Group #11783510 — subgroups

Subgroups — #11783510

Order 1152.

360 conjugacy classes of subgroups; only the 174 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 174 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	C₂×C₉×#97	C₂	1	1	yes	maximal, characteristic
2	#10588612	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₉⋊C₈	C₂	1	1	yes	maximal, characteristic
4	#10588228	C₂	1	4	yes	maximal
5	#69806	—	3	1	no	maximal
6	C₂²×C₈×C₉	C₂²	1	2	yes	—
7	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
8	C₂×C₄×Dic₉	C₂²	1	2	yes	—
9	C₂²×C₉⋊C₈	C₂²	1	2	yes	—
10	C₉×#97	C₄	1	4	yes	complemented
11	C₉⋊#95	C₄	1	4	yes	—
12	C₄×C₉⋊C₈	C₄	1	4	yes	complemented
13	C₂×C₃×#97	D₃	1	1	yes	characteristic
14	#4932	—	3	1	no	—
15	C₂×C₄×C₃⋊C₈	—	3	1	no	—
16	#4550	—	3	4	no	—
17	C₂²×C₄×C₉	C₂×C₄	1	2	yes	—
18	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
19	C₂²×Dic₉	C₂×C₄	1	4	yes	—
20	C₂×C₈×C₉	—	2	4	no	—
21	C₂×C₈×C₉	C₂×C₄	1	4	yes	—
22	C₄²×C₉	C₂×C₄	1	2	yes	—
23	C₄²×C₉	C₂×C₄	1	2	yes	—
24	C₄×Dic₉	—	2	4	no	—
25	C₂×C₉⋊C₈	—	2	4	no	—
26	C₂×C₉⋊C₈	C₂×C₄	1	4	yes	—
27	#1746	—	9	1	no	Sylow
28	C₂²×C₃×C₈	C₂×D₃	1	2	yes	—
29	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
30	C₂×C₄×Dic₃	—	3	2	no	—
31	C₂²×C₃⋊C₈	—	3	2	no	—
32	C₃×#97	Dic₃	1	4	yes	—
33	C₃⋊#95	—	3	4	no	—
34	C₄×C₃⋊C₈	—	3	4	no	—
35	C₂³×C₉	C₂²×C₄	1	1	yes	characteristic
36	C₂×C₄×C₉	—	2	4	no	—
37	C₂×C₄×C₉	C₄²	1	4	yes	—
38	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
39	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
40	C₂×C₄×C₉	#41	1	4	yes	—
41	C₂×Dic₉	—	2	4	no	—
42	C₂×Dic₉	—	2	8	no	—
43	C₈×C₉	—	2	4	no	—
44	C₉⋊C₈	—	2	4	no	—
45	C₂×#97	D₉	1	1	yes	characteristic
46	C₂×C₄×C₈	—	9	1	no	—
47	#376	—	9	1	no	—
48	#336	—	9	4	no	—
49	C₂²×C₃×C₄	C₄×D₃	1	2	yes	—
50	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
51	C₂²×Dic₃	—	3	4	no	—
52	C₂×C₃×C₈	—	2	4	no	—
53	C₂×C₃×C₈	C₂×Dic₃	1	4	yes	—
54	C₃×C₄²	C₄×D₃	1	2	yes	—
55	C₃×C₄²	C₂×Dic₃	1	2	yes	—
56	C₄×Dic₃	—	6	4	no	—
57	C₂×C₃⋊C₈	—	3	4	no	—
58	C₂×C₃⋊C₈	—	6	4	no	—
