Finite Group Databasebeta

← #469×D139 #31815996

Subgroups — #469×D139 #31815996

Order 17792.

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×D139C211yesmaximal, characteristic, complemented
2C2×M16×D139C211yesmaximal, characteristic, complemented
3#121×D139C212yesmaximal, complemented
4#22581207C211yesmaximal, characteristic, complemented
5#22581206C211yesmaximal, characteristic, complemented
6#22581205C212yesmaximal, complemented
7#22581204C212yesmaximal, complemented
8#22581203C211yesmaximal, characteristic, complemented
9#106×D139C211yesmaximal, characteristic, complemented
10#102×D139C212yesmaximal, complemented
11#469×C139C211yesmaximal, characteristic, complemented
12C2×D4×D139—22no—
13C2×D4×D139C2212yes—
14C22×C4×D139C2211yescharacteristic
15C2×D1112C2211yescharacteristic, complemented
16C2×#14555770C2212yescomplemented
17D8×D139—24no—
18C2×#14555769C2211yescharacteristic, complemented
19C2×#14555768C2211yescharacteristic, complemented
20C2×#14555768C2211yescharacteristic, complemented
21M16×D139—24no—
22C2×C8×D139C2211yescharacteristic
23C2×C8×D139C2211yescharacteristic
24#17984817C2212yescomplemented
25#17984816C2212yescomplemented
26#17984815—22no—
27#17984814—22no—
28#17984813C2212yescomplemented
29C4⋊C4×D139C2212yes—
30C22⋊C4×D139—22no—
31#17984774C2211yescharacteristic, complemented
32#17984773C2212yescomplemented
33#17984764C2212yescomplemented
34#17984763C2212yescomplemented
35#17984762C2212yescomplemented
36C2×D8×C139C2211yescharacteristic, complemented
37C2×M16×C139C2211yescharacteristic, complemented
38#121×C139C2212yescomplemented
39#106×C139C2211yescharacteristic, complemented
40#102×C139C2212yescomplemented
41C23×D139—22no—
42C23×D139D411yescharacteristic
43C2×D556—22no—
44C2×D556C2312yes—
45C2×C22⋊D139—22no—
46C2×C22⋊D139—22no—
47C2×C22⋊D139—22no—
48D4×D139—24no—
49D4×D139—24no—
50D4×D139—48no—
51C22×Dic139D411yescharacteristic
52C2×C4×D139—22no—
53C2×C4×D139—22no—
54C2×C4×D139—22no—
55C2×C4×D139D411yescharacteristic
56C2×C4×D139D411yescharacteristic
57C2×C4×D139C2311yescharacteristic
58C2×C4×D139C2311yescharacteristic
59D1112—22no—
60#14555770—24no—
61#14555769—22no—
62#14555768—22no—
63#14555768—22no—
64C2×C139⋊C8C2311yescharacteristic
65C2×C139⋊C8C2311yescharacteristic
66C8×D139—22no—
67C8×D139D414yescomplemented
68C4⋊Dic139C2312yes—
69Dic139⋊C4—22no—
70C22⋊Dic139—22no—
71(C2×D139)⋊C4—22no—
72(C2×D139)⋊C4—22no—
73C2×D4×C139—22no—
74C2×D4×C139C2312yes—
75C22×C4×C139C2311yescharacteristic
76D8×C139—22no—
77M16×C139—22no—
78C2×C8×C139C2311yescharacteristic
79C2×C8×C139C2311yescharacteristic
80C4⋊C4×C139C2312yes—
81C22⋊C4×C139—22no—
82C22×D139—22no—
83C22×D139—24no—
84C22×D139—22no—
85C22×D139—44no—
86C22×D139—44no—
87C22×D139—44no—
88C22×D139C2×D411yescharacteristic
89C22×D139C2×D411yescharacteristic
90D556—22no—
91D556—22no—
