Finite Group Databasebeta

← #28556233

Subgroups — #28556233

Order 15104.

996 conjugacy classes of subgroups.

The subgroup lattice has 952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21438145C211yesmaximal, characteristic
2#21426729C211yesmaximal, characteristic, complemented
3#21422674C211yesmaximal, characteristic, complemented
4#21422669C211yesmaximal, characteristic, complemented
5#21422661C211yesmaximal, characteristic, complemented
6#21422653C211yesmaximal, characteristic, complemented
7#21422648C211yesmaximal, characteristic, complemented
8#21422640C211yesmaximal, characteristic, complemented
9#21422635C211yesmaximal, characteristic, complemented
10#21422630C211yesmaximal, characteristic, complemented
11#21422617C211yesmaximal, characteristic, complemented
12#21422601C211yesmaximal, characteristic, complemented
13#21422588C211yesmaximal, characteristic, complemented
14C2×#16837140C211yesmaximal, characteristic, complemented
15C59×#2974C211yesmaximal, characteristic, complemented
16#16838122C411yescharacteristic, complemented
17#16838107—21no—
18#16838092C411yescharacteristic, complemented
19#16838092C411yescharacteristic, complemented
20#16838078—21no—
21#16838078—21no—
22D4×Dic118C411yescharacteristic, complemented
23#16838061C411yescharacteristic, complemented
24#16838061C411yescharacteristic, complemented
25#16838057C411yescharacteristic, complemented
26#16838056C411yescharacteristic, complemented
27#16838046—21no—
28#16838017—21no—
29#16837994—21no—
30#16837994—21no—
31#16837959C2211yescharacteristic
32#16837936C2211yescharacteristic
33#16837913C2211yescharacteristic
34#16837913C2211yescharacteristic
35C2×#14273706C2211yescharacteristic
36C2×#14273706C2211yescharacteristic
37#16837881—21no—
38#16837295—21no—
39#16837288—21no—
40#16837282—21no—
41#16837277—21no—
42#16837270C2211yescharacteristic
43#16837268C2211yescharacteristic
44#16837265C2211yescharacteristic
45#16837262C2211yescharacteristic
46C4×C22⋊Dic59C2211yescharacteristic
47C2×C59⋊#95C2211yescharacteristic
48#16837140C2211yescharacteristic
49#16837140C2211yescharacteristic
50#16837140C2211yescharacteristic
51#16837140C2211yescharacteristic
52#16837140C2211yescharacteristic
53#16837140C2211yescharacteristic
54#16837140C2211yescharacteristic
55#16837140C2211yescharacteristic
56#16837140C2211yescharacteristic
57#16837140C2211yescharacteristic
58#16837140C2211yescharacteristic
59#16837140C2211yescharacteristic
60#16837137C2211yescharacteristic
61#16837137C2211yescharacteristic
62#16837137C2211yescharacteristic
63#16837137C2211yescharacteristic
64C2×C4×D4×C59C2211yescharacteristic
65C59×#436—21no—
66C59×#435—21no—
67C59×#435—21no—
68C8×D4×C59—21no—
69C59×#432C2211yescharacteristic
70C59×#431C2211yescharacteristic
71C59×#407C2211yescharacteristic
72C59×#407C2211yescharacteristic
73C2×C22⋊C8×C59C2211yescharacteristic
74C2×C22⋊C8×C59C2211yescharacteristic
75C2×#11745685C2×C411yescharacteristic
