Subgroups — C₃×#827 #63613

Order 288.

63 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×D₈	C₂	1	1	yes	maximal, characteristic
2	C₃×Dic₁₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×SD₃₂	—	3	1	no	maximal
5	#827	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₃²×D₄	—	2	1	no	—
7	C₃×Dic₆	—	2	1	no	—
8	C₃²×C₈	C₂²	1	1	yes	characteristic
9	C₃×Q₁₆	—	3	1	no	—
10	C₃×D₈	—	2	1	no	—
11	C₃×D₈	D₃	1	1	yes	characteristic
12	C₃×D₈	C₂×C₃	1	1	yes	characteristic
13	Dic₁₂	C₂×C₃	1	1	yes	characteristic, complemented
14	C₃×C₁₆	—	3	1	no	—
15	C₃⋊C₁₆	C₂×C₃	1	1	yes	characteristic, complemented
16	C₂²×C₃²	—	4	1	no	—
17	C₃²×C₄	D₄	1	1	yes	characteristic
18	C₃×Dic₃	—	4	1	no	—
19	SD₃₂	—	3	1	no	Sylow
20	C₃×Q₈	—	6	1	no	—
21	C₃×D₄	—	2	2	no	—
22	C₃×D₄	—	2	1	no	—
23	C₃×D₄	—	2	1	no	—
24	Dic₆	—	2	1	no	—
25	C₃×C₈	—	2	1	no	—
26	C₃×C₈	C₂×D₃	1	1	yes	characteristic
27	C₃×C₈	C₂²×C₃	1	1	yes	characteristic
28	C₂×C₃²	—	8	1	no	—
29	C₂×C₃²	D₈	1	1	yes	characteristic
30	Q₁₆	—	3	1	no	—
31	D₈	C₃×D₃	1	1	yes	characteristic
32	C₁₆	—	3	1	no	—
33	C₂²×C₃	—	4	2	no	—
34	C₂²×C₃	—	4	1	no	—
35	C₂²×C₃	—	4	1	no	—
36	C₃×C₄	—	2	1	no	—
37	C₃×C₄	—	12	1	no	—
38	C₃×C₄	#67	1	1	yes	characteristic
39	C₃×C₄	C₃×D₄	1	1	yes	characteristic
40	Dic₃	—	4	1	no	—
41	C₃²	SD₃₂	1	1	yes	characteristic, complemented, Sylow
42	Q₈	—	6	1	no	—
43	D₄	—	2	1	no	—
44	C₈	C₂×C₃×D₃	1	1	yes	characteristic
45	C₂×C₃	—	2	1	no	—
46	C₂×C₃	—	8	2	no	—
47	C₂×C₃	—	8	1	no	—
48	C₂×C₃	—	8	1	no	—
49	C₂×C₃	#213	1	1	yes	characteristic
50	C₂×C₃	C₃×D₈	1	1	yes	characteristic
51	C₂²	—	4	1	no	—
52	C₄	—	12	1	no	—
53	C₄	C₃×#67	1	1	yes	characteristic
54	C₃	—	2	1	no	—
55	C₃	#827	1	1	yes	characteristic, direct product factor
56	C₃	C₃×SD₃₂	1	1	yes	characteristic, complemented
57	C₂	—	8	1	no	—
58	C₂	C₃×#213	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	#213
commutator, cosocle	C₃×C₈	C₂²×C₃
Frattini	C₈	C₂×C₃×D₃
Fitting, prime radical	C₃²×D₈	C₂
socle	C₂×C₃²	D₈
hypercenter	C₃×D₈	D₃
hypocenter	C₃	C₃×SD₃₂
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄ ◁ C₃×C₈ ◁ C₃×D₈

Complements

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

N	H ≅ G/N	type
2. C₃×Dic₁₂	C₂	semidirect
3. C₃×C₃⋊C₁₆	C₂	semidirect
5. #827	C₃	direct (N × H)
13. Dic₁₂	C₂×C₃	semidirect
15. C₃⋊C₁₆	C₂×C₃	semidirect
41. C₃²	SD₃₂	semidirect
55. C₃	#827	direct (N × H)
56. C₃	C₃×SD₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₃²×D₈	2
C₃×Dic₁₂	2
C₃×C₃⋊C₁₆	2
C₃×SD₃₂	3
#827	3

Subgroups — C3×#827 #63613

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#827 #63613