Finite Group Databasebeta

← #28571405

Subgroups — #28571405

Order 15104.

596 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21434678C211yesmaximal, characteristic, complemented
2#21433884C211yesmaximal, characteristic
3#21433063C211yesmaximal, characteristic
4#21423680C211yesmaximal, characteristic, complemented
5#21423676C211yesmaximal, characteristic, complemented
6#21423673C211yesmaximal, characteristic, complemented
7#21423669C211yesmaximal, characteristic, complemented
8#21423622C211yesmaximal, characteristic, complemented
9#21423617C211yesmaximal, characteristic, complemented
10#21423588C211yesmaximal, characteristic, complemented
11#21423583C211yesmaximal, characteristic, complemented
12C2×#16837152C211yesmaximal, characteristic, complemented
13#21422754C211yesmaximal, characteristic, complemented
14#21422753C211yesmaximal, characteristic, complemented
15C59×#3076C211yesmaximal, characteristic
16#16837959C2211yescharacteristic
17#16837805C2211yescharacteristic
18#16837781C2211yescharacteristic
19#16837754C2211yescharacteristic
20#16837752C2211yescharacteristic
21#16837709—21no—
22#16837702—21no—
23#16837697C2211yescharacteristic
24#16837692C2211yescharacteristic
25#16837687C2211yescharacteristic
26#16837682C2211yescharacteristic
27#16837641—21no—
28#16837641—21no—
29#16837533C2211yescharacteristic
30#16837533C2211yescharacteristic
31C4×#11745672—21no—
32C4×#11745672—21no—
33#16837480C2211yescharacteristic
34#16837480C2211yescharacteristic
35#16837474—21no—
36#16837474—21no—
37#16837455—21no—
38#16837455C2211yescharacteristic
39#16837438—21no—
40C2×C4⋊(C59⋊C8)C2211yescharacteristic
41#16837398—21no—
42C4×#11745664—21no—
43C2×C4×C59⋊C8C2211yescharacteristic
44#16837152C2211yescharacteristic
45#16837152C2211yescharacteristic
46#16837152C2211yescharacteristic
47#16837152C2211yescharacteristic
48#16837151C2211yescharacteristic
49#16837151C2211yescharacteristic
50#16837150C2211yescharacteristic
51#16837150C2211yescharacteristic
52#16837148C2211yescharacteristic
53#16837148C2211yescharacteristic
54#16837147C2211yescharacteristic
55#16837147C2211yescharacteristic
56C59×#533C2211yescharacteristic
57C4×#41×C59C2211yescharacteristic
58C59×#479—21no—
59C59×#478—21no—
60C59×#477C2211yescharacteristic
61C59×#476C2211yescharacteristic
62C59×#475C2211yescharacteristic
63C59×#474C2211yescharacteristic
64C59×#427—21no—
65C2×C4⋊C8×C59C2211yescharacteristic
66C59×#416—21no—
67C2×#11745672—21no—
68C2×#11745672—21no—
69C2×#11745664—21no—
70C2×#11745664—21no—
71C22×C59⋊C8—21no—
72C22×C59⋊C8D411yescharacteristic
73C22×C59⋊C8D411yescharacteristic
74#14273727C2311yescharacteristic
75#14273727C2311yescharacteristic
76#14273719—21no—
77#14273706—21no—
78#14273706—21no—
79C4×Dic118—21no—
80C4×Dic118—21no—
81#14273686—21no—
82#14273660—21no—
83#14273660—21no—
84#14273660—21no—
85#14273660—21no—
86#14273658—21no—
87#14273658—21no—
88C4⋊(C59⋊C8)—21no—
89C4⋊(C59⋊C8)—21no—
90C4⋊(C59⋊C8)—21no—
91C4⋊(C59⋊C8)C2311yescharacteristic
92C4⋊(C59⋊C8)C2311yescharacteristic
93C4⋊(C59⋊C8)C2311yescharacteristic
94C4⋊(C59⋊C8)C2311yescharacteristic
95#14273651—21no—
96#14273651—21no—
97#14273651—21no—
98#14273651—21no—
99#14273650—21no—
100#14273650—21no—
101#14273648—21no—
102#14273648—21no—
103C22⋊(C59⋊C8)—21no—
104C22⋊(C59⋊C8)—21no—
105C22⋊(C59⋊C8)—21no—
106#14273638—21no—
107#14273638—21no—
