Subgroups — AΣL(1,𝔽₂₇)×C₃₁⋊C₃ #21419373

Order 7533.

252 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₃₁⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
2	3₋¹⁺²×C₃₁⋊C₃	C₃	1	2	yes	maximal, complemented
3	H(3,𝔽₃)×C₃₁⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
4	#14578895	C₃	1	4	yes	maximal, complemented
5	#14578894	C₃	1	2	yes	maximal, complemented
6	#14578893	C₃	1	2	yes	maximal, complemented
7	C₃₁×AΣL(1,𝔽₂₇)	C₃	1	1	yes	maximal, characteristic, complemented
8	C₃³×C₃₁	C₃²	1	1	yes	characteristic, complemented
9	C₃²×C₃₁⋊C₃	—	3	2	no	—
10	C₃²×C₃₁⋊C₃	—	3	1	no	—
11	C₃²×C₃₁⋊C₃	—	3	9	no	—
12	C₃²×C₃₁⋊C₃	—	3	1	no	—
13	C₃²×C₃₁⋊C₃	C₃²	1	1	yes	characteristic
14	C₃²×C₃₁⋊C₃	C₃²	1	2	yes	complemented
15	3₋¹⁺²×C₃₁	C₃²	1	2	yes	complemented
16	H(3,𝔽₃)×C₃₁	C₃²	1	1	yes	characteristic, complemented
17	C₃²⋊(C₃₁⋊C₃)	—	3	2	no	—
18	C₃²⋊(C₃₁⋊C₃)	C₃²	1	2	yes	complemented
19	#11719689	C₃²	1	4	yes	complemented
20	#11719687	—	3	2	no	—
21	#11719686	—	3	2	no	—
22	C₉×C₃₁⋊C₃	—	3	2	no	—
23	C₃²×C₃₁	—	3	3	no	—
24	C₃²×C₃₁	—	3	1	no	—
25	C₃²×C₃₁	—	3	1	no	—
26	C₃²×C₃₁	C₃³	1	1	yes	characteristic
27	C₃×C₃₁⋊C₃	—	3	18	no	—
28	C₃×C₃₁⋊C₃	—	3	2	no	—
29	C₃×C₃₁⋊C₃	—	3	9	no	—
30	C₃×C₃₁⋊C₃	—	3	3	no	—
31	C₃×C₃₁⋊C₃	—	3	6	no	—
32	C₃×C₃₁⋊C₃	—	3	2	no	—
33	C₃×C₃₁⋊C₃	—	9	3	no	—
34	C₃×C₃₁⋊C₃	H(3,𝔽₃)	1	2	yes	—
35	C₃×C₃₁⋊C₃	H(3,𝔽₃)	1	1	yes	characteristic
36	C₉×C₃₁	—	3	2	no	—
37	C₃₁⋊C₉	—	3	4	no	—
38	C₃×AΣL(1,𝔽₂₇)	—	31	1	no	maximal, Sylow
39	C₃×C₃₁	—	3	3	no	—
40	C₃×C₃₁	—	3	1	no	—
41	C₃×C₃₁	—	9	1	no	—
42	C₃×C₃₁	C₃×H(3,𝔽₃)	1	1	yes	characteristic
43	C₃₁⋊C₃	—	3	6	no	—
44	C₃₁⋊C₃	—	3	2	no	—
45	C₃₁⋊C₃	—	9	2	no	—
46	C₃₁⋊C₃	AΣL(1,𝔽₂₇)	1	3	yes	direct product factor
47	C₃⁴	—	31	1	no	—
48	C₃×3₋¹⁺²	—	31	2	no	—
49	C₃×H(3,𝔽₃)	—	31	1	no	—
50	AΣL(1,𝔽₂₇)	—	31	2	no	—
51	AΣL(1,𝔽₂₇)	—	31	4	no	—
52	AΣL(1,𝔽₂₇)	—	31	2	no	—
53	AΣL(1,𝔽₂₇)	C₃₁⋊C₃	1	1	yes	characteristic, direct product factor
54	C₃₁	C₃×AΣL(1,𝔽₂₇)	1	1	yes	characteristic, complemented, Sylow
55	C₃³	—	31	1	no	—
56	C₃³	—	31	2	no	—
57	C₃³	—	93	1	no	—
58	C₃³	—	93	1	no	—
59	C₃³	—	93	2	no	—
60	C₃³	—	93	9	no	—
61	C₃³	C₃×C₃₁⋊C₃	1	1	yes	characteristic, complemented
62	3₋¹⁺²	—	31	4	no	—
63	3₋¹⁺²	—	93	2	no	—
64	3₋¹⁺²	—	93	2	no	—
65	3₋¹⁺²	C₃×C₃₁⋊C₃	1	2	yes	complemented
66	H(3,𝔽₃)	—	31	2	no	—
67	H(3,𝔽₃)	—	93	2	no	—
68	H(3,𝔽₃)	C₃×C₃₁⋊C₃	1	1	yes	characteristic, complemented
69	C₃×C₉	—	93	2	no	—
70	C₃²	—	3	3	no	—
71	C₃²	—	3	1	no	—
72	C₃²	—	3	1	no	—
73	C₃²	—	279	3	no	—
74	C₃²	—	31	1	no	—
75	C₃²	—	31	2	no	—
76	C₃²	—	93	3	no	—
77	C₃²	—	93	9	no	—
78	C₃²	—	93	6	no	—
79	C₃²	—	93	18	no	—
80	C₃²	—	93	2	no	—
81	C₃²	—	93	2	no	—
82	C₃²	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
83	C₉	—	3	2	no	—
84	C₉	—	93	4	no	—
85	C₃	—	3	1	no	—
86	C₃	—	3	3	no	—
87	C₃	—	9	1	no	—
88	C₃	—	279	2	no	—
89	C₃	—	31	3	no	—
90	C₃	—	93	2	no	—
91	C₃	—	93	6	no	—
92	C₃	H(3,𝔽₃)×C₃₁⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₃	H(3,𝔽₃)×C₃₁⋊C₃
commutator	C₃²×C₃₁	C₃³
Frattini	C₃²	C₃²×C₃₁⋊C₃
Fitting	C₃₁×AΣL(1,𝔽₂₇)	C₃
socle	C₃×C₃₁	C₃×H(3,𝔽₃)
hypercenter	AΣL(1,𝔽₂₇)	C₃₁⋊C₃
hypocenter	C₃₁	C₃×AΣL(1,𝔽₂₇)
LCS	G ▷ C₃²×C₃₁ ▷ C₃×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₃ ◁ C₃² ◁ AΣL(1,𝔽₂₇)

