Group #11782584 — subgroups

Subgroups — #11782584

Order 1152.

420 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 98 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×#493	C₂	1	1	yes	maximal, characteristic, complemented
2	#10588755	C₂	1	4	yes	maximal, complemented
3	#10588377	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈×C₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	#71276	—	3	1	no	maximal
6	C₂×C₉×D₈	—	2	2	no	—
7	C₉×#127	C₂²	1	2	yes	—
8	C₂×#3673	—	2	8	no	—
9	C₂×D₇₂	—	2	2	no	—
10	#63436	C₂²	1	2	yes	—
11	C₄×C₈×C₉	C₂²	1	1	yes	characteristic
12	C₄×C₉⋊C₈	C₂²	1	2	yes	—
13	C₃×#493	D₃	1	1	yes	characteristic
14	#5073	—	3	4	no	—
15	#4695	—	3	1	no	—
16	C₈×C₃⋊C₈	—	3	1	no	—
17	C₂×D₄×C₉	—	2	4	no	—
18	C₂×D₄×C₉	—	2	2	no	—
19	C₂×D₃₆	—	2	4	no	—
20	C₂×D₃₆	—	2	2	no	—
21	C₉×D₈	—	4	4	no	—
22	C₂×C₈×C₉	D₄	1	2	yes	—
23	C₄²×C₉	C₂³	1	1	yes	characteristic
24	#3673	—	4	16	no	—
25	C₂×C₉⋊C₈	D₄	1	4	yes	—
26	D₇₂	—	4	4	no	—
27	#1712	—	9	1	no	Sylow
28	C₂×C₃×D₈	—	2	2	no	—
29	C₃×#127	C₂×D₃	1	2	yes	—
30	C₂×#213	—	6	8	no	—
31	C₂×D₂₄	—	6	2	no	—
32	#874	—	3	2	no	—
33	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic
34	C₄×C₃⋊C₈	—	3	2	no	—
35	C₂³×C₉	—	4	2	no	—
36	C₂²×D₉	—	4	2	no	—
37	D₄×C₉	—	4	8	no	—
38	D₄×C₉	—	4	4	no	—
39	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
40	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
41	D₃₆	—	4	4	no	—
42	D₃₆	—	4	8	no	—
43	C₈×C₉	D₈	1	4	yes	complemented
44	C₉⋊C₈	D₈	1	8	yes	complemented
45	#493	—	9	4	no	—
46	#493	—	9	1	no	—
47	#493	D₉	1	1	yes	characteristic, complemented
48	C₈²	—	9	1	no	—
49	C₂×C₃×D₄	—	2	4	no	—
50	C₂×C₃×D₄	—	2	2	no	—
51	C₂×D₁₂	—	6	4	no	—
52	C₂×D₁₂	—	6	2	no	—
53	C₃×D₈	—	4	4	no	—
54	C₂×C₃×C₈	#67	1	2	yes	—
55	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
56	#213	—	12	16	no	—
57	C₂×C₃⋊C₈	—	3	4	no	—
58	D₂₄	—	12	4	no	—
