Finite Group Databasebeta

← #28402177

Subgroups — #28402177

Order 14464.

546 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 125 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×#16813649C212yesmaximal, complemented
2#20299251C211yesmaximal, characteristic, complemented
3D4×D452C211yesmaximal, characteristic, complemented
4#20298972C211yesmaximal, characteristic, complemented
5#20298847C212yesmaximal, complemented
6#20298794C211yesmaximal, characteristic, complemented
7#20298747C212yesmaximal, complemented
8#20298746C212yesmaximal, complemented
9C4×#14268632C211yesmaximal, characteristic, complemented
10#20298675C211yesmaximal, characteristic, complemented
11#461×C113C211yesmaximal, characteristic, complemented
12C2×#14268648C2212yescomplemented
13C22×D452—21no—
14C2×D4×D113C2212yes—
15#16813649—28no—
16C2×#14268634C2212yescomplemented
17C2×#14268634C2212yescomplemented
18C2×D904C2212yescomplemented
19C2×#14268632C2211yescharacteristic
20C2×#14268630C2212yescomplemented
21#16813619C2211yescharacteristic
22#16813607—22no—
23#16813598C2212yescomplemented
24#16813597—21no—
25#16813597C2212yes—
26#16813596—21no—
27#16813592—22no—
28C4×D452C2211yescharacteristic
29C4×D452C2211yescharacteristic, complemented
30C4⋊C4×D113—21no—
31#16813555C2211yescharacteristic, complemented
32#16813544C2212yescomplemented
33#16813543C2211yescharacteristic
34#16813542C2211yescharacteristic, complemented
35#16813534C2212yescomplemented
36C4×#11744751C2211yescharacteristic, complemented
37C2×SD16×C113C2212yes—
38C4⋊Q8×C113C2211yescharacteristic, complemented
39C4×D4×C113C2211yescharacteristic
40C4⋊C8×C113C2211yescharacteristic, complemented
41#103×C113C2212yescomplemented
42C23×D113—22no—
43#14268648—24no—
44#14268648—42no—
45C2×D452—22no—
46C2×D452—22no—
47C2×D452—21no—
48C2×D452—21no—
49C2×D452—44no—
50C2×D452D411yescharacteristic
51C2×D452C2312yes—
52C2×D452C2311yescharacteristic
53C2×C22⋊D113—22no—
54D4×D113—24no—
55D4×D113—42no—
56C2×C4×D113—21no—
57C2×C4×D113—22no—
58C2×C4×D113C2312yes—
59#14268634—24no—
60#14268634—42no—
61D904—24no—
62#14268632D414yescomplemented
63#14268630—24no—
64C2×#11744751C2311yescharacteristic
65C2×#11744751C2311yescharacteristic
66C4⋊Dic113D411yescharacteristic
67C4⋊Dic113C2311yescharacteristic
68#14268626—22no—
69#14268624—22no—
70#14268624—21no—
71#14268624—22no—
72#14268624D412yes—
73C2×Q8×C113C2312yes—
74C2×D4×C113C2311yescharacteristic
75C22×C4×C113—21no—
76SD16×C113—24no—
77C2×C8×C113C2312yes—
78C4⋊C4×C113—21no—
79C4⋊C4×C113—21no—
80C4⋊C4×C113C2311yescharacteristic
81C22⋊C4×C113—21no—
82C42×C113C2311yescharacteristic
83C23×C113—21no—
84C22×D113—21no—
85C22×D113—22no—
86C22×D113—44no—
87C22×D113—44no—
88C22×D113—82no—
89C22×D113C2×D412yes—
90Q8×C113—22no—
91Q8×C113—22no—
92D4×C113—21no—
93D4×C113C2×D412yes—
94C2×C4×C113—21no—
95C2×C4×C113—22no—
96C2×C4×C113—42no—
97C2×C4×C113C2×D411yescharacteristic
98C2×C4×C113C2×D411yescharacteristic
99C2×C4×C113C2411yescharacteristic
100C22⋊D113—44no—
101C2×Dic113—21no—
102C2×Dic113C2×D412yes—
103D452—22no—
104D452—22no—
105D452—21no—
106D452—22no—
107D452—44no—
108D452—44no—
109D452—42no—
110D452—81no—
111D452C2×D412yescomplemented
112C4×D113—22no—
113C4×D113—22no—
114C4×D113—44no—
115C4×D113—42no—
116C8×C113—22no—
117#11744751—21no—
118#11744751C2×D412yescomplemented
119C22×C113—22no—
120C22×C113—41no—
121C22×C113—41no—
122C22×C113C22×D411yescharacteristic
123C2×D113—22no—
124C2×D113—22no—
125C2×D113—22no—
126C2×D113—22no—
127C2×D113—41no—
128C2×D113—41no—
129C2×D113—42no—
130C2×D113—42no—
131C2×D113—42no—
132C2×D113—88no—
133C4×C113—21no—
134C4×C113—42no—
135C4×C113—41no—
136C4×C113AGL(1,ℤ/8)12yescomplemented
137C4×C113C22×D411yescharacteristic
138C4×C113H(5,𝔽2)11yescharacteristic
139Dic113—22no—
140Dic113—41no—
141C2×C113—42no—
142C2×C113D4211yescharacteristic
143C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
144C2×C113#57711yescharacteristic
145D113—42no—
146D113—42no—
147D113—82no—
148#3272—1131nomaximal, Sylow
149C113#327211yescharacteristic, complemented, Sylow
150C2×AGL(1,ℤ/8)—1132no—
