Finite Group Databasebeta

← #28399820

Subgroups — #28399820

Order 14464.

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

normal subgroups only

This group has 758 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
1C22×#14268648C211yesmaximal, characteristic, complemented
2C2×#16813653C211yesmaximal, characteristic, complemented
3C2×#16813650C211yesmaximal, characteristic, complemented
4#20299110C211yesmaximal, characteristic, complemented
5#20298763C214yesmaximal, complemented
6#20298746C214yesmaximal, complemented
7#20298602C211yesmaximal, characteristic, complemented
8#20298561C211yesmaximal, characteristic, complemented
9#419×C113C211yesmaximal, characteristic, complemented
10C2×#14268648—24no—
11C2×#14268648—22no—
12C2×#14268648—24no—
13C2×#14268648C2214yes—
14C2×#14268647C2211yescharacteristic
15C22×D452—21no—
16C22×D452C2211yescharacteristic
17C22×C4×D113—21no—
18C22×C4×D113C2211yescharacteristic
19#16813653—24no—
20#16813650—24no—
21C2×#14268637C2212yescomplemented
22C2×#14268636C2212yescomplemented
23C2×#14268634C2212yescomplemented
24C2×D904C2212yescomplemented
25C2×#14268631C2211yescharacteristic
26#16813606—21no—
27#16813602C2212yescomplemented
28#16813597C2212yescomplemented
29#16813592—21no—
30C4×D452—22no—
31#16813542C2214yescomplemented
32#16813534C2214yescomplemented
33C22×Q8×C113C2211yescharacteristic
34C2×M16×C113C2211yescharacteristic
35#117×C113C2211yescharacteristic
36#103×C113C2214yescomplemented
37C23×D113—21no—
38C23×D113D411yescharacteristic
39#14268648—216no—
40#14268648—28no—
41#14268648—28no—
42#14268647—22no—
43#14268647—22no—
44C2×Dic226C2311yescharacteristic
45C2×D452—28no—
46C2×D452—24no—
47C2×D452—21no—
48C2×D452—22no—
49C2×D452—22no—
50C2×D452D414yescomplemented
51C2×D452C2311yescharacteristic
52C2×D452C2312yes—
53C2×C22⋊D113—21no—
54C22×Dic113D411yescharacteristic
55C2×C4×D113—28no—
56C2×C4×D113—22no—
57C2×C4×D113—22no—
58C2×C4×D113—24no—
59C2×C4×D113—21no—
60C2×C4×D113D412yes—
61C2×C4×D113C2312yes—
62#14268637—24no—
63#14268636—24no—
64#14268634—24no—
65D904—24no—
66#14268631—22no—
67C2×#11744751C2312yes—
68C4⋊Dic113—22no—
69#14268624—22no—
70#14268624—22no—
71C2×Q8×C113—22no—
72C2×Q8×C113—21no—
73C2×Q8×C113D414yescomplemented
74C2×Q8×C113C2312yes—
75C22×C4×C113—21no—
76C22×C4×C113C2311yescharacteristic
77M16×C113—22no—
78C2×C8×C113C2312yes—
79C4⋊C4×C113C2312yes—
80C22⋊C4×C113—21no—
81C42×C113—21no—
82C23×C113C2×D411yescharacteristic
83C22×D113—22no—
84C22×D113—24no—
85C22×D113—22no—
86C22×D113—21no—
87C22×D113—42no—
88C22×D113—44no—
89C22×D113C2×D412yes—
90Q8×C113—24no—
91Q8×C113—22no—
92Q8×C113C2×D414yes—
93C2×C4×C113—24no—
94C2×C4×C113—22no—
95C2×C4×C113—22no—
96C2×C4×C113C2×D411yescharacteristic
97C2×C4×C113C2×D412yes—
98C2×C4×C113C2×D412yes—
99C2×C4×C113C2411yescharacteristic
100C22⋊D113—42no—
101C2×Dic113—22no—
102C2×Dic113—21no—
103C2×Dic113C2×D412yes—
104D452—216no—
105D452—24no—
106D452—22no—
107D452—21no—
108D452—21no—
109D452—44no—
110D452C2×D414yes—
111C4×D113—216no—
112C4×D113—24no—
113C4×D113—22no—
114C4×D113—22no—
115C4×D113—42no—
116Dic226—21no—
117Dic226—21no—
118C8×C113—22no—
119#11744751—22no—
120C22×C113—22no—
121C22×C113#12012yes—
122C22×C113C22×D411yescharacteristic
123C2×D113—22no—
124C2×D113—24no—
125C2×D113—22no—
126C2×D113—22no—
127C2×D113—44no—
128C2×D113—48no—
129C2×D113—44no—
130C2×D113—41no—
131C2×D113—42no—
132C4×C113—24no—
133C4×C113—42no—
134C4×C113#12012yes—
135C4×C113C22×D411yescharacteristic
136C4×C113C22×D411yescharacteristic
137Dic113—22no—
138Dic113—41no—
139C2×C113—22no—
140C2×C113C2×#12011yescharacteristic
141C2×C113#57512yes—
142D113—42no—
143D113—44no—
144D113—81no—
145#3005—1131nomaximal, Sylow
146C113#300511yescharacteristic, complemented, Sylow
