Subgroups — #15690857

Order 3104.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13095511	C₂	1	3	yes	maximal, complemented
2	#13095510	C₂	1	6	yes	maximal, complemented
3	C₂×Dic₁₉₄	C₂	1	3	yes	maximal, complemented
4	Q₈×D₉₇	C₂	1	2	yes	maximal, complemented
5	#41×C₉₇	C₂	1	1	yes	maximal, characteristic, complemented
6	Q₈×C₉₇	C₂²	1	1	yes	characteristic
7	D₄×C₉₇	C₂²	1	3	yes	—
8	C₂×C₄×C₉₇	C₂²	1	3	yes	—
9	C₂²⋊D₉₇	C₂²	1	6	yes	—
10	C₂×Dic₉₇	C₂²	1	6	yes	—
11	D₃₈₈	C₂²	1	1	yes	characteristic
12	C₄×D₉₇	C₂²	1	6	yes	—
13	Dic₁₉₄	C₂²	1	6	yes	—
14	Dic₁₉₄	C₂²	1	3	yes	—
15	C₂²×C₉₇	C₂³	1	3	yes	—
16	C₂×D₉₇	C₂³	1	2	yes	—
17	C₄×C₉₇	C₂³	1	1	yes	characteristic
18	C₄×C₉₇	C₂³	1	3	yes	—
19	Dic₉₇	C₂³	1	6	yes	—
20	C₂×C₉₇	—	2	3	no	—
21	C₂×C₉₇	C₂⁴	1	1	yes	characteristic
22	D₉₇	—	2	2	no	—
23	C₉₇	2₋¹⁺⁴	1	1	yes	characteristic, complemented, Sylow
24	2₋¹⁺⁴	—	97	1	no	maximal, Sylow
25	#41	—	97	6	no	—
26	#41	—	97	3	no	—
27	#41	D₉₇	1	1	yes	characteristic, complemented
28	C₂×Q₈	—	97	2	no	—
29	C₂×Q₈	—	97	3	no	—
30	Q₈	—	97	6	no	—
31	Q₈	—	97	3	no	—
32	Q₈	C₂×D₉₇	1	1	yes	characteristic
33	D₄	—	97	6	no	—
34	D₄	—	97	1	no	—
35	D₄	C₂×D₉₇	1	3	yes	—
36	C₂×C₄	—	97	6	no	—
37	C₂×C₄	—	97	6	no	—
38	C₂×C₄	C₂×D₉₇	1	3	yes	—
39	C₂²	—	97	2	no	—
40	C₂²	C₂²×D₉₇	1	3	yes	—
41	C₄	—	97	6	no	—
42	C₄	C₂²×D₉₇	1	3	yes	—
43	C₄	C₂²×D₉₇	1	1	yes	characteristic
44	C₂	—	2	3	no	—
45	C₂	—	194	2	no	—
46	C₂	C₂³×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.