Finite Group Databasebeta

← #28400490

Subgroups — #28400490

Order 14464.

420 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 121 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#20299111C211yesmaximal, characteristic
2C2×#16813580C211yesmaximal, characteristic, complemented
3#20298938C212yesmaximal, complemented
4#20298926C211yesmaximal, characteristic, complemented
5#20298925C212yesmaximal, complemented
6#20298916C211yesmaximal, characteristic, complemented
7#20298912C211yesmaximal, characteristic, complemented
8#20298635C212yesmaximal, complemented
9#20298593C212yesmaximal, complemented
10C22⋊C8×D113C211yesmaximal, characteristic, complemented
11#484×C113C211yesmaximal, characteristic, complemented
12C2×#14268648C2211yescharacteristic
13C22×C4×D113C2211yescharacteristic
14C2×C8×D113C2212yes—
15#16813607—21no—
16#16813598C2211yescharacteristic
17#16813597C2211yescharacteristic
18#16813596C2211yescharacteristic
19#16813592—21no—
20#16813584—21no—
21#16813582—21no—
22#16813580—21no—
23#16813580—21no—
24#16813580C2212yes—
25#16813580C2212yes—
26#16813580C2211yescharacteristic
27C2×C4⋊Dic113C2211yescharacteristic
28C2×#14268624—21no—
29C2×C4×Dic113—21no—
30#16813556C2212yescomplemented
31#16813553C2212yescomplemented
32#16813553C2212yescomplemented
33#16813546C2212yescomplemented
34#16813544C2212yescomplemented
35#16813542C2212yescomplemented
36C22⋊#11744751C2211yescharacteristic
37#16813534C2212yes—
38C22⋊Q8×C113C2211yescharacteristic
39C2×C4⋊C4×C113C2211yescharacteristic
40#107×C113C2212yescomplemented
41#103×C113C2212yescomplemented
42C22⋊C8×C113C2211yescharacteristic
43C23×D113D411yescharacteristic
44#14268648—24no—
45C2×D452—21no—
46C2×D452—21no—
47C2×D452C2311yescharacteristic
48C2×C22⋊D113—21no—
49C22×Dic113—21no—
50C22×Dic113D411yescharacteristic
51C2×C4×D113—24no—
52C2×C4×D113—21no—
53C2×C4×D113D411yescharacteristic
54C2×C4×D113D411yescharacteristic
55C2×C4×D113C2311yescharacteristic
56C2×C4×D113C2311yescharacteristic
57C2×#11744751C2312yes—
58C8×D113—24no—
59C4⋊Dic113—21no—
60C4⋊Dic113C2312yes—
61C4⋊Dic113C2311yescharacteristic
62#14268626—21no—
63#14268624—22no—
64#14268624—22no—
65#14268624—21no—
66#14268624—21no—
67#14268624—21no—
68#14268624—21no—
69C4×Dic113—22no—
70C4×Dic113—22no—
71C4×Dic113—21no—
72C2×Q8×C113C2311yescharacteristic
73C22×C4×C113—21no—
74C22×C4×C113C2311yescharacteristic
75C2×C8×C113C2312yes—
76C4⋊C4×C113—21no—
77C4⋊C4×C113—21no—
78C4⋊C4×C113C2312yes—
79C4⋊C4×C113C2311yescharacteristic
80C22⋊C4×C113—21no—
81C23×C113C2×D411yescharacteristic
82C22×D113—22no—
83C22×D113—22no—
84C22×D113—21no—
85C22×D113—41no—
86C22×D113C2×D411yescharacteristic
87C22×D113C2×D411yescharacteristic
88Q8×C113—22no—
89C2×C4×C113—22no—
90C2×C4×C113—21no—
91C2×C4×C113—21no—
92C2×C4×C113—22no—
93C2×C4×C113—42no—
94C2×C4×C113C2×D411yescharacteristic
95C2×C4×C113C2411yescharacteristic
96C22⋊D113—42no—
97C2×Dic113—22no—
98C2×Dic113—22no—
99C2×Dic113—21no—
100C2×Dic113—42no—
101C2×Dic113C2×D411yescharacteristic
102C2×Dic113C2×D411yescharacteristic
103D452—22no—
104D452—42no—
105D452—42no—
106C4×D113—22no—
107C4×D113—22no—
108C4×D113—22no—
109C4×D113—42no—
110C4×D113#4114yes—
111C8×C113—22no—
112#11744751—22no—
113C22×C113—21no—
114C22×C113—21no—
115C22×C113#13512yes—
116C22×C113C22×D411yescharacteristic
117C2×D113—21no—
118C2×D113—21no—
119C2×D113—21no—
120C2×D113—21no—
121C2×D113—21no—
122C2×D113—44no—
123C2×D113—41no—
124C2×D113—41no—
125C2×D113—41no—
126C2×D113#12312yes—
127C4×C113—21no—
128C4×C113—41no—
129C4×C113—41no—
130C4×C113—42no—
131C4×C113C2×#4112yes—
132Dic113—21no—
133Dic113—42no—
134Dic113—41no—
135Dic113#12312yes—
136C2×C113—22no—
137C2×C113C2×#12311yescharacteristic
138C2×C113C2×#13511yescharacteristic