59	C₂²×C₉	C₂×C₄²	1	1	yes	characteristic
60	C₂²×C₉	#117	1	2	yes	—
61	C₂²×C₉	#131	1	4	yes	—
62	C₄×C₉	—	2	4	no	—
63	C₄×C₉	#117	1	2	yes	—
64	C₄×C₉	#117	1	2	yes	—
65	Dic₉	—	4	4	no	—
66	C₂²×C₈	—	9	2	no	—
67	C₂²×C₈	C₂×D₉	1	2	yes	—
68	C₂×C₄²	—	9	2	no	—
69	C₂×C₄²	C₂×D₉	1	1	yes	characteristic
70	#97	Dic₉	1	4	yes	complemented
71	C₄×C₈	—	9	4	no	—
72	#95	—	9	4	no	—
73	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
74	C₂×C₃×C₄	—	2	4	no	—
75	C₂×C₃×C₄	C₄×Dic₃	1	4	yes	—
76	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
77	C₂×C₃×C₄	#235	1	4	yes	—
78	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
79	C₂×Dic₃	—	6	4	no	—
80	C₂×Dic₃	—	6	8	no	—
81	C₃×C₈	—	2	4	no	—
82	C₃⋊C₈	—	6	4	no	—
83	C₂×C₉	#376	1	1	yes	characteristic
84	C₂×C₉	#405	1	2	yes	—
85	C₂×C₉	#433	1	4	yes	—
86	C₂²×C₄	—	9	4	no	—
87	C₂²×C₄	C₄×D₉	1	2	yes	—
88	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
89	C₂×C₈	—	2	4	no	—
90	C₂×C₈	—	9	4	no	—
91	C₂×C₈	—	18	4	no	—
92	C₂×C₈	C₂×Dic₉	1	4	yes	—
93	C₄²	—	18	4	no	—
94	C₄²	C₄×D₉	1	2	yes	—
95	C₄²	C₂×Dic₉	1	2	yes	—
96	C₂²×C₃	#872	1	2	yes	—
97	C₂²×C₃	#907	1	4	yes	—
98	C₂²×C₃	C₂×C₄×Dic₃	1	1	yes	characteristic
99	C₃×C₄	—	2	4	no	—
100	C₃×C₄	#872	1	2	yes	—
101	C₃×C₄	#926	1	2	yes	—
102	Dic₃	—	12	4	no	—
103	C₉	#1746	1	1	yes	characteristic, complemented, Sylow
104	C₂³	C₂×C₄×D₉	1	1	yes	characteristic
105	C₂×C₄	—	2	4	no	—
106	C₂×C₄	—	18	4	no	—
107	C₂×C₄	—	18	8	no	—
108	C₂×C₄	C₄×Dic₉	1	4	yes	—
109	C₂×C₄	C₂×C₄×D₉	1	1	yes	characteristic
110	C₂×C₄	#3697	1	4	yes	—
111	C₂×C₄	C₂²×Dic₉	1	1	yes	characteristic
112	C₈	—	2	4	no	—
113	C₈	—	18	4	no	—
114	C₂×C₃	#4709	1	4	yes	—
115	C₂×C₃	#4932	1	1	yes	characteristic
116	C₂×C₃	#5122	1	2	yes	—
117	C₂²	#63434	1	2	yes	—
118	C₂²	#63469	1	4	yes	—
119	C₂²	C₂×C₄×Dic₉	1	1	yes	characteristic
120	C₄	—	2	4	no	—
121	C₄	—	36	4	no	—
122	C₄	#63434	1	2	yes	—
123	C₄	#63488	1	2	yes	—
124	C₃	#69806	1	1	yes	characteristic
125	C₂	#10588390	1	4	yes	—
126	C₂	#10588612	1	1	yes	characteristic
127	C₂	#10588797	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₉×#97

