Subgroups — C₃×#888 #64011

Order 288.

149 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Dic₆	C₂	1	2	yes	maximal
2	C₃²×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₃×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic
4	C₃×Dic₃⋊C₄	C₂	1	2	yes	maximal
5	C₃×C₄×Dic₃	C₂	1	1	yes	maximal, characteristic
6	C₃×C₄⋊Q₈	—	3	1	no	maximal
7	#888	C₃	1	1	yes	maximal, characteristic, direct product factor
8	C₂×C₃²×C₄	C₂²	1	2	yes	—
9	C₂×C₃²×C₄	C₂²	1	1	yes	characteristic
10	C₂×C₃×Dic₃	C₂²	1	2	yes	—
11	C₂×C₃×Dic₃	C₂²	1	1	yes	characteristic
12	C₂×C₃×Dic₃	C₂²	1	1	yes	characteristic
13	C₃×Dic₆	—	2	4	no	—
14	C₂×C₃×Q₈	—	3	2	no	—
15	C₂×Dic₆	C₂×C₃	1	2	yes	—
16	C₃×C₄⋊C₄	—	2	1	no	—
17	C₃×C₄⋊C₄	—	3	2	no	—
18	C₃×C₄⋊C₄	—	3	1	no	—
19	C₃×C₄⋊C₄	D₃	1	1	yes	characteristic
20	C₃×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
21	C₃×C₄²	—	3	1	no	—
22	C₄⋊Dic₃	C₂×C₃	1	1	yes	characteristic
23	Dic₃⋊C₄	C₂×C₃	1	2	yes	—
24	C₄×Dic₃	C₂×C₃	1	1	yes	characteristic
25	C₂²×C₃²	C₂³	1	1	yes	characteristic
26	C₃²×C₄	—	2	2	no	—
27	C₃²×C₄	Q₈	1	2	yes	complemented
28	C₃×Dic₃	—	2	2	no	—
29	C₃×Dic₃	D₄	1	2	yes	—
30	C₃×Dic₃	Q₈	1	2	yes	complemented
31	C₄⋊Q₈	—	3	1	no	Sylow
32	C₃×Q₈	—	6	4	no	—
33	C₂×C₃×C₄	—	2	1	no	—
34	C₂×C₃×C₄	—	2	2	no	—
35	C₂×C₃×C₄	—	3	1	no	—
36	C₂×C₃×C₄	—	3	1	no	—
37	C₂×C₃×C₄	—	3	2	no	—
38	C₂×C₃×C₄	C₂×D₃	1	2	yes	—
39	C₂×C₃×C₄	C₂×D₃	1	1	yes	characteristic
40	C₂×C₃×C₄	C₂²×C₃	1	2	yes	—
41	C₂×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
42	C₂×Dic₃	C₂²×C₃	1	2	yes	—
43	C₂×Dic₃	C₂²×C₃	1	1	yes	characteristic
44	C₂×Dic₃	C₂²×C₃	1	1	yes	characteristic
45	Dic₆	—	2	4	no	—
46	C₂×C₃²	C₂×D₄	1	1	yes	characteristic
47	C₂×C₃²	C₂×Q₈	1	1	yes	characteristic
48	C₂×C₃²	C₂×Q₈	1	1	yes	characteristic
49	C₂×Q₈	—	3	2	no	—
50	C₄⋊C₄	—	3	2	no	—
51	C₄⋊C₄	—	3	1	no	—
52	C₄⋊C₄	C₃×D₃	1	1	yes	characteristic
53	C₄²	—	3	1	no	—
54	C₂²×C₃	—	2	1	no	—
55	C₂²×C₃	C₂²×D₃	1	1	yes	characteristic
56	C₂²×C₃	C₂³×C₃	1	1	yes	characteristic
57	C₃×C₄	—	2	2	no	—
58	C₃×C₄	—	2	2	no	—
59	C₃×C₄	—	2	2	no	—
60	C₃×C₄	—	3	2	no	—
61	C₃×C₄	—	3	2	no	—
62	C₃×C₄	—	4	2	no	—
63	C₃×C₄	—	6	2	no	—
64	C₃×C₄	Dic₆	1	2	yes	complemented
65	C₃×C₄	C₃×Q₈	1	2	yes	complemented
66	Dic₃	—	2	2	no	—
67	Dic₃	C₃×D₄	1	2	yes	—
68	Dic₃	C₃×Q₈	1	2	yes	complemented
69	C₃²	C₄⋊Q₈	1	1	yes	characteristic, complemented, Sylow
70	Q₈	—	6	4	no	—
71	C₂×C₄	—	3	1	no	—
72	C₂×C₄	—	3	1	no	—
73	C₂×C₄	—	3	2	no	—
74	C₂×C₄	C₂×C₃×D₃	1	2	yes	—
75	C₂×C₄	C₂×C₃×D₃	1	1	yes	characteristic
76	C₂×C₃	—	2	1	no	—
77	C₂×C₃	—	2	1	no	—
78	C₂×C₃	—	2	1	no	—
79	C₂×C₃	C₂×Dic₆	1	1	yes	characteristic
80	C₂×C₃	D₃×D₄	1	1	yes	characteristic
81	C₂×C₃	D₃×Q₈	1	1	yes	characteristic
82	C₂×C₃	C₂×C₃×D₄	1	1	yes	characteristic
83	C₂×C₃	C₂×C₃×Q₈	1	1	yes	characteristic
84	C₂×C₃	C₂×C₃×Q₈	1	1	yes	characteristic
85	C₂²	C₂²×C₃×D₃	1	1	yes	characteristic
86	C₄	—	2	2	no	—
87	C₄	—	3	2	no	—
88	C₄	—	3	2	no	—
89	C₄	—	6	2	no	—
90	C₄	C₃×Dic₆	1	2	yes	complemented
91	C₃	—	2	1	no	—
92	C₃	#888	1	1	yes	characteristic, direct product factor
93	C₃	C₃×C₄⋊Q₈	1	1	yes	characteristic, complemented
94	C₂	C₂×C₃×Dic₆	1	1	yes	characteristic
95	C₂	C₃×D₃×D₄	1	1	yes	characteristic
96	C₂	C₃×D₃×Q₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂²×D₃
commutator, cosocle	C₂²×C₃	C₂³×C₃
Frattini	C₂²	C₂²×C₃×D₃
Fitting	C₃²×C₄⋊C₄	C₂
socle, prime radical	C₂²×C₃²	C₂³
hypercenter	C₃×C₄⋊C₄	D₃
hypocenter	C₃	C₃×C₄⋊Q₈
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
7. #888	C₃	direct (N × H)
27. C₃²×C₄	Q₈	semidirect
30. C₃×Dic₃	Q₈	semidirect
64. C₃×C₄	Dic₆	semidirect
65. C₃×C₄	C₃×Q₈	semidirect
68. Dic₃	C₃×Q₈	semidirect
69. C₃²	C₄⋊Q₈	semidirect
90. C₄	C₃×Dic₆	semidirect
92. C₃	#888	direct (N × H)
93. C₃	C₃×C₄⋊Q₈	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
C₃×C₄⋊Dic₃	2
C₃×Dic₃⋊C₄	2
C₃×C₄×Dic₃	2
C₃×C₄⋊Q₈	3
#888	3

Subgroups — C3×#888 #64011

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#888 #64011