Finite Group Databasebeta

← #29452506

Subgroups — #29452506

Order 15104.

2038 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21437297C211yesmaximal, characteristic
2#21432761C212yesmaximal, complemented
3#21432759C214yesmaximal, complemented
4#21432752C214yesmaximal, complemented
5#21432750C212yesmaximal, complemented
6#21432745C211yesmaximal, characteristic, complemented
7#21432744C212yesmaximal, complemented
8#21432738C211yesmaximal, characteristic, complemented
9#21432737C212yesmaximal, complemented
10#21432734C211yesmaximal, characteristic, complemented
11#21432730C212yesmaximal, complemented
12#433×D59C212yesmaximal, complemented
13#21432661C212yesmaximal, complemented
14#21432542C212yesmaximal
15#21432521C211yesmaximal, characteristic, complemented
16C4×#14273733C211yesmaximal, characteristic, complemented
17C2×C59×#433C211yesmaximal, characteristic, complemented
18C22×#11745685C2211yescharacteristic
19C2×#14273733C2212yes—
20C2×#14273733C2212yes—
21#16837883C414yes—
22#16837882C412yes—
23#16837882C412yes—
24#16837879C412yes—
25#16837876C412yes—
26#16837875C414yes—
27C4×#11745685C2211yescharacteristic
28C4×#11745685C2211yescharacteristic
29C4×#11745685C2211yescharacteristic
30C4×#11745685C2211yescharacteristic
31#16837870C2212yes—
32#16837870C2212yes—
33C2×#14273686C2211yescharacteristic
34#117×D59C2212yes—
35#117×D59C2212yes—
36#16837464C2212yescomplemented
37#16837464C2212yescomplemented
38#16837463C2212yes—
39#16837463C2212yes—
40#16837463C2212yescomplemented
41#16837463C2212yescomplemented
42#16837462C2214yescomplemented
43#16837462C2214yescomplemented
44#16837461C2212yescomplemented
45#16837461C2212yescomplemented
46#16837460C2214yes—
47#16837460C2214yes—
48#16837458C2214yescomplemented
49#16837457C2214yescomplemented
50#16837456C2214yescomplemented
51#16837454C2214yescomplemented
52#16837453C2214yescomplemented
53#16837452C2214yescomplemented
54#16837428C2212yescomplemented
55#16837428C2212yescomplemented
56#16837427C2214yescomplemented
57#16837427C2214yescomplemented
58#16837426C2212yescomplemented
59#16837424C2214yescomplemented
60C4⋊C8×D59C2214yescomplemented
61#16837368C2212yes—
62#16837368C2212yes—
63#16837367C2214yes—
64#16837367C2214yes—
65#16837366C2212yes—
66#16837364C2214yes—
67C22⋊C8×D59C2214yes—
68#16837359C2214yescomplemented
69#16837357C2212yescomplemented
70#16837357C2212yescomplemented
71#16837356C2214yescomplemented
72C4×#11745664C2211yescharacteristic, complemented
73C4×#11745664C2211yescharacteristic, complemented
74#16837354C2212yescomplemented
75C4×#11745659C2212yescomplemented
76#97×D59C2212yescomplemented
77C4×C8×D59C2212yescomplemented
78C2×#117×C59C2211yescharacteristic
79C59×#433C2211yescharacteristic
80C59×#433C2211yescharacteristic
