Finite Group Databasebeta

← #28560629

Subgroups — #28560629

Order 15104.

612 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21434685C211yesmaximal, characteristic
2#21433258C211yesmaximal, characteristic, complemented
3#21422998C211yesmaximal, characteristic, complemented
4#21422979C211yesmaximal, characteristic, complemented
5#21422972C211yesmaximal, characteristic, complemented
6#21422960C211yesmaximal, characteristic, complemented
7#21422932C211yesmaximal, characteristic, complemented
8#21422923C211yesmaximal, characteristic, complemented
9#21422918C211yesmaximal, characteristic, complemented
10C8×#11745670C211yesmaximal, characteristic, complemented
11#21422849C211yesmaximal, characteristic, complemented
12#21422502C211yesmaximal, characteristic, complemented
13#21422495C211yesmaximal, characteristic, complemented
14#21422391C211yesmaximal, characteristic, complemented
15C59×#2979C211yesmaximal, characteristic, complemented
16#16837936C2211yescharacteristic
17#16837808C411yescharacteristic
18#16837789C411yescharacteristic
19#16837766C411yescharacteristic
20#16837764C411yescharacteristic
21#16837653C411yescharacteristic
22#16837653C411yescharacteristic
23#16837646C411yescharacteristic
24#16837646C411yescharacteristic
25#16837532C2211yescharacteristic
26C8×Dic118C2211yescharacteristic
27C4×#11745670C2211yescharacteristic
28C4×#11745670C2211yescharacteristic
29C4×#11745669C2211yescharacteristic
30C4×#11745669C2211yescharacteristic
31#16837481C2211yescharacteristic
32#16837470—21no—
33C8×D236C2211yescharacteristic
34(C22⋊D59)⋊C8—21no—
35#16837462—21no—
36#16837455C2211yescharacteristic
37#16837427—21no—
38C2×C4⋊(C59⋊C8)C2211yescharacteristic
39C4×#11745664C2211yescharacteristic
40#16837154C2211yescharacteristic
41#16837154C2211yescharacteristic
42#16837152C2211yescharacteristic
43#16837152C2211yescharacteristic
44#16837132C2211yescharacteristic
45#16837132C2211yescharacteristic
46D4⋊(C59⋊C8)C2211yescharacteristic
47D4⋊(C59⋊C8)C2211yescharacteristic
48D4⋊(C59⋊C8)C2211yescharacteristic
49D4⋊(C59⋊C8)C2211yescharacteristic
50#16837129C2211yescharacteristic
51#16837129C2211yescharacteristic
52#16837124C2211yescharacteristic
53#16837124C2211yescharacteristic
54#16837123C2211yescharacteristic
55C8×C59⋊C8C2211yescharacteristic
56C59×#532C2211yescharacteristic
57C59×#436—21no—
58C59×#436C2211yescharacteristic
59C59×#436C2211yescharacteristic
60C8×D4×C59—21no—
61C8×D4×C59C2211yescharacteristic
62C8×D4×C59C2211yescharacteristic
63C59×#431C2211yescharacteristic
64C59×#431C2211yescharacteristic
65C59×#408—21no—
66C59×#408—21no—
67C2×#11745670C2×C411yescharacteristic
68C2×#11745670C2×C411yescharacteristic
69C2×#11745669C2×C411yescharacteristic
70C2×#11745669C2×C411yescharacteristic
71C2×#11745664C2×C411yescharacteristic
72C2×#11745664C2×C411yescharacteristic
73C2×#11745659—21no—
74C22×C59⋊C8—21no—
75C2×C8×D59—21no—
76#14273721—21no—
77#14273719C2×C411yescharacteristic
78#14273715C2×C411yescharacteristic
79#14273710—21no—
