Subgroups — #20260538

Order 6208.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₃₈₈	C₂	1	1	yes	maximal, characteristic
2	C₂×#13095486	C₂	1	1	yes	maximal, characteristic
3	#107×C₉₇	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₁₉₄	—	2	1	no	—
5	Dic₃₈₈	—	2	1	no	—
6	Dic₃₈₈	C₄	1	2	yes	complemented
7	#13095486	—	2	1	no	—
8	C₂×C₈×C₉₇	C₂²	1	1	yes	characteristic
9	C₄⋊C₄×C₉₇	—	2	1	no	—
10	C₂×C₄×C₉₇	—	4	1	no	—
11	C₂×C₄×C₉₇	D₄	1	1	yes	characteristic
12	C₂×Dic₉₇	—	4	1	no	—
13	Dic₁₉₄	—	2	2	no	—
14	Dic₁₉₄	—	4	1	no	—
15	C₈×C₉₇	C₂×C₄	1	1	yes	characteristic
16	C₈×C₉₇	D₄	1	1	yes	characteristic
17	C₂²×C₉₇	D₈	1	1	yes	characteristic
18	C₄×C₉₇	—	8	1	no	—
19	C₄×C₉₇	C₂²⋊C₄	1	1	yes	characteristic
20	C₄×C₉₇	SD₁₆	1	1	yes	characteristic
21	Dic₉₇	—	4	2	no	—
22	C₂×C₉₇	#102	1	1	yes	characteristic
23	C₂×C₉₇	SD₃₂	1	1	yes	characteristic
24	C₂×C₉₇	Q₃₂	1	1	yes	characteristic
25	C₉₇	#358	1	1	yes	characteristic, complemented, Sylow
26	#358	—	97	1	no	maximal, Sylow
27	C₂×Q₁₆	—	97	1	no	—
28	C₂×C₁₆	—	97	1	no	—
29	#107	D₉₇	1	1	yes	characteristic
30	C₂×Q₈	—	194	1	no	—
31	Q₁₆	—	97	2	no	—
32	Q₁₆	—	194	1	no	—
33	C₂×C₈	C₂×D₉₇	1	1	yes	characteristic
34	C₄⋊C₄	—	2	1	no	—
35	C₁₆	—	194	1	no	—
36	Q₈	—	388	1	no	—
37	Q₈	—	194	2	no	—
38	C₂×C₄	—	4	1	no	—
39	C₂×C₄	—	388	1	no	—
40	C₂×C₄	C₂²⋊D₉₇	1	1	yes	characteristic
41	C₈	C₄×D₉₇	1	1	yes	characteristic
42	C₈	D₃₈₈	1	1	yes	characteristic
43	C₂²	#13095496	1	1	yes	characteristic
44	C₄	—	8	1	no	—
45	C₄	—	388	2	no	—
46	C₄	#13095488	1	1	yes	characteristic
47	C₄	#13095498	1	1	yes	characteristic
48	C₂	#15690730	1	1	yes	characteristic
49	C₂	#15690754	1	1	yes	characteristic
50	C₂	#15690756	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#13095496
commutator	C₈×C₉₇	C₂×C₄
Frattini	C₂×C₈	C₂×D₉₇
Fitting	#107×C₉₇	C₂
socle	C₂²×C₉₇	D₈
hypercenter	#107	D₉₇
hypocenter	C₉₇	#358
LCS	G ▷ C₈×C₉₇ ▷ C₄×C₉₇ ▷ C₂×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #107

Complements

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

N	H ≅ G/N	type
6. Dic₃₈₈	C₄	semidirect
25. C₉₇	#358	semidirect