Subgroups — #20261092

Order 6208.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15690798	C₂	1	1	yes	maximal, characteristic
2	#15690733	C₂	1	2	yes	maximal, complemented
3	#15690730	C₂	1	2	yes	maximal
4	C₄×#11715895	C₂	1	1	yes	maximal, characteristic, complemented
5	#125×C₉₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Dic₁₉₄	C₂²	1	1	yes	characteristic
7	C₂×D₃₈₈	C₂²	1	1	yes	characteristic
8	C₂×#11715895	C₂²	1	2	yes	—
9	#13095488	—	2	2	no	—
10	C₄⋊C₄×C₉₇	—	2	2	no	—
11	C₄⋊C₄×C₉₇	C₂²	1	2	yes	—
12	C₄²×C₉₇	C₂²	1	1	yes	characteristic
13	C₂²×D₉₇	—	2	1	no	—
14	C₂×C₄×C₉₇	—	2	2	no	—
15	C₂×C₄×C₉₇	D₄	1	2	yes	—
16	C₂×C₄×C₉₇	C₂³	1	1	yes	characteristic
17	C₂×Dic₉₇	—	2	1	no	—
18	D₃₈₈	—	2	2	no	—
19	Dic₁₉₄	—	2	2	no	—
20	#11715895	—	2	2	no	—
21	C₂²×C₉₇	C₂×D₄	1	1	yes	characteristic
22	C₂×D₉₇	—	4	1	no	—
23	C₂×D₉₇	—	4	2	no	—
24	C₄×C₉₇	—	2	2	no	—
25	C₄×C₉₇	—	4	2	no	—
26	C₄×C₉₇	#41	1	2	yes	—
27	Dic₉₇	—	4	1	no	—
28	C₂×C₉₇	#124	1	1	yes	characteristic
29	C₂×C₉₇	#135	1	2	yes	—
30	D₉₇	—	8	1	no	—
31	C₉₇	#488	1	1	yes	characteristic, complemented, Sylow
32	#488	—	97	1	no	maximal, Sylow
33	#125	D₉₇	1	1	yes	characteristic, complemented
34	#124	—	97	1	no	—
35	#103	—	97	2	no	—
36	#102	—	97	2	no	—
37	C₄×C₈	—	97	1	no	—
38	C₂×Q₈	—	97	1	no	—
39	C₂×D₄	—	97	1	no	—
40	C₂×C₈	—	97	2	no	—
41	C₄⋊C₄	—	2	2	no	—
42	C₄⋊C₄	C₂×D₉₇	1	2	yes	—
43	C₂²⋊C₄	—	194	2	no	—
44	C₄²	C₂×D₉₇	1	1	yes	characteristic
45	C₂³	—	194	1	no	—
46	Q₈	—	194	2	no	—
47	D₄	—	194	2	no	—
48	C₂×C₄	—	2	2	no	—
49	C₂×C₄	—	194	1	no	—
50	C₂×C₄	C₂²⋊D₉₇	1	2	yes	—
51	C₂×C₄	C₂²×D₉₇	1	1	yes	characteristic
52	C₈	—	194	2	no	—
53	C₂²	—	388	1	no	—
54	C₂²	—	388	2	no	—
55	C₂²	C₂×C₂²⋊D₉₇	1	1	yes	characteristic
56	C₄	—	2	2	no	—
57	C₄	—	4	2	no	—
58	C₄	—	388	1	no	—
59	C₄	#13095512	1	2	yes	—
60	C₂	—	776	1	no	—
61	C₂	#15690799	1	1	yes	characteristic
62	C₂	#15690830	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₉₇
commutator	C₂×C₄×C₉₇	C₂³
Frattini	C₂×C₄	C₂²×D₉₇
Fitting	#125×C₉₇	C₂
socle	C₂²×C₉₇	C₂×D₄
hypercenter	#125	D₉₇
hypocenter	C₉₇	#488
LCS	G ▷ C₂×C₄×C₉₇ ▷ C₂×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #125

Complements

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

N	H ≅ G/N	type
2. #15690733	C₂	semidirect
4. C₄×#11715895	C₂	semidirect
5. #125×C₉₇	C₂	semidirect
31. C₉₇	#488	semidirect
33. #125	D₉₇	semidirect