Subgroups — #14519476

Order 1944.

21312 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃⁵	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃⋊(C₃⋊(C₃⋊(C₃⋊D₃)))	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃⋊(C₃⋊(C₃⋊(C₃⋊Dic₃)))	C₂	1	1	yes	maximal, characteristic, complemented
4	#10620179	—	3	121	no	maximal
5	C₂×C₃⁵	—	2	1	no	—
6	C₂×C₃⁵	C₂²	1	1	yes	characteristic
7	C₃⋊(C₃⋊(C₃⋊(C₃⋊D₃)))	—	2	1	no	—
8	C₂²×C₃⁴	D₃	1	121	yes	complemented
9	C₂×C₃⋊(C₃⋊(C₃⋊D₃))	—	3	121	no	—
10	C₃⋊(C₃⋊(C₃⋊Dic₃))	—	3	121	no	—
11	C₃⁵	D₄	1	1	yes	characteristic, complemented, Sylow
12	#6312	—	9	1210	no	—
13	C₂×C₃⁴	—	2	121	no	—
14	C₂×C₃⁴	C₂×D₃	1	121	yes	—
15	C₃⋊(C₃⋊(C₃⋊D₃))	—	6	121	no	—
16	C₂²×C₃³	C₃⋊D₃	1	1210	yes	complemented
17	C₂×C₃⋊(C₃⋊D₃)	—	9	1210	no	—
18	C₃⋊(C₃⋊Dic₃)	—	9	1210	no	—
19	C₃⁴	#67	1	121	yes	complemented
20	#638	—	27	1210	no	—
21	C₂×C₃³	—	2	1210	no	—
22	C₂×C₃³	C₂×C₃⋊D₃	1	1210	yes	—
23	C₃⋊(C₃⋊D₃)	—	18	1210	no	—
24	C₂²×C₃²	C₃⋊(C₃⋊D₃)	1	1210	yes	complemented
25	C₂×C₃⋊D₃	—	27	1210	no	—
26	C₃⋊Dic₃	—	27	1210	no	—
27	C₃³	#638	1	1210	yes	complemented
28	#67	—	81	121	no	—
29	C₂×C₃²	—	2	1210	no	—
30	C₂×C₃²	C₂×C₃⋊(C₃⋊D₃)	1	1210	yes	—
31	C₃⋊D₃	—	54	1210	no	—
32	C₂²×C₃	C₃⋊(C₃⋊(C₃⋊D₃))	1	121	yes	complemented
33	C₂×D₃	—	81	121	no	—
34	Dic₃	—	81	121	no	—
35	C₃²	#6312	1	1210	yes	complemented
36	D₄	—	243	1	no	Sylow
37	C₂×C₃	—	2	121	no	—
38	C₂×C₃	C₂×C₃⋊(C₃⋊(C₃⋊D₃))	1	121	yes	—
39	D₃	—	162	121	no	—
40	C₂²	—	243	1	no	—
41	C₂²	C₃⋊(C₃⋊(C₃⋊(C₃⋊D₃)))	1	1	yes	characteristic, complemented
42	C₄	—	243	1	no	—
43	C₃	#10620179	1	121	yes	complemented
44	C₂	—	2	1	no	—
45	C₂	—	486	1	no	—
46	C₂	C₂×C₃⋊(C₃⋊(C₃⋊(C₃⋊D₃)))	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂×C₃⋊(C₃⋊(C₃⋊(C₃⋊D₃)))
commutator, socle, cosocle	C₂×C₃⁵	C₂²
Fitting	C₂²×C₃⁵	C₂
hypercenter	C₂²	C₃⋊(C₃⋊(C₃⋊(C₃⋊D₃)))
hypocenter	C₃⁵	D₄
LCS	G ▷ C₂×C₃⁵ ▷ C₃⁵
UCS	C₁ ◁ C₂ ◁ C₂²

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃⁵	C₂	semidirect
2. C₂×C₃⋊(C₃⋊(C₃⋊(C₃⋊D₃)))	C₂	semidirect
3. C₃⋊(C₃⋊(C₃⋊(C₃⋊Dic₃)))	C₂	semidirect
8. C₂²×C₃⁴	D₃	semidirect
11. C₃⁵	D₄	semidirect
16. C₂²×C₃³	C₃⋊D₃	semidirect
19. C₃⁴	#67	semidirect
24. C₂²×C₃²	C₃⋊(C₃⋊D₃)	semidirect
27. C₃³	#638	semidirect
32. C₂²×C₃	C₃⋊(C₃⋊(C₃⋊D₃))	semidirect
35. C₃²	#6312	semidirect
41. C₂²	C₃⋊(C₃⋊(C₃⋊(C₃⋊D₃)))	semidirect
43. C₃	#10620179	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃⁵	2
C₂×C₃⋊(C₃⋊(C₃⋊(C₃⋊D₃)))	2
C₃⋊(C₃⋊(C₃⋊(C₃⋊Dic₃)))	2
#10620179	3