Finite Group Databasebeta

← #28400713

Subgroups — #28400713

Order 14464.

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

normal subgroups only

This group has 450 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#20299134C211yesmaximal, characteristic, complemented
2C2×D4×Dic113C211yesmaximal, characteristic, complemented
3#20298926C211yesmaximal, characteristic, complemented
4#20298912C211yesmaximal, characteristic, complemented
5#20298896C212yesmaximal, complemented
6#20298815C212yesmaximal, complemented
7#20298732C211yesmaximal, characteristic
8#20298707C212yesmaximal, complemented
9#20298699C212yesmaximal, complemented
10#20298652C211yesmaximal, characteristic, complemented
11#450×C113C211yesmaximal, characteristic, complemented
12C23×Dic113—21no—
13C2×#14268632C2212yes—
14#16813617—21no—
15#16813613C2211yescharacteristic, complemented
16#16813611C2211yescharacteristic, complemented
17#16813606—21no—
18#16813596C2211yescharacteristic
19Q8×Dic113C2211yescharacteristic, complemented
20D4×Dic113—21no—
21D4×Dic113—21no—
22D4×Dic113C2212yes—
23D4×Dic113C2212yes—
24#16813584C2211yescharacteristic, complemented
25#16813582—21no—
26#16813580—21no—
27C2×C4⋊Dic113C2211yescharacteristic
28C2×C22⋊Dic113—21no—
29C2×C4×Dic113C2211yescharacteristic
30#16813556C2212yescomplemented
31#16813553C2212yescomplemented
32#16813551C2212yescomplemented
33#16813546C2212yescomplemented
34#16813544C2212yescomplemented
35#16813543C2212yes—
36C22⋊#11744751C2211yescharacteristic
37#16813532C2212yescomplemented
38C22×D4×C113C2211yescharacteristic
39C2×SD16×C113C2212yes—
40C22⋊Q8×C113C2211yescharacteristic
41#102×C113C2212yes—
42C22⋊C8×C113C2211yescharacteristic
43C2×D452C2311yescharacteristic
44C2×C22⋊D113—21no—
45C22×Dic113—21no—
46C22×Dic113—22no—
47C22×Dic113—22no—
48C22×Dic113—44no—
49C22×Dic113D411yescharacteristic
50C22×Dic113D411yescharacteristic
51C2×C4×D113—21no—
52#14268632—24no—
53C2×#11744751C2312yes—
54C4⋊Dic113—21no—
55C4⋊Dic113—21no—
56C4⋊Dic113—21no—
57C4⋊Dic113C2312yes—
58C4⋊Dic113C2311yescharacteristic
59#14268626—21no—
60C22⋊Dic113—22no—
61C22⋊Dic113—22no—
62#14268624—21no—
63#14268624—21no—
64#14268624—21no—
65#14268624—21no—
66C4×Dic113—21no—
67C4×Dic113D411yescharacteristic
68C4×Dic113D411yescharacteristic
69C4×Dic113C2311yescharacteristic
70C4×Dic113C2311yescharacteristic
71C24×C113—21no—
72C2×Q8×C113C2311yescharacteristic
73C2×D4×C113—24no—
74C2×D4×C113—21no—
75C2×D4×C113C2312yes—
76C22×C4×C113C2311yescharacteristic
77SD16×C113—24no—
78C2×C8×C113C2312yes—
79C4⋊C4×C113—21no—
80C4⋊C4×C113C2311yescharacteristic
81C22⋊C4×C113—21no—
82C23×C113—24no—
83C23×C113—22no—
84C23×C113—42no—
85C23×C113—42no—
86C23×C113C2×D411yescharacteristic
87C22×D113—21no—
88Q8×C113—22no—
89D4×C113—24no—
90D4×C113—22no—
91D4×C113#4114yes—
92C2×C4×C113—22no—
93C2×C4×C113—21no—
94C2×C4×C113—21no—
95C2×C4×C113C2×D411yescharacteristic
96C2×C4×C113C2411yescharacteristic
97C22⋊D113—42no—
98C2×Dic113—22no—
99C2×Dic113—21no—
100C2×Dic113—22no—
101C2×Dic113—41no—
102C2×Dic113—44no—
103C2×Dic113—44no—
104C2×Dic113—42no—
105C2×Dic113C2×D411yescharacteristic
106C2×Dic113C2×D411yescharacteristic
107C2×Dic113C2×D411yescharacteristic
108C2×Dic113C2×D411yescharacteristic
109D452—22no—
110C4×D113—42no—
111C8×C113—22no—
112#11744751—22no—
113C22×C113—21no—
114C22×C113—21no—
115C22×C113—24no—
116C22×C113—48no—
117C22×C113—42no—
118C22×C113—42no—
119C22×C113AGL(1,ℤ/8)12yes—
120C22×C113C22×D411yescharacteristic
121C2×D113—41no—
122C2×D113—41no—
123C2×D113—41no—
124C4×C113—21no—
125C4×C113—41no—
126C4×C113—41no—
127C4×C113C2×#4112yes—
128Dic113—21no—
129Dic113—21no—
130Dic113—21no—
131Dic113—21no—
132Dic113—42no—
133Dic113—41no—
134C2×C113—22no—
135C2×C113—44no—
