Finite Group Databasebeta

← #31815795

Subgroups — #31815795

Order 17792.

766 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 766 conjugacy classes of subgroups — too many to draw. Only its 145 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#22581789C211yesmaximal, characteristic, complemented
2#22581464C212yesmaximal, complemented
3#22581142C214yesmaximal, complemented
4#22581139C214yesmaximal, complemented
5#22580927C211yesmaximal, characteristic, complemented
6#22580926C212yesmaximal, complemented
7#525×C139C211yesmaximal, characteristic, complemented
8#17984890—21no—
9#17984889—22no—
10#17984888—22no—
11#17984887—21no—
12#17984887C2214yes—
13C2×#14555785—22no—
14C2×#14555785C2212yes—
15#41×D139—24no—
16#17984825C2214yescomplemented
17#17984821—22no—
18#17984816—22no—
19#17984811C2214yescomplemented
20C4×C22⋊D139—24no—
21#17984801C2212yescomplemented
22#17984757C2214yescomplemented
23#17984756C2218yescomplemented
24C2×#41×C139C2211yescharacteristic
25C23×C4×C139C2211yescharacteristic, complemented
26#123×C139C2212yescomplemented
27C22⋊Q8×C139—21no—
28#121×C139—21no—
29#120×C139C2212yescomplemented
30C4×D4×C139—22no—
31#117×C139C2211yescharacteristic, complemented
32#14555786—24no—
33#14555785—24no—
34#14555785—24no—
35#14555785—22no—
36#14555785—22no—
37#14555785—24no—
38#14555785—22no—
39#14555785—22no—
40#14555784—24no—
41#14555784—28no—
42C2×Dic278—22no—
43C2×Dic278D412yescomplemented
44Q8×D139—24no—
45C2×D556—22no—
46C2×D556D412yescomplemented
47C2×C22⋊D139—24no—
48C2×C22⋊D139—24no—
49C2×C22⋊D139C2314yes—
50D4×D139—24no—
51D4×D139—28no—
52C2×C4×D139—24no—
53C2×C4×D139D414yescomplemented
54C4⋊Dic139—22no—
55Dic139⋊C4—24no—
56C22⋊Dic139—24no—
57C22⋊Dic139C2314yes—
58(C2×D139)⋊C4—24no—
59C4×Dic139—22no—
60C24×C139C2311yescharacteristic
61#41×C139—22no—
62#41×C139—22no—
63C2×Q8×C139D411yescharacteristic, complemented
64C2×D4×C139—22no—
65C2×D4×C139D411yescharacteristic, complemented
66C2×D4×C139C2312yes—
67C22×C4×C139—22no—
68C22×C4×C139—22no—
69C22×C4×C139—21no—
70C22×C4×C139—21no—
71C22×C4×C139D412yescomplemented
72C22×C4×C139C2311yescharacteristic
73C22×C4×C139C2311yescharacteristic
74C4⋊C4×C139—21no—
75C4⋊C4×C139—22no—
76C22⋊C4×C139—22no—
77C22⋊C4×C139—22no—
78C22⋊C4×C139C2312yes—
79C42×C139—21no—
80C22×D139—24no—
81C22×D139C2×D414yes—
82Dic278—24no—
83Dic278—22no—
84Dic278—22no—
85D556—24no—
86D556—22no—
87D556—22no—
88C22⋊D139—28no—
89C22⋊D139—24no—
90C22⋊D139—24no—
91C22⋊D139—48no—
92C2×Dic139—24no—
93C2×Dic139—24no—
94C2×Dic139C2×D414yes—
95C4×D139—28no—
96C4×D139—24no—
97C4×D139—24no—
98C23×C139—21no—
99C23×C139—22no—
100C23×C139—42no—
101C23×C139C2×D412yes—
102C23×C139C2411yescharacteristic
103Q8×C139—22no—
104D4×C139—24no—
105D4×C139—22no—
106D4×C139—44no—
107C2×C4×C139—22no—
108C2×C4×C139—22no—
109C2×C4×C139—22no—
110C2×C4×C139—21no—
111C2×C4×C139—22no—
112C2×C4×C139—41no—
113C2×C4×C139—42no—
114C2×C4×C139—41no—
115C2×C4×C139C2×D412yes—
116C2×C4×C139C2×D412yes—
117C2×C4×C139C2×D412yes—
118C2×C4×C139C2×D411yescharacteristic
119C2×C4×C139C2×D411yescharacteristic
120C22×C139—22no—
121C22×C139—24no—
122C22×C139—22no—
123C22×C139—41no—
124C22×C139—42no—
125C22×C139—42no—
126C22×C139—41no—
127C22×C139—41no—
128C22×C139C22×D412yes—
129C22×C139C22×D411yescharacteristic
130C2×D139—24no—
131C2×D139—44no—
132C2×D139—84no—
133C4×C139—22no—
134C4×C139—42no—
135C4×C139—41no—
136C4×C139#12011yescharacteristic
137C4×C139#12012yes—
138C4×C139#12011yescharacteristic
139Dic139—24no—
140Dic139—44no—
141C2×C139—22no—
142C2×C139—21no—
143C2×C139—42no—
144C2×C139—42no—
145C2×C139C2×#12011yescharacteristic
146D139—44no—
147C139#302511yescharacteristic, complemented, Sylow
148#3025—1391nomaximal, Sylow
149#585—1391no—
150#525—1392no—
151#525D13911yescharacteristic, complemented
152#458—1394no—
153B(4,𝔽2)—1394no—
154#410—1391no—
155#410—1392no—
1562−1+4—2782no—
