Finite Group Databasebeta

← #46781274

Subgroups — #46781274

Order 33664.

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

normal subgroups only

This group has 326 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#121×D263C211yesmaximal, characteristic
2#30681900C211yesmaximal, characteristic, complemented
3#30681800C211yesmaximal, characteristic, complemented
4#30681673C211yesmaximal, characteristic, complemented
5#30681672C211yesmaximal, characteristic, complemented
6#30681671C211yesmaximal, characteristic, complemented
7#327×C263C211yesmaximal, characteristic, complemented
8C2×D4×D263—21no—
9C2×D4×D263C411yescharacteristic, complemented
10C22×C4×D263C2211yescharacteristic
11C2×#16862359—21no—
12#22554445C411yescharacteristic, complemented
13#22554444C2211yescharacteristic
14#22554443—21no—
15#22554442—21no—
16#22554441C411yescharacteristic, complemented
17C4⋊C4×D263C411yescharacteristic, complemented
18C2×(C2×D263)⋊C4—21no—
19C22⋊C4×D263—21no—
20C22⋊(C263⋊C8)C2211yescharacteristic, complemented
21(C2×D263)⋊C8—21no—
22C263⋊#95—21no—
23C263⋊#95C2211yescharacteristic, complemented
24#121×C263C2211yescharacteristic
25C22⋊C8×C263C2211yescharacteristic, complemented
26#95×C263C2211yescharacteristic, complemented
27C23×D263—21no—
28C23×D263D411yescharacteristic
29C2×D1052—21no—
30C2×D1052C2×C411yescharacteristic
31C2×C22⋊D263—21no—
32C2×C22⋊D263—21no—
33C2×C22⋊D263—21no—
34D4×D263—42no—
35D4×D263—42no—
36D4×D263—42no—
37C22×Dic263—21no—
38C22×Dic263D411yescharacteristic
39C2×C4×D263—21no—
40C2×C4×D263—42no—
41C2×C4×D263C2×C411yescharacteristic
42C2×C4×D263C2×C411yescharacteristic
43C2×C4×D263D411yescharacteristic
44C2×C4×D263D411yescharacteristic
45#16862359—42no—
46C2×C263⋊C8—21no—
47C4⋊Dic263C2×C411yescharacteristic
48Dic263⋊C4—21no—
49C22⋊Dic263—21no—
50(C2×D263)⋊C4—21no—
51(C2×D263)⋊C4—21no—
52(C2×D263)⋊C4—42no—
53C2×D4×C263—21no—
54C2×D4×C263C2×C411yescharacteristic
55C22×C4×C263—21no—
56C22×C4×C263C2311yescharacteristic
57C2×C8×C263—21no—
58C4⋊C4×C263C2×C411yescharacteristic
59C22⋊C4×C263—21no—
60C22×D263—21no—
61C22×D263—21no—
62C22×D263—22no—
63C22×D263—21no—
64C22×D263—41no—
65C22×D263—42no—
66C22×D263—42no—
67C22×D263—42no—
68C22×D263C22⋊C411yescharacteristic
69C22×D263C22⋊C411yescharacteristic
70D1052—41no—
71D1052—42no—
72C22⋊D263—42no—
73C22⋊D263—42no—
74C22⋊D263—41no—
75C22⋊D263—41no—
76C2×Dic263—21no—
77C2×Dic263—41no—
78C2×Dic263—41no—
79C2×Dic263—41no—
80C2×Dic263—41no—
81C2×Dic263C22⋊C411yescharacteristic
82C2×Dic263C22⋊C411yescharacteristic
83C4×D263—22no—
84C4×D263—22no—
85C4×D263—41no—
86C4×D263—41no—
87C4×D263—42no—
88C263⋊C8—41no—
89C23×C263—21no—
90C23×C263C2×D411yescharacteristic
91D4×C263—41no—
92D4×C263—41no—
93D4×C263—41no—
94C2×C4×C263—21no—
95C2×C4×C263—41no—
96C2×C4×C263—41no—
97C2×C4×C263—41no—
98C2×C4×C263—41no—
99C2×C4×C263C22×C411yescharacteristic
100C2×C4×C263C2×D411yescharacteristic
101C8×C263—41no—
102C22×C263—21no—
103C22×C263—21no—
104C22×C263—41no—
105C22×C263—41no—
106C22×C263—41no—
107C22×C263C2×C22⋊C411yescharacteristic
108C22×C263AGL(1,ℤ/8)11yescharacteristic
109C22×C263AGL(1,ℤ/8)11yescharacteristic
110C2×D263—21no—
111C2×D263—21no—
112C2×D263—21no—
113C2×D263—21no—
114C2×D263—21no—
115C2×D263—42no—
116C2×D263—42no—
117C2×D263—41no—
118C2×D263—41no—
119C2×D263—41no—
120C2×D263—84no—
121C2×D263#9912yes—
122C4×C263—21no—
123C4×C263—21no—
124C4×C263—41no—
125C4×C263—81no—
126Dic263—21no—
127Dic263—21no—
128Dic263—41no—
129Dic263—81no—
130C2×C263—21no—
131C2×C263—21no—
132C2×C263—81no—
133C2×C263C2×#9911yescharacteristic
134C2×C263#41811yescharacteristic
