Finite Group Databasebeta

← #31816539

Subgroups — #31816539

Order 17792.

450 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 117 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#22581484C211yesmaximal, characteristic, complemented
2C2×#17984804C211yesmaximal, characteristic, complemented
3#22581283C211yesmaximal, characteristic, complemented
4#22581256C212yesmaximal, complemented
5#22581167C212yesmaximal, complemented
6#22581106C211yesmaximal, characteristic, complemented
7#22581086C211yesmaximal, characteristic
8#22581062C212yesmaximal, complemented
9#22581052C212yesmaximal, complemented
10#22581007C211yesmaximal, characteristic, complemented
11#480×C139C211yesmaximal, characteristic, complemented
12C22×D556C2211yescharacteristic
13C22×C4×D139—21no—
14C2×#14555774C2212yes—
15C2×#14555770C2212yes—
16#17984835—21no—
17#17984833C2211yescharacteristic, complemented
18#17984829C2211yescharacteristic, complemented
19#17984823—21no—
20#17984821C2211yescharacteristic
21#17984807C2211yescharacteristic, complemented
22D4×Dic139—21no—
23D4×Dic139C2211yescharacteristic, complemented
24#17984804—21no—
25#17984804—21no—
26#17984804C2212yes—
27#17984804C2212yes—
28#17984798—21no—
29C2×(C2×D139)⋊C4—21no—
30C2×C4×Dic139C2211yescharacteristic
31#17984773C2212yescomplemented
32Dic139⋊C8C2212yescomplemented
33#17984765C2212yescomplemented
34#17984764C2212yes—
35#17984762C2212yes—
36C22⋊(C139⋊C8)C2211yescharacteristic
37#17984752C2212yescomplemented
38#121×C139C2211yescharacteristic
39C2×C4⋊C4×C139C2211yescharacteristic
40#107×C139C2212yescomplemented
41#102×C139C2212yescomplemented
42C22⋊C8×C139C2211yescharacteristic
43C23×D139—21no—
44C2×Dic278C2311yescharacteristic
45C2×D556—24no—
46C2×D556—21no—
47C2×D556C2312yes—
48C22×Dic139—21no—
49C22×Dic139D411yescharacteristic
50C22×Dic139D411yescharacteristic
51C2×C4×D139—22no—
52C2×C4×D139—22no—
53C2×C4×D139—44no—
54#14555774—24no—
55#14555770—24no—
56C2×C139⋊C8C2312yes—
57C4⋊Dic139—21no—
58C4⋊Dic139C2311yescharacteristic
59Dic139⋊C4—21no—
60Dic139⋊C4—21no—
61Dic139⋊C4—21no—
62C22⋊Dic139—21no—
63C22⋊Dic139—21no—
64C22⋊Dic139—21no—
65C22⋊Dic139—21no—
66(C2×D139)⋊C4—22no—
67(C2×D139)⋊C4—22no—
68C4×Dic139—21no—
69C4×Dic139D411yescharacteristic
70C4×Dic139D411yescharacteristic
71C4×Dic139C2311yescharacteristic
72C4×Dic139C2311yescharacteristic
73C2×D4×C139—21no—
74C2×D4×C139C2311yescharacteristic
75C22×C4×C139—21no—
76C22×C4×C139C2311yescharacteristic
77C2×C8×C139C2312yes—
78C4⋊C4×C139—21no—
79C4⋊C4×C139C2312yes—
80C4⋊C4×C139C2311yescharacteristic
81C22⋊C4×C139—21no—
82C22×D139—24no—
83C22×D139—22no—
84C22×D139—42no—
85C22×D139—42no—
86Dic278—22no—
87D556—24no—
88D556—22no—
89D556#4114yes—
90C2×Dic139—22no—
91C2×Dic139—21no—
92C2×Dic139—21no—
93C2×Dic139—41no—
94C2×Dic139—42no—
95C2×Dic139C2×D411yescharacteristic
96C2×Dic139C2×D411yescharacteristic
97C2×Dic139C2×D411yescharacteristic
98C2×Dic139C2×D411yescharacteristic
99C4×D139—44no—
100C4×D139—44no—
101C139⋊C8—22no—
102C23×C139—21no—
103C23×C139C2×D411yescharacteristic
104D4×C139—22no—
105D4×C139—42no—
106C2×C4×C139—22no—
107C2×C4×C139—21no—
108C2×C4×C139—22no—
109C2×C4×C139—42no—
110C2×C4×C139C2×D411yescharacteristic
111C2×C4×C139C2411yescharacteristic
112C8×C139—22no—
113C22×C139—21no—
114C22×C139—21no—
115C22×C139—41no—
116C22×C139—41no—
117C22×C139—41no—
118C22×C139AGL(1,ℤ/8)12yes—
119C22×C139C22×D411yescharacteristic
120C2×D139—24no—
121C2×D139—48no—
122C2×D139—42no—
123C2×D139—42no—
124C4×C139—21no—
125C4×C139—42no—
126C4×C139—41no—
127C4×C139C2×#4112yes—
128Dic139—21no—
129Dic139—21no—
130Dic139—21no—
131Dic139—21no—
132Dic139—41no—
133Dic139—41no—
134C2×C139—22no—
135C2×C139—81no—
136C2×C139#52511yescharacteristic
137C2×C139C2×AGL(1,ℤ/8)11yescharacteristic
