Subgroups — #20261589

Order 6208.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15690867	C₂	1	1	yes	maximal, characteristic
2	(C₂×#87604)⋊C₄	C₂	1	1	yes	maximal, characteristic
3	#15690786	C₂	1	1	yes	maximal, characteristic
4	C₂²×#87604	—	2	1	no	—
5	C₂×#11715897	—	2	1	no	—
6	C₂×C₄×D₉₇	C₂²	1	1	yes	characteristic
7	C₄⋊Dic₉₇	C₄	1	1	yes	characteristic, complemented
8	#13095490	—	2	1	no	—
9	#13095488	—	2	1	no	—
10	C₂×Q₈×C₉₇	C₄	1	1	yes	characteristic, complemented
11	C₂²×D₉₇	D₄	1	1	yes	characteristic
12	C₂×#87604	—	2	2	no	—
13	C₂×#87604	—	4	1	no	—
14	C₂×#87604	—	4	1	no	—
15	Q₈×C₉₇	—	4	1	no	—
16	C₂×C₄×C₉₇	—	2	1	no	—
17	C₂×C₄×C₉₇	C₂×C₄	1	1	yes	characteristic
18	C₂×Dic₉₇	—	2	1	no	—
19	C₂×Dic₉₇	D₄	1	1	yes	characteristic
20	C₄×D₉₇	—	4	1	no	—
21	#11715897	—	4	1	no	—
22	C₂²×C₉₇	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×D₉₇	—	2	1	no	—
24	C₂×D₉₇	—	2	1	no	—
25	C₂×D₉₇	SD₁₆	1	1	yes	characteristic
26	C₂×D₉₇	Q₁₆	1	1	yes	characteristic
27	#87604	—	4	2	no	—
28	C₄×C₉₇	—	2	1	no	—
29	C₄×C₉₇	—	4	1	no	—
30	Dic₉₇	—	2	1	no	—
31	Dic₉₇	—	4	1	no	—
32	C₂×C₉₇	#99	1	1	yes	characteristic
33	C₂×C₉₇	#103	1	1	yes	characteristic
34	C₂×C₉₇	#104	1	1	yes	characteristic
35	D₉₇	—	2	1	no	—
36	D₉₇	—	2	1	no	—
37	C₉₇	#328	1	1	yes	characteristic, complemented, Sylow
38	#328	—	97	1	no	maximal, Sylow
39	C₂²⋊Q₈	—	97	1	no	—
40	C₂²⋊C₈	—	97	1	no	—
41	#95	—	97	1	no	—
42	C₂×Q₈	#87604	1	1	yes	characteristic, complemented
43	C₂²×C₄	—	97	1	no	—
44	C₂²×C₄	—	194	1	no	—
45	C₂×C₈	—	194	1	no	—
46	C₄⋊C₄	—	97	1	no	—
47	C₄⋊C₄	—	194	1	no	—
48	C₂²⋊C₄	—	194	1	no	—
49	C₂³	—	97	1	no	—
50	Q₈	—	4	1	no	—
51	C₂×C₄	—	2	1	no	—
52	C₂×C₄	—	97	1	no	—
53	C₂×C₄	—	388	1	no	—
54	C₂×C₄	—	388	1	no	—
55	C₂×C₄	—	388	1	no	—
56	C₂×C₄	—	194	2	no	—
57	C₂×C₄	—	194	1	no	—
58	C₂×C₄	C₂×#87604	1	1	yes	characteristic
59	C₈	—	388	1	no	—
60	C₂²	—	97	1	no	—
61	C₂²	—	97	1	no	—
62	C₂²	—	194	1	no	—
63	C₂²	—	194	1	no	—
64	C₂²	C₂²⋊#87604	1	1	yes	characteristic
65	C₄	—	2	1	no	—
66	C₄	—	4	1	no	—
67	C₄	—	388	2	no	—
68	C₄	—	388	1	no	—
69	C₄	—	194	1	no	—
70	C₂	—	194	1	no	—
71	C₂	—	194	1	no	—
72	C₂	#15690868	1	1	yes	characteristic
73	C₂	#15690873	1	1	yes	characteristic
74	C₂	#15690875	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊#87604
commutator	C₂×C₄×C₉₇	C₂×C₄
Frattini	C₂×C₄	C₂×#87604
Fitting	C₂×Q₈×C₉₇	C₄
socle	C₂²×C₉₇	C₂²⋊C₄
hypercenter	C₂×Q₈	#87604
hypocenter	C₉₇	#328
LCS	G ▷ C₂×C₄×C₉₇ ▷ C₂²×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
7. C₄⋊Dic₉₇	C₄	semidirect
10. C₂×Q₈×C₉₇	C₄	semidirect
37. C₉₇	#328	semidirect
42. C₂×Q₈	#87604	semidirect