Finite Group Databasebeta

← #28400714

Subgroups — #28400714

Order 14464.

450 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 125 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#20299132C211yesmaximal, characteristic, complemented
2C2×C4×D452C211yesmaximal, characteristic, complemented
3#20298929C211yesmaximal, characteristic, complemented
4#20298912C211yesmaximal, characteristic, complemented
5#20298899C212yesmaximal, complemented
6#20298814C212yesmaximal, complemented
7#20298751C211yesmaximal, characteristic, complemented
8#20298734C211yesmaximal, characteristic
9#20298711C212yesmaximal, complemented
10#20298700C212yesmaximal, complemented
11#432×C113C211yesmaximal, characteristic, complemented
12C22×D452C2211yescharacteristic
13C22×C4×D113—21no—
14C2×#14268636C2212yes—
15C2×D904C2212yes—
16#16813616—21no—
17#16813614C2211yescharacteristic, complemented
18#16813610C2211yescharacteristic, complemented
19#16813605—21no—
20#16813601C2211yescharacteristic
21#16813596C2211yescharacteristic
22C4×Dic226C2211yescharacteristic, complemented
23C4×D452—21no—
24C4×D452—21no—
25C4×D452C2212yes—
26C4×D452C2212yes—
27C4×D452C2211yescharacteristic, complemented
28C4×C22⋊D113—21no—
29#16813579—21no—
30C2×C4⋊Dic113C2211yescharacteristic
31C2×#14268624—21no—
32#16813556C2212yescomplemented
33#16813554C2212yescomplemented
34#16813547C2212yescomplemented
35#16813544C2212yes—
36#16813544C2212yes—
37#16813544C2212yescomplemented
38C2×C42×C113C2211yescharacteristic
39C4⋊C8×C113C2212yescomplemented
40C22⋊C8×C113C2211yescharacteristic
41C22⋊C8×C113C2211yescharacteristic
42#97×C113C2212yescomplemented
43C23×D113—21no—
44C2×Dic226C2311yescharacteristic
45C2×D452—21no—
46C2×D452—24no—
47C2×D452C2311yescharacteristic
48C2×D452C2312yes—
49C2×C22⋊D113—21no—
50C22×Dic113—21no—
51C2×C4×D113—21no—
52C2×C4×D113—22no—
53C2×C4×D113—22no—
54C2×C4×D113—44no—
55#14268636—24no—
56D904—24no—
57C4⋊Dic113—21no—
58C4⋊Dic113C2312yes—
59C4⋊Dic113C2311yescharacteristic
60C4⋊Dic113C2311yescharacteristic
61#14268626—21no—
62#14268626—21no—
63#14268626—21no—
64#14268626—21no—
65C22⋊Dic113—21no—
66#14268624—22no—
67#14268624—22no—
68#14268624—21no—
69#14268624—21no—
70#14268624—21no—
71#14268624—21no—
72C4×Dic113—21no—
73C22×C4×C113D411yescharacteristic
74C22×C4×C113D411yescharacteristic
75C22×C4×C113C2311yescharacteristic
76C2×C8×C113C2312yes—
77C2×C8×C113C2312yes—
78C42×C113D411yescharacteristic
79C42×C113D411yescharacteristic
80C42×C113C2311yescharacteristic
81C42×C113C2311yescharacteristic
82C23×C113C2×D411yescharacteristic
83C22×D113—24no—
84C22×D113—22no—
85C22×D113—21no—
86C22×D113—42no—
87C22×D113—42no—
88C2×C4×C113—22no—
89C2×C4×C113—22no—
90C2×C4×C113—41no—
91C2×C4×C113C2×D411yescharacteristic
92C2×C4×C113C2×D411yescharacteristic
93C2×C4×C113C2×D411yescharacteristic
94C2×C4×C113C2×D411yescharacteristic
95C2×C4×C113C2×D411yescharacteristic
96C2×C4×C113C2411yescharacteristic
97C22⋊D113—42no—
98C2×Dic113—21no—
99C2×Dic113—21no—
100C2×Dic113—22no—
101C2×Dic113—21no—
102C2×Dic113—42no—
103D452—24no—
104D452—22no—
105D452—22no—
106D452#4114yes—
107C4×D113—42no—
108C4×D113—44no—
109C4×D113—44no—
110Dic226—22no—
111C8×C113—22no—
112C8×C113—22no—
113C22×C113—21no—
114C22×C113—21no—
115C22×C113AGL(1,ℤ/8)12yes—
116C22×C113C22×D411yescharacteristic
117C2×D113—24no—
118C2×D113—48no—
119C2×D113—42no—
120C2×D113—42no—
121C2×D113—41no—
122C2×D113—41no—
123C2×D113—41no—
124C4×C113—21no—
125C4×C113—21no—
126C4×C113—21no—
127C4×C113—21no—
128C4×C113—21no—
129C4×C113C2×#4112yes—
130Dic113—41no—
131Dic113—42no—
132Dic113—41no—
133Dic113—41no—
134C2×C113—22no—
135C2×C113#52511yescharacteristic
