Subgroups — C₃×#926 #64049

Order 288.

179 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃²×C₄	C₂	1	1	yes	maximal, characteristic
2	C₃×#217	C₂	1	2	yes	maximal
3	C₃×C₄⋊Dic₃	C₂	1	2	yes	maximal, complemented
4	C₃×C₄×Dic₃	C₂	1	2	yes	maximal, complemented
5	C₃×#117	—	3	1	no	maximal
6	#926	C₃	1	1	yes	maximal, characteristic, direct product factor
7	C₂³×C₃²	C₂²	1	1	yes	characteristic
8	C₂×C₃²×C₄	C₄	1	4	yes	complemented
9	C₂×C₃²×C₄	C₂²	1	1	yes	characteristic
10	C₂×C₃²×C₄	C₂²	1	1	yes	characteristic
11	C₂×C₃×Dic₃	C₂²	1	4	yes	—
12	C₂²×C₃×C₄	—	2	1	no	—
13	C₂²×C₃×C₄	D₃	1	1	yes	characteristic
14	C₂²×C₃×C₄	C₂×C₃	1	1	yes	characteristic
15	C₃×C₄⋊C₄	—	3	2	no	—
16	C₃×C₂²⋊C₄	—	3	2	no	—
17	C₃×C₄²	—	3	2	no	—
18	#217	C₂×C₃	1	2	yes	—
19	C₄⋊Dic₃	C₂×C₃	1	2	yes	complemented
20	C₄×Dic₃	C₂×C₃	1	2	yes	complemented
21	C₂²×C₃²	—	2	2	no	—
22	C₂²×C₃²	C₂×C₄	1	2	yes	—
23	C₂²×C₃²	C₂³	1	1	yes	characteristic
24	C₃²×C₄	C₂×C₄	1	2	yes	—
25	C₃²×C₄	C₂×C₄	1	2	yes	—
26	C₃×Dic₃	—	2	4	no	—
27	#117	—	3	1	no	Sylow
28	C₂³×C₃	—	2	1	no	—
29	C₂³×C₃	C₂×D₃	1	1	yes	characteristic
30	C₂³×C₃	C₂²×C₃	1	1	yes	characteristic
31	C₂×C₃×C₄	—	2	4	no	—
32	C₂×C₃×C₄	—	2	1	no	—
33	C₂×C₃×C₄	—	2	1	no	—
34	C₂×C₃×C₄	—	3	4	no	—
35	C₂×C₃×C₄	Dic₃	1	4	yes	complemented
36	C₂×C₃×C₄	C₃×C₄	1	4	yes	complemented
37	C₂×C₃×C₄	C₂×D₃	1	1	yes	characteristic
38	C₂×C₃×C₄	C₂×D₃	1	1	yes	characteristic
39	C₂×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
40	C₂×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
41	C₂×Dic₃	C₂²×C₃	1	4	yes	—
42	C₂×C₃²	—	2	2	no	—
43	C₂×C₃²	C₂²×C₄	1	1	yes	characteristic
44	C₂×C₃²	#41	1	2	yes	—
45	C₂²×C₄	C₃×D₃	1	1	yes	characteristic
46	C₄⋊C₄	—	3	2	no	—
47	C₂²⋊C₄	—	3	2	no	—
48	C₄²	—	3	2	no	—
49	C₂²×C₃	—	2	4	no	—
50	C₂²×C₃	—	2	2	no	—
51	C₂²×C₃	—	2	2	no	—
52	C₂²×C₃	—	2	2	no	—
53	C₂²×C₃	—	2	1	no	—
54	C₂²×C₃	C₂×Dic₃	1	2	yes	—
55	C₂²×C₃	C₂×C₃×C₄	1	2	yes	—
56	C₂²×C₃	C₂²×D₃	1	1	yes	characteristic
57	C₂²×C₃	C₂³×C₃	1	1	yes	characteristic
58	C₃×C₄	—	2	2	no	—
59	C₃×C₄	—	2	2	no	—
60	C₃×C₄	—	6	4	no	—
61	C₃×C₄	C₂×Dic₃	1	2	yes	—
62	C₃×C₄	C₂×Dic₃	1	2	yes	—
63	C₃×C₄	C₂×C₃×C₄	1	2	yes	—
64	C₃×C₄	C₂×C₃×C₄	1	2	yes	—
65	Dic₃	—	2	4	no	—
66	C₃²	#117	1	1	yes	characteristic, complemented, Sylow
67	C₂³	C₂×C₃×D₃	1	1	yes	characteristic
68	C₂×C₄	—	3	4	no	—
69	C₂×C₄	C₃×Dic₃	1	4	yes	complemented
70	C₂×C₄	C₂×C₃×D₃	1	1	yes	characteristic
71	C₂×C₄	C₂×C₃×D₃	1	1	yes	characteristic
72	C₂×C₃	—	2	4	no	—
73	C₂×C₃	—	2	2	no	—
74	C₂×C₃	—	2	2	no	—
75	C₂×C₃	—	2	2	no	—
76	C₂×C₃	—	2	1	no	—
77	C₂×C₃	#235	1	2	yes	—
78	C₂×C₃	C₂²×Dic₃	1	1	yes	characteristic
79	C₂×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
80	C₂×C₃	C₃×#41	1	2	yes	—
81	C₂²	—	2	2	no	—
82	C₂²	C₂×C₃×Dic₃	1	2	yes	—
83	C₂²	C₂²×C₃×D₃	1	1	yes	characteristic
84	C₄	—	6	4	no	—
85	C₄	C₂×C₃×Dic₃	1	2	yes	—
86	C₄	C₂×C₃×Dic₃	1	2	yes	—
87	C₃	—	2	1	no	—
88	C₃	#926	1	1	yes	characteristic, direct product factor
89	C₃	C₃×#117	1	1	yes	characteristic, complemented
90	C₂	—	2	2	no	—
91	C₂	C₃×#235	1	2	yes	—
92	C₂	C₂²×C₃×Dic₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂×D₃
commutator	C₂×C₃	C₂²×C₃×C₄
Frattini	C₂²	C₂²×C₃×D₃
Fitting	C₂²×C₃²×C₄	C₂
socle	C₂²×C₃²	C₂³
prime radical	C₂³×C₃²	C₂²
cosocle	C₂²×C₃	C₂³×C₃
hypercenter	C₂²×C₃×C₄	D₃
hypocenter	C₃	C₃×#117
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂²×C₃×C₄

Complements

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

N	H ≅ G/N	type
3. C₃×C₄⋊Dic₃	C₂	semidirect
4. C₃×C₄×Dic₃	C₂	semidirect
6. #926	C₃	direct (N × H)
8. C₂×C₃²×C₄	C₄	semidirect
19. C₄⋊Dic₃	C₂×C₃	semidirect
20. C₄×Dic₃	C₂×C₃	semidirect
35. C₂×C₃×C₄	Dic₃	semidirect
36. C₂×C₃×C₄	C₃×C₄	semidirect
66. C₃²	#117	semidirect
69. C₂×C₄	C₃×Dic₃	semidirect
88. C₃	#926	direct (N × H)
89. C₃	C₃×#117	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃²×C₄	2
C₃×#217	2
C₃×C₄⋊Dic₃	2
C₃×C₄×Dic₃	2
C₃×#117	3
#926	3

Subgroups — C3×#926 #64049

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#926 #64049