Finite Group Databasebeta

← #29453218

Subgroups — #29453218

Order 15104.

1878 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21437481C211yesmaximal, characteristic
2#21433081C214yesmaximal, complemented
3#21433077C214yesmaximal, complemented
4#21433071C214yesmaximal, complemented
5#21433067C214yesmaximal, complemented
6#21433034C211yesmaximal, characteristic, complemented
7#21433028C211yesmaximal, characteristic, complemented
8#21432812C211yesmaximal, characteristic, complemented
9#21432806C211yesmaximal, characteristic, complemented
10#21432801C211yesmaximal, characteristic, complemented
11#21432797C211yesmaximal, characteristic, complemented
12#21432792C211yesmaximal, characteristic, complemented
13#21432788C211yesmaximal, characteristic, complemented
14#21432748C211yesmaximal, characteristic, complemented
15#21432747C211yesmaximal, characteristic, complemented
16#21432732C211yesmaximal, characteristic, complemented
17C4×#14273733C211yesmaximal, characteristic, complemented
18C2×#16837356C211yesmaximal, characteristic, complemented
19C4×#131×C59C211yesmaximal, characteristic, complemented
20C2×#14273733C2211yescharacteristic
21C2×#14273733C2211yescharacteristic
22C22×#11745659C2211yescharacteristic
23C22×C8×D59C2211yescharacteristic
24#16838024C412yes—
25#16838017C412yes—
26#16838010C412yes—
27#16838003C412yes—
28#16837994C414yes—
29#16837985C414yes—
30#16837955C2211yescharacteristic
31#16837948C2211yescharacteristic
32#16837936C2214yes—
33#16837930C2214yes—
34#16837914C2211yescharacteristic
35#16837909C2211yescharacteristic
36C4×#11745685C2211yescharacteristic
37C2×#14273684C2211yescharacteristic
38#16837532C2214yescomplemented
39#16837530C2214yescomplemented
40#16837530C2214yescomplemented
41C8×Dic118C2214yescomplemented
42#16837481C2214yes—
43#16837478C2214yes—
44#16837478C2214yescomplemented
45#16837475C2214yes—
46#16837475C2214yes—
47#16837473C2214yes—
48#16837473C2214yescomplemented
49#16837471C2214yes—
50#16837471C2214yescomplemented
51C8×D236C2214yes—
52C8×C22⋊D59C2214yes—
53C8×C22⋊D59C2214yescomplemented
54#16837464C2214yes—
55#16837463C2214yescomplemented
56#16837461C2214yes—
57#16837461C2214yescomplemented
58#16837459C2214yescomplemented
59#16837457C2214yescomplemented
60#16837430C2211yescharacteristic
61#16837430C2211yescharacteristic
62#16837429C2211yescharacteristic
63#16837429C2211yescharacteristic
64#16837425C2211yescharacteristic
65#16837425C2211yescharacteristic
66#16837370C2211yescharacteristic
67#16837370C2211yescharacteristic
68#16837369C2211yescharacteristic
69#16837369C2211yescharacteristic
70#16837365C2211yescharacteristic
71#16837365C2211yescharacteristic
72#16837357C2211yescharacteristic
73#16837357C2211yescharacteristic
74#16837356C2212yes—
75#16837356C2212yes—
76#16837356C2212yes—
77#16837356C2212yes—
