Subgroups — #19151426

Order 5696.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15667946	C₂	1	2	yes	maximal
2	C₂×C₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₄⋊Dic₈₉	—	2	2	no	—
4	C₂×C₈×C₈₉	C₂²	1	1	yes	characteristic
5	C₁₆×C₈₉	C₄	1	2	yes	complemented
6	C₂×C₄×C₈₉	D₄	1	1	yes	characteristic
7	C₂×Dic₈₉	—	4	2	no	—
8	C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
9	C₈×C₈₉	Q₈	1	1	yes	characteristic
10	C₂²×C₈₉	D₈	1	1	yes	characteristic
11	C₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
12	C₄×C₈₉	Q₁₆	1	1	yes	characteristic
13	Dic₈₉	—	8	2	no	—
14	C₂×C₈₉	#107	1	1	yes	characteristic
15	C₂×C₈₉	SD₃₂	1	2	yes	—
16	C₈₉	#367	1	1	yes	characteristic, complemented, Sylow
17	#367	—	89	1	no	maximal, Sylow
18	C₂×C₁₆	D₈₉	1	1	yes	characteristic
19	#107	—	89	2	no	—
20	C₂×C₈	C₂×D₈₉	1	1	yes	characteristic
21	C₄⋊C₄	—	178	2	no	—
22	C₁₆	Dic₈₉	1	2	yes	complemented
23	C₂×C₄	—	356	2	no	—
24	C₂×C₄	D₃₅₆	1	1	yes	characteristic
25	C₈	Dic₁₇₈	1	1	yes	characteristic
26	C₈	C₂×Dic₈₉	1	1	yes	characteristic
27	C₂²	D₇₁₂	1	1	yes	characteristic
28	C₄	—	712	2	no	—
29	C₄	C₄⋊Dic₈₉	1	1	yes	characteristic
30	C₄	Dic₃₅₆	1	1	yes	characteristic
31	C₂	#15667946	1	1	yes	characteristic
32	C₂	#15667957	1	2	yes	—

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