Subgroups — #20260856

Order 6208.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15690832	C₂	1	1	yes	maximal, characteristic
2	#15690818	C₂	1	2	yes	maximal, complemented
3	#15690736	C₂	1	2	yes	maximal, complemented
4	#15690720	C₂	1	1	yes	maximal, characteristic, complemented
5	#108×C₉₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#13095511	C₂²	1	2	yes	—
7	Dic₃₈₈	C₄	1	1	yes	characteristic, complemented
8	#13095500	C₄	1	2	yes	complemented
9	D₇₇₆	C₄	1	1	yes	characteristic, complemented
10	#13095494	—	2	2	no	—
11	C₂×#11715895	C₂²	1	1	yes	characteristic
12	C₈×D₉₇	—	2	2	no	—
13	C₄×Dic₉₇	C₂²	1	1	yes	characteristic
14	M₁₆×C₉₇	C₂²	1	2	yes	—
15	C₂×C₈×C₉₇	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₉₇	C₂³	1	1	yes	characteristic
17	C₂²⋊D₉₇	—	2	2	no	—
18	C₂×Dic₉₇	—	2	1	no	—
19	D₃₈₈	C₂×C₄	1	2	yes	—
20	C₄×D₉₇	—	2	2	no	—
21	Dic₁₉₄	C₂×C₄	1	2	yes	—
22	C₈×C₉₇	—	2	2	no	—
23	C₈×C₉₇	C₂×C₄	1	1	yes	characteristic
24	C₈×C₉₇	C₂×C₄	1	1	yes	characteristic
25	#11715895	D₄	1	2	yes	—
26	C₂²×C₉₇	#41	1	1	yes	characteristic
27	C₂×D₉₇	—	2	2	no	—
28	C₄×C₉₇	C₂²×C₄	1	1	yes	characteristic
29	C₄×C₉₇	C₂×D₄	1	1	yes	characteristic
30	Dic₉₇	—	2	2	no	—
31	Dic₉₇	—	4	1	no	—
32	C₂×C₉₇	—	2	1	no	—
33	C₂×C₉₇	C₄×D₄	1	1	yes	characteristic
34	D₉₇	—	4	2	no	—
35	C₉₇	#444	1	1	yes	characteristic, complemented, Sylow
36	#444	—	97	1	no	maximal, Sylow
37	#135	—	97	1	no	—
38	#131	—	97	2	no	—
39	#108	D₉₇	1	1	yes	characteristic, complemented
40	#104	—	97	2	no	—
41	#97	—	97	1	no	—
42	#41	—	97	2	no	—
43	Q₁₆	—	97	1	no	—
44	SD₁₆	—	97	2	no	—
45	D₈	—	97	1	no	—
46	M₁₆	—	194	2	no	—
47	M₁₆	C₂×D₉₇	1	2	yes	—
48	C₂×C₈	—	97	1	no	—
49	C₂×C₈	—	194	2	no	—
50	C₂×C₈	C₂×D₉₇	1	1	yes	characteristic
51	C₄²	—	97	1	no	—
52	Q₈	—	97	2	no	—
53	D₄	—	97	2	no	—
54	D₄	—	194	2	no	—
55	C₂×C₄	—	194	1	no	—
56	C₂×C₄	—	194	2	no	—
57	C₂×C₄	C₂²×D₉₇	1	1	yes	characteristic
58	C₈	—	2	2	no	—
59	C₈	—	97	2	no	—
60	C₈	C₄×D₉₇	1	1	yes	characteristic
61	C₈	C₄×D₉₇	1	1	yes	characteristic
62	C₂²	—	194	2	no	—
63	C₂²	#13095512	1	1	yes	characteristic
64	C₄	—	388	1	no	—
65	C₄	—	194	2	no	—
66	C₄	C₂×C₄×D₉₇	1	1	yes	characteristic
67	C₄	D₄×D₉₇	1	1	yes	characteristic
68	C₂	—	2	1	no	—
69	C₂	—	388	2	no	—
70	C₂	#15690772	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₄×D₉₇
commutator	C₄×C₉₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₉₇
Fitting	#108×C₉₇	C₂
socle	C₂×C₉₇	C₄×D₄
hypercenter	#108	D₉₇
hypocenter	C₉₇	#444
LCS	G ▷ C₄×C₉₇ ▷ C₂×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ #108

Complements

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

N	H ≅ G/N	type
2. #15690818	C₂	semidirect
3. #15690736	C₂	semidirect
4. #15690720	C₂	semidirect
5. #108×C₉₇	C₂	semidirect
7. Dic₃₈₈	C₄	semidirect
8. #13095500	C₄	semidirect
9. D₇₇₆	C₄	semidirect
35. C₉₇	#444	semidirect
39. #108	D₉₇	semidirect