Subgroups — #14518224

Order 1944.

220 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11757764	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₉⋊D₉	C₃	1	1	yes	maximal, characteristic, complemented
3	#10619770	—	3	4	no	maximal
4	#92312	—	4	1	no	maximal
5	C₂²×C₉²	C₂×C₃	1	1	yes	characteristic, complemented
6	C₂×C₉⋊D₉	—	3	1	no	—
7	C₂×C₉⋊D₉	—	3	1	no	—
8	(C₃×A₄)⋊C₉	D₃	1	4	yes	—
9	(C₂²⋊C₉)⋊C₉	—	2	4	no	—
10	#6898	—	4	1	no	Sylow
11	A₄×C₃⋊D₃	—	9	1	no	—
12	C₂²×C₃⋊D₉	—	3	4	no	—
13	C₂×C₉²	—	3	1	no	—
14	C₉⋊D₉	—	3	1	no	—
15	C₉⋊D₉	A₄	1	1	yes	characteristic, complemented
16	#4169	—	12	4	no	—
17	C₃²×A₄	C₃⋊D₃	1	1	yes	characteristic
18	C₂²×C₃×C₉	C₃×D₃	1	4	yes	—
19	C₂×C₃⋊D₉	—	9	4	no	—
20	C₂×C₃⋊D₉	—	9	4	no	—
21	C₃×C₂²⋊C₉	—	2	4	no	—
22	C₉⋊C₉	—	8	4	no	—
23	C₃²⋊C₉	—	4	4	no	—
24	C₉²	C₂×A₄	1	1	yes	characteristic, complemented
25	C₂²×C₃⋊D₃	—	9	1	no	—
26	D₃×A₄	—	27	4	no	—
27	C₂²×D₉	—	27	4	no	—
28	C₃×C₃⋊D₃	—	36	1	no	—
29	C₂×C₃×C₉	—	3	4	no	—
30	C₃⋊D₉	—	3	4	no	—
31	C₃⋊D₉	—	9	4	no	—
32	C₂²×C₃²	C₃×C₃⋊D₃	1	1	yes	characteristic
33	C₂×C₃⋊D₃	—	27	1	no	—
34	C₂×C₃⋊D₃	—	27	1	no	—
35	C₃×A₄	—	3	4	no	—
36	C₂²×C₉	—	3	4	no	—
37	C₂×D₉	—	27	12	no	—
38	C₂×D₉	—	27	12	no	—
39	C₂²⋊C₉	—	6	4	no	—
40	C₃³	—	4	1	no	—
41	C₃×C₉	—	8	4	no	—
42	C₃×C₉	D₃×A₄	1	4	yes	—
43	C₂²×D₃	—	27	4	no	—
44	C₂×A₄	—	81	1	no	—
45	C₂×C₃²	—	3	1	no	—
46	C₃⋊D₃	—	9	1	no	—
47	C₃⋊D₃	—	27	1	no	—
48	C₃×D₃	—	108	4	no	—
49	C₂×C₉	—	3	12	no	—
50	D₉	—	27	4	no	—
51	D₉	—	27	12	no	—
52	C₂²×C₃	#4207	1	4	yes	—
53	C₂×D₃	—	81	4	no	—
54	C₂×D₃	—	81	4	no	—
55	A₄	—	9	1	no	—
56	C₃²	—	12	4	no	—
57	C₃²	A₄×C₃⋊D₃	1	1	yes	characteristic
58	C₉	—	3	4	no	—
59	C₉	—	24	4	no	—
60	C₂³	—	81	1	no	Sylow
61	C₂×C₃	—	3	4	no	—
62	C₂×C₃	—	324	1	no	—
63	D₃	—	27	4	no	—
64	D₃	—	81	4	no	—
65	C₂²	—	243	1	no	—
66	C₂²	—	243	1	no	—
67	C₂²	#92312	1	1	yes	characteristic, complemented
68	C₃	—	36	1	no	—
69	C₃	#10620070	1	4	yes	—
70	C₂	—	3	1	no	—
71	C₂	—	81	1	no	—
72	C₂	—	243	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₂²×C₉²	C₂×C₃
Frattini	C₃²	A₄×C₃⋊D₃
socle	C₂²×C₃²	C₃×C₃⋊D₃
LCS	G ▷ C₂²×C₉²
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. #11757764	C₂	semidirect
2. C₂²×C₉⋊D₉	C₃	semidirect
5. C₂²×C₉²	C₂×C₃	semidirect
15. C₉⋊D₉	A₄	semidirect
24. C₉²	C₂×A₄	semidirect
67. C₂²	#92312	semidirect

Maximal subgroups

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

subgroup	index
#11757764	2
C₂²×C₉⋊D₉	3
#10619770	3
#92312	4