Subgroups — #36442091

Order 22784.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26018450	C₂	1	1	yes	maximal, characteristic
2	#26018328	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#2253	C₂	1	1	yes	maximal, characteristic
4	#19151432	—	2	1	no	—
5	#19151419	—	2	1	no	—
6	#499×C₈₉	—	2	1	no	—
7	#367×C₈₉	C₄	1	2	yes	—
8	#366×C₈₉	—	2	1	no	—
9	C₄×C₁₆×C₈₉	C₂²	1	1	yes	characteristic
10	#15667952	—	4	1	no	—
11	#15667918	—	4	1	no	—
12	#125×C₈₉	—	4	1	no	—
13	C₂×C₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
14	C₂×C₁₆×C₈₉	D₄	1	1	yes	characteristic
15	#107×C₈₉	—	2	2	no	—
16	#106×C₈₉	—	4	1	no	—
17	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
18	#13083549	—	8	1	no	—
19	C₂×C₈×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
20	C₂×C₈×C₈₉	D₈	1	1	yes	characteristic
21	C₄⋊C₄×C₈₉	—	4	2	no	—
22	C₄⋊C₄×C₈₉	—	8	2	no	—
23	C₄²×C₈₉	SD₁₆	1	1	yes	characteristic
24	C₁₆×C₈₉	—	2	1	no	—
25	C₁₆×C₈₉	SD₁₆	1	1	yes	characteristic
26	C₁₆×C₈₉	Q₁₆	1	1	yes	characteristic
27	C₂×C₄×C₈₉	—	2	1	no	—
28	C₂×C₄×C₈₉	—	8	2	no	—
29	C₂×C₄×C₈₉	#102	1	1	yes	characteristic
30	C₈×C₈₉	#101	1	1	yes	characteristic
31	C₈×C₈₉	#103	1	1	yes	characteristic
32	C₈×C₈₉	SD₃₂	1	1	yes	characteristic
33	C₈×C₈₉	Q₃₂	1	1	yes	characteristic
34	C₂²×C₈₉	#361	1	1	yes	characteristic
35	C₄×C₈₉	—	4	1	no	—
36	C₄×C₈₉	—	16	2	no	—
37	C₄×C₈₉	#332	1	1	yes	characteristic
38	C₄×C₈₉	#358	1	1	yes	characteristic
39	#7454	—	89	1	no	maximal, Sylow
40	C₂×C₈₉	—	2	1	no	—
41	C₂×C₈₉	#1365	1	1	yes	characteristic
42	#2253	D₈₉	1	1	yes	characteristic
43	#1422	—	89	1	no	—
44	#1373	—	89	1	no	—
45	C₈₉	#7454	1	1	yes	characteristic, complemented, Sylow
46	#499	—	2	1	no	—
47	M₆₄	—	178	1	no	—
48	#367	Dic₈₉	1	2	yes	—
49	#366	—	2	1	no	—
50	#364	—	178	1	no	—
51	C₄×C₁₆	C₂×D₈₉	1	1	yes	characteristic
52	#125	—	4	1	no	—
53	M₃₂	—	356	1	no	—
54	C₂×C₁₆	C₂×Dic₈₉	1	1	yes	characteristic
55	C₂×C₁₆	C₂²⋊D₈₉	1	1	yes	characteristic
56	#107	—	2	2	no	—
57	#106	—	4	1	no	—
58	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
59	C₃₂	—	356	1	no	—
60	C₂×C₈	C₂²⋊Dic₈₉	1	1	yes	characteristic
61	C₂×C₈	#13083559	1	1	yes	characteristic
62	C₄⋊C₄	—	4	2	no	—
63	C₄⋊C₄	—	8	2	no	—
64	C₄²	#13083562	1	1	yes	characteristic
65	C₁₆	—	2	1	no	—
66	C₁₆	—	712	1	no	—
67	C₁₆	#13083561	1	1	yes	characteristic
68	C₁₆	#13083564	1	1	yes	characteristic
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	8	2	no	—
71	C₂×C₄	#15667933	1	1	yes	characteristic
72	C₈	#15667931	1	1	yes	characteristic
73	C₈	#15667936	1	1	yes	characteristic
74	C₈	#15667955	1	1	yes	characteristic
75	C₈	#15667958	1	1	yes	characteristic
76	C₂²	#19151411	1	1	yes	characteristic
77	C₄	—	4	1	no	—
78	C₄	—	16	2	no	—
79	C₄	#19151344	1	1	yes	characteristic
80	C₄	#19151402	1	1	yes	characteristic
81	C₂	—	2	1	no	—
82	C₂	#26018310	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#26018310
commutator	C₂×C₁₆×C₈₉	C₂×C₄
Frattini	C₄×C₁₆	C₂×D₈₉
Fitting	C₈₉×#2253	C₂
socle	C₂×C₈₉	#1365
prime radical	C₂²×C₈₉	#361
cosocle	C₄×C₁₆×C₈₉	C₂²
hypercenter	#2253	D₈₉
hypocenter	C₈₉	#7454
LCS	G ▷ C₂×C₁₆×C₈₉ ▷ C₂×C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #2253

Complements

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

N	H ≅ G/N	type
45. C₈₉	#7454	semidirect

Maximal subgroups

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

subgroup	index
#26018450	2
#26018328	2
C₈₉×#2253	2
#7454	89