Subgroups — C₃²×#16812183 #44525144

Order 30861.

576 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₁₂₇⋊C₃	C₃	1	1	yes	maximal, characteristic
2	C₃×#16812183	C₃	1	36	yes	maximal, direct product factor
3	C₃²×#11765917	C₃	1	2	yes	maximal, complemented
4	C₃²×C₉×C₁₂₇	C₃	1	1	yes	maximal, characteristic, complemented
5	C₃²×C₁₂₇⋊C₃	—	3	9	no	—
6	C₃²×C₁₂₇⋊C₃	C₃²	1	12	yes	—
7	#16812183	C₃²	1	81	yes	direct product factor
8	C₃×#11765917	C₃²	1	24	yes	complemented
9	C₃³×C₁₂₇	C₃²	1	1	yes	characteristic
10	C₃×C₉×C₁₂₇	C₃²	1	12	yes	complemented
11	C₃²×C₁₂₇	3₋¹⁺²	1	9	yes	complemented
12	C₃²×C₁₂₇	C₃³	1	4	yes	—
13	C₃×C₁₂₇⋊C₃	—	3	36	no	—
14	C₃×C₁₂₇⋊C₃	C₃³	1	9	yes	—
15	C₉×C₁₂₇	C₃³	1	9	yes	complemented
16	#11765917	C₃³	1	18	yes	complemented
17	C₃×C₁₂₇	C₃×3₋¹⁺²	1	12	yes	complemented
18	C₃×C₁₂₇	C₃⁴	1	1	yes	characteristic
19	C₁₂₇⋊C₃	—	3	9	no	—
20	C₃²×3₋¹⁺²	—	127	1	no	maximal, Sylow
21	C₁₂₇	C₃²×3₋¹⁺²	1	1	yes	characteristic, complemented, Sylow
22	C₃⁴	—	127	1	no	—
23	C₃×3₋¹⁺²	—	127	36	no	—
24	C₃²×C₉	—	127	2	no	—
25	C₃²×C₉	C₁₂₇⋊C₃	1	1	yes	characteristic, complemented
26	C₃³	—	381	9	no	—
27	C₃³	—	127	12	no	—
28	C₃³	C₃×C₁₂₇⋊C₃	1	1	yes	characteristic
29	3₋¹⁺²	—	127	81	no	—
30	C₃×C₉	—	127	24	no	—
31	C₃×C₉	C₃×C₁₂₇⋊C₃	1	12	yes	complemented
32	C₃²	—	381	36	no	—
33	C₃²	—	127	9	no	—
34	C₃²	#16812183	1	9	yes	direct product factor
35	C₃²	C₃²×C₁₂₇⋊C₃	1	4	yes	—
36	C₉	—	127	18	no	—
37	C₉	C₃²×C₁₂₇⋊C₃	1	9	yes	complemented
38	C₃	—	381	9	no	—
39	C₃	C₃×#16812183	1	12	yes	direct product factor
40	C₃	C₃³×C₁₂₇⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₃³	C₃×C₁₂₇⋊C₃
commutator, cosocle	C₃×C₁₂₇	C₃⁴
Frattini	C₃	C₃³×C₁₂₇⋊C₃
Fitting	C₃²×C₉×C₁₂₇	C₃
socle	C₃³×C₁₂₇	C₃²
prime radical	C₃³×C₁₂₇⋊C₃	C₃
hypercenter	C₃²×C₉	C₁₂₇⋊C₃
hypocenter	C₁₂₇	C₃²×3₋¹⁺²
LCS	G ▷ C₃×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₃³ ◁ C₃²×C₉

Complements

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

N	H ≅ G/N	type
2. C₃×#16812183	C₃	direct (N × H)
3. C₃²×#11765917	C₃	semidirect
4. C₃²×C₉×C₁₂₇	C₃	semidirect
7. #16812183	C₃²	direct (N × H)
8. C₃×#11765917	C₃²	semidirect
10. C₃×C₉×C₁₂₇	C₃²	semidirect
11. C₃²×C₁₂₇	3₋¹⁺²	semidirect
15. C₉×C₁₂₇	C₃³	semidirect
16. #11765917	C₃³	semidirect
17. C₃×C₁₂₇	C₃×3₋¹⁺²	semidirect
21. C₁₂₇	C₃²×3₋¹⁺²	semidirect
25. C₃²×C₉	C₁₂₇⋊C₃	semidirect
31. C₃×C₉	C₃×C₁₂₇⋊C₃	semidirect
34. C₃²	#16812183	direct (N × H)
37. C₉	C₃²×C₁₂₇⋊C₃	semidirect
39. C₃	C₃×#16812183	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃³×C₁₂₇⋊C₃	3
C₃×#16812183	3
C₃²×#11765917	3
C₃²×C₉×C₁₂₇	3
C₃²×3₋¹⁺²	127

Subgroups — C32×#16812183 #44525144

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#16812183 #44525144