Finite Group Databasebeta

← #28401562

Subgroups — #28401562

Order 14464.

444 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 111 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#20299149C211yesmaximal, characteristic, complemented
2#124×D113C211yesmaximal, characteristic, complemented
3#20298988C211yesmaximal, characteristic, complemented
4#20298987C211yesmaximal, characteristic, complemented
5#20298960C211yesmaximal, characteristic, complemented
6#20298816C212yesmaximal, complemented
7#20298812C212yesmaximal, complemented
8#20298738C212yesmaximal, complemented
9#20298733C212yesmaximal, complemented
10#20298653C211yesmaximal, characteristic, complemented
11#489×C113C211yesmaximal, characteristic, complemented
12C2×#14268648—21no—
13C2×Q8×D113C2211yescharacteristic
14C2×D4×D113C2211yescharacteristic
15C2×#14268636C2212yescomplemented
16C2×#14268634C2212yescomplemented
17C2×D904C2212yes—
18C2×#14268632C2212yes—
19#16813619C2211yescharacteristic, complemented
20#16813611—21no—
21#16813611C2211yescharacteristic
22#16813610C2211yescharacteristic
23#16813609C2211yescharacteristic
24#16813608—21no—
25#16813608—21no—
26#16813597—21no—
27#16813597C2212yes—
28#16813584—21no—
29#16813584C2212yescomplemented
30C22⋊C4×D113—21no—
31C22⋊C4×D113—21no—
32C42×D113C2211yescharacteristic
33#16813551C2212yescomplemented
34#16813545C2212yescomplemented
35#16813542C2212yes—
36#16813534C2212yes—
37#16813533C2211yescharacteristic, complemented
38C4⋊Q8×C113C2211yescharacteristic, complemented
39#124×C113C2211yescharacteristic
40#103×C113C2212yescomplemented
41#102×C113C2212yes—
42#97×C113C2211yescharacteristic, complemented
43C23×D113—21no—
44#14268648—44no—
45C2×Dic226—21no—
46C2×Dic226C2311yescharacteristic
47Q8×D113—42no—
48C2×D452—22no—
49C2×D452—21no—
50C2×D452—21no—
51C2×D452C2312yes—
52C2×D452C2311yescharacteristic
53C2×C22⋊D113—21no—
54D4×D113—42no—
55C2×C4×D113—21no—
56C2×C4×D113—22no—
57C2×C4×D113D411yescharacteristic
58C2×C4×D113D411yescharacteristic
59C2×C4×D113C2311yescharacteristic
60#14268636—42no—
61#14268634—42no—
62D904—42no—
63#14268632—42no—
64C2×#11744751C2312yes—
65C22⋊Dic113—21no—
66C22⋊Dic113—21no—
67#14268624—21no—
68#14268624—21no—
69#14268624—21no—
70#14268624—21no—
71#14268624—22no—
72#14268624—22no—
73C4×Dic113D411yescharacteristic
74C4×Dic113D411yescharacteristic
75C4×Dic113C2311yescharacteristic
76C2×Q8×C113—21no—
77C2×Q8×C113C2311yescharacteristic
78C2×D4×C113C2311yescharacteristic
79C2×C8×C113C2312yes—
80C4⋊C4×C113—21no—
81C4⋊C4×C113C2312yes—
82C22⋊C4×C113—21no—
83C22⋊C4×C113—21no—
84C42×C113C2311yescharacteristic
85C23×C113—21no—
86C22×D113—21no—
87C22×D113—22no—
88C22×D113—42no—
89C22×D113—42no—
90C22×D113—42no—
91C22×D113C2×D411yescharacteristic
92Q8×C113—22no—
93Q8×C113—42no—
94D4×C113—22no—
95C2×C4×C113—21no—
96C2×C4×C113—22no—
97C2×C4×C113C2×D411yescharacteristic
98C2×C4×C113C2×D411yescharacteristic
99C2×C4×C113C2411yescharacteristic
100C22⋊D113—42no—
101C2×Dic113—21no—
102C2×Dic113C2×D411yescharacteristic
103C2×Dic113C2×D411yescharacteristic
104C2×Dic113C2×D411yescharacteristic
105D452—22no—
106D452—22no—
107D452—22no—
108D452—42no—
109D452—42no—
110D452—44no—
111C4×D113—22no—
112C4×D113—22no—
113C4×D113—41no—
114C4×D113—44no—
115C4×D113—42no—
116Dic226—22no—
117Dic226—42no—
118C8×C113—22no—
119#11744751—22no—
120C22×C113—41no—
121C22×C113—41no—
122C22×C113—41no—
123C22×C113C22×D411yescharacteristic
124C2×D113—21no—
125C2×D113—21no—
126C2×D113—41no—
127C2×D113—42no—
128C2×D113—42no—
129C2×D113—41no—
130C2×D113—42no—
131C2×D113—41no—
132C2×D113—84no—
133C2×D113AGL(1,ℤ/8)12yes—
134C4×C113—21no—
135C4×C113—21no—
136C4×C113—41no—
137C4×C113—42no—
138C4×C113H(5,𝔽2)12yes—
139Dic113—21no—
140Dic113—21no—
141Dic113—21no—
142Dic113—41no—
143C2×C113—81no—
144C2×C113#53511yescharacteristic
145C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
146C2×C113#57511yescharacteristic
