Subgroups — #20261132

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	#15690742	C₂	1	1	yes	maximal, characteristic
3	#15690741	C₂	1	2	yes	maximal
4	C₈×Dic₉₇	C₂	1	1	yes	maximal, characteristic
5	#106×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	2	yes	—
17	Dic₁₉₄	—	4	4	no	—
18	C₈×C₉₇	Q₈	1	2	yes	complemented
19	#11715895	Q₈	1	2	yes	complemented
20	C₂²×C₉₇	C₂×D₄	1	1	yes	characteristic
21	C₄×C₉₇	—	4	2	no	—
22	C₄×C₉₇	C₂×Q₈	1	1	yes	characteristic
23	C₄×C₉₇	C₂×Q₈	1	1	yes	characteristic
24	Dic₉₇	—	4	2	no	—
25	Dic₉₇	SD₁₆	1	4	yes	—
26	C₂×C₉₇	C₄⋊Q₈	1	1	yes	characteristic
27	C₂×C₉₇	C₂×SD₁₆	1	2	yes	—
28	C₉₇	#498	1	1	yes	characteristic, complemented, Sylow
29	#498	—	97	1	no	maximal, Sylow
30	C₄⋊Q₈	—	97	2	no	—
31	#106	—	97	1	no	—
32	#106	—	97	2	no	—
33	#106	D₉₇	1	1	yes	characteristic
34	C₄×C₈	—	97	1	no	—
35	C₂×Q₈	—	194	2	no	—
36	C₂×C₈	—	97	1	no	—
37	C₂×C₈	C₂×D₉₇	1	1	yes	characteristic
38	C₄⋊C₄	—	97	2	no	—
39	C₄⋊C₄	—	194	2	no	—
40	C₄⋊C₄	C₂×D₉₇	1	2	yes	—
41	C₄²	—	97	1	no	—
42	Q₈	—	388	4	no	—
43	C₂×C₄	—	2	2	no	—
44	C₂×C₄	—	97	2	no	—
45	C₂×C₄	—	194	2	no	—
46	C₂×C₄	C₂²×D₉₇	1	1	yes	characteristic
47	C₈	—	97	2	no	—
48	C₈	Dic₁₉₄	1	2	yes	complemented
49	C₂²	D₄×D₉₇	1	1	yes	characteristic
50	C₄	—	4	2	no	—
51	C₄	—	97	4	no	—
52	C₄	—	388	2	no	—
53	C₄	Q₈×D₉₇	1	1	yes	characteristic
54	C₄	C₂×Dic₁₉₄	1	1	yes	characteristic
55	C₂	#15690809	1	1	yes	characteristic
56	C₂	SD₁₆×D₉₇	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄×D₉₇
commutator	C₂×C₄×C₉₇	C₂³
Frattini	C₂×C₄	C₂²×D₉₇
Fitting	#106×C₉₇	C₂
socle	C₂²×C₉₇	C₂×D₄
hypercenter	#106	D₉₇
hypocenter	C₉₇	#498
LCS	G ▷ C₂×C₄×C₉₇ ▷ C₂×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

Complements

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

N	H ≅ G/N	type
18. C₈×C₉₇	Q₈	semidirect
19. #11715895	Q₈	semidirect
28. C₉₇	#498	semidirect
48. C₈	Dic₁₉₄	semidirect