Finite Group Databasebeta

← #29452679

Subgroups — #29452679

Order 15104.

2742 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838167C211yesmaximal, characteristic, complemented
2#41×C22⋊D59C211yesmaximal, characteristic
3#21432838C213yesmaximal, complemented
4M16×C22⋊D59C213yesmaximal, complemented
5#21432821C213yesmaximal, complemented
6#21432818C213yesmaximal, complemented
7#21432806C213yesmaximal, complemented
8#21432799C213yesmaximal, complemented
9#21432797C213yesmaximal, complemented
10C2×#16837478C213yesmaximal, complemented
11#21432662C211yesmaximal, characteristic, complemented
12#21432545C211yesmaximal, characteristic, complemented
13#21432543C211yesmaximal, characteristic, complemented
14#131×Dic59C211yesmaximal, characteristic, complemented
15C2×C59×#568C211yesmaximal, characteristic, complemented
16C2×#41×D59C2211yescharacteristic
17#16838167—28no—
18C2×#14273735C2213yescomplemented
19C2×#14273734C2211yescharacteristic
20C2×#14273734C2211yescharacteristic
21C2×#14273733C2213yescomplemented
22C22×#11745659C2213yescomplemented
23C2×M16×D59C2213yescomplemented
24#16838071C411yescharacteristic
25Q8×C22⋊D59C411yescharacteristic
26#16838063C411yescharacteristic
27#16838059C411yescharacteristic
28#16838051C413yes—
29#16838046C413yes—
30#16838040C413yes—
31D4×C22⋊D59C413yes—
32#16837948C2213yes—
33#16837913C2213yes—
34#16837909C2213yes—
35#41×Dic59C2211yescharacteristic
36C2×C4×C22⋊D59C2213yes—
37#16837478C2211yescharacteristic
38#16837478C2213yes—
39#16837478C2213yescomplemented
40#16837478C2213yescomplemented
41#16837478C2213yescomplemented
42#16837478C2213yescomplemented
43#16837478C2213yescomplemented
44#16837478C2213yescomplemented
45#16837478C2216yescomplemented
46#16837473C2216yescomplemented
47#16837473C2216yescomplemented
48#16837471C2216yescomplemented
49#16837471C2216yescomplemented
50C8×C22⋊D59C2216yescomplemented
51C8×C22⋊D59C2216yescomplemented
52#16837430C2213yescomplemented
53#16837428C2213yescomplemented
54#16837425C2213yescomplemented
55C2×Dic59⋊C8C2213yescomplemented
56#16837370C2213yescomplemented
57#16837369C2213yescomplemented
58#16837369C2213yescomplemented
59#16837368C2213yescomplemented
60#16837366C2213yescomplemented
61#16837365C2213yescomplemented
62C2×C22⋊(C59⋊C8)C2213yescomplemented
63C2×(C2×D59)⋊C8C2213yescomplemented
64#16837360C2213yescomplemented
65#16837357C2213yescomplemented
66M16×Dic59C2213yescomplemented
67C2×C8×Dic59C2213yescomplemented
68C22×#41×C59C2211yescharacteristic
69C59×#568—28no—
70C2×#131×C59C2211yescharacteristic
71C2×#131×C59C2211yescharacteristic
72C2×#131×C59C2213yescomplemented
73C2×#131×C59C2213yescomplemented
74C22×M16×C59C2213yescomplemented
