Finite Group Databasebeta

← #28745545

Subgroups — #28745545

Order 15104.

580 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21436494C211yesmaximal, characteristic, complemented
2#21435781C211yesmaximal, characteristic, complemented
3#21426326C211yesmaximal, characteristic, complemented
4#21426298C211yesmaximal, characteristic, complemented
5#21426286C211yesmaximal, characteristic, complemented
6#21426255C211yesmaximal, characteristic, complemented
7#21426192C211yesmaximal, characteristic, complemented
8#21426181C211yesmaximal, characteristic, complemented
9#21426150C211yesmaximal, characteristic, complemented
10#21426020C211yesmaximal, characteristic, complemented
11#21426008C211yesmaximal, characteristic, complemented
12#21425940C211yesmaximal, characteristic, complemented
13C16×C22⋊D59C211yesmaximal, characteristic, complemented
14#21425800C211yesmaximal, characteristic, complemented
15C2×C59×#357C211yesmaximal, characteristic, complemented
16C2×#14273746C2211yescharacteristic
17#16838100—21no—
18#16838046—21no—
19C2×#14273672C2211yescharacteristic, complemented
20C2×#14273668C2211yescharacteristic
21C2×#14273668C2211yescharacteristic
22C2×C16×D59C2211yescharacteristic, complemented
23#16837803C2211yescharacteristic, complemented
24#16837785C2211yescharacteristic
25#16837729—21no—
26#16837720—21no—
27#16837705—21no—
28#16837643C2211yescharacteristic
29#16837639C2211yescharacteristic, complemented
30#16837638C2211yescharacteristic
31#16837635C2211yescharacteristic
32#16837615—21no—
33#16837553—21no—
34#16837544—21no—
35D8×Dic59C2211yescharacteristic
36#16837484C2211yescharacteristic, complemented
37C8×C22⋊D59C2211yescharacteristic
38#16837439C2211yescharacteristic, complemented
39#16837230C2211yescharacteristic, complemented
40#16837227C2211yescharacteristic, complemented
41#16837227C2211yescharacteristic, complemented
42Dic59⋊C16C2211yescharacteristic, complemented
43#16837207C2211yescharacteristic, complemented
44#16837205C2211yescharacteristic, complemented
45#16837205C2211yescharacteristic, complemented
46#16837204C2211yescharacteristic, complemented
47#16837203C2211yescharacteristic
48#16837203C2211yescharacteristic
49C22⋊(C59⋊C16)C2211yescharacteristic
50(C2×D59)⋊C16C2211yescharacteristic, complemented
51C16×Dic59C2211yescharacteristic, complemented
52C22×D8×C59C2211yescharacteristic
53C22×C16×C59C2211yescharacteristic
54C2×#107×C59C2211yescharacteristic
55C59×#357C2211yescharacteristic
56C59×#357C2211yescharacteristic
57C59×#357C2211yescharacteristic
58C59×#357C2211yescharacteristic
59C2×#11745687—21no—
60#14273746—22no—
61#14273746—41no—
62C2×Dic236C2311yescharacteristic
63C2×#11745670—21no—
64C2×#11745670—21no—
65C2×D472C2311yescharacteristic
66C2×C8×D59C2311yescharacteristic
67#14273722—41no—
68#14273718—21no—
69#14273714—21no—
70#14273712—41no—
71#14273708—41no—
72#14273706—21no—
73#14273702—21no—
74#14273701—21no—
75#14273701—41no—
76#14273699—41no—
77#14273698—21no—
78#14273696—41no—
79D4×Dic59—21no—
80#14273689—21no—
81C4×C22⋊D59—41no—
82C4×C22⋊D59D411yescharacteristic
83#14273685—21no—
84C2×C22⋊Dic59—41no—
85#14273672—41no—
86#14273668—22no—
87#14273668—41no—
88C2×C59⋊C16C2311yescharacteristic
89C2×C59⋊C16C2311yescharacteristic
90C16×D59—41no—
91#14273661C2311yescharacteristic
92#14273661C2311yescharacteristic
93#14273658—21no—
94#14273658—21no—
95Dic59⋊C8D411yescharacteristic
96#14273652—21no—
97#14273649—21no—
98#14273648—21no—
99#14273648—21no—
100#14273647—21no—
101#14273647—21no—
102C22⋊(C59⋊C8)D411yescharacteristic
103(C2×D59)⋊C8D411yescharacteristic
104C8×Dic59C2311yescharacteristic
105C22×D4×C59—21no—
106C2×D8×C59—22no—
107C2×D8×C59—21no—
108C2×D8×C59—41no—
109C2×D8×C59C2311yescharacteristic
110C2×D8×C59C2311yescharacteristic
111C22×C8×C59C2311yescharacteristic
112C2×C4⋊C4×C59—21no—
113C2×C16×C59—41no—
114C2×C16×C59C2311yescharacteristic
115C2×C16×C59C2311yescharacteristic
116#107×C59—21no—
117#107×C59C2311yescharacteristic
118#107×C59C2311yescharacteristic
119C24×C59—41no—
120C2×D4×C59—21no—