136C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
137C2×C113#57511yescharacteristic
138D113—44no—
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#450—1131no—
149#447—1131no—
150#442—1132no—
151#440—1132no—
152#432D11311yescharacteristic, complemented
153C22×D4—1131no—
154C23×C4—2261no—
155C2×SD16—1132no—
156C2×D8—1132no—
157#126—2261no—
158#125—1131no—
159#124—1131no—
160#123—2261no—
161C22⋊Q8—1131no—
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×C42C2×D11311yescharacteristic
174#107—1132no—
175#106—1132no—
176C4⋊C8C2×D11312yescomplemented
177#103—1132no—
178#102—1132no—
179#102—1132no—
180#102—1132no—
181C22⋊C8C2×D11311yescharacteristic
182C22⋊C8C2×D11311yescharacteristic
183#97C2×D11312yescomplemented
184C24—2261no—
185C2×Q8—1131no—
186C2×D4—1132no—
187C2×D4—1131no—
188C2×D4—2264no—
189C2×D4—2261no—
190C2×D4—2261no—
191C22×C4—4524no—
192C22×C4—2261no—
193C22×C4—2261no—
194C22×C4—2262no—
195C22×C4—2262no—
196C22×C4D45211yescharacteristic
197C22×C4D45211yescharacteristic
198C22×C4C22×D11311yescharacteristic
199SD16—2264no—
200D8—2264no—
201C2×C8C22×D11312yes—
202C2×C8C22×D11312yes—
203C4⋊C4—1131no—
204C4⋊C4—1131no—
205C4⋊C4—1132no—
206C4⋊C4—2261no—
207C4⋊C4—2261no—
208C4⋊C4—2261no—
209C4⋊C4—2261no—
210C4⋊C4—2261no—
211C22⋊C4—2261no—
212C22⋊C4—2262no—
213C22⋊C4—2262no—
214C22⋊C4—2261no—
215C22⋊C4—2261no—
216C22⋊C4—2261no—
217C22⋊C4—2261no—
218C42—2261no—
219C42D45211yescharacteristic
220C42D45211yescharacteristic
221C42C22×D11311yescharacteristic
222C42C22×D11311yescharacteristic
223C23—4522no—
224C23—4522no—
225C23—2264no—
226C23—2261no—
227C23—2262no—
228C23C2×D45211yescharacteristic
229Q8—2262no—
230D4—1134no—
231D4—4522no—
232D4—2264no—
233D4—2262no—
234D4—2262no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—41no—
238C2×C4—4524no—
239C2×C4—4524no—
240C2×C4—4522no—
241C2×C4—4522no—
242C2×C4—2261no—
243C2×C4—2261no—
244C2×C4—2261no—
245C2×C4—2262no—
246C2×C4C2×D45211yescharacteristic
247C2×C4C2×D45211yescharacteristic
248C2×C4C2×D45211yescharacteristic
249C2×C4C2×D45211yescharacteristic
250C2×C4C2×D45211yescharacteristic
251C2×C4C23×D11311yescharacteristic
252C8—22no—
253C8—22no—
254C22—21no—
255C22—21no—
256C22—4528no—
257C22—4521no—
258C22—4521no—
259C22—4521no—
260C22—4522no—
261C22—4522no—
262C22—2264no—
263C22#1681365012yes—
264C22C22×D45211yescharacteristic
265C4—21no—
266C4—21no—
267C4—21no—
268C4—21no—
269C4—21no—
270C4—4521no—
271C4—4522no—
272C4—4521no—
273C4—4521no—
274C4#41×D11312yes—
275C2—22no—
276C2—9041no—
277C2—4524no—
278C2#2029911011yescharacteristic
279C2C2×#1681365011yescharacteristic
280C2#2029939811yescharacteristic
subgroupG/H
centerC22C22×D452
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#432×C113C2
socleC22×C113C22×D4
prime radical#20298734C2
hypercenter#432D113
hypocenterC113#3114
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
1. #20299132C2semidirect
2. C2×C4×D452C2semidirect
3. #20298929C2semidirect
4. #20298912C2semidirect
5. #20298899C2semidirect
6. #20298814C2semidirect
7. #20298751C2semidirect
9. #20298711C2semidirect
10. #20298700C2semidirect
11. #432×C113C2semidirect
17. #16813614C22semidirect
18. #16813610C22semidirect
22. C4×Dic226C22semidirect
27. C4×D452C22semidirect
32. #16813556C22semidirect
33. #16813554C22semidirect
34. #16813547C22semidirect
37. #16813544C22semidirect
39. C4⋊C8×C113C22semidirect
42. #97×C113C22semidirect
141. C113#3114semidirect
152. #432D113semidirect
176. C4⋊C8C2×D113semidirect
183. #97C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202991322
C2×C4×D4522
#202989292
#202989122
#202988992
#202988142
#202987512
#202987342
#202987112
#202987002
#432×C1132
#3114113