Finite Group Databasebeta

← #31818165

Subgroups — #31818165

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#22581764C211yesmaximal, characteristic, complemented
2#22581763C211yesmaximal, characteristic, complemented
3#22581757C211yesmaximal, characteristic, complemented
4#22581756C211yesmaximal, characteristic, complemented
5#22581340C211yesmaximal, characteristic, complemented
6#22581222C211yesmaximal, characteristic, complemented
7#22581221C211yesmaximal, characteristic, complemented
8#22581215C211yesmaximal, characteristic, complemented
9#22581214C211yesmaximal, characteristic, complemented
10#22581132C211yesmaximal, characteristic, complemented
11#22581127C211yesmaximal, characteristic, complemented
12#22581120C211yesmaximal, characteristic, complemented
13#22581072C211yesmaximal, characteristic, complemented
14#22581072C211yesmaximal, characteristic, complemented
15#453×C139C211yesmaximal, characteristic, complemented
16#17984889C2211yescharacteristic, complemented
17#17984888C2211yescharacteristic
18#17984887C2211yescharacteristic, complemented
19#17984875C2211yescharacteristic, complemented
20#17984872—21no—
21#17984872C2211yescharacteristic, complemented
22#17984871—21no—
23#17984870C2211yescharacteristic, complemented
24#17984869—21no—
25#17984868—21no—
26#17984868—21no—
27#17984868C2211yescharacteristic
28#17984868C2211yescharacteristic, complemented
29#17984867—21no—
30#17984867C2211yescharacteristic, complemented
31#17984866—21no—
32#17984866—21no—
33#17984863—21no—
34#17984862—21no—
35#17984862—21no—
36#17984862C2211yescharacteristic
37#17984862C2211yescharacteristic
38#17984861—21no—
39C2×#14555773—21no—
40C2×#14555773C2211yescharacteristic, complemented
41C2×#14555773C2211yescharacteristic, complemented
42SD16×D139—21no—
43C2×#14555770—21no—
44C2×#14555770C2211yescharacteristic, complemented
45C2×#14555770C2211yescharacteristic, complemented
46D8×D139—21no—
47#17984850C2211yescharacteristic, complemented
48#17984850C2211yescharacteristic, complemented
49#17984849C2211yescharacteristic, complemented
50#17984849C2211yescharacteristic, complemented
51#17984830C2211yescharacteristic, complemented
52#17984777C2211yescharacteristic, complemented
53#17984777C2211yescharacteristic, complemented
54#17984770C2211yescharacteristic, complemented
55#17984770C2211yescharacteristic, complemented
56#17984760C2211yescharacteristic, complemented
57#17984759C2211yescharacteristic, complemented
58#17984758C2211yescharacteristic, complemented
59#17984753C2211yescharacteristic, complemented
60H(5,𝔽2)×C139C2211yescharacteristic, complemented
61AGL(1,ℤ/8)×C139C2211yescharacteristic
62AGL(1,ℤ/8)×C139C2211yescharacteristic, complemented
63#127×C139C2211yescharacteristic, complemented
64#104×C139C2211yescharacteristic, complemented
65#104×C139C2211yescharacteristic, complemented
66#100×C139C2211yescharacteristic, complemented
67#14555786—21no—
68#14555785—21no—
69#14555785—21no—
70#14555785C2311yescharacteristic
71#14555785C2311yescharacteristic
72#14555784—21no—
73#14555784—21no—
74#14555784—21no—
75#14555784—41no—
76C2×Dic278—21no—
77C2×Dic278C2311yescharacteristic
78Q8×D139—21no—
79C2×D556—21no—
80C2×D556C2311yescharacteristic
81C2×C22⋊D139—41no—
82D4×D139—21no—
83D4×D139—21no—
84D4×D139—21no—
85D4×D139—41no—
86Dic556—21no—
87#14555775—21no—
88#14555775D411yescharacteristic, complemented
89#14555775D411yescharacteristic, complemented
90#14555774—21no—
91#14555774—21no—
92#14555773—21no—
93#14555773—21no—
94#14555773—21no—
95#14555773—21no—
96#14555773—21no—
97#14555773—21no—
98#14555773—21no—
99#14555773D411yescharacteristic, complemented
100#14555773D411yescharacteristic, complemented
101#14555772—21no—
102#14555772D411yescharacteristic, complemented
103#14555772D411yescharacteristic, complemented
104D1112—21no—
105#14555770—21no—
106#14555770—21no—
107#14555770—21no—
108#14555770—21no—
109#14555770—21no—
110#14555770—21no—
111#14555770—21no—
112#14555770D411yescharacteristic, complemented
113#14555770D411yescharacteristic, complemented
114#14555769—21no—
115#14555769—21no—
116#14555769C2311yescharacteristic
117#14555769C2311yescharacteristic
118#14555768—21no—
119#14555768—21no—
120C2×C139⋊C8—21no—
121C2×C139⋊C8—21no—
122C2×C139⋊C8C2311yescharacteristic
123C2×C139⋊C8C2311yescharacteristic
124C8×D139—21no—
125C8×D139—21no—
126(C2×D139)⋊C4—41no—
127#41×C139—21no—
128#41×C139—21no—
129#41×C139C2311yescharacteristic
130#41×C139C2311yescharacteristic
131C2×D4×C139—21no—
132C2×D4×C139—21no—
133C2×D4×C139—41no—
134C2×D4×C139—41no—
135C2×D4×C139C2311yescharacteristic
136C2×D4×C139C2311yescharacteristic
137SD16×C139—21no—
138SD16×C139—21no—
139D8×C139—21no—
140D8×C139—21no—
141M16×C139C2311yescharacteristic
142M16×C139C2311yescharacteristic
143C42×C139C2311yescharacteristic
144C22×D139—21no—
145C22×D139—41no—
146C22×D139—41no—
147Dic278—21no—
148Dic278—21no—
149Dic278—41no—
150Dic278C2×D411yescharacteristic
151Dic278C2×D411yescharacteristic
152D556—21no—
153D556—21no—
