Subgroups — C₄⋊(C₃⋊D₈₁) #14516148

Order 1944.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃⋊D₈₁	C₂	1	2	yes	maximal, complemented
2	C₃×C₄×C₈₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄⋊(C₃⋊D₂₇)	—	3	1	no	maximal
4	D₃₂₄	—	3	3	no	maximal
5	C₂×C₃×C₈₁	C₂²	1	1	yes	characteristic
6	C₃⋊D₈₁	—	2	2	no	—
7	C₂×C₃⋊D₂₇	—	3	2	no	—
8	C₃×C₄×C₂₇	D₃	1	1	yes	characteristic
9	C₂×D₈₁	—	3	6	no	—
10	C₄×C₈₁	D₃	1	3	yes	complemented
11	C₃×C₈₁	D₄	1	1	yes	characteristic, complemented, Sylow
12	C₄⋊(C₃⋊D₉)	—	9	1	no	—
13	D₁₀₈	—	9	2	no	—
14	D₁₀₈	—	9	1	no	—
15	C₂×C₃×C₂₇	C₂×D₃	1	1	yes	characteristic
16	C₃⋊D₂₇	—	6	2	no	—
17	C₂×C₈₁	C₂×D₃	1	3	yes	—
18	D₈₁	—	6	6	no	—
19	C₂×C₃⋊D₉	—	9	2	no	—
20	C₃×C₄×C₉	D₉	1	1	yes	characteristic
21	C₂×D₂₇	—	9	4	no	—
22	C₂×D₂₇	—	9	2	no	—
23	C₄×C₂₇	D₉	1	2	yes	—
24	C₄×C₂₇	C₃⋊D₃	1	1	yes	characteristic
25	C₃×C₂₇	D₁₂	1	1	yes	characteristic
26	C₈₁	D₁₂	1	3	yes	complemented
27	C₄⋊(C₃⋊D₃)	—	27	1	no	—
28	D₃₆	—	27	2	no	—
29	D₃₆	—	27	1	no	—
30	C₂×C₃×C₉	C₂×D₉	1	1	yes	characteristic
31	C₃⋊D₉	—	18	2	no	—
32	C₂×C₂₇	C₂×D₉	1	2	yes	—
33	C₂×C₂₇	C₂×C₃⋊D₃	1	1	yes	characteristic
34	D₂₇	—	18	4	no	—
35	D₂₇	—	18	2	no	—
36	C₂×C₃⋊D₃	—	27	2	no	—
37	C₃²×C₄	D₂₇	1	1	yes	characteristic
38	C₂×D₉	—	27	4	no	—
39	C₂×D₉	—	27	2	no	—
40	C₄×C₉	D₂₇	1	2	yes	—
41	C₄×C₉	C₃⋊D₉	1	1	yes	characteristic
42	C₃×C₉	D₃₆	1	1	yes	characteristic
43	C₂₇	D₃₆	1	2	yes	—
44	C₂₇	C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
45	D₁₂	—	81	3	no	—
46	D₁₂	—	81	1	no	—
47	C₂×C₃²	C₂×D₂₇	1	1	yes	characteristic
48	C₃⋊D₃	—	54	2	no	—
49	C₂×C₉	C₂×D₂₇	1	2	yes	—
50	C₂×C₉	C₂×C₃⋊D₉	1	1	yes	characteristic
51	D₉	—	54	4	no	—
52	D₉	—	54	2	no	—
53	C₂×D₃	—	81	6	no	—
54	C₂×D₃	—	81	2	no	—
55	C₃×C₄	D₈₁	1	3	yes	complemented
56	C₃×C₄	C₃⋊D₂₇	1	1	yes	characteristic
57	C₃²	D₁₀₈	1	1	yes	characteristic
58	C₉	D₁₀₈	1	2	yes	—
59	C₉	C₄⋊(C₃⋊D₉)	1	1	yes	characteristic
60	D₄	—	243	1	no	Sylow
61	C₂×C₃	C₂×D₈₁	1	3	yes	—
62	C₂×C₃	C₂×C₃⋊D₂₇	1	1	yes	characteristic
63	D₃	—	162	2	no	—
64	D₃	—	162	6	no	—
65	C₂²	—	243	2	no	—
66	C₄	C₃⋊D₈₁	1	1	yes	characteristic, complemented
67	C₃	D₃₂₄	1	3	yes	complemented
68	C₃	C₄⋊(C₃⋊D₂₇)	1	1	yes	characteristic
69	C₂	—	486	2	no	—
70	C₂	C₂×C₃⋊D₈₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×C₃⋊D₈₁
commutator, cosocle	C₂×C₃×C₈₁	C₂²
Frattini	C₂×C₂₇	C₂×C₃⋊D₃
Fitting	C₃×C₄×C₈₁	C₂
socle	C₂×C₃²	C₂×D₂₇
hypercenter	C₄	C₃⋊D₈₁
hypocenter	C₃×C₈₁	D₄
LCS	G ▷ C₂×C₃×C₈₁ ▷ C₃×C₈₁
UCS	C₁ ◁ C₂ ◁ C₄

Complements

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

N	H ≅ G/N	type
1. C₂×C₃⋊D₈₁	C₂	semidirect
2. C₃×C₄×C₈₁	C₂	semidirect
10. C₄×C₈₁	D₃	semidirect
11. C₃×C₈₁	D₄	semidirect
26. C₈₁	D₁₂	semidirect
55. C₃×C₄	D₈₁	semidirect
66. C₄	C₃⋊D₈₁	semidirect
67. C₃	D₃₂₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃⋊D₈₁	2
C₃×C₄×C₈₁	2
C₄⋊(C₃⋊D₂₇)	3
D₃₂₄	3

Subgroups — C4⋊(C3⋊D81) #14516148

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄⋊(C₃⋊D₈₁) #14516148