Finite Group Databasebeta

← #28745553

Subgroups — #28745553

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#21436501C211yesmaximal, characteristic, complemented
2#21435781C211yesmaximal, characteristic, complemented
3#21426326C211yesmaximal, characteristic, complemented
4#21426299C211yesmaximal, characteristic, complemented
5#21426285C211yesmaximal, characteristic, complemented
6#21426251C211yesmaximal, characteristic, complemented
7#21426190C211yesmaximal, characteristic, complemented
8#21426179C211yesmaximal, characteristic, complemented
9#21426149C211yesmaximal, characteristic, complemented
10#21426016C211yesmaximal, characteristic, complemented
11D16×Dic59C211yesmaximal, characteristic, complemented
12(C22⋊D59)⋊C16C211yesmaximal, characteristic, complemented
13#21425800C211yesmaximal, characteristic, complemented
14C2×#16837203C211yesmaximal, characteristic, complemented
15C59×#2184C211yesmaximal, characteristic, complemented
16C2×#14273746C2211yescharacteristic
17#16838104—21no—
18#16838046—21no—
19C2×#14273671C2211yescharacteristic, complemented
20C22×C59⋊C16C2211yescharacteristic
21C2×C16×D59C2211yescharacteristic, complemented
22#16837803C2211yescharacteristic, complemented
23#16837785C2211yescharacteristic
24#16837724—21no—
25#16837718—21no—
26#16837700—21no—
27#16837643C2211yescharacteristic
28#16837635C2211yescharacteristic
29#16837635C2211yescharacteristic, complemented
30#16837615—21no—
31#16837553—21no—
32#16837544—21no—
33D8×Dic59C2211yescharacteristic
34D8×Dic59C2211yescharacteristic, complemented
35C8×C22⋊D59C2211yescharacteristic
36#16837439C2211yescharacteristic, complemented
37C2×#14273661C2211yescharacteristic
38#16837229C2211yescharacteristic, complemented
39#16837228C2211yescharacteristic, complemented
40#16837228C2211yescharacteristic, complemented
41Dic59⋊C16C2211yescharacteristic, complemented
42#16837207C2211yescharacteristic, complemented
43#16837207C2211yescharacteristic, complemented
44#16837205C2211yescharacteristic, complemented
45#16837203C2211yescharacteristic
46#16837203C2211yescharacteristic
47#16837203C2211yescharacteristic
48#16837203C2211yescharacteristic
49#16837203C2211yescharacteristic, complemented
50(C2×D59)⋊C16C2211yescharacteristic, complemented
51C16×Dic59C2211yescharacteristic, complemented
52C22×D8×C59C2211yescharacteristic
53C2×D16×C59C2211yescharacteristic
54C2×D16×C59C2211yescharacteristic
55C59×#466C2211yescharacteristic
56C59×#357C2211yescharacteristic
57C59×#357C2211yescharacteristic
58C59×C22⋊C16C2211yescharacteristic
59C2×#11745687—21no—
60#14273746—22no—
61#14273746—41no—
62C2×Dic236C2311yescharacteristic
63C2×#11745670—21no—
64C2×#11745670—21no—
65C2×C8×D59C2311yescharacteristic
66#14273720—41no—
67#14273718—21no—
68#14273714—21no—
69#14273711—41no—
70#14273708—41no—
71#14273706—21no—
72#14273699—41no—
73#14273699—41no—
74#14273698—21no—
75#14273698—21no—
76#14273696—41no—
77D4×Dic59—21no—
78D4×Dic59—21no—
79D4×Dic59—41no—
80C4×C22⋊D59D411yescharacteristic
81#14273685—21no—
82C2×C4⋊Dic59—21no—
83C2×C22⋊Dic59—41no—
84#14273671—41no—
85C2×C59⋊C16—41no—
86C2×C59⋊C16C2311yescharacteristic
87C2×C59⋊C16C2311yescharacteristic
88C16×D59—41no—
89#14273661—21no—
90#14273661C2311yescharacteristic
91#14273661C2311yescharacteristic
92#14273661C2311yescharacteristic
93#14273658—21no—
94#14273658—21no—
95Dic59⋊C8D411yescharacteristic
96#14273652—21no—
97#14273648—21no—
