Finite Group Databasebeta

← #28401514

Subgroups — #28401514

Order 14464.

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

normal subgroups only

This group has 488 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#20299152C211yesmaximal, characteristic, complemented
2#127×D113C211yesmaximal, characteristic
3#20298969C212yesmaximal, complemented
4#20298943C212yesmaximal, complemented
5#20298799C211yesmaximal, characteristic, complemented
6#20298798C211yesmaximal, characteristic, complemented
7#20298795C211yesmaximal, characteristic, complemented
8#20298750C212yesmaximal, complemented
9#20298747C212yesmaximal, complemented
10#20298650C211yesmaximal, characteristic, complemented
11#460×C113C211yesmaximal, characteristic, complemented
12C2×D4×D113—21no—
13C2×D4×D113—21no—
14C2×D4×D113C2212yes—
15C2×#14268636C2212yescomplemented
16C2×#14268635C2212yescomplemented
17C2×#14268634C2212yescomplemented
18#16813621C2211yescharacteristic, complemented
19#16813620C2211yescharacteristic, complemented
20#16813619C2211yescharacteristic
21#16813618—21no—
22#16813618—21no—
23#16813618C2212yes—
24#16813612—21no—
25#16813602C2211yescharacteristic
26#16813600—21no—
27#16813598C2211yescharacteristic
28C4×Dic226—21no—
29C4×Dic226C2211yescharacteristic, complemented
30#16813579—21no—
31C42×D113C2211yescharacteristic
32C4⋊#11744751C2211yescharacteristic, complemented
33#16813544C2212yescomplemented
34#16813543C2212yescomplemented
35#16813542C2212yescomplemented
36#16813534C2212yes—
37C8×Dic113C2212yescomplemented
38C2×SD16×C113C2212yescomplemented
39#127×C113C2211yescharacteristic
40C4×Q8×C113C2211yescharacteristic, complemented
41C4⋊C8×C113C2211yescharacteristic, complemented
42#102×C113C2212yescomplemented
43C23×D113—22no—
44C2×Dic226—21no—
45C2×Dic226C2311yescharacteristic
46C2×D452—21no—
47C2×D452—21no—
48C2×D452C2312yes—
49C2×C22⋊D113—22no—
50C2×C22⋊D113—22no—
51C2×C22⋊D113—22no—
52D4×D113—42no—
53D4×D113—42no—
54D4×D113—44no—
55D4×D113—44no—
56C2×C4×D113D411yescharacteristic
57C2×C4×D113D411yescharacteristic
58C2×C4×D113C2311yescharacteristic
59#14268636—42no—
60#14268635—42no—
61#14268634—42no—
62C2×#11744751C2312yes—
63C4⋊Dic113—21no—
64C4⋊Dic113C2311yescharacteristic
65#14268626—21no—
66#14268626—21no—
67#14268626—21no—
68#14268626—21no—
69#14268626—21no—
70#14268624—21no—
71#14268624—21no—
72C4×Dic113—21no—
73C4×Dic113D411yescharacteristic
74C4×Dic113D411yescharacteristic
75C4×Dic113C2311yescharacteristic
76C2×Q8×C113C2311yescharacteristic
77C2×D4×C113—21no—
78C2×D4×C113—21no—
79C2×D4×C113C2312yes—
80SD16×C113—42no—
81C2×C8×C113C2312yes—
82C4⋊C4×C113—21no—
83C4⋊C4×C113C2311yescharacteristic
84C42×C113—21no—
85C42×C113C2311yescharacteristic
86C23×C113—22no—
87C22×D113—22no—
88C22×D113—44no—
