Finite Group Databasebeta

← #469×D103 #27204736

Subgroups — #469×D103 #27204736

Order 13184.

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×D103C211yesmaximal, characteristic, complemented
2C2×M16×D103C211yesmaximal, characteristic, complemented
3#121×D103C212yesmaximal, complemented
4#20268045C211yesmaximal, characteristic, complemented
5#20268044C211yesmaximal, characteristic, complemented
6#20268043C212yesmaximal, complemented
7#20268042C212yesmaximal, complemented
8#20268041C211yesmaximal, characteristic, complemented
9#106×D103C211yesmaximal, characteristic, complemented
10#102×D103C212yesmaximal, complemented
11#469×C103C211yesmaximal, characteristic, complemented
12C2×D4×D103—22no—
13C2×D4×D103C2212yes—
14C22×C4×D103C2211yescharacteristic
15C2×D824C2211yescharacteristic, complemented
16C2×#13110090C2212yescomplemented
17D8×D103—24no—
18C2×#13110089C2211yescharacteristic, complemented
19C2×#13110088C2211yescharacteristic, complemented
20C2×#13110088C2211yescharacteristic, complemented
21M16×D103—24no—
22C2×C8×D103C2211yescharacteristic
23C2×C8×D103C2211yescharacteristic
24#15692996C2212yescomplemented
25#15692995C2212yescomplemented
26#15692994—22no—
27#15692993—22no—
28#15692992C2212yescomplemented
29C4⋊C4×D103C2212yes—
30C22⋊C4×D103—22no—
31#15692953C2211yescharacteristic, complemented
32#15692952C2212yescomplemented
33#15692943C2212yescomplemented
34#15692942C2212yescomplemented
35#15692941C2212yescomplemented
36C2×D8×C103C2211yescharacteristic, complemented
37C2×M16×C103C2211yescharacteristic, complemented
38#121×C103C2212yescomplemented
39#106×C103C2211yescharacteristic, complemented
40#102×C103C2212yescomplemented
41C23×D103—22no—
42C23×D103D411yescharacteristic
43C2×D412—22no—
44C2×D412C2312yes—
45C2×C22⋊D103—22no—
46C2×C22⋊D103—22no—
47C2×C22⋊D103—22no—
48D4×D103—24no—
49D4×D103—24no—
50D4×D103—48no—
51C22×Dic103D411yescharacteristic
52C2×C4×D103—22no—
53C2×C4×D103—22no—
54C2×C4×D103—22no—
55C2×C4×D103D411yescharacteristic
56C2×C4×D103D411yescharacteristic
57C2×C4×D103C2311yescharacteristic
58C2×C4×D103C2311yescharacteristic
59D824—22no—
60#13110090—24no—
61#13110089—22no—
62#13110088—22no—
63#13110088—22no—
64C2×C103⋊C8C2311yescharacteristic
65C2×C103⋊C8C2311yescharacteristic
66C8×D103—22no—
67C8×D103D414yescomplemented
68C4⋊Dic103C2312yes—
69Dic103⋊C4—22no—
70C22⋊Dic103—22no—
71(C2×D103)⋊C4—22no—
72(C2×D103)⋊C4—22no—
73C2×D4×C103—22no—
74C2×D4×C103C2312yes—
75C22×C4×C103C2311yescharacteristic
76D8×C103—22no—
77M16×C103—22no—
78C2×C8×C103C2311yescharacteristic
79C2×C8×C103C2311yescharacteristic
80C4⋊C4×C103C2312yes—
81C22⋊C4×C103—22no—
82C23×C103—22no—
83C23×C103C2×D411yescharacteristic
84C22×D103—22no—
85C22×D103—24no—
86C22×D103—22no—
87C22×D103—44no—
88C22×D103—44no—
89C22×D103—44no—
90C22×D103C2×D411yescharacteristic
