Subgroups — #36345073

Order 21780.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₃×#10597244	C₂	1	1	yes	maximal, characteristic
2	C₃²×#10597244	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₁×C₁₁⋊#157	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	D₃×#10597244	—	6	2	no	—
5	#14559056	—	9	1	no	maximal, Hall
6	C₁₁²×C₃⋊D₃	C₂×C₅	1	1	yes	characteristic
7	(C₁₁⋊C₅)⋊#157	—	11	1	no	maximal
8	#157×C₁₁⋊C₅	—	11	1	no	maximal
9	C₃×#10597244	—	2	2	no	—
10	C₂×#10597244	—	9	1	no	—
11	C₃²×C₁₁²	C₄×C₅	1	1	yes	characteristic, complemented, Hall
12	C₃⋊D₃×C₁₁⋊C₅	—	11	1	no	—
13	C₃⋊D₃×C₁₁⋊C₅	—	11	1	no	—
14	D₃×C₁₁²	—	6	2	no	—
15	#10597244	#157	1	1	yes	characteristic, complemented, Hall
16	C₃²×C₁₁⋊C₅	—	11	1	no	—
17	C₃²×C₁₁⋊C₅	—	11	1	no	—
18	C₁₁×Dic₁₁	—	9	1	no	Hall
19	C₁₁⋊#157	C₁₁⋊C₅	1	1	yes	characteristic, complemented
20	C₁₁×#157	—	11	1	no	—
21	C₃×C₁₁²	—	2	2	no	—
22	D₃×C₁₁⋊C₅	—	66	2	no	—
23	D₃×C₁₁⋊C₅	—	66	2	no	—
24	C₂×C₁₁²	—	9	1	no	—
25	C₄×C₁₁⋊C₅	—	99	1	no	—
26	Dic₁₁⋊C₅	—	99	1	no	—
27	C₁₁×C₃⋊D₃	—	10	1	no	—
28	C₁₁×C₃⋊D₃	AGL(1,𝔽₁₁)	1	1	yes	characteristic
29	C₁₁×C₃⋊D₃	C₂×C₁₁⋊C₅	1	1	yes	characteristic
30	C₅×#157	—	121	1	no	Hall
31	C₃×C₁₁⋊C₅	—	22	2	no	—
32	C₃×C₁₁⋊C₅	—	22	2	no	—
33	C₁₁²	C₅×#157	1	1	yes	characteristic, complemented, Sylow
34	C₂×C₁₁⋊C₅	—	99	1	no	—
35	C₂×C₁₁⋊C₅	—	99	1	no	—
36	C₃²×C₁₁	—	10	1	no	—
37	C₃²×C₁₁	Dic₁₁⋊C₅	1	1	yes	characteristic, complemented
38	C₃²×C₁₁	C₄×C₁₁⋊C₅	1	1	yes	characteristic, complemented
39	C₅×C₃⋊D₃	—	121	1	no	—
40	D₃×C₁₁	—	6	2	no	—
41	D₃×C₁₁	—	6	2	no	—
42	D₃×C₁₁	—	30	4	no	—
43	C₁₁⋊C₅	—	11	1	no	—
44	C₁₁⋊C₅	—	11	1	no	—
45	C₃²×C₅	—	121	1	no	Hall
46	C₄×C₁₁	—	99	1	no	—
47	Dic₁₁	—	9	1	no	—
48	#157	—	11	1	no	Hall
49	C₃×C₁₁	—	2	2	no	—
50	C₃×C₁₁	—	2	2	no	—
51	C₃×C₁₁	—	10	4	no	—
52	C₅×D₃	—	726	2	no	—
53	C₂×C₁₁	—	9	1	no	—
54	C₂×C₁₁	—	9	1	no	—
55	C₂×C₁₁	—	90	1	no	—
56	C₄×C₅	—	1089	1	no	Hall
57	C₃⋊D₃	#11925897	1	1	yes	characteristic
58	C₃×C₅	—	242	2	no	—
59	C₁₁	—	10	1	no	—
60	C₁₁	#157×C₁₁⋊C₅	1	1	yes	characteristic, complemented
61	C₁₁	(C₁₁⋊C₅)⋊#157	1	1	yes	characteristic, complemented
62	C₂×C₅	—	1089	1	no	—
63	C₃²	#14559056	1	1	yes	characteristic, complemented, Sylow
64	D₃	—	6	2	no	—
65	C₅	—	121	1	no	Sylow
66	C₄	—	99	1	no	Sylow
67	C₃	—	2	2	no	—
68	C₂	—	9	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₁₁²	C₄×C₅
prime radical	C₃⋊D₃×#10597244	C₂
cosocle	C₁₁²×C₃⋊D₃	C₂×C₅
LCS	G ▷ C₃²×C₁₁²
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. C₃²×#10597244	C₄	semidirect
3. C₁₁×C₁₁⋊#157	C₅	semidirect
11. C₃²×C₁₁²	C₄×C₅	semidirect
15. #10597244	#157	semidirect
19. C₁₁⋊#157	C₁₁⋊C₅	semidirect
33. C₁₁²	C₅×#157	semidirect
37. C₃²×C₁₁	Dic₁₁⋊C₅	semidirect
38. C₃²×C₁₁	C₄×C₁₁⋊C₅	semidirect
60. C₁₁	#157×C₁₁⋊C₅	semidirect
61. C₁₁	(C₁₁⋊C₅)⋊#157	semidirect
63. C₃²	#14559056	semidirect

Maximal subgroups

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

subgroup	index
C₃⋊D₃×#10597244	2
C₁₁×C₁₁⋊#157	5
#14559056	9
(C₁₁⋊C₅)⋊#157	11
#157×C₁₁⋊C₅	11