Subgroups — #19152037

Order 5696.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15668031	C₂	1	1	yes	maximal, characteristic
2	Q₁₆×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	Dic₇₁₂	C₂	1	1	yes	maximal, characteristic, complemented
4	#15667958	C₂	1	1	yes	maximal, characteristic, complemented
5	#15667956	C₂	1	1	yes	maximal, characteristic, complemented
6	#15667951	C₂	1	1	yes	maximal, characteristic, complemented
7	SD₃₂×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#13083573	—	2	1	no	—
9	Q₈×D₈₉	—	2	1	no	—
10	Dic₃₅₆	C₂²	1	1	yes	characteristic
11	Dic₃₅₆	C₂²	1	1	yes	characteristic
12	#13083564	—	2	1	no	—
13	#13083562	—	2	1	no	—
14	C₈×D₈₉	C₂²	1	1	yes	characteristic
15	#13083549	C₂²	1	1	yes	characteristic
16	Q₁₆×C₈₉	C₂²	1	1	yes	characteristic
17	D₈×C₈₉	C₂²	1	1	yes	characteristic
18	C₁₆×C₈₉	C₂²	1	1	yes	characteristic
19	Q₈×C₈₉	—	2	1	no	—
20	D₄×C₈₉	—	2	1	no	—
21	C₂²⋊D₈₉	—	4	1	no	—
22	C₂×Dic₈₉	—	4	1	no	—
23	C₄×D₈₉	—	4	1	no	—
24	C₄×D₈₉	D₄	1	1	yes	characteristic
25	Dic₁₇₈	—	2	1	no	—
26	Dic₁₇₈	—	2	1	no	—
27	Dic₁₇₈	—	4	1	no	—
28	C₈×C₈₉	C₂³	1	1	yes	characteristic
29	#10623494	D₄	1	1	yes	characteristic
30	C₂²×C₈₉	—	4	1	no	—
31	C₂×D₈₉	D₈	1	1	yes	characteristic
32	C₄×C₈₉	—	4	1	no	—
33	C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
34	Dic₈₉	—	4	1	no	—
35	Dic₈₉	—	4	1	no	—
36	Dic₈₉	D₈	1	1	yes	characteristic
37	C₂×C₈₉	—	8	1	no	—
38	C₂×C₈₉	C₂×D₈	1	1	yes	characteristic
39	D₈₉	—	2	1	no	—
40	C₈₉	#510	1	1	yes	characteristic, complemented, Sylow
41	#510	—	89	1	no	maximal, Sylow
42	#135	—	89	1	no	—
43	C₂×Q₁₆	—	89	1	no	—
44	Q₃₂	—	89	1	no	—
45	Q₃₂	—	89	1	no	—
46	SD₃₂	—	89	1	no	—
47	SD₃₂	D₈₉	1	1	yes	characteristic, complemented
48	M₃₂	—	89	1	no	—
49	#41	—	178	1	no	—
50	C₂×Q₈	—	178	1	no	—
51	Q₁₆	—	89	1	no	—
52	Q₁₆	—	89	1	no	—
53	Q₁₆	—	178	1	no	—
54	Q₁₆	C₂×D₈₉	1	1	yes	characteristic
55	SD₁₆	—	178	1	no	—
56	D₈	C₂×D₈₉	1	1	yes	characteristic
57	C₂×C₈	—	89	1	no	—
58	C₁₆	—	89	1	no	—
59	C₁₆	C₂×D₈₉	1	1	yes	characteristic
60	Q₈	—	2	1	no	—
61	Q₈	—	356	1	no	—
62	Q₈	—	178	1	no	—
63	Q₈	—	178	1	no	—
64	D₄	—	2	1	no	—
65	D₄	—	356	1	no	—
66	C₂×C₄	—	89	1	no	—
67	C₂×C₄	—	356	1	no	—
68	C₂×C₄	—	356	1	no	—
69	C₈	—	89	1	no	—
70	C₈	C₂²×D₈₉	1	1	yes	characteristic
71	C₂²	—	4	1	no	—
72	C₂²	—	89	1	no	—
73	C₄	—	4	1	no	—
74	C₄	—	89	1	no	—
75	C₄	—	356	1	no	—
76	C₄	—	356	1	no	—
77	C₄	D₄×D₈₉	1	1	yes	characteristic
78	C₂	—	8	1	no	—
79	C₂	—	178	1	no	—
80	C₂	D₈×D₈₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×D₈₉
commutator	C₈×C₈₉	C₂³
Frattini	C₈	C₂²×D₈₉
Fitting	SD₃₂×C₈₉	C₂
socle	C₂×C₈₉	C₂×D₈
hypercenter	SD₃₂	D₈₉
hypocenter	C₈₉	#510
LCS	G ▷ C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ SD₃₂

Complements

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

N	H ≅ G/N	type
2. Q₁₆×D₈₉	C₂	semidirect
3. Dic₇₁₂	C₂	semidirect
4. #15667958	C₂	semidirect
5. #15667956	C₂	semidirect
6. #15667951	C₂	semidirect
7. SD₃₂×C₈₉	C₂	semidirect
40. C₈₉	#510	semidirect
47. SD₃₂	D₈₉	semidirect