Subgroups — C₃×#869 #63992

Order 288.

151 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Dic₆	C₂	1	2	yes	maximal
2	C₃²×C₄²	C₂	1	1	yes	maximal, characteristic
3	C₃×C₄⋊Dic₃	C₂	1	4	yes	maximal
4	C₃×C₄⋊Q₈	—	3	1	no	maximal
5	#869	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₂×C₃²×C₄	C₂²	1	1	yes	characteristic
7	C₂×C₃²×C₄	C₂²	1	2	yes	—
8	C₂×C₃×Dic₃	C₂²	1	4	yes	—
9	C₃×Dic₆	—	2	4	no	—
10	C₂×C₃×Q₈	—	3	2	no	—
11	C₂×Dic₆	C₂×C₃	1	2	yes	—
12	C₃×C₄⋊C₄	—	3	4	no	—
13	C₃×C₄²	—	2	1	no	—
14	C₃×C₄²	D₃	1	1	yes	characteristic
15	C₃×C₄²	C₂×C₃	1	1	yes	characteristic
16	C₄⋊Dic₃	C₂×C₃	1	4	yes	—
17	C₂²×C₃²	C₂³	1	1	yes	characteristic
18	C₃²×C₄	D₄	1	2	yes	—
19	C₃²×C₄	Q₈	1	4	yes	complemented
20	C₃×Dic₃	—	2	4	no	—
21	C₄⋊Q₈	—	3	1	no	Sylow
22	C₃×Q₈	—	6	4	no	—
23	C₂×C₃×C₄	—	2	2	no	—
24	C₂×C₃×C₄	—	2	1	no	—
25	C₂×C₃×C₄	—	3	4	no	—
26	C₂×C₃×C₄	C₂×D₃	1	2	yes	—
27	C₂×C₃×C₄	C₂×D₃	1	1	yes	characteristic
28	C₂×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
29	C₂×C₃×C₄	C₂²×C₃	1	2	yes	—
30	C₂×Dic₃	C₂²×C₃	1	4	yes	—
31	Dic₆	—	2	4	no	—
32	C₂×C₃²	C₂×D₄	1	1	yes	characteristic
33	C₂×C₃²	C₂×Q₈	1	2	yes	—
34	C₂×Q₈	—	3	2	no	—
35	C₄⋊C₄	—	3	4	no	—
36	C₄²	C₃×D₃	1	1	yes	characteristic
37	C₂²×C₃	—	2	1	no	—
38	C₂²×C₃	C₂²×D₃	1	1	yes	characteristic
39	C₂²×C₃	C₂³×C₃	1	1	yes	characteristic
40	C₃×C₄	—	2	4	no	—
41	C₃×C₄	—	2	2	no	—
42	C₃×C₄	—	6	4	no	—
43	C₃×C₄	Dic₆	1	4	yes	complemented
44	C₃×C₄	D₁₂	1	2	yes	—
45	C₃×C₄	C₃×D₄	1	2	yes	—
46	C₃×C₄	C₃×Q₈	1	4	yes	complemented
47	Dic₃	—	2	4	no	—
48	C₃²	C₄⋊Q₈	1	1	yes	characteristic, complemented, Sylow
49	Q₈	—	6	4	no	—
50	C₂×C₄	—	3	4	no	—
51	C₂×C₄	C₂×C₃×D₃	1	2	yes	—
52	C₂×C₄	C₂×C₃×D₃	1	1	yes	characteristic
53	C₂×C₃	—	2	2	no	—
54	C₂×C₃	—	2	1	no	—
55	C₂×C₃	C₂×Dic₆	1	2	yes	—
56	C₂×C₃	C₂×D₁₂	1	1	yes	characteristic
57	C₂×C₃	C₂×C₃×D₄	1	1	yes	characteristic
58	C₂×C₃	C₂×C₃×Q₈	1	2	yes	—
59	C₂²	C₂²×C₃×D₃	1	1	yes	characteristic
60	C₄	—	6	4	no	—
61	C₄	C₃×Dic₆	1	4	yes	complemented
62	C₄	C₃×D₁₂	1	2	yes	—
63	C₃	—	2	1	no	—
64	C₃	#869	1	1	yes	characteristic, direct product factor
65	C₃	C₃×C₄⋊Q₈	1	1	yes	characteristic, complemented
66	C₂	C₂×C₃×Dic₆	1	2	yes	—
67	C₂	C₂×C₃×D₁₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂²×D₃
commutator, cosocle	C₂²×C₃	C₂³×C₃
Frattini	C₂²	C₂²×C₃×D₃
Fitting	C₃²×C₄²	C₂
socle, prime radical	C₂²×C₃²	C₂³
hypercenter	C₃×C₄²	D₃
hypocenter	C₃	C₃×C₄⋊Q₈
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
5. #869	C₃	direct (N × H)
19. C₃²×C₄	Q₈	semidirect
43. C₃×C₄	Dic₆	semidirect
46. C₃×C₄	C₃×Q₈	semidirect
48. C₃²	C₄⋊Q₈	semidirect
61. C₄	C₃×Dic₆	semidirect
64. C₃	#869	direct (N × H)
65. C₃	C₃×C₄⋊Q₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×Dic₆	2
C₃²×C₄²	2
C₃×C₄⋊Dic₃	2
C₃×C₄⋊Q₈	3
#869	3

Subgroups — C3×#869 #63992

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#869 #63992