Finite Group Databasebeta

← #46782663

Subgroups — #46782663

Order 33664.

612 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 612 conjugacy classes of subgroups — too many to draw. Only its 101 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
1C22×#16862375C211yesmaximal, characteristic
2C2×#22554385C211yesmaximal, characteristic, complemented
3C2×#22554384C212yesmaximal, complemented
4#30681799C212yesmaximal, complemented
5C2×#99×C263C211yesmaximal, characteristic, complemented
6C2×#16862375—24no—
7C2×#16862375—24no—
8C2×#16862375—22no—
9C2×#16862375—22no—
10C22×Dic526C411yescharacteristic, complemented
11C22×C22⋊D263C411yescharacteristic, complemented
12C22×C22⋊D263C2211yescharacteristic
13C23×Dic263C411yescharacteristic, complemented
14C23×Dic263C2211yescharacteristic
15C22×C4×D263C411yescharacteristic, complemented
16C2×C22⋊Dic263C2212yes—
17#22554385—22no—
18#22554384—24no—
19C263⋊#95—24no—
20C22×D4×C263C2211yescharacteristic
21C2×C22⋊C4×C263C2212yes—
22#99×C263—22no—
23C23×D263C2×C411yescharacteristic
24#16862375—216no—
25#16862375—216no—
26C2×Dic526—22no—
27C2×Dic526—22no—
28C2×Dic526—22no—
29C2×C22⋊D263—22no—
30C2×C22⋊D263—22no—
31C2×C22⋊D263—22no—
32C2×C22⋊D263—22no—
33C2×C22⋊D263—21no—
34C2×C22⋊D263—21no—
35C2×C22⋊D263D414yes—
36C22×Dic263—22no—
37C22×Dic263—22no—
38C22×Dic263—22no—
39C22×Dic263—22no—
40C22×Dic263—21no—
41C22×Dic263—21no—
42C22×Dic263—22no—
43C22×Dic263C2×C411yescharacteristic
44C22×Dic263C2×C411yescharacteristic
45C22×Dic263C2×C411yescharacteristic
46C22×Dic263D414yes—
47C2×C4×D263—22no—
48C2×C4×D263—22no—
49C2×C4×D263—22no—
50C22⋊Dic263—22no—
51C22⋊Dic263—22no—
52C24×C263C2×C411yescharacteristic
53C24×C263C2311yescharacteristic
54C2×D4×C263—22no—
55C2×D4×C263—22no—
56C2×D4×C263D412yes—
57C2×D4×C263D412yes—
58C22×C4×C263—22no—
59C22×C4×C263C2×C411yescharacteristic
60C22⋊C4×C263—22no—
61C22⋊C4×C263—22no—
62C22×D263—21no—
63C22×D263—21no—
64C22×D263—42no—
65C22×D263C22⋊C412yes—
66Dic526—28no—
67C22⋊D263—28no—
68C22⋊D263—24no—
69C22⋊D263—24no—
70C2×Dic263—28no—
71C2×Dic263—21no—
72C2×Dic263—21no—
73C2×Dic263—21no—
74C2×Dic263—21no—
75C2×Dic263—21no—
76C2×Dic263—21no—
77C2×Dic263—24no—
78C2×Dic263—24no—
79C2×Dic263—44no—
80C2×Dic263—42no—
81C2×Dic263C22⋊C412yes—
82C2×Dic263C22⋊C412yes—
83C2×Dic263C22⋊C412yes—
84C4×D263—28no—
85C23×C263—21no—
86C23×C263—21no—
87C23×C263—42no—
88C23×C263—42no—
89C23×C263C22⋊C412yes—
90C23×C263C22×C411yescharacteristic
91C23×C263C2×D412yes—
92C23×C263C2×D412yes—
93C23×C263C2×D411yescharacteristic
94C23×C263C2×D411yescharacteristic
95D4×C263—24no—
96D4×C263—24no—
97C2×C4×C263—21no—
98C2×C4×C263—21no—
99C2×C4×C263—44no—
100C2×C4×C263—42no—
101C2×C4×C263C22⋊C412yes—
102C22×C263—24no—
103C22×C263—22no—
104C22×C263—22no—
105C22×C263—42no—
106C22×C263—41no—
107C22×C263—41no—
108C22×C263—42no—
109C22×C263—42no—
110C22×C263—42no—
111C22×C263C2×C22⋊C411yescharacteristic
112C22×C263C2×C22⋊C411yescharacteristic
113C22×C263C2×C22⋊C411yescharacteristic
114C22×C263#12012yes—
115C22×C263#12012yes—
116C2×D263—22no—
117C2×D263—42no—
118C2×D263—42no—
119C2×D263—42no—
120C4×C263—22no—
121C4×C263—82no—
122Dic263—22no—
123Dic263—22no—
124Dic263—22no—
125Dic263—82no—
126C2×C263—22no—
127C2×C263—22no—
128C2×C263—21no—
129C2×C263—21no—
130C2×C263—42no—
131C2×C263#37911yescharacteristic