C₂

yes

maximal, characteristic

#10588612

C₂

yes

maximal, characteristic

C₂×C₄×C₉⋊C₈

C₂

yes

maximal, characteristic

#10588228

C₂

yes

maximal

#69806

—

maximal

C₂²×C₈×C₉

C₂²

yes

—

C₂×C₄²×C₉

C₂²

yes

characteristic

C₂×C₄×Dic₉

C₂²

yes

—

C₂²×C₉⋊C₈

C₂²

yes

—

C₉×#97

C₄

yes

complemented

C₉⋊#95

C₄

yes

—

C₄×C₉⋊C₈

C₄

yes

complemented

C₂×C₃×#97

D₃

yes

characteristic

#4932

—

C₂×C₄×C₃⋊C₈

—

#4550

—

C₂²×C₄×C₉

C₂×C₄

yes

—

C₂²×C₄×C₉

C₂³

yes

characteristic

C₂²×Dic₉

C₂×C₄

yes

—

C₂×C₈×C₉

—

C₂×C₈×C₉

C₂×C₄

yes

—

C₄²×C₉

C₂×C₄

yes

—

C₄²×C₉

C₂×C₄

yes

—

C₄×Dic₉

—

C₂×C₉⋊C₈

—

C₂×C₉⋊C₈

C₂×C₄

yes

—

#1746

—

Sylow

C₂²×C₃×C₈

C₂×D₃

yes

—

C₂×C₃×C₄²

C₂×D₃

yes

characteristic

C₂×C₄×Dic₃

—

C₂²×C₃⋊C₈

—

C₃×#97

Dic₃

yes

—

C₃⋊#95

—

C₄×C₃⋊C₈

—

C₂³×C₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₉

—

C₂×C₄×C₉

C₄²

yes

—

C₂×C₄×C₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₉

#41

yes

—

C₂×Dic₉

—

C₂×Dic₉

—

C₈×C₉

—

C₉⋊C₈

—

C₂×#97

D₉

yes

characteristic

C₂×C₄×C₈

—

#376

—

#336

—

C₂²×C₃×C₄

C₄×D₃

yes

—

C₂²×C₃×C₄

C₂²×D₃

yes

characteristic

C₂²×Dic₃

—

C₂×C₃×C₈

—

C₂×C₃×C₈

C₂×Dic₃

yes

—

C₃×C₄²

C₄×D₃

yes

—

C₃×C₄²

C₂×Dic₃

yes

—

C₄×Dic₃

—

C₂×C₃⋊C₈

—

C₂×C₃⋊C₈

—

C₂²×C₉

C₂×C₄²

yes

characteristic

C₂²×C₉

#117

yes

—

C₂²×C₉

#131

yes

—

C₄×C₉

—

C₄×C₉

#117

yes

—

C₄×C₉

#117

yes

—

Dic₉

—

C₂²×C₈

—

C₂²×C₈

C₂×D₉

yes

—

C₂×C₄²

—

C₂×C₄²

C₂×D₉

yes

characteristic

#97

Dic₉

yes

complemented

C₄×C₈

—

#95

—

C₂³×C₃

C₂×C₄×D₃

yes

characteristic

C₂×C₃×C₄

—

C₂×C₃×C₄

C₄×Dic₃

yes

—

C₂×C₃×C₄

C₂×C₄×D₃

yes

characteristic

C₂×C₃×C₄

#235

yes

—

C₂×C₃×C₄

C₂²×Dic₃

yes

characteristic

C₂×Dic₃

—

C₂×Dic₃

—

C₃×C₈

—

C₃⋊C₈

—

C₂×C₉

#376

yes

characteristic

C₂×C₉

#405

yes

—

C₂×C₉

#433

yes

—

C₂²×C₄

—

C₂²×C₄

C₄×D₉

yes

—

C₂²×C₄

C₂²×D₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×Dic₉

yes

—

C₄²

—

C₄²

C₄×D₉

yes

—

C₄²

C₂×Dic₉

yes

—

C₂²×C₃

#872

yes

—

C₂²×C₃

#907

yes

—

C₂²×C₃

C₂×C₄×Dic₃

yes

characteristic

C₃×C₄

—

100

C₃×C₄

#872

yes

—

101

C₃×C₄

#926

yes

—

102

Dic₃

—

103

C₉

#1746

yes

characteristic, complemented, Sylow

104

C₂³

C₂×C₄×D₉

yes

characteristic

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

C₄×Dic₉

yes

—

109

C₂×C₄

C₂×C₄×D₉

yes

characteristic

110

C₂×C₄

#3697

yes

—

111

C₂×C₄

C₂²×Dic₉

yes

characteristic

112

C₈

—

113

C₈

—

114

C₂×C₃

#4709

yes

—

115

C₂×C₃

#4932

yes

characteristic

116

C₂×C₃

#5122

yes

—

117

C₂²

#63434

yes

—

118

C₂²

#63469

yes

—

119

C₂²

C₂×C₄×Dic₉

yes

characteristic

120

C₄

—

121

C₄

—

122

C₄

#63434

yes

—

123

C₄

#63488

yes

—

124

C₃

#69806

yes

characteristic

125

C₂

#10588390

yes

—

126

C₂

#10588612

yes

characteristic

127

C₂

#10588797

yes

—

	subgroup	G/H
center	C₂²×C₄	C₂²×D₉
commutator	C₂²×C₉	C₂×C₄²
Frattini	C₂²×C₃×C₄	C₂²×D₃
Fitting	C₂×C₉×#97	C₂
socle, prime radical	C₂³×C₃	C₂×C₄×D₃
cosocle	C₂²×C₄×C₉	C₂³
hypercenter	C₂×#97	D₉
hypocenter	C₉	#1746
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#97

subgroup

G/H

center

C₂²×C₄

C₂²×D₉

commutator

C₂²×C₉

C₂×C₄²

Frattini

C₂²×C₃×C₄

C₂²×D₃

Fitting

C₂×C₉×#97

C₂

socle, prime radical

C₂³×C₃

C₂×C₄×D₃

cosocle

C₂²×C₄×C₉

C₂³

hypercenter

C₂×#97

D₉

C₉

G ▷ C₂²×C₉ ▷ C₉

C₁ ◁ C₂²×C₄ ◁ C₂×#97

N	H ≅ G/N	type
10. C₉×#97	C₄	semidirect
12. C₄×C₉⋊C₈	C₄	semidirect
70. #97	Dic₉	semidirect
103. C₉	#1746	semidirect

H ≅ G/N

type

10. C₉×#97

C₄

semidirect

12. C₄×C₉⋊C₈

C₄

semidirect

70. #97

Dic₉

semidirect

103. C₉

#1746

semidirect

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

subgroup	index
C₂×C₉×#97	2
#10588612	2
C₂×C₄×C₉⋊C₈	2
#10588228	2
#69806	3

subgroup

index

C₂×C₉×#97

#10588612

C₂×C₄×C₉⋊C₈

#10588228

#69806

Subgroups — #11783510

Conjugacy classes of subgroups

Complements

Maximal subgroups