76C2×#11745685C2×C411yescharacteristic, complemented
77C2×#11745687—21no—
78C22×Dic118C2×C411yescharacteristic
79C22×Dic118C2×C411yescharacteristic, complemented
80C23×Dic59—21no—
81#14273727C2×C411yescharacteristic, complemented
82#14273727C2×C411yescharacteristic, complemented
83#14273726—21no—
84#14273721—21no—
85#14273720—21no—
86#14273720—21no—
87#14273720—21no—
88#14273720—21no—
89#14273719—21no—
90#14273719C2×C411yescharacteristic, complemented
91#14273717—21no—
92#14273717—21no—
93#14273715C2×C411yescharacteristic, complemented
94#14273714—21no—
95#14273713—21no—
96#14273713—21no—
97#14273711—21no—
98#14273711—21no—
99#14273710—21no—
100#14273710—21no—
101#14273710—21no—
102#14273709—21no—
103#14273709—21no—
104#14273708—21no—
105#14273708—21no—
106#14273707—21no—
107#14273706—21no—
108#14273706—21no—
109#14273706—21no—
110#14273706—21no—
111#14273706—21no—
112#14273706C2×C411yescharacteristic
113#14273706C2×C411yescharacteristic
114#14273706C2×C411yescharacteristic
115#14273706C2×C411yescharacteristic, complemented
116#14273706C2×C411yescharacteristic, complemented
117#14273706C2×C411yescharacteristic, complemented
118#14273706C2311yescharacteristic
119#14273706C2311yescharacteristic
120#14273706C2311yescharacteristic
121#14273705—21no—
122#14273705—21no—
123#14273704—21no—
124#14273704—21no—
125#14273701C2×C411yescharacteristic
126#14273701C2×C411yescharacteristic, complemented
127#14273701C2311yescharacteristic
128#14273699—21no—
129#14273699—21no—
130#14273698—21no—
131#14273696—21no—
132#14273696—21no—
133C4×Dic118—21no—
134C4×Dic118C2×C411yescharacteristic, complemented
135C4×Dic118C2×C411yescharacteristic, complemented
136C4×Dic118C2×C411yescharacteristic, complemented
137#14273692—21no—
138C4×D236C2×C411yescharacteristic, complemented
139D4×Dic59—21no—
140C4×C22⋊D59—21no—
141C4×C22⋊D59—21no—
142C4×C22⋊D59—21no—
143C4×C22⋊D59—21no—
144C4×C22⋊D59—21no—
145(C22⋊D59)⋊C4—21no—
146(C22⋊D59)⋊C4—21no—
147#14273686—21no—
148#14273686C2×C411yescharacteristic
149#14273686C2×C411yescharacteristic, complemented
150#14273684—21no—
151#14273683—21no—
152#14273683—21no—
153C2×C4⋊Dic59—21no—
154C2×C4⋊Dic59—21no—
155C2×C4⋊Dic59C2×C411yescharacteristic
156C2×C4⋊Dic59C2×C411yescharacteristic, complemented
157C2×Dic59⋊C4—21no—
158C2×Dic59⋊C4—21no—
159C4⋊C4×D59—21no—
160C2×C22⋊Dic59—21no—
161C2×C22⋊Dic59—21no—
162C2×C22⋊Dic59—21no—
163C2×C22⋊Dic59—21no—
164C2×C22⋊Dic59—21no—
165C2×C4×Dic59—21no—
166C59⋊#95—21no—
167C59⋊#95—21no—
168C59⋊#95—21no—
169C59⋊#95—21no—
170C59⋊#95—21no—
171C59⋊#95C2311yescharacteristic
172C59⋊#95C2311yescharacteristic
173C59⋊#95C2311yescharacteristic
174C59⋊#95C2311yescharacteristic
175C22×D4×C59D411yescharacteristic
176C23×C4×C59C2311yescharacteristic
177C23×C4×C59C2311yescharacteristic
178C2×M16×C59—21no—
179C2×M16×C59—21no—
180C22×C8×C59—21no—
181C22×C8×C59—21no—
182C4×D4×C59C2×C411yescharacteristic
183C4×D4×C59C2×C411yescharacteristic
