Subgroups — #15692252

Order 3232.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄₀₄	C₂	1	6	yes	maximal, complemented
2	C₄²×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×D₁₀₁	C₂²	1	4	yes	—
4	C₂×C₄×C₁₀₁	C₂²	1	3	yes	—
5	D₄₀₄	—	2	12	no	—
6	C₂²×C₁₀₁	C₂³	1	1	yes	characteristic
7	C₂×D₁₀₁	—	2	12	no	—
8	C₄×C₁₀₁	D₄	1	6	yes	complemented
9	C₂×C₁₀₁	C₂×D₄	1	3	yes	—
10	D₁₀₁	—	4	4	no	—
11	C₁₀₁	#127	1	1	yes	characteristic, complemented, Sylow
12	#127	—	101	1	no	maximal, Sylow
13	C₂×D₄	—	101	6	no	—
14	C₄²	D₁₀₁	1	1	yes	characteristic, complemented
15	C₂³	—	101	4	no	—
16	D₄	—	202	12	no	—
17	C₂×C₄	C₂×D₁₀₁	1	3	yes	—
18	C₂²	—	202	12	no	—
19	C₂²	C₂²×D₁₀₁	1	1	yes	characteristic
20	C₄	D₄₀₄	1	6	yes	complemented
21	C₂	—	404	4	no	—
22	C₂	C₂×D₄₀₄	1	3	yes	—

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.