Subgroups — #15690779

Order 3104.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂²⋊D₉₇	C₂	1	3	yes	maximal, complemented
2	C₂²⋊Dic₉₇	C₂	1	3	yes	maximal, complemented
3	C₂⁴×C₉₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂³×C₉₇	—	2	6	no	—
5	C₂³×C₉₇	C₂²	1	3	yes	—
6	C₂²×D₉₇	C₂²	1	1	yes	characteristic, complemented
7	C₂²⋊D₉₇	—	2	6	no	—
8	C₂×Dic₉₇	C₂²	1	3	yes	complemented
9	C₂²×C₉₇	—	2	8	no	—
10	C₂²×C₉₇	—	2	6	no	—
11	C₂²×C₉₇	D₄	1	6	yes	complemented
12	C₂²×C₉₇	C₂³	1	1	yes	characteristic
13	C₂×D₉₇	—	2	3	no	—
14	Dic₉₇	—	2	3	no	—
15	C₂×C₉₇	—	2	6	no	—
16	C₂×C₉₇	C₂×D₄	1	3	yes	—
17	D₉₇	—	4	1	no	—
18	C₉₇	#120	1	1	yes	characteristic, complemented, Sylow
19	#120	—	97	1	no	maximal, Sylow
20	C₂⁴	D₉₇	1	1	yes	characteristic, complemented
21	C₂×D₄	—	97	3	no	—
22	C₂²⋊C₄	—	97	3	no	—
23	C₂³	—	2	6	no	—
24	C₂³	—	97	1	no	—
25	C₂³	C₂×D₉₇	1	3	yes	—
26	D₄	—	194	6	no	—
27	C₂×C₄	—	97	3	no	—
28	C₂²	—	2	8	no	—
29	C₂²	—	2	6	no	—
30	C₂²	—	194	3	no	—
31	C₂²	C₂²⋊D₉₇	1	6	yes	complemented
32	C₂²	C₂²×D₉₇	1	1	yes	characteristic
33	C₄	—	194	3	no	—
34	C₂	—	2	6	no	—
35	C₂	—	388	1	no	—
36	C₂	C₂×C₂²⋊D₉₇	1	3	yes	—

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

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.