98#14273648—21no—
99#14273648—21no—
100#14273648—21no—
101C22⋊(C59⋊C8)D411yescharacteristic
102(C2×D59)⋊C8D411yescharacteristic
103C8×Dic59C2311yescharacteristic
104C22×D4×C59—21no—
105C2×D8×C59—22no—
106C2×D8×C59—21no—
107C2×D8×C59—41no—
108C2×D8×C59C2311yescharacteristic
109C2×D8×C59C2311yescharacteristic
110C2×D8×C59C2311yescharacteristic
111C22×C8×C59C2311yescharacteristic
112#121×C59—21no—
113D16×C59—22no—
114D16×C59—41no—
115C2×C16×C59C2311yescharacteristic
116C2×C16×C59C2311yescharacteristic
117#107×C59C2311yescharacteristic
118#102×C59—21no—
119C24×C59—41no—
120C2×D4×C59—21no—
121C2×D4×C59—21no—
122C2×D4×C59—21no—
123C2×D4×C59—42no—
124C2×D4×C59—41no—
125C2×D4×C59—41no—
126C2×D4×C59—81no—
127C22×C4×C59C2×D411yescharacteristic
128C2×C22⋊D59—41no—
129C2×C22⋊D59—41no—
130C2×C22⋊D59—41no—
131C2×C22⋊D59D811yescharacteristic
132C22×Dic59—41no—
133C22×Dic59—41no—
134C22×Dic59—41no—
135C22×Dic59—41no—
136#11745687—42no—
137#11745687—81no—
138C2×C4×D59C2×D411yescharacteristic
139C2×Dic118—21no—
140D8×C59—21no—
141D8×C59—21no—
142D8×C59—21no—
143D8×C59—21no—
144D8×C59—21no—
145D8×C59—42no—
146D8×C59#4112yes—
147C2×C8×C59—21no—
148C2×C8×C59—21no—
149C2×C8×C59C2×D411yescharacteristic
150C2×C8×C59C2411yescharacteristic
151C4⋊C4×C59—21no—
152C22⋊C4×C59—41no—
153C22⋊Dic59—41no—
154C22⋊Dic59—41no—
155C22⋊Dic59—41no—
156C22⋊Dic59—41no—
157C22⋊Dic59—41no—
158C22⋊Dic59—41no—
159C22⋊Dic59—41no—
160C22⋊Dic59D811yescharacteristic
161#11745670—42no—
162#11745670—81no—
163(C2×D59)⋊C4—41no—
164(C2×D59)⋊C4D811yescharacteristic
165C4⋊Dic59—21no—
166C4⋊Dic59—21no—
167C4⋊Dic59—21no—
168C4⋊Dic59—41no—
169C4⋊Dic59—41no—
170Dic59⋊C4—41no—
171Dic59⋊C4—41no—
172Dic59⋊C4D811yescharacteristic
173C4×Dic59—41no—
174C4×Dic59C2×D411yescharacteristic
175C2×C59⋊C8C2×D411yescharacteristic
176C2×C59⋊C8C2×D411yescharacteristic
177Dic236—21no—
178Dic236—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—41no—
188C23×C59—82no—
189C23×C59—82no—
190C23×C59—161no—
191C23×C59C2×D811yescharacteristic
192C22×D59C2×D811yescharacteristic
193D4×C59—22no—
194D4×C59—41no—
195D4×C59—41no—
196D4×C59—41no—
197D4×C59—41no—
198D4×C59—41no—
199D4×C59—82no—
200D4×C59—82no—
201C2×C4×C59—21no—
202C2×C4×C59—21no—
203C2×C4×C59—41no—
204C2×C4×C59C2×D811yescharacteristic
205C2×C4×C59C22×D411yescharacteristic
206C22⋊D59—22no—
207C22⋊D59—82no—
208C22⋊D59—161no—
209C22⋊D59—161no—
210C2×Dic59—41no—
211C2×Dic59—41no—
212C2×Dic59—41no—
213C2×Dic59—41no—
214C2×Dic59—82no—
215C2×Dic59—161no—
216C2×Dic59—161no—
217C2×Dic59—161no—
218C2×Dic59C2×D811yescharacteristic
219C2×Dic59C2×D811yescharacteristic
220C2×Dic59C2×D811yescharacteristic
221C4×D59—21no—
222C4×D59—21no—
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—81no—
240C22×C59—81no—
241C22×C59—81no—
242C22×C59—164no—
243C22×C59#50812yes—
244C22×C59C22×D811yescharacteristic
245C2×D59—21no—
246C2×D59—21no—
247C2×D59—21no—
248C4×C59—21no—
249C4×C59—81no—
250C4×C59#54611yescharacteristic
251C4×C59#57711yescharacteristic
252Dic59—21no—
253Dic59—21no—
254Dic59—21no—
255Dic59—81no—
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#2184D5911yescharacteristic, complemented
270C4×D16—591no—
271D4×C16—591no—
272#2138—591no—
273C2×#357—591no—
274C2×C59—22no—
275C2×C59—82no—
276C2×C59—161no—
277C2×C59—161no—
278C2×C59#329411yescharacteristic
279C2×C59C2×#50811yescharacteristic
280C2×C59#341511yescharacteristic
281D59—41no—
282C2×#135—591no—
