Finite Group Databasebeta

← #31817881

Subgroups — #31817881

Order 17792.

568 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17984869C211yesmaximal, characteristic, complemented
2C22×D1112C211yesmaximal, characteristic, complemented
3#22581594C211yesmaximal, characteristic, complemented
4#22581587C211yesmaximal, characteristic, complemented
5#22581339C211yesmaximal, characteristic, complemented
6#22581207C211yesmaximal, characteristic, complemented
7#22581171C211yesmaximal, characteristic, complemented
8#22581147C211yesmaximal, characteristic, complemented
9#22581103C211yesmaximal, characteristic, complemented
10#22581101C211yesmaximal, characteristic, complemented
11#22581088C211yesmaximal, characteristic, complemented
12#22581086C211yesmaximal, characteristic, complemented
13#22581064C211yesmaximal, characteristic, complemented
14#22581024C211yesmaximal, characteristic, complemented
15#465×C139C211yesmaximal, characteristic, complemented
16C2×#14555786C2211yescharacteristic, complemented
17C22×D556C2211yescharacteristic
18C22×D556C2211yescharacteristic, complemented
19C2×D4×D139—21no—
20C2×D4×D139C2211yescharacteristic, complemented
21#17984869—24no—
22C2×#14555772C2211yescharacteristic, complemented
23C2×#14555772C2211yescharacteristic, complemented
24C2×D1112—24no—
25C2×D1112C2211yescharacteristic
26C2×D1112C2211yescharacteristic
27C2×D1112C2211yescharacteristic, complemented
28C2×D1112C2211yescharacteristic, complemented
29C2×#14555770C2211yescharacteristic, complemented
30C2×#14555770C2211yescharacteristic, complemented
31C2×#14555768C2211yescharacteristic, complemented
32#17984838C2211yescharacteristic, complemented
33#17984831C2211yescharacteristic, complemented
34#17984827—21no—
35#17984817—21no—
36#17984817C2211yescharacteristic, complemented
37#17984817C2211yescharacteristic, complemented
38#17984815—21no—
39#17984812—21no—
40#17984812—21no—
41#17984810—21no—
42#17984804C2211yescharacteristic, complemented
43#17984804C2211yescharacteristic, complemented
44C4×C22⋊D139C2211yescharacteristic
45C22⋊C4×D139—21no—
46Dic139⋊C8C2211yescharacteristic, complemented
47#17984762C2211yescharacteristic, complemented
48#17984762C2211yescharacteristic, complemented
49#17984762C2211yescharacteristic, complemented
50#17984762C2211yescharacteristic, complemented
51C22⋊(C139⋊C8)C2211yescharacteristic, complemented
52(C2×D139)⋊C8C2211yescharacteristic, complemented
53#17984752C2211yescharacteristic, complemented
54C2×SD16×C139C2211yescharacteristic, complemented
55C22×C8×C139C2211yescharacteristic, complemented
56C22⋊Q8×C139C2211yescharacteristic, complemented
57#121×C139C2211yescharacteristic
58#106×C139C2211yescharacteristic, complemented
59#103×C139C2211yescharacteristic, complemented
60#102×C139C2211yescharacteristic, complemented
61C23×D139—21no—
62C23×D139—21no—
63C23×D139—21no—
64#14555786—22no—
65#14555786—41no—
66C2×D556—22no—
67C2×D556—22no—
68C2×D556—21no—
69C2×D556—21no—
70C2×D556—21no—
71C2×D556—21no—
72C2×D556—21no—
73C2×D556—41no—
74C2×D556—41no—
75C2×D556C2311yescharacteristic
76C2×D556C2311yescharacteristic
77C2×D556C2311yescharacteristic
78C2×D556C2311yescharacteristic
