Finite Group Databasebeta

← D181⋊#352 #37549970

Subgroups — D181⋊#352 #37549970

Order 23168.

278 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 54 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
1D181⋊#100C211yesmaximal, characteristic
2D181⋊#99C211yesmaximal, characteristic
3#26042182C212yesmaximal, complemented
4#26042181C212yesmaximal, complemented
5#123×D181C211yesmaximal, characteristic
6D181⋊M16—21no—
7C2×C22⋊#10624382—21no—
8#19153876—21no—
9#19153876C2212yes—
10#19153875—21no—
11#19153874C2212yes—
12C2×D4×D181C2211yescharacteristic
13C22×C4×D181C411yescharacteristic, complemented
14#19153801—21no—
15#19153800C2211yescharacteristic
16#19153799C2211yescharacteristic
17#19153798—21no—
18#19153797C411yescharacteristic, complemented
19C4⋊C4×D181—21no—
20C22⋊C4×D181—21no—
21C22⋊C4×D181C411yescharacteristic, complemented
22#123×C181C411yescharacteristic, complemented
23C22×#10624382—41no—
24#15668459—41no—
25#15668458—22no—
26D181⋊C8—41no—
27C22⋊#10624382—22no—
28C22⋊#10624382—41no—
29C23×D181C2×C411yescharacteristic
30C23×D181D411yescharacteristic
31C2×D724D411yescharacteristic
32C2×C22⋊D181D411yescharacteristic
33C2×C22⋊D181C2311yescharacteristic
34D4×D181—41no—
35D4×D181—41no—
36C22×Dic181C2×C411yescharacteristic, complemented
37C2×C4×D181—21no—
38C2×C4×D181—21no—
39C2×C4×D181—21no—
40C2×C4×D181—41no—
41C2×C4×D181—41no—
42C2×C4×D181D411yescharacteristic
43C4⋊Dic181—21no—
44#15668428—21no—
45#15668428—21no—
46C22⋊Dic181—21no—
47C22⋊Dic181C2×C411yescharacteristic, complemented
48#15668426—21no—
49#15668426—21no—
50#15668426—21no—
51C2×D4×C181C2×C411yescharacteristic
52C22×C4×C181C2×C411yescharacteristic, complemented
53C4⋊C4×C181—21no—
54C22⋊C4×C181—21no—
55C22⋊C4×C181C2×C411yescharacteristic, complemented
56C2×#10624382—42no—
57C2×#10624382—82no—
58#13089685—42no—
59C22×D181—21no—
60C22×D181—21no—
61C22×D181—21no—
62C22×D181—21no—
63C22×D181—42no—
64C22×D181—42no—
65C22×D181C22⋊C411yescharacteristic
66C22×D181C22⋊C411yescharacteristic
67C22×D181C2×D411yescharacteristic
68D724—41no—
69C22⋊D181—41no—
70C22⋊D181—41no—
71C2×Dic181—21no—
72C2×Dic181—21no—
73C2×Dic181—41no—
74C2×Dic181C2×D411yescharacteristic
75C4×D181—21no—
76C4×D181—21no—
77C4×D181—42no—
78C4×D181—42no—
79C4×D181—41no—
80C4×D181—41no—
81C23×C181C22⋊C411yescharacteristic
82C23×C181C22×C411yescharacteristic
83D4×C181—41no—
84C2×C4×C181—21no—
85C2×C4×C181—21no—
86C2×C4×C181—41no—
87C2×C4×C181C22⋊C411yescharacteristic
88C22×C181—21no—
89C22×C181—21no—
90C22×C181—41no—
91C22×C181—41no—
92C22×C181C2×C22⋊C411yescharacteristic
93C2×D181—22no—
94C2×D181—21no—
95C2×D181—21no—
96C2×D181—42no—
97C2×D181—42no—
98C2×D181—42no—
99C2×D181—41no—
100C2×D181—41no—
101C2×D181—81no—
102C2×D181#9911yescharacteristic
103C2×D181#9911yescharacteristic
104#10624382—82no—
105C4×C181—21no—
106C4×C181—41no—
107C4×C181—41no—
108Dic181—21no—
109Dic181—41no—
110Dic181—41no—
111C2×C181—21no—
112C2×C181—41no—
113C2×C181—41no—
114C2×C181C2×#9911yescharacteristic
115D181—21no—
116D181—41no—
117D181—41no—
118D181#35212yescomplemented
119C181C2×#35211yescharacteristic, complemented, Sylow
120C2×#352—1811nomaximal, Sylow
