Finite Group Databasebeta

← #31816753

Subgroups — #31816753

Order 17792.

404 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22581580C211yesmaximal, characteristic, complemented
2#22581516C211yesmaximal, characteristic
3#22581317C211yesmaximal, characteristic, complemented
4#22581316C211yesmaximal, characteristic, complemented
5#22581315C211yesmaximal, characteristic, complemented
6#22581311C211yesmaximal, characteristic, complemented
7#22581308C211yesmaximal, characteristic, complemented
8#22581306C211yesmaximal, characteristic, complemented
9#22581298C211yesmaximal, characteristic, complemented
10#22580956C211yesmaximal, characteristic, complemented
11#22580951C211yesmaximal, characteristic, complemented
12#22580946C211yesmaximal, characteristic, complemented
13#102×D139C211yesmaximal, characteristic, complemented
14#22580907C211yesmaximal, characteristic, complemented
15#486×C139C211yesmaximal, characteristic, complemented
16C2×#14555784C2211yescharacteristic
17C2×D4×D139C2211yescharacteristic
18C2×#14555768C2211yescharacteristic
19C2×C8×D139C2211yescharacteristic
20#17984841C2211yescharacteristic, complemented
21#17984840—21no—
22#17984838C2211yescharacteristic
23#17984834C2211yescharacteristic, complemented
24#17984833C2211yescharacteristic, complemented
25#17984832—21no—
26#17984830C2211yescharacteristic
27#17984829C2211yescharacteristic
28#17984820—21no—
29#17984818—21no—
30#17984814—21no—
31#17984814—21no—
32#17984810—21no—
33#17984810—21no—
34#17984800C2211yescharacteristic
35#17984799C2211yescharacteristic
36C4⋊C4×D139C2211yescharacteristic
37#17984767C2211yescharacteristic, complemented
38#17984767C2211yescharacteristic, complemented
39#17984765C2211yescharacteristic, complemented
40#17984765C2211yescharacteristic, complemented
41#17984764C2211yescharacteristic
42#17984764C2211yescharacteristic
43#17984763C2211yescharacteristic
44#17984763C2211yescharacteristic
45#17984763C2211yescharacteristic, complemented
46#17984763C2211yescharacteristic, complemented
47#17984762C2211yescharacteristic
48#17984762C2211yescharacteristic
49#17984753C2211yescharacteristic, complemented
50#17984752C2211yescharacteristic, complemented
51C8×Dic139C2211yescharacteristic, complemented
52C4⋊Q8×C139C2211yescharacteristic, complemented
53#127×C139C2211yescharacteristic
54#102×C139C2211yescharacteristic
55#102×C139C2211yescharacteristic
56#102×C139C2211yescharacteristic, complemented
57#102×C139C2211yescharacteristic, complemented
58C4×C8×C139C2211yescharacteristic, complemented
59C23×D139—21no—
60#14555784—22no—
61#14555784—22no—
62C2×Dic278—21no—
63C2×Dic278C2311yescharacteristic
64C2×D556C2311yescharacteristic
65C2×C22⋊D139—21no—
66C2×C22⋊D139—21no—
67C2×C22⋊D139—21no—
68C2×C22⋊D139—21no—
69D4×D139—22no—
70D4×D139—22no—
71C22×Dic139—21no—
72C2×C4×D139—21no—
73C2×C4×D139C2311yescharacteristic
74#14555768—22no—
75C2×C139⋊C8C2311yescharacteristic
76C2×C139⋊C8C2311yescharacteristic
77C8×D139—22no—
78C4⋊Dic139—21no—
79C4⋊Dic139C2311yescharacteristic
80C4⋊Dic139C2311yescharacteristic
81Dic139⋊C4—21no—
82Dic139⋊C4—21no—
83Dic139⋊C4—21no—
84Dic139⋊C4—21no—
85Dic139⋊C4—21no—
86Dic139⋊C4D411yescharacteristic
87Dic139⋊C4D411yescharacteristic
88C22⋊Dic139—21no—
89C22⋊Dic139—21no—
90(C2×D139)⋊C4—21no—
91(C2×D139)⋊C4—21no—
92(C2×D139)⋊C4—21no—
93(C2×D139)⋊C4D411yescharacteristic
94(C2×D139)⋊C4D411yescharacteristic
95C4×Dic139—21no—