79C2×C22⋊D139—21no—
80C2×C22⋊D139—21no—
81C2×C22⋊D139—21no—
82C2×C22⋊D139D411yescharacteristic
83D4×D139—22no—
84D4×D139—41no—
85D4×D139—44no—
86C2×C4×D139—21no—
87C2×C4×D139—21no—
88C2×C4×D139—21no—
89C2×C4×D139C2311yescharacteristic
90#14555772—22no—
91#14555772—41no—
92D1112—22no—
93D1112—22no—
94D1112—22no—
95D1112D414yescomplemented
96#14555770—22no—
97#14555770—41no—
98#14555768—22no—
99C2×C139⋊C8C2311yescharacteristic
100C2×C139⋊C8C2311yescharacteristic
101Dic139⋊C4D411yescharacteristic
102C22⋊Dic139D411yescharacteristic
103(C2×D139)⋊C4—21no—
104(C2×D139)⋊C4—21no—
105(C2×D139)⋊C4—21no—
106(C2×D139)⋊C4—21no—
107(C2×D139)⋊C4—21no—
108(C2×D139)⋊C4—21no—
109(C2×D139)⋊C4D411yescharacteristic
110C4×Dic139C2311yescharacteristic
111C2×Q8×C139C2311yescharacteristic
112C2×D4×C139—21no—
113C2×D4×C139C2311yescharacteristic
114C22×C4×C139C2311yescharacteristic
115SD16×C139—22no—
116C2×C8×C139—22no—
117C2×C8×C139C2311yescharacteristic
118C2×C8×C139C2311yescharacteristic
119C4⋊C4×C139—21no—
120C4⋊C4×C139C2311yescharacteristic
121C4⋊C4×C139C2311yescharacteristic
122C22⋊C4×C139—21no—
123C22⋊C4×C139—21no—
124C22×D139—21no—
125C22×D139—21no—
126C22×D139—21no—
127C22×D139—21no—
128C22×D139—42no—
129C22×D139—42no—
130C22×D139—42no—
131C22×D139—42no—
132C22×D139—42no—
133C22×D139—42no—
134C22×D139—81no—
135C22×D139—81no—
136C22×D139—81no—
137C22×D139C2×D411yescharacteristic
138D556—21no—
139D556—21no—
140D556—21no—
141D556—21no—
142D556—21no—
143D556—21no—
144D556—42no—
145D556—42no—
146D556—42no—
147D556—42no—
148D556—81no—
149D556C2×D412yes—
150D556C2×D412yescomplemented
151C22⋊D139—22no—
152C22⋊D139—42no—
153C22⋊D139—42no—
154C22⋊D139—81no—
155C2×Dic139C2×D411yescharacteristic
156C2×Dic139C2×D411yescharacteristic
157C2×Dic139C2×D411yescharacteristic
158C4×D139—21no—
159C4×D139—21no—
160C4×D139—42no—
161C4×D139—42no—
162C4×D139—81no—
163C139⋊C8—21no—
164C139⋊C8—21no—
165C23×C139—21no—
166C23×C139C2×D411yescharacteristic
167Q8×C139—21no—
168Q8×C139—21no—
169D4×C139—21no—
170D4×C139—21no—
171D4×C139—42no—
172C2×C4×C139—21no—
173C2×C4×C139—21no—
174C2×C4×C139—21no—
175C2×C4×C139—21no—
176C2×C4×C139—21no—
177C2×C4×C139C2×D411yescharacteristic
178C2×C4×C139C2411yescharacteristic
179C8×C139—21no—
180C8×C139C2×D412yescomplemented
181C22×C139—21no—
182C22×C139—21no—
183C22×C139—41no—
184C22×C139—41no—
185C22×C139—41no—
186C22×C139AGL(1,ℤ/8)12yescomplemented
187C22×C139C22×D411yescharacteristic
188C2×D139—21no—
189C2×D139—22no—
190C2×D139—22no—
191C2×D139—21no—
192C2×D139—21no—
193C2×D139—41no—
194C2×D139—41no—
195C2×D139—41no—
196C2×D139—41no—
197C2×D139—41no—
198C2×D139—41no—
199C2×D139—41no—
200C2×D139—41no—
201C2×D139—41no—
202C2×D139—41no—
203C2×D139—84no—
204C2×D139—84no—
205C2×D139—84no—
206C4×C139—21no—
207C4×C139—41no—
208C4×C139—41no—
209C4×C139—41no—
210C4×C139C22×D411yescharacteristic
211C4×C139H(5,𝔽2)11yescharacteristic
212Dic139—21no—
213Dic139—21no—
214Dic139—21no—
215C2×C139—22no—
216C2×C139—81no—
217C2×C139D4211yescharacteristic
218C2×C139C2×AGL(1,ℤ/8)11yescharacteristic
219C2×C139#57611yescharacteristic
220D139—41no—
221D139—42no—
222D139—42no—
223D139—81no—
