Finite Group Databasebeta

← #31818365

Subgroups — #31818365

Order 17792.

442 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22581607C211yesmaximal, characteristic, complemented
2#22581312C211yesmaximal, characteristic, complemented
3#22581281C211yesmaximal, characteristic, complemented
4#22581269C211yesmaximal, characteristic, complemented
5#22581243C211yesmaximal, characteristic, complemented
6#22581204C211yesmaximal, characteristic, complemented
7#22581184C211yesmaximal, characteristic, complemented
8#22581165C211yesmaximal, characteristic, complemented
9#22581098C211yesmaximal, characteristic, complemented
10#22581087C211yesmaximal, characteristic, complemented
11#22581063C211yesmaximal, characteristic, complemented
12#22581025C211yesmaximal, characteristic, complemented
13#22580954C211yesmaximal, characteristic, complemented
14C2×#17984763C211yesmaximal, characteristic, complemented
15#546×C139C211yesmaximal, characteristic, complemented
16C2×#14555784—21no—
17C2×#14555772C2211yescharacteristic, complemented
18C2×#14555770C2211yescharacteristic
19C2×#14555770C2211yescharacteristic
20C2×#14555769C2211yescharacteristic, complemented
21C22×C139⋊C8C2211yescharacteristic
22#17984842C2211yescharacteristic, complemented
23#17984826—21no—
24#17984826—21no—
25#17984822—21no—
26#17984816C2211yescharacteristic
27#17984816C2211yescharacteristic, complemented
28C4×D556C2211yescharacteristic, complemented
29C2×C4⋊Dic139C2211yescharacteristic
30C2×C4⋊Dic139C2211yescharacteristic, complemented
31#17984773C2211yescharacteristic, complemented
32#17984773C2211yescharacteristic, complemented
33#17984773C2211yescharacteristic, complemented
34C4⋊(C139⋊C8)C2211yescharacteristic, complemented
35#17984766C2211yescharacteristic, complemented
36#17984766C2211yescharacteristic, complemented
37#17984766C2211yescharacteristic, complemented
38#17984763C2211yescharacteristic
39#17984763C2211yescharacteristic
40#17984763C2211yescharacteristic
41#17984763C2211yescharacteristic
42#17984763C2211yescharacteristic
43#17984763C2211yescharacteristic
44#17984762C2211yescharacteristic, complemented
45C22⋊(C139⋊C8)C2211yescharacteristic
46C22⋊(C139⋊C8)C2211yescharacteristic, complemented
47#17984753C2211yescharacteristic, complemented
48C2×#41×C139C2211yescharacteristic
49C22×D4×C139C2211yescharacteristic
50#124×C139C2211yescharacteristic
51#123×C139—21no—
52C22⋊Q8×C139C2211yescharacteristic
53#121×C139—21no—
54#121×C139C2211yescharacteristic
55#120×C139—21no—
56C4×D4×C139C2211yescharacteristic
57C4×D4×C139C2211yescharacteristic
58C2×C22⋊C4×C139—21no—
59#14555784—44no—
60C2×Dic278—21no—
61C2×D556C2311yescharacteristic
62C2×C22⋊D139—21no—
63C2×C22⋊D139—21no—
64C22×Dic139—21no—
65C22×Dic139—21no—
66C2×C4×D139—21no—
67#14555772—41no—
68#14555770—22no—
69#14555770—41no—
70#14555769—41no—
71C2×C139⋊C8—41no—
72C2×C139⋊C8C2311yescharacteristic
73C2×C139⋊C8C2311yescharacteristic
74C2×C139⋊C8C2311yescharacteristic
75C2×C139⋊C8C2311yescharacteristic
76C4⋊Dic139—21no—
77C4⋊Dic139—21no—
78C4⋊Dic139—21no—
79C4⋊Dic139C2311yescharacteristic
80C4⋊Dic139C2311yescharacteristic
81C4⋊Dic139C2311yescharacteristic
82(C2×D139)⋊C4—21no—
83(C2×D139)⋊C4—21no—
84(C2×D139)⋊C4—21no—
85C24×C139—21no—
86#41×C139—22no—
87#41×C139—41no—
88C2×Q8×C139C2311yescharacteristic
89C2×D4×C139—22no—
90C2×D4×C139—21no—
91C2×D4×C139—21no—
92C2×D4×C139—21no—
93C2×D4×C139—41no—
94C2×D4×C139D411yescharacteristic
95C2×D4×C139C2311yescharacteristic
96C2×D4×C139C2311yescharacteristic
97C22×C4×C139—21no—
98C22×C4×C139—21no—
