Finite Group Databasebeta

← #31818234

Subgroups — #31818234

Order 17792.

408 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22581637C211yesmaximal, characteristic, complemented
2#22581600C211yesmaximal, characteristic
3#22581306C211yesmaximal, characteristic, complemented
4#22581285C211yesmaximal, characteristic, complemented
5#22581274C211yesmaximal, characteristic, complemented
6#22581252C211yesmaximal, characteristic, complemented
7#22581193C211yesmaximal, characteristic, complemented
8#22581173C211yesmaximal, characteristic, complemented
9#22581113C211yesmaximal, characteristic, complemented
10#22581102C211yesmaximal, characteristic, complemented
11#22581038C211yesmaximal, characteristic, complemented
12C8×C22⋊D139C211yesmaximal, characteristic, complemented
13#22580950C211yesmaximal, characteristic, complemented
14#102×D139C211yesmaximal, characteristic, complemented
15#465×C139C211yesmaximal, characteristic, complemented
16C2×#14555785C2211yescharacteristic
17C2×D4×D139C2211yescharacteristic
18C2×#14555775C2211yescharacteristic, complemented
19C2×#14555772C2211yescharacteristic
20C2×C8×D139C2211yescharacteristic
21#17984835—21no—
22#17984833C2211yescharacteristic, complemented
23#17984832—21no—
24#17984829C2211yescharacteristic
25#17984824—21no—
26#17984824—21no—
27#17984822C2211yescharacteristic
28#17984818C2211yescharacteristic
29#17984813—21no—
30#17984810—21no—
31Q8×Dic139C2211yescharacteristic, complemented
32#17984804C2211yescharacteristic
33C4×C22⋊D139C2211yescharacteristic
34#17984801C2211yescharacteristic, complemented
35#17984800—21no—
36C4⋊C4×D139C2211yescharacteristic
37C22⋊C4×D139—21no—
38#17984775C2211yescharacteristic, complemented
39#17984773C2211yescharacteristic, complemented
40Dic139⋊C8C2211yescharacteristic, complemented
41#17984767C2211yescharacteristic, complemented
42#17984767C2211yescharacteristic, complemented
43#17984765C2211yescharacteristic, complemented
44#17984764C2211yescharacteristic
45#17984764C2211yescharacteristic
46#17984763C2211yescharacteristic
47#17984763C2211yescharacteristic
48#17984762C2211yescharacteristic
49C22⋊(C139⋊C8)C2211yescharacteristic, complemented
50(C2×D139)⋊C8C2211yescharacteristic
51C8×Dic139C2211yescharacteristic, complemented
52C2×SD16×C139C2211yescharacteristic
53C22×C8×C139C2211yescharacteristic, complemented
54C22⋊Q8×C139C2211yescharacteristic, complemented
55#121×C139C2211yescharacteristic
56#106×C139C2211yescharacteristic, complemented
57#103×C139C2211yescharacteristic, complemented
58#102×C139C2211yescharacteristic
59C23×D139—21no—
60#14555785—22no—
61#14555785—41no—
62C2×Dic278C2311yescharacteristic
63C2×D556C2311yescharacteristic
64C2×C22⋊D139—21no—
65C2×C22⋊D139—21no—
66C2×C22⋊D139D411yescharacteristic
67D4×D139—22no—
68D4×D139—41no—
69C2×C4×D139—21no—
70C2×C4×D139—21no—
71C2×C4×D139—21no—
72C2×C4×D139C2311yescharacteristic
73#14555775—41no—
74#14555772—22no—
75C2×C139⋊C8C2311yescharacteristic
76C2×C139⋊C8C2311yescharacteristic
77C8×D139—41no—
78C4⋊Dic139—21no—
79C4⋊Dic139—21no—
80C4⋊Dic139—21no—
81C4⋊Dic139C2311yescharacteristic
82C4⋊Dic139C2311yescharacteristic
83Dic139⋊C4—21no—
84Dic139⋊C4—21no—
85Dic139⋊C4—21no—
86Dic139⋊C4D411yescharacteristic
87C22⋊Dic139—21no—
88C22⋊Dic139—21no—
89C22⋊Dic139—21no—
90C22⋊Dic139D411yescharacteristic
91(C2×D139)⋊C4—21no—
92(C2×D139)⋊C4—21no—
93(C2×D139)⋊C4—21no—
94(C2×D139)⋊C4D411yescharacteristic
95C4×Dic139—21no—
96C4×Dic139—21no—
