Finite Group Databasebeta

← #28401354

Subgroups — #28401354

Order 14464.

420 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 115 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#20299108C211yesmaximal, characteristic
2C2×#16813602C211yesmaximal, characteristic, complemented
3#20298941C212yesmaximal, complemented
4#20298928C211yesmaximal, characteristic, complemented
5#20298840C212yesmaximal, complemented
6#20298826C212yesmaximal, complemented
7#20298761C212yesmaximal, complemented
8#20298756C211yesmaximal, characteristic, complemented
9#20298736C211yesmaximal, characteristic, complemented
10C22⋊C8×D113C211yesmaximal, characteristic, complemented
11#480×C113C211yesmaximal, characteristic, complemented
12C2×#14268646C2211yescharacteristic
13C22×Dic226C2211yescharacteristic
14C22×C4×D113C2211yescharacteristic
15C2×Dic452C2212yescomplemented
16C2×#14268635C2212yescomplemented
17C2×C8×D113C2212yes—
18#16813604—21no—
19#16813602—21no—
20#16813602—21no—
21#16813602C2212yes—
22#16813602C2212yes—
23#16813602C2211yescharacteristic
24#16813601C2211yescharacteristic
25#16813593C2211yescharacteristic
26#16813590—21no—
27D4×Dic113—21no—
28#16813582—21no—
29#16813580C2211yescharacteristic
30C2×C4⋊Dic113—21no—
31C2×#14268624—21no—
32#16813553C2212yescomplemented
33#16813547C2212yescomplemented
34#16813545C2212yescomplemented
35#16813545C2212yescomplemented
36C22⋊#11744751C2211yescharacteristic
37#16813534C2212yes—
38#121×C113C2211yescharacteristic
39C2×C4⋊C4×C113C2211yescharacteristic
40#107×C113C2212yescomplemented
41#102×C113C2212yescomplemented
42C22⋊C8×C113C2211yescharacteristic
43C23×D113D411yescharacteristic
44#14268646—42no—
45C2×Dic226—21no—
46C2×Dic226—42no—
47C2×Dic226C2311yescharacteristic
48C2×Dic226C2312yes—
49C2×C22⋊D113—21no—
50C2×C22⋊D113—21no—
51C22×Dic113—21no—
52C22×Dic113—21no—
53C22×Dic113D411yescharacteristic
54C2×C4×D113—42no—
55C2×C4×D113D411yescharacteristic
56C2×C4×D113D411yescharacteristic
57C2×C4×D113C2311yescharacteristic
58C2×C4×D113C2311yescharacteristic
59Dic452—42no—
60#14268635—42no—
61C2×#11744751C2312yes—
62C8×D113—42no—
63C4⋊Dic113—22no—
64C4⋊Dic113—22no—
65C4⋊Dic113—21no—
66C4⋊Dic113C2311yescharacteristic
67#14268626—21no—
68C22⋊Dic113—21no—
69C22⋊Dic113—21no—
70#14268624—22no—
71#14268624—22no—
72#14268624—21no—
73#14268624—21no—
74C4×Dic113—21no—
75C2×D4×C113—21no—
76C2×D4×C113C2311yescharacteristic
77C22×C4×C113—21no—
78C22×C4×C113C2311yescharacteristic
79C2×C8×C113C2312yes—
80C4⋊C4×C113—21no—
81C4⋊C4×C113C2311yescharacteristic
82C4⋊C4×C113C2312yes—
83C22⋊C4×C113—21no—
84C23×C113—21no—
85C23×C113C2×D411yescharacteristic
86C22×D113—22no—
87C22×D113—22no—
88C22×D113—41no—
89C22×D113C2×D411yescharacteristic
90C22×D113C2×D411yescharacteristic
91D4×C113—22no—
92D4×C113—42no—
93C2×C4×C113—22no—
94C2×C4×C113—21no—
95C2×C4×C113—22no—
96C2×C4×C113—42no—
97C2×C4×C113C2×D411yescharacteristic
98C2×C4×C113C2411yescharacteristic
99C22⋊D113—42no—
100C22⋊D113—42no—
101C2×Dic113—21no—
102C2×Dic113—22no—
103C2×Dic113—21no—
104C2×Dic113—41no—
105C2×Dic113—42no—
106C2×Dic113—42no—
107C2×Dic113C2×D411yescharacteristic
108C2×Dic113C2×D411yescharacteristic
109C4×D113—22no—
110C4×D113—22no—
111C4×D113—41no—
112C4×D113—41no—
113Dic226—22no—
114Dic226—22no—
115Dic226—22no—
116Dic226—42no—
117C8×C113—22no—
118#11744751—22no—
119C22×C113—21no—
120C22×C113—21no—
121C22×C113—41no—
122C22×C113—41no—
123C22×C113—41no—
124C22×C113#13512yes—
125C22×C113C22×D411yescharacteristic
126C2×D113—21no—
127C2×D113—21no—
128C2×D113—21no—
129C2×D113—21no—
130C2×D113—21no—
131C2×D113—44no—
132C2×D113#13712yes—
133C4×C113—21no—
134C4×C113—42no—
135C4×C113—41no—
136C4×C113H(5,𝔽2)12yes—
137Dic113—21no—
138Dic113—21no—
139Dic113—42no—
140Dic113—41no—
141Dic113—41no—
142C2×C113—22no—
143C2×C113—81no—
144C2×C113#53411yescharacteristic
