Finite Group Databasebeta

← #28400667

Subgroups — #28400667

Order 14464.

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

normal subgroups only

This group has 488 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#20299149C211yesmaximal, characteristic, complemented
2C4×D4×D113C211yesmaximal, characteristic, complemented
3#20298918C212yesmaximal, complemented
4#20298885C211yesmaximal, characteristic, complemented
5#20298794C211yesmaximal, characteristic, complemented
6#20298793C211yesmaximal, characteristic, complemented
7#20298733C212yesmaximal, complemented
8#20298709C212yesmaximal, complemented
9#20298707C212yesmaximal, complemented
10#20298654C211yesmaximal, characteristic, complemented
11#476×C113C211yesmaximal, characteristic, complemented
12C2×#14268648—21no—
13C2×D4×D113C2211yescharacteristic
14C22×C4×D113—21no—
15C2×D904C2212yes—
16C2×#14268632C2212yes—
17#16813619C2211yescharacteristic, complemented
18#16813611—21no—
19#16813597—21no—
20#16813597C2212yes—
21C4×D452C2211yescharacteristic
22D4×Dic113C2211yescharacteristic
23#16813584—21no—
24#16813584C2211yescharacteristic
25#16813584C2212yescomplemented
26C4×C22⋊D113—21no—
27#16813582—21no—
28C4⋊C4×D113C2211yescharacteristic
29C22⋊C4×D113—21no—
30C42×D113C2211yescharacteristic
31#16813553C2212yescomplemented
32C4⋊#11744751C2211yescharacteristic, complemented
33#16813544C2212yescomplemented
34#16813542C2212yes—
35#16813542C2212yescomplemented
36#16813534C2212yes—
37#16813532C2212yescomplemented
38C4⋊Q8×C113C2211yescharacteristic, complemented
39C4×D4×C113C2211yescharacteristic
40#106×C113C2212yescomplemented
41C4⋊C8×C113C2211yescharacteristic, complemented
42#102×C113C2212yes—
43C23×D113—21no—
44#14268648—44no—
45C2×D452—22no—
46C2×D452—21no—
47C2×D452—21no—
48C2×D452C2312yes—
49C2×D452C2311yescharacteristic
50C2×C22⋊D113—21no—
51D4×D113—22no—
52D4×D113—22no—
53C22×Dic113—21no—
54C2×C4×D113—21no—
55C2×C4×D113—21no—
56C2×C4×D113—21no—
57C2×C4×D113—22no—
58C2×C4×D113—44no—
59C2×C4×D113D411yescharacteristic
60C2×C4×D113D411yescharacteristic
61C2×C4×D113C2311yescharacteristic
62D904—24no—
63#14268632—24no—
64C2×#11744751C2312yes—
65C4⋊Dic113C2311yescharacteristic
66#14268626—21no—
67C22⋊Dic113—21no—
68#14268624—21no—
69#14268624—21no—
70#14268624—22no—
71#14268624—22no—
72C4×Dic113D411yescharacteristic
73C4×Dic113D411yescharacteristic
74C4×Dic113C2311yescharacteristic
75C2×Q8×C113—21no—
76C2×D4×C113C2311yescharacteristic
77C22×C4×C113—21no—
78C2×C8×C113C2312yes—
79C4⋊C4×C113—21no—
80C4⋊C4×C113C2311yescharacteristic
81C4⋊C4×C113C2312yes—
82C22⋊C4×C113—21no—
83C42×C113C2311yescharacteristic
84C23×C113—21no—
85C22×D113—24no—
86C22×D113—21no—
87C22×D113—22no—
88C22×D113—42no—
89C22×D113—42no—
90C22×D113C2×D411yescharacteristic