89C22×D113—44no—
90C22×D113—44no—
91C22×D113C2×D411yescharacteristic
92Q8×C113—21no—
93Q8×C113—21no—
94D4×C113—22no—
95D4×C113—22no—
96D4×C113—42no—
97D4×C113—42no—
98C2×C4×C113—21no—
99C2×C4×C113—21no—
100C2×C4×C113C2×D411yescharacteristic
101C2×C4×C113C2×D411yescharacteristic
102C2×C4×C113C2411yescharacteristic
103C22⋊D113—44no—
104C22⋊D113—44no—
105C22⋊D113—44no—
106C2×Dic113—21no—
107C2×Dic113—21no—
108C2×Dic113C2×D411yescharacteristic
109C2×Dic113C2×D411yescharacteristic
110C2×Dic113C2×D411yescharacteristic
111D452—22no—
112D452—22no—
113D452—42no—
114D452—42no—
115C4×D113—21no—
116C4×D113—21no—
117C4×D113—22no—
118C4×D113SD1614yescomplemented
119Dic226—21no—
120Dic226—21no—
121Dic226—42no—
122C8×C113—22no—
123#11744751—22no—
124C22×C113—42no—
125C22×C113—42no—
126C22×C113—42no—
127C22×C113C22×D411yescharacteristic
128C2×D113—21no—
129C2×D113—21no—
130C2×D113—42no—
131C2×D113—42no—
132C2×D113—42no—
133C2×D113—88no—
134C2×D113C2×SD1612yes—
135C4×C113—21no—
136C4×C113—41no—
137C4×C113—41no—
138C4×C113C2×SD1612yes—
139C4×C113H(5,𝔽2)11yescharacteristic
140C4×C113H(5,𝔽2)11yescharacteristic
141Dic113—21no—
142Dic113—41no—
143Dic113—41no—
144Dic113C2×SD1612yes—
145Dic113AGL(1,ℤ/8)12yes—
146C2×C113—82no—
147C2×C113#53511yescharacteristic
148C2×C113C22×SD1611yescharacteristic
149C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
150D113—22no—
151D113—82no—
152#3208—1131nomaximal, Sylow
153C113#320811yescharacteristic, complemented, Sylow
154#533—1131no—
155C2×#127—1131no—
156#492—1132no—
157#486—1132no—
158#460—1131no—
159#460—1131no—
160#460—1131no—
161#460D11311yescharacteristic, complemented
162#450—1132no—
163#450—1132no—
164#431—1131no—
165C22×D4—1132no—
166C22×D4—2261no—
167C22×D4—2261no—
168C2×SD16—1132no—
169C2×SD16—1132no—
170C2×SD16—1132no—
171C2×SD16C2×D11312yescomplemented
172C4⋊Q8—1131no—
173C4⋊Q8—1131no—
174#127—1132no—
175#127—1131no—
176#127—2261no—
177#127—2261no—
178#127C2×D11311yescharacteristic
179#125—2261no—
180C22⋊Q8—1131no—
181C22⋊Q8—1131no—
182C22⋊Q8—2261no—
183C4×Q8—1131no—
184C4×Q8—2261no—
185C4×Q8C2×D11311yescharacteristic, complemented
186#117—2261no—
187C2×C42—1131no—
188C4⋊C8—1131no—
189C4⋊C8C2×D11311yescharacteristic, complemented
190#102—1132no—
191#102—1132no—
192#102—1132no—
193#102C2×D11312yescomplemented
194C22⋊C8—1132no—
195C4×C8—1132no—
196C24—2262no—
197C2×Q8—1131no—
198C2×Q8—2261no—
199C2×Q8C22×D11311yescharacteristic
200C2×D4—21no—
201C2×D4—21no—
202C2×D4—1132no—
203C2×D4—4524no—
204C2×D4—4522no—
205C2×D4—4522no—
206C2×D4—4524no—
207C2×D4—2262no—
208C2×D4—2262no—
209C2×D4—2262no—
210C2×D4—2261no—
211C2×D4—2261no—
212C2×D4C22×D11312yes—
213C22×C4—1131no—
214C22×C4—1131no—
215C22×C4—1131no—
216SD16—42no—
217SD16—4522no—
218SD16—4522no—