135C2×C263#42111yescharacteristic
136D263—22no—
137D263—41no—
138D263—81no—
139C263#151011yescharacteristic, complemented, Sylow
140#1510—2631nomaximal, Sylow
141C2×#121—2631no—
142#407—2631no—
143#381—2631no—
144#327—2631no—
145#327—2631no—
146#327—2631no—
147#327D26311yescharacteristic, complemented
148C22×D4—2631no—
149C22×D4—5261no—
150C23×C4—2631no—
151C2×M16—5261no—
152#121—2631no—
153#121—2631no—
154#121—2631no—
155#121—5261no—
156#121—5261no—
157#121C2×D26311yescharacteristic
158C2×C4⋊C4—2631no—
159C2×C22⋊C4—5261no—
160C2×C22⋊C4—5261no—
161C22⋊C8—2631no—
162C22⋊C8—5261no—
163C22⋊C8C2×D26311yescharacteristic, complemented
164#95—2631no—
165#95—5261no—
166#95C2×D26311yescharacteristic, complemented
167C24—2631no—
168C24—5261no—
169C2×D4—21no—
170C2×D4—2631no—
171C2×D4—5261no—
172C2×D4—5261no—
173C2×D4—5261no—
174C2×D4—5261no—
175C2×D4—10522no—
176C2×D4—10522no—
177C2×D4—10522no—
178C2×D4C4×D26311yescharacteristic
179C22×C4—21no—
180C22×C4—2631no—
181C22×C4—2631no—
182C22×C4—2631no—
183C22×C4—2631no—
184C22×C4—2631no—
185C22×C4—5261no—
186C22×C4—5261no—
187C22×C4—10522no—
188C22×C4C22×D26311yescharacteristic
189M16—10522no—
190C2×C8—21no—
191C2×C8—5261no—
192C4⋊C4—2631no—
193C4⋊C4—5261no—
194C4⋊C4C4×D26311yescharacteristic
195C22⋊C4—21no—
196C22⋊C4—5261no—
197C22⋊C4—5261no—
198C22⋊C4—5261no—
199C22⋊C4—10522no—
200C23—21no—
201C23—2631no—
202C23—2631no—
203C23—5262no—
204C23—5261no—
205C23—5261no—
206C23—5261no—
207C23—10521no—
208C23—10522no—
209C23—10522no—
210C23—10522no—
211C23D4×D26311yescharacteristic
212D4—41no—
213D4—41no—
214D4—41no—
215D4—10521no—
216D4—10522no—
217D4—10522no—
218D4—10522no—
219D4—10521no—
220D4—10521no—
221C2×C4—21no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—2631no—
227C2×C4—2631no—
228C2×C4—5262no—
229C2×C4—5262no—
230C2×C4—5261no—
231C2×C4—10521no—
232C2×C4—10521no—
233C2×C4—10522no—
234C2×C4—10521no—
235C2×C4—10521no—
236C2×C4—10521no—
237C2×C4—10521no—
238C2×C4C2×C4×D26311yescharacteristic
239C2×C4D4×D26311yescharacteristic
240C8—41no—
241C8—10521no—
242C22—21no—
243C22—21no—
244C22—41no—
245C22—41no—
246C22—41no—
247C22—2632no—
248C22—5261no—
249C22—5261no—
250C22—5261no—
251C22—5261no—
252C22—5261no—
253C22—10522no—
254C22—10522no—
255C22—10521no—
256C22—10521no—
257C22—10521no—
258C22—21044no—
259C22C22⋊C4×D26311yescharacteristic
260C22#2255449411yescharacteristic
261C22#2255449711yescharacteristic
262C4—21no—
263C4—21no—
264C4—41no—
265C4—81no—
266C4—5261no—
267C4—5261no—
268C4—10521no—
269C4—21041no—
270C2—21no—
271C2—21no—
272C2—81no—
273C2—5262no—
274C2—10521no—
275C2—21041no—
276C2#99×D26311yescharacteristic
277C2#3068194111yescharacteristic
278C2#3068195311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D263
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#327×C263C2
socleC22×C263C2×C22⋊C4
prime radical#121×D263C2
cosocleC22×C4×C263C23
hypercenter#327D263
hypocenterC263#1510
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. #30681900C2semidirect
3. #30681800C2semidirect
4. #30681673C2semidirect
5. #30681672C2semidirect
6. #30681671C2semidirect
7. #327×C263C2semidirect
9. C2×D4×D263C4semidirect
12. #22554445C4semidirect
16. #22554441C4semidirect
17. C4⋊C4×D263C4semidirect
20. C22⋊(C263⋊C8)C22semidirect
23. C263⋊#95C22semidirect
25. C22⋊C8×C263C22semidirect
26. #95×C263C22semidirect
139. C263#1510semidirect
147. #327D263semidirect
163. C22⋊C8C2×D263semidirect
166. #95C2×D263semidirect

Maximal subgroups

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

subgroupindex
#121×D2632
#306819002
#306818002
#306816732
#306816722
#306816712
#327×C2632
#1510263