Subgroups — C₃×#944 #64067

Order 288.

155 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×Dic₆	C₂	1	1	yes	maximal, characteristic
3	C₃×Dic₃⋊C₄	C₂	1	4	yes	maximal
4	C₃×C₄×Dic₃	C₂	1	1	yes	maximal, characteristic
5	C₃×C₄⋊Q₈	—	3	1	no	maximal
6	#944	C₃	1	1	yes	maximal, characteristic, direct product factor
7	C₃²×Q₈	—	2	2	no	—
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	2	yes	—
12	C₃×Dic₆	—	2	2	no	—
13	C₂×C₃×Q₈	—	2	1	no	—
14	C₂×C₃×Q₈	—	3	1	no	—
15	C₂×C₃×Q₈	D₃	1	1	yes	characteristic
16	C₂×C₃×Q₈	C₂×C₃	1	1	yes	characteristic
17	C₂×Dic₆	C₂×C₃	1	1	yes	characteristic
18	C₃×C₄⋊C₄	—	3	4	no	—
19	C₃×C₄²	—	3	1	no	—
20	Dic₃⋊C₄	C₂×C₃	1	4	yes	—
21	C₄×Dic₃	C₂×C₃	1	1	yes	characteristic
22	C₂²×C₃²	C₂³	1	1	yes	characteristic
23	C₃²×C₄	—	2	2	no	—
24	C₃²×C₄	D₄	1	2	yes	—
25	C₃×Dic₃	—	2	2	no	—
26	C₃×Dic₃	Q₈	1	4	yes	complemented
27	C₄⋊Q₈	—	3	1	no	Sylow
28	C₃×Q₈	—	2	4	no	—
29	C₃×Q₈	—	2	2	no	—
30	C₃×Q₈	—	2	2	no	—
31	C₃×Q₈	—	6	2	no	—
32	C₂×C₃×C₄	—	2	2	no	—
33	C₂×C₃×C₄	—	2	1	no	—
34	C₂×C₃×C₄	—	3	2	no	—
35	C₂×C₃×C₄	—	3	2	no	—
36	C₂×C₃×C₄	C₂×D₃	1	2	yes	—
37	C₂×C₃×C₄	C₂×D₃	1	1	yes	characteristic
38	C₂×C₃×C₄	C₂²×C₃	1	2	yes	—
39	C₂×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
40	C₂×Dic₃	C₂²×C₃	1	2	yes	—
41	C₂×Dic₃	C₂²×C₃	1	2	yes	—
42	Dic₆	—	2	2	no	—
43	C₂×C₃²	C₂×D₄	1	1	yes	characteristic
44	C₂×C₃²	C₂×Q₈	1	2	yes	—
45	C₂×Q₈	—	3	1	no	—
46	C₂×Q₈	C₃×D₃	1	1	yes	characteristic
47	C₄⋊C₄	—	3	4	no	—
48	C₄²	—	3	1	no	—
49	C₂²×C₃	—	2	1	no	—
50	C₂²×C₃	C₂²×D₃	1	1	yes	characteristic
51	C₂²×C₃	C₂³×C₃	1	1	yes	characteristic
52	C₃×C₄	—	2	4	no	—
53	C₃×C₄	—	2	2	no	—
54	C₃×C₄	—	2	2	no	—
55	C₃×C₄	—	2	2	no	—
56	C₃×C₄	—	3	4	no	—
57	C₃×C₄	—	6	2	no	—
58	C₃×C₄	#67	1	2	yes	—
59	C₃×C₄	C₃×D₄	1	2	yes	—
60	Dic₃	—	2	2	no	—
61	Dic₃	C₃×Q₈	1	4	yes	complemented
62	C₃²	C₄⋊Q₈	1	1	yes	characteristic, complemented, Sylow
63	Q₈	—	2	2	no	—
64	Q₈	—	6	2	no	—
65	C₂×C₄	—	3	2	no	—
66	C₂×C₄	—	3	2	no	—
67	C₂×C₄	C₂×C₃×D₃	1	2	yes	—
68	C₂×C₄	C₂×C₃×D₃	1	1	yes	characteristic
69	C₂×C₃	—	2	2	no	—
70	C₂×C₃	—	2	1	no	—
71	C₂×C₃	D₃×Q₈	1	2	yes	—
72	C₂×C₃	C₂×#67	1	1	yes	characteristic
73	C₂×C₃	C₂×C₃×D₄	1	1	yes	characteristic
74	C₂×C₃	C₂×C₃×Q₈	1	2	yes	—
75	C₂²	C₂²×C₃×D₃	1	1	yes	characteristic
76	C₄	—	2	2	no	—
77	C₄	—	3	4	no	—
78	C₄	—	6	2	no	—
79	C₄	C₃×#67	1	2	yes	—
80	C₃	—	2	1	no	—
81	C₃	#944	1	1	yes	characteristic, direct product factor
82	C₃	C₃×C₄⋊Q₈	1	1	yes	characteristic, complemented
83	C₂	C₃×D₃×Q₈	1	2	yes	—
84	C₂	C₂×C₃×#67	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
6. #944	C₃	direct (N × H)
26. C₃×Dic₃	Q₈	semidirect
61. Dic₃	C₃×Q₈	semidirect
62. C₃²	C₄⋊Q₈	semidirect
81. C₃	#944	direct (N × H)
82. 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×C₃²×Q₈	2
C₂×C₃×Dic₆	2
C₃×Dic₃⋊C₄	2
C₃×C₄×Dic₃	2
C₃×C₄⋊Q₈	3
#944	3

Subgroups — C3×#944 #64067

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#944 #64067