121C2×#123—1811no—
122C2×#100—1811no—
123C2×#99—1811no—
124#352—1812no—
125#352—1812no—
126C22×D4—1811no—
127C23×C4—1811no—
128C2×M16—3621no—
129#123—3621no—
130#123—3621no—
131#123—1811no—
132#123—1811no—
133#123—1811no—
134#123#1062438211yescharacteristic, complemented
135C2×C4⋊C4—3621no—
136C2×C22⋊C4—3621no—
137C2×C22⋊C4—3621no—
138C2×C22⋊C4—1811no—
139#100—3621no—
140#100—1812no—
141#99—3621no—
142#99—1812no—
143C24—1811no—
144C24—1811no—
145C2×D4—1811no—
146C2×D4—1811no—
147C2×D4—1811no—
148C2×D4—7241no—
149C2×D4—7241no—
150C2×D4C2×#1062438211yescharacteristic
151C22×C4—3621no—
152C22×C4—3621no—
153C22×C4—3621no—
154C22×C4—1811no—
155C22×C4—1811no—
156C22×C4—7241no—
157C22×C4—7241no—
158C22×C4—7241no—
159C22×C4C2×#1062438211yescharacteristic, complemented
160M16—3622no—
161M16—7241no—
162C2×C8—7241no—
163C4⋊C4—21no—
164C4⋊C4—3621no—
165C4⋊C4—3621no—
166C4⋊C4—3621no—
167C22⋊C4—21no—
168C22⋊C4—3621no—
169C22⋊C4—3621no—
170C22⋊C4—3621no—
171C22⋊C4—3621no—
172C22⋊C4—3622no—
173C22⋊C4—1811no—
174C22⋊C4—7241no—
175C22⋊C4C2×#1062438211yescharacteristic, complemented
176C23—3621no—
177C23—3621no—
178C23—3621no—
179C23—3621no—
180C23—1811no—
181C23—1811no—
182C23—1811no—
183C23—7242no—
184C23—7242no—
185C23C22⋊#1062438211yescharacteristic
186C23C22×#1062438211yescharacteristic
187D4—41no—
188D4—7241no—
189D4—7241no—
190D4—7241no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—41no—
194C2×C4—3621no—
195C2×C4—3621no—
196C2×C4—3621no—
197C2×C4—3621no—
198C2×C4—14482no—
199C2×C4—1811no—
200C2×C4—7242no—
201C2×C4—7242no—
202C2×C4—7241no—
203C2×C4—7241no—
204C2×C4—7242no—
205C2×C4—7241no—
206C2×C4C22⋊#1062438211yescharacteristic
207C8—7242no—
208C22—21no—
209C22—21no—
210C22—41no—
211C22—41no—
212C22—3622no—
213C22—3621no—
214C22—3621no—
215C22—14481no—
216C22—1811no—
217C22—1811no—
218C22—7241no—
219C22—7241no—
220C22—7242no—
221C22—7242no—
222C22—7242no—
223C22C2×C22⋊#1062438211yescharacteristic
224C4—21no—
225C4—41no—
226C4—41no—
227C4—3621no—
228C4—14482no—
229C4—7241no—
230C4—7241no—
231C2—21no—
232C2—41no—
233C2—41no—
234C2—3621no—
235C2—1812no—
236C2—7241no—
237C2—7241no—
238C2D181⋊#9911yescharacteristic
subgroupG/H
centerC2D181⋊#99
commutatorC23×C181C22×C4
FrattiniC23C22×#10624382
Fitting#123×C181C4
socleC2×C181C2×#99
prime radicalC2×D4×D181C22
cosocleC2×C22⋊D181C23
hypercenter#123#10624382
hypocenterC181C2×#352
LCSG ▷ C23×C181 ▷ C22×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #123

Complements

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

NH ≅ G/Ntype
3. #26042182C2semidirect
4. #26042181C2semidirect
13. C22×C4×D181C4semidirect
18. #19153797C4semidirect
21. C22⋊C4×D181C4semidirect
22. #123×C181C4semidirect
36. C22×Dic181C2×C4semidirect
47. C22⋊Dic181C2×C4semidirect
52. C22×C4×C181C2×C4semidirect
55. C22⋊C4×C181C2×C4semidirect
118. D181#352semidirect
119. C181C2×#352semidirect
134. #123#10624382semidirect
159. C22×C4C2×#10624382semidirect
175. C22⋊C4C2×#10624382semidirect

Maximal subgroups

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

subgroupindex
D181⋊#1002
D181⋊#992
#260421822
#260421812
#123×D1812
C2×#352181