59	C₂²×C₉	—	8	4	no	—
60	C₂²×C₉	—	8	2	no	—
61	C₂²×C₉	#127	1	1	yes	characteristic
62	C₂×D₉	—	8	4	no	—
63	C₂×D₉	—	8	2	no	—
64	C₄×C₉	C₂×D₈	1	4	yes	—
65	C₄×C₉	C₂×D₈	1	2	yes	—
66	C₂×D₈	—	2	2	no	—
67	C₂×D₈	—	18	8	no	—
68	C₂×D₈	—	18	2	no	—
69	#127	—	9	2	no	—
70	#127	C₂×D₉	1	2	yes	—
71	C₄×C₈	—	9	2	no	—
72	C₄×C₈	C₂×D₉	1	1	yes	characteristic
73	C₂³×C₃	—	4	2	no	—
74	C₂²×D₃	—	12	2	no	—
75	C₃×D₄	—	4	8	no	—
76	C₃×D₄	—	4	4	no	—
77	C₂×C₃×C₄	D₃×D₄	1	2	yes	—
78	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
79	D₁₂	—	12	8	no	—
80	D₁₂	—	12	4	no	—
81	C₃×C₈	#213	1	4	yes	—
82	C₃⋊C₈	—	3	8	no	—
83	C₂×C₉	—	16	2	no	—
84	C₂×C₉	#493	1	2	yes	—
85	C₂×C₉	#493	1	1	yes	characteristic
86	D₉	—	16	2	no	—
87	C₂×D₄	—	2	4	no	—
88	C₂×D₄	—	2	2	no	—
89	C₂×D₄	—	18	4	no	—
90	C₂×D₄	—	18	2	no	—
91	D₈	—	4	4	no	—
92	D₈	—	36	16	no	—
93	D₈	—	36	4	no	—
94	C₂×C₈	—	9	4	no	—
95	C₂×C₈	#611	1	2	yes	—
96	C₄²	C₂²×D₉	1	1	yes	characteristic
97	C₂²×C₃	—	8	4	no	—
98	C₂²×C₃	—	8	2	no	—
99	C₂²×C₃	#940	1	1	yes	characteristic
100	C₂×D₃	—	24	4	no	—
101	C₂×D₃	—	24	2	no	—
102	C₃×C₄	D₃×D₈	1	4	yes	—
103	C₃×C₄	C₂×#213	1	2	yes	—
104	C₉	#1712	1	1	yes	characteristic, complemented, Sylow
105	C₂³	—	4	2	no	—
106	C₂³	—	36	2	no	—
107	D₄	—	4	4	no	—
108	D₄	—	4	8	no	—
109	D₄	—	36	4	no	—
110	D₄	—	36	8	no	—
111	C₂×C₄	D₄×D₉	1	2	yes	—
112	C₂×C₄	C₂×#611	1	1	yes	characteristic
113	C₈	—	9	8	no	—
114	C₈	#3673	1	4	yes	complemented
115	C₂×C₃	—	16	2	no	—
116	C₂×C₃	#5073	1	1	yes	characteristic
117	C₂×C₃	#5151	1	2	yes	—
118	D₃	—	48	2	no	—
119	C₂²	—	8	2	no	—
120	C₂²	—	8	4	no	—
121	C₂²	—	72	2	no	—
122	C₂²	—	72	4	no	—
123	C₂²	#63502	1	1	yes	characteristic
124	C₄	D₈×D₉	1	4	yes	—
125	C₄	C₂×#3673	1	2	yes	—
126	C₃	#71276	1	1	yes	characteristic
127	C₂	—	16	2	no	—
128	C₂	—	144	2	no	—
129	C₂	#10588755	1	1	yes	characteristic
130	C₂	#10588831	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₉×#493

