Subgroups — #36380953

Order 22599.

290 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#14578892	C₃	1	2	yes	maximal
2	#21419296	C₃	1	1	yes	maximal, characteristic
3	#21419221	C₃	1	3	yes	maximal, complemented
4	#21419220	C₃	1	3	yes	maximal, complemented
5	C₂₇×C₃₁⋊C₉	C₃	1	3	yes	maximal, complemented
6	C₃²×C₂₇×C₃₁	C₃	1	1	yes	maximal, characteristic
7	#14578892	C₉	1	18	yes	complemented
8	C₃×C₃₁⋊C₂₇	C₃²	1	6	yes	—
9	#14578887	C₉	1	3	yes	—
10	#14578886	C₉	1	3	yes	—
11	C₃²⋊(C₃₁⋊C₉)	C₉	1	3	yes	—
12	C₉×C₃₁⋊C₉	C₃²	1	3	yes	—
13	C₃²×C₉×C₃₁	C₃²	1	1	yes	characteristic
14	C₃×C₂₇×C₃₁	C₉	1	9	yes	complemented
15	C₃×C₂₇×C₃₁	C₃²	1	1	yes	characteristic
16	C₃×C₂₇×C₃₁	C₃²	1	1	yes	characteristic
17	C₃×C₂₇×C₃₁	C₃²	1	1	yes	characteristic
18	C₃³×C₃₁	C₃×C₉	1	1	yes	characteristic
19	C₃×C₉×C₃₁	C₃×C₉	1	1	yes	characteristic
20	C₃×C₉×C₃₁	C₃×C₉	1	1	yes	characteristic
21	C₃×C₉×C₃₁	C₃×C₉	1	6	yes	—
22	C₃×C₉×C₃₁	C₃×C₉	1	3	yes	—
23	C₃×C₉×C₃₁	C₃³	1	1	yes	characteristic
24	C₃×C₃₁⋊C₉	C₃×C₉	1	9	yes	—
25	C₂₇×C₃₁	C₃×C₉	1	3	yes	—
26	C₂₇×C₃₁	C₃×C₉	1	3	yes	—
27	C₂₇×C₃₁	C₃×C₉	1	3	yes	—
28	C₃₁⋊C₂₇	C₃×C₉	1	18	yes	—
29	#10624681	—	31	1	no	maximal, Sylow
30	C₃²×C₃₁	—	3	3	no	—
31	C₃²×C₃₁	C₉²	1	3	yes	—
32	C₃²×C₃₁	C₃²×C₉	1	1	yes	characteristic
33	C₉×C₃₁	C₉²	1	3	yes	—
34	C₉×C₃₁	C₉²	1	3	yes	—
35	C₉×C₃₁	C₃²×C₉	1	2	yes	—
36	C₉×C₃₁	C₃²×C₉	1	1	yes	characteristic
37	C₃₁⋊C₉	—	3	9	no	—
38	C₃×C₂₇⋊C₃	—	31	2	no	—
39	C₃²×C₂₇	C₃₁⋊C₃	1	1	yes	characteristic
40	#6887	—	31	1	no	—
41	#6864	—	31	3	no	—
42	#6864	—	31	3	no	—
43	C₉×C₂₇	—	31	3	no	—
44	C₃×C₃₁	—	3	3	no	—
45	C₃×C₃₁	C₃×C₉²	1	1	yes	characteristic
46	C₃×C₃₁	#6903	1	3	yes	—
47	C₃²×C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
48	C₂₇⋊C₃	—	31	18	no	—
49	C₃×C₂₇	—	31	6	no	—
50	C₃×C₂₇	C₃₁⋊C₉	1	9	yes	complemented
51	C₃×C₂₇	C₃×C₃₁⋊C₃	1	1	yes	characteristic
52	C₃×C₂₇	C₃×C₃₁⋊C₃	1	1	yes	characteristic
53	C₃×C₂₇	C₃×C₃₁⋊C₃	1	1	yes	characteristic
54	C₉⋊C₉	—	31	3	no	—
55	C₉⋊C₉	—	31	3	no	—
56	C₃²⋊C₉	—	31	3	no	—
57	C₉²	—	31	3	no	—
58	C₃₁	#10624681	1	1	yes	characteristic, complemented, Sylow
59	C₃³	C₉×C₃₁⋊C₃	1	1	yes	characteristic
60	C₃×C₉	—	31	9	no	—
61	C₃×C₉	C₉×C₃₁⋊C₃	1	1	yes	characteristic
62	C₃×C₉	C₉×C₃₁⋊C₃	1	1	yes	characteristic
63	C₃×C₉	C₉×C₃₁⋊C₃	1	6	yes	—
64	C₃×C₉	C₃×C₃₁⋊C₉	1	3	yes	—
65	C₃×C₉	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
66	C₂₇	—	31	18	no	—
67	C₂₇	C₃×C₃₁⋊C₉	1	3	yes	—
68	C₂₇	C₃×C₃₁⋊C₉	1	3	yes	—
69	C₂₇	C₃×C₃₁⋊C₉	1	3	yes	—
70	C₃²	—	3	3	no	—
71	C₃²	C₉×C₃₁⋊C₉	1	3	yes	—
72	C₃²	C₃×C₉×C₃₁⋊C₃	1	1	yes	characteristic
73	C₉	—	93	9	no	—
74	C₉	C₉×C₃₁⋊C₉	1	3	yes	—
75	C₉	C₉×C₃₁⋊C₉	1	3	yes	—
76	C₉	C₃×C₉×C₃₁⋊C₃	1	2	yes	—
77	C₉	C₃²×C₃₁⋊C₉	1	1	yes	characteristic
78	C₃	—	3	3	no	—
79	C₃	C₃×C₉×C₃₁⋊C₉	1	1	yes	characteristic
80	C₃	#21419370	1	3	yes	—

	subgroup	G/H
center	C₃×C₂₇	C₃×C₃₁⋊C₃
commutator	C₃×C₃₁	C₃×C₉²
Frattini	C₃×C₉	C₃²×C₃₁⋊C₃
Fitting	C₃²×C₂₇×C₃₁	C₃
socle	C₃²×C₃₁	C₃²×C₉
prime radical	C₃³×C₃₁	C₃×C₉
cosocle	C₃×C₉×C₃₁	C₃³
hypercenter	C₃²×C₂₇	C₃₁⋊C₃
hypocenter	C₃₁	#10624681
LCS	G ▷ C₃×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₃×C₂₇ ◁ C₃²×C₂₇

Complements

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

N	H ≅ G/N	type
3. #21419221	C₃	semidirect
4. #21419220	C₃	semidirect
5. C₂₇×C₃₁⋊C₉	C₃	semidirect
7. #14578892	C₉	semidirect
14. C₃×C₂₇×C₃₁	C₉	semidirect
50. C₃×C₂₇	C₃₁⋊C₉	semidirect
58. C₃₁	#10624681	semidirect

Maximal subgroups

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

subgroup	index
C₃×#14578892	3
#21419296	3
#21419221	3
#21419220	3
C₂₇×C₃₁⋊C₉	3
C₃²×C₂₇×C₃₁	3
#10624681	31