Finite Group Databasebeta

← #31817878

Subgroups — #31817878

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×D8×D139C211yesmaximal, characteristic, complemented
2#22581591C211yesmaximal, characteristic, complemented
3D4×C22⋊D139C211yesmaximal, characteristic, complemented
4#22581339C211yesmaximal, characteristic, complemented
5#22581206C211yesmaximal, characteristic, complemented
6#22581179C211yesmaximal, characteristic, complemented
7#22581170C211yesmaximal, characteristic, complemented
8#22581146C211yesmaximal, characteristic, complemented
9#22581102C211yesmaximal, characteristic, complemented
10#22581098C211yesmaximal, characteristic, complemented
11#22581087C211yesmaximal, characteristic, complemented
12#22581085C211yesmaximal, characteristic, complemented
13#22581065C211yesmaximal, characteristic, complemented
14#22581022C211yesmaximal, characteristic, complemented
15C2×AGL(1,ℤ/8)×C139C211yesmaximal, characteristic, complemented
16C22×C22⋊D139—21no—
17C2×D4×D139C2211yescharacteristic
18C2×D4×D139C2211yescharacteristic, complemented
19C2×#14555772C2211yescharacteristic, complemented
20C2×D1112C2211yescharacteristic, complemented
21C2×#14555770C2211yescharacteristic
22C2×#14555770C2211yescharacteristic, complemented
23C2×#14555770C2211yescharacteristic, complemented
24D8×D139—24no—
25C2×C8×D139C2211yescharacteristic, complemented
26#17984838C2211yescharacteristic, complemented
27#17984831C2211yescharacteristic, complemented
28#17984825—21no—
29#17984818C2211yescharacteristic, complemented
30#17984816C2211yescharacteristic, complemented
31#17984816C2211yescharacteristic, complemented
32#17984814—21no—
33#17984814—21no—
34#17984813C2211yescharacteristic
35#17984811—21no—
36#17984810—21no—
37#17984810—21no—
38D4×Dic139C2211yescharacteristic, complemented
39D4×Dic139C2211yescharacteristic, complemented
40C4×C22⋊D139C2211yescharacteristic
41C2×(C2×D139)⋊C4—21no—
42#17984774C2211yescharacteristic, complemented
43Dic139⋊C8C2211yescharacteristic, complemented
44#17984766C2211yescharacteristic, complemented
45#17984764C2211yescharacteristic, complemented
46#17984764C2211yescharacteristic, complemented
47#17984763C2211yescharacteristic, complemented
48#17984763C2211yescharacteristic, complemented
49#17984763C2211yescharacteristic, complemented
50C22⋊(C139⋊C8)C2211yescharacteristic, complemented
51(C2×D139)⋊C8C2211yescharacteristic, complemented
52#17984752C2211yescharacteristic, complemented
53C2×#41×C139C2211yescharacteristic, complemented
54C22×D4×C139C2211yescharacteristic, complemented
55AGL(1,ℤ/8)×C139—24no—
56C2×SD16×C139C2211yescharacteristic, complemented
57C2×SD16×C139C2211yescharacteristic, complemented
58C2×D8×C139C2211yescharacteristic
59C2×D8×C139C2211yescharacteristic, complemented
60C2×M16×C139C2211yescharacteristic, complemented
61C23×D139—21no—
62C23×D139—21no—
63C2×D556C2311yescharacteristic
64C2×D556C2311yescharacteristic
65C2×C22⋊D139—21no—
66C2×C22⋊D139—21no—
67C2×C22⋊D139—21no—
68C2×C22⋊D139—21no—
69C2×C22⋊D139—21no—
70C2×C22⋊D139—21no—
