	1	no	—
76	C₄	—	194	1	no	—
77	C₄	—	194	1	no	—
78	C₄	Q₈×D₉₇	1	1	yes	characteristic
79	C₄	C₂×Dic₁₉₄	1	1	yes	characteristic
80	C₂	#15690809	1	1	yes	characteristic
81	C₂	#15690834	1	1	yes	characteristic
82	C₂	#15690842	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	#501
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
27. C₈×C₉₇	Q₈	semidirect
28. #11715895	Q₈	semidirect
41. C₉₇	#501	semidirect
70. C₈	Dic₁₉₄	semidirect