Subgroups — C₃⋊((C₂²⋊C₈₁)⋊C₂) #14516475

Order 1944.

114 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, complemented
2	#10619677	—	3	1	no	maximal
3	(C₂²⋊C₈₁)⋊C₂	—	3	3	no	maximal
4	C₃⋊D₈₁	—	4	1	no	maximal
5	C₂²×C₃×C₂₇	D₃	1	1	yes	characteristic
6	C₂×C₃⋊D₂₇	—	3	1	no	—
7	C₃⋊Dic₂₇	—	3	1	no	—
8	C₂²⋊C₈₁	D₃	1	3	yes	complemented
9	C₃×C₈₁	—	4	1	no	Sylow
10	#6233	—	9	1	no	—
11	#6171	—	9	2	no	—
12	#6171	—	9	1	no	—
13	C₂×C₃×C₂₇	—	3	1	no	—
14	C₃⋊D₂₇	—	6	1	no	—
15	D₈₁	—	12	3	no	—
16	C₂²×C₃×C₉	D₉	1	1	yes	characteristic
17	C₂×C₃⋊D₉	—	9	1	no	—
18	C₃⋊Dic₉	—	9	1	no	—
19	C₂²×C₂₇	D₉	1	2	yes	—
20	C₂²×C₂₇	C₃⋊D₃	1	1	yes	characteristic
21	C₂×D₂₇	—	9	2	no	—
22	C₂×D₂₇	—	9	1	no	—
23	Dic₂₇	—	9	2	no	—
24	Dic₂₇	—	9	1	no	—
25	C₃×C₂₇	S₄	1	1	yes	characteristic
26	C₈₁	—	4	3	no	—
27	#638	—	27	1	no	—
28	#611	—	27	2	no	—
29	#611	—	27	1	no	—
30	C₂×C₃×C₉	—	3	1	no	—
31	C₃⋊D₉	—	18	1	no	—
32	C₂×C₂₇	—	3	2	no	—
33	C₂×C₂₇	—	3	1	no	—
34	D₂₇	—	18	2	no	—
35	D₂₇	—	18	1	no	—
36	C₂²×C₃²	D₂₇	1	1	yes	characteristic
37	C₂×C₃⋊D₃	—	27	1	no	—
38	C₃⋊Dic₃	—	27	1	no	—
39	C₂²×C₉	D₂₇	1	2	yes	—
40	C₂²×C₉	C₃⋊D₉	1	1	yes	characteristic
41	C₂×D₉	—	27	1	no	—
42	C₂×D₉	—	27	2	no	—
43	Dic₉	—	27	1	no	—
44	Dic₉	—	27	2	no	—
45	C₃×C₉	(C₂²⋊C₉)⋊C₂	1	1	yes	characteristic
46	C₂₇	(C₂²⋊C₉)⋊C₂	1	2	yes	—
47	C₂₇	C₃⋊S₄	1	1	yes	characteristic
48	#67	—	81	3	no	—
49	#67	—	81	1	no	—
50	C₂×C₃²	—	3	1	no	—
51	C₃⋊D₃	—	54	1	no	—
52	C₂×C₉	—	3	2	no	—
53	C₂×C₉	—	3	1	no	—
54	D₉	—	54	2	no	—
55	D₉	—	54	1	no	—
56	C₂²×C₃	D₈₁	1	3	yes	complemented
57	C₂²×C₃	C₃⋊D₂₇	1	1	yes	characteristic
58	C₂×D₃	—	81	1	no	—
59	C₂×D₃	—	81	3	no	—
60	Dic₃	—	81	1	no	—
61	Dic₃	—	81	3	no	—
62	C₃²	(C₂²⋊C₂₇)⋊C₂	1	1	yes	characteristic
63	C₉	(C₂²⋊C₂₇)⋊C₂	1	2	yes	—
64	C₉	C₃⋊((C₂²⋊C₉)⋊C₂)	1	1	yes	characteristic
65	D₄	—	243	1	no	Sylow
66	C₂×C₃	—	3	1	no	—
67	C₂×C₃	—	3	3	no	—
68	D₃	—	162	1	no	—
69	D₃	—	162	3	no	—
70	C₂²	—	243	1	no	—
71	C₂²	C₃⋊D₈₁	1	1	yes	characteristic, complemented
72	C₄	—	243	1	no	—
73	C₃	(C₂²⋊C₈₁)⋊C₂	1	3	yes	complemented
74	C₃	C₃⋊((C₂²⋊C₂₇)⋊C₂)	1	1	yes	characteristic
75	C₂	—	3	1	no	—
76	C₂	—	486	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₃×C₂²⋊C₈₁	C₂
Frattini	C₂₇	C₃⋊S₄
Fitting	C₂²×C₃×C₂₇	D₃
socle	C₂²×C₃²	D₂₇
LCS	G ▷ C₃×C₂²⋊C₈₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₂²⋊C₈₁	C₂	semidirect
8. C₂²⋊C₈₁	D₃	semidirect
56. C₂²×C₃	D₈₁	semidirect
71. C₂²	C₃⋊D₈₁	semidirect
73. C₃	(C₂²⋊C₈₁)⋊C₂	semidirect

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
#10619677	3
(C₂²⋊C₈₁)⋊C₂	3
C₃⋊D₈₁	4

Subgroups — C3⋊((C22⋊C81)⋊C2) #14516475

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊((C₂²⋊C₈₁)⋊C₂) #14516475