75C22×M16×C59C2213yescomplemented
76C2×#11745689C2×C411yescharacteristic
77C2×#11745685C2313yes—
78C2×#11745687C2×C413yes—
79#41×D59—24no—
80#41×D59—24no—
81C2×Q8×D59C2×C411yescharacteristic
82C22×C22⋊D59C2×C413yes—
83C2×D4×D59C2×C413yes—
84C22×C4×D59C2313yes—
85#14273735—212no—
86#14273734—24no—
87#14273734—24no—
88#14273733—212no—
89C2×#11745664C2313yes—
90C2×#11745664C2313yes—
91C2×#11745659—212no—
92C2×#11745659C2313yes—
93C2×#11745659C2311yescharacteristic
94C2×#11745659C2313yes—
95C2×#11745659C2313yes—
96M16×D59—212no—
97C22×C59⋊C8C2313yes—
98C22×C59⋊C8C2313yes—
99C2×C8×D59C2316yes—
100#14273725C2×C413yes—
101#14273723C2×C413yes—
102#14273716C2×C413yes—
103#14273714C2×C413yes—
104#14273710C2×C416yes—
105#14273708C2×C416yes—
106#14273706C2×C413yes—
107#14273706C2×C413yes—
108#14273703C2×C413yes—
109#14273703C2×C413yes—
110#14273701C2×C413yes—
111#14273701C2×C413yes—
112#14273699C2×C416yes—
113#14273699C2×C416yes—
114#14273698C2×C413yes—
115#14273698C2×C413yes—
116#14273696C2×C416yes—
117#14273695C2×C416yes—
118Q8×Dic59C2×C411yescharacteristic
119Q8×Dic59C2×C411yescharacteristic
120D4×Dic59C2×C413yes—
121D4×Dic59C2×C413yes—
122C4×C22⋊D59C2×C413yes—
123C4×C22⋊D59C2×C413yes—
124C4×C22⋊D59C2×C413yes—
125C4×C22⋊D59C2×C413yes—
126C4×C22⋊D59C2313yes—
127C4×C22⋊D59C2316yes—
128C4×C22⋊D59C2313yes—
129C4×C22⋊D59C2313yes—
130C4×C22⋊D59C2311yescharacteristic
131#14273686C2313yes—
132C2×Dic59⋊C4C2×C413yes—
133C2×C22⋊Dic59C2×C413yes—
134C2×(C2×D59)⋊C4C2×C413yes—
135C2×C4×Dic59C2313yes—
136Dic59⋊C8C2311yescharacteristic
137Dic59⋊C8C2313yes—
138Dic59⋊C8C2313yes—
139Dic59⋊C8C2313yes—
140Dic59⋊C8C2316yes—
141C22⋊(C59⋊C8)C2313yes—
142C22⋊(C59⋊C8)C2316yes—
143C22⋊(C59⋊C8)C2313yes—
144C22⋊(C59⋊C8)C2313yes—
145C22⋊(C59⋊C8)C2311yescharacteristic
146(C2×D59)⋊C8C2313yes—
147(C2×D59)⋊C8C2316yes—
148(C2×D59)⋊C8C2313yes—
149(C2×D59)⋊C8C2313yes—
150(C2×D59)⋊C8C2311yescharacteristic
151#14273637C2316yes—
152C8×Dic59C2313yes—
153C8×Dic59C2313yes—
154C8×Dic59C2311yescharacteristic
155C8×Dic59C2313yes—
156C2×#41×C59—24no—
157C2×#41×C59—24no—
158C2×#41×C59C2×C413yes—
159C2×#41×C59C2×C411yescharacteristic
160C2×#41×C59C2313yes—
161C2×#41×C59C2311yescharacteristic
162C22×Q8×C59C2×C411yescharacteristic
163C22×D4×C59C2×C413yes—
164C23×C4×C59C2313yes—
165#131×C59—24no—
166#131×C59—212no—
167#131×C59—212no—
168#131×C59D418yescomplemented
169C2×M16×C59—212no—
170C2×M16×C59—212no—
171C2×M16×C59C2313yes—
172C2×M16×C59C2313yes—
173C2×M16×C59C2313yes—
174C2×M16×C59C2311yescharacteristic
175C2×M16×C59C2313yes—
176C2×M16×C59C2313yes—
177C22×C8×C59C2313yes—
178C22×C8×C59C2316yes—
179C22×C8×C59C2313yes—
180C24×C59C22×C413yes—
181C23×D59C22×C413yes—
182#41×C59—24no—
