Subgroups — #36442312

Order 22784.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19151317	C₂	1	1	yes	maximal, characteristic, complemented
2	#26018456	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2262	C₂	1	1	yes	maximal, characteristic
4	#19151428	—	2	1	no	—
5	#19151317	—	2	1	no	—
6	#508×C₈₉	—	2	1	no	—
7	Q₆₄×C₈₉	C₄	1	1	yes	characteristic
8	SD₆₄×C₈₉	—	2	1	no	—
9	D₃₂×C₈₉	C₄	1	1	yes	characteristic
10	C₂×C₃₂×C₈₉	C₂²	1	1	yes	characteristic
11	#15667948	—	4	1	no	—
12	#135×C₈₉	—	4	1	no	—
13	Q₃₂×C₈₉	—	2	1	no	—
14	SD₃₂×C₈₉	—	4	1	no	—
15	D₁₆×C₈₉	—	2	1	no	—
16	C₂×C₁₆×C₈₉	D₄	1	1	yes	characteristic
17	C₃₂×C₈₉	C₂×C₄	1	1	yes	characteristic
18	C₃₂×C₈₉	D₄	1	1	yes	characteristic
19	#13083558	—	8	1	no	—
20	#41×C₈₉	—	8	1	no	—
21	Q₁₆×C₈₉	—	4	1	no	—
22	SD₁₆×C₈₉	—	8	1	no	—
23	D₈×C₈₉	—	4	1	no	—
24	C₂×C₈×C₈₉	D₈	1	1	yes	characteristic
25	C₁₆×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
26	C₁₆×C₈₉	SD₁₆	1	1	yes	characteristic
27	Q₈×C₈₉	—	8	1	no	—
28	D₄×C₈₉	—	8	1	no	—
29	D₄×C₈₉	—	16	1	no	—
30	C₂×C₄×C₈₉	—	16	1	no	—
31	C₂×C₄×C₈₉	D₁₆	1	1	yes	characteristic
32	C₈×C₈₉	#102	1	1	yes	characteristic
33	C₈×C₈₉	SD₃₂	1	1	yes	characteristic
34	#10623494	—	16	1	no	—
35	C₂²×C₈₉	—	16	1	no	—
36	C₂²×C₈₉	SD₆₄	1	1	yes	characteristic
37	C₄×C₈₉	—	16	1	no	—
38	C₄×C₈₉	#357	1	1	yes	characteristic
39	C₄×C₈₉	D₃₂	1	1	yes	characteristic
40	#7539	—	89	1	no	maximal, Sylow
41	C₂×C₈₉	—	2	1	no	—
42	C₂×C₈₉	—	32	1	no	—
43	C₂×C₈₉	#1415	1	1	yes	characteristic
44	#2262	D₈₉	1	1	yes	characteristic
45	C₂×C₆₄	—	89	1	no	—
46	#1425	—	89	1	no	—
47	C₈₉	#7539	1	1	yes	characteristic, complemented, Sylow
48	#508	—	2	1	no	—
49	Q₆₄	Dic₈₉	1	1	yes	characteristic
50	SD₆₄	—	2	1	no	—
51	D₃₂	Dic₈₉	1	1	yes	characteristic
52	C₂×C₃₂	C₂×D₈₉	1	1	yes	characteristic
53	#368	—	178	1	no	—
54	C₆₄	—	178	1	no	—
55	#135	—	4	1	no	—
56	Q₃₂	—	2	1	no	—
57	SD₃₂	—	4	1	no	—
58	D₁₆	—	2	1	no	—
59	C₂×C₁₆	C₂²⋊D₈₉	1	1	yes	characteristic
60	#108	—	356	1	no	—
61	C₃₂	C₂×Dic₈₉	1	1	yes	characteristic
62	C₃₂	C₂²⋊D₈₉	1	1	yes	characteristic
63	#41	—	8	1	no	—
64	Q₁₆	—	4	1	no	—
65	SD₁₆	—	8	1	no	—
66	D₈	—	4	1	no	—
67	M₁₆	—	712	1	no	—
68	C₂×C₈	#13083559	1	1	yes	characteristic
69	C₁₆	C₂²⋊Dic₈₉	1	1	yes	characteristic
70	C₁₆	#13083562	1	1	yes	characteristic
71	Q₈	—	8	1	no	—
72	D₄	—	8	1	no	—
73	D₄	—	16	1	no	—
74	C₂×C₄	—	16	1	no	—
75	C₂×C₄	#15667953	1	1	yes	characteristic
76	C₈	—	1424	1	no	—
77	C₈	#15667933	1	1	yes	characteristic
78	C₈	#15667956	1	1	yes	characteristic
79	C₂²	—	16	1	no	—
80	C₂²	#19151436	1	1	yes	characteristic
81	C₄	—	16	1	no	—
82	C₄	#19151399	1	1	yes	characteristic
83	C₄	#19151433	1	1	yes	characteristic
84	C₂	—	2	1	no	—
85	C₂	—	32	1	no	—
86	C₂	#26018430	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#19151433
commutator	C₃₂×C₈₉	C₂×C₄
Frattini	C₂×C₃₂	C₂×D₈₉
Fitting, prime radical	C₈₉×#2262	C₂
socle	C₂×C₈₉	#1415
cosocle	C₂×C₃₂×C₈₉	C₂²
hypercenter	#2262	D₈₉
hypocenter	C₈₉	#7539
LCS	G ▷ C₃₂×C₈₉ ▷ C₁₆×C₈₉ ▷ C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ #2262

Complements

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

N	H ≅ G/N	type
1. C₂×#19151317	C₂	semidirect
2. #26018456	C₂	semidirect
47. C₈₉	#7539	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#19151317	2
#26018456	2
C₈₉×#2262	2
#7539	89