Subgroups — Dic₃⋊(C₃⋊C₈) #63571

Order 288.

87 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×Dic₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic
4	Dic₃⋊C₈	—	3	1	no	maximal
5	C₄⋊(C₃⋊C₈)	—	3	1	no	maximal
6	C₂×C₃²×C₄	C₂²	1	1	yes	characteristic
7	C₂×C₃×Dic₃	C₄	1	1	yes	characteristic
8	C₂×C₃×Dic₃	C₄	1	1	yes	characteristic
9	C₃⋊(C₃⋊C₈)	—	2	1	no	—
10	C₃×C₃⋊C₈	—	2	1	no	—
11	C₂×C₃×C₈	—	3	1	no	—
12	C₃×C₄²	—	3	1	no	—
13	C₄×Dic₃	D₃	1	1	yes	characteristic
14	C₂×C₃⋊C₈	—	3	1	no	—
15	C₂×C₃⋊C₈	—	3	1	no	—
16	C₂×C₃⋊C₈	—	6	1	no	—
17	C₂×C₃⋊C₈	D₃	1	1	yes	characteristic
18	C₂²×C₃²	C₂×C₄	1	1	yes	characteristic
19	C₃²×C₄	D₄	1	1	yes	characteristic
20	C₃²×C₄	Q₈	1	1	yes	characteristic
21	C₃×Dic₃	—	2	1	no	—
22	C₃×Dic₃	C₈	1	2	yes	complemented
23	C₄⋊C₈	—	9	1	no	Sylow
24	C₂×C₃×C₄	—	2	1	no	—
25	C₂×C₃×C₄	—	3	1	no	—
26	C₂×C₃×C₄	—	3	1	no	—
27	C₂×C₃×C₄	C₂×D₃	1	1	yes	characteristic
28	C₂×C₃×C₄	C₂×D₃	1	1	yes	characteristic
29	C₂×Dic₃	Dic₃	1	1	yes	characteristic
30	C₂×Dic₃	Dic₃	1	1	yes	characteristic
31	C₃×C₈	—	6	1	no	—
32	C₃⋊C₈	—	2	1	no	—
33	C₃⋊C₈	—	6	2	no	—
34	C₃⋊C₈	—	6	1	no	—
35	C₃⋊C₈	—	6	1	no	—
36	C₂×C₃²	C₄⋊C₄	1	1	yes	characteristic
37	C₂×C₃²	C₂×C₈	1	1	yes	characteristic
38	C₂×C₃²	M₁₆	1	1	yes	characteristic
39	C₂×C₈	—	3	1	no	—
40	C₂×C₈	—	9	1	no	—
41	C₄²	—	3	1	no	—
42	C₂²×C₃	—	2	1	no	—
43	C₂²×C₃	C₄×D₃	1	1	yes	characteristic
44	C₂²×C₃	C₂×Dic₃	1	1	yes	characteristic
45	C₃×C₄	—	2	1	no	—
46	C₃×C₄	—	2	1	no	—
47	C₃×C₄	—	3	2	no	—
48	C₃×C₄	—	6	1	no	—
49	C₃×C₄	Dic₆	1	1	yes	characteristic
50	C₃×C₄	Dic₆	1	1	yes	characteristic
51	C₃×C₄	D₁₂	1	1	yes	characteristic
52	C₃×C₄	#67	1	1	yes	characteristic
53	Dic₃	—	2	1	no	—
54	Dic₃	C₃⋊C₈	1	2	yes	complemented
55	C₃²	C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
56	C₂×C₄	—	3	1	no	—
57	C₂×C₄	—	3	1	no	—
58	C₂×C₄	D₃²	1	1	yes	characteristic
59	C₈	—	6	1	no	—
60	C₈	—	18	1	no	—
61	C₂×C₃	—	2	1	no	—
62	C₂×C₃	—	2	1	no	—
63	C₂×C₃	—	2	1	no	—
64	C₂×C₃	D₃×C₈	1	1	yes	characteristic
65	C₂×C₃	ΓL(1,𝔽₂₅)	1	1	yes	characteristic
66	C₂×C₃	C₂×C₃⋊C₈	1	1	yes	characteristic
67	C₂×C₃	#208	1	1	yes	characteristic
68	C₂×C₃	Dic₃⋊C₄	1	1	yes	characteristic
69	C₂×C₃	C₄⋊Dic₃	1	1	yes	characteristic
70	C₂²	D₃×Dic₃	1	1	yes	characteristic
71	C₄	—	3	2	no	—
72	C₄	—	6	1	no	—
73	C₄	#626	1	1	yes	characteristic
74	C₄	#627	1	1	yes	characteristic
75	C₃	—	2	1	no	—
76	C₃	C₄⋊(C₃⋊C₈)	1	1	yes	characteristic, complemented
77	C₃	Dic₃⋊C₈	1	1	yes	characteristic, complemented
78	C₂	D₃×C₃⋊C₈	1	1	yes	characteristic
79	C₂	#3711	1	1	yes	characteristic
80	C₂	Dic₃⋊Dic₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂×C₄	D₃²
commutator	C₂×C₃²	C₂×C₈
Fitting, cosocle	C₂×C₃²×C₄	C₂²
socle, prime radical	C₂²×C₃²	C₂×C₄
hypocenter	C₃²	C₄⋊C₈
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
22. C₃×Dic₃	C₈	semidirect
54. Dic₃	C₃⋊C₈	semidirect
55. C₃²	C₄⋊C₈	semidirect
76. C₃	C₄⋊(C₃⋊C₈)	semidirect
77. C₃	Dic₃⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃⋊(C₃⋊C₈)	2
C₃×C₄×Dic₃	2
C₂×C₃×C₃⋊C₈	2
Dic₃⋊C₈	3
C₄⋊(C₃⋊C₈)	3

Subgroups — Dic3⋊(C3⋊C8) #63571

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₃⋊(C₃⋊C₈) #63571