99C22×C4×C139C2311yescharacteristic
100C22×C4×C139C2311yescharacteristic
101C4⋊C4×C139—21no—
102C4⋊C4×C139D411yescharacteristic
103C4⋊C4×C139C2311yescharacteristic
104C22⋊C4×C139—21no—
105C22⋊C4×C139—21no—
106C22⋊C4×C139—21no—
107C22⋊C4×C139—21no—
108C22⋊C4×C139—21no—
109C22⋊C4×C139D411yescharacteristic
110C22⋊C4×C139D411yescharacteristic
111C42×C139C2311yescharacteristic
112C22×D139—21no—
113Dic278—42no—
114D556—21no—
115D556—21no—
116C22⋊D139—42no—
117C22⋊D139—42no—
118C2×Dic139—21no—
119C2×Dic139—21no—
120C2×Dic139—21no—
121C2×Dic139—42no—
122C2×Dic139—42no—
123C4×D139—42no—
124C139⋊C8—21no—
125C139⋊C8—21no—
126C139⋊C8—21no—
127C139⋊C8—21no—
128C23×C139—21no—
129C23×C139—21no—
130C23×C139—42no—
131C23×C139—42no—
132C23×C139—81no—
133C23×C139C2×D411yescharacteristic
134C23×C139C2×D411yescharacteristic
135Q8×C139—21no—
136Q8×C139—21no—
137D4×C139—22no—
138D4×C139—21no—
139D4×C139—21no—
140D4×C139—21no—
141D4×C139—42no—
142D4×C139—42no—
143D4×C139—81no—
144D4×C139#4112yescomplemented
145C2×C4×C139—21no—
146C2×C4×C139—21no—
147C2×C4×C139—21no—
148C2×C4×C139—21no—
149C2×C4×C139—21no—
150C2×C4×C139—21no—
151C2×C4×C139—42no—
152C2×C4×C139—81no—
153C2×C4×C139C2×D411yescharacteristic
154C2×C4×C139C2×D411yescharacteristic
155C2×C4×C139C2×D411yescharacteristic
156C2×C4×C139C2×D411yescharacteristic
157C2×C4×C139C2411yescharacteristic
158C22×C139—21no—
159C22×C139—21no—
160C22×C139—21no—
161C22×C139—22no—
162C22×C139—21no—
163C22×C139—21no—
164C22×C139—41no—
165C22×C139—41no—
166C22×C139—41no—
167C22×C139—41no—
168C22×C139—41no—
169C22×C139—84no—
170C22×C139AGL(1,ℤ/8)12yes—
171C22×C139C22×D411yescharacteristic
172C2×D139—41no—
173C2×D139—41no—
174C2×D139—41no—
175C4×C139—21no—
176C4×C139—21no—
177C4×C139—21no—
178C4×C139—21no—
179C4×C139—41no—
180C4×C139—41no—
181C4×C139C2×#4111yescharacteristic
182C4×C139H(5,𝔽2)11yescharacteristic
183Dic139—41no—
184Dic139—41no—
185Dic139—41no—
186C2×C139—22no—
187C2×C139—41no—
188C2×C139—42no—
189C2×C139—81no—
190C2×C139#54611yescharacteristic
191C2×C139C2×AGL(1,ℤ/8)11yescharacteristic
192C2×C139#57711yescharacteristic
193D139—81no—
194C139#330611yescharacteristic, complemented, Sylow
195#3306—1391nomaximal, Sylow
196#547—1391no—
197#546D13911yescharacteristic, complemented
198#489—1391no—
199#483—1391no—
200#481—1391no—
201#476—1391no—
202#469—1391no—
203#465—1391no—
204#463—1391no—
205#449—1391no—
206#447—1391no—
207#442—1391no—
208#435—1391no—
209#417—1391no—
210C2×#102—1391no—
211C2×#41—2781no—
212C2×#41C2×D13911yescharacteristic
213C22×D4C2×D13911yescharacteristic
214C2×SD16—1391no—
215C2×D8—1391no—
216C2×D8—1391no—
217C2×M16—1391no—
218C22×C8—1391no—
219C4⋊Q8—1391no—
220#124C2×D13911yescharacteristic
221#123—21no—
222#123—2781no—
223#123—2781no—
224C22⋊Q8—2781no—
225C22⋊Q8C2×D13911yescharacteristic
226#121—21no—
227#121—1391no—
228#121—1391no—
229#121C2×D13911yescharacteristic
230#120—21no—
231C4×D4—1391no—
232C4×D4C2×D13911yescharacteristic
233C4×D4C2×D13911yescharacteristic
234C2×C4⋊C4—1391no—
235C2×C4⋊C4—1391no—
236C2×C22⋊C4—21no—
237#106—1391no—
238#106—1391no—
239#106—1391no—
240C4⋊C8—1391no—
241#103—1391no—
242#103—1391no—
243#103—1391no—
244#102—1391no—
245#102—1391no—
246#102—1391no—
247#102—1391no—
248#102—1391no—
249#102—1391no—
250#102—1391no—
251C22⋊C8—1391no—
252C22⋊C8—1391no—
253#97—1391no—
254C24—21no—
255#41—22no—
256#41—41no—
257#41—5564no—
258C2×Q8—2781no—
259C2×Q8C22×D13911yescharacteristic
260C2×D4—22no—
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—41no—
265C2×D4—2781no—
266C2×D4—2781no—
267C2×D4—1391no—
