Subgroups — #20261681

Order 6208.

186 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊#87604	C₂	1	6	yes	maximal
2	C₄²×D₉₇	C₂	1	1	yes	maximal, characteristic
3	C₂²×#87604	C₂²	1	4	yes	—
4	C₄⋊#87604	—	2	12	no	—
5	C₂×C₄×D₉₇	C₂²	1	3	yes	—
6	C₄×Dic₉₇	C₄	1	3	yes	complemented
7	C₄²×C₉₇	C₄	1	1	yes	characteristic, complemented
8	C₂²×D₉₇	C₂³	1	1	yes	characteristic
9	C₂×#87604	—	2	12	no	—
10	C₂×C₄×C₉₇	C₂×C₄	1	3	yes	—
11	C₂×Dic₉₇	C₂×C₄	1	3	yes	—
12	C₄×D₉₇	D₄	1	6	yes	—
13	C₄×D₉₇	Q₈	1	6	yes	—
14	C₂²×C₉₇	C₂²×C₄	1	1	yes	characteristic
15	C₂×D₉₇	C₂×D₄	1	3	yes	—
16	C₂×D₉₇	C₂×Q₈	1	3	yes	—
17	#87604	—	4	4	no	—
18	C₄×C₉₇	C₄⋊C₄	1	6	yes	complemented
19	Dic₉₇	C₄⋊C₄	1	6	yes	complemented
20	C₂×C₉₇	C₂×C₄⋊C₄	1	3	yes	—
21	D₉₇	#127	1	1	yes	characteristic
22	D₉₇	C₄⋊Q₈	1	3	yes	—
23	C₉₇	#384	1	1	yes	characteristic, complemented, Sylow
24	#384	—	97	1	no	maximal, Sylow
25	C₂×C₄⋊C₄	—	97	6	no	—
26	C₂×C₄²	—	97	1	no	—
27	C₂²×C₄	—	97	3	no	—
28	C₂²×C₄	—	97	4	no	—
29	C₄⋊C₄	—	194	12	no	—
30	C₄²	—	97	3	no	—
31	C₄²	#87604	1	1	yes	characteristic, complemented
32	C₂³	—	97	1	no	—
33	C₂×C₄	—	97	3	no	—
34	C₂×C₄	—	97	6	no	—
35	C₂×C₄	—	97	6	no	—
36	C₂×C₄	—	194	12	no	—
37	C₂×C₄	C₂×#87604	1	3	yes	—
38	C₂²	—	97	3	no	—
39	C₂²	—	97	3	no	—
40	C₂²	C₂²×#87604	1	1	yes	characteristic
41	C₄	—	97	6	no	—
42	C₄	—	388	4	no	—
43	C₄	C₄⋊#87604	1	6	yes	complemented
44	C₂	—	97	1	no	—
45	C₂	—	97	3	no	—
46	C₂	C₂×C₄⋊#87604	1	3	yes	—

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