Finite Group Databasebeta

← #28559960

Subgroups — #28559960

Order 15104.

592 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21434178C211yesmaximal, characteristic
2#21433258C211yesmaximal, characteristic
3#21433183C211yesmaximal, characteristic, complemented
4#21423006C211yesmaximal, characteristic, complemented
5#21423000C211yesmaximal, characteristic, complemented
6#21422948C211yesmaximal, characteristic, complemented
7#21422948C211yesmaximal, characteristic, complemented
8#21422941C211yesmaximal, characteristic, complemented
9#21422934C211yesmaximal, characteristic, complemented
10#21422916C211yesmaximal, characteristic, complemented
11#21422910C211yesmaximal, characteristic, complemented
12#21422881C211yesmaximal, characteristic, complemented
13#21422557C211yesmaximal, characteristic
14C2×#16837134C211yesmaximal, characteristic, complemented
15C59×#1452C211yesmaximal, characteristic, complemented
16#16837936C2211yescharacteristic
17C2×C4×Dic118C2211yescharacteristic
18#16837733C411yescharacteristic
19#16837716C411yescharacteristic
20#16837710C411yescharacteristic
21#16837710C411yescharacteristic
22#16837625C411yescharacteristic
23#16837625C411yescharacteristic
24#16837560C411yescharacteristic
25#16837543C411yescharacteristic
26#16837532C2211yescharacteristic
27#16837532C2211yescharacteristic
28#16837532C2211yescharacteristic
29#16837531—21no—
30#16837531—21no—
31C8×Dic118C2211yescharacteristic
32C8×Dic118C2211yescharacteristic
33C8×Dic118C2211yescharacteristic
34C4×Dic236C2211yescharacteristic
35C4×Dic236C2211yescharacteristic
36C4×#11745660C2211yescharacteristic
37C4×#11745660C2211yescharacteristic
38#16837481C2211yescharacteristic
39#16837470—21no—
40C8×D236C2211yescharacteristic
41(C22⋊D59)⋊C8—21no—
42#16837462—21no—
43#16837459C2211yescharacteristic
44#16837456—21no—
45#16837452—21no—
46#16837427—21no—
47C2×C4⋊(C59⋊C8)C2211yescharacteristic
48#16837155C2211yescharacteristic
49#16837155C2211yescharacteristic
50#16837153C2211yescharacteristic
51#16837153C2211yescharacteristic
52#16837134C2211yescharacteristic
53#16837134C2211yescharacteristic
54#16837134C2211yescharacteristic
55#16837134C2211yescharacteristic
56#16837134C2211yescharacteristic
57#16837134C2211yescharacteristic
58#16837131C2211yescharacteristic
59#16837131C2211yescharacteristic
60C59×#431C2211yescharacteristic
61C59×#431C2211yescharacteristic
62C2×C4×C8×C59C2211yescharacteristic
63C59×#322C2211yescharacteristic
64C59×#322C2211yescharacteristic
65C59×#322C2211yescharacteristic
66C59×#322C2211yescharacteristic
67C22×Dic118C2×C411yescharacteristic
68C2×Dic236C2×C411yescharacteristic
69C2×Dic236C2×C411yescharacteristic
70C2×#11745660C2×C411yescharacteristic
71C2×#11745660C2×C411yescharacteristic
72C2×#11745659—21no—
73C22×C59⋊C8—21no—
74C2×C8×D59—21no—
75#14273721—21no—
76#14273719C2×C411yescharacteristic
77#14273715C2×C411yescharacteristic
78#14273710—21no—
