Finite Group Databasebeta

← #31817880

Subgroups — #31817880

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×#17984868C211yesmaximal, characteristic, complemented
2C22×#14555770C211yesmaximal, characteristic, complemented
3#22581599C211yesmaximal, characteristic, complemented
4#22581340C211yesmaximal, characteristic, complemented
5#22581204C211yesmaximal, characteristic, complemented
6#22581180C211yesmaximal, characteristic, complemented
7#22581168C211yesmaximal, characteristic, complemented
8#22581145C211yesmaximal, characteristic, complemented
9#22581104C211yesmaximal, characteristic, complemented
10#22581096C211yesmaximal, characteristic, complemented
11#22581087C211yesmaximal, characteristic, complemented
12#22581086C211yesmaximal, characteristic, complemented
13#22581063C211yesmaximal, characteristic, complemented
14#22581025C211yesmaximal, characteristic, complemented
15D42×C139C211yesmaximal, characteristic, complemented
16C2×#14555785C2211yescharacteristic, complemented
17C22×D556C2211yescharacteristic, complemented
18#17984868—24no—
19C2×#14555773C2211yescharacteristic, complemented
20C2×#14555773C2211yescharacteristic, complemented
21C2×#14555773C2211yescharacteristic, complemented
22C2×#14555770—24no—
23C2×#14555770C2211yescharacteristic
24C2×#14555770C2211yescharacteristic
25C2×#14555770C2211yescharacteristic, complemented
26C2×#14555770C2211yescharacteristic, complemented
27C2×#14555770C2211yescharacteristic, complemented
28C2×#14555770C2211yescharacteristic, complemented
29C2×#14555769C2211yescharacteristic, complemented
30C22×C139⋊C8C2211yescharacteristic, complemented
31#17984830C2211yescharacteristic, complemented
32#17984827—21no—
33#17984821C2211yescharacteristic, complemented
34#17984816C2211yescharacteristic, complemented
35#17984815—21no—
36#17984810—21no—
37C4×D556C2211yescharacteristic, complemented
38C22⋊C4×D139—21no—
39#17984773C2211yescharacteristic, complemented
40C4⋊(C139⋊C8)C2211yescharacteristic, complemented
41#17984765C2211yescharacteristic, complemented
42#17984763C2211yescharacteristic, complemented
43#17984763C2211yescharacteristic, complemented
44#17984763C2211yescharacteristic, complemented
45#17984762C2211yescharacteristic, complemented
46#17984762C2211yescharacteristic, complemented
47C22⋊(C139⋊C8)C2211yescharacteristic, complemented
48C22⋊(C139⋊C8)C2211yescharacteristic, complemented
49#17984753C2211yescharacteristic, complemented
50C22×D4×C139—21no—
51C22×D4×C139C2211yescharacteristic
52C22×D4×C139C2211yescharacteristic, complemented
53#127×C139C2211yescharacteristic, complemented
54#121×C139—21no—
55#121×C139C2211yescharacteristic
56#121×C139C2211yescharacteristic, complemented
57#120×C139—21no—
58#120×C139—21no—
59C4×D4×C139C2211yescharacteristic
60C4×D4×C139C2211yescharacteristic, complemented
61C23×D139—21no—
62#14555785—22no—
63#14555785—41no—
64C2×Dic278C2311yescharacteristic
65C2×D556—22no—
66C2×D556—21no—
67C2×D556—41no—
68C2×D556C2311yescharacteristic
69C2×D556C2311yescharacteristic
70C2×C22⋊D139—21no—
71C2×C22⋊D139—21no—
72C2×C4×D139—21no—
73C2×C4×D139—21no—
74#14555773—22no—
75#14555773—22no—
