Subgroups — C₂×C₃×C₂²⋊C₈₁ #14516593

Order 1944.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₂²⋊C₈₁	C₂	1	1	yes	maximal, characteristic, direct product factor
2	C₂³×C₃×C₂₇	C₃	1	1	yes	maximal, characteristic
3	C₂×C₂²⋊C₈₁	C₃	1	3	yes	maximal, direct product factor
4	C₂×C₃×C₈₁	—	4	1	no	maximal
5	C₂²×C₃×C₂₇	—	3	1	no	—
6	C₂²×C₃×C₂₇	—	3	1	no	—
7	C₂²×C₃×C₂₇	C₂×C₃	1	1	yes	characteristic
8	C₂²⋊C₈₁	C₂×C₃	1	3	yes	direct product factor
9	C₃×C₈₁	—	4	1	no	Sylow
10	C₂³×C₃×C₉	C₉	1	1	yes	characteristic
11	C₂³×C₂₇	C₉	1	2	yes	—
12	C₂³×C₂₇	C₃²	1	1	yes	characteristic
13	C₂×C₃×C₂₇	—	3	1	no	—
14	C₂×C₃×C₂₇	—	3	1	no	—
15	C₂×C₃×C₂₇	A₄	1	1	yes	characteristic
16	C₂×C₈₁	—	4	3	no	—
17	C₂²×C₃×C₉	—	3	1	no	—
18	C₂²×C₃×C₉	—	3	1	no	—
19	C₂²×C₃×C₉	C₂×C₉	1	1	yes	characteristic
20	C₂²×C₂₇	—	3	2	no	—
21	C₂²×C₂₇	—	3	1	no	—
22	C₂²×C₂₇	—	3	2	no	—
23	C₂²×C₂₇	—	3	1	no	—
24	C₂²×C₂₇	C₂×C₉	1	2	yes	—
25	C₂²×C₂₇	C₂×C₃²	1	1	yes	characteristic
26	C₃×C₂₇	C₂×A₄	1	1	yes	characteristic
27	C₈₁	—	4	3	no	—
28	C₂³×C₃²	C₂₇	1	1	yes	characteristic
29	C₂³×C₉	C₂₇	1	2	yes	—
30	C₂³×C₉	C₃×C₉	1	1	yes	characteristic
31	C₂×C₃×C₉	—	3	1	no	—
32	C₂×C₃×C₉	—	3	1	no	—
33	C₂×C₃×C₉	C₂²⋊C₉	1	1	yes	characteristic
34	C₂×C₂₇	—	3	2	no	—
35	C₂×C₂₇	—	3	2	no	—
36	C₂×C₂₇	—	3	1	no	—
37	C₂×C₂₇	—	3	1	no	—
38	C₂×C₂₇	C₂²⋊C₉	1	2	yes	—
39	C₂×C₂₇	C₃×A₄	1	1	yes	characteristic
40	C₂²×C₃²	—	3	1	no	—
41	C₂²×C₃²	—	3	1	no	—
42	C₂²×C₃²	C₂×C₂₇	1	1	yes	characteristic
43	C₂²×C₉	—	3	1	no	—
44	C₂²×C₉	—	3	2	no	—
45	C₂²×C₉	—	3	2	no	—
46	C₂²×C₉	—	3	1	no	—
47	C₂²×C₉	C₂×C₂₇	1	2	yes	—
48	C₂²×C₉	C₂×C₃×C₉	1	1	yes	characteristic
49	C₃×C₉	C₂×C₂²⋊C₉	1	1	yes	characteristic
50	C₂₇	C₂×C₂²⋊C₉	1	2	yes	—
51	C₂₇	C₂×C₃×A₄	1	1	yes	characteristic
52	C₂³×C₃	C₈₁	1	3	yes	complemented
53	C₂³×C₃	C₃×C₂₇	1	1	yes	characteristic
54	C₂×C₃²	—	3	1	no	—
55	C₂×C₃²	—	3	1	no	—
56	C₂×C₃²	C₂²⋊C₂₇	1	1	yes	characteristic
57	C₂×C₉	—	3	2	no	—
58	C₂×C₉	—	3	2	no	—
59	C₂×C₉	—	3	1	no	—
60	C₂×C₉	—	3	1	no	—
61	C₂×C₉	C₂²⋊C₂₇	1	2	yes	—
62	C₂×C₉	C₃×C₂²⋊C₉	1	1	yes	characteristic
63	C₂²×C₃	—	3	3	no	—
64	C₂²×C₃	—	3	1	no	—
65	C₂²×C₃	—	3	3	no	—
66	C₂²×C₃	—	3	1	no	—
67	C₂²×C₃	C₂×C₈₁	1	3	yes	complemented
68	C₂²×C₃	C₂×C₃×C₂₇	1	1	yes	characteristic
69	C₃²	C₂×C₂²⋊C₂₇	1	1	yes	characteristic
70	C₉	C₂×C₂²⋊C₂₇	1	2	yes	—
71	C₉	C₂×C₃×C₂²⋊C₉	1	1	yes	characteristic
72	C₂³	C₃×C₈₁	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₃	—	3	3	no	—
74	C₂×C₃	—	3	3	no	—
75	C₂×C₃	—	3	1	no	—
76	C₂×C₃	—	3	1	no	—
77	C₂×C₃	C₂²⋊C₈₁	1	3	yes	direct product factor
78	C₂×C₃	C₃×C₂²⋊C₂₇	1	1	yes	characteristic
79	C₂²	—	3	1	no	—
80	C₂²	—	3	1	no	—
81	C₂²	C₂×C₃×C₈₁	1	1	yes	characteristic, complemented
82	C₃	C₂×C₂²⋊C₈₁	1	3	yes	direct product factor
83	C₃	C₂×C₃×C₂²⋊C₂₇	1	1	yes	characteristic
84	C₂	—	3	1	no	—
85	C₂	—	3	1	no	—
86	C₂	C₃×C₂²⋊C₈₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₂₇	A₄
commutator, hypocenter	C₂²	C₂×C₃×C₈₁
Frattini	C₂₇	C₂×C₃×A₄
Fitting	C₂³×C₃×C₂₇	C₃
socle, prime radical	C₂³×C₃²	C₂₇
cosocle	C₂²×C₂₇	C₂×C₃²
LCS	G ▷ C₂²
UCS	C₁ ◁ C₂×C₃×C₂₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₂²⋊C₈₁	C₂	direct (N × H)
3. C₂×C₂²⋊C₈₁	C₃	direct (N × H)
8. C₂²⋊C₈₁	C₂×C₃	direct (N × H)
52. C₂³×C₃	C₈₁	semidirect
67. C₂²×C₃	C₂×C₈₁	semidirect
72. C₂³	C₃×C₈₁	semidirect
77. C₂×C₃	C₂²⋊C₈₁	direct (N × H)
81. C₂²	C₂×C₃×C₈₁	semidirect
82. C₃	C₂×C₂²⋊C₈₁	direct (N × H)
86. C₂	C₃×C₂²⋊C₈₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₂²⋊C₈₁	2
C₂³×C₃×C₂₇	3
C₂×C₂²⋊C₈₁	3
C₂×C₃×C₈₁	4

Subgroups — C2×C3×C22⋊C81 #14516593

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₂²⋊C₈₁ #14516593