Finite Group Databasebeta

← #46781302

Subgroups — #46781302

Order 33664.

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

normal subgroups only

This group has 284 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#30682451C211yesmaximal, characteristic
2C22⋊C8×D263C211yesmaximal, characteristic, complemented
3#30681800C211yesmaximal, characteristic, complemented
4#30681675C211yesmaximal, characteristic, complemented
5#30681673C211yesmaximal, characteristic, complemented
6#30681671C211yesmaximal, characteristic, complemented
7#328×C263C211yesmaximal, characteristic, complemented
8C2×#16862377C411yescharacteristic, complemented
9C22×C4×D263C2211yescharacteristic
10C2×C8×D263—21no—
11#22554455—21no—
12#22554446C411yescharacteristic, complemented
13#22554445C411yescharacteristic, complemented
14#22554444C2211yescharacteristic
15#22554440—21no—
16#22554432—21no—
17(C22⋊D263)⋊C4—21no—
18#22554428C411yescharacteristic, complemented
19C2×(C2×D263)⋊C4—21no—
20C22⋊(C263⋊C8)C2211yescharacteristic
21(C2×D263)⋊C8—21no—
22C263⋊#95—21no—
23C263⋊#95C2211yescharacteristic
24C22⋊Q8×C263C2211yescharacteristic
25C22⋊C8×C263C2211yescharacteristic
26#95×C263C2211yescharacteristic
27C23×D263D411yescharacteristic
28#16862377—42no—
29C2×D1052—21no—
30C2×D1052—21no—
31C2×D1052C2×C411yescharacteristic
32C2×C22⋊D263—21no—
33C22×Dic263—21no—
34C22×Dic263D411yescharacteristic
35C2×C4×D263—21no—
36C2×C4×D263—42no—
37C2×C4×D263C2×C411yescharacteristic
38C2×C4×D263C2×C411yescharacteristic
39C2×C4×D263D411yescharacteristic
40C2×C4×D263D411yescharacteristic
41C2×C263⋊C8—21no—
42C8×D263—42no—
43C4⋊Dic263C2×C411yescharacteristic
44Dic263⋊C4—21no—
45(C2×D263)⋊C4—21no—
46(C2×D263)⋊C4—21no—
47(C2×D263)⋊C4—21no—
48(C2×D263)⋊C4—21no—
49(C2×D263)⋊C4—42no—
50C4×Dic263—21no—
51C2×Q8×C263C2×C411yescharacteristic
52C22×C4×C263—21no—
53C22×C4×C263C2311yescharacteristic
54C2×C8×C263—21no—
55C4⋊C4×C263—21no—
56C4⋊C4×C263C2×C411yescharacteristic
57C22⋊C4×C263—21no—
58C22×D263—21no—
59C22×D263—21no—
60C22×D263—22no—
61C22×D263—21no—
62C22×D263—41no—
63C22×D263C22⋊C411yescharacteristic
64C22×D263C22⋊C411yescharacteristic
65D1052—41no—
66D1052—42no—
67D1052—42no—
68C22⋊D263—41no—
69C22⋊D263—41no—
70C2×Dic263—21no—
71C2×Dic263—41no—
72C2×Dic263—41no—
73C2×Dic263—41no—
74C2×Dic263—41no—
75C2×Dic263C22⋊C411yescharacteristic
76C2×Dic263C22⋊C411yescharacteristic
77C4×D263—22no—
78C4×D263—22no—
79C4×D263—41no—
80C4×D263—41no—
81C4×D263—42no—
82C263⋊C8—41no—
83C23×C263C2×D411yescharacteristic
84Q8×C263—41no—
85C2×C4×C263—21no—
86C2×C4×C263—21no—
87C2×C4×C263—41no—
88C2×C4×C263—41no—
89C2×C4×C263—41no—
90C2×C4×C263—41no—
91C2×C4×C263C22×C411yescharacteristic
92C2×C4×C263C2×D411yescharacteristic
93C8×C263—41no—
94C22×C263—21no—
95C22×C263—21no—
96C22×C263C2×C22⋊C411yescharacteristic
97C22×C263#13511yescharacteristic
98C22×C263#13511yescharacteristic
99C2×D263—21no—
100C2×D263—21no—
101C2×D263—21no—
102C2×D263—21no—
103C2×D263—21no—
104C2×D263—42no—
105C2×D263—42no—
106C2×D263—41no—
107C2×D263—41no—
108C2×D263—41no—
109C2×D263#9912yes—
110C4×C263—21no—
111C4×C263—21no—
112C4×C263—41no—
113C4×C263—41no—
114C4×C263—81no—
115Dic263—21no—
116Dic263—21no—
117Dic263—41no—
118Dic263—81no—
119C2×C263—21no—
120C2×C263—21no—
121C2×C263C2×#9911yescharacteristic
