Finite Group Databasebeta

← #31818171

Subgroups — #31818171

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#22581765C211yesmaximal, characteristic, complemented
2#22581760C211yesmaximal, characteristic, complemented
3#22581758C211yesmaximal, characteristic, complemented
4#22581755C211yesmaximal, characteristic, complemented
5#22581342C211yesmaximal, characteristic, complemented
6#22581224C211yesmaximal, characteristic, complemented
7#22581223C211yesmaximal, characteristic, complemented
8#22581217C211yesmaximal, characteristic, complemented
9#22581216C211yesmaximal, characteristic, complemented
10#22581132C211yesmaximal, characteristic, complemented
11#22581127C211yesmaximal, characteristic, complemented
12#22581122C211yesmaximal, characteristic, complemented
13#22581122C211yesmaximal, characteristic, complemented
14#22581076C211yesmaximal, characteristic, complemented
15#444×C139C211yesmaximal, characteristic, complemented
16#17984889C2211yescharacteristic, complemented
17#17984888C2211yescharacteristic
18#17984888C2211yescharacteristic, complemented
19#17984888C2211yescharacteristic, complemented
20#17984875—21no—
21#17984875C2211yescharacteristic, complemented
22#17984874—21no—
23#17984872C2211yescharacteristic, complemented
24#17984870—21no—
25#17984870—21no—
26#17984870—21no—
27#17984870C2211yescharacteristic
28#17984870C2211yescharacteristic, complemented
29#17984870C2211yescharacteristic, complemented
30#17984869—21no—
31#17984869—21no—
32#17984867C2211yescharacteristic
33#17984867C2211yescharacteristic, complemented
34#17984867C2211yescharacteristic, complemented
35#17984866—21no—
36#17984865—21no—
37#17984864—21no—
38#17984864—21no—
39#17984864C2211yescharacteristic
40#17984863—21no—
41C2×#14555774—21no—
42C2×#14555774C2211yescharacteristic, complemented
43C2×#14555774C2211yescharacteristic, complemented
44SD16×D139—21no—
45C2×D1112—21no—
46C2×D1112C2211yescharacteristic, complemented
47C2×D1112C2211yescharacteristic, complemented
48D8×D139—21no—
49#17984848C2211yescharacteristic, complemented
50#17984848C2211yescharacteristic, complemented
51#17984839C2211yescharacteristic, complemented
52#17984830C2211yescharacteristic, complemented
53#17984778C2211yescharacteristic, complemented
54#17984770C2211yescharacteristic, complemented
55#17984770C2211yescharacteristic, complemented
56#17984760C2211yescharacteristic, complemented
57#17984758C2211yescharacteristic, complemented
58#17984758C2211yescharacteristic, complemented
59#17984758C2211yescharacteristic, complemented
60#135×C139C2211yescharacteristic
61#131×C139C2211yescharacteristic, complemented
62#131×C139C2211yescharacteristic, complemented
63#108×C139C2211yescharacteristic, complemented
64#104×C139C2211yescharacteristic, complemented
65#104×C139C2211yescharacteristic, complemented
66#97×C139C2211yescharacteristic, complemented
67#14555786—21no—
68#14555786—21no—
69#14555786—21no—
70#14555785—21no—
71#14555785—21no—
72#14555785—21no—
73#14555785—21no—
74#14555785C2311yescharacteristic
75#14555785C2311yescharacteristic
76#14555784—21no—
77#14555784—41no—
78C2×Dic278—21no—
79C2×Dic278C2311yescharacteristic
80Q8×D139—21no—
81C2×D556—21no—
82C2×D556—21no—
83C2×D556—21no—
84C2×D556—41no—
85C2×D556C2311yescharacteristic
86C2×D556C2311yescharacteristic
87C2×D556C2311yescharacteristic
88D4×D139—21no—
89D4×D139—21no—
90D4×D139—21no—
91D4×D139—41no—
92D4×D139—41no—
93D4×D139—41no—
94Dic556—21no—
95Dic556D411yescharacteristic, complemented
96#14555775—21no—
97#14555774—21no—
98#14555774—21no—
99#14555774—21no—
100#14555774—21no—
101#14555774—21no—
