Subgroups — C₂×#11757618 #14517677

Order 1944.

428 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#6900	C₂	1	1	yes	maximal, characteristic
2	#11757618	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃⋊(3₋¹⁺²⋊C₄)	—	3	4	no	maximal
4	C₂×C₉⋊Dic₉	C₃	1	1	yes	maximal, characteristic, complemented
5	C₂×#6900	C₄	1	2	yes	complemented
6	C₂×#6900	C₂²	1	1	yes	characteristic
7	C₂²×C₃×3₋¹⁺²	D₃	1	4	yes	—
8	C₃⋊(3₋¹⁺²⋊C₄)	—	3	8	no	—
9	C₂²×C₉⋊C₉	—	2	4	no	—
10	C₂²×C₉²	C₂×C₃	1	1	yes	characteristic
11	C₉⋊Dic₉	C₂×C₃	1	2	yes	complemented
12	#6900	C₂×C₄	1	1	yes	characteristic, complemented, Sylow
13	C₂×C₃×C₃⋊Dic₃	—	9	1	no	—
14	C₂×C₃⋊Dic₉	—	3	4	no	—
15	C₂×3₋¹⁺²⋊C₄	—	9	12	no	—
16	C₂×C₃×3₋¹⁺²	Dic₃	1	8	yes	—
17	C₂×C₃×3₋¹⁺²	C₂×D₃	1	4	yes	—
18	C₂×C₉⋊C₉	—	2	8	no	—
19	C₂×C₉⋊C₉	—	2	4	no	—
20	C₂×C₉²	C₃×C₄	1	2	yes	complemented
21	C₂×C₉²	C₂²×C₃	1	1	yes	characteristic
22	C₂²×C₃³	C₃⋊D₃	1	1	yes	characteristic
23	C₃×C₃⋊Dic₃	—	9	2	no	—
24	C₂²×3₋¹⁺²	—	3	12	no	—
25	C₂²×C₃×C₉	—	2	4	no	—
26	C₂²×C₃×C₉	C₃×D₃	1	4	yes	—
27	C₃⋊Dic₉	—	3	8	no	—
28	3₋¹⁺²⋊C₄	—	9	24	no	—
29	C₃×3₋¹⁺²	C₂×Dic₃	1	4	yes	—
30	C₉⋊C₉	—	2	4	no	—
31	C₉²	C₂×C₃×C₄	1	1	yes	characteristic, complemented
32	C₂×C₃⋊Dic₃	—	9	1	no	—
33	C₂×C₃×Dic₃	—	27	4	no	—
34	C₂×Dic₉	—	9	12	no	—
35	C₂×C₃³	C₃⋊Dic₃	1	2	yes	—
36	C₂×C₃³	C₂×C₃⋊D₃	1	1	yes	characteristic
37	C₂×3₋¹⁺²	—	3	24	no	—
38	C₂×3₋¹⁺²	—	3	12	no	—
39	C₂×C₃×C₉	—	2	8	no	—
40	C₂×C₃×C₉	—	2	4	no	—
41	C₂×C₃×C₉	C₃×Dic₃	1	8	yes	—
42	C₂×C₃×C₉	C₂×C₃×D₃	1	4	yes	—
43	C₂²×C₃²	—	3	4	no	—
44	C₂²×C₃²	C₃×C₃⋊D₃	1	1	yes	characteristic
45	C₃⋊Dic₃	—	9	2	no	—
46	C₃×Dic₃	—	27	8	no	—
47	C₂²×C₉	—	6	4	no	—
48	C₂²×C₉	AGL(1,ℤ/9)	1	12	yes	—
49	Dic₉	—	9	24	no	—
50	C₃³	C₂×C₃⋊Dic₃	1	1	yes	characteristic
51	3₋¹⁺²	—	3	12	no	—
52	C₃×C₉	—	2	4	no	—
53	C₃×C₉	C₂×C₃×Dic₃	1	4	yes	—
54	C₂×C₃×C₄	—	81	1	no	—
55	C₂×Dic₃	—	27	4	no	—
56	C₂×C₃²	—	3	8	no	—
57	C₂×C₃²	—	3	4	no	—
58	C₂×C₃²	C₃×C₃⋊Dic₃	1	2	yes	—
59	C₂×C₃²	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
60	C₂×C₉	—	6	8	no	—
61	C₂×C₉	—	6	4	no	—
62	C₂×C₉	3₋¹⁺²⋊C₄	1	24	yes	complemented
63	C₂×C₉	C₂×AGL(1,ℤ/9)	1	12	yes	—
64	C₂²×C₃	—	9	1	no	—
65	C₂²×C₃	C₃⋊AGL(1,ℤ/9)	1	4	yes	—
66	C₃×C₄	—	81	2	no	—
67	Dic₃	—	27	8	no	—
68	C₃²	—	3	4	no	—
69	C₃²	C₂×C₃×C₃⋊Dic₃	1	1	yes	characteristic
70	C₉	—	6	4	no	—
71	C₉	C₂×3₋¹⁺²⋊C₄	1	12	yes	complemented
72	C₂×C₄	—	81	1	no	Sylow
73	C₂×C₃	—	9	2	no	—
74	C₂×C₃	—	9	1	no	—
75	C₂×C₃	C₃⋊(3₋¹⁺²⋊C₄)	1	8	yes	—
76	C₂×C₃	C₂×C₃⋊AGL(1,ℤ/9)	1	4	yes	—
77	C₂²	#92314	1	1	yes	characteristic
78	C₄	—	81	2	no	—
79	C₃	—	9	1	no	—
80	C₃	C₂×C₃⋊(3₋¹⁺²⋊C₄)	1	4	yes	—
81	C₂	#11757618	1	2	yes	direct product factor
82	C₂	C₂×#92314	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²	#92314
commutator, hypocenter	C₉²	C₂×C₃×C₄
Frattini	C₂×C₃²	C₂×C₃×C₃⋊D₃
Fitting	C₂²×#6900	C₂
socle	C₂²×C₃²	C₃×C₃⋊D₃
prime radical	C₂²×C₃³	C₃⋊D₃
cosocle	C₂×C₉²	C₂²×C₃
LCS	G ▷ C₉²
UCS	C₁ ◁ C₂²

Complements

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

N	H ≅ G/N	type
2. #11757618	C₂	direct (N × H)
4. C₂×C₉⋊Dic₉	C₃	semidirect
5. C₂×#6900	C₄	semidirect
11. C₉⋊Dic₉	C₂×C₃	semidirect
12. #6900	C₂×C₄	semidirect
20. C₂×C₉²	C₃×C₄	semidirect
31. C₉²	C₂×C₃×C₄	semidirect
62. C₂×C₉	3₋¹⁺²⋊C₄	semidirect
71. C₉	C₂×3₋¹⁺²⋊C₄	semidirect
81. C₂	#11757618	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#6900	2
#11757618	2
C₂×C₃⋊(3₋¹⁺²⋊C₄)	3
C₂×C₉⋊Dic₉	3

Subgroups — C2×#11757618 #14517677

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11757618 #14517677