Subgroups — #14552606

Order 2187.

872 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₉²	C₃	1	1	yes	maximal, characteristic
2	#10624559	C₃	1	24	yes	maximal, complemented
3	#10624558	C₃	1	4	yes	maximal
4	#10624556	C₃	1	8	yes	maximal
5	#10624551	C₃	1	3	yes	maximal, complemented
6	C₃²×3₋¹⁺²	C₃²	1	1	yes	characteristic
7	C₃³×C₉	C₃²	1	4	yes	—
8	C₃×C₉⋊C₉	C₃²	1	24	yes	—
9	C₃×C₃²⋊C₉	C₃²	1	8	yes	—
10	C₃×C₉²	—	3	9	no	—
11	C₃×C₉²	C₃²	1	8	yes	—
12	C₃×C₉²	C₃²	1	1	yes	characteristic
13	#6855	C₃²	1	24	yes	—
14	#6855	C₃²	1	12	yes	—
15	#6855	C₃²	1	24	yes	—
16	#6855	C₃²	1	24	yes	—
17	C₃⁴	C₃³	1	1	yes	characteristic
18	C₃×3₋¹⁺²	—	3	12	no	—
19	C₃²×C₉	—	3	12	no	—
20	C₃²×C₉	—	3	12	no	—
21	C₃²×C₉	—	3	24	no	—
22	C₃²×C₉	C₃³	1	3	yes	—
23	C₃²×C₉	C₃³	1	24	yes	—
24	C₃²×C₉	C₃³	1	4	yes	—
25	C₃²×C₉	C₃³	1	8	yes	—
26	C₉⋊C₉	—	3	72	no	—
27	C₃²⋊C₉	—	3	24	no	—
28	C₉²	—	3	24	no	—
29	C₉²	3₋¹⁺²	1	9	yes	complemented
30	C₃³	—	3	1	no	—
31	C₃³	—	3	8	no	—
32	C₃³	#737	1	12	yes	—
33	C₃³	C₃⁴	1	1	yes	characteristic
34	3₋¹⁺²	—	9	9	no	—
35	C₃×C₉	—	3	108	no	—
36	C₃×C₉	—	3	8	no	—
37	C₃×C₉	—	3	4	no	—
38	C₃×C₉	—	3	8	no	—
39	C₃×C₉	—	3	8	no	—
40	C₃×C₉	—	3	8	no	—
41	C₃×C₉	—	3	24	no	—
42	C₃×C₉	—	3	72	no	—
43	C₃×C₉	—	3	12	no	—
44	C₃×C₉	C₃×3₋¹⁺²	1	12	yes	—
45	C₃×C₉	#737	1	24	yes	—
46	C₃²	—	3	12	no	—
47	C₃²	—	3	24	no	—
48	C₃²	#6897	1	9	yes	—
49	C₃²	C₃²×3₋¹⁺²	1	1	yes	characteristic
50	C₃²	C₃×#737	1	4	yes	—
51	C₃²	C₃×#737	1	8	yes	—
52	C₉	—	3	12	no	—
53	C₉	—	3	24	no	—
54	C₉	—	9	3	no	—
55	C₉	—	9	24	no	—
56	C₃	—	3	9	no	—
57	C₃	#10624872	1	4	yes	—
58	C₃	C₃×#6897	1	1	yes	characteristic
59	C₃	#10624877	1	8	yes	—

	subgroup	G/H
center, commutator, Frattini, socle, cosocle	C₃³	C₃⁴
prime radical	C₃⁴	C₃³
LCS	G ▷ C₃³ ▷ C₁
UCS	C₁ ◁ C₃³ ◁ G
LECS	G ▷ C₃³ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. #10624559	C₃	semidirect
5. #10624551	C₃	semidirect
29. C₉²	3₋¹⁺²	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₉²	3
#10624559	3
#10624558	3
#10624556	3
#10624551	3