Subgroups — #13097073

Order 1584.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×D₃₃	C₂	1	1	yes	maximal, characteristic
2	C₃⋊(C₃⋊(C₁₁⋊C₈))	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₁×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#10587194	—	3	1	no	maximal
5	#10587138	—	3	1	no	maximal
6	C₂×C₃×D₃₃	C₄	1	1	yes	characteristic
7	C₃²×C₄×C₁₁	C₂²	1	1	yes	characteristic
8	C₃×Dic₃₃	C₄	1	1	yes	characteristic
9	C₄×D₃₃	D₃	1	1	yes	characteristic
10	C₃×C₄×D₁₁	—	3	1	no	—
11	C₃×C₈×C₁₁	—	3	1	no	—
12	C₃⋊(C₁₁⋊C₈)	—	3	1	no	—
13	C₃⋊(C₁₁⋊C₈)	—	3	1	no	—
14	C₃⋊(C₁₁⋊C₈)	—	6	1	no	—
15	C₁₁×C₃⋊C₈	D₃	1	1	yes	characteristic, complemented
16	C₂×C₃²×C₁₁	C₂×C₄	1	1	yes	characteristic
17	C₃×D₃₃	—	2	1	no	—
18	#4313	—	9	1	no	Hall
19	#3711	—	11	1	no	maximal, Hall
20	C₂×D₃₃	Dic₃	1	1	yes	characteristic
21	C₂×C₃×D₁₁	—	3	1	no	—
22	C₃×C₄×C₁₁	—	2	1	no	—
23	C₃×C₄×C₁₁	C₂×D₃	1	1	yes	characteristic
24	C₃×C₄×C₁₁	C₂×D₃	1	1	yes	characteristic
25	Dic₃₃	Dic₃	1	1	yes	characteristic
26	C₃×Dic₁₁	—	3	1	no	—
27	C₃²×C₁₁	M₁₆	1	1	yes	characteristic, complemented, Hall
28	C₄×D₁₁	—	3	1	no	—
29	C₈×C₁₁	—	3	1	no	—
30	C₁₁⋊C₈	—	9	1	no	—
31	C₃×C₄×D₃	—	11	1	no	—
32	C₃⋊(C₃⋊C₈)	—	11	1	no	—
33	C₃×C₃⋊C₈	D₁₁	1	1	yes	characteristic, complemented
34	C₂×C₃×C₁₁	—	2	1	no	—
35	C₂×C₃×C₁₁	C₄×D₃	1	1	yes	characteristic
36	C₂×C₃×C₁₁	C₂×Dic₃	1	1	yes	characteristic
37	D₃₃	—	2	1	no	—
38	C₃×D₁₁	—	6	1	no	—
39	#208	—	33	1	no	—
40	ΓL(1,𝔽₂₅)	—	33	1	no	—
41	C₂×D₁₁	—	3	1	no	—
42	C₄×C₁₁	D₃²	1	1	yes	characteristic
43	Dic₁₁	—	3	1	no	—
44	C₂×C₃×D₃	—	11	1	no	—
45	C₃²×C₄	C₂×D₁₁	1	1	yes	characteristic
46	C₃×Dic₃	—	11	1	no	—
47	C₃×C₁₁	—	2	1	no	—
48	C₃×C₁₁	ΓL(1,𝔽₂₅)	1	1	yes	characteristic, complemented
49	C₃×C₁₁	#208	1	1	yes	characteristic, complemented
50	C₂×C₃×C₄	—	33	1	no	—
51	C₄×D₃	—	11	1	no	—
52	C₃×C₈	—	3	1	no	—
53	C₃⋊C₈	—	33	1	no	—
54	C₃⋊C₈	—	33	1	no	—
55	C₃⋊C₈	—	66	1	no	—
56	C₃⋊C₈	D₃₃	1	1	yes	characteristic, complemented
57	C₂×C₁₁	D₃×Dic₃	1	1	yes	characteristic
58	D₁₁	—	6	1	no	—
59	C₂×C₃²	C₄×D₁₁	1	1	yes	characteristic
60	C₃×D₃	—	22	1	no	—
61	M₁₆	—	99	1	no	Sylow
62	C₂²×C₃	—	33	1	no	—
63	C₂×D₃	—	11	1	no	—
64	C₃×C₄	—	2	1	no	—
65	C₃×C₄	—	33	1	no	—
66	C₃×C₄	D₃×D₁₁	1	1	yes	characteristic
67	C₃×C₄	C₂×D₃₃	1	1	yes	characteristic
68	Dic₃	—	11	1	no	—
69	C₁₁	#3711	1	1	yes	characteristic, complemented, Sylow
70	C₃²	#4313	1	1	yes	characteristic, complemented, Sylow
71	C₂×C₄	—	33	1	no	—
72	C₈	—	3	1	no	—
73	C₈	—	99	1	no	—
74	C₂×C₃	—	2	1	no	—
75	C₂×C₃	—	66	1	no	—
76	C₂×C₃	Dic₃×D₁₁	1	1	yes	characteristic
77	C₂×C₃	C₄×D₃₃	1	1	yes	characteristic
78	D₃	—	22	1	no	—
79	C₂²	—	33	1	no	—
80	C₄	—	33	1	no	—
81	C₄	D₃×D₃₃	1	1	yes	characteristic
82	C₃	—	2	1	no	—
83	C₃	#10587138	1	1	yes	characteristic, complemented
84	C₃	#10587194	1	1	yes	characteristic, complemented
85	C₂	—	66	1	no	—
86	C₂	Dic₃×D₃₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₄	D₃×D₃₃
commutator, socle	C₂×C₃²×C₁₁	C₂×C₄
Fitting, cosocle	C₃²×C₄×C₁₁	C₂²
prime radical	C₂×C₃×D₃₃	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
3. C₃×C₁₁×C₃⋊C₈	C₂	semidirect
15. C₁₁×C₃⋊C₈	D₃	semidirect
27. C₃²×C₁₁	M₁₆	semidirect
33. C₃×C₃⋊C₈	D₁₁	semidirect
48. C₃×C₁₁	ΓL(1,𝔽₂₅)	semidirect
49. C₃×C₁₁	#208	semidirect
56. C₃⋊C₈	D₃₃	semidirect
69. C₁₁	#3711	semidirect
70. C₃²	#4313	semidirect
83. C₃	#10587138	semidirect
84. C₃	#10587194	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄×D₃₃	2
C₃⋊(C₃⋊(C₁₁⋊C₈))	2
C₃×C₁₁×C₃⋊C₈	2
#10587194	3
#10587138	3
#3711	11