136C2×C113#52511yescharacteristic
137C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
138C2×C113#57511yescharacteristic
139D113—81no—
140#3114—1131nomaximal, Sylow
141C113#311411yescharacteristic, complemented, Sylow
142#529—1131no—
143C2×C4×D4—1131no—
144#483—1131no—
145#480—1131no—
146#478—1132no—
147#463—1132no—
148#450D11311yescharacteristic, complemented
149#447—1131no—
150#442—1132no—
151#440—1132no—
152#432—1131no—
153C22×D4C2×D11311yescharacteristic
154C23×C4—2261no—
155C2×SD16C2×D11312yes—
156C2×D8—1132no—
157#126—2261no—
158#125—1131no—
159#124—1131no—
160#123—2261no—
161C22⋊Q8C2×D11311yescharacteristic
162#121—1131no—
163C4×Q8—1131no—
164C4×D4—1132no—
165C4×D4—1132no—
166C4×D4—1131no—
167C4×D4—2261no—
168C4×D4—2261no—
169C4×D4—2261no—
170#117—2261no—
171C2×C4⋊C4—1131no—
172C2×C22⋊C4—2261no—
173C2×C42—1131no—
174#107—1132no—
175#106—1132no—
176C4⋊C8—1132no—
177#103—1132no—
178#102—1132no—
179#102—1132no—
180#102C2×D11312yes—
181C22⋊C8—1131no—
182C22⋊C8C2×D11311yescharacteristic
183#97—1132no—
184C24—21no—
185C2×Q8C22×D11311yescharacteristic
186C2×D4—24no—
187C2×D4—21no—
188C2×D4—1131no—
189C2×D4—2261no—
190C2×D4C22×D11312yes—
191C22×C4—1131no—
192C22×C4—1131no—
193C22×C4—4524no—
194C22×C4—2261no—
195C22×C4—2262no—
196C22×C4—2262no—
197C22×C4—2261no—
198C22×C4C22×D11311yescharacteristic
199SD16—24no—
200D8—2264no—
201C2×C8—1132no—
202C2×C8C22×D11312yes—
203C4⋊C4—21no—
204C4⋊C4—1131no—
205C4⋊C4—1132no—
206C4⋊C4—2261no—
207C4⋊C4—2261no—
208C4⋊C4—2261no—
209C4⋊C4—2261no—
210C4⋊C4C22×D11311yescharacteristic
211C22⋊C4—21no—
212C22⋊C4—2261no—
213C22⋊C4—2261no—
214C22⋊C4—2261no—
215C22⋊C4—2262no—
216C22⋊C4—2262no—
217C22⋊C4—2261no—
218C42—1131no—
219C42—1131no—
220C42—1131no—
221C42—1131no—
222C42—2261no—
223C23—24no—
224C23—22no—
225C23—42no—
226C23—42no—
227C23—2261no—
228C23D4×D11311yescharacteristic
229Q8—22no—
230D4—24no—
231D4—22no—
232D4—4522no—
233D4—2262no—
234D4#1426864614yes—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—1131no—
239C2×C4—1131no—
240C2×C4—1131no—
241C2×C4—1131no—
242C2×C4—4522no—
243C2×C4—4522no—
244C2×C4—4524no—
245C2×C4—4524no—
246C2×C4—4521no—
247C2×C4—2261no—
248C2×C4—2262no—
249C2×C4—2262no—
250C2×C4D4×D11311yescharacteristic
251C2×C4C23×D11311yescharacteristic
252C8—22no—
253C8—2262no—
254C22—21no—
255C22—21no—
256C22—24no—
257C22—48no—
258C22—42no—
259C22—42no—
260C22—4521no—
261C22—4521no—
262C22—4521no—
263C22#1681364912yes—
264C22C2×D4×D11311yescharacteristic
265C4—21no—
266C4—41no—
267C4—41no—
268C4—4522no—
269C4—4521no—
270C4—2261no—
271C4—2261no—
272C4—2261no—
273C4—2261no—
274C4C2×#1426864612yes—
275C2—22no—
276C2—44no—
277C2—9041no—
278C2#2029910411yescharacteristic
279C2C2×#1681364911yescharacteristic
280C2#2029939411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#450×C113C2
socleC22×C113C22×D4
prime radical#20298732C2
hypercenter#450D113
hypocenterC113#3114
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #20299134C2semidirect
2. C2×D4×Dic113C2semidirect
3. #20298926C2semidirect
4. #20298912C2semidirect
5. #20298896C2semidirect
6. #20298815C2semidirect
8. #20298707C2semidirect
9. #20298699C2semidirect
10. #20298652C2semidirect
11. #450×C113C2semidirect
15. #16813613C22semidirect
16. #16813611C22semidirect
19. Q8×Dic113C22semidirect
24. #16813584C22semidirect
30. #16813556C22semidirect
31. #16813553C22semidirect
32. #16813551C22semidirect
33. #16813546C22semidirect
34. #16813544C22semidirect
37. #16813532C22semidirect
141. C113#3114semidirect
148. #450D113semidirect

Maximal subgroups

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

subgroupindex
#202991342
C2×D4×Dic1132
#202989262
#202989122
#202988962
#202988152
#202987322
#202987072
#202986992
#202986522
#450×C1132
#3114113