145C2×C113C2×#13511yescharacteristic
146C2×C113C2×#13711yescharacteristic
147D113—22no—
148D113—41no—
149#3190—1131nomaximal, Sylow
150C113#319011yescharacteristic, complemented, Sylow
151#525—1131no—
152C2×C22⋊Q8—1131no—
153#485—1132no—
154#483—1131no—
155#480D11311yescharacteristic, complemented
156#467—1132no—
157#465—1132no—
158#452—1132no—
159#451—1131no—
160#448—1131no—
161C2×C22⋊C8—1131no—
162C2×#41—1131no—
163C22×Q8—1131no—
164C23×C4—1131no—
165C2×Q16—1132no—
166C2×SD16—1132no—
167C22×C8—1132no—
168#123—2261no—
169C22⋊Q8—1131no—
170C22⋊Q8—1132no—
171C22⋊Q8—1132no—
172C22⋊Q8—1131no—
173C22⋊Q8—2261no—
174C22⋊Q8—2261no—
175#121—1131no—
176#121C2×D11311yescharacteristic
177#120—2261no—
178C4×D4—2261no—
179C4×D4—2261no—
180#117—1131no—
181C2×C4⋊C4—2261no—
182C2×C4⋊C4C2×D11311yescharacteristic
183C2×C22⋊C4—2261no—
184#107C2×D11312yescomplemented
185#106—1132no—
186#103—1132no—
187#103—1132no—
188#103—1132no—
189#102C2×D11312yescomplemented
190C22⋊C8—1131no—
191C22⋊C8—1132no—
192C22⋊C8C2×D11311yescharacteristic
193C24—1131no—
194#41—4522no—
195C2×Q8—1132no—
196C2×Q8—1131no—
197C2×Q8—4522no—
198C2×Q8—2261no—
199C2×D4—21no—
200C2×D4—2261no—
201C2×D4—2261no—
202C2×D4C22×D11311yescharacteristic
203C22×C4—21no—
204C22×C4—1131no—
205C22×C4—1131no—
206C22×C4—1131no—
207C22×C4—1131no—
208C22×C4—1131no—
209C22×C4—4522no—
210C22×C4—2261no—
211C22×C4—2261no—
212C22×C4C22×D11311yescharacteristic
213Q16—4522no—
214SD16—4522no—
215C2×C8—1132no—
216C2×C8—4522no—
217C2×C8C22×D11312yes—
218C4⋊C4—21no—
219C4⋊C4—1131no—
220C4⋊C4—2262no—
221C4⋊C4—2262no—
222C4⋊C4—2261no—
223C4⋊C4—2261no—
224C4⋊C4C22×D11312yes—
225C4⋊C4C22×D11311yescharacteristic
226C22⋊C4—21no—
227C22⋊C4—2262no—
228C22⋊C4—2262no—
229C22⋊C4—2261no—
230C22⋊C4—2261no—
231C22⋊C4—2261no—
232C22⋊C4—2261no—
233C42—2261no—
234C23—21no—
235C23—1131no—
236C23—1131no—
237C23—4521no—
238C23—2262no—
239C23—2262no—
240C23D4×D11311yescharacteristic
241Q8—4522no—
242Q8—2262no—
243Q8—2262no—
244Q8—2262no—
245D4—22no—
246D4—42no—
247D4—4522no—
248D4—4522no—
249C2×C4—22no—
250C2×C4—21no—
251C2×C4—22no—
252C2×C4—42no—
253C2×C4—1131no—
254C2×C4—1131no—
255C2×C4—4521no—
256C2×C4—4521no—
257C2×C4—4522no—
258C2×C4—4522no—
259C2×C4—4521no—
260C2×C4—2261no—
261C2×C4—2261no—
262C2×C4—2262no—
263C2×C4—2262no—
264C2×C4—2262no—
265C2×C4D4×D11311yescharacteristic
266C2×C4C23×D11311yescharacteristic
267C8—22no—
268C8—2262no—
269C22—21no—
270C22—21no—
271C22—41no—
272C22—41no—
273C22—41no—
274C22—1132no—
275C22—4524no—
276C22—2261no—
277C22—2261no—
278C22—2261no—
279C22—2261no—
280C22—2261no—
281C22#1681364112yes—
282C22C2×D4×D11311yescharacteristic
283C4—21no—
284C4—42no—
285C4—41no—
286C4—4521no—
287C4—4521no—
288C4—4522no—
289C4—2261no—
290C4—2261no—
291C4#1681366812yes—
292C2—22no—
293C2—81no—
294C2—4521no—
295C2—2262no—
296C2#2029915911yescharacteristic
297C2C2×#1681364111yescharacteristic
298C2#137×D11311yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#480×C113C2
socleC22×C113C22×D4
prime radical#20299108C2
hypercenter#480D113
hypocenterC113#3190
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. C2×#16813602C2semidirect
3. #20298941C2semidirect
4. #20298928C2semidirect
5. #20298840C2semidirect
6. #20298826C2semidirect
7. #20298761C2semidirect
8. #20298756C2semidirect
9. #20298736C2semidirect
10. C22⋊C8×D113C2semidirect
11. #480×C113C2semidirect
15. C2×Dic452C22semidirect
16. C2×#14268635C22semidirect
32. #16813553C22semidirect
33. #16813547C22semidirect
34. #16813545C22semidirect
35. #16813545C22semidirect
40. #107×C113C22semidirect
41. #102×C113C22semidirect
150. C113#3190semidirect
155. #480D113semidirect
184. #107C2×D113semidirect
189. #102C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202991082
C2×#168136022
#202989412
#202989282
#202988402
#202988262
#202987612
#202987562
#202987362
C22⋊C8×D1132
#480×C1132
#3190113