184C4×D4×C59C2×C411yescharacteristic
185C4×D4×C59C2×C411yescharacteristic
186C4×D4×C59D411yescharacteristic
187C4×D4×C59D411yescharacteristic
188C4×D4×C59D411yescharacteristic
189C4×D4×C59D411yescharacteristic
190C2×C4⋊C4×C59D411yescharacteristic
191C2×C22⋊C4×C59D411yescharacteristic
192C2×C22⋊C4×C59D411yescharacteristic
193C2×C42×C59C2311yescharacteristic
194C4⋊C8×C59—21no—
195C4⋊C8×C59—21no—
196C22⋊C8×C59—21no—
197C22⋊C8×C59—21no—
198C22⋊C8×C59—21no—
199C22⋊C8×C59—21no—
200C22⋊C8×C59C2311yescharacteristic
201C22⋊C8×C59C2311yescharacteristic
202C22⋊C8×C59C2311yescharacteristic
203C22⋊C8×C59C2311yescharacteristic
204#97×C59—21no—
205C4×C8×C59—21no—
206C24×C59C2×D411yescharacteristic
207C24×C59C2×D411yescharacteristic
208C2×D4×C59—42no—
209C2×D4×C59C22⋊C411yescharacteristic
210C2×D4×C59C22⋊C411yescharacteristic
211C2×D4×C59C22⋊C411yescharacteristic
212C2×D4×C59C22⋊C411yescharacteristic
213C22×C4×C59—81no—
214C22×C4×C59—81no—
215C22×C4×C59C22×C411yescharacteristic
216C22×C4×C59C22×C411yescharacteristic
217C22×C4×C59C22×C411yescharacteristic
218C22×C4×C59C22×C411yescharacteristic
219C22×C4×C59C2×D411yescharacteristic
220C22×C4×C59C2×D411yescharacteristic
221C22×C4×C59C2×D411yescharacteristic
222C22×C4×C59C2×D411yescharacteristic
223C22×C4×C59C2×D411yescharacteristic
224C22×C4×C59C2×D411yescharacteristic
225C22×C4×C59C2×D411yescharacteristic
226C22×C4×C59C2×D411yescharacteristic
227C22×C4×C59C2411yescharacteristic
228C2×C22⋊D59—21no—
229C2×C22⋊D59—21no—
230C2×C22⋊D59—21no—
231C2×C22⋊D59—21no—
232C2×C22⋊D59—21no—
233C22×Dic59—21no—
234C22×Dic59—21no—
235C22×Dic59—21no—
236C22×Dic59—21no—
237C22×Dic59—21no—
238C22×Dic59—21no—
239C22×Dic59—21no—
240C22×Dic59—21no—
241C22×Dic59—42no—
242C22×Dic59—81no—
243C22×Dic59—81no—
244#11745687—44no—
245#11745685—81no—
246#11745685—81no—
247C2×D236C22×C411yescharacteristic
248C2×C4×D59—21no—
249C2×C4×D59—21no—
250C2×C4×D59—21no—
251C2×Dic118—21no—
252C2×Dic118—21no—
253C2×Dic118—21no—
254C2×Dic118—81no—
255C2×Dic118—81no—
256C2×Dic118C22×C411yescharacteristic
257C2×Dic118C22×C411yescharacteristic
258C2×Dic118C22×C411yescharacteristic
259M16×C59—81no—
260M16×C59—81no—
261C2×C8×C59—21no—
262C2×C8×C59—21no—
263C2×C8×C59—21no—
264C2×C8×C59—21no—
265C2×C8×C59—81no—
266C2×C8×C59—81no—
267C4⋊C4×C59C22⋊C411yescharacteristic
268C4⋊C4×C59C22⋊C411yescharacteristic
269C4⋊C4×C59C22⋊C411yescharacteristic
270C4⋊C4×C59C22⋊C411yescharacteristic
271C22⋊C4×C59C22⋊C411yescharacteristic
272C22⋊C4×C59C22⋊C411yescharacteristic
273C22⋊C4×C59C22⋊C411yescharacteristic
274C22⋊C4×C59C22⋊C411yescharacteristic
275C22⋊C4×C59C22⋊C411yescharacteristic
276C22⋊C4×C59C22⋊C411yescharacteristic
277C22⋊C4×C59C22⋊C411yescharacteristic
278C22⋊C4×C59C22⋊C411yescharacteristic
279C42×C59C22×C411yescharacteristic
280C42×C59C22×C411yescharacteristic
281C42×C59C2×D411yescharacteristic
282C42×C59C2×D411yescharacteristic
283C22⋊Dic59—21no—
284C22⋊Dic59—21no—
285C22⋊Dic59—21no—
286C22⋊Dic59—21no—