96C4×Dic139C2311yescharacteristic
97C2×Q8×C139—21no—
98C2×D4×C139—21no—
99C2×D4×C139—21no—
100C2×D4×C139C2311yescharacteristic
101C2×D4×C139C2311yescharacteristic
102C2×C8×C139C2311yescharacteristic
103C2×C8×C139C2311yescharacteristic
104C4⋊C4×C139—21no—
105C4⋊C4×C139C2311yescharacteristic
106C4⋊C4×C139C2311yescharacteristic
107C42×C139C2311yescharacteristic
108C22×D139—21no—
109C22×D139—42no—
110C22×D139—81no—
111C22×D139—81no—
112C22×D139C2×D411yescharacteristic
113Dic278—21no—
114Dic278—21no—
115Dic278—81no—
116D556—21no—
117D556—21no—
118C22⋊D139—42no—
119C22⋊D139—42no—
120C22⋊D139—81no—
121C22⋊D139—81no—
122C2×Dic139—21no—
123C2×Dic139—21no—
124C2×Dic139—21no—
125C2×Dic139—42no—
126C2×Dic139C2×D411yescharacteristic
127C2×Dic139C2×D411yescharacteristic
128C2×Dic139C2×D411yescharacteristic
129C4×D139—81no—
130C4×D139#4112yes—
131C4×D139#4112yes—
132C139⋊C8—21no—
133C139⋊C8—21no—
134C23×C139—21no—
135C23×C139—21no—
136Q8×C139—81no—
137D4×C139—21no—
138D4×C139—21no—
139D4×C139—21no—
140D4×C139—21no—
141D4×C139—81no—
142D4×C139—81no—
143C2×C4×C139—21no—
144C2×C4×C139—21no—
145C2×C4×C139C2×D411yescharacteristic
146C2×C4×C139C2×D411yescharacteristic
147C2×C4×C139C2411yescharacteristic
148C8×C139—21no—
149C8×C139—21no—
150C22×C139—41no—
151C22×C139—41no—
152C22×C139—41no—
153C22×C139—41no—
154C22×C139—41no—
155C22×C139—41no—
156C22×C139C22×D411yescharacteristic
157C2×D139—21no—
158C2×D139—21no—
159C2×D139—41no—
160C2×D139—41no—
161C2×D139—41no—
162C2×D139—84no—
163C2×D139#12412yes—
164C4×C139—21no—
165C4×C139—21no—
166C4×C139—41no—
167C4×C139—41no—
168C4×C139C2×#4111yescharacteristic
169C4×C139C2×#4111yescharacteristic
170Dic139—21no—
171Dic139—21no—
172Dic139—41no—
173Dic139—41no—
174Dic139—41no—
175Dic139#12412yes—
176C2×C139—81no—
177C2×C139—81no—
178C2×C139C2×#12411yescharacteristic
179C2×C139#57611yescharacteristic
180C2×C139#57711yescharacteristic
181D139—22no—
182D139—81no—
183C139#313611yescharacteristic, complemented, Sylow
184#3136—1391nomaximal, Sylow
185#544—1391no—
186#535—1391no—
187#490—1391no—
188#490—1391no—
189#489—1391no—
190#489—1391no—
191#488—1391no—
192#488—1391no—
193#486—1391no—
194#486D13911yescharacteristic, complemented
195#418—1391no—
196#417—1391no—
197#416—1391no—
198C2×#102—1391no—
199#405—1391no—
200C2×#41—1391no—
201C22×D4—1391no—
202C2×M16—1391no—
203C22×C8—1391no—
204C4⋊Q8—2781no—
205C4⋊Q8—1391no—
206C4⋊Q8C2×D13911yescharacteristic, complemented
207#127—1391no—
208#127C2×D13911yescharacteristic
209#125—2781no—
210#125—1391no—
211#125—1391no—
212#124—1391no—
213#124—1391no—
214C22⋊Q8—2781no—
215C22⋊Q8—2781no—
216#121—2781no—
217#121—2781no—
218#120—2781no—
219#120—2781no—
220#117—1391no—
221#117—1391no—
222C2×C4⋊C4—1391no—
223#103—1391no—
224#103—1391no—
225#103—1391no—
226#103—1391no—
227#102—1391no—
228#102—1391no—
229#102—1391no—
230#102—1391no—
231#102—1391no—
232#102—1391no—
233#102—1391no—
234#102—1391no—
235#102C2×D13911yescharacteristic
236#102C2×D13911yescharacteristic
237#102C2×D13911yescharacteristic, complemented
238#102C2×D13911yescharacteristic, complemented
239#97—1391no—
240#97—1391no—
241C4×C8—1391no—
242C4×C8C2×D13911yescharacteristic, complemented
243C24—2781no—
244#41—2782no—
245#41—2782no—
246C2×Q8—21no—
247C2×Q8—2781no—
248C2×Q8—1391no—
249C2×D4—21no—
250C2×D4—21no—
251C2×D4—2781no—
252C2×D4—2782no—
253C2×D4—2782no—
254C2×D4—2781no—
255C2×D4—2781no—
256C2×D4—2781no—
