Subgroups — #10624473⋊C₂ #13090498

Order 1458.

81 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624473	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃⋊(D₂₇⋊C₃)	C₃	1	1	yes	maximal, characteristic
3	#92294	—	3	1	no	maximal
4	C₃×C₂₇⋊C₃	—	2	1	no	—
5	C₃×C₂₇⋊C₃	C₂×C₃	1	1	yes	characteristic
6	#6887	D₃	1	1	yes	characteristic
7	C₃×C₃⋊D₉	—	3	1	no	—
8	C₃⋊D₂₇	C₉	1	1	yes	characteristic, complemented
9	D₂₇⋊C₃	—	9	1	no	—
10	D₉⋊C₉	—	9	1	no	—
11	D₉⋊C₉	—	9	1	no	—
12	(C₃⋊D₃)⋊C₉	—	9	1	no	—
13	C₉×D₉	—	9	1	no	—
14	C₃²×C₉	C₃×D₃	1	1	yes	characteristic
15	C₂₇⋊C₃	—	2	3	no	—
16	C₂₇⋊C₃	—	3	1	no	—
17	C₂₇⋊C₃	—	6	1	no	—
18	C₂₇⋊C₃	—	6	1	no	—
19	C₂₇⋊C₃	—	6	1	no	—
20	C₃×C₂₇	—	2	1	no	—
21	C₃×C₂₇	—	6	1	no	—
22	C₃×C₂₇	C₂×C₉	1	1	yes	characteristic, complemented
23	C₉⋊C₉	—	2	1	no	—
24	C₉⋊C₉	—	3	1	no	—
25	C₉⋊C₉	D₉	1	1	yes	characteristic
26	C₃²⋊C₉	—	3	1	no	—
27	C₉²	—	3	1	no	—
28	C₃×C₃⋊D₃	—	9	1	no	—
29	C₃⋊D₉	—	3	1	no	—
30	D₃×C₉	—	27	1	no	—
31	C₃×D₉	—	9	1	no	—
32	C₃×D₉	—	9	1	no	—
33	C₃×D₉	—	9	1	no	—
34	D₂₇	—	9	1	no	—
35	C₃³	AGL(1,ℤ/9)	1	1	yes	characteristic
36	C₃×C₉	—	2	1	no	—
37	C₃×C₉	—	2	1	no	—
38	C₃×C₉	—	2	1	no	—
39	C₃×C₉	—	2	1	no	—
40	C₃×C₉	—	3	1	no	—
41	C₃×C₉	—	6	1	no	—
42	C₃×C₉	C₃×D₉	1	1	yes	characteristic
43	C₃×C₉	D₃×C₉	1	1	yes	characteristic
44	C₃×C₉	(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
45	C₃×C₉	AGL(1,ℤ/9)	1	1	yes	characteristic
46	C₂₇	—	3	1	no	—
47	C₂₇	—	6	3	no	—
48	C₂₇	—	6	1	no	—
49	C₃⋊D₃	—	9	1	no	—
50	C₃×D₃	—	27	1	no	—
51	C₃×D₃	—	81	1	no	—
52	C₂×C₉	—	81	1	no	—
53	D₉	—	9	1	no	—
54	D₉	—	9	1	no	—
55	D₉	—	9	1	no	—
56	C₃²	—	2	1	no	—
57	C₃²	—	9	1	no	—
58	C₃²	#4169	1	1	yes	characteristic
59	C₃²	D₉⋊C₉	1	1	yes	characteristic
60	C₉	—	2	1	no	—
61	C₉	—	2	1	no	—
62	C₉	—	2	1	no	—
63	C₉	—	9	1	no	—
64	C₉	—	18	1	no	—
65	C₉	C₉×D₉	1	1	yes	characteristic
66	C₉	(C₃⋊D₃)⋊C₉	1	1	yes	characteristic
67	C₉	D₉⋊C₉	1	1	yes	characteristic
68	C₂×C₃	—	81	1	no	—
69	D₃	—	27	1	no	—
70	D₃	—	81	1	no	—
71	C₃	—	3	1	no	—
72	C₃	—	3	1	no	—
73	C₃	—	6	1	no	—
74	C₃	#92158	1	1	yes	characteristic
75	C₂	—	81	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, hypocenter	C₃×C₂₇	C₂×C₉
Frattini	C₃²×C₉	C₃×D₃
Fitting	#10624473	C₂
socle	C₃	#92158
prime radical	C₃⋊(D₂₇⋊C₃)	C₃
cosocle	C₃×C₂₇⋊C₃	C₂×C₃
LCS	G ▷ C₃×C₂₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. #10624473	C₂	semidirect
8. C₃⋊D₂₇	C₉	semidirect
22. C₃×C₂₇	C₂×C₉	semidirect

Maximal subgroups

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

subgroup	index
#10624473	2
C₃⋊(D₂₇⋊C₃)	3
#92294	3

Subgroups — #10624473⋊C2 #13090498

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #10624473⋊C₂ #13090498