108C4×C59⋊C8—21no—
109C4×C59⋊C8D411yescharacteristic
110C4×C59⋊C8D411yescharacteristic
111C4×C59⋊C8C2311yescharacteristic
112C4×C59⋊C8C2311yescharacteristic
113C2×#41×C59D411yescharacteristic
114C22×C8×C59—21no—
115C4⋊Q8×C59C2311yescharacteristic
116C4⋊Q8×C59C2311yescharacteristic
117#125×C59—21no—
118C22⋊Q8×C59—21no—
119C22⋊Q8×C59—21no—
120C4×Q8×C59—21no—
121C4×Q8×C59—21no—
122C4×Q8×C59D411yescharacteristic
123C4×Q8×C59C2311yescharacteristic
124C4×D4×C59—21no—
125C4×D4×C59—21no—
126C4×D4×C59D411yescharacteristic
127C4×D4×C59C2311yescharacteristic
128#117×C59—21no—
129#117×C59—21no—
130#117×C59D411yescharacteristic
131C2×C42×C59—21no—
132C2×C42×C59C2311yescharacteristic
133#107×C59—21no—
134#107×C59—21no—
135#106×C59—21no—
136#106×C59—21no—
137C4⋊C8×C59—21no—
138C4⋊C8×C59C2311yescharacteristic
139C4⋊C8×C59C2311yescharacteristic
140#103×C59—21no—
141#103×C59—21no—
142#102×C59—21no—
143#102×C59—21no—
144#41×C59—22no—
145#41×C59—22no—
146C2×Q8×C59—21no—
147C2×Q8×C59—21no—
148C2×Q8×C59C2×D411yescharacteristic
149C2×D4×C59—21no—
150C2×D4×C59C2×D411yescharacteristic
151C22×C4×C59—21no—
152C22×C4×C59—21no—
153C22×C4×C59—21no—
154C22×C4×C59C2×D411yescharacteristic
155C22×C4×C59C2×D411yescharacteristic
156C22×C4×C59#4111yescharacteristic
157C2×Dic118—21no—
158C2×Dic118—21no—
159C2×C8×C59—21no—
160C2×C8×C59—21no—
161C2×C8×C59—42no—
162C4⋊C4×C59—21no—
163C4⋊C4×C59—21no—
164C4⋊C4×C59—21no—
165C4⋊C4×C59—21no—
166C4⋊C4×C59—21no—
167C4⋊C4×C59—21no—
168C4⋊C4×C59—41no—
169C4⋊C4×C59—41no—
170C4⋊C4×C59C2×D411yescharacteristic
171C4⋊C4×C59C2×D411yescharacteristic
172C22⋊C4×C59—21no—
173C22⋊C4×C59—21no—
174C22⋊C4×C59—21no—
175C22⋊C4×C59—41no—
176C42×C59—21no—
177C42×C59—21no—
178C42×C59—21no—
179C42×C59—41no—
180C42×C59C2×D411yescharacteristic
181C42×C59C2×D411yescharacteristic
182C42×C59#4111yescharacteristic
183C42×C59C2411yescharacteristic
184C22⋊Dic59—41no—
185#11745672—42no—
186#11745672—42no—
187C4⋊Dic59—21no—
188C4⋊Dic59—21no—
189C4⋊Dic59—21no—
190C4⋊Dic59—21no—
191Dic59⋊C4—41no—
192Dic59⋊C4—41no—
193C4×Dic59—41no—
194#11745664—42no—
195#11745664—42no—
196C2×C59⋊C8—22no—
197C2×C59⋊C8—21no—
198C2×C59⋊C8—21no—
199C2×C59⋊C8—21no—
200C2×C59⋊C8—21no—
201C2×C59⋊C8—41no—
202C2×C59⋊C8—42no—
203C2×C59⋊C8C2×D411yescharacteristic
204C2×C59⋊C8C2×D411yescharacteristic
205C2×C59⋊C8C2×D411yescharacteristic
206C2×C59⋊C8C2×D411yescharacteristic
207C23×C59—21no—
208C23×C59#12111yescharacteristic
209Q8×C59—21no—
210Q8×C59—21no—
211Q8×C59—41no—
212Q8×C59—41no—
213Q8×C59—81no—
214D4×C59—21no—
215D4×C59—21no—
216D4×C59—42no—
217C2×C4×C59—21no—
218C2×C4×C59—21no—
219C2×C4×C59—21no—
220C2×C4×C59—21no—
221C2×C4×C59—21no—
222C2×C4×C59—41no—
223C2×C4×C59—42no—
224C2×C4×C59—41no—
225C2×C4×C59—41no—
226C2×C4×C59—42no—
227C2×C4×C59—41no—
228C2×C4×C59—41no—
229C2×C4×C59#12111yescharacteristic
230C2×C4×C59#12111yescharacteristic
231C2×C4×C59#12111yescharacteristic
232C2×C4×C59#13712yes—
233C2×C4×C59#13712yes—
234C2×C4×C59C22×D411yescharacteristic
235C2×C4×C59C22×D411yescharacteristic
236C2×C4×C59C2×#4111yescharacteristic
237C2×Dic59—41no—
238C2×Dic59—41no—
239Dic118—41no—
240Dic118—41no—
241Dic118—81no—
242C8×C59—41no—
243C8×C59—41no—
244C59⋊C8—21no—
245C59⋊C8—21no—
246C59⋊C8—21no—
247C59⋊C8—41no—
248C59⋊C8—41no—
249C59⋊C8—41no—
250C59⋊C8—41no—
251C59⋊C8#13512yes—
252#19158—591nomaximal, Sylow
