Subgroups — C₃⋊#26012784 #45686107

Order 33300.

224 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅²×C₃₇⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#16814867	C₃	1	1	yes	maximal, characteristic, complemented
3	#26012784	—	3	1	no	maximal
4	C₃×C₅²×C₃₇⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃⋊(Dic₁₈₅⋊C₃)	—	5	6	no	maximal
6	C₂×C₅²×C₃₇⋊C₃	—	2	1	no	—
7	C₂×C₅²×C₃₇⋊C₃	D₃	1	1	yes	characteristic
8	C₂×C₃×C₅²×C₃₇	C₂×C₃	1	1	yes	characteristic
9	#16814867	—	3	1	no	Hall
10	C₂×C₃×C₅×C₃₇⋊C₃	D₅	1	6	yes	—
11	C₅²×C₃₇⋊C₃	—	2	1	no	—
12	C₅²×C₃₇⋊C₃	Dic₃	1	1	yes	characteristic, complemented
13	C₃×C₅²×C₃₇	C₃×C₄	1	1	yes	characteristic, complemented
14	Dic₅₅₅	—	5	6	no	—
15	Dic₁₈₅⋊C₃	—	15	6	no	—
16	C₂×C₅²×C₃₇	C₃×D₃	1	1	yes	characteristic
17	C₃×C₅×C₃₇⋊C₃	Dic₅	1	6	yes	complemented
18	C₃⋊(Dic₃₇⋊C₃)	—	25	1	no	Hall
19	C₂×C₃×C₅×C₃₇	C₃×D₅	1	6	yes	—
20	C₂×C₅×C₃₇⋊C₃	—	2	6	no	—
21	C₂×C₅×C₃₇⋊C₃	D₁₅	1	6	yes	—
22	C₅²×C₃₇	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
23	C₃×C₃⋊#1039	—	37	1	no	maximal, Hall
24	Dic₁₈₅	—	15	6	no	—
25	C₂×C₃×C₃₇⋊C₃	C₅⋊D₅	1	1	yes	characteristic
26	C₃×C₅×C₃₇	C₃×Dic₅	1	6	yes	complemented
27	C₅×C₃₇⋊C₃	—	2	6	no	—
28	C₅×C₃₇⋊C₃	Dic₁₅	1	6	yes	complemented
29	C₂×C₃²×C₅²	—	37	1	no	—
30	Dic₁₁₁	—	25	1	no	—
31	Dic₃₇⋊C₃	—	75	1	no	—
32	C₂×C₅×C₃₇	C₃×D₁₅	1	6	yes	—
33	C₃×C₃₇⋊C₃	#1039	1	1	yes	characteristic, complemented, Hall
34	C₃⋊#1039	—	37	1	no	—
35	C₃×#1039	—	111	1	no	—
36	C₃²×C₅²	—	37	1	no	Hall
37	C₂×C₃×C₃₇	C₃×C₅⋊D₅	1	1	yes	characteristic
38	C₂×C₃₇⋊C₃	—	2	1	no	—
39	C₂×C₃₇⋊C₃	C₃⋊(C₅⋊D₅)	1	1	yes	characteristic
40	C₅×C₃₇	C₃×Dic₁₅	1	6	yes	complemented
41	C₃×Dic₁₅	—	185	6	no	—
42	C₂×C₃×C₅²	—	37	1	no	—
43	C₂×C₃×C₅²	—	74	1	no	—
44	C₂×C₃×C₅²	D₃₇⋊C₃	1	1	yes	characteristic
45	Dic₃₇	—	75	1	no	Hall
46	C₃×C₃₇	C₃×#1039	1	1	yes	characteristic, complemented
47	C₃₇⋊C₃	—	2	1	no	—
48	C₃₇⋊C₃	C₃⋊#1039	1	1	yes	characteristic, complemented
49	#1039	—	111	1	no	Hall
50	C₂×C₃²×C₅	—	37	6	no	—
51	C₃×C₅²	—	37	1	no	—
52	C₃×C₅²	—	74	1	no	—
