Finite Group Databasebeta

← #31818166

Subgroups — #31818166

Order 17792.

464 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22581761C211yesmaximal, characteristic, complemented
2#22581756C211yesmaximal, characteristic, complemented
3#22581755C211yesmaximal, characteristic, complemented
4#22581339C211yesmaximal, characteristic, complemented
5#22581223C211yesmaximal, characteristic, complemented
6#22581221C211yesmaximal, characteristic, complemented
7#22581218C211yesmaximal, characteristic, complemented
8#22581213C211yesmaximal, characteristic, complemented
9#22581129C211yesmaximal, characteristic, complemented
10#22581126C211yesmaximal, characteristic, complemented
11#22581121C211yesmaximal, characteristic, complemented
12#22581119C211yesmaximal, characteristic, complemented
13#22581075C211yesmaximal, characteristic, complemented
14#22581073C211yesmaximal, characteristic, complemented
15#577×C139C211yesmaximal, characteristic, complemented
16#17984888C2211yescharacteristic
17#17984888C2211yescharacteristic, complemented
18#17984873—21no—
19#17984873C2211yescharacteristic, complemented
20#17984869—21no—
21#17984869—21no—
22#17984868—21no—
23#17984868C2211yescharacteristic
24#17984867—21no—
25#17984867—21no—
26#17984867C2211yescharacteristic
27#17984867C2211yescharacteristic, complemented
28#17984867C2211yescharacteristic, complemented
29#17984867C2211yescharacteristic, complemented
30#17984865—21no—
31#17984862—21no—
32#17984862—21no—
33#17984862C2211yescharacteristic
34C2×#14555772—21no—
35C2×#14555772C2211yescharacteristic, complemented
36C2×D1112C2211yescharacteristic, complemented
37C2×#14555770—21no—
38C2×#14555770C2211yescharacteristic, complemented
39D8×D139—21no—
40#17984849C2211yescharacteristic, complemented
41#17984849C2211yescharacteristic, complemented
42#17984848C2211yescharacteristic, complemented
43#17984838C2211yescharacteristic, complemented
44#17984831C2211yescharacteristic, complemented
45#17984778C2211yescharacteristic, complemented
46#17984777C2211yescharacteristic, complemented
47#17984769C2211yescharacteristic, complemented
48#17984769C2211yescharacteristic, complemented
49#17984769C2211yescharacteristic, complemented
50#17984768C2211yescharacteristic, complemented
51#17984761C2211yescharacteristic, complemented
52#17984759C2211yescharacteristic, complemented
53#17984758C2211yescharacteristic, complemented
54#17984758C2211yescharacteristic, complemented
55#17984752C2211yescharacteristic, complemented
562−1+4×C139C2211yescharacteristic, complemented
57H(5,𝔽2)×C139C2211yescharacteristic, complemented
58#137×C139—21no—
59#137×C139C2211yescharacteristic, complemented
60AGL(1,ℤ/8)×C139—21no—
61AGL(1,ℤ/8)×C139C2211yescharacteristic, complemented
62#135×C139—21no—
63#135×C139C2211yescharacteristic
64C2×SD16×C139—21no—
65C2×SD16×C139C2211yescharacteristic, complemented
66#131×C139C2211yescharacteristic, complemented
67#14555786—21no—
68#14555786—21no—
69#14555785—21no—
70#14555785—21no—
71#14555785C2311yescharacteristic
72C2×D556—21no—
73C2×D556—21no—
74C2×D556C2311yescharacteristic
75C2×D556C2311yescharacteristic
76C2×C22⋊D139—41no—
77D4×D139—21no—
78D4×D139—21no—
79D4×D139—41no—
80D4×D139—41no—
81#14555775—21no—
82#14555775D411yescharacteristic, complemented
83#14555773—21no—
84#14555773D411yescharacteristic, complemented
85#14555772—21no—
86#14555772—21no—
87#14555772—21no—
88#14555772—21no—
89#14555772—21no—
90#14555772—21no—
91#14555772—21no—
92#14555772D411yescharacteristic, complemented
93D1112—21no—
94D1112—21no—
95#14555770—21no—
96#14555770—21no—
97#14555770—21no—
98#14555770—21no—
99#14555770—21no—
100#14555770—21no—
101#14555770—21no—
102#14555770D411yescharacteristic, complemented