80#14273706C2×C411yescharacteristic
81#14273701C2×C411yescharacteristic
82C4×Dic118C2311yescharacteristic
83C4×D236C2311yescharacteristic
84C4×C22⋊D59—21no—
85#14273684—21no—
86#14273660C2×C411yescharacteristic
87#14273660C2×C411yescharacteristic
88#14273658C2×C411yescharacteristic
89#14273658C2×C411yescharacteristic
90C4⋊(C59⋊C8)—21no—
91C4⋊(C59⋊C8)—21no—
92C4⋊(C59⋊C8)C2311yescharacteristic
93C4⋊(C59⋊C8)C2311yescharacteristic
94Dic59⋊C8—21no—
95Dic59⋊C8—21no—
96#14273650C2×C411yescharacteristic
97#14273650C2×C411yescharacteristic
98#14273648C2×C411yescharacteristic
99#14273648C2×C411yescharacteristic
100#14273648C2×C411yescharacteristic
101#14273648C2×C411yescharacteristic
102#14273647C2×C411yescharacteristic
103#14273647C2×C411yescharacteristic
104C22⋊(C59⋊C8)—21no—
105(C2×D59)⋊C8—21no—
106(C2×D59)⋊C8—21no—
107#14273638C2×C411yescharacteristic
108#14273638C2×C411yescharacteristic
109#14273637—21no—
110C4×C59⋊C8C2311yescharacteristic
111C4×C59⋊C8C2311yescharacteristic
112C4×C59⋊C8C2311yescharacteristic
113C4×C59⋊C8C2311yescharacteristic
114C8×Dic59—21no—
115C2×#41×C59—21no—
116C2×M16×C59—21no—
117C2×M16×C59—21no—
118C22×C8×C59—21no—
119C22×C8×C59—21no—
120C4⋊Q8×C59C2×C411yescharacteristic
121#127×C59C2×C411yescharacteristic
122#124×C59—21no—
123#121×C59—21no—
124#121×C59C2×C411yescharacteristic
125#121×C59C2×C411yescharacteristic
126C4×D4×C59—21no—
127C4×D4×C59C2311yescharacteristic
128C4×D4×C59C2311yescharacteristic
129C2×C42×C59C2311yescharacteristic
130C4⋊C8×C59D411yescharacteristic
131C4⋊C8×C59D411yescharacteristic
132C4⋊C8×C59C2311yescharacteristic
133C4⋊C8×C59C2311yescharacteristic
134C22⋊C8×C59—21no—
135C22⋊C8×C59—21no—
136C22⋊C8×C59—21no—
137C22⋊C8×C59—21no—
138C22⋊C8×C59—21no—
139C22⋊C8×C59D411yescharacteristic
140C22⋊C8×C59D411yescharacteristic
141C4×C8×C59—21no—
142C4×C8×C59C2311yescharacteristic
143C4×C8×C59C2311yescharacteristic
144#41×C59—81no—
145#41×C59—81no—
146C2×Q8×C59—21no—
147C2×D4×C59—21no—
148C2×D4×C59—21no—
149C2×D4×C59—21no—
150C2×D4×C59—21no—
151C2×D4×C59C22×C411yescharacteristic
152C2×D4×C59C22×C411yescharacteristic
153C22×C4×C59—21no—
154C22×C4×C59—21no—
155C22×C4×C59C22×C411yescharacteristic
156C22×C4×C59C2×D411yescharacteristic
157C22×C4×C59#4111yescharacteristic
158C2×C22⋊D59—21no—
159C2×D236C22×C411yescharacteristic
160C2×C4×D59—21no—
161C2×Dic118C22×C411yescharacteristic
162M16×C59—81no—
163M16×C59—81no—
164C2×C8×C59—21no—
165C2×C8×C59—21no—
166C2×C8×C59—81no—
167C2×C8×C59—81no—
168C2×C8×C59C2×D411yescharacteristic
169C2×C8×C59C2×D411yescharacteristic
170C2×C8×C59C2×D411yescharacteristic
171C2×C8×C59C2×D411yescharacteristic
172C4⋊C4×C59—21no—
173C4⋊C4×C59C22×C411yescharacteristic
174C4⋊C4×C59C22×C411yescharacteristic
175C22⋊C4×C59—21no—
176C22⋊C4×C59—21no—
177C22⋊C4×C59—21no—
178C22⋊C4×C59—21no—
179C42×C59C22×C411yescharacteristic
180C42×C59C2×D411yescharacteristic
181C42×C59#4111yescharacteristic
182C42×C59C2411yescharacteristic
183C22⋊Dic59—21no—
184#11745670—22no—
