Finite Group Databasebeta

← #29453888

Subgroups — #29453888

Order 15104.

1864 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21437393C211yesmaximal, characteristic
2#21433265C214yesmaximal, complemented
3#21433234C214yesmaximal, complemented
4#21433220C214yesmaximal, complemented
5#21433212C214yesmaximal, complemented
6#21433037C211yesmaximal, characteristic, complemented
7#21432824C212yesmaximal, complemented
8#21432820C212yesmaximal, complemented
9#21432815C211yesmaximal, characteristic, complemented
10#21432813C211yesmaximal, characteristic, complemented
11#21432760C212yesmaximal, complemented
12C2×#16837457C211yesmaximal, characteristic, complemented
13#21432663C212yesmaximal, complemented
14#423×D59C211yesmaximal, characteristic, complemented
15C59×#2961C211yesmaximal, characteristic, complemented
16C2×#14273735C2212yes—
17C2×#14273733C2212yes—
18C2×M16×D59C2212yes—
19#16837957C411yescharacteristic
20#16837957C411yescharacteristic
21#16837953C411yescharacteristic
22#16837953C411yescharacteristic
23#16837952C2211yescharacteristic
24#16837939C2212yes—
25#16837939C2212yes—
26#16837938C412yes—
27#16837938C412yes—
28#16837937C412yes—
29#16837937C412yes—
30#16837915C412yes—
31#16837915C412yes—
32#16837914C2212yes—
33C4×#11745689C2212yes—
34C4×#11745689C2212yes—
35#16837870C2212yes—
36C2×C42×D59C2211yescharacteristic
37#16837533C2214yescomplemented
38#16837533C2214yescomplemented
39#16837481C2214yes—
40#16837479C2214yes—
41#16837475C2214yes—
42#16837475C2214yes—
43#16837475C2214yescomplemented
44#16837475C2214yescomplemented
45#16837472C2214yes—
46#16837472C2214yes—
47#16837472C2214yescomplemented
48#16837472C2214yescomplemented
49C8×D236C2214yes—
50#16837467C2214yes—
51#16837464C2214yescomplemented
52#16837461C2214yescomplemented
53#16837457C2212yes—
54#16837457C2212yes—
55#16837457C2212yes—
56#16837457C2212yes—
57#16837457C2214yescomplemented
58#16837453C2214yescomplemented
59#16837429C2212yes—
60#16837427C2214yescomplemented
61#16837427C2214yescomplemented
62#16837426C2211yescharacteristic
63#16837425C2212yes—
64#16837424C2212yes—
65#16837424C2212yes—
66#16837424C2214yescomplemented
67C2×Dic59⋊C8C2211yescharacteristic
68C2×Dic59⋊C8C2211yescharacteristic
69C4⋊C8×D59C2212yes—
70C4⋊C8×D59C2212yes—
71C4⋊C8×D59C2214yescomplemented
72#16837370C2212yes—
73#16837368C2212yes—
74C2×(C2×D59)⋊C8C2211yescharacteristic
75C2×(C2×D59)⋊C8C2211yescharacteristic
76#16837358C2212yes—
77C2×#14273638C2211yescharacteristic
78C59×#533C2211yescharacteristic
79C59×#446C2214yescomplemented
80C59×#446C2214yescomplemented
81C59×#424C2212yes—
82C59×#423C2211yescharacteristic
83C59×#405C2212yes—
84C2×#97×C59C2211yescharacteristic
85C2×#11745689C2×C412yes—
86C2×#11745689C2×C412yes—
