Subgroups — C₃×#948 #64071

Order 288.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#41	C₂	1	1	yes	maximal, characteristic
2	C₃×#208	C₂	1	3	yes	maximal, complemented
3	C₂×C₃×C₃⋊C₈	C₂	1	3	yes	maximal, complemented
4	C₃×#131	—	3	1	no	maximal
5	#948	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₃²×Q₈	C₄	1	1	yes	characteristic
7	C₃²×D₄	C₄	1	3	yes	—
8	C₂×C₃²×C₄	C₂²	1	3	yes	—
9	C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
10	C₃×C₃⋊C₈	C₂²	1	3	yes	—
11	C₃×#41	—	2	1	no	—
12	C₃×#41	D₃	1	1	yes	characteristic
13	C₃×#41	C₂×C₃	1	1	yes	characteristic
14	C₃×M₁₆	—	3	3	no	—
15	C₂×C₃×C₈	—	3	3	no	—
16	#208	C₂×C₃	1	3	yes	complemented
17	C₂×C₃⋊C₈	C₂×C₃	1	3	yes	complemented
18	C₂²×C₃²	C₂×C₄	1	3	yes	—
19	C₃²×C₄	C₂×C₄	1	3	yes	—
20	C₃²×C₄	C₂³	1	1	yes	characteristic
21	#131	—	3	1	no	Sylow
22	C₃×Q₈	—	2	1	no	—
23	C₃×Q₈	Dic₃	1	1	yes	characteristic
24	C₃×Q₈	C₃×C₄	1	1	yes	characteristic
25	C₃×D₄	—	2	3	no	—
26	C₃×D₄	Dic₃	1	3	yes	—
27	C₃×D₄	C₃×C₄	1	3	yes	—
28	C₂×C₃×C₄	—	2	3	no	—
29	C₂×C₃×C₄	C₂×D₃	1	3	yes	—
30	C₂×C₃×C₄	C₂²×C₃	1	3	yes	—
31	C₃×C₈	—	3	1	no	—
32	C₃×C₈	—	3	3	no	—
33	C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
34	C₃⋊C₈	C₂²×C₃	1	3	yes	—
35	C₂×C₃²	—	2	3	no	—
36	C₂×C₃²	C₂²×C₄	1	1	yes	characteristic
37	#41	C₃×D₃	1	1	yes	characteristic
38	M₁₆	—	3	3	no	—
39	C₂×C₈	—	3	3	no	—
40	C₂²×C₃	—	2	3	no	—
41	C₂²×C₃	C₂×Dic₃	1	3	yes	—
42	C₂²×C₃	C₂×C₃×C₄	1	3	yes	—
43	C₃×C₄	—	2	3	no	—
44	C₃×C₄	—	2	1	no	—
45	C₃×C₄	C₂×Dic₃	1	3	yes	—
46	C₃×C₄	C₂×C₃×C₄	1	3	yes	—
47	C₃×C₄	C₂²×D₃	1	1	yes	characteristic
48	C₃×C₄	C₂³×C₃	1	1	yes	characteristic
49	C₃²	#131	1	1	yes	characteristic, complemented, Sylow
50	Q₈	C₃×Dic₃	1	1	yes	characteristic
51	D₄	C₃×Dic₃	1	3	yes	—
52	C₂×C₄	C₂×C₃×D₃	1	3	yes	—
53	C₈	—	3	1	no	—
54	C₈	—	3	3	no	—
55	C₂×C₃	—	2	3	no	—
56	C₂×C₃	—	2	3	no	—
57	C₂×C₃	—	2	1	no	—
58	C₂×C₃	—	4	3	no	—
59	C₂×C₃	C₂²×Dic₃	1	1	yes	characteristic
60	C₂×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
61	C₂²	C₂×C₃×Dic₃	1	3	yes	—
62	C₄	C₂×C₃×Dic₃	1	3	yes	—
63	C₄	C₂²×C₃×D₃	1	1	yes	characteristic
64	C₃	—	2	1	no	—
65	C₃	#948	1	1	yes	characteristic, direct product factor
66	C₃	C₃×#131	1	1	yes	characteristic, complemented
67	C₂	—	2	3	no	—
68	C₂	C₂²×C₃×Dic₃	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	C₂²×D₃
commutator	C₂×C₃	C₂²×C₃×C₄
Frattini	C₄	C₂²×C₃×D₃
Fitting, prime radical	C₃²×#41	C₂
socle	C₂×C₃²	C₂²×C₄
cosocle	C₃×C₄	C₂³×C₃
hypercenter	C₃×#41	D₃
hypocenter	C₃	C₃×#131
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₃×C₄ ◁ C₃×#41

Complements

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

N	H ≅ G/N	type
2. C₃×#208	C₂	semidirect
3. C₂×C₃×C₃⋊C₈	C₂	semidirect
5. #948	C₃	direct (N × H)
16. #208	C₂×C₃	semidirect
17. C₂×C₃⋊C₈	C₂×C₃	semidirect
49. C₃²	#131	semidirect
65. C₃	#948	direct (N × H)
66. C₃	C₃×#131	semidirect

Maximal subgroups

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

subgroup	index
C₃²×#41	2
C₃×#208	2
C₂×C₃×C₃⋊C₈	2
C₃×#131	3
#948	3

Subgroups — C3×#948 #64071

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#948 #64071