Subgroups — #44525075

Order 30861.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#16812184	C₃	1	3	yes	maximal
2	#23779835	C₃	1	1	yes	maximal, characteristic, complemented
3	#23779834	C₃	1	1	yes	maximal, characteristic, complemented
4	#23779833	C₃	1	6	yes	maximal, complemented
5	C₉×#11765917	C₃	1	1	yes	maximal, characteristic, complemented
6	C₃×3₋¹⁺²×C₁₂₇	C₃	1	1	yes	maximal, characteristic
7	#16812184	—	3	9	no	—
8	C₃×#11765917	C₃²	1	3	yes	—
9	C₃×#11765917	C₃²	1	3	yes	—
10	C₃×#11765917	C₃²	1	3	yes	—
11	C₃³×C₁₂₇	C₃²	1	1	yes	characteristic
12	3₋¹⁺²×C₁₂₇	—	3	3	no	—
13	C₃×C₉×C₁₂₇	C₃²	1	2	yes	—
14	C₃×C₉×C₁₂₇	C₃²	1	1	yes	characteristic
15	C₃²×C₁₂₇	—	3	1	no	—
16	C₃²×C₁₂₇	—	3	3	no	—
17	C₃²×C₁₂₇	C₃³	1	1	yes	characteristic
18	C₉×C₁₂₇	—	3	2	no	—
19	C₉×C₁₂₇	3₋¹⁺²	1	3	yes	complemented
20	#11765917	—	3	3	no	—
21	#11765917	—	3	3	no	—
22	#11765917	3₋¹⁺²	1	9	yes	complemented
23	C₃×C₁₂₇	—	9	1	no	—
24	C₃×C₁₂₇	C₃×3₋¹⁺²	1	3	yes	—
25	C₃×C₁₂₇	C₃×3₋¹⁺²	1	1	yes	characteristic
26	#6900	—	127	1	no	maximal, Sylow
27	C₁₂₇	#6900	1	1	yes	characteristic, complemented, Sylow
28	C₃×3₋¹⁺²	—	127	3	no	—
29	C₃×3₋¹⁺²	C₁₂₇⋊C₃	1	1	yes	characteristic
30	C₉⋊C₉	—	127	6	no	—
31	C₉⋊C₉	—	127	1	no	—
32	C₉⋊C₉	—	127	1	no	—
33	C₉²	—	127	1	no	—
34	C₃³	C₃×C₁₂₇⋊C₃	1	1	yes	characteristic
35	3₋¹⁺²	—	3	3	no	—
36	3₋¹⁺²	—	381	9	no	—
37	C₃×C₉	—	127	3	no	—
38	C₃×C₉	—	127	3	no	—
39	C₃×C₉	—	127	3	no	—
40	C₃×C₉	C₃×C₁₂₇⋊C₃	1	2	yes	—
41	C₃×C₉	C₃×C₁₂₇⋊C₃	1	1	yes	characteristic
42	C₃²	—	3	3	no	—
43	C₃²	—	3	1	no	—
44	C₃²	C₃²×C₁₂₇⋊C₃	1	1	yes	characteristic
45	C₉	—	3	2	no	—
46	C₉	—	381	3	no	—
47	C₉	—	381	3	no	—
48	C₉	—	127	9	no	—
49	C₉	#16812184	1	3	yes	complemented
50	C₃	—	9	1	no	—
51	C₃	3₋¹⁺²×C₁₂₇⋊C₃	1	3	yes	—
52	C₃	C₃×#16812184	1	1	yes	characteristic

	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	#6900
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. #23779835	C₃	semidirect
3. #23779834	C₃	semidirect
4. #23779833	C₃	semidirect
5. C₉×#11765917	C₃	semidirect
19. C₉×C₁₂₇	3₋¹⁺²	semidirect
22. #11765917	3₋¹⁺²	semidirect
27. C₁₂₇	#6900	semidirect
49. C₉	#16812184	semidirect

Maximal subgroups

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

subgroup	index
C₃×#16812184	3
#23779835	3
#23779834	3
#23779833	3
C₉×#11765917	3
C₃×3₋¹⁺²×C₁₂₇	3
#6900	127