Subgroups — C₃×#23779844 #44525094

Order 30861.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#16812184	C₃	1	2	yes	maximal, complemented
2	C₃²×#11765917	C₃	1	1	yes	maximal, characteristic, complemented
3	#23779844	C₃	1	9	yes	maximal, direct product factor
4	C₃×H(3,𝔽₃)×C₁₂₇	C₃	1	1	yes	maximal, characteristic
5	#16812184	—	3	4	no	—
6	#16812184	C₃²	1	6	yes	complemented
7	C₃×#11765917	—	3	2	no	—
8	C₃×#11765917	—	3	1	no	—
9	C₃×#11765917	—	3	2	no	—
10	C₃×#11765917	C₃²	1	3	yes	complemented
11	C₃³×C₁₂₇	—	3	1	no	—
12	C₃³×C₁₂₇	C₃²	1	1	yes	characteristic
13	H(3,𝔽₃)×C₁₂₇	—	3	2	no	—
14	H(3,𝔽₃)×C₁₂₇	C₃²	1	3	yes	—
15	C₃²×C₁₂₇	—	3	3	no	—
16	C₃²×C₁₂₇	—	3	3	no	—
17	C₃²×C₁₂₇	—	9	3	no	—
18	C₃²×C₁₂₇	H(3,𝔽₃)	1	2	yes	—
19	C₃²×C₁₂₇	H(3,𝔽₃)	1	1	yes	characteristic
20	C₃²×C₁₂₇	C₃³	1	1	yes	characteristic
21	#11765917	—	3	3	no	—
22	#11765917	—	3	6	no	—
23	C₃×C₁₂₇	—	3	2	no	—
24	C₃×C₁₂₇	—	3	1	no	—
25	C₃×C₁₂₇	—	9	3	no	—
26	C₃×C₁₂₇	#731	1	3	yes	complemented
27	C₃×C₁₂₇	C₃×H(3,𝔽₃)	1	1	yes	characteristic
28	C₃×#731	—	127	1	no	maximal, Sylow
29	C₁₂₇	C₃×#731	1	1	yes	characteristic, complemented, Sylow
30	C₃×3₋¹⁺²	—	127	2	no	—
31	C₃×H(3,𝔽₃)	C₁₂₇⋊C₃	1	1	yes	characteristic
32	C₃²×C₉	—	127	1	no	—
33	#731	—	127	9	no	—
34	C₃³	—	3	1	no	—
35	C₃³	C₃×C₁₂₇⋊C₃	1	1	yes	characteristic
36	3₋¹⁺²	—	381	4	no	—
37	3₋¹⁺²	—	127	6	no	—
38	H(3,𝔽₃)	—	3	2	no	—
39	H(3,𝔽₃)	C₃×C₁₂₇⋊C₃	1	3	yes	—
40	C₃×C₉	—	381	2	no	—
41	C₃×C₉	—	381	1	no	—
42	C₃×C₉	—	381	2	no	—
43	C₃×C₉	—	127	3	no	—
44	C₃²	—	3	3	no	—
45	C₃²	—	3	3	no	—
46	C₃²	—	9	3	no	—
47	C₃²	C₃²⋊(C₁₂₇⋊C₃)	1	2	yes	—
48	C₃²	C₃²⋊(C₁₂₇⋊C₃)	1	1	yes	characteristic
49	C₃²	C₃²×C₁₂₇⋊C₃	1	1	yes	characteristic
50	C₉	—	381	3	no	—
51	C₉	—	381	6	no	—
52	C₃	—	3	2	no	—
53	C₃	—	3	1	no	—
54	C₃	—	9	3	no	—
55	C₃	#23779844	1	3	yes	direct product factor
56	C₃	C₃×C₃²⋊(C₁₂₇⋊C₃)	1	1	yes	characteristic

	subgroup	G/H
center	C₃²	C₃²⋊(C₁₂₇⋊C₃)
commutator, cosocle	C₃²×C₁₂₇	C₃³
Frattini	C₃²	C₃²×C₁₂₇⋊C₃
Fitting, prime radical	C₃×H(3,𝔽₃)×C₁₂₇	C₃
socle	C₃²×C₁₂₇	H(3,𝔽₃)
hypercenter	C₃×H(3,𝔽₃)	C₁₂₇⋊C₃
hypocenter	C₁₂₇	C₃×#731
LCS	G ▷ C₃²×C₁₂₇ ▷ C₃×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₃² ◁ C₃³ ◁ C₃×H(3,𝔽₃)

Complements

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

N	H ≅ G/N	type
1. C₃×#16812184	C₃	semidirect
2. C₃²×#11765917	C₃	semidirect
3. #23779844	C₃	direct (N × H)
6. #16812184	C₃²	semidirect
10. C₃×#11765917	C₃²	semidirect
26. C₃×C₁₂₇	#731	semidirect
29. C₁₂₇	C₃×#731	semidirect
55. C₃	#23779844	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#16812184	3
C₃²×#11765917	3
#23779844	3
C₃×H(3,𝔽₃)×C₁₂₇	3
C₃×#731	127

Subgroups — C3×#23779844 #44525094

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#23779844 #44525094