151#547—1131no—
152D42—1131no—
153#492—1131no—
154#468—1132no—
155#461D11311yescharacteristic, complemented
156#459—1131no—
157#450—1132no—
158#449—1132no—
159C4×D8—1131no—
160#436—1131no—
161C2×#41—1132no—
162C22×D4—1132no—
163C22×D4—2261no—
164AGL(1,ℤ/8)—2268no—
165C2×SD16—1132no—
166C2×SD16—1132no—
167C2×SD16C2×D11312yes—
168C2×D8—1131no—
169C2×D8—1132no—
170C2×M16—1132no—
171C4⋊Q8C2×D11311yescharacteristic, complemented
172#127—1131no—
173#123—2262no—
174C22⋊Q8—1132no—
175#121—1132no—
176#121—2261no—
177#121—2261no—
178#120—2262no—
179C4×D4—1131no—
180C4×D4—1131no—
181C4×D4C2×D11311yescharacteristic
182C2×C4⋊C4—2261no—
183#107—1131no—
184C4⋊C8C2×D11311yescharacteristic, complemented
185#103C2×D11312yescomplemented
186#102—1131no—
187#102—1132no—
188#102—1131no—
189C22⋊C8—1132no—
190C4×C8—1131no—
191C24—2262no—
192#41—4522no—
193#41—2264no—
194C2×Q8C22×D11312yes—
195C2×D4—1131no—
196C2×D4—1131no—
197C2×D4—1132no—
198C2×D4—4524no—
199C2×D4—4522no—
200C2×D4—2262no—
201C2×D4—2262no—
202C2×D4—2262no—
203C2×D4—2264no—
204C2×D4—2261no—
205C2×D4—2261no—
206C2×D4C22×D11311yescharacteristic
207C22×C4—21no—
208C22×C4—1132no—
209C22×C4—2262no—
210C22×C4—2261no—
211SD16—24no—
212SD16—4522no—
213SD16—2264no—
214D8—1134no—
215D8—2264no—
216M16—2264no—
217C2×C8—1131no—
218C2×C8—1131no—
219C2×C8C22×D11312yes—
220C4⋊C4—21no—
221C4⋊C4—21no—
222C4⋊C4—1131no—
223C4⋊C4—1131no—
224C4⋊C4—2262no—
225C4⋊C4C22×D11311yescharacteristic
226C22⋊C4—21no—
227C22⋊C4—1132no—
228C22⋊C4—2262no—
229C22⋊C4—2262no—
230C22⋊C4—2261no—
231C42C22×D11311yescharacteristic
232C23—21no—
233C23—1132no—
234C23—9042no—
235C23—4524no—
236C23—4524no—
237C23—2262no—
238C23—2261no—
239Q8—22no—
240Q8—22no—
241D4—21no—
242D4—1132no—
243D4—9041no—
244D4—4524no—
245D4—4524no—
246D4—4524no—
247D4—4522no—
248D4—2262no—
249D4—2262no—
250D4—2262no—
251D4—2261no—
252D4D4×D11312yes—
253C2×C4—21no—
254C2×C4—22no—
255C2×C4—42no—
256C2×C4—1132no—
257C2×C4—4524no—
258C2×C4—4522no—
259C2×C4—2261no—
260C2×C4—2262no—
261C2×C4—2262no—
262C2×C4D4×D11311yescharacteristic
263C2×C4D4×D11311yescharacteristic
264C2×C4C23×D11311yescharacteristic
265C8—22no—
266C8—1132no—
267C8—2261no—
268C22—22no—
269C22—41no—
270C22—41no—
271C22—9048no—
272C22—4522no—
273C22—4522no—
274C22—4522no—
275C22—4521no—
276C22—4521no—
277C22—2262no—
278C22—2262no—
279C22—2262no—
280C22—2262no—
281C22C2×D4×D11311yescharacteristic
282C4—21no—
283C4—41no—
284C4—42no—
285C4—4521no—
286C4—2262no—
287C4#1681364912yescomplemented
288C4C2×D4×D11311yescharacteristic
289C4#1681366811yescharacteristic
290C2—42no—
291C2—9042no—
292C2—4522no—
293C2—4522no—
294C2#2029923211yescharacteristic
295C2C2×#1681364911yescharacteristic
296C2#2029940711yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#461×C113C2
socleC22×C113C22×D4
hypercenter#461D113
hypocenterC113#3272
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
1. C2×#16813649C2semidirect
2. #20299251C2semidirect
3. D4×D452C2semidirect
4. #20298972C2semidirect
5. #20298847C2semidirect
6. #20298794C2semidirect
7. #20298747C2semidirect
8. #20298746C2semidirect
9. C4×#14268632C2semidirect
10. #20298675C2semidirect
11. #461×C113C2semidirect
12. C2×#14268648C22semidirect
16. C2×#14268634C22semidirect
17. C2×#14268634C22semidirect
18. C2×D904C22semidirect
20. C2×#14268630C22semidirect
23. #16813598C22semidirect
29. C4×D452C22semidirect
31. #16813555C22semidirect
32. #16813544C22semidirect
34. #16813542C22semidirect
35. #16813534C22semidirect
36. C4×#11744751C22semidirect
38. C4⋊Q8×C113C22semidirect
40. C4⋊C8×C113C22semidirect
41. #103×C113C22semidirect
62. #14268632D4semidirect
111. D452C2×D4semidirect
118. #11744751C2×D4semidirect
136. C4×C113AGL(1,ℤ/8)semidirect
149. C113#3272semidirect
155. #461D113semidirect
171. C4⋊Q8C2×D113semidirect
184. C4⋊C8C2×D113semidirect
185. #103C2×D113semidirect
287. C4#16813649semidirect

Maximal subgroups

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

subgroupindex
C2×#168136492
#202992512
D4×D4522
#202989722
#202988472
#202987942
#202987472
#202987462
C4×#142686322
#202986752
#461×C1132
#3272113