Finite Group Databasebeta

← #28401556

Subgroups — #28401556

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#20299146C211yesmaximal, characteristic, complemented
2#124×D113C211yesmaximal, characteristic, complemented
3#20298985C211yesmaximal, characteristic, complemented
4#20298958C211yesmaximal, characteristic, complemented
5#20298957C211yesmaximal, characteristic, complemented
6#20298815C212yesmaximal, complemented
7#20298811C212yesmaximal, complemented
8#20298735C212yesmaximal, complemented
9#20298730C212yesmaximal, complemented
10#20298653C211yesmaximal, characteristic, complemented
11#496×C113C211yesmaximal, characteristic, complemented
12C2×#14268646—21no—
13C2×Q8×D113C2211yescharacteristic
14C2×D4×D113C2211yescharacteristic
15C2×#14268635C2212yescomplemented
16C2×#14268632C2212yes—
17#16813622C2211yescharacteristic, complemented
18#16813611C2211yescharacteristic
19#16813610C2211yescharacteristic
20#16813609—21no—
21#16813609C2211yescharacteristic
22#16813608—21no—
23#16813608—21no—
24#16813593—21no—
25#16813593C2212yes—
26D4×Dic113—21no—
27D4×Dic113C2212yescomplemented
28C22⋊C4×D113—21no—
29C22⋊C4×D113—21no—
30C42×D113C2211yescharacteristic
31#16813551C2212yescomplemented
32#16813547C2212yescomplemented
33#16813546C2212yescomplemented
34#16813544C2212yes—
35#16813543C2212yes—
36#16813534C2212yes—
37#16813533C2211yescharacteristic, complemented
38C2×SD16×C113C2212yescomplemented
39C2×D8×C113C2212yes—
40#127×C113C2211yescharacteristic, complemented
41#124×C113C2211yescharacteristic
42#97×C113C2211yescharacteristic, complemented
43C23×D113—21no—
44#14268646—44no—
45C2×Dic226—21no—
46C2×Dic226—21no—
47C2×Dic226C2311yescharacteristic
48Q8×D113—42no—
49C2×D452C2311yescharacteristic
50C2×C22⋊D113—22no—
51C2×C22⋊D113—21no—
52D4×D113—42no—
53C22×Dic113—22no—
54C2×C4×D113—21no—
55C2×C4×D113D411yescharacteristic
56C2×C4×D113D411yescharacteristic
57C2×C4×D113C2311yescharacteristic
58#14268635—42no—
59#14268632—42no—
60C2×#11744751C2312yes—
61C4⋊Dic113—21no—
62C4⋊Dic113C2312yes—
63C22⋊Dic113—21no—
64C22⋊Dic113—21no—
65C22⋊Dic113—22no—
66C22⋊Dic113—22no—
67#14268624—21no—
68#14268624—21no—
69#14268624—21no—
70#14268624—21no—
71C4×Dic113D411yescharacteristic
72C4×Dic113D411yescharacteristic
73C4×Dic113C2311yescharacteristic
74C2×Q8×C113C2311yescharacteristic
75C2×D4×C113—21no—
76C2×D4×C113—21no—
77C2×D4×C113C2312yes—
78C2×D4×C113C2311yescharacteristic
79SD16×C113—42no—
80D8×C113—42no—
81C2×C8×C113C2312yes—
82C22⋊C4×C113—21no—
83C22⋊C4×C113—21no—
84C42×C113C2311yescharacteristic
85C23×C113—21no—
86C23×C113—22no—
87C22×D113—21no—
88C22×D113—42no—
89C22×D113—42no—
90C22×D113—42no—
91C22×D113C2×D411yescharacteristic
92Q8×C113—22no—
93D4×C113—22no—
94D4×C113—22no—
95D4×C113—22no—
96D4×C113—42no—
97D4×C113—42no—
98C2×C4×C113—21no—
99C2×C4×C113C2×D411yescharacteristic
100C2×C4×C113C2×D411yescharacteristic
101C2×C4×C113C2411yescharacteristic
102C22⋊D113—42no—
103C22⋊D113—44no—
104C2×Dic113—21no—
105C2×Dic113—22no—
106C2×Dic113—44no—
107C2×Dic113C2×D411yescharacteristic
108C2×Dic113C2×D411yescharacteristic
109C2×Dic113C2×D411yescharacteristic
110D452—22no—
111C4×D113—22no—
112C4×D113—22no—
113C4×D113—41no—
114C4×D113—42no—
115Dic226—22no—
116Dic226—42no—
117Dic226—42no—
118C8×C113—22no—
119#11744751—22no—
120C22×C113—41no—
121C22×C113—42no—
122C22×C113—42no—
123C22×C113—41no—
124C22×C113—42no—
125C22×C113—41no—
126C22×C113C22×D411yescharacteristic
127C2×D113—21no—
128C2×D113—21no—
129C2×D113—41no—
130C2×D113—41no—
131C2×D113—41no—
132C2×D113—84no—
133C2×D113AGL(1,ℤ/8)12yes—
134C4×C113—21no—
135C4×C113—21no—
136C4×C113—41no—
137C4×C113H(5,𝔽2)12yes—
138Dic113—21no—
139Dic113—21no—
140Dic113—21no—