185#11745670—41no—
186#11745669—22no—
187#11745669—41no—
188(C2×D59)⋊C4—21no—
189(C2×D59)⋊C4—21no—
190(C2×D59)⋊C4—21no—
191(C2×D59)⋊C4—21no—
192C4⋊Dic59C22×C411yescharacteristic
193C4⋊Dic59C22×C411yescharacteristic
194Dic59⋊C4—21no—
195Dic59⋊C4—21no—
196Dic59⋊C4—21no—
197Dic59⋊C4—21no—
198C4×Dic59—21no—
199#11745664—22no—
200#11745664—41no—
201C2×C59⋊C8—21no—
202C2×C59⋊C8—21no—
203C2×C59⋊C8—21no—
204C2×C59⋊C8—21no—
205C2×C59⋊C8—81no—
206C2×C59⋊C8C22×C411yescharacteristic
207C2×C59⋊C8C22×C411yescharacteristic
208C2×C59⋊C8C22×C411yescharacteristic
209C2×C59⋊C8C22×C411yescharacteristic
210#11745659—81no—
211C8×D59—81no—
212C23×C59—21no—
213C23×C59—21no—
214C23×C59C4×D411yescharacteristic
215C22×D59—21no—
216Q8×C59—81no—
217D4×C59—21no—
218D4×C59—21no—
219D4×C59—21no—
220D4×C59—21no—
221D4×C59—42no—
222D4×C59—81no—
223D4×C59—81no—
224D4×C59—81no—
225C2×C4×C59—21no—
226C2×C4×C59—21no—
227C2×C4×C59—21no—
228C2×C4×C59—21no—
229C2×C4×C59—21no—
230C2×C4×C59—21no—
231C2×C4×C59—41no—
232C2×C4×C59—41no—
233C2×C4×C59—41no—
234C2×C4×C59—41no—
235C2×C4×C59—41no—
236C2×C4×C59C4×D411yescharacteristic
237C2×C4×C59C4×D411yescharacteristic
238C2×C4×C59C4×D411yescharacteristic
239C2×C4×C59C23×C411yescharacteristic
240C2×C4×C59C22×D411yescharacteristic
241C2×C4×C59C2×#4111yescharacteristic
242C22⋊D59—42no—
243C2×Dic59—21no—
244C2×Dic59—21no—
245C2×Dic59—21no—
246D236—21no—
247D236—21no—
248C4×D59—41no—
249C4×D59—41no—
250Dic118—21no—
251Dic118—21no—
252C8×C59—21no—
253C8×C59—21no—
254C8×C59—21no—
255C8×C59—21no—
256C8×C59—41no—
257C8×C59—41no—
258C59⋊C8—21no—
259C59⋊C8—21no—
260C59⋊C8—21no—
261C59⋊C8—41no—
262C59⋊C8—41no—
263C59⋊C8—41no—
264C59⋊C8—41no—
265C59⋊C8#13112yes—
266#18082—591nomaximal, Sylow
267C22×C59—21no—
268C22×C59—21no—
269C22×C59—21no—
270C22×C59—41no—
271C22×C59—41no—
272C22×C59—41no—
273C22×C59—41no—
274C22×C59—41no—
275C22×C59—41no—
276C22×C59C2×C4×D411yescharacteristic
277C2×D59—41no—
278C2×D59—41no—
279C2×D59—41no—
280C4×C59—21no—
281C4×C59—21no—
282C4×C59—21no—
283C4×C59—21no—
284C4×C59—41no—
285C4×C59—41no—
286C4×C59C2×#13111yescharacteristic
287C4×C59#56811yescharacteristic
288C4×C59#57611yescharacteristic
289C4×C59#57711yescharacteristic
290Dic59—41no—
291Dic59—41no—
292Dic59—41no—
293#3171—591no—
294#2994—591no—
295#2979D5911yescharacteristic, complemented
296#1592—591no—
297#1589—591no—
298#1588—591no—
299#1586—591no—
300#1582—591no—
301#1581—591no—
302#1580—591no—
303C8×SD16—591no—
304#1565—591no—
305#1482—591no—
306#1480—591no—
307#1453—591no—
308C2×C59—41no—
309C2×C59—81no—
310C2×C59—81no—
311C2×C59#293511yescharacteristic
312C2×C59#294611yescharacteristic
313C2×C59#295511yescharacteristic
314D59—81no—
315#532C2×D5911yescharacteristic
316#529—591no—
317#501—591no—
318#496—591no—
319#490—591no—
320#489—591no—
321#469—591no—
322#469—591no—
323#468—591no—
324#468—591no—
325#446—591no—
326C8×Q8—591no—
327C4×SD16—591no—
328C4×SD16—591no—
329C4×D8—591no—
330C4×D8—591no—
331#436—21no—
332#436—591no—
333#436C2×D5911yescharacteristic