91Q8×C113—42no—
92D4×C113—21no—
93D4×C113#4112yescomplemented
94C2×C4×C113—21no—
95C2×C4×C113—22no—
96C2×C4×C113—42no—
97C2×C4×C113C2×D411yescharacteristic
98C2×C4×C113C2×D411yescharacteristic
99C2×C4×C113C2411yescharacteristic
100C22⋊D113—24no—
101C2×Dic113—21no—
102C2×Dic113—42no—
103C2×Dic113C2×D411yescharacteristic
104C2×Dic113C2×D411yescharacteristic
105C2×Dic113C2×D411yescharacteristic
106D452—21no—
107D452—22no—
108D452—22no—
109D452—42no—
110D452—44no—
111D452—42no—
112D452#4112yescomplemented
113C4×D113—22no—
114C4×D113—22no—
115C4×D113—21no—
116C4×D113—21no—
117C4×D113—42no—
118C4×D113—44no—
119C4×D113—42no—
120C4×D113—42no—
121C8×C113—22no—
122#11744751—22no—
123C22×C113—22no—
124C22×C113—41no—
125C22×C113—41no—
126C22×C113C22×D411yescharacteristic
127C2×D113—21no—
128C2×D113—21no—
129C2×D113—22no—
130C2×D113—48no—
131C2×D113—41no—
132C2×D113—41no—
133C2×D113—42no—
134C2×D113—42no—
135C2×D113—42no—
136C2×D113AGL(1,ℤ/8)12yes—
137C4×C113—21no—
138C4×C113—41no—
139C4×C113—42no—
140C4×C113AGL(1,ℤ/8)12yes—
141C4×C113C2×#4111yescharacteristic
142C4×C113C2×#4111yescharacteristic
143Dic113—21no—
144Dic113—21no—
145Dic113—21no—
146Dic113—41no—
147C2×C113—42no—
148C2×C113#52511yescharacteristic
149C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
150C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
151D113—22no—
152D113—42no—
153D113—82no—
154#3109—1131nomaximal, Sylow
155C113#310911yescharacteristic, complemented, Sylow
156#532—1131no—
157C2×C4×D4—1131no—
158#481—1132no—
159#476—1131no—
160#476D11311yescharacteristic, complemented
161#459—1131no—
162#459—1131no—
163#447—1132no—
164#442—1132no—
165#442—1132no—
166#432—1131no—
167C2×#41—2261no—
168C22×D4—1131no—
169C23×C4—2261no—
170C2×D8—1132no—
171C2×D8—1132no—
172C4⋊Q8C2×D11311yescharacteristic, complemented
173#127—1131no—
174#124—2261no—
175#121—1132no—
176#121—2261no—
177C4×D4—1131no—
178C4×D4—1131no—
179C4×D4—1132no—
180C4×D4—1131no—
181C4×D4—2261no—
182C4×D4—2261no—
183C4×D4—2261no—
184C4×D4C2×D11311yescharacteristic
185C2×C4⋊C4—1131no—
186C2×C22⋊C4—2261no—
187C2×C42—1131no—
188#106—1132no—
189#106C2×D11312yescomplemented
190C4⋊C8—1131no—
191C4⋊C8C2×D11311yescharacteristic, complemented
192#102—1132no—
193#102—1132no—
194#102—1132no—
195#102C2×D11312yes—
196C22⋊C8—1132no—
197#97—1132no—
198C24—2261no—
199#41—4524no—
200C2×Q8—21no—
201C2×D4—1131no—
202C2×D4—1132no—
203C2×D4—2262no—
204C2×D4—2261no—
205C2×D4—2262no—
206C2×D4—2262no—
207C2×D4—2261no—
208C2×D4—2261no—
209C2×D4C22×D11311yescharacteristic
210C22×C4—21no—
211C22×C4—1131no—
212C22×C4—1131no—
213C22×C4—1131no—
214C22×C4—4524no—
215C22×C4—2261no—
216C22×C4—2262no—
217C22×C4—2261no—
218C22×C4—2261no—
219C22×C4—2261no—
220D8—2264no—
