Subgroups — #15690873

Order 3104.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13095519	C₂	1	1	yes	maximal, characteristic
2	C₄⋊#87604	C₂	1	1	yes	maximal, characteristic
3	Q₈×D₉₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#87604	—	2	1	no	—
5	Q₈×C₉₇	C₄	1	1	yes	characteristic, complemented
6	C₄×D₉₇	—	2	1	no	—
7	C₄×D₉₇	C₂²	1	1	yes	characteristic
8	Dic₁₉₄	—	2	1	no	—
9	Dic₁₉₄	C₄	1	1	yes	characteristic, complemented
10	#11715897	—	2	1	no	—
11	C₂×D₉₇	D₄	1	1	yes	characteristic
12	#87604	—	4	1	no	—
13	C₄×C₉₇	—	2	1	no	—
14	C₄×C₉₇	C₂×C₄	1	1	yes	characteristic
15	Dic₉₇	—	2	1	no	—
16	Dic₉₇	D₄	1	1	yes	characteristic
17	C₂×C₉₇	C₂²⋊C₄	1	1	yes	characteristic
18	D₉₇	SD₁₆	1	1	yes	characteristic
19	D₉₇	Q₁₆	1	1	yes	characteristic
20	C₉₇	#103	1	1	yes	characteristic, complemented, Sylow
21	#103	—	97	1	no	maximal, Sylow
22	C₂×Q₈	—	97	1	no	—
23	C₂×C₈	—	97	1	no	—
24	C₄⋊C₄	—	97	1	no	—
25	Q₈	—	97	1	no	—
26	Q₈	—	194	1	no	—
27	Q₈	#87604	1	1	yes	characteristic, complemented
28	C₂×C₄	—	97	1	no	—
29	C₂×C₄	—	194	1	no	—
30	C₂×C₄	—	194	1	no	—
31	C₈	—	194	1	no	—
32	C₂²	—	97	1	no	—
33	C₄	—	2	1	no	—
34	C₄	—	97	1	no	—
35	C₄	—	388	1	no	—
36	C₄	—	194	1	no	—
37	C₄	C₂×#87604	1	1	yes	characteristic
38	C₂	—	97	1	no	—
39	C₂	—	97	1	no	—
40	C₂	C₂²⋊#87604	1	1	yes	characteristic

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.