Group #13090375 — subgroups

Subgroups — C₂×#10624889 #13090375

Order 1458.

620 conjugacy classes of subgroups; only the 440 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 440 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624889	C₂	1	1	yes	maximal, characteristic, direct product factor, Sylow
2	C₂×#6897	C₃	1	18	yes	maximal, complemented
3	C₂×#6896	C₃	1	9	yes	maximal, complemented
4	C₂×#6894	C₃	1	6	yes	maximal, complemented
5	C₂×#6891	C₃	1	2	yes	maximal
6	C₂×#6891	C₃	1	1	yes	maximal, characteristic
7	C₂×C₉×3₋¹⁺²	C₃	1	3	yes	maximal, complemented
8	C₂×C₃×C₃²⋊C₉	C₃	1	1	yes	maximal, characteristic
9	#6897	C₂×C₃	1	18	yes	complemented
10	#6896	C₂×C₃	1	9	yes	complemented
11	#6894	C₂×C₃	1	6	yes	complemented
12	#6891	C₂×C₃	1	2	yes	—
13	#6891	C₂×C₃	1	1	yes	characteristic
14	C₉×3₋¹⁺²	C₂×C₃	1	3	yes	complemented
15	C₃×C₃²⋊C₉	C₂×C₃	1	1	yes	characteristic
16	C₂×C₃⁴	C₃²	1	1	yes	characteristic
17	C₂×C₃×3₋¹⁺²	C₃²	1	3	yes	—
18	C₂×C₃×3₋¹⁺²	C₃²	1	6	yes	—
19	C₂×C₃²×C₉	C₃²	1	1	yes	characteristic
20	C₂×C₃²×C₉	C₃²	1	2	yes	—
21	C₂×C₉⋊C₉	C₃²	1	18	yes	complemented
22	C₂×C₉⋊C₉	C₃²	1	54	yes	complemented
23	C₂×C₃²⋊C₉	C₃²	1	3	yes	—
24	C₂×C₃²⋊C₉	C₃²	1	6	yes	—
25	C₂×C₃²⋊C₉	C₃²	1	6	yes	—
26	C₂×C₃²⋊C₉	C₃²	1	3	yes	—
27	C₂×C₃²⋊C₉	C₃²	1	6	yes	—
28	C₂×C₃²⋊C₉	C₃²	1	12	yes	—
29	C₂×C₉²	C₃²	1	9	yes	complemented
30	C₃⁴	C₂×C₃²	1	1	yes	characteristic
31	C₃×3₋¹⁺²	C₂×C₃²	1	3	yes	—
32	C₃×3₋¹⁺²	C₂×C₃²	1	6	yes	—
33	C₃²×C₉	C₂×C₃²	1	1	yes	characteristic
34	C₃²×C₉	C₂×C₃²	1	2	yes	—
35	C₉⋊C₉	C₂×C₃²	1	18	yes	complemented
36	C₉⋊C₉	C₂×C₃²	1	54	yes	complemented
37	C₃²⋊C₉	C₂×C₃²	1	3	yes	—
38	C₃²⋊C₉	C₂×C₃²	1	6	yes	—
39	C₃²⋊C₉	C₂×C₃²	1	6	yes	—
40	C₃²⋊C₉	C₂×C₃²	1	3	yes	—
41	C₃²⋊C₉	C₂×C₃²	1	6	yes	—
42	C₃²⋊C₉	C₂×C₃²	1	12	yes	—
43	C₉²	C₂×C₃²	1	9	yes	complemented