92D556—44no—
93C22⋊D139—44no—
94C22⋊D139—44no—
95C22⋊D139—44no—
96C2×Dic139—22no—
97C2×Dic139—22no—
98C2×Dic139C2×D411yescharacteristic
99C2×Dic139C2×D411yescharacteristic
100C4×D139—22no—
101C4×D139—21no—
102C4×D139—21no—
103C4×D139—22no—
104C4×D139—44no—
105C4×D139C2×D412yes—
106C4×D139#4112yes—
107C139⋊C8—21no—
108C139⋊C8C2×D412yescomplemented
109C23×C139—22no—
110C23×C139C2×D411yescharacteristic
111D4×C139—22no—
112D4×C139—22no—
113D4×C139—44no—
114C2×C4×C139—21no—
115C2×C4×C139—21no—
116C2×C4×C139—22no—
117C2×C4×C139C2×D411yescharacteristic
118C2×C4×C139C2411yescharacteristic
119C8×C139—21no—
120C8×C139C2×D412yescomplemented
121C22×C139—21no—
122C22×C139—22no—
123C22×C139—42no—
124C22×C139—42no—
125C22×C139—42no—
126C22×C139C22×D411yescharacteristic
127C2×D139—21no—
128C2×D139—22no—
129C2×D139—44no—
130C2×D139—42no—
131C2×D139—42no—
132C2×D139—42no—
133C2×D139—88no—
134C2×D139#12112yes—
135C2×D139AGL(1,ℤ/8)14yes—
136C4×C139—21no—
137C4×C139—42no—
138C4×C139C22×D411yescharacteristic
139C4×C139C2×#4111yescharacteristic
140Dic139—21no—
141Dic139—42no—
142Dic139#12112yes—
143C2×C139—41no—
144C2×C139—82no—
145C2×C139C2×#12111yescharacteristic
146C2×C139C2×AGL(1,ℤ/8)12yes—
147D139—41no—
148D139—82no—
149D139#46914yesdirect product factor
150C139C2×#46911yescharacteristic, complemented, Sylow
151C2×#469—1391nomaximal, Sylow
152C22×D8—1391no—
153C22×M16—1391no—
154C2×#121—1392no—
155#469—1391no—
156#469—1391no—
157#469—1392no—
158#469—1391no—
159#469—1392no—
160#469D13911yescharacteristic, direct product factor
161C2×#106—1391no—
162C2×#102—1392no—
163C22×D4—2782no—
164C22×D4—1392no—
165C23×C4—1391no—
166C2×D8—2784no—
167C2×D8—1392no—
168C2×D8—1391no—
169C2×D8C2×D13911yescharacteristic, complemented
170C2×M16—2784no—
171C2×M16—1391no—
172C2×M16—1391no—
173C2×M16—1391no—
174C2×M16C2×D13911yescharacteristic, complemented
175C22×C8—1391no—
176C22×C8—1391no—
177#121—2782no—
178#121—2782no—
179#121—1392no—
180#121—1392no—
181#121—1392no—
182#121C2×D13912yescomplemented
183C2×C4⋊C4—1392no—
184C2×C22⋊C4—2782no—
185#106—1391no—
186#106—1392no—
187#106C2×D13911yescharacteristic, complemented
188#102—1392no—
189#102—1392no—
190#102—1392no—
191#102C2×D13912yescomplemented
192C24—2782no—
193C24—1391no—
194C2×D4—22no—
195C2×D4—2782no—
196C2×D4—2782no—
197C2×D4—2782no—
198C2×D4—2784no—
199C2×D4—2784no—
200C2×D4—2782no—
201C2×D4—5568no—
202C2×D4—1392no—
203C2×D4C22×D13912yes—
204C22×C4—2782no—
205C22×C4—2782no—
206C22×C4—2782no—
207C22×C4—1391no—
208C22×C4—1391no—
209C22×C4—1391no—
210C22×C4—1391no—
211C22×C4—1391no—
212C22×C4C22×D13911yescharacteristic
213D8—22no—
214D8—2784no—
215D8—2782no—
216M16—22no—
217M16—2782no—
218M16—2782no—
219M16—2782no—
220C2×C8—2782no—
221C2×C8—1391no—
222C2×C8—1391no—
223C2×C8—1394no—
224C2×C8C22×D13911yescharacteristic