Complements

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

N	H ≅ G/N	type
1. C₃³×C₃₁⋊C₃	C₃	semidirect
2. 3₋¹⁺²×C₃₁⋊C₃	C₃	semidirect
3. H(3,𝔽₃)×C₃₁⋊C₃	C₃	semidirect
4. #14578895	C₃	semidirect
5. #14578894	C₃	semidirect
6. #14578893	C₃	semidirect
7. C₃₁×AΣL(1,𝔽₂₇)	C₃	semidirect
8. C₃³×C₃₁	C₃²	semidirect
14. C₃²×C₃₁⋊C₃	C₃²	semidirect
15. 3₋¹⁺²×C₃₁	C₃²	semidirect
16. H(3,𝔽₃)×C₃₁	C₃²	semidirect
18. C₃²⋊(C₃₁⋊C₃)	C₃²	semidirect
19. #11719689	C₃²	semidirect
46. C₃₁⋊C₃	AΣL(1,𝔽₂₇)	direct (N × H)
53. AΣL(1,𝔽₂₇)	C₃₁⋊C₃	direct (N × H)
54. C₃₁	C₃×AΣL(1,𝔽₂₇)	semidirect
61. C₃³	C₃×C₃₁⋊C₃	semidirect
65. 3₋¹⁺²	C₃×C₃₁⋊C₃	semidirect
68. H(3,𝔽₃)	C₃×C₃₁⋊C₃	semidirect

Subgroups — AΣL(1,𝔽27)×C31⋊C3 #21419373

Conjugacy classes of subgroups

Complements

Subgroups — AΣL(1,𝔽₂₇)×C₃₁⋊C₃ #21419373