121C2×D4×C59—21no—
122C2×D4×C59—42no—
123C2×D4×C59—41no—
124C2×D4×C59—81no—
125C22×C4×C59—41no—
126C22×C4×C59C2×D411yescharacteristic
127C2×C22⋊D59—41no—
128C2×C22⋊D59—41no—
129C2×C22⋊D59—41no—
130C2×C22⋊D59D811yescharacteristic
131C22×Dic59—41no—
132C22×Dic59—41no—
133#11745687—42no—
134#11745687—81no—
135C2×D236—21no—
136C2×D236—41no—
137C2×C4×D59—41no—
138C2×C4×D59C2×D411yescharacteristic
139C2×Dic118—21no—
140D8×C59—21no—
141D8×C59—21no—
142D8×C59—21no—
143D8×C59—42no—
144D8×C59#4112yes—
145C2×C8×C59—21no—
146C2×C8×C59—21no—
147C2×C8×C59C2×D411yescharacteristic
148C2×C8×C59C2411yescharacteristic
149C4⋊C4×C59—21no—
150C4⋊C4×C59—21no—
151C4⋊C4×C59—41no—
152C22⋊Dic59—41no—
153C22⋊Dic59—41no—
154C22⋊Dic59—41no—
155C22⋊Dic59—41no—
156C22⋊Dic59—41no—
157C22⋊Dic59D811yescharacteristic
158#11745670—42no—
159#11745670—81no—
160(C2×D59)⋊C4—41no—
161(C2×D59)⋊C4—41no—
162(C2×D59)⋊C4—41no—
163(C2×D59)⋊C4—41no—
164(C2×D59)⋊C4D811yescharacteristic
165C4⋊Dic59—21no—
166C4⋊Dic59—21no—
167C4⋊Dic59—41no—
168Dic59⋊C4—41no—
169Dic59⋊C4—41no—
170Dic59⋊C4D811yescharacteristic
171C4×Dic59—41no—
172C4×Dic59C2×D411yescharacteristic
173C2×C59⋊C8C2×D411yescharacteristic
174C2×C59⋊C8C2×D411yescharacteristic
175Dic236—21no—
176Dic236—21no—
177D472—21no—
178D472—21no—
179C8×D59—21no—
180C8×D59—21no—
181C16×C59—21no—
182C16×C59—21no—
183C59⋊C16—21no—
184C59⋊C16—21no—
185C23×C59—41no—
186C23×C59—41no—
187C23×C59—82no—
188C23×C59—82no—
189C23×C59—161no—
190C23×C59C2×D811yescharacteristic
191C22×D59—41no—
192C22×D59C2×D811yescharacteristic
193D4×C59—22no—
194D4×C59—41no—
195D4×C59—41no—
196D4×C59—41no—
197D4×C59—82no—
198C2×C4×C59—21no—
199C2×C4×C59—21no—
200C2×C4×C59—41no—
201C2×C4×C59—41no—
202C2×C4×C59—161no—
203C2×C4×C59C2×D811yescharacteristic
204C2×C4×C59C22×D411yescharacteristic
205C22⋊D59—22no—
206C22⋊D59—82no—
207C22⋊D59—82no—
208C22⋊D59—161no—
209C2×Dic59—41no—
210C2×Dic59—41no—
211C2×Dic59—41no—
212C2×Dic59—82no—
213C2×Dic59—161no—
214C2×Dic59C2×D811yescharacteristic
215C2×Dic59C2×D811yescharacteristic
216C2×Dic59C2×D811yescharacteristic
217D236—41no—
218D236—41no—
219D236—161no—
220C4×D59—21no—
221C4×D59—21no—
222C4×D59—161no—
223Dic118—41no—
224Dic118—41no—
225C8×C59—21no—
226C8×C59C2×#4111yescharacteristic
227C8×C59H(5,𝔽2)11yescharacteristic
228C59⋊C8—21no—
229C59⋊C8—21no—
230#33864—591nomaximal, Sylow
231C22×C59—21no—
232C22×C59—21no—
233C22×C59—42no—
234C22×C59—81no—
235C22×C59—81no—
236C22×C59—81no—
237C22×C59—81no—
238C22×C59—81no—
239C22×C59—164no—
240C22×C59#50812yes—
241C22×C59C22×D811yescharacteristic
242C2×D59—21no—
243C2×D59—21no—
244C2×D59—21no—
245C2×D59—81no—
246C2×D59—81no—
247C2×D59—81no—
248C4×C59—21no—
249C4×C59—81no—
250C4×C59—81no—
251C4×C59#54611yescharacteristic
252C4×C59#57711yescharacteristic
253Dic59—21no—
254Dic59—21no—
255Dic59—21no—
256Dic59—81no—
257Dic59—81no—
258Dic59—81no—
259#3339—591no—
260#3280—591no—
261#2242—591no—
262#2236—591no—
263#2234—591no—
264#2228—591no—
265#2217—591no—
266#2215—591no—
267#2210—591no—
268#2186—591no—
269#2184—591no—
270C4×D16—591no—
271D4×C16—591no—
272#2138—591no—
273C2×#357D5911yescharacteristic, complemented
274C2×C59—22no—
275C2×C59—82no—
276C2×C59—161no—
277C2×C59#329411yescharacteristic
278C2×C59C2×#50811yescharacteristic
279C2×C59#341511yescharacteristic
280D59—41no—
281D59—161no—
282C2×#135—591no—
283C22×D8C2×D5911yescharacteristic
284#553—1181no—
285#546—1181no—
286C2×SD32—591no—
287C2×D16—591no—
288C2×D16—591no—
289C22×C16—591no—
290C22×C16C2×D5911yescharacteristic
291#499—591no—
292#495—591no—
293#482—1181no—
294#481—1181no—
295#478—1181no—
296#467—591no—
297#466—591no—
298#466—591no—
299#466—591no—
300#463—1181no—
301#450—1181no—
302#449—1181no—
303C4×D8—591no—
304C4×D8—591no—
305C8×D4—591no—
306#427—591no—
307C2×#107C2×D5911yescharacteristic
308#367—591no—
309#366—591no—
310#366—591no—
311C4⋊C16—591no—
312#358—591no—
313#358—591no—
314#358—591no—
315#357—591no—
316#357—591no—
317#357—591no—
318#357C2×D5911yescharacteristic
319#357C2×D5911yescharacteristic
320#357C2×D5911yescharacteristic