287C22⋊Dic59—21no—
288C22⋊Dic59—21no—
289C22⋊Dic59—21no—
290C22⋊Dic59—21no—
291C22⋊Dic59—21no—
292C22⋊Dic59—21no—
293C22⋊Dic59—21no—
294C22⋊Dic59—42no—
295C22⋊Dic59—81no—
296C22⋊Dic59—81no—
297(C2×D59)⋊C4—21no—
298(C2×D59)⋊C4—21no—
299(C2×D59)⋊C4—21no—
300(C2×D59)⋊C4—21no—
301(C2×D59)⋊C4—21no—
302(C2×D59)⋊C4—21no—
303C4⋊Dic59—21no—
304C4⋊Dic59—21no—
305C4⋊Dic59—21no—
306C4⋊Dic59—21no—
307C4⋊Dic59—21no—
308C4⋊Dic59—81no—
309C4⋊Dic59—81no—
310C4⋊Dic59C22×C411yescharacteristic
311C4⋊Dic59C22×C411yescharacteristic
312C4⋊Dic59C22×C411yescharacteristic
313C4⋊Dic59C22×C411yescharacteristic
314Dic59⋊C4—21no—
315Dic59⋊C4—21no—
316Dic59⋊C4—21no—
317Dic59⋊C4—21no—
318Dic59⋊C4—21no—
319Dic59⋊C4—21no—
320Dic59⋊C4—21no—
321Dic59⋊C4—21no—
322Dic59⋊C4—21no—
323Dic59⋊C4—21no—
324Dic59⋊C4—21no—
325Dic59⋊C4—21no—
326Dic59⋊C4—21no—
327Dic59⋊C4—21no—
328C4×Dic59—21no—
329C4×Dic59—21no—
330C4×Dic59—21no—
331C4×Dic59—21no—
332C4×Dic59—21no—
333C4×Dic59—81no—
334C23×C59—21no—
335C23×C59—21no—
336C23×C59—22no—
337C23×C59—21no—
338C23×C59—21no—
339C23×C59—41no—
340C23×C59—41no—
341C23×C59—41no—
342C23×C59C2×C22⋊C411yescharacteristic
343C23×C59C2×C22⋊C411yescharacteristic
344C23×C59C2×C22⋊C411yescharacteristic
345C23×C59C2×C22⋊C411yescharacteristic
346C23×C59C22×D411yescharacteristic
347C22×D59—21no—
348D4×C59—22no—
349D4×C59—22no—
350D4×C59—41no—
351D4×C59—41no—
352C2×C4×C59—21no—
353C2×C4×C59—21no—
354C2×C4×C59—41no—
355C2×C4×C59—41no—
356C2×C4×C59—41no—
357C2×C4×C59—41no—
358C2×C4×C59—41no—
359C2×C4×C59—41no—
360C2×C4×C59—41no—
361C2×C4×C59—41no—
362C2×C4×C59—41no—
363C2×C4×C59—41no—
364C2×C4×C59—41no—
365C2×C4×C59—41no—
366C2×C4×C59C2×C22⋊C411yescharacteristic
367C2×C4×C59C2×C22⋊C411yescharacteristic
368C2×C4×C59C2×C22⋊C411yescharacteristic
369C2×C4×C59C2×C22⋊C411yescharacteristic
370C2×C4×C59C2×C22⋊C411yescharacteristic
371C2×C4×C59C2×C22⋊C411yescharacteristic
372C2×C4×C59C2×C22⋊C411yescharacteristic
373C2×C4×C59C2×C22⋊C411yescharacteristic
374C2×C4×C59C23×C411yescharacteristic
375C2×C4×C59C22×D411yescharacteristic
376C22⋊D59—42no—
377C22⋊D59—41no—
378C22⋊D59—41no—
379C22⋊D59—42no—
380C22⋊D59—81no—
381C22⋊D59—81no—
382C2×Dic59—21no—
383C2×Dic59—21no—
384C2×Dic59—21no—
385C2×Dic59—21no—
386C2×Dic59—21no—
387C2×Dic59—21no—
388C2×Dic59—21no—
389C2×Dic59—42no—
390C2×Dic59—42no—
391C2×Dic59—41no—
392C2×Dic59—41no—
393C2×Dic59—41no—
394C2×Dic59—41no—
395C2×Dic59—41no—
396C2×Dic59—41no—
397C2×Dic59—41no—
398C2×Dic59—41no—
399C2×Dic59—41no—
400C2×Dic59—41no—
401C2×Dic59—41no—
402C2×Dic59—41no—
403C2×Dic59—81no—
404C2×Dic59—81no—
405C2×Dic59—84no—
406D236—41no—
407C4×D59—42no—
408C4×D59—81no—
409C4×D59—81no—
410Dic118—42no—
411Dic118—41no—
412Dic118—41no—
413Dic118—41no—
414Dic118—81no—
415Dic118—81no—
416C8×C59—41no—
417C8×C59—41no—
418C8×C59—41no—
419C8×C59—41no—
420#17598—591nomaximal, Sylow
421C22×C59—21no—
422C22×C59—21no—
423C22×C59—21no—
424C22×C59—21no—
425C22×C59—21no—
426C22×C59—21no—