87C2×#11745685C2312yes—
88C22×C4×D59C2×C411yescharacteristic
89C22×C4×D59C2×C411yescharacteristic
90C22×C4×D59C2311yescharacteristic
91#14273735—44no—
92#14273733—44no—
93C2×#11745664C2312yes—
94C2×#11745659C2314yes—
95C2×#11745659C2314yes—
96C2×#11745659C2314yes—
97M16×D59—44no—
98C22×C59⋊C8C2311yescharacteristic
99C22×C59⋊C8C2311yescharacteristic
100C2×C8×D59C2314yes—
101C2×C8×D59C2314yes—
102C2×C8×D59C2314yes—
103#14273727C2×C411yescharacteristic
104#14273724C2×C411yescharacteristic
105#14273722C2×C414yes—
106#14273722C2×C414yes—
107#14273718C2×C412yes—
108#14273718C2×C412yes—
109#14273716C2×C412yes—
110#14273716C2×C412yes—
111#14273715C2×C412yes—
112#14273712C2×C414yes—
113#14273712C2×C414yes—
114#14273711C2×C414yes—
115#14273707C2×C412yes—
116#14273707C2×C412yes—
117#14273703C2×C412yes—
118#14273703C2×C412yes—
119#14273702C2×C412yes—
120#14273702C2×C412yes—
121#14273702C2×C412yes—
122#14273702C2×C412yes—
123#14273701C2×C412yes—
124#14273701C2×C412yes—
125#14273697C2×C414yes—
126Q8×Dic59C2×C412yes—
127Q8×Dic59C2×C412yes—
128#14273692C2×C412yes—
129#14273692C2×C412yes—
130C4×D236C2314yes—
131C4×D236C2314yes—
132C4×D236C2312yes—
133C4×D236C2312yes—
134#14273689C2×C414yes—
135#14273689C2×C414yes—
136#14273689C2×C412yes—
137#14273689C2×C412yes—
138#14273689C2×C412yes—
139#14273689C2×C412yes—
140(C22⋊D59)⋊C4C2×C414yes—
141(C22⋊D59)⋊C4C2×C414yes—
142#14273685C2×C412yes—
143#14273685C2×C412yes—
144#14273685C2×C414yes—
145#14273685C2×C414yes—
146#14273684C2314yes—
147C2×C4×Dic59C2×C411yescharacteristic
148C2×C4×Dic59C2×C411yescharacteristic
149C2×C4×Dic59C2311yescharacteristic
150C42×D59C2×C411yescharacteristic
151C42×D59C2×C411yescharacteristic
152C42×D59C2×C411yescharacteristic
153C42×D59C2×C411yescharacteristic
154C42×D59C2311yescharacteristic
155C42×D59C2311yescharacteristic
156C42×D59C2314yes—
157C42×D59C2311yescharacteristic
158C42×D59C2311yescharacteristic
159C4⋊(C59⋊C8)C2312yes—
160C4⋊(C59⋊C8)C2312yes—
161C4⋊(C59⋊C8)C2314yes—
162C4⋊(C59⋊C8)C2314yes—
163Dic59⋊C8C2314yes—
164Dic59⋊C8C2314yes—
165Dic59⋊C8C2312yes—
166Dic59⋊C8C2312yes—
167Dic59⋊C8C2312yes—
168Dic59⋊C8C2312yes—
169(C2×D59)⋊C8C2314yes—
170(C2×D59)⋊C8C2314yes—
171(C2×D59)⋊C8C2312yes—
172(C2×D59)⋊C8C2312yes—
173(C2×D59)⋊C8C2312yes—
174(C2×D59)⋊C8C2312yes—
175(C2×D59)⋊C8C2314yes—
176(C2×D59)⋊C8C2314yes—
177#14273638C2312yes—
178#14273638C2312yes—
179#14273638C2314yes—
180C4×C59⋊C8C2314yes—
181C2×M16×C59C2312yes—
182C22×C8×C59C2311yescharacteristic
183C22×C8×C59C2311yescharacteristic
184C4⋊Q8×C59C2×C411yescharacteristic
185C4⋊Q8×C59C2×C411yescharacteristic
186#125×C59C2×C412yes—
187C22⋊Q8×C59C2×C412yes—
188C22⋊Q8×C59C2×C412yes—
189C4×Q8×C59C2312yes—
190C4×Q8×C59C2312yes—
191#117×C59C2312yes—
192C2×C42×C59C2311yescharacteristic
