Finite Group Databasebeta

← #469×D113 #28400166

Subgroups — #469×D113 #28400166

Order 14464.

596 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 135 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×D8×D113C211yesmaximal, characteristic, complemented
2C2×M16×D113C211yesmaximal, characteristic, complemented
3#121×D113C212yesmaximal, complemented
4#20298852C211yesmaximal, characteristic, complemented
5#20298851C211yesmaximal, characteristic, complemented
6#20298850C212yesmaximal, complemented
7#20298849C212yesmaximal, complemented
8#20298848C211yesmaximal, characteristic, complemented
9#106×D113C211yesmaximal, characteristic, complemented
10#102×D113C212yesmaximal, complemented
11#469×C113C211yesmaximal, characteristic, complemented
12C2×D4×D113—22no—
13C2×D4×D113C2212yes—
14C22×C4×D113C2211yescharacteristic
15C2×D904C2211yescharacteristic, complemented
16C2×#14268632C2212yescomplemented
17D8×D113—24no—
18C2×#14268631C2211yescharacteristic, complemented
19C2×#14268630C2211yescharacteristic, complemented
20C2×#14268630C2211yescharacteristic, complemented
21M16×D113—24no—
22C2×C8×D113C2211yescharacteristic
23C2×C8×D113C2211yescharacteristic
24#16813597C2212yescomplemented
25#16813596C2212yescomplemented
26#16813595—22no—
27#16813594—22no—
28#16813593C2212yescomplemented
29C4⋊C4×D113C2212yes—
30C22⋊C4×D113—22no—
31#16813554C2211yescharacteristic, complemented
32#16813553C2212yescomplemented
33#16813544C2212yescomplemented
34#16813543C2212yescomplemented
35#16813542C2212yescomplemented
36C2×D8×C113C2211yescharacteristic, complemented
37C2×M16×C113C2211yescharacteristic, complemented
38#121×C113C2212yescomplemented
39#106×C113C2211yescharacteristic, complemented
40#102×C113C2212yescomplemented
41C23×D113—22no—
42C23×D113D411yescharacteristic
43C2×D452—22no—
44C2×D452C2312yes—
45C2×C22⋊D113—22no—
46C2×C22⋊D113—22no—
47C2×C22⋊D113—22no—
48D4×D113—24no—
49D4×D113—24no—
50D4×D113—48no—
51C22×Dic113D411yescharacteristic
52C2×C4×D113—22no—
53C2×C4×D113—22no—
54C2×C4×D113—22no—
55C2×C4×D113D411yescharacteristic
56C2×C4×D113D411yescharacteristic
57C2×C4×D113C2311yescharacteristic
58C2×C4×D113C2311yescharacteristic
59D904—22no—
60#14268632—24no—
61#14268631—22no—
62#14268630—22no—
63#14268630—22no—
64C2×#11744751C2311yescharacteristic
65C2×#11744751C2311yescharacteristic
66C8×D113—22no—
67C8×D113D414yescomplemented
68C4⋊Dic113C2312yes—
69#14268626—22no—
70C22⋊Dic113—22no—
71#14268624—22no—
72#14268624—22no—
73C2×D4×C113—22no—
74C2×D4×C113C2312yes—
75C22×C4×C113C2311yescharacteristic
76D8×C113—22no—
77M16×C113—22no—
78C2×C8×C113C2311yescharacteristic
79C2×C8×C113C2311yescharacteristic
80C4⋊C4×C113C2312yes—
81C22⋊C4×C113—22no—
82C23×C113—22no—
83C23×C113C2×D411yescharacteristic
84C22×D113—22no—
85C22×D113—24no—
86C22×D113—22no—
87C22×D113—44no—
88C22×D113—44no—
