Subgroups — #19152032

Order 5696.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15668031	C₂	1	1	yes	maximal, characteristic, complemented
2	D₈×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#15667957	C₂	1	1	yes	maximal, characteristic, complemented
4	#15667956	C₂	1	1	yes	maximal, characteristic, complemented
5	#15667953	C₂	1	1	yes	maximal, characteristic, complemented
6	#15667951	C₂	1	1	yes	maximal, characteristic, complemented
7	D₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#13083573	—	2	1	no	—
9	D₄×D₈₉	—	2	1	no	—
10	Dic₃₅₆	C₂²	1	1	yes	characteristic, complemented
11	#13083562	—	2	1	no	—
12	D₇₁₂	C₂²	1	1	yes	characteristic
13	#13083559	—	2	1	no	—
14	C₈×D₈₉	C₂²	1	1	yes	characteristic
15	#13083549	C₂²	1	1	yes	characteristic, complemented
16	D₈×C₈₉	C₂²	1	1	yes	characteristic
17	D₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
18	C₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
19	C₂²×D₈₉	—	4	1	no	—
20	D₄×C₈₉	—	2	1	no	—
21	D₄×C₈₉	—	2	1	no	—
22	C₂²⋊D₈₉	—	4	1	no	—
23	C₂²⋊D₈₉	—	4	1	no	—
24	C₂×Dic₈₉	—	4	1	no	—
25	D₃₅₆	—	2	1	no	—
26	C₄×D₈₉	D₄	1	1	yes	characteristic
27	Dic₁₇₈	—	2	1	no	—
28	C₈×C₈₉	C₂³	1	1	yes	characteristic
29	#10623494	D₄	1	1	yes	characteristic
30	C₂²×C₈₉	—	4	1	no	—
31	C₂²×C₈₉	—	4	1	no	—
32	C₂×D₈₉	—	4	1	no	—
33	C₂×D₈₉	—	8	2	no	—
34	C₂×D₈₉	D₈	1	1	yes	characteristic
35	C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
36	Dic₈₉	—	4	1	no	—
37	Dic₈₉	D₈	1	1	yes	characteristic
38	C₂×C₈₉	—	8	1	no	—
39	C₂×C₈₉	—	8	1	no	—
40	C₂×C₈₉	C₂×D₈	1	1	yes	characteristic
41	D₈₉	—	2	1	no	—
42	D₈₉	—	8	1	no	—
43	C₈₉	#509	1	1	yes	characteristic, complemented, Sylow
44	#509	—	89	1	no	maximal, Sylow
45	#135	—	89	1	no	—
46	C₂×D₈	—	89	1	no	—
47	SD₃₂	—	89	1	no	—
48	SD₃₂	—	89	1	no	—
49	D₁₆	—	89	1	no	—
50	D₁₆	D₈₉	1	1	yes	characteristic, complemented
51	M₃₂	—	89	1	no	—
52	#41	—	178	1	no	—
53	C₂×D₄	—	178	1	no	—
54	Q₁₆	—	89	1	no	—
55	SD₁₆	—	178	1	no	—
56	D₈	—	89	1	no	—
57	D₈	—	178	1	no	—
58	D₈	C₂×D₈₉	1	1	yes	characteristic
59	D₈	C₂×D₈₉	1	1	yes	characteristic, complemented
60	C₂×C₈	—	89	1	no	—
61	C₁₆	—	89	1	no	—
62	C₁₆	C₂×D₈₉	1	1	yes	characteristic, complemented
63	C₂³	—	356	1	no	—
64	Q₈	—	178	1	no	—
65	D₄	—	2	1	no	—
66	D₄	—	2	1	no	—
67	D₄	—	356	1	no	—
68	D₄	—	356	1	no	—
69	D₄	—	178	1	no	—
70	C₂×C₄	—	89	1	no	—
71	C₂×C₄	—	356	1	no	—
72	C₈	—	89	1	no	—
73	C₈	C₂²×D₈₉	1	1	yes	characteristic
74	C₂²	—	4	1	no	—
75	C₂²	—	4	1	no	—
76	C₂²	—	89	1	no	—
77	C₂²	—	356	1	no	—
78	C₂²	—	712	2	no	—
79	C₄	—	89	1	no	—
80	C₄	—	356	1	no	—
81	C₄	D₄×D₈₉	1	1	yes	characteristic
82	C₂	—	8	1	no	—
83	C₂	—	8	1	no	—
84	C₂	—	178	1	no	—
85	C₂	—	712	1	no	—
86	C₂	D₈×D₈₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×D₈₉
commutator	C₈×C₈₉	C₂³
Frattini	C₈	C₂²×D₈₉
Fitting	D₁₆×C₈₉	C₂
socle	C₂×C₈₉	C₂×D₈
hypercenter	D₁₆	D₈₉
hypocenter	C₈₉	#509
LCS	G ▷ C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ D₁₆

Complements

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

N	H ≅ G/N	type
1. #15668031	C₂	semidirect
2. D₈×D₈₉	C₂	semidirect
3. #15667957	C₂	semidirect
4. #15667956	C₂	semidirect
5. #15667953	C₂	semidirect
6. #15667951	C₂	semidirect
7. D₁₆×C₈₉	C₂	semidirect
10. Dic₃₅₆	C₂²	semidirect
15. #13083549	C₂²	semidirect
17. D₈×C₈₉	C₂²	semidirect
18. C₁₆×C₈₉	C₂²	semidirect
43. C₈₉	#509	semidirect
50. D₁₆	D₈₉	semidirect
59. D₈	C₂×D₈₉	semidirect
62. C₁₆	C₂×D₈₉	semidirect