79#14273706C2×C411yescharacteristic
80#14273701C2×C411yescharacteristic
81C4×Dic118—21no—
82C4×Dic118—21no—
83C4×Dic118C2×C411yescharacteristic
84C4×Dic118C2×C411yescharacteristic
85C4×Dic118C2311yescharacteristic
86C4×Dic118C2311yescharacteristic
87C4×Dic118C2311yescharacteristic
88C4×D236C2311yescharacteristic
89C4×C22⋊D59—21no—
90#14273684—21no—
91C2×C4⋊Dic59C2×C411yescharacteristic
92C2×Dic59⋊C4—21no—
93C2×C4×Dic59—21no—
94#14273661C2×C411yescharacteristic
95#14273661C2×C411yescharacteristic
96#14273659C2×C411yescharacteristic
97#14273659C2×C411yescharacteristic
98C4⋊(C59⋊C8)—21no—
99C4⋊(C59⋊C8)C2311yescharacteristic
100C4⋊(C59⋊C8)C2311yescharacteristic
101C4⋊(C59⋊C8)C2311yescharacteristic
102C4⋊(C59⋊C8)C2311yescharacteristic
103Dic59⋊C8—21no—
104Dic59⋊C8—21no—
105Dic59⋊C8—21no—
106Dic59⋊C8—21no—
107Dic59⋊C8—21no—
108Dic59⋊C8—21no—
109#14273652C2×C411yescharacteristic
110#14273652C2×C411yescharacteristic
111#14273652C2×C411yescharacteristic
112#14273652C2×C411yescharacteristic
113#14273652C2×C411yescharacteristic
114#14273652C2×C411yescharacteristic
115#14273649C2×C411yescharacteristic
116#14273649C2×C411yescharacteristic
117C22⋊(C59⋊C8)—21no—
118(C2×D59)⋊C8—21no—
119(C2×D59)⋊C8—21no—
120#14273638—21no—
121#14273637—21no—
122#14273637—21no—
123#14273637—21no—
124C8×Dic59—21no—
125C8×Dic59—21no—
126C8×Dic59—21no—
127C22×C8×C59—21no—
128C2×C42×C59C2311yescharacteristic
129C4⋊C8×C59C2×C411yescharacteristic
130C4⋊C8×C59C2×C411yescharacteristic
131C4⋊C8×C59D411yescharacteristic
132C4⋊C8×C59D411yescharacteristic
133C22⋊C8×C59C2×C411yescharacteristic
134C22⋊C8×C59C2×C411yescharacteristic
135C22⋊C8×C59D411yescharacteristic
136C22⋊C8×C59D411yescharacteristic
137C4×C8×C59—21no—
138C4×C8×C59C2311yescharacteristic
139C4×C8×C59C2311yescharacteristic
140C4×C8×C59C2311yescharacteristic
141C4×C8×C59C2311yescharacteristic
142C4×C8×C59C2311yescharacteristic
143C4×C8×C59C2311yescharacteristic
144C22×C4×C59C22×C411yescharacteristic
145C22×C4×C59C2×D411yescharacteristic
146C22×C4×C59#4111yescharacteristic
147C2×C22⋊D59—21no—
148C22×Dic59—21no—
149C22×Dic59—21no—
150C2×D236C22×C411yescharacteristic
151C2×C4×D59—21no—
152C2×Dic118—22no—
153C2×Dic118—21no—
154C2×Dic118—41no—
155C2×Dic118C22×C411yescharacteristic
156C2×Dic118C22×C411yescharacteristic
157C2×Dic118C22×C411yescharacteristic
158C2×C8×C59—21no—
159C2×C8×C59—21no—
160C2×C8×C59—42no—
161C2×C8×C59C22×C411yescharacteristic
162C2×C8×C59C22×C411yescharacteristic
163C2×C8×C59C22×C411yescharacteristic
164C2×C8×C59C22×C411yescharacteristic
165C2×C8×C59C2×D411yescharacteristic
166C2×C8×C59C2×D411yescharacteristic
167C2×C8×C59C2×D411yescharacteristic
168C2×C8×C59C2×D411yescharacteristic
169C42×C59C22×C411yescharacteristic
170C42×C59C2×D411yescharacteristic
171C42×C59#4111yescharacteristic
172C42×C59C2411yescharacteristic
173C22⋊Dic59—21no—
174(C2×D59)⋊C4—21no—
175(C2×D59)⋊C4—21no—