1572−1+4—2781no—
158H(5,𝔽2)—2782no—
159H(5,𝔽2)—2781no—
160H(5,𝔽2)—1394no—
161C2×#41—2784no—
162C2×#41—2782no—
163C2×#41—1392no—
164C2×#41C2×D13911yescharacteristic
165C23×C4C2×D13911yescharacteristic, complemented
166#123—1394no—
167#123C2×D13912yescomplemented
168C22⋊Q8—21no—
169C22⋊Q8—2782no—
170#121—21no—
171#121—2782no—
172#120—1394no—
173#120C2×D13912yescomplemented
174C4×D4—22no—
175C4×D4—2784no—
176#117—1392no—
177#117C2×D13911yescharacteristic, complemented
178#99—1394no—
179#99—1398no—
180C24C22×D13911yescharacteristic
181#41—22no—
182#41—22no—
183#41—2784no—
184#41—2784no—
185#41—2784no—
186#41—2784no—
187#41—2788no—
188#41—2782no—
189#41—2782no—
190#41—2782no—
191#41—2784no—
192#41—2782no—
193C2×Q8—2782no—
194C2×Q8—2784no—
195C2×Q8—1392no—
196C2×Q8C22⋊D13911yescharacteristic, complemented
197C2×D4—22no—
198C2×D4—2782no—
199C2×D4—2784no—
200C2×D4—2788no—
201C2×D4—2784no—
202C2×D4—2784no—
203C2×D4—1394no—
204C2×D4—1392no—
205C2×D4C22⋊D13911yescharacteristic, complemented
206C2×D4C22×D13912yes—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—2784no—
212C22×C4—1394no—
213C22×C4C22⋊D13912yescomplemented
214C22×C4C22×D13911yescharacteristic
215C22×C4C22×D13911yescharacteristic
216C4⋊C4—21no—
217C4⋊C4—22no—
218C4⋊C4—2784no—
219C4⋊C4—2782no—
220C22⋊C4—22no—
221C22⋊C4—22no—
222C22⋊C4—2784no—
223C22⋊C4—2784no—
224C22⋊C4—1394no—
225C22⋊C4C22×D13912yes—
226C42—21no—
227C42—2782no—
228C23—22no—
229C23—21no—
230C23—42no—
231C23—2784no—
232C23—1394no—
233C23C2×C22⋊D13912yes—
234C23C23×D13911yescharacteristic
235Q8—22no—
236Q8—2784no—
237Q8—2782no—
238Q8—2782no—
239D4—24no—
240D4—22no—
241D4—44no—
242D4—2784no—
243D4—2788no—
244D4—2784no—
245D4—2784no—
246D4—2782no—
247D4—2782no—
248D4—5568no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—21no—
254C2×C4—41no—
255C2×C4—42no—
256C2×C4—41no—
257C2×C4—2788no—
258C2×C4—2784no—
259C2×C4—2784no—
260C2×C4—2784no—
261C2×C4—2784no—
262C2×C4—1394no—
263C2×C4D4×D13912yes—
264C2×C4D4×D13912yes—
265C2×C4C2×C22⋊D13912yes—
266C2×C4C2×C22⋊D13911yescharacteristic
267C2×C4C2×C22⋊D13911yescharacteristic
268C22—22no—
269C22—24no—
270C22—22no—
271C22—41no—
272C22—42no—
273C22—41no—
274C22—42no—
275C22—41no—
276C22—2784no—
277C22—5564no—
278C22—11124no—
279C22C2×D4×D13912yes—
280C22C22×C22⋊D13911yescharacteristic
281C4—22no—
282C4—42no—
283C4—41no—
284C4—2784no—
285C4—5564no—
286C4#1798481011yescharacteristic
287C4#1798481012yes—
288C4#1798481011yescharacteristic
289C2—21no—
290C2—22no—
291C2—42no—
292C2—42no—
293C2—5564no—
294C2C2×#1798481011yescharacteristic
subgroupG/H
centerC4#17984810
commutator, cosocleC23×C139C24
FrattiniC23C23×D139
Fitting#525×C139C2
socleC2×C139C2×#120
hypercenter#525D139
hypocenterC139#3025
LCSG ▷ C23×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C4 ◁ C22×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. #22581789C2semidirect
2. #22581464C2semidirect
3. #22581142C2semidirect
4. #22581139C2semidirect
5. #22580927C2semidirect
6. #22580926C2semidirect
7. #525×C139C2semidirect
16. #17984825C22semidirect
19. #17984811C22semidirect
21. #17984801C22semidirect
22. #17984757C22semidirect
23. #17984756C22semidirect
25. C23×C4×C139C22semidirect
26. #123×C139C22semidirect
29. #120×C139C22semidirect
31. #117×C139C22semidirect
43. C2×Dic278D4semidirect
46. C2×D556D4semidirect
53. C2×C4×D139D4semidirect
63. C2×Q8×C139D4semidirect
65. C2×D4×C139D4semidirect
71. C22×C4×C139D4semidirect
147. C139#3025semidirect
151. #525D139semidirect
165. C23×C4C2×D139semidirect
167. #123C2×D139semidirect
173. #120C2×D139semidirect
177. #117C2×D139semidirect
196. C2×Q8C22⋊D139semidirect
205. C2×D4C22⋊D139semidirect
213. C22×C4C22⋊D139semidirect

Maximal subgroups

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

subgroupindex
#225817892
#225814642
#225811422
#225811392
#225809272
#225809262
#525×C1392
#3025139