Subgroups — C₃⋊(C₃⋊#14559055) #36345002

Order 21780.

156 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×#10597245	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#14559055	—	3	4	no	maximal
3	C₃²×#10597245	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₁×C₃⋊Dic₃₃	C₅	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂×C₃×#10597245	D₃	1	4	yes	—
6	#14559055	—	9	1	no	Hall
7	C₂×C₃²×C₁₁²	C₂×C₅	1	1	yes	characteristic
8	C₃⋊(C₃⋊(Dic₁₁⋊C₅))	—	11	1	no	maximal
9	C₃⋊Dic₃×C₁₁⋊C₅	—	11	1	no	maximal
10	C₃×#10597245	Dic₃	1	4	yes	complemented
11	C₁₁×Dic₃₃	—	3	4	no	—
12	C₂×#10597245	C₃⋊D₃	1	1	yes	characteristic
13	C₃²×C₁₁²	C₄×C₅	1	1	yes	characteristic, complemented, Hall
14	C₂×C₃²×C₁₁⋊C₅	—	11	1	no	—
15	C₂×C₃²×C₁₁⋊C₅	—	11	1	no	—
16	C₂×C₃×C₁₁²	C₅×D₃	1	4	yes	—
17	C₃⋊(Dic₁₁⋊C₅)	—	33	4	no	—
18	Dic₃×C₁₁⋊C₅	—	33	4	no	—
19	#10597245	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
20	C₃²×C₁₁⋊C₅	—	11	1	no	—
21	C₃²×C₁₁⋊C₅	—	11	1	no	—
22	C₁₁×Dic₁₁	—	9	1	no	Hall
23	C₃⋊Dic₃₃	C₁₁⋊C₅	1	1	yes	characteristic, complemented
24	C₁₁×C₃⋊Dic₃	—	11	1	no	—
25	C₃×C₁₁²	C₅×Dic₃	1	4	yes	complemented
26	C₂×C₃×C₁₁⋊C₅	—	11	4	no	—
27	C₂×C₃×C₁₁⋊C₅	—	11	4	no	—
28	C₂×C₁₁²	C₅×C₃⋊D₃	1	1	yes	characteristic
29	C₄×C₁₁⋊C₅	—	99	1	no	—
30	Dic₁₁⋊C₅	—	99	1	no	—
31	C₂×C₃²×C₁₁	—	10	1	no	—
32	C₂×C₃²×C₁₁	AGL(1,𝔽₁₁)	1	1	yes	characteristic
33	C₂×C₃²×C₁₁	C₂×C₁₁⋊C₅	1	1	yes	characteristic
34	C₅×C₃⋊Dic₃	—	121	1	no	Hall
35	C₃×C₁₁⋊C₅	—	11	4	no	—
36	C₃×C₁₁⋊C₅	—	11	4	no	—
37	Dic₃₃	—	3	4	no	—
38	C₁₁×Dic₃	—	33	4	no	—
39	C₁₁²	C₅×C₃⋊Dic₃	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₁₁⋊C₅	—	11	1	no	—
41	C₂×C₁₁⋊C₅	—	11	1	no	—
42	C₃²×C₁₁	—	10	1	no	—
43	C₃²×C₁₁	Dic₁₁⋊C₅	1	1	yes	characteristic, complemented
44	C₃²×C₁₁	C₄×C₁₁⋊C₅	1	1	yes	characteristic, complemented
45	C₂×C₃²×C₅	—	121	1	no	—
46	C₂×C₃×C₁₁	—	10	4	no	—
47	C₂×C₃×C₁₁	D₃×C₁₁⋊C₅	1	4	yes	—
48	C₂×C₃×C₁₁	C₃⋊AGL(1,𝔽₁₁)	1	4	yes	—
49	C₅×Dic₃	—	363	4	no	—
50	C₁₁⋊C₅	—	11	1	no	—
51	C₁₁⋊C₅	—	11	1	no	—
52	C₃²×C₅	—	121	1	no	Hall
53	C₄×C₁₁	—	99	1	no	—
54	Dic₁₁	—	9	1	no	—
55	C₃⋊Dic₃	—	11	1	no	Hall
56	C₃×C₁₁	—	10	4	no	—
57	C₃×C₁₁	Dic₃×C₁₁⋊C₅	1	4	yes	complemented
58	C₃×C₁₁	C₃⋊(Dic₁₁⋊C₅)	1	4	yes	complemented
59	C₂×C₃×C₅	—	121	4	no	—
60	C₂×C₁₁	—	10	1	no	—
61	C₂×C₁₁	C₃⋊D₃×C₁₁⋊C₅	1	1	yes	characteristic
62	C₂×C₁₁	C₃⋊(C₃⋊AGL(1,𝔽₁₁))	1	1	yes	characteristic
63	C₄×C₅	—	1089	1	no	Hall
64	C₂×C₃²	#11925896	1	1	yes	characteristic
65	C₃×C₅	—	121	4	no	—
66	Dic₃	—	33	4	no	—
67	C₁₁	—	10	1	no	—
68	C₁₁	C₃⋊Dic₃×C₁₁⋊C₅	1	1	yes	characteristic, complemented
69	C₁₁	C₃⋊(C₃⋊(Dic₁₁⋊C₅))	1	1	yes	characteristic, complemented
70	C₂×C₅	—	121	1	no	—
71	C₃²	#14559055	1	1	yes	characteristic, complemented, Sylow
72	C₂×C₃	C₃⋊#11925896	1	4	yes	—
73	C₅	—	121	1	no	Sylow
74	C₄	—	99	1	no	Sylow
75	C₃	C₃⋊#14559055	1	4	yes	complemented
76	C₂	C₃⋊(C₃⋊#11925896)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₃⋊(C₃⋊#11925896)
commutator, hypocenter	C₃²×C₁₁²	C₄×C₅
Fitting, socle, cosocle	C₂×C₃²×C₁₁²	C₂×C₅
prime radical	C₂×C₃²×#10597245	C₂
LCS	G ▷ C₃²×C₁₁²
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
3. C₃²×#10597245	C₄	semidirect
4. C₁₁×C₃⋊Dic₃₃	C₅	semidirect
10. C₃×#10597245	Dic₃	semidirect
13. C₃²×C₁₁²	C₄×C₅	semidirect
19. #10597245	C₃⋊Dic₃	semidirect
23. C₃⋊Dic₃₃	C₁₁⋊C₅	semidirect
25. C₃×C₁₁²	C₅×Dic₃	semidirect
39. C₁₁²	C₅×C₃⋊Dic₃	semidirect
43. C₃²×C₁₁	Dic₁₁⋊C₅	semidirect
44. C₃²×C₁₁	C₄×C₁₁⋊C₅	semidirect
57. C₃×C₁₁	Dic₃×C₁₁⋊C₅	semidirect
58. C₃×C₁₁	C₃⋊(Dic₁₁⋊C₅)	semidirect
68. C₁₁	C₃⋊Dic₃×C₁₁⋊C₅	semidirect
69. C₁₁	C₃⋊(C₃⋊(Dic₁₁⋊C₅))	semidirect
71. C₃²	#14559055	semidirect
75. C₃	C₃⋊#14559055	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×#10597245	2
C₃⋊#14559055	3
C₁₁×C₃⋊Dic₃₃	5
C₃⋊(C₃⋊(Dic₁₁⋊C₅))	11
C₃⋊Dic₃×C₁₁⋊C₅	11

Subgroups — C3⋊(C3⋊#14559055) #36345002

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(C₃⋊#14559055) #36345002