81C59×#433C2212yes—
82C59×#433C2211yescharacteristic, complemented
83C59×#433C2211yescharacteristic, complemented
84C59×#433C2212yescomplemented
85C2×C4⋊C8×C59C2212yescomplemented
86C2×C22⋊C8×C59C2212yes—
87C2×#97×C59C2211yescharacteristic, complemented
88C2×C4×C8×C59C2211yescharacteristic, complemented
89C2×#11745685—28no—
90C2×#11745685C2×C411yescharacteristic
91C2×#11745685C2×C411yescharacteristic
92C2×#11745685C2×C412yes—
93C2×#11745685C2312yes—
94C2×#11745685C2311yescharacteristic
95C2×#11745685C2311yescharacteristic
96C22×Dic118C2×C411yescharacteristic
97C22×D236C2×C411yescharacteristic
98C22×C22⋊D59C2×C412yes—
99C22×C4×D59C2312yes—
100#14273733—28no—
101#14273733—28no—
102C2×#11745664C2312yes—
103C2×#11745664C2312yes—
104C2×#11745659C2314yes—
105C2×#11745659C2314yes—
106C2×C8×D59C2314yes—
107C2×C8×D59C2314yes—
108C4×Dic118C2×C412yes—
109C4×Dic118C2×C412yes—
110C4×Dic118C2×C412yes—
111C4×Dic118C2×C412yes—
112#14273692C2×C414yes—
113#14273692C2×C414yes—
114C4×D236C2×C412yes—
115C4×D236C2×C412yes—
116C4×D236C2×C412yes—
117C4×D236C2×C412yes—
118#14273689C2×C414yes—
119#14273689C2×C414yes—
120C4×C22⋊D59C2×C414yes—
121C4×C22⋊D59C2×C414yes—
122C4×C22⋊D59C2×C414yes—
123C4×C22⋊D59C2×C414yes—
124(C22⋊D59)⋊C4C2×C414yes—
125(C22⋊D59)⋊C4C2×C414yes—
126(C22⋊D59)⋊C4C2×C414yes—
127(C22⋊D59)⋊C4C2×C414yes—
128#14273686C2×C412yes—
129#14273686C2×C412yes—
130#14273686C2311yescharacteristic
131#14273686C2312yes—
132#14273686C2311yescharacteristic
133#14273685C2×C414yes—
134#14273685C2×C414yes—
135#14273684C2312yes—
136#14273684C2312yes—
137#14273684C2312yes—
138#14273684C2312yes—
139#14273683C2×C414yes—
140#14273683C2×C414yes—
141C2×C4⋊Dic59C2×C412yes—
142C4⋊C4×D59C2×C414yes—
143C4⋊C4×D59C2×C414yes—
144C2×C22⋊Dic59C2×C412yes—
145C22⋊C4×D59C2×C414yes—
146C22⋊C4×D59C2×C414yes—
147C2×C4×Dic59C2312yes—
148C42×D59C2312yes—
149C42×D59C2312yes—
150C42×D59C2312yes—
151C42×D59C2312yes—
152C4⋊(C59⋊C8)C2314yes—
153C4⋊(C59⋊C8)C2314yes—
154Dic59⋊C8C2314yes—
155Dic59⋊C8C2314yes—
156Dic59⋊C8C2314yes—
157Dic59⋊C8C2314yes—
158C22⋊(C59⋊C8)C2314yes—
159C22⋊(C59⋊C8)C2314yes—
160(C2×D59)⋊C8C2314yes—
161(C2×D59)⋊C8C2314yes—
162(C2×D59)⋊C8C2314yes—
163(C2×D59)⋊C8C2314yes—
164#14273638C2312yes—
165#14273638C2312yes—
166#14273637C2314yes—
167#14273637C2314yes—
168C4×C59⋊C8C2312yes—
169C4×C59⋊C8C2312yes—
170C8×Dic59C2314yes—
171C8×Dic59C2314yes—
172C23×C4×C59C2311yescharacteristic
173C22×C8×C59C2312yes—
174C22×C8×C59C2312yes—
175#117×C59C2×C412yes—
176#117×C59C2×C412yes—
177#117×C59C2311yescharacteristic
178#117×C59C2311yescharacteristic
179#117×C59C2311yescharacteristic
180#117×C59C2311yescharacteristic
181C2×C4⋊C4×C59C2×C412yes—
182C2×C22⋊C4×C59C2×C412yes—
183C2×C42×C59C2311yescharacteristic