141Dic113—41no—
142Dic113—42no—
143C2×C113—81no—
144C2×C113—82no—
145C2×C113#53511yescharacteristic
146C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
147C2×C113#57511yescharacteristic
148D113—22no—
149D113—81no—
150#3213—1131nomaximal, Sylow
151C113#321311yescharacteristic, complemented, Sylow
152#532—1131no—
153C2×#124—1131no—
154#496—1131no—
155#496D11311yescharacteristic, complemented
156#489—1131no—
157#489—1131no—
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×SD16C2×D11312yescomplemented
168C2×D8—1132no—
169C2×D8C2×D11312yes—
170C4⋊Q8—1131no—
171#127C2×D11311yescharacteristic, complemented
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#103—1132no—
189#102—1132no—
190#102—1132no—
191C22⋊C8—1132no—
192#97—1131no—
193#97C2×D11311yescharacteristic, complemented
194C24—2261no—
195#41—4524no—
196C2×Q8—1131no—
197C2×Q8—4522no—
198C2×Q8—2261no—
199C2×Q8—2261no—
200C2×Q8C22×D11311yescharacteristic
201C2×D4—21no—
202C2×D4—21no—
203C2×D4—1131no—
204C2×D4—4522no—
205C2×D4—2261no—
206C2×D4—2262no—
207C2×D4C22×D11311yescharacteristic
208C2×D4C22×D11312yes—
209C22×C4—1131no—
210C22×C4—1131no—
211C22×C4—1131no—
212C22×C4—2261no—
213C22×C4—2262no—
214SD16—42no—
215SD16—4522no—
216D8—42no—
217D8—4522no—
218C2×C8—1132no—
219C2×C8C22×D11312yes—
220C4⋊C4—1132no—
221C4⋊C4—2261no—
222C22⋊C4—21no—
223C22⋊C4—21no—
224C22⋊C4—2261no—
225C22⋊C4—2261no—
226C22⋊C4—2261no—
227C22⋊C4—2261no—
228C22⋊C4—2262no—
229C22⋊C4—2262no—
230C22⋊C4—2261no—
231C22⋊C4—2261no—
232C42—1131no—
233C42—1131no—
234C42—1131no—
235C42C22×D11311yescharacteristic
236C23—21no—
237C23—22no—
238C23—1131no—
239C23—4522no—
240C23—4522no—
241C23—4522no—
242C23—2261no—
243Q8—22no—
244Q8—4522no—
245Q8—4522no—
246Q8—2262no—
247D4—22no—
248D4—22no—
249D4—22no—
250D4—42no—
251D4—42no—
252D4—4524no—
253D4—4522no—
254D4—2262no—
255C2×C4—21no—
256C2×C4—1131no—
257C2×C4—1131no—
258C2×C4—1131no—
259C2×C4—4521no—
260C2×C4—4522no—
261C2×C4—4524no—
262C2×C4—2262no—
263C2×C4—2261no—
264C2×C4—2262no—
265C2×C4—2262no—
266C2×C4D4×D11311yescharacteristic
267C2×C4D4×D11311yescharacteristic
268C2×C4C23×D11311yescharacteristic
269C8—22no—
270C8—2262no—
271C22—42no—
272C22—41no—
273C22—42no—
274C22—41no—
275C22—41no—
276C22—42no—
277C22—1132no—
278C22—9044no—
279C22—4521no—
280C22—4521no—
281C22—4521no—
282C22—2261no—
283C22—2261no—
284C22C2×D4×D11311yescharacteristic
285C4—21no—
286C4—21no—
287C4—41no—
288C4—4522no—
289C4—4521no—
290C4—2261no—
291C4—2261no—
292C4—2261no—
293C4#1681366712yes—
294C2—81no—
295C2—82no—
296C2—9041no—
297C2—2262no—
298C2#2029916111yescharacteristic
299C2AGL(1,ℤ/8)×D11311yescharacteristic
300C2#2029939411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#496×C113C2
socleC22×C113C22×D4
hypercenter#496D113
hypocenterC113#3213
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. #20299146C2semidirect
2. #124×D113C2semidirect
3. #20298985C2semidirect
4. #20298958C2semidirect
5. #20298957C2semidirect
6. #20298815C2semidirect
7. #20298811C2semidirect
8. #20298735C2semidirect
9. #20298730C2semidirect
10. #20298653C2semidirect
11. #496×C113C2semidirect
15. C2×#14268635C22semidirect
17. #16813622C22semidirect
27. D4×Dic113C22semidirect
31. #16813551C22semidirect
32. #16813547C22semidirect
33. #16813546C22semidirect
37. #16813533C22semidirect
38. C2×SD16×C113C22semidirect
40. #127×C113C22semidirect
42. #97×C113C22semidirect
151. C113#3213semidirect
155. #496D113semidirect
167. C2×SD16C2×D113semidirect
171. #127C2×D113semidirect
193. #97C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202991462
#124×D1132
#202989852
#202989582
#202989572
#202988152
#202988112
#202987352
#202987302
#202986532
#496×C1132
#3213113