89C22×D113—44no—
90C22×D113C2×D411yescharacteristic
91C22×D113C2×D411yescharacteristic
92D4×C113—22no—
93D4×C113—22no—
94D4×C113—44no—
95C2×C4×C113—21no—
96C2×C4×C113—21no—
97C2×C4×C113—22no—
98C2×C4×C113C2×D411yescharacteristic
99C2×C4×C113C2411yescharacteristic
100C22⋊D113—44no—
101C22⋊D113—44no—
102C22⋊D113—44no—
103C2×Dic113—22no—
104C2×Dic113—22no—
105C2×Dic113C2×D411yescharacteristic
106C2×Dic113C2×D411yescharacteristic
107D452—22no—
108D452—22no—
109D452—44no—
110C4×D113—22no—
111C4×D113—21no—
112C4×D113—21no—
113C4×D113—22no—
114C4×D113—44no—
115C4×D113C2×D412yes—
116C4×D113#4112yes—
117C8×C113—21no—
118C8×C113C2×D412yescomplemented
119#11744751—21no—
120#11744751C2×D412yescomplemented
121C22×C113—21no—
122C22×C113—22no—
123C22×C113—42no—
124C22×C113—42no—
125C22×C113—42no—
126C22×C113C22×D411yescharacteristic
127C2×D113—21no—
128C2×D113—22no—
129C2×D113—44no—
130C2×D113—42no—
131C2×D113—42no—
132C2×D113—42no—
133C2×D113—88no—
134C2×D113#12112yes—
135C2×D113AGL(1,ℤ/8)14yes—
136C4×C113—21no—
137C4×C113—42no—
138C4×C113C22×D411yescharacteristic
139C4×C113C2×#4111yescharacteristic
140Dic113—21no—
141Dic113—42no—
142Dic113#12112yes—
143C2×C113—41no—
144C2×C113—82no—
145C2×C113C2×#12111yescharacteristic
146C2×C113C2×AGL(1,ℤ/8)12yes—
147D113—41no—
148D113—82no—
149D113#46914yesdirect product factor
150C2×#469—1131nomaximal, Sylow
151C113C2×#46911yescharacteristic, complemented, Sylow
152C22×D8—1131no—
153C22×M16—1131no—
154C2×#121—1132no—
155#469—1131no—
156#469—1131no—
157#469—1132no—
158#469—1131no—
159#469—1132no—
160#469D11311yescharacteristic, direct product factor
161C2×#106—1131no—
162C2×#102—1132no—
163C22×D4—1132no—
164C22×D4—2262no—
165C23×C4—1131no—
166C2×D8—1132no—
167C2×D8—1131no—
168C2×D8—2264no—
169C2×D8C2×D11311yescharacteristic, complemented
170C2×M16—1131no—
171C2×M16—1131no—
172C2×M16—1131no—
173C2×M16—2264no—
174C2×M16C2×D11311yescharacteristic, complemented
175C22×C8—1131no—
176C22×C8—1131no—
177#121—1132no—
178#121—1132no—
179#121—1132no—
180#121—2262no—
181#121—2262no—
182#121C2×D11312yescomplemented
183C2×C4⋊C4—1132no—
184C2×C22⋊C4—2262no—
185#106—1131no—
186#106—1132no—
187#106C2×D11311yescharacteristic, complemented
188#102—1132no—
189#102—1132no—
190#102—1132no—
191#102C2×D11312yescomplemented
192C24—1131no—
193C24—2262no—
194C2×D4—22no—
195C2×D4—1132no—
196C2×D4—4528no—
197C2×D4—2262no—
198C2×D4—2264no—
199C2×D4—2264no—
200C2×D4—2262no—
201C2×D4—2262no—
202C2×D4—2262no—
203C2×D4C22×D11312yes—
204C22×C4—1131no—
205C22×C4—1131no—
206C22×C4—1131no—
207C22×C4—1131no—
208C22×C4—1131no—
209C22×C4—2262no—
210C22×C4—2262no—
211C22×C4—2262no—
212C22×C4C22×D11311yescharacteristic
213D8—22no—
214D8—2264no—
215D8—2262no—
216M16—22no—
217M16—2262no—
218M16—2262no—
219M16—2262no—
220C2×C8—1131no—
221C2×C8—1134no—
222C2×C8—1131no—
223C2×C8—2262no—