184C2×C42×C59C2311yescharacteristic
185C4⋊C8×C59C2312yes—
186C4⋊C8×C59C2312yes—
187C4⋊C8×C59C2312yes—
188C4⋊C8×C59C2312yes—
189C22⋊C8×C59C2312yes—
190C22⋊C8×C59C2312yes—
191C22⋊C8×C59C2312yes—
192C22⋊C8×C59C2312yes—
193#97×C59C2312yes—
194#97×C59C2311yescharacteristic
195#97×C59C2311yescharacteristic
196C4×C8×C59C2312yes—
197C4×C8×C59C2311yescharacteristic
198C4×C8×C59C2311yescharacteristic
199C24×C59C22×C411yescharacteristic
200C23×D59C22×C412yes—
201C22×C4×C59—24no—
202C22×C4×C59C22×C411yescharacteristic
203C22×C4×C59C22×C411yescharacteristic
204C22×C4×C59C22×C411yescharacteristic
205C22×C4×C59C22×C412yes—
206C22×C4×C59C22×C412yes—
207C22×C4×C59C2411yescharacteristic
208C22×C4×C59C2411yescharacteristic
209C22×C4×C59C2411yescharacteristic
210C2×C22⋊D59—28no—
211C2×C22⋊D59C22×C412yes—
212C2×C22⋊D59C22×C412yes—
213C2×C22⋊D59C22×C412yes—
214C2×C22⋊D59C22×C412yes—
215C22×Dic59C22×C412yes—
216C22×Dic59C22×C414yes—
217#11745685—24no—
218#11745685—28no—
219#11745685—24no—
220#11745685—28no—
221#11745685—24no—
222#11745685#4118yes—
223C2×D236—24no—
224C2×D236C22×C412yes—
225C2×D236C22×C411yescharacteristic
226C2×D236C22×C411yescharacteristic
227C2×C4×D59—28no—
228C2×C4×D59C22×C412yes—
229C2×C4×D59C22×C412yes—
230C2×C4×D59C22×C414yes—
231C2×C4×D59C22×C414yes—
232C2×C4×D59C22×C414yes—
233C2×C4×D59C22×C414yes—
234C2×C4×D59C2412yes—
235C2×C4×D59C2412yes—
236C2×Dic118—24no—
237C2×Dic118C22×C412yes—
238C2×Dic118C22×C411yescharacteristic
239C2×Dic118C22×C411yescharacteristic
240C2×C8×C59—24no—
241C2×C8×C59—24no—
242C2×C8×C59C2412yes—
243C2×C8×C59C2412yes—
244C2×C8×C59C2412yes—
245C2×C8×C59C2412yes—
246C4⋊C4×C59C22×C412yes—
247C4⋊C4×C59C22×C412yes—
248C4⋊C4×C59C22×C412yes—
249C4⋊C4×C59C22×C412yes—
250C22⋊C4×C59C22×C412yes—
251C22⋊C4×C59C22×C412yes—
252C22⋊C4×C59C22×C412yes—
253C22⋊C4×C59C22×C412yes—
254C42×C59C22×C412yes—
255C42×C59C22×C412yes—
256C42×C59C2411yescharacteristic
257C42×C59C2411yescharacteristic
258C42×C59C2411yescharacteristic
259C42×C59C2411yescharacteristic
260C22⋊Dic59C22×C414yes—
261C22⋊Dic59C22×C412yes—
262C22⋊Dic59C22×C412yes—
263(C2×D59)⋊C4C22×C414yes—
264(C2×D59)⋊C4C22×C414yes—
265(C2×D59)⋊C4C22×C414yes—
266(C2×D59)⋊C4C22×C414yes—
267C4⋊Dic59C22×C414yes—
268C4⋊Dic59C22×C412yes—
269C4⋊Dic59C22×C412yes—
270Dic59⋊C4C22×C414yes—
271Dic59⋊C4C22×C414yes—
272Dic59⋊C4C22×C414yes—
273Dic59⋊C4C22×C414yes—
274C4×Dic59C22×C414yes—
275C4×Dic59C22×C414yes—
276C4×Dic59C22×C414yes—
277C4×Dic59C22×C414yes—
278C4×Dic59C22×C414yes—
279C4×Dic59C2412yes—
280C4×Dic59C2412yes—
281#11745664—24no—
282#11745664—24no—
283C2×C59⋊C8C2414yes—
284C2×C59⋊C8C2414yes—
285#11745659—28no—
286#11745659—28no—
287C8×D59—28no—
288C8×D59—28no—
289C23×C59—22no—
290C23×C59—42no—
291C23×C59C23×C411yescharacteristic
