Subgroups — #14517719

Order 1944.

756 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×C₉²	C₂	1	1	yes	maximal, characteristic
2	C₃⋊(C₉⋊Dic₉)	C₂	1	2	yes	maximal
3	#10619985	—	3	4	no	maximal
4	#10619651	—	3	9	no	maximal
5	C₂×C₃×C₉²	C₂²	1	1	yes	characteristic
6	C₃²×C₄×C₉	D₃	1	4	yes	—
7	C₃⋊(C₃⋊Dic₉)	—	3	8	no	—
8	C₄×C₉²	D₃	1	9	yes	—
9	C₉⋊Dic₉	—	3	18	no	—
10	C₃×C₉²	Q₈	1	1	yes	characteristic, complemented, Sylow
11	#6308	—	9	1	no	—
12	#6226	—	9	36	no	—
13	#6226	—	9	12	no	—
14	C₂×C₃²×C₉	C₂×D₃	1	4	yes	—
15	C₂×C₉²	C₂×D₃	1	9	yes	—
16	C₃³×C₄	C₃⋊D₃	1	1	yes	characteristic
17	C₃⋊(C₃⋊Dic₃)	—	9	2	no	—
18	C₃×C₄×C₉	D₉	1	36	yes	—
19	C₃×C₄×C₉	C₃⋊D₃	1	12	yes	—
20	C₃⋊Dic₉	—	9	72	no	—
21	C₃⋊Dic₉	—	9	24	no	—
22	C₃²×C₉	Dic₆	1	4	yes	—
23	C₉²	Dic₆	1	9	yes	complemented
24	#634	—	27	12	no	—
25	#634	—	27	1	no	—
26	Dic₁₈	—	27	36	no	—
27	C₂×C₃³	C₂×C₃⋊D₃	1	1	yes	characteristic
28	C₂×C₃×C₉	C₂×D₉	1	36	yes	—
29	C₂×C₃×C₉	C₂×C₃⋊D₃	1	12	yes	—
30	C₃²×C₄	C₃⋊D₉	1	12	yes	—
31	C₃²×C₄	C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
32	C₃⋊Dic₃	—	27	24	no	—
33	C₃⋊Dic₃	—	27	2	no	—
34	C₄×C₉	C₃⋊D₉	1	36	yes	—
35	Dic₉	—	27	72	no	—
36	C₃³	#634	1	1	yes	characteristic
37	C₃×C₉	Dic₁₈	1	36	yes	complemented
38	C₃×C₉	#634	1	12	yes	—
39	Dic₆	—	81	9	no	—
40	Dic₆	—	81	4	no	—
41	C₂×C₃²	C₂×C₃⋊D₉	1	12	yes	—
42	C₂×C₃²	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
43	C₂×C₉	C₂×C₃⋊D₉	1	36	yes	—
44	C₃×C₄	C₉⋊D₉	1	9	yes	—
45	C₃×C₄	C₃⋊(C₃⋊D₉)	1	4	yes	—
46	Dic₃	—	81	18	no	—
47	Dic₃	—	81	8	no	—
48	C₃²	#6226	1	12	yes	—
49	C₃²	#6308	1	1	yes	characteristic
50	C₉	#6226	1	36	yes	complemented
51	Q₈	—	243	1	no	Sylow
52	C₂×C₃	C₂×C₉⋊D₉	1	9	yes	—
53	C₂×C₃	C₂×C₃⋊(C₃⋊D₉)	1	4	yes	—
54	C₄	—	243	2	no	—
55	C₄	C₃⋊(C₉⋊D₉)	1	1	yes	characteristic
56	C₃	#10619651	1	9	yes	complemented
57	C₃	#10619985	1	4	yes	—
58	C₂	C₂×C₃⋊(C₉⋊D₉)	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×C₃⋊(C₉⋊D₉)
commutator, cosocle	C₂×C₃×C₉²	C₂²
Frattini	C₂×C₃²	C₂×C₃⋊(C₃⋊D₃)
Fitting	C₃×C₄×C₉²	C₂
socle, prime radical	C₂×C₃³	C₂×C₃⋊D₃
hypercenter	C₄	C₃⋊(C₉⋊D₉)
hypocenter	C₃×C₉²	Q₈
LCS	G ▷ C₂×C₃×C₉² ▷ C₃×C₉²
UCS	C₁ ◁ C₂ ◁ C₄

Complements

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

N	H ≅ G/N	type
10. C₃×C₉²	Q₈	semidirect
23. C₉²	Dic₆	semidirect
37. C₃×C₉	Dic₁₈	semidirect
50. C₉	#6226	semidirect
56. C₃	#10619651	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄×C₉²	2
C₃⋊(C₉⋊Dic₉)	2
#10619985	3
#10619651	3