Subgroups — #44525196

Order 30861.

138 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23779867	C₃	1	3	yes	maximal, complemented
2	#23779866	C₃	1	3	yes	maximal, complemented
3	C₃²⋊#11765919	C₃	1	3	yes	maximal
4	C₉×#11765919	C₃	1	3	yes	maximal, complemented
5	C₃×C₉×C₁₂₇⋊C₃	C₃	1	1	yes	maximal, characteristic
6	C₃×#11765919	C₃²	1	9	yes	—
7	C₃²×C₁₂₇⋊C₃	C₃²	1	1	yes	characteristic
8	C₃×#11765917	C₉	1	2	yes	complemented
9	C₉×C₁₂₇⋊C₃	C₉	1	2	yes	complemented
10	C₉×C₁₂₇⋊C₃	C₉	1	2	yes	complemented
11	C₉×C₁₂₇⋊C₃	C₉	1	2	yes	complemented
12	C₉×C₁₂₇⋊C₃	C₃²	1	1	yes	characteristic
13	C₉×C₁₂₇⋊C₃	C₃²	1	1	yes	characteristic
14	C₉×C₁₂₇⋊C₃	C₃²	1	1	yes	characteristic
15	C₃×C₉×C₁₂₇	C₉	1	1	yes	characteristic, complemented
16	C₃²×C₁₂₇	C₃×C₉	1	1	yes	characteristic
17	C₃×C₁₂₇⋊C₃	—	3	3	no	—
18	C₃×C₁₂₇⋊C₃	C₃×C₉	1	2	yes	—
19	C₃×C₁₂₇⋊C₃	C₃³	1	1	yes	characteristic
20	#11765919	—	3	9	no	—
21	C₉×C₁₂₇	C₃×C₉	1	1	yes	characteristic
22	C₉×C₁₂₇	C₃×C₉	1	1	yes	characteristic
23	C₉×C₁₂₇	C₃×C₉	1	1	yes	characteristic
24	#11765917	C₃×C₉	1	2	yes	—
25	#11765917	C₃×C₉	1	2	yes	—
26	#11765917	C₃×C₉	1	2	yes	—
27	C₃×C₁₂₇	—	3	1	no	—
28	C₃×C₁₂₇	C₃²×C₉	1	1	yes	characteristic
29	C₁₂₇⋊C₃	—	3	2	no	—
30	C₁₂₇⋊C₃	#737	1	3	yes	—
31	#6887	—	127	1	no	maximal, Sylow
32	C₁₂₇	#6887	1	1	yes	characteristic, complemented, Sylow
33	C₃²×C₉	—	127	1	no	—
34	C₉⋊C₉	—	127	3	no	—
35	C₉⋊C₉	—	127	3	no	—
36	C₃²⋊C₉	—	127	3	no	—
37	C₉²	—	127	3	no	—
38	C₃³	—	127	1	no	—
39	C₃×C₉	—	127	9	no	—
40	C₃×C₉	—	127	2	no	—
41	C₃×C₉	—	127	2	no	—
42	C₃×C₉	—	127	2	no	—
43	C₃×C₉	—	127	1	no	—
44	C₃×C₉	—	127	1	no	—
45	C₃×C₉	—	127	2	no	—
46	C₃×C₉	—	127	1	no	—
47	C₃×C₉	#11765919	1	1	yes	characteristic, complemented
48	C₃²	—	381	3	no	—
49	C₃²	—	127	2	no	—
50	C₃²	—	127	1	no	—
51	C₃²	C₃×#11765919	1	1	yes	characteristic
52	C₉	—	381	9	no	—
53	C₉	—	127	2	no	—
54	C₉	—	127	2	no	—
55	C₉	—	127	2	no	—
56	C₉	C₃×#11765919	1	1	yes	characteristic
57	C₉	C₃×#11765919	1	1	yes	characteristic
58	C₉	C₃×#11765919	1	1	yes	characteristic
59	C₃	—	3	1	no	—
60	C₃	—	381	2	no	—
61	C₃	—	127	3	no	—
62	C₃	C₃²×#11765919	1	1	yes	characteristic

	subgroup	G/H
center	C₉	C₃×#11765919
commutator, socle	C₃×C₁₂₇	C₃²×C₉
Frattini	C₃	C₃²×#11765919
Fitting	C₃×C₉×C₁₂₇	C₉
prime radical	C₃²×C₁₂₇⋊C₃	C₃²
cosocle	C₃×C₁₂₇⋊C₃	C₃³
hypercenter	C₃×C₉	#11765919
hypocenter	C₁₂₇	#6887
LCS	G ▷ C₃×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₉ ◁ C₃×C₉

Complements

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

N	H ≅ G/N	type
1. #23779867	C₃	semidirect
2. #23779866	C₃	semidirect
4. C₉×#11765919	C₃	semidirect
8. C₃×#11765917	C₉	semidirect
9. C₉×C₁₂₇⋊C₃	C₉	semidirect
10. C₉×C₁₂₇⋊C₃	C₉	semidirect
11. C₉×C₁₂₇⋊C₃	C₉	semidirect
15. C₃×C₉×C₁₂₇	C₉	semidirect
32. C₁₂₇	#6887	semidirect
47. C₃×C₉	#11765919	semidirect

Maximal subgroups

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

subgroup	index
#23779867	3
#23779866	3
C₃²⋊#11765919	3
C₉×#11765919	3
C₃×C₉×C₁₂₇⋊C₃	3
#6887	127