Subgroups — #20261583

Order 6208.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#11715897	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#11715897	C₂	1	1	yes	maximal, characteristic, complemented
3	#15690772	C₂	1	1	yes	maximal, characteristic
4	C₂×#11715897	—	2	1	no	—
5	C₂×#11715897	—	2	1	no	—
6	C₂×D₃₈₈	C₄	1	1	yes	characteristic
7	C₂×C₄×D₉₇	—	2	1	no	—
8	#13095488	—	2	1	no	—
9	C₄×Dic₉₇	C₂²	1	1	yes	characteristic
10	C₄⋊C₄×C₉₇	C₄	1	1	yes	characteristic
11	C₂²×D₉₇	—	2	1	no	—
12	C₂×C₄×C₉₇	—	2	1	no	—
13	C₂×C₄×C₉₇	C₂×C₄	1	1	yes	characteristic
14	C₂×Dic₉₇	D₄	1	1	yes	characteristic
15	C₂×Dic₉₇	D₄	1	1	yes	characteristic
16	D₃₈₈	—	2	1	no	—
17	D₃₈₈	C₈	1	2	yes	complemented
18	C₄×D₉₇	—	4	1	no	—
19	C₄×D₉₇	—	4	1	no	—
20	#11715897	—	2	2	no	—
21	#11715897	—	4	1	no	—
22	C₂²×C₉₇	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×D₉₇	—	2	2	no	—
24	C₂×D₉₇	—	4	1	no	—
25	C₂×D₉₇	—	4	1	no	—
26	C₄×C₉₇	—	4	1	no	—
27	C₄×C₉₇	C₂×C₈	1	1	yes	characteristic
28	C₄×C₉₇	M₁₆	1	1	yes	characteristic
29	Dic₉₇	—	2	1	no	—
30	Dic₉₇	D₈	1	1	yes	characteristic
31	Dic₉₇	SD₁₆	1	1	yes	characteristic
32	C₂×C₉₇	C₂²⋊C₈	1	1	yes	characteristic
33	C₂×C₉₇	#102	1	1	yes	characteristic
34	C₂×C₉₇	#104	1	1	yes	characteristic
35	D₉₇	—	4	2	no	—
36	C₉₇	D₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
37	D₄⋊C₈	—	97	1	no	maximal, Sylow
38	C₄×D₄	—	97	1	no	—
39	C₄⋊C₈	—	97	1	no	—
40	C₄×C₈	—	97	1	no	—
41	C₂×D₄	—	97	1	no	—
42	C₂²×C₄	—	194	1	no	—
43	C₂×C₈	—	194	1	no	—
44	C₂×C₈	—	194	1	no	—
45	C₄⋊C₄	#87604	1	1	yes	characteristic
46	C₂²⋊C₄	—	194	1	no	—
47	C₄²	—	97	1	no	—
48	C₂³	—	194	1	no	—
49	D₄	—	97	2	no	—
50	D₄	—	194	1	no	—
51	C₂×C₄	—	2	1	no	—
52	C₂×C₄	—	97	1	no	—
53	C₂×C₄	—	97	1	no	—
54	C₂×C₄	—	388	1	no	—
55	C₂×C₄	—	388	1	no	—
56	C₂×C₄	C₂×#87604	1	1	yes	characteristic
57	C₈	—	388	1	no	—
58	C₈	—	194	2	no	—
59	C₂²	—	388	1	no	—
60	C₂²	—	388	1	no	—
61	C₂²	—	194	2	no	—
62	C₂²	C₂²⋊#87604	1	1	yes	characteristic
63	C₄	—	4	1	no	—
64	C₄	—	97	1	no	—
65	C₄	—	97	1	no	—
66	C₄	—	194	1	no	—
67	C₄	#13095519	1	1	yes	characteristic
68	C₄	#13095521	1	1	yes	characteristic
69	C₂	—	388	2	no	—
70	C₂	#15690867	1	1	yes	characteristic
71	C₂	#15690872	1	1	yes	characteristic
72	C₂	#15690875	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊#87604
commutator	C₄×C₉₇	C₂×C₈
Frattini	C₂×C₄	C₂×#87604
Fitting	C₄⋊C₄×C₉₇	C₄
socle	C₂²×C₉₇	C₂²⋊C₄
hypercenter	C₄⋊C₄	#87604
hypocenter	C₉₇	D₄⋊C₈
LCS	G ▷ C₄×C₉₇ ▷ C₂×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊C₄

Complements

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

N	H ≅ G/N	type
1. C₄⋊#11715897	C₂	semidirect
2. C₄×#11715897	C₂	semidirect
17. D₃₈₈	C₈	semidirect
36. C₉₇	D₄⋊C₈	semidirect