Subgroups — C₃³×(C₂²⋊C₉)⋊C₂ #14519190

Order 1944.

894 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₂²⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃³×#67	—	3	1	no	maximal
3	C₃²×(C₂²⋊C₉)⋊C₂	C₃	1	13	yes	maximal, direct product factor
4	C₃³×D₉	—	4	1	no	maximal
5	C₂²×C₃⁴	D₃	1	1	yes	characteristic
6	C₂×C₃³×D₃	—	3	1	no	—
7	C₃³×Dic₃	—	3	1	no	—
8	C₃²×C₂²⋊C₉	—	2	13	no	—
9	C₃²×C₂²⋊C₉	C₂×C₃	1	13	yes	complemented
10	C₃³×C₉	—	4	1	no	Sylow
11	C₃³×D₄	—	9	1	no	—
12	C₃²×#67	—	3	13	no	—
13	C₃×(C₂²⋊C₉)⋊C₂	C₃²	1	13	yes	direct product factor
14	C₂×C₃⁴	—	3	1	no	—
15	C₃³×D₃	—	6	1	no	—
16	C₃²×D₉	—	4	13	no	—
17	C₂²×C₃³	—	2	13	no	—
18	C₂²×C₃³	—	9	1	no	—
19	C₂²×C₃³	D₉	1	1	yes	characteristic, complemented
20	C₂²×C₃³	C₃×D₃	1	13	yes	—
21	C₂×C₃²×D₃	—	3	13	no	—
22	C₃³×C₄	—	9	1	no	—
23	C₃²×Dic₃	—	3	13	no	—
24	C₃×C₂²⋊C₉	—	2	52	no	—
25	C₃×C₂²⋊C₉	C₂×C₃²	1	13	yes	complemented
26	C₃⁴	S₄	1	1	yes	characteristic
27	C₃²×C₉	—	4	13	no	—
28	C₃²×C₉	—	8	13	no	—
29	C₃²×D₄	—	9	13	no	—
30	C₃×#67	—	3	13	no	—
31	(C₂²⋊C₉)⋊C₂	C₃³	1	1	yes	characteristic, direct product factor
32	C₂×C₃³	—	3	1	no	—
33	C₂×C₃³	—	3	13	no	—
34	C₂×C₃³	—	6	13	no	—
35	C₂×C₃³	—	18	1	no	—
36	C₃²×D₃	—	6	13	no	—
37	C₃×D₉	—	4	13	no	—
38	C₂²×C₃²	—	2	52	no	—
39	C₂²×C₃²	—	9	13	no	—
40	C₂²×C₃²	C₃×D₉	1	13	yes	complemented
41	C₂²×C₃²	C₃²×D₃	1	13	yes	—
42	C₂×C₃×D₃	—	3	13	no	—
43	C₃²×C₄	—	9	13	no	—
44	C₃×Dic₃	—	3	13	no	—
45	C₂²⋊C₉	—	2	13	no	—
46	C₂²⋊C₉	C₂×C₃³	1	1	yes	characteristic, complemented
47	C₃³	—	2	13	no	—
48	C₃³	(C₂²⋊C₉)⋊C₂	1	1	yes	characteristic, direct product factor
49	C₃³	C₃×S₄	1	13	yes	—
50	C₃×C₉	—	4	13	no	—
51	C₃×C₉	—	8	52	no	—
52	C₃×D₄	—	9	13	no	—
53	#67	—	3	1	no	—
54	C₂×C₃²	—	3	13	no	—
55	C₂×C₃²	—	3	13	no	—
56	C₂×C₃²	—	6	52	no	—
57	C₂×C₃²	—	18	13	no	—
58	C₃×D₃	—	6	13	no	—
59	D₉	—	4	1	no	—
60	C₂²×C₃	—	2	13	no	—
61	C₂²×C₃	—	9	13	no	—
62	C₂²×C₃	C₃²×D₉	1	13	yes	complemented
63	C₂²×C₃	C₃³×D₃	1	1	yes	characteristic
64	C₂×D₃	—	3	1	no	—
65	C₃×C₄	—	9	13	no	—
66	Dic₃	—	3	1	no	—
67	C₃²	—	2	52	no	—
68	C₃²	C₃×(C₂²⋊C₉)⋊C₂	1	13	yes	direct product factor
69	C₃²	C₃²×S₄	1	13	yes	—
70	C₉	—	4	1	no	—
71	C₉	—	8	13	no	—
72	D₄	—	9	1	no	Sylow
73	C₂×C₃	—	3	1	no	—
74	C₂×C₃	—	3	13	no	—
75	C₂×C₃	—	6	13	no	—
76	C₂×C₃	—	18	13	no	—
77	D₃	—	6	1	no	—
78	C₂²	—	9	1	no	—
79	C₂²	C₃³×D₉	1	1	yes	characteristic, complemented
80	C₄	—	9	1	no	—
81	C₃	—	2	13	no	—
82	C₃	C₃²×(C₂²⋊C₉)⋊C₂	1	13	yes	direct product factor
83	C₃	C₃³×S₄	1	1	yes	characteristic
84	C₂	—	3	1	no	—
85	C₂	—	18	1	no	—

	subgroup	G/H
center, hypercenter	C₃³	(C₂²⋊C₉)⋊C₂
commutator, cosocle, hypocenter	C₂²⋊C₉	C₂×C₃³
Frattini	C₃	C₃³×S₄
Fitting, socle	C₂²×C₃⁴	D₃
LCS	G ▷ C₂²⋊C₉
UCS	C₁ ◁ C₃³

Complements

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

N	H ≅ G/N	type
1. C₃³×C₂²⋊C₉	C₂	semidirect
3. C₃²×(C₂²⋊C₉)⋊C₂	C₃	direct (N × H)
9. C₃²×C₂²⋊C₉	C₂×C₃	semidirect
13. C₃×(C₂²⋊C₉)⋊C₂	C₃²	direct (N × H)
19. C₂²×C₃³	D₉	semidirect
25. C₃×C₂²⋊C₉	C₂×C₃²	semidirect
31. (C₂²⋊C₉)⋊C₂	C₃³	direct (N × H)
40. C₂²×C₃²	C₃×D₉	semidirect
46. C₂²⋊C₉	C₂×C₃³	semidirect
48. C₃³	(C₂²⋊C₉)⋊C₂	direct (N × H)
62. C₂²×C₃	C₃²×D₉	semidirect
68. C₃²	C₃×(C₂²⋊C₉)⋊C₂	direct (N × H)
79. C₂²	C₃³×D₉	semidirect
82. C₃	C₃²×(C₂²⋊C₉)⋊C₂	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃³×C₂²⋊C₉	2
C₃³×#67	3
C₃²×(C₂²⋊C₉)⋊C₂	3
C₃³×D₉	4

Subgroups — C33×(C22⋊C9)⋊C2 #14519190

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃³×(C₂²⋊C₉)⋊C₂ #14519190