224C2×C8C22×D11311yescharacteristic
225C2×C8C22×D11311yescharacteristic
226C4⋊C4—1132no—
227C4⋊C4—2262no—
228C4⋊C4C22×D11312yes—
229C22⋊C4—22no—
230C22⋊C4—2262no—
231C22⋊C4—2262no—
232C22⋊C4—2262no—
233C23—22no—
234C23—1131no—
235C23—1131no—
236C23—4524no—
237C23—4524no—
238C23—4524no—
239C23—2262no—
240C23—2264no—
241C23—2262no—
242C23D4×D11311yescharacteristic
243D4—22no—
244D4—22no—
245D4—44no—
246D4—4524no—
247D4—4524no—
248D4—4524no—
249D4—4524no—
250D4—2262no—
251D4—2262no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—22no—
255C2×C4—1131no—
256C2×C4—1132no—
257C2×C4—1132no—
258C2×C4—1131no—
259C2×C4—4524no—
260C2×C4—2262no—
261C2×C4—2262no—
262C2×C4—2262no—
263C2×C4—2262no—
264C2×C4—2261no—
265C2×C4—2261no—
266C2×C4D4×D11311yescharacteristic
267C2×C4C23×D11311yescharacteristic
268C8—21no—
269C8—1132no—
270C8—2261no—
271C8D4×D11312yescomplemented
272C22—21no—
273C22—22no—
274C22—42no—
275C22—42no—
276C22—42no—
277C22—1132no—
278C22—1134no—
279C22—9048no—
280C22—4524no—
281C22—4522no—
282C22—4522no—
283C22—4522no—
284C22—2261no—
285C22—2262no—
286C22C2×D4×D11311yescharacteristic
287C4—21no—
288C4—42no—
289C4—1132no—
290C4—4522no—
291C4—2261no—
292C4C2×D4×D11311yescharacteristic
293C4#41×D11311yescharacteristic
294C2—41no—
295C2—82no—
296C2—1134no—
297C2—9042no—
298C2—4521no—
299C2#121×D11311yescharacteristic
300C2AGL(1,ℤ/8)×D11312yes—
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#469×C113C2
socleC22×C113C22×D4
hypercenter#469D113
hypocenterC113C2×#469
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. C2×D8×D113C2semidirect
2. C2×M16×D113C2semidirect
3. #121×D113C2semidirect
4. #20298852C2semidirect
5. #20298851C2semidirect
6. #20298850C2semidirect
7. #20298849C2semidirect
8. #20298848C2semidirect
9. #106×D113C2semidirect
10. #102×D113C2semidirect
11. #469×C113C2semidirect
15. C2×D904C22semidirect
16. C2×#14268632C22semidirect
18. C2×#14268631C22semidirect
19. C2×#14268630C22semidirect
20. C2×#14268630C22semidirect
24. #16813597C22semidirect
25. #16813596C22semidirect
28. #16813593C22semidirect
31. #16813554C22semidirect
32. #16813553C22semidirect
33. #16813544C22semidirect
34. #16813543C22semidirect
35. #16813542C22semidirect
36. C2×D8×C113C22semidirect
37. C2×M16×C113C22semidirect
38. #121×C113C22semidirect
39. #106×C113C22semidirect
40. #102×C113C22semidirect
67. C8×D113D4semidirect
118. C8×C113C2×D4semidirect
120. #11744751C2×D4semidirect
149. D113#469direct (N × H)
151. C113C2×#469semidirect
160. #469D113direct (N × H)
169. C2×D8C2×D113semidirect
174. C2×M16C2×D113semidirect
182. #121C2×D113semidirect
187. #106C2×D113semidirect
191. #102C2×D113semidirect
271. C8D4×D113semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D1132
C2×M16×D1132
#121×D1132
#202988522
#202988512
#202988502
#202988492
#202988482
#106×D1132
#102×D1132
#469×C1132
C2×#469113