Subgroups — #36442329

Order 22784.

66 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
2	#26018452	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#1423	C₂	1	1	yes	maximal, characteristic
4	#19151424	—	2	1	no	—
5	#19151317	C₄	1	2	yes	complemented
6	C₂×C₃₂×C₈₉	C₂²	1	1	yes	characteristic
7	#366×C₈₉	—	2	1	no	—
8	#15667946	—	4	1	no	—
9	C₂×C₁₆×C₈₉	D₄	1	1	yes	characteristic
10	#107×C₈₉	—	4	1	no	—
11	C₃₂×C₈₉	C₂×C₄	1	1	yes	characteristic
12	C₃₂×C₈₉	Q₈	1	1	yes	characteristic
13	C₄⋊Dic₈₉	—	8	1	no	—
14	C₂×C₈×C₈₉	D₈	1	1	yes	characteristic
15	C₄⋊C₄×C₈₉	—	8	1	no	—
16	C₁₆×C₈₉	C₄⋊C₄	1	1	yes	characteristic
17	C₁₆×C₈₉	Q₁₆	1	1	yes	characteristic
18	C₂×C₄×C₈₉	—	16	1	no	—
19	C₂×C₄×C₈₉	D₁₆	1	1	yes	characteristic
20	C₂×Dic₈₉	—	16	1	no	—
21	C₈×C₈₉	#107	1	1	yes	characteristic
22	C₈×C₈₉	Q₃₂	1	1	yes	characteristic
23	C₂²×C₈₉	D₃₂	1	1	yes	characteristic
24	C₄×C₈₉	—	32	1	no	—
25	C₄×C₈₉	#366	1	1	yes	characteristic
26	C₄×C₈₉	Q₆₄	1	1	yes	characteristic
27	Dic₈₉	—	32	1	no	—
28	#7546	—	89	1	no	maximal, Sylow
29	C₂×C₈₉	#1423	1	1	yes	characteristic
30	C₂×C₈₉	SD₁₂₈	1	1	yes	characteristic
31	C₂×C₈₉	SD₁₂₈	1	1	yes	characteristic
32	C₂×C₆₄	—	89	1	no	—
33	#1423	—	89	1	no	—
34	#1423	D₈₉	1	1	yes	characteristic
35	C₈₉	#7546	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₃₂	C₂×D₈₉	1	1	yes	characteristic
37	#366	—	2	1	no	—
38	#366	—	178	1	no	—
39	C₆₄	—	89	2	no	—
40	C₂×C₁₆	C₂²⋊D₈₉	1	1	yes	characteristic
41	#107	—	4	1	no	—
42	#107	—	356	1	no	—
43	C₃₂	Dic₁₇₈	1	1	yes	characteristic
44	C₃₂	C₄×D₈₉	1	1	yes	characteristic
45	C₂×C₈	#13083559	1	1	yes	characteristic
46	C₄⋊C₄	—	8	1	no	—
47	C₄⋊C₄	—	712	1	no	—
48	C₁₆	#13083553	1	1	yes	characteristic
49	C₁₆	#13083564	1	1	yes	characteristic
50	C₂×C₄	—	16	1	no	—
51	C₂×C₄	—	1424	1	no	—
52	C₂×C₄	#15667953	1	1	yes	characteristic
53	C₈	#15667945	1	1	yes	characteristic
54	C₈	#15667958	1	1	yes	characteristic
55	C₂²	#19151433	1	1	yes	characteristic
56	C₄	—	32	1	no	—
57	C₄	—	2848	1	no	—
58	C₄	#19151423	1	1	yes	characteristic
59	C₄	#19151438	1	1	yes	characteristic
60	C₂	#26018451	1	1	yes	characteristic
61	C₂	#26018466	1	1	yes	characteristic
62	C₂	#26018467	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#19151433
commutator	C₃₂×C₈₉	C₂×C₄
Frattini	C₂×C₃₂	C₂×D₈₉
Fitting	C₈₉×#1423	C₂
socle, prime radical	C₂²×C₈₉	D₃₂
cosocle	C₂×C₃₂×C₈₉	C₂²
hypercenter	#1423	D₈₉
hypocenter	C₈₉	#7546
LCS	G ▷ C₃₂×C₈₉ ▷ C₁₆×C₈₉ ▷ C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ #1423

Complements

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

N	H ≅ G/N	type
5. #19151317	C₄	semidirect
35. C₈₉	#7546	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
#26018452	2
C₈₉×#1423	2
#7546	89