176(C2×D59)⋊C4—21no—
177(C2×D59)⋊C4—21no—
178C4⋊Dic59—21no—
179C4⋊Dic59C22×C411yescharacteristic
180C4⋊Dic59C22×C411yescharacteristic
181C4⋊Dic59C22×C411yescharacteristic
182C4⋊Dic59C22×C411yescharacteristic
183Dic59⋊C4—21no—
184Dic59⋊C4—21no—
185Dic59⋊C4—21no—
186Dic59⋊C4—21no—
187Dic59⋊C4—21no—
188Dic59⋊C4—21no—
189Dic59⋊C4—21no—
190Dic59⋊C4—21no—
191C4×Dic59—21no—
192C4×Dic59—21no—
193C4×Dic59—21no—
194C4×Dic59—21no—
195C4×Dic59—21no—
196C2×C59⋊C8—21no—
197C2×C59⋊C8—21no—
198C2×C59⋊C8—21no—
199C2×C59⋊C8—21no—
200C2×C59⋊C8—81no—
201Dic236—22no—
202Dic236—41no—
203#11745660—22no—
204#11745660—41no—
205#11745659—81no—
206C8×D59—81no—
207C23×C59C4×D411yescharacteristic
208C22×D59—21no—
209C2×C4×C59—22no—
210C2×C4×C59—21no—
211C2×C4×C59—21no—
212C2×C4×C59—21no—
213C2×C4×C59—21no—
214C2×C4×C59C4×D411yescharacteristic
215C2×C4×C59C4×D411yescharacteristic
216C2×C4×C59C4×D411yescharacteristic
217C2×C4×C59C23×C411yescharacteristic
218C2×C4×C59C22×D411yescharacteristic
219C2×C4×C59C2×#4111yescharacteristic
220C22⋊D59—42no—
221C2×Dic59—21no—
222C2×Dic59—21no—
223C2×Dic59—21no—
224C2×Dic59—21no—
225C2×Dic59—21no—
226C2×Dic59—21no—
227C2×Dic59—21no—
228C2×Dic59—42no—
229C2×Dic59—42no—
230D236—21no—
231D236—21no—
232C4×D59—41no—
233C4×D59—41no—
234Dic118—21no—
235Dic118—21no—
236Dic118—21no—
237Dic118—21no—
238Dic118—21no—
239Dic118—42no—
240Dic118#13112yes—
241C8×C59—21no—
242C8×C59—21no—
243C8×C59—21no—
244C8×C59—21no—
245C8×C59—21no—
246C8×C59—21no—
247C8×C59—21no—
248C8×C59—21no—
249C8×C59—41no—
250C8×C59—41no—
251C59⋊C8—41no—
252C59⋊C8—41no—
253C59⋊C8—41no—
254C59⋊C8—41no—
255#18023—591nomaximal, Sylow
256C22×C59—21no—
257C22×C59—21no—
258C22×C59#44412yes—
259C22×C59C2×C4×D411yescharacteristic
260C2×D59—41no—
261C2×D59—41no—
262C2×D59—41no—
263C4×C59—21no—
264C4×C59—21no—
265C4×C59—21no—
266C4×C59—21no—
267C4×C59C2×#13111yescharacteristic
268C4×C59#56811yescharacteristic
269C4×C59#57711yescharacteristic
270C4×C59#57811yescharacteristic
271Dic59—22no—
272Dic59—41no—
273Dic59—41no—
274Dic59—41no—
275Dic59—41no—
276Dic59—41no—
277Dic59—41no—
278#3108—591no—
279#2994—591no—
280#2984—591no—
281#1593—591no—
282#1592—591no—
283#1584—591no—
284#1584—591no—
285#1583—591no—
286#1582—591no—
287#1579—591no—
288SD16⋊C8—591no—
289#1573—591no—
290#1494—591no—
291C2×Q8⋊C8—591no—
292#1452D5911yescharacteristic, complemented
293C2×C59—22no—
294C2×C59#293311yescharacteristic
295C2×C59#294711yescharacteristic
296C2×C59C2×#44411yescharacteristic
297D59—81no—
298#529—591no—
299C2×C4×Q8—591no—
300#483—591no—
301#480—591no—
302#479—591no—
303#479—591no—
304#464—591no—
305#464—591no—
306#451—591no—
307#448—591no—
308#446—591no—
309#446—591no—
310#446—591no—
311#446—1181no—
312#446—1181no—
313C8×Q8—591no—
314C8×Q8—591no—
315C8×Q8—591no—
316C4×Q16—591no—
317C4×Q16—591no—
318C4×SD16—591no—
319C4×SD16—591no—
320#436—591no—
321#435—1181no—
322C8×D4—591no—
323C8×D4—1181no—