139C2×C113#57511yescharacteristic
140D113—22no—
141D113—41no—
142D113—81no—
143#3091—1131nomaximal, Sylow
144C113#309111yescharacteristic, complemented, Sylow
145#525—1131no—
146C2×#117—1131no—
147#485—1132no—
148#484D11311yescharacteristic, complemented
149#483—1131no—
150#482—1132no—
151#481—1131no—
152#480—1131no—
153#427—1132no—
154#416—1132no—
155C2×C22⋊C8—1131no—
156C2×#41—1131no—
157C23×C4—1131no—
158C22×C8—1132no—
159#123—2261no—
160C22⋊Q8—1131no—
161C22⋊Q8C2×D11311yescharacteristic
162#121—1131no—
163#121—1131no—
164#120—2261no—
165C4×D4—2261no—
166C4×D4—2261no—
167#117—1132no—
168#117—1132no—
169#117—1131no—
170#117—2261no—
171#117—2261no—
172C2×C4⋊C4—1131no—
173C2×C4⋊C4C2×D11311yescharacteristic
174C2×C22⋊C4—2261no—
175C2×C42—2261no—
176#107—1132no—
177#107C2×D11312yescomplemented
178#106—1132no—
179#106—1132no—
180#103—1132no—
181#103C2×D11312yescomplemented
182#102—1132no—
183#102—1132no—
184C22⋊C8—1131no—
185C22⋊C8—1132no—
186C22⋊C8C2×D11311yescharacteristic
187C24—1131no—
188#41—2264no—
189C2×Q8C22×D11311yescharacteristic
190C2×D4—1131no—
191C2×D4—2261no—
192C2×D4—2261no—
193C2×D4—2261no—
194C22×C4—21no—
195C22×C4—1131no—
196C22×C4—1131no—
197C22×C4—1131no—
198C22×C4—1131no—
199C22×C4—1131no—
200C22×C4—2261no—
201C22×C4—2264no—
202C22×C4—2261no—
203C22×C4C22×D11311yescharacteristic
204C2×C8—1132no—
205C2×C8—2264no—
206C2×C8C22×D11312yes—
207C4⋊C4—21no—
208C4⋊C4—21no—
209C4⋊C4—1132no—
210C4⋊C4—1131no—
211C4⋊C4—2261no—
212C4⋊C4—2261no—
213C4⋊C4C22×D11312yes—
214C4⋊C4C22×D11311yescharacteristic
215C22⋊C4—21no—
216C22⋊C4—2261no—
217C22⋊C4—2262no—
218C22⋊C4—2262no—
219C22⋊C4—2261no—
220C22⋊C4—2261no—
221C22⋊C4—2261no—
222C42—2262no—
223C42—2262no—
224C42—2261no—
225C23—1131no—
226C23—1131no—
227C23—4521no—
228C23—2262no—
229C23—2261no—
230C23—2262no—
231C23D4×D11311yescharacteristic
232Q8—22no—
233D4—4522no—
234D4—4522no—
235D4—4522no—
236D4—2262no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—42no—
242C2×C4—1131no—
243C2×C4—1134no—
244C2×C4—1131no—
245C2×C4—4522no—
246C2×C4—4522no—
247C2×C4—2262no—
248C2×C4—2262no—
249C2×C4—2262no—
250C2×C4—2262no—
251C2×C4—2261no—
252C2×C4—2262no—
253C2×C4D4×D11311yescharacteristic
254C2×C4C23×D11311yescharacteristic
255C8—22no—
256C8—2262no—
257C22—21no—
258C22—21no—
259C22—1132no—
260C22—4524no—
261C22—4521no—
262C22—4521no—
263C22—4521no—
264C22—2261no—
265C22—2261no—
266C22—2261no—
267C22—2261no—
268C22—2261no—
269C22#1681364512yes—
270C22C2×D4×D11311yescharacteristic
271C4—21no—
272C4—41no—
273C4—42no—
274C4—41no—
275C4—1132no—
276C4—4522no—
277C4—4521no—
278C4—2261no—
279C4#41×D11312yes—
280C2—22no—
281C2—9041no—
282C2—4521no—
283C2—2262no—
284C2#123×D11311yescharacteristic
285C2C2×#1681364511yescharacteristic
286C2#2029939411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#484×C113C2
socleC22×C113C22×D4
prime radical#20299111C2
hypercenter#484D113
hypocenterC113#3091
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
2. C2×#16813580C2semidirect
3. #20298938C2semidirect
4. #20298926C2semidirect
5. #20298925C2semidirect
6. #20298916C2semidirect
7. #20298912C2semidirect
8. #20298635C2semidirect
9. #20298593C2semidirect
10. C22⋊C8×D113C2semidirect
11. #484×C113C2semidirect
30. #16813556C22semidirect
31. #16813553C22semidirect
32. #16813553C22semidirect
33. #16813546C22semidirect
34. #16813544C22semidirect
35. #16813542C22semidirect
40. #107×C113C22semidirect
41. #103×C113C22semidirect
144. C113#3091semidirect
148. #484D113semidirect
177. #107C2×D113semidirect
181. #103C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202991112
C2×#168135802
#202989382
#202989262
#202989252
#202989162
#202989122
#202986352
#202985932
C22⋊C8×D1132
#484×C1132
#3091113