78#16837356C2212yescomplemented
79#16837356C2212yescomplemented
80C4×#11745664C2211yescharacteristic
81C4×#11745659C2212yescomplemented
82C2×#14273638C2211yescharacteristic
83C2×#14273637C2211yescharacteristic
84C2×C8×Dic59C2211yescharacteristic
85C4×C8×D59C2212yescomplemented
86C2×#131×C59C2211yescharacteristic
87C2×#131×C59C2211yescharacteristic
88C4×#41×C59C2211yescharacteristic
89C59×#405C2211yescharacteristic
90C59×#405C2211yescharacteristic
91C59×#405C2212yescomplemented
92C59×#405C2212yescomplemented
93C4×M16×C59C2211yescharacteristic
94C4×M16×C59C2212yescomplemented
95C2×C4×C8×C59C2211yescharacteristic
96C2×C4×C8×C59C2212yescomplemented
97C2×#11745685C2311yescharacteristic
98C22×C4×D59C2311yescharacteristic
99#14273733—24no—
100#14273733—24no—
101C2×#11745664C2311yescharacteristic
102C2×#11745664C2311yescharacteristic
103C2×#11745659—24no—
104C2×#11745659C2312yes—
105C2×#11745659C2312yes—
106C2×#11745659C2312yes—
107C2×#11745659C2312yes—
108C22×C59⋊C8C2311yescharacteristic
109C22×C59⋊C8C2311yescharacteristic
110C2×C8×D59—24no—
111C2×C8×D59C2312yes—
112C2×C8×D59C2312yes—
113C2×C8×D59C2312yes—
114C2×C8×D59C2312yes—
115#14273726C2×C412yes—
116#14273725C2×C411yescharacteristic
117#14273723C2×C411yescharacteristic
118#14273722C2×C414yes—
119#14273721C2×C414yes—
120#14273721C2×C414yes—
121#14273720C2×C414yes—
122#14273719C2×C414yes—
123#14273718C2×C412yes—
124#14273717C2×C414yes—
125#14273716C2×C411yescharacteristic
126#14273715C2×C414yes—
127#14273714C2×C411yescharacteristic
128#14273713C2×C414yes—
129#14273712C2×C414yes—
130#14273711C2×C412yes—
131#14273710C2×C414yes—
132#14273710C2×C414yes—
133#14273709C2×C414yes—
134#14273708C2×C412yes—
135#14273707C2×C412yes—
136#14273706C2×C414yes—
137#14273705C2×C414yes—
138#14273704C2×C414yes—
139#14273703C2×C412yes—
140#14273702C2×C412yes—
141#14273701C2×C414yes—
142#14273700C2×C414yes—
143#14273699C2×C414yes—
144#14273698C2×C412yes—
145#14273697C2×C412yes—
146#14273695C2×C412yes—
147C4×Dic118C2×C412yes—
148C4×Dic118C2314yes—
149C4×D236C2×C412yes—
150C4×D236C2314yes—
151C4×C22⋊D59C2×C414yes—
152C4×C22⋊D59C2314yes—
153C4×C22⋊D59C2314yes—
154#14273686C2311yescharacteristic
155#14273684C2×C412yes—
156#14273684C2×C412yes—
157#14273684C2312yes—
158#14273684C2312yes—
159#14273684C2312yes—
160C2×Dic59⋊C4C2×C412yes—
161C2×(C2×D59)⋊C4C2×C412yes—
162C2×C4×Dic59C2311yescharacteristic
163C42×D59C2312yes—
164C4⋊(C59⋊C8)C2314yes—
165C4⋊(C59⋊C8)C2314yes—
166Dic59⋊C8C2314yes—
167Dic59⋊C8C2314yes—
168Dic59⋊C8C2314yes—
169Dic59⋊C8C2314yes—
170C22⋊(C59⋊C8)C2314yes—
171C22⋊(C59⋊C8)C2314yes—
172(C2×D59)⋊C8C2314yes—
173(C2×D59)⋊C8C2314yes—
174(C2×D59)⋊C8C2314yes—
175(C2×D59)⋊C8C2314yes—
176#14273638C2312yes—
177#14273638C2312yes—
178#14273638C2312yes—
179#14273637C2312yes—
180#14273637C2312yes—