132C2×C263#41012yes—
133D263—42no—
134C263#178211yescharacteristic, complemented, Sylow
135#1782—2631nomaximal, Sylow
136C22×#41—2631no—
137C2×#99—2631no—
138C2×#99—2632no—
139C2×#99D26311yescharacteristic, complemented
140#381—2632no—
141C2×#41—5264no—
142C2×#41—5264no—
143C2×#41—5262no—
144C2×#41—5262no—
145C22×Q8—2631no—
146C22×D4—2631no—
147C22×D4—2631no—
148C22×D4C2×D26311yescharacteristic
149C23×C4—2631no—
150C23×C4—2631no—
151C23×C4—2631no—
152C2×C22⋊C4—2632no—
153C2×C22⋊C4C2×D26312yes—
154#99—22no—
155#99—5264no—
156#99—5262no—
157#95—5264no—
158C24—2631no—
159C24C4×D26311yescharacteristic
160C24C22×D26311yescharacteristic
161#41—52616no—
162#41—52616no—
163C2×Q8—5262no—
164C2×Q8—5262no—
165C2×Q8—5262no—
166C2×D4—22no—
167C2×D4—22no—
168C2×D4—2634no—
169C2×D4—5262no—
170C2×D4—5262no—
171C2×D4—5262no—
172C2×D4—5262no—
173C2×D4—5261no—
174C2×D4—5261no—
175C2×D4C22⋊D26312yes—
176C2×D4D105212yes—
177C22×C4—22no—
178C22×C4—2631no—
179C22×C4—2631no—
180C22×C4—2631no—
181C22×C4—2634no—
182C22×C4—5262no—
183C22×C4—5262no—
184C22×C4—5262no—
185C22×C4—5262no—
186C22×C4—5262no—
187C22×C4—5262no—
188C22×C4—5261no—
189C22×C4—5261no—
190C22×C4—5262no—
191C22×C4—5262no—
192C22×C4C4×D26311yescharacteristic
193C22⋊C4—22no—
194C22⋊C4—22no—
195C22⋊C4—5262no—
196C22⋊C4—5262no—
197C23—21no—
198C23—21no—
199C23—42no—
200C23—42no—
201C23—2632no—
202C23—5261no—
203C23—5261no—
204C23—10522no—
205C23(C2×D263)⋊C412yes—
206C23C2×C4×D26311yescharacteristic
207C23D4×D26312yes—
208C23D4×D26312yes—
209C23C2×C22⋊D26311yescharacteristic
210C23C2×D105211yescharacteristic
211Q8—5268no—
212D4—24no—
213D4—24no—
214D4—5268no—
215D4—5264no—
216D4—5264no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—44no—
220C2×C4—42no—
221C2×C4—2632no—
222C2×C4—2632no—
223C2×C4—2632no—
224C2×C4—5268no—
225C2×C4—5268no—
226C2×C4—5261no—
227C2×C4—5261no—
228C2×C4—5261no—
229C2×C4—5261no—
230C2×C4—5261no—
231C2×C4—5261no—
232C2×C4—5264no—
233C2×C4—5264no—
234C2×C4—10524no—
235C2×C4—10522no—
236C2×C4(C2×D263)⋊C412yes—
237C22—24no—
238C22—22no—
239C22—22no—
240C22—42no—
241C22—41no—
242C22—41no—
243C22—42no—
244C22—42no—
245C22—42no—
246C22—5262no—
247C22—10522no—
248C22—10522no—
249C22—10522no—
250C22C22⋊C4×D26311yescharacteristic
251C22C22⋊C4×D26311yescharacteristic
252C22C2×(C2×D263)⋊C411yescharacteristic
253C22#2255443812yes—
254C22#2255444012yes—
255C4—22no—
256C4—82no—
257C4—5262no—
258C4—5262no—
259C4—5262no—
260C4—21042no—
261C2—22no—
262C2—22no—
263C2—21no—
264C2—21no—
265C2—42no—
266C2—10522no—
267C2#3068179311yescharacteristic
268C2#3068191012yes—
subgroupG/H
centerC22C22⋊C4×D263
commutatorC23×C263C22×C4
FrattiniC24C22×D263
FittingC2×#99×C263C2
socleC22×C263C2×C22⋊C4
prime radicalC22×#16862375C2
cosocleC24×C263C23
hypercenterC2×#99D263
hypocenterC263#1782
LCSG ▷ C23×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
2. C2×#22554385C2semidirect
3. C2×#22554384C2semidirect
4. #30681799C2semidirect
5. C2×#99×C263C2semidirect
10. C22×Dic526C4semidirect
11. C22×C22⋊D263C4semidirect
13. C23×Dic263C4semidirect
15. C22×C4×D263C4semidirect
134. C263#1782semidirect
139. C2×#99D263semidirect

Maximal subgroups

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

subgroupindex
C22×#168623752
C2×#225543852
C2×#225543842
#306817992
C2×#99×C2632
#1782263