Finite Group Databasebeta

← #37542058

Subgroups — #37542058

Order 23168.

564 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 169 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
1C2×#19153793C211yesmaximal, characteristic
2C22×C4×Dic181C211yesmaximal, characteristic
3#26041183C212yesmaximal, complemented
4#26041176C212yesmaximal, complemented
5#26041166C212yesmaximal, complemented
6#26041162C212yesmaximal, complemented
7#26041154C211yesmaximal, characteristic
8#26041151C211yesmaximal, characteristic
9#26041142C211yesmaximal, characteristic
10#26041137C211yesmaximal, characteristic
11#381×C181C211yesmaximal, characteristic
12C22×Dic362C2211yescharacteristic
13C23×Dic181C2211yescharacteristic
14C23×Dic181C2211yescharacteristic
15#19153793—24no—
16C2×C4⋊Dic181C2212yes—
17C2×C4⋊Dic181C2211yescharacteristic
18C2×#15668428C2212yes—
19C2×#15668428C2212yes—
20C2×#15668428C2211yescharacteristic
21C2×#15668428C2211yescharacteristic
22C2×C22⋊Dic181C2211yescharacteristic
23C2×C22⋊Dic181C2211yescharacteristic
24C2×C4×Dic181—24no—
25C2×C4×Dic181C2212yes—
26C2×C4×Dic181C2212yes—
27#19153723C2212yes—
28#19153723C2212yes—
29#19153723C2212yes—
30#19153723C2212yes—
31#19153723C2212yes—
32C23×C4×C181C2211yescharacteristic
33C2×C22⋊C4×C181C2211yescharacteristic
34C2×C22⋊C4×C181C2211yescharacteristic
35#95×C181C2212yes—
36#95×C181C2212yes—
37C2×Dic362—22no—
38C2×Dic362—24no—
39C22×Dic181—24no—
40C22×Dic181—24no—
41C22×Dic181—22no—
42C22×Dic181D414yes—
43C22×Dic181C2312yes—
44C22×Dic181C2311yescharacteristic
45C22×Dic181C2311yescharacteristic
46C22×Dic181C2311yescharacteristic
47C22×Dic181C2312yes—
48C22×Dic181C2311yescharacteristic
49C4⋊Dic181—22no—
50C4⋊Dic181—24no—
51#15668428—22no—
52#15668428—22no—
53#15668428—24no—
54#15668428—24no—
55C22⋊Dic181—22no—
56C22⋊Dic181—22no—
57C4×Dic181—24no—
58C4×Dic181—24no—
59C24×C181C2311yescharacteristic
60C22×C4×C181—22no—
61C22×C4×C181—22no—
62C22×C4×C181Q814yescomplemented
63C22×C4×C181C2312yes—
64C22×C4×C181C2311yescharacteristic
65C22×C4×C181C2311yescharacteristic
66C22×C4×C181C2312yes—
67C22⋊C4×C181—22no—
68C22⋊C4×C181—22no—
69Dic362—44no—
70C2×Dic181—28no—
71C2×Dic181—22no—
72C2×Dic181—22no—
73C2×Dic181—22no—
74C2×Dic181—28no—
75C2×Dic181—21no—
76C2×Dic181—21no—
77C2×Dic181—22no—
78C2×Dic181—22no—
79C2×Dic181—22no—
80C2×Dic181—22no—
81C2×Dic181—22no—
82C2×Dic181C2×D412yes—
83C2×Dic181C2×D412yes—
84C2×Dic181#4114yes—
85C2×Dic181#4114yes—
86C23×C181—22no—
87C23×C181—22no—
88C23×C181C2×D412yes—
89C23×C181C2×Q812yes—
90C23×C181#4112yes—
91C23×C181C2411yescharacteristic
92C2×C4×C181—28no—
93C2×C4×C181—22no—
94C2×C4×C181—22no—
95C2×C4×C181—21no—
96C2×C4×C181—21no—
97C2×C4×C181—22no—
98C2×C4×C181—22no—
99C2×C4×C181—22no—
100C2×C4×C181—22no—
101C2×C4×C181—22no—
102C2×C4×C181C2×Q814yes—
103C22×C181—22no—
104C22×C181—22no—
105C22×C181—24no—
106C22×C181—24no—
107C22×C181C22⋊Q814yes—
108C22×C181C22×D411yescharacteristic
109C22×C181C22×Q811yescharacteristic
110C22×C181C2×#4112yes—
111C22×C181C2×#4112yes—
112C22×C181C2×#4111yescharacteristic
113C4×C181—24no—
114C4×C181—41no—
115C4×C181—41no—
116C4×C181—42no—
117Dic181—22no—
118Dic181—24no—
119Dic181—41no—
120Dic181—41no—
121Dic181—42no—
122Dic181#12314yes—
123C2×C181—24no—