193C4⋊C8×C59C2312yes—
194C4⋊C8×C59C2312yes—
195C4⋊C8×C59C2314yes—
196C4⋊C8×C59C2314yes—
197#97×C59C2312yes—
198#97×C59C2312yes—
199#97×C59C2314yes—
200C4×C8×C59C2314yes—
201C23×D59C22×C411yescharacteristic
202C2×Q8×C59C22×C412yes—
203C2×Q8×C59C22×C412yes—
204C22×C4×C59C22×C411yescharacteristic
205C22×C4×C59C22×C411yescharacteristic
206C22×C4×C59C2411yescharacteristic
207C2×C22⋊D59C22×C414yes—
208C22×Dic59C22×C411yescharacteristic
209C22×Dic59C22×C411yescharacteristic
210C22×Dic59C22×C411yescharacteristic
211#11745689—44no—
212#11745689—44no—
213#11745685—24no—
214#11745685—24no—
215C2×D236C22×C412yes—
216C2×D236C22×C414yes—
217C2×D236C22×C414yes—
218C2×D236C22×C412yes—
219C2×D236C22×C412yes—
220C2×C4×D59—22no—
221C2×C4×D59—22no—
222C2×C4×D59—42no—
223C2×C4×D59—42no—
224C2×C4×D59C22×C411yescharacteristic
225C2×C4×D59C22×C411yescharacteristic
226C2×C4×D59C22×C411yescharacteristic
227C2×C4×D59C22×C411yescharacteristic
228C2×C4×D59C22×C411yescharacteristic
229C2×C4×D59C22×C411yescharacteristic
230C2×C4×D59C22×C414yes—
231C2×C4×D59C22×C411yescharacteristic
232C2×C4×D59C22×C411yescharacteristic
233C2×C4×D59C22×C411yescharacteristic
234C2×C4×D59C22×C411yescharacteristic
235C2×C4×D59C22×C414yes—
236C2×C4×D59C2411yescharacteristic
237C2×C4×D59C2411yescharacteristic
238C2×C4×D59C2414yes—
239C2×Dic118C22×C412yes—
240M16×C59—24no—
241C2×C8×C59—22no—
242C2×C8×C59—22no—
243C2×C8×C59C2412yes—
244C2×C8×C59C2414yes—
245C2×C8×C59C2412yes—
246C4⋊C4×C59C22×C412yes—
247C4⋊C4×C59C22×C412yes—
248C4⋊C4×C59C22×C414yes—
249C4⋊C4×C59C22×C414yes—
250C4⋊C4×C59C22×C412yes—
251C4⋊C4×C59C22×C412yes—
252C22⋊C4×C59C22×C414yes—
253C42×C59C22×C411yescharacteristic
254C42×C59C22×C411yescharacteristic
255C42×C59C2414yes—
256C42×C59C2411yescharacteristic
257C42×C59C2411yescharacteristic
258(C2×D59)⋊C4C22×C414yes—
259(C2×D59)⋊C4C22×C414yes—
260(C2×D59)⋊C4C22×C414yes—
261(C2×D59)⋊C4C22×C414yes—
262(C2×D59)⋊C4C22×C414yes—
263(C2×D59)⋊C4C22×C414yes—
264(C2×D59)⋊C4C22×C414yes—
265(C2×D59)⋊C4C22×C414yes—
266C4⋊Dic59C22×C412yes—
267C4⋊Dic59C22×C412yes—
268C4⋊Dic59C22×C414yes—
269C4⋊Dic59C22×C414yes—
270Dic59⋊C4C22×C414yes—
271Dic59⋊C4C22×C414yes—
272C4×Dic59C22×C411yescharacteristic
273C4×Dic59C22×C411yescharacteristic
274C4×Dic59C22×C411yescharacteristic
275C4×Dic59C22×C411yescharacteristic
276C4×Dic59C22×C411yescharacteristic
277C4×Dic59C22×C411yescharacteristic
278C4×Dic59C22×C411yescharacteristic
279C4×Dic59C22×C411yescharacteristic
280C4×Dic59C22×C411yescharacteristic
281C4×Dic59C22×C411yescharacteristic
282C4×Dic59C22×C414yes—
283C4×Dic59C22×C414yes—
284C4×Dic59C2411yescharacteristic
285C4×Dic59C2411yescharacteristic
286#11745664—24no—
287C2×C59⋊C8—22no—
288C2×C59⋊C8—22no—
289C2×C59⋊C8C2412yes—
