Subgroups — #44525055

Order 30861.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#16812183	C₃	1	1	yes	maximal, characteristic
2	C₃×#16812182	C₃	1	1	yes	maximal, characteristic
3	#23779835	C₃	1	2	yes	maximal, complemented
4	#23779834	C₃	1	2	yes	maximal, complemented
5	#23779833	C₃	1	4	yes	maximal, complemented
6	#23779831	C₃	1	2	yes	maximal
7	C₉²×C₁₂₇	C₃	1	1	yes	maximal, characteristic, complemented
8	C₃²×C₁₂₇⋊C₃	C₃²	1	1	yes	characteristic
9	#16812183	—	3	3	no	—
10	#16812182	—	3	3	no	—
11	C₃×#11765917	C₃²	1	2	yes	—
12	C₃×#11765917	C₃²	1	2	yes	—
13	C₃×#11765917	C₃²	1	4	yes	—
14	C₃×C₉×C₁₂₇	C₃²	1	2	yes	—
15	C₃×C₉×C₁₂₇	C₃²	1	1	yes	characteristic
16	C₃×C₉×C₁₂₇	C₃²	1	1	yes	characteristic
17	C₃²×C₁₂₇	C₃³	1	1	yes	characteristic
18	C₃×C₁₂₇⋊C₃	—	3	1	no	—
19	C₃×C₁₂₇⋊C₃	—	3	1	no	—
20	C₃×C₁₂₇⋊C₃	—	3	2	no	—
21	C₉×C₁₂₇	—	3	2	no	—
22	C₉×C₁₂₇	3₋¹⁺²	1	3	yes	complemented
23	C₉×C₁₂₇	3₋¹⁺²	1	3	yes	complemented
24	#11765917	—	3	2	no	—
25	#11765917	—	3	2	no	—
26	#11765917	—	3	4	no	—
27	C₃×C₁₂₇	C₃×3₋¹⁺²	1	1	yes	characteristic
28	C₃×C₁₂₇	C₃×3₋¹⁺²	1	1	yes	characteristic
29	C₃×C₁₂₇	#737	1	2	yes	—
30	C₁₂₇⋊C₃	—	9	1	no	—
31	#6896	—	127	1	no	maximal, Sylow
32	C₁₂₇	#6896	1	1	yes	characteristic, complemented, Sylow
33	C₃×3₋¹⁺²	—	127	1	no	—
34	C₃×3₋¹⁺²	—	127	1	no	—
35	C₉⋊C₉	—	127	4	no	—
36	C₉⋊C₉	—	127	2	no	—
37	C₉⋊C₉	—	127	2	no	—
38	C₃²⋊C₉	—	127	2	no	—
39	C₉²	C₁₂₇⋊C₃	1	1	yes	characteristic, complemented
40	C₃³	—	127	1	no	—
41	3₋¹⁺²	—	381	3	no	—
42	3₋¹⁺²	—	381	3	no	—
43	C₃×C₉	—	127	4	no	—
44	C₃×C₉	—	127	2	no	—
45	C₃×C₉	—	127	2	no	—
46	C₃×C₉	C₃×C₁₂₇⋊C₃	1	2	yes	—
47	C₃×C₉	C₃×C₁₂₇⋊C₃	1	1	yes	characteristic
48	C₃×C₉	C₃×C₁₂₇⋊C₃	1	1	yes	characteristic
49	C₃²	—	381	1	no	—
50	C₃²	—	381	1	no	—
51	C₃²	—	381	2	no	—
52	C₃²	C₃²×C₁₂₇⋊C₃	1	1	yes	characteristic
53	C₉	—	3	2	no	—
54	C₉	—	381	2	no	—
55	C₉	—	381	2	no	—
56	C₉	—	381	4	no	—
57	C₉	#16812182	1	3	yes	complemented
58	C₉	#16812183	1	3	yes	complemented
59	C₃	—	1143	1	no	—
60	C₃	C₃×#16812182	1	1	yes	characteristic
61	C₃	C₃×#16812183	1	1	yes	characteristic
62	C₃	#23779860	1	2	yes	—

	subgroup	G/H
center, Frattini	C₃²	C₃²×C₁₂₇⋊C₃
commutator, socle, cosocle	C₃²×C₁₂₇	C₃³
Fitting	C₉²×C₁₂₇	C₃
prime radical	C₃²×C₁₂₇⋊C₃	C₃²
hypercenter	C₉²	C₁₂₇⋊C₃
hypocenter	C₁₂₇	#6896
LCS	G ▷ C₃²×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₃² ◁ C₉²

Complements

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

N	H ≅ G/N	type
3. #23779835	C₃	semidirect
4. #23779834	C₃	semidirect
5. #23779833	C₃	semidirect
7. C₉²×C₁₂₇	C₃	semidirect
22. C₉×C₁₂₇	3₋¹⁺²	semidirect
23. C₉×C₁₂₇	3₋¹⁺²	semidirect
32. C₁₂₇	#6896	semidirect
39. C₉²	C₁₂₇⋊C₃	semidirect
57. C₉	#16812182	semidirect
58. C₉	#16812183	semidirect

Maximal subgroups

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

subgroup	index
C₃×#16812183	3
C₃×#16812182	3
#23779835	3
#23779834	3
#23779833	3
#23779831	3
C₉²×C₁₂₇	3
#6896	127