Subgroups — #20260866

Order 6208.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#11715895	C₂	1	1	yes	maximal, characteristic
2	C₄⋊#11715895	C₂	1	2	yes	maximal
3	#15690721	C₂	1	2	yes	maximal
4	C₄×#11715895	C₂	1	1	yes	maximal, characteristic
5	C₄×Q₈×C₉₇	C₂	1	1	yes	maximal, characteristic
6	C₂×#11715895	C₂²	1	1	yes	characteristic
7	C₂×#11715895	C₂²	1	2	yes	—
8	C₂×#11715895	C₂²	1	1	yes	characteristic
9	C₂×Q₈×C₉₇	C₄	1	1	yes	characteristic
10	C₄⋊C₄×C₉₇	C₄	1	2	yes	—
11	C₄⋊C₄×C₉₇	C₄	1	1	yes	characteristic
12	C₄²×C₉₇	C₂²	1	1	yes	characteristic
13	C₄²×C₉₇	C₂²	1	2	yes	—
14	Q₈×C₉₇	—	2	2	no	—
15	C₂×C₄×C₉₇	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₉₇	C₂×C₄	1	2	yes	—
17	C₂×C₄×C₉₇	C₂×C₄	1	2	yes	—
18	C₂×C₄×C₉₇	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄×C₉₇	C₂³	1	1	yes	characteristic
20	#11715895	—	2	1	no	—
21	#11715895	—	2	2	no	—
22	#11715895	Q₈	1	2	yes	complemented
23	C₂²×C₉₇	C₂²×C₄	1	1	yes	characteristic
24	C₄×C₉₇	—	2	2	no	—
25	C₄×C₉₇	—	2	1	no	—
26	C₄×C₉₇	—	2	2	no	—
27	C₄×C₉₇	M₁₆	1	2	yes	—
28	C₄×C₉₇	C₂×Q₈	1	1	yes	characteristic
29	C₄×C₉₇	#41	1	1	yes	characteristic
30	C₂×C₉₇	C₄×Q₈	1	1	yes	characteristic
31	C₂×C₉₇	C₂×M₁₆	1	1	yes	characteristic
32	C₂×C₉₇	#131	1	1	yes	characteristic
33	C₉₇	#446	1	1	yes	characteristic, complemented, Sylow
34	#446	—	97	1	no	maximal, Sylow
35	C₄×Q₈	D₉₇	1	1	yes	characteristic
36	C₄⋊C₈	—	97	1	no	—
37	C₄⋊C₈	—	97	2	no	—
38	#97	—	97	2	no	—
39	C₄×C₈	—	97	1	no	—
40	C₂×Q₈	Dic₉₇	1	1	yes	characteristic
41	C₂×C₈	—	97	1	no	—
42	C₂×C₈	—	97	1	no	—
43	C₂×C₈	—	97	2	no	—
44	C₄⋊C₄	Dic₉₇	1	2	yes	—
45	C₄⋊C₄	Dic₉₇	1	1	yes	characteristic
46	C₄²	C₂×D₉₇	1	1	yes	characteristic
47	C₄²	C₂×D₉₇	1	2	yes	—
48	Q₈	—	2	2	no	—
49	C₂×C₄	C₂×Dic₉₇	1	1	yes	characteristic
50	C₂×C₄	C₂×Dic₉₇	1	2	yes	—
51	C₂×C₄	C₂×Dic₉₇	1	2	yes	—
52	C₂×C₄	C₂×Dic₉₇	1	1	yes	characteristic
53	C₂×C₄	C₂²×D₉₇	1	1	yes	characteristic
54	C₈	—	97	2	no	—
55	C₈	—	194	1	no	—
56	C₈	—	194	2	no	—
57	C₂²	C₂²×Dic₉₇	1	1	yes	characteristic
58	C₄	—	2	2	no	—
59	C₄	—	2	1	no	—
60	C₄	—	2	2	no	—
61	C₄	#13095495	1	2	yes	—
62	C₄	Q₈×D₉₇	1	1	yes	characteristic
63	C₄	#13095512	1	1	yes	characteristic
64	C₂	Q₈×Dic₉₇	1	1	yes	characteristic
65	C₂	C₂×#13095495	1	1	yes	characteristic
66	C₂	#15690817	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₉₇
commutator, socle	C₂²×C₉₇	C₂²×C₄
Fitting	C₄×Q₈×C₉₇	C₂
hypercenter	C₄×Q₈	D₉₇
hypocenter	C₉₇	#446
LCS	G ▷ C₂²×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
22. #11715895	Q₈	semidirect
33. C₉₇	#446	semidirect