183#41×C59—212no—
184#41×C59—26no—
185#41×C59—26no—
186#41×C59C2×D414yes—
187#41×C59#4114yes—
188C2×Q8×C59—24no—
189C2×Q8×C59C22×C413yes—
190C2×Q8×C59C22×C411yescharacteristic
191C2×D4×C59—212no—
192C2×D4×C59C22×C416yes—
193C2×D4×C59C22×C413yes—
194C2×D4×C59C22×C413yes—
195C22×C4×C59—26no—
196C22×C4×C59—26no—
197C22×C4×C59C22×C413yes—
198C22×C4×C59C22×C413yes—
199C22×C4×C59C22×C413yes—
200C22×C4×C59C2413yes—
201C22×C4×C59C2411yescharacteristic
202C22×C4×C59C2413yes—
203C2×C22⋊D59—46no—
204C2×C22⋊D59C22×C411yescharacteristic
205C2×C22⋊D59C22×C413yes—
206C2×C22⋊D59C22×C416yes—
207C2×C22⋊D59C22×C413yes—
208C2×C22⋊D59C22×C413yes—
209C2×C22⋊D59C22×C416yes—
210C22×Dic59C22×C413yes—
211C22×Dic59C22×C413yes—
212C22×Dic59C22×C413yes—
213#11745689—24no—
214Q8×D59—24no—
215#11745687—212no—
216D4×D59—212no—
217#11745685—26no—
218#11745685—26no—
219C2×D236C22×C413yes—
220C2×C4×D59—26no—
221C2×C4×D59—26no—
222C2×C4×D59C22×C413yes—
223C2×C4×D59C22×C413yes—
224C2×C4×D59C2413yes—
225C2×C4×D59C2411yescharacteristic
226C2×Dic118C22×C413yes—
227M16×C59—26no—
228M16×C59—26no—
229M16×C59—22no—
230M16×C59—26no—
231M16×C59—26no—
232M16×C59C2×D4112yescomplemented
233C2×C8×C59—26no—
234C2×C8×C59—212no—
235C2×C8×C59C2×D4112yescomplemented
236C2×C8×C59C2411yescharacteristic
237C2×C8×C59C2413yes—
238C2×C8×C59C2411yescharacteristic
239C2×C8×C59C2413yes—
240C22⋊Dic59C22×C411yescharacteristic
241C22⋊Dic59C22×C413yes—
242C22⋊Dic59C22×C413yes—
243C22⋊Dic59C22×C413yes—
244C22⋊Dic59C22×C416yes—
245C22⋊Dic59C22×C416yes—
246(C2×D59)⋊C4C22×C411yescharacteristic
247(C2×D59)⋊C4C22×C413yes—
248(C2×D59)⋊C4C22×C413yes—
249(C2×D59)⋊C4C22×C413yes—
250(C2×D59)⋊C4C22×C416yes—
251C4⋊Dic59C22×C413yes—
252C4⋊Dic59C22×C413yes—
253Dic59⋊C4C22×C411yescharacteristic
254Dic59⋊C4C22×C413yes—
255Dic59⋊C4C22×C413yes—
256Dic59⋊C4C22×C413yes—
257Dic59⋊C4C22×C416yes—
258C4×Dic59C22×C413yes—
259C4×Dic59C22×C413yes—
260C4×Dic59C2411yescharacteristic
261C4×Dic59C2413yes—
262#11745664—26no—
263#11745664—26no—
264C2×C59⋊C8—26no—
265C2×C59⋊C8—26no—
266C2×C59⋊C8C2411yescharacteristic
267C2×C59⋊C8C2413yes—
268C2×C59⋊C8C2413yes—
269C2×C59⋊C8C2411yescharacteristic
270#11745659—26no—
271#11745659—22no—
272#11745659—26no—
273#11745659—26no—
274C8×D59—212no—
275C23×C59—26no—
276C23×C59—43no—
277C23×C59—43no—
278C23×C59C23×C411yescharacteristic
279C23×C59C23×C413yes—
280C23×C59C23×C413yes—
281C22×D59—26no—
282C22×D59—43no—
283C22×D59—43no—
284C22×D59C23×C411yescharacteristic
285C22×D59C23×C413yes—
286Q8×C59—26no—
287Q8×C59C4×D414yes—
288D4×C59—212no—
289D4×C59—26no—
290D4×C59C4×D4112yes—
291C2×C4×C59—26no—
292C2×C4×C59—26no—
293C2×C4×C59—26no—
294C2×C4×C59—23no—
295C2×C4×C59—21no—
296C2×C4×C59—21no—