C₂

yes

maximal, characteristic, complemented

#10588755

C₂

yes

maximal, complemented

#10588377

C₂

yes

maximal, characteristic, complemented

C₈×C₉⋊C₈

C₂

yes

maximal, characteristic, complemented

#71276

—

maximal

C₂×C₉×D₈

—

C₉×#127

C₂²

yes

—

C₂×#3673

—

C₂×D₇₂

—

#63436

C₂²

yes

—

C₄×C₈×C₉

C₂²

yes

characteristic

C₄×C₉⋊C₈

C₂²

yes

—

C₃×#493

D₃

yes

characteristic

#5073

—

#4695

—

C₈×C₃⋊C₈

—

C₂×D₄×C₉

—

C₂×D₄×C₉

—

C₂×D₃₆

—

C₂×D₃₆

—

C₉×D₈

—

C₂×C₈×C₉

D₄

yes

—

C₄²×C₉

C₂³

yes

characteristic

#3673

—

C₂×C₉⋊C₈

D₄

yes

—

D₇₂

—

#1712

—

Sylow

C₂×C₃×D₈

—

C₃×#127

C₂×D₃

yes

—

C₂×#213

—

C₂×D₂₄

—

#874

—

C₃×C₄×C₈

C₂×D₃

yes

characteristic

C₄×C₃⋊C₈

—

C₂³×C₉

—

C₂²×D₉

—

D₄×C₉

—

D₄×C₉

—

C₂×C₄×C₉

C₂×D₄

yes

—

C₂×C₄×C₉

C₂×D₄

yes

characteristic

D₃₆

—

D₃₆

—

C₈×C₉

D₈

yes

complemented

C₉⋊C₈

D₈

yes

—

—

D₉

yes

characteristic, complemented

C₈²

—

C₂×C₃×D₄

—

C₂×C₃×D₄

—

C₂×D₁₂

—

C₂×D₁₂

—

C₃×D₈

—

C₂×C₃×C₈

#67

yes

—

C₃×C₄²

C₂²×D₃

yes

characteristic

#213

—

C₂×C₃⋊C₈

—

D₂₄

—

C₂²×C₉

—

C₂²×C₉

—

C₂²×C₉

#127

yes

characteristic

C₂×D₉

—

C₂×D₉

—

C₄×C₉

C₂×D₈

yes

—

C₄×C₉

C₂×D₈

yes

—

C₂×D₈

—

C₂×D₈

—

C₂×D₈

—

#127

—

#127

C₂×D₉

yes

—

C₄×C₈

—

C₄×C₈

C₂×D₉

yes

characteristic

C₂³×C₃

—

C₂²×D₃

—

C₃×D₄

—

C₃×D₄

—

C₂×C₃×C₄

D₃×D₄

yes

—

C₂×C₃×C₄

C₂×#67

yes

characteristic

D₁₂

—

D₁₂

—

C₃×C₈

#213

yes

—

C₃⋊C₈

—

C₂×C₉

—

C₂×C₉

#493

yes

—

C₂×C₉

#493

yes

characteristic

D₉

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

D₈

—

D₈

—

D₈

—

C₂×C₈

—

C₂×C₈

#611

yes

—

C₄²

C₂²×D₉

yes

characteristic

C₂²×C₃

—

C₂²×C₃

—

C₂²×C₃

#940

yes

characteristic

100

C₂×D₃

—

101

C₂×D₃

—

102

C₃×C₄

D₃×D₈

yes

—

103

C₃×C₄

C₂×#213

yes

—

104

C₉

#1712

yes

characteristic, complemented, Sylow

105

C₂³

—

106

C₂³

—

107

D₄

—

108

D₄

—

109

D₄

—

110

D₄

—

111

C₂×C₄

D₄×D₉

yes

—

112

C₂×C₄

C₂×#611

yes

characteristic

113

C₈

—

114

C₈

#3673

yes

complemented

115

C₂×C₃

—

116

C₂×C₃

#5073

yes

characteristic

117

C₂×C₃

#5151

yes

—

118

D₃

—

119

C₂²

—

120

C₂²

—

121

C₂²

—

122

C₂²

—

123

C₂²

#63502

yes

characteristic

124

C₄

D₈×D₉

yes

—

125

C₄

C₂×#3673

yes

—

126

C₃

#71276

yes

characteristic

127

C₂

—

128

C₂

—

144

—

129

C₂

#10588755

yes

characteristic

130

C₂

#10588831

yes

—

	subgroup	G/H
center	C₂²	#63502
commutator, cosocle	C₄²×C₉	C₂³
Frattini	C₃×C₄²	C₂²×D₃
Fitting	C₉×#493	C₂
socle	C₂²×C₃	#940
hypercenter	#493	D₉
hypocenter	C₉	#1712
LCS	G ▷ C₄²×C₉ ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #493

subgroup

G/H

center

C₂²

#63502

commutator, cosocle

C₄²×C₉

C₂³

Frattini

C₃×C₄²

C₂²×D₃

C₂

C₂²×C₃

D₉

C₉

G ▷ C₄²×C₉ ▷ C₂²×C₉ ▷ C₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #493

N	H ≅ G/N	type
1. C₉×#493	C₂	semidirect
2. #10588755	C₂	semidirect
3. #10588377	C₂	semidirect
4. C₈×C₉⋊C₈	C₂	semidirect
43. C₈×C₉	D₈	semidirect
44. C₉⋊C₈	D₈	semidirect
47. #493	D₉	semidirect
104. C₉	#1712	semidirect
114. C₈	#3673	semidirect

H ≅ G/N

type

1. C₉×#493

C₂

semidirect

2. #10588755

C₂

semidirect

3. #10588377

C₂

semidirect

4. C₈×C₉⋊C₈

C₂

semidirect

43. C₈×C₉

D₈

semidirect

44. C₉⋊C₈

D₈

semidirect

47. #493

D₉

semidirect

104. C₉

#1712

semidirect

114. C₈

#3673

semidirect

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

subgroup	index
C₉×#493	2
#10588755	2
#10588377	2
C₈×C₉⋊C₈	2
#71276	3

subgroup

index

C₈×C₉⋊C₈

Subgroups — #11782584

Conjugacy classes of subgroups

Complements

Maximal subgroups