Subgroups — #20261632

Order 6208.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15690884	C₂	1	2	yes	maximal, complemented
2	C₂×#13095494	C₂	1	1	yes	maximal, characteristic
3	#13095514	—	2	2	no	—
4	C₂×C₄×D₉₇	C₄	1	1	yes	characteristic
5	#13095494	—	2	2	no	—
6	C₂×#11715895	C₂²	1	1	yes	characteristic
7	C₂×C₈×C₉₇	C₄	1	1	yes	characteristic
8	C₂²×D₉₇	C₈	1	1	yes	characteristic
9	C₂×C₄×C₉₇	C₂×C₄	1	1	yes	characteristic
10	C₂×Dic₉₇	C₈	1	1	yes	characteristic
11	C₄×D₉₇	—	2	1	no	—
12	C₄×D₉₇	—	2	1	no	—
13	C₈×C₉₇	—	2	1	no	—
14	#11715895	D₄	1	2	yes	—
15	C₂²×C₉₇	C₂×C₈	1	1	yes	characteristic
16	C₂×D₉₇	—	2	1	no	—
17	C₂×D₉₇	—	4	1	no	—
18	C₄×C₉₇	C₂²⋊C₄	1	1	yes	characteristic
19	C₄×C₉₇	M₁₆	1	1	yes	characteristic
20	Dic₉₇	—	2	1	no	—
21	C₂×C₉₇	—	2	1	no	—
22	C₂×C₉₇	C₂²⋊C₈	1	1	yes	characteristic
23	D₉₇	—	4	1	no	—
24	C₉₇	#349	1	1	yes	characteristic, complemented, Sylow
25	#349	—	97	1	no	maximal, Sylow
26	C₂×M₁₆	—	97	1	no	—
27	M₃₂	—	97	2	no	—
28	C₂²×C₄	—	97	1	no	—
29	M₁₆	—	194	2	no	—
30	C₂×C₈	—	97	1	no	—
31	C₂×C₈	#87604	1	1	yes	characteristic
32	C₁₆	—	194	2	no	—
33	C₂³	—	97	1	no	—
34	C₂×C₄	—	97	1	no	—
35	C₂×C₄	—	194	1	no	—
36	C₂×C₄	—	194	1	no	—
37	C₂×C₄	C₂×#87604	1	1	yes	characteristic
38	C₈	—	2	1	no	—
39	C₈	—	97	2	no	—
40	C₂²	—	388	1	no	—
41	C₂²	—	194	1	no	—
42	C₂²	#13095519	1	1	yes	characteristic
43	C₄	—	194	1	no	—
44	C₄	C₂²⋊#87604	1	1	yes	characteristic
45	C₄	#13095521	1	1	yes	characteristic
46	C₂	—	2	1	no	—
47	C₂	—	388	1	no	—
48	C₂	#15690867	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. #15690884	C₂	semidirect
24. C₉₇	#349	semidirect