334#436C2×D5911yescharacteristic
335#435—1181no—
336C8×D4—21no—
337C8×D4—591no—
338C8×D4—1181no—
339C8×D4C2×D5911yescharacteristic
340C8×D4C2×D5911yescharacteristic
341#433—1181no—
342#431—591no—
343#431C2×D5911yescharacteristic
344#431C2×D5911yescharacteristic
345#424—1181no—
346C2×C4⋊C8—591no—
347#408—21no—
348#408—21no—
349C4×M16—591no—
350#335—591no—
351#335—591no—
352#334—591no—
353#334—591no—
354Q8⋊C8—591no—
355Q8⋊C8—591no—
356D4⋊C8—591no—
357D4⋊C8—591no—
358D4⋊C8—591no—
359D4⋊C8—591no—
360D4⋊C8—591no—
361D4⋊C8—591no—
362#322—591no—
363#322—591no—
364#322—591no—
365C82—591no—
366C59#1808211yescharacteristic, complemented, Sylow
367C2×#41—21no—
368C2×SD16—591no—
369C2×SD16—591no—
370C2×D8—591no—
371C2×D8—591no—
372C2×M16—21no—
373C2×M16—21no—
374C2×M16—591no—
375C2×M16—591no—
376C2×M16—1181no—
377C22×C8—21no—
378C22×C8—21no—
379C22×C8—1181no—
380C22×C8—1181no—
381C4⋊Q8C4×D5911yescharacteristic
382#127C4×D5911yescharacteristic
383#126—1181no—
384#125—591no—
385#124—21no—
386#124—591no—
387#123—1181no—
388C22⋊Q8—591no—
389#121—21no—
390#121—591no—
391#121C4×D5911yescharacteristic
392#121C4×D5911yescharacteristic
393C4×Q8—591no—
394C4×D4—21no—
395C4×D4—591no—
396C4×D4—1181no—
397C4×D4C22×D5911yescharacteristic
398C4×D4C22×D5911yescharacteristic
399#117—1181no—
400C2×C42C22×D5911yescharacteristic
401#107—591no—
402#107—591no—
403#106—591no—
404#106—591no—
405C4⋊C8—591no—
406C4⋊C8—591no—
407C4⋊C8—1181no—
408C4⋊C8—1181no—
409C4⋊C8—1181no—
410C4⋊C8—1181no—
411C4⋊C8C22⋊D5911yescharacteristic
412C4⋊C8C22⋊D5911yescharacteristic
413C4⋊C8C22×D5911yescharacteristic
414C4⋊C8C22×D5911yescharacteristic
415#103—591no—
416#103—591no—
417#102—591no—
418#102—591no—
419#102—591no—
420#102—591no—
421#102—591no—
422#102—591no—
423C22⋊C8—21no—
424C22⋊C8—21no—
425C22⋊C8—21no—
426C22⋊C8—21no—
427C22⋊C8—21no—
428C22⋊C8—1181no—
429C22⋊C8—1181no—
430C22⋊C8—1181no—
431C22⋊C8C22⋊D5911yescharacteristic
432C22⋊C8C22⋊D5911yescharacteristic
433#97—591no—
434#97—591no—
435#97—1181no—
436C4×C8—21no—
437C4×C8—591no—
438C4×C8—591no—
439C4×C8—591no—
440C4×C8—591no—
441C4×C8—1181no—
442C4×C8C22×D5911yescharacteristic
443C4×C8C22×D5911yescharacteristic
444#41—81no—
445#41—81no—
446C2×Q8—21no—
447C2×Q8—591no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—591no—
453C2×D4—1181no—
454C2×D4C2×C4×D5911yescharacteristic
455C2×D4C2×C4×D5911yescharacteristic
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—1181no—
459C22×C4C2×C4×D5911yescharacteristic
460C22×C4#1174568511yescharacteristic
461C22×C4C2×C22⋊D5911yescharacteristic
462SD16—1182no—
463SD16—2361no—
464D8—1182no—
465D8—2361no—
466M16—81no—
467M16—81no—
468M16—1182no—
469M16—4721no—
470M16—2361no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—81no—
474C2×C8—81no—
475C2×C8—591no—
476C2×C8—591no—
477C2×C8—591no—
478C2×C8—591no—
479C2×C8—1181no—
480C2×C8—1181no—
481C2×C8—1181no—
482C2×C8—1181no—
483C2×C8—4721no—
484C2×C8—4721no—
485C2×C8C2×C22⋊D5911yescharacteristic
