Subgroups — #44525042

Order 30861.

124 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	#23779833	C₃	1	3	yes	maximal, complemented
4	C₃²⋊#11765917	C₃	1	2	yes	maximal
5	C₃×3₋¹⁺²×C₁₂₇	C₃	1	1	yes	maximal, characteristic
6	C₃×#11765917	—	3	3	no	—
7	C₃×#11765917	C₃²	1	2	yes	—
8	C₃×#11765917	C₃²	1	6	yes	—
9	C₃×#11765917	C₃²	1	1	yes	characteristic
10	C₃³×C₁₂₇	C₃²	1	1	yes	characteristic
11	3₋¹⁺²×C₁₂₇	—	3	3	no	—
12	C₃×C₉×C₁₂₇	C₃²	1	3	yes	—
13	C₃²×C₁₂₇	—	3	1	no	—
14	C₃²×C₁₂₇	—	3	2	no	—
15	C₃²×C₁₂₇	3₋¹⁺²	1	3	yes	—
16	C₃²×C₁₂₇	C₃³	1	1	yes	characteristic
17	C₉×C₁₂₇	—	3	3	no	—
18	#11765917	—	3	2	no	—
19	#11765917	—	3	6	no	—
20	#11765917	3₋¹⁺²	1	3	yes	complemented
21	C₃×C₁₂₇	—	3	3	no	—
22	C₃×C₁₂₇	C₃×3₋¹⁺²	1	1	yes	characteristic
23	C₃×C₁₂₇	C₃×3₋¹⁺²	1	1	yes	characteristic
24	C₃×C₁₂₇	#737	1	2	yes	—
25	#6894	—	127	1	no	maximal, Sylow
26	C₁₂₇	#6894	1	1	yes	characteristic, complemented, Sylow
27	C₃×3₋¹⁺²	C₁₂₇⋊C₃	1	1	yes	characteristic
28	C₃²×C₉	—	127	1	no	—
29	C₉⋊C₉	—	127	6	no	—
30	C₉⋊C₉	—	127	3	no	—
31	C₃²⋊C₉	—	127	2	no	—
32	C₃³	C₃×C₁₂₇⋊C₃	1	1	yes	characteristic
33	3₋¹⁺²	—	3	3	no	—
34	C₃×C₉	—	381	3	no	—
35	C₃×C₉	—	127	6	no	—
36	C₃×C₉	—	127	2	no	—
37	C₃×C₉	—	127	1	no	—
38	C₃×C₉	C₃×C₁₂₇⋊C₃	1	3	yes	—
39	C₃²	—	3	1	no	—
40	C₃²	—	3	2	no	—
41	C₃²	#16812184	1	3	yes	—
42	C₃²	C₃²×C₁₂₇⋊C₃	1	1	yes	characteristic
43	C₉	—	3	3	no	—
44	C₉	—	381	2	no	—
45	C₉	—	381	6	no	—
46	C₉	—	127	3	no	—
47	C₃	—	3	3	no	—
48	C₃	3₋¹⁺²×C₁₂₇⋊C₃	1	1	yes	characteristic
49	C₃	C₃×#16812184	1	1	yes	characteristic
50	C₃	#23779861	1	2	yes	—

	subgroup	G/H
center, Frattini	C₃²	C₃²×C₁₂₇⋊C₃
commutator, socle, cosocle	C₃²×C₁₂₇	C₃³
Fitting	C₃×3₋¹⁺²×C₁₂₇	C₃
prime radical	C₃³×C₁₂₇	C₃²
hypercenter	C₃×3₋¹⁺²	C₁₂₇⋊C₃
hypocenter	C₁₂₇	#6894
LCS	G ▷ C₃²×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₃² ◁ C₃×3₋¹⁺²

Complements

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

N	H ≅ G/N	type
2. #23779833	C₃	semidirect
3. #23779833	C₃	semidirect
20. #11765917	3₋¹⁺²	semidirect
26. C₁₂₇	#6894	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
C₃×3₋¹⁺²×C₁₂₇	3
#6894	127