Subgroups — D₃₂₂₈₄ #72302003

Order 64568.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₈₀₇₁	C₂	1	2	yes	maximal, complemented
2	C₄×C₇×C₁₁₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×C₁₁₅₃	C₂²	1	1	yes	characteristic
4	D₈₀₇₁	—	2	2	no	—
5	D₄₆₁₂	—	7	1	no	maximal, Hall
6	C₇×C₁₁₅₃	D₄	1	1	yes	characteristic, complemented, Hall
7	C₂×D₁₁₅₃	—	7	2	no	—
8	C₄×C₁₁₅₃	D₇	1	1	yes	characteristic, complemented
9	C₂×C₁₁₅₃	C₂×D₇	1	1	yes	characteristic
10	D₁₁₅₃	—	14	2	no	—
11	C₁₁₅₃	D₂₈	1	1	yes	characteristic, complemented, Sylow
12	D₂₈	—	1153	1	no	maximal, Hall
13	C₂×D₇	—	1153	2	no	—
14	C₄×C₇	D₁₁₅₃	1	1	yes	characteristic, complemented
15	C₂×C₇	C₂×D₁₁₅₃	1	1	yes	characteristic
16	D₇	—	2306	2	no	—
17	D₄	—	8071	1	no	Sylow
18	C₇	D₄₆₁₂	1	1	yes	characteristic, complemented, Sylow
19	C₂²	—	8071	2	no	—
20	C₄	D₈₀₇₁	1	1	yes	characteristic, complemented
21	C₂	—	16142	2	no	—
22	C₂	C₂×D₈₀₇₁	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.