Subgroups — D₃₂₂₉₆ #72302014

Order 64592.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₆₁₄₈	C₂	1	2	yes	maximal, complemented
2	C₈×C₁₁×C₃₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₄₀₃₇	—	2	2	no	—
4	C₄×C₁₁×C₃₆₇	C₂²	1	1	yes	characteristic
5	C₂×C₁₁×C₃₆₇	D₄	1	1	yes	characteristic
6	D₄₀₃₇	—	4	2	no	—
7	D₂₉₃₆	—	11	1	no	maximal, Hall
8	C₁₁×C₃₆₇	D₈	1	1	yes	characteristic, complemented, Hall
9	D₁₄₆₈	—	11	2	no	—
10	C₈×C₃₆₇	D₁₁	1	1	yes	characteristic, complemented
11	C₂×D₃₆₇	—	22	2	no	—
12	C₄×C₃₆₇	C₂×D₁₁	1	1	yes	characteristic
13	C₂×C₃₆₇	D₄₄	1	1	yes	characteristic
14	D₃₆₇	—	44	2	no	—
15	C₃₆₇	D₈₈	1	1	yes	characteristic, complemented, Sylow
16	D₈₈	—	367	1	no	maximal, Hall
17	D₄₄	—	367	2	no	—
18	C₈×C₁₁	D₃₆₇	1	1	yes	characteristic, complemented
19	C₂×D₁₁	—	734	2	no	—
20	C₄×C₁₁	C₂×D₃₆₇	1	1	yes	characteristic
21	C₂×C₁₁	D₁₄₆₈	1	1	yes	characteristic
22	D₁₁	—	1468	2	no	—
23	D₈	—	4037	1	no	Sylow
24	C₁₁	D₂₉₃₆	1	1	yes	characteristic, complemented, Sylow
25	D₄	—	4037	2	no	—
26	C₈	D₄₀₃₇	1	1	yes	characteristic, complemented
27	C₂²	—	8074	2	no	—
28	C₄	C₂×D₄₀₃₇	1	1	yes	characteristic
29	C₂	—	16148	2	no	—
30	C₂	D₁₆₁₄₈	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.