154D556—41no—
155D556C2×D411yescharacteristic
156D556C2×D411yescharacteristic
157C22⋊D139—21no—
158C22⋊D139—21no—
159C22⋊D139—41no—
160C22⋊D139—41no—
161C22⋊D139—41no—
162C22⋊D139—41no—
163C2×Dic139—21no—
164C2×Dic139—41no—
165C2×Dic139—41no—
166C4×D139—21no—
167C4×D139—21no—
168C4×D139—41no—
169C4×D139—41no—
170C139⋊C8—21no—
171C139⋊C8—21no—
172C139⋊C8C2×D411yescharacteristic
173C139⋊C8C2×D411yescharacteristic
174C139⋊C8C2×D411yescharacteristic
175C139⋊C8C2×D411yescharacteristic
176C23×C139—21no—
177C23×C139—21no—
178C23×C139—41no—
179Q8×C139C2×D411yescharacteristic
180Q8×C139C2×D411yescharacteristic
181D4×C139—21no—
182D4×C139—21no—
183D4×C139—21no—
184D4×C139—21no—
185D4×C139—21no—
186D4×C139—21no—
187D4×C139—41no—
188D4×C139—41no—
189D4×C139—82no—
190D4×C139C2×D411yescharacteristic
191D4×C139C2×D411yescharacteristic
192C2×C4×C139—21no—
193C2×C4×C139—21no—
194C2×C4×C139—21no—
195C2×C4×C139—41no—
196C2×C4×C139C2411yescharacteristic
197C8×C139—21no—
198C8×C139—21no—
199C22×C139—21no—
200C22×C139—21no—
201C22×C139—41no—
202C22×C139—41no—
203C22×C139—81no—
204C22×C139—81no—
205C22×C139—161no—
206C22×C139H(5,𝔽2)11yescharacteristic
207C2×D139—21no—
208C2×D139—21no—
209C2×D139—41no—
210C2×D139—81no—
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×C139—81no—
225C2×C139—81no—
226C2×C139D4211yescharacteristic
227D139—41no—
228D139—41no—
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#453D13911yescharacteristic, complemented
245#444—1391no—
246#444—1391no—
2472−1+4—1391no—
248H(5,𝔽2)—1391no—
249H(5,𝔽2)—1391no—
250H(5,𝔽2)C2×D13911yescharacteristic, complemented
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)C2×D13911yescharacteristic
266AGL(1,ℤ/8)C2×D13911yescharacteristic, complemented
267#135—2781no—
268#135—2781no—
269#135—2781no—
270#135—2781no—
271#135—1391no—
272#135—1391no—
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#131—1391no—
284#131—1391no—
285#127C2×D13911yescharacteristic, complemented
286#124—1391no—
287#108—1391no—
288#108—1391no—
289#104—1391no—
290#104—1391no—
291#104C2×D13911yescharacteristic, complemented
292#104C2×D13911yescharacteristic, complemented
293#101—1391no—
294#100—1391no—
295#100—1391no—
296#100C2×D13911yescharacteristic, complemented
297#97—1391no—
298#41—21no—
299#41—21no—
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—21no—
315C2×D4—21no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—2781no—
319C2×D4—2781no—
320C2×D4—2781no—
321C2×D4—2781no—
322C2×D4—5561no—
323C2×D4—5561no—
324C2×D4—1391no—
325C2×D4C22×D13911yescharacteristic
326C2×D4C22×D13911yescharacteristic
327Q16—2781no—
328Q16—2781no—
329Q16—1391no—
330Q16—1391no—
331SD16—21no—
332SD16—21no—
333SD16—2781no—
334SD16—2781no—
335SD16—2781no—
336SD16—2781no—
337SD16—2781no—
338SD16—2781no—
339SD16—2781no—
340SD16—2781no—
341SD16—2781no—
342SD16—2781no—
343SD16—1391no—
344SD16—1391no—
345SD16—1391no—
346SD16—1391no—
347D8—21no—
348D8—21no—
349D8—2781no—
350D8—2781no—
351D8—2781no—
352D8—2781no—
353D8—2781no—
354D8—2781no—
355D8—2781no—
356D8—2781no—
357D8—1391no—
358D8—1391no—
359M16—2781no—
360M16—2781no—
361M16—2781no—
362M16—2781no—
363M16—1391no—
364M16—1391no—
365M16C22×D13911yescharacteristic
366M16C22×D13911yescharacteristic
367C2×C8—2781no—
368C2×C8—2781no—
369C2×C8—2781no—
370C2×C8—2781no—
371C2×C8—1391no—
372C2×C8—1391no—
373C22⋊C4—5561no—
374C42C22×D13911yescharacteristic
375C23—21no—
376C23—21no—
377C23—41no—
378C23—2781no—
379C23—5561no—
380C23—5561no—
381Q8—2781no—
382Q8—2781no—
383Q8—5561no—
384Q8—1391no—
385Q8—1391no—
386Q8D4×D13911yescharacteristic
387Q8D4×D13911yescharacteristic
388D4—21no—
389D4—21no—
390D4—21no—
391D4—21no—
392D4—21no—
393D4—21no—
394D4—41no—
395D4—41no—
396D4—82no—
397D4—2781no—
398D4—2781no—
399D4—2781no—
400D4—2781no—
401D4—5561no—
402D4—5561no—
403D4—5561no—
404D4—5561no—
405D4—5561no—
406D4—1391no—
407D4—1391no—
408D4D4×D13911yescharacteristic
409D4D4×D13911yescharacteristic
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—41no—
414C2×C4—2781no—
415C2×C4—2781no—
416C2×C4—2781no—
417C2×C4—5561no—
418C2×C4—5561no—
419C2×C4—5561no—
420C2×C4—5561no—
421C2×C4C23×D13911yescharacteristic
422C8—21no—
423C8—21no—
424C8—2781no—
425C8—2781no—
426C8—1391no—
427C8—1391no—
428C8—1391no—
429C8—1391no—
430C22—21no—
431C22—21no—
432C22—41no—
433C22—41no—
434C22—81no—
435C22—81no—
436C22—161no—
437C22—2781no—
438C22—2781no—
439C22—5561no—
440C22—11121no—
441C22—22241no—
442C22—22241no—
443C22#1798488711yescharacteristic
444C4—21no—
445C4—21no—
446C4—41no—
447C4—2781no—
448C4—2781no—
449C4—5561no—
450C4C2×D4×D13911yescharacteristic
451C4C2×D4×D13911yescharacteristic
452C2—21no—
453C2—41no—
454C2—41no—
455C2—81no—
456C2—81no—
457C2—5561no—
458C2—5561no—
459C2—11121no—
460C2#2258158511yescharacteristic
subgroupG/H
centerC2#22581585
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#453×C139C2
socleC2×C139D42
hypercenter#453D139
hypocenterC139#3288
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C2 ◁ C2×C4 ◁ #453

