Subgroups — D₁₁₃₉₂ #36442341

Order 22784.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅₆₉₆	C₂	1	2	yes	maximal, complemented
2	C₈₉×C₁₂₈	C₂	1	1	yes	maximal, characteristic, complemented
3	D₂₈₄₈	—	2	2	no	—
4	C₆₄×C₈₉	C₂²	1	1	yes	characteristic
5	D₁₄₂₄	—	4	2	no	—
6	C₃₂×C₈₉	D₄	1	1	yes	characteristic
7	D₇₁₂	—	8	2	no	—
8	C₁₆×C₈₉	D₈	1	1	yes	characteristic
9	D₃₅₆	—	16	2	no	—
10	C₈×C₈₉	D₁₆	1	1	yes	characteristic
11	C₂×D₈₉	—	32	2	no	—
12	C₄×C₈₉	D₃₂	1	1	yes	characteristic
13	D₁₂₈	—	89	1	no	maximal, Sylow
14	C₂×C₈₉	D₆₄	1	1	yes	characteristic
15	D₈₉	—	64	2	no	—
16	D₆₄	—	89	2	no	—
17	C₁₂₈	D₈₉	1	1	yes	characteristic, complemented
18	C₈₉	D₁₂₈	1	1	yes	characteristic, complemented, Sylow
19	D₃₂	—	178	2	no	—
20	C₆₄	C₂×D₈₉	1	1	yes	characteristic
21	D₁₆	—	356	2	no	—
22	C₃₂	D₃₅₆	1	1	yes	characteristic
23	D₈	—	712	2	no	—
24	C₁₆	D₇₁₂	1	1	yes	characteristic
25	D₄	—	1424	2	no	—
26	C₈	D₁₄₂₄	1	1	yes	characteristic
27	C₂²	—	2848	2	no	—
28	C₄	D₂₈₄₈	1	1	yes	characteristic
29	C₂	—	5696	2	no	—
30	C₂	D₅₆₉₆	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.