297C2×C4×C59—23no—
298C2×C4×C59C23×C411yescharacteristic
299C2×C4×C59C23×C413yes—
300C2×C4×C59C23×C413yes—
301C2×C4×C59C22×D416yes—
302C2×C4×C59C2×#4116yes—
303C2×C4×C59C2511yescharacteristic
304C22⋊D59—212no—
305C22⋊D59—22no—
306C22⋊D59—26no—
307C22⋊D59—43no—
308C22⋊D59—43no—
309C22⋊D59—46no—
310C2×Dic59—26no—
311C2×Dic59—26no—
312C2×Dic59—43no—
313C2×Dic59C23×C411yescharacteristic
314C2×Dic59C23×C413yes—
315C2×Dic59C23×C413yes—
316C2×Dic59C23×C413yes—
317C2×Dic59C23×C411yescharacteristic
318C2×Dic59C23×C411yescharacteristic
319D236—26no—
320C4×D59—26no—
321C4×D59—26no—
322C4×D59—23no—
323C4×D59—21no—
324C4×D59—21no—
325C4×D59—23no—
326Dic118—26no—
327C8×C59—21no—
328C8×C59—23no—
329C8×C59C22×D416yes—
330C8×C59C22×D412yes—
331C59⋊C8—23no—
332C59⋊C8—21no—
333C59⋊C8—21no—
334C59⋊C8—23no—
335#60147—591nomaximal, Sylow
336C22×C59—23no—
337C22×C59—23no—
338C22×C59—21no—
339C22×C59—23no—
340C22×C59—21no—
341C22×C59—23no—
342C22×C59—23no—
343C22×C59—21no—
344C22×C59—86no—
345C22×C59C2×C4×D416yes—
346C22×C59C24×C411yescharacteristic
347C2×D59—21no—
348C2×D59—23no—
349C2×D59—21no—
350C2×D59—23no—
351C2×D59—23no—
352C2×D59—21no—
353C2×D59—86no—
354C4×C59—21no—
355C4×C59—23no—
356C4×C59C2×C4×D416yes—
357C4×C59C23×D411yescharacteristic
358C4×C59C22×#4111yescharacteristic
359Dic59—23no—
360Dic59—21no—
361Dic59—23no—
362Dic59—21no—
363Dic59—23no—
364Dic59#56812yescomplemented
365C2×#568—591no—
366C2×#568D5911yescharacteristic, complemented
367D4×#41—591no—
368#2935—593no—
369D4×M16—593no—
370#2933—593no—
371#2933—593no—
372#2931—593no—
373#2930—593no—
374#2930—593no—
375C2×#436—593no—
376#2906—591no—
377#2880—591no—
378#2880—591no—
379C4×#131—591no—
380C2×C59—26no—
381C2×C59—43no—
382C2×C59—41no—
383C2×C59C22×C4×D411yescharacteristic
384C2×C59C2×#56811yescharacteristic
385C2×C59#357311yescharacteristic
386D59—43no—
387D59—41no—
388C22×#41—591no—
389C22×#41C2×D5911yescharacteristic
390#568—28no—
391#568—1188no—
392C2×#131—591no—
393C2×#131—591no—
394C2×#131—593no—
395C2×#131—593no—
396C2×#131C2×D5911yescharacteristic
397C2×#131C2×D5911yescharacteristic
398C2×#131C2×D5913yescomplemented
399C2×#131C2×D5913yescomplemented
400C22×M16—593no—
401C22×M16—593no—
402C22×M16C2×D5913yescomplemented
403C22×M16C2×D5913yescomplemented
404#550—591no—
405D4×Q8—591no—
406#548—591no—
407#548—591no—
408#547—593no—
409#546—593no—
410#546—593no—
411D42—593no—
412#532—593no—
413#525—593no—
414#525—593no—
415C4×#41—591no—
416C2×C4×D4—593no—
417#436—591no—
418#436—593no—
419#436—593no—
420#436—593no—
421#436—593no—
422#436—593no—
423#436—593no—
424#436—593no—
425#436—596no—
426#435—596no—
427#435—596no—
428#435—596no—
429#435—596no—
430C8×D4—596no—
431C8×D4—596no—
