Subgroups — #13097098

Order 1584.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₁×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	C₃×C₃⋊(C₁₁⋊C₈)	C₂	1	2	yes	maximal, complemented
3	#10587139	—	3	2	no	maximal
4	C₂×C₁₁×C₃⋊D₃	C₄	1	1	yes	characteristic
5	C₃²×C₄×C₁₁	C₂²	1	1	yes	characteristic
6	C₁₁×C₃⋊Dic₃	C₄	1	1	yes	characteristic
7	C₄×D₃×C₁₁	—	3	2	no	—
8	C₄×D₃×C₁₁	—	6	1	no	—
9	C₃⋊(C₁₁⋊C₈)	D₃	1	2	yes	complemented
10	C₃×C₁₁⋊C₈	—	3	2	no	—
11	C₂×C₃²×C₁₁	C₂×C₄	1	1	yes	characteristic
12	C₁₁×C₃⋊D₃	—	2	1	no	—
13	#4318	—	9	1	no	Hall
14	#3712	—	11	1	no	maximal, Hall
15	C₂×D₃×C₁₁	—	3	2	no	—
16	C₂×D₃×C₁₁	—	6	1	no	—
17	C₃×C₄×C₁₁	—	2	1	no	—
18	C₃×C₄×C₁₁	C₂×D₃	1	2	yes	—
19	C₁₁×Dic₃	—	3	2	no	—
20	C₁₁×Dic₃	—	6	1	no	—
21	C₃²×C₁₁	M₁₆	1	1	yes	characteristic, complemented, Hall
22	C₂×C₄×C₁₁	—	9	1	no	—
23	C₁₁⋊C₈	—	3	2	no	—
24	C₄×C₃⋊D₃	D₁₁	1	1	yes	characteristic
25	C₃×C₃⋊C₈	—	11	2	no	—
26	C₂×C₃×C₁₁	—	2	1	no	—
27	C₂×C₃×C₁₁	C₄×D₃	1	2	yes	—
28	D₃×C₁₁	—	6	2	no	—
29	D₃×C₁₁	—	6	2	no	—
30	ΓL(1,𝔽₂₅)	—	33	2	no	—
31	C₂²×C₁₁	—	9	1	no	—
32	C₄×C₁₁	—	9	1	no	—
33	C₄×C₁₁	D₃²	1	1	yes	characteristic
34	C₂×C₃⋊D₃	Dic₁₁	1	1	yes	characteristic
35	C₃²×C₄	C₂×D₁₁	1	1	yes	characteristic
36	C₃⋊Dic₃	Dic₁₁	1	1	yes	characteristic
37	C₃×C₁₁	—	2	1	no	—
38	C₃×C₁₁	ΓL(1,𝔽₂₅)	1	2	yes	complemented
39	C₄×D₃	—	3	2	no	—
40	C₄×D₃	—	6	1	no	—
41	C₃×C₈	—	33	2	no	—
42	C₃⋊C₈	—	11	2	no	—
43	C₂×C₁₁	—	18	1	no	—
44	C₂×C₁₁	#624	1	1	yes	characteristic
45	C₂×C₃²	C₂×Dic₁₁	1	1	yes	characteristic
46	C₃⋊D₃	—	2	1	no	—
47	M₁₆	—	99	1	no	Sylow
48	C₂×D₃	—	3	2	no	—
49	C₂×D₃	—	6	1	no	—
50	C₃×C₄	—	2	1	no	—
51	C₃×C₄	D₃×D₁₁	1	2	yes	—
52	Dic₃	—	3	2	no	—
53	Dic₃	—	6	1	no	—
54	C₁₁	#3712	1	1	yes	characteristic, complemented, Sylow
55	C₃²	#4318	1	1	yes	characteristic, complemented, Sylow
56	C₂×C₄	—	9	1	no	—
57	C₈	—	33	2	no	—
58	C₂×C₃	—	2	1	no	—
59	C₂×C₃	D₃×Dic₁₁	1	2	yes	—
60	D₃	—	6	2	no	—
61	D₃	—	6	2	no	—
62	C₂²	—	9	1	no	—
63	C₄	—	9	1	no	—
64	C₄	(C₃⋊D₃)⋊D₁₁	1	1	yes	characteristic
65	C₃	—	2	1	no	—
66	C₃	#10587139	1	2	yes	complemented
67	C₂	—	18	1	no	—
68	C₂	#11716245	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₄	(C₃⋊D₃)⋊D₁₁
commutator, socle	C₂×C₃²×C₁₁	C₂×C₄
Fitting, cosocle	C₃²×C₄×C₁₁	C₂²
prime radical	C₂×C₁₁×C₃⋊D₃	C₄
hypocenter	C₃²×C₁₁	M₁₆
LCS	G ▷ C₂×C₃²×C₁₁ ▷ C₃²×C₁₁
UCS	C₁ ◁ C₄

Complements

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

N	H ≅ G/N	type
2. C₃×C₃⋊(C₁₁⋊C₈)	C₂	semidirect
9. C₃⋊(C₁₁⋊C₈)	D₃	semidirect
21. C₃²×C₁₁	M₁₆	semidirect
38. C₃×C₁₁	ΓL(1,𝔽₂₅)	semidirect
54. C₁₁	#3712	semidirect
55. C₃²	#4318	semidirect
66. C₃	#10587139	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₁₁×C₃⋊D₃	2
C₃×C₃⋊(C₁₁⋊C₈)	2
#10587139	3
#3712	11