122C2×C263#41611yescharacteristic
123C2×C263#42111yescharacteristic
124D263—22no—
125D263—41no—
126D263—81no—
127C263#151611yescharacteristic, complemented, Sylow
128#1516—2631nomaximal, Sylow
129#525—2631no—
130C2×C22⋊C8—2631no—
131#381—2631no—
132#328—2631no—
133#328D26311yescharacteristic, complemented
134#327—2631no—
135#327—2631no—
136C2×#41—2631no—
137C23×C4—2631no—
138C22×C8—5261no—
139#123—5261no—
140C22⋊Q8—2631no—
141C22⋊Q8C2×D26311yescharacteristic
142#121—2631no—
143#121—2631no—
144#120—5261no—
145C4×D4—5261no—
146C4×D4—5261no—
147#117—2631no—
148C2×C22⋊C4—5261no—
149C22⋊C8—2631no—
150C22⋊C8—5261no—
151C22⋊C8C2×D26311yescharacteristic
152#95—2631no—
153#95—5261no—
154#95C2×D26311yescharacteristic
155C24—2631no—
156#41—10522no—
157C2×Q8C4×D26311yescharacteristic
158C2×D4—2631no—
159C2×D4—5261no—
160C2×D4—5261no—
161C2×D4—5261no—
162C22×C4—21no—
163C22×C4—2631no—
164C22×C4—2631no—
165C22×C4—2631no—
166C22×C4—2631no—
167C22×C4—2631no—
168C22×C4—5261no—
169C22×C4—5261no—
170C22×C4—10522no—
171C22×C4C22×D26311yescharacteristic
172C2×C8—21no—
173C2×C8—5261no—
174C2×C8—10522no—
175C4⋊C4—21no—
176C4⋊C4—2631no—
177C4⋊C4—5261no—
178C4⋊C4C4×D26311yescharacteristic
179C22⋊C4—21no—
180C22⋊C4—5261no—
181C22⋊C4—5261no—
182C22⋊C4—5261no—
183C22⋊C4—5261no—
184C22⋊C4—10522no—
185C42—5261no—
186C23—2631no—
187C23—2631no—
188C23—5262no—
189C23—5261no—
190C23—5261no—
191C23—5261no—
192C23—10521no—
193C23D4×D26311yescharacteristic
194Q8—41no—
195D4—10521no—
196D4—10522no—
197D4—10522no—
198D4—10521no—
199D4—10521no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—2631no—
207C2×C4—2631no—
208C2×C4—5262no—
209C2×C4—5262no—
210C2×C4—5261no—
211C2×C4—10521no—
212C2×C4—10521no—
213C2×C4—10522no—
214C2×C4—10521no—
215C2×C4—10521no—
216C2×C4—10521no—
217C2×C4—10521no—
218C2×C4C2×C4×D26311yescharacteristic
219C2×C4D4×D26311yescharacteristic
220C8—41no—
221C8—10521no—
222C22—21no—
223C22—21no—
224C22—2632no—
225C22—5261no—
226C22—5261no—
227C22—5261no—
228C22—5261no—
229C22—5261no—
230C22—10522no—
231C22—10522no—
232C22—10521no—
233C22—10521no—
234C22—10521no—
235C22C22⋊C4×D26311yescharacteristic
236C22#2255449111yescharacteristic
237C22#2255449311yescharacteristic
238C4—21no—
239C4—21no—
240C4—41no—
241C4—41no—
242C4—81no—
243C4—5261no—
244C4—5261no—
245C4—10521no—
246C4—21041no—
247C2—21no—
248C2—21no—
249C2—5262no—
250C2—10521no—
251C2—21041no—
252C2#99×D26311yescharacteristic
253C2#3068193311yescharacteristic
254C2#3068195311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D263
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#328×C263C2
socleC22×C263C2×C22⋊C4
prime radical#30682451C2
cosocleC22×C4×C263C23
hypercenter#328D263
hypocenterC263#1516
LCSG ▷ C2×C4×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. C22⋊C8×D263C2semidirect
3. #30681800C2semidirect
4. #30681675C2semidirect
5. #30681673C2semidirect
6. #30681671C2semidirect
7. #328×C263C2semidirect
8. C2×#16862377C4semidirect
12. #22554446C4semidirect
13. #22554445C4semidirect
18. #22554428C4semidirect
127. C263#1516semidirect
133. #328D263semidirect

Maximal subgroups

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

subgroupindex
#306824512
C22⋊C8×D2632
#306818002
#306816752
#306816732
#306816712
#328×C2632
#1516263