290C2×C59⋊C8C2414yes—
291C2×C59⋊C8C2412yes—
292#11745659—44no—
293#11745659—44no—
294#11745659—44no—
295C8×D59—44no—
296C8×D59—44no—
297C8×D59—44no—
298C23×C59C23×C411yescharacteristic
299C22×D59—22no—
300C22×D59—22no—
301C22×D59—41no—
302C22×D59C23×C414yes—
303C22×D59C23×C411yescharacteristic
304C22×D59C23×C411yescharacteristic
305Q8×C59—42no—
306Q8×C59—42no—
307C2×C4×C59—41no—
308C2×C4×C59—41no—
309C2×C4×C59C23×C411yescharacteristic
310C2×C4×C59C23×C411yescharacteristic
311C2×C4×C59C23×C411yescharacteristic
312C2×C4×C59C23×C411yescharacteristic
313C2×C4×C59C23×C414yes—
314C2×C4×C59C23×C414yes—
315C2×C4×C59C23×C411yescharacteristic
316C2×C4×C59H(5,𝔽2)12yes—
317C2×C4×C592−1+412yes—
318C2×C4×C59C2511yescharacteristic
319C22⋊D59—28no—
320C2×Dic59—22no—
321C2×Dic59—22no—
322C2×Dic59—41no—
323C2×Dic59C23×C411yescharacteristic
324C2×Dic59C23×C411yescharacteristic
325C2×Dic59C23×C411yescharacteristic
326C2×Dic59C23×C411yescharacteristic
327C2×Dic59C23×C411yescharacteristic
328C2×Dic59C23×C414yes—
329C2×Dic59C23×C411yescharacteristic
330D236—28no—
331D236—24no—
332D236—42no—
333D236—42no—
334D236—44no—
335C4×D59—22no—
336C4×D59—22no—
337C4×D59—22no—
338C4×D59—22no—
339C4×D59—21no—
340C4×D59—24no—
341C4×D59—21no—
342C4×D59—21no—
343C4×D59—21no—
344C4×D59—24no—
345C4×D59—22no—
346C4×D59—22no—
347C4×D59—28no—
348C4×D59—41no—
349C4×D59—41no—
350C4×D59—41no—
351C4×D59—41no—
352C4×D59—44no—
353Dic118—24no—
354C8×C59—22no—
355C8×C59—24no—
356C8×C59—22no—
357C59⋊C8—22no—
358C59⋊C8—24no—
359C59⋊C8—22no—
360#60269—591nomaximal, Sylow
361C22×C59—21no—
362C22×C59—21no—
363C22×C59#52012yes—
364C22×C59C24×C411yescharacteristic
365C2×D59—21no—
366C2×D59—21no—
367C2×D59—21no—
368C2×D59—24no—
369C2×D59—21no—
370C2×D59—24no—
371C2×D59—21no—
372C2×D59—24no—
373C2×D59—44no—
374C2×D59#56812yes—
375C4×C59—21no—
376C4×C59—21no—
377C4×C59—21no—
378C4×C59—21no—
379C4×C59—24no—
380C4×C59—24no—
381C4×C59#52012yes—
382C4×C59C2×H(5,𝔽2)11yescharacteristic
383C4×C59C2×2−1+411yescharacteristic
384Dic59—24no—
385Dic59—21no—
386Dic59—21no—
387Dic59—21no—
388Dic59—21no—
389Dic59—21no—
390Dic59#56812yes—
391#3444—591no—
392#2995—594no—
393#2992—594no—
394#2990—594no—
395#2989—594no—
396#2961—591no—
397#2961D5911yescharacteristic, complemented
398#2933—592no—
399#2933—592no—
400#2932—591no—
401#2932—591no—
402#2925—592no—
403C2×#432—591no—
404#2906—592no—
405C2×#423—591no—
406C2×C59—22no—
407C2×C59C2×#52011yescharacteristic
408C2×C59C2×#56811yescharacteristic
409C2×C59C2×#56811yescharacteristic
410D59—22no—
411D59—44no—
412D59—41no—
413C2×#131—592no—
414C2×#131—592no—
415C22×M16—592no—
416#533—591no—
417#533—591no—
418#533C2×D5911yescharacteristic
419#532—591no—
420#532—591no—
421#532—591no—
422#529—592no—
423#529—592no—