71C2×C22⋊D139—21no—
72C2×C22⋊D139—44no—
73C2×C22⋊D139D411yescharacteristic
74D4×D139—22no—
75D4×D139—22no—
76D4×D139—41no—
77D4×D139—41no—
78C22×Dic139—21no—
79C22×Dic139—21no—
80C2×C4×D139C2311yescharacteristic
81#14555772—41no—
82D1112—22no—
83#14555770—22no—
84#14555770—22no—
85#14555770—41no—
86C2×C139⋊C8C2311yescharacteristic
87C2×C139⋊C8C2311yescharacteristic
88C8×D139—22no—
89C4⋊Dic139C2311yescharacteristic
90C4⋊Dic139C2311yescharacteristic
91Dic139⋊C4—21no—
92Dic139⋊C4D411yescharacteristic
93C22⋊Dic139—21no—
94C22⋊Dic139—21no—
95C22⋊Dic139—21no—
96C22⋊Dic139D411yescharacteristic
97(C2×D139)⋊C4—21no—
98(C2×D139)⋊C4—21no—
99(C2×D139)⋊C4—21no—
100(C2×D139)⋊C4—21no—
101(C2×D139)⋊C4—21no—
102(C2×D139)⋊C4D411yescharacteristic
103C4×Dic139C2311yescharacteristic
104C24×C139—21no—
105#41×C139—22no—
106#41×C139—41no—
107C2×Q8×C139C2311yescharacteristic
108C2×D4×C139—22no—
109C2×D4×C139—21no—
110C2×D4×C139—21no—
111C2×D4×C139—41no—
112C2×D4×C139C2311yescharacteristic
113C2×D4×C139C2311yescharacteristic
114C2×D4×C139C2311yescharacteristic
115C22×C4×C139—21no—
116C22×C4×C139C2311yescharacteristic
117SD16×C139—22no—
118SD16×C139—22no—
119D8×C139—22no—
120D8×C139D414yescomplemented
121M16×C139—22no—
122C2×C8×C139C2311yescharacteristic
123C2×C8×C139C2311yescharacteristic
124C22×D139—21no—
125C22×D139—21no—
126C22×D139—42no—
127C22×D139—42no—
128C22×D139—42no—
129C22×D139—42no—
130C22×D139—81no—
131C22×D139—81no—
132C22×D139C2×D411yescharacteristic
133D556—21no—
134D556—21no—
135D556—21no—
136D556—21no—
137C22⋊D139—22no—
138C22⋊D139—42no—
139C22⋊D139—42no—
140C22⋊D139—42no—
141C22⋊D139—42no—
142C22⋊D139—42no—
143C22⋊D139—81no—
144C22⋊D139—81no—
145C2×Dic139—21no—
146C2×Dic139—21no—
147C2×Dic139—42no—
148C2×Dic139—81no—
149C2×Dic139C2×D411yescharacteristic
150C2×Dic139C2×D411yescharacteristic
151C2×Dic139C2×D411yescharacteristic
152C4×D139—21no—
153C4×D139—21no—
154C139⋊C8—21no—
155C139⋊C8—21no—
156C23×C139—21no—
157C23×C139—21no—
158C23×C139—21no—
159C23×C139—42no—
160C23×C139—42no—
161C23×C139—81no—
162C23×C139C2×D411yescharacteristic
163Q8×C139—21no—
164Q8×C139—21no—
165D4×C139—21no—
166D4×C139—21no—
167D4×C139—21no—
168D4×C139—21no—
169D4×C139—42no—
170D4×C139—42no—
171D4×C139C2×D412yes—
172D4×C139C2×D412yescomplemented
173C2×C4×C139—21no—
174C2×C4×C139—21no—
175C2×C4×C139—21no—
176C2×C4×C139—42no—
177C2×C4×C139C2×D411yescharacteristic
178C2×C4×C139C2411yescharacteristic
179C8×C139—21no—
180C8×C139C2×D412yescomplemented
181C22×C139—21no—
182C22×C139—22no—
183C22×C139—22no—
184C22×C139—21no—
185C22×C139—21no—
186C22×C139—41no—
187C22×C139—41no—
188C22×C139—41no—
189C22×C139—41no—
190C22×C139—41no—
191C22×C139—41no—
192C22×C139—41no—
193C22×C139—84no—
194C22×C139C22×D411yescharacteristic
195C2×D139—21no—
196C2×D139—21no—
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×D139AGL(1,ℤ/8)12yescomplemented
206C4×C139—21no—
207C4×C139—41no—
208C4×C139C22×D411yescharacteristic
209C4×C139H(5,𝔽2)11yescharacteristic
210Dic139—21no—
211Dic139—21no—