76#14555773—41no—
77#14555770—22no—
78#14555770—22no—
79#14555770—22no—
80#14555770—22no—
81#14555770—41no—
82#14555770D414yescomplemented
83#14555769—22no—
84C2×C139⋊C8—22no—
85C2×C139⋊C8C2311yescharacteristic
86C2×C139⋊C8C2311yescharacteristic
87C2×C139⋊C8C2311yescharacteristic
88C2×C139⋊C8C2311yescharacteristic
89C4⋊Dic139C2311yescharacteristic
90Dic139⋊C4—21no—
91C22⋊Dic139—21no—
92(C2×D139)⋊C4—21no—
93(C2×D139)⋊C4—21no—
94(C2×D139)⋊C4—21no—
95(C2×D139)⋊C4—21no—
96C24×C139—21no—
97C24×C139—21no—
98C2×D4×C139—22no—
99C2×D4×C139—22no—
100C2×D4×C139—21no—
101C2×D4×C139—21no—
102C2×D4×C139—21no—
103C2×D4×C139—21no—
104C2×D4×C139—21no—
105C2×D4×C139—21no—
106C2×D4×C139—41no—
107C2×D4×C139—41no—
108C2×D4×C139—44no—
109C2×D4×C139D411yescharacteristic
110C2×D4×C139C2311yescharacteristic
111C2×D4×C139C2311yescharacteristic
112C2×D4×C139C2311yescharacteristic
113C22×C4×C139—21no—
114C22×C4×C139C2311yescharacteristic
115C22×C4×C139C2311yescharacteristic
116C4⋊C4×C139D411yescharacteristic
117C4⋊C4×C139C2311yescharacteristic
118C22⋊C4×C139—21no—
119C22⋊C4×C139—21no—
120C22⋊C4×C139—21no—
121C22⋊C4×C139D411yescharacteristic
122C22⋊C4×C139D411yescharacteristic
123C42×C139C2311yescharacteristic
124C22×D139—21no—
125C22×D139—21no—
126C22×D139—42no—
127C22×D139—42no—
128C22×D139—81no—
129Dic278—21no—
130Dic278—21no—
131D556—21no—
132D556—21no—
133D556—21no—
134D556—42no—
135D556C2×D412yescomplemented
136C22⋊D139—42no—
137C22⋊D139—81no—
138C2×Dic139—21no—
139C2×Dic139—21no—
140C4×D139—42no—
141C4×D139—81no—
142C139⋊C8—21no—
143C139⋊C8—21no—
144C139⋊C8—21no—
145C139⋊C8C2×D412yescomplemented
146C23×C139—21no—
147C23×C139—21no—
148C23×C139—21no—
149C23×C139—42no—
150C23×C139—42no—
151C23×C139—42no—
152C23×C139—42no—
153C23×C139—81no—
154C23×C139—81no—
155C23×C139C2×D411yescharacteristic
156C23×C139C2×D411yescharacteristic
157D4×C139—22no—
158D4×C139—21no—
159D4×C139—21no—
160D4×C139—21no—
161D4×C139—21no—
162D4×C139—21no—
163D4×C139—42no—
164D4×C139—42no—
165D4×C139—42no—
166D4×C139—42no—
167D4×C139—42no—
168D4×C139—81no—
169D4×C139C2×D412yes—
170C2×C4×C139—21no—
171C2×C4×C139—21no—
172C2×C4×C139—21no—
173C2×C4×C139—21no—
174C2×C4×C139—21no—
175C2×C4×C139—42no—
176C2×C4×C139C2×D411yescharacteristic
177C2×C4×C139C2×D411yescharacteristic
178C2×C4×C139C2×D411yescharacteristic
179C2×C4×C139C2×D411yescharacteristic
180C2×C4×C139C2411yescharacteristic
181C22×C139—21no—
182C22×C139—21no—
183C22×C139—21no—
184C22×C139—22no—
185C22×C139—21no—
186C22×C139—21no—
187C22×C139—41no—
188C22×C139—41no—
189C22×C139—41no—
190C22×C139—41no—
191C22×C139—41no—
192C22×C139—41no—
193C22×C139—41no—
194C22×C139—41no—
195C22×C139—84no—
196C22×C139—84no—
197C22×C139AGL(1,ℤ/8)12yescomplemented
198C22×C139C22×D411yescharacteristic
199C2×D139—22no—
200C2×D139—41no—
201C2×D139—41no—
202C2×D139—41no—
203C2×D139—41no—
204C2×D139—41no—
205C2×D139—84no—
206C4×C139—21no—
207C4×C139—21no—
208C4×C139—21no—
209C4×C139—21no—
210C4×C139—41no—
211C4×C139C22×D411yescharacteristic
212C4×C139H(5,𝔽2)11yescharacteristic
213Dic139—41no—
214Dic139—41no—
215C2×C139—22no—
216C2×C139—41no—
217C2×C139—42no—
