Subgroups — #20261097

Order 6208.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15690798	C₂	1	1	yes	maximal, characteristic
2	#15690733	C₂	1	2	yes	maximal, complemented
3	#15690730	C₂	1	2	yes	maximal
4	#15690721	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄⋊Q₈×C₉₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Dic₁₉₄	C₂²	1	1	yes	characteristic
7	C₂×D₃₈₈	C₂²	1	1	yes	characteristic
8	C₂×#11715895	C₂²	1	2	yes	—
9	#13095488	—	2	1	no	—
10	#13095488	—	2	1	no	—
11	C₂×Q₈×C₉₇	—	2	1	no	—
12	C₄⋊C₄×C₉₇	—	2	1	no	—
13	C₄⋊C₄×C₉₇	C₂²	1	2	yes	—
14	C₄²×C₉₇	C₂²	1	1	yes	characteristic
15	C₂²×D₉₇	—	2	1	no	—
16	Q₈×C₉₇	—	4	2	no	—
17	C₂×C₄×C₉₇	—	2	2	no	—
18	C₂×C₄×C₉₇	D₄	1	1	yes	characteristic
19	C₂×C₄×C₉₇	D₄	1	1	yes	characteristic
20	C₂×C₄×C₉₇	C₂³	1	1	yes	characteristic
21	C₂×Dic₉₇	—	2	1	no	—
22	D₃₈₈	—	2	2	no	—
23	Dic₁₉₄	—	2	2	no	—
24	#11715895	—	2	2	no	—
25	C₂²×C₉₇	C₂×D₄	1	1	yes	characteristic
26	C₂×D₉₇	—	4	1	no	—
27	C₂×D₉₇	—	4	1	no	—
28	C₂×D₉₇	—	4	1	no	—
29	C₄×C₉₇	—	2	1	no	—
30	C₄×C₉₇	—	2	1	no	—
31	C₄×C₉₇	—	4	2	no	—
32	C₄×C₉₇	#41	1	2	yes	—
33	Dic₉₇	—	4	1	no	—
34	C₂×C₉₇	#124	1	1	yes	characteristic
35	C₂×C₉₇	AGL(1,ℤ/8)	1	1	yes	characteristic
36	C₂×C₉₇	#137	1	1	yes	characteristic
37	D₉₇	—	8	1	no	—
38	C₉₇	#489	1	1	yes	characteristic, complemented, Sylow
39	#489	—	97	1	no	maximal, Sylow
40	C₄⋊Q₈	D₉₇	1	1	yes	characteristic, complemented
41	#124	—	97	1	no	—
42	#103	—	97	2	no	—
43	#102	—	97	2	no	—
44	#97	—	97	1	no	—
45	C₂×Q₈	—	2	1	no	—
46	C₂×Q₈	—	97	1	no	—
47	C₂×D₄	—	97	1	no	—
48	C₂×C₈	—	97	2	no	—
49	C₄⋊C₄	—	2	1	no	—
50	C₄⋊C₄	C₂×D₉₇	1	2	yes	—
51	C₂²⋊C₄	—	194	1	no	—
52	C₂²⋊C₄	—	194	1	no	—
53	C₄²	C₂×D₉₇	1	1	yes	characteristic
54	C₂³	—	194	1	no	—
55	Q₈	—	4	2	no	—
56	Q₈	—	194	2	no	—
57	D₄	—	194	2	no	—
58	C₂×C₄	—	2	2	no	—
59	C₂×C₄	—	194	1	no	—
60	C₂×C₄	C₂²⋊D₉₇	1	1	yes	characteristic
61	C₂×C₄	C₂²⋊D₉₇	1	1	yes	characteristic
62	C₂×C₄	C₂²×D₉₇	1	1	yes	characteristic
63	C₈	—	194	2	no	—
64	C₂²	—	388	1	no	—
65	C₂²	—	388	1	no	—
66	C₂²	—	388	1	no	—
67	C₂²	C₂×C₂²⋊D₉₇	1	1	yes	characteristic
68	C₄	—	2	1	no	—
69	C₄	—	2	1	no	—
70	C₄	—	4	2	no	—
71	C₄	—	388	1	no	—
72	C₄	#13095512	1	2	yes	—
73	C₂	—	776	1	no	—
74	C₂	#15690799	1	1	yes	characteristic
75	C₂	#15690836	1	1	yes	characteristic
76	C₂	#15690841	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₉₇
commutator	C₂×C₄×C₉₇	C₂³
Frattini	C₂×C₄	C₂²×D₉₇
Fitting	C₄⋊Q₈×C₉₇	C₂
socle	C₂²×C₉₇	C₂×D₄
hypercenter	C₄⋊Q₈	D₉₇
hypocenter	C₉₇	#489
LCS	G ▷ C₂×C₄×C₉₇ ▷ C₂×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
2. #15690733	C₂	semidirect
4. #15690721	C₂	semidirect
5. C₄⋊Q₈×C₉₇	C₂	semidirect
38. C₉₇	#489	semidirect
40. C₄⋊Q₈	D₉₇	semidirect