Finite Group Databasebeta

← #46783775

Subgroups — #46783775

Order 33664.

394 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 73 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
2#30682502C211yesmaximal, characteristic
3C2×#22554458C211yesmaximal, characteristic, complemented
4#30681948C211yesmaximal, characteristic, complemented
5C2×#22554386C211yesmaximal, characteristic, complemented
6#30681698C211yesmaximal, characteristic, complemented
7C2×#104×C263C211yesmaximal, characteristic, complemented
8C22×Dic526C2211yescharacteristic
9C22×D1052C2211yescharacteristic
10#22554500—22no—
11#22554500—22no—
12C2×#16862366—21no—
13C2×#16862364—21no—
14C2×#16862360C2211yescharacteristic
15#22554466—21no—
16#22554459—21no—
17#22554458—22no—
18#22554458—22no—
19#22554444—22no—
20#22554438—22no—
21#22554429C2211yescharacteristic
22C2×(C2×D263)⋊C4—22no—
23#22554395—22no—
24#22554386—22no—
25C2×#41×C263C2211yescharacteristic
26C2×M16×C263C2211yescharacteristic
27C2×C42×C263C2211yescharacteristic
28#104×C263—22no—
29C23×D263D412yes—
30C2×Dic526—21no—
31C2×Dic526—21no—
32C2×Dic526—21no—
33C2×Dic526—21no—
34C2×Dic526—21no—
35C2×Dic526D412yescomplemented
36C2×D1052—21no—
37C2×D1052—21no—
38C2×D1052—21no—
39C2×D1052—21no—
40C2×D1052—21no—
41C2×D1052—21no—
42C2×C22⋊D263—24no—
43C22×Dic263—21no—
44#16862366—24no—
45#16862364—24no—
46#16862360—21no—
47#16862360D412yescomplemented
48C2×C263⋊C8—21no—
49C4⋊Dic263D412yes—
50C22⋊Dic263—21no—
51(C2×D263)⋊C4—28no—
52(C2×D263)⋊C4—24no—
53C4×Dic263—21no—
54#41×C263—21no—
55#41×C263—21no—
56#41×C263—21no—
57#41×C263—21no—
58C2×Q8×C263D411yescharacteristic
59C2×D4×C263—21no—
60C2×D4×C263D411yescharacteristic
61C22×C4×C263—21no—
62C22×C4×C263—21no—
63C22×C4×C263C2311yescharacteristic
64M16×C263—21no—
65M16×C263—21no—
66C2×C8×C263—21no—
67C42×C263—21no—
68C42×C263D412yescomplemented
69C22×D263—22no—
70C22×D263—22no—
71C22×D263—22no—
72C22×D263—44no—
73Dic526—22no—
74Dic526—22no—
75Dic526—41no—
76Dic526—41no—
77D1052—41no—
78D1052—41no—
79D1052—41no—
80D1052—41no—
81C22⋊D263—84no—
82C2×Dic263—22no—
83C2×Dic263—22no—
84C2×Dic263—41no—
85C2×Dic263—41no—
86C263⋊C8—22no—
87C23×C263—21no—
88C23×C263C2×D411yescharacteristic
89Q8×C263—21no—
90Q8×C263—21no—
91D4×C263—21no—
92D4×C263—21no—
93D4×C263—41no—
94D4×C263—41no—
95C2×C4×C263—22no—
96C2×C4×C263—21no—
97C2×C4×C263—42no—
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—41no—
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—42no—
118C4×C263—41no—
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×#137—2631no—
134#535—2631no—
135C2×#124—2631no—
136C2×#104D26311yescharacteristic, complemented
137#419—2631no—
138C2×#100—2631no—
139#339—2631no—
140C2×#41C2×D26311yescharacteristic
141C22×Q8—2631no—
142C22×D4—2631no—
143#137—5262no—
144#137—5262no—
145C2×Q16—5261no—
146C2×SD16—5261no—
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×C42C2×D26311yescharacteristic
158#104—22no—
159#103—5262no—
160#100—5262no—
161C24—2632no—
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×Q8D105211yescharacteristic
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×D4D105211yescharacteristic
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—5261no—
185C22×C4C22×D26311yescharacteristic
186Q16—5264no—
187SD16—5264no—
188M16—21no—
189M16—21no—
190M16—2632no—
191M16—5261no—
192C2×C8—21no—
193C2×C8—5261no—
194C4⋊C4—2632no—
195C22⋊C4—5268no—
196C22⋊C4—5264no—
197C22⋊C4—5261no—
198C42—21no—
199C42—5261no—
200C42C22⋊D26312yescomplemented
201C23—21no—
202C23—5262no—
203C23—5262no—
204C23—5262no—
205C23—10524no—
206C23D4×D26311yescharacteristic
207Q8—21no—
208Q8—21no—
209Q8—5262no—
210Q8—5262no—
211Q8—10521no—
212Q8—10521no—
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—42no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—5262no—
228C2×C4—5262no—
229C2×C4—10521no—
230C2×C4—10521no—
231C2×C4D4×D26311yescharacteristic
232C2×C4D4×D26311yescharacteristic
233C2×C4D4×D26311yescharacteristic
234C2×C4C2×C22⋊D26311yescharacteristic
235C2×C4C2×D105211yescharacteristic
236C2×C4#1686237611yescharacteristic
237C8—41no—
238C8—5262no—
239C22—22no—
240C22—42no—
241C22—41no—
242C22—10524no—
243C22—10524no—
244C22—10522no—
245C22—21042no—
246C22#2255443811yescharacteristic
247C22#2255444011yescharacteristic
248C22#2255444311yescharacteristic
249C4—42no—
250C4—41no—
251C4—10522no—
252C4—10522no—
253C4#2255444011yescharacteristic
254C4#2255444311yescharacteristic
255C4#2255444411yescharacteristic
256C4#2255446611yescharacteristic
257C2—21no—
258C2—21no—
259C2—81no—
260C2—21042no—
261C2#3068184711yescharacteristic
262C2#3068211712yes—
subgroupG/H
centerC22#22554440
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
FittingC2×#104×C263C2
socleC22×C263#120
prime radical#30682502C2
hypercenterC2×#104D263
hypocenterC263#2004
LCSG ▷ C22×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
1. C2×#22554500C2semidirect
3. C2×#22554458C2semidirect
4. #30681948C2semidirect
5. C2×#22554386C2semidirect
6. #30681698C2semidirect
7. C2×#104×C263C2semidirect
35. C2×Dic526D4semidirect
47. #16862360D4semidirect
68. C42×C263D4semidirect
131. C263#2004semidirect
136. C2×#104D263semidirect
200. C42C22⋊D263semidirect

Maximal subgroups

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

subgroupindex
C2×#225545002
#306825022
C2×#225544582
#306819482
C2×#225543862
#306816982
C2×#104×C2632
#2004263