97C4×Dic139C2311yescharacteristic
98C2×Q8×C139C2311yescharacteristic
99C2×D4×C139—21no—
100C2×D4×C139C2311yescharacteristic
101C22×C4×C139C2311yescharacteristic
102SD16×C139—41no—
103C2×C8×C139—41no—
104C2×C8×C139C2311yescharacteristic
105C2×C8×C139C2311yescharacteristic
106C4⋊C4×C139—21no—
107C4⋊C4×C139C2311yescharacteristic
108C4⋊C4×C139C2311yescharacteristic
109C22⋊C4×C139—21no—
110C22⋊C4×C139—21no—
111C22×D139—21no—
112C22×D139—42no—
113C22×D139—42no—
114C22×D139—81no—
115C22×D139C2×D411yescharacteristic
116Dic278—21no—
117Dic278—21no—
118D556—21no—
119D556#4112yes—
120C22⋊D139—22no—
121C22⋊D139—42no—
122C22⋊D139—42no—
123C2×Dic139—21no—
124C2×Dic139—21no—
125C2×Dic139—21no—
126C2×Dic139C2×D411yescharacteristic
127C2×Dic139C2×D411yescharacteristic
128C2×Dic139C2×D411yescharacteristic
129C4×D139—21no—
130C4×D139—21no—
131C4×D139—42no—
132C4×D139—42no—
133C4×D139—81no—
134C139⋊C8—21no—
135C139⋊C8—21no—
136C23×C139—21no—
137C23×C139C2×D411yescharacteristic
138Q8×C139—21no—
139Q8×C139—21no—
140D4×C139—21no—
141D4×C139—21no—
142D4×C139—81no—
143C2×C4×C139—21no—
144C2×C4×C139—21no—
145C2×C4×C139—21no—
146C2×C4×C139—21no—
147C2×C4×C139—21no—
148C2×C4×C139C2×D411yescharacteristic
149C2×C4×C139C2411yescharacteristic
150C8×C139—21no—
151C8×C139—21no—
152C22×C139—21no—
153C22×C139—21no—
154C22×C139—21no—
155C22×C139—41no—
156C22×C139—41no—
157C22×C139—41no—
158C22×C139C22×D411yescharacteristic
159C2×D139—21no—
160C2×D139—21no—
161C2×D139—22no—
162C2×D139—41no—
163C2×D139—41no—
164C2×D139—84no—
165C2×D139#13512yes—
166C4×C139—21no—
167C4×C139—41no—
168C4×C139—41no—
169C4×C139—41no—
170C4×C139C2×#4111yescharacteristic
171C4×C139H(5,𝔽2)11yescharacteristic
172Dic139—21no—
173Dic139—21no—
174Dic139—21no—
175Dic139—41no—
176Dic139—41no—
177Dic139—41no—
178C2×C139—41no—
179C2×C139—81no—
180C2×C139#54611yescharacteristic
181C2×C139C2×#13511yescharacteristic
182C2×C139#57711yescharacteristic
183D139—22no—
184D139—42no—
185C139#329611yescharacteristic, complemented, Sylow
186#3296—1391nomaximal, Sylow
187#552—1391no—
188#546—1391no—
189#488—1391no—
190#483—1391no—
191#482—1391no—
192#478—1391no—
193#467—1391no—
194#465D13911yescharacteristic, complemented
195#464—1391no—
196#452—1391no—
197#450—1391no—
198C4×SD16—1391no—
199C8×D4—1391no—
200#416—1391no—
201C2×#102—1391no—
202C2×#41—1391no—
203C22×D4—1391no—
204C2×Q16—1391no—
205C2×SD16—1391no—
206C2×SD16C2×D13911yescharacteristic
207C22×C8—1391no—
208C22×C8C2×D13911yescharacteristic, complemented
209#126—2781no—
210#125—2781no—
211#125—1391no—
212#124—1391no—
213#123—2781no—
214#123—2781no—
215C22⋊Q8—1391no—
216C22⋊Q8—1391no—
217C22⋊Q8C2×D13911yescharacteristic, complemented
218#121—2781no—
219#121C2×D13911yescharacteristic
220#120—2781no—
221C4×Q8—1391no—
222C4×D4—1391no—
223C4×D4—1391no—
224#117—2781no—
225#117—1391no—
226C2×C4⋊C4—1391no—
227C2×C22⋊C4—2781no—
228#107—1391no—
229#106—1391no—
230#106C2×D13911yescharacteristic, complemented
231C4⋊C8—1391no—
232#103—1391no—
233#103—1391no—
234#103—1391no—
235#103C2×D13911yescharacteristic, complemented
236#102—1391no—
237#102—1391no—
238#102—1391no—
239#102—1391no—
240#102—1391no—
241#102C2×D13911yescharacteristic
242C22⋊C8—1391no—
243C22⋊C8—1391no—
244C4×C8—1391no—
245C24—2781no—
246#41—2782no—
247#41—5561no—
248C2×Q8—1391no—
249C2×Q8C22×D13911yescharacteristic
250C2×D4—21no—
251C2×D4—2782no—
252C2×D4—2781no—
253C2×D4—2781no—
254C2×D4—5561no—
255C2×D4—1391no—
256C2×D4—1391no—
