Subgroups — C₃×C₄⋊(C₃⋊C₈) #63590

Order 288.

91 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₂×C₃×C₄	C₂×D₃
commutator	C₂×C₃	C₂×C₃×C₈
Frattini	C₂×C₄	C₂×C₃×D₃
Fitting	C₃²×C₄²	C₂
socle, prime radical	C₂²×C₃²	C₂×C₄
cosocle	C₂×C₃×C₄	C₂²×C₃
hypercenter	C₃×C₄²	D₃
hypocenter	C₃	C₃×C₄⋊C₈
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×C₄²

Complements

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

N	H ≅ G/N	type
4. C₄⋊(C₃⋊C₈)	C₃	direct (N × H)
16. C₃²×C₄	C₈	semidirect
45. C₃×C₄	C₃⋊C₈	semidirect
46. C₃×C₄	C₃×C₈	semidirect
51. C₃²	C₄⋊C₈	semidirect
67. C₄	C₃×C₃⋊C₈	semidirect
71. C₃	C₄⋊(C₃⋊C₈)	direct (N × H)
72. C₃	C₃×C₄⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₄²	2
C₂×C₃×C₃⋊C₈	2
C₃×C₄⋊C₈	3
C₄⋊(C₃⋊C₈)	3

Subgroups — C3×C4⋊(C3⋊C8) #63590

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄⋊(C₃⋊C₈) #63590