Subgroups — C₃×#904 #64027

Order 288.

135 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#235	C₂	1	2	yes	maximal, complemented
2	C₂×C₃²×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×Dic₁₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×D₂₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#204	C₂	1	2	yes	maximal, complemented
6	C₃×#135	—	3	1	no	maximal
7	#904	C₃	1	1	yes	maximal, characteristic, direct product factor
8	C₂×C₃²×C₄	C₂²	1	1	yes	characteristic
9	C₃×#67	—	2	2	no	—
10	C₃×D₁₂	C₂²	1	2	yes	—
11	C₃×C₄×D₃	—	2	2	no	—
12	C₃×Dic₆	C₂²	1	2	yes	—
13	C₃²×C₈	C₂²	1	1	yes	characteristic
14	C₃²×C₈	C₂²	1	1	yes	characteristic
15	C₃×#41	—	3	2	no	—
16	#235	C₂×C₃	1	2	yes	complemented
17	C₃×Q₁₆	—	3	1	no	—
18	C₃×SD₁₆	—	3	2	no	—
19	C₃×D₈	—	3	1	no	—
20	C₂×C₃×C₈	—	2	1	no	—
21	C₂×C₃×C₈	D₃	1	1	yes	characteristic, complemented
22	C₂×C₃×C₈	C₂×C₃	1	1	yes	characteristic, complemented
23	Dic₁₂	C₂×C₃	1	1	yes	characteristic, complemented
24	D₂₄	C₂×C₃	1	1	yes	characteristic, complemented
25	#204	C₂×C₃	1	2	yes	complemented
26	C₂²×C₃²	D₄	1	1	yes	characteristic
27	C₂×C₃×D₃	—	2	2	no	—
28	C₃²×C₄	D₄	1	1	yes	characteristic
29	C₃²×C₄	C₂³	1	1	yes	characteristic
30	C₃×Dic₃	—	2	2	no	—
31	#135	—	3	1	no	Sylow
32	C₃×Q₈	—	3	2	no	—
33	C₃×D₄	—	3	2	no	—
34	C₃×D₄	—	6	2	no	—
35	C₂×C₃×C₄	—	2	1	no	—
36	C₂×C₃×C₄	—	6	2	no	—
37	C₂×C₃×C₄	C₂×D₃	1	1	yes	characteristic
38	C₂×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
39	#67	—	2	2	no	—
40	D₁₂	C₂²×C₃	1	2	yes	—
41	C₄×D₃	—	2	2	no	—
42	Dic₆	C₂²×C₃	1	2	yes	—
43	C₃×C₈	—	2	1	no	—
44	C₃×C₈	—	2	1	no	—
45	C₃×C₈	C₂×D₃	1	1	yes	characteristic
46	C₃×C₈	C₂×D₃	1	1	yes	characteristic
47	C₃×C₈	C₂²×C₃	1	1	yes	characteristic
48	C₃×C₈	C₂²×C₃	1	1	yes	characteristic
49	C₂×C₃²	—	2	1	no	—
50	C₂×C₃²	C₂×D₄	1	1	yes	characteristic
51	C₃×D₃	—	4	2	no	—
52	#41	—	3	2	no	—
53	Q₁₆	—	3	1	no	—
54	SD₁₆	—	3	2	no	—
55	D₈	—	3	1	no	—
56	C₂×C₈	C₃×D₃	1	1	yes	characteristic, complemented
57	C₂²×C₃	—	2	1	no	—
58	C₂²×C₃	—	6	2	no	—
59	C₂²×C₃	D₁₂	1	1	yes	characteristic
60	C₂²×C₃	C₃×D₄	1	1	yes	characteristic
61	C₂×D₃	—	2	2	no	—
62	C₃×C₄	—	2	1	no	—
63	C₃×C₄	—	2	1	no	—
64	C₃×C₄	—	6	2	no	—
65	C₃×C₄	D₁₂	1	1	yes	characteristic
66	C₃×C₄	C₃×D₄	1	1	yes	characteristic
67	C₃×C₄	C₂²×D₃	1	1	yes	characteristic
68	C₃×C₄	C₂³×C₃	1	1	yes	characteristic
69	Dic₃	—	2	2	no	—
70	C₃²	#135	1	1	yes	characteristic, complemented, Sylow
71	Q₈	—	3	2	no	—
72	D₄	—	3	2	no	—
73	D₄	—	6	2	no	—
74	C₂×C₄	—	6	2	no	—
75	C₂×C₄	C₂×C₃×D₃	1	1	yes	characteristic
76	C₈	C₂×C₃×D₃	1	1	yes	characteristic
77	C₈	C₂×C₃×D₃	1	1	yes	characteristic
78	C₂×C₃	—	2	2	no	—
79	C₂×C₃	—	2	1	no	—
80	C₂×C₃	—	2	1	no	—
81	C₂×C₃	—	2	1	no	—
82	C₂×C₃	—	12	2	no	—
83	C₂×C₃	C₂×D₁₂	1	1	yes	characteristic
84	C₂×C₃	C₂×C₃×D₄	1	1	yes	characteristic
85	D₃	—	4	2	no	—
86	C₂²	—	6	2	no	—
87	C₂²	C₃×D₁₂	1	1	yes	characteristic
88	C₄	—	6	2	no	—
89	C₄	C₃×D₁₂	1	1	yes	characteristic
90	C₄	C₂²×C₃×D₃	1	1	yes	characteristic
91	C₃	—	2	1	no	—
92	C₃	#904	1	1	yes	characteristic, direct product factor
93	C₃	C₃×#135	1	1	yes	characteristic, complemented
94	C₂	—	2	1	no	—
95	C₂	—	12	2	no	—
96	C₂	C₂×C₃×D₁₂	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	D₁₂
commutator, cosocle	C₃×C₄	C₂³×C₃
Frattini	C₄	C₂²×C₃×D₃
Fitting	C₂×C₃²×C₈	C₂
socle	C₂×C₃²	C₂×D₄
hypercenter	C₂×C₃×C₈	D₃
hypocenter	C₃	C₃×#135
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₃×C₄ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₈

Complements

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

N	H ≅ G/N	type
1. C₃×#235	C₂	semidirect
2. C₂×C₃²×C₈	C₂	semidirect
3. C₃×Dic₁₂	C₂	semidirect
4. C₃×D₂₄	C₂	semidirect
5. C₃×#204	C₂	semidirect
7. #904	C₃	direct (N × H)
16. #235	C₂×C₃	semidirect
21. C₂×C₃×C₈	D₃	semidirect
22. C₂×C₃×C₈	C₂×C₃	semidirect
23. Dic₁₂	C₂×C₃	semidirect
24. D₂₄	C₂×C₃	semidirect
25. #204	C₂×C₃	semidirect
56. C₂×C₈	C₃×D₃	semidirect
70. C₃²	#135	semidirect
92. C₃	#904	direct (N × H)
93. 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×#235	2
C₂×C₃²×C₈	2
C₃×Dic₁₂	2
C₃×D₂₄	2
C₃×#204	2
C₃×#135	3
#904	3

Subgroups — C3×#904 #64027

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#904 #64027