Subgroups — C₄⋊#92314 #14517564

Order 1944.

404 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#92314	C₂	1	2	yes	maximal, complemented
2	C₄×#6900	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄⋊(C₃⋊AGL(1,ℤ/9))	—	3	4	no	maximal
4	C₄⋊(C₉⋊D₉)	C₃	1	1	yes	maximal, characteristic, complemented
5	C₂×#6900	C₂²	1	1	yes	characteristic
6	#92314	—	2	2	no	—
7	C₂×C₃⋊AGL(1,ℤ/9)	—	3	8	no	—
8	C₃×C₄×3₋¹⁺²	D₃	1	4	yes	—
9	C₂×C₉⋊D₉	C₂×C₃	1	2	yes	complemented
10	C₄×C₉⋊C₉	—	2	4	no	—
11	C₄×C₉²	C₂×C₃	1	1	yes	characteristic, complemented
12	#6900	D₄	1	1	yes	characteristic, complemented, Sylow
13	C₃×C₄⋊(C₃⋊D₃)	—	9	1	no	—
14	C₄⋊(C₃⋊D₉)	—	3	4	no	—
15	C₄⋊AGL(1,ℤ/9)	—	9	12	no	—
16	C₂×C₃×3₋¹⁺²	C₂×D₃	1	4	yes	—
17	C₃⋊AGL(1,ℤ/9)	—	6	8	no	—
18	C₂×C₉⋊C₉	—	2	4	no	—
19	C₂×C₉²	C₂²×C₃	1	1	yes	characteristic
20	C₉⋊D₉	—	2	2	no	—
21	C₂×C₃×C₃⋊D₃	—	9	2	no	—
22	C₃³×C₄	C₃⋊D₃	1	1	yes	characteristic
23	C₂×C₃⋊D₉	—	3	8	no	—
24	C₂×AGL(1,ℤ/9)	—	9	24	no	—
25	C₄×3₋¹⁺²	—	3	12	no	—
26	C₃×C₄×C₉	—	2	4	no	—
27	C₃×C₄×C₉	C₃×D₃	1	4	yes	—
28	C₃×3₋¹⁺²	D₁₂	1	4	yes	—
29	C₉⋊C₉	—	2	4	no	—
30	C₉²	C₃×D₄	1	1	yes	characteristic, complemented
31	C₄⋊(C₃⋊D₃)	—	9	1	no	—
32	C₃×D₁₂	—	27	4	no	—
33	D₃₆	—	9	12	no	—
34	C₂×C₃³	C₂×C₃⋊D₃	1	1	yes	characteristic
35	C₃×C₃⋊D₃	—	18	2	no	—
36	C₂×3₋¹⁺²	—	3	12	no	—
37	C₂×C₃×C₉	—	2	4	no	—
38	C₂×C₃×C₉	C₂×C₃×D₃	1	4	yes	—
39	C₃⋊D₉	—	6	8	no	—
40	AGL(1,ℤ/9)	—	18	24	no	—
41	C₂×C₃⋊D₃	—	9	2	no	—
42	C₂×C₃×D₃	—	27	8	no	—
43	C₃²×C₄	—	3	4	no	—
44	C₃²×C₄	C₃×C₃⋊D₃	1	1	yes	characteristic
45	C₂×D₉	—	9	24	no	—
46	C₄×C₉	—	6	4	no	—
47	C₄×C₉	AGL(1,ℤ/9)	1	12	yes	complemented
48	C₃³	C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
49	3₋¹⁺²	—	3	12	no	—
50	C₃×C₉	—	2	4	no	—
51	C₃×C₉	C₃×D₁₂	1	4	yes	—
52	C₃×D₄	—	81	1	no	—
53	D₁₂	—	27	4	no	—
54	C₂×C₃²	—	3	4	no	—
55	C₂×C₃²	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
56	C₃⋊D₃	—	18	2	no	—
57	C₃×D₃	—	54	8	no	—
58	C₂×C₉	—	6	4	no	—
59	C₂×C₉	C₂×AGL(1,ℤ/9)	1	12	yes	—
60	D₉	—	18	24	no	—
61	C₂²×C₃	—	81	2	no	—
62	C₂×D₃	—	27	8	no	—
63	C₃×C₄	—	9	1	no	—
64	C₃×C₄	C₃⋊AGL(1,ℤ/9)	1	4	yes	—
65	C₃²	—	3	4	no	—
66	C₃²	C₃×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
67	C₉	—	6	4	no	—
68	C₉	C₄⋊AGL(1,ℤ/9)	1	12	yes	complemented
69	D₄	—	81	1	no	Sylow
70	C₂×C₃	—	9	1	no	—
71	C₂×C₃	—	162	2	no	—
72	C₂×C₃	C₂×C₃⋊AGL(1,ℤ/9)	1	4	yes	—
73	D₃	—	54	8	no	—
74	C₂²	—	81	2	no	—
75	C₄	#92314	1	1	yes	characteristic, complemented
76	C₃	—	9	1	no	—
77	C₃	C₄⋊(C₃⋊AGL(1,ℤ/9))	1	4	yes	—
78	C₂	—	162	2	no	—
79	C₂	C₂×#92314	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×#92314
commutator, cosocle	C₂×C₉²	C₂²×C₃
Frattini, socle	C₂×C₃²	C₂×C₃×C₃⋊D₃
Fitting	C₄×#6900	C₂
hypercenter	C₄	#92314
hypocenter	C₉²	C₃×D₄
LCS	G ▷ C₂×C₉² ▷ C₉²
UCS	C₁ ◁ C₂ ◁ C₄

Complements

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

N	H ≅ G/N	type
1. C₂×#92314	C₂	semidirect
2. C₄×#6900	C₂	semidirect
4. C₄⋊(C₉⋊D₉)	C₃	semidirect
9. C₂×C₉⋊D₉	C₂×C₃	semidirect
11. C₄×C₉²	C₂×C₃	semidirect
12. #6900	D₄	semidirect
30. C₉²	C₃×D₄	semidirect
47. C₄×C₉	AGL(1,ℤ/9)	semidirect
68. C₉	C₄⋊AGL(1,ℤ/9)	semidirect
75. C₄	#92314	semidirect

Maximal subgroups

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

subgroup	index
C₂×#92314	2
C₄×#6900	2
C₄⋊(C₃⋊AGL(1,ℤ/9))	3
C₄⋊(C₉⋊D₉)	3

Subgroups — C4⋊#92314 #14517564

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄⋊#92314 #14517564