Finite Group Databasebeta

← #46783773

Subgroups — #46783773

Order 33664.

394 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 75 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#30682502C211yesmaximal, characteristic
2C2×#22554459C211yesmaximal, characteristic, complemented
3C2×#22554397C211yesmaximal, characteristic, complemented
4#30681947C211yesmaximal, characteristic, complemented
5C2×#22554386C211yesmaximal, characteristic, complemented
6#30681699C211yesmaximal, characteristic, complemented
7C2×#137×C263C211yesmaximal, characteristic, complemented
8C22×D1052C2211yescharacteristic
9C2×#16862360C2211yescharacteristic
10#22554466—21no—
11#22554459—22no—
12#22554459—21no—
13#22554459—22no—
14#22554444—22no—
15#22554438—22no—
16#22554429C2211yescharacteristic
17C2×(C2×D263)⋊C4—22no—
18C2×C4×Dic263C2211yescharacteristic
19#22554397—22no—
20#22554394—22no—
21#22554386—22no—
22C2×#41×C263C2211yescharacteristic
23C22×Q8×C263C2211yescharacteristic
24#137×C263—22no—
25#137×C263—22no—
26C2×Q16×C263—21no—
27C2×SD16×C263—21no—
28C2×M16×C263C2211yescharacteristic
29C23×D263D412yes—
30C2×D1052—21no—
31C2×D1052—21no—
32C2×D1052—21no—
33C2×D1052—21no—
34C2×D1052—21no—
35C2×D1052—21no—
36C2×C22⋊D263—24no—
37C22×Dic263—21no—
38#16862360—21no—
39#16862360—21no—
40C2×C263⋊C8—21no—
41C4⋊Dic263D412yes—
42C22⋊Dic263—21no—
43(C2×D263)⋊C4—28no—
44(C2×D263)⋊C4—24no—
45C4×Dic263—21no—
46C4×Dic263—21no—
47C4×Dic263D412yescomplemented
48#41×C263—21no—
49#41×C263—21no—
50#41×C263—21no—
51#41×C263—21no—
52C2×Q8×C263—21no—
53C2×Q8×C263—21no—
54C2×Q8×C263—21no—
55C2×Q8×C263—21no—
56C2×Q8×C263—21no—
57C2×Q8×C263D411yescharacteristic
58C2×Q8×C263D412yescomplemented
59C2×D4×C263—21no—
60C2×D4×C263D411yescharacteristic
61C22×C4×C263—21no—
62C22×C4×C263—21no—
63C22×C4×C263C2311yescharacteristic
64Q16×C263—24no—
65SD16×C263—24no—
66M16×C263—21no—
67M16×C263D412yescomplemented
68C2×C8×C263—21no—
69C22×D263—22no—
70C22×D263—22no—
71C22×D263—22no—
72C22×D263—44no—
73D1052—41no—
74D1052—41no—
75D1052—41no—
76D1052—41no—
77C22⋊D263—84no—
78C2×Dic263—22no—
79C2×Dic263—22no—
80C2×Dic263—42no—
81C263⋊C8—41no—
82C23×C263—21no—
83C23×C263C2×D411yescharacteristic
84Q8×C263—22no—
85Q8×C263—21no—
86Q8×C263—22no—
87Q8×C263—21no—
88Q8×C263—41no—
89Q8×C263—41no—
90D4×C263—21no—
91D4×C263—21no—
92D4×C263—41no—
93D4×C263—41no—
94C2×C4×C263—21no—
95C2×C4×C263—22no—
96C2×C4×C263—41no—
97C2×C4×C263—41no—
98C2×C4×C263—41no—
99C2×C4×C263—41no—
100C2×C4×C263C2×D411yescharacteristic
101C2×C4×C263C2×D411yescharacteristic
102C2×C4×C263C2×D411yescharacteristic
103C2×C4×C263C2×D411yescharacteristic
104C2×C4×C263C2×D411yescharacteristic
105C2×C4×C263#4111yescharacteristic
106C8×C263—22no—
107C22×C263—22no—
108C22×C263—41no—
109C22×C263—42no—
110C22×C263#12011yescharacteristic
111C22×C263#12011yescharacteristic
112C22×C263#12111yescharacteristic
113C2×D263—44no—
114C2×D263—42no—
115C2×D263—44no—
116C2×D263—82no—
117C4×C263—41no—
118C4×C263—42no—
119C4×C263#12011yescharacteristic
120C4×C263#12111yescharacteristic
121C4×C263#12111yescharacteristic
122C4×C263#12711yescharacteristic
123Dic263—42no—
124Dic263—42no—
125C2×C263—21no—
126C2×C263—21no—
127C2×C263—81no—
128C2×C263#39211yescharacteristic
129C2×C263#45512yes—
130D263—82no—
131C263#200411yescharacteristic, complemented, Sylow
