Subgroups — #44525012

Order 30861.

138 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23779835	C₃	1	3	yes	maximal, complemented
2	#23779834	C₃	1	3	yes	maximal, complemented
3	C₃²⋊#11765917	C₃	1	3	yes	maximal
4	C₉×#11765917	C₃	1	3	yes	maximal, complemented
5	C₃²×C₉×C₁₂₇	C₃	1	1	yes	maximal, characteristic
6	C₃×#11765917	C₃²	1	9	yes	—
7	C₃³×C₁₂₇	C₃²	1	1	yes	characteristic
8	C₃×C₉×C₁₂₇	C₉	1	9	yes	complemented
9	C₃×C₉×C₁₂₇	C₃²	1	1	yes	characteristic
10	C₃×C₉×C₁₂₇	C₃²	1	1	yes	characteristic
11	C₃×C₉×C₁₂₇	C₃²	1	1	yes	characteristic
12	C₃²×C₁₂₇	—	3	3	no	—
13	C₃²×C₁₂₇	C₃×C₉	1	3	yes	—
14	C₃²×C₁₂₇	C₃³	1	1	yes	characteristic
15	C₉×C₁₂₇	C₃×C₉	1	3	yes	—
16	C₉×C₁₂₇	C₃×C₉	1	3	yes	—
17	C₉×C₁₂₇	C₃×C₉	1	3	yes	—
18	#11765917	—	3	9	no	—
19	C₃×C₁₂₇	—	3	3	no	—
20	C₃×C₁₂₇	C₃²×C₉	1	1	yes	characteristic
21	C₃×C₁₂₇	#737	1	3	yes	—
22	#6887	—	127	1	no	maximal, Sylow
23	C₁₂₇	#6887	1	1	yes	characteristic, complemented, Sylow
24	C₃²×C₉	C₁₂₇⋊C₃	1	1	yes	characteristic
25	C₉⋊C₉	—	127	3	no	—
26	C₉⋊C₉	—	127	3	no	—
27	C₃²⋊C₉	—	127	3	no	—
28	C₉²	—	127	3	no	—
29	C₃³	C₃×C₁₂₇⋊C₃	1	1	yes	characteristic
30	C₃×C₉	—	127	9	no	—
31	C₃×C₉	#11765917	1	9	yes	complemented
32	C₃×C₉	C₃×C₁₂₇⋊C₃	1	1	yes	characteristic
33	C₃×C₉	C₃×C₁₂₇⋊C₃	1	1	yes	characteristic
34	C₃×C₉	C₃×C₁₂₇⋊C₃	1	1	yes	characteristic
35	C₃²	—	3	3	no	—
36	C₃²	C₃×#11765917	1	3	yes	—
37	C₃²	C₃²×C₁₂₇⋊C₃	1	1	yes	characteristic
38	C₉	—	381	9	no	—
39	C₉	C₃×#11765917	1	3	yes	—
40	C₉	C₃×#11765917	1	3	yes	—
41	C₉	C₃×#11765917	1	3	yes	—
42	C₃	—	3	3	no	—
43	C₃	C₃²×#11765917	1	1	yes	characteristic
44	C₃	#23779860	1	3	yes	—

	subgroup	G/H
center	C₃×C₉	C₃×C₁₂₇⋊C₃
commutator	C₃×C₁₂₇	C₃²×C₉
Frattini	C₃²	C₃²×C₁₂₇⋊C₃
Fitting	C₃²×C₉×C₁₂₇	C₃
socle, cosocle	C₃²×C₁₂₇	C₃³
prime radical	C₃³×C₁₂₇	C₃²
hypercenter	C₃²×C₉	C₁₂₇⋊C₃
hypocenter	C₁₂₇	#6887
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. #23779835	C₃	semidirect
2. #23779834	C₃	semidirect
4. C₉×#11765917	C₃	semidirect
8. C₃×C₉×C₁₂₇	C₉	semidirect
23. C₁₂₇	#6887	semidirect
31. C₃×C₉	#11765917	semidirect

Maximal subgroups

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

subgroup	index
#23779835	3
#23779834	3
C₃²⋊#11765917	3
C₉×#11765917	3
C₃²×C₉×C₁₂₇	3
#6887	127