103#14555769—21no—
104#14555769—21no—
105#14555769C2311yescharacteristic
106#14555769C2311yescharacteristic
107#14555769C2311yescharacteristic
108#14555768—21no—
109C2×C139⋊C8—21no—
110C2×C139⋊C8—21no—
111C2×C139⋊C8C2311yescharacteristic
112C8×D139—21no—
113(C2×D139)⋊C4—41no—
114C4×Dic139C2311yescharacteristic
115#41×C139—21no—
116#41×C139—21no—
117#41×C139—21no—
118#41×C139—21no—
119#41×C139—41no—
120#41×C139C2311yescharacteristic
121#41×C139C2311yescharacteristic
122#41×C139C2311yescharacteristic
123C2×Q8×C139—21no—
124C2×Q8×C139—21no—
125C2×Q8×C139C2311yescharacteristic
126C2×D4×C139—21no—
127C2×D4×C139—21no—
128C2×D4×C139—41no—
129C2×D4×C139C2311yescharacteristic
130Q16×C139—21no—
131Q16×C139D411yescharacteristic, complemented
132SD16×C139—21no—
133SD16×C139—21no—
134SD16×C139—21no—
135SD16×C139—21no—
136SD16×C139D411yescharacteristic, complemented
137SD16×C139D411yescharacteristic, complemented
138D8×C139—21no—
139D8×C139D411yescharacteristic, complemented
140M16×C139—21no—
141M16×C139C2311yescharacteristic
142C2×C8×C139—21no—
143C2×C8×C139C2311yescharacteristic
144C22×D139—21no—
145C22×D139—21no—
146C22×D139—41no—
147C22×D139—41no—
148Dic278C2×D411yescharacteristic
149D556—21no—
150D556—21no—
151D556—21no—
152D556—21no—
153D556—41no—
154D556—41no—
155D556C2×D411yescharacteristic
156C22⋊D139—21no—
157C22⋊D139—41no—
158C22⋊D139—41no—
159C22⋊D139—82no—
160C2×Dic139—21no—
161C4×D139—21no—
162C4×D139—41no—
163C4×D139—41no—
164C139⋊C8—21no—
165C139⋊C8—21no—
166C139⋊C8—21no—
167C139⋊C8C2×D411yescharacteristic
168C139⋊C8C2×D411yescharacteristic
169C23×C139—21no—
170C23×C139—41no—
171Q8×C139—21no—
172Q8×C139—21no—
173Q8×C139—41no—
174Q8×C139C2×D411yescharacteristic
175Q8×C139C2×D411yescharacteristic
176Q8×C139C2×D411yescharacteristic
177D4×C139—21no—
178D4×C139—21no—
179D4×C139—21no—
180D4×C139—21no—
181D4×C139—21no—
182D4×C139—41no—
183D4×C139—41no—
184D4×C139—41no—
185D4×C139C2×D411yescharacteristic
186D4×C139C2×D411yescharacteristic
187D4×C139C2×D411yescharacteristic
188C2×C4×C139—21no—
189C2×C4×C139—21no—
190C2×C4×C139—21no—
191C2×C4×C139—21no—
192C2×C4×C139—41no—
193C2×C4×C139—41no—
194C2×C4×C139—41no—
195C2×C4×C139C2411yescharacteristic
196C8×C139—21no—
197C8×C139C2×D411yescharacteristic
198C8×C139C2×D411yescharacteristic
199C22×C139—21no—
200C22×C139—21no—
201C22×C139—21no—
202C22×C139—41no—
203C22×C139—81no—
204C22×C139—161no—
205C22×C139H(5,𝔽2)11yescharacteristic
206C2×D139—21no—
207C2×D139—41no—
208C2×D139—41no—
209C2×D139—81no—
210C2×D139—81no—
211C2×D139—161no—
212C2×D139—161no—
213C4×C139—21no—
214C4×C139—21no—
215C4×C139—21no—
216C4×C139—41no—
217C4×C139C22×D411yescharacteristic
218C4×C139C22×D411yescharacteristic
219Dic139—21no—
220Dic139—41no—
221C2×C139—21no—
222C2×C139—41no—
223C2×C139—41no—
224C2×C139—41no—
225C2×C139—81no—
226C2×C139D4211yescharacteristic
227D139—41no—
228D139—81no—
229D139—81no—
230C139#328811yescharacteristic, complemented, Sylow
231#3288—1391nomaximal, Sylow
232#577—1391no—
233#577D13911yescharacteristic, complemented
234#576—1391no—
235#576—1391no—
236#496—1391no—
237#472—1391no—
238#472—1391no—
239#471—1391no—
240#471—1391no—
241#455—1391no—
242#454—1391no—
243#453—1391no—
244#453—1391no—
245#444—1391no—
246#444—1391no—
2472−1+4C2×D13911yescharacteristic, complemented
248H(5,𝔽2)—1391no—
249H(5,𝔽2)—1391no—
250H(5,𝔽2)C2×D13911yescharacteristic, complemented
251#137—21no—
252#137—2781no—
253#137—1391no—
254#137C2×D13911yescharacteristic, complemented
255AGL(1,ℤ/8)—21no—
256AGL(1,ℤ/8)—2781no—
257AGL(1,ℤ/8)—2781no—
258AGL(1,ℤ/8)—2781no—
259AGL(1,ℤ/8)—2781no—
260AGL(1,ℤ/8)—2781no—
261AGL(1,ℤ/8)—1391no—
262AGL(1,ℤ/8)—1391no—
263AGL(1,ℤ/8)—1391no—
264AGL(1,ℤ/8)—1391no—
265AGL(1,ℤ/8)—1391no—
