Subgroups — C₃×#14578895 #21419376

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	C₃×#11719689	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃×C₃²⋊(C₃₁⋊C₃)	C₃	1	1	yes	maximal, characteristic, complemented
4	#14578895	C₃	1	9	yes	maximal, direct product factor
5	C₃×3₋¹⁺²×C₃₁	C₃	1	1	yes	maximal, characteristic, complemented
6	C₃³×C₃₁	C₃²	1	1	yes	characteristic
7	C₃²×C₃₁⋊C₃	—	3	2	no	—
8	C₃²×C₃₁⋊C₃	—	3	1	no	—
9	C₃²×C₃₁⋊C₃	—	3	9	no	—
10	C₃²×C₃₁⋊C₃	—	3	1	no	—
11	C₃²×C₃₁⋊C₃	C₃²	1	3	yes	complemented
12	3₋¹⁺²×C₃₁	—	3	2	no	—
13	3₋¹⁺²×C₃₁	C₃²	1	3	yes	complemented
14	C₃×C₉×C₃₁	—	3	1	no	—
15	C₃²⋊(C₃₁⋊C₃)	—	3	2	no	—
16	C₃²⋊(C₃₁⋊C₃)	C₃²	1	3	yes	complemented
17	#11719689	—	3	2	no	—
18	#11719689	C₃²	1	3	yes	complemented
19	C₃×C₃₁⋊C₉	—	3	1	no	—
20	C₃²×C₃₁	—	3	3	no	—
21	C₃²×C₃₁	H(3,𝔽₃)	1	2	yes	—
22	C₃²×C₃₁	H(3,𝔽₃)	1	1	yes	characteristic
23	C₃²×C₃₁	C₃³	1	1	yes	characteristic
24	C₃×C₃₁⋊C₃	—	3	18	no	—
25	C₃×C₃₁⋊C₃	—	3	9	no	—
26	C₃×C₃₁⋊C₃	—	3	3	no	—
27	C₃×C₃₁⋊C₃	—	3	9	no	—
28	C₃×C₃₁⋊C₃	—	3	3	no	—
29	C₃×C₃₁⋊C₃	—	9	3	no	—
30	C₉×C₃₁	—	3	3	no	—
31	C₃₁⋊C₉	—	3	3	no	—
32	C₃×AΣL(1,𝔽₂₇)	—	31	1	no	maximal, Sylow
33	C₃×C₃₁	—	3	2	no	—
34	C₃×C₃₁	—	3	1	no	—
35	C₃×C₃₁	AΣL(1,𝔽₂₇)	1	3	yes	complemented
36	C₃×C₃₁	C₃×H(3,𝔽₃)	1	1	yes	characteristic
37	C₃₁⋊C₃	—	3	9	no	—
38	C₃₁⋊C₃	—	9	3	no	—
39	C₃⁴	—	31	1	no	—
40	C₃×3₋¹⁺²	—	31	1	no	—
41	C₃×3₋¹⁺²	C₃₁⋊C₃	1	1	yes	characteristic, complemented
42	C₃×H(3,𝔽₃)	—	31	1	no	—
43	AΣL(1,𝔽₂₇)	—	31	9	no	—
44	C₃₁	C₃×AΣL(1,𝔽₂₇)	1	1	yes	characteristic, complemented, Sylow
45	C₃³	—	31	3	no	—
46	C₃³	—	93	9	no	—
47	C₃³	—	93	1	no	—
48	C₃³	—	93	2	no	—
49	C₃³	—	93	1	no	—
50	C₃³	C₃×C₃₁⋊C₃	1	1	yes	characteristic
51	3₋¹⁺²	—	3	2	no	—
52	3₋¹⁺²	—	31	3	no	—
53	3₋¹⁺²	—	93	2	no	—
54	3₋¹⁺²	C₃×C₃₁⋊C₃	1	3	yes	complemented
55	H(3,𝔽₃)	—	31	3	no	—
56	H(3,𝔽₃)	—	93	2	no	—
57	C₃×C₉	—	3	1	no	—
58	C₃×C₉	—	93	1	no	—
59	C₃²	—	3	3	no	—
60	C₃²	—	279	3	no	—
61	C₃²	—	93	9	no	—
62	C₃²	—	93	18	no	—
63	C₃²	—	93	3	no	—
64	C₃²	—	93	9	no	—
65	C₃²	—	93	3	no	—
66	C₃²	C₃²⋊(C₃₁⋊C₃)	1	2	yes	—
67	C₃²	C₃²⋊(C₃₁⋊C₃)	1	1	yes	characteristic
68	C₃²	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
69	C₉	—	3	3	no	—
70	C₉	—	93	3	no	—
71	C₃	—	3	2	no	—
72	C₃	—	3	1	no	—
73	C₃	—	279	3	no	—
74	C₃	—	93	9	no	—
75	C₃	#14578895	1	3	yes	direct product factor
76	C₃	C₃×C₃²⋊(C₃₁⋊C₃)	1	1	yes	characteristic

	subgroup	G/H
center	C₃²	C₃²⋊(C₃₁⋊C₃)
commutator	C₃²×C₃₁	C₃³
Frattini	C₃²	C₃²×C₃₁⋊C₃
Fitting	C₃×3₋¹⁺²×C₃₁	C₃
socle	C₃²×C₃₁	H(3,𝔽₃)
hypercenter	C₃×3₋¹⁺²	C₃₁⋊C₃
hypocenter	C₃₁	C₃×AΣL(1,𝔽₂₇)
LCS	G ▷ C₃²×C₃₁ ▷ C₃×C₃₁ ▷ C₃₁
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×C₃₁⋊C₃	C₃	semidirect
2. C₃×#11719689	C₃	semidirect
3. C₃×C₃²⋊(C₃₁⋊C₃)	C₃	semidirect
4. #14578895	C₃	direct (N × H)
5. C₃×3₋¹⁺²×C₃₁	C₃	semidirect
11. C₃²×C₃₁⋊C₃	C₃²	semidirect
13. 3₋¹⁺²×C₃₁	C₃²	semidirect
16. C₃²⋊(C₃₁⋊C₃)	C₃²	semidirect
18. #11719689	C₃²	semidirect
35. C₃×C₃₁	AΣL(1,𝔽₂₇)	semidirect
41. C₃×3₋¹⁺²	C₃₁⋊C₃	semidirect
44. C₃₁	C₃×AΣL(1,𝔽₂₇)	semidirect
54. 3₋¹⁺²	C₃×C₃₁⋊C₃	semidirect
75. C₃	#14578895	direct (N × H)

Subgroups — C3×#14578895 #21419376

Conjugacy classes of subgroups

Complements

Subgroups — C₃×#14578895 #21419376