Subgroups — C₃×#23779843 #44525092

Order 30861.

252 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₁₂₇⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
2	C₃×#16812184	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃×C₃²⋊(C₁₂₇⋊C₃)	C₃	1	1	yes	maximal, characteristic, complemented
4	#23779843	C₃	1	9	yes	maximal, direct product factor
5	C₃×3₋¹⁺²×C₁₂₇	C₃	1	1	yes	maximal, characteristic, complemented
6	C₃²×C₁₂₇⋊C₃	—	3	2	no	—
7	C₃²×C₁₂₇⋊C₃	—	3	1	no	—
8	C₃²×C₁₂₇⋊C₃	—	3	9	no	—
9	C₃²×C₁₂₇⋊C₃	—	3	1	no	—
10	C₃²×C₁₂₇⋊C₃	C₃²	1	3	yes	complemented
11	#16812184	—	3	2	no	—
12	#16812184	C₃²	1	3	yes	complemented
13	C₃²⋊(C₁₂₇⋊C₃)	—	3	2	no	—
14	C₃²⋊(C₁₂₇⋊C₃)	C₃²	1	3	yes	complemented
15	C₃×#11765917	—	3	1	no	—
16	C₃³×C₁₂₇	C₃²	1	1	yes	characteristic
17	3₋¹⁺²×C₁₂₇	—	3	2	no	—
18	3₋¹⁺²×C₁₂₇	C₃²	1	3	yes	complemented
19	C₃×C₉×C₁₂₇	—	3	1	no	—
20	C₃²×C₁₂₇	—	3	3	no	—
21	C₃²×C₁₂₇	H(3,𝔽₃)	1	2	yes	—
22	C₃²×C₁₂₇	H(3,𝔽₃)	1	1	yes	characteristic
23	C₃²×C₁₂₇	C₃³	1	1	yes	characteristic
24	C₃×C₁₂₇⋊C₃	—	3	18	no	—
25	C₃×C₁₂₇⋊C₃	—	3	9	no	—
26	C₃×C₁₂₇⋊C₃	—	3	3	no	—
27	C₃×C₁₂₇⋊C₃	—	3	9	no	—
28	C₃×C₁₂₇⋊C₃	—	3	3	no	—
29	C₃×C₁₂₇⋊C₃	—	9	3	no	—
30	C₉×C₁₂₇	—	3	3	no	—
31	#11765917	—	3	3	no	—
32	C₃×C₁₂₇	—	3	2	no	—
33	C₃×C₁₂₇	—	3	1	no	—
34	C₃×C₁₂₇	AΣL(1,𝔽₂₇)	1	3	yes	complemented
35	C₃×C₁₂₇	C₃×H(3,𝔽₃)	1	1	yes	characteristic
36	C₁₂₇⋊C₃	—	3	9	no	—
37	C₁₂₇⋊C₃	—	9	3	no	—
38	C₃×AΣL(1,𝔽₂₇)	—	127	1	no	maximal, Sylow
39	C₁₂₇	C₃×AΣL(1,𝔽₂₇)	1	1	yes	characteristic, complemented, Sylow
40	C₃⁴	—	127	1	no	—
41	C₃×3₋¹⁺²	—	127	1	no	—
42	C₃×3₋¹⁺²	C₁₂₇⋊C₃	1	1	yes	characteristic, complemented
43	C₃×H(3,𝔽₃)	—	127	1	no	—
44	AΣL(1,𝔽₂₇)	—	127	9	no	—
45	C₃³	—	381	9	no	—
46	C₃³	—	381	1	no	—
47	C₃³	—	381	2	no	—
48	C₃³	—	381	1	no	—
49	C₃³	—	127	3	no	—
50	C₃³	C₃×C₁₂₇⋊C₃	1	1	yes	characteristic
51	3₋¹⁺²	—	3	2	no	—
52	3₋¹⁺²	—	381	2	no	—
53	3₋¹⁺²	—	127	3	no	—
54	3₋¹⁺²	C₃×C₁₂₇⋊C₃	1	3	yes	complemented
55	H(3,𝔽₃)	—	381	2	no	—
56	H(3,𝔽₃)	—	127	3	no	—
57	C₃×C₉	—	3	1	no	—
58	C₃×C₉	—	381	1	no	—
59	C₃²	—	3	3	no	—
60	C₃²	—	1143	3	no	—
61	C₃²	—	381	9	no	—
62	C₃²	—	381	18	no	—
63	C₃²	—	381	3	no	—
64	C₃²	—	381	9	no	—
65	C₃²	—	381	3	no	—
66	C₃²	C₃²⋊(C₁₂₇⋊C₃)	1	2	yes	—
67	C₃²	C₃²⋊(C₁₂₇⋊C₃)	1	1	yes	characteristic
68	C₃²	C₃²×C₁₂₇⋊C₃	1	1	yes	characteristic
69	C₉	—	3	3	no	—
70	C₉	—	381	3	no	—
71	C₃	—	3	2	no	—
72	C₃	—	3	1	no	—
73	C₃	—	1143	3	no	—
74	C₃	—	381	9	no	—
75	C₃	#23779843	1	3	yes	direct product factor
76	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	C₃×3₋¹⁺²×C₁₂₇	C₃
socle	C₃²×C₁₂₇	H(3,𝔽₃)
hypercenter	C₃×3₋¹⁺²	C₁₂₇⋊C₃
hypocenter	C₁₂₇	C₃×AΣL(1,𝔽₂₇)
LCS	G ▷ C₃²×C₁₂₇ ▷ C₃×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₃² ◁ C₃³ ◁ C₃×3₋¹⁺²

Complements

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

N	H ≅ G/N	type
1. C₃³×C₁₂₇⋊C₃	C₃	semidirect
2. C₃×#16812184	C₃	semidirect
3. C₃×C₃²⋊(C₁₂₇⋊C₃)	C₃	semidirect
4. #23779843	C₃	direct (N × H)
5. C₃×3₋¹⁺²×C₁₂₇	C₃	semidirect
10. C₃²×C₁₂₇⋊C₃	C₃²	semidirect
12. #16812184	C₃²	semidirect
14. C₃²⋊(C₁₂₇⋊C₃)	C₃²	semidirect
18. 3₋¹⁺²×C₁₂₇	C₃²	semidirect
34. C₃×C₁₂₇	AΣL(1,𝔽₂₇)	semidirect
39. C₁₂₇	C₃×AΣL(1,𝔽₂₇)	semidirect
42. C₃×3₋¹⁺²	C₁₂₇⋊C₃	semidirect
54. 3₋¹⁺²	C₃×C₁₂₇⋊C₃	semidirect
75. C₃	#23779843	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃³×C₁₂₇⋊C₃	3
C₃×#16812184	3
C₃×C₃²⋊(C₁₂₇⋊C₃)	3
#23779843	3
C₃×3₋¹⁺²×C₁₂₇	3
C₃×AΣL(1,𝔽₂₇)	127

Subgroups — C3×#23779843 #44525092

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#23779843 #44525092