224D139—81no—
225C139#326411yescharacteristic, complemented, Sylow
226#3264—1391nomaximal, Sylow
227C2×AGL(1,ℤ/8)—1391no—
228C22×D8—1391no—
229#546—1391no—
230D42—1391no—
231#496—1391no—
232#469—1391no—
233#465D13911yescharacteristic, complemented
234#463—1391no—
235#459—1391no—
236#450—1391no—
237#449—1391no—
238#447—1391no—
239#447—1391no—
240#442—1391no—
241#435—1391no—
242C2×#41—1391no—
243C22×D4—2781no—
244C22×D4—1391no—
245C22×D4—1391no—
246C22×D4—1391no—
247AGL(1,ℤ/8)—2784no—
248C2×SD16—1391no—
249C2×SD16—1391no—
250C2×SD16C2×D13911yescharacteristic, complemented
251C2×D8—2784no—
252C2×D8—1391no—
253C2×D8—1391no—
254C2×D8—1391no—
255C2×D8—1391no—
256C2×D8—1391no—
257C2×D8—1391no—
258C2×M16—1391no—
259C22×C8C2×D13911yescharacteristic, complemented
260#127—1391no—
261#124—1391no—
262#123—2781no—
263C22⋊Q8C2×D13911yescharacteristic, complemented
264#121—2781no—
265#121—2781no—
266#121—1391no—
267#121—1391no—
268#121C2×D13911yescharacteristic
269#120—2781no—
270#120—2781no—
271#120—2781no—
272C4×D4—1391no—
273C4×D4—1391no—
274C4×D4—1391no—
275C2×C22⋊C4—2781no—
276#106C2×D13911yescharacteristic, complemented
277C4⋊C8—1391no—
278#103C2×D13911yescharacteristic, complemented
279#102—1391no—
280#102—1391no—
281#102—1391no—
282#102—1391no—
283#102C2×D13911yescharacteristic, complemented
284C22⋊C8—1391no—
285C22⋊C8—1391no—
286#97—1391no—
287C24—2781no—
288C24—2781no—
289C24—2781no—
290#41—2782no—
291#41—5561no—
292C2×Q8C22×D13911yescharacteristic
293C2×D4—21no—
294C2×D4—2782no—
295C2×D4—2782no—
296C2×D4—2781no—
297C2×D4—2781no—
298C2×D4—2781no—
299C2×D4—2782no—
300C2×D4—2781no—
301C2×D4—2781no—
302C2×D4—2781no—
303C2×D4—2781no—
304C2×D4—2781no—
305C2×D4—5561no—
306C2×D4—5561no—
307C2×D4—5561no—
308C2×D4—5564no—
309C2×D4—1391no—
310C2×D4—1391no—
311C2×D4—1391no—
312C2×D4—1391no—
313C2×D4—1391no—
314C2×D4C22×D13911yescharacteristic
315C22×C4—2781no—
316C22×C4—2781no—
317C22×C4—2781no—
318C22×C4—1391no—
319C22×C4C22×D13911yescharacteristic
320SD16—22no—
321SD16—2782no—
322SD16—5561no—
323D8—2782no—
324D8—2782no—
325D8—2782no—
326D8—2782no—
327D8—5561no—
328D8—1394no—
329M16—2782no—
330C2×C8—22no—
331C2×C8—1391no—
332C2×C8—1391no—
333C2×C8C22×D13911yescharacteristic
334C2×C8C22×D13911yescharacteristic
335C4⋊C4—21no—
336C4⋊C4—1391no—
337C4⋊C4C22×D13911yescharacteristic
338C4⋊C4C22×D13911yescharacteristic
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—2781no—
342C22⋊C4—2781no—
343C22⋊C4—2781no—
344C22⋊C4—2781no—
345C22⋊C4—2781no—
346C22⋊C4—2781no—
347C22⋊C4—1391no—
348C22⋊C4—1391no—
349C42—1391no—
350C23—21no—
351C23—2781no—
352C23—2781no—
353C23—2781no—
354C23—2781no—
355C23—5562no—
356C23—5562no—
357C23—5562no—
358C23—5562no—
359C23—5562no—
360C23—5562no—
361C23—11121no—
362C23—11121no—
363C23—11121no—
364C23—1391no—
365C23D4×D13911yescharacteristic
366Q8—21no—
367Q8—21no—
368D4—21no—
369D4—21no—
370D4—42no—
371D4—2782no—
372D4—2781no—
373D4—2781no—
374D4—2781no—
375D4—2781no—
376D4—2781no—
377D4—2781no—
378D4—5562no—
379D4—5562no—
380D4—5562no—
381D4—5562no—
382D4—5562no—
383D4—5562no—
384D4—11121no—
385D4—11121no—
386D4—1392no—
387D4—1392no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—2781no—
