Subgroups — #19151435

Order 5696.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₄₂₄	C₂	1	1	yes	maximal, characteristic
2	#15667918	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₃₂×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	D₇₁₂	—	2	1	no	—
5	Q₁₆×C₈₉	—	2	1	no	—
6	C₁₆×C₈₉	C₂²	1	1	yes	characteristic
7	Q₈×C₈₉	—	4	1	no	—
8	D₃₅₆	—	4	1	no	—
9	C₈×C₈₉	D₄	1	1	yes	characteristic
10	C₂×D₈₉	—	8	1	no	—
11	C₄×C₈₉	—	8	1	no	—
12	C₄×C₈₉	D₈	1	1	yes	characteristic
13	C₂×C₈₉	D₁₆	1	1	yes	characteristic
14	D₈₉	—	16	1	no	—
15	C₈₉	SD₆₄	1	1	yes	characteristic, complemented, Sylow
16	SD₆₄	—	89	1	no	maximal, Sylow
17	Q₃₂	D₈₉	1	1	yes	characteristic, complemented
18	D₁₆	—	89	1	no	—
19	C₃₂	—	89	1	no	—
20	Q₁₆	—	2	1	no	—
21	D₈	—	178	1	no	—
22	C₁₆	C₂×D₈₉	1	1	yes	characteristic
23	Q₈	—	4	1	no	—
24	D₄	—	356	1	no	—
25	C₈	C₂²⋊D₈₉	1	1	yes	characteristic
26	C₂²	—	712	1	no	—
27	C₄	—	8	1	no	—
28	C₄	#13083559	1	1	yes	characteristic
29	C₂	—	1424	1	no	—
30	C₂	#15667953	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.