292C23×C59C23×C411yescharacteristic
293C23×C59C23×C411yescharacteristic
294C22×D59—24no—
295C22×D59—44no—
296C22×D59C23×C412yes—
297C22×D59C23×C412yes—
298C2×C4×C59—22no—
299C2×C4×C59—22no—
300C2×C4×C59—22no—
301C2×C4×C59—22no—
302C2×C4×C59—22no—
303C2×C4×C59—42no—
304C2×C4×C59—42no—
305C2×C4×C59C23×C411yescharacteristic
306C2×C4×C59C23×C412yes—
307C2×C4×C59C23×C412yes—
308C2×C4×C59C23×C412yes—
309C2×C4×C59C23×C412yes—
310C2×C4×C59C23×C411yescharacteristic
311C2×C4×C59C23×C411yescharacteristic
312C2×C4×C59C2×#4114yes—
313C2×C4×C59C2511yescharacteristic
314C22⋊D59—24no—
315C22⋊D59—24no—
316C22⋊D59—24no—
317C22⋊D59#11718yes—
318C2×Dic59—24no—
319C2×Dic59—44no—
320C2×Dic59C23×C412yes—
321C2×Dic59C23×C414yes—
322C2×Dic59C23×C414yes—
323C2×Dic59C23×C412yes—
324D236—24no—
325D236—22no—
326D236#11714yes—
327C4×D59—24no—
328C4×D59—24no—
329C4×D59—24no—
330C4×D59—44no—
331C4×D59—44no—
332C4×D59—44no—
333C4×D59—44no—
334C4×D59C2×#4118yes—
335Dic118—22no—
336Dic118—24no—
337Dic118#11714yes—
338C8×C59—22no—
339C8×C59—22no—
340C8×C59—22no—
341C8×C59—22no—
342C59⋊C8—24no—
343C59⋊C8—24no—
344#60129—591nomaximal, Sylow
345C22×C59—22no—
346C22×C59—21no—
347C22×C59—21no—
348C22×C59—22no—
349C22×C59—22no—
350C22×C59—82no—
351C22×C59C2×#11712yes—
352C22×C59C24×C411yescharacteristic
353C2×D59—24no—
354C2×D59—22no—
355C2×D59—24no—
356C2×D59—84no—
357C2×D59C2×#11714yes—
358C4×C59—21no—
359C4×C59—21no—
360C4×C59—22no—
361C4×C59—22no—
362C4×C59—22no—
363C4×C59—22no—
364C4×C59C2×#11712yes—
365C4×C59C22×#4112yes—
366Dic59—22no—
367Dic59—24no—
368Dic59—24no—
369Dic59C2×#11714yes—
370#3428—591no—
371#2925—594no—
372#2925—592no—
373#2924—594no—
374#2924—592no—
375#2923—592no—
376#2923—591no—
377#2922—592no—
378#2922—591no—
379#2921—592no—
380#2921—591no—
381C2×#433—592no—
382C2×#433D5911yescharacteristic, complemented
383#2906—592no—
384#2880—592no—
385#2875—591no—
386C4×#131—591no—
387C2×C59—22no—
388C2×C59—41no—
389C2×C59—41no—
390C2×C59C22×#11711yescharacteristic
391C2×C59#357312yes—
392D59—24no—
393D59—42no—
394C22×#41—591no—
395C2×#131—592no—
396C2×#131—592no—
397#520—592no—
398#520—592no—
399#520—594no—
400#519—592no—
401#518—592no—
402#518—594no—
403C4×#41—592no—
404C4×#41—592no—
405C4×#41—591no—
406C4×#41—591no—
407C4×#41—591no—
408C4×#41—591no—
409C2×#117—591no—
410C2×#117—592no—
411C2×#117—592no—
412C2×#117C2×D5911yescharacteristic
413#433—592no—
414#433—592no—
415#433—592no—
416#433—592no—
417#433—594no—
418#433—594no—
419#433—594no—
420#433—594no—
421#433—592no—
422#433—592no—
423#433—592no—
424#433—592no—
425#433C2×D5911yescharacteristic
426#433C2×D5911yescharacteristic
427#433C2×D5912yes—
428#433C2×D5911yescharacteristic, complemented
429#433C2×D5911yescharacteristic, complemented