427C22×C59—21no—
428C22×C59—21no—
429C22×C59—21no—
430C22×C59—21no—
431C22×C59—21no—
432C22×C59—21no—
433C22×C59—21no—
434C22×C59—42no—
435C22×C59—42no—
436C22×C59—81no—
437C22×C59—81no—
438C22×C59#42112yes—
439C22×C59C22×C22⋊C411yescharacteristic
440C22×C59#57711yescharacteristic
441C22×C59#57811yescharacteristic
442C2×D59—41no—
443C2×D59—41no—
444C2×D59—41no—
445C4×C59—21no—
446C4×C59—21no—
447C4×C59—21no—
448C4×C59—21no—
449C4×C59—21no—
450C4×C59—21no—
451C4×C59—21no—
452C4×C59—21no—
453C4×C59—21no—
454C4×C59—21no—
455Dic59—41no—
456Dic59—41no—
457Dic59—41no—
458Dic59—41no—
459Dic59—41no—
460Dic59—41no—
461Dic59—41no—
462Dic59—81no—
463Dic59—81no—
464Dic59—81no—
465Dic59—81no—
466#3520—591no—
467#2974D5911yescharacteristic, complemented
468#2318—591no—
469#1521—591no—
470#1520—591no—
471#1518—591no—
472#1516—591no—
473#1515—591no—
474#1513—591no—
475#1512—591no—
476#1511—591no—
477#1508—591no—
478#1504—591no—
479#1501—591no—
480C2×#328—591no—
481C2×C59—21no—
482C2×C59—21no—
483C2×C59—22no—
484C2×C59—41no—
485C2×C59—41no—
486C2×C59—41no—
487C2×C59#288311yescharacteristic
488C2×C59#289811yescharacteristic
489C2×C59C2×#42111yescharacteristic
490D59—81no—
491#556—591no—
492#554—1181no—
493#552—591no—
494#552—591no—
495#551—1181no—
496#551—1181no—
497D4×Q8—591no—
498#548—591no—
499#548—591no—
500#547—591no—
501#547—591no—
502#546—1181no—
503#542—1181no—
504#539—1181no—
505#539—1181no—
506#533—591no—
507#529—591no—
508#525—591no—
509#525—591no—
510C2×C22⋊Q8—591no—
511C2×C22⋊Q8—591no—
512#520—1181no—
513C2×C4×D4C2×D5911yescharacteristic
514#436—21no—
515#435—21no—
516#435—21no—
517C8×D4—21no—
518#432C2×D5911yescharacteristic
519#431C2×D5911yescharacteristic
520#407C2×D5911yescharacteristic
521#407C2×D5911yescharacteristic
522C2×C22⋊C8C2×D5911yescharacteristic
523C2×C22⋊C8C2×D5911yescharacteristic
524#388—1181no—
525#387—1181no—
526#386—1181no—
527#385—1181no—
528#383—591no—
529#382—591no—
530#381—591no—
531#380—591no—
532C4×C22⋊C4—591no—
533C2×#95—591no—
534#328—591no—
535#328—591no—
536#328—591no—
537#328—591no—
538#328—591no—
539#328—591no—
540#328—591no—
541#328—591no—
542#328—591no—
543#328—591no—
544#328—591no—
545#328—591no—
546#327—591no—
547#327—591no—
548#327—591no—
549#327—591no—
550C59#1759811yescharacteristic, complemented, Sylow
551C2×#41—591no—
552C2×#41—591no—
553C2×#41—1181no—
554C22×Q8—591no—
555C22×Q8—591no—
556C22×D4D23611yescharacteristic
557C23×C4—1181no—
558C23×C4C22×D5911yescharacteristic
559C23×C4C22×D5911yescharacteristic
560C2×M16—21no—
561C2×M16—21no—
562C22×C8—21no—
563C22×C8—21no—
564C4⋊Q8—591no—
565C4⋊Q8—591no—
566C4⋊Q8—1181no—
567#126—1181no—
568#126—1181no—
569#126—1181no—
570#126—1181no—
571#126—1181no—
572#125—591no—
573#125—1181no—
574#125—1181no—
575#125—1181no—
576#124—591no—
577#124—1181no—
578#124—1181no—
579#124—1181no—
580#123—1181no—
581#123—1181no—
582#123—1181no—
583#123—1181no—
584#123—1181no—
585#123—1181no—
586#123—1181no—
