Finite Group Databasebeta

← #28401498

Subgroups — #28401498

Order 14464.

428 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 123 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#20299145C211yesmaximal, characteristic
2C4⋊Q8×D113C211yesmaximal, characteristic, complemented
3#20298969C212yesmaximal, complemented
4#20298947C212yesmaximal, complemented
5#20298804C211yesmaximal, characteristic, complemented
6#20298803C211yesmaximal, characteristic, complemented
7#20298800C211yesmaximal, characteristic, complemented
8#20298738C212yesmaximal, complemented
9#20298735C212yesmaximal, complemented
10#20298650C211yesmaximal, characteristic, complemented
11#461×C113C211yesmaximal, characteristic, complemented
12C2×#14268647—21no—
13C2×Q8×D113C2212yes—
14C2×#14268636C2212yes—
15C2×#14268635C2212yes—
16C2×#14268634C2212yes—
17#16813622C2211yescharacteristic
18#16813621—21no—
19#16813621—21no—
20#16813621C2211yescharacteristic
21#16813620C2212yes—
22#16813618C2211yescharacteristic
23#16813608—21no—
24#16813597C2211yescharacteristic
25#16813595—21no—
26#16813593C2211yescharacteristic
27C4×D452C2211yescharacteristic
28C4×C22⋊D113—21no—
29C4⋊C4×D113—21no—
30C4⋊C4×D113—21no—
31C42×D113C2211yescharacteristic
32C4⋊#11744751C2211yescharacteristic
33#16813547C2212yes—
34#16813546C2212yes—
35#16813545C2212yes—
36#16813534C2212yes—
37C8×Dic113C2212yes—
38C2×SD16×C113C2212yes—
39C4⋊Q8×C113C2211yescharacteristic
40C4×D4×C113C2211yescharacteristic
41C4⋊C8×C113C2211yescharacteristic
42#103×C113C2212yes—
43#14268647—44no—
44C2×Dic226—21no—
45C2×Dic226—22no—
46C2×Dic226C2312yes—
47Q8×D113—42no—
48Q8×D113—42no—
49C2×D452—21no—
50C2×D452C2311yescharacteristic
51C2×C22⋊D113—21no—
52C2×C22⋊D113—21no—
53C2×C22⋊D113—21no—
54C2×C4×D113—22no—
55C2×C4×D113—21no—
56C2×C4×D113D411yescharacteristic
57C2×C4×D113D411yescharacteristic
58C2×C4×D113C2311yescharacteristic
59#14268636—42no—
60#14268635—42no—
61#14268634—42no—
62C2×#11744751C2312yes—
63C4⋊Dic113—21no—
64C4⋊Dic113—21no—
65C4⋊Dic113C2311yescharacteristic
66#14268626—22no—
67#14268626—22no—
68#14268626—21no—
69C22⋊Dic113—21no—
70#14268624—21no—
71#14268624—21no—
72C4×Dic113D411yescharacteristic
73C4×Dic113D411yescharacteristic
74C4×Dic113C2311yescharacteristic
75C2×Q8×C113C2312yes—
76C2×D4×C113C2311yescharacteristic
77C22×C4×C113—21no—
78SD16×C113—42no—
79C2×C8×C113C2312yes—
80C4⋊C4×C113—21no—
81C4⋊C4×C113—21no—
82C4⋊C4×C113C2311yescharacteristic
83C22⋊C4×C113—21no—
84C42×C113C2311yescharacteristic
85C23×C113—21no—
86C22×D113—21no—
87C22×D113C2×D411yescharacteristic
88Q8×C113—22no—
89Q8×C113—22no—
90D4×C113—21no—
91D4×C113—21no—
92C2×C4×C113—21no—
93C2×C4×C113—22no—
94C2×C4×C113—42no—
95C2×C4×C113C2×D411yescharacteristic
96C2×C4×C113C2×D411yescharacteristic
97C2×C4×C113C2411yescharacteristic
98C22⋊D113—42no—
99C22⋊D113—42no—
100C22⋊D113—42no—
101C2×Dic113—21no—
102C2×Dic113—22no—
103C2×Dic113C2×D411yescharacteristic
104C2×Dic113C2×D411yescharacteristic
105C2×Dic113C2×D411yescharacteristic
106D452—21no—
107D452—21no—
108D452—42no—
109C4×D113—21no—
110C4×D113—21no—
111C4×D113—22no—
112C4×D113—44no—
113C4×D113—42no—
114C4×D113SD1614yescomplemented
115Dic226—22no—
116Dic226—22no—
117Dic226—44no—
118Dic226—42no—
119C8×C113—22no—
120#11744751—22no—
121C22×C113—41no—
122C22×C113—41no—
123C22×C113—41no—
124C22×C113C22×D411yescharacteristic
125C2×D113—21no—
126C2×D113—21no—
127C2×D113—41no—
128C2×D113—41no—
129C2×D113—41no—
130C2×D113C2×SD1612yes—
131C4×C113—21no—
132C4×C113—42no—
133C4×C113—41no—
134C4×C113C2×SD1612yes—
135C4×C113H(5,𝔽2)11yescharacteristic
136C4×C113H(5,𝔽2)11yescharacteristic
137Dic113—21no—
138Dic113—42no—
139Dic113—41no—
140Dic113C2×SD1612yes—
141Dic113#13712yes—