430#433C2×D5912yescomplemented
431#432—594no—
432#432—594no—
433#432—594no—
434#431—594no—
435#431—594no—
436#431—594no—
437#424—592no—
438#424—592no—
439#424—594no—
440#424—594no—
441#423—592no—
442#423—594no—
443C2×C4⋊C8—594no—
444C2×C4⋊C8C2×D5912yescomplemented
445#408—592no—
446#408—592no—
447#408—594no—
448#408—594no—
449#407—592no—
450#407—594no—
451C2×C22⋊C8—594no—
452C2×C22⋊C8C2×D5912yes—
453#405—592no—
454#405—592no—
455#405—594no—
456#405—594no—
457C4×M16—591no—
458C4×M16—591no—
459C4×M16—592no—
460C4×M16—592no—
461C2×#97—592no—
462C2×#97C2×D5911yescharacteristic, complemented
463C2×C4×C8—592no—
464C2×C4×C8C2×D5911yescharacteristic, complemented
465C59#6012911yescharacteristic, complemented, Sylow
466C2×#41—591no—
467C2×#41—591no—
468C2×#41—592no—
469C2×#41—591no—
470C2×#41—592no—
471C2×#41—591no—
472C2×#41—1188no—
473C22×Q8—591no—
474C22×D4—592no—
475C22×D4—591no—
476C23×C4—592no—
477C23×C4C22×D5911yescharacteristic
478#131—1188no—
479#131—1188no—
480C2×M16—592no—
481C2×M16—592no—
482C2×M16—594no—
483C2×M16—594no—
484C22×C8—594no—
485C22×C8—594no—
486C22×C8C22×D5912yes—
487C22×C8C22×D5912yes—
488C4×Q8—594no—
489C4×Q8—594no—
490C4×Q8—592no—
491C4×Q8—592no—
492C4×Q8—592no—
493C4×Q8—592no—
494C4×D4—594no—
495C4×D4—594no—
496C4×D4—594no—
497C4×D4—594no—
498C4×D4—594no—
499C4×D4—594no—
500C4×D4—594no—
501C4×D4—594no—
502C4×D4—594no—
503C4×D4—594no—
504C4×D4—592no—
505C4×D4—592no—
506C4×D4—592no—
507C4×D4—592no—
508#117—592no—
509#117—592no—
510#117—592no—
511#117—591no—
512#117—591no—
513#117—594no—
514#117—594no—
515#117—594no—
516#117—594no—
517#117—592no—
518#117—592no—
519#117—592no—
520#117—592no—
521#117C4×D5912yes—
522#117C4×D5912yes—
523#117C22×D5911yescharacteristic
524#117C22×D5911yescharacteristic
525#117C22×D5911yescharacteristic
526#117C22×D5911yescharacteristic
527C2×C4⋊C4—592no—
528C2×C4⋊C4—594no—
529C2×C4⋊C4—594no—
530C2×C4⋊C4C4×D5912yes—
531C2×C22⋊C4—592no—
532C2×C22⋊C4—594no—
533C2×C22⋊C4—594no—
534C2×C22⋊C4C4×D5912yes—
535C2×C42—592no—
536C2×C42—592no—
537C2×C42—592no—
538C2×C42—592no—
539C2×C42—592no—
540C2×C42C22×D5911yescharacteristic
541C2×C42C22×D5911yescharacteristic
542C4⋊C8—594no—
543C4⋊C8—594no—
544C4⋊C8—594no—
545C4⋊C8—594no—
546C4⋊C8—594no—
547C4⋊C8—594no—
548C4⋊C8C22×D5912yes—
549C4⋊C8C22×D5912yes—
550C4⋊C8C22×D5912yes—
551C4⋊C8C22×D5912yes—
552C22⋊C8—594no—
553C22⋊C8—594no—
554C22⋊C8—594no—
555C22⋊C8—594no—
556C22⋊C8—594no—
557C22⋊C8—594no—
558C22⋊C8C22×D5912yes—
559C22⋊C8C22×D5912yes—
560C22⋊C8C22×D5912yes—
561C22⋊C8C22×D5912yes—
562#97—594no—
563#97—594no—
564#97—592no—
565#97—592no—
566#97C22×D5911yescharacteristic
567#97C22×D5911yescharacteristic
568#97C22×D5912yes—
569C4×C8—594no—
570C4×C8—594no—
571C4×C8—592no—
572C4×C8—592no—