266AGL(1,ℤ/8)C2×D13911yescharacteristic, complemented
267#135—21no—
268#135—2781no—
269#135—2781no—
270#135—2781no—
271#135—1391no—
272#135C2×D13911yescharacteristic
273C2×SD16—21no—
274C2×SD16—2781no—
275C2×SD16—1391no—
276C2×SD16C2×D13911yescharacteristic, complemented
277C2×D8—2781no—
278C2×D8—2781no—
279C2×D8—1391no—
280C2×D8—1391no—
281#131—1391no—
282#131—1391no—
283#131—1391no—
284#131C2×D13911yescharacteristic, complemented
285#127—1391no—
286#124—1391no—
287#108—1391no—
288#108—1391no—
289#104—1391no—
290#104—1391no—
291#104—1391no—
292#104—1391no—
293#101—1391no—
294#100—1391no—
295#100—1391no—
296#100—1391no—
297#97—1391no—
298#41—21no—
299#41—21no—
300#41—21no—
301#41—21no—
302#41—41no—
303#41—2781no—
304#41—2781no—
305#41—2781no—
306#41—2781no—
307#41—1391no—
308#41C22×D13911yescharacteristic
309#41C22×D13911yescharacteristic
310#41C22×D13911yescharacteristic
311C2×Q8—21no—
312C2×Q8—21no—
313C2×Q8C22×D13911yescharacteristic
314C2×D4—21no—
315C2×D4—21no—
316C2×D4—41no—
317C2×D4—2781no—
318C2×D4—2781no—
319C2×D4—2781no—
320C2×D4—2781no—
321C2×D4—5561no—
322C2×D4—5561no—
323C2×D4—5561no—
324C2×D4—1391no—
325C2×D4—1391no—
326C2×D4C22×D13911yescharacteristic
327Q16—21no—
328Q16—2781no—
329Q16—1391no—
330Q16C22⋊D13911yescharacteristic, complemented
331SD16—21no—
332SD16—21no—
333SD16—21no—
334SD16—21no—
335SD16—2781no—
336SD16—2781no—
337SD16—2781no—
338SD16—2781no—
339SD16—2781no—
340SD16—2781no—
341SD16—2781no—
342SD16—2781no—
343SD16—1391no—
344SD16—1391no—
345SD16C22⋊D13911yescharacteristic, complemented
346SD16C22⋊D13911yescharacteristic, complemented
347D8—21no—
348D8—2781no—
349D8—2781no—
350D8—2781no—
351D8—2781no—
352D8—2781no—
353D8—2781no—
354D8—2781no—
355D8—2781no—
356D8—2781no—
357D8—1391no—
358D8C22⋊D13911yescharacteristic, complemented
359M16—21no—
360M16—2781no—
361M16—2781no—
362M16—2781no—
363M16—1391no—
364M16—1391no—
365M16—1391no—
366M16C22×D13911yescharacteristic
367C2×C8—21no—
368C2×C8—2781no—
369C2×C8—2781no—
370C2×C8—2781no—
371C2×C8—1391no—
372C2×C8C22×D13911yescharacteristic
373C22⋊C4—5561no—
374C42—1391no—
375C23—21no—
376C23—41no—
377C23—2781no—
378C23—2781no—
379C23—5561no—
380C23—5561no—
381Q8—21no—
382Q8—21no—
383Q8—41no—
384Q8—1391no—
385Q8D4×D13911yescharacteristic
386Q8C2×C22⋊D13911yescharacteristic
387Q8C2×C22⋊D13911yescharacteristic
388D4—21no—
389D4—21no—
390D4—21no—
391D4—21no—
392D4—21no—
393D4—41no—
394D4—41no—
395D4—41no—
396D4—2781no—
397D4—2781no—
398D4—2781no—
399D4—2781no—
400D4—2781no—
401D4—5561no—
402D4—5561no—
403D4—5561no—
404D4—5561no—
405D4—11122no—
406D4—1391no—
407D4D4×D13911yescharacteristic
408D4C2×C22⋊D13911yescharacteristic
409D4C2×C22⋊D13911yescharacteristic
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—2781no—
418C2×C4—2781no—
419C2×C4—5561no—
420C2×C4—5561no—
421C2×C4C23×D13911yescharacteristic
422C8—21no—
423C8—2781no—
424C8—2781no—
425C8—2781no—
426C8—1391no—
427C8—1391no—
428C8C2×C22⋊D13911yescharacteristic
429C8C2×C22⋊D13911yescharacteristic
430C22—21no—
431C22—21no—
432C22—21no—
433C22—41no—
434C22—81no—
435C22—161no—
436C22—2781no—
437C22—5561no—
438C22—5561no—
439C22—11121no—
440C22—11121no—
441C22—22241no—
442C22—22241no—
443C22#1798488711yescharacteristic
444C4—21no—
445C4—21no—
446C4—21no—
447C4—41no—
448C4—2781no—
449C4—5561no—
450C4C2×D4×D13911yescharacteristic
451C4C22×C22⋊D13911yescharacteristic
452C2—21no—
453C2—41no—
454C2—41no—
455C2—41no—
456C2—81no—
457C2—5561no—
458C2—11121no—
459C2—11121no—
460C2D4×C22⋊D13911yescharacteristic
subgroupG/H
centerC2D4×C22⋊D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#577×C139C2
socleC2×C139D42
hypercenter#577D139
hypocenterC139#3288
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C2 ◁ C2×C4 ◁ #577

