Finite Group Databasebeta

← #46783774

Subgroups — #46783774

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
1C2×#22554500C211yesmaximal, characteristic, complemented
2C2×#22554457C211yesmaximal, characteristic, complemented
3C2×#22554397C211yesmaximal, characteristic, complemented
4#30681946C211yesmaximal, characteristic, complemented
5C2×#22554387C211yesmaximal, characteristic, complemented
6#30681697C211yesmaximal, characteristic, complemented
7#535×C263C211yesmaximal, characteristic
8C22×Dic526C2211yescharacteristic
9#22554500—22no—
10#22554500—22no—
11C2×#16862366—21no—
12C2×#16862364—21no—
13C2×#16862360C2211yescharacteristic
14C2×#16862360C2211yescharacteristic
15#22554457—22no—
16#22554457—22no—
17C2×C22⋊Dic263—22no—
18C2×C4×Dic263C2211yescharacteristic
19#22554397—22no—
20#22554393—22no—
21#22554387—22no—
22C2×#41×C263C2211yescharacteristic
23C22×D4×C263C2211yescharacteristic
24#127×C263—21no—
25#124×C263—21no—
26#121×C263—22no—
27#120×C263—22no—
28#117×C263C2211yescharacteristic
29C2×Dic526—21no—
30C2×Dic526—21no—
31C2×Dic526—21no—
32C2×Dic526—21no—
33C2×Dic526—21no—
34C2×Dic526D412yescomplemented
35C22×Dic263—21no—
36C22×Dic263—21no—
37#16862366—24no—
38#16862364—24no—
39#16862360—21no—
40#16862360—21no—
41#16862360—21no—
42#16862360D412yescomplemented
43C2×C263⋊C8—21no—
44C2×C263⋊C8—21no—
45C22⋊Dic263—28no—
46C4×Dic263—21no—
47C4×Dic263D412yescomplemented
48C24×C263D412yes—
49#41×C263—21no—
50#41×C263—21no—
51#41×C263—21no—
52#41×C263—21no—
53C2×Q8×C263D411yescharacteristic
54C2×D4×C263—21no—
55C2×D4×C263—24no—
56C2×D4×C263—21no—
57C2×D4×C263—21no—
58C2×D4×C263—21no—
59C2×D4×C263—21no—
60C2×D4×C263—21no—
61C2×D4×C263—21no—
62C2×D4×C263D411yescharacteristic
63C22×C4×C263—21no—
64C22×C4×C263C2311yescharacteristic
65C4⋊C4×C263D412yes—
66C22⋊C4×C263—24no—
67C22⋊C4×C263—21no—
68C42×C263—21no—
69Dic526—22no—
70Dic526—22no—
71Dic526—41no—
72Dic526—41no—
73C2×Dic263—22no—
74C2×Dic263—22no—
75C2×Dic263—42no—
76C2×Dic263—41no—
77C2×Dic263—41no—
78C263⋊C8—22no—
79C263⋊C8—41no—
80C23×C263—22no—
81C23×C263—21no—
82C23×C263—22no—
83C23×C263—22no—
84C23×C263—44no—
85C23×C263C2×D411yescharacteristic
86Q8×C263—21no—
87Q8×C263—21no—
88D4×C263—21no—
89D4×C263—21no—
90D4×C263—41no—
91D4×C263—41no—
92D4×C263—41no—
93D4×C263—41no—
94D4×C263—41no—
95D4×C263—41no—
96D4×C263—84no—
97C2×C4×C263—22no—
98C2×C4×C263—21no—
99C2×C4×C263—41no—
100C2×C4×C263—41no—
101C2×C4×C263C2×D411yescharacteristic
102C2×C4×C263C2×D411yescharacteristic
103C2×C4×C263C2×D411yescharacteristic
104C2×C4×C263C2×D411yescharacteristic
105C2×C4×C263C2×D411yescharacteristic
106C2×C4×C263#4111yescharacteristic
107C22×C263—22no—
108C22×C263—44no—
109C22×C263—41no—
110C22×C263—42no—
111C22×C263—42no—
112C22×C263—44no—
113C22×C263—82no—
114C22×C263#12011yescharacteristic
115C22×C263#12011yescharacteristic
116C22×C263#12111yescharacteristic
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—82no—
129C2×C263#39211yescharacteristic
130C2×C263#45512yes—
131C263#200411yescharacteristic, complemented, Sylow
132#2004—2631nomaximal, Sylow
133C2×#137—2631no—
134#535D26311yescharacteristic
135C2×#124—2631no—
136C2×#104—2631no—
