Subgroups — #20260654

Order 6208.

182 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13095490	C₂	1	3	yes	maximal
2	#15690717	C₂	1	3	yes	maximal
3	C₂²×Q₈×C₉₇	C₂	1	1	yes	maximal, characteristic
4	C₂²×Dic₉₇	C₂²	1	1	yes	characteristic
5	C₂²×Dic₉₇	C₂²	1	3	yes	—
6	#13095490	—	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	Q₈×C₉₇	—	2	8	no	—
11	C₂×C₄×C₉₇	—	2	6	no	—
12	C₂×C₄×C₉₇	D₄	1	6	yes	—
13	C₂×Dic₉₇	—	2	3	no	—
14	C₂×Dic₉₇	—	2	3	no	—
15	C₂×Dic₉₇	—	2	3	no	—
16	C₂×Dic₉₇	Q₈	1	6	yes	complemented
17	C₂²×C₉₇	C₂×D₄	1	3	yes	—
18	C₂²×C₉₇	C₂×Q₈	1	3	yes	—
19	C₂²×C₉₇	#41	1	1	yes	characteristic
20	C₄×C₉₇	—	2	6	no	—
21	Dic₉₇	—	2	6	no	—
22	Dic₉₇	—	4	1	no	—
23	C₂×C₉₇	#120	1	1	yes	characteristic
24	C₂×C₉₇	C₂²⋊Q₈	1	3	yes	—
25	C₂×C₉₇	C₄⋊Q₈	1	3	yes	—
26	C₉₇	#395	1	1	yes	characteristic, complemented, Sylow
27	#395	—	97	1	no	maximal, Sylow
28	C₂²×Q₈	D₉₇	1	1	yes	characteristic
29	C₂×C₄⋊C₄	—	97	3	no	—
30	#95	—	97	3	no	—
31	C₂×Q₈	—	2	6	no	—
32	C₂²×C₄	—	97	3	no	—
33	C₂²×C₄	—	97	1	no	—
34	C₂²×C₄	C₂×D₉₇	1	3	yes	—
35	C₄⋊C₄	—	194	6	no	—
36	C₂³	C₂²×D₉₇	1	1	yes	characteristic
37	Q₈	—	2	8	no	—
38	C₂×C₄	—	2	6	no	—
39	C₂×C₄	—	97	6	no	—
40	C₂×C₄	—	194	3	no	—
41	C₂×C₄	—	194	3	no	—
42	C₂×C₄	—	194	3	no	—
43	C₂×C₄	C₂²⋊D₉₇	1	6	yes	—
44	C₂²	C₂×C₂²⋊D₉₇	1	3	yes	—
45	C₂²	Q₈×D₉₇	1	3	yes	—
46	C₂²	#13095512	1	1	yes	characteristic
47	C₄	—	2	6	no	—
48	C₄	—	388	1	no	—
49	C₄	—	194	6	no	—
50	C₂	#15690779	1	1	yes	characteristic
51	C₂	#15690786	1	3	yes	—
52	C₂	#15690808	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	#395
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
16. C₂×Dic₉₇	Q₈	semidirect
26. C₉₇	#395	semidirect