283C22×D8C2×D5911yescharacteristic
284#553—1181no—
285#546—1181no—
286C2×SD32—591no—
287C2×D16C2×D5911yescharacteristic
288C2×D16C2×D5911yescharacteristic
289C22×C16—591no—
290C22×C16—591no—
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#466C2×D5911yescharacteristic
300#463—1181no—
301#450—1181no—
302#449—1181no—
303C4×D8—591no—
304C4×D8—591no—
305C8×D4—591no—
306#427—591no—
307C2×#107—591no—
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#357—591no—
319#357—591no—
320#357C2×D5911yescharacteristic
321#357C2×D5911yescharacteristic
322C22⋊C16—591no—
323C22⋊C16C2×D5911yescharacteristic
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×D8C22×D5911yescharacteristic
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—21no—
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—1181no—
359C2×C22⋊C4—2361no—
360SD32—2361no—
361D16—22no—
362D16—41no—
363C2×C16—591no—
364C2×C16—591no—
365C2×C16—2361no—
366C2×C16—2361no—
367C2×C16C22×D5911yescharacteristic
368C2×C16C22×D5911yescharacteristic
369#107—591no—
370#107—591no—
371#107—591no—
372#107—1181no—
373#107C22×D5911yescharacteristic
374#106—1181no—
375#106—1181no—
376C4⋊C8—591no—
377#103—1181no—
378#102—21no—
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—21no—
393C2×D4—42no—
394C2×D4—41no—
395C2×D4—41no—
396C2×D4—81no—
397C2×D4—591no—
398C2×D4—2361no—
399C2×D4—2361no—
400C2×D4—2361no—
401C22×C4—591no—
402C22×C4—2361no—
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—21no—
415D8—21no—
416D8—42no—
417D8#1174568712yes—
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—591no—
428C4⋊C4—1181no—
429C4⋊C4—1181no—
430C4⋊C4—1181no—
431C4⋊C4—2361no—
432C4⋊C4—2361no—
433C4⋊C4—2361no—
434C4⋊C4—2361no—
435C22⋊C4—41no—
436C22⋊C4—591no—
437C22⋊C4—591no—
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—41no—
455C23—82no—
456C23—82no—
457C23—161no—
458C23—591no—
459C23D8×D5911yescharacteristic
460Q8—2361no—
461Q8—2361no—
462D4—22no—
463D4—41no—
464D4—41no—
465D4—41no—
466D4—41no—
467D4—41no—
468D4—82no—
469D4—82no—
470D4—1182no—
471D4—9441no—
472D4—9441no—
473D4—4722no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—41no—
477C2×C4—591no—
478C2×C4—591no—
479C2×C4—591no—
480C2×C4—1181no—
481C2×C4—1181no—
482C2×C4—9441no—
483C2×C4—9441no—
484C2×C4—9441no—
485C2×C4—4722no—
486C2×C4—2361no—
487C2×C4—2361no—
488C2×C4—2361no—
489C2×C4—2361no—
490C2×C4D8×D5911yescharacteristic
491C2×C4C2×D4×D5911yescharacteristic
492C8—21no—
493C8—1181no—
494C8—1181no—
495C8C2×#1174568711yescharacteristic
496C8#1427377211yescharacteristic
497C22—21no—
498C22—21no—
499C22—42no—
500C22—81no—
501C22—81no—
502C22—81no—
503C22—81no—
504C22—81no—
505C22—81no—
506C22—81no—
507C22—81no—
508C22—164no—
509C22—1181no—
510C22—1181no—
511C22—1181no—
512C22#1683783112yes—
513C22C2×D8×D5911yescharacteristic
514C4—21no—
515C4—81no—
516C4—1181no—
517C4—1181no—
518C4—1181no—
519C4—4721no—
520C4—4721no—
521C4—4721no—
522C4—4721no—
523C4#1683803911yescharacteristic
524C4#1683821211yescharacteristic
525C2—22no—
526C2—82no—
527C2—161no—
528C2—161no—
529C2—2361no—
530C2#2143590211yescharacteristic
531C2C2×#1683783111yescharacteristic
532C2#2143723611yescharacteristic
subgroupG/H
centerC22C2×D8×D59
commutator, cosocleC2×C8×C59C24
FrattiniC2×C8C23×D59
FittingC59×#2184C2
socleC22×C59C22×D8
hypercenter#2184D59
hypocenterC59#33864
LCSG ▷ C2×C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2184