137#419—2631no—
138C2×#100—2631no—
139#339—2631no—
140C2×#41C2×D26311yescharacteristic
141C22×Q8—2631no—
142C22×D4C2×D26311yescharacteristic
143#137—5262no—
144#137—5262no—
145C2×Q16—5261no—
146C2×SD16—5261no—
147C2×M16—2631no—
148C2×M16—2631no—
149#127—21no—
150#124—21no—
151#124—5262no—
152#124—5262no—
153#121—22no—
154#120—22no—
155#117C2×D26311yescharacteristic
156C2×C22⋊C4—5262no—
157C2×C42—2631no—
158#104—5262no—
159#103—5262no—
160#100—5262no—
161C24C22⋊D26312yes—
162#41—21no—
163#41—21no—
164#41—21no—
165#41—21no—
166C2×Q8—2632no—
167C2×Q8—5261no—
168C2×Q8—5261no—
169C2×Q8—5261no—
170C2×Q8—5261no—
171C2×Q8—5261no—
172C2×Q8C22⋊D26311yescharacteristic
173C2×D4—21no—
174C2×D4—24no—
175C2×D4—21no—
176C2×D4—21no—
177C2×D4—21no—
178C2×D4—21no—
179C2×D4—21no—
180C2×D4—21no—
181C2×D4C22⋊D26311yescharacteristic
182C22×C4—21no—
183C22×C4—5261no—
184C22×C4—5261no—
185C22×C4C22×D26311yescharacteristic
186Q16—5264no—
187SD16—5264no—
188M16—2632no—
189M16—5261no—
190M16—5261no—
191M16—5261no—
192C2×C8—5261no—
193C2×C8—5261no—
194C4⋊C4C22⋊D26312yes—
195C22⋊C4—24no—
196C22⋊C4—21no—
197C22⋊C4—5268no—
198C42—21no—
199C42—2632no—
200C42—5261no—
201C23—22no—
202C23—22no—
203C23—21no—
204C23—22no—
205C23—44no—
206C23C2×C22⋊D26311yescharacteristic
207Q8—21no—
208Q8—21no—
209Q8—5262no—
210Q8—5262no—
211Q8—10521no—
212Q8—10521no—
213D4—21no—
214D4—21no—
215D4—41no—
216D4—41no—
217D4—41no—
218D4—41no—
219D4—41no—
220D4—41no—
221D4—84no—
222C2×C4—22no—
223C2×C4—21no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—5262no—
227C2×C4—5262no—
228C2×C4—10522no—
229C2×C4—10521no—
230C2×C4—10521no—
231C2×C4D4×D26311yescharacteristic
232C2×C4D4×D26311yescharacteristic
233C2×C4D4×D26311yescharacteristic
234C2×C4C2×C22⋊D26311yescharacteristic
235C2×C4C2×C22⋊D26311yescharacteristic
236C2×C4#1686237511yescharacteristic
237C8—5262no—
238C8—10521no—
239C22—22no—
240C22—44no—
241C22—42no—
242C22—44no—
243C22—41no—
244C22—42no—
245C22—82no—
246C22#2255443811yescharacteristic
247C22#2255443911yescharacteristic
248C22#2255444211yescharacteristic
249C4—42no—
250C4—41no—
251C4—10522no—
252C4—10522no—
253C4#2255443811yescharacteristic
254C4#2255444111yescharacteristic
255C4#2255444211yescharacteristic
256C4#2255446611yescharacteristic
257C2—21no—
258C2—21no—
259C2—82no—
260C2—81no—
261C2#3068184611yescharacteristic
262C2#3068211612yes—
subgroupG/H
centerC22#22554439
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
Fitting, prime radical#535×C263C2
socleC22×C263#120
hypercenter#535D263
hypocenterC263#2004
LCSG ▷ C22×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ #535

Complements

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

NH ≅ G/Ntype
1. C2×#22554500C2semidirect
2. C2×#22554457C2semidirect
3. C2×#22554397C2semidirect
4. #30681946C2semidirect
5. C2×#22554387C2semidirect
6. #30681697C2semidirect
34. C2×Dic526D4semidirect
42. #16862360D4semidirect
47. C4×Dic263D4semidirect
131. C263#2004semidirect

Maximal subgroups

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

subgroupindex
C2×#225545002
C2×#225544572
C2×#225543972
#306819462
C2×#225543872
#306816972
#535×C2632
#2004263