268C2×D4C22⋊D13911yescharacteristic
269C2×D4C22×D13911yescharacteristic
270C2×D4C22×D13911yescharacteristic
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—2781no—
274C22×C4—2781no—
275C22×C4—2781no—
276C22×C4C22×D13911yescharacteristic
277C22×C4C22×D13911yescharacteristic
278SD16—5561no—
279D8—2782no—
280D8—5561no—
281M16—5561no—
282C2×C8—5561no—
283C2×C8—1391no—
284C2×C8—1391no—
285C2×C8—1391no—
286C2×C8—1391no—
287C4⋊C4—21no—
288C4⋊C4—2781no—
289C4⋊C4—2781no—
290C4⋊C4—2781no—
291C4⋊C4—1391no—
292C4⋊C4—1391no—
293C4⋊C4—1391no—
294C4⋊C4C22⋊D13911yescharacteristic
295C4⋊C4C22×D13911yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—2781no—
302C22⋊C4—2781no—
303C22⋊C4—2781no—
304C22⋊C4C22⋊D13911yescharacteristic
305C22⋊C4C22⋊D13911yescharacteristic
306C42C22×D13911yescharacteristic
307C23—21no—
308C23—21no—
309C23—42no—
310C23—42no—
311C23—81no—
312C23—2781no—
313C23C2×C22⋊D13911yescharacteristic
314C23C2×C22⋊D13911yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—5562no—
318D4—22no—
319D4—21no—
320D4—21no—
321D4—21no—
322D4—42no—
323D4—42no—
324D4—81no—
325D4—2781no—
326D4—2781no—
327D4—5562no—
328D4—5562no—
329D4#1455578412yescomplemented
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—42no—
337C2×C4—81no—
338C2×C4—2781no—
339C2×C4—2781no—
340C2×C4—2781no—
341C2×C4—5562no—
342C2×C4—5562no—
343C2×C4—5562no—
344C2×C4C2×C22⋊D13911yescharacteristic
345C2×C4C2×C22⋊D13911yescharacteristic
346C2×C4C2×C22⋊D13911yescharacteristic
347C2×C4C2×C22⋊D13911yescharacteristic
348C2×C4C23×D13911yescharacteristic
349C8—2781no—
350C8—2781no—
351C8—2781no—
352C8—2781no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—22no—
358C22—21no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—84no—
365C22—5561no—
366C22—5561no—
367C22—5561no—
368C22#1798486712yes—
369C22C22×C22⋊D13911yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—41no—
375C4—41no—
376C4—5561no—
377C4—5561no—
378C4—5561no—
379C4C2×#1455578411yescharacteristic
380C4#1798488711yescharacteristic
381C2—22no—
382C2—41no—
383C2—42no—
384C2—81no—
385C2—11121no—
386C2#2258159711yescharacteristic
387C2C2×#1798486711yescharacteristic
388C2#2258176411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#546×C139C2
socleC22×C139C22×D4
hypercenter#546D139
hypocenterC139#3306
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. #22581607C2semidirect
2. #22581312C2semidirect
3. #22581281C2semidirect
4. #22581269C2semidirect
5. #22581243C2semidirect
6. #22581204C2semidirect
7. #22581184C2semidirect
8. #22581165C2semidirect
9. #22581098C2semidirect
10. #22581087C2semidirect
11. #22581063C2semidirect
12. #22581025C2semidirect
13. #22580954C2semidirect
14. C2×#17984763C2semidirect
15. #546×C139C2semidirect
17. C2×#14555772C22semidirect
20. C2×#14555769C22semidirect
22. #17984842C22semidirect
27. #17984816C22semidirect
28. C4×D556C22semidirect
30. C2×C4⋊Dic139C22semidirect
31. #17984773C22semidirect
32. #17984773C22semidirect
33. #17984773C22semidirect
34. C4⋊(C139⋊C8)C22semidirect
35. #17984766C22semidirect
36. #17984766C22semidirect
37. #17984766C22semidirect
44. #17984762C22semidirect
46. C22⋊(C139⋊C8)C22semidirect
47. #17984753C22semidirect
144. D4×C139#41semidirect
194. C139#3306semidirect
197. #546D139semidirect
329. D4#14555784semidirect

Maximal subgroups

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

subgroupindex
#225816072
#225813122
#225812812
#225812692
#225812432
#225812042
#225811842
#225811652
#225810982
#225810872
#225810632
#225810252
#225809542
C2×#179847632
#546×C1392
#3306139