Subgroups — #14518221

Order 1944.

300 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11757761	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃⋊(D₉⋊A₄)	—	3	4	no	maximal
3	C₂²×C₉⋊D₉	C₃	1	1	yes	maximal, characteristic, complemented
4	#92314	—	4	1	no	maximal
5	C₃×C₉⋊A₄	D₃	1	4	yes	—
6	C₂²×C₉²	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂×C₉⋊D₉	—	3	1	no	—
8	C₂×C₉⋊D₉	—	3	1	no	—
9	C₉⋊(C₂²⋊C₉)	—	2	4	no	—
10	#6900	—	4	1	no	Sylow
11	A₄×C₃⋊D₃	—	9	1	no	—
12	C₂²×C₃⋊D₉	—	3	4	no	—
13	D₉⋊A₄	—	9	12	no	—
14	C₃⋊AGL(1,ℤ/9)	—	12	4	no	—
15	C₂×C₉²	—	3	1	no	—
16	C₉⋊D₉	—	3	1	no	—
17	C₉⋊D₉	A₄	1	1	yes	characteristic, complemented
18	C₃²×A₄	C₃⋊D₃	1	1	yes	characteristic
19	C₂²×C₃×C₉	C₃×D₃	1	4	yes	—
20	C₂×C₃⋊D₉	—	9	4	no	—
21	C₂×C₃⋊D₉	—	9	4	no	—
22	C₃×C₂²⋊C₉	—	2	4	no	—
23	C₉⋊A₄	—	3	12	no	—
24	C₃×3₋¹⁺²	—	4	4	no	—
25	C₉⋊C₉	—	8	4	no	—
26	C₉²	C₂×A₄	1	1	yes	characteristic, complemented
27	C₂²×C₃⋊D₃	—	9	1	no	—
28	D₃×A₄	—	27	4	no	—
29	C₂²×D₉	—	9	12	no	—
30	C₃×C₃⋊D₃	—	36	1	no	—
31	C₂×C₃×C₉	—	3	4	no	—
32	C₃⋊D₉	—	3	4	no	—
33	C₃⋊D₉	—	9	4	no	—
34	AGL(1,ℤ/9)	—	36	12	no	—
35	C₂²×C₃²	C₃×C₃⋊D₃	1	1	yes	characteristic
36	C₂×C₃⋊D₃	—	27	1	no	—
37	C₂×C₃⋊D₃	—	27	1	no	—
38	C₃×A₄	—	3	4	no	—
39	C₂²×C₉	AGL(1,ℤ/9)	1	12	yes	complemented
40	C₂×D₉	—	27	12	no	—
41	C₂×D₉	—	27	12	no	—
42	C₂²⋊C₉	—	6	4	no	—
43	C₃³	—	4	1	no	—
44	3₋¹⁺²	—	12	12	no	—
45	C₃×C₉	—	8	4	no	—
46	C₃×C₉	D₃×A₄	1	4	yes	—
47	C₂²×D₃	—	27	4	no	—
48	C₂×A₄	—	81	1	no	—
49	C₂×C₃²	—	3	1	no	—
50	C₃⋊D₃	—	9	1	no	—
51	C₃⋊D₃	—	27	1	no	—
52	C₃×D₃	—	108	4	no	—
53	C₂×C₉	—	3	12	no	—
54	D₉	—	9	12	no	—
55	D₉	—	27	12	no	—
56	C₂²×C₃	C₃⋊AGL(1,ℤ/9)	1	4	yes	—
57	C₂×D₃	—	81	4	no	—
58	C₂×D₃	—	81	4	no	—
59	A₄	—	9	1	no	—
60	C₃²	—	12	4	no	—
61	C₃²	A₄×C₃⋊D₃	1	1	yes	characteristic
62	C₉	—	24	4	no	—
63	C₉	D₉⋊A₄	1	12	yes	complemented
64	C₂³	—	81	1	no	Sylow
65	C₂×C₃	—	3	4	no	—
66	C₂×C₃	—	324	1	no	—
67	D₃	—	27	4	no	—
68	D₃	—	81	4	no	—
69	C₂²	—	243	1	no	—
70	C₂²	—	243	1	no	—
71	C₂²	#92314	1	1	yes	characteristic, complemented
72	C₃	—	36	1	no	—
73	C₃	C₃⋊(D₉⋊A₄)	1	4	yes	—
74	C₂	—	3	1	no	—
75	C₂	—	81	1	no	—
76	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. #11757761	C₂	semidirect
3. C₂²×C₉⋊D₉	C₃	semidirect
6. C₂²×C₉²	C₂×C₃	semidirect
17. C₉⋊D₉	A₄	semidirect
26. C₉²	C₂×A₄	semidirect
39. C₂²×C₉	AGL(1,ℤ/9)	semidirect
63. C₉	D₉⋊A₄	semidirect
71. C₂²	#92314	semidirect

Maximal subgroups

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

subgroup	index
#11757761	2
C₃⋊(D₉⋊A₄)	3
C₂²×C₉⋊D₉	3
#92314	4