324#433—1181no—
325#432—591no—
326#432—1181no—
327#431—1181no—
328#431C2×D5911yescharacteristic
329#431C2×D5911yescharacteristic
330#424—1181no—
331C2×C4⋊C8—591no—
332C2×C4×C8C2×D5911yescharacteristic
333#335—591no—
334#335—591no—
335#334—591no—
336#334—591no—
337Q8⋊C8—591no—
338Q8⋊C8—591no—
339Q8⋊C8—591no—
340Q8⋊C8—591no—
341Q8⋊C8—591no—
342Q8⋊C8—591no—
343D4⋊C8—591no—
344D4⋊C8—591no—
345#322C2×D5911yescharacteristic
346#322C2×D5911yescharacteristic
347#322C2×D5911yescharacteristic
348#322C2×D5911yescharacteristic
349C59#1802311yescharacteristic, complemented, Sylow
350C22×Q8—591no—
351C2×Q16—591no—
352C2×Q16—591no—
353C2×SD16—591no—
354C2×SD16—591no—
355C2×M16—1181no—
356C22×C8—21no—
357C22×C8—1181no—
358C22×C8—1181no—
359#126—1181no—
360#125—591no—
361#124—591no—
362#123—1181no—
363C22⋊Q8—591no—
364#121—591no—
365C4×Q8—591no—
366C4×Q8—591no—
367C4×Q8—591no—
368C4×Q8—591no—
369C4×Q8—591no—
370C4×Q8—1181no—
371C4×Q8—1181no—
372C4×D4—591no—
373C4×D4—1181no—
374#117—1181no—
375C2×C4⋊C4—591no—
376C2×C4⋊C4—1181no—
377C2×C42—1181no—
378C2×C42C22×D5911yescharacteristic
379#107—591no—
380#107—591no—
381#106—591no—
382#106—591no—
383C4⋊C8—591no—
384C4⋊C8—591no—
385C4⋊C8—591no—
386C4⋊C8—591no—
387C4⋊C8—1181no—
388C4⋊C8—1181no—
389C4⋊C8—1181no—
390C4⋊C8—1181no—
391C4⋊C8—1181no—
392C4⋊C8—1181no—
393C4⋊C8—1181no—
394C4⋊C8C4×D5911yescharacteristic
395C4⋊C8C4×D5911yescharacteristic
396C4⋊C8D23611yescharacteristic
397C4⋊C8D23611yescharacteristic
398#103—591no—
399#103—591no—
400#103—591no—
401#103—591no—
402#103—591no—
403#103—591no—
404#102—591no—
405#102—591no—
406C22⋊C8—1181no—
407C22⋊C8—1181no—
408C22⋊C8—1181no—
409C22⋊C8C4×D5911yescharacteristic
410C22⋊C8C4×D5911yescharacteristic
411C22⋊C8D23611yescharacteristic
412C22⋊C8D23611yescharacteristic
413#97—1181no—
414#97—1181no—
415#97—1181no—
416#97—1181no—
417C4×C8—21no—
418C4×C8—1181no—
419C4×C8—1181no—
420C4×C8—1181no—
421C4×C8C22×D5911yescharacteristic
422C4×C8C22×D5911yescharacteristic
423C4×C8C22×D5911yescharacteristic
424C4×C8C22×D5911yescharacteristic
425C4×C8C22×D5911yescharacteristic
426C4×C8C22×D5911yescharacteristic
427C2×Q8—591no—
428C2×Q8—591no—
429C2×Q8—591no—
430C2×Q8—1182no—
431C2×Q8—1181no—
432C2×Q8—2361no—
433C2×D4—591no—
434C2×D4—1181no—
435C22×C4—1181no—
436C22×C4—1181no—
437C22×C4—1181no—
438C22×C4C2×C4×D5911yescharacteristic
439C22×C4C2×D23611yescharacteristic
440C22×C4#1174568511yescharacteristic
441Q16—1182no—
442Q16—2361no—
443SD16—1182no—
444SD16—2361no—
445M16—4721no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—42no—
449C2×C8—1181no—
450C2×C8—1181no—
451C2×C8—1181no—
452C2×C8—1181no—
453C2×C8—4721no—
454C2×C8—4721no—
455C2×C8C2×C4×D5911yescharacteristic
456C2×C8C2×C4×D5911yescharacteristic
457C2×C8C2×C4×D5911yescharacteristic
458C2×C8C2×C4×D5911yescharacteristic
459C2×C8C2×D23611yescharacteristic
460C2×C8C2×D23611yescharacteristic
461C2×C8C2×D23611yescharacteristic
