Finite Group Databasebeta

← #28399861

Subgroups — #28399861

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×#16813670C211yesmaximal, characteristic, complemented
2C2×#16813650C211yesmaximal, characteristic, complemented
3C22×#14268634C211yesmaximal, characteristic, complemented
4#20299167C211yesmaximal, characteristic, complemented
5#20298746C214yesmaximal, complemented
6#20298738C214yesmaximal, complemented
7#20298592C211yesmaximal, characteristic, complemented
8#20298566C211yesmaximal, characteristic, complemented
9#419×C113C211yesmaximal, characteristic, complemented
10#16813670—24no—
11#16813670—24no—
12C2×#14268648—21no—
13C2×#14268648C2212yescomplemented
14C2×#14268647—22no—
15C2×#14268647C2211yescharacteristic
16C2×#14268647C2211yescharacteristic
17C2×Q8×D113—21no—
18C2×Q8×D113C2212yescomplemented
19C22×D452C2211yescharacteristic
20#16813650—24no—
21C2×#14268636C2212yes—
22C2×#14268634—24no—
23C2×#14268634C2214yes—
24C2×D904C2212yes—
25C22×#11744751C2211yescharacteristic
26#16813619—21no—
27#16813610—21no—
28#16813597C2214yes—
29#16813592—22no—
30#16813545C2212yescomplemented
31#16813542C2212yescomplemented
32#16813534C2214yescomplemented
33C22×Q8×C113C2211yescharacteristic
34C2×M16×C113C2211yescharacteristic
35#117×C113C2211yescharacteristic
36#103×C113C2214yescomplemented
37C23×D113—21no—
38#14268648—28no—
39#14268648—24no—
40#14268648—24no—
41#14268647—216no—
42#14268647—22no—
43#14268647—22no—
44#14268647—22no—
45#14268647D414yescomplemented
46C2×Dic226—22no—
47C2×Dic226D411yescharacteristic
48C2×Dic226C2311yescharacteristic
49Q8×D113—28no—
50Q8×D113—24no—
51Q8×D113—24no—
52C2×D452—22no—
53C2×D452—22no—
54C2×D452—22no—
55C2×D452—21no—
56C2×D452—24no—
57C2×D452D411yescharacteristic
58C2×D452C2312yes—
59C2×D452C2311yescharacteristic
60C2×C22⋊D113—21no—
61C2×C22⋊D113D412yes—
62C2×C4×D113—22no—
63C2×C4×D113—21no—
64C2×C4×D113—22no—
65C2×C4×D113C2312yes—
66#14268636—24no—
67#14268634—28no—
68D904—24no—
69C2×#11744751—22no—
70C2×#11744751C2312yes—
71#14268624—24no—
72C2×Q8×C113—21no—
73C2×Q8×C113—22no—
74C2×Q8×C113D414yescomplemented
75C2×Q8×C113C2312yes—
76C22×C4×C113—21no—
77C22×C4×C113C2311yescharacteristic
78M16×C113—22no—
79C2×C8×C113C2312yes—
80C4⋊C4×C113C2312yes—
81C22⋊C4×C113—21no—
82C42×C113—21no—
83C23×C113C2×D411yescharacteristic
84C22×D113—21no—
85C22×D113—22no—
86C22×D113—42no—
87C22×D113—82no—
88C22×D113C2×D412yes—
89Q8×C113—24no—
90Q8×C113—22no—
91Q8×C113C2×D414yes—
92C2×C4×C113—24no—
93C2×C4×C113—22no—
94C2×C4×C113—22no—
95C2×C4×C113C2×D411yescharacteristic
96C2×C4×C113C2×D412yes—
97C2×C4×C113C2×D412yes—
98C2×C4×C113C2411yescharacteristic
99C22⋊D113—24no—
100C22⋊D113—24no—
101C2×Dic113—21no—
102C2×Dic113C2×D412yes—
103D452—28no—
104D452—22no—
105D452—21no—
106D452—22no—
107D452—22no—
108D452—42no—
109D452—84no—
110D452C2×D412yes—
111C4×D113—28no—
112C4×D113—28no—
113C4×D113—24no—
114C4×D113—22no—
115C4×D113—22no—
116Dic226—28no—
117Dic226—22no—
118Dic226—21no—
119Dic226C2×D412yes—
120C8×C113—22no—
121#11744751—22no—
122C22×C113—22no—
123C22×C113#12012yes—
124C22×C113C22×D411yescharacteristic
125C2×D113—22no—
126C2×D113—22no—
127C2×D113—24no—
128C2×D113—42no—
129C2×D113—42no—
130C2×D113—44no—
131C2×D113—84no—
132C4×C113—24no—
133C4×C113—42no—
134C4×C113#12012yes—
135C4×C113C22×D411yescharacteristic
136C4×C113C22×D411yescharacteristic
137Dic113—22no—
138Dic113—22no—
139C2×C113—22no—
140C2×C113C2×#12011yescharacteristic
141C2×C113#57712yes—
142D113—42no—
143D113—42no—
144D113—82no—
145#3010—1131nomaximal, Sylow
146C113#301011yescharacteristic, complemented, Sylow