424#529—592no—
425#529—592no—
426#529—592no—
427#529—592no—
428#525—592no—
429#525—592no—
430#525—592no—
431C4×#41—592no—
432C4×#41—592no—
433C4×#41—592no—
434C22×C42—591no—
435#446—594no—
436#446—594no—
437#446C2×D5914yescomplemented
438#446C2×D5914yescomplemented
439#436—594no—
440#436—594no—
441#435—594no—
442#435—594no—
443#435—594no—
444#435—594no—
445#435—594no—
446#435—594no—
447#435—594no—
448#435—594no—
449C8×D4—594no—
450C8×D4—594no—
451#433—594no—
452#433—594no—
453#432—592no—
454#432—592no—
455#432—592no—
456#432—592no—
457#432—594no—
458#431—594no—
459#424—592no—
460#424—594no—
461#424—594no—
462#424C2×D5912yes—
463#423—592no—
464#423—591no—
465#423—592no—
466#423—592no—
467#423—594no—
468#423C2×D5911yescharacteristic
469C2×C4⋊C8—591no—
470C2×C4⋊C8—591no—
471C2×C4⋊C8—592no—
472C2×C4⋊C8—592no—
473C2×C4⋊C8—594no—
474#408—592no—
475#408—592no—
476C2×C22⋊C8—591no—
477C2×C22⋊C8—591no—
478#405—592no—
479#405C2×D5912yes—
480C2×#97—591no—
481C2×#97C2×D5911yescharacteristic
482C59#6026911yescharacteristic, complemented, Sylow
483C2×#41—592no—
484C2×#41—592no—
485C2×#41—592no—
486C23×C4—591no—
487C23×C4—591no—
488C23×C4—591no—
489#131—2364no—
490#131—2364no—
491C2×M16—592no—
492C2×M16—594no—
493C2×M16—594no—
494C2×M16—594no—
495C2×M16—2364no—
496C2×M16C22×D5912yes—
497C22×C8—591no—
498C22×C8—591no—
499C22×C8—594no—
500C22×C8—594no—
501C22×C8—594no—
502C22×C8C22×D5911yescharacteristic
503C22×C8C22×D5911yescharacteristic
504C4⋊Q8—591no—
505C4⋊Q8C4×D5911yescharacteristic
506C4⋊Q8C4×D5911yescharacteristic
507#127—591no—
508#126—594no—
509#126—594no—
510#125—592no—
511#125—592no—
512#125C4×D5912yes—
513#124—592no—
514#124—592no—
515#124—592no—
516#123—594no—
517#123—594no—
518#123—594no—
519C22⋊Q8—592no—
520C22⋊Q8—592no—
521C22⋊Q8—592no—
522C22⋊Q8—592no—
523C22⋊Q8C4×D5912yes—
524C22⋊Q8C4×D5912yes—
525#121—592no—
526#121—592no—
527#121—592no—
528#121—592no—
529#121—592no—
530#121—592no—
531#120—594no—
532C4×Q8—592no—
533C4×Q8—592no—
534C4×Q8—592no—
535C4×Q8—592no—
536C4×Q8C22×D5912yes—
537C4×Q8C22×D5912yes—
538C4×D4—594no—
539C4×D4—594no—
540C4×D4—592no—
541C4×D4—592no—
542C4×D4—592no—
543C4×D4—592no—
544C4×D4—594no—
545C4×D4—594no—
546C4×D4—594no—
547C4×D4—594no—
548C4×D4—592no—
549C4×D4—592no—
550#117—592no—
551#117—592no—
552#117—594no—
553#117—594no—
554#117—594no—
555#117C22×D5912yes—
556C2×C42—591no—
557C2×C42—591no—
558C2×C42—591no—
559C2×C42—591no—
560C2×C42—591no—
561C2×C42—591no—
562C2×C42—591no—
563C2×C42—594no—
564C2×C42—591no—
565C2×C42—591no—
566C2×C42—591no—
567C2×C42—591no—
568C2×C42C22×D5911yescharacteristic
569C4⋊C8—592no—
570C4⋊C8—594no—
571C4⋊C8—594no—
572C4⋊C8—592no—
573C4⋊C8—592no—
574C4⋊C8—592no—
575C4⋊C8—592no—
576C4⋊C8—592no—
577C4⋊C8—594no—
578C4⋊C8—594no—
