Subgroups — #20261552

Order 6208.

248 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15690857	C₂	1	2	yes	maximal, complemented
2	#15690843	C₂	1	6	yes	maximal, complemented
3	#15690832	C₂	1	3	yes	maximal, complemented
4	C₂×Dic₃₈₈	C₂	1	3	yes	maximal, complemented
5	#131×C₉₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#13095511	C₂²	1	6	yes	—
7	#13095510	—	2	6	no	—
8	C₂×Dic₁₉₄	C₂²	1	6	yes	—
9	Q₈×D₉₇	—	2	2	no	—
10	Dic₃₈₈	C₂²	1	3	yes	—
11	Dic₃₈₈	C₂²	1	6	yes	—
12	#13095500	C₂²	1	6	yes	—
13	D₇₇₆	C₂²	1	1	yes	characteristic
14	#41×C₉₇	C₂²	1	1	yes	characteristic
15	M₁₆×C₉₇	C₂²	1	3	yes	—
16	C₂×C₈×C₉₇	C₂²	1	3	yes	—
17	Q₈×C₉₇	D₄	1	1	yes	characteristic
18	D₄×C₉₇	D₄	1	3	yes	—
19	C₂×C₄×C₉₇	C₂³	1	3	yes	—
20	C₂²⋊D₉₇	—	2	6	no	—
21	C₂×Dic₉₇	—	2	6	no	—
22	D₃₈₈	C₂³	1	2	yes	—
23	C₄×D₉₇	—	2	6	no	—
24	Dic₁₉₄	—	2	6	no	—
25	Dic₁₉₄	C₂³	1	6	yes	—
26	C₈×C₉₇	C₂³	1	1	yes	characteristic
27	C₈×C₉₇	C₂³	1	3	yes	—
28	C₂²×C₉₇	C₂×D₄	1	3	yes	—
29	C₂×D₉₇	—	2	2	no	—
30	C₄×C₉₇	C₂×D₄	1	3	yes	—
31	C₄×C₉₇	C₂⁴	1	1	yes	characteristic
32	Dic₉₇	—	2	6	no	—
33	C₂×C₉₇	—	2	3	no	—
34	C₂×C₉₇	C₂²×D₄	1	1	yes	characteristic
35	D₉₇	—	4	2	no	—
36	C₉₇	#578	1	1	yes	characteristic, complemented, Sylow
37	#578	—	97	1	no	maximal, Sylow
38	2₋¹⁺⁴	—	97	2	no	—
39	#137	—	97	6	no	—
40	#135	—	97	3	no	—
41	C₂×Q₁₆	—	97	3	no	—
42	#131	D₉₇	1	1	yes	characteristic, complemented
43	#41	—	97	6	no	—
44	#41	—	194	6	no	—
45	#41	C₂×D₉₇	1	1	yes	characteristic
46	C₂×Q₈	—	97	6	no	—
47	C₂×Q₈	—	194	2	no	—
48	Q₁₆	—	97	3	no	—
49	Q₁₆	—	97	6	no	—
50	SD₁₆	—	97	6	no	—
51	D₈	—	97	1	no	—
52	M₁₆	C₂×D₉₇	1	3	yes	—
53	C₂×C₈	C₂×D₉₇	1	3	yes	—
54	Q₈	—	97	6	no	—
55	Q₈	—	194	6	no	—
56	Q₈	D₃₈₈	1	1	yes	characteristic
57	D₄	—	97	2	no	—
58	D₄	—	194	6	no	—
59	D₄	D₃₈₈	1	3	yes	—
60	C₂×C₄	—	194	6	no	—
61	C₂×C₄	—	194	6	no	—
62	C₂×C₄	C₂²×D₉₇	1	3	yes	—
63	C₈	C₂²×D₉₇	1	1	yes	characteristic
64	C₈	C₂²×D₉₇	1	3	yes	—
65	C₂²	—	194	2	no	—
66	C₂²	C₂×D₃₈₈	1	3	yes	—
67	C₄	—	194	6	no	—
68	C₄	C₂×D₃₈₈	1	3	yes	—
69	C₄	C₂³×D₉₇	1	1	yes	characteristic
70	C₂	—	2	3	no	—
71	C₂	—	388	2	no	—
72	C₂	C₂²×D₃₈₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²×D₃₈₈
commutator	C₄×C₉₇	C₂⁴
Frattini	C₄	C₂³×D₉₇
Fitting	#131×C₉₇	C₂
socle	C₂×C₉₇	C₂²×D₄
hypercenter	#131	D₉₇
hypocenter	C₉₇	#578
LCS	G ▷ C₄×C₉₇ ▷ C₂×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₂ ◁ #41 ◁ #131

Complements

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

N	H ≅ G/N	type
1. #15690857	C₂	semidirect
2. #15690843	C₂	semidirect
3. #15690832	C₂	semidirect
4. C₂×Dic₃₈₈	C₂	semidirect
5. #131×C₉₇	C₂	semidirect
36. C₉₇	#578	semidirect
42. #131	D₉₇	semidirect