Finite Group Databasebeta

← #46783192

Subgroups — #46783192

Order 33664.

358 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 83 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#30682445C211yesmaximal, characteristic
2C2×#22554427C211yesmaximal, characteristic, complemented
3C2×#22554397C211yesmaximal, characteristic, complemented
4#30681901C211yesmaximal, characteristic, complemented
5#30681699C211yesmaximal, characteristic, complemented
6#30681698C211yesmaximal, characteristic, complemented
7C2×#104×C263C211yesmaximal, characteristic, complemented
8C22×C4×D263C2211yescharacteristic
9C2×#16862360C2211yescharacteristic
10#22554451—21no—
11#22554446C412yescomplemented
12#22554441C412yescomplemented
13#22554438—21no—
14C4×C22⋊D263—22no—
15#22554429C2211yescharacteristic
16#22554427—22no—
17#22554427—22no—
18C2×Dic263⋊C4—21no—
19C2×(C2×D263)⋊C4—21no—
20C2×C4×Dic263C2211yescharacteristic
21#22554397—22no—
22(C2×D263)⋊C8—22no—
23C2×#41×C263C2211yescharacteristic
24C2×M16×C263C2211yescharacteristic
25C2×C42×C263C2211yescharacteristic
26#104×C263—22no—
27C23×D263D411yescharacteristic
28C2×C22⋊D263—22no—
29C22×Dic263—21no—
30C22×Dic263D411yescharacteristic
31C2×C4×D263—21no—
32C2×C4×D263—21no—
33C2×C4×D263—21no—
34C2×C4×D263—21no—
35C2×C4×D263C2×C412yes—
36C2×C4×D263D412yes—
37#16862360—21no—
38#16862360—21no—
39C2×C263⋊C8—21no—
40C4⋊Dic263C2×C412yes—
41Dic263⋊C4—24no—
42Dic263⋊C4—22no—
43C22⋊Dic263—22no—
44C22⋊Dic263—21no—
45(C2×D263)⋊C4—24no—
46(C2×D263)⋊C4—22no—
47C4×Dic263—21no—
48C4×Dic263—21no—
49C4×Dic263D412yescomplemented
50#41×C263—21no—
51#41×C263—21no—
52#41×C263—21no—
53#41×C263—21no—
54C2×Q8×C263C2×C411yescharacteristic
55C2×D4×C263—21no—
56C2×D4×C263C2×C411yescharacteristic
57C22×C4×C263—21no—
58C22×C4×C263—21no—
59C22×C4×C263C2311yescharacteristic
60M16×C263—21no—
61M16×C263—21no—
62C2×C8×C263—21no—
63C42×C263—21no—
64C42×C263D412yescomplemented
65C22×D263—21no—
66C22×D263—21no—
67C22×D263—42no—
68C22×D263C22⋊C412yes—
69C22⋊D263—44no—
70C2×Dic263—21no—
71C2×Dic263—21no—
72C2×Dic263—22no—
73C2×Dic263—22no—
74C2×Dic263—42no—
75C2×Dic263C22⋊C412yes—
76C4×D263—22no—
77C4×D263—22no—
78C4×D263—22no—
79C4×D263—22no—
80C263⋊C8—41no—
81C23×C263—21no—
82C23×C263C2×D411yescharacteristic
83Q8×C263—21no—
84Q8×C263—21no—
85D4×C263—21no—
86D4×C263—21no—
87D4×C263—41no—
88D4×C263—41no—
89C2×C4×C263—21no—
90C2×C4×C263—22no—
91C2×C4×C263—42no—
92C2×C4×C263—41no—
93C2×C4×C263—41no—
94C2×C4×C263C22×C411yescharacteristic
95C2×C4×C263C2×D411yescharacteristic
96C2×C4×C263C2×D411yescharacteristic
97C2×C4×C263C2×D411yescharacteristic
98C2×C4×C263#4111yescharacteristic
99C2×C4×C263#4111yescharacteristic
100C8×C263—41no—
101C22×C263—22no—
102C22×C263—41no—
103C22×C263—42no—
104C22×C263C2×C22⋊C411yescharacteristic
105C22×C263#12011yescharacteristic
106C22×C263#12311yescharacteristic
107C2×D263—22no—
108C2×D263—22no—
109C2×D263—22no—
110C2×D263—42no—
111C2×D263—42no—
112C4×C263—42no—
113C4×C263—41no—
114C4×C263C4×D411yescharacteristic
115C4×C263C4×D411yescharacteristic
116C4×C263#12111yescharacteristic
117C4×C263#12111yescharacteristic
118Dic263—22no—
119Dic263—42no—
120Dic263—42no—
121C2×C263—21no—
122C2×C263—21no—
123C2×C263—81no—
124C2×C263#38611yescharacteristic
125C2×C263#42112yes—
126D263—42no—
127C263#189711yescharacteristic, complemented, Sylow