573C4×C8C22×D5911yescharacteristic
574C4×C8C22×D5911yescharacteristic
575C4×C8C22×D5912yes—
576C24—592no—
577C24C2×C4×D5911yescharacteristic
578#41—598no—
579#41—1188no—
580#41—1188no—
581#41—1184no—
582#41—1184no—
583#41—1184no—
584C2×Q8—591no—
585C2×Q8—592no—
586C2×Q8—591no—
587C2×Q8—1184no—
588C2×D4—592no—
589C2×D4—592no—
590C2×D4—592no—
591C2×D4—592no—
592C2×D4—591no—
593C2×D4—592no—
594C2×D4—591no—
595C2×D4—1184no—
596C2×D4—1188no—
597C22×C4—24no—
598C22×C4—592no—
599C22×C4—592no—
600C22×C4—594no—
601C22×C4—592no—
602C22×C4—592no—
603C22×C4—592no—
604C22×C4—594no—
605C22×C4—594no—
606C22×C4—594no—
607C22×C4—594no—
608C22×C4—1188no—
609C22×C4C2×C4×D5911yescharacteristic
610C22×C4C2×C4×D5911yescharacteristic
611C22×C4C2×C4×D5911yescharacteristic
612C22×C4C2×C4×D5912yes—
613C22×C4C2×C4×D5912yes—
614C22×C4C23×D5911yescharacteristic
615C22×C4C23×D5911yescharacteristic
616C22×C4C23×D5911yescharacteristic
617M16—1188no—
618M16—1188no—
619M16—1184no—
620M16—1184no—
621C2×C8—24no—
622C2×C8—24no—
623C2×C8—594no—
624C2×C8—594no—
625C2×C8—1188no—
626C2×C8—1188no—
627C2×C8C23×D5912yes—
628C2×C8C23×D5912yes—
629C2×C8C23×D5912yes—
630C2×C8C23×D5912yes—
631C4⋊C4—594no—
632C4⋊C4—594no—
633C4⋊C4—594no—
634C4⋊C4—594no—
635C4⋊C4—594no—
636C4⋊C4—592no—
637C4⋊C4—592no—
638C4⋊C4C2×C4×D5912yes—
639C4⋊C4C2×C4×D5912yes—
640C4⋊C4C2×C4×D5912yes—
641C4⋊C4C2×C4×D5912yes—
642C22⋊C4—594no—
643C22⋊C4—592no—
644C22⋊C4—592no—
645C22⋊C4—594no—
646C22⋊C4—594no—
647C22⋊C4—594no—
648C22⋊C4—594no—
649C22⋊C4C2×C4×D5912yes—
650C22⋊C4C2×C4×D5912yes—
651C22⋊C4C2×C4×D5912yes—
652C22⋊C4C2×C4×D5912yes—
653C42—594no—
654C42—594no—
655C42—594no—
656C42—594no—
657C42—594no—
658C42—592no—
659C42—592no—
660C42C2×C4×D5912yes—
661C42C2×C4×D5912yes—
662C42C23×D5911yescharacteristic
663C42C23×D5911yescharacteristic
664C42C23×D5911yescharacteristic
665C42C23×D5911yescharacteristic
666C23—22no—
667C23—42no—
668C23—592no—
669C23—592no—
670C23—1184no—
671C23—2364no—
672C23C22×C4×D5911yescharacteristic
673C23C22×C4×D5911yescharacteristic
674C23C22×C4×D5911yescharacteristic
675Q8—594no—
676Q8—1184no—
677Q8—1182no—
678D4—598no—
679D4—594no—
680D4—1184no—
681D4—1184no—
682D4—1184no—
683D4—1184no—
684D4—1182no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—592no—
693C2×C4—598no—
694C2×C4—594no—
695C2×C4—594no—
696C2×C4—592no—
697C2×C4—1184no—
698C2×C4—1184no—
699C2×C4—1184no—
700C2×C4—1184no—
701C2×C4—2364no—
702C2×C4—2364no—
703C2×C4—2364no—
704C2×C4—2364no—
705C2×C4—2364no—
706C2×C4C22×C4×D5911yescharacteristic
707C2×C4C22×C4×D5912yes—
708C2×C4C22×C4×D5912yes—
709C2×C4C22×C4×D5912yes—
710C2×C4C22×C4×D5912yes—
711C2×C4C22×C4×D5911yescharacteristic
712C2×C4C22×C4×D5911yescharacteristic
713C2×C4#41×D5914yes—
714C2×C4C24×D5911yescharacteristic