432#424—593no—
433#424—593no—
434#423—593no—
435C2×C4⋊C8—593no—
436#408—593no—
437#408—593no—
438#408—593no—
439#408—593no—
440#407—593no—
441#407—593no—
442C2×C22⋊C8—593no—
443C2×C22⋊C8—593no—
444#405—593no—
445#405—593no—
446C4×M16—593no—
447C2×C4×C8—593no—
448C59#6014711yescharacteristic, complemented, Sylow
449C2×#41—24no—
450C2×#41—24no—
451C2×#41—591no—
452C2×#41—593no—
453C2×#41—593no—
454C2×#41—1184no—
455C2×#41—1184no—
456C2×#41C4×D5913yes—
457C2×#41C4×D5911yescharacteristic
458C2×#41C22×D5913yes—
459C2×#41C22×D5911yescharacteristic
460C22×Q8—591no—
461C22×Q8C4×D5911yescharacteristic
462C22×D4—593no—
463C22×D4—593no—
464C22×D4C4×D5913yes—
465C23×C4—593no—
466C23×C4C22×D5913yes—
467#131—24no—
468#131—212no—
469#131—212no—
470#131—1184no—
471#131—1184no—
472#131—11812no—
473#131—11812no—
474#131C22⋊D5918yescomplemented
475C2×M16—212no—
476C2×M16—212no—
477C2×M16—593no—
478C2×M16—593no—
479C2×M16—593no—
480C2×M16—591no—
481C2×M16—593no—
482C2×M16—593no—
483C2×M16—11812no—
484C2×M16—11812no—
485C2×M16C22×D5913yes—
486C2×M16C22×D5911yescharacteristic
487C2×M16C22×D5913yes—
488C2×M16C22×D5913yes—
489C2×M16C22×D5913yes—
490C2×M16C22×D5913yes—
491C22×C8—593no—
492C22×C8—593no—
493C22×C8—596no—
494C22×C8C22×D5913yes—
495C22×C8C22×D5916yes—
496C22×C8C22×D5913yes—
497C4⋊Q8—593no—
498#127—593no—
499#124—593no—
500#124—593no—
501#123—596no—
502#123—596no—
503C22⋊Q8—593no—
504C22⋊Q8—593no—
505C22⋊Q8—593no—
506C22⋊Q8—593no—
507#121—593no—
508#121—593no—
509#121—596no—
510#121—596no—
511#121—593no—
512#121—593no—
513#120—596no—
514#120—596no—
515C4×Q8—591no—
516C4×Q8—591no—
517C4×D4—593no—
518C4×D4—593no—
519C4×D4—593no—
520C4×D4—593no—
521C4×D4—593no—
522C4×D4—593no—
523C4×D4—591no—
524C4×D4—593no—
525C4×D4—593no—
526C4×D4—593no—
527C4×D4—596no—
528#117—593no—
529C2×C4⋊C4—593no—
530C2×C22⋊C4—593no—
531C2×C22⋊C4—593no—
532C2×C42—593no—
533C4⋊C8—591no—
534C4⋊C8—593no—
535C4⋊C8—593no—
536C4⋊C8—593no—
537C4⋊C8—596no—
538C22⋊C8—591no—
539C22⋊C8—593no—
540C22⋊C8—593no—
541C22⋊C8—593no—
542C22⋊C8—596no—
543C22⋊C8—591no—
544C22⋊C8—593no—
545C22⋊C8—593no—
546C22⋊C8—593no—
547C22⋊C8—596no—
548#97—596no—
549C4×C8—591no—
550C4×C8—593no—
551C4×C8—593no—
552C4×C8—593no—
553C24—593no—
554C24C2×C4×D5913yes—
555#41—24no—
556#41—212no—
557#41—26no—
558#41—26no—
559#41—1184no—
560#41—11812no—
561#41—1186no—
562#41—1186no—
563#41#1174568514yes—
564#41C2×C22⋊D5914yes—
565C2×Q8—24no—
566C2×Q8—593no—
567C2×Q8—1184no—
568C2×Q8C2×C4×D5913yes—
569C2×Q8C2×C4×D5911yescharacteristic
570C2×D4—212no—
571C2×D4—591no—
572C2×D4—593no—
573C2×D4—596no—
574C2×D4—593no—
575C2×D4—593no—
576C2×D4—596no—
577C2×D4—593no—
578C2×D4—11812no—
579C2×D4—2366no—