321#357C2×D5911yescharacteristic
322C22⋊C16—591no—
323C22⋊C16—591no—
324C4×C16—591no—
325C59#3386411yescharacteristic, complemented, Sylow
326C2×#41—1181no—
327C22×D4—21no—
328#135—1182no—
329#135—2361no—
330C2×Q16—591no—
331C2×SD16—1181no—
332C2×SD16—1181no—
333C2×D8—22no—
334C2×D8—21no—
335C2×D8—41no—
336C2×D8—591no—
337C2×D8C22×D5911yescharacteristic
338C2×D8C22×D5911yescharacteristic
339C22×C8—591no—
340C22×C8C22×D5911yescharacteristic
341#126—2361no—
342#125—1181no—
343#124—1181no—
344#123—2361no—
345#123—2361no—
346C22⋊Q8—1181no—
347#121—1181no—
348#121—1181no—
349#121—1181no—
350#121—2361no—
351#121—2361no—
352#120—2361no—
353C4×D4—591no—
354C4×D4—1181no—
355C4×D4—1181no—
356C4×D4—2361no—
357#117—1181no—
358C2×C4⋊C4—21no—
359C2×C22⋊C4—2361no—
360SD32—2361no—
361D16—1182no—
362D16—2361no—
363C2×C16—41no—
364C2×C16—591no—
365C2×C16—591no—
366C2×C16—2361no—
367C2×C16C22×D5911yescharacteristic
368C2×C16C22×D5911yescharacteristic
369#107—21no—
370#107—591no—
371#107—591no—
372#107C22×D5911yescharacteristic
373#107C22×D5911yescharacteristic
374#106—1181no—
375#106—1181no—
376C4⋊C8—591no—
377#103—1181no—
378#102—1181no—
379#102—1181no—
380#102—1181no—
381#102—1181no—
382#102—1181no—
383C22⋊C8—591no—
384C22⋊C8—591no—
385C4×C8—591no—
386C24—41no—
387#41—4721no—
388#41—2362no—
389C2×Q8—1181no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—42no—
393C2×D4—41no—
394C2×D4—81no—
395C2×D4—591no—
396C2×D4—1181no—
397C2×D4—2361no—
398C2×D4—2361no—
399C2×D4—2361no—
400C2×D4—2361no—
401C22×C4—41no—
402C22×C4—591no—
403C22×C4—2361no—
404C22×C4—2361no—
405C22×C4—2361no—
406C22×C4D4×D5911yescharacteristic
407Q16—1181no—
408Q16—1181no—
409SD16—4721no—
410SD16—2362no—
411D8—21no—
412D8—21no—
413D8—21no—
414D8—42no—
415D8—1181no—
416D8—1181no—
417D8#1174568512yes—
418C2×C8—21no—
419C2×C8—21no—
420C2×C8—591no—
421C2×C8—591no—
422C2×C8—1181no—
423C2×C8—1181no—
424C2×C8D4×D5911yescharacteristic
425C2×C8C23×D5911yescharacteristic
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—41no—
429C4⋊C4—591no—
430C4⋊C4—1181no—
431C4⋊C4—1181no—
432C4⋊C4—2361no—
433C4⋊C4—2361no—
434C4⋊C4—2361no—
435C22⋊C4—591no—
436C22⋊C4—591no—
437C22⋊C4—2361no—
438C22⋊C4—2361no—
439C22⋊C4—2361no—
440C22⋊C4—2361no—
441C22⋊C4—2361no—
442C22⋊C4—2361no—
443C22⋊C4—2361no—
444C22⋊C4—2361no—
445C22⋊C4—2361no—
446C42—591no—
447C42—2361no—
448C16—21no—
449C16—21no—
450C16—1181no—
451C16—1181no—
452C23—41no—
453C23—41no—
454C23—82no—
455C23—82no—
456C23—161no—
457C23—591no—
458C23—2361no—
459C23D8×D5911yescharacteristic
460Q8—2361no—
461Q8—2361no—
462D4—22no—
463D4—41no—
464D4—41no—
465D4—41no—
466D4—82no—
467D4—1182no—
468D4—9441no—
469D4—9441no—
470D4—4722no—
471D4—4722no—
472D4—2361no—
473D4—2361no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—161no—
479C2×C4—591no—
480C2×C4—591no—
481C2×C4—591no—
482C2×C4—1181no—
483C2×C4—1181no—
484C2×C4—9441no—
485C2×C4—9441no—
486C2×C4—4722no—
487C2×C4—2361no—
488C2×C4—2361no—
489C2×C4—2361no—
490C2×C4D8×D5911yescharacteristic
491C2×C4C2×D4×D5911yescharacteristic
492C8—21no—
493C8—1181no—
494C8—1181no—
495C8C2×#1174568511yescharacteristic
496C8#1427377211yescharacteristic
497C22—21no—
498C22—21no—
499C22—42no—
500C22—81no—
501C22—81no—
502C22—81no—
503C22—81no—
504C22—81no—
505C22—164no—
506C22—1181no—
507C22—1181no—
508C22—1181no—
509C22—4721no—
510C22—4721no—
511C22—4721no—
512C22#1683783312yes—
513C22C2×D8×D5911yescharacteristic
514C4—21no—
515C4—81no—
516C4—81no—
517C4—1181no—
518C4—1181no—
519C4—1181no—
520C4—4721no—
521C4—4721no—
522C4—4721no—
523C4#1683804211yescharacteristic
524C4#1683820811yescharacteristic
525C2—22no—
526C2—82no—
527C2—161no—
528C2—9441no—
529C2—2361no—
530C2#2143590511yescharacteristic
531C2C2×#1683783311yescharacteristic
532C2#2143723311yescharacteristic
subgroupG/H
centerC22C2×D8×D59
commutator, cosocleC2×C8×C59C24
FrattiniC2×C8C23×D59
FittingC2×C59×#357C2
socleC22×C59C22×D8
hypercenterC2×#357D59
hypocenterC59#33864
LCSG ▷ C2×C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#357

