Subgroups — C₃×#810 #63596

Order 288.

97 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Dic₆	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₃×#103	—	3	1	no	maximal
5	#810	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₂×C₃²×C₄	—	2	1	no	—
7	C₂×C₃²×C₄	C₂²	1	1	yes	characteristic
8	C₂×C₃×Dic₃	—	2	1	no	—
9	C₃×Dic₆	—	2	1	no	—
10	C₃×Dic₆	C₄	1	2	yes	complemented
11	C₃×C₃⋊C₈	—	2	1	no	—
12	C₂×C₃×Q₈	—	3	1	no	—
13	C₂×Dic₆	C₂×C₃	1	1	yes	characteristic
14	C₂×C₃×C₈	—	3	1	no	—
15	C₃×C₄⋊C₄	—	2	1	no	—
16	C₃×C₄⋊C₄	D₃	1	1	yes	characteristic
17	C₃×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
18	C₂×C₃⋊C₈	C₂×C₃	1	1	yes	characteristic
19	C₂²×C₃²	D₄	1	1	yes	characteristic
20	C₃²×C₄	—	4	1	no	—
21	C₃²×C₄	C₂×C₄	1	1	yes	characteristic
22	C₃²×C₄	D₄	1	1	yes	characteristic
23	C₃×Dic₃	—	2	2	no	—
24	#103	—	3	1	no	Sylow
25	C₃×Q₈	—	3	2	no	—
26	C₃×Q₈	—	6	1	no	—
27	C₂×C₃×C₄	—	2	2	no	—
28	C₂×C₃×C₄	—	2	1	no	—
29	C₂×C₃×C₄	—	2	1	no	—
30	C₂×C₃×C₄	—	2	1	no	—
31	C₂×C₃×C₄	—	6	1	no	—
32	C₂×C₃×C₄	C₂×D₃	1	1	yes	characteristic
33	C₂×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
34	C₂×Dic₃	—	2	1	no	—
35	Dic₆	—	2	1	no	—
36	Dic₆	C₃×C₄	1	2	yes	complemented
37	C₃×C₈	—	6	1	no	—
38	C₃⋊C₈	—	2	1	no	—
39	C₂×C₃²	C₂²⋊C₄	1	1	yes	characteristic
40	C₂×C₃²	SD₁₆	1	1	yes	characteristic
41	C₂×C₃²	Q₁₆	1	1	yes	characteristic
42	C₂×Q₈	—	3	1	no	—
43	C₂×C₈	—	3	1	no	—
44	C₄⋊C₄	C₃×D₃	1	1	yes	characteristic
45	C₂²×C₃	—	2	1	no	—
46	C₂²×C₃	#67	1	1	yes	characteristic
47	C₂²×C₃	C₃×D₄	1	1	yes	characteristic
48	C₃×C₄	—	2	1	no	—
49	C₃×C₄	—	2	1	no	—
50	C₃×C₄	—	4	2	no	—
51	C₃×C₄	—	4	1	no	—
52	C₃×C₄	—	4	1	no	—
53	C₃×C₄	—	6	2	no	—
54	C₃×C₄	C₄×D₃	1	1	yes	characteristic
55	C₃×C₄	D₁₂	1	1	yes	characteristic
56	C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
57	C₃×C₄	C₃×D₄	1	1	yes	characteristic
58	Dic₃	—	2	2	no	—
59	C₃²	#103	1	1	yes	characteristic, complemented, Sylow
60	Q₈	—	3	2	no	—
61	Q₈	—	6	1	no	—
62	C₂×C₄	—	2	1	no	—
63	C₂×C₄	—	6	1	no	—
64	C₂×C₄	C₂×C₃×D₃	1	1	yes	characteristic
65	C₈	—	6	1	no	—
66	C₂×C₃	—	2	1	no	—
67	C₂×C₃	—	2	1	no	—
68	C₂×C₃	—	2	1	no	—
69	C₂×C₃	(C₂×D₃)⋊C₄	1	1	yes	characteristic
70	C₂×C₃	#214	1	1	yes	characteristic
71	C₂×C₃	#216	1	1	yes	characteristic
72	C₂×C₃	C₃×C₂²⋊C₄	1	1	yes	characteristic
73	C₂×C₃	C₃×SD₁₆	1	1	yes	characteristic
74	C₂×C₃	C₃×Q₁₆	1	1	yes	characteristic
75	C₂²	C₃×#67	1	1	yes	characteristic
76	C₄	—	4	1	no	—
77	C₄	—	6	2	no	—
78	C₄	C₃×C₄×D₃	1	1	yes	characteristic
79	C₄	C₃×D₁₂	1	1	yes	characteristic
80	C₃	—	2	1	no	—
81	C₃	#810	1	1	yes	characteristic, direct product factor
82	C₃	C₃×#103	1	1	yes	characteristic, complemented
83	C₂	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
84	C₂	C₃×#214	1	1	yes	characteristic
85	C₂	C₃×#216	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	#67
commutator	C₃×C₄	C₂×C₃×C₄
Frattini	C₂×C₄	C₂×C₃×D₃
Fitting	C₃²×C₄⋊C₄	C₂
socle, prime radical	C₂²×C₃²	D₄
cosocle	C₂×C₃×C₄	C₂²×C₃
hypercenter	C₃×C₄⋊C₄	D₃
hypocenter	C₃	C₃×#103
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄ ◁ C₃×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
5. #810	C₃	direct (N × H)
10. C₃×Dic₆	C₄	semidirect
36. Dic₆	C₃×C₄	semidirect
59. C₃²	#103	semidirect
81. C₃	#810	direct (N × H)
82. C₃	C₃×#103	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×C₄⋊C₄	2
C₂×C₃×C₃⋊C₈	2
C₃×#103	3
#810	3

Subgroups — C3×#810 #63596

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#810 #63596