580C2×D4C2×C4×D5916yes—
581C2×D4C2×C4×D5913yes—
582C2×D4C2×C4×D5913yes—
583C22×C4—26no—
584C22×C4—26no—
585C22×C4—593no—
586C22×C4—593no—
587C22×C4—593no—
588C22×C4—593no—
589C22×C4—593no—
590C22×C4—593no—
591C22×C4—591no—
592C22×C4—1186no—
593C22×C4—1186no—
594C22×C4C2×C4×D5913yes—
595C22×C4C2×C4×D5913yes—
596C22×C4C2×C4×D5913yes—
597C22×C4C23×D5913yes—
598C22×C4C23×D5911yescharacteristic
599C22×C4C23×D5913yes—
600M16—26no—
601M16—26no—
602M16—22no—
603M16—26no—
604M16—26no—
605M16—1186no—
606M16—1186no—
607M16—1186no—
608M16—1182no—
609M16—1186no—
610M16—1186no—
611M16C2×C22⋊D59112yescomplemented
612C2×C8—26no—
613C2×C8—212no—
614C2×C8—591no—
615C2×C8—593no—
616C2×C8—591no—
617C2×C8—593no—
618C2×C8—1186no—
619C2×C8—1186no—
620C2×C8—11812no—
621C2×C8C2×C22⋊D59112yescomplemented
622C2×C8C23×D5911yescharacteristic
623C2×C8C23×D5913yes—
624C2×C8C23×D5911yescharacteristic
625C2×C8C23×D5913yes—
626C4⋊C4—591no—
627C4⋊C4—593no—
628C4⋊C4—593no—
629C4⋊C4—593no—
630C4⋊C4—593no—
631C4⋊C4—593no—
632C4⋊C4—596no—
633C22⋊C4—591no—
634C22⋊C4—593no—
635C22⋊C4—593no—
636C22⋊C4—593no—
637C22⋊C4—596no—
638C22⋊C4—596no—
639C22⋊C4—591no—
640C22⋊C4—593no—
641C22⋊C4—593no—
642C22⋊C4—593no—
643C22⋊C4—596no—
644C42—593no—
645C42—593no—
646C42—591no—
647C42—593no—
648C23—26no—
649C23—43no—
650C23—43no—
651C23—591no—
652C23—593no—
653C23—1186no—
654C23—2363no—
655C23—2363no—
656C23C22×C4×D5911yescharacteristic
657C23C22×C4×D5913yes—
658C23C22×C4×D5913yes—
659Q8—26no—
660Q8—1186no—
661Q8C4×C22⋊D5914yes—
662D4—212no—
663D4—26no—
664D4—1186no—
665D4—1182no—
666D4—11812no—
667D4—1186no—
668D4—2366no—
669D4—2363no—
670D4—2363no—
671D4C4×C22⋊D59112yes—
672C2×C4—26no—
673C2×C4—23no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—23no—
677C2×C4—26no—
678C2×C4—26no—
679C2×C4—591no—
680C2×C4—591no—
681C2×C4—593no—
682C2×C4—593no—
683C2×C4—591no—
684C2×C4—593no—
685C2×C4—1186no—
686C2×C4—1186no—
687C2×C4—1183no—
688C2×C4—1181no—
689C2×C4—1181no—
690C2×C4—1183no—
691C2×C4—1186no—
692C2×C4—1186no—
693C2×C4—2363no—
694C2×C4C22×C4×D5911yescharacteristic
695C2×C4C22×C4×D5913yes—
696C2×C4C22×C4×D5913yes—
697C2×C4C22×C22⋊D5916yes—
698C2×C4C2×#1174568516yes—
699C2×C4C24×D5911yescharacteristic
700C8—21no—
701C8—23no—
702C8—1183no—
703C8—1181no—
704C8—1181no—
705C8—1183no—
706C8C22×C22⋊D5916yes—
707C8C22×C22⋊D5912yes—
708C22—23no—
709C22—23no—
710C22—21no—
711C22—23no—
712C22—21no—
713C22—23no—
714C22—23no—
715C22—21no—
716C22—86no—
717C22—1181no—
718C22—1183no—
719C22—1181no—
720C22—1183no—
721C22—1183no—
722C22—1181no—
723C22—4726no—
724C22C2×C4×C22⋊D5916yes—
725C22C23×C4×D5911yescharacteristic
726C4—21no—
727C4—23no—
728C4—592no—
729C4—1181no—
730C4—1183no—
