Subgroups — #14516342

Order 1944.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#6896	C₂	1	1	yes	maximal, characteristic
2	C₃⋊(3₋¹⁺²⋊C₈)	—	3	2	no	maximal
3	C₉⋊(C₉⋊C₈)	C₃	1	1	yes	maximal, characteristic, complemented
4	#10619495	—	3	2	no	maximal
5	C₂×#6896	C₄	1	1	yes	characteristic
6	C₃×C₄×3₋¹⁺²	D₃	1	2	yes	—
7	C₄×C₉⋊C₉	—	2	2	no	—
8	C₄×C₉⋊C₉	—	2	2	no	—
9	C₄×C₃²⋊C₉	D₃	1	2	yes	—
10	C₄×C₉²	C₂×C₃	1	1	yes	characteristic
11	#6896	C₈	1	1	yes	characteristic, complemented, Sylow
12	C₃×C₃⋊(C₃⋊C₈)	—	9	1	no	—
13	C₃⋊(C₉⋊C₈)	—	3	2	no	—
14	C₃⋊(C₉⋊C₈)	—	3	2	no	—
15	3₋¹⁺²⋊C₈	—	9	6	no	—
16	C₂×C₃×3₋¹⁺²	Dic₃	1	2	yes	—
17	C₂×C₉⋊C₉	—	2	2	no	—
18	C₂×C₉⋊C₉	—	2	2	no	—
19	C₂×C₃²⋊C₉	Dic₃	1	2	yes	—
20	C₂×C₉²	C₃×C₄	1	1	yes	characteristic
21	C₃³×C₄	C₃⋊D₃	1	1	yes	characteristic
22	C₄×3₋¹⁺²	—	3	6	no	—
23	C₃×C₄×C₉	—	2	2	no	—
24	C₃×C₄×C₉	—	2	2	no	—
25	C₃×C₄×C₉	C₃×D₃	1	2	yes	—
26	C₃×C₄×C₉	C₃×D₃	1	2	yes	—
27	C₃×3₋¹⁺²	C₃⋊C₈	1	2	yes	—
28	C₉⋊C₉	—	2	2	no	—
29	C₉⋊C₉	—	2	2	no	—
30	C₃²⋊C₉	C₃⋊C₈	1	2	yes	—
31	C₉²	C₃×C₈	1	1	yes	characteristic, complemented
32	C₃⋊(C₃⋊C₈)	—	9	1	no	—
33	C₃×C₃⋊C₈	—	27	2	no	—
34	C₃×C₃⋊C₈	—	27	2	no	—
35	C₉⋊C₈	—	9	6	no	—
36	C₉⋊C₈	—	27	2	no	—
37	C₂×C₃³	C₃⋊Dic₃	1	1	yes	characteristic
38	C₂×3₋¹⁺²	—	3	6	no	—
39	C₂×C₃×C₉	—	2	2	no	—
40	C₂×C₃×C₉	—	2	2	no	—
41	C₂×C₃×C₉	C₃×Dic₃	1	2	yes	—
42	C₂×C₃×C₉	C₃×Dic₃	1	2	yes	—
43	C₃²×C₄	—	3	2	no	—
44	C₃²×C₄	—	3	2	no	—
45	C₃²×C₄	C₃×C₃⋊D₃	1	1	yes	characteristic
46	C₄×C₉	—	3	2	no	—
47	C₄×C₉	—	6	2	no	—
48	C₄×C₉	—	6	2	no	—
49	C₄×C₉	AGL(1,ℤ/9)	1	6	yes	—
50	C₃³	C₃⋊(C₃⋊C₈)	1	1	yes	characteristic
51	3₋¹⁺²	—	3	6	no	—
52	C₃×C₉	—	2	2	no	—
53	C₃×C₉	—	2	2	no	—
54	C₃×C₉	C₃×C₃⋊C₈	1	2	yes	—
55	C₃×C₉	C₃×C₃⋊C₈	1	2	yes	—
56	C₃×C₈	—	81	1	no	—
57	C₃⋊C₈	—	27	2	no	—
58	C₃⋊C₈	—	27	2	no	—
59	C₂×C₃²	—	3	2	no	—
60	C₂×C₃²	—	3	2	no	—
61	C₂×C₃²	C₃×C₃⋊Dic₃	1	1	yes	characteristic
62	C₂×C₉	—	3	2	no	—
63	C₂×C₉	—	6	2	no	—
64	C₂×C₉	—	6	2	no	—
65	C₂×C₉	3₋¹⁺²⋊C₄	1	6	yes	—
66	C₃×C₄	—	9	1	no	—
67	C₃×C₄	C₃⋊AGL(1,ℤ/9)	1	2	yes	—
68	C₃×C₄	#4207	1	2	yes	—
69	C₃²	—	3	2	no	—
70	C₃²	—	3	2	no	—
71	C₃²	C₃×C₃⋊(C₃⋊C₈)	1	1	yes	characteristic
72	C₉	—	3	2	no	—
73	C₉	—	6	2	no	—
74	C₉	—	6	2	no	—
75	C₉	3₋¹⁺²⋊C₈	1	6	yes	complemented
76	C₈	—	81	1	no	Sylow
77	C₂×C₃	—	9	1	no	—
78	C₂×C₃	C₃⋊(3₋¹⁺²⋊C₄)	1	2	yes	—
79	C₂×C₃	#66409	1	2	yes	—
80	C₄	#92309	1	1	yes	characteristic
81	C₃	—	9	1	no	—
82	C₃	C₃⋊(3₋¹⁺²⋊C₈)	1	2	yes	—
83	C₃	#10619724	1	2	yes	—
84	C₂	#11757613	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄	#92309
commutator, hypocenter	C₉²	C₃×C₈
Frattini	C₃²×C₄	C₃×C₃⋊D₃
Fitting	C₄×#6896	C₂
socle	C₂×C₃²	C₃×C₃⋊Dic₃
prime radical	C₂×C₃³	C₃⋊Dic₃
cosocle	C₄×C₉²	C₂×C₃
LCS	G ▷ C₉²
UCS	C₁ ◁ C₄

Complements

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

N	H ≅ G/N	type
3. C₉⋊(C₉⋊C₈)	C₃	semidirect
11. #6896	C₈	semidirect
31. C₉²	C₃×C₈	semidirect
75. C₉	3₋¹⁺²⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
C₄×#6896	2
C₃⋊(3₋¹⁺²⋊C₈)	3
C₉⋊(C₉⋊C₈)	3
#10619495	3