Finite Group Databasebeta

← #28745836

Subgroups — #28745836

Order 15104.

622 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21436494C211yesmaximal, characteristic, complemented
2D8×C22⋊D59C211yesmaximal, characteristic, complemented
3#21426336C211yesmaximal, characteristic, complemented
4#21426285C211yesmaximal, characteristic, complemented
5#21426281C211yesmaximal, characteristic, complemented
6#21426251C211yesmaximal, characteristic, complemented
7#21426198C211yesmaximal, characteristic, complemented
8#21426182C211yesmaximal, characteristic, complemented
9#21426130C211yesmaximal, characteristic, complemented
10#21426009C211yesmaximal, characteristic, complemented
11#21426008C211yesmaximal, characteristic, complemented
12#21425969C211yesmaximal, characteristic, complemented
13#21425921C211yesmaximal, characteristic, complemented
14#21425810C211yesmaximal, characteristic, complemented
15C2×C59×#357C211yesmaximal, characteristic, complemented
16C2×D8×D59C2211yescharacteristic
17#16838100—21no—
18D4×C22⋊D59—21no—
19C2×D944C2211yescharacteristic, complemented
20C2×#14273668C2211yescharacteristic
21C2×#14273668C2211yescharacteristic, complemented
22C2×#14273666C2211yescharacteristic, complemented
23#16837803C2211yescharacteristic, complemented
24#16837777C2211yescharacteristic
25#16837729—21no—
26#16837720—21no—
27#16837705—21no—
28#16837639C2211yescharacteristic, complemented
29#16837638C2211yescharacteristic
30#16837638C2211yescharacteristic, complemented
31#16837635C2211yescharacteristic
32#16837595—21no—
33#16837536—21no—
34#16837534—21no—
35D8×Dic59C2211yescharacteristic
36#16837484C2211yescharacteristic, complemented
37C8×C22⋊D59C2211yescharacteristic
38#16837439C2211yescharacteristic, complemented
39#16837229C2211yescharacteristic, complemented
40#16837229C2211yescharacteristic, complemented
41#16837228C2211yescharacteristic, complemented
42Dic59⋊C16C2211yescharacteristic, complemented
43#16837204C2211yescharacteristic, complemented
44#16837204C2211yescharacteristic, complemented
45#16837203C2211yescharacteristic
46#16837203C2211yescharacteristic, complemented
47#16837202C2211yescharacteristic, complemented
48#16837202C2211yescharacteristic, complemented
49C22⋊(C59⋊C16)C2211yescharacteristic, complemented
50(C2×D59)⋊C16C2211yescharacteristic, complemented
51#16837177C2211yescharacteristic, complemented
52C22×D8×C59C2211yescharacteristic
53C22×C16×C59C2211yescharacteristic, complemented
54C2×#107×C59C2211yescharacteristic, complemented
55C59×#357C2211yescharacteristic
56C59×#357C2211yescharacteristic
57C59×#357C2211yescharacteristic, complemented
58C59×#357C2211yescharacteristic, complemented
59C22×C22⋊D59—41no—
60C2×D4×D59—21no—
61C2×D472C2311yescharacteristic
62C2×D472C2311yescharacteristic
63C2×#11745669—21no—
64C2×#11745669—21no—
65D8×D59—22no—
66D8×D59—41no—
67C2×C8×D59C2311yescharacteristic
68#14273723—21no—
69#14273722—41no—
70#14273718—21no—
71#14273712—41no—
72#14273702—21no—
73#14273701—21no—
74#14273701—21no—
75#14273701—41no—
76#14273699—41no—
77#14273698—21no—
78#14273696—41no—
79#14273695—41no—
80D4×Dic59—21no—
81#14273689—21no—
82C4×C22⋊D59—41no—
83C4×C22⋊D59D411yescharacteristic
84#14273685—21no—
85D944—41no—
86#14273668—22no—
87#14273668—41no—
88#14273666—41no—
89C2×C59⋊C16C2311yescharacteristic
90C2×C59⋊C16C2311yescharacteristic
