Subgroups — #20261595

Order 6208.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15690877	C₂	1	2	yes	maximal
2	#15690808	C₂	1	1	yes	maximal, characteristic
3	C₂×#11715897	—	2	2	no	—
4	C₂×Dic₁₉₄	C₄	1	1	yes	characteristic
5	#13095490	—	2	2	no	—
6	C₄×Dic₉₇	C₂²	1	1	yes	characteristic
7	C₂×Q₈×C₉₇	C₄	1	1	yes	characteristic
8	Q₈×C₉₇	—	4	1	no	—
9	C₂×C₄×C₉₇	—	2	1	no	—
10	C₂×C₄×C₉₇	C₂×C₄	1	1	yes	characteristic
11	C₂×Dic₉₇	—	2	1	no	—
12	C₂×Dic₉₇	D₄	1	2	yes	—
13	Dic₁₉₄	—	4	1	no	—
14	#11715897	—	4	2	no	—
15	C₂²×C₉₇	C₂²⋊C₄	1	1	yes	characteristic
16	C₄×C₉₇	—	2	1	no	—
17	C₄×C₉₇	—	4	1	no	—
18	Dic₉₇	—	4	1	no	—
19	Dic₉₇	SD₁₆	1	2	yes	—
20	Dic₉₇	Q₁₆	1	2	yes	—
21	C₂×C₉₇	#100	1	1	yes	characteristic
22	C₂×C₉₇	#103	1	2	yes	—
23	C₉₇	#333	1	1	yes	characteristic, complemented, Sylow
24	#333	—	97	1	no	maximal, Sylow
25	C₄⋊Q₈	—	97	1	no	—
26	C₄⋊C₈	—	97	2	no	—
27	C₂×Q₈	—	97	1	no	—
28	C₂×Q₈	#87604	1	1	yes	characteristic
29	C₂×C₈	—	194	2	no	—
30	C₄⋊C₄	—	194	2	no	—
31	C₄²	—	97	1	no	—
32	Q₈	—	4	1	no	—
33	Q₈	—	388	1	no	—
34	C₂×C₄	—	2	1	no	—
35	C₂×C₄	—	97	2	no	—
36	C₂×C₄	—	194	1	no	—
37	C₂×C₄	C₂×#87604	1	1	yes	characteristic
38	C₈	—	388	2	no	—
39	C₂²	C₂²⋊#87604	1	1	yes	characteristic
40	C₄	—	2	1	no	—
41	C₄	—	4	1	no	—
42	C₄	—	97	2	no	—
43	C₄	—	97	2	no	—
44	C₄	—	388	1	no	—
45	C₂	#15690870	1	1	yes	characteristic
46	C₂	#15690873	1	2	yes	—

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

N	H ≅ G/N	type
23. C₉₇	#333	semidirect