Subgroups — #44525009

Order 30861.

138 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#11765917	C₃	1	1	yes	maximal, characteristic
2	#23779833	C₃	1	6	yes	maximal, complemented
3	C₃²⋊#11765917	C₃	1	2	yes	maximal
4	C₉×#11765917	C₃	1	3	yes	maximal, complemented
5	C₃²⋊C₉×C₁₂₇	C₃	1	1	yes	maximal, characteristic
6	C₃×#11765917	C₉	1	9	yes	complemented
7	C₃×#11765917	C₃²	1	6	yes	—
8	C₃×#11765917	C₃²	1	1	yes	characteristic
9	C₃×#11765917	C₃²	1	2	yes	—
10	C₃³×C₁₂₇	C₃²	1	1	yes	characteristic
11	C₃×C₉×C₁₂₇	C₃²	1	3	yes	—
12	C₃²×C₁₂₇	—	3	1	no	—
13	C₃²×C₁₂₇	—	3	2	no	—
14	C₃²×C₁₂₇	C₃×C₉	1	3	yes	—
15	C₃²×C₁₂₇	C₃³	1	1	yes	characteristic
16	C₉×C₁₂₇	—	3	3	no	—
17	#11765917	—	3	6	no	—
18	#11765917	C₃×C₉	1	3	yes	—
19	#11765917	C₃×C₉	1	6	yes	—
20	C₃×C₁₂₇	—	3	3	no	—
21	C₃×C₁₂₇	C₃²×C₉	1	1	yes	characteristic
22	C₃×C₁₂₇	#737	1	1	yes	characteristic
23	C₃×C₁₂₇	#737	1	2	yes	—
24	#6887	—	127	1	no	maximal, Sylow
25	C₁₂₇	#6887	1	1	yes	characteristic, complemented, Sylow
26	C₃²×C₉	—	127	1	no	—
27	C₉⋊C₉	—	127	6	no	—
28	C₃²⋊C₉	—	127	2	no	—
29	C₃²⋊C₉	C₁₂₇⋊C₃	1	1	yes	characteristic
30	C₉²	—	127	3	no	—
31	C₃³	C₃×C₁₂₇⋊C₃	1	1	yes	characteristic
32	C₃×C₉	—	127	6	no	—
33	C₃×C₉	—	127	9	no	—
34	C₃×C₉	—	127	1	no	—
35	C₃×C₉	—	127	2	no	—
36	C₃×C₉	C₃×C₁₂₇⋊C₃	1	3	yes	—
37	C₃²	—	3	1	no	—
38	C₃²	—	3	2	no	—
39	C₃²	C₉×C₁₂₇⋊C₃	1	3	yes	—
40	C₃²	C₃²×C₁₂₇⋊C₃	1	1	yes	characteristic
41	C₉	—	3	3	no	—
42	C₉	—	381	6	no	—
43	C₉	—	127	3	no	—
44	C₉	—	127	6	no	—
45	C₃	—	3	3	no	—
46	C₃	C₃×C₉×C₁₂₇⋊C₃	1	1	yes	characteristic
47	C₃	#23779859	1	1	yes	characteristic
48	C₃	#23779861	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. #23779833	C₃	semidirect
4. C₉×#11765917	C₃	semidirect
6. C₃×#11765917	C₉	semidirect
25. C₁₂₇	#6887	semidirect

Maximal subgroups

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

subgroup	index
C₃²×#11765917	3
#23779833	3
C₃²⋊#11765917	3
C₉×#11765917	3
C₃²⋊C₉×C₁₂₇	3
#6887	127