253C22×C59—21no—
254C22×C59—21no—
255C22×C59—41no—
256C22×C59—41no—
257C22×C59—41no—
258C22×C59#47012yes—
259C22×C59C2×#12111yescharacteristic
260C4×C59—21no—
261C4×C59—21no—
262C4×C59—21no—
263C4×C59—41no—
264C4×C59—41no—
265C4×C59—41no—
266C4×C59—81no—
267C4×C59—81no—
268C4×C59#47012yes—
269C4×C59C2×#13511yescharacteristic
270C4×C59C2×#13711yescharacteristic
271C4×C59C2×#13711yescharacteristic
272C4×C59#57511yescharacteristic
273Dic59—81no—
274Dic59—81no—
275#3170—591no—
276#3076—591no—
277#3076D5911yescharacteristic
278#2965—591no—
279#1704—591no—
280#1704—591no—
281#1703—591no—
282#1703—591no—
283#1696—591no—
284#1695—591no—
285#1690—591no—
286#1689—591no—
287C2×#334—591no—
288#1542—591no—
289#1542—591no—
290C2×C59—22no—
291C2×C59—81no—
292C2×C59#303511yescharacteristic
293C2×C59C2×#47011yescharacteristic
294C2×C59#306711yescharacteristic
295#533—591no—
296#533C2×D5911yescharacteristic
297C4×#41C2×D5911yescharacteristic
298#500—591no—
299#494—591no—
300#487—591no—
301#487—591no—
302#479—21no—
303#479—1181no—
304#478—21no—
305#478—1181no—
306#477—591no—
307#477C2×D5911yescharacteristic
308#476—591no—
309#476C2×D5911yescharacteristic
310#475—591no—
311#475C2×D5911yescharacteristic
312#474—591no—
313#474C2×D5911yescharacteristic
314#467—1181no—
315#467—1181no—
316#446—591no—
317#446—591no—
318C4×Q16—1181no—
319C4×Q16—1181no—
320#436—591no—
321#436—591no—
322#435—1181no—
323#435—1181no—
324#431—591no—
325#431—1181no—
326#427—21no—
327#427—1181no—
328C2×C4⋊C8—591no—
329C2×C4⋊C8C2×D5911yescharacteristic
330#416—21no—
331#416—1181no—
332C4×M16—1181no—
333C2×C4×C8—591no—
334#334—591no—
335#334—591no—
336#334—591no—
337#334—591no—
338#333—591no—
339#333—591no—
340#333—591no—
341#333—591no—
342#332—591no—
343#332—591no—
344#332—591no—
345#332—591no—
346C59#1915811yescharacteristic, complemented, Sylow
347C2×#41C22⋊D5911yescharacteristic
348C2×Q16—1181no—
349C2×Q16—1181no—
350C2×M16—1181no—
351C2×M16—1181no—
352C22×C8—21no—
353C22×C8—591no—
354C22×C8—591no—
355C22×C8—1181no—
356C4⋊Q8—591no—
357C4⋊Q8—591no—
358C4⋊Q8C22×D5911yescharacteristic
359C4⋊Q8C22×D5911yescharacteristic
360#125—21no—
361#125—1181no—
362C22⋊Q8—21no—
363C22⋊Q8—21no—
364C22⋊Q8—1181no—
365C22⋊Q8—1181no—
366C4×Q8—21no—
367C4×Q8—21no—
368C4×Q8—1181no—
369C4×Q8—1181no—
370C4×Q8C22⋊D5911yescharacteristic
371C4×Q8C22×D5911yescharacteristic
372C4×D4—21no—
373C4×D4—21no—
374C4×D4C22⋊D5911yescharacteristic
375C4×D4C22×D5911yescharacteristic
376#117—21no—
377#117—21no—
378#117—1181no—
379#117C22⋊D5911yescharacteristic
380C2×C42—21no—
381C2×C42C22×D5911yescharacteristic
382#107—21no—
383#107—21no—
384#107—1181no—
385#107—1181no—
386#107—1181no—
387#107—1181no—
388#106—21no—
389#106—21no—
390#106—1181no—
391#106—1181no—
392C4⋊C8—21no—
393C4⋊C8—591no—
394C4⋊C8—591no—
395C4⋊C8—591no—
396C4⋊C8—591no—
397C4⋊C8—1181no—
398C4⋊C8—1181no—
399C4⋊C8—1181no—
400C4⋊C8C22×D5911yescharacteristic
401C4⋊C8C22×D5911yescharacteristic
402#103—21no—
403#103—21no—
404#103—1181no—
405#103—1181no—
406#103—1181no—
407#103—1181no—
408#103—1181no—
409#103—1181no—
410#102—21no—
411#102—21no—
412#102—1181no—
413#102—1181no—
414C22⋊C8—1181no—
415C22⋊C8—1181no—
416C22⋊C8—1181no—
417#97—1181no—
418#97—1181no—
419C4×C8—591no—
420C4×C8—591no—
421C4×C8—591no—
422C4×C8—591no—
423C4×C8—1181no—
424#41—22no—
425#41—22no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—1181no—
