Subgroups — #36382957

Order 22599.

936 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21419438	C₃	1	2	yes	maximal
2	C₃×#14578911	C₃	1	1	yes	maximal, characteristic
3	#21419409	C₃	1	24	yes	maximal, complemented
4	C₃×#14578901	C₃	1	12	yes	maximal, complemented
5	C₃₁×3₋¹⁺⁴	C₃	1	1	yes	maximal, characteristic
6	#14578911	—	3	9	no	—
7	#14578911	—	3	18	no	—
8	C₃×#11719689	C₃²	1	24	yes	—
9	C₃×#11719689	C₃²	1	8	yes	—
10	C₃²×C₃₁⋊C₉	C₃²	1	4	yes	—
11	#14578901	C₃²	1	9	yes	—
12	#14578901	C₃²	1	72	yes	—
13	C₃₁×#737	—	3	9	no	—
14	C₃×3₋¹⁺²×C₃₁	C₃²	1	12	yes	—
15	C₃×H(3,𝔽₃)×C₃₁	C₃²	1	1	yes	characteristic
16	C₃³×C₃₁	C₃³	1	4	yes	—
17	3₋¹⁺²×C₃₁	—	3	24	no	—
18	3₋¹⁺²×C₃₁	C₃³	1	9	yes	—
19	H(3,𝔽₃)×C₃₁	H(3,𝔽₃)	1	9	yes	—
20	C₃×C₉×C₃₁	—	3	12	no	—
21	#11719689	—	3	48	no	—
22	#11719689	—	3	24	no	—
23	#11719689	C₃³	1	18	yes	—
24	C₃×C₃₁⋊C₉	—	3	12	no	—
25	C₃×C₃₁⋊C₉	—	3	24	no	—
26	C₃×C₃₁⋊C₉	C₃³	1	1	yes	characteristic
27	C₃×C₃₁⋊C₉	C₃³	1	8	yes	—
28	#10624933	—	31	1	no	maximal, Sylow
29	C₃²×C₃₁	—	9	4	no	—
30	C₃²×C₃₁	C₃×H(3,𝔽₃)	1	12	yes	—
31	C₃²×C₃₁	C₃⁴	1	1	yes	characteristic
32	C₉×C₃₁	—	3	9	no	—
33	C₃₁⋊C₉	—	3	1	no	—
34	C₃₁⋊C₉	—	3	18	no	—
35	C₃₁⋊C₉	—	3	8	no	—
36	3₋¹⁺⁴	—	31	2	no	—
37	3₋¹⁺⁴	C₃₁⋊C₃	1	1	yes	characteristic
38	C₃×#737	—	31	1	no	—
39	#6912	—	31	24	no	—
40	C₃×#733	—	31	12	no	—
41	C₃×C₃₁	—	3	1	no	—
42	C₃×C₃₁	—	3	12	no	—
43	C₃×C₃₁	C₃²×H(3,𝔽₃)	1	1	yes	characteristic
44	#737	—	3	9	no	—
45	#737	—	93	9	no	—
46	#737	—	93	18	no	—
47	C₃×3₋¹⁺²	—	31	8	no	—
48	C₃×3₋¹⁺²	—	31	24	no	—
49	C₃×3₋¹⁺²	C₃×C₃₁⋊C₃	1	12	yes	—
50	C₃×H(3,𝔽₃)	C₃×C₃₁⋊C₃	1	1	yes	characteristic
51	C₃²×C₉	—	31	4	no	—
52	#733	—	31	72	no	—
53	#733	—	31	9	no	—
54	C₃₁	#10624933	1	1	yes	characteristic, complemented, Sylow
55	C₃³	C₃²×C₃₁⋊C₃	1	4	yes	—
56	3₋¹⁺²	—	3	24	no	—
57	3₋¹⁺²	—	31	18	no	—
58	3₋¹⁺²	—	93	24	no	—
59	3₋¹⁺²	—	93	48	no	—
60	3₋¹⁺²	C₃²×C₃₁⋊C₃	1	9	yes	—
61	H(3,𝔽₃)	C₃²⋊(C₃₁⋊C₃)	1	9	yes	—
62	C₃×C₉	—	3	12	no	—
63	C₃×C₉	—	31	1	no	—
64	C₃×C₉	—	31	8	no	—
65	C₃×C₉	—	93	12	no	—
66	C₃×C₉	—	93	24	no	—
67	C₃²	—	9	4	no	—
68	C₃²	C₃×C₃²⋊(C₃₁⋊C₃)	1	12	yes	—
69	C₃²	C₃³×C₃₁⋊C₃	1	1	yes	characteristic
70	C₉	—	3	9	no	—
71	C₉	—	93	1	no	—
72	C₉	—	93	8	no	—
73	C₉	—	93	18	no	—
74	C₃	—	3	1	no	—
75	C₃	—	3	12	no	—
76	C₃	C₃²×C₃²⋊(C₃₁⋊C₃)	1	1	yes	characteristic

	subgroup	G/H
center	C₃	C₃²×C₃²⋊(C₃₁⋊C₃)
commutator, cosocle	C₃²×C₃₁	C₃⁴
Frattini	C₃²	C₃³×C₃₁⋊C₃
Fitting	C₃₁×3₋¹⁺⁴	C₃
socle	C₃×C₃₁	C₃²×H(3,𝔽₃)
prime radical	C₃×H(3,𝔽₃)×C₃₁	C₃²
hypercenter	3₋¹⁺⁴	C₃₁⋊C₃
hypocenter	C₃₁	#10624933
LCS	G ▷ C₃²×C₃₁ ▷ C₃×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₃ ◁ C₃×H(3,𝔽₃) ◁ 3₋¹⁺⁴

Complements

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

N	H ≅ G/N	type
3. #21419409	C₃	semidirect
4. C₃×#14578901	C₃	semidirect
54. C₃₁	#10624933	semidirect

Maximal subgroups

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

subgroup	index
#21419438	3
C₃×#14578911	3
#21419409	3
C₃×#14578901	3
C₃₁×3₋¹⁺⁴	3
#10624933	31