Finite Group Databasebeta

← #31816500

Subgroups — #31816500

Order 17792.

444 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 119 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#22581505C211yesmaximal, characteristic, complemented
2C2×#17984804C211yesmaximal, characteristic
3#22581288C211yesmaximal, characteristic, complemented
4#22581232C212yesmaximal, complemented
5#22581157C212yesmaximal, complemented
6#22581106C211yesmaximal, characteristic
7#22581103C211yesmaximal, characteristic
8#22581056C212yesmaximal, complemented
9#22581052C212yesmaximal, complemented
10#22581007C211yesmaximal, characteristic, complemented
11#484×C139C211yesmaximal, characteristic, complemented
12C22×D556C2211yescharacteristic
13C22×C4×D139—21no—
14C2×#14555774C2212yes—
15C2×#14555772C2212yes—
16#17984841C2211yescharacteristic, complemented
17#17984840C2211yescharacteristic, complemented
18#17984832—21no—
19#17984821C2211yescharacteristic
20#17984819—21no—
21Q8×Dic139C2211yescharacteristic, complemented
22#17984807—21no—
23#17984807C2211yescharacteristic, complemented
24#17984804—21no—
25#17984804—21no—
26#17984804C2212yes—
27#17984804C2212yes—
28#17984798—21no—
29C2×(C2×D139)⋊C4—21no—
30C2×C4×Dic139C2211yescharacteristic
31#17984775C2212yescomplemented
32Dic139⋊C8C2212yescomplemented
33#17984765C2212yescomplemented
34#17984764C2212yes—
35#17984762C2212yes—
36C22⋊(C139⋊C8)C2211yescharacteristic
37#17984752C2212yescomplemented
38C22⋊Q8×C139C2211yescharacteristic
39C2×C4⋊C4×C139C2211yescharacteristic
40#107×C139C2212yescomplemented
41#103×C139C2212yescomplemented
42C22⋊C8×C139C2211yescharacteristic
43C23×D139—21no—
44C2×Dic278—21no—
45C2×Dic278C2311yescharacteristic
46C2×D556—24no—
47C2×D556—21no—
48C2×D556C2312yes—
49C22×Dic139D411yescharacteristic
50C22×Dic139D411yescharacteristic
51C2×C4×D139—22no—
52C2×C4×D139—22no—
53C2×C4×D139—44no—
54#14555774—24no—
55#14555772—24no—
56C2×C139⋊C8C2312yes—
57C4⋊Dic139—21no—
58C4⋊Dic139C2311yescharacteristic
59Dic139⋊C4—21no—
60Dic139⋊C4—21no—
61Dic139⋊C4—21no—
62Dic139⋊C4—21no—
63Dic139⋊C4—21no—
64C22⋊Dic139—21no—
65(C2×D139)⋊C4—22no—
66(C2×D139)⋊C4—22no—
67C4×Dic139—21no—
68C4×Dic139—21no—
69C4×Dic139D411yescharacteristic
70C4×Dic139D411yescharacteristic
71C4×Dic139C2311yescharacteristic
72C4×Dic139C2311yescharacteristic
73C2×Q8×C139C2311yescharacteristic
74C22×C4×C139—21no—
75C22×C4×C139C2311yescharacteristic
76C2×C8×C139C2312yes—
77C4⋊C4×C139—21no—
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—
87Dic278—42no—
88D556—24no—
89D556—22no—
90D556#4114yes—
91C2×Dic139—22no—
92C2×Dic139—22no—
93C2×Dic139—21no—
94C2×Dic139—21no—
95C2×Dic139C2×D411yescharacteristic
96C2×Dic139C2×D411yescharacteristic
97C2×Dic139C2×D411yescharacteristic
98C2×Dic139C2×D411yescharacteristic
99C4×D139—44no—
100C4×D139—44no—
101C139⋊C8—22no—
102C23×C139C2×D411yescharacteristic
103Q8×C139—22no—
104C2×C4×C139—22no—
105C2×C4×C139—21no—
106C2×C4×C139—21no—
107C2×C4×C139—22no—
108C2×C4×C139—42no—
109C2×C4×C139C2×D411yescharacteristic
110C2×C4×C139C2411yescharacteristic
111C8×C139—22no—
112C22×C139—21no—
113C22×C139—21no—
114C22×C139#13712yes—
115C22×C139C22×D411yescharacteristic
116C2×D139—24no—
117C2×D139—48no—
118C2×D139—42no—
119C2×D139—42no—
120C4×C139—21no—
121C4×C139—41no—
122C4×C139—42no—
123C4×C139—41no—
124C4×C139C2×#4112yes—
125Dic139—21no—
126Dic139—21no—
127Dic139—21no—
128Dic139—41no—
129Dic139—41no—
130Dic139AGL(1,ℤ/8)12yes—
131C2×C139—22no—
132C2×C139#52511yescharacteristic
133C2×C139C2×AGL(1,ℤ/8)11yescharacteristic
134C2×C139C2×#13711yescharacteristic
135D139—44no—
136C139#311011yescharacteristic, complemented, Sylow
