Finite Group Databasebeta

← #46783198

Subgroups — #46783198

Order 33664.

598 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 598 conjugacy classes of subgroups — too many to draw. Only its 97 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×#22554439C211yesmaximal, characteristic
2C22×C22⋊Dic263C211yesmaximal, characteristic, complemented
3C2×#22554384C212yesmaximal, complemented
4#30681704C212yesmaximal, complemented
5#379×C263C211yesmaximal, characteristic, complemented
6C22×C22⋊D263C412yescomplemented
7C22×C22⋊D263C2211yescharacteristic
8C23×Dic263—21no—
9#22554439—22no—
10#22554439—21no—
11#22554439—21no—
12C2×C22⋊Dic263—24no—
13C2×C22⋊Dic263—21no—
14C2×C22⋊Dic263C412yescomplemented
15C2×C22⋊Dic263C2211yescharacteristic
16C2×C22⋊Dic263C2212yes—
17#22554384—24no—
18C25×C263C2211yescharacteristic
19C2×C22⋊C4×C263—22no—
20C2×C22⋊C4×C263C2212yes—
21C23×D263C2×C411yescharacteristic, complemented
22C2×C22⋊D263—22no—
23C2×C22⋊D263—22no—
24C2×C22⋊D263—22no—
25C2×C22⋊D263—21no—
26C2×C22⋊D263—21no—
27C2×C22⋊D263—22no—
28C2×C22⋊D263—44no—
29C22×Dic263—24no—
30C22×Dic263—22no—
31C22×Dic263—44no—
32C22×Dic263C2×C411yescharacteristic, complemented
33C22×Dic263C2×C412yescomplemented
34C22⋊Dic263—24no—
35C22⋊Dic263—22no—
36C22⋊Dic263—22no—
37C22⋊Dic263—22no—
38C22⋊Dic263—21no—
39C22⋊Dic263—21no—
40C22⋊Dic263D414yescomplemented
41C24×C263—22no—
42C24×C263—22no—
43C24×C263—44no—
44C24×C263C2×C412yes—
45C24×C263D412yes—
46C24×C263D411yescharacteristic
47C24×C263D411yescharacteristic
48C24×C263C2311yescharacteristic
49C22×C4×C263—22no—
50C22⋊C4×C263—22no—
51C22⋊C4×C263—22no—
52C22⋊C4×C263—44no—
53C22×D263—21no—
54C22×D263—22no—
55C22×D263—42no—
56C22⋊D263—44no—
57C22⋊D263—44no—
58C22⋊D263—41no—
59C22⋊D263—42no—
60C22⋊D263—41no—
61C2×Dic263—21no—
62C2×Dic263—22no—
63C2×Dic263—22no—
64C2×Dic263—24no—
65C2×Dic263—48no—
66C2×Dic263—44no—
67C2×Dic263—42no—
68C23×C263—24no—
69C23×C263—21no—
70C23×C263—21no—
71C23×C263—24no—
72C23×C263—24no—
73C23×C263—24no—
74C23×C263—21no—
75C23×C263—24no—
76C23×C263—21no—
77C23×C263—42no—
78C23×C263—42no—
79C23×C263—42no—
80C23×C263—42no—
81C23×C263—48no—
82C23×C263—48no—
83C23×C263C22⋊C412yes—
84C23×C263C22⋊C412yes—
85C23×C263C22×C411yescharacteristic
86C23×C263C2×D412yes—
87C23×C263C2×D411yescharacteristic
88C23×C263C2×D411yescharacteristic
89C23×C263#4112yes—
90C2×C4×C263—44no—
91C2×C4×C263—42no—
92C22×C263—24no—
93C22×C263—24no—
94C22×C263—22no—
95C22×C263—22no—
96C22×C263—22no—
97C22×C263—22no—
98C22×C263—22no—
99C22×C263—22no—
100C22×C263—22no—
101C22×C263—22no—
102C22×C263—42no—
103C22×C263—42no—
104C22×C263—48no—
105C22×C263—48no—
106C22×C263—42no—
107C22×C263—42no—
108C22×C263#9914yescomplemented
109C22×C263C2×C22⋊C411yescharacteristic
110C22×C263C4×D412yes—
111C22×C263#12011yescharacteristic
112C22×C263#12112yes—
113C22×C263#12311yescharacteristic
114C2×D263—41no—
115C2×D263—42no—
116C2×D263—82no—
117C4×C263—82no—
118Dic263—44no—
119Dic263—41no—
120Dic263—42no—
121C2×C263—21no—
122C2×C263—22no—
123C2×C263—22no—
124C2×C263—24no—
125C2×C263—21no—
126C2×C263—42no—
127C2×C263#38611yescharacteristic
128C2×C263C2×#9912yes—
129D263—81no—
130C263#189811yescharacteristic, complemented, Sylow
131#1898—2631nomaximal, Sylow
132C2×#120—2631no—