394C2×C4—2781no—
395C2×C4—5562no—
396C2×C4—5562no—
397C2×C4—11121no—
398C2×C4—1391no—
399C2×C4—1391no—
400C2×C4—1391no—
401C2×C4D4×D13911yescharacteristic
402C2×C4C23×D13911yescharacteristic
403C8—21no—
404C8—2781no—
405C8—2781no—
406C8D4×D13912yescomplemented
407C22—21no—
408C22—21no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—2781no—
413C22—2782no—
414C22—2782no—
415C22—2781no—
416C22—2781no—
417C22—5561no—
418C22—5561no—
419C22—5561no—
420C22—5561no—
421C22—5561no—
422C22—5561no—
423C22—5561no—
424C22—5561no—
425C22—5561no—
426C22—5561no—
427C22—11124no—
428C22—11124no—
429C22—11124no—
430C22#1798486912yescomplemented
431C22C2×D4×D13911yescharacteristic
432C4—21no—
433C4—41no—
434C4—41no—
435C4—41no—
436C4—2781no—
437C4—2781no—
438C4—2781no—
439C4C2×D4×D13911yescharacteristic
440C4#1798488811yescharacteristic
441C2—22no—
442C2—81no—
443C2—5561no—
444C2—5562no—
445C2—5562no—
446C2—11121no—
447C2—11121no—
448C2#2258158711yescharacteristic
449C2C2×#1798486911yescharacteristic
450C2#2258175511yescharacteristic
subgroupG/H
centerC22C2×D4×D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#465×C139C2
socleC22×C139C22×D4
hypercenter#465D139
hypocenterC139#3264
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. C2×#17984869C2semidirect
2. C22×D1112C2semidirect
3. #22581594C2semidirect
4. #22581587C2semidirect
5. #22581339C2semidirect
6. #22581207C2semidirect
7. #22581171C2semidirect
8. #22581147C2semidirect
9. #22581103C2semidirect
10. #22581101C2semidirect
11. #22581088C2semidirect
12. #22581086C2semidirect
13. #22581064C2semidirect
14. #22581024C2semidirect
15. #465×C139C2semidirect
16. C2×#14555786C22semidirect
18. C22×D556C22semidirect
20. C2×D4×D139C22semidirect
22. C2×#14555772C22semidirect
23. C2×#14555772C22semidirect
27. C2×D1112C22semidirect
28. C2×D1112C22semidirect
29. C2×#14555770C22semidirect
30. C2×#14555770C22semidirect
31. C2×#14555768C22semidirect
32. #17984838C22semidirect
33. #17984831C22semidirect
36. #17984817C22semidirect
37. #17984817C22semidirect
42. #17984804C22semidirect
43. #17984804C22semidirect
46. Dic139⋊C8C22semidirect
47. #17984762C22semidirect
48. #17984762C22semidirect
49. #17984762C22semidirect
50. #17984762C22semidirect
51. C22⋊(C139⋊C8)C22semidirect
52. (C2×D139)⋊C8C22semidirect
53. #17984752C22semidirect
54. C2×SD16×C139C22semidirect
55. C22×C8×C139C22semidirect
56. C22⋊Q8×C139C22semidirect
58. #106×C139C22semidirect
59. #103×C139C22semidirect
60. #102×C139C22semidirect
95. D1112D4semidirect
150. D556C2×D4semidirect
180. C8×C139C2×D4semidirect
186. C22×C139AGL(1,ℤ/8)semidirect
225. C139#3264semidirect
233. #465D139semidirect
250. C2×SD16C2×D139semidirect
259. C22×C8C2×D139semidirect
263. C22⋊Q8C2×D139semidirect
276. #106C2×D139semidirect
278. #103C2×D139semidirect
283. #102C2×D139semidirect
406. C8D4×D139semidirect
430. C22#17984869semidirect

Maximal subgroups

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

subgroupindex
C2×#179848692
C22×D11122
#225815942
#225815872
#225813392
#225812072
#225811712
#225811472
#225811032
#225811012
#225810882
#225810862
#225810642
#225810242
#465×C1392
#3264139