181#14273637C2312yes—
182#14273637C2312yes—
183C4×C59⋊C8C2312yes—
184C8×Dic59C2312yes—
185C8×Dic59C2312yes—
186C8×Dic59C2312yes—
187C8×Dic59C2312yes—
188C2×#41×C59C2311yescharacteristic
189#131×C59—24no—
190#131×C59—24no—
191C2×M16×C59C2311yescharacteristic
192C2×M16×C59C2311yescharacteristic
193C2×M16×C59C2312yes—
194C2×M16×C59C2312yes—
195C22×C8×C59C2312yes—
196C22×C8×C59C2312yes—
197C22×C8×C59C2311yescharacteristic
198C22×C8×C59C2311yescharacteristic
199C4×Q8×C59C2×C412yes—
200C4×D4×C59C2×C414yes—
201C4×D4×C59C2×C412yes—
202#117×C59C2311yescharacteristic
203#117×C59C2312yes—
204C2×C42×C59C2312yes—
205C2×C42×C59C2311yescharacteristic
206#97×C59C2312yes—
207#97×C59C2312yes—
208#97×C59C2312yes—
209C4×C8×C59C2311yescharacteristic
210C4×C8×C59C2311yescharacteristic
211C4×C8×C59C2311yescharacteristic
212C4×C8×C59C2311yescharacteristic
213C4×C8×C59C2312yes—
214C4×C8×C59C2312yes—
215C4×C8×C59C2312yes—
216C23×D59C22×C411yescharacteristic
217#41×C59—22no—
218#41×C59—22no—
219C2×Q8×C59C22×C411yescharacteristic
220C2×D4×C59C22×C412yes—
221C2×D4×C59C22×C411yescharacteristic
222C22×C4×C59C22×C412yes—
223C22×C4×C59C22×C414yes—
224C22×C4×C59C2412yes—
225C22×C4×C59C2411yescharacteristic
226C2×C22⋊D59C22×C412yes—
227C2×C22⋊D59C22×C414yes—
228C2×C22⋊D59C22×C414yes—
229C22×Dic59C22×C411yescharacteristic
230C22×Dic59C22×C412yes—
231#11745685—22no—
232#11745685—22no—
233C2×D236C22×C411yescharacteristic
234C2×D236C22×C414yes—
235C2×C4×D59—22no—
236C2×C4×D59—22no—
237C2×C4×D59C22×C412yes—
238C2×C4×D59C22×C414yes—
239C2×C4×D59C2412yes—
240C2×C4×D59C2412yes—
241C2×Dic118C22×C411yescharacteristic
242C2×Dic118C22×C414yes—
243M16×C59—22no—
244M16×C59—22no—
245M16×C59—24no—
246M16×C59—24no—
247C2×C8×C59—24no—
248C2×C8×C59—24no—
249C2×C8×C59#4114yes—
250C2×C8×C59#4114yes—
251C2×C8×C59C2412yes—
252C2×C8×C59C2412yes—
253C2×C8×C59C2411yescharacteristic
254C2×C8×C59C2411yescharacteristic
255C2×C8×C59C2411yescharacteristic
256C2×C8×C59C2411yescharacteristic
257C4⋊C4×C59C22×C412yes—
258C4⋊C4×C59C22×C414yes—
259C22⋊C4×C59C22×C412yes—
260C22⋊C4×C59C22×C414yes—
261C42×C59C22×C412yes—
262C42×C59C22×C414yes—
263C42×C59C2411yescharacteristic
264C42×C59C2411yescharacteristic
265C42×C59C2412yes—
266C22⋊Dic59C22×C412yes—
267C22⋊Dic59C22×C414yes—
268C22⋊Dic59C22×C414yes—
269(C2×D59)⋊C4C22×C412yes—
270(C2×D59)⋊C4C22×C412yes—
271(C2×D59)⋊C4C22×C412yes—
272(C2×D59)⋊C4C22×C412yes—
273(C2×D59)⋊C4C22×C414yes—
274(C2×D59)⋊C4C22×C414yes—
275(C2×D59)⋊C4C22×C414yes—
276(C2×D59)⋊C4C22×C414yes—
277(C2×D59)⋊C4C22×C414yes—
278C4⋊Dic59C22×C412yes—
279C4⋊Dic59C22×C414yes—
280C4⋊Dic59C22×C414yes—
281Dic59⋊C4C22×C412yes—
282Dic59⋊C4C22×C412yes—
283Dic59⋊C4C22×C412yes—
284Dic59⋊C4C22×C412yes—
285Dic59⋊C4C22×C414yes—
286Dic59⋊C4C22×C414yes—
287Dic59⋊C4C22×C414yes—
288Dic59⋊C4C22×C414yes—
289Dic59⋊C4C22×C414yes—