44	C₂×C₃³	—	3	3	no	—
45	C₂×C₃³	—	9	1	no	—
46	C₂×C₃³	—	9	2	no	—
47	C₂×C₃³	C₃³	1	2	yes	—
48	C₂×C₃³	C₃³	1	1	yes	characteristic
49	C₂×C₃³	C₃³	1	1	yes	characteristic
50	C₂×3₋¹⁺²	—	3	9	no	—
51	C₂×3₋¹⁺²	—	9	6	no	—
52	C₂×C₃×C₉	—	9	1	no	—
53	C₂×C₃×C₉	—	9	2	no	—
54	C₂×C₃×C₉	C₃³	1	3	yes	—
55	C₂×C₃×C₉	C₃³	1	9	yes	—
56	C₂×C₃×C₉	C₃³	1	18	yes	—
57	C₂×C₃×C₉	C₃³	1	6	yes	—
58	C₃³	—	3	3	no	—
59	C₃³	—	9	1	no	—
60	C₃³	—	9	2	no	—
61	C₃³	C₂×C₃³	1	2	yes	—
62	C₃³	C₂×C₃³	1	1	yes	characteristic
63	C₃³	C₂×C₃³	1	1	yes	characteristic
64	3₋¹⁺²	—	3	9	no	—
65	3₋¹⁺²	—	9	6	no	—
66	C₃×C₉	—	9	1	no	—
67	C₃×C₉	—	9	2	no	—
68	C₃×C₉	C₂×C₃³	1	3	yes	—
69	C₃×C₉	C₂×C₃³	1	9	yes	—
70	C₃×C₉	C₂×C₃³	1	18	yes	—
71	C₃×C₉	C₂×C₃³	1	6	yes	—
72	C₂×C₃²	—	3	1	no	—
73	C₂×C₃²	—	3	2	no	—
74	C₂×C₃²	—	3	2	no	—
75	C₂×C₃²	—	3	1	no	—
76	C₂×C₃²	—	3	2	no	—
77	C₂×C₃²	—	3	2	no	—
78	C₂×C₃²	—	3	4	no	—
79	C₂×C₃²	—	3	1	no	—
80	C₂×C₃²	—	9	9	no	—
81	C₂×C₃²	#737	1	3	yes	—
82	C₂×C₃²	C₃⁴	1	1	yes	characteristic
83	C₂×C₉	—	3	9	no	—
84	C₂×C₉	—	3	3	no	—
85	C₂×C₉	—	3	6	no	—
86	C₂×C₉	—	3	18	no	—
87	C₃²	—	3	1	no	—
88	C₃²	—	3	2	no	—
89	C₃²	—	3	2	no	—
90	C₃²	—	3	1	no	—
91	C₃²	—	3	2	no	—
92	C₃²	—	3	2	no	—
93	C₃²	—	3	4	no	—
94	C₃²	—	3	1	no	—
95	C₃²	—	9	9	no	—
96	C₃²	C₂×#737	1	3	yes	—
97	C₃²	C₂×C₃⁴	1	1	yes	characteristic
98	C₉	—	3	9	no	—
99	C₉	—	3	3	no	—
100	C₉	—	3	6	no	—
101	C₉	—	3	18	no	—
102	C₂×C₃	—	3	3	no	—
103	C₂×C₃	—	9	1	no	—
104	C₂×C₃	—	9	2	no	—
105	C₂×C₃	C₃×#737	1	1	yes	characteristic
106	C₂×C₃	3₋¹⁺⁴	1	1	yes	characteristic
107	C₂×C₃	3₋¹⁺⁴	1	2	yes	—
108	C₃	—	3	3	no	—
109	C₃	—	9	1	no	—
110	C₃	—	9	2	no	—
111	C₃	C₂×C₃×#737	1	1	yes	characteristic
112	C₃	C₂×3₋¹⁺⁴	1	1	yes	characteristic
113	C₃	C₂×3₋¹⁺⁴	1	2	yes	—
114	C₂	#10624889	1	1	yes	characteristic, direct product factor, Sylow

