Group #11766025 — subgroups

Subgroups — C₉×#1304 #11766025

Order 1152.

594 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 594 conjugacy classes of subgroups — too many to draw. Only its 108 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	C₉×#379	C₂	1	3	yes	maximal
2	C₃×#1304	C₃	1	1	yes	maximal, characteristic
3	C₂⁵×C₉	C₂²	1	1	yes	characteristic
4	C₂×C₉×C₂²⋊C₄	—	2	6	no	—
5	C₂×C₉×C₂²⋊C₄	C₄	1	6	yes	complemented
6	C₃×#379	C₂×C₃	1	3	yes	—
7	C₂⁴×C₉	—	4	6	no	—
8	C₂⁴×C₉	C₂×C₄	1	3	yes	—
9	C₂⁴×C₉	D₄	1	3	yes	—
10	C₂⁴×C₉	Q₈	1	1	yes	characteristic
11	C₂²×C₄×C₉	—	2	6	no	—
12	C₉×C₂²⋊C₄	—	4	12	no	—
13	C₉×C₂²⋊C₄	—	4	6	no	—
14	#1304	C₉	1	1	yes	characteristic, direct product factor, Sylow
15	C₂⁵×C₃	C₂²×C₃	1	1	yes	characteristic
16	C₂×C₃×C₂²⋊C₄	—	2	6	no	—
17	C₂×C₃×C₂²⋊C₄	C₃×C₄	1	6	yes	—
18	C₂³×C₉	—	2	6	no	—
19	C₂³×C₉	—	2	12	no	—
20	C₂³×C₉	—	4	6	no	—
21	C₂³×C₉	—	4	3	no	—
22	C₂³×C₉	—	4	3	no	—
23	C₂³×C₉	—	4	16	no	—
24	C₂³×C₉	C₄²	1	1	yes	characteristic
25	C₂³×C₉	C₂²⋊C₄	1	3	yes	—
26	C₂³×C₉	C₄⋊C₄	1	3	yes	—
27	C₂×C₄×C₉	—	4	12	no	—
28	C₂×C₄×C₉	—	4	6	no	—
29	#379	C₂×C₉	1	3	yes	—
30	C₂⁴×C₃	—	4	6	no	—
31	C₂⁴×C₃	C₂×C₃×C₄	1	3	yes	—
32	C₂⁴×C₃	C₃×D₄	1	3	yes	—
33	C₂⁴×C₃	C₃×Q₈	1	1	yes	characteristic
34	C₂²×C₃×C₄	—	2	6	no	—
35	C₃×C₂²⋊C₄	—	4	12	no	—
36	C₃×C₂²⋊C₄	—	4	6	no	—
37	C₂²×C₉	—	2	6	no	—
38	C₂²×C₉	—	2	3	no	—
39	C₂²×C₉	—	2	3	no	—
40	C₂²×C₉	—	2	6	no	—
41	C₂²×C₉	—	4	12	no	—
42	C₂²×C₉	—	4	12	no	—
43	C₂²×C₉	—	4	4	no	—
44	C₂²×C₉	#95	1	1	yes	characteristic
45	C₂²×C₉	#99	1	6	yes	—
46	C₄×C₉	—	8	6	no	—
47	C₂⁵	C₂²×C₉	1	1	yes	characteristic
48	C₂×C₂²⋊C₄	—	2	6	no	—
