Subgroups — C₂×D₈₀₈ #15692266

Order 3232.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄₀₄	C₂	1	2	yes	maximal, complemented
2	D₈₀₈	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₈×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₁₀₁	—	2	2	no	—
5	C₂×C₄×C₁₀₁	C₂²	1	1	yes	characteristic
6	D₄₀₄	—	2	2	no	—
7	D₄₀₄	C₂²	1	4	yes	complemented
8	C₈×C₁₀₁	C₂²	1	2	yes	complemented
9	C₂²×C₁₀₁	D₄	1	1	yes	characteristic
10	C₂×D₁₀₁	—	2	4	no	—
11	C₂×D₁₀₁	—	4	4	no	—
12	C₄×C₁₀₁	D₄	1	1	yes	characteristic
13	C₄×C₁₀₁	C₂³	1	1	yes	characteristic
14	C₂×C₁₀₁	D₈	1	2	yes	complemented
15	C₂×C₁₀₁	C₂×D₄	1	1	yes	characteristic
16	D₁₀₁	—	4	4	no	—
17	C₁₀₁	C₂×D₈	1	1	yes	characteristic, complemented, Sylow
18	C₂×D₈	—	101	1	no	maximal, Sylow
19	C₂×D₄	—	101	2	no	—
20	D₈	—	101	4	no	—
21	C₂×C₈	D₁₀₁	1	1	yes	characteristic, complemented
22	C₂³	—	202	2	no	—
23	D₄	—	101	4	no	—
24	D₄	—	202	2	no	—
25	C₂×C₄	C₂×D₁₀₁	1	1	yes	characteristic
26	C₈	C₂×D₁₀₁	1	2	yes	complemented
27	C₂²	—	404	4	no	—
28	C₂²	—	202	4	no	—
29	C₂²	D₄₀₄	1	1	yes	characteristic
30	C₄	D₄₀₄	1	1	yes	characteristic
31	C₄	C₂²×D₁₀₁	1	1	yes	characteristic
32	C₂	—	404	4	no	—
33	C₂	D₈₀₈	1	2	yes	direct product factor
34	C₂	C₂×D₄₀₄	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.