102#14555774—21no—
103#14555774—21no—
104#14555774—21no—
105#14555774D411yescharacteristic, complemented
106#14555774D411yescharacteristic, complemented
107#14555773—21no—
108#14555772—21no—
109#14555772—21no—
110#14555772—21no—
111D1112—21no—
112D1112—21no—
113D1112—21no—
114D1112—21no—
115D1112—21no—
116D1112—21no—
117D1112—21no—
118D1112D411yescharacteristic, complemented
119#14555770—21no—
120#14555770—21no—
121#14555770—21no—
122#14555769C2311yescharacteristic
123#14555769C2311yescharacteristic
124#14555768—21no—
125#14555768—21no—
126C8×D139—21no—
127C8×D139—21no—
128(C2×D139)⋊C4—41no—
129#41×C139C2311yescharacteristic
130#41×C139C2311yescharacteristic
131Q16×C139D411yescharacteristic, complemented
132SD16×C139D411yescharacteristic, complemented
133SD16×C139D411yescharacteristic, complemented
134D8×C139D411yescharacteristic, complemented
135M16×C139—21no—
136M16×C139—21no—
137M16×C139C2311yescharacteristic
138M16×C139C2311yescharacteristic
139C2×C8×C139—21no—
140C2×C8×C139—21no—
141C2×C8×C139C2311yescharacteristic
142C2×C8×C139C2311yescharacteristic
143C42×C139C2311yescharacteristic
144C22×D139—21no—
145C22×D139—21no—
146C22×D139—21no—
147C22×D139—41no—
148C22×D139—41no—
149C22×D139—41no—
150Dic278—21no—
151Dic278—21no—
152Dic278—41no—
153Dic278C2×D411yescharacteristic
154Dic278C2×D411yescharacteristic
155D556—21no—
156D556—21no—
157D556—21no—
158D556—21no—
159D556—21no—
160D556—21no—
161D556—41no—
162D556—41no—
163D556—41no—
164D556—82no—
165D556C2×D411yescharacteristic
166D556C2×D411yescharacteristic
167C22⋊D139—21no—
168C22⋊D139—21no—
169C22⋊D139—41no—
170C22⋊D139—41no—
171C22⋊D139—41no—
172C22⋊D139—41no—
173C2×Dic139—21no—
174C2×Dic139—41no—
175C4×D139—21no—
176C4×D139—21no—
177C4×D139—41no—
178C4×D139—41no—
179C4×D139—41no—
180C4×D139—41no—
181C139⋊C8—21no—
182C139⋊C8—21no—
183Q8×C139C2×D411yescharacteristic
184Q8×C139C2×D411yescharacteristic
185D4×C139—21no—
186D4×C139—21no—
187D4×C139C2×D411yescharacteristic
188D4×C139C2×D411yescharacteristic
189C2×C4×C139—21no—
190C2×C4×C139—21no—
191C2×C4×C139—21no—
192C2×C4×C139C2411yescharacteristic
193C8×C139—21no—
194C8×C139—21no—
195C8×C139C2×D411yescharacteristic
196C8×C139C2×D411yescharacteristic
197C8×C139C2×D411yescharacteristic
198C8×C139C2×D411yescharacteristic
199C22×C139—21no—
200C22×C139—21no—
201C22×C139H(5,𝔽2)11yescharacteristic
202C2×D139—21no—
203C2×D139—21no—
204C2×D139—41no—
205C2×D139—41no—
206C2×D139—41no—
207C2×D139—81no—
208C2×D139—81no—
209C2×D139—81no—
210C2×D139—161no—
211C2×D139—161no—
212C2×D139—161no—
213C4×C139—21no—
214C4×C139—21no—
215C4×C139—41no—
216C4×C139C22×D411yescharacteristic
217C4×C139C22×D411yescharacteristic
218Dic139—21no—
219Dic139—21no—
220Dic139—41no—
221C2×C139—21no—
222C2×C139—41no—
223C2×C139—41no—
224C2×C139D4211yescharacteristic
225D139—41no—
226D139—41no—
227D139—81no—
228D139—81no—
229D139—81no—
230C139#328811yescharacteristic, complemented, Sylow
231#3288—1391nomaximal, Sylow
232#577—1391no—
233#577—1391no—
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#444D13911yescharacteristic, complemented
2472−1+4—1391no—
248H(5,𝔽2)—1391no—
249H(5,𝔽2)—1391no—
250H(5,𝔽2)—1391no—
251#137—2781no—
252#137—2781no—
253#137—1391no—
254#137—1391no—
255AGL(1,ℤ/8)—2781no—
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)—1391no—
267#135—2781no—
268#135—2781no—
269#135—2781no—
270#135—2781no—
271#135—1391no—
272#135C2×D13911yescharacteristic
273C2×SD16—2781no—
274C2×SD16—2781no—
275C2×SD16—1391no—
276C2×SD16—1391no—
277C2×D8—2781no—
278C2×D8—2781no—
279C2×D8—1391no—
280C2×D8—1391no—
281#131—1391no—
282#131—1391no—
