Subgroups — #20260646

Order 6208.

202 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13095488	C₂	1	3	yes	maximal
2	#15690717	C₂	1	3	yes	maximal, complemented
3	C₂²×Q₈×C₉₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂³×D₉₇	C₂²	1	1	yes	characteristic
5	C₂²×Dic₉₇	C₂²	1	3	yes	—
6	#13095488	—	2	6	no	—
7	C₂×Q₈×C₉₇	—	2	6	no	—
8	C₂²×C₄×C₉₇	C₂²	1	3	yes	—
9	C₂³×C₉₇	C₂³	1	1	yes	characteristic
10	C₂²×D₉₇	—	2	3	no	—
11	C₂²×D₉₇	—	2	3	no	—
12	C₂²×D₉₇	Q₈	1	2	yes	complemented
13	Q₈×C₉₇	—	2	8	no	—
14	C₂×C₄×C₉₇	—	2	6	no	—
15	C₂×C₄×C₉₇	D₄	1	6	yes	—
16	C₂×Dic₉₇	—	2	3	no	—
17	C₂×Dic₉₇	—	2	6	no	—
18	C₂²×C₉₇	C₂×D₄	1	3	yes	—
19	C₂²×C₉₇	C₂×Q₈	1	1	yes	characteristic
20	C₂²×C₉₇	#41	1	3	yes	—
21	C₂×D₉₇	—	2	6	no	—
22	C₂×D₉₇	—	4	1	no	—
23	C₂×D₉₇	—	4	3	no	—
24	C₄×C₉₇	—	2	6	no	—
25	Dic₉₇	—	4	3	no	—
26	C₂×C₉₇	#120	1	1	yes	characteristic
27	C₂×C₉₇	C₂²⋊Q₈	1	3	yes	—
28	C₂×C₉₇	#124	1	3	yes	—
29	D₉₇	—	4	2	no	—
30	C₉₇	#393	1	1	yes	characteristic, complemented, Sylow
31	#393	—	97	1	no	maximal, Sylow
32	C₂²×Q₈	D₉₇	1	1	yes	characteristic, complemented
33	C₂×C₂²⋊C₄	—	97	3	no	—
34	#95	—	97	3	no	—
35	C₂⁴	—	97	1	no	—
36	C₂×Q₈	—	2	6	no	—
37	C₂²×C₄	—	97	3	no	—
38	C₂²×C₄	C₂×D₉₇	1	3	yes	—
39	C₂²⋊C₄	—	194	6	no	—
40	C₂³	—	97	2	no	—
41	C₂³	—	194	3	no	—
42	C₂³	—	194	3	no	—
43	C₂³	C₂²×D₉₇	1	1	yes	characteristic
44	Q₈	—	2	8	no	—
45	C₂×C₄	—	2	6	no	—
46	C₂×C₄	—	194	3	no	—
47	C₂×C₄	—	194	6	no	—
48	C₂×C₄	C₂²⋊D₉₇	1	6	yes	—
49	C₂²	—	388	1	no	—
50	C₂²	—	388	3	no	—
51	C₂²	—	194	6	no	—
52	C₂²	C₂×C₂²⋊D₉₇	1	3	yes	—
53	C₂²	Q₈×D₉₇	1	1	yes	characteristic
54	C₂²	#13095512	1	3	yes	—
55	C₄	—	2	6	no	—
56	C₄	—	388	3	no	—
57	C₂	—	388	2	no	—
58	C₂	#15690779	1	1	yes	characteristic
59	C₂	#15690786	1	3	yes	—
60	C₂	#15690799	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₉₇
commutator, socle	C₂³×C₉₇	C₂³
Fitting	C₂²×Q₈×C₉₇	C₂
hypercenter	C₂²×Q₈	D₉₇
hypocenter	C₉₇	#393
LCS	G ▷ C₂³×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₂³ ◁ C₂²×Q₈

Complements

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

N	H ≅ G/N	type
2. #15690717	C₂	semidirect
3. C₂²×Q₈×C₉₇	C₂	semidirect
12. C₂²×D₉₇	Q₈	semidirect
30. C₉₇	#393	semidirect
32. C₂²×Q₈	D₉₇	semidirect