Finite Group Databasebeta

← #28401588

Subgroups — #28401588

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#20299127C211yesmaximal, characteristic, complemented
3#20298988C211yesmaximal, characteristic, complemented
4#20298963C211yesmaximal, characteristic, complemented
5#20298962C211yesmaximal, characteristic, complemented
6#20298796C212yesmaximal, complemented
7#20298791C212yesmaximal, complemented
8#20298747C212yesmaximal, complemented
9#20298730C212yesmaximal, complemented
10#20298653C211yesmaximal, characteristic, complemented
11#496×C113C211yesmaximal, characteristic, complemented
12C2×D4×D113—21no—
13C2×D4×D113—21no—
14C2×D4×D113C2212yes—
15C2×#14268634C2212yescomplemented
16C2×#14268632C2212yescomplemented
17#16813619C2211yescharacteristic
18#16813618—21no—
19#16813618—21no—
20#16813618C2212yes—
21#16813615—21no—
22#16813614C2211yescharacteristic, complemented
23#16813604—21no—
24#16813598C2211yescharacteristic
25#16813593C2211yescharacteristic
26Q8×Dic113C2211yescharacteristic, complemented
27D4×Dic113C2211yescharacteristic, complemented
28#16813582—21no—
29#16813578—21no—
30C42×D113C2211yescharacteristic
31#16813551C2212yescomplemented
32#16813544C2212yescomplemented
33#16813544C2212yescomplemented
34#16813543C2212yescomplemented
35#16813543C2212yescomplemented
36#16813534C2212yes—
37#16813533C2211yescharacteristic, complemented
38C2×SD16×C113C2212yescomplemented
39C2×D8×C113C2212yescomplemented
40#127×C113C2211yescharacteristic
41#124×C113C2211yescharacteristic, complemented
42#97×C113C2211yescharacteristic, complemented
43C23×D113—22no—
44C2×D452—21no—
45C2×D452—21no—
46C2×D452C2312yes—
47C2×C22⋊D113—21no—
48C2×C22⋊D113—22no—
49C2×C22⋊D113—22no—
50C2×C22⋊D113—22no—
51D4×D113—42no—
52D4×D113—42no—
53D4×D113—44no—
54D4×D113—44no—
55C22×Dic113—21no—
56C2×C4×D113D411yescharacteristic
57C2×C4×D113D411yescharacteristic
58C2×C4×D113C2311yescharacteristic
59#14268634—42no—
60#14268632—42no—
61C2×#11744751C2312yes—
62C4⋊Dic113—21no—
63C4⋊Dic113C2311yescharacteristic
64C4⋊Dic113C2311yescharacteristic
65#14268626—21no—
66#14268626—21no—
67#14268626—21no—
68C22⋊Dic113—21no—
69C22⋊Dic113—21no—
70#14268624—21no—
71C4×Dic113—21no—
72C4×Dic113D411yescharacteristic
73C4×Dic113D411yescharacteristic
74C4×Dic113C2311yescharacteristic
75C2×Q8×C113C2311yescharacteristic
76C2×D4×C113—21no—
77C2×D4×C113—21no—
78C2×D4×C113C2311yescharacteristic
79C2×D4×C113C2312yes—
80SD16×C113—42no—
81D8×C113—42no—
82C2×C8×C113C2312yes—
83C22⋊C4×C113—21no—
84C22⋊C4×C113—21no—
85C42×C113C2311yescharacteristic
86C23×C113—21no—
87C23×C113—22no—
88C22×D113—22no—
89C22×D113—44no—
90C22×D113—44no—
91C22×D113—44no—
92C22×D113C2×D411yescharacteristic
93Q8×C113—22no—
94D4×C113—22no—
95D4×C113—22no—
96D4×C113—22no—
97D4×C113—42no—
98D4×C113—42no—
99C2×C4×C113—21no—
100C2×C4×C113C2×D411yescharacteristic
101C2×C4×C113C2×D411yescharacteristic
102C2×C4×C113C2411yescharacteristic
103C22⋊D113—44no—
104C22⋊D113—44no—
105C22⋊D113—42no—
106C22⋊D113—44no—
107C2×Dic113—21no—
108C2×Dic113—21no—
109C2×Dic113—42no—
110C2×Dic113C2×D411yescharacteristic
111C2×Dic113C2×D411yescharacteristic
112C2×Dic113C2×D411yescharacteristic
113D452—22no—
114D452—22no—
115D452—42no—
116D452—42no—
117C4×D113—22no—
118C4×D113—22no—
119C4×D113—22no—
120C8×C113—22no—
121#11744751—22no—
122C22×C113—42no—
123C22×C113—41no—
124C22×C113—41no—
125C22×C113—42no—
126C22×C113—42no—
127C22×C113—41no—
128C22×C113C22×D411yescharacteristic
129C2×D113—21no—
130C2×D113—21no—
131C2×D113—42no—
132C2×D113—42no—
133C2×D113—42no—
134C2×D113—88no—
135C2×D113AGL(1,ℤ/8)12yes—
136C4×C113—21no—
137C4×C113—21no—
138C4×C113—41no—
139C4×C113H(5,𝔽2)12yes—
140Dic113—21no—
141Dic113—21no—
142Dic113—41no—
143Dic113—41no—
144Dic113AGL(1,ℤ/8)12yes—
145C2×C113—82no—
146C2×C113—81no—
147C2×C113#53511yescharacteristic
