Subgroups — #20260917

Order 6208.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15690858	C₂	1	1	yes	maximal, characteristic
2	#15690841	C₂	1	2	yes	maximal, complemented
3	#15690738	C₂	1	2	yes	maximal, complemented
4	#15690729	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄⋊Q₈×C₉₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#13095512	—	2	2	no	—
7	#13095511	—	2	2	no	—
8	#13095511	C₂²	1	2	yes	—
9	Q₈×D₉₇	—	2	2	no	—
10	#13095501	—	2	2	no	—
11	#13095498	—	2	2	no	—
12	#13095495	C₂²	1	2	yes	—
13	C₂×Q₈×C₉₇	C₂²	1	1	yes	characteristic
14	C₂×Q₈×C₉₇	C₂²	1	1	yes	characteristic
15	C₄⋊C₄×C₉₇	—	2	2	no	—
16	C₄²×C₉₇	C₂²	1	1	yes	characteristic
17	Q₈×C₉₇	—	2	2	no	—
18	Q₈×C₉₇	—	2	2	no	—
19	C₂×C₄×C₉₇	—	2	1	no	—
20	C₂×C₄×C₉₇	—	2	1	no	—
21	C₂×C₄×C₉₇	D₄	1	2	yes	—
22	C₂×C₄×C₉₇	C₂³	1	1	yes	characteristic
23	C₂²⋊D₉₇	—	2	2	no	—
24	D₃₈₈	—	2	2	no	—
25	D₃₈₈	D₄	1	2	yes	—
26	C₄×D₉₇	—	2	4	no	—
27	C₄×D₉₇	—	2	2	no	—
28	Dic₁₉₄	—	2	2	no	—
29	Dic₁₉₄	D₄	1	2	yes	—
30	#11715895	—	2	2	no	—
31	C₂²×C₉₇	C₂×D₄	1	1	yes	characteristic
32	C₂×D₉₇	—	2	2	no	—
33	C₄×C₉₇	—	2	2	no	—
34	C₄×C₉₇	—	2	2	no	—
35	C₄×C₉₇	—	4	1	no	—
36	C₄×C₉₇	C₂×D₄	1	2	yes	—
37	Dic₉₇	—	2	2	no	—
38	C₂×C₉₇	—	2	1	no	—
39	C₂×C₉₇	#120	1	1	yes	characteristic
40	D₉₇	—	4	2	no	—
41	C₉₇	#456	1	1	yes	characteristic, complemented, Sylow
42	#456	—	97	1	no	maximal, Sylow
43	2₋¹⁺⁴	—	97	1	no	—
44	#137	—	97	2	no	—
45	C₄⋊Q₈	D₉₇	1	1	yes	characteristic, complemented
46	#104	—	97	2	no	—
47	#101	—	97	1	no	—
48	#41	—	97	2	no	—
49	#41	—	194	2	no	—
50	#41	—	194	2	no	—
51	C₂×Q₈	—	194	2	no	—
52	C₂×Q₈	C₂×D₉₇	1	1	yes	characteristic
53	C₂×Q₈	C₂×D₉₇	1	1	yes	characteristic
54	Q₁₆	—	194	2	no	—
55	SD₁₆	—	194	2	no	—
56	M₁₆	—	97	2	no	—
57	C₄⋊C₄	—	2	2	no	—
58	C₄²	C₂×D₉₇	1	1	yes	characteristic
59	Q₈	—	2	2	no	—
60	Q₈	—	2	2	no	—
61	Q₈	—	97	2	no	—
62	Q₈	—	194	2	no	—
63	D₄	—	97	2	no	—
64	D₄	—	194	2	no	—
65	D₄	—	194	2	no	—
66	C₂×C₄	—	2	1	no	—
67	C₂×C₄	—	2	1	no	—
68	C₂×C₄	—	194	4	no	—
69	C₂×C₄	—	194	2	no	—
70	C₂×C₄	C₂²⋊D₉₇	1	2	yes	—
71	C₂×C₄	C₂²×D₉₇	1	1	yes	characteristic
72	C₈	—	194	2	no	—
73	C₂²	—	194	2	no	—
74	C₂²	C₂×C₂²⋊D₉₇	1	1	yes	characteristic
75	C₄	—	2	2	no	—
76	C₄	—	2	2	no	—
77	C₄	—	4	1	no	—
78	C₄	—	194	2	no	—
79	C₄	D₄×D₉₇	1	2	yes	—
80	C₂	—	2	1	no	—
81	C₂	—	388	2	no	—
82	C₂	#15690778	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#15690778
commutator	C₂×C₄×C₉₇	C₂³
Frattini	C₂×C₄	C₂²×D₉₇
Fitting	C₄⋊Q₈×C₉₇	C₂
socle	C₂×C₉₇	#120
hypercenter	C₄⋊Q₈	D₉₇
hypocenter	C₉₇	#456
LCS	G ▷ C₂×C₄×C₉₇ ▷ C₂×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
2. #15690841	C₂	semidirect
3. #15690738	C₂	semidirect
4. #15690729	C₂	semidirect
5. C₄⋊Q₈×C₉₇	C₂	semidirect
41. C₉₇	#456	semidirect
45. C₄⋊Q₈	D₉₇	semidirect