91#14273661C2311yescharacteristic
92#14273661C2311yescharacteristic
93#14273658—21no—
94#14273658—21no—
95Dic59⋊C8D411yescharacteristic
96#14273649—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—
120C23×D59—41no—
121C2×D4×C59—21no—
122C2×D4×C59—21no—
123C2×D4×C59—42no—
124C2×D4×C59—41no—
125C2×D4×C59—81no—
126C22×C4×C59—41no—
127C22×C4×C59C2×D411yescharacteristic
128C2×C22⋊D59—41no—
129C2×C22⋊D59—41no—
130C2×C22⋊D59—41no—
131C2×C22⋊D59—41no—
132C2×C22⋊D59—41no—
133C2×C22⋊D59—41no—
134C2×C22⋊D59—84no—
135C2×C22⋊D59D811yescharacteristic
136C22×Dic59—41no—
137D4×D59—42no—
138D4×D59—81no—
139C2×D236—21no—
140C2×D236—21no—
141C2×D236—41no—
142C2×C4×D59—41no—
143C2×C4×D59C2×D411yescharacteristic
144D8×C59—21no—
145D8×C59—21no—
146D8×C59—21no—
147D8×C59—42no—
148D8×C59#4112yes—
149C2×C8×C59—21no—
150C2×C8×C59—21no—
151C2×C8×C59C2×D411yescharacteristic
152C2×C8×C59C2411yescharacteristic
153C4⋊C4×C59—21no—
154C4⋊C4×C59—21no—
155C4⋊C4×C59—41no—
156C22⋊Dic59—41no—
157C22⋊Dic59—41no—
158C22⋊Dic59D811yescharacteristic
159#11745669—42no—
160#11745669—81no—
161(C2×D59)⋊C4—41no—
162(C2×D59)⋊C4—41no—
163(C2×D59)⋊C4—41no—
164(C2×D59)⋊C4—41no—
165(C2×D59)⋊C4—41no—
166(C2×D59)⋊C4D811yescharacteristic
167C4⋊Dic59—21no—
168C4⋊Dic59—21no—
169C4⋊Dic59—41no—
170Dic59⋊C4—41no—
171Dic59⋊C4D811yescharacteristic
172C4×Dic59—41no—
173C4×Dic59C2×D411yescharacteristic
174C2×C59⋊C8C2×D411yescharacteristic
175C2×C59⋊C8C2×D411yescharacteristic
176D472—21no—
177D472—21no—
178D472—21no—
179D472—21no—
180C8×D59—21no—
181C8×D59—21no—
182C16×C59—21no—
183C16×C59—21no—
184C59⋊C16—21no—
185C59⋊C16—21no—
186C23×C59—41no—
187C23×C59—41no—
188C23×C59—82no—
189C23×C59—82no—
190C23×C59—161no—
191C23×C59C2×D811yescharacteristic
192C22×D59—41no—
193C22×D59—41no—
194C22×D59—82no—
195C22×D59—82no—
196C22×D59—161no—
197C22×D59C2×D811yescharacteristic
198D4×C59—22no—
199D4×C59—41no—
200D4×C59—41no—
201D4×C59—41no—
202D4×C59—82no—
203C2×C4×C59—21no—
204C2×C4×C59—21no—
205C2×C4×C59—41no—
206C2×C4×C59—41no—
207C2×C4×C59—161no—
208C2×C4×C59C2×D811yescharacteristic
209C2×C4×C59C22×D411yescharacteristic
210C22⋊D59—22no—
211C22⋊D59—82no—
212C22⋊D59—82no—
213C22⋊D59—82no—
214C22⋊D59—82no—
215C22⋊D59—82no—
216C22⋊D59—161no—
217C2×Dic59—41no—
218C2×Dic59—41no—
219C2×Dic59—82no—
220C2×Dic59C2×D811yescharacteristic
221C2×Dic59C2×D811yescharacteristic
222C2×Dic59C2×D811yescharacteristic
223D236—41no—
224D236—41no—
225D236—41no—
226D236—41no—
227D236—161no—
228C4×D59—21no—
229C4×D59—21no—
230C4×D59—161no—
231C8×C59—21no—
232C8×C59C2×#4111yescharacteristic
233C8×C59H(5,𝔽2)11yescharacteristic
234C59⋊C8—21no—
235C59⋊C8—21no—
236#33885—591nomaximal, Sylow
237C22×C59—21no—
238C22×C59—21no—
239C22×C59—42no—
240C22×C59—81no—
241C22×C59—81no—
242C22×C59—81no—
243C22×C59—81no—
244C22×C59—81no—
245C22×C59—164no—
246C22×C59#50912yes—
247C22×C59C22×D811yescharacteristic
248C2×D59—21no—
249C2×D59—21no—
250C2×D59—21no—
251C2×D59—81no—
252C2×D59—81no—
253C2×D59—81no—
254C2×D59—81no—
255C2×D59—81no—
256C2×D59—81no—
257C2×D59—164no—
258C4×C59—21no—
259C4×C59—81no—
260C4×C59—81no—
261C4×C59#54611yescharacteristic
262C4×C59#57711yescharacteristic
263Dic59—21no—
264Dic59—21no—
265Dic59—21no—
266Dic59—81no—
267Dic59—81no—
268#3339—591no—
269D4×D8—591no—
270#2244—591no—
271#2234—591no—
272#2233—591no—
273#2228—591no—
274#2218—591no—
275#2215—591no—
