Subgroups — C₃×C₉×#11765919 #44525192

Order 30861.

252 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#11765919	C₃	1	3	yes	maximal
2	C₉×#11765919	C₃	1	9	yes	maximal, direct product factor
3	C₃×C₉×C₁₂₇⋊C₃	C₃	1	1	yes	maximal, characteristic
4	C₃×#11765919	C₉	1	27	yes	direct product factor
5	C₃×#11765919	C₃²	1	9	yes	—
6	C₃²×C₁₂₇⋊C₃	C₃²	1	1	yes	characteristic
7	C₃×#11765917	C₉	1	2	yes	complemented
8	C₉×C₁₂₇⋊C₃	C₉	1	6	yes	complemented
9	C₉×C₁₂₇⋊C₃	C₃²	1	3	yes	—
10	C₃×C₉×C₁₂₇	C₉	1	1	yes	characteristic, complemented
11	C₃²×C₁₂₇	C₃×C₉	1	1	yes	characteristic
12	C₃×C₁₂₇⋊C₃	C₃×C₉	1	2	yes	—
13	C₃×C₁₂₇⋊C₃	C₃×C₉	1	9	yes	—
14	C₃×C₁₂₇⋊C₃	C₃³	1	1	yes	characteristic
15	#11765919	C₃×C₉	1	27	yes	direct product factor
16	C₉×C₁₂₇	C₃×C₉	1	3	yes	complemented
17	#11765917	C₃×C₉	1	6	yes	complemented
18	C₃×C₁₂₇	C₉²	1	3	yes	complemented
19	C₃×C₁₂₇	C₃²×C₉	1	1	yes	characteristic
20	C₁₂₇⋊C₃	C₉²	1	6	yes	complemented
21	C₁₂₇⋊C₃	C₃²×C₉	1	3	yes	—
22	C₃×C₉²	—	127	1	no	maximal, Sylow
23	C₁₂₇	C₃×C₉²	1	1	yes	characteristic, complemented, Sylow
24	C₃²×C₉	—	127	3	no	—
25	C₃²×C₉	—	127	1	no	—
26	C₉²	—	127	9	no	—
27	C₃³	—	127	1	no	—
28	C₃×C₉	—	127	27	no	—
29	C₃×C₉	—	127	9	no	—
30	C₃×C₉	—	127	2	no	—
31	C₃×C₉	—	127	6	no	—
32	C₃×C₉	—	127	3	no	—
33	C₃×C₉	#11765919	1	1	yes	characteristic, direct product factor
34	C₃²	—	127	9	no	—
35	C₃²	—	127	1	no	—
36	C₃²	—	127	2	no	—
37	C₃²	C₃×#11765919	1	1	yes	characteristic
38	C₉	—	127	27	no	—
39	C₉	—	127	6	no	—
40	C₉	C₃×#11765919	1	3	yes	direct product factor
41	C₃	—	127	3	no	—
42	C₃	—	127	6	no	—
43	C₃	C₉×#11765919	1	3	yes	direct product factor
44	C₃	C₃²×#11765919	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃×C₉	#11765919
commutator, hypocenter	C₁₂₇	C₃×C₉²
Frattini	C₃	C₃²×#11765919
Fitting	C₃×C₉×C₁₂₇	C₉
socle	C₃²×C₁₂₇	C₃×C₉
prime radical	C₃²×C₁₂₇⋊C₃	C₃²
cosocle	C₃×C₁₂₇⋊C₃	C₃³
LCS	G ▷ C₁₂₇
UCS	C₁ ◁ C₃×C₉

Complements

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

N	H ≅ G/N	type
2. C₉×#11765919	C₃	direct (N × H)
4. C₃×#11765919	C₉	direct (N × H)
7. C₃×#11765917	C₉	semidirect
8. C₉×C₁₂₇⋊C₃	C₉	semidirect
10. C₃×C₉×C₁₂₇	C₉	semidirect
15. #11765919	C₃×C₉	direct (N × H)
16. C₉×C₁₂₇	C₃×C₉	semidirect
17. #11765917	C₃×C₉	semidirect
18. C₃×C₁₂₇	C₉²	semidirect
20. C₁₂₇⋊C₃	C₉²	semidirect
23. C₁₂₇	C₃×C₉²	semidirect
33. C₃×C₉	#11765919	direct (N × H)
40. C₉	C₃×#11765919	direct (N × H)
43. C₃	C₉×#11765919	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×#11765919	3
C₉×#11765919	3
C₃×C₉×C₁₂₇⋊C₃	3
C₃×C₉²	127

Subgroups — C3×C9×#11765919 #44525192

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₉×#11765919 #44525192