Subgroups — #20260484

Order 6208.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#11715895	C₂	1	2	yes	maximal
2	C₄⋊Q₈×C₉₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#11715895	—	2	2	no	—
4	C₂×Q₈×C₉₇	C₄	1	2	yes	—
5	C₄⋊C₄×C₉₇	—	2	2	no	—
6	C₄²×C₉₇	C₂²	1	1	yes	characteristic
7	Q₈×C₉₇	—	4	2	no	—
8	C₂×C₄×C₉₇	—	2	2	no	—
9	C₂×C₄×C₉₇	C₂×C₄	1	1	yes	characteristic
10	C₂×C₄×C₉₇	D₄	1	2	yes	—
11	#11715895	—	4	2	no	—
12	C₂²×C₉₇	C₂²⋊C₄	1	1	yes	characteristic
13	C₄×C₉₇	—	2	1	no	—
14	C₄×C₉₇	—	4	2	no	—
15	C₄×C₉₇	SD₁₆	1	2	yes	—
16	C₄×C₉₇	Q₁₆	1	2	yes	—
17	C₂×C₉₇	#100	1	1	yes	characteristic
18	C₂×C₉₇	#103	1	2	yes	—
19	C₉₇	#333	1	1	yes	characteristic, complemented, Sylow
20	#333	—	97	1	no	maximal, Sylow
21	C₄⋊Q₈	D₉₇	1	1	yes	characteristic
22	C₄⋊C₈	—	97	2	no	—
23	C₂×Q₈	Dic₉₇	1	2	yes	—
24	C₂×C₈	—	194	2	no	—
25	C₄⋊C₄	—	2	2	no	—
26	C₄²	C₂×D₉₇	1	1	yes	characteristic
27	Q₈	—	4	2	no	—
28	C₂×C₄	—	2	2	no	—
29	C₂×C₄	C₂×Dic₉₇	1	1	yes	characteristic
30	C₂×C₄	C₂²⋊D₉₇	1	2	yes	—
31	C₈	—	388	2	no	—
32	C₂²	C₂²⋊Dic₉₇	1	1	yes	characteristic
33	C₄	—	2	1	no	—
34	C₄	—	4	2	no	—
35	C₄	#13095498	1	2	yes	—
36	C₄	#13095501	1	2	yes	—
37	C₂	#15690727	1	1	yes	characteristic
38	C₂	#15690734	1	2	yes	—

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

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