290C4×Dic59C22×C414yes—
291C4×Dic59C22×C411yescharacteristic
292C4×Dic59C22×C411yescharacteristic
293C4×Dic59C2412yes—
294C4×Dic59C2412yes—
295#11745664—22no—
296#11745664—22no—
297C2×C59⋊C8—22no—
298C2×C59⋊C8—22no—
299C2×C59⋊C8C2412yes—
300C2×C59⋊C8C2412yes—
301C2×C59⋊C8C2412yes—
302C2×C59⋊C8C2412yes—
303#11745659—24no—
304#11745659—24no—
305#11745659—24no—
306#11745659—24no—
307C8×D59—24no—
308C8×D59—24no—
309C8×D59—24no—
310C8×D59—24no—
311C23×C59C23×C412yes—
312C23×C59C23×C411yescharacteristic
313C22×D59—22no—
314C22×D59—42no—
315C22×D59C23×C412yes—
316C22×D59C23×C412yes—
317Q8×C59—22no—
318D4×C59—24no—
319D4×C59—22no—
320C2×C4×C59—22no—
321C2×C4×C59—22no—
322C2×C4×C59—44no—
323C2×C4×C59—42no—
324C2×C4×C59C23×C412yes—
325C2×C4×C59C23×C412yes—
326C2×C4×C59C23×C412yes—
327C2×C4×C59C23×C414yes—
328C2×C4×C59C23×C411yescharacteristic
329C2×C4×C59C2×#4112yes—
330C2×C4×C59C2×#4112yes—
331C2×C4×C59C2511yescharacteristic
332C22⋊D59—24no—
333C22⋊D59—44no—
334C22⋊D59—44no—
335C2×Dic59—22no—
336C2×Dic59—42no—
337C2×Dic59C23×C412yes—
338C2×Dic59C23×C412yes—
339C2×Dic59C23×C414yes—
340C2×Dic59C23×C412yes—
341C2×Dic59C23×C412yes—
342D236—22no—
343D236—44no—
344C4×D59—24no—
345C4×D59—22no—
346C4×D59—22no—
347C4×D59—22no—
348C4×D59—22no—
349C4×D59—44no—
350Dic118—22no—
351Dic118—44no—
352C8×C59—22no—
353C8×C59—22no—
354C8×C59C2×#4112yes—
355C8×C59C2×#4112yes—
356C8×C59C2×#4112yes—
357C8×C59C2×#4112yes—
358C59⋊C8—22no—
359C59⋊C8—22no—
360C59⋊C8—22no—
361C59⋊C8—22no—
362#60206—591nomaximal, Sylow
363C22×C59—22no—
364C22×C59—22no—
365C22×C59—24no—
366C22×C59C4×#4112yes—
367C22×C59C24×C411yescharacteristic
368C2×D59—22no—
369C2×D59—22no—
370C2×D59—24no—
371C2×D59—22no—
372C2×D59—22no—
373C2×D59—44no—
374C4×C59—22no—
375C4×C59—24no—
376C4×C59—22no—
377C4×C59—22no—
378C4×C59C4×#4112yes—
379C4×C59C22×#4111yescharacteristic
380C4×C59C22×#4111yescharacteristic
381Dic59—22no—
382Dic59—22no—
383Dic59—22no—
384Dic59—24no—
385Dic59—22no—
386#3455—591no—
387#2967—594no—
388#2967—594no—
389#2966—594no—
390#2966—594no—
391#2961—591no—
392#2960—591no—
393#2932—591no—
394#2931—591no—
395#2930—591no—
396#2930—591no—
397#2929—591no—
398#2929—591no—
399#2923—591no—
400#2923—591no—
401#2921—591no—
402C4×#131—591no—
403C4×#131D5911yescharacteristic, complemented
404C2×#405—591no—
405C2×C59—22no—
406C2×C59—42no—
407C2×C59C2×C4×#4111yescharacteristic
408C2×C59#357312yes—
409D59—42no—
410D59—42no—
411C2×#131—591no—
412C2×#131—591no—
413C2×#131C2×D5911yescharacteristic
414C2×#131C2×D5911yescharacteristic
415C22×M16—591no—
416C23×C8—591no—
417#542—592no—
418#542—592no—
419#541—592no—
420#540—592no—
421#539—594no—
422#538—594no—
423#533—591no—
424#532—591no—
425#529—594no—
426#529—594no—
427#525—591no—
428#525—591no—
429C4×#41—591no—
430C4×#41C2×D5911yescharacteristic
