Subgroups — C₃×#23779840 #44525085

Order 30861.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23779840	C₃	1	9	yes	maximal, direct product factor
2	C₃×#16812178	C₃	1	3	yes	maximal, complemented
3	C₃²×C₉×C₁₂₇	C₃	1	1	yes	maximal, characteristic
4	#16812178	C₃²	1	9	yes	complemented
5	C₃³×C₁₂₇	C₉	1	1	yes	characteristic
6	C₃×C₉×C₁₂₇	C₉	1	6	yes	—
7	C₃×C₉×C₁₂₇	C₉	1	2	yes	—
8	C₃×C₉×C₁₂₇	C₃²	1	3	yes	—
9	C₃×C₉×C₁₂₇	C₃²	1	1	yes	characteristic
10	C₃²×C₁₂₇	—	3	3	no	—
11	C₃²×C₁₂₇	C₃×C₉	1	3	yes	—
12	C₃²×C₁₂₇	C₃×C₉	1	1	yes	characteristic
13	C₉×C₁₂₇	C₃×C₉	1	6	yes	—
14	C₉×C₁₂₇	C₃×C₉	1	2	yes	—
15	C₉×C₁₂₇	C₃³	1	1	yes	characteristic
16	C₃×C₁₂₇	—	3	3	no	—
17	C₃×C₁₂₇	C₂₇⋊C₃	1	3	yes	complemented
18	C₃×C₁₂₇	C₃²×C₉	1	1	yes	characteristic
19	C₃×C₂₇⋊C₃	—	127	1	no	maximal, Sylow
20	C₁₂₇	C₃×C₂₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
21	C₃²×C₉	C₁₂₇⋊C₃	1	1	yes	characteristic
22	C₂₇⋊C₃	—	127	9	no	—
23	C₃×C₂₇	—	127	3	no	—
24	C₃³	#11765917	1	1	yes	characteristic
25	C₃×C₉	#11765917	1	2	yes	—
26	C₃×C₉	#11765917	1	6	yes	—
27	C₃×C₉	C₃×C₁₂₇⋊C₃	1	3	yes	—
28	C₃×C₉	C₃×C₁₂₇⋊C₃	1	1	yes	characteristic
29	C₂₇	—	127	9	no	—
30	C₃²	—	3	3	no	—
31	C₃²	C₃×#11765917	1	3	yes	—
32	C₃²	C₃×#11765917	1	1	yes	characteristic
33	C₉	C₃×#11765917	1	6	yes	—
34	C₉	C₃×#11765917	1	2	yes	—
35	C₉	C₃²×C₁₂₇⋊C₃	1	1	yes	characteristic
36	C₃	—	3	3	no	—
37	C₃	#23779840	1	3	yes	direct product factor
38	C₃	C₃²×#11765917	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₉	C₃×C₁₂₇⋊C₃
commutator	C₃×C₁₂₇	C₃²×C₉
Frattini	C₉	C₃²×C₁₂₇⋊C₃
Fitting	C₃²×C₉×C₁₂₇	C₃
socle	C₃²×C₁₂₇	C₃×C₉
prime radical	C₃³×C₁₂₇	C₉
cosocle	C₉×C₁₂₇	C₃³
hypercenter	C₃²×C₉	C₁₂₇⋊C₃
hypocenter	C₁₂₇	C₃×C₂₇⋊C₃
LCS	G ▷ C₃×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₃×C₉ ◁ C₃²×C₉

Complements

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

N	H ≅ G/N	type
1. #23779840	C₃	direct (N × H)
2. C₃×#16812178	C₃	semidirect
4. #16812178	C₃²	semidirect
17. C₃×C₁₂₇	C₂₇⋊C₃	semidirect
20. C₁₂₇	C₃×C₂₇⋊C₃	semidirect
37. C₃	#23779840	direct (N × H)

Maximal subgroups

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

subgroup	index
#23779840	3
C₃×#16812178	3
C₃²×C₉×C₁₂₇	3
C₃×C₂₇⋊C₃	127

Subgroups — C3×#23779840 #44525085

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#23779840 #44525085