132#2004—2631nomaximal, Sylow
133C2×#137D26311yescharacteristic, complemented
134#535—2631no—
135C2×#124—2631no—
136C2×#104—2631no—
137#419—2631no—
138C2×#100—2631no—
139#339—2631no—
140C2×#41C2×D26311yescharacteristic
141C22×Q8C2×D26311yescharacteristic
142C22×D4—2631no—
143#137—22no—
144#137—22no—
145C2×Q16—21no—
146C2×SD16—21no—
147C2×M16—2631no—
148C2×M16C2×D26311yescharacteristic
149#127—5261no—
150#124—5262no—
151#124—5261no—
152#124—5262no—
153#121—5262no—
154#120—5262no—
155#117—2631no—
156C2×C22⋊C4—5262no—
157C2×C42—2631no—
158#104—5262no—
159#103—5262no—
160#100—5262no—
161C24—2632no—
162#41—21no—
163#41—21no—
164#41—21no—
165#41—21no—
166C2×Q8—21no—
167C2×Q8—21no—
168C2×Q8—21no—
169C2×Q8—21no—
170C2×Q8—21no—
171C2×Q8C22⋊D26311yescharacteristic
172C2×Q8C22⋊D26312yescomplemented
173C2×D4—21no—
174C2×D4—5264no—
175C2×D4—5261no—
176C2×D4—5261no—
177C2×D4—5261no—
178C2×D4—5261no—
179C2×D4—5261no—
180C2×D4—5261no—
181C2×D4C22⋊D26311yescharacteristic
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—5261no—
185C22×C4C22×D26311yescharacteristic
186Q16—24no—
187SD16—24no—
188M16—21no—
189M16—5261no—
190M16—5261no—
191M16C22⋊D26312yescomplemented
192C2×C8—21no—
193C2×C8—5261no—
194C4⋊C4—2632no—
195C22⋊C4—5268no—
196C22⋊C4—5264no—
197C22⋊C4—5261no—
198C42—2632no—
199C42—5261no—
200C42—5261no—
201C23—21no—
202C23—5262no—
203C23—5262no—
204C23—5262no—
205C23—10524no—
206C23D4×D26311yescharacteristic
207Q8—22no—
208Q8—21no—
209Q8—22no—
210Q8—21no—
211Q8—41no—
212Q8—41no—
213D4—21no—
214D4—21no—
215D4—41no—
216D4—41no—
217D4—10521no—
218D4—10521no—
219D4—10521no—
220D4—10521no—
221D4—21044no—
222C2×C4—22no—
223C2×C4—21no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—5262no—
229C2×C4—5262no—
230C2×C4—10522no—
231C2×C4D4×D26311yescharacteristic
232C2×C4D4×D26311yescharacteristic
233C2×C4C2×C22⋊D26311yescharacteristic
234C2×C4C2×C22⋊D26311yescharacteristic
235C2×C4C2×C22⋊D26311yescharacteristic
236C2×C4#1686237511yescharacteristic
237C8—22no—
238C8—10521no—
239C22—22no—
240C22—42no—
241C22—41no—
242C22—10524no—
243C22—10524no—
244C22—10522no—
245C22—21042no—
246C22#2255443811yescharacteristic
247C22#2255443811yescharacteristic
248C22#2255444111yescharacteristic
249C4—41no—
250C4—42no—
251C4—10522no—
252C4—10522no—
253C4#2255443911yescharacteristic
254C4#2255444211yescharacteristic
255C4#2255444211yescharacteristic
256C4#2255446611yescharacteristic
257C2—21no—
258C2—21no—
259C2—81no—
260C2—21042no—
261C2#3068184611yescharacteristic
262C2#3068211412yes—
subgroupG/H
centerC22#22554438
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
FittingC2×#137×C263C2
socleC22×C263#120
prime radical#30682502C2
hypercenterC2×#137D263
hypocenterC263#2004
LCSG ▷ C22×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
2. C2×#22554459C2semidirect
3. C2×#22554397C2semidirect
4. #30681947C2semidirect
5. C2×#22554386C2semidirect
6. #30681699C2semidirect
7. C2×#137×C263C2semidirect
47. C4×Dic263D4semidirect
58. C2×Q8×C263D4semidirect
67. M16×C263D4semidirect
131. C263#2004semidirect
133. C2×#137D263semidirect
172. C2×Q8C22⋊D263semidirect
191. M16C22⋊D263semidirect

Maximal subgroups

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

subgroupindex
#306825022
C2×#225544592
C2×#225543972
#306819472
C2×#225543862
#306816992
C2×#137×C2632
#2004263