429C2×Q8—1181no—
430C2×Q8C2×C22⋊D5911yescharacteristic
431C2×D4—21no—
432C2×D4C2×C22⋊D5911yescharacteristic
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4D4×D5911yescharacteristic
437C22×C4#1174568711yescharacteristic
438C22×C4C2×C22⋊D5911yescharacteristic
439Q16—2362no—
440Q16—2362no—
441M16—2362no—
442M16—2362no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—42no—
446C2×C8—591no—
447C2×C8—591no—
448C2×C8—591no—
449C2×C8—591no—
450C2×C8—1182no—
451C2×C8—1181no—
452C2×C8—1181no—
453C2×C8—1181no—
454C2×C8—1181no—
455C2×C8—2361no—
456C2×C8—2362no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4—1181no—
466C4⋊C4—1181no—
467C4⋊C4—1181no—
468C4⋊C4—1181no—
469C4⋊C4—2361no—
470C4⋊C4—2361no—
471C4⋊C4C2×C22⋊D5911yescharacteristic
472C4⋊C4C2×C22⋊D5911yescharacteristic
473C22⋊C4—21no—
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—41no—
477C22⋊C4—2361no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—41no—
482C42—2361no—
483C42D4×D5911yescharacteristic
484C42#1174568711yescharacteristic
485C42C2×C22⋊D5911yescharacteristic
486C42C23×D5911yescharacteristic
487C23—21no—
488C23#1427369911yescharacteristic
489Q8—21no—
490Q8—21no—
491Q8—41no—
492Q8—41no—
493Q8—81no—
494Q8—4721no—
495Q8—2361no—
496Q8—2361no—
497D4—21no—
498D4—21no—
499D4—42no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—41no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—2361no—
513C2×C4—2361no—
514C2×C4#1427369911yescharacteristic
515C2×C4#1427369911yescharacteristic
516C2×C4#1427369911yescharacteristic
517C2×C4#1427375712yes—
518C2×C4#1427375812yes—
519C2×C4C2×D4×D5911yescharacteristic
520C2×C4C22×C22⋊D5911yescharacteristic
521C2×C4C2×#1174568711yescharacteristic
522C8—41no—
523C8—41no—
524C8—592no—
525C8—1181no—
526C8—1181no—
527C8—1181no—
528C8—2361no—
529C8—2361no—
530C8—2361no—
531C8—2361no—
532C22—21no—
533C22—21no—
534C22—41no—
535C22—41no—
536C22—41no—
537C22#1683765812yes—
538C22C2×#1427369911yescharacteristic
539C4—21no—
540C4—21no—
541C4—21no—
542C4—41no—
543C4—41no—
544C4—41no—
545C4—81no—
546C4—81no—
547C4—4721no—
548C4—4721no—
549C4#1683765812yes—
550C4#135×D5911yescharacteristic
551C4C2×#1427375711yescharacteristic
552C4C2×#1427375811yescharacteristic
553C4#1683819911yescharacteristic
554C2—22no—
555C2—81no—
556C2#2143354711yescharacteristic
557C2C2×#1683765811yescharacteristic
558C2#2143381311yescharacteristic
subgroupG/H
centerC2×C4#14273699
commutator, cosocleC42×C59C24
FrattiniC42C23×D59
FittingC59×#3076C2
socleC22×C59C2×#121
prime radicalC2×#41×C59D4
hypercenter#3076D59
hypocenterC59#19158
LCSG ▷ C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3076

Complements

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

NH ≅ G/Ntype
1. #21434678C2semidirect
4. #21423680C2semidirect
5. #21423676C2semidirect
6. #21423673C2semidirect
7. #21423669C2semidirect
8. #21423622C2semidirect
9. #21423617C2semidirect
10. #21423588C2semidirect
11. #21423583C2semidirect
12. C2×#16837152C2semidirect
13. #21422754C2semidirect
14. #21422753C2semidirect
346. C59#19158semidirect

Maximal subgroups

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

subgroupindex
#214346782
#214338842
#214330632
#214236802
#214236762
#214236732
#214236692
#214236222
#214236172
#214235882
#214235832
C2×#168371522
#214227542
#214227532
C59×#30762
#1915859