Subgroups — #19152000

Order 5696.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15668004	C₂	1	2	yes	maximal
2	#15667946	C₂	1	2	yes	maximal
3	#15667944	C₂	1	2	yes	maximal
4	C₄×C₈×C₈₉	C₂	1	1	yes	maximal, characteristic
5	C₄⋊Dic₈₉	C₂²	1	4	yes	—
6	#13083553	—	2	4	no	—
7	C₂×C₈×C₈₉	C₂²	1	1	yes	characteristic
8	C₂×C₈×C₈₉	C₂²	1	1	yes	characteristic
9	C₄²×C₈₉	C₂²	1	1	yes	characteristic
10	C₂×C₄×C₈₉	D₄	1	2	yes	—
11	C₂×C₄×C₈₉	C₂³	1	1	yes	characteristic
12	C₂×Dic₈₉	—	2	4	no	—
13	C₈×C₈₉	Q₈	1	2	yes	—
14	C₈×C₈₉	Q₈	1	2	yes	—
15	C₂²×C₈₉	C₂×D₄	1	1	yes	characteristic
16	C₄×C₈₉	—	2	2	no	—
17	C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
18	C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
19	Dic₈₉	—	4	4	no	—
20	C₂×C₈₉	C₄⋊Q₈	1	1	yes	characteristic
21	C₂×C₈₉	#135	1	2	yes	—
22	C₈₉	#499	1	1	yes	characteristic, complemented, Sylow
23	#499	—	89	1	no	maximal, Sylow
24	#125	—	89	2	no	—
25	#107	—	89	2	no	—
26	#106	—	89	2	no	—
27	C₄×C₈	D₈₉	1	1	yes	characteristic
28	C₂×C₈	C₂×D₈₉	1	1	yes	characteristic
29	C₂×C₈	C₂×D₈₉	1	1	yes	characteristic
30	C₄⋊C₄	—	89	4	no	—
31	C₄⋊C₄	—	178	4	no	—
32	C₄²	C₂×D₈₉	1	1	yes	characteristic
33	C₂×C₄	—	178	4	no	—
34	C₂×C₄	D₃₅₆	1	2	yes	—
35	C₂×C₄	C₂²×D₈₉	1	1	yes	characteristic
36	C₈	Dic₁₇₈	1	2	yes	—
37	C₈	Dic₁₇₈	1	2	yes	—
38	C₂²	C₂×D₃₅₆	1	1	yes	characteristic
39	C₄	—	2	2	no	—
40	C₄	—	356	4	no	—
41	C₄	C₂×Dic₁₇₈	1	1	yes	characteristic
42	C₄	C₂×Dic₁₇₈	1	1	yes	characteristic
43	C₂	#15668012	1	1	yes	characteristic
44	C₂	#15668034	1	2	yes	—

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

N	H ≅ G/N	type
22. C₈₉	#499	semidirect