Subgroups — #36442090

Order 22784.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26022531	C₂	1	1	yes	maximal, characteristic
2	#26018328	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#1422	C₂	1	1	yes	maximal, characteristic
4	#19152000	—	2	1	no	—
5	#19151426	C₄	1	2	yes	—
6	#19151424	—	2	1	no	—
7	#19151419	—	2	1	no	—
8	M₆₄×C₈₉	—	2	1	no	—
9	C₄×C₁₆×C₈₉	C₂²	1	1	yes	characteristic
10	#15668004	—	4	1	no	—
11	#15667952	—	4	1	no	—
12	#15667946	—	2	2	no	—
13	#15667944	—	4	1	no	—
14	C₂×C₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
15	C₂×C₁₆×C₈₉	D₄	1	1	yes	characteristic
16	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
17	C₃₂×C₈₉	—	4	1	no	—
18	C₄⋊Dic₈₉	—	4	2	no	—
19	#13083553	—	8	2	no	—
20	#13083549	—	8	1	no	—
21	C₂×C₈×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
22	C₂×C₈×C₈₉	D₈	1	1	yes	characteristic
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	#102	1	1	yes	characteristic
29	C₂×Dic₈₉	—	8	2	no	—
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	#332	1	1	yes	characteristic
37	C₄×C₈₉	#358	1	1	yes	characteristic
38	Dic₈₉	—	16	2	no	—
39	#7454	—	89	1	no	maximal, Sylow
40	C₂×C₈₉	—	2	1	no	—
41	C₂×C₈₉	#1365	1	1	yes	characteristic
42	#2253	—	89	1	no	—
43	#1422	D₈₉	1	1	yes	characteristic
44	#1373	—	89	1	no	—
45	C₈₉	#7454	1	1	yes	characteristic, complemented, Sylow
46	#499	—	178	1	no	—
47	M₆₄	—	2	1	no	—
48	#367	—	89	2	no	—
49	#366	—	178	1	no	—
50	#364	—	178	1	no	—
51	C₄×C₁₆	C₂×D₈₉	1	1	yes	characteristic
52	#125	—	356	1	no	—
53	M₃₂	—	356	1	no	—
54	C₂×C₁₆	C₄×D₈₉	1	1	yes	characteristic
55	C₂×C₁₆	C₂²⋊D₈₉	1	1	yes	characteristic
56	#107	—	178	2	no	—
57	#106	—	356	1	no	—
58	C₄×C₈	D₃₅₆	1	1	yes	characteristic
59	C₃₂	—	4	1	no	—
60	C₂×C₈	#13083551	1	1	yes	characteristic
61	C₂×C₈	D₇₁₂	1	1	yes	characteristic
62	C₄⋊C₄	—	356	2	no	—
63	C₄⋊C₄	—	712	2	no	—
64	C₄²	#13083563	1	1	yes	characteristic
65	C₁₆	—	2	1	no	—
66	C₁₆	—	712	1	no	—
67	C₁₆	#13083562	1	1	yes	characteristic
68	C₁₆	#13083564	1	1	yes	characteristic
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	712	2	no	—
71	C₂×C₄	#15667934	1	1	yes	characteristic
72	C₈	#15667930	1	1	yes	characteristic
73	C₈	#15667935	1	1	yes	characteristic
74	C₈	#15667957	1	1	yes	characteristic
75	C₈	Dic₇₁₂	1	1	yes	characteristic
76	C₂²	#19151412	1	1	yes	characteristic
77	C₄	—	4	1	no	—
78	C₄	—	1424	2	no	—
79	C₄	#19151343	1	1	yes	characteristic
80	C₄	#19151403	1	1	yes	characteristic
81	C₂	—	2	1	no	—
82	C₂	#26018309	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#26018309
commutator	C₂×C₁₆×C₈₉	C₂×C₄
Frattini	C₄×C₁₆	C₂×D₈₉
Fitting	C₈₉×#1422	C₂
socle	C₂×C₈₉	#1365
prime radical	C₂²×C₈₉	#361
cosocle	C₄×C₁₆×C₈₉	C₂²
hypercenter	#1422	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 ◁ #1422

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
#26022531	2
#26018328	2
C₈₉×#1422	2
#7454	89