212Dic139—21no—
213Dic139—41no—
214Dic139—41no—
215C2×C139—42no—
216C2×C139—42no—
217C2×C139—41no—
218C2×C139—81no—
219C2×C139D4211yescharacteristic
220C2×C139C2×AGL(1,ℤ/8)11yescharacteristic
221C2×C139#57611yescharacteristic
222D139—22no—
223D139—81no—
224D139—81no—
225C139#326411yescharacteristic, complemented, Sylow
226#3264—1391nomaximal, Sylow
227C2×AGL(1,ℤ/8)D13911yescharacteristic, complemented
228C22×D8—1391no—
229#546—1391no—
230D42—1391no—
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×#41C2×D13911yescharacteristic, complemented
243C22×D4—2781no—
244C22×D4—1391no—
245C22×D4—1391no—
246C22×D4C2×D13911yescharacteristic, complemented
247AGL(1,ℤ/8)—24no—
248C2×SD16—1391no—
249C2×SD16C2×D13911yescharacteristic, complemented
250C2×SD16C2×D13911yescharacteristic, complemented
251C2×D8—2784no—
252C2×D8—1391no—
253C2×D8—1391no—
254C2×D8—1391no—
255C2×D8—1391no—
256C2×D8C2×D13911yescharacteristic
257C2×D8C2×D13911yescharacteristic, complemented
258C2×M16C2×D13911yescharacteristic, complemented
259C22×C8—1391no—
260#127—1391no—
261#124—1391no—
262#123—2781no—
263C22⋊Q8—1391no—
264#121—2781no—
265#121—2781no—
266#121—1391no—
267#121—1391no—
268#121—1391no—
269#120—2781no—
270#120—2781no—
271#120—2781no—
272C4×D4—1391no—
273C4×D4—1391no—
274C4×D4—1391no—
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—2781no—
289C24—2781no—
290#41—22no—
291#41—41no—
292C2×Q8C22×D13911yescharacteristic
293C2×D4—22no—
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—41no—
297C2×D4—2782no—
298C2×D4—2782no—
299C2×D4—2781no—
300C2×D4—2781no—
301C2×D4—2781no—
302C2×D4—2781no—
303C2×D4—2781no—
304C2×D4—2781no—
305C2×D4—2781no—
306C2×D4—5561no—
307C2×D4—5561no—
308C2×D4—5564no—
309C2×D4—1391no—
310C2×D4—1391no—
311C2×D4—1391no—
312C2×D4C22×D13911yescharacteristic
313C2×D4C22×D13911yescharacteristic
314C2×D4C22×D13911yescharacteristic
315C22×C4—21no—
316C22×C4—2781no—
317C22×C4—2781no—
318C22×C4—1391no—
319C22×C4C22×D13911yescharacteristic
320SD16—22no—
321SD16—22no—
322SD16—5561no—
323D8—22no—
324D8—2782no—
325D8—2782no—
326D8—2782no—
327D8—5561no—
328D8C22⋊D13914yescomplemented
329M16—22no—
330C2×C8—2782no—
331C2×C8—1391no—
332C2×C8—1391no—
333C2×C8C22×D13911yescharacteristic
334C2×C8C22×D13911yescharacteristic
335C4⋊C4—2781no—
336C4⋊C4—1391no—
337C4⋊C4—1391no—
338C4⋊C4—1391no—
339C22⋊C4—2781no—
340C22⋊C4—2781no—
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—21no—
352C23—21no—
353C23—42no—
354C23—42no—
355C23—81no—
356C23—2781no—
357C23—2781no—
358C23—5562no—
359C23—5562no—
360C23—5562no—
361C23—5562no—
362C23—11121no—
363C23—11121no—
364C23—1391no—
365C23D4×D13911yescharacteristic
366Q8—21no—
367Q8—21no—
368D4—21no—
369D4—21no—
370D4—21no—
371D4—21no—
372D4—42no—
373D4—42no—
374D4—2782no—
375D4—2781no—
376D4—2781no—
377D4—2781no—
378D4—2781no—
379D4—5562no—
380D4—5562no—
381D4—5562no—
382D4—5562no—
383D4—5562no—
384D4—11121no—
385D4—11121no—
386D4C2×C22⋊D13912yes—
387D4C2×C22⋊D13912yescomplemented
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—42no—