49	C₂×C₂²⋊C₄	C₄×C₉	1	6	yes	complemented
50	C₂³×C₃	—	2	6	no	—
51	C₂³×C₃	—	2	12	no	—
52	C₂³×C₃	—	4	6	no	—
53	C₂³×C₃	—	4	3	no	—
54	C₂³×C₃	—	4	3	no	—
55	C₂³×C₃	—	4	16	no	—
56	C₂³×C₃	C₃×C₄²	1	1	yes	characteristic
57	C₂³×C₃	C₃×C₂²⋊C₄	1	3	yes	—
58	C₂³×C₃	C₃×C₄⋊C₄	1	3	yes	—
59	C₂×C₃×C₄	—	4	12	no	—
60	C₂×C₃×C₄	—	4	6	no	—
61	C₂×C₉	—	2	6	no	—
62	C₂×C₉	—	4	1	no	—
63	C₂×C₉	—	4	3	no	—
64	C₂×C₉	#342	1	3	yes	—
65	C₂⁴	—	4	6	no	—
66	C₂⁴	C₂×C₄×C₉	1	3	yes	—
67	C₂⁴	D₄×C₉	1	3	yes	—
68	C₂⁴	Q₈×C₉	1	1	yes	characteristic
69	C₂²×C₄	—	2	6	no	—
70	C₂²⋊C₄	—	4	12	no	—
71	C₂²⋊C₄	—	4	6	no	—
72	C₂²×C₃	—	2	6	no	—
73	C₂²×C₃	—	2	3	no	—
74	C₂²×C₃	—	2	3	no	—
75	C₂²×C₃	—	2	6	no	—
76	C₂²×C₃	—	4	12	no	—
77	C₂²×C₃	—	4	12	no	—
78	C₂²×C₃	—	4	4	no	—
79	C₂²×C₃	C₃×#95	1	1	yes	characteristic
80	C₂²×C₃	C₃×#99	1	6	yes	—
81	C₃×C₄	—	8	6	no	—
82	C₉	#1304	1	1	yes	characteristic, direct product factor, Sylow
83	C₂³	—	2	6	no	—
84	C₂³	—	2	12	no	—
85	C₂³	—	4	6	no	—
86	C₂³	—	4	3	no	—
87	C₂³	—	4	3	no	—
88	C₂³	—	4	16	no	—
89	C₂³	C₄²×C₉	1	1	yes	characteristic
90	C₂³	C₉×C₂²⋊C₄	1	3	yes	—
91	C₂³	C₉×C₄⋊C₄	1	3	yes	—
92	C₂×C₄	—	4	12	no	—
93	C₂×C₄	—	4	6	no	—
94	C₂×C₃	—	2	6	no	—
95	C₂×C₃	—	4	1	no	—
96	C₂×C₃	—	4	3	no	—
97	C₂×C₃	C₃×#342	1	3	yes	—
98	C₂²	—	2	6	no	—
99	C₂²	—	2	3	no	—
100	C₂²	—	2	3	no	—
101	C₂²	—	2	6	no	—
102	C₂²	—	4	12	no	—
103	C₂²	—	4	12	no	—
104	C₂²	—	4	4	no	—
105	C₂²	C₉×#95	1	1	yes	characteristic
106	C₂²	C₉×#99	1	6	yes	—
107	C₄	—	8	6	no	—
108	C₃	C₃×#1304	1	1	yes	characteristic
109	C₂	—	2	6	no	—
110	C₂	—	4	1	no	—
111	C₂	—	4	3	no	—
112	C₂	C₉×#342	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₉×#379