587#123—1181no—
588#123—1181no—
589C22⋊Q8—591no—
590C22⋊Q8—591no—
591C22⋊Q8—591no—
592C22⋊Q8—591no—
593C22⋊Q8—591no—
594C22⋊Q8—591no—
595C22⋊Q8—591no—
596C22⋊Q8—591no—
597C22⋊Q8—591no—
598C22⋊Q8—1181no—
599C22⋊Q8—1181no—
600C22⋊Q8—1181no—
601C22⋊Q8—1181no—
602C22⋊Q8—1181no—
603C22⋊Q8—1181no—
604C22⋊Q8—1181no—
605C22⋊Q8—1181no—
606C22⋊Q8—1181no—
607C22⋊Q8—1181no—
608#121—591no—
609#121—591no—
610#121—591no—
611#121—1181no—
612#121—1181no—
613#121—1181no—
614#120—1181no—
615#120—1181no—
616C4×Q8—591no—
617C4×Q8—591no—
618C4×Q8—591no—
619C4×Q8—1181no—
620C4×Q8—1181no—
621C4×D4—591no—
622C4×D4—1181no—
623C4×D4—1181no—
624C4×D4—1181no—
625C4×D4—1181no—
626C4×D4—1181no—
627C4×D4—1181no—
628C4×D4—1181no—
629C4×D4—1181no—
630C4×D4C4×D5911yescharacteristic
631C4×D4C4×D5911yescharacteristic
632C4×D4C4×D5911yescharacteristic
633C4×D4C4×D5911yescharacteristic
634C4×D4C22⋊D5911yescharacteristic
635C4×D4C22⋊D5911yescharacteristic
636C4×D4C22⋊D5911yescharacteristic
637C4×D4C22⋊D5911yescharacteristic
638#117—591no—
639#117—591no—
640#117—1181no—
641#117—1181no—
642#117—1181no—
643#117—1181no—
644C2×C4⋊C4—591no—
645C2×C4⋊C4—591no—
646C2×C4⋊C4—1181no—
647C2×C4⋊C4—1181no—
648C2×C4⋊C4—1181no—
649C2×C4⋊C4—1181no—
650C2×C4⋊C4—1181no—
651C2×C4⋊C4D23611yescharacteristic
652C2×C22⋊C4—1181no—
653C2×C22⋊C4—1181no—
654C2×C22⋊C4—1181no—
655C2×C22⋊C4—1181no—
656C2×C22⋊C4—1181no—
657C2×C22⋊C4D23611yescharacteristic
658C2×C22⋊C4D23611yescharacteristic
659C2×C42—1181no—
660C2×C42C22×D5911yescharacteristic
661C4⋊C8—21no—
662C4⋊C8—21no—
663C22⋊C8—21no—
664C22⋊C8—21no—
665C22⋊C8—21no—
666C22⋊C8—21no—
667C22⋊C8C22×D5911yescharacteristic
668C22⋊C8C22×D5911yescharacteristic
669C22⋊C8C22×D5911yescharacteristic
670C22⋊C8C22×D5911yescharacteristic
671#97—21no—
672C4×C8—21no—
673#95—591no—
674#95—591no—
675#95—591no—
676#95—591no—
677#95—1181no—
678#95—1181no—
679#95—1181no—
680#95—1181no—
681#95—1181no—
682C24C2×D23611yescharacteristic
683C24C2×D23611yescharacteristic
684#41—4721no—
685#41—4721no—
686#41—2364no—
687C2×Q8—591no—
688C2×Q8—591no—
689C2×Q8—591no—
690C2×Q8—1181no—
691C2×Q8—1181no—
692C2×Q8—1181no—
693C2×Q8—4721no—
694C2×Q8—4721no—
695C2×D4—42no—
696C2×D4—591no—
697C2×D4—1181no—
698C2×D4—1181no—
699C2×D4—1181no—
700C2×D4—1181no—
701C2×D4—1181no—
702C2×D4(C2×D59)⋊C411yescharacteristic
703C2×D4(C2×D59)⋊C411yescharacteristic
704C2×D4(C2×D59)⋊C411yescharacteristic
705C2×D4(C2×D59)⋊C411yescharacteristic
706C22×C4—81no—
707C22×C4—81no—
708C22×C4—1181no—
709C22×C4—1181no—
710C22×C4—1181no—
711C22×C4—1181no—
712C22×C4—1181no—
713C22×C4—1181no—
714C22×C4—1181no—
715C22×C4—1181no—
716C22×C4—1181no—
717C22×C4—1181no—
718C22×C4—1181no—
719C22×C4—4721no—
720C22×C4—4721no—
721C22×C4—2362no—
722C22×C4C2×C4×D5911yescharacteristic
723C22×C4C2×C4×D5911yescharacteristic
724C22×C4C2×C4×D5911yescharacteristic
725C22×C4C2×C4×D5911yescharacteristic
726C22×C4C2×D23611yescharacteristic
727C22×C4C2×D23611yescharacteristic
