Finite Group Databasebeta

← #28743797

Subgroups — #28743797

Order 15104.

568 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21434735C211yesmaximal, characteristic, complemented
2#21426304C211yesmaximal, characteristic, complemented
3#21426287C211yesmaximal, characteristic, complemented
4#21426243C211yesmaximal, characteristic, complemented
5#21426233C211yesmaximal, characteristic, complemented
6#21426151C211yesmaximal, characteristic, complemented
7#21426151C211yesmaximal, characteristic, complemented
8#21426025C211yesmaximal, characteristic, complemented
9#21426008C211yesmaximal, characteristic
10#21425970C211yesmaximal, characteristic, complemented
11#21425960C211yesmaximal, characteristic, complemented
12C4×#14273671C211yesmaximal, characteristic, complemented
13C4×#14273668C211yesmaximal, characteristic, complemented
14#21425903C211yesmaximal, characteristic, complemented
15C59×#2948C211yesmaximal, characteristic, complemented
16#16838023—21no—
17C2×#14273671C2211yescharacteristic
18C2×#14273671C2211yescharacteristic
19C2×#14273668C2211yescharacteristic
20C2×#14273668C2211yescharacteristic
21#16837807C2211yescharacteristic, complemented
22#16837786C2211yescharacteristic, complemented
23#16837762—21no—
24#16837648—21no—
25#16837643C2211yescharacteristic
26#16837638C2211yescharacteristic
27#16837504—21no—
28C4×Dic236C2211yescharacteristic, complemented
29C4×D472C2211yescharacteristic, complemented
30#16837229C2211yescharacteristic, complemented
31#16837229C2211yescharacteristic, complemented
32#16837227C2211yescharacteristic, complemented
33#16837227C2211yescharacteristic, complemented
34C4⋊(C59⋊C16)C2211yescharacteristic, complemented
35C4⋊(C59⋊C16)C2211yescharacteristic, complemented
36#16837205C2211yescharacteristic, complemented
37#16837205C2211yescharacteristic, complemented
38#16837203C2211yescharacteristic
39#16837203C2211yescharacteristic
40#16837203C2211yescharacteristic
41#16837203C2211yescharacteristic
42#16837202C2211yescharacteristic, complemented
43#16837202C2211yescharacteristic, complemented
44C22⋊(C59⋊C16)C2211yescharacteristic
45C22⋊(C59⋊C16)C2211yescharacteristic
46#16837178C2211yescharacteristic, complemented
47C4×C59⋊C16C2211yescharacteristic, complemented
48C22×D8×C59C2211yescharacteristic
49C59×#518—21no—
50C59×#442—21no—
51C59×#442—21no—
52C4×D8×C59C2211yescharacteristic
53C4×D8×C59C2211yescharacteristic
54C4×D8×C59C2211yescharacteristic
55C4×D8×C59C2211yescharacteristic
56C59×#427C2211yescharacteristic
57C59×#418—21no—
58C59×#405C2211yescharacteristic
59C2×Dic236C2311yescharacteristic
60C2×#11745660—21no—
61C2×D472C2311yescharacteristic
62#14273727—21no—
63#14273722—41no—
64#14273715—21no—
65#14273713—41no—
66#14273709—41no—
67#14273706—21no—
68#14273705—41no—
69#14273701—21no—
70C4×Dic118—21no—
71C4×D236—21no—
72#14273671—22no—
73#14273671—22no—
74#14273668—22no—
75#14273668—22no—
76C2×C59⋊C16C2311yescharacteristic
77C2×C59⋊C16C2311yescharacteristic
78C2×C59⋊C16C2311yescharacteristic
79C2×C59⋊C16C2311yescharacteristic
80#14273661—21no—
81#14273661C2311yescharacteristic
82#14273661C2311yescharacteristic
83#14273652—21no—
84#14273652—21no—
85#14273649—21no—
86#14273649—21no—
87C22×D4×C59—21no—
88C2×D8×C59—22no—
89C2×D8×C59—22no—
90C2×D8×C59—21no—
91C2×D8×C59C2311yescharacteristic
92C2×D8×C59C2311yescharacteristic
93C2×M16×C59D411yescharacteristic
94C22×C8×C59C2311yescharacteristic
95C4×D4×C59—21no—
96C4×D4×C59—21no—
97C4×D4×C59—21no—
98C4×D4×C59—21no—
99C4×D4×C59—41no—
100C4×D4×C59—41no—
101#117×C59—21no—
102#117×C59D411yescharacteristic
103C2×C22⋊C4×C59—41no—
104C2×C22⋊C4×C59—41no—
105#107×C59C2311yescharacteristic
106#107×C59C2311yescharacteristic
107#106×C59—21no—
108#102×C59—21no—
109#102×C59—21no—
110#102×C59—21no—
111#102×C59—21no—
112#97×C59D411yescharacteristic
113#97×C59D411yescharacteristic
114C4×C8×C59C2311yescharacteristic
115C4×C8×C59C2311yescharacteristic
116C24×C59—41no—
117C2×D4×C59—24no—
118C2×D4×C59—21no—
