Finite Group Databasebeta

← #46781240

Subgroups — #46781240

Order 33664.

284 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 71 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#30681988C211yesmaximal, characteristic, complemented
3#30681789C211yesmaximal, 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×Dic263⋊C4—21no—
18C2×C4×Dic263—21no—
19C2×C4×Dic263C2211yescharacteristic
20Dic263⋊C8—21no—
21C22⋊(C263⋊C8)C2211yescharacteristic
22C8×Dic263—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—24no—
42Dic263⋊C4—21no—
43C22⋊Dic263—21no—
44(C2×D263)⋊C4—21no—
45(C2×D263)⋊C4—21no—
46C4×Dic263—42no—
47C4×Dic263C2×C411yescharacteristic
48C4×Dic263C2×C411yescharacteristic
49C4×Dic263D411yescharacteristic
50C4×Dic263D411yescharacteristic
51C2×D4×C263—21no—
52C2×D4×C263C2×C411yescharacteristic
53C22×C4×C263—21no—
54C22×C4×C263C2311yescharacteristic
55C2×C8×C263—21no—
56C4⋊C4×C263C2×C411yescharacteristic
57C22⋊C4×C263—21no—
58C22×D263—21no—
59Dic526—42no—
60D1052—41no—
61C22⋊D263—41no—
62C22⋊D263—41no—
63C22⋊D263—42no—
64C22⋊D263—42no—
65C2×Dic263—22no—
66C2×Dic263—22no—
67C2×Dic263—21no—
68C2×Dic263—41no—
69C2×Dic263—41no—
70C2×Dic263—42no—
71C2×Dic263C22⋊C411yescharacteristic
72C2×Dic263C22⋊C411yescharacteristic
73C2×Dic263C22⋊C411yescharacteristic
74C2×Dic263C22⋊C411yescharacteristic
75C2×Dic263D812yes—
76C2×Dic263SD1612yes—
77C4×D263—42no—
78C263⋊C8—41no—
79C23×C263—21no—
80C23×C263C2×D411yescharacteristic
81D4×C263—41no—
82D4×C263—41no—
83D4×C263—41no—
84C2×C4×C263—22no—
85C2×C4×C263—21no—
86C2×C4×C263—41no—
87C2×C4×C263—41no—
88C2×C4×C263—41no—
89C2×C4×C263C22×C411yescharacteristic
90C2×C4×C263C2×D411yescharacteristic
91C8×C263—41no—
92C22×C263—21no—
93C22×C263—21no—
94C22×C263—41no—
95C22×C263—41no—
96C22×C263—41no—
97C22×C263C2×C22⋊C411yescharacteristic
98C22×C263C2×D811yescharacteristic
99C22×C263C2×SD1611yescharacteristic
100C2×D263—41no—
101C2×D263—41no—
102C2×D263—41no—
103C4×C263—21no—
104C4×C263—21no—
105C4×C263—42no—
106C4×C263—41no—
107Dic263—21no—
108Dic263—42no—
109Dic263—41no—
110Dic263#10212yes—
111Dic263#10212yes—
112Dic263#10412yes—
113C2×C263—21no—
114C2×C263—21no—
115C2×C263—81no—
116C2×C263#41011yescharacteristic
117C2×C263C2×#10211yescharacteristic
118C2×C263C2×#10411yescharacteristic
119D263—81no—
120C263#150211yescharacteristic, complemented, Sylow
121#1502—2631nomaximal, Sylow
122#532—2631no—
123#431—2631no—
124C4×C4⋊C4—2631no—
125#327—2631no—
126#327—2631no—
127#327—2631no—
128#327D26311yescharacteristic, complemented
129C2×#41—5261no—
130C4⋊Q8—2631no—
131#127—2631no—
132#124—5261no—
133#121—2631no—
134#121—5261no—
135#121C2×D26311yescharacteristic
136C4×D4—2631no—
137C4×D4—2631no—
138C4×D4—5261no—
139C2×C4⋊C4—5261no—
140C2×C42—2631no—
141C2×C42—5261no—
142C4⋊C8—5261no—
143C22⋊C8—2631no—
144C22⋊C8C2×D26311yescharacteristic
145C4×C8—5261no—
146#95—2631no—
147#95C2×D26311yescharacteristic
148#41—10522no—
149#41—10522no—
150C2×Q8—5261no—
151C2×D4—21no—
152C2×D4—2631no—
153C2×D4—5261no—
154C2×D4—5261no—
155C2×D4—5261no—
156C2×D4C4×D26311yescharacteristic
157C22×C4—21no—
158C22×C4—2631no—
159C22×C4—2631no—
160C22×C4—5261no—
161C22×C4—5261no—
162C22×C4—5261no—
163C22×C4C22×D26311yescharacteristic
164C2×C8—21no—
165C2×C8—5261no—
166C4⋊C4—2631no—
167C4⋊C4—5261no—
168C4⋊C4—5264no—
169C4⋊C4C4×D26311yescharacteristic
170C22⋊C4—21no—
171C22⋊C4—5261no—
172C22⋊C4—5261no—
173C22⋊C4—5261no—
174C42—2631no—
175C42—2631no—
176C42—2631no—
177C42—2631no—
178C42—10522no—
179C23—21no—
180C23—5261no—
181C23D4×D26311yescharacteristic
182Q8—10522no—
183D4—41no—
184D4—41no—
185D4—41no—
186D4—10521no—
187D4—10522no—
188D4—10522no—
189D4—10521no—
190D4—10521no—
191C2×C4—22no—
192C2×C4—21no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—2631no—
197C2×C4—2631no—
198C2×C4—2631no—
199C2×C4—2632no—
200C2×C4—2632no—
201C2×C4—2631no—
202C2×C4—5262no—
203C2×C4—5262no—
204C2×C4—5261no—
205C2×C4—10522no—
206C2×C4—10522no—
207C2×C4—10521no—
208C2×C4—10521no—
209C2×C4C2×C4×D26311yescharacteristic
210C2×C4D4×D26311yescharacteristic
211C8—41no—
212C8—10521no—
213C22—21no—
214C22—21no—
215C22—41no—
216C22—41no—
217C22—41no—
218C22—10521no—
219C22—10521no—
220C22—10521no—
221C22C22⋊C4×D26311yescharacteristic
222C22D8×D26311yescharacteristic
223C22SD16×D26311yescharacteristic
224C4—21no—
225C4—21no—
226C4—42no—
227C4—41no—
228C4—2632no—
229C4—2632no—
230C4—2632no—
231C4—5261no—
232C4—10522no—
233C4—10521no—
234C2—21no—
235C2—21no—
236C2—81no—
237C2—21041no—
238C2#3068191011yescharacteristic
239C2#102×D26311yescharacteristic
240C2#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#1502
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. #30681988C2semidirect
3. #30681789C2semidirect
4. #30681673C2semidirect
5. #30681672C2semidirect
6. #30681671C2semidirect
7. #327×C263C2semidirect
9. #22554469C4semidirect
10. #22554466C4semidirect
14. D4×Dic263C4semidirect
15. #22554432C4semidirect
120. C263#1502semidirect
128. #327D263semidirect

Maximal subgroups

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

subgroupindex
#306824832
#306819882
#306817892
#306816732
#306816722
#306816712
#327×C2632
#1502263