128#1897—2631nomaximal, Sylow
129#525—2631no—
130C2×#117—2631no—
131C2×#104—2631no—
132C2×#104D26311yescharacteristic, complemented
133#407—2631no—
134#339—2631no—
135#339—2631no—
136C2×#41C2×D26311yescharacteristic
137C23×C4—2631no—
138C2×M16—2631no—
139C2×M16C2×D26311yescharacteristic
140#123—5261no—
141C22⋊Q8—2632no—
142#121—2632no—
143#120—5261no—
144C4×D4—5262no—
145#117—2631no—
146#117—5262no—
147#117—5262no—
148C2×C4⋊C4—5261no—
149C2×C22⋊C4—5261no—
150C2×C42—2631no—
151C2×C42C2×D26311yescharacteristic
152#104—22no—
153#104—5262no—
154C22⋊C8—5262no—
155C24—2631no—
156#41—21no—
157#41—21no—
158#41—21no—
159#41—21no—
160C2×Q8C4×D26311yescharacteristic
161C2×D4—21no—
162C2×D4—5262no—
163C2×D4C4×D26311yescharacteristic
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—2631no—
167C22×C4—2632no—
168C22×C4—2632no—
169C22×C4—5261no—
170C22×C4—5261no—
171C22×C4—5261no—
172C22×C4—5261no—
173C22×C4—5261no—
174C22×C4C22×D26311yescharacteristic
175M16—21no—
176M16—21no—
177M16—5261no—
178M16—5261no—
179C2×C8—21no—
180C2×C8—5261no—
181C4⋊C4—2632no—
182C4⋊C4—5262no—
183C4⋊C4—5264no—
184C22⋊C4—5262no—
185C22⋊C4—5264no—
186C22⋊C4—5262no—
187C22⋊C4—5261no—
188C42—21no—
189C42—2632no—
190C42—5261no—
191C42—5261no—
192C42C22⋊D26312yescomplemented
193C23—21no—
194C23—2632no—
195C23—5261no—
196C23—5261no—
197C23—10522no—
198C23D4×D26311yescharacteristic
199Q8—21no—
200Q8—21no—
201D4—21no—
202D4—21no—
203D4—41no—
204D4—41no—
205D4—10524no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—42no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—2632no—
212C2×C4—5261no—
213C2×C4—5261no—
214C2×C4—5262no—
215C2×C4—5262no—
216C2×C4—5262no—
217C2×C4—5262no—
218C2×C4—5262no—
219C2×C4—5262no—
220C2×C4—10522no—
221C2×C4C2×C4×D26311yescharacteristic
222C2×C4D4×D26311yescharacteristic
223C2×C4D4×D26311yescharacteristic
224C2×C4C2×C22⋊D26311yescharacteristic
225C2×C4#1686237511yescharacteristic
226C2×C4#1686237611yescharacteristic
227C8—41no—
228C8—10521no—
229C22—22no—
230C22—42no—
231C22—41no—
232C22—5262no—
233C22—5262no—
234C22—5262no—
235C22—10522no—
236C22—10522no—
237C22C22⋊C4×D26311yescharacteristic
238C22#2255443811yescharacteristic
239C22#2255445211yescharacteristic
240C4—42no—
241C4—41no—
242C4—5262no—
243C4—10522no—
244C4—10522no—
245C4(C22⋊D263)⋊C411yescharacteristic
246C4C4×C22⋊D26311yescharacteristic
247C4#2255444111yescharacteristic
248C4#2255444311yescharacteristic
249C2—21no—
250C2—21no—
251C2—81no—
252C2—10522no—
253C2#3068181411yescharacteristic
254C2#3068195312yes—
subgroupG/H
centerC2×C4D4×D263
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
FittingC2×#104×C263C2
socleC22×C263C2×C22⋊C4
prime radical#30682445C2
cosocleC22×C4×C263C23
hypercenterC2×#104D263
hypocenterC263#1897
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. C2×#22554427C2semidirect
3. C2×#22554397C2semidirect
4. #30681901C2semidirect
5. #30681699C2semidirect
6. #30681698C2semidirect
7. C2×#104×C263C2semidirect
11. #22554446C4semidirect
12. #22554441C4semidirect
49. C4×Dic263D4semidirect
64. C42×C263D4semidirect
127. C263#1897semidirect
132. C2×#104D263semidirect
192. C42C22⋊D263semidirect

Maximal subgroups

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

subgroupindex
#306824452
C2×#225544272
C2×#225543972
#306819012
#306816992
#306816982
C2×#104×C2632
#1897263