Subgroups — #10624828⋊C₂ #13091269

Order 1458.

97 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624828	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃⋊(D₉⋊C₉)	—	3	1	no	maximal
3	#6869⋊C₂	C₃	1	1	yes	maximal, characteristic
4	AGL(1,ℤ/27)	—	3	3	no	maximal
5	C₃×C₉⋊C₉	D₃	1	1	yes	characteristic
6	#6875	—	2	3	no	—
7	#6875	D₃	1	3	yes	complemented
8	#6869	—	2	1	no	—
9	#6869	C₂×C₃	1	1	yes	characteristic
10	C₉×C₃⋊D₃	—	9	1	no	—
11	C₃×C₃⋊D₉	—	3	1	no	—
12	D₂₇⋊C₃	—	3	3	no	—
13	D₉⋊C₉	—	9	2	no	—
14	D₉⋊C₉	—	9	1	no	—
15	C₃²×C₉	—	3	1	no	—
16	C₃²×C₉	C₃×D₃	1	1	yes	characteristic
17	C₂₇⋊C₃	—	2	3	no	—
18	C₂₇⋊C₃	C₃×D₃	1	3	yes	—
19	C₉⋊C₉	—	2	1	no	—
20	C₉⋊C₉	—	3	2	no	—
21	C₉⋊C₉	C₃⋊D₃	1	1	yes	characteristic
22	C₃×C₃⋊D₃	—	9	1	no	—
23	C₃⋊D₉	—	3	1	no	—
24	D₃×C₉	—	27	1	no	—
25	D₃×C₉	—	27	3	no	—
26	C₃×D₉	—	9	2	no	—
27	C₃×D₉	—	9	1	no	—
28	D₂₇	—	3	3	no	—
29	C₃³	AGL(1,ℤ/9)	1	1	yes	characteristic
30	C₃×C₉	—	3	1	no	—
31	C₃×C₉	—	3	1	no	—
32	C₃×C₉	—	6	1	no	—
33	C₃×C₉	—	6	1	no	—
34	C₃×C₉	—	9	3	no	—
35	C₃×C₉	AGL(1,ℤ/9)	1	2	yes	—
36	C₃×C₉	C₃×C₃⋊D₃	1	1	yes	characteristic
37	C₂₇	—	3	3	no	—
38	C₂₇	—	6	3	no	—
39	C₃⋊D₃	—	9	1	no	—
40	C₃×D₃	—	27	3	no	—
41	C₃×D₃	—	27	1	no	—
42	C₂×C₉	—	81	1	no	—
43	D₉	—	9	2	no	—
44	D₉	—	9	1	no	—
45	C₃²	—	3	3	no	—
46	C₃²	—	3	1	no	—
47	C₃²	C₃⋊AGL(1,ℤ/9)	1	1	yes	characteristic
48	C₉	—	2	1	no	—
49	C₉	—	3	2	no	—
50	C₉	—	9	1	no	—
51	C₉	—	18	1	no	—
52	C₉	#4208	1	1	yes	characteristic
53	C₂×C₃	—	81	1	no	—
54	D₃	—	27	3	no	—
55	D₃	—	27	1	no	—
56	C₃	—	3	3	no	—
57	C₃	—	3	1	no	—
58	C₃	#6895⋊C₂	1	1	yes	characteristic
59	C₂	—	81	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	#6869	C₂×C₃
Frattini	C₃×C₉	C₃×C₃⋊D₃
Fitting	#10624828	C₂
socle	C₃	#6895⋊C₂
prime radical	#6869⋊C₂	C₃
LCS	G ▷ #6869
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. #10624828	C₂	semidirect
7. #6875	D₃	semidirect

Maximal subgroups

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

subgroup	index
#10624828	2
C₃⋊(D₉⋊C₉)	3
#6869⋊C₂	3
AGL(1,ℤ/27)	3

Subgroups — #10624828⋊C2 #13091269

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #10624828⋊C₂ #13091269