Subgroups — #44525010

Order 30861.

138 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×C₁₂₇⋊C₃	C₃	1	1	yes	maximal, characteristic
2	#23779833	C₃	1	6	yes	maximal, complemented
3	#23779831	C₃	1	3	yes	maximal
4	C₉×#11765917	C₃	1	2	yes	maximal, complemented
5	C₉²×C₁₂₇	C₃	1	1	yes	maximal, characteristic, complemented
6	C₃²×C₁₂₇⋊C₃	C₃²	1	1	yes	characteristic
7	C₃×#11765917	C₃²	1	6	yes	—
8	C₃×#11765917	C₃²	1	2	yes	—
9	C₉×C₁₂₇⋊C₃	C₉	1	9	yes	complemented
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	3	no	—
14	C₃×C₁₂₇⋊C₃	C₃×C₉	1	3	yes	—
15	C₉×C₁₂₇	—	3	3	no	—
16	C₉×C₁₂₇	C₃×C₉	1	3	yes	—
17	#11765917	—	3	6	no	—
18	#11765917	C₃×C₉	1	6	yes	—
19	C₃×C₁₂₇	C₃²×C₉	1	1	yes	characteristic
20	C₃×C₁₂₇	#737	1	3	yes	—
21	C₁₂₇⋊C₃	—	3	3	no	—
22	#6887	—	127	1	no	maximal, Sylow
23	C₁₂₇	#6887	1	1	yes	characteristic, complemented, Sylow
24	C₃²×C₉	—	127	1	no	—
25	C₉⋊C₉	—	127	6	no	—
26	C₃²⋊C₉	—	127	3	no	—
27	C₉²	—	127	2	no	—
28	C₉²	C₁₂₇⋊C₃	1	1	yes	characteristic, complemented
29	C₃³	—	127	1	no	—
30	C₃×C₉	—	127	6	no	—
31	C₃×C₉	—	127	2	no	—
32	C₃×C₉	—	127	9	no	—
33	C₃×C₉	C₃×C₁₂₇⋊C₃	1	3	yes	—
34	C₃×C₉	C₃×C₁₂₇⋊C₃	1	1	yes	characteristic
35	C₃²	—	381	3	no	—
36	C₃²	—	127	3	no	—
37	C₃²	C₃²×C₁₂₇⋊C₃	1	1	yes	characteristic
38	C₉	—	3	3	no	—
39	C₉	—	381	6	no	—
40	C₉	—	127	6	no	—
41	C₉	C₉×C₁₂₇⋊C₃	1	3	yes	—
42	C₃	—	381	3	no	—
43	C₃	C₃×C₉×C₁₂₇⋊C₃	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	C₉²×C₁₂₇	C₃
socle, cosocle	C₃²×C₁₂₇	C₃³
prime radical	C₃²×C₁₂₇⋊C₃	C₃²
hypercenter	C₉²	C₁₂₇⋊C₃
hypocenter	C₁₂₇	#6887
LCS	G ▷ C₃×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₃×C₉ ◁ C₉²

Complements

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

N	H ≅ G/N	type
2. #23779833	C₃	semidirect
4. C₉×#11765917	C₃	semidirect
5. C₉²×C₁₂₇	C₃	semidirect
9. C₉×C₁₂₇⋊C₃	C₉	semidirect
23. C₁₂₇	#6887	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×C₉×C₁₂₇⋊C₃	3
#23779833	3
#23779831	3
C₉×#11765917	3
C₉²×C₁₂₇	3
#6887	127