Subgroups — #31772625

Order 17312.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₂₁₆₄	C₂	1	6	yes	maximal, complemented
2	C₄²×C₅₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×D₅₄₁	C₂²	1	4	yes	—
4	D₂₁₆₄	—	2	12	no	—
5	C₂×C₄×C₅₄₁	C₂²	1	3	yes	—
6	C₂²×C₅₄₁	C₂³	1	1	yes	characteristic
7	C₂×D₅₄₁	—	2	12	no	—
8	C₄×C₅₄₁	D₄	1	6	yes	complemented
9	C₂×C₅₄₁	C₂×D₄	1	3	yes	—
10	D₅₄₁	—	4	4	no	—
11	C₅₄₁	#127	1	1	yes	characteristic, complemented, Sylow
12	#127	—	541	1	no	maximal, Sylow
13	C₂×D₄	—	541	6	no	—
14	C₄²	D₅₄₁	1	1	yes	characteristic, complemented
15	C₂³	—	541	4	no	—
16	D₄	—	1082	12	no	—
17	C₂×C₄	C₂×D₅₄₁	1	3	yes	—
18	C₂²	—	1082	12	no	—
19	C₂²	C₂²×D₅₄₁	1	1	yes	characteristic
20	C₄	D₂₁₆₄	1	6	yes	complemented
21	C₂	—	2164	4	no	—
22	C₂	C₂×D₂₁₆₄	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.