Subgroups — #36442340

Order 22784.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅₆₉₆	C₂	1	1	yes	maximal, characteristic, complemented
2	#26018071	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×D₆₄	C₂	1	1	yes	maximal, characteristic, complemented
4	D₂₈₄₈	—	2	1	no	—
5	D₃₂×C₈₉	—	2	1	no	—
6	C₆₄×C₈₉	C₂²	1	1	yes	characteristic
7	D₁₄₂₄	—	4	1	no	—
8	D₁₆×C₈₉	—	4	1	no	—
9	C₃₂×C₈₉	D₄	1	1	yes	characteristic
10	D₇₁₂	—	8	1	no	—
11	D₈×C₈₉	—	8	1	no	—
12	C₁₆×C₈₉	D₈	1	1	yes	characteristic
13	D₄×C₈₉	—	16	1	no	—
14	D₃₅₆	—	16	1	no	—
15	C₈×C₈₉	D₁₆	1	1	yes	characteristic
16	C₂²×C₈₉	—	32	1	no	—
17	C₂×D₈₉	—	32	1	no	—
18	C₄×C₈₉	D₃₂	1	1	yes	characteristic
19	D₁₂₈	—	89	1	no	maximal, Sylow
20	C₂×C₈₉	—	64	1	no	—
21	C₂×C₈₉	D₆₄	1	1	yes	characteristic
22	D₈₉	—	64	1	no	—
23	D₆₄	—	89	1	no	—
24	D₆₄	D₈₉	1	1	yes	characteristic, complemented
25	C₁₂₈	—	89	1	no	—
26	C₈₉	D₁₂₈	1	1	yes	characteristic, complemented, Sylow
27	D₃₂	—	2	1	no	—
28	D₃₂	—	178	1	no	—
29	C₆₄	C₂×D₈₉	1	1	yes	characteristic
30	D₁₆	—	4	1	no	—
31	D₁₆	—	356	1	no	—
32	C₃₂	C₂²⋊D₈₉	1	1	yes	characteristic
33	D₈	—	8	1	no	—
34	D₈	—	712	1	no	—
35	C₁₆	#13083559	1	1	yes	characteristic
36	D₄	—	16	1	no	—
37	D₄	—	1424	1	no	—
38	C₈	#15667953	1	1	yes	characteristic
39	C₂²	—	32	1	no	—
40	C₂²	—	2848	1	no	—
41	C₄	#19151433	1	1	yes	characteristic
42	C₂	—	64	1	no	—
43	C₂	—	5696	1	no	—
44	C₂	#26018464	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.