486C2×C8C2×C22⋊D5911yescharacteristic
487C2×C8C2×C22⋊D5911yescharacteristic
488C2×C8C2×C22⋊D5911yescharacteristic
489C4⋊C4—21no—
490C4⋊C4—591no—
491C4⋊C4—591no—
492C4⋊C4—1181no—
493C4⋊C4—1181no—
494C4⋊C4—1181no—
495C4⋊C4—1181no—
496C4⋊C4C2×C4×D5911yescharacteristic
497C4⋊C4C2×C4×D5911yescharacteristic
498C22⋊C4—21no—
499C22⋊C4—21no—
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—1181no—
503C22⋊C4—1181no—
504C22⋊C4—1181no—
505C22⋊C4—1181no—
506C22⋊C4—1181no—
507C42—1181no—
508C42C2×C4×D5911yescharacteristic
509C42#1174568511yescharacteristic
510C42C2×C22⋊D5911yescharacteristic
511C42C23×D5911yescharacteristic
512C23—21no—
513C23—21no—
514C23—1181no—
515C23C4×C22⋊D5911yescharacteristic
516Q8—81no—
517Q8—1181no—
518Q8—1181no—
519D4—21no—
520D4—21no—
521D4—21no—
522D4—21no—
523D4—42no—
524D4—81no—
525D4—81no—
526D4—81no—
527D4—1181no—
528D4—1181no—
529D4—2362no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—1181no—
542C2×C4—1181no—
543C2×C4—1181no—
544C2×C4—2361no—
545C2×C4—2361no—
546C2×C4C4×C22⋊D5911yescharacteristic
547C2×C4C4×C22⋊D5911yescharacteristic
548C2×C4C4×C22⋊D5911yescharacteristic
549C2×C4C22×C4×D5911yescharacteristic
550C2×C4C22×C22⋊D5911yescharacteristic
551C2×C4C2×#1174568511yescharacteristic
552C8—21no—
553C8—21no—
554C8—21no—
555C8—21no—
556C8—41no—
557C8—41no—
558C8—592no—
559C8—1181no—
560C8—1181no—
561C8—1181no—
562C8—2361no—
563C8—2361no—
564C8—2361no—
565C8—2361no—
566C22—21no—
567C22—21no—
568C22—21no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—2361no—
576C22—2361no—
577C22—2361no—
578C22C2×C4×C22⋊D5911yescharacteristic
579C4—21no—
580C4—21no—
581C4—21no—
582C4—21no—
583C4—41no—
584C4—41no—
585C4—2361no—
586C4—2361no—
587C4—2361no—
588C4#131×D5911yescharacteristic
589C4#1683816711yescharacteristic
590C4#1683820511yescharacteristic
591C4#1683821311yescharacteristic
592C2—41no—
593C2—81no—
594C2—81no—
595C2—4721no—
596C2#2143283811yescharacteristic
597C2#2143292811yescharacteristic
598C2#2143299711yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC42C23×D59
FittingC59×#2979C2
socleC22×C59C2×C4×D4
prime radical#21434685C2
cosocleC42×C59C24
hypercenter#2979D59
hypocenterC59#18082
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2979

Complements

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

NH ≅ G/Ntype
2. #21433258C2semidirect
3. #21422998C2semidirect
4. #21422979C2semidirect
5. #21422972C2semidirect
6. #21422960C2semidirect
7. #21422932C2semidirect
8. #21422923C2semidirect
9. #21422918C2semidirect
10. C8×#11745670C2semidirect
11. #21422849C2semidirect
12. #21422502C2semidirect
13. #21422495C2semidirect
14. #21422391C2semidirect
15. C59×#2979C2semidirect
295. #2979D59semidirect
366. C59#18082semidirect

Maximal subgroups

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

subgroupindex
#214346852
#214332582
#214229982
#214229792
#214229722
#214229602
#214229322
#214229232
#214229182
C8×#117456702
#214228492
#214225022
#214224952
#214223912
C59×#29792
#1808259