Finite Group Databasebeta

← #37537011

Subgroups — #37537011

Order 23168.

504 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 167 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×Q8×Dic181C211yesmaximal, characteristic
2C2×#19153781C211yesmaximal, characteristic
3#26041212C212yesmaximal
4#26041211C211yesmaximal, characteristic
5#26041209C211yesmaximal, characteristic
6#26041200C212yesmaximal
7#26041198C211yesmaximal, characteristic
8C4⋊C4×Dic181C212yesmaximal
9#26041130C212yesmaximal
10#26041124C211yesmaximal, characteristic
11#395×C181C211yesmaximal, characteristic
12C22×Dic362C2211yescharacteristic
13Q8×Dic181—24no—
14#19153781—24no—
15C2×C4⋊Dic181C2212yes—
16C2×C4⋊Dic181C2212yes—
17C2×C4⋊Dic181C2211yescharacteristic
18C2×#15668428C2212yes—
19C2×#15668428C2212yes—
20C2×#15668428C2211yescharacteristic
21C2×#15668428C2211yescharacteristic
22C2×C4×Dic181C2211yescharacteristic
23C2×C4×Dic181C2212yes—
24C2×C4×Dic181C2211yescharacteristic
25C2×C4×Dic181C2211yescharacteristic
26C2×C4×Dic181C2212yes—
27#19153723C2211yescharacteristic
28#19153723C2212yes—
29#19153723C2212yes—
30#19153723C2212yes—
31#19153723C2212yes—
32C22×Q8×C181C2211yescharacteristic
33C2×C4⋊C4×C181C2212yes—
34C2×C4⋊C4×C181C2211yescharacteristic
35#95×C181C2211yescharacteristic
36#95×C181C2212yes—
37C2×Dic362—22no—
38C2×Dic362—22no—
39C2×Dic362—22no—
40C22×Dic181C2311yescharacteristic
41C22×Dic181C2312yes—
42C22×Dic181C2311yescharacteristic
43C22×Dic181C2312yes—
44C22×Dic181C2311yescharacteristic
45C22×Dic181C2311yescharacteristic
46C4⋊Dic181—24no—
47C4⋊Dic181—24no—
48C4⋊Dic181—22no—
49#15668428—22no—
50#15668428—22no—
51#15668428—24no—
52#15668428—24no—
53C4×Dic181—22no—
54C4×Dic181—22no—
55C4×Dic181—24no—
56C4×Dic181D414yes—
57C4×Dic181Q818yescomplemented
58C2×Q8×C181—22no—
59C2×Q8×C181—24no—
60C22×C4×C181C2311yescharacteristic
61C22×C4×C181C2311yescharacteristic
62C22×C4×C181C2312yes—
63C22×C4×C181C2311yescharacteristic
64C22×C4×C181C2312yes—
65C4⋊C4×C181—22no—
66C4⋊C4×C181—24no—
67Dic362—28no—
68C2×Dic181—21no—
69C2×Dic181—22no—
70C2×Dic181—22no—
71C2×Dic181—21no—
72C2×Dic181—21no—
73C2×Dic181—21no—
74C2×Dic181—21no—
75C2×Dic181—22no—
76C2×Dic181—22no—
77C2×Dic181—22no—
78C2×Dic181—22no—
79C2×Dic181C2×D412yes—
80C2×Dic181C2×D412yes—
81C2×Dic181C2×Q814yes—
82C2×Dic181C2×Q814yes—
83C2×Dic181#4112yes—
84C23×C181C2411yescharacteristic
85Q8×C181—28no—
86C2×C4×C181—21no—
87C2×C4×C181—22no—
88C2×C4×C181—22no—
89C2×C4×C181—22no—
90C2×C4×C181—22no—
91C2×C4×C181—22no—
92C2×C4×C181—21no—
93C2×C4×C181—21no—
94C2×C4×C181—22no—
95C2×C4×C181C2×D412yes—
96C2×C4×C181C2×Q814yes—
97C2×C4×C181#4114yes—
98C2×C4×C181#4112yes—
99C22×C181C22×D411yescharacteristic
100C22×C181C22×Q812yes—
101C22×C181C2×#4111yescharacteristic
102C22×C181C2×#4112yes—
103C22×C181C2×#4111yescharacteristic
104C4×C181—22no—
105C4×C181—24no—
106C4×C181—22no—
107C4×C181—24no—
108C4×C181—41no—
109Dic181—22no—
110Dic181—22no—
111Dic181—24no—
112Dic181—41no—