53	C₃×C₅²	Dic₃₇⋊C₃	1	1	yes	characteristic, complemented
54	C₂×C₃₇	C₃×C₃⋊(C₅⋊D₅)	1	1	yes	characteristic
55	Dic₁₅	—	185	6	no	—
56	C₃×Dic₅	—	555	6	no	—
57	C₂×C₅²	C₃⋊(D₃₇⋊C₃)	1	1	yes	characteristic
58	C₃²×C₅	—	37	6	no	—
59	C₃₇	C₃×C₃⋊#1039	1	1	yes	characteristic, complemented, Sylow
60	C₃×Dic₃	—	925	1	no	Hall
61	C₂×C₃×C₅	—	37	6	no	—
62	C₂×C₃×C₅	—	74	6	no	—
63	C₂×C₃×C₅	C₅⋊(D₃₇⋊C₃)	1	6	yes	—
64	C₅²	C₃⋊(Dic₃₇⋊C₃)	1	1	yes	characteristic, complemented, Sylow
65	Dic₅	—	555	6	no	—
66	C₂×C₃²	—	37	1	no	—
67	C₃×C₅	—	37	6	no	—
68	C₃×C₅	—	74	6	no	—
69	C₃×C₅	Dic₁₈₅⋊C₃	1	6	yes	complemented
70	C₃×C₄	—	2775	1	no	—
71	Dic₃	—	925	1	no	—
72	C₂×C₅	C₃⋊(C₅⋊(D₃₇⋊C₃))	1	6	yes	—
73	C₃²	—	37	1	no	Sylow
74	C₂×C₃	—	37	1	no	—
75	C₂×C₃	—	74	1	no	—
76	C₂×C₃	C₅⋊(C₅⋊(D₃₇⋊C₃))	1	1	yes	characteristic
77	C₅	C₃⋊(Dic₁₈₅⋊C₃)	1	6	yes	complemented
78	C₄	—	2775	1	no	Sylow
79	C₃	—	37	1	no	—
80	C₃	—	74	1	no	—
81	C₃	#26012784	1	1	yes	characteristic, complemented
82	C₂	C₃⋊(C₅⋊(C₅⋊(D₃₇⋊C₃)))	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₃⋊(C₅⋊(C₅⋊(D₃₇⋊C₃)))
commutator, hypocenter	C₃×C₅²×C₃₇	C₃×C₄
Fitting, socle, cosocle	C₂×C₃×C₅²×C₃₇	C₂×C₃
prime radical	C₂×C₃×C₅²×C₃₇⋊C₃	C₂
LCS	G ▷ C₃×C₅²×C₃₇
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
2. C₃⋊#16814867	C₃	semidirect
4. C₃×C₅²×C₃₇⋊C₃	C₄	semidirect
12. C₅²×C₃₇⋊C₃	Dic₃	semidirect
13. C₃×C₅²×C₃₇	C₃×C₄	semidirect
17. C₃×C₅×C₃₇⋊C₃	Dic₅	semidirect
22. C₅²×C₃₇	C₃×Dic₃	semidirect
26. C₃×C₅×C₃₇	C₃×Dic₅	semidirect
28. C₅×C₃₇⋊C₃	Dic₁₅	semidirect
33. C₃×C₃₇⋊C₃	#1039	semidirect
40. C₅×C₃₇	C₃×Dic₁₅	semidirect
46. C₃×C₃₇	C₃×#1039	semidirect
48. C₃₇⋊C₃	C₃⋊#1039	semidirect
53. C₃×C₅²	Dic₃₇⋊C₃	semidirect
59. C₃₇	C₃×C₃⋊#1039	semidirect
64. C₅²	C₃⋊(Dic₃₇⋊C₃)	semidirect
69. C₃×C₅	Dic₁₈₅⋊C₃	semidirect
77. C₅	C₃⋊(Dic₁₈₅⋊C₃)	semidirect
81. C₃	#26012784	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅²×C₃₇⋊C₃	2
C₃⋊#16814867	3
#26012784	3
C₃⋊(Dic₁₈₅⋊C₃)	5
C₃×C₃⋊#1039	37

Subgroups — C3⋊#26012784 #45686107

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊#26012784 #45686107