Subgroups — #13097042

Order 1584.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11716270	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×C₄⋊(C₃⋊D₃)	C₂	1	1	yes	maximal, characteristic
3	C₃²×C₁₁⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#10587148	—	3	4	no	maximal
5	C₂×C₁₁×C₃⋊D₃	—	2	1	no	—
6	C₃²×C₄×C₁₁	C₂²	1	1	yes	characteristic
7	C₃⋊Dic₃₃	—	2	1	no	—
8	Dic₆₆	—	3	4	no	—
9	C₁₁×D₁₂	—	3	4	no	—
10	C₃×C₁₁⋊C₈	D₃	1	4	yes	complemented
11	C₂×C₃²×C₁₁	D₄	1	1	yes	characteristic
12	C₁₁×C₃⋊D₃	—	4	1	no	—
13	#4324	—	9	1	no	Hall
14	#3744	—	11	1	no	maximal, Hall
15	C₂×D₃×C₁₁	—	6	4	no	—
16	C₃×C₄×C₁₁	C₂×D₃	1	4	yes	—
17	Dic₃₃	—	6	4	no	—
18	C₃²×C₁₁	SD₁₆	1	1	yes	characteristic, complemented, Hall
19	D₄×C₁₁	—	9	1	no	—
20	Dic₂₂	—	9	1	no	—
21	C₁₁⋊C₈	C₃⋊D₃	1	1	yes	characteristic, complemented
22	C₄⋊(C₃⋊D₃)	D₁₁	1	1	yes	characteristic
23	#634	—	11	1	no	—
24	C₃²×C₈	—	11	1	no	—
25	C₂×C₃×C₁₁	D₁₂	1	4	yes	—
26	D₃×C₁₁	—	12	4	no	—
27	#204	—	33	4	no	—
28	C₂²×C₁₁	—	18	1	no	—
29	C₄×C₁₁	C₂×C₃⋊D₃	1	1	yes	characteristic
30	Dic₁₁	—	18	1	no	—
31	C₂×C₃⋊D₃	—	2	1	no	—
32	C₃²×C₄	C₂×D₁₁	1	1	yes	characteristic
33	C₃⋊Dic₃	—	22	1	no	—
34	C₃×C₁₁	#204	1	4	yes	complemented
35	D₁₂	—	3	4	no	—
36	Dic₆	—	33	4	no	—
37	C₃×C₈	—	11	4	no	—
38	C₂×C₁₁	—	36	1	no	—
39	C₂×C₁₁	C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
40	C₂×C₃²	C₂²⋊D₁₁	1	1	yes	characteristic
41	C₃⋊D₃	—	4	1	no	—
42	SD₁₆	—	99	1	no	Sylow
43	C₂×D₃	—	6	4	no	—
44	C₃×C₄	D₃×D₁₁	1	4	yes	—
45	Dic₃	—	66	4	no	—
46	C₁₁	#3744	1	1	yes	characteristic, complemented, Sylow
47	C₃²	#4324	1	1	yes	characteristic, complemented, Sylow
48	Q₈	—	99	1	no	—
49	D₄	—	9	1	no	—
50	C₈	—	11	1	no	—
51	C₂×C₃	#63142	1	4	yes	—
52	D₃	—	12	4	no	—
53	C₂²	—	18	1	no	—
54	C₄	—	198	1	no	—
55	C₄	C₃⋊D₃×D₁₁	1	1	yes	characteristic
56	C₃	#10587148	1	4	yes	complemented
57	C₂	—	36	1	no	—
58	C₂	#11716230	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11716230
commutator, Fitting, cosocle	C₃²×C₄×C₁₁	C₂²
Frattini, hypercenter	C₄	C₃⋊D₃×D₁₁
socle	C₂×C₃²×C₁₁	D₄
prime radical	C₁₁×C₄⋊(C₃⋊D₃)	C₂
hypocenter	C₃²×C₁₁	SD₁₆
LCS	G ▷ C₃²×C₄×C₁₁ ▷ C₂×C₃²×C₁₁ ▷ C₃²×C₁₁
UCS	C₁ ◁ C₂ ◁ C₄

Complements

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

N	H ≅ G/N	type
1. #11716270	C₂	semidirect
3. C₃²×C₁₁⋊C₈	C₂	semidirect
10. C₃×C₁₁⋊C₈	D₃	semidirect
18. C₃²×C₁₁	SD₁₆	semidirect
21. C₁₁⋊C₈	C₃⋊D₃	semidirect
34. C₃×C₁₁	#204	semidirect
46. C₁₁	#3744	semidirect
47. C₃²	#4324	semidirect
56. C₃	#10587148	semidirect

Maximal subgroups

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

subgroup	index
#11716270	2
C₁₁×C₄⋊(C₃⋊D₃)	2
C₃²×C₁₁⋊C₈	2
#10587148	3
#3744	11