subgroup

G/H

class size

multiplicity

normal?

properties

#10624889

C₂

yes

maximal, characteristic, direct product factor, Sylow

C₂×#6897

C₃

yes

maximal, complemented

C₂×#6896

C₃

yes

maximal, complemented

C₂×#6894

C₃

yes

maximal, complemented

C₂×#6891

C₃

yes

maximal

C₂×#6891

C₃

yes

maximal, characteristic

C₂×C₉×3₋¹⁺²

C₃

yes

maximal, complemented

C₂×C₃×C₃²⋊C₉

C₃

yes

maximal, characteristic

#6897

C₂×C₃

yes

complemented

#6896

C₂×C₃

yes

complemented

#6894

C₂×C₃

yes

complemented

#6891

C₂×C₃

yes

—

#6891

C₂×C₃

yes

characteristic

C₉×3₋¹⁺²

C₂×C₃

yes

complemented

C₃×C₃²⋊C₉

C₂×C₃

yes

characteristic

C₂×C₃⁴

C₃²

yes

characteristic

C₂×C₃×3₋¹⁺²

C₃²

yes

—

C₂×C₃×3₋¹⁺²

C₃²

yes

—

C₂×C₃²×C₉

C₃²

yes

characteristic

C₂×C₃²×C₉

C₃²

yes

—

C₂×C₉⋊C₉

C₃²

yes

complemented

C₂×C₉⋊C₉

C₃²

yes

complemented

C₂×C₃²⋊C₉

C₃²

yes

—

C₂×C₃²⋊C₉

C₃²

yes

—

C₂×C₃²⋊C₉

C₃²

yes

—

C₂×C₃²⋊C₉

C₃²

yes

—

C₂×C₃²⋊C₉

C₃²

yes

—

C₂×C₃²⋊C₉

C₃²

yes

—

C₂×C₉²

C₃²

yes

complemented

C₃⁴

C₂×C₃²

yes

characteristic

C₃×3₋¹⁺²

C₂×C₃²

yes

—

C₃×3₋¹⁺²

C₂×C₃²

yes

—

C₃²×C₉

C₂×C₃²

yes

characteristic

C₃²×C₉

C₂×C₃²

yes

—

C₉⋊C₉

C₂×C₃²

yes

complemented

C₉⋊C₉

C₂×C₃²

yes

complemented

C₃²⋊C₉

C₂×C₃²

yes

—

C₃²⋊C₉

C₂×C₃²

yes

—

C₃²⋊C₉

C₂×C₃²

yes

—

C₃²⋊C₉

C₂×C₃²

yes

—

C₃²⋊C₉

C₂×C₃²

yes

—

C₃²⋊C₉

C₂×C₃²

yes

—

C₉²

C₂×C₃²

yes

complemented

C₂×C₃³

—

C₂×C₃³

—

C₂×C₃³

—

C₂×C₃³

C₃³

yes

—

C₂×C₃³

C₃³

yes

characteristic

C₂×C₃³

C₃³

yes

characteristic

C₂×3₋¹⁺²

—

C₂×3₋¹⁺²

—

C₂×C₃×C₉

—

C₂×C₃×C₉

—

C₂×C₃×C₉

C₃³

yes

—

C₂×C₃×C₉

C₃³

yes

—

C₂×C₃×C₉

C₃³

yes

—

C₂×C₃×C₉

C₃³

yes

—

C₃³

—

C₃³

—

C₃³

—

C₃³

C₂×C₃³

yes

—

C₃³

C₂×C₃³

yes

characteristic

C₃³

C₂×C₃³

yes

characteristic

3₋¹⁺²

—

3₋¹⁺²

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

C₂×C₃³

yes

—

C₃×C₉

C₂×C₃³

yes

—

C₃×C₉

C₂×C₃³

yes

—

C₃×C₉

C₂×C₃³

yes

—

C₂×C₃²

—

C₂×C₃²

—

C₂×C₃²

—

C₂×C₃²

—

C₂×C₃²

—

C₂×C₃²

—

C₂×C₃²

—

C₂×C₃²

—

C₂×C₃²

—

C₂×C₃²

#737

yes

—

C₂×C₃²

C₃⁴

yes

characteristic

C₂×C₉

—

C₂×C₉

—

C₂×C₉

—

C₂×C₉

—

C₃²

—

C₃²

—

C₃²

—