276#2206—591no—
277#2184—591no—
278#2184—591no—
279#2177—591no—
280#2168—591no—
281#2140—591no—
282C2×#357D5911yescharacteristic, complemented
283C2×C59—22no—
284C2×C59—82no—
285C2×C59—161no—
286C2×C59#329411yescharacteristic
287C2×C59C2×#50911yescharacteristic
288C2×C59#341511yescharacteristic
289D59—41no—
290D59—161no—
291D59—161no—
292C22×D8—591no—
293C22×D8C2×D5911yescharacteristic
294#553—1181no—
295D42—1181no—
296C2×D16—591no—
297C2×D16—591no—
298C2×D16—591no—
299C2×M32—591no—
300C22×C16C2×D5911yescharacteristic, complemented
301#499—591no—
302#493—591no—
303#482—1181no—
304#481—1181no—
305#478—1181no—
306#466—591no—
307#466—591no—
308#466—591no—
309#466—591no—
310#459—1181no—
311#447—1181no—
312#447—1181no—
313C4×D8—591no—
314C4×D8—591no—
315C8×D4—591no—
316#427—591no—
317C2×#107C2×D5911yescharacteristic, complemented
318#367—591no—
319#367—591no—
320#366—591no—
321C4⋊C16—591no—
322#357—591no—
323#357—591no—
324#357—591no—
325#357—591no—
326#357—591no—
327#357—591no—
328#357C2×D5911yescharacteristic
329#357C2×D5911yescharacteristic
330#357C2×D5911yescharacteristic, complemented
331#357C2×D5911yescharacteristic, complemented
332C22⋊C16—591no—
333C22⋊C16—591no—
334#346—591no—
335C59#3388511yescharacteristic, complemented, Sylow
336C22×D4—21no—
337C22×D4—1181no—
338C22×D4—2361no—
339C2×D8—22no—
340C2×D8—21no—
341C2×D8—41no—
342C2×D8—591no—
343C2×D8—591no—
344C2×D8—1181no—
345C2×D8—1181no—
346C2×D8—1182no—
347C2×D8—2361no—
348C2×D8C22×D5911yescharacteristic
349C2×D8C22×D5911yescharacteristic
350C22×C8—591no—
351C22×C8C22×D5911yescharacteristic
352#127—1181no—
353#126—2361no—
354#125—1181no—
355#123—2361no—
356#121—1181no—
357#121—1181no—
358#121—1181no—
359#121—1181no—
360#121—2361no—
361#121—2361no—
362#120—2361no—
363#120—2361no—
364C4×D4—591no—
365C4×D4—1181no—
366C4×D4—1181no—
367C4×D4—2361no—
368#117—1181no—
369C2×C4⋊C4—21no—
370D16—1182no—
371D16—2361no—
372D16—2361no—
373M32—2361no—
374C2×C16—41no—
375C2×C16—591no—
376C2×C16—591no—
377C2×C16C22×D5911yescharacteristic
378C2×C16C22×D5911yescharacteristic
379#107—21no—
380#107—591no—
381#107—591no—
382#107C22×D5911yescharacteristic
383#107C22×D5911yescharacteristic
384#106—1181no—
385#106—1181no—
386C4⋊C8—591no—
387#102—1181no—
388#102—1181no—
389#102—1181no—
390#102—1181no—
391#102—1181no—
392#102—1181no—
393C22⋊C8—591no—
394C22⋊C8—591no—
395C4×C8—591no—
396C24—41no—
397C24—2361no—
398C2×D4—21no—
399C2×D4—21no—
400C2×D4—42no—
401C2×D4—41no—
402C2×D4—81no—
403C2×D4—591no—
404C2×D4—1181no—
405C2×D4—1181no—
406C2×D4—4721no—
407C2×D4—4724no—
408C2×D4—2361no—
409C2×D4—2361no—
410C2×D4—2361no—
411C2×D4—2361no—
412C2×D4—2362no—
413C2×D4—2361no—
414C2×D4—2361no—
415C2×D4—2361no—
416C22×C4—41no—
417C22×C4—591no—
418C22×C4—2361no—
419C22×C4—2361no—
420C22×C4D4×D5911yescharacteristic
421D8—21no—
422D8—21no—
423D8—21no—
424D8—42no—
425D8—1181no—
426D8—1181no—
427D8—1181no—
428D8—1181no—
429D8—4721no—
430D8—2362no—
431D8#1174568512yes—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—591no—
435C2×C8—591no—
436C2×C8—1181no—
437C2×C8—1181no—
438C2×C8D4×D5911yescharacteristic
439C2×C8C23×D5911yescharacteristic
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—41no—
443C4⋊C4—591no—
444C4⋊C4—1181no—
445C4⋊C4—1181no—
446C4⋊C4—2361no—
447C4⋊C4—2361no—
448C22⋊C4—591no—
449C22⋊C4—591no—
450C22⋊C4—2361no—
451C22⋊C4—2361no—
