Subgroups — C₃×#912 #64035

Order 288.

135 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#237	C₂	1	2	yes	maximal, complemented
2	C₃²×D₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#214	C₂	1	2	yes	maximal, complemented
4	C₃×Dic₁₂	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×D₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#135	—	3	1	no	maximal
7	#912	C₃	1	1	yes	maximal, characteristic, direct product factor
8	C₃²×D₄	C₂²	1	2	yes	—
9	C₃×#67	—	2	2	no	—
10	C₂×C₃×Dic₃	—	2	2	no	—
11	C₃×C₄×D₃	C₂²	1	1	yes	characteristic
12	C₃×Dic₆	C₂²	1	2	yes	—
13	C₃²×C₈	C₂²	1	1	yes	characteristic
14	C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
15	C₃×#41	—	3	2	no	—
16	#237	C₂×C₃	1	2	yes	complemented
17	C₃×Q₁₆	—	3	1	no	—
18	C₃×SD₁₆	—	3	2	no	—
19	C₃×D₈	—	2	1	no	—
20	C₃×D₈	D₃	1	1	yes	characteristic, complemented
21	C₃×D₈	C₂×C₃	1	1	yes	characteristic, complemented
22	C₂×C₃×C₈	—	3	1	no	—
23	#214	C₂×C₃	1	2	yes	complemented
24	Dic₁₂	C₂×C₃	1	1	yes	characteristic, complemented
25	D₃×C₈	C₂×C₃	1	1	yes	characteristic, complemented
26	C₂²×C₃²	—	2	2	no	—
27	C₂×C₃×D₃	D₄	1	1	yes	characteristic
28	C₃²×C₄	C₂³	1	1	yes	characteristic
29	C₃×Dic₃	—	2	2	no	—
30	C₃×Dic₃	D₄	1	1	yes	characteristic
31	#135	—	3	1	no	Sylow
32	C₃×Q₈	—	3	2	no	—
33	C₃×D₄	—	2	2	no	—
34	C₃×D₄	—	6	2	no	—
35	C₃×D₄	C₂×D₃	1	2	yes	—
36	C₃×D₄	C₂²×C₃	1	2	yes	—
37	C₂×C₃×C₄	—	3	1	no	—
38	C₂×C₃×C₄	—	6	2	no	—
39	#67	—	2	2	no	—
40	C₂×Dic₃	—	2	2	no	—
41	C₄×D₃	C₂²×C₃	1	1	yes	characteristic
42	Dic₆	C₂²×C₃	1	2	yes	—
43	C₃×C₈	—	2	1	no	—
44	C₃×C₈	—	3	1	no	—
45	C₃×C₈	C₂×D₃	1	1	yes	characteristic
46	C₃×C₈	C₂²×C₃	1	1	yes	characteristic
47	C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
48	C₂×C₃²	—	4	2	no	—
49	C₂×C₃²	C₂×D₄	1	1	yes	characteristic
50	C₃×D₃	—	2	1	no	—
51	#41	—	3	2	no	—
52	Q₁₆	—	3	1	no	—
53	SD₁₆	—	3	2	no	—
54	D₈	C₃×D₃	1	1	yes	characteristic, complemented
55	C₂×C₈	—	3	1	no	—
56	C₂²×C₃	—	2	2	no	—
57	C₂²×C₃	—	2	2	no	—
58	C₂²×C₃	—	3	1	no	—
59	C₂²×C₃	—	4	2	no	—
60	C₂×D₃	C₃×D₄	1	1	yes	characteristic
61	C₃×C₄	—	2	1	no	—
62	C₃×C₄	—	3	1	no	—
63	C₃×C₄	—	6	2	no	—
64	C₃×C₄	C₂²×D₃	1	1	yes	characteristic
65	C₃×C₄	C₂³×C₃	1	1	yes	characteristic
66	Dic₃	—	2	2	no	—
67	Dic₃	C₃×D₄	1	1	yes	characteristic
68	C₃²	#135	1	1	yes	characteristic, complemented, Sylow
69	Q₈	—	3	2	no	—
70	D₄	—	6	2	no	—
71	D₄	C₂×C₃×D₃	1	2	yes	—
72	C₂×C₄	—	3	1	no	—
73	C₂×C₄	—	6	2	no	—
74	C₈	—	3	1	no	—
75	C₈	C₂×C₃×D₃	1	1	yes	characteristic
76	C₂×C₃	—	2	1	no	—
77	C₂×C₃	—	4	2	no	—
78	C₂×C₃	—	4	2	no	—
79	C₂×C₃	—	6	1	no	—
80	C₂×C₃	—	8	2	no	—
81	C₂×C₃	D₃×D₄	1	1	yes	characteristic
82	C₂×C₃	C₂×C₃×D₄	1	1	yes	characteristic
83	D₃	—	2	1	no	—
84	C₂²	—	2	2	no	—
85	C₂²	—	3	1	no	—
86	C₄	—	3	1	no	—
87	C₄	—	6	2	no	—
88	C₄	C₂²×C₃×D₃	1	1	yes	characteristic
89	C₃	—	2	1	no	—
90	C₃	#912	1	1	yes	characteristic, direct product factor
91	C₃	C₃×#135	1	1	yes	characteristic, complemented
92	C₂	—	4	2	no	—
93	C₂	—	6	1	no	—
94	C₂	C₃×D₃×D₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	D₃×D₄
commutator, cosocle	C₃×C₄	C₂³×C₃
Frattini	C₄	C₂²×C₃×D₃
Fitting	C₃²×D₈	C₂
socle	C₂×C₃²	C₂×D₄
hypercenter	C₃×D₈	D₃
hypocenter	C₃	C₃×#135
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄ ◁ C₃×D₈

Complements

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

N	H ≅ G/N	type
1. C₃×#237	C₂	semidirect
2. C₃²×D₈	C₂	semidirect
3. C₃×#214	C₂	semidirect
4. C₃×Dic₁₂	C₂	semidirect
5. C₃×D₃×C₈	C₂	semidirect
7. #912	C₃	direct (N × H)
16. #237	C₂×C₃	semidirect
20. C₃×D₈	D₃	semidirect
21. C₃×D₈	C₂×C₃	semidirect
23. #214	C₂×C₃	semidirect
24. Dic₁₂	C₂×C₃	semidirect
25. D₃×C₈	C₂×C₃	semidirect
54. D₈	C₃×D₃	semidirect
68. C₃²	#135	semidirect
90. C₃	#912	direct (N × H)
91. C₃	C₃×#135	semidirect

Maximal subgroups

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

subgroup	index
C₃×#237	2
C₃²×D₈	2
C₃×#214	2
C₃×Dic₁₂	2
C₃×D₃×C₈	2
C₃×#135	3
#912	3

Subgroups — C3×#912 #64035

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#912 #64035