Subgroups — C₃×#805 #63591

Order 288.

103 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#235	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₄²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#208	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#104	—	3	1	no	maximal
5	#805	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	C₃×#67	—	2	1	no	—
9	C₃×D₁₂	C₄	1	1	yes	characteristic, complemented
10	C₃×C₄×D₃	—	2	1	no	—
11	C₃×Dic₆	C₄	1	1	yes	characteristic, complemented
12	C₃×C₃⋊C₈	—	2	1	no	—
13	C₃×#41	—	3	1	no	—
14	#235	C₂×C₃	1	1	yes	characteristic
15	C₃×M₁₆	—	3	1	no	—
16	C₃×C₄²	—	2	1	no	—
17	C₃×C₄²	D₃	1	1	yes	characteristic, complemented
18	C₃×C₄²	C₂×C₃	1	1	yes	characteristic, complemented
19	#208	C₂×C₃	1	1	yes	characteristic, complemented
20	C₂²×C₃²	D₄	1	1	yes	characteristic
21	C₂×C₃×D₃	—	2	1	no	—
22	C₃²×C₄	—	2	2	no	—
23	C₃²×C₄	C₂×C₄	1	1	yes	characteristic
24	C₃²×C₄	D₄	1	1	yes	characteristic
25	C₃×Dic₃	—	2	1	no	—
26	#104	—	3	1	no	Sylow
27	C₃×Q₈	—	3	1	no	—
28	C₃×D₄	—	3	1	no	—
29	C₃×D₄	—	6	1	no	—
30	C₂×C₃×C₄	—	2	2	no	—
31	C₂×C₃×C₄	—	2	1	no	—
32	C₂×C₃×C₄	—	2	1	no	—
33	C₂×C₃×C₄	—	2	1	no	—
34	C₂×C₃×C₄	—	6	1	no	—
35	C₂×C₃×C₄	C₂×D₃	1	1	yes	characteristic
36	C₂×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
37	#67	—	2	1	no	—
38	D₁₂	C₃×C₄	1	1	yes	characteristic, complemented
39	C₄×D₃	—	2	1	no	—
40	Dic₆	C₃×C₄	1	1	yes	characteristic, complemented
41	C₃×C₈	—	6	1	no	—
42	C₃⋊C₈	—	2	1	no	—
43	C₂×C₃²	—	2	1	no	—
44	C₂×C₃²	C₂²⋊C₄	1	1	yes	characteristic
45	C₃×D₃	—	4	1	no	—
46	#41	—	3	1	no	—
47	M₁₆	—	3	1	no	—
48	C₄²	C₃×D₃	1	1	yes	characteristic, complemented
49	C₂²×C₃	—	2	1	no	—
50	C₂²×C₃	—	6	1	no	—
51	C₂²×C₃	#67	1	1	yes	characteristic
52	C₂²×C₃	C₃×D₄	1	1	yes	characteristic
53	C₂×D₃	—	2	1	no	—
54	C₃×C₄	—	2	4	no	—
55	C₃×C₄	—	2	2	no	—
56	C₃×C₄	—	2	2	no	—
57	C₃×C₄	—	2	1	no	—
58	C₃×C₄	—	2	1	no	—
59	C₃×C₄	—	6	1	no	—
60	C₃×C₄	C₄×D₃	1	1	yes	characteristic
61	C₃×C₄	D₁₂	1	1	yes	characteristic
62	C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
63	C₃×C₄	C₃×D₄	1	1	yes	characteristic
64	Dic₃	—	2	1	no	—
65	C₃²	#104	1	1	yes	characteristic, complemented, Sylow
66	Q₈	—	3	1	no	—
67	D₄	—	3	1	no	—
68	D₄	—	6	1	no	—
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	6	1	no	—
71	C₂×C₄	C₂×C₃×D₃	1	1	yes	characteristic
72	C₈	—	6	1	no	—
73	C₂×C₃	—	2	2	no	—
74	C₂×C₃	—	2	1	no	—
75	C₂×C₃	—	2	1	no	—
76	C₂×C₃	—	2	1	no	—
77	C₂×C₃	—	12	1	no	—
78	C₂×C₃	(C₂×D₃)⋊C₄	1	1	yes	characteristic
79	C₂×C₃	C₃×C₂²⋊C₄	1	1	yes	characteristic
80	D₃	—	4	1	no	—
81	C₂²	—	6	1	no	—
82	C₂²	C₃×#67	1	1	yes	characteristic
83	C₄	—	2	2	no	—
84	C₄	—	6	1	no	—
85	C₄	C₃×C₄×D₃	1	1	yes	characteristic
86	C₄	C₃×D₁₂	1	1	yes	characteristic
87	C₃	—	2	1	no	—
88	C₃	#805	1	1	yes	characteristic, direct product factor
89	C₃	C₃×#104	1	1	yes	characteristic, complemented
90	C₂	—	2	1	no	—
91	C₂	—	12	1	no	—
92	C₂	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	D₁₂
commutator	C₃×C₄	C₂×C₃×C₄
Frattini	C₂×C₄	C₂×C₃×D₃
Fitting	C₃²×C₄²	C₂
socle	C₂×C₃²	C₂²⋊C₄
prime radical	C₃×#235	C₂
cosocle	C₂×C₃×C₄	C₂²×C₃
hypercenter	C₃×C₄²	D₃
hypocenter	C₃	C₃×#104
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₃×C₄ ◁ C₂×C₃×C₄ ◁ C₃×C₄²

Complements

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

N	H ≅ G/N	type
2. C₃²×C₄²	C₂	semidirect
3. C₃×#208	C₂	semidirect
5. #805	C₃	direct (N × H)
9. C₃×D₁₂	C₄	semidirect
11. C₃×Dic₆	C₄	semidirect
17. C₃×C₄²	D₃	semidirect
18. C₃×C₄²	C₂×C₃	semidirect
19. #208	C₂×C₃	semidirect
38. D₁₂	C₃×C₄	semidirect
40. Dic₆	C₃×C₄	semidirect
48. C₄²	C₃×D₃	semidirect
65. C₃²	#104	semidirect
88. C₃	#805	direct (N × H)
89. C₃	C₃×#104	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
C₃²×C₄²	2
C₃×#208	2
C₃×#104	3
#805	3

Subgroups — C3×#805 #63591

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#805 #63591