225C2×C8C22×D13911yescharacteristic
226C4⋊C4—2782no—
227C4⋊C4—1392no—
228C4⋊C4C22×D13912yes—
229C22⋊C4—22no—
230C22⋊C4—2782no—
231C22⋊C4—2782no—
232C22⋊C4—2782no—
233C23—22no—
234C23—2782no—
235C23—2784no—
236C23—2782no—
237C23—5564no—
238C23—5564no—
239C23—5564no—
240C23—1391no—
241C23—1391no—
242C23D4×D13911yescharacteristic
243D4—22no—
244D4—22no—
245D4—44no—
246D4—2782no—
247D4—2782no—
248D4—5564no—
249D4—5564no—
250D4—5564no—
251D4—5564no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—22no—
255C2×C4—2782no—
256C2×C4—2782no—
257C2×C4—2782no—
258C2×C4—2781no—
259C2×C4—2781no—
260C2×C4—2782no—
261C2×C4—5564no—
262C2×C4—1391no—
263C2×C4—1391no—
264C2×C4—1392no—
265C2×C4—1392no—
266C2×C4D4×D13911yescharacteristic
267C2×C4C23×D13911yescharacteristic
268C8—21no—
269C8—2781no—
270C8—1392no—
271C8D4×D13912yescomplemented
272C22—21no—
273C22—22no—
274C22—42no—
275C22—42no—
276C22—42no—
277C22—2781no—
278C22—2782no—
279C22—5564no—
280C22—5562no—
281C22—5562no—
282C22—5562no—
283C22—11128no—
284C22—1392no—
285C22—1394no—
286C22C2×D4×D13911yescharacteristic
287C4—21no—
288C4—42no—
289C4—2781no—
290C4—5562no—
291C4—1392no—
292C4C2×D4×D13911yescharacteristic
293C4#41×D13911yescharacteristic
294C2—41no—
295C2—82no—
296C2—5561no—
297C2—11122no—
298C2—1394no—
299C2#121×D13911yescharacteristic
300C2AGL(1,ℤ/8)×D13912yes—
subgroupG/H
centerC22C2×D4×D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#469×C139C2
socleC22×C139C22×D4
hypercenter#469D139
hypocenterC139C2×#469
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. C2×D8×D139C2semidirect
2. C2×M16×D139C2semidirect
3. #121×D139C2semidirect
4. #22581207C2semidirect
5. #22581206C2semidirect
6. #22581205C2semidirect
7. #22581204C2semidirect
8. #22581203C2semidirect
9. #106×D139C2semidirect
10. #102×D139C2semidirect
11. #469×C139C2semidirect
15. C2×D1112C22semidirect
16. C2×#14555770C22semidirect
18. C2×#14555769C22semidirect
19. C2×#14555768C22semidirect
20. C2×#14555768C22semidirect
24. #17984817C22semidirect
25. #17984816C22semidirect
28. #17984813C22semidirect
31. #17984774C22semidirect
32. #17984773C22semidirect
33. #17984764C22semidirect
34. #17984763C22semidirect
35. #17984762C22semidirect
36. C2×D8×C139C22semidirect
37. C2×M16×C139C22semidirect
38. #121×C139C22semidirect
39. #106×C139C22semidirect
40. #102×C139C22semidirect
67. C8×D139D4semidirect
108. C139⋊C8C2×D4semidirect
120. C8×C139C2×D4semidirect
149. D139#469direct (N × H)
150. C139C2×#469semidirect
160. #469D139direct (N × H)
169. C2×D8C2×D139semidirect
174. C2×M16C2×D139semidirect
182. #121C2×D139semidirect
187. #106C2×D139semidirect
191. #102C2×D139semidirect
271. C8D4×D139semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D1392
C2×M16×D1392
#121×D1392
#225812072
#225812062
#225812052
#225812042
#225812032
#106×D1392
#102×D1392
#469×C1392
C2×#469139