257C2×D4—1391no—
258C2×D4C22×D13911yescharacteristic
259C2×D4C22×D13911yescharacteristic
260C22×C4—2781no—
261C22×C4—2781no—
262C22×C4—1391no—
263M16—2782no—
264C2×C8—2782no—
265C2×C8—1391no—
266C2×C8—1391no—
267C2×C8C22×D13911yescharacteristic
268C2×C8C22×D13911yescharacteristic
269C4⋊C4—21no—
270C4⋊C4—2781no—
271C4⋊C4—2781no—
272C4⋊C4—2781no—
273C4⋊C4—2781no—
274C4⋊C4—2781no—
275C4⋊C4—2781no—
276C4⋊C4—1391no—
277C4⋊C4—1391no—
278C4⋊C4—1391no—
279C4⋊C4—1391no—
280C4⋊C4C22×D13911yescharacteristic
281C4⋊C4C22×D13911yescharacteristic
282C22⋊C4—2781no—
283C22⋊C4—2781no—
284C22⋊C4—2781no—
285C22⋊C4—2781no—
286C22⋊C4—2781no—
287C22⋊C4—1391no—
288C22⋊C4—1391no—
289C42—2781no—
290C42—1391no—
291C42C22×D13911yescharacteristic
292C23—21no—
293C23—21no—
294C23—2781no—
295C23—5562no—
296C23—11121no—
297C23—11121no—
298C23—1391no—
299Q8—81no—
300Q8—2781no—
301Q8—2781no—
302Q8—11121no—
303D4—21no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—81no—
308D4—81no—
309D4—2781no—
310D4—2781no—
311D4—5562no—
312D4—5562no—
313D4—11121no—
314D4—11121no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—2781no—
318C2×C4—2781no—
319C2×C4—2781no—
320C2×C4—5562no—
321C2×C4—11121no—
322C2×C4—1391no—
323C2×C4—1391no—
324C2×C4—1391no—
325C2×C4—1392no—
326C2×C4—1392no—
327C2×C4D4×D13911yescharacteristic
328C2×C4D4×D13911yescharacteristic
329C2×C4C23×D13911yescharacteristic
330C8—21no—
331C8—21no—
332C8—2781no—
333C8—2781no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—2781no—
341C22—2781no—
342C22—5561no—
343C22—5561no—
344C22—5561no—
345C22—11124no—
346C22—1392no—
347C22C2×D4×D13911yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—2781no—
353C4—2781no—
354C4—5561no—
355C4—5561no—
356C4—5561no—
357C4—1392no—
358C4#41×D13911yescharacteristic
359C4#41×D13911yescharacteristic
360C2—81no—
361C2—81no—
362C2—2782no—
363C2—11121no—
364C2#124×D13911yescharacteristic
365C2#2258175411yescharacteristic
366C2#2258175911yescharacteristic
subgroupG/H
centerC22C2×D4×D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#486×C139C2
socleC22×C139C22×D4
prime radical#22581516C2
hypercenter#486D139
hypocenterC139#3136
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #22581580C2semidirect
3. #22581317C2semidirect
4. #22581316C2semidirect
5. #22581315C2semidirect
6. #22581311C2semidirect
7. #22581308C2semidirect
8. #22581306C2semidirect
9. #22581298C2semidirect
10. #22580956C2semidirect
11. #22580951C2semidirect
12. #22580946C2semidirect
13. #102×D139C2semidirect
14. #22580907C2semidirect
15. #486×C139C2semidirect
20. #17984841C22semidirect
23. #17984834C22semidirect
24. #17984833C22semidirect
37. #17984767C22semidirect
38. #17984767C22semidirect
39. #17984765C22semidirect
40. #17984765C22semidirect
45. #17984763C22semidirect
46. #17984763C22semidirect
49. #17984753C22semidirect
50. #17984752C22semidirect
51. C8×Dic139C22semidirect
52. C4⋊Q8×C139C22semidirect
56. #102×C139C22semidirect
57. #102×C139C22semidirect
58. C4×C8×C139C22semidirect
183. C139#3136semidirect
194. #486D139semidirect
206. C4⋊Q8C2×D139semidirect
237. #102C2×D139semidirect
238. #102C2×D139semidirect
242. C4×C8C2×D139semidirect

Maximal subgroups

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

subgroupindex
#225815802
#225815162
#225813172
#225813162
#225813152
#225813112
#225813082
#225813062
#225812982
#225809562
#225809512
#225809462
#102×D1392
#225809072
#486×C1392
#3136139