Subgroups — #15690832

Order 3104.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13095511	C₂	1	2	yes	maximal, complemented
2	Dic₃₈₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#13095500	C₂	1	2	yes	maximal, complemented
4	D₇₇₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₈×C₉₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×C₉₇	C₂²	1	1	yes	characteristic
7	C₂²⋊D₉₇	—	2	2	no	—
8	D₃₈₈	C₂²	1	2	yes	—
9	C₄×D₉₇	—	2	2	no	—
10	Dic₁₉₄	C₂²	1	2	yes	—
11	C₈×C₉₇	C₂²	1	1	yes	characteristic
12	C₈×C₉₇	C₂²	1	1	yes	characteristic
13	C₂²×C₉₇	D₄	1	1	yes	characteristic
14	C₂×D₉₇	—	2	2	no	—
15	C₄×C₉₇	D₄	1	1	yes	characteristic
16	C₄×C₉₇	C₂³	1	1	yes	characteristic
17	Dic₉₇	—	2	2	no	—
18	C₂×C₉₇	—	2	1	no	—
19	C₂×C₉₇	C₂×D₄	1	1	yes	characteristic
20	D₉₇	—	4	2	no	—
21	C₉₇	#135	1	1	yes	characteristic, complemented, Sylow
22	#135	—	97	1	no	maximal, Sylow
23	#41	—	97	2	no	—
24	Q₁₆	—	97	1	no	—
25	SD₁₆	—	97	2	no	—
26	D₈	—	97	1	no	—
27	C₂×C₈	D₉₇	1	1	yes	characteristic, complemented
28	Q₈	—	97	2	no	—
29	D₄	—	97	2	no	—
30	D₄	—	194	2	no	—
31	C₂×C₄	—	194	2	no	—
32	C₂×C₄	C₂×D₉₇	1	1	yes	characteristic
33	C₈	C₂×D₉₇	1	1	yes	characteristic
34	C₈	C₂×D₉₇	1	1	yes	characteristic
35	C₂²	—	194	2	no	—
36	C₂²	D₃₈₈	1	1	yes	characteristic
37	C₄	—	194	2	no	—
38	C₄	D₃₈₈	1	1	yes	characteristic
39	C₄	C₂²×D₉₇	1	1	yes	characteristic
40	C₂	—	2	1	no	—
41	C₂	—	388	2	no	—
42	C₂	C₂×D₃₈₈	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.