Subgroups — #14546405

Order 2187.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624845	C₃	1	1	yes	maximal, characteristic
2	#10624649	C₃	1	1	yes	maximal, characteristic, complemented
3	#10624522	C₃	1	1	yes	maximal, characteristic, complemented
4	#10624465	C₃	1	1	yes	maximal, characteristic, complemented
5	#6908	—	3	1	no	—
6	C₃×C₂₇⋊C₃	—	3	1	no	—
7	#6894	—	3	1	no	—
8	#6887	C₃²	1	1	yes	characteristic
9	#6883	—	3	1	no	—
10	#6882	—	3	1	no	—
11	#6881	—	3	1	no	—
12	#6869	—	3	1	no	—
13	#6861	—	3	1	no	—
14	#6860	—	3	1	no	—
15	#6858	—	3	1	no	—
16	#737	—	9	1	no	—
17	C₃×3₋¹⁺²	—	3	1	no	—
18	C₃²×C₉	H(3,𝔽₃)	1	1	yes	characteristic
19	#733	—	3	1	no	—
20	#733	—	3	1	no	—
21	#732	—	3	1	no	—
22	#731	—	9	1	no	—
23	AΣL(1,𝔽₂₇)	—	9	1	no	—
24	C₂₇⋊C₃	—	9	1	no	—
25	C₂₇⋊C₃	—	9	1	no	—
26	C₂₇⋊C₃	—	9	1	no	—
27	C₂₇⋊C₃	—	9	1	no	—
28	C₃×C₂₇	—	3	3	no	—
29	C₉⋊C₉	—	3	1	no	—
30	C₉⋊C₉	—	3	1	no	—
31	C₉⋊C₉	—	9	1	no	—
32	C₉⋊C₉	—	9	1	no	—
33	C₉⋊C₉	—	9	1	no	—
34	C₃²⋊C₉	—	3	1	no	—
35	C₃²⋊C₉	—	3	1	no	—
36	C₃²⋊C₉	—	3	1	no	—
37	C₉²	—	3	1	no	—
38	C₃³	AΣL(1,𝔽₂₇)	1	1	yes	characteristic
39	3₋¹⁺²	—	9	1	no	—
40	3₋¹⁺²	—	9	1	no	—
41	3₋¹⁺²	—	27	1	no	—
42	3₋¹⁺²	—	27	1	no	—
43	3₋¹⁺²	—	27	1	no	—
44	H(3,𝔽₃)	—	9	1	no	—
45	C₃×C₉	—	3	1	no	—
46	C₃×C₉	—	3	1	no	—
47	C₃×C₉	—	3	1	no	—
48	C₃×C₉	—	9	1	no	—
49	C₃×C₉	—	9	1	no	—
50	C₃×C₉	—	9	1	no	—
51	C₃×C₉	—	9	1	no	—
52	C₃×C₉	—	27	1	no	—
53	C₃×C₉	AΣL(1,𝔽₂₇)	1	1	yes	characteristic
54	C₃×C₉	#732	1	1	yes	characteristic
55	C₃×C₉	#732	1	1	yes	characteristic
56	C₂₇	—	9	3	no	—
57	C₂₇	—	27	1	no	—
58	C₃²	—	3	1	no	—
59	C₃²	—	9	1	no	—
60	C₃²	—	27	1	no	—
61	C₃²	#6856	1	1	yes	characteristic
62	C₉	—	3	1	no	—
63	C₉	—	3	1	no	—
64	C₉	—	27	1	no	—
65	C₉	—	27	1	no	—
66	C₉	—	27	1	no	—
67	C₉	—	27	1	no	—
68	C₉	—	27	1	no	—
69	C₉	—	27	1	no	—
70	C₉	#6878	1	1	yes	characteristic
71	C₉	#6881	1	1	yes	characteristic
72	C₉	#6883	1	1	yes	characteristic
73	C₃	—	3	1	no	—
74	C₃	—	9	1	no	—
75	C₃	—	81	1	no	—
76	C₃	#10624481	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₃	#10624481
commutator, Frattini, cosocle	#6887	C₃²
prime radical	#10624845	C₃
LCS	G ▷ #6887 ▷ C₃²×C₉ ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃ ◁ C₃×C₉ ◁ C₃²×C₉ ◁ #6887 ◁ G
LECS	G ▷ #6887 ▷ C₃²×C₉ ▷ C₃² ▷ C₃ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. #10624649	C₃	semidirect
3. #10624522	C₃	semidirect
4. #10624465	C₃	semidirect

Maximal subgroups

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

subgroup	index
#10624845	3
#10624649	3
#10624522	3
#10624465	3