218C2×C139—81no—
219C2×C139—81no—
220C2×C139D4211yescharacteristic
221C2×C139C2×AGL(1,ℤ/8)11yescharacteristic
222C2×C139#57611yescharacteristic
223D139—42no—
224D139—81no—
225C139#326411yescharacteristic, complemented, Sylow
226#3264—1391nomaximal, Sylow
227C2×AGL(1,ℤ/8)—1391no—
228C22×D8—1391no—
229#546—1391no—
230D42D13911yescharacteristic, complemented
231#496—1391no—
232#469—1391no—
233#465—1391no—
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—21no—
244C22×D4—1391no—
245C22×D4C2×D13911yescharacteristic
246C22×D4C2×D13911yescharacteristic, complemented
247AGL(1,ℤ/8)—2784no—
248C2×SD16—1391no—
249C2×SD16—1391no—
250C2×SD16—1391no—
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×C8—1391no—
260#127C2×D13911yescharacteristic, complemented
261#124—1391no—
262#123—2781no—
263C22⋊Q8—1391no—
264#121—21no—
265#121—2781no—
266#121—1391no—
267#121C2×D13911yescharacteristic
268#121C2×D13911yescharacteristic, complemented
269#120—21no—
270#120—21no—
271#120—2781no—
272C4×D4—1391no—
273C4×D4C2×D13911yescharacteristic
274C4×D4C2×D13911yescharacteristic, complemented
275C2×C22⋊C4—2781no—
276#106—1391no—
277C4⋊C8—1391no—
278#103—1391no—
279#102—1391no—
280#102—1391no—
281#102—1391no—
282#102—1391no—
283#102—1391no—
284C22⋊C8—1391no—
285C22⋊C8—1391no—
286#97—1391no—
287C24—21no—
288C24—21no—
289C24—2781no—
290#41—2782no—
291#41—5561no—
292C2×Q8—1391no—
293C2×D4—22no—
294C2×D4—22no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—21no—
298C2×D4—21no—
299C2×D4—21no—
300C2×D4—21no—
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—44no—
304C2×D4—2782no—
305C2×D4—2781no—
306C2×D4—2781no—
307C2×D4—2781no—
308C2×D4—5561no—
309C2×D4—1391no—
310C2×D4—1391no—
311C2×D4C22⋊D13911yescharacteristic
312C2×D4C22×D13911yescharacteristic
313C2×D4C22×D13911yescharacteristic
314C2×D4C22×D13911yescharacteristic
315C22×C4—21no—
316C22×C4—2781no—
317C22×C4—2781no—
318C22×C4C22×D13911yescharacteristic
319C22×C4C22×D13911yescharacteristic
320SD16—2782no—
321SD16—2782no—
322SD16—5561no—
323D8—2782no—
324D8—2782no—
325D8—2782no—
326D8—2782no—
327D8—5561no—
328D8—1394no—
329M16—2782no—
330C2×C8—2782no—
331C2×C8—1391no—
332C2×C8—1391no—
333C2×C8—1391no—
334C2×C8—1391no—
335C4⋊C4—2781no—
336C4⋊C4—1391no—
337C4⋊C4C22⋊D13911yescharacteristic
338C4⋊C4C22×D13911yescharacteristic
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—21no—
342C22⋊C4—2781no—
343C22⋊C4—2781no—
344C22⋊C4—2781no—
345C22⋊C4—2781no—
346C22⋊C4—2781no—
347C22⋊C4C22⋊D13911yescharacteristic
348C22⋊C4C22⋊D13911yescharacteristic
349C42C22×D13911yescharacteristic
350C23—21no—
351C23—21no—
352C23—21no—
353C23—42no—
354C23—42no—
355C23—42no—
356C23—42no—
357C23—81no—
358C23—81no—
359C23—2781no—
360C23—2781no—
361C23—5562no—
362C23—5562no—
363C23—11121no—
364C23C2×C22⋊D13911yescharacteristic
365C23C2×C22⋊D13911yescharacteristic
366Q8—2781no—
367Q8—2781no—
368D4—22no—
369D4—21no—
370D4—21no—
371D4—21no—
372D4—21no—
373D4—21no—
374D4—42no—
375D4—42no—
376D4—42no—
377D4—42no—
378D4—42no—
379D4—81no—
380D4—2781no—
381D4—2781no—
382D4—2781no—
383D4—5562no—
384D4—5562no—
385D4—11121no—
386D4—1392no—