Complements

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

NH ≅ G/Ntype
1. #21436501C2semidirect
2. #21435781C2semidirect
3. #21426326C2semidirect
4. #21426299C2semidirect
5. #21426285C2semidirect
6. #21426251C2semidirect
7. #21426190C2semidirect
8. #21426179C2semidirect
9. #21426149C2semidirect
10. #21426016C2semidirect
11. D16×Dic59C2semidirect
12. (C22⋊D59)⋊C16C2semidirect
13. #21425800C2semidirect
14. C2×#16837203C2semidirect
15. C59×#2184C2semidirect
19. C2×#14273671C22semidirect
21. C2×C16×D59C22semidirect
22. #16837803C22semidirect
29. #16837635C22semidirect
34. D8×Dic59C22semidirect
36. #16837439C22semidirect
38. #16837229C22semidirect
39. #16837228C22semidirect
40. #16837228C22semidirect
41. Dic59⋊C16C22semidirect
42. #16837207C22semidirect
43. #16837207C22semidirect
44. #16837205C22semidirect
49. #16837203C22semidirect
50. (C2×D59)⋊C16C22semidirect
51. C16×Dic59C22semidirect
269. #2184D59semidirect
325. C59#33864semidirect

Maximal subgroups

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

subgroupindex
#214365012
#214357812
#214263262
#214262992
#214262852
#214262512
#214261902
#214261792
#214261492
#214260162
D16×Dic592
(C22⋊D59)⋊C162
#214258002
C2×#168372032
C59×#21842
#3386459