Complements

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

NH ≅ G/Ntype
1. #22581761C2semidirect
2. #22581756C2semidirect
3. #22581755C2semidirect
4. #22581339C2semidirect
5. #22581223C2semidirect
6. #22581221C2semidirect
7. #22581218C2semidirect
8. #22581213C2semidirect
9. #22581129C2semidirect
10. #22581126C2semidirect
11. #22581121C2semidirect
12. #22581119C2semidirect
13. #22581075C2semidirect
14. #22581073C2semidirect
15. #577×C139C2semidirect
17. #17984888C22semidirect
19. #17984873C22semidirect
27. #17984867C22semidirect
28. #17984867C22semidirect
29. #17984867C22semidirect
35. C2×#14555772C22semidirect
36. C2×D1112C22semidirect
38. C2×#14555770C22semidirect
40. #17984849C22semidirect
41. #17984849C22semidirect
42. #17984848C22semidirect
43. #17984838C22semidirect
44. #17984831C22semidirect
45. #17984778C22semidirect
46. #17984777C22semidirect
47. #17984769C22semidirect
48. #17984769C22semidirect
49. #17984769C22semidirect
50. #17984768C22semidirect
51. #17984761C22semidirect
52. #17984759C22semidirect
53. #17984758C22semidirect
54. #17984758C22semidirect
55. #17984752C22semidirect
56. 2−1+4×C139C22semidirect
57. H(5,𝔽2)×C139C22semidirect
59. #137×C139C22semidirect
61. AGL(1,ℤ/8)×C139C22semidirect
65. C2×SD16×C139C22semidirect
66. #131×C139C22semidirect
82. #14555775D4semidirect
84. #14555773D4semidirect
92. #14555772D4semidirect
102. #14555770D4semidirect
131. Q16×C139D4semidirect
136. SD16×C139D4semidirect
137. SD16×C139D4semidirect
139. D8×C139D4semidirect
230. C139#3288semidirect
233. #577D139semidirect
247. 2−1+4C2×D139semidirect
250. H(5,𝔽2)C2×D139semidirect
254. #137C2×D139semidirect
266. AGL(1,ℤ/8)C2×D139semidirect
276. C2×SD16C2×D139semidirect
284. #131C2×D139semidirect
330. Q16C22⋊D139semidirect
345. SD16C22⋊D139semidirect
346. SD16C22⋊D139semidirect
358. D8C22⋊D139semidirect

Maximal subgroups

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

subgroupindex
#225817612
#225817562
#225817552
#225813392
#225812232
#225812212
#225812182
#225812132
#225811292
#225811262
#225811212
#225811192
#225810752
#225810732
#577×C1392
#3288139