Subgroups — #15690818

Order 3104.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13095511	C₂	1	1	yes	maximal, characteristic
2	#13095494	C₂	1	2	yes	maximal, complemented
3	C₂×#11715895	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈×D₉₇	C₂	1	2	yes	maximal, complemented
5	M₁₆×C₉₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×C₉₇	C₂²	1	1	yes	characteristic
7	C₂²⋊D₉₇	C₄	1	2	yes	—
8	D₃₈₈	C₄	1	1	yes	characteristic
9	C₄×D₉₇	C₂²	1	2	yes	—
10	Dic₁₉₄	C₄	1	1	yes	characteristic
11	C₈×C₉₇	C₂²	1	2	yes	—
12	#11715895	C₂²	1	1	yes	characteristic
13	#11715895	C₂²	1	1	yes	characteristic
14	C₂²×C₉₇	C₂×C₄	1	1	yes	characteristic
15	C₂×D₉₇	C₂×C₄	1	2	yes	—
16	C₄×C₉₇	C₂×C₄	1	1	yes	characteristic
17	C₄×C₉₇	C₂³	1	1	yes	characteristic
18	Dic₉₇	C₂×C₄	1	2	yes	—
19	C₂×C₉₇	—	2	1	no	—
20	C₂×C₉₇	C₂²×C₄	1	1	yes	characteristic
21	D₉₇	—	2	2	no	—
22	C₉₇	#131	1	1	yes	characteristic, complemented, Sylow
23	#131	—	97	1	no	maximal, Sylow
24	#41	—	97	1	no	—
25	M₁₆	—	97	2	no	—
26	M₁₆	D₉₇	1	1	yes	characteristic, complemented
27	C₂×C₈	—	97	1	no	—
28	C₂×C₈	—	97	2	no	—
29	Q₈	—	97	1	no	—
30	D₄	—	97	2	no	—
31	D₄	—	97	1	no	—
32	C₂×C₄	—	97	2	no	—
33	C₂×C₄	C₂×D₉₇	1	1	yes	characteristic
34	C₈	—	97	1	no	—
35	C₈	—	97	1	no	—
36	C₈	C₂×D₉₇	1	2	yes	—
37	C₂²	—	97	2	no	—
38	C₂²	C₄×D₉₇	1	1	yes	characteristic
39	C₄	—	97	2	no	—
40	C₄	C₄×D₉₇	1	1	yes	characteristic
41	C₄	C₂²×D₉₇	1	1	yes	characteristic
42	C₂	—	2	1	no	—
43	C₂	—	194	2	no	—
44	C₂	C₂×C₄×D₉₇	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.