219SD16—4522no—
220C2×C8—1132no—
221C2×C8C22×D11312yes—
222C4⋊C4—21no—
223C4⋊C4—1131no—
224C4⋊C4—2261no—
225C4⋊C4—2261no—
226C4⋊C4—2261no—
227C4⋊C4—2261no—
228C4⋊C4—2261no—
229C4⋊C4—2261no—
230C4⋊C4C22×D11311yescharacteristic
231C22⋊C4—2261no—
232C22⋊C4—2261no—
233C42—21no—
234C42—1131no—
235C42—1131no—
236C42—1131no—
237C42—2261no—
238C42C22×D11311yescharacteristic
239C23—22no—
240C23—1131no—
241C23—4524no—
242C23—4524no—
243C23—4524no—
244C23—2262no—
245Q8—21no—
246Q8—21no—
247Q8—4522no—
248Q8—2261no—
249Q8—2261no—
250D4—22no—
251D4—22no—
252D4—42no—
253D4—42no—
254D4—4522no—
255D4—4524no—
256D4—4524no—
257D4—4524no—
258D4—4522no—
259D4—2262no—
260D4—2262no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—1131no—
264C2×C4—1131no—
265C2×C4—1134no—
266C2×C4—1131no—
267C2×C4—2262no—
268C2×C4—2261no—
269C2×C4—2261no—
270C2×C4—2261no—
271C2×C4—2261no—
272C2×C4D4×D11311yescharacteristic
273C2×C4D4×D11311yescharacteristic
274C2×C4C23×D11311yescharacteristic
275C8—22no—
276C8—2262no—
277C22—42no—
278C22—42no—
279C22—42no—
280C22—1132no—
281C22—9048no—
282C22—4522no—
283C22—4522no—
284C22—4522no—
285C22—2261no—
286C22—2261no—
287C22C2×D4×D11311yescharacteristic
288C4—21no—
289C4—41no—
290C4—41no—
291C4—1132no—
292C4—1132no—
293C4—4521no—
294C4—4521no—
295C4—2261no—
296C4SD16×D11312yes—
297C4#1681366711yescharacteristic
298C4#1681366811yescharacteristic
299C2—82no—
300C2—9042no—
301C2—2262no—
302C2#2029916411yescharacteristic
303C2C2×SD16×D11311yescharacteristic
304C2AGL(1,ℤ/8)×D11311yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#460×C113C2
socleC22×C113C22×D4
prime radical#127×D113C2
hypercenter#460D113
hypocenterC113#3208
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. #20299152C2semidirect
3. #20298969C2semidirect
4. #20298943C2semidirect
5. #20298799C2semidirect
6. #20298798C2semidirect
7. #20298795C2semidirect
8. #20298750C2semidirect
9. #20298747C2semidirect
10. #20298650C2semidirect
11. #460×C113C2semidirect
15. C2×#14268636C22semidirect
16. C2×#14268635C22semidirect
17. C2×#14268634C22semidirect
18. #16813621C22semidirect
19. #16813620C22semidirect
29. C4×Dic226C22semidirect
32. C4⋊#11744751C22semidirect
33. #16813544C22semidirect
34. #16813543C22semidirect
35. #16813542C22semidirect
37. C8×Dic113C22semidirect
38. C2×SD16×C113C22semidirect
40. C4×Q8×C113C22semidirect
41. C4⋊C8×C113C22semidirect
42. #102×C113C22semidirect
118. C4×D113SD16semidirect
153. C113#3208semidirect
161. #460D113semidirect
171. C2×SD16C2×D113semidirect
185. C4×Q8C2×D113semidirect
189. C4⋊C8C2×D113semidirect
193. #102C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202991522
#127×D1132
#202989692
#202989432
#202987992
#202987982
#202987952
#202987502
#202987472
#202986502
#460×C1132
#3208113