Finite Group Databasebeta

← D59×#3497 #29496858

Subgroups — D59×#3497 #29496858

Order 15104.

11210 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×2−1+4×D59C212yesmaximal, complemented
2#21437867C211yesmaximal, characteristic, complemented
3#21437866C214yesmaximal, complemented
4#21437865C216yesmaximal, complemented
5#21437864C218yesmaximal, complemented
6#21437863C212yesmaximal, complemented
7#21437862C216yesmaximal, complemented
8#21437861C214yesmaximal, complemented
9#550×D59C214yesmaximal, complemented
10D4×Q8×D59C214yesmaximal, