Subgroups — #44525070

Order 30861.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#16812183	C₃	1	1	yes	maximal, characteristic
2	#23779834	C₃	1	2	yes	maximal, complemented
3	#23779833	C₃	1	6	yes	maximal, complemented
4	#23779831	C₃	1	3	yes	maximal
5	C₉²×C₁₂₇	C₃	1	1	yes	maximal, characteristic, complemented
6	C₃²×C₁₂₇⋊C₃	C₃²	1	1	yes	characteristic
7	#16812183	—	3	3	no	—
8	C₃×#11765917	C₃²	1	2	yes	—
9	C₃×#11765917	C₃²	1	6	yes	—
10	C₃×C₉×C₁₂₇	C₃²	1	3	yes	—
11	C₃×C₉×C₁₂₇	C₃²	1	1	yes	characteristic
12	C₃²×C₁₂₇	C₃³	1	1	yes	characteristic
13	C₃×C₁₂₇⋊C₃	—	3	1	no	—
14	C₃×C₁₂₇⋊C₃	—	3	3	no	—
15	C₉×C₁₂₇	—	3	3	no	—
16	C₉×C₁₂₇	3₋¹⁺²	1	3	yes	—
17	#11765917	—	3	2	no	—
18	#11765917	—	3	6	no	—
19	C₃×C₁₂₇	C₃×3₋¹⁺²	1	1	yes	characteristic
20	C₃×C₁₂₇	#737	1	3	yes	—
21	C₁₂₇⋊C₃	—	9	1	no	—
22	#6899	—	127	1	no	maximal, Sylow
23	C₁₂₇	#6899	1	1	yes	characteristic, complemented, Sylow
24	C₃×3₋¹⁺²	—	127	1	no	—
25	C₉⋊C₉	—	127	6	no	—
26	C₉⋊C₉	—	127	2	no	—
27	C₃²⋊C₉	—	127	3	no	—
28	C₉²	C₁₂₇⋊C₃	1	1	yes	characteristic, complemented
29	C₃³	—	127	1	no	—
30	3₋¹⁺²	—	381	3	no	—
31	C₃×C₉	—	127	6	no	—
32	C₃×C₉	—	127	2	no	—
33	C₃×C₉	C₃×C₁₂₇⋊C₃	1	3	yes	—
34	C₃×C₉	C₃×C₁₂₇⋊C₃	1	1	yes	characteristic
35	C₃²	—	381	1	no	—
36	C₃²	—	381	3	no	—
37	C₃²	C₃²×C₁₂₇⋊C₃	1	1	yes	characteristic
38	C₉	—	3	3	no	—
39	C₉	—	381	2	no	—
40	C₉	—	381	6	no	—
41	C₉	#16812183	1	3	yes	—
42	C₃	—	1143	1	no	—
43	C₃	C₃×#16812183	1	1	yes	characteristic
44	C₃	#23779860	1	3	yes	—

	subgroup	G/H
center, Frattini	C₃²	C₃²×C₁₂₇⋊C₃
commutator, socle, cosocle	C₃²×C₁₂₇	C₃³
Fitting	C₉²×C₁₂₇	C₃
prime radical	C₃²×C₁₂₇⋊C₃	C₃²
hypercenter	C₉²	C₁₂₇⋊C₃
hypocenter	C₁₂₇	#6899
LCS	G ▷ C₃²×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₃² ◁ C₉²

Complements

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

N	H ≅ G/N	type
2. #23779834	C₃	semidirect
3. #23779833	C₃	semidirect
5. C₉²×C₁₂₇	C₃	semidirect
23. C₁₂₇	#6899	semidirect
28. C₉²	C₁₂₇⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₃×#16812183	3
#23779834	3
#23779833	3
#23779831	3
C₉²×C₁₂₇	3
#6899	127