C₃²

—

C₃²

—

C₃²

—

C₃²

—

C₃²

—

C₃²

—

C₃²

C₂×#737

yes

—

C₃²

C₂×C₃⁴

yes

characteristic

C₉

—

C₉

—

100

C₉

—

101

C₉

—

102

C₂×C₃

—

103

C₂×C₃

—

104

C₂×C₃

—

105

C₂×C₃

C₃×#737

yes

characteristic

106

C₂×C₃

3₋¹⁺⁴

yes

characteristic

107

C₂×C₃

3₋¹⁺⁴

yes

—

108

C₃

—

109

C₃

—

110

C₃

—

111

C₃

C₂×C₃×#737

yes

characteristic

112

C₃

C₂×3₋¹⁺⁴

yes

characteristic

113

C₃

C₂×3₋¹⁺⁴

yes

—

114

C₂

#10624889

yes

characteristic, direct product factor, Sylow

	subgroup	G/H
center, socle	C₂×C₃²	C₃⁴
commutator, Frattini, cosocle	C₃²	C₂×C₃⁴
prime radical	C₂×C₃⁴	C₃²
LCS	G ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₂×C₃² ◁ G

subgroup

G/H

center, socle

C₂×C₃²

C₃⁴

commutator, Frattini, cosocle

C₃²

C₂×C₃⁴

prime radical

C₂×C₃⁴

C₃²

LCS

G ▷ C₃² ▷ C₁

UCS

C₁ ◁ C₂×C₃² ◁ G

N	H ≅ G/N	type
1. #10624889	C₂	direct (N × H)
2. C₂×#6897	C₃	semidirect
3. C₂×#6896	C₃	semidirect
4. C₂×#6894	C₃	semidirect
7. C₂×C₉×3₋¹⁺²	C₃	semidirect
9. #6897	C₂×C₃	semidirect
10. #6896	C₂×C₃	semidirect
11. #6894	C₂×C₃	semidirect
14. C₉×3₋¹⁺²	C₂×C₃	semidirect
21. C₂×C₉⋊C₉	C₃²	semidirect
22. C₂×C₉⋊C₉	C₃²	semidirect
29. C₂×C₉²	C₃²	semidirect
35. C₉⋊C₉	C₂×C₃²	semidirect
36. C₉⋊C₉	C₂×C₃²	semidirect
43. C₉²	C₂×C₃²	semidirect
114. C₂	#10624889	direct (N × H)

H ≅ G/N

type

1. #10624889

C₂

direct (N × H)

2. C₂×#6897

C₃

semidirect

3. C₂×#6896

C₃

semidirect

4. C₂×#6894

C₃

semidirect

7. C₂×C₉×3₋¹⁺²

C₃

semidirect

9. #6897

C₂×C₃

semidirect

10. #6896

C₂×C₃

semidirect

11. #6894

C₂×C₃

semidirect

14. C₉×3₋¹⁺²

C₂×C₃

semidirect

21. C₂×C₉⋊C₉

C₃²

semidirect

22. C₂×C₉⋊C₉

C₃²

semidirect

29. C₂×C₉²

C₃²

semidirect

35. C₉⋊C₉

C₂×C₃²

semidirect

36. C₉⋊C₉

C₂×C₃²

semidirect

43. C₉²

C₂×C₃²

semidirect

114. C₂

#10624889

direct (N × H)

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

subgroup	index
#10624889	2
C₂×#6897	3
C₂×#6896	3
C₂×#6894	3
C₂×#6891	3
C₂×C₉×3₋¹⁺²	3
C₂×C₃×C₃²⋊C₉	3

subgroup

index

C₂×C₉×3₋¹⁺²

C₂×C₃×C₃²⋊C₉

Subgroups — C₂×#10624889 #13090375

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×#10624889 #13090375

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10624889 #13090375