Subgroups — C₃×#874 #63997

Order 288.

231 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₁₂	C₂	1	6	yes	maximal, complemented
2	C₃²×C₄²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#127	—	3	1	no	maximal
4	#874	C₃	1	1	yes	maximal, characteristic, direct product factor
5	C₂²×C₃×D₃	C₂²	1	4	yes	—
6	C₂×C₃²×C₄	C₂²	1	3	yes	—
7	C₃×D₁₂	—	2	12	no	—
8	C₂×C₃×D₄	—	3	6	no	—
9	C₂×D₁₂	C₂×C₃	1	6	yes	complemented
10	C₃×C₄²	—	2	1	no	—
11	C₃×C₄²	D₃	1	1	yes	characteristic, complemented
12	C₃×C₄²	C₂×C₃	1	1	yes	characteristic, complemented
13	C₂²×C₃²	C₂³	1	1	yes	characteristic
14	C₂×C₃×D₃	—	2	12	no	—
15	C₃²×C₄	D₄	1	6	yes	complemented
16	#127	—	3	1	no	Sylow
17	C₂³×C₃	—	3	4	no	—
18	C₂²×D₃	C₂²×C₃	1	4	yes	—
19	C₃×D₄	—	6	12	no	—
20	C₂×C₃×C₄	—	2	3	no	—
21	C₂×C₃×C₄	C₂×D₃	1	3	yes	—
22	C₂×C₃×C₄	C₂²×C₃	1	3	yes	—
23	D₁₂	—	2	12	no	—
24	C₂×C₃²	C₂×D₄	1	3	yes	—
25	C₃×D₃	—	4	4	no	—
26	C₂×D₄	—	3	6	no	—
27	C₄²	C₃×D₃	1	1	yes	characteristic, complemented
28	C₂²×C₃	—	2	1	no	—
29	C₂²×C₃	—	6	12	no	—
30	C₂²×C₃	C₂²×D₃	1	1	yes	characteristic
31	C₂²×C₃	C₂³×C₃	1	1	yes	characteristic
32	C₂×D₃	—	2	12	no	—
33	C₃×C₄	—	2	6	no	—
34	C₃×C₄	D₁₂	1	6	yes	complemented
35	C₃×C₄	C₃×D₄	1	6	yes	complemented
36	C₃²	#127	1	1	yes	characteristic, complemented, Sylow
37	C₂³	—	3	4	no	—
38	D₄	—	6	12	no	—
39	C₂×C₄	C₂×C₃×D₃	1	3	yes	—
40	C₂×C₃	—	2	3	no	—
41	C₂×C₃	—	12	4	no	—
42	C₂×C₃	C₂×D₁₂	1	3	yes	—
43	C₂×C₃	C₂×C₃×D₄	1	3	yes	—
44	D₃	—	4	4	no	—
45	C₂²	—	6	12	no	—
46	C₂²	C₂²×C₃×D₃	1	1	yes	characteristic
47	C₄	C₃×D₁₂	1	6	yes	complemented
48	C₃	—	2	1	no	—
49	C₃	#874	1	1	yes	characteristic, direct product factor
50	C₃	C₃×#127	1	1	yes	characteristic, complemented
51	C₂	—	12	4	no	—
52	C₂	C₂×C₃×D₁₂	1	3	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂²×D₃
commutator, cosocle	C₂²×C₃	C₂³×C₃
Frattini	C₂²	C₂²×C₃×D₃
Fitting	C₃²×C₄²	C₂
socle	C₂²×C₃²	C₂³
hypercenter	C₃×C₄²	D₃
hypocenter	C₃	C₃×#127
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄²

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×D₁₂	C₂	semidirect
2. C₃²×C₄²	C₂	semidirect
4. #874	C₃	direct (N × H)
9. C₂×D₁₂	C₂×C₃	semidirect
11. C₃×C₄²	D₃	semidirect
12. C₃×C₄²	C₂×C₃	semidirect
15. C₃²×C₄	D₄	semidirect
27. C₄²	C₃×D₃	semidirect
34. C₃×C₄	D₁₂	semidirect
35. C₃×C₄	C₃×D₄	semidirect
36. C₃²	#127	semidirect
47. C₄	C₃×D₁₂	semidirect
49. C₃	#874	direct (N × H)
50. C₃	C₃×#127	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×D₁₂	2
C₃²×C₄²	2
C₃×#127	3
#874	3

Subgroups — C3×#874 #63997

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#874 #63997