431C2×#117—591no—
432#446—594no—
433#446—594no—
434#446—594no—
435C8×Q8—594no—
436#436—594no—
437#436—594no—
438#436—594no—
439#435—594no—
440#435—594no—
441#435—594no—
442#435—594no—
443#435—594no—
444#435—594no—
445C8×D4—594no—
446C8×D4—594no—
447C8×D4—594no—
448#433—594no—
449#433—594no—
450#433—594no—
451#433—594no—
452#432—594no—
453#432—594no—
454#424—591no—
455#424—591no—
456#424—591no—
457#424—591no—
458#423—591no—
459#423—591no—
460#408—591no—
461#408—591no—
462#408—591no—
463#408—591no—
464#407—591no—
465#407—591no—
466#405—591no—
467#405—591no—
468#405—592no—
469#405—592no—
470#405—592no—
471#405—592no—
472#405—592no—
473#405—592no—
474#405C2×D5911yescharacteristic
475#405C2×D5911yescharacteristic
476#405C2×D5912yescomplemented
477#405C2×D5912yescomplemented
478C4×M16—591no—
479C4×M16—592no—
480C4×M16C2×D5911yescharacteristic
481C4×M16C2×D5912yescomplemented
482C2×#97—591no—
483C2×#97—591no—
484C2×C4×C8—591no—
485C2×C4×C8—592no—
486C2×C4×C8C2×D5911yescharacteristic
487C2×C4×C8C2×D5912yescomplemented
488C59#6020611yescharacteristic, complemented, Sylow
489C2×#41—591no—
490C2×#41C22×D5911yescharacteristic
491C23×C4—591no—
492#131—24no—
493#131—24no—
494#131—1184no—
495#131—1184no—
496C2×M16—591no—
497C2×M16—591no—
498C2×M16—592no—
499C2×M16—592no—
500C2×M16—592no—
501C2×M16—592no—
502C2×M16—1184no—
503C2×M16C22×D5911yescharacteristic
504C2×M16C22×D5911yescharacteristic
505C2×M16C22×D5912yes—
506C2×M16C22×D5912yes—
507C22×C8—591no—
508C22×C8—591no—
509C22×C8—592no—
510C22×C8—592no—
511C22×C8—592no—
512C22×C8—592no—
513C22×C8—1184no—
514C22×C8C22×D5912yes—
515C22×C8C22×D5912yes—
516C22×C8C22×D5911yescharacteristic
517C22×C8C22×D5911yescharacteristic
518C4⋊Q8—591no—
519C4⋊Q8—592no—
520#127—591no—
521#126—594no—
522#126—594no—
523#126—594no—
524#126—594no—
525#125—594no—
526#125—592no—
527#125—594no—
528#124—591no—
529#124—591no—
530#124—594no—
531#124—594no—
532#123—592no—
533#123—594no—
534#123—594no—
535#123—594no—
536#123—592no—
537#123—594no—
538C22⋊Q8—592no—
539C22⋊Q8—594no—
540C22⋊Q8—592no—
541C22⋊Q8—594no—
542C22⋊Q8—594no—
543#121—592no—
544#121—594no—
545#121—594no—
546#121—592no—
547#121—594no—
548#120—592no—
549#120—592no—
550C4×Q8—592no—
551C4×Q8—594no—
552C4×Q8C4×D5912yes—
553C4×D4—594no—
554C4×D4—594no—
555C4×D4—594no—
556C4×D4—592no—
557C4×D4—594no—
558C4×D4C4×D5914yes—
559C4×D4C4×D5912yes—
560#117—591no—
561#117—592no—
562#117—592no—
563#117—592no—
564#117—592no—
565#117—592no—
566#117C22×D5911yescharacteristic
567#117C22×D5912yes—
568C2×C4⋊C4—592no—
569C2×C22⋊C4—592no—
570C2×C42—591no—
571C2×C42—592no—
572C2×C42C22×D5911yescharacteristic
573C2×C42C22×D5912yes—
574C4⋊C8—594no—
575C4⋊C8—594no—
576C4⋊C8—594no—
577C4⋊C8—594no—
578C4⋊C8—594no—
579C4⋊C8—594no—
580C22⋊C8—594no—
581C22⋊C8—594no—
582C22⋊C8—594no—
583C22⋊C8—594no—
