Group #11919611 — subgroups

Subgroups — #3391⋊C₉ #11919611

Order 1152.

221 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 221 conjugacy classes of subgroups — too many to draw. Only its 49 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	C₄⋊(#41⋊C₉)	C₂	1	2	yes	maximal, complemented
2	C₈×Q₈⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#3391	C₃	1	1	yes	maximal, characteristic
4	C₂×#41⋊C₉	—	2	2	no	—
5	C₄×Q₈⋊C₉	C₂²	1	1	yes	characteristic
6	C₉×#107	—	4	1	no	maximal
7	C₃×#550	C₂×C₃	1	2	yes	—
8	C₃×#493	—	3	1	no	—
9	C₃×#459	—	3	2	no	—
10	C₃×C₈×Q₈	C₂×C₃	1	1	yes	characteristic
11	C₃×C₄×D₈	—	3	1	no	—
12	#41⋊C₉	—	4	2	no	—
13	C₂×Q₈⋊C₉	D₄	1	1	yes	characteristic
14	C₂×C₈×C₉	—	4	1	no	—
15	C₉×C₄⋊C₄	—	4	2	no	—
16	#3391	C₉	1	1	yes	characteristic, complemented, Sylow
17	C₂×C₃×#41	—	2	2	no	—
18	C₂×C₃×D₈	—	3	2	no	—
19	C₂×C₃×D₈	—	3	1	no	—
20	C₃×#127	—	3	2	no	—
21	C₃×#121	—	6	2	no	—
22	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
23	C₃×C₄×D₄	—	3	2	no	—
24	C₃×#107	A₄	1	1	yes	characteristic
25	C₃×C₄⋊C₈	—	3	1	no	—
26	C₃×#102	—	3	2	no	—
27	C₃×C₄×C₈	—	3	1	no	—
28	C₂×C₄×C₉	—	4	1	no	—
29	C₂×C₄×C₉	—	8	2	no	—
30	Q₈⋊C₉	D₈	1	1	yes	characteristic, complemented
31	C₈×C₉	—	4	2	no	—
32	#550	C₂×C₉	1	2	yes	—
33	#493	—	3	1	no	—
34	#459	—	3	2	no	—
35	C₈×Q₈	C₂×C₉	1	1	yes	characteristic
36	C₄×D₈	—	3	1	no	—
37	C₃×#41	—	4	2	no	—
38	C₃×#41	—	12	2	no	—
39	C₂×C₃×Q₈	C₃×D₄	1	1	yes	characteristic
40	C₂×C₃×D₄	—	3	2	no	—
41	C₂×C₃×D₄	—	6	2	no	—
42	C₂×C₃×D₄	—	6	2	no	—
43	C₂²×C₃×C₄	—	6	2	no	—
44	C₃×D₈	—	6	2	no	—
45	C₃×D₈	—	12	2	no	—
46	C₂×C₃×C₈	—	3	1	no	—
47	C₂×C₃×C₈	C₂×A₄	1	1	yes	characteristic
48	C₃×C₄⋊C₄	—	3	1	no	—
49	C₃×C₄⋊C₄	C₂×A₄	1	2	yes	—
50	C₃×C₂²⋊C₄	—	6	2	no	—
51	C₃×C₄²	—	3	1	no	—
52	C₂²×C₉	—	4	1	no	—
53	C₄×C₉	—	4	1	no	—
54	C₄×C₉	—	4	1	no	—
55	C₄×C₉	—	16	2	no	—
56	C₂×#41	—	2	2	no	—
57	C₂×D₈	—	3	2	no	—
58	C₂×D₈	—	3	1	no	—
59	#127	—	3	2	no	—
60	#121	—	6	2	no	—
61	C₄×Q₈	C₂²×C₉	1	1	yes	characteristic
62	C₄×D₄	—	3	2	no	—
63	#107	C₂²⋊C₉	1	1	yes	characteristic
64	C₄⋊C₈	—	3	1	no	—
65	#102	—	3	2	no	—
66	C₄×C₈	—	3	1	no	—
67	C₂³×C₃	—	6	2	no	—
