Subgroups — 3₋¹⁺²×C₃₁⋊C₉ #21419305

Order 7533.

148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₃₁⋊C₉	C₃	1	1	yes	maximal, characteristic
2	#14578887	C₃	1	3	yes	maximal, complemented
3	#14578886	C₃	1	3	yes	maximal, complemented
4	C₃²⋊(C₃₁⋊C₉)	C₃	1	2	yes	maximal
5	C₉×C₃₁⋊C₉	C₃	1	3	yes	maximal, complemented
6	C₃×3₋¹⁺²×C₃₁	C₃	1	1	yes	maximal, characteristic
7	C₃³×C₃₁	C₃²	1	1	yes	characteristic
8	3₋¹⁺²×C₃₁	C₉	1	9	yes	complemented
9	C₃×C₉×C₃₁	C₃²	1	3	yes	—
10	C₃×C₃₁⋊C₉	—	3	3	no	—
11	C₃×C₃₁⋊C₉	C₃²	1	6	yes	—
12	C₃×C₃₁⋊C₉	C₃²	1	1	yes	characteristic
13	C₃×C₃₁⋊C₉	C₃²	1	1	yes	characteristic
14	C₃×C₃₁⋊C₉	C₃²	1	1	yes	characteristic
15	C₃²×C₃₁	—	3	1	no	—
16	C₃²×C₃₁	—	3	2	no	—
17	C₃²×C₃₁	C₃×C₉	1	3	yes	—
18	C₃²×C₃₁	C₃³	1	1	yes	characteristic
19	C₉×C₃₁	C₃×C₉	1	9	yes	complemented
20	C₃₁⋊C₉	—	3	1	no	—
21	C₃₁⋊C₉	—	3	1	no	—
22	C₃₁⋊C₉	—	3	6	no	—
23	C₃₁⋊C₉	3₋¹⁺²	1	3	yes	direct product factor
24	C₉×3₋¹⁺²	—	31	1	no	maximal, Sylow
25	C₃×C₃₁	—	3	3	no	—
26	C₃×C₃₁	C₃²×C₉	1	1	yes	characteristic
27	C₃×C₃₁	C₃×3₋¹⁺²	1	1	yes	characteristic
28	C₃×C₃₁	#737	1	2	yes	—
29	C₃×3₋¹⁺²	C₃₁⋊C₃	1	1	yes	characteristic
30	C₃²×C₉	—	31	1	no	—
31	C₉⋊C₉	—	31	3	no	—
32	C₉⋊C₉	—	31	3	no	—
33	C₃²⋊C₉	—	31	2	no	—
34	C₉²	—	31	3	no	—
35	C₃₁	C₉×3₋¹⁺²	1	1	yes	characteristic, complemented, Sylow
36	C₃³	C₃×C₃₁⋊C₃	1	1	yes	characteristic
37	3₋¹⁺²	C₃₁⋊C₉	1	9	yes	direct product factor
38	C₃×C₉	—	31	1	no	—
39	C₃×C₉	—	31	6	no	—
40	C₃×C₉	—	31	1	no	—
41	C₃×C₉	—	31	1	no	—
42	C₃×C₉	—	93	3	no	—
43	C₃×C₉	C₃×C₃₁⋊C₃	1	3	yes	—
44	C₃²	—	3	1	no	—
45	C₃²	—	3	2	no	—
46	C₃²	C₃×C₃₁⋊C₉	1	3	yes	—
47	C₃²	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
48	C₉	—	31	3	no	—
49	C₉	—	93	1	no	—
50	C₉	—	93	1	no	—
51	C₉	—	93	6	no	—
52	C₉	C₃×C₃₁⋊C₉	1	9	yes	complemented
53	C₃	—	3	3	no	—
54	C₃	C₃²×C₃₁⋊C₉	1	1	yes	characteristic
55	C₃	3₋¹⁺²×C₃₁⋊C₃	1	1	yes	characteristic
56	C₃	#14578913	1	2	yes	—

	subgroup	G/H
center, Frattini	C₃²	C₃²×C₃₁⋊C₃
commutator	C₃×C₃₁	C₃²×C₉
Fitting	C₃×3₋¹⁺²×C₃₁	C₃
socle	C₃²×C₃₁	C₃³
hypercenter	C₃×3₋¹⁺²	C₃₁⋊C₃
hypocenter	C₃₁	C₉×3₋¹⁺²
LCS	G ▷ C₃×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₃² ◁ C₃×3₋¹⁺²

Complements

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

N	H ≅ G/N	type
2. #14578887	C₃	semidirect
3. #14578886	C₃	semidirect
5. C₉×C₃₁⋊C₉	C₃	semidirect
8. 3₋¹⁺²×C₃₁	C₉	semidirect
19. C₉×C₃₁	C₃×C₉	semidirect
23. C₃₁⋊C₉	3₋¹⁺²	direct (N × H)
35. C₃₁	C₉×3₋¹⁺²	semidirect
37. 3₋¹⁺²	C₃₁⋊C₉	direct (N × H)
52. C₉	C₃×C₃₁⋊C₉	semidirect

Subgroups — 3−1+2×C31⋊C9 #21419305

Conjugacy classes of subgroups

Complements

Subgroups — 3₋¹⁺²×C₃₁⋊C₉ #21419305