584C22⋊C8—594no—
585C22⋊C8—594no—
586#97—592no—
587#97—592no—
588#97—592no—
589#97—592no—
590#97—592no—
591#97—592no—
592#97—592no—
593#97C22×D5912yes—
594#97C22×D5912yes—
595#97C22×D5912yes—
596C4×C8—592no—
597C4×C8—592no—
598C4×C8—592no—
599C4×C8—592no—
600C4×C8—592no—
601C4×C8C22×D5911yescharacteristic
602C4×C8C22×D5911yescharacteristic
603C4×C8C22×D5912yes—
604C4×C8C22×D5912yes—
605C4×C8C22×D5911yescharacteristic
606C4×C8C22×D5911yescharacteristic
607C4×C8C22×D5912yes—
608C24—591no—
609#41—22no—
610#41—22no—
611#41—1182no—
612#41—1182no—
613C2×Q8—591no—
614C2×Q8—594no—
615C2×Q8C2×C4×D5911yescharacteristic
616C2×D4—592no—
617C2×D4—594no—
618C2×D4—594no—
619C2×D4—591no—
620C2×D4—594no—
621C2×D4C2×C4×D5912yes—
622C2×D4C2×C4×D5911yescharacteristic
623C22×C4—591no—
624C22×C4—592no—
625C22×C4—592no—
626C22×C4—592no—
627C22×C4—592no—
628C22×C4—594no—
629C22×C4—1182no—
630C22×C4—1182no—
631C22×C4C2×C4×D5912yes—
632C22×C4C2×C4×D5914yes—
633C22×C4C23×D5912yes—
634C22×C4C23×D5911yescharacteristic
635M16—22no—
636M16—22no—
637M16—24no—
638M16—24no—
639M16—1182no—
640M16—1182no—
641M16—1184no—
642M16—1184no—
643M16—1184no—
644M16—1184no—
645C2×C8—24no—
646C2×C8—24no—
647C2×C8—592no—
648C2×C8—592no—
649C2×C8—592no—
650C2×C8—592no—
651C2×C8—1182no—
652C2×C8—1182no—
653C2×C8—1184no—
654C2×C8—1184no—
655C2×C8—1184no—
656C2×C8—1184no—
657C2×C8#1174568514yes—
658C2×C8#1174568514yes—
659C2×C8C23×D5912yes—
660C2×C8C23×D5912yes—
661C2×C8C23×D5911yescharacteristic
662C2×C8C23×D5911yescharacteristic
663C2×C8C23×D5911yescharacteristic
664C2×C8C23×D5911yescharacteristic
665C4⋊C4—592no—
666C4⋊C4—592no—
667C4⋊C4—592no—
668C4⋊C4—592no—
669C4⋊C4—592no—
670C4⋊C4—594no—
671C4⋊C4—594no—
672C4⋊C4—594no—
673C4⋊C4—594no—
674C4⋊C4—594no—
675C4⋊C4—594no—
676C4⋊C4—594no—
677C4⋊C4C2×C4×D5912yes—
678C4⋊C4C2×C4×D5914yes—
679C22⋊C4—592no—
680C22⋊C4—594no—
681C22⋊C4—594no—
682C22⋊C4—592no—
683C22⋊C4—592no—
684C22⋊C4—592no—
685C22⋊C4—592no—
686C22⋊C4—594no—
687C22⋊C4—594no—
688C22⋊C4—594no—
689C22⋊C4—594no—
690C22⋊C4—594no—
691C22⋊C4C2×C4×D5912yes—
692C22⋊C4C2×C4×D5914yes—
693C42—591no—
694C42—591no—
695C42—594no—
696C42—592no—
697C42—592no—
698C42C2×C4×D5912yes—
699C42C2×C4×D5914yes—
700C42C23×D5911yescharacteristic
701C42C23×D5911yescharacteristic
702C42C23×D5912yes—
703C23—592no—
704C23—592no—
705C23—1182no—
706C23—2362no—
707C23C22×C4×D5912yes—
708C23C22×C4×D5911yescharacteristic
709Q8—22no—
710Q8—1182no—
711Q8—2364no—
712D4—24no—
713D4—22no—
714D4—1184no—
715D4—1182no—
716D4—2364no—
717D4—2364no—
718D4—2364no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—42no—
722C2×C4—44no—
723C2×C4—592no—
724C2×C4—594no—
725C2×C4—592no—
726C2×C4—592no—
727C2×C4—592no—
728C2×C4—1182no—
729C2×C4—1182no—
730C2×C4—1182no—
731C2×C4—1182no—
732C2×C4—1182no—
733C2×C4—1184no—