138C2×C139#57511yescharacteristic
139D139—44no—
140C139#311411yescharacteristic, complemented, Sylow
141#3114—1391nomaximal, Sylow
142#529—1391no—
143C2×C4×D4—1391no—
144#483—1391no—
145#480D13911yescharacteristic, complemented
146#478—1392no—
147#463—1392no—
148#450—1391no—
149#447—1391no—
150#442—1392no—
151#440—1392no—
152#432—1391no—
153C22×D4—1391no—
154C23×C4—2781no—
155C2×SD16—1392no—
156C2×D8—1392no—
157#126—2781no—
158#125—1391no—
159#124—1391no—
160#123—2781no—
161C22⋊Q8—1391no—
162#121C2×D13911yescharacteristic
163C4×Q8—1391no—
164C4×D4—2781no—
165C4×D4—2781no—
166C4×D4—2781no—
167C4×D4—1391no—
168C4×D4—1392no—
169C4×D4—1392no—
170#117—2781no—
171C2×C4⋊C4C2×D13911yescharacteristic
172C2×C22⋊C4—2781no—
173C2×C42—1391no—
174#107C2×D13912yescomplemented
175#106—1392no—
176C4⋊C8—1392no—
177#103—1392no—
178#102—1392no—
179#102—1392no—
180#102C2×D13912yescomplemented
181C22⋊C8—1391no—
182C22⋊C8C2×D13911yescharacteristic
183#97—1392no—
184C24—2781no—
185C2×Q8—1391no—
186C2×D4—21no—
187C2×D4—2784no—
188C2×D4—2781no—
189C2×D4—1392no—
190C2×D4C22×D13911yescharacteristic
191C22×C4—21no—
192C22×C4—2782no—
193C22×C4—2782no—
194C22×C4—2781no—
195C22×C4—5564no—
196C22×C4—1391no—
197C22×C4—1391no—
198C22×C4C22×D13911yescharacteristic
199SD16—2784no—
200D8—2784no—
201C2×C8—1392no—
202C2×C8C22×D13912yes—
203C4⋊C4—21no—
204C4⋊C4—2781no—
205C4⋊C4—2781no—
206C4⋊C4—2781no—
207C4⋊C4—2781no—
208C4⋊C4—1391no—
209C4⋊C4C22×D13911yescharacteristic
210C4⋊C4C22×D13912yes—
211C22⋊C4—21no—
212C22⋊C4—2782no—
213C22⋊C4—2782no—
214C22⋊C4—2781no—
215C22⋊C4—2781no—
216C22⋊C4—2781no—
217C22⋊C4—2781no—
218C42—2781no—
219C42—1391no—
220C42—1391no—
221C42—1391no—
222C42—1391no—
223C23—21no—
224C23—2784no—
225C23—2782no—
226C23—5562no—
227C23—5562no—
228C23D4×D13911yescharacteristic
229Q8—2782no—
230D4—22no—
231D4—42no—
232D4—2784no—
233D4—2782no—
234D4—1394no—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—42no—
239C2×C4—2782no—
240C2×C4—2781no—
241C2×C4—2781no—
242C2×C4—5564no—
243C2×C4—5564no—
244C2×C4—5561no—
245C2×C4—5562no—
246C2×C4—1391no—
247C2×C4—1391no—
248C2×C4—1391no—
249C2×C4—1391no—
250C2×C4D4×D13911yescharacteristic
251C2×C4C23×D13911yescharacteristic
252C8—22no—
253C8—2782no—
254C22—21no—
255C22—21no—
256C22—41no—
257C22—41no—
258C22—41no—
259C22—2784no—
260C22—5568no—
261C22—5562no—
262C22—5562no—
263C22#1798486612yes—
264C22C2×D4×D13911yescharacteristic
265C4—21no—
266C4—42no—
267C4—41no—
268C4—2781no—
269C4—2781no—
270C4—2781no—
271C4—2781no—
272C4—5561no—
273C4—5561no—
274C4#41×D13912yes—
275C2—22no—
276C2—81no—
277C2—5564no—
278C2#2258146111yescharacteristic
279C2C2×#1798486611yescharacteristic
280C2#2258175211yescharacteristic
subgroupG/H
centerC22C2×D4×D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#480×C139C2
socleC22×C139C22×D4
prime radical#22581086C2
hypercenter#480D139
hypocenterC139#3114
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. #22581484C2semidirect
2. C2×#17984804C2semidirect
3. #22581283C2semidirect
4. #22581256C2semidirect
5. #22581167C2semidirect
6. #22581106C2semidirect
8. #22581062C2semidirect
9. #22581052C2semidirect
10. #22581007C2semidirect
11. #480×C139C2semidirect
17. #17984833C22semidirect
18. #17984829C22semidirect
21. #17984807C22semidirect
23. D4×Dic139C22semidirect
31. #17984773C22semidirect
32. Dic139⋊C8C22semidirect
33. #17984765C22semidirect
37. #17984752C22semidirect
40. #107×C139C22semidirect
41. #102×C139C22semidirect
140. C139#3114semidirect
145. #480D139semidirect
174. #107C2×D139semidirect
180. #102C2×D139semidirect

Maximal subgroups

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

subgroupindex
#225814842
C2×#179848042
#225812832
#225812562
#225811672
#225811062
#225810862
#225810622
#225810522
#225810072
#480×C1392
#3114139