142C2×C113—81no—
143C2×C113#53511yescharacteristic
144C2×C113C22×SD1611yescharacteristic
145C2×C113C2×#13711yescharacteristic
146D113—22no—
147D113—81no—
148#3206—1131nomaximal, Sylow
149C113#320611yescharacteristic, complemented, Sylow
150#532—1131no—
151C2×C4⋊Q8—1131no—
152#492—1132no—
153#487—1132no—
154#461—1131no—
155#461—1131no—
156#461—1131no—
157#461D11311yescharacteristic, complemented
158#448—1132no—
159#448—1132no—
160#431—1131no—
161C2×#41—2261no—
162C22×Q8—1132no—
163C2×SD16—1132no—
164C2×SD16—1132no—
165C2×SD16—1132no—
166C2×SD16C2×D11312yes—
167C4⋊Q8—1131no—
168C4⋊Q8—1132no—
169C4⋊Q8—1131no—
170C4⋊Q8—2261no—
171C4⋊Q8—2261no—
172C4⋊Q8C2×D11311yescharacteristic
173#127—1131no—
174#124—2261no—
175#121—1131no—
176#121—1131no—
177#121—2261no—
178C4×D4—1131no—
179C4×D4—2261no—
180C4×D4C2×D11311yescharacteristic
181C2×C4⋊C4—2261no—
182C2×C4⋊C4—2261no—
183C2×C42—1131no—
184C4⋊C8—1131no—
185C4⋊C8C2×D11311yescharacteristic
186#103—1132no—
187#103—1132no—
188#103—1132no—
189#103C2×D11312yes—
190C22⋊C8—1132no—
191C4×C8—1132no—
192#41—4524no—
193C2×Q8—1132no—
194C2×Q8—4522no—
195C2×Q8—4522no—
196C2×Q8—2261no—
197C2×Q8—2262no—
198C2×Q8C22×D11312yes—
199C2×D4—1131no—
200C2×D4—2261no—
201C2×D4—2261no—
202C2×D4—2261no—
203C2×D4—2261no—
204C2×D4C22×D11311yescharacteristic
205C22×C4—21no—
206C22×C4—1131no—
207C22×C4—1131no—
208C22×C4—1131no—
209C22×C4—2262no—
210C22×C4—2261no—
211SD16—42no—
212SD16—4522no—
213SD16—4522no—
214SD16—4522no—
215C2×C8—1132no—
216C2×C8C22×D11312yes—
217C4⋊C4—21no—
218C4⋊C4—21no—
219C4⋊C4—1131no—
220C4⋊C4—2262no—
221C4⋊C4—2262no—
222C4⋊C4—2261no—
223C4⋊C4—2261no—
224C4⋊C4—2261no—
225C4⋊C4C22×D11311yescharacteristic
226C22⋊C4—21no—
227C22⋊C4—2261no—
228C22⋊C4—2261no—
229C22⋊C4—2261no—
230C42—1131no—
231C42—1131no—
232C42—1131no—
233C42C22×D11311yescharacteristic
234C23—21no—
235C23—1131no—
236C23—2261no—
237Q8—22no—
238Q8—22no—
239Q8—4522no—
240Q8—4524no—
241Q8—2262no—
242Q8—2262no—
243D4—21no—
244D4—21no—
245D4—4522no—
246D4—4522no—
247D4—4522no—
248D4—4522no—
249D4—2261no—
250D4—2261no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—42no—
254C2×C4—1131no—
255C2×C4—1131no—
256C2×C4—1134no—
257C2×C4—1131no—
258C2×C4—4524no—
259C2×C4—4522no—
260C2×C4—2262no—
261C2×C4—2261no—
262C2×C4—2262no—
263C2×C4—2261no—
264C2×C4—2261no—
265C2×C4D4×D11311yescharacteristic
266C2×C4D4×D11311yescharacteristic
267C2×C4C23×D11311yescharacteristic
268C8—22no—
269C8—2262no—
270C22—41no—
271C22—41no—
272C22—41no—
273C22—1132no—
274C22—4521no—
275C22—4521no—
276C22—4521no—
277C22—2261no—
278C22—2261no—
279C22C2×D4×D11311yescharacteristic
280C4—21no—
281C4—41no—
282C4—42no—
283C4—1132no—
284C4—1132no—
285C4—4521no—
286C4—4522no—
287C4—2261no—
288C4SD16×D11312yes—
289C4#1681366711yescharacteristic
290C4#1681366811yescharacteristic
291C2—81no—
292C2—9041no—
293C2—2262no—
294C2#2029916411yescharacteristic
295C2C2×SD16×D11311yescharacteristic
296C2#137×D11311yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#461×C113C2
socleC22×C113C22×D4
prime radical#20299145C2
hypercenter#461D113
hypocenterC113#3206
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
2. C4⋊Q8×D113C2semidirect
3. #20298969C2semidirect
4. #20298947C2semidirect
5. #20298804C2semidirect
6. #20298803C2semidirect
7. #20298800C2semidirect
8. #20298738C2semidirect
9. #20298735C2semidirect
10. #20298650C2semidirect
11. #461×C113C2semidirect
114. C4×D113SD16semidirect
149. C113#3206semidirect
157. #461D113semidirect

Maximal subgroups

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

subgroupindex
#202991452
C4⋊Q8×D1132
#202989692
#202989472
#202988042
#202988032
#202988002
#202987382
#202987352
#202986502
#461×C1132
#3206113