Subgroups — C₄×C₃⋊D₈₁ #14516147

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	1	yes	maximal, characteristic
2	C₃×C₄×C₈₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃⋊Dic₈₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₃⋊D₂₇	—	3	1	no	maximal
5	C₄×D₈₁	—	3	3	no	maximal
6	C₂×C₃×C₈₁	C₂²	1	1	yes	characteristic
7	C₃⋊D₈₁	C₄	1	2	yes	direct product factor
8	C₂×C₃⋊D₂₇	—	3	1	no	—
9	C₃×C₄×C₂₇	D₃	1	1	yes	characteristic
10	C₃⋊Dic₂₇	—	3	1	no	—
11	C₂×D₈₁	—	3	3	no	—
12	C₄×C₈₁	D₃	1	3	yes	complemented
13	Dic₈₁	—	3	3	no	—
14	C₃×C₈₁	C₂×C₄	1	1	yes	characteristic, complemented, Sylow
15	C₄×C₃⋊D₉	—	9	1	no	—
16	C₄×D₂₇	—	9	2	no	—
17	C₄×D₂₇	—	9	1	no	—
18	C₂×C₃×C₂₇	C₂×D₃	1	1	yes	characteristic
19	C₃⋊D₂₇	—	3	2	no	—
20	C₂×C₈₁	C₂×D₃	1	3	yes	—
21	D₈₁	—	3	6	no	—
22	C₂×C₃⋊D₉	—	9	1	no	—
23	C₃×C₄×C₉	D₉	1	1	yes	characteristic
24	C₃⋊Dic₉	—	9	1	no	—
25	C₂×D₂₇	—	9	2	no	—
26	C₂×D₂₇	—	9	1	no	—
27	C₄×C₂₇	D₉	1	2	yes	—
28	C₄×C₂₇	C₃⋊D₃	1	1	yes	characteristic
29	Dic₂₇	—	9	2	no	—
30	Dic₂₇	—	9	1	no	—
31	C₃×C₂₇	C₄×D₃	1	1	yes	characteristic
32	C₈₁	C₄×D₃	1	3	yes	complemented
33	C₄×C₃⋊D₃	—	27	1	no	—
34	C₄×D₉	—	27	2	no	—
35	C₄×D₉	—	27	1	no	—
36	C₂×C₃×C₉	C₂×D₉	1	1	yes	characteristic
37	C₃⋊D₉	—	9	2	no	—
38	C₂×C₂₇	C₂×D₉	1	2	yes	—
39	C₂×C₂₇	C₂×C₃⋊D₃	1	1	yes	characteristic
40	D₂₇	—	9	4	no	—
41	D₂₇	—	9	2	no	—
42	C₂×C₃⋊D₃	—	27	1	no	—
43	C₃²×C₄	D₂₇	1	1	yes	characteristic
44	C₃⋊Dic₃	—	27	1	no	—
45	C₂×D₉	—	27	2	no	—
46	C₂×D₉	—	27	1	no	—
47	C₄×C₉	D₂₇	1	2	yes	—
48	C₄×C₉	C₃⋊D₉	1	1	yes	characteristic
49	Dic₉	—	27	2	no	—
50	Dic₉	—	27	1	no	—
51	C₃×C₉	C₄×D₉	1	1	yes	characteristic
52	C₂₇	C₄×D₉	1	2	yes	—
53	C₂₇	C₄×C₃⋊D₃	1	1	yes	characteristic
54	C₄×D₃	—	81	3	no	—
55	C₄×D₃	—	81	1	no	—
56	C₂×C₃²	C₂×D₂₇	1	1	yes	characteristic
57	C₃⋊D₃	—	27	2	no	—
58	C₂×C₉	C₂×D₂₇	1	2	yes	—
59	C₂×C₉	C₂×C₃⋊D₉	1	1	yes	characteristic
60	D₉	—	27	4	no	—
61	D₉	—	27	2	no	—
62	C₂×D₃	—	81	3	no	—
63	C₂×D₃	—	81	1	no	—
64	C₃×C₄	D₈₁	1	3	yes	complemented
65	C₃×C₄	C₃⋊D₂₇	1	1	yes	characteristic
66	Dic₃	—	81	3	no	—
67	Dic₃	—	81	1	no	—
68	C₃²	C₄×D₂₇	1	1	yes	characteristic
69	C₉	C₄×D₂₇	1	2	yes	—
70	C₉	C₄×C₃⋊D₉	1	1	yes	characteristic
71	C₂×C₄	—	243	1	no	Sylow
72	C₂×C₃	C₂×D₈₁	1	3	yes	—
73	C₂×C₃	C₂×C₃⋊D₂₇	1	1	yes	characteristic
74	D₃	—	81	2	no	—
75	D₃	—	81	6	no	—
76	C₂²	—	243	1	no	—
77	C₄	—	243	1	no	—
78	C₄	C₃⋊D₈₁	1	1	yes	characteristic, direct product factor
79	C₃	C₄×D₈₁	1	3	yes	complemented
80	C₃	C₄×C₃⋊D₂₇	1	1	yes	characteristic
81	C₂	—	243	2	no	—
82	C₂	C₂×C₃⋊D₈₁	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₃×C₄×C₈₁	C₂	semidirect
3. C₃⋊Dic₈₁	C₂	semidirect
7. C₃⋊D₈₁	C₄	direct (N × H)
12. C₄×C₈₁	D₃	semidirect
14. C₃×C₈₁	C₂×C₄	semidirect
32. C₈₁	C₄×D₃	semidirect
64. C₃×C₄	D₈₁	semidirect
78. C₄	C₃⋊D₈₁	direct (N × H)
79. C₃	C₄×D₈₁	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
C₃⋊Dic₈₁	2
C₄×C₃⋊D₂₇	3
C₄×D₈₁	3

Subgroups — C4×C3⋊D81 #14516147

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₃⋊D₈₁ #14516147