C₂

yes

maximal

C₃×#1304

C₃

yes

maximal, characteristic

C₂⁵×C₉

C₂²

yes

characteristic

C₂×C₉×C₂²⋊C₄

—

C₂×C₉×C₂²⋊C₄

C₄

yes

complemented

C₃×#379

C₂×C₃

yes

—

C₂⁴×C₉

—

C₂⁴×C₉

C₂×C₄

yes

—

C₂⁴×C₉

D₄

yes

—

C₂⁴×C₉

Q₈

yes

characteristic

C₂²×C₄×C₉

—

C₉×C₂²⋊C₄

—

C₉×C₂²⋊C₄

—

#1304

C₉

yes

characteristic, direct product factor, Sylow

C₂⁵×C₃

C₂²×C₃

yes

characteristic

C₂×C₃×C₂²⋊C₄

—

C₂×C₃×C₂²⋊C₄

C₃×C₄

yes

—

C₂³×C₉

—

C₂³×C₉

—

C₂³×C₉

—

C₂³×C₉

—

C₂³×C₉

—

C₂³×C₉

—

C₂³×C₉

C₄²

yes

characteristic

C₂³×C₉

C₂²⋊C₄

yes

—

C₂³×C₉

C₄⋊C₄

yes

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

#379

C₂×C₉

yes

—

C₂⁴×C₃

—

C₂⁴×C₃

C₂×C₃×C₄

yes

—

C₂⁴×C₃

C₃×D₄

yes

—

C₂⁴×C₃

C₃×Q₈

yes

characteristic

C₂²×C₃×C₄

—

C₃×C₂²⋊C₄

—

C₃×C₂²⋊C₄

—

C₂²×C₉

—

C₂²×C₉

—

C₂²×C₉

—

C₂²×C₉

—

C₂²×C₉

—

C₂²×C₉

—

C₂²×C₉

—

C₂²×C₉

#95

yes

characteristic

C₂²×C₉

#99

yes

—

C₄×C₉

—

C₂⁵

C₂²×C₉

yes

characteristic

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

C₄×C₉

yes

complemented

C₂³×C₃

—

C₂³×C₃

—

C₂³×C₃

—

C₂³×C₃

—

C₂³×C₃

—

C₂³×C₃

—

C₂³×C₃

C₃×C₄²

yes

characteristic

C₂³×C₃

C₃×C₂²⋊C₄

yes

—

C₂³×C₃

C₃×C₄⋊C₄

yes

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₉

—

C₂×C₉

—

C₂×C₉

—

C₂×C₉

#342

yes

—

C₂⁴

—

C₂⁴

C₂×C₄×C₉

yes

—

C₂⁴

D₄×C₉

yes

—

C₂⁴

Q₈×C₉

yes

characteristic

C₂²×C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²×C₃

—

C₂²×C₃

—

C₂²×C₃

—

C₂²×C₃

—

C₂²×C₃

—

C₂²×C₃

—

C₂²×C₃

—

C₂²×C₃

C₃×#95

yes

characteristic

C₂²×C₃

C₃×#99

yes

—

C₃×C₄

—

C₉

#1304

yes

characteristic, direct product factor, Sylow

C₂³

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

C₂³

C₄²×C₉

yes

characteristic

C₂³

C₉×C₂²⋊C₄

yes

—

C₂³

C₉×C₄⋊C₄

yes

—

C₂×C₄

—

C₂×C₄

—

C₂×C₃

—

C₂×C₃

—

C₂×C₃

—

C₂×C₃

C₃×#342

yes

—

C₂²

—

C₂²

—

100

C₂²

—

101

C₂²

—

102

C₂²

—

103

C₂²

—

104

C₂²

—

105

C₂²

C₉×#95

yes

characteristic

106

C₂²

C₉×#99

yes

—

107

C₄

—

108

C₃

C₃×#1304

yes

characteristic

109

C₂

—

110

C₂

—

111

C₂

—

112

C₂

C₉×#342

yes

—

	subgroup	G/H
center	C₂²×C₉	#95
commutator	C₂³	C₄²×C₉
Frattini, prime radical, cosocle	C₂⁵×C₃	C₂²×C₃
socle	C₂²×C₃	C₃×#95
LCS	G ▷ C₂³ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₉ ◁ C₂⁵×C₉ ◁ G

subgroup

G/H

center

C₂²×C₉

#95

commutator

C₂³

C₄²×C₉

Frattini, prime radical, cosocle

C₂⁵×C₃

C₂²×C₃

socle

C₂²×C₃

C₃×#95

LCS

G ▷ C₂³ ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₉ ◁ C₂⁵×C₉ ◁ G

N	H ≅ G/N	type
5. C₂×C₉×C₂²⋊C₄	C₄	semidirect
14. #1304	C₉	direct (N × H)
49. C₂×C₂²⋊C₄	C₄×C₉	semidirect
82. C₉	#1304	direct (N × H)

H ≅ G/N

type

5. C₂×C₉×C₂²⋊C₄

C₄

semidirect

14. #1304

C₉

direct (N × H)

49. C₂×C₂²⋊C₄

C₄×C₉

semidirect

82. C₉

#1304

direct (N × H)

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

subgroup	index
C₉×#379	2
C₃×#1304	3

subgroup

index

C₉×#379

C₃×#1304

Subgroups — C₉×#1304 #11766025

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C9×#1304 #11766025

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#1304 #11766025