68	C₃×Q₈	—	3	1	no	—
69	C₃×Q₈	C₃×D₈	1	1	yes	characteristic
70	C₃×D₄	—	6	2	no	—
71	C₃×D₄	—	6	2	no	—
72	C₃×D₄	—	12	2	no	—
73	C₃×D₄	—	12	2	no	—
74	C₃×D₄	—	24	2	no	—
75	C₂×C₃×C₄	—	2	2	no	—
76	C₂×C₃×C₄	—	3	1	no	—
77	C₂×C₃×C₄	—	3	1	no	—
78	C₂×C₃×C₄	—	12	2	no	—
79	C₂×C₃×C₄	—	12	2	no	—
80	C₂×C₃×C₄	C₂²×A₄	1	1	yes	characteristic
81	C₃×C₈	—	6	1	no	—
82	C₃×C₈	#41⋊C₃	1	2	yes	—
83	C₂×C₉	—	4	1	no	—
84	C₂×C₉	—	4	1	no	—
85	C₂×C₉	—	4	1	no	—
86	#41	—	4	2	no	—
87	#41	—	12	2	no	—
88	C₂×Q₈	D₄×C₉	1	1	yes	characteristic
89	C₂×D₄	—	3	2	no	—
90	C₂×D₄	—	6	2	no	—
91	C₂×D₄	—	6	2	no	—
92	C₂²×C₄	—	6	2	no	—
93	D₈	—	6	2	no	—
94	D₈	—	12	2	no	—
95	C₂×C₈	—	3	1	no	—
96	C₂×C₈	C₂×C₂²⋊C₉	1	1	yes	characteristic
97	C₄⋊C₄	—	3	1	no	—
98	C₄⋊C₄	C₂×C₂²⋊C₉	1	2	yes	—
99	C₂²⋊C₄	—	6	2	no	—
100	C₄²	—	3	1	no	—
101	C₂²×C₃	—	12	2	no	—
102	C₂²×C₃	—	12	2	no	—
103	C₂²×C₃	—	12	2	no	—
104	C₂²×C₃	D₄×A₄	1	1	yes	characteristic
105	C₃×C₄	—	3	1	no	—
106	C₃×C₄	—	3	1	no	—
107	C₃×C₄	—	4	2	no	—
108	C₃×C₄	—	6	1	no	—
109	C₃×C₄	C₂×#41⋊C₃	1	1	yes	characteristic
110	C₃×C₄	#994	1	1	yes	characteristic
111	C₉	—	4	1	no	Sylow
112	C₂³	—	6	2	no	—
113	Q₈	—	3	1	no	—
114	Q₈	C₉×D₈	1	1	yes	characteristic
115	D₄	—	6	2	no	—
116	D₄	—	6	2	no	—
117	D₄	—	12	2	no	—
118	D₄	—	12	2	no	—
119	D₄	—	24	2	no	—
120	C₂×C₄	—	2	2	no	—
121	C₂×C₄	—	3	1	no	—
122	C₂×C₄	—	3	1	no	—
123	C₂×C₄	—	12	2	no	—
124	C₂×C₄	—	12	2	no	—
125	C₂×C₄	C₂²×C₂²⋊C₉	1	1	yes	characteristic
126	C₈	—	6	1	no	—
127	C₈	#41⋊C₉	1	2	yes	complemented
128	C₂×C₃	—	24	2	no	—
129	C₂×C₃	C₄⋊(#41⋊C₃)	1	1	yes	characteristic
130	C₂×C₃	A₄×D₈	1	1	yes	characteristic
131	C₂×C₃	#576⋊C₃	1	1	yes	characteristic
132	C₂²	—	12	2	no	—
133	C₂²	—	12	2	no	—
134	C₂²	—	12	2	no	—
135	C₂²	D₄×C₂²⋊C₉	1	1	yes	characteristic
136	C₄	—	3	1	no	—
137	C₄	—	3	1	no	—
138	C₄	—	4	2	no	—
139	C₄	—	6	1	no	—
140	C₄	C₂×#41⋊C₉	1	1	yes	characteristic
141	C₄	#63700	1	1	yes	characteristic
142	C₃	#3391⋊C₃	1	1	yes	characteristic
143	C₂	—	24	2	no	—
144	C₂	C₄⋊(#41⋊C₉)	1	1	yes	characteristic
145	C₂	D₈×C₂²⋊C₉	1	1	yes	characteristic
146	C₂	#576⋊C₉	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄⋊(#41⋊C₉)

