Finite Group Databasebeta

← #28399858

Subgroups — #28399858

Order 14464.

732 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 732 conjugacy classes of subgroups — too many to draw. Only its 149 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
1C2×#16813669C211yesmaximal, characteristic, complemented
2C2×#16813648C211yesmaximal, characteristic, complemented
3C22×#14268635C211yesmaximal, characteristic, complemented
4#20298741C214yesmaximal, complemented
5#20298736C214yesmaximal, complemented
6#20298606C211yesmaximal, characteristic, complemented
7#20298592C211yesmaximal, characteristic, complemented
8#20298565C211yesmaximal, characteristic, complemented
9#535×C113C211yesmaximal, characteristic, complemented
10#16813669—24no—
11#16813669—24no—
12C2×#14268647C2211yescharacteristic
13C2×#14268647C2212yescomplemented
14C2×#14268646—22no—
15C2×#14268646—21no—
16C22×Dic226C2211yescharacteristic
17C22×Dic226C2212yescomplemented
18C2×Q8×D113—21no—
19#16813648—24no—
20C2×#14268635—24no—
21C2×#14268635C2214yes—
22C2×#14268635C2212yes—
23C2×#14268632C2212yes—
24C2×#14268631C2211yescharacteristic
25C22×#11744751C2211yescharacteristic
26#16813545C2212yescomplemented
27#16813545C2214yescomplemented
28#16813542C2212yescomplemented
29C22⋊#11744751C2214yescomplemented
30C2×#41×C113C2211yescharacteristic
31C22×D4×C113C2211yescharacteristic
32#127×C113—21no—
33#124×C113—21no—
34#121×C113C2214yes—
35#120×C113—22no—
36#117×C113C2211yescharacteristic
37#14268647—22no—
38#14268647—24no—
39#14268647—24no—
40#14268647D414yescomplemented
41#14268646—216no—
42#14268646—28no—
43C2×Dic226—21no—
44C2×Dic226—22no—
45C2×Dic226—22no—
46C2×Dic226—24no—
47C2×Dic226—24no—
48C2×Dic226D414yescomplemented
49C2×Dic226C2312yes—
50C2×Dic226C2311yescharacteristic
51Q8×D113—28no—
52C2×D452C2311yescharacteristic
53C2×C22⋊D113—21no—
54C2×C22⋊D113—22no—
55C22×Dic113—21no—
56C22×Dic113—22no—
57C2×C4×D113—21no—
58C2×C4×D113—22no—
59#14268635—28no—
60#14268635—24no—
61#14268632—24no—
62#14268631—22no—
63C2×#11744751—22no—
64C2×#11744751C2312yes—
65C2×#11744751C2312yes—
66C24×C113—21no—
67#41×C113—22no—
68#41×C113—22no—
69C2×Q8×C113D411yescharacteristic
70C2×D4×C113—24no—
71C2×D4×C113—22no—
72C2×D4×C113—22no—
73C2×D4×C113—21no—
74C2×D4×C113D412yes—
75C2×D4×C113D411yescharacteristic
76C2×D4×C113C2312yes—
77C22×C4×C113C2312yes—
78C22×C4×C113C2311yescharacteristic
79C4⋊C4×C113C2312yes—
80C22⋊C4×C113—21no—
81C22⋊C4×C113—24no—
82C42×C113—21no—
83C23×C113—22no—
84C23×C113—42no—
85C23×C113—82no—
86C23×C113C2×D412yes—
87C23×C113C2×D411yescharacteristic
88C22×D113—21no—
89Q8×C113—22no—
90D4×C113—24no—
91D4×C113—22no—
92D4×C113—22no—
93D4×C113—22no—
94D4×C113—42no—
95D4×C113—84no—
96C2×C4×C113—22no—
97C2×C4×C113—22no—
98C2×C4×C113—22no—
99C2×C4×C113C2×D412yes—
100C2×C4×C113C2×D412yes—
101C2×C4×C113C2×D412yes—
102C2×C4×C113C2×D411yescharacteristic
103C2×C4×C113C2411yescharacteristic
104C22⋊D113—28no—
105C22⋊D113—24no—
106C2×Dic113—28no—
107C2×Dic113—24no—
108C2×Dic113—21no—
109C2×Dic113—22no—
110D452—21no—
111D452C2×D412yes—
112C4×D113—28no—
113C4×D113—24no—
114Dic226—28no—
115Dic226—24no—
116Dic226—22no—
117Dic226—21no—
118Dic226C2×D412yes—
119Dic226C2×D414yes—
120#11744751—22no—
121#11744751—22no—
122C22×C113—22no—
123C22×C113—22no—
124C22×C113—24no—
125C22×C113—42no—
126C22×C113—44no—
127C22×C113—84no—
128C22×C113#12012yes—
129C22×C113C22×D411yescharacteristic
130C2×D113—22no—
131C2×D113—42no—
132C4×C113—22no—
133C4×C113—42no—
134C4×C113#12012yes—
135C4×C113C22×D411yescharacteristic
136C4×C113C22×D411yescharacteristic
137Dic113—22no—
138Dic113—24no—
139C2×C113—22no—
140C2×C113—42no—
141C2×C113—82no—
142C2×C113C2×#12011yescharacteristic