452C22⋊C4—2361no—
453C22⋊C4—2361no—
454C22⋊C4—2361no—
455C22⋊C4—2361no—
456C22⋊C4—2361no—
457C42—591no—
458C42—2361no—
459C16—21no—
460C16—21no—
461C16—1181no—
462C16—1181no—
463C23—41no—
464C23—41no—
465C23—82no—
466C23—82no—
467C23—161no—
468C23—591no—
469C23—9441no—
470C23—4722no—
471C23—4722no—
472C23—2361no—
473C23—2361no—
474C23D8×D5911yescharacteristic
475D4—22no—
476D4—41no—
477D4—41no—
478D4—41no—
479D4—82no—
480D4—1182no—
481D4—9441no—
482D4—9441no—
483D4—4722no—
484D4—4722no—
485D4—4722no—
486D4—4722no—
487D4—4722no—
488D4—2361no—
489D4—2361no—
490D4—2361no—
491D4—2361no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—161no—
497C2×C4—591no—
498C2×C4—591no—
499C2×C4—591no—
500C2×C4—1181no—
501C2×C4—1181no—
502C2×C4—9441no—
503C2×C4—4722no—
504C2×C4—2361no—
505C2×C4—2361no—
506C2×C4D8×D5911yescharacteristic
507C2×C4C2×D4×D5911yescharacteristic
508C8—21no—
509C8—1181no—
510C8—1181no—
511C8C2×#1174568511yescharacteristic
512C8#1427377211yescharacteristic
513C22—21no—
514C22—21no—
515C22—42no—
516C22—81no—
517C22—81no—
518C22—81no—
519C22—81no—
520C22—81no—
521C22—164no—
522C22—1181no—
523C22—1181no—
524C22—1181no—
525C22—9444no—
526C22—4721no—
527C22—4721no—
528C22—4721no—
529C22—4721no—
530C22—4721no—
531C22—4721no—
532C22#1683783912yes—
533C22C2×D8×D5911yescharacteristic
534C4—21no—
535C4—81no—
536C4—81no—
537C4—1181no—
538C4—1181no—
539C4—1181no—
540C4—4721no—
541C4—4721no—
542C4#1683804211yescharacteristic
543C4#1683820811yescharacteristic
544C2—22no—
545C2—82no—
546C2—161no—
547C2—9441no—
548C2—9441no—
549C2—2361no—
550C2#2143590511yescharacteristic
551C2C2×#1683783911yescharacteristic
552C2#2143723311yescharacteristic
subgroupG/H
centerC22C2×D8×D59
commutator, cosocleC2×C8×C59C24
FrattiniC2×C8C23×D59
FittingC2×C59×#357C2
socleC22×C59C22×D8
hypercenterC2×#357D59
hypocenterC59#33885
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. D8×C22⋊D59C2semidirect
3. #21426336C2semidirect
4. #21426285C2semidirect
5. #21426281C2semidirect
6. #21426251C2semidirect
7. #21426198C2semidirect
8. #21426182C2semidirect
9. #21426130C2semidirect
10. #21426009C2semidirect
11. #21426008C2semidirect
12. #21425969C2semidirect
13. #21425921C2semidirect
14. #21425810C2semidirect
15. C2×C59×#357C2semidirect
19. C2×D944C22semidirect
21. C2×#14273668C22semidirect
22. C2×#14273666C22semidirect
23. #16837803C22semidirect
28. #16837639C22semidirect
30. #16837638C22semidirect
36. #16837484C22semidirect
38. #16837439C22semidirect
39. #16837229C22semidirect
40. #16837229C22semidirect
41. #16837228C22semidirect
42. Dic59⋊C16C22semidirect
43. #16837204C22semidirect
44. #16837204C22semidirect
46. #16837203C22semidirect
47. #16837202C22semidirect
48. #16837202C22semidirect
49. C22⋊(C59⋊C16)C22semidirect
50. (C2×D59)⋊C16C22semidirect
51. #16837177C22semidirect
53. C22×C16×C59C22semidirect
54. C2×#107×C59C22semidirect
57. C59×#357C22semidirect
58. C59×#357C22semidirect
282. C2×#357D59semidirect
300. C22×C16C2×D59semidirect
317. C2×#107C2×D59semidirect
330. #357C2×D59semidirect
331. #357C2×D59semidirect
335. C59#33885semidirect

Maximal subgroups

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

subgroupindex
#214364942
D8×C22⋊D592
#214263362
#214262852
#214262812
#214262512
#214261982
#214261822
#214261302
#214260092
#214260082
#214259692
#214259212
#214258102
C2×C59×#3572
#3388559