148C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
149C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
150D113—22no—
151D113—82no—
152#3217—1131nomaximal, Sylow
153C113#321711yescharacteristic, complemented, Sylow
154C2×#127—1131no—
155#529—1131no—
156#496—1131no—
157#496D11311yescharacteristic, complemented
158#490—1131no—
159#490—1131no—
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×SD16C2×D11312yescomplemented
170C2×D8—1132no—
171C2×D8C2×D11312yescomplemented
172#127—1132no—
173#127—1131no—
174#127—2261no—
175#127—2261no—
176#127C2×D11311yescharacteristic
177#126—2261no—
178#125—1131no—
179#124C2×D11311yescharacteristic, complemented
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#102—1132no—
192#102—1132no—
193C22⋊C8—1132no—
194#97—1131no—
195#97C2×D11311yescharacteristic, complemented
196C24—2262no—
197C2×Q8C22×D11311yescharacteristic
198C2×D4—21no—
199C2×D4—21no—
200C2×D4—1132no—
201C2×D4—4522no—
202C2×D4—4522no—
203C2×D4—4524no—
204C2×D4—4524no—
205C2×D4—2262no—
206C2×D4—2262no—
207C2×D4—2262no—
208C2×D4—2261no—
209C2×D4—2261no—
210C2×D4—2261no—
211C2×D4C22×D11312yes—
212C2×D4C22×D11311yescharacteristic
213C22×C4—1131no—
214C22×C4—1131no—
215C22×C4—1131no—
216C22×C4—2261no—
217SD16—42no—
218SD16—4522no—
219D8—42no—
220D8—4522no—
221C2×C8—1132no—
222C2×C8C22×D11312yes—
223C4⋊C4—1131no—
224C4⋊C4—1131no—
225C4⋊C4—2261no—
226C4⋊C4—2261no—
227C4⋊C4—2261no—
228C4⋊C4—2261no—
229C22⋊C4—21no—
230C22⋊C4—21no—
231C22⋊C4—2261no—
232C22⋊C4—2261no—
233C22⋊C4—2261no—
234C42—1131no—
235C42—1131no—
236C42—1131no—
237C42—2261no—
238C42C22×D11311yescharacteristic
239C23—21no—
240C23—22no—
241C23—1131no—
242C23—4524no—
243C23—4524no—
244C23—4524no—
245C23—2262no—
246Q8—22no—
247D4—22no—
248D4—22no—
249D4—22no—
250D4—42no—
251D4—42no—
252D4—4522no—
253D4—4522no—
254D4—4524no—
255D4—4522no—
256D4—4524no—
257D4—4524no—
258D4—2262no—
259D4—2262no—
260C2×C4—21no—
261C2×C4—1131no—
262C2×C4—1131no—
263C2×C4—1131no—
264C2×C4—4522no—
265C2×C4—2262no—
266C2×C4—2262no—
267C2×C4—2261no—
268C2×C4—2261no—
269C2×C4—2262no—
270C2×C4D4×D11311yescharacteristic
271C2×C4D4×D11311yescharacteristic
272C2×C4C23×D11311yescharacteristic
273C8—22no—
274C8—2262no—
275C22—41no—
276C22—42no—
277C22—42no—
278C22—41no—
279C22—42no—
280C22—41no—
281C22—1132no—
282C22—9048no—
283C22—4522no—
284C22—4522no—
285C22—4522no—
286C22—2261no—
287C22—2261no—
288C22C2×D4×D11311yescharacteristic
289C4—21no—
290C4—21no—
291C4—41no—
292C4—1132no—
293C4—4521no—
294C4—4521no—
295C4—2261no—
296C4—2261no—
297C4#1681366712yes—
298C2—82no—
299C2—81no—
300C2—9042no—
301C2—2262no—
302C2#2029916111yescharacteristic
303C2AGL(1,ℤ/8)×D11311yescharacteristic
304C2AGL(1,ℤ/8)×D11311yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#496×C113C2
socleC22×C113C22×D4
hypercenter#496D113
hypocenterC113#3217
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #127×D113C2semidirect
2. #20299127C2semidirect
3. #20298988C2semidirect
4. #20298963C2semidirect
5. #20298962C2semidirect
6. #20298796C2semidirect
7. #20298791C2semidirect
8. #20298747C2semidirect
9. #20298730C2semidirect
10. #20298653C2semidirect
11. #496×C113C2semidirect
15. C2×#14268634C22semidirect
16. C2×#14268632C22semidirect
22. #16813614C22semidirect
26. Q8×Dic113C22semidirect
27. D4×Dic113C22semidirect
31. #16813551C22semidirect
32. #16813544C22semidirect
33. #16813544C22semidirect
34. #16813543C22semidirect
35. #16813543C22semidirect
37. #16813533C22semidirect
38. C2×SD16×C113C22semidirect
39. C2×D8×C113C22semidirect
41. #124×C113C22semidirect
42. #97×C113C22semidirect
153. C113#3217semidirect
157. #496D113semidirect
169. C2×SD16C2×D113semidirect
171. C2×D8C2×D113semidirect
179. #124C2×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
#202991272
#202989882
#202989632
#202989622
#202987962
#202987912
#202987472
#202987302
#202986532
#496×C1132
#3217113