143C2×C113#57712yes—
144D113—42no—
145#3010—1131nomaximal, Sylow
146C113#301011yescharacteristic, complemented, Sylow
147C2×2−1+4—1131no—
148C2×AGL(1,ℤ/8)—1131no—
149C22×SD16—1131no—
150#535D11311yescharacteristic, complemented
151#449—1134no—
152#448—1134no—
153#419—1131no—
154#416—1131no—
155#408—1131no—
1562−1+4—2264no—
1572−1+4—2264no—
158C2×#41—1131no—
159C2×#41—1132no—
160C2×#41—2262no—
161C2×#41—2261no—
162C2×#41C2×D11311yescharacteristic
163C22×Q8—1131no—
164C22×Q8—1132no—
165C22×Q8—2261no—
166C22×D4C2×D11311yescharacteristic
167AGL(1,ℤ/8)—2264no—
168C2×SD16—1134no—
169C2×SD16—1132no—
170C2×SD16—2264no—
171C2×D8—1132no—
172C2×M16—1131no—
173C22×C8—1131no—
174#127—21no—
175#124—21no—
176#121C2×D11314yes—
177#120—22no—
178#117C2×D11311yescharacteristic
179#103—1132no—
180#103—1134no—
181#102—1132no—
182C22⋊C8—1134no—
183C24—21no—
184#41—22no—
185#41—22no—
186#41—1134no—
187#41—2264no—
188#41—2264no—
189#41—22616no—
190#41—2268no—
191#41—2262no—
192C2×Q8—1134no—
193C2×Q8—1132no—
194C2×Q8—1131no—
195C2×Q8—2264no—
196C2×Q8—2264no—
197C2×Q8—2268no—
198C2×Q8—2262no—
199C2×Q8—2262no—
200C2×Q8—2261no—
201C2×Q8C22⋊D11311yescharacteristic
202C2×D4—24no—
203C2×D4—22no—
204C2×D4—22no—
205C2×D4—21no—
206C2×D4—1131no—
207C2×D4—2262no—
208C2×D4—2261no—
209C2×D4C22⋊D11312yes—
210C2×D4C22⋊D11311yescharacteristic
211C2×D4C22×D11312yes—
212C22×C4—2262no—
213C22×C4—2261no—
214C22×C4—2262no—
215C22×C4—2261no—
216C22×C4C22×D11312yes—
217C22×C4C22×D11311yescharacteristic
218SD16—2268no—
219SD16—2264no—
220D8—2264no—
221M16—2262no—
222C2×C8—1132no—
223C2×C8—1132no—
224C2×C8—2262no—
225C4⋊C4C22×D11312yes—
226C22⋊C4—21no—
227C22⋊C4—24no—
228C42—21no—
229C23—22no—
230C23—42no—
231C23—82no—
232C23—2261no—
233C23C2×C22⋊D11312yes—
234C23C2×C22⋊D11311yescharacteristic
235Q8—22no—
236Q8—1134no—
237Q8—1132no—
238Q8—2268no—
239Q8—2264no—
240Q8—2262no—
241Q8—2261no—
242D4—24no—
243D4—22no—
244D4—22no—
245D4—22no—
246D4—42no—
247D4—84no—
248D4—1132no—
249D4—2268no—
250D4—2264no—
251D4—2261no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—2268no—
256C2×C4—2268no—
257C2×C4—2264no—
258C2×C4—2262no—
259C2×C4—2261no—
260C2×C4—2264no—
261C2×C4D4×D11312yes—
262C2×C4D4×D11312yes—
263C2×C4C2×C22⋊D11312yes—
264C2×C4C2×C22⋊D11311yescharacteristic
265C2×C4C23×D11311yescharacteristic
266C8—2262no—
267C8—2262no—
268C22—22no—
269C22—22no—
270C22—24no—
271C22—42no—
272C22—44no—
273C22—84no—
274C22—4522no—
275C22—2262no—
276C22#1681359012yes—
277C22C22×C22⋊D11311yescharacteristic
278C4—22no—
279C4—42no—
280C4—2264no—
281C4—2262no—
282C4#1681359012yes—
283C4C2×D4×D11311yescharacteristic
284C4C2×D4×D11311yescharacteristic
285C2—22no—
286C2—42no—
287C2—82no—
288C2—4522no—
289C2C2×#1681359011yescharacteristic
290C2#2029940912yes—
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#535×C113C2
socleC22×C113C22×D4
hypercenter#535D113
hypocenterC113#3010
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C2×#41 ◁ #535

Complements

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

NH ≅ G/Ntype
1. C2×#16813669C2semidirect
2. C2×#16813648C2semidirect
3. C22×#14268635C2semidirect
4. #20298741C2semidirect
5. #20298736C2semidirect
6. #20298606C2semidirect
7. #20298592C2semidirect
8. #20298565C2semidirect
9. #535×C113C2semidirect
13. C2×#14268647C22semidirect
17. C22×Dic226C22semidirect
26. #16813545C22semidirect
27. #16813545C22semidirect
28. #16813542C22semidirect
29. C22⋊#11744751C22semidirect
40. #14268647D4semidirect
48. C2×Dic226D4semidirect
146. C113#3010semidirect
150. #535D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136692
C2×#168136482
C22×#142686352
#202987412
#202987362
#202986062
#202985922
#202985652
#535×C1132
#3010113