119C2×D4×C59—21no—
120C2×D4×C59—42no—
121C2×D4×C59—41no—
122C22×C4×C59—41no—
123C22×C4×C59—41no—
124C22×C4×C59—41no—
125C22×C4×C59—41no—
126C22×C4×C59C2×D411yescharacteristic
127C2×C22⋊D59—41no—
128C2×D236—21no—
129C2×C4×D59—41no—
130C2×Dic118—21no—
131C2×Dic118—41no—
132D8×C59—24no—
133D8×C59—21no—
134D8×C59—21no—
135D8×C59#4112yes—
136D8×C59#4112yes—
137M16×C59—41no—
138C2×C8×C59—21no—
139C2×C8×C59—21no—
140C2×C8×C59C2×D411yescharacteristic
141C2×C8×C59C2×D411yescharacteristic
142C2×C8×C59C2×D411yescharacteristic
143C2×C8×C59C2411yescharacteristic
144C4⋊C4×C59—21no—
145C4⋊C4×C59—21no—
146C4⋊C4×C59D811yescharacteristic
147C4⋊C4×C59D811yescharacteristic
148C22⋊C4×C59—41no—
149C22⋊C4×C59—41no—
150C22⋊C4×C59—41no—
151C22⋊C4×C59—41no—
152C22⋊C4×C59—41no—
153C22⋊C4×C59D811yescharacteristic
154C22⋊C4×C59D811yescharacteristic
155C42×C59—41no—
156C42×C59C2×D411yescharacteristic
157C42×C59C2×D411yescharacteristic
158C22⋊Dic59—41no—
159(C2×D59)⋊C4—41no—
160(C2×D59)⋊C4—41no—
161(C2×D59)⋊C4—41no—
162(C2×D59)⋊C4—41no—
163C4⋊Dic59—21no—
164C4⋊Dic59—21no—
165C4⋊Dic59—41no—
166Dic59⋊C4—41no—
167Dic59⋊C4—41no—
168C4×Dic59—41no—
169Dic236—21no—
170Dic236—21no—
171D472—21no—
172D472—21no—
173#11745660—42no—
174C59⋊C16—21no—
175C59⋊C16—21no—
176C59⋊C16—21no—
177C59⋊C16—21no—
178C23×C59—44no—
179C23×C59—41no—
180C23×C59—41no—
181C23×C59—161no—
182C23×C59—161no—
183C23×C59C2×D811yescharacteristic
184C22×D59—41no—
185D4×C59—22no—
186D4×C59—22no—
187D4×C59—44no—
188D4×C59—41no—
189D4×C59—41no—
190C2×C4×C59—21no—
191C2×C4×C59—21no—
192C2×C4×C59—41no—
193C2×C4×C59—41no—
194C2×C4×C59—161no—
195C2×C4×C59—161no—
196C2×C4×C59—161no—
197C2×C4×C59—161no—
198C2×C4×C59C2×D811yescharacteristic
199C2×C4×C59C2×D811yescharacteristic
200C2×C4×C59C2×D811yescharacteristic
201C2×C4×C59C2×D811yescharacteristic
202C2×C4×C59C2×D811yescharacteristic
203C2×C4×C59C22×D411yescharacteristic
204C22⋊D59—161no—
205C2×Dic59—41no—
206C2×Dic59—41no—
207C2×Dic59—41no—
208D236—41no—
209D236—41no—
210C4×D59—161no—
211Dic118—41no—
212Dic118—41no—
213Dic118—161no—
214C8×C59—21no—
215C8×C59—21no—
216C8×C59—21no—
217C8×C59C2×#4111yescharacteristic
218C8×C59C2×#4111yescharacteristic
219#33678—591nomaximal, Sylow
220C22×C59—21no—
221C22×C59—21no—
222C22×C59—21no—
223C22×C59—42no—
224C22×C59—42no—
225C22×C59—81no—
226C22×C59—81no—
227C22×C59—81no—
228C22×C59—81no—
229C22×C59—164no—
230C22×C59C22×D811yescharacteristic
231C2×D59—81no—
232C2×D59—81no—
233C2×D59—81no—
234C4×C59—21no—
235C4×C59—21no—
236C4×C59—21no—
237C4×C59—21no—
238C4×C59—21no—
239C4×C59—81no—
240C4×C59—81no—
241C4×C59#52511yescharacteristic
242C4×C59#57511yescharacteristic
243Dic59—81no—
244Dic59—81no—
245Dic59—81no—
246#3175—591no—
247#2948D5911yescharacteristic, complemented
248#2237—591no—
249#2234—591no—
250#2226—591no—
251#2224—591no—
252#2210—591no—
253#2210—591no—
254#2187—591no—
255#2184—591no—
256#2177—591no—
257#2175—591no—
258C4×SD32—591no—
259C4×D16—591no—
260#2164—591no—
261C2×C59—41no—
262C2×C59—82no—
263C2×C59—82no—
264C2×C59#310011yescharacteristic
265C2×C59#341511yescharacteristic
266C2×C59#341611yescharacteristic
267D59—161no—
268C22×D8C2×D5911yescharacteristic
269#542—1181no—
270#518—21no—
271C2×SD32—591no—
272C2×SD32—591no—
273C2×D16—591no—
274C2×D16—591no—
275#500—591no—
276#495—591no—
277#489—1181no—
278#468—1181no—
279#467—591no—
280#466—591no—
281#442—21no—
282#442—21no—
283#440—1181no—
284C4×Q16—591no—
285C4×D8—591no—
286C4×D8C2×D5911yescharacteristic
287C4×D8C2×D5911yescharacteristic
288C4×D8C2×D5911yescharacteristic
289C4×D8C2×D5911yescharacteristic
290#427C2×D5911yescharacteristic
291#418—21no—
292#405C2×D5911yescharacteristic
293#367—591no—
294#367—591no—
295#366—591no—
296#366—591no—
297C4⋊C16—591no—
298C4⋊C16—591no—
299#358—591no—
300#358—591no—
301#357—591no—
302#357—591no—
303#357—591no—
304#357—591no—
305#357—591no—
306#357—591no—
307C22⋊C16—591no—
308C22⋊C16—591no—
309#346—591no—
310C4×C16—591no—
311C59#3367811yescharacteristic, complemented, Sylow
