Finite Group Databasebeta

← #46781253

Subgroups — #46781253

Order 33664.

272 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 63 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#30682483C211yesmaximal, characteristic
2#30681992C211yesmaximal, characteristic, complemented
3#30681783C211yesmaximal, characteristic, complemented
4#30681673C211yesmaximal, characteristic, complemented
5#30681672C211yesmaximal, characteristic, complemented
6#30681671C211yesmaximal, characteristic, complemented
7#327×C263C211yesmaximal, characteristic, complemented
8C2×#16862375—21no—
9#22554469C411yescharacteristic, complemented
10#22554466C411yescharacteristic, complemented
11#22554456—21no—
12#22554444C2211yescharacteristic
13#22554442—21no—
14D4×Dic263C411yescharacteristic, complemented
15#22554432C411yescharacteristic, complemented
16(C22⋊D263)⋊C4—21no—
17C2×C4×Dic263—21no—
18C2×C4×Dic263C2211yescharacteristic
19Dic263⋊C8—21no—
20C22⋊(C263⋊C8)C2211yescharacteristic
21#22554380—21no—
22C263⋊#95—21no—
23C263⋊#95C2211yescharacteristic
24#121×C263C2211yescharacteristic
25C22⋊C8×C263C2211yescharacteristic
26#95×C263C2211yescharacteristic
27#16862375—42no—
28#16862375—42no—
29C2×Dic526—21no—
30C2×D1052C2×C411yescharacteristic
31C2×C22⋊D263—21no—
32C2×C22⋊D263—21no—
33C2×C22⋊D263—21no—
34C22×Dic263—21no—
35C22×Dic263—21no—
36C22×Dic263D411yescharacteristic
37C22×Dic263D411yescharacteristic
38C2×C4×D263—21no—
39C2×C263⋊C8—21no—
40C4⋊Dic263C2×C411yescharacteristic
41Dic263⋊C4—21no—
42C22⋊Dic263—21no—
43(C2×D263)⋊C4—21no—
44(C2×D263)⋊C4—21no—
45C4×Dic263—24no—
46C4×Dic263C2×C411yescharacteristic
47C4×Dic263C2×C411yescharacteristic
48C4×Dic263D411yescharacteristic
49C4×Dic263D411yescharacteristic
50C2×D4×C263—21no—
51C2×D4×C263C2×C411yescharacteristic
52C22×C4×C263—21no—
53C22×C4×C263C2311yescharacteristic
54C2×C8×C263—21no—
55C4⋊C4×C263C2×C411yescharacteristic
56C22⋊C4×C263—21no—
57C22×D263—21no—
58Dic526—42no—
59D1052—41no—
60C22⋊D263—42no—
61C22⋊D263—41no—
62C22⋊D263—41no—
63C22⋊D263—42no—
64C2×Dic263—21no—
65C2×Dic263—21no—
66C2×Dic263—22no—
67C2×Dic263—22no—
68C2×Dic263—21no—
69C2×Dic263—42no—
70C2×Dic263—41no—
71C2×Dic263—41no—
72C2×Dic263C22⋊C411yescharacteristic
73C2×Dic263C22⋊C411yescharacteristic
74C2×Dic263C22⋊C411yescharacteristic
75C2×Dic263C22⋊C411yescharacteristic
76C4×D263—42no—
77C263⋊C8—41no—
78C23×C263—21no—
79C23×C263C2×D411yescharacteristic
80D4×C263—41no—
81D4×C263—41no—
82D4×C263—41no—
83C2×C4×C263—22no—
84C2×C4×C263—21no—
85C2×C4×C263—41no—
86C2×C4×C263—41no—
87C2×C4×C263—41no—
88C2×C4×C263C22×C411yescharacteristic
89C2×C4×C263C2×D411yescharacteristic
90C8×C263—41no—
91C22×C263—21no—
92C22×C263—21no—
93C22×C263—41no—
94C22×C263—41no—
95C22×C263—41no—
96C22×C263C2×C22⋊C411yescharacteristic
97C22×C263AGL(1,ℤ/8)11yescharacteristic
98C22×C263AGL(1,ℤ/8)11yescharacteristic
99C2×D263—41no—
100C2×D263—41no—
101C2×D263—41no—
102C4×C263—21no—
103C4×C263—21no—
104C4×C263—42no—
105C4×C263—41no—
106Dic263—21no—
107Dic263—21no—
108Dic263—21no—
109Dic263—42no—
110Dic263—41no—
111Dic263#10412yes—
112C2×C263—21no—
113C2×C263—21no—
114C2×C263—81no—
