Finite Group Databasebeta

← #28401593

Subgroups — #28401593

Order 14464.

490 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 113 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#127×D113C211yesmaximal, characteristic, complemented
2#20299133C211yesmaximal, characteristic, complemented
3#20298987C211yesmaximal, characteristic, complemented
4#20298985C211yesmaximal, characteristic, complemented
5#20298964C211yesmaximal, characteristic, complemented
6#20298797C212yesmaximal, complemented
7#20298792C212yesmaximal, complemented
8#20298750C212yesmaximal, complemented
9#20298733C212yesmaximal, complemented
10#20298653C211yesmaximal, characteristic, complemented
11#490×C113C211yesmaximal, characteristic, complemented
12C2×D4×D113—21no—
13C2×D4×D113—21no—
14C2×D4×D113C2212yes—
15C2×#14268636C2212yescomplemented
16C2×#14268635C2212yescomplemented
17C2×D904C2212yescomplemented
18C2×#14268632C2212yescomplemented
19#16813619C2211yescharacteristic
20#16813618—21no—
21#16813618—21no—
22#16813618C2212yes—
23#16813617—21no—
24#16813610C2211yescharacteristic, complemented
25#16813607—21no—
26#16813602C2211yescharacteristic
27#16813597C2211yescharacteristic
28#16813587C2211yescharacteristic, complemented
29#16813584—21no—
30#16813584C2211yescharacteristic, complemented
31#16813580—21no—
32C42×D113C2211yescharacteristic
33#16813551C2212yescomplemented
34#16813542C2212yescomplemented
35#16813542C2212yescomplemented
36#16813534C2212yes—
37#16813533C2211yescharacteristic, complemented
38#127×C113C2211yescharacteristic
39#125×C113C2211yescharacteristic, complemented
40#102×C113C2212yescomplemented
41#102×C113C2212yescomplemented
42#97×C113C2211yescharacteristic, complemented
43C23×D113—22no—
44C2×Dic226C2311yescharacteristic
45C2×D452—21no—
46C2×D452—21no—
47C2×D452—21no—
48C2×D452C2311yescharacteristic
49C2×D452C2312yes—
50C2×C22⋊D113—22no—
51C2×C22⋊D113—22no—
52C2×C22⋊D113—22no—
53D4×D113—42no—
54D4×D113—42no—
55D4×D113—44no—
56D4×D113—44no—
57C2×C4×D113—21no—
58C2×C4×D113D411yescharacteristic
59C2×C4×D113D411yescharacteristic
60C2×C4×D113C2311yescharacteristic
61#14268636—42no—
62#14268635—42no—
63D904—42no—
64#14268632—42no—
65C2×#11744751C2312yes—
66C4⋊Dic113—21no—
67#14268626—21no—
68#14268624—21no—
69#14268624—21no—
70#14268624—21no—
71#14268624—21no—
72#14268624—21no—
73C4×Dic113—21no—
74C4×Dic113D411yescharacteristic
75C4×Dic113D411yescharacteristic
76C4×Dic113C2311yescharacteristic
77C2×D4×C113—21no—
78C2×D4×C113—21no—
79C2×D4×C113C2312yes—
80C2×C8×C113C2312yes—
81C4⋊C4×C113—21no—
82C4⋊C4×C113—21no—
83C4⋊C4×C113C2311yescharacteristic
84C4⋊C4×C113C2311yescharacteristic
85C42×C113C2311yescharacteristic
86C23×C113—22no—
87C22×D113—21no—
88C22×D113—22no—
89C22×D113—44no—
90C22×D113—44no—
91C22×D113—44no—
92C22×D113C2×D411yescharacteristic
93D4×C113—22no—
94D4×C113—22no—
95D4×C113—42no—
96D4×C113—42no—
97C2×C4×C113—21no—
98C2×C4×C113—21no—
99C2×C4×C113C2×D411yescharacteristic
100C2×C4×C113C2×D411yescharacteristic
101C2×C4×C113C2411yescharacteristic
102C22⋊D113—44no—
103C22⋊D113—44no—
104C22⋊D113—44no—
105C2×Dic113—21no—
106C2×Dic113C2×D411yescharacteristic
107C2×Dic113C2×D411yescharacteristic
108C2×Dic113C2×D411yescharacteristic
109D452—22no—
110D452—22no—
111D452—22no—
112D452—42no—
113D452—42no—
114D452—42no—
115C4×D113—22no—
116C4×D113—22no—
117C4×D113—22no—
118C4×D113—42no—
119Dic226—22no—
120C8×C113—22no—
121#11744751—22no—
122C22×C113—42no—
123C22×C113—42no—
124C22×C113—42no—
125C22×C113C22×D411yescharacteristic
126C2×D113—21no—
127C2×D113—21no—
128C2×D113—42no—
129C2×D113—41no—
130C2×D113—41no—
131C2×D113—42no—
132C2×D113—42no—
133C2×D113—41no—
134C2×D113—88no—
135C2×D113AGL(1,ℤ/8)12yes—
136C4×C113—21no—
137C4×C113—21no—
138C4×C113—41no—
139C4×C113—41no—
140C4×C113H(5,𝔽2)12yes—
141Dic113—21no—
142Dic113—21no—
143Dic113—41no—
144Dic113AGL(1,ℤ/8)12yes—
145C2×C113—82no—
146C2×C113#53511yescharacteristic
147C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
148C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