147C22×#41—1131no—
148C2×#137—1131no—
149C2×AGL(1,ℤ/8)—1131no—
150#525—1131no—
151#452—1134no—
152#449—1134no—
153#419D11311yescharacteristic, complemented
154#418—1131no—
155#407—1131no—
156C2×#41—1134no—
157C2×#41—1131no—
158C2×#41—2262no—
159C2×#41—2264no—
160C2×#41—2264no—
161C22×Q8C2×D11311yescharacteristic
162C22×D4—1131no—
163C22×D4—2261no—
164C23×C4—1131no—
165C23×C4—2261no—
166#137—2264no—
167AGL(1,ℤ/8)—2264no—
168C2×Q16—1132no—
169C2×SD16—1132no—
170C2×SD16—1132no—
171C2×D8—1132no—
172C2×M16—1131no—
173C2×M16C2×D11311yescharacteristic
174#123—2261no—
175C22⋊Q8—1132no—
176#121—1132no—
177#120—2261no—
178C4×D4—2262no—
179#117C2×D11311yescharacteristic
180#103C2×D11314yescomplemented
181#102—1134no—
182C22⋊C8—1134no—
183C24—1131no—
184C24—2261no—
185#41—2262no—
186#41—2262no—
187#41—2268no—
188#41—22616no—
189#41—2268no—
190C2×Q8—22no—
191C2×Q8—21no—
192C2×Q8—1131no—
193C2×Q8D45214yescomplemented
194C2×Q8C22×D11312yes—
195C2×D4—1134no—
196C2×D4—1132no—
197C2×D4—1131no—
198C2×D4—2262no—
199C2×D4—2264no—
200C2×D4—2268no—
201C2×D4—2261no—
202C2×D4—2261no—
203C2×D4—2262no—
204C22×C4—21no—
205C22×C4—1131no—
206C22×C4—1132no—
207C22×C4—1132no—
208C22×C4—2264no—
209C22×C4—2268no—
210C22×C4—2261no—
211C22×C4—2262no—
212C22×C4—2262no—
213C22×C4C22×D11311yescharacteristic
214Q16—2264no—
215SD16—2264no—
216SD16—2264no—
217D8—2264no—
218M16—22no—
219M16—2262no—
220C2×C8—1132no—
221C2×C8C22×D11312yes—
222C4⋊C4—2262no—
223C4⋊C4C22×D11312yes—
224C22⋊C4—21no—
225C22⋊C4—2262no—
226C22⋊C4—2262no—
227C42—21no—
228C23—1132no—
229C23—4524no—
230C23—4522no—
231C23—2261no—
232C23—2264no—
233C23—2262no—
234C23—2262no—
235C23D4×D11311yescharacteristic
236Q8—24no—
237Q8—22no—
238Q8—2261no—
239Q8—2261no—
240Q8C2×D45214yes—
241D4—1134no—
242D4—4524no—
243D4—4522no—
244D4—22616no—
245D4—2264no—
246D4—2261no—
247D4—2261no—
248D4—2262no—
249C2×C4—24no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—1132no—
253C2×C4—4522no—
254C2×C4—22616no—
255C2×C4—2261no—
256C2×C4—2262no—
257C2×C4—2264no—
258C2×C4—2262no—
259C2×C4—2262no—
260C2×C4D4×D11311yescharacteristic
261C2×C4D4×D11312yes—
262C2×C4C2×D45212yes—
263C2×C4C23×D11311yescharacteristic
264C8—22no—
265C8—2262no—
266C22—22no—
267C22—4528no—
268C22—4524no—
269C22—4521no—
270C22—4522no—
271C22—4524no—
272C22—2264no—
273C22—2262no—
274C22—2262no—
275C22—2262no—
276C22#1681359212yes—
277C22C2×D4×D11311yescharacteristic
278C4—24no—
279C4—42no—
280C4—4521no—
281C4—2262no—
282C4#1681359212yes—
283C4C2×D4×D11311yescharacteristic
284C4C22×D45211yescharacteristic
285C2—22no—
286C2—9041no—
287C2—4524no—
288C2—4522no—
289C2C2×#1681359211yescharacteristic
290C2#2029939712yes—
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#419×C113C2
socleC22×C113C22×D4
hypercenter#419D113
hypocenterC113#3005
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. C22×#14268648C2semidirect
2. C2×#16813653C2semidirect
3. C2×#16813650C2semidirect
4. #20299110C2semidirect
5. #20298763C2semidirect
6. #20298746C2semidirect
7. #20298602C2semidirect
8. #20298561C2semidirect
9. #419×C113C2semidirect
21. C2×#14268637C22semidirect
22. C2×#14268636C22semidirect
23. C2×#14268634C22semidirect
24. C2×D904C22semidirect
27. #16813602C22semidirect
28. #16813597C22semidirect
31. #16813542C22semidirect
32. #16813534C22semidirect
36. #103×C113C22semidirect
50. C2×D452D4semidirect
73. C2×Q8×C113D4semidirect
146. C113#3005semidirect
153. #419D113semidirect
180. #103C2×D113semidirect
193. C2×Q8D452semidirect

Maximal subgroups

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

subgroupindex
C22×#142686482
C2×#168136532
C2×#168136502
#202991102
#202987632
#202987462
#202986022
#202985612
#419×C1132
#3005113