579C4⋊C8C22×D5912yes—
580C4⋊C8C22×D5912yes—
581C4⋊C8C22×D5914yes—
582C4⋊C8C22×D5914yes—
583C22⋊C8—592no—
584C22⋊C8—592no—
585C22⋊C8—592no—
586C22⋊C8—592no—
587C22⋊C8—594no—
588C22⋊C8—594no—
589C22⋊C8—594no—
590C22⋊C8—594no—
591#97—592no—
592#97—592no—
593#97—594no—
594#97C22×D5912yes—
595#97C22×D5912yes—
596#97C22×D5914yes—
597C4×C8—594no—
598C4×C8C22×D5914yes—
599C24—591no—
600#41—1184no—
601#41—1184no—
602#41—2364no—
603#41—2364no—
604C2×Q8—592no—
605C2×Q8C2×C4×D5912yes—
606C2×Q8C2×C4×D5912yes—
607C2×D4—594no—
608C2×D4—594no—
609C2×D4—592no—
610C2×D4—594no—
611C2×D4—592no—
612C2×D4—592no—
613C22×C4—591no—
614C22×C4—591no—
615C22×C4—591no—
616C22×C4—591no—
617C22×C4—591no—
618C22×C4—591no—
619C22×C4—591no—
620C22×C4—591no—
621C22×C4—591no—
622C22×C4—594no—
623C22×C4—591no—
624C22×C4—591no—
625C22×C4—594no—
626C22×C4—591no—
627C22×C4—591no—
628C22×C4—591no—
629C22×C4—591no—
630C22×C4—594no—
631C22×C4—1182no—
632C22×C4—1182no—
633C22×C4—2362no—
634C22×C4—2362no—
635C22×C4C2×C4×D5911yescharacteristic
636C22×C4C2×C4×D5911yescharacteristic
637C22×C4C23×D5911yescharacteristic
638M16—24no—
639M16—1184no—
640M16—2364no—
641M16—2364no—
642M16—2364no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—592no—
646C2×C8—594no—
647C2×C8—592no—
648C2×C8—1182no—
649C2×C8—1182no—
650C2×C8—2364no—
651C2×C8—2364no—
652C2×C8—2364no—
653C2×C8C23×D5912yes—
654C2×C8C23×D5914yes—
655C2×C8C23×D5912yes—
656C4⋊C4—592no—
657C4⋊C4—592no—
658C4⋊C4—594no—
659C4⋊C4—594no—
660C4⋊C4—594no—
661C4⋊C4—594no—
662C4⋊C4C2×C4×D5912yes—
663C4⋊C4C2×C4×D5912yes—
664C4⋊C4C2×C4×D5914yes—
665C4⋊C4C2×C4×D5914yes—
666C4⋊C4C2×C4×D5912yes—
667C4⋊C4C2×C4×D5912yes—
668C22⋊C4—594no—
669C22⋊C4—594no—
670C22⋊C4—594no—
671C22⋊C4—594no—
672C22⋊C4—594no—
673C22⋊C4—594no—
674C22⋊C4—594no—
675C22⋊C4—594no—
676C22⋊C4C2×C4×D5914yes—
677C42—591no—
678C42—591no—
679C42—591no—
680C42—591no—
681C42—591no—
682C42—591no—
683C42—591no—
684C42—591no—
685C42—591no—
686C42—591no—
687C42—594no—
688C42—594no—
689C42—591no—
690C42—591no—
691C42C2×C4×D5911yescharacteristic
692C42C2×C4×D5911yescharacteristic
693C42C23×D5914yes—
694C42C23×D5911yescharacteristic
695C42C23×D5911yescharacteristic
696C23—591no—
697C23—594no—
698C23—591no—
699C23—1182no—
700C23—1182no—
701C23—2361no—
702C23C22×C4×D5911yescharacteristic
703Q8—42no—
704Q8—42no—
705Q8—1184no—
706D4—1188no—
707D4—1188no—
708D4—1184no—
709D4—2362no—
710D4—2362no—
711D4—2364no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—591no—
715C2×C4—591no—
716C2×C4—591no—
717C2×C4—591no—
718C2×C4—591no—
719C2×C4—591no—
720C2×C4—594no—
721C2×C4—1182no—
722C2×C4—1182no—
723C2×C4—1188no—
724C2×C4—1182no—
725C2×C4—1182no—
726C2×C4—1182no—
727C2×C4—1182no—
728C2×C4—1181no—
729C2×C4—1184no—