C₂

yes

maximal, complemented

C₈×Q₈⋊C₉

C₂

yes

maximal, characteristic, complemented

C₃×#3391

C₃

yes

maximal, characteristic

C₂×#41⋊C₉

—

C₄×Q₈⋊C₉

C₂²

yes

—

C₂×C₃

yes

—

C₃×#493

—

C₃×#459

—

C₃×C₈×Q₈

C₂×C₃

yes

characteristic

C₃×C₄×D₈

—

#41⋊C₉

—

C₂×Q₈⋊C₉

D₄

yes

characteristic

C₂×C₈×C₉

—

C₉×C₄⋊C₄

—

#3391

C₉

yes

characteristic, complemented, Sylow

C₂×C₃×#41

—

C₂×C₃×D₈

—

C₂×C₃×D₈

—

C₃×#127

—

C₃×#121

—

C₃×C₄×Q₈

C₂²×C₃

yes

characteristic

C₃×C₄×D₄

—

C₃×#107

A₄

yes

characteristic

C₃×C₄⋊C₈

—

C₃×#102

—

C₃×C₄×C₈

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

Q₈⋊C₉

D₈

yes

characteristic, complemented

C₈×C₉

—

#550

C₂×C₉

yes

—

#493

—

#459

—

C₈×Q₈

C₂×C₉

yes

characteristic

C₄×D₈

—

C₃×#41

—

C₃×#41

—

C₂×C₃×Q₈

C₃×D₄

yes

characteristic

C₂×C₃×D₄

—

C₂×C₃×D₄

—

C₂×C₃×D₄

—

C₂²×C₃×C₄

—

C₃×D₈

—

C₃×D₈

—

C₂×C₃×C₈

—

C₂×C₃×C₈

C₂×A₄

yes

characteristic

C₃×C₄⋊C₄

—

C₃×C₄⋊C₄

C₂×A₄

yes

—

C₃×C₂²⋊C₄

—

C₃×C₄²

—

C₂²×C₉

—

C₄×C₉

—

C₄×C₉

—

C₄×C₉

—

C₂×#41

—

C₂×D₈

—

C₂×D₈

—

#127

—

#121

—

C₄×Q₈

C₂²×C₉

yes

characteristic

C₄×D₄

—

#107

C₂²⋊C₉

yes

characteristic

C₄⋊C₈

—

#102

—

C₄×C₈

—

C₂³×C₃

—

C₃×Q₈

—

C₃×Q₈

C₃×D₈

yes

characteristic

C₃×D₄

—

C₃×D₄

—

C₃×D₄

—

C₃×D₄

—

C₃×D₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

C₂²×A₄

yes

characteristic

C₃×C₈

—

C₃×C₈

#41⋊C₃

yes

—

C₂×C₉

—

C₂×C₉

—

C₂×C₉

—

#41

—

#41

—

C₂×Q₈

D₄×C₉

yes

characteristic

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

D₈

—

D₈

—

C₂×C₈

—

C₂×C₈

C₂×C₂²⋊C₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

C₂×C₂²⋊C₉

yes

—

C₂²⋊C₄

—

100

C₄²

—

101

C₂²×C₃

—

102

C₂²×C₃

—

103

C₂²×C₃

—

104

C₂²×C₃

D₄×A₄

yes

characteristic

105

C₃×C₄

—

106

C₃×C₄

—

107

C₃×C₄

—

108

C₃×C₄

—

109

C₃×C₄

C₂×#41⋊C₃

yes

characteristic

110

C₃×C₄

#994

yes

characteristic

111

C₉

—

Sylow

112

C₂³

—

113

Q₈

—

114

Q₈

C₉×D₈

yes

characteristic

115

D₄

—

116

D₄

—

117

D₄

—

118

D₄

—

119

D₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

C₂²×C₂²⋊C₉

yes

characteristic

126

C₈

—

127

C₈

#41⋊C₉

yes

complemented

128

C₂×C₃

—

129

C₂×C₃

C₄⋊(#41⋊C₃)

yes

characteristic

130

C₂×C₃

A₄×D₈

yes

characteristic

131

C₂×C₃

#576⋊C₃

yes

characteristic

132

C₂²

—

133

C₂²

—

134

C₂²

—

135

C₂²

D₄×C₂²⋊C₉

yes

characteristic

136

C₄

—

137

C₄

—

138

C₄

—

139

C₄

—

140

C₄

C₂×#41⋊C₉

yes

characteristic

141

C₄

#63700

yes

characteristic

142

C₃

#3391⋊C₃

yes

characteristic

143

C₂

—

144

C₂

C₄⋊(#41⋊C₉)

yes

characteristic

145

C₂

D₈×C₂²⋊C₉

yes

characteristic

146

C₂

#576⋊C₉

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₃	D₄×A₄
commutator	C₄×Q₈	C₂²×C₉
Frattini	C₂×C₃×C₄	C₂²×A₄
Fitting, prime radical	C₃×#3391	C₃
cosocle	C₃×C₄×Q₈	C₂²×C₃
hypercenter	C₃×#107	A₄
hypocenter	Q₈	C₉×D₈
LCS	G ▷ C₄×Q₈ ▷ C₂×Q₈ ▷ Q₈
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄ ◁ C₃×#107

subgroup

G/H

center, socle

C₂²×C₃

D₄×A₄

commutator

C₄×Q₈

C₂²×C₉

Frattini

C₂×C₃×C₄

C₂²×A₄

Fitting, prime radical

C₃×#3391

C₃

cosocle

C₃×C₄×Q₈

C₂²×C₃

hypercenter

C₃×#107

A₄

hypocenter

Q₈

C₉×D₈

LCS

G ▷ C₄×Q₈ ▷ C₂×Q₈ ▷ Q₈

UCS

C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄ ◁ C₃×#107

N	H ≅ G/N	type
1. C₄⋊(#41⋊C₉)	C₂	semidirect
2. C₈×Q₈⋊C₉	C₂	semidirect
16. #3391	C₉	semidirect
30. Q₈⋊C₉	D₈	semidirect
127. C₈	#41⋊C₉	semidirect

H ≅ G/N

type

1. C₄⋊(#41⋊C₉)

C₂

semidirect

2. C₈×Q₈⋊C₉

C₂

semidirect

16. #3391

C₉

semidirect

30. Q₈⋊C₉

D₈

semidirect

127. C₈

#41⋊C₉

semidirect

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

subgroup	index
C₄⋊(#41⋊C₉)	2
C₈×Q₈⋊C₉	2
C₃×#3391	3
C₉×#107	4

subgroup

index

C₄⋊(#41⋊C₉)

C₈×Q₈⋊C₉

C₃×#3391

C₉×#107

Subgroups — #3391⋊C₉ #11919611

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3391⋊C9 #11919611

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3391⋊C₉ #11919611