137#3110—1391nomaximal, Sylow
138#533—1391no—
139C2×C4×D4—1391no—
140#484—1391no—
141#484D13911yescharacteristic, complemented
142#474—1392no—
143#461—1392no—
144#450—1391no—
145#450—1391no—
146#440—1392no—
147#440—1392no—
148#432—1391no—
149C22×D4—1391no—
150C23×C4—2781no—
151C2×SD16—1392no—
152C2×SD16—1392no—
153C4⋊Q8—1391no—
154C4⋊Q8—1391no—
155#125—2781no—
156C22⋊Q8—2781no—
157C22⋊Q8—1391no—
158C22⋊Q8C2×D13911yescharacteristic
159C4×Q8—2781no—
160C4×Q8—1391no—
161C4×Q8—1391no—
162C4×D4—2781no—
163C4×D4—2781no—
164C4×D4—1392no—
165C4×D4—1392no—
166#117—2781no—
167C2×C4⋊C4C2×D13911yescharacteristic
168C2×C22⋊C4—2781no—
169C2×C42—1391no—
170#107—1392no—
171#107C2×D13912yescomplemented
172C4⋊C8—1392no—
173#103—1392no—
174#103C2×D13912yescomplemented
175#102—1392no—
176#102—1392no—
177C22⋊C8—1391no—
178C22⋊C8C2×D13911yescharacteristic
179#97—1392no—
180C24—2781no—
181C2×Q8—2781no—
182C2×Q8—1391no—
183C2×Q8C22×D13911yescharacteristic
184C2×D4—2784no—
185C2×D4—2781no—
186C2×D4—1392no—
187C22×C4—21no—
188C22×C4—2782no—
189C22×C4—2782no—
190C22×C4—5564no—
191C22×C4—1391no—
192C22×C4—1391no—
193C22×C4C22×D13911yescharacteristic
194SD16—2784no—
195SD16—2784no—
196C2×C8—1392no—
197C2×C8C22×D13912yes—
198C4⋊C4—21no—
199C4⋊C4—21no—
200C4⋊C4—2781no—
201C4⋊C4—2781no—
202C4⋊C4—2781no—
203C4⋊C4—2781no—
204C4⋊C4—2781no—
205C4⋊C4—2781no—
206C4⋊C4—1391no—
207C4⋊C4C22×D13911yescharacteristic
208C4⋊C4C22×D13912yes—
209C22⋊C4—21no—
210C22⋊C4—2782no—
211C22⋊C4—2782no—
212C22⋊C4—2781no—
213C42—2781no—
214C42—2781no—
215C42—1391no—
216C42—1391no—
217C42—1391no—
218C42—1391no—
219C23—2784no—
220C23—2782no—
221C23—5562no—
222C23—5562no—
223C23D4×D13911yescharacteristic
224Q8—22no—
225Q8—2782no—
226Q8—5562no—
227D4—2784no—
228D4—2782no—
229D4—1394no—
230C2×C4—22no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—42no—
235C2×C4—2782no—
236C2×C4—2782no—
237C2×C4—2781no—
238C2×C4—2781no—
239C2×C4—5564no—
240C2×C4—5564no—
241C2×C4—1391no—
242C2×C4—1391no—
243C2×C4—1391no—
244C2×C4—1391no—
245C2×C4D4×D13911yescharacteristic
246C2×C4C23×D13911yescharacteristic
247C8—22no—
248C8—2782no—
249C22—21no—
250C22—21no—
251C22—2784no—
252C22—5568no—
253C22—5562no—
254C22—5562no—
255C22#1798487412yes—
256C22C2×D4×D13911yescharacteristic
257C4—21no—
258C4—41no—
259C4—42no—
260C4—41no—
261C4—2781no—
262C4—2781no—
263C4—2781no—
264C4—5561no—
265C4—5561no—
266C4—1392no—
267C4#41×D13912yes—
268C2—22no—
269C2—5564no—
270C2#2258146111yescharacteristic
271C2AGL(1,ℤ/8)×D13911yescharacteristic
272C2C2×#1798487411yescharacteristic
subgroupG/H
centerC22C2×D4×D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#484×C139C2
socleC22×C139C22×D4
prime radicalC22×D556C22
hypercenter#484D139
hypocenterC139#3110
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
1. #22581505C2semidirect
3. #22581288C2semidirect
4. #22581232C2semidirect
5. #22581157C2semidirect
8. #22581056C2semidirect
9. #22581052C2semidirect
10. #22581007C2semidirect
11. #484×C139C2semidirect
16. #17984841C22semidirect
17. #17984840C22semidirect
21. Q8×Dic139C22semidirect
23. #17984807C22semidirect
31. #17984775C22semidirect
32. Dic139⋊C8C22semidirect
33. #17984765C22semidirect
37. #17984752C22semidirect
40. #107×C139C22semidirect
41. #103×C139C22semidirect
136. C139#3110semidirect
141. #484D139semidirect
171. #107C2×D139semidirect
174. #103C2×D139semidirect

Maximal subgroups

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

subgroupindex
#225815052
C2×#179848042
#225812882
#225812322
#225811572
#225811062
#225811032
#225810562
#225810522
#225810072
#484×C1392
#3110139