115C2×C263#41011yescharacteristic
116C2×C263#41811yescharacteristic
117C2×C263C2×#10411yescharacteristic
118D263—81no—
119C263#150511yescharacteristic, complemented, Sylow
120#1505—2631nomaximal, Sylow
121#532—2631no—
122#432—2631no—
123#376—2631no—
124#327—2631no—
125#327—2631no—
126#327—2631no—
127#327D26311yescharacteristic, complemented
128C2×#41—5261no—
129C4⋊Q8—2631no—
130#127—2631no—
131#124—5261no—
132#121—2631no—
133#121—5261no—
134#121C2×D26311yescharacteristic
135C4×D4—2631no—
136C4×D4—2631no—
137C4×D4—5261no—
138C2×C42—2631no—
139C2×C42—5261no—
140C4⋊C8—5261no—
141C22⋊C8—2631no—
142C22⋊C8C2×D26311yescharacteristic
143#97—5261no—
144#95—2631no—
145#95—5261no—
146#95C2×D26311yescharacteristic
147#41—10522no—
148#41—10522no—
149C2×Q8—5261no—
150C2×D4—21no—
151C2×D4—2631no—
152C2×D4—5261no—
153C2×D4—5261no—
154C2×D4—5261no—
155C2×D4C4×D26311yescharacteristic
156C22×C4—21no—
157C22×C4—2631no—
158C22×C4—2631no—
159C22×C4—5261no—
160C22×C4—5261no—
161C22×C4—5261no—
162C22×C4C22×D26311yescharacteristic
163C2×C8—21no—
164C2×C8—5261no—
165C4⋊C4—2631no—
166C4⋊C4—5261no—
167C4⋊C4C4×D26311yescharacteristic
168C22⋊C4—21no—
169C22⋊C4—5261no—
170C22⋊C4—5261no—
171C22⋊C4—5261no—
172C42—2631no—
173C42—2631no—
174C42—2631no—
175C42—2631no—
176C42—5264no—
177C23—21no—
178C23—5261no—
179C23D4×D26311yescharacteristic
180Q8—10522no—
181D4—41no—
182D4—41no—
183D4—41no—
184D4—10521no—
185D4—10522no—
186D4—10522no—
187D4—10521no—
188D4—10521no—
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—2631no—
195C2×C4—2631no—
196C2×C4—2631no—
197C2×C4—2631no—
198C2×C4—5262no—
199C2×C4—5261no—
200C2×C4—5261no—
201C2×C4—5262no—
202C2×C4—5261no—
203C2×C4—10522no—
204C2×C4—10522no—
205C2×C4—10521no—
206C2×C4—10521no—
207C2×C4C2×C4×D26311yescharacteristic
208C2×C4D4×D26311yescharacteristic
209C8—41no—
210C8—10521no—
211C22—21no—
212C22—21no—
213C22—41no—
214C22—41no—
215C22—41no—
216C22—10521no—
217C22—10521no—
218C22—10521no—
219C22C22⋊C4×D26311yescharacteristic
220C22#2255449411yescharacteristic
221C22#2255449711yescharacteristic
222C4—21no—
223C4—21no—
224C4—42no—
225C4—41no—
226C4—2632no—
227C4—5261no—
228C4—5261no—
229C4—5261no—
230C4—10522no—
231C4—10521no—
232C2—21no—
233C2—21no—
234C2—81no—
235C2—21041no—
236C2#3068191011yescharacteristic
237C2#3068194111yescharacteristic
238C2#104×D26311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D263
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#327×C263C2
socleC22×C263C2×C22⋊C4
prime radical#30682483C2
cosocleC22×C4×C263C23
hypercenter#327D263
hypocenterC263#1505
LCSG ▷ C2×C4×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #30681992C2semidirect
3. #30681783C2semidirect
4. #30681673C2semidirect
5. #30681672C2semidirect
6. #30681671C2semidirect
7. #327×C263C2semidirect
9. #22554469C4semidirect
10. #22554466C4semidirect
14. D4×Dic263C4semidirect
15. #22554432C4semidirect
119. C263#1505semidirect
127. #327D263semidirect

Maximal subgroups

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

subgroupindex
#306824832
#306819922
#306817832
#306816732
#306816722
#306816712
#327×C2632
#1505263