462C2×C8C2×D23611yescharacteristic
463C4⋊C4—591no—
464C4⋊C4—591no—
465C4⋊C4—591no—
466C4⋊C4—591no—
467C4⋊C4—1181no—
468C4⋊C4—1181no—
469C4⋊C4—1181no—
470C4⋊C4—1181no—
471C4⋊C4—1181no—
472C4⋊C4—1181no—
473C4⋊C4—1181no—
474C4⋊C4—1181no—
475C4⋊C4—1181no—
476C22⋊C4—1181no—
477C22⋊C4—1181no—
478C22⋊C4—1181no—
479C22⋊C4—1181no—
480C22⋊C4—1181no—
481C42—1181no—
482C42—1181no—
483C42—1181no—
484C42—1181no—
485C42—1181no—
486C42C2×C4×D5911yescharacteristic
487C42C2×D23611yescharacteristic
488C42#1174568511yescharacteristic
489C42C23×D5911yescharacteristic
490C23—1181no—
491C23C4×D23611yescharacteristic
492Q8—592no—
493Q8—1181no—
494Q8—1181no—
495Q8—1181no—
496Q8—1181no—
497Q8—1181no—
498Q8—2362no—
499D4—1181no—
500D4—1181no—
501D4—2362no—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—1181no—
508C2×C4—1181no—
509C2×C4—1181no—
510C2×C4—1181no—
511C2×C4—1181no—
512C2×C4—1181no—
513C2×C4—1181no—
514C2×C4—2362no—
515C2×C4—2362no—
516C2×C4—2361no—
517C2×C4—2361no—
518C2×C4C4×D23611yescharacteristic
519C2×C4C4×D23611yescharacteristic
520C2×C4C4×D23611yescharacteristic
521C2×C4C22×C4×D5911yescharacteristic
522C2×C4C22×D23611yescharacteristic
523C2×C4C2×#1174568511yescharacteristic
524C8—21no—
525C8—21no—
526C8—21no—
527C8—21no—
528C8—21no—
529C8—21no—
530C8—21no—
531C8—21no—
532C8—41no—
533C8—41no—
534C8—2361no—
535C8—2361no—
536C8—2361no—
537C8—2361no—
538C22—21no—
539C22—21no—
540C22—2361no—
541C22—2361no—
542C22—2361no—
543C22#1683752512yes—
544C22C2×C4×D23611yescharacteristic
545C4—21no—
546C4—21no—
547C4—21no—
548C4—21no—
549C4—1182no—
550C4—2361no—
551C4—2361no—
552C4—2361no—
553C4—2361no—
554C4—2361no—
555C4—2361no—
556C4#131×D5911yescharacteristic
557C4#1683816711yescharacteristic
558C4#1683821411yescharacteristic
559C4#1683821911yescharacteristic
560C2—22no—
561C2—4721no—
562C2#2143282411yescharacteristic
563C2#2143294111yescharacteristic
564C2C2×#1683752511yescharacteristic
subgroupG/H
centerC2×C4C22×D236
commutatorC2×C4×C59C23×C4
FrattiniC42C23×D59
FittingC59×#1452C2
socleC22×C59C2×C4×D4
prime radical#14273701C2×C4
cosocleC42×C59C24
hypercenter#1452D59
hypocenterC59#18023
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ #431 ◁ #1452

Complements

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

NH ≅ G/Ntype
3. #21433183C2semidirect
4. #21423006C2semidirect
5. #21423000C2semidirect
6. #21422948C2semidirect
7. #21422948C2semidirect
8. #21422941C2semidirect
9. #21422934C2semidirect
10. #21422916C2semidirect
11. #21422910C2semidirect
12. #21422881C2semidirect
14. C2×#16837134C2semidirect
15. C59×#1452C2semidirect
292. #1452D59semidirect
349. C59#18023semidirect

Maximal subgroups

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

subgroupindex
#214341782
#214332582
#214331832
#214230062
#214230002
#214229482
#214229412
#214229342
#214229162
#214229102
#214228812
#214225572
C2×#168371342
C59×#14522
#1802359