Subgroups — #20260480

Order 6208.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15690810	C₂	1	1	yes	maximal, characteristic
2	C₄⋊#11715895	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₈×C₉₇	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₁₉₄	—	2	1	no	—
5	C₂×#11715895	—	2	1	no	—
6	C₄⋊Dic₉₇	—	2	1	no	—
7	C₄⋊Dic₉₇	C₄	1	2	yes	—
8	C₂×C₈×C₉₇	—	2	1	no	—
9	C₄²×C₉₇	C₂²	1	1	yes	characteristic
10	C₂×C₄×C₉₇	C₂×C₄	1	1	yes	characteristic
11	C₂×C₄×C₉₇	D₄	1	1	yes	characteristic
12	C₂×C₄×C₉₇	D₄	1	1	yes	characteristic
13	C₂×Dic₉₇	—	2	2	no	—
14	Dic₁₉₄	—	4	1	no	—
15	Dic₁₉₄	—	4	1	no	—
16	C₈×C₉₇	—	4	1	no	—
17	#11715895	—	4	1	no	—
18	C₂²×C₉₇	C₂²⋊C₄	1	1	yes	characteristic
19	C₄×C₉₇	—	2	1	no	—
20	C₄×C₉₇	D₈	1	1	yes	characteristic
21	C₄×C₉₇	SD₁₆	1	1	yes	characteristic
22	C₄×C₉₇	SD₁₆	1	1	yes	characteristic
23	C₄×C₉₇	Q₁₆	1	1	yes	characteristic
24	Dic₉₇	—	4	2	no	—
25	C₂×C₉₇	#101	1	1	yes	characteristic
26	C₂×C₉₇	#102	1	1	yes	characteristic
27	C₂×C₉₇	#103	1	1	yes	characteristic
28	C₉₇	#332	1	1	yes	characteristic, complemented, Sylow
29	#332	—	97	1	no	maximal, Sylow
30	C₄⋊Q₈	—	97	1	no	—
31	C₄⋊C₈	—	97	1	no	—
32	C₄⋊C₈	D₉₇	1	1	yes	characteristic
33	C₂×Q₈	—	194	1	no	—
34	C₂×C₈	—	2	1	no	—
35	C₂×C₈	—	194	1	no	—
36	C₄⋊C₄	—	97	2	no	—
37	C₄⋊C₄	—	194	1	no	—
38	C₄²	C₂×D₉₇	1	1	yes	characteristic
39	Q₈	—	388	1	no	—
40	Q₈	—	388	1	no	—
41	C₂×C₄	—	194	2	no	—
42	C₂×C₄	C₄×D₉₇	1	1	yes	characteristic
43	C₂×C₄	D₃₈₈	1	1	yes	characteristic
44	C₂×C₄	C₂²⋊D₉₇	1	1	yes	characteristic
45	C₈	—	4	1	no	—
46	C₈	—	388	1	no	—
47	C₂²	#13095488	1	1	yes	characteristic
48	C₄	—	2	1	no	—
49	C₄	—	388	2	no	—
50	C₄	D₇₇₆	1	1	yes	characteristic
51	C₄	#13095499	1	1	yes	characteristic
52	C₄	#13095500	1	1	yes	characteristic
53	C₄	#13095501	1	1	yes	characteristic
54	C₂	#15690728	1	1	yes	characteristic
55	C₂	#15690732	1	1	yes	characteristic
56	C₂	#15690733	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#13095488
commutator	C₂×C₄×C₉₇	C₂×C₄
Frattini	C₄²	C₂×D₉₇
Fitting	C₄⋊C₈×C₉₇	C₂
socle	C₂²×C₉₇	C₂²⋊C₄
hypercenter	C₄⋊C₈	D₉₇
hypocenter	C₉₇	#332
LCS	G ▷ C₂×C₄×C₉₇ ▷ C₂²×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
28. C₉₇	#332	semidirect