257C2×D4C22×D13911yescharacteristic
258C22×C4—2781no—
259C22×C4—2781no—
260C22×C4—2781no—
261C22×C4—1391no—
262C22×C4C22×D13911yescharacteristic
263Q16—5561no—
264SD16—41no—
265SD16—2782no—
266C2×C8—41no—
267C2×C8—5561no—
268C2×C8—1391no—
269C2×C8—1391no—
270C2×C8C22×D13911yescharacteristic
271C2×C8C22×D13911yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—2781no—
274C4⋊C4—2781no—
275C4⋊C4—2781no—
276C4⋊C4—2781no—
277C4⋊C4—2781no—
278C4⋊C4—2781no—
279C4⋊C4—1391no—
280C4⋊C4—1391no—
281C4⋊C4—1391no—
282C4⋊C4C22×D13911yescharacteristic
283C4⋊C4C22×D13911yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—2781no—
287C22⋊C4—2781no—
288C22⋊C4—2781no—
289C22⋊C4—2781no—
290C22⋊C4—2781no—
291C22⋊C4—2781no—
292C22⋊C4—1391no—
293C22⋊C4—1391no—
294C42—2781no—
295C42—2781no—
296C42—1391no—
297C23—21no—
298C23—2781no—
299C23—5562no—
300C23—5562no—
301C23—11121no—
302C23—1391no—
303C23D4×D13911yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—2781no—
307Q8—2781no—
308D4—21no—
309D4—21no—
310D4—81no—
311D4—2782no—
312D4—2781no—
313D4—5562no—
314D4—5562no—
315D4—1392no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—2781no—
322C2×C4—2781no—
323C2×C4—2781no—
324C2×C4—2781no—
325C2×C4—2781no—
326C2×C4—5562no—
327C2×C4—5562no—
328C2×C4—11121no—
329C2×C4—1391no—
330C2×C4—1391no—
331C2×C4—1391no—
332C2×C4D4×D13911yescharacteristic
333C2×C4C23×D13911yescharacteristic
334C8—21no—
335C8—21no—
336C8—2781no—
337C8—2781no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—2781no—
345C22—2781no—
346C22—2782no—
347C22—5561no—
348C22—5561no—
349C22—11124no—
350C22—1392no—
351C22C2×D4×D13911yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—2781no—
357C4—2781no—
358C4—2781no—
359C4—5561no—
360C4—5561no—
361C4—5561no—
362C4#41×D13911yescharacteristic
363C4#1798488711yescharacteristic
364C2—41no—
365C2—81no—
366C2—2782no—
367C2—5562no—
368C2#2258159211yescharacteristic
369C2#135×D13911yescharacteristic
370C2#2258175911yescharacteristic
subgroupG/H
centerC22C2×D4×D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#465×C139C2
socleC22×C139C22×D4
prime radical#22581600C2
hypercenter#465D139
hypocenterC139#3296
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #22581637C2semidirect
3. #22581306C2semidirect
4. #22581285C2semidirect
5. #22581274C2semidirect
6. #22581252C2semidirect
7. #22581193C2semidirect
8. #22581173C2semidirect
9. #22581113C2semidirect
10. #22581102C2semidirect
11. #22581038C2semidirect
12. C8×C22⋊D139C2semidirect
13. #22580950C2semidirect
14. #102×D139C2semidirect
15. #465×C139C2semidirect
18. C2×#14555775C22semidirect
22. #17984833C22semidirect
31. Q8×Dic139C22semidirect
34. #17984801C22semidirect
38. #17984775C22semidirect
39. #17984773C22semidirect
40. Dic139⋊C8C22semidirect
41. #17984767C22semidirect
42. #17984767C22semidirect
43. #17984765C22semidirect
49. C22⋊(C139⋊C8)C22semidirect
51. C8×Dic139C22semidirect
53. C22×C8×C139C22semidirect
54. C22⋊Q8×C139C22semidirect
56. #106×C139C22semidirect
57. #103×C139C22semidirect
185. C139#3296semidirect
194. #465D139semidirect
208. C22×C8C2×D139semidirect
217. C22⋊Q8C2×D139semidirect
230. #106C2×D139semidirect
235. #103C2×D139semidirect

Maximal subgroups

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

subgroupindex
#225816372
#225816002
#225813062
#225812852
#225812742
#225812522
#225811932
#225811732
#225811132
#225811022
#225810382
C8×C22⋊D1392
#225809502
#102×D1392
#465×C1392
#3296139