149D113—22no—
150D113—81no—
151D113—82no—
152#3217—1131nomaximal, Sylow
153C113#321711yescharacteristic, complemented, Sylow
154C2×#127—1131no—
155#529—1131no—
156#496—1131no—
157#496—1131no—
158#490—1131no—
159#490D11311yescharacteristic, complemented
160#460—1132no—
161#459—1132no—
162#450—1132no—
163#447—1132no—
164#432—1131no—
165C22×D4—1132no—
166C22×D4—2261no—
167C22×D4—2261no—
168C2×SD16—1132no—
169C2×SD16—1132no—
170C2×D8—1132no—
171C2×D8—1132no—
172#127—1132no—
173#127—1131no—
174#127—2261no—
175#127—2261no—
176#127C2×D11311yescharacteristic
177#126—2261no—
178#125C2×D11311yescharacteristic, complemented
179#124—1131no—
180#123—2261no—
181C22⋊Q8—1131no—
182#121—1131no—
183C4×Q8—1131no—
184C4×D4—1131no—
185C4×D4—2261no—
186#117—2261no—
187C2×C42—1131no—
188C4⋊C8—1132no—
189#102—1132no—
190#102—1132no—
191#102C2×D11312yescomplemented
192#102C2×D11312yescomplemented
193C22⋊C8—1132no—
194#97—1131no—
195#97C2×D11311yescharacteristic, complemented
196C24—2262no—
197C2×Q8—1131no—
198C2×D4—21no—
199C2×D4—21no—
200C2×D4—1132no—
201C2×D4—1131no—
202C2×D4—4522no—
203C2×D4—4522no—
204C2×D4—4524no—
205C2×D4—4524no—
206C2×D4—2261no—
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—
216C22×C4—2261no—
217SD16—4522no—
218SD16—4522no—
219D8—4522no—
220D8—4522no—
221C2×C8—1132no—
222C2×C8C22×D11312yes—
223C4⋊C4—21no—
224C4⋊C4—21no—
225C4⋊C4—2261no—
226C4⋊C4—2261no—
227C4⋊C4C22×D11311yescharacteristic
228C4⋊C4C22×D11311yescharacteristic
229C22⋊C4—2261no—
230C22⋊C4—2261no—
231C22⋊C4—2261no—
232C22⋊C4—2261no—
233C22⋊C4—2261no—
234C42—1131no—
235C42—1131no—
236C42—1131no—
237C42—2261no—
238C42C22×D11311yescharacteristic
239C23—22no—
240C23—1131no—
241C23—4524no—
242C23—4524no—
243C23—4524no—
244C23—2261no—
245C23—2262no—
246Q8—2262no—
247D4—22no—
248D4—22no—
249D4—42no—
250D4—42no—
251D4—4522no—
252D4—4522no—
253D4—4522no—
254D4—4524no—
255D4—4524no—
256D4—4524no—
257D4—2262no—
258D4—2262no—
259D4—2262no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—1131no—
263C2×C4—1131no—
264C2×C4—1131no—
265C2×C4—4522no—
266C2×C4—2262no—
267C2×C4—2262no—
268C2×C4—2261no—
269C2×C4—2262no—
270C2×C4D4×D11311yescharacteristic
271C2×C4D4×D11311yescharacteristic
272C2×C4C23×D11311yescharacteristic
273C8—22no—
274C8—2262no—
275C22—42no—
276C22—42no—
277C22—42no—
278C22—1132no—
279C22—9048no—
280C22—4521no—
281C22—4522no—
282C22—4522no—
283C22—4521no—
284C22—4522no—
285C22—4521no—
286C22—2261no—
287C22—2261no—
288C22C2×D4×D11311yescharacteristic
289C4—21no—
290C4—21no—
291C4—41no—
292C4—41no—
293C4—1132no—
294C4—4521no—
295C4—2261no—
296C4—2261no—
297C4#1681366812yes—
298C2—82no—
299C2—9042no—
300C2—9041no—
301C2—2262no—
302C2#2029916611yescharacteristic
303C2AGL(1,ℤ/8)×D11311yescharacteristic
304C2AGL(1,ℤ/8)×D11311yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#490×C113C2
socleC22×C113C22×D4
hypercenter#490D113
hypocenterC113#3217
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #127×D113C2semidirect
2. #20299133C2semidirect
3. #20298987C2semidirect
4. #20298985C2semidirect
5. #20298964C2semidirect
6. #20298797C2semidirect
7. #20298792C2semidirect
8. #20298750C2semidirect
9. #20298733C2semidirect
10. #20298653C2semidirect
11. #490×C113C2semidirect
15. C2×#14268636C22semidirect
16. C2×#14268635C22semidirect
17. C2×D904C22semidirect
18. C2×#14268632C22semidirect
24. #16813610C22semidirect
28. #16813587C22semidirect
30. #16813584C22semidirect
33. #16813551C22semidirect
34. #16813542C22semidirect
35. #16813542C22semidirect
37. #16813533C22semidirect
39. #125×C113C22semidirect
40. #102×C113C22semidirect
41. #102×C113C22semidirect
42. #97×C113C22semidirect
153. C113#3217semidirect
159. #490D113semidirect
178. #125C2×D113semidirect
191. #102C2×D113semidirect
192. #102C2×D113semidirect
195. #97C2×D113semidirect

Maximal subgroups

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

subgroupindex
#127×D1132
#202991332
#202989872
#202989852
#202989642
#202987972
#202987922
#202987502
#202987332
#202986532
#490×C1132
#3217113