283#131C2×D13911yescharacteristic, complemented
284#131C2×D13911yescharacteristic, complemented
285#127—1391no—
286#124—1391no—
287#108—1391no—
288#108C2×D13911yescharacteristic, complemented
289#104—1391no—
290#104—1391no—
291#104C2×D13911yescharacteristic, complemented
292#104C2×D13911yescharacteristic, complemented
293#101—1391no—
294#100—1391no—
295#100—1391no—
296#100—1391no—
297#97C2×D13911yescharacteristic, complemented
298#41—2781no—
299#41—2781no—
300#41—2781no—
301#41—2781no—
302#41—2781no—
303#41—2781no—
304#41—2781no—
305#41—2781no—
306#41—5561no—
307#41—1391no—
308#41—1391no—
309#41C22×D13911yescharacteristic
310#41C22×D13911yescharacteristic
311C2×Q8—2781no—
312C2×Q8—2781no—
313C2×Q8—1391no—
314C2×D4—2781no—
315C2×D4—2781no—
316C2×D4—2781no—
317C2×D4—2781no—
318C2×D4—2781no—
319C2×D4—2781no—
320C2×D4—5561no—
321C2×D4—5561no—
322C2×D4—5561no—
323C2×D4—5561no—
324C2×D4—1391no—
325C2×D4—1391no—
326C2×D4—1391no—
327Q16—2781no—
328Q16—2781no—
329Q16—1391no—
330Q16D55611yescharacteristic, complemented
331SD16—2781no—
332SD16—2781no—
333SD16—2781no—
334SD16—2781no—
335SD16—2781no—
336SD16—2781no—
337SD16—2781no—
338SD16—2781no—
339SD16—2781no—
340SD16—2781no—
341SD16—2781no—
342SD16—2781no—
343SD16—1391no—
344SD16—1391no—
345SD16D55611yescharacteristic, complemented
346SD16D55611yescharacteristic, complemented
347D8—2781no—
348D8—2781no—
349D8—2781no—
350D8—2781no—
351D8—2781no—
352D8—2781no—
353D8—2781no—
354D8—2781no—
355D8—2781no—
356D8—2781no—
357D8—1391no—
358D8D55611yescharacteristic, complemented
359M16—21no—
360M16—21no—
361M16—2781no—
362M16—2781no—
363M16—1391no—
364M16—1391no—
365M16C22×D13911yescharacteristic
366M16C22×D13911yescharacteristic
367C2×C8—21no—
368C2×C8—21no—
369C2×C8—2781no—
370C2×C8—2781no—
371C2×C8C22×D13911yescharacteristic
372C2×C8C22×D13911yescharacteristic
373C22⋊C4—5561no—
374C42C22×D13911yescharacteristic
375C23—2781no—
376C23—2781no—
377C23—2781no—
378C23—5561no—
379C23—5561no—
380C23—5561no—
381Q8—2781no—
382Q8—2781no—
383Q8—5561no—
384Q8—1391no—
385Q8—1391no—
386Q8C2×D55611yescharacteristic
387Q8C2×D55611yescharacteristic
388D4—21no—
389D4—21no—
390D4—2781no—
391D4—2781no—
392D4—2781no—
393D4—2781no—
394D4—2781no—
395D4—2781no—
396D4—2781no—
397D4—2781no—
398D4—5561no—
399D4—5561no—
400D4—5561no—
401D4—5561no—
402D4—5561no—
403D4—5561no—
404D4—5561no—
405D4—11122no—
406D4—1391no—
407D4—1391no—
408D4C2×D55611yescharacteristic
409D4C2×D55611yescharacteristic
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—2781no—
414C2×C4—2781no—
415C2×C4—2781no—
416C2×C4—5561no—
417C2×C4—5561no—
418C2×C4—5561no—
419C2×C4—5561no—
420C2×C4—5561no—
421C2×C4C23×D13911yescharacteristic
422C8—21no—
423C8—21no—
424C8—2781no—
425C8—2781no—
426C8D4×D13911yescharacteristic
427C8D4×D13911yescharacteristic
428C8C2×D55611yescharacteristic
429C8C2×D55611yescharacteristic
430C22—21no—
431C22—21no—
432C22—2781no—
433C22—2781no—
434C22—5561no—
435C22—5561no—
436C22—5561no—
437C22—11121no—
438C22—11121no—
439C22—11121no—
440C22—22241no—
441C22—22241no—
442C22—22241no—
443C22#1798488811yescharacteristic
444C4—21no—
445C4—21no—
446C4—41no—
447C4—2781no—
448C4—2781no—
449C4—5561no—
450C4C2×D4×D13911yescharacteristic
451C4C22×D55611yescharacteristic
452C2—21no—
453C2—41no—
454C2—41no—
455C2—5561no—
456C2—5561no—
457C2—11121no—
458C2—11121no—
459C2—11121no—
460C2D4×D55611yescharacteristic
subgroupG/H
centerC2D4×D556
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#444×C139C2
socleC2×C139D42
hypercenter#444D139
hypocenterC139#3288
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C2 ◁ C2×C4 ◁ #444