221D8—2264no—
222C2×C8—1132no—
223C2×C8C22×D11312yes—
224C4⋊C4—21no—
225C4⋊C4—1131no—
226C4⋊C4—2261no—
227C4⋊C4C22×D11311yescharacteristic
228C4⋊C4C22×D11312yes—
229C22⋊C4—21no—
230C22⋊C4—2261no—
231C22⋊C4—2262no—
232C22⋊C4—2262no—
233C22⋊C4—2261no—
234C22⋊C4—2261no—
235C42—1131no—
236C42—1131no—
237C42—1131no—
238C42C22×D11311yescharacteristic
239C23—21no—
240C23—1131no—
241C23—4522no—
242C23—4522no—
243C23—2264no—
244C23—2262no—
245C23—2261no—
246Q8—42no—
247D4—21no—
248D4—1132no—
249D4—4522no—
250D4—4524no—
251D4—4522no—
252D4—2264no—
253D4—2262no—
254D4—2262no—
255D4—2261no—
256D4#1426864812yescomplemented
257C2×C4—21no—
258C2×C4—22no—
259C2×C4—42no—
260C2×C4—1131no—
261C2×C4—1131no—
262C2×C4—1131no—
263C2×C4—4522no—
264C2×C4—4522no—
265C2×C4—4524no—
266C2×C4—4522no—
267C2×C4—4522no—
268C2×C4—2262no—
269C2×C4—2261no—
270C2×C4—2262no—
271C2×C4—2261no—
272C2×C4—2261no—
273C2×C4D4×D11311yescharacteristic
274C2×C4D4×D11311yescharacteristic
275C2×C4C23×D11311yescharacteristic
276C8—22no—
277C8—2262no—
278C22—22no—
279C22—41no—
280C22—41no—
281C22—1132no—
282C22—4528no—
283C22—4522no—
284C22—4522no—
285C22—4522no—
286C22—4521no—
287C22—4521no—
288C22—2262no—
289C22—2261no—
290C22—2261no—
291C22C2×D4×D11311yescharacteristic
292C4—21no—
293C4—42no—
294C4—41no—
295C4—4521no—
296C4—2261no—
297C4—2261no—
298C4—2261no—
299C4#1681364912yes—
300C4#41×D11311yescharacteristic
301C4C2×#1426864811yescharacteristic
302C2—42no—
303C2—9042no—
304C2—4522no—
305C2—2262no—
306C2#2029911111yescharacteristic
307C2AGL(1,ℤ/8)×D11311yescharacteristic
308C2C2×#1681364911yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#476×C113C2
socleC22×C113C22×D4
hypercenter#476D113
hypocenterC113#3109
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #20299149C2semidirect
2. C4×D4×D113C2semidirect
3. #20298918C2semidirect
4. #20298885C2semidirect
5. #20298794C2semidirect
6. #20298793C2semidirect
7. #20298733C2semidirect
8. #20298709C2semidirect
9. #20298707C2semidirect
10. #20298654C2semidirect
11. #476×C113C2semidirect
17. #16813619C22semidirect
25. #16813584C22semidirect
31. #16813553C22semidirect
32. C4⋊#11744751C22semidirect
33. #16813544C22semidirect
35. #16813542C22semidirect
37. #16813532C22semidirect
38. C4⋊Q8×C113C22semidirect
40. #106×C113C22semidirect
41. C4⋊C8×C113C22semidirect
93. D4×C113#41semidirect
112. D452#41semidirect
155. C113#3109semidirect
160. #476D113semidirect
172. C4⋊Q8C2×D113semidirect
189. #106C2×D113semidirect
191. C4⋊C8C2×D113semidirect
256. D4#14268648semidirect

Maximal subgroups

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

subgroupindex
#202991492
C4×D4×D1132
#202989182
#202988852
#202987942
#202987932
#202987332
#202987092
#202987072
#202986542
#476×C1132
#3109113