113Dic181—42no—
114Dic181C4⋊Q814yes—
115C2×C181#52511yescharacteristic
116C2×C181#52511yescharacteristic
117C2×C181C2×C4⋊Q811yescharacteristic
118C2×C181#53312yes—
119C2×C181#53312yes—
120C181#239911yescharacteristic, complemented, Sylow
121#2399—1811nomaximal, Sylow
122C2×C4×Q8—1811no—
123C2×C4×Q8—1811no—
124#398—1811no—
125#398—1812no—
126#398—1811no—
127#395—1811no—
128#395—1812no—
129#395D18111yescharacteristic
130C4×C4⋊C4—1812no—
131C4×C4⋊C4—1812no—
132#376—1811no—
133C22×Q8—1811no—
134C22×Q8C2×D18111yescharacteristic
135C4×Q8—3624no—
136C4×Q8—3624no—
137C2×C4⋊C4—1811no—
138C2×C4⋊C4—1811no—
139C2×C4⋊C4—1812no—
140C2×C4⋊C4—1811no—
141C2×C4⋊C4—1812no—
142C2×C4⋊C4—1812no—
143C2×C4⋊C4—1812no—
144C2×C4⋊C4C2×D18111yescharacteristic
145C2×C4⋊C4C2×D18112yes—
146C2×C42—1812no—
147C2×C42—1811no—
148C2×C42—1811no—
149C2×C42—1811no—
150C2×C42—1812no—
151#95—1811no—
152#95—1812no—
153#95—1812no—
154#95—1812no—
155#95—1812no—
156#95C2×D18111yescharacteristic
157#95C2×D18112yes—
158C2×Q8—22no—
159C2×Q8—24no—
160C2×Q8—3622no—
161C2×Q8—3622no—
162C2×Q8—3622no—
163C22×C4—1812no—
164C22×C4—1811no—
165C22×C4—1812no—
166C22×C4—1811no—
167C22×C4—1811no—
168C22×C4—1811no—
169C22×C4C22×D18111yescharacteristic
170C22×C4C22×D18111yescharacteristic
171C22×C4C22×D18112yes—
172C22×C4C22×D18112yes—
173C22×C4C22×D18111yescharacteristic
174C4⋊C4—22no—
175C4⋊C4—24no—
176C4⋊C4—3622no—
177C4⋊C4—3624no—
178C4⋊C4—3624no—
179C4⋊C4—3622no—
180C4⋊C4—3622no—
181C4⋊C4—3624no—
182C4⋊C4—3624no—
183C42—3622no—
184C42—3624no—
185C42—3622no—
186C42—1814no—
187C42—1818no—
188C23C23×D18111yescharacteristic
189Q8—28no—
190Q8—3628no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—22no—
200C2×C4—3621no—
201C2×C4—3621no—
202C2×C4—3622no—
203C2×C4—3622no—
204C2×C4—3621no—
205C2×C4—3621no—
206C2×C4—3621no—
207C2×C4—3622no—
208C2×C4—3622no—
209C2×C4—3622no—
210C2×C4—3622no—
211C2×C4—1812no—
212C2×C4—1814no—
213C2×C4—1812no—
214C2×C4—1812no—
215C2×C4—1814no—
216C2×C4D4×D18112yes—
217C2×C4Q8×D18114yes—
218C2×C4#1566844814yes—
219C2×C4#1566845012yes—
220C22C2×D4×D18111yescharacteristic
221C22C2×Q8×D18112yes—
222C22#41×D18111yescharacteristic
223C22C2×#1566844812yes—
224C22C2×#1566845011yescharacteristic
225C4—22no—
226C4—24no—
227C4—22no—
228C4—24no—
229C4—41no—
230C4—3622no—
231C4—3622no—
232C4—3624no—
233C4—1814no—
234C4—7241no—
235C4—7242no—
236C2#2604178511yescharacteristic
237C2#2604179211yescharacteristic
238C2C4⋊Q8×D18111yescharacteristic
239C2#2604183112yes—
240C2#2604183412yes—
subgroupG/H
center, FrattiniC23C23×D181
commutator, socle, prime radical, cosocleC23×C181C24
Fitting#395×C181C2
hypercenter#395D181
hypocenterC181#2399
LCSG ▷ C23×C181 ▷ C181
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
57. C4×Dic181Q8semidirect
120. C181#2399semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×Dic1812
C2×#191537812
#260412122
#260412112
#260412092
#260412002
#260411982
C4⋊C4×Dic1812
#260411302
#260411242
#395×C1812
#2399181