728C22×C4C2×D23611yescharacteristic
729C22×C4C2×D23611yescharacteristic
730C22×C4C2×C22⋊D5911yescharacteristic
731C22×C4C2×C22⋊D5911yescharacteristic
732C22×C4C2×C22⋊D5911yescharacteristic
733C22×C4C2×C22⋊D5911yescharacteristic
734C22×C4C23×D5911yescharacteristic
735M16—81no—
736M16—81no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—81no—
742C2×C8—81no—
743C4⋊C4—591no—
744C4⋊C4—591no—
745C4⋊C4—591no—
746C4⋊C4—591no—
747C4⋊C4—1181no—
748C4⋊C4—1181no—
749C4⋊C4—1181no—
750C4⋊C4—1181no—
751C4⋊C4—1181no—
752C4⋊C4—1181no—
753C4⋊C4—1181no—
754C4⋊C4—1181no—
755C4⋊C4—1181no—
756C4⋊C4—1181no—
757C4⋊C4—1181no—
758C4⋊C4—1181no—
759C4⋊C4—1181no—
760C4⋊C4—1181no—
761C4⋊C4—1181no—
762C4⋊C4—1181no—
763C4⋊C4—1181no—
764C4⋊C4—1181no—
765C4⋊C4—1181no—
766C4⋊C4—4721no—
767C4⋊C4—4721no—
768C4⋊C4(C2×D59)⋊C411yescharacteristic
769C4⋊C4(C2×D59)⋊C411yescharacteristic
770C4⋊C4(C2×D59)⋊C411yescharacteristic
771C4⋊C4(C2×D59)⋊C411yescharacteristic
772C22⋊C4—1181no—
773C22⋊C4—1181no—
774C22⋊C4—1181no—
775C22⋊C4—1181no—
776C22⋊C4—1181no—
777C22⋊C4—1181no—
778C22⋊C4—1181no—
779C22⋊C4—1181no—
780C22⋊C4—1181no—
781C22⋊C4—1181no—
782C22⋊C4—1181no—
783C22⋊C4—1181no—
784C22⋊C4—1181no—
785C22⋊C4—1181no—
786C22⋊C4—1181no—
787C22⋊C4—1181no—
788C22⋊C4—1181no—
789C22⋊C4—4721no—
790C22⋊C4—4721no—
791C22⋊C4—2362no—
792C22⋊C4(C2×D59)⋊C411yescharacteristic
793C22⋊C4(C2×D59)⋊C411yescharacteristic
794C22⋊C4(C2×D59)⋊C411yescharacteristic
795C22⋊C4(C2×D59)⋊C411yescharacteristic
796C22⋊C4(C2×D59)⋊C411yescharacteristic
797C22⋊C4(C2×D59)⋊C411yescharacteristic
798C22⋊C4(C2×D59)⋊C411yescharacteristic
799C22⋊C4(C2×D59)⋊C411yescharacteristic
800C42—1181no—
801C42—1181no—
802C42—1181no—
803C42—1181no—
804C42—1181no—
805C42—4721no—
806C42C2×C4×D5911yescharacteristic
807C42C2×C4×D5911yescharacteristic
808C42C2×C22⋊D5911yescharacteristic
809C42C2×C22⋊D5911yescharacteristic
810C23—22no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—1181no—
819C23C2×(C2×D59)⋊C411yescharacteristic
820C23C2×(C2×D59)⋊C411yescharacteristic
821C23C2×(C2×D59)⋊C411yescharacteristic
822C23C2×(C2×D59)⋊C411yescharacteristic
823C23C22×D23611yescharacteristic
824Q8—4721no—
825Q8—4721no—
826Q8—2361no—
827Q8—2361no—
828Q8—2361no—
829Q8—2362no—
830D4—22no—
831D4—22no—
832D4—41no—
833D4—41no—
834D4—4721no—
835D4—4721no—
836D4—2361no—
837D4—2362no—
838D4—2362no—
839D4—2361no—
840D4—2361no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—1181no—
856C2×C4—1181no—
857C2×C4—1181no—
858C2×C4—1181no—
859C2×C4—1181no—
860C2×C4—1181no—
861C2×C4—1181no—
862C2×C4—4721no—
863C2×C4—4721no—
864C2×C4—4724no—
865C2×C4—4721no—
866C2×C4—4721no—
867C2×C4—2362no—
868C2×C4—2361no—
869C2×C4—2361no—
870C2×C4—2361no—
871C2×C4—2361no—
872C2×C4—2361no—
873C2×C4—2361no—
874C2×C4—2361no—
875C2×C4—2361no—
876C2×C4—2361no—
877C2×C4—2361no—
878C2×C4—2361no—
879C2×C4—2361no—
880C2×C4—2362no—
881C2×C4—2362no—
882C2×C4C2×(C2×D59)⋊C411yescharacteristic
883C2×C4C2×(C2×D59)⋊C411yescharacteristic