91C22×D103C2×D411yescharacteristic
92D4×C103—22no—
93D4×C103—22no—
94D4×C103—44no—
95C2×C4×C103—21no—
96C2×C4×C103—21no—
97C2×C4×C103—22no—
98C2×C4×C103C2×D411yescharacteristic
99C2×C4×C103C2411yescharacteristic
100C22⋊D103—44no—
101C22⋊D103—44no—
102C22⋊D103—44no—
103C2×Dic103—22no—
104C2×Dic103—22no—
105C2×Dic103C2×D411yescharacteristic
106C2×Dic103C2×D411yescharacteristic
107D412—22no—
108D412—22no—
109D412—44no—
110C4×D103—22no—
111C4×D103—21no—
112C4×D103—21no—
113C4×D103—22no—
114C4×D103—44no—
115C4×D103C2×D412yes—
116C4×D103#4112yes—
117C8×C103—21no—
118C8×C103C2×D412yescomplemented
119C103⋊C8—21no—
120C103⋊C8C2×D412yescomplemented
121C22×C103—21no—
122C22×C103—22no—
123C22×C103—42no—
124C22×C103—42no—
125C22×C103—42no—
126C22×C103C22×D411yescharacteristic
127C2×D103—21no—
128C2×D103—22no—
129C2×D103—44no—
130C2×D103—42no—
131C2×D103—42no—
132C2×D103—42no—
133C2×D103—88no—
134C2×D103#12112yes—
135C2×D103AGL(1,ℤ/8)14yes—
136C4×C103—21no—
137C4×C103—42no—
138C4×C103C22×D411yescharacteristic
139C4×C103C2×#4111yescharacteristic
140Dic103—21no—
141Dic103—42no—
142Dic103#12112yes—
143C2×C103—41no—
144C2×C103—82no—
145C2×C103C2×#12111yescharacteristic
146C2×C103C2×AGL(1,ℤ/8)12yes—
147D103—41no—
148D103—82no—
149D103#46914yesdirect product factor
150C2×#469—1031nomaximal, Sylow
151C103C2×#46911yescharacteristic, complemented, Sylow
152C22×D8—1031no—
153C22×M16—1031no—
154C2×#121—1032no—
155#469—1031no—
156#469—1031no—
157#469—1032no—
158#469—1031no—
159#469—1032no—
160#469D10311yescharacteristic, direct product factor
161C2×#106—1031no—
162C2×#102—1032no—
163C22×D4—1032no—
164C22×D4—2062no—
165C23×C4—1031no—
166C2×D8—1032no—
167C2×D8—1031no—
168C2×D8—2064no—
169C2×D8C2×D10311yescharacteristic, complemented
170C2×M16—1031no—
171C2×M16—1031no—
172C2×M16—1031no—
173C2×M16—2064no—
174C2×M16C2×D10311yescharacteristic, complemented
175C22×C8—1031no—
176C22×C8—1031no—
177#121—1032no—
178#121—1032no—
179#121—1032no—
180#121—2062no—
181#121—2062no—
182#121C2×D10312yescomplemented
183C2×C4⋊C4—1032no—
184C2×C22⋊C4—2062no—
185#106—1031no—
186#106—1032no—
187#106C2×D10311yescharacteristic, complemented
188#102—1032no—
189#102—1032no—
190#102—1032no—
191#102C2×D10312yescomplemented
192C24—1031no—
193C24—2062no—
194C2×D4—22no—
195C2×D4—1032no—
196C2×D4—4128no—
197C2×D4—2062no—
198C2×D4—2064no—
199C2×D4—2064no—
200C2×D4—2062no—
201C2×D4—2062no—
202C2×D4—2062no—
203C2×D4C22×D10312yes—
204C22×C4—1031no—
205C22×C4—1031no—
206C22×C4—1031no—
207C22×C4—1031no—
208C22×C4—1031no—
209C22×C4—2062no—
210C22×C4—2062no—
211C22×C4—2062no—
212C22×C4C22×D10311yescharacteristic
213D8—22no—
214D8—2064no—
215D8—2062no—
216M16—22no—
217M16—2062no—
218M16—2062no—
219M16—2062no—
220C2×C8—1031no—
221C2×C8—1034no—
222C2×C8—1031no—
223C2×C8—2062no—
224C2×C8C22×D10311yescharacteristic