312C22×D4—21no—
313C2×Q16—591no—
314C2×SD16—1181no—
315C2×D8—22no—
316C2×D8—22no—
317C2×D8—21no—
318C2×D8—591no—
319C2×D8C22×D5911yescharacteristic
320C2×D8C22×D5911yescharacteristic
321C2×M16C22⋊D5911yescharacteristic
322C22×C8C22×D5911yescharacteristic
323C4⋊Q8—1181no—
324#126—2361no—
325#124—1181no—
326#124—2361no—
327#123—2361no—
328C22⋊Q8—1181no—
329C22⋊Q8—2361no—
330#121—1181no—
331C4×Q8—1181no—
332C4×D4—21no—
333C4×D4—21no—
334C4×D4—21no—
335C4×D4—21no—
336C4×D4—41no—
337C4×D4—41no—
338C4×D4—1181no—
339#117—21no—
340#117C22⋊D5911yescharacteristic
341C2×C22⋊C4—41no—
342C2×C22⋊C4—41no—
343SD32—1182no—
344SD32—1182no—
345D16—1182no—
346D16—1182no—
347C2×C16—591no—
348C2×C16—591no—
349C2×C16—591no—
350C2×C16—591no—
351#107—591no—
352#107—591no—
353#107—1181no—
354#107C22×D5911yescharacteristic
355#107C22×D5911yescharacteristic
356#106—21no—
357#103—1181no—
358#103—1181no—
359#102—21no—
360#102—21no—
361#102—21no—
362#102—21no—
363#102—1181no—
364#102—1181no—
365#97C22⋊D5911yescharacteristic
366#97C22⋊D5911yescharacteristic
367C4×C8C22×D5911yescharacteristic
368C4×C8C22×D5911yescharacteristic
369C24—41no—
370C2×Q8—1181no—
371C2×Q8—2361no—
372C2×D4—24no—
373C2×D4—21no—
374C2×D4—21no—
375C2×D4—42no—
376C2×D4—41no—
377C2×D4—1181no—
378C2×D4—2361no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—2361no—
384C22×C4C2×C22⋊D5911yescharacteristic
385Q16—1181no—
386Q16—1181no—
387SD16—2362no—
388D8—24no—
389D8—21no—
390D8—21no—
391D8—1181no—
392D8—1181no—
393D8#1174568512yes—
394D8#1174568512yes—
395M16—41no—
396C2×C8—21no—
397C2×C8—21no—
398C2×C8C2×C22⋊D5911yescharacteristic
399C2×C8C2×C22⋊D5911yescharacteristic
400C2×C8C2×C22⋊D5911yescharacteristic
401C2×C8C23×D5911yescharacteristic
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—1181no—
405C4⋊C4—1181no—
406C4⋊C4—2361no—
407C4⋊C4—2361no—
408C4⋊C4—2361no—
409C4⋊C4#1174566911yescharacteristic
410C4⋊C4#1174566911yescharacteristic
411C22⋊C4—41no—
412C22⋊C4—41no—
413C22⋊C4—41no—
414C22⋊C4—41no—
415C22⋊C4—41no—
416C22⋊C4—2361no—
417C22⋊C4—2361no—
418C22⋊C4—2361no—
419C22⋊C4—2361no—
420C22⋊C4—2361no—
421C22⋊C4#1174566911yescharacteristic
422C22⋊C4#1174566911yescharacteristic
423C42—41no—
424C42—2361no—
425C42C2×C22⋊D5911yescharacteristic
426C42C2×C22⋊D5911yescharacteristic
427C16—1181no—
428C16—1181no—
429C16—1181no—
430C16—1181no—
431C23—44no—
432C23—41no—
433C23—41no—
434C23—161no—
435C23—161no—
436C23—2361no—
437C23C2×#1174566911yescharacteristic
438Q8—9441no—
439Q8—2361no—
440Q8—2361no—
441D4—22no—
442D4—22no—
443D4—44no—
444D4—41no—
445D4—41no—
446D4—9441no—
447D4—2361no—
448D4—2361no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—161no—
454C2×C4—161no—
455C2×C4—161no—
456C2×C4—161no—
457C2×C4—9441no—
458C2×C4—2361no—
459C2×C4—2361no—
460C2×C4—2361no—
461C2×C4C2×#1174566911yescharacteristic
462C2×C4C2×#1174566911yescharacteristic
463C2×C4C2×#1174566911yescharacteristic
464C2×C4C2×#1174566911yescharacteristic
465C2×C4C2×#1174566911yescharacteristic
466C2×C4C22×C22⋊D5911yescharacteristic
467C8—21no—
468C8—21no—
469C8—21no—
470C8C2×#1174568511yescharacteristic
471C8C2×#1174568511yescharacteristic
472C22—21no—
473C22—21no—
474C22—21no—
475C22—42no—
476C22—42no—
477C22—81no—
478C22—81no—
479C22—81no—
480C22—81no—
481C22—164no—
482C22—4721no—
483C22—4721no—
484C22—4721no—
485C22C22×#1174566911yescharacteristic
486C4—21no—
487C4—21no—
488C4—21no—
489C4—21no—
490C4—21no—
491C4—81no—
492C4—81no—
493C4—4721no—
494C4—4721no—
495C4—4721no—
496C4#1683791311yescharacteristic
497C4#1683820011yescharacteristic
498C2—41no—
499C2—82no—
500C2—82no—
501C2—9441no—
502C2#2143409611yescharacteristic
503C2#2143723511yescharacteristic
504C2#2143724311yescharacteristic
subgroupG/H
centerC22C22×#11745669
commutator, cosocleC2×C8×C59C24
FrattiniC2×C8C23×D59
FittingC59×#2948C2
socleC22×C59C22×D8
prime radical#21426008C2
hypercenter#2948D59
hypocenterC59#33678
LCSG ▷ C2×C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #2948