731C4—1183no—
732C4—1181no—
733C4—1183no—
734C4C2×C4×C22⋊D5916yes—
735C4C23×C22⋊D5911yescharacteristic
736C4C22×#1174568511yescharacteristic
737C2—26no—
738C2—41no—
739C2—43no—
740C2—2361no—
741C2—2363no—
742C2C22×C4×C22⋊D5911yescharacteristic
743C2#568×D5911yescharacteristic
744C2#2143880911yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D59
commutator, socleC22×C59C24×C4
FittingC2×C59×#568C2
prime radical#41×C22⋊D59C2
cosocleC2×C4×C59C25
hypercenterC2×#568D59
hypocenterC59#60147
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×#568

Complements

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

NH ≅ G/Ntype
1. C2×#16838167C2semidirect
3. #21432838C2semidirect
4. M16×C22⋊D59C2semidirect
5. #21432821C2semidirect
6. #21432818C2semidirect
7. #21432806C2semidirect
8. #21432799C2semidirect
9. #21432797C2semidirect
10. C2×#16837478C2semidirect
11. #21432662C2semidirect
12. #21432545C2semidirect
13. #21432543C2semidirect
14. #131×Dic59C2semidirect
15. C2×C59×#568C2semidirect
18. C2×#14273735C22semidirect
21. C2×#14273733C22semidirect
22. C22×#11745659C22semidirect
23. C2×M16×D59C22semidirect
39. #16837478C22semidirect
40. #16837478C22semidirect
41. #16837478C22semidirect
42. #16837478C22semidirect
43. #16837478C22semidirect
44. #16837478C22semidirect
45. #16837478C22semidirect
46. #16837473C22semidirect
47. #16837473C22semidirect
48. #16837471C22semidirect
49. #16837471C22semidirect
50. C8×C22⋊D59C22semidirect
51. C8×C22⋊D59C22semidirect
52. #16837430C22semidirect
53. #16837428C22semidirect
54. #16837425C22semidirect
55. C2×Dic59⋊C8C22semidirect
56. #16837370C22semidirect
57. #16837369C22semidirect
58. #16837369C22semidirect
59. #16837368C22semidirect
60. #16837366C22semidirect
61. #16837365C22semidirect
62. C2×C22⋊(C59⋊C8)C22semidirect
63. C2×(C2×D59)⋊C8C22semidirect
64. #16837360C22semidirect
65. #16837357C22semidirect
66. M16×Dic59C22semidirect
67. C2×C8×Dic59C22semidirect
72. C2×#131×C59C22semidirect
73. C2×#131×C59C22semidirect
74. C22×M16×C59C22semidirect
75. C22×M16×C59C22semidirect
168. #131×C59D4semidirect
232. M16×C59C2×D4semidirect
235. C2×C8×C59C2×D4semidirect
364. Dic59#568semidirect
366. C2×#568D59semidirect
398. C2×#131C2×D59semidirect
399. C2×#131C2×D59semidirect
402. C22×M16C2×D59semidirect
403. C22×M16C2×D59semidirect
448. C59#60147semidirect
474. #131C22⋊D59semidirect
611. M16C2×C22⋊D59semidirect
621. C2×C8C2×C22⋊D59semidirect

Maximal subgroups

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

subgroupindex
C2×#168381672
#41×C22⋊D592
#214328382
M16×C22⋊D592
#214328212
#214328182
#214328062
#214327992
#214327972
C2×#168374782
#214326622
#214325452
#214325432
#131×Dic592
C2×C59×#5682
#6014759