225C2×C8C22×D10311yescharacteristic
226C4⋊C4—1032no—
227C4⋊C4—2062no—
228C4⋊C4C22×D10312yes—
229C22⋊C4—22no—
230C22⋊C4—2062no—
231C22⋊C4—2062no—
232C22⋊C4—2062no—
233C23—22no—
234C23—1031no—
235C23—1031no—
236C23—4124no—
237C23—4124no—
238C23—4124no—
239C23—2062no—
240C23—2064no—
241C23—2062no—
242C23D4×D10311yescharacteristic
243D4—22no—
244D4—22no—
245D4—44no—
246D4—4124no—
247D4—4124no—
248D4—4124no—
249D4—4124no—
250D4—2062no—
251D4—2062no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—22no—
255C2×C4—1031no—
256C2×C4—1032no—
257C2×C4—1032no—
258C2×C4—1031no—
259C2×C4—4124no—
260C2×C4—2062no—
261C2×C4—2062no—
262C2×C4—2062no—
263C2×C4—2062no—
264C2×C4—2061no—
265C2×C4—2061no—
266C2×C4D4×D10311yescharacteristic
267C2×C4C23×D10311yescharacteristic
268C8—21no—
269C8—1032no—
270C8—2061no—
271C8D4×D10312yescomplemented
272C22—22no—
273C22—21no—
274C22—42no—
275C22—42no—
276C22—42no—
277C22—8248no—
278C22—1034no—
279C22—1032no—
280C22—4124no—
281C22—4122no—
282C22—4122no—
283C22—4122no—
284C22—2062no—
285C22—2061no—
286C22C2×D4×D10311yescharacteristic
287C4—21no—
288C4—42no—
289C4—1032no—
290C4—4122no—
291C4—2061no—
292C4C2×D4×D10311yescharacteristic
293C4#41×D10311yescharacteristic
294C2—41no—
295C2—82no—
296C2—8242no—
297C2—1034no—
298C2—4121no—
299C2#121×D10311yescharacteristic
300C2AGL(1,ℤ/8)×D10312yes—
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#469×C103C2
socleC22×C103C22×D4
hypercenter#469D103
hypocenterC103C2×#469
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. C2×D8×D103C2semidirect
2. C2×M16×D103C2semidirect
3. #121×D103C2semidirect
4. #20268045C2semidirect
5. #20268044C2semidirect
6. #20268043C2semidirect
7. #20268042C2semidirect
8. #20268041C2semidirect
9. #106×D103C2semidirect
10. #102×D103C2semidirect
11. #469×C103C2semidirect
15. C2×D824C22semidirect
16. C2×#13110090C22semidirect
18. C2×#13110089C22semidirect
19. C2×#13110088C22semidirect
20. C2×#13110088C22semidirect
24. #15692996C22semidirect
25. #15692995C22semidirect
28. #15692992C22semidirect
31. #15692953C22semidirect
32. #15692952C22semidirect
33. #15692943C22semidirect
34. #15692942C22semidirect
35. #15692941C22semidirect
36. C2×D8×C103C22semidirect
37. C2×M16×C103C22semidirect
38. #121×C103C22semidirect
39. #106×C103C22semidirect
40. #102×C103C22semidirect
67. C8×D103D4semidirect
118. C8×C103C2×D4semidirect
120. C103⋊C8C2×D4semidirect
149. D103#469direct (N × H)
151. C103C2×#469semidirect
160. #469D103direct (N × H)
169. C2×D8C2×D103semidirect
174. C2×M16C2×D103semidirect
182. #121C2×D103semidirect
187. #106C2×D103semidirect
191. #102C2×D103semidirect
271. C8D4×D103semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D1032
C2×M16×D1032
#121×D1032
#202680452
#202680442
#202680432
#202680422
#202680412
#106×D1032
#102×D1032
#469×C1032
C2×#469103