Complements

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

NH ≅ G/Ntype
1. #22581765C2semidirect
2. #22581760C2semidirect
3. #22581758C2semidirect
4. #22581755C2semidirect
5. #22581342C2semidirect
6. #22581224C2semidirect
7. #22581223C2semidirect
8. #22581217C2semidirect
9. #22581216C2semidirect
10. #22581132C2semidirect
11. #22581127C2semidirect
12. #22581122C2semidirect
13. #22581122C2semidirect
14. #22581076C2semidirect
15. #444×C139C2semidirect
16. #17984889C22semidirect
18. #17984888C22semidirect
19. #17984888C22semidirect
21. #17984875C22semidirect
23. #17984872C22semidirect
28. #17984870C22semidirect
29. #17984870C22semidirect
33. #17984867C22semidirect
34. #17984867C22semidirect
42. C2×#14555774C22semidirect
43. C2×#14555774C22semidirect
46. C2×D1112C22semidirect
47. C2×D1112C22semidirect
49. #17984848C22semidirect
50. #17984848C22semidirect
51. #17984839C22semidirect
52. #17984830C22semidirect
53. #17984778C22semidirect
54. #17984770C22semidirect
55. #17984770C22semidirect
56. #17984760C22semidirect
57. #17984758C22semidirect
58. #17984758C22semidirect
59. #17984758C22semidirect
61. #131×C139C22semidirect
62. #131×C139C22semidirect
63. #108×C139C22semidirect
64. #104×C139C22semidirect
65. #104×C139C22semidirect
66. #97×C139C22semidirect
95. Dic556D4semidirect
105. #14555774D4semidirect
106. #14555774D4semidirect
118. D1112D4semidirect
131. Q16×C139D4semidirect
132. SD16×C139D4semidirect
133. SD16×C139D4semidirect
134. D8×C139D4semidirect
230. C139#3288semidirect
246. #444D139semidirect
283. #131C2×D139semidirect
284. #131C2×D139semidirect
288. #108C2×D139semidirect
291. #104C2×D139semidirect
292. #104C2×D139semidirect
297. #97C2×D139semidirect
330. Q16D556semidirect
345. SD16D556semidirect
346. SD16D556semidirect
358. D8D556semidirect

Maximal subgroups

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

subgroupindex
#225817652
#225817602
#225817582
#225817552
#225813422
#225812242
#225812232
#225812172
#225812162
#225811322
#225811272
#225811222
#225810762
#444×C1392
#3288139