392C2×C4—2781no—
393C2×C4—2781no—
394C2×C4—2781no—
395C2×C4—2781no—
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—
406C8C2×C22⋊D13912yescomplemented
407C22—21no—
408C22—22no—
409C22—22no—
410C22—21no—
411C22—21no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—41no—
417C22—41no—
418C22—41no—
419C22—84no—
420C22—2781no—
421C22—2781no—
422C22—5561no—
423C22—5561no—
424C22—5561no—
425C22—5561no—
426C22—5561no—
427C22—5561no—
428C22—11124no—
429C22—11124no—
430C22—1392no—
431C22C2×D4×D13911yescharacteristic
432C4—21no—
433C4—41no—
434C4—2781no—
435C4—2781no—
436C4—2781no—
437C4—5561no—
438C4—5561no—
439C4C22×C22⋊D13911yescharacteristic
440C4#1798488711yescharacteristic
441C2—41no—
442C2—42no—
443C2—42no—
444C2—81no—
445C2—2782no—
446C2—11121no—
447C2—11121no—
448C2D4×C22⋊D13911yescharacteristic
449C2AGL(1,ℤ/8)×D13911yescharacteristic
450C2#2258175711yescharacteristic
subgroupG/H
centerC22C2×D4×D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
FittingC2×AGL(1,ℤ/8)×C139C2
socleC22×C139C22×D4
hypercenterC2×AGL(1,ℤ/8)D139
hypocenterC139#3264
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×D8×D139C2semidirect
2. #22581591C2semidirect
3. D4×C22⋊D139C2semidirect
4. #22581339C2semidirect
5. #22581206C2semidirect
6. #22581179C2semidirect
7. #22581170C2semidirect
8. #22581146C2semidirect
9. #22581102C2semidirect
10. #22581098C2semidirect
11. #22581087C2semidirect
12. #22581085C2semidirect
13. #22581065C2semidirect
14. #22581022C2semidirect
15. C2×AGL(1,ℤ/8)×C139C2semidirect
18. C2×D4×D139C22semidirect
19. C2×#14555772C22semidirect
20. C2×D1112C22semidirect
22. C2×#14555770C22semidirect
23. C2×#14555770C22semidirect
25. C2×C8×D139C22semidirect
26. #17984838C22semidirect
27. #17984831C22semidirect
29. #17984818C22semidirect
30. #17984816C22semidirect
31. #17984816C22semidirect
38. D4×Dic139C22semidirect
39. D4×Dic139C22semidirect
42. #17984774C22semidirect
43. Dic139⋊C8C22semidirect
44. #17984766C22semidirect
45. #17984764C22semidirect
46. #17984764C22semidirect
47. #17984763C22semidirect
48. #17984763C22semidirect
49. #17984763C22semidirect
50. C22⋊(C139⋊C8)C22semidirect
51. (C2×D139)⋊C8C22semidirect
52. #17984752C22semidirect
53. C2×#41×C139C22semidirect
54. C22×D4×C139C22semidirect
56. C2×SD16×C139C22semidirect
57. C2×SD16×C139C22semidirect
59. C2×D8×C139C22semidirect
60. C2×M16×C139C22semidirect
120. D8×C139D4semidirect
172. D4×C139C2×D4semidirect
180. C8×C139C2×D4semidirect
205. C2×D139AGL(1,ℤ/8)semidirect
225. C139#3264semidirect
227. C2×AGL(1,ℤ/8)D139semidirect
242. C2×#41C2×D139semidirect
246. C22×D4C2×D139semidirect
249. C2×SD16C2×D139semidirect
250. C2×SD16C2×D139semidirect
257. C2×D8C2×D139semidirect
258. C2×M16C2×D139semidirect
328. D8C22⋊D139semidirect
387. D4C2×C22⋊D139semidirect
406. C8C2×C22⋊D139semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D1392
#225815912
D4×C22⋊D1392
#225813392
#225812062
#225811792
#225811702
#225811462
#225811022
#225810982
#225810872
#225810852
#225810652
#225810222
C2×AGL(1,ℤ/8)×C1392
#3264139