133C22×C22⋊C4—2631no—
134C2×#99—2632no—
135#379D26311yescharacteristic, complemented
136#342—2632no—
137C25C2×D26311yescharacteristic
138C22×D4—2631no—
139C22×D4—2632no—
140C23×C4—5261no—
141#120—5262no—
142#120—5261no—
143#120—5261no—
144C2×C22⋊C4—22no—
145C2×C22⋊C4—2632no—
146C2×C22⋊C4—2632no—
147C2×C22⋊C4—2631no—
148C2×C22⋊C4—5264no—
149C2×C22⋊C4—5261no—
150C2×C22⋊C4C2×D26312yes—
151#99—5264no—
152C24—22no—
153C24—22no—
154C24—44no—
155C24—2631no—
156C24C4×D26312yes—
157C24C22⋊D26312yes—
158C24D105211yescharacteristic
159C24D105211yescharacteristic
160C24C22×D26311yescharacteristic
161C2×D4—5262no—
162C2×D4—5262no—
163C2×D4—5262no—
164C2×D4—5261no—
165C2×D4—5261no—
166C2×D4—5262no—
167C2×D4—10524no—
168C22×C4—22no—
169C22×C4—2631no—
170C22×C4—2632no—
171C22×C4—5264no—
172C22×C4—5262no—
173C22×C4—10524no—
174C22⋊C4—22no—
175C22⋊C4—22no—
176C22⋊C4—44no—
177C22⋊C4—2634no—
178C22⋊C4—5264no—
179C22⋊C4—5262no—
180C22⋊C4—5262no—
181C22⋊C4—5262no—
182C22⋊C4—5261no—
183C22⋊C4—5261no—
184C23—24no—
185C23—21no—
186C23—21no—
187C23—24no—
188C23—24no—
189C23—24no—
190C23—21no—
191C23—24no—
192C23—21no—
193C23—42no—
194C23—42no—
195C23—42no—
196C23—42no—
197C23—48no—
198C23—48no—
199C23—5261no—
200C23—5262no—
201C23—10522no—
202C23(C2×D263)⋊C412yes—
203C23(C2×D263)⋊C412yes—
204C23C2×C4×D26311yescharacteristic
205C23D4×D26312yes—
206C23C2×C22⋊D26311yescharacteristic
207C23C2×D105211yescharacteristic
208C23#1686237512yes—
209D4—10524no—
210D4—10524no—
211D4—10521no—
212D4—10522no—
213D4—10521no—
214C2×C4—44no—
215C2×C4—42no—
216C2×C4—5262no—
217C2×C4—5261no—
218C2×C4—5262no—
219C2×C4—5264no—
220C2×C4—10528no—
221C2×C4—10524no—
222C2×C4—10522no—
223C22—24no—
224C22—24no—
225C22—22no—
226C22—22no—
227C22—22no—
228C22—22no—
229C22—22no—
230C22—22no—
231C22—22no—
232C22—22no—
233C22—42no—
234C22—42no—
235C22—48no—
236C22—48no—
237C22—42no—
238C22—42no—
239C22—10522no—
240C22—10521no—
241C22—21042no—
242C22#2255438414yescomplemented
243C22C2×(C2×D263)⋊C411yescharacteristic
244C22(C22⋊D263)⋊C412yes—
245C22#2255444011yescharacteristic
246C22#2255444212yes—
247C22#2255445411yescharacteristic
248C4—82no—
249C4—10524no—
250C4—10522no—
251C4—10521no—
252C2—22no—
253C2—21no—
254C2—24no—
255C2—21no—
256C2—22no—
257C2—42no—
258C2—21041no—
259C2#3068181511yescharacteristic
260C2C2×#2255438412yes—
subgroupG/H
centerC22C2×(C2×D263)⋊C4
commutatorC23×C263C22×C4
FrattiniC24C22×D263
Fitting#379×C263C2
socleC22×C263C2×C22⋊C4
prime radicalC2×#22554439C2
cosocleC24×C263C23
hypercenter#379D263
hypocenterC263#1898
LCSG ▷ C23×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C25 ◁ #379

Complements

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

NH ≅ G/Ntype
2. C22×C22⋊Dic263C2semidirect
3. C2×#22554384C2semidirect
4. #30681704C2semidirect
5. #379×C263C2semidirect
6. C22×C22⋊D263C4semidirect
14. C2×C22⋊Dic263C4semidirect
21. C23×D263C2×C4semidirect
32. C22×Dic263C2×C4semidirect
33. C22×Dic263C2×C4semidirect
40. C22⋊Dic263D4semidirect
108. C22×C263#99semidirect
130. C263#1898semidirect
135. #379D263semidirect
242. C22#22554384semidirect

Maximal subgroups

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

subgroupindex
C2×#225544392
C22×C22⋊Dic2632
C2×#225543842
#306817042
#379×C2632
#1898263