124C2×C181C2×C22⋊Q811yescharacteristic
125C2×C181C2×#12311yescharacteristic
126C2×C181#52511yescharacteristic
127C2×C181#52912yes—
128C2×C181#53312yes—
129C181#285511yescharacteristic, complemented, Sylow
130#2855—1811nomaximal, Sylow
131C2×C22⋊Q8—1811no—
132C22×C42—1811no—
133#391—1812no—
134#389—1812no—
135#387—1812no—
136#387—1812no—
137#385—1811no—
138#385—1811no—
139#381—1811no—
140#381D18111yescharacteristic
141#380—1811no—
142C22×Q8—1811no—
143C23×C4—1811no—
144C23×C4—1811no—
145C23×C4C2×D18111yescharacteristic
146C22⋊Q8—3624no—
147C2×C4⋊C4—1811no—
148C2×C4⋊C4—1811no—
149C2×C4⋊C4—1811no—
150C2×C4⋊C4—1812no—
151C2×C4⋊C4—1812no—
152C2×C4⋊C4—1812no—
153C2×C22⋊C4—1811no—
154C2×C22⋊C4—1811no—
155C2×C22⋊C4C2×D18111yescharacteristic
156C2×C22⋊C4C2×D18111yescharacteristic
157C2×C42—3624no—
158C2×C42—1812no—
159C2×C42—1812no—
160#95—1812no—
161#95—1812no—
162#95—1812no—
163#95—1812no—
164#95—1812no—
165#95C2×D18112yes—
166#95C2×D18112yes—
167C24C22×D18111yescharacteristic
168C2×Q8—3622no—
169C2×Q8—3624no—
170C22×C4—22no—
171C22×C4—22no—
172C22×C4—3622no—
173C22×C4—3624no—
174C22×C4—3624no—
175C22×C4—1812no—
176C22×C4—1811no—
177C22×C4—1811no—
178C22×C4—1814no—
179C22×C4—1812no—
180C22×C4—1811no—
181C22×C4—1811no—
182C22×C4Dic36214yescomplemented
183C22×C4C22×D18112yes—
184C22×C4C22×D18111yescharacteristic
185C22×C4C22×D18111yescharacteristic
186C22×C4C22×D18112yes—
187C4⋊C4—3622no—
188C4⋊C4—3622no—
189C4⋊C4—3622no—
190C4⋊C4—3624no—
191C4⋊C4—3624no—
192C4⋊C4—3624no—
193C22⋊C4—22no—
194C22⋊C4—22no—
195C22⋊C4—3622no—
196C22⋊C4—3622no—
197C42—3624no—
198C42—3624no—
199C23—22no—
200C23—22no—
201C23D4×D18112yes—
202C23C2×Dic36212yes—
203C23#1566844812yes—
204C23C23×D18111yescharacteristic
205Q8—7244no—
206C2×C4—28no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—3628no—
217C2×C4—3622no—
218C2×C4—3622no—
219C2×C4—3622no—
220C2×C4—3628no—
221C2×C4—3621no—
222C2×C4—3621no—
223C2×C4—3622no—
224C2×C4—3622no—
225C2×C4—3622no—
226C2×C4—3622no—
227C2×C4—3622no—
228C2×C4—1812no—
229C2×C4—1814no—
230C2×C4—1812no—
231C2×C4—1814no—
232C2×C4C2×Dic36214yes—
233C22—22no—
234C22—22no—
235C22—24no—
236C22—24no—
237C22#1915379314yes—
238C22C2×D4×D18111yescharacteristic
239C22C22×Dic36211yescharacteristic
240C22#41×D18112yes—
241C22#41×D18112yes—
242C22C2×#1566844811yescharacteristic
243C4—24no—
244C4—41no—
245C4—41no—
246C4—42no—
247C4—3622no—
248C4—3624no—
249C4—1814no—
250C4—7241no—
251C4—7241no—
252C4—7242no—
253C2—24no—
254C2C2×#1915379311yescharacteristic
255C2#123×D18111yescharacteristic
256C2#2604178711yescharacteristic
257C2#2604180612yes—
258C2#2604183212yes—
subgroupG/H
center, FrattiniC23C23×D181
commutator, socle, cosocleC23×C181C24
Fitting#381×C181C2
prime radicalC24×C181C23
hypercenter#381D181
hypocenterC181#2855
LCSG ▷ C23×C181 ▷ C181
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
3. #26041183C2semidirect
4. #26041176C2semidirect
5. #26041166C2semidirect
6. #26041162C2semidirect
62. C22×C4×C181Q8semidirect
129. C181#2855semidirect
182. C22×C4Dic362semidirect

Maximal subgroups

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

subgroupindex
C2×#191537932
C22×C4×Dic1812
#260411832
#260411762
#260411662
#260411622
#260411542
#260411512
#260411422
#260411372
#381×C1812
#2855181