Subgroups — #36345110

Order 21780.

156 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊(C₃⋊#11925893)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₃⋊#11925890	C₂	1	2	yes	maximal, complemented
3	#11925890⋊D₃	—	3	2	no	maximal
4	C₃²×#10597245	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₃₃²	—	5	1	no	maximal, Hall
6	C₃⋊#11925890	D₃	1	2	yes	complemented
7	C₃⋊#11925893	—	3	2	no	—
8	C₃⋊#11925893	—	6	1	no	—
9	C₃×#11925890	—	3	2	no	—
10	#11925890⋊C₂	—	9	1	no	Hall
11	C₃⋊(C₃⋊(C₁₁⋊D₁₁))	D₅	1	1	yes	characteristic, complemented
12	C₃×C₁₁×D₃₃	—	5	2	no	—
13	C₃×#10597245	—	2	1	no	—
14	C₃×#10597245	C₂×D₃	1	2	yes	complemented
15	D₁₁×D₃₃	—	15	2	no	—
16	#11925893	—	9	1	no	—
17	#11925890	—	3	2	no	—
18	C₃²×C₁₁²	C₂×D₅	1	1	yes	characteristic, complemented, Hall
19	C₃⋊(C₃⋊AGL(1,𝔽₁₁))	—	22	1	no	—
20	C₃⋊(C₁₁⋊D₁₁)	—	3	2	no	—
21	C₃⋊(C₁₁⋊D₁₁)	—	6	1	no	—
22	C₁₁×D₃₃	—	5	2	no	—
23	C₃×C₁₁×D₁₁	—	15	2	no	—
24	#10597245	D₃²	1	1	yes	characteristic, complemented, Hall
25	C₃²×C₁₁⋊C₅	—	22	1	no	—
26	D₁₁²	—	45	1	no	Hall
27	D₃×D₃₃	—	55	2	no	—
28	C₃×C₁₁²	—	2	1	no	—
29	C₃×C₁₁²	D₃×D₅	1	2	yes	complemented
30	C₃⋊AGL(1,𝔽₁₁)	—	66	2	no	—
31	C₃⋊AGL(1,𝔽₁₁)	—	66	2	no	—
32	C₁₁⋊D₁₁	—	9	1	no	—
33	C₁₁×D₁₁	—	15	2	no	—
34	C₃⋊D₃₃	—	22	1	no	—
35	C₃⋊D₃₃	—	55	2	no	—
36	C₃×D₃₃	—	5	2	no	—
37	C₃×D₃×C₁₁	—	55	2	no	—
38	(C₃⋊D₃)⋊D₅	—	121	1	no	maximal, Hall
39	C₃×C₁₁⋊C₅	—	22	2	no	—
40	C₃×C₁₁⋊C₅	—	22	2	no	—
41	C₂×D₃₃	—	165	2	no	—
42	D₃×D₁₁	—	165	2	no	—
43	C₁₁²	(C₃⋊D₃)⋊D₅	1	1	yes	characteristic, complemented, Sylow
44	AGL(1,𝔽₁₁)	—	198	1	no	—
45	C₃²×C₁₁	—	2	1	no	—
46	C₃²×C₁₁	—	5	2	no	—
47	C₅×C₃⋊D₃	—	121	1	no	—
48	C₃×D₁₅	—	121	2	no	—
49	C₂×C₃×C₁₁	—	165	2	no	—
50	D₃₃	—	5	2	no	—
51	D₃₃	—	66	2	no	—
52	D₃₃	—	66	2	no	—
53	D₃₃	—	330	2	no	—
54	D₃₃	—	165	2	no	—
55	D₃₃	—	165	2	no	—
56	C₃×D₁₁	—	15	2	no	—
57	D₃×C₁₁	—	55	2	no	—
58	D₃×D₅	—	363	2	no	—
59	C₁₁⋊C₅	—	22	1	no	—
60	C₃²×C₅	—	121	1	no	Hall
61	C₂×D₁₁	—	495	2	no	—
62	D₃²	—	605	1	no	Hall
63	C₃×C₁₁	—	2	2	no	—
64	C₃×C₁₁	—	2	2	no	—
65	C₃×C₁₁	—	5	2	no	—
66	C₃×C₁₁	—	5	2	no	—
67	C₃×C₁₁	—	10	2	no	—
68	D₁₅	—	121	2	no	—
69	C₃×D₅	—	363	2	no	—
70	C₅×D₃	—	363	2	no	—
71	C₅×D₃	—	726	1	no	—
72	C₂×C₁₁	—	165	2	no	—
73	D₁₁	—	15	2	no	—
74	D₁₁	—	198	1	no	—
75	D₁₁	—	495	2	no	—
76	C₂×D₅	—	1089	1	no	Hall
77	C₃⋊D₃	—	121	1	no	—
78	C₃×D₃	—	55	2	no	—
79	C₃×C₅	—	121	2	no	—
80	C₃×C₅	—	242	1	no	—
81	C₂×D₃	—	1815	2	no	—
82	C₁₁	—	2	1	no	—
83	C₁₁	—	5	2	no	—
84	C₂×C₅	—	1089	1	no	—
85	D₅	—	363	2	no	—
86	C₃²	#11925890⋊C₂	1	1	yes	characteristic, complemented, Sylow
87	C₂×C₃	—	165	2	no	—
88	D₃	—	55	2	no	—
89	D₃	—	363	2	no	—
90	D₃	—	726	1	no	—
91	C₅	—	121	1	no	Sylow
92	C₂²	—	5445	1	no	Sylow
93	C₃	—	2	1	no	—
94	C₃	#11925890⋊D₃	1	2	yes	complemented
95	C₂	—	1089	1	no	—
96	C₂	—	165	2	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₃²×#10597245	C₂²
Fitting, socle	C₃²×C₁₁²	C₂×D₅
LCS	G ▷ C₃²×#10597245
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃⋊(C₃⋊#11925893)	C₂	semidirect
2. C₃×C₃⋊#11925890	C₂	semidirect
4. C₃²×#10597245	C₂²	semidirect
6. C₃⋊#11925890	D₃	semidirect
11. C₃⋊(C₃⋊(C₁₁⋊D₁₁))	D₅	semidirect
14. C₃×#10597245	C₂×D₃	semidirect
18. C₃²×C₁₁²	C₂×D₅	semidirect
24. #10597245	D₃²	semidirect
29. C₃×C₁₁²	D₃×D₅	semidirect
43. C₁₁²	(C₃⋊D₃)⋊D₅	semidirect
86. C₃²	#11925890⋊C₂	semidirect
94. C₃	#11925890⋊D₃	semidirect

Maximal subgroups

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

subgroup	index
C₃⋊(C₃⋊#11925893)	2
C₃×C₃⋊#11925890	2
#11925890⋊D₃	3
D₃₃²	5
(C₃⋊D₃)⋊D₅	121