Subgroups — #15692278

Order 3232.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13108075	C₂	1	2	yes	maximal, complemented
2	#13108061	C₂	1	2	yes	maximal, complemented
3	D₈₀₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈×D₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
5	Q₁₆×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
6	Q₈×C₁₀₁	C₂²	1	2	yes	—
7	D₄₀₄	—	2	2	no	—
8	D₄₀₄	C₂²	1	2	yes	—
9	C₄×D₁₀₁	—	2	2	no	—
10	C₄×D₁₀₁	C₂²	1	1	yes	characteristic
11	C₈×C₁₀₁	C₂²	1	1	yes	characteristic
12	#11717579	C₂²	1	1	yes	characteristic
13	C₂×D₁₀₁	—	2	2	no	—
14	C₂×D₁₀₁	D₄	1	1	yes	characteristic
15	C₄×C₁₀₁	—	2	2	no	—
16	C₄×C₁₀₁	C₂³	1	1	yes	characteristic
17	Dic₁₀₁	D₄	1	1	yes	characteristic
18	C₂×C₁₀₁	C₂×D₄	1	1	yes	characteristic
19	D₁₀₁	—	2	1	no	—
20	D₁₀₁	—	4	2	no	—
21	C₁₀₁	#135	1	1	yes	characteristic, complemented, Sylow
22	#135	—	101	1	no	maximal, Sylow
23	#41	—	101	2	no	—
24	Q₁₆	D₁₀₁	1	1	yes	characteristic, complemented
25	SD₁₆	—	101	2	no	—
26	D₈	—	101	1	no	—
27	C₂×C₈	—	101	1	no	—
28	Q₈	C₂×D₁₀₁	1	2	yes	—
29	D₄	—	101	2	no	—
30	D₄	—	202	2	no	—
31	C₂×C₄	—	101	1	no	—
32	C₂×C₄	—	202	2	no	—
33	C₈	—	101	1	no	—
34	C₈	C₂×D₁₀₁	1	1	yes	characteristic
35	C₂²	—	101	1	no	—
36	C₂²	—	202	2	no	—
37	C₄	—	2	2	no	—
38	C₄	—	101	1	no	—
39	C₄	C₂²×D₁₀₁	1	1	yes	characteristic
40	C₂	—	404	2	no	—
41	C₂	—	202	1	no	—
42	C₂	D₄×D₁₀₁	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.