Subgroups — #20261137

Order 6208.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15690802	C₂	1	2	yes	maximal
2	#15690744	C₂	1	2	yes	maximal
3	#15690742	C₂	1	2	yes	maximal
4	C₄×C₈×C₉₇	C₂	1	1	yes	maximal, characteristic
5	C₄⋊Dic₉₇	C₂²	1	4	yes	—
6	#13095490	—	2	4	no	—
7	C₂×C₈×C₉₇	C₂²	1	1	yes	characteristic
8	C₂×C₈×C₉₇	C₂²	1	1	yes	characteristic
9	C₄²×C₉₇	C₂²	1	1	yes	characteristic
10	C₂×C₄×C₉₇	D₄	1	2	yes	—
11	C₂×C₄×C₉₇	C₂³	1	1	yes	characteristic
12	C₂×Dic₉₇	—	2	4	no	—
13	C₈×C₉₇	Q₈	1	2	yes	—
14	C₈×C₉₇	Q₈	1	2	yes	—
15	C₂²×C₉₇	C₂×D₄	1	1	yes	characteristic
16	C₄×C₉₇	—	2	2	no	—
17	C₄×C₉₇	C₂×Q₈	1	1	yes	characteristic
18	C₄×C₉₇	C₂×Q₈	1	1	yes	characteristic
19	Dic₉₇	—	4	4	no	—
20	C₂×C₉₇	C₄⋊Q₈	1	1	yes	characteristic
21	C₂×C₉₇	#135	1	2	yes	—
22	C₉₇	#499	1	1	yes	characteristic, complemented, Sylow
23	#499	—	97	1	no	maximal, Sylow
24	#125	—	97	2	no	—
25	#107	—	97	2	no	—
26	#106	—	97	2	no	—
27	C₄×C₈	D₉₇	1	1	yes	characteristic
28	C₂×C₈	C₂×D₉₇	1	1	yes	characteristic
29	C₂×C₈	C₂×D₉₇	1	1	yes	characteristic
30	C₄⋊C₄	—	97	4	no	—
31	C₄⋊C₄	—	194	4	no	—
32	C₄²	C₂×D₉₇	1	1	yes	characteristic
33	C₂×C₄	—	194	4	no	—
34	C₂×C₄	D₃₈₈	1	2	yes	—
35	C₂×C₄	C₂²×D₉₇	1	1	yes	characteristic
36	C₈	Dic₁₉₄	1	2	yes	—
37	C₈	Dic₁₉₄	1	2	yes	—
38	C₂²	C₂×D₃₈₈	1	1	yes	characteristic
39	C₄	—	2	2	no	—
40	C₄	—	388	4	no	—
41	C₄	C₂×Dic₁₉₄	1	1	yes	characteristic
42	C₄	C₂×Dic₁₉₄	1	1	yes	characteristic
43	C₂	#15690810	1	1	yes	characteristic
44	C₂	#15690832	1	2	yes	—

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

N	H ≅ G/N	type
22. C₉₇	#499	semidirect