147C2×2−1+4—1131no—
148C2×AGL(1,ℤ/8)—1131no—
149C22×SD16—1131no—
150#535—1131no—
151#449—1134no—
152#448—1134no—
153#419D11311yescharacteristic, complemented
154#416—1131no—
155#408—1131no—
1562−1+4—2264no—
1572−1+4—2264no—
158C2×#41—1131no—
159C2×#41—1132no—
160C2×#41—1131no—
161C2×#41—2262no—
162C2×#41—2261no—
163C22×Q8—1132no—
164C22×Q8—2261no—
165C22×Q8C2×D11311yescharacteristic
166C22×D4—1131no—
167AGL(1,ℤ/8)—2264no—
168C2×SD16—1134no—
169C2×SD16—1132no—
170C2×SD16—2264no—
171C2×D8—1132no—
172C2×M16C2×D11311yescharacteristic
173C22×C8—1131no—
174#127—2261no—
175#124—2261no—
176#121—1134no—
177#120—2262no—
178#117C2×D11311yescharacteristic
179#103—1132no—
180#103C2×D11314yescomplemented
181#102—1132no—
182C22⋊C8—1134no—
183C24—2261no—
184#41—1134no—
185#41—22616no—
186#41—2264no—
187#41—2268no—
188#41—2264no—
189#41—2262no—
190#41—2262no—
191#41—2262no—
192C2×Q8—21no—
193C2×Q8—22no—
194C2×Q8—1131no—
195C2×Q8—1131no—
196C2×Q8—2262no—
197C2×Q8—2264no—
198C2×Q8—2268no—
199C2×Q8—2264no—
200C2×Q8D45214yescomplemented
201C2×Q8C22×D11312yes—
202C2×D4—1132no—
203C2×D4—1131no—
204C2×D4—1131no—
205C2×D4—1132no—
206C2×D4—2264no—
207C2×D4—2262no—
208C2×D4—2261no—
209C2×D4—2261no—
210C2×D4—2262no—
211C2×D4—2262no—
212C22×C4—21no—
213C22×C4—1132no—
214C22×C4—2262no—
215C22×C4—2262no—
216C22×C4—2261no—
217C22×C4C22×D11311yescharacteristic
218SD16—2264no—
219SD16—2268no—
220D8—2264no—
221M16—22no—
222C2×C8—1132no—
223C2×C8—2262no—
224C2×C8C22×D11312yes—
225C4⋊C4C22×D11312yes—
226C22⋊C4—21no—
227C22⋊C4—2264no—
228C42—21no—
229C23—1132no—
230C23—9042no—
231C23—4522no—
232C23—2262no—
233C23—2261no—
234C23D4×D11311yescharacteristic
235Q8—24no—
236Q8—22no—
237Q8—1132no—
238Q8—2268no—
239Q8—2262no—
240Q8—2261no—
241Q8C2×D45214yes—
242D4—1132no—
243D4—9044no—
244D4—4522no—
245D4—2268no—
246D4—2264no—
247D4—2264no—
248D4—2262no—
249D4—2262no—
250D4—2262no—
251D4—2261no—
252C2×C4—24no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—1132no—
256C2×C4—2268no—
257C2×C4—2268no—
258C2×C4—2261no—
259C2×C4—2264no—
260C2×C4—2262no—
261C2×C4—2262no—
262C2×C4D4×D11311yescharacteristic
263C2×C4D4×D11312yes—
264C2×C4C2×D45212yes—
265C2×C4C23×D11311yescharacteristic
266C8—22no—
267C8—2262no—
268C22—22no—
269C22—9044no—
270C22—4522no—
271C22—4524no—
272C22—4522no—
273C22—2262no—
274C22—2262no—
275C22—2264no—
276C22#1681359212yes—
277C22C2×D4×D11311yescharacteristic
278C4—24no—
279C4—42no—
280C4—2262no—
281C4—2262no—
282C4#1681359212yes—
283C4C2×D4×D11311yescharacteristic
284C4C22×D45211yescharacteristic
285C2—22no—
286C2—9042no—
287C2—4522no—
288C2—4522no—
289C2C2×#1681359211yescharacteristic
290C2#2029940712yes—
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#419×C113C2
socleC22×C113C22×D4
hypercenter#419D113
hypocenterC113#3010
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
1. C2×#16813670C2semidirect
2. C2×#16813650C2semidirect
3. C22×#14268634C2semidirect
4. #20299167C2semidirect
5. #20298746C2semidirect
6. #20298738C2semidirect
7. #20298592C2semidirect
8. #20298566C2semidirect
9. #419×C113C2semidirect
13. C2×#14268648C22semidirect
18. C2×Q8×D113C22semidirect
30. #16813545C22semidirect
31. #16813542C22semidirect
32. #16813534C22semidirect
36. #103×C113C22semidirect
45. #14268647D4semidirect
74. C2×Q8×C113D4semidirect
146. C113#3010semidirect
153. #419D113semidirect
180. #103C2×D113semidirect
200. C2×Q8D452semidirect

Maximal subgroups

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

subgroupindex
C2×#168136702
C2×#168136502
C22×#142686342
#202991672
#202987462
#202987382
#202985922
#202985662
#419×C1132
#3010113