147D113—22no—
148D113—82no—
149D113—81no—
150#3213—1131nomaximal, Sylow
151C113#321311yescharacteristic, complemented, Sylow
152#532—1131no—
153C2×#124—1131no—
154#496—1131no—
155#496—1131no—
156#489—1131no—
157#489D11311yescharacteristic, complemented
158#463—1132no—
159#463—1132no—
160#448—1132no—
161#447—1132no—
162#432—1131no—
163C2×#41—2261no—
164C22×Q8—1131no—
165C22×D4—1131no—
166C2×SD16—1132no—
167C2×SD16—1132no—
168C2×D8—1132no—
169C2×D8—1132no—
170C4⋊Q8C2×D11311yescharacteristic, complemented
171#127—1131no—
172#124—1131no—
173#124—1131no—
174#124—1131no—
175#124—2261no—
176#124—2261no—
177#124—2261no—
178#124C2×D11311yescharacteristic
179#121—1132no—
180#121—2261no—
181C4×D4—1132no—
182C4×D4—2261no—
183C2×C22⋊C4—2261no—
184C2×C22⋊C4—2261no—
185C2×C42—1131no—
186C4⋊C8—1132no—
187#103—1132no—
188#103C2×D11312yescomplemented
189#102—1132no—
190#102C2×D11312yes—
191C22⋊C8—1132no—
192#97—1131no—
193#97C2×D11311yescharacteristic, complemented
194C24—2261no—
195#41—4524no—
196C2×Q8—21no—
197C2×Q8—1131no—
198C2×Q8—4522no—
199C2×Q8—2261no—
200C2×Q8C22×D11311yescharacteristic
201C2×D4—1131no—
202C2×D4—1132no—
203C2×D4—4522no—
204C2×D4—2262no—
205C2×D4—2261no—
206C2×D4—2261no—
207C2×D4—2261no—
208C2×D4C22×D11311yescharacteristic
209C22×C4—1131no—
210C22×C4—1131no—
211C22×C4—1131no—
212C22×C4—2262no—
213C22×C4—2261no—
214SD16—4522no—
215SD16—4522no—
216D8—4522no—
217D8—4522no—
218C2×C8—1132no—
219C2×C8C22×D11312yes—
220C4⋊C4—21no—
221C4⋊C4C22×D11312yes—
222C22⋊C4—21no—
223C22⋊C4—21no—
224C22⋊C4—2261no—
225C22⋊C4—2261no—
226C22⋊C4—2262no—
227C22⋊C4—2262no—
228C22⋊C4—2261no—
229C22⋊C4—2261no—
230C22⋊C4—2261no—
231C22⋊C4—2261no—
232C42—1131no—
233C42—1131no—
234C42—1131no—
235C42C22×D11311yescharacteristic
236C23—21no—
237C23—1131no—
238C23—4522no—
239C23—4522no—
240C23—4522no—
241C23—2261no—
242C23—2262no—
243Q8—22no—
244Q8—42no—
245Q8—4522no—
246Q8—2262no—
247D4—22no—
248D4—4522no—
249D4—4522no—
250D4—4524no—
251D4—4522no—
252D4—2262no—
253D4—2262no—
254D4—2262no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—1131no—
258C2×C4—1131no—
259C2×C4—1131no—
260C2×C4—4521no—
261C2×C4—4522no—
262C2×C4—4524no—
263C2×C4—2262no—
264C2×C4—2261no—
265C2×C4—2262no—
266C2×C4D4×D11311yescharacteristic
267C2×C4D4×D11311yescharacteristic
268C2×C4C23×D11311yescharacteristic
269C8—22no—
270C8—2262no—
271C22—41no—
272C22—41no—
273C22—41no—
274C22—1132no—
275C22—9044no—
276C22—4522no—
277C22—4521no—
278C22—4522no—
279C22—4521no—
280C22—4521no—
281C22—4522no—
282C22—2261no—
283C22—2261no—
284C22C2×D4×D11311yescharacteristic
285C4—21no—
286C4—21no—
287C4—42no—
288C4—41no—
289C4—4521no—
290C4—2261no—
291C4—2261no—
292C4—2261no—
293C4#1681366812yes—
294C2—81no—
295C2—9041no—
296C2—9042no—
297C2—2262no—
298C2#2029916611yescharacteristic
299C2AGL(1,ℤ/8)×D11311yescharacteristic
300C2#2029939711yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#489×C113C2
socleC22×C113C22×D4
hypercenter#489D113
hypocenterC113#3213
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #20299149C2semidirect
2. #124×D113C2semidirect
3. #20298988C2semidirect
4. #20298987C2semidirect
5. #20298960C2semidirect
6. #20298816C2semidirect
7. #20298812C2semidirect
8. #20298738C2semidirect
9. #20298733C2semidirect
10. #20298653C2semidirect
11. #489×C113C2semidirect
15. C2×#14268636C22semidirect
16. C2×#14268634C22semidirect
19. #16813619C22semidirect
29. #16813584C22semidirect
33. #16813551C22semidirect
34. #16813545C22semidirect
37. #16813533C22semidirect
38. C4⋊Q8×C113C22semidirect
40. #103×C113C22semidirect
42. #97×C113C22semidirect
151. C113#3213semidirect
157. #489D113semidirect
170. C4⋊Q8C2×D113semidirect
188. #103C2×D113semidirect
193. #97C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202991492
#124×D1132
#202989882
#202989872
#202989602
#202988162
#202988122
#202987382
#202987332
#202986532
#489×C1132
#3213113