Finite Group Databasebeta

← #37534167

Subgroups — #37534167

Order 23168.

358 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.

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

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041790C211yesmaximal, characteristic
2C2×#19153775C211yesmaximal, characteristic, complemented
3C2×#19153742C212yesmaximal, complemented
4#26041040C212yesmaximal, complemented
5#407×C181C211yesmaximal, characteristic, complemented
6C2×#15668449C2211yescharacteristic
7#19153799—21no—
8#19153795C412yescomplemented
9#19153790C412yescomplemented
10#19153785—21no—
11C4×C22⋊D181—22no—
12#19153775—24no—
13#19153775C2211yescharacteristic
14C2×C4⋊Dic181—21no—
15C2×C22⋊Dic181—21no—
16C2×C4×Dic181C2212yes—
17#19153742—24no—
18C23×C4×C181C2211yescharacteristic
19C2×M16×C181C2212yes—
20C22⋊C8×C181—22no—
21#15668449—22no—
22#15668449—22no—
23C2×Dic362C2×C411yescharacteristic
24C2×D724C2×C411yescharacteristic
25C2×C22⋊D181—22no—
26C2×C22⋊D181—21no—
27C22×Dic181—22no—
28C2×C4×D181—21no—
29C4⋊Dic181—24no—
30C4⋊Dic181C2×C412yes—
31#15668428—22no—
32C22⋊Dic181—24no—
33C22⋊Dic181—22no—
34C22⋊Dic181—21no—
35#15668426—22no—
36C4×Dic181—22no—
37C4×Dic181—21no—
38C4×Dic181D414yescomplemented
39C24×C181D411yescharacteristic
40C22×C4×C181—22no—
41C22×C4×C181—22no—
42C22×C4×C181C2×C412yes—
43C22×C4×C181D412yes—
44C22×C4×C181D411yescharacteristic
45C22×C4×C181C2311yescharacteristic
46M16×C181—22no—
47M16×C181—22no—
48C2×C8×C181—22no—
49C22×D181—21no—
50Dic362—22no—
51D724—22no—
52C22⋊D181—44no—
53C22⋊D181—41no—
54C22⋊D181—41no—
55C2×Dic181—22no—
56C2×Dic181—21no—
57C2×Dic181—24no—
58C2×Dic181—44no—
59C4×D181—42no—
60C23×C181—21no—
61C23×C181—21no—
62C23×C181—42no—
63C23×C181C22⋊C412yes—
64C23×C181C2×D411yescharacteristic
65C2×C4×C181—21no—
66C2×C4×C181—21no—
67C2×C4×C181—24no—
68C2×C4×C181—24no—
69C2×C4×C181C22⋊C412yes—
70C2×C4×C181C22×C411yescharacteristic
71C2×C4×C181C2×D412yes—
72C2×C4×C181C2×D411yescharacteristic
73C2×C4×C181#4112yes—
74C8×C181—42no—
75C22×C181—22no—
76C22×C181—22no—
77C22×C181—22no—
78C22×C181—22no—
79C22×C181—42no—
80C22×C181—42no—
81C22×C181C2×C22⋊C411yescharacteristic
82C22×C181#12011yescharacteristic
83C22×C181#12311yescharacteristic
84C2×D181—41no—
85C2×D181—42no—
86C4×C181—22no—
87C4×C181C4×D412yes—
88C4×C181#12112yes—
89Dic181—44no—
90Dic181—41no—
91Dic181—42no—
92C2×C181—21no—
93C2×C181—21no—
94C2×C181—42no—
95C2×C181#38611yescharacteristic
96C2×C181#42112yes—
97D181—81no—
98C181#189711yescharacteristic, complemented, Sylow
99#1897—1811nomaximal, Sylow
100#525—1811no—
101C2×#117—1811no—
102C2×#104—1812no—
103#407D18111yescharacteristic, complemented
104#339—1812no—
105C2×#41—1811no—
106C23×C4C2×D18111yescharacteristic
107C2×M16C2×D18112yes—
108#123—3621no—
109C22⋊Q8—1812no—
110#121—1812no—
111#120—3621no—
112C4×D4—3622no—
113#117—3624no—
114#117—1811no—
115C2×C4⋊C4—3621no—
116C2×C22⋊C4—3621no—
117C2×C42—1812no—
118#104—3624no—
119C22⋊C8—22no—
120C24D72411yescharacteristic
121#41—3622no—
122#41—3622no—
123C2×Q8—1811no—
124C2×D4—3622no—
125C2×D4—3621no—
126C2×D4—1811no—
127C22×C4—22no—
128C22×C4—22no—
129C22×C4—3622no—
130C22×C4—3621no—
131C22×C4C4×D18112yes—
132C22×C4C22⋊D18112yes—
133C22×C4D72411yescharacteristic
134C22×C4C22×D18111yescharacteristic
135M16—22no—
136M16—22no—
137C2×C8—22no—
138C4⋊C4—3624no—
139C4⋊C4—3622no—
140C4⋊C4—1812no—
141C22⋊C4—3624no—
142C22⋊C4—3622no—
143C22⋊C4—3621no—
144C22⋊C4—3622no—
145C42—3622no—
146C42—3621no—
147C42—1814no—
148C23—21no—
149C23—21no—
150C23—42no—
151C23—3621no—
152C23#1566842612yes—
153C23C2×D72411yescharacteristic
154Q8—3622no—
155D4—3622no—
156D4—7244no—
157D4—7241no—
158D4—7241no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—24no—
162C2×C4—24no—
163C2×C4—3622no—
164C2×C4—3621no—
165C2×C4—3624no—
166C2×C4—7244no—
167C2×C4—7242no—
168C2×C4#1566842612yes—
169C2×C4C2×C4×D18111yescharacteristic
170C2×C4D4×D18112yes—
171C2×C4C2×C22⋊D18111yescharacteristic
172C2×C4#1566844812yes—
173C8—42no—
174C22—22no—
175C22—22no—
176C22—22no—
177C22—22no—
178C22—42no—
179C22—42no—
180C22—7241no—
181C22—7242no—
182C22C2×#1566842611yescharacteristic
183C22#1915378611yescharacteristic
184C22#1915380011yescharacteristic
185C4—22no—
186C4—7244no—
187C4—7241no—
188C4—7242no—
189C4#1915377612yes—
190C4#1915378812yes—
191C2—21no—
192C2—21no—
193C2—42no—
194C2—14481no—
195C2#2604115611yescharacteristic
196C2#2604129512yes—
subgroupG/H
centerC2×C4C2×C22⋊D181
commutatorC2×C4×C181C22×C4
FrattiniC22×C4C22×D181
Fitting#407×C181C2
socleC22×C181C2×C22⋊C4
prime radical#26041790C2
cosocleC22×C4×C181C23
hypercenter#407D181
hypocenterC181#1897
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #407

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#19153775C2semidirect
3. C2×#19153742C2semidirect
4. #26041040C2semidirect
5. #407×C181C2semidirect
8. #19153795C4semidirect
9. #19153790C4semidirect
38. C4×Dic181D4semidirect
98. C181#1897semidirect
103. #407D181semidirect

Maximal subgroups

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

subgroupindex
#260417902
C2×#191537752
C2×#191537422
#260410402
#407×C1812
#1897181