Subgroups — #44525064

Order 30861.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23779835	C₃	1	1	yes	maximal, characteristic, complemented
2	#23779834	C₃	1	1	yes	maximal, characteristic, complemented
3	#23779833	C₃	1	2	yes	maximal, complemented
4	#23779833	C₃	1	2	yes	maximal, complemented
5	#23779833	C₃	1	2	yes	maximal, complemented
6	C₃²⋊#11765917	C₃	1	2	yes	maximal
7	C₃²⋊#11765917	C₃	1	1	yes	maximal, characteristic
8	C₉×#11765917	C₃	1	1	yes	maximal, characteristic, complemented
9	C₃²⋊C₉×C₁₂₇	C₃	1	1	yes	maximal, characteristic
10	C₃×#11765917	C₃²	1	2	yes	—
11	C₃×#11765917	C₃²	1	1	yes	characteristic
12	C₃×#11765917	C₃²	1	2	yes	—
13	C₃×#11765917	C₃²	1	2	yes	—
14	C₃×#11765917	C₃²	1	2	yes	—
15	C₃³×C₁₂₇	C₃²	1	1	yes	characteristic
16	C₃×C₉×C₁₂₇	C₃²	1	1	yes	characteristic
17	C₃×C₉×C₁₂₇	C₃²	1	1	yes	characteristic
18	C₃×C₉×C₁₂₇	C₃²	1	1	yes	characteristic
19	C₃²×C₁₂₇	—	3	1	no	—
20	C₃²×C₁₂₇	—	3	1	no	—
21	C₃²×C₁₂₇	—	3	2	no	—
22	C₃²×C₁₂₇	C₃³	1	1	yes	characteristic
23	C₉×C₁₂₇	—	3	1	no	—
24	C₉×C₁₂₇	—	3	1	no	—
25	C₉×C₁₂₇	—	3	1	no	—
26	#11765917	—	3	1	no	—
27	#11765917	—	3	2	no	—
28	#11765917	—	3	2	no	—
29	#11765917	—	3	2	no	—
30	#11765917	—	3	2	no	—
31	C₃×C₁₂₇	—	9	1	no	—
32	C₃×C₁₂₇	#737	1	1	yes	characteristic
33	C₃×C₁₂₇	#737	1	1	yes	characteristic
34	C₃×C₁₂₇	#737	1	2	yes	—
35	#6898	—	127	1	no	maximal, Sylow
36	C₁₂₇	#6898	1	1	yes	characteristic, complemented, Sylow
37	C₉⋊C₉	—	127	2	no	—
38	C₉⋊C₉	—	127	2	no	—
39	C₉⋊C₉	—	127	2	no	—
40	C₉⋊C₉	—	127	1	no	—
41	C₉⋊C₉	—	127	1	no	—
42	C₃²⋊C₉	—	127	1	no	—
43	C₃²⋊C₉	—	127	2	no	—
44	C₃²⋊C₉	C₁₂₇⋊C₃	1	1	yes	characteristic
45	C₉²	—	127	1	no	—
46	C₃³	C₃×C₁₂₇⋊C₃	1	1	yes	characteristic
47	C₃×C₉	—	127	1	no	—
48	C₃×C₉	—	127	2	no	—
49	C₃×C₉	—	127	2	no	—
50	C₃×C₉	—	127	2	no	—
51	C₃×C₉	—	127	2	no	—
52	C₃×C₉	C₃×C₁₂₇⋊C₃	1	1	yes	characteristic
53	C₃×C₉	C₃×C₁₂₇⋊C₃	1	1	yes	characteristic
54	C₃×C₉	C₃×C₁₂₇⋊C₃	1	1	yes	characteristic
55	C₃²	—	3	1	no	—
56	C₃²	—	3	1	no	—
57	C₃²	—	3	2	no	—
58	C₃²	C₃²×C₁₂₇⋊C₃	1	1	yes	characteristic
59	C₉	—	3	1	no	—
60	C₉	—	3	1	no	—
61	C₉	—	3	1	no	—
62	C₉	—	381	1	no	—
63	C₉	—	381	2	no	—
64	C₉	—	381	2	no	—
65	C₉	—	381	2	no	—
66	C₉	—	381	2	no	—
67	C₃	—	9	1	no	—
68	C₃	#23779859	1	1	yes	characteristic
69	C₃	#23779860	1	1	yes	characteristic
70	C₃	#23779861	1	2	yes	—

	subgroup	G/H
center, Frattini	C₃²	C₃²×C₁₂₇⋊C₃
commutator, socle, cosocle	C₃²×C₁₂₇	C₃³
Fitting	C₃²⋊C₉×C₁₂₇	C₃
prime radical	C₃³×C₁₂₇	C₃²
hypercenter	C₃²⋊C₉	C₁₂₇⋊C₃
hypocenter	C₁₂₇	#6898
LCS	G ▷ C₃²×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₃² ◁ C₃²⋊C₉

Complements

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

N	H ≅ G/N	type
1. #23779835	C₃	semidirect
2. #23779834	C₃	semidirect
3. #23779833	C₃	semidirect
4. #23779833	C₃	semidirect
5. #23779833	C₃	semidirect
8. C₉×#11765917	C₃	semidirect
36. C₁₂₇	#6898	semidirect

Maximal subgroups

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

subgroup	index
#23779835	3
#23779834	3
#23779833	3
C₃²⋊#11765917	3
C₉×#11765917	3
C₃²⋊C₉×C₁₂₇	3
#6898	127