734C2×C4—2364no—
735C2×C4—2362no—
736C2×C4C22×C4×D5912yes—
737C2×C4C22×C4×D5912yes—
738C2×C4C22×C4×D5912yes—
739C2×C4C22×C4×D5914yes—
740C2×C4C22×C4×D5911yescharacteristic
741C2×C4C2×#1174568512yes—
742C2×C4C2×#1174568512yes—
743C2×C4C24×D5911yescharacteristic
744C8—22no—
745C8—22no—
746C8—1182no—
747C8—1182no—
748C8—1182no—
749C8—1182no—
750C8C2×#1174568512yes—
751C8C2×#1174568512yes—
752C8C2×#1174568512yes—
753C8C2×#1174568512yes—
754C22—22no—
755C22—24no—
756C22—22no—
757C22—1184no—
758C22—1182no—
759C22—1182no—
760C22—1182no—
761C22—1182no—
762C22—2364no—
763C22C4×#1174568512yes—
764C22C23×C4×D5911yescharacteristic
765C4—22no—
766C4—22no—
767C4—24no—
768C4—22no—
769C4—1182no—
770C4—1184no—
771C4—1182no—
772C4—1182no—
773C4—1182no—
774C4C4×#1174568512yes—
775C4C22×#1174568511yescharacteristic
776C4C22×#1174568511yescharacteristic
777C2—22no—
778C2—42no—
779C2—2362no—
780C2—2362no—
781C2C2×C4×#1174568511yescharacteristic
782C2#2143880712yes—
subgroupG/H
centerC2×C8C23×D59
commutator, socleC22×C59C24×C4
FrattiniC2×C4C24×D59
FittingC4×#131×C59C2
prime radical#21437481C2
cosocleC2×C4×C59C25
hypercenterC4×#131D59
hypocenterC59#60206
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C2×C8 ◁ C4×#131

Complements

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

NH ≅ G/Ntype
2. #21433081C2semidirect
3. #21433077C2semidirect
4. #21433071C2semidirect
5. #21433067C2semidirect
6. #21433034C2semidirect
7. #21433028C2semidirect
8. #21432812C2semidirect
9. #21432806C2semidirect
10. #21432801C2semidirect
11. #21432797C2semidirect
12. #21432792C2semidirect
13. #21432788C2semidirect
14. #21432748C2semidirect
15. #21432747C2semidirect
16. #21432732C2semidirect
17. C4×#14273733C2semidirect
18. C2×#16837356C2semidirect
19. C4×#131×C59C2semidirect
38. #16837532C22semidirect
39. #16837530C22semidirect
40. #16837530C22semidirect
41. C8×Dic118C22semidirect
44. #16837478C22semidirect
48. #16837473C22semidirect
50. #16837471C22semidirect
53. C8×C22⋊D59C22semidirect
55. #16837463C22semidirect
57. #16837461C22semidirect
58. #16837459C22semidirect
59. #16837457C22semidirect
78. #16837356C22semidirect
79. #16837356C22semidirect
81. C4×#11745659C22semidirect
85. C4×C8×D59C22semidirect
91. C59×#405C22semidirect
92. C59×#405C22semidirect
94. C4×M16×C59C22semidirect
96. C2×C4×C8×C59C22semidirect
403. C4×#131D59semidirect
476. #405C2×D59semidirect
477. #405C2×D59semidirect
481. C4×M16C2×D59semidirect
487. C2×C4×C8C2×D59semidirect
488. C59#60206semidirect

Maximal subgroups

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

subgroupindex
#214374812
#214330812
#214330772
#214330712
#214330672
#214330342
#214330282
#214328122
#214328062
#214328012
#214327972
#214327922
#214327882
#214327482
#214327472
#214327322
C4×#142737332
C2×#168373562
C4×#131×C592
#6020659