Complements

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

NH ≅ G/Ntype
1. #21436494C2semidirect
2. #21435781C2semidirect
3. #21426326C2semidirect
4. #21426298C2semidirect
5. #21426286C2semidirect
6. #21426255C2semidirect
7. #21426192C2semidirect
8. #21426181C2semidirect
9. #21426150C2semidirect
10. #21426020C2semidirect
11. #21426008C2semidirect
12. #21425940C2semidirect
13. C16×C22⋊D59C2semidirect
14. #21425800C2semidirect
15. C2×C59×#357C2semidirect
19. C2×#14273672C22semidirect
22. C2×C16×D59C22semidirect
23. #16837803C22semidirect
29. #16837639C22semidirect
36. #16837484C22semidirect
38. #16837439C22semidirect
39. #16837230C22semidirect
40. #16837227C22semidirect
41. #16837227C22semidirect
42. Dic59⋊C16C22semidirect
43. #16837207C22semidirect
44. #16837205C22semidirect
45. #16837205C22semidirect
46. #16837204C22semidirect
50. (C2×D59)⋊C16C22semidirect
51. C16×Dic59C22semidirect
273. C2×#357D59semidirect
325. C59#33864semidirect

Maximal subgroups

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

subgroupindex
#214364942
#214357812
#214263262
#214262982
#214262862
#214262552
#214261922
#214261812
#214261502
#214260202
#214260082
#214259402
C16×C22⋊D592
#214258002
C2×C59×#3572
#3386459