Subgroups — #14550337

Order 2187.

314 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#6887	C₃	1	1	yes	maximal, characteristic
2	#10624683	C₃	1	2	yes	maximal
3	C₃×C₃²⋊C₂₇	C₃	1	1	yes	maximal, characteristic
4	#10624468	C₃	1	9	yes	maximal, complemented
5	C₃³×C₉	C₃²	1	1	yes	characteristic
6	C₃×C₂₇⋊C₃	C₃²	1	6	yes	—
7	C₃²×C₂₇	C₃²	1	3	yes	—
8	#6887	—	3	2	no	—
9	#6887	—	3	4	no	—
10	#6887	C₉	1	6	yes	—
11	#6887	C₃²	1	3	yes	—
12	C₃×C₉⋊C₉	—	3	2	no	—
13	C₃×C₃²⋊C₉	C₉	1	2	yes	—
14	C₃×C₃²⋊C₉	C₉	1	1	yes	characteristic
15	C₃×C₉²	—	3	1	no	—
16	C₃²⋊C₂₇	—	3	1	no	—
17	C₃²⋊C₂₇	—	3	2	no	—
18	C₃²⋊C₂₇	—	3	2	no	—
19	C₃²⋊C₂₇	—	3	4	no	—
20	C₃⁴	C₃×C₉	1	1	yes	characteristic
21	C₃²×C₉	—	3	3	no	—
22	C₃²×C₉	—	3	6	no	—
23	C₃²×C₉	—	3	2	no	—
24	C₃²×C₉	—	3	1	no	—
25	C₃²×C₉	C₃×C₉	1	2	yes	—
26	C₃²×C₉	H(3,𝔽₃)	1	1	yes	characteristic
27	C₃²×C₉	H(3,𝔽₃)	1	2	yes	—
28	C₃²×C₉	3₋¹⁺²	1	2	yes	—
29	C₃²×C₉	3₋¹⁺²	1	4	yes	—
30	C₃²×C₉	C₃³	1	1	yes	characteristic
31	C₂₇⋊C₃	—	3	18	no	—
32	C₃×C₂₇	—	3	3	no	—
33	C₃×C₂₇	—	3	6	no	—
34	C₃×C₂₇	—	3	9	no	—
35	C₉⋊C₉	—	3	12	no	—
36	C₉⋊C₉	—	3	6	no	—
37	C₃²⋊C₉	—	3	2	no	—
38	C₃²⋊C₉	—	3	4	no	—
39	C₃²⋊C₉	C₃×C₉	1	3	yes	—
40	C₃²⋊C₉	C₃×C₉	1	6	yes	—
41	C₉²	—	3	6	no	—
42	C₉²	—	3	3	no	—
43	C₃³	—	3	3	no	—
44	C₃³	—	3	3	no	—
45	C₃³	—	9	2	no	—
46	C₃³	C₃²⋊C₉	1	2	yes	—
47	C₃³	C₃²⋊C₉	1	1	yes	characteristic
48	C₃³	C₃²×C₉	1	1	yes	characteristic
49	C₃×C₉	—	3	6	no	—
50	C₃×C₉	—	3	1	no	—
51	C₃×C₉	—	3	2	no	—
52	C₃×C₉	—	3	2	no	—
53	C₃×C₉	—	3	4	no	—
54	C₃×C₉	—	3	6	no	—
55	C₃×C₉	—	3	12	no	—
56	C₃×C₉	—	3	3	no	—
57	C₃×C₉	—	3	6	no	—
58	C₃×C₉	—	9	6	no	—
59	C₃×C₉	—	9	3	no	—
60	C₃×C₉	C₃²⋊C₉	1	2	yes	—
61	C₃×C₉	C₃²⋊C₉	1	4	yes	—
62	C₃×C₉	C₃×H(3,𝔽₃)	1	1	yes	characteristic
63	C₃×C₉	C₃×3₋¹⁺²	1	2	yes	—
64	C₃×C₉	#737	1	3	yes	—
65	C₃×C₉	#737	1	6	yes	—
66	C₂₇	—	9	3	no	—
67	C₂₇	—	9	6	no	—
68	C₃²	—	3	1	no	—
69	C₃²	—	3	1	no	—
70	C₃²	—	3	2	no	—
71	C₃²	—	3	2	no	—
72	C₃²	—	3	2	no	—
73	C₃²	—	3	2	no	—
74	C₃²	—	3	4	no	—
75	C₃²	—	9	9	no	—
76	C₃²	#6873	1	3	yes	—
77	C₃²	C₃×C₃²⋊C₉	1	1	yes	characteristic
78	C₃²	#6887	1	3	yes	—
79	C₉	—	3	2	no	—
80	C₉	—	3	4	no	—
81	C₉	—	9	3	no	—
82	C₉	—	9	6	no	—
83	C₉	#6893	1	1	yes	characteristic
84	C₉	#6893	1	2	yes	—
85	C₉	#6895	1	6	yes	—
86	C₃	—	3	3	no	—
87	C₃	—	3	3	no	—
88	C₃	—	9	2	no	—
89	C₃	#10624549	1	1	yes	characteristic
90	C₃	C₃×#6873	1	1	yes	characteristic
91	C₃	#10624704	1	2	yes	—

	subgroup	G/H
center	C₃×C₉	C₃×H(3,𝔽₃)
commutator	C₃³	C₃²×C₉
Frattini, cosocle	C₃²×C₉	C₃³
socle	C₃²	C₃×C₃²⋊C₉
prime radical	C₃⁴	C₃×C₉
LCS	G ▷ C₃³ ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₉ ◁ C₃³×C₉ ◁ G
LECS	G ▷ C₃²×C₉ ▷ C₃ ▷ C₁

Complements

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

N	H ≅ G/N	type
4. #10624468	C₃	semidirect

Maximal subgroups

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

subgroup	index
C₃×#6887	3
#10624683	3
C₃×C₃²⋊C₂₇	3
#10624468	3