Subgroups — #26018314

Order 11392.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19152000	C₂	1	1	yes	maximal, characteristic
2	#19151419	C₂	1	1	yes	maximal, characteristic
3	#364×C₈₉	C₂	1	1	yes	maximal, characteristic
4	#15668004	C₄	1	2	yes	—
5	#15667952	—	2	1	no	—
6	#15667946	—	2	1	no	—
7	#15667944	—	2	1	no	—
8	M₃₂×C₈₉	—	2	1	no	—
9	C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
10	C₄⋊Dic₈₉	—	2	2	no	—
11	#13083553	—	4	2	no	—
12	#13083549	—	4	1	no	—
13	C₂×C₈×C₈₉	D₄	1	1	yes	characteristic
14	C₂×C₈×C₈₉	D₄	1	1	yes	characteristic
15	C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
16	C₁₆×C₈₉	—	4	1	no	—
17	C₂×C₄×C₈₉	—	2	1	no	—
18	C₂×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
19	C₂×Dic₈₉	—	4	2	no	—
20	C₈×C₈₉	SD₁₆	1	1	yes	characteristic
21	C₈×C₈₉	SD₁₆	1	1	yes	characteristic
22	C₈×C₈₉	Q₁₆	1	1	yes	characteristic
23	C₈×C₈₉	Q₁₆	1	1	yes	characteristic
24	C₂²×C₈₉	#100	1	1	yes	characteristic
25	C₄×C₈₉	—	4	1	no	—
26	C₄×C₈₉	#103	1	1	yes	characteristic
27	C₄×C₈₉	#103	1	1	yes	characteristic
28	Dic₈₉	—	8	2	no	—
29	C₂×C₈₉	—	2	1	no	—
30	C₂×C₈₉	#333	1	1	yes	characteristic
31	#1366	—	89	1	no	maximal, Sylow
32	C₈₉	#1366	1	1	yes	characteristic, complemented, Sylow
33	#499	—	89	1	no	—
34	#364	—	89	1	no	—
35	#364	D₈₉	1	1	yes	characteristic
36	#125	—	89	2	no	—
37	M₃₂	—	2	1	no	—
38	M₃₂	—	178	1	no	—
39	#107	—	178	1	no	—
40	#106	—	178	1	no	—
41	C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
42	C₂×C₈	D₃₅₆	1	1	yes	characteristic
43	C₂×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
44	C₄⋊C₄	—	356	2	no	—
45	C₄⋊C₄	—	178	2	no	—
46	C₄²	C₄×D₈₉	1	1	yes	characteristic
47	C₁₆	—	4	1	no	—
48	C₁₆	—	356	1	no	—
49	C₂×C₄	—	2	1	no	—
50	C₂×C₄	—	356	2	no	—
51	C₂×C₄	#13083551	1	1	yes	characteristic
52	C₈	#13083562	1	1	yes	characteristic
53	C₈	#13083563	1	1	yes	characteristic
54	C₈	#13083564	1	1	yes	characteristic
55	C₈	Dic₃₅₆	1	1	yes	characteristic
56	C₂²	#15667928	1	1	yes	characteristic
57	C₄	—	4	1	no	—
58	C₄	—	712	2	no	—
59	C₄	#15667935	1	1	yes	characteristic
60	C₄	#15667937	1	1	yes	characteristic
61	C₂	—	2	1	no	—
62	C₂	#19151346	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#19151346
commutator	C₄²×C₈₉	C₂×C₄
Frattini	C₄×C₈	C₂×D₈₉
Fitting	#364×C₈₉	C₂
socle	C₂×C₈₉	#333
prime radical	C₂²×C₈₉	#100
cosocle	C₄×C₈×C₈₉	C₂²
hypercenter	#364	D₈₉
hypocenter	C₈₉	#1366
LCS	G ▷ C₄²×C₈₉ ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #364

Complements

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

N	H ≅ G/N	type
32. C₈₉	#1366	semidirect

Maximal subgroups

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

subgroup	index
#19152000	2
#19151419	2
#364×C₈₉	2
#1366	89