387D4D4×D13912yes—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—42no—
394C2×C4—2781no—
395C2×C4—2781no—
396C2×C4—5562no—
397C2×C4—11121no—
398C2×C4C2×C22⋊D13911yescharacteristic
399C2×C4C2×C22⋊D13911yescharacteristic
400C2×C4C2×C22⋊D13911yescharacteristic
401C2×C4C2×C22⋊D13911yescharacteristic
402C2×C4C23×D13911yescharacteristic
403C8—2781no—
404C8—2781no—
405C8—2781no—
406C8—1392no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—22no—
411C22—21no—
412C22—21no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—41no—
417C22—41no—
418C22—41no—
419C22—41no—
420C22—41no—
421C22—84no—
422C22—84no—
423C22—2782no—
424C22—5561no—
425C22—5561no—
426C22—5561no—
427C22—5561no—
428C22—5561no—
429C22—11124no—
430C22#1798486812yescomplemented
431C22C22×C22⋊D13911yescharacteristic
432C4—21no—
433C4—21no—
434C4—21no—
435C4—21no—
436C4—41no—
437C4—5561no—
438C4—5561no—
439C4C2×D4×D13911yescharacteristic
440C4#1798488711yescharacteristic
441C2—22no—
442C2—41no—
443C2—42no—
444C2—81no—
445C2—81no—
446C2—5562no—
447C2—11121no—
448C2D4×C22⋊D13911yescharacteristic
449C2C2×#1798486811yescharacteristic
450C2#2258175611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
FittingD42×C139C2
socleC22×C139C22×D4
hypercenterD42D139
hypocenterC139#3264
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. C2×#17984868C2semidirect
2. C22×#14555770C2semidirect
3. #22581599C2semidirect
4. #22581340C2semidirect
5. #22581204C2semidirect
6. #22581180C2semidirect
7. #22581168C2semidirect
8. #22581145C2semidirect
9. #22581104C2semidirect
10. #22581096C2semidirect
11. #22581087C2semidirect
12. #22581086C2semidirect
13. #22581063C2semidirect
14. #22581025C2semidirect
15. D42×C139C2semidirect
16. C2×#14555785C22semidirect
17. C22×D556C22semidirect
19. C2×#14555773C22semidirect
20. C2×#14555773C22semidirect
21. C2×#14555773C22semidirect
25. C2×#14555770C22semidirect
26. C2×#14555770C22semidirect
27. C2×#14555770C22semidirect
28. C2×#14555770C22semidirect
29. C2×#14555769C22semidirect
30. C22×C139⋊C8C22semidirect
31. #17984830C22semidirect
33. #17984821C22semidirect
34. #17984816C22semidirect
37. C4×D556C22semidirect
39. #17984773C22semidirect
40. C4⋊(C139⋊C8)C22semidirect
41. #17984765C22semidirect
42. #17984763C22semidirect
43. #17984763C22semidirect
44. #17984763C22semidirect
45. #17984762C22semidirect
46. #17984762C22semidirect
47. C22⋊(C139⋊C8)C22semidirect
48. C22⋊(C139⋊C8)C22semidirect
49. #17984753C22semidirect
52. C22×D4×C139C22semidirect
53. #127×C139C22semidirect
56. #121×C139C22semidirect
60. C4×D4×C139C22semidirect
82. #14555770D4semidirect
135. D556C2×D4semidirect
145. C139⋊C8C2×D4semidirect
197. C22×C139AGL(1,ℤ/8)semidirect
225. C139#3264semidirect
230. D42D139semidirect
246. C22×D4C2×D139semidirect
260. #127C2×D139semidirect
268. #121C2×D139semidirect
274. C4×D4C2×D139semidirect
430. C22#17984868semidirect

Maximal subgroups

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

subgroupindex
C2×#179848682
C22×#145557702
#225815992
#225813402
#225812042
#225811802
#225811682
#225811452
#225811042
#225810962
#225810872
#225810862
#225810632
#225810252
D42×C1392
#3264139