Complements

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

NH ≅ G/Ntype
1. #22581764C2semidirect
2. #22581763C2semidirect
3. #22581757C2semidirect
4. #22581756C2semidirect
5. #22581340C2semidirect
6. #22581222C2semidirect
7. #22581221C2semidirect
8. #22581215C2semidirect
9. #22581214C2semidirect
10. #22581132C2semidirect
11. #22581127C2semidirect
12. #22581120C2semidirect
13. #22581072C2semidirect
14. #22581072C2semidirect
15. #453×C139C2semidirect
16. #17984889C22semidirect
18. #17984887C22semidirect
19. #17984875C22semidirect
21. #17984872C22semidirect
23. #17984870C22semidirect
28. #17984868C22semidirect
30. #17984867C22semidirect
40. C2×#14555773C22semidirect
41. C2×#14555773C22semidirect
44. C2×#14555770C22semidirect
45. C2×#14555770C22semidirect
47. #17984850C22semidirect
48. #17984850C22semidirect
49. #17984849C22semidirect
50. #17984849C22semidirect
51. #17984830C22semidirect
52. #17984777C22semidirect
53. #17984777C22semidirect
54. #17984770C22semidirect
55. #17984770C22semidirect
56. #17984760C22semidirect
57. #17984759C22semidirect
58. #17984758C22semidirect
59. #17984753C22semidirect
60. H(5,𝔽2)×C139C22semidirect
62. AGL(1,ℤ/8)×C139C22semidirect
63. #127×C139C22semidirect
64. #104×C139C22semidirect
65. #104×C139C22semidirect
66. #100×C139C22semidirect
88. #14555775D4semidirect
89. #14555775D4semidirect
99. #14555773D4semidirect
100. #14555773D4semidirect
102. #14555772D4semidirect
103. #14555772D4semidirect
112. #14555770D4semidirect
113. #14555770D4semidirect
230. C139#3288semidirect
244. #453D139semidirect
250. H(5,𝔽2)C2×D139semidirect
266. AGL(1,ℤ/8)C2×D139semidirect
285. #127C2×D139semidirect
291. #104C2×D139semidirect
292. #104C2×D139semidirect
296. #100C2×D139semidirect

Maximal subgroups

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

subgroupindex
#225817642
#225817632
#225817572
#225817562
#225813402
#225812222
#225812212
#225812152
#225812142
#225811322
#225811272
#225811202
#225810722
#453×C1392
#3288139