715C8—22no—
716C8—22no—
717C8—22no—
718C8—22no—
719C8—1184no—
720C8—1184no—
721C22—22no—
722C22—21no—
723C22—21no—
724C22—22no—
725C22—22no—
726C22—82no—
727C22—594no—
728C22—1184no—
729C22—1182no—
730C22—1184no—
731C22—4724no—
732C22#117×D5912yes—
733C22C23×C4×D5911yescharacteristic
734C4—21no—
735C4—21no—
736C4—22no—
737C4—22no—
738C4—22no—
739C4—22no—
740C4—594no—
741C4—1182no—
742C4—1184no—
743C4—1184no—
744C4#117×D5912yes—
745C4C2×#41×D5912yes—
746C2—22no—
747C2—41no—
748C2—41no—
749C2—1184no—
750C2—2362no—
751C2C2×#117×D5911yescharacteristic
752C2#2143880712yes—
subgroupG/H
center, FrattiniC2×C4C24×D59
commutator, socleC22×C59C24×C4
FittingC2×C59×#433C2
prime radicalC22×#11745685C22
cosocleC2×C4×C59C25
hypercenterC2×#433D59
hypocenterC59#60129
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
2. #21432761C2semidirect
3. #21432759C2semidirect
4. #21432752C2semidirect
5. #21432750C2semidirect
6. #21432745C2semidirect
7. #21432744C2semidirect
8. #21432738C2semidirect
9. #21432737C2semidirect
10. #21432734C2semidirect
11. #21432730C2semidirect
12. #433×D59C2semidirect
13. #21432661C2semidirect
15. #21432521C2semidirect
16. C4×#14273733C2semidirect
17. C2×C59×#433C2semidirect
36. #16837464C22semidirect
37. #16837464C22semidirect
40. #16837463C22semidirect
41. #16837463C22semidirect
42. #16837462C22semidirect
43. #16837462C22semidirect
44. #16837461C22semidirect
45. #16837461C22semidirect
48. #16837458C22semidirect
49. #16837457C22semidirect
50. #16837456C22semidirect
51. #16837454C22semidirect
52. #16837453C22semidirect
53. #16837452C22semidirect
54. #16837428C22semidirect
55. #16837428C22semidirect
56. #16837427C22semidirect
57. #16837427C22semidirect
58. #16837426C22semidirect
59. #16837424C22semidirect
60. C4⋊C8×D59C22semidirect
68. #16837359C22semidirect
69. #16837357C22semidirect
70. #16837357C22semidirect
71. #16837356C22semidirect
72. C4×#11745664C22semidirect
73. C4×#11745664C22semidirect
74. #16837354C22semidirect
75. C4×#11745659C22semidirect
76. #97×D59C22semidirect
77. C4×C8×D59C22semidirect
82. C59×#433C22semidirect
83. C59×#433C22semidirect
84. C59×#433C22semidirect
85. C2×C4⋊C8×C59C22semidirect
87. C2×#97×C59C22semidirect
88. C2×C4×C8×C59C22semidirect
382. C2×#433D59semidirect
428. #433C2×D59semidirect
429. #433C2×D59semidirect
430. #433C2×D59semidirect
444. C2×C4⋊C8C2×D59semidirect
462. C2×#97C2×D59semidirect
464. C2×C4×C8C2×D59semidirect
465. C59#60129semidirect

Maximal subgroups

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

subgroupindex
#214372972
#214327612
#214327592
#214327522
#214327502
#214327452
#214327442
#214327382
#214327372
#214327342
#214327302
#433×D592
#214326612
#214325422
#214325212
C4×#142737332
C2×C59×#4332
#6012959