Subgroups — 3₋¹⁺²×#11765919 #44525198

Order 30861.

148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#11765919	C₃	1	1	yes	maximal, characteristic
2	#23779867	C₃	1	3	yes	maximal, complemented
3	#23779866	C₃	1	3	yes	maximal, complemented
4	C₃²⋊#11765919	C₃	1	2	yes	maximal
5	C₉×#11765919	C₃	1	3	yes	maximal, complemented
6	3₋¹⁺²×C₁₂₇⋊C₃	C₃	1	1	yes	maximal, characteristic
7	C₃×#11765919	—	3	3	no	—
8	C₃×#11765919	C₃²	1	6	yes	—
9	C₃×#11765919	C₃²	1	1	yes	characteristic
10	C₃×#11765919	C₃²	1	1	yes	characteristic
11	C₃×#11765919	C₃²	1	1	yes	characteristic
12	C₃²×C₁₂₇⋊C₃	C₃²	1	1	yes	characteristic
13	#16812184	C₉	1	2	yes	complemented
14	#16812183	C₉	1	3	yes	complemented
15	#16812182	C₉	1	3	yes	complemented
16	C₉×C₁₂₇⋊C₃	C₃²	1	3	yes	—
17	3₋¹⁺²×C₁₂₇	C₉	1	1	yes	characteristic, complemented
18	C₃²×C₁₂₇	C₃×C₉	1	1	yes	characteristic
19	C₃×C₁₂₇⋊C₃	—	3	1	no	—
20	C₃×C₁₂₇⋊C₃	—	3	2	no	—
21	C₃×C₁₂₇⋊C₃	C₃×C₉	1	1	yes	characteristic
22	C₃×C₁₂₇⋊C₃	C₃×C₉	1	1	yes	characteristic
23	C₃×C₁₂₇⋊C₃	C₃³	1	1	yes	characteristic
24	#11765919	—	3	1	no	—
25	#11765919	—	3	1	no	—
26	#11765919	—	3	6	no	—
27	#11765919	3₋¹⁺²	1	3	yes	direct product factor
28	C₉×C₁₂₇	C₃×C₉	1	3	yes	complemented
29	#11765917	C₃×C₉	1	6	yes	complemented
30	C₃×C₁₂₇	—	3	1	no	—
31	C₃×C₁₂₇	C₃²×C₉	1	1	yes	characteristic
32	C₁₂₇⋊C₃	—	3	1	no	—
33	C₁₂₇⋊C₃	—	3	1	no	—
34	C₁₂₇⋊C₃	C₃×3₋¹⁺²	1	1	yes	characteristic
35	C₁₂₇⋊C₃	#737	1	2	yes	—
36	C₉×3₋¹⁺²	—	127	1	no	maximal, Sylow
37	C₁₂₇	C₉×3₋¹⁺²	1	1	yes	characteristic, complemented, Sylow
38	C₃×3₋¹⁺²	—	127	1	no	—
39	C₃²×C₉	—	127	1	no	—
40	C₉⋊C₉	—	127	3	no	—
41	C₉⋊C₉	—	127	3	no	—
42	C₃²⋊C₉	—	127	2	no	—
43	C₉²	—	127	3	no	—
44	C₃³	—	127	1	no	—
45	3₋¹⁺²	—	127	2	no	—
46	3₋¹⁺²	—	127	3	no	—
47	3₋¹⁺²	—	127	3	no	—
48	3₋¹⁺²	#11765919	1	1	yes	characteristic, direct product factor
49	C₃×C₉	—	381	3	no	—
50	C₃×C₉	—	127	6	no	—
51	C₃×C₉	—	127	1	no	—
52	C₃×C₉	—	127	1	no	—
53	C₃×C₉	—	127	1	no	—
54	C₃×C₉	—	127	3	no	—
55	C₃²	—	381	1	no	—
56	C₃²	—	381	2	no	—
57	C₃²	—	127	1	no	—
58	C₃²	—	127	1	no	—
59	C₃²	—	127	1	no	—
60	C₃²	C₃×#11765919	1	1	yes	characteristic
61	C₉	—	381	1	no	—
62	C₉	—	381	1	no	—
63	C₉	—	381	6	no	—
64	C₉	—	127	3	no	—
65	C₉	—	127	6	no	—
66	C₉	C₃×#11765919	1	3	yes	complemented
67	C₃	—	3	1	no	—
68	C₃	—	381	1	no	—
69	C₃	—	381	1	no	—
70	C₃	—	127	2	no	—
71	C₃	—	127	1	no	—
72	C₃	C₃²×#11765919	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₃	C₃²×#11765919
commutator, socle	C₃×C₁₂₇	C₃²×C₉
Fitting	3₋¹⁺²×C₁₂₇	C₉
prime radical	C₃²×C₁₂₇⋊C₃	C₃²
cosocle	C₃×C₁₂₇⋊C₃	C₃³
hypercenter	3₋¹⁺²	#11765919
hypocenter	C₁₂₇	C₉×3₋¹⁺²
LCS	G ▷ C₃×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₃ ◁ 3₋¹⁺²

Complements

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

N	H ≅ G/N	type
2. #23779867	C₃	semidirect
3. #23779866	C₃	semidirect
5. C₉×#11765919	C₃	semidirect
13. #16812184	C₉	semidirect
14. #16812183	C₉	semidirect
15. #16812182	C₉	semidirect
17. 3₋¹⁺²×C₁₂₇	C₉	semidirect
27. #11765919	3₋¹⁺²	direct (N × H)
28. C₉×C₁₂₇	C₃×C₉	semidirect
29. #11765917	C₃×C₉	semidirect
37. C₁₂₇	C₉×3₋¹⁺²	semidirect
48. 3₋¹⁺²	#11765919	direct (N × H)
66. C₉	C₃×#11765919	semidirect

Maximal subgroups

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

subgroup	index
C₃²×#11765919	3
#23779867	3
#23779866	3
C₃²⋊#11765919	3
C₉×#11765919	3
3₋¹⁺²×C₁₂₇⋊C₃	3
C₉×3₋¹⁺²	127

Subgroups — 3−1+2×#11765919 #44525198

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — 3₋¹⁺²×#11765919 #44525198