Complements

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

NH ≅ G/Ntype
1. #21434735C2semidirect
2. #21426304C2semidirect
3. #21426287C2semidirect
4. #21426243C2semidirect
5. #21426233C2semidirect
6. #21426151C2semidirect
7. #21426151C2semidirect
8. #21426025C2semidirect
10. #21425970C2semidirect
11. #21425960C2semidirect
12. C4×#14273671C2semidirect
13. C4×#14273668C2semidirect
14. #21425903C2semidirect
15. C59×#2948C2semidirect
21. #16837807C22semidirect
22. #16837786C22semidirect
28. C4×Dic236C22semidirect
29. C4×D472C22semidirect
30. #16837229C22semidirect
31. #16837229C22semidirect
32. #16837227C22semidirect
33. #16837227C22semidirect
34. C4⋊(C59⋊C16)C22semidirect
35. C4⋊(C59⋊C16)C22semidirect
36. #16837205C22semidirect
37. #16837205C22semidirect
42. #16837202C22semidirect
43. #16837202C22semidirect
46. #16837178C22semidirect
47. C4×C59⋊C16C22semidirect
247. #2948D59semidirect
311. C59#33678semidirect

Maximal subgroups

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

subgroupindex
#214347352
#214263042
#214262872
#214262432
#214262332
#214261512
#214260252
#214260082
#214259702
#214259602
C4×#142736712
C4×#142736682
#214259032
C59×#29482
#3367859