730C2×C4—1181no—
731C2×C4—1181no—
732C2×C4—1181no—
733C2×C4—1184no—
734C2×C4—1182no—
735C2×C4—1182no—
736C2×C4—2361no—
737C2×C4—2361no—
738C2×C4—2361no—
739C2×C4—2361no—
740C2×C4—2364no—
741C2×C4—2361no—
742C2×C4C22×C4×D5911yescharacteristic
743C2×C4C22×C4×D5911yescharacteristic
744C2×C4C22×C4×D5911yescharacteristic
745C2×C4C22×C4×D5911yescharacteristic
746C2×C4C22×C4×D5914yes—
747C2×C4C22×C4×D5914yes—
748C2×C4C22×C4×D5911yescharacteristic
749C2×C4#1427377312yes—
750C2×C4#1427377512yes—
751C2×C4C24×D5911yescharacteristic
752C8—22no—
753C8—24no—
754C8—22no—
755C8—1182no—
756C8—1184no—
757C8—1182no—
758C22—21no—
759C22—21no—
760C22—592no—
761C22—1181no—
762C22—1181no—
763C22—1181no—
764C22—1184no—
765C22—1181no—
766C22—1184no—
767C22—1181no—
768C22—1184no—
769C22—2364no—
770C22#1683788412yes—
771C22C23×C4×D5911yescharacteristic
772C4—21no—
773C4—21no—
774C4—21no—
775C4—21no—
776C4—24no—
777C4—24no—
778C4—592no—
779C4—1181no—
780C4—1181no—
781C4—1181no—
782C4—1181no—
783C4—1181no—
784C4—1184no—
785C4#1683788412yes—
786C4C2×#1427377311yescharacteristic
787C4C2×#1427377511yescharacteristic
788C2—22no—
789C2—1182no—
790C2—2361no—
791C2—2364no—
792C2C2×#1683788411yescharacteristic
793C2#568×D5911yescharacteristic
794C2#568×D5911yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D59
commutator, socleC22×C59C24×C4
FittingC59×#2961C2
prime radical#21437393C2
cosocleC2×C4×C59C25
hypercenter#2961D59
hypocenterC59#60269
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ #2961

Complements

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

NH ≅ G/Ntype
2. #21433265C2semidirect
3. #21433234C2semidirect
4. #21433220C2semidirect
5. #21433212C2semidirect
6. #21433037C2semidirect
7. #21432824C2semidirect
8. #21432820C2semidirect
9. #21432815C2semidirect
10. #21432813C2semidirect
11. #21432760C2semidirect
12. C2×#16837457C2semidirect
13. #21432663C2semidirect
14. #423×D59C2semidirect
15. C59×#2961C2semidirect
37. #16837533C22semidirect
38. #16837533C22semidirect
43. #16837475C22semidirect
44. #16837475C22semidirect
47. #16837472C22semidirect
48. #16837472C22semidirect
51. #16837464C22semidirect
52. #16837461C22semidirect
57. #16837457C22semidirect
58. #16837453C22semidirect
60. #16837427C22semidirect
61. #16837427C22semidirect
66. #16837424C22semidirect
71. C4⋊C8×D59C22semidirect
79. C59×#446C22semidirect
80. C59×#446C22semidirect
397. #2961D59semidirect
437. #446C2×D59semidirect
438. #446C2×D59semidirect
482. C59#60269semidirect

Maximal subgroups

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

subgroupindex
#214373932
#214332652
#214332342
#214332202
#214332122
#214330372
#214328242
#214328202
#214328152
#214328132
#214327602
C2×#168374572
#214326632
#423×D592
C59×#29612
#6026959