884C2×C4C2×(C2×D59)⋊C411yescharacteristic
885C2×C4C2×(C2×D59)⋊C411yescharacteristic
886C2×C4C2×(C2×D59)⋊C411yescharacteristic
887C2×C4C2×(C2×D59)⋊C411yescharacteristic
888C2×C4C2×(C2×D59)⋊C411yescharacteristic
889C2×C4C2×(C2×D59)⋊C411yescharacteristic
890C2×C4C22×C4×D5911yescharacteristic
891C2×C4C22×C22⋊D5911yescharacteristic
892C8—41no—
893C8—41no—
894C8—41no—
895C8—41no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—21no—
903C22—21no—
904C22—21no—
905C22—21no—
906C22—21no—
907C22—21no—
908C22—21no—
909C22—42no—
910C22—42no—
911C22—81no—
912C22—81no—
913C22—2361no—
914C22—2361no—
915C22—2361no—
916C22#1683741812yes—
917C22C22×(C2×D59)⋊C411yescharacteristic
918C22#1683821411yescharacteristic
919C22#1683821911yescharacteristic
920C4—21no—
921C4—21no—
922C4—21no—
923C4—21no—
924C4—21no—
925C4—21no—
926C4—21no—
927C4—21no—
928C4—21no—
929C4—21no—
930C4—4721no—
931C4—4721no—
932C4—4721no—
933C4—4721no—
934C4—2361no—
935C4—2361no—
936C4—2361no—
937C4—2361no—
938C4—2361no—
939C4—2361no—
940C4—2361no—
941C2—21no—
942C2—21no—
943C2—22no—
944C2—41no—
945C2—41no—
946C2—41no—
947C2—4721no—
948C2#2143255611yescharacteristic
949C2#2143263011yescharacteristic
950C2C2×#1683741811yescharacteristic
subgroupG/H
centerC22C22×(C2×D59)⋊C4
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#2974C2
socleC22×C59C22×C22⋊C4
prime radical#21438145C2
cosocleC22×C4×C59C24
hypercenter#2974D59
hypocenterC59#17598
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2974

Complements

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

NH ≅ G/Ntype
2. #21426729C2semidirect
3. #21422674C2semidirect
4. #21422669C2semidirect
5. #21422661C2semidirect
6. #21422653C2semidirect
7. #21422648C2semidirect
8. #21422640C2semidirect
9. #21422635C2semidirect
10. #21422630C2semidirect
11. #21422617C2semidirect
12. #21422601C2semidirect
13. #21422588C2semidirect
14. C2×#16837140C2semidirect
15. C59×#2974C2semidirect
16. #16838122C4semidirect
18. #16838092C4semidirect
19. #16838092C4semidirect
22. D4×Dic118C4semidirect
23. #16838061C4semidirect
24. #16838061C4semidirect
25. #16838057C4semidirect
26. #16838056C4semidirect
76. C2×#11745685C2×C4semidirect
79. C22×Dic118C2×C4semidirect
81. #14273727C2×C4semidirect
82. #14273727C2×C4semidirect
90. #14273719C2×C4semidirect
93. #14273715C2×C4semidirect
115. #14273706C2×C4semidirect
116. #14273706C2×C4semidirect
117. #14273706C2×C4semidirect
126. #14273701C2×C4semidirect
134. C4×Dic118C2×C4semidirect
135. C4×Dic118C2×C4semidirect
136. C4×Dic118C2×C4semidirect
138. C4×D236C2×C4semidirect
149. #14273686C2×C4semidirect
156. C2×C4⋊Dic59C2×C4semidirect
467. #2974D59semidirect
550. C59#17598semidirect

Maximal subgroups

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

subgroupindex
#214381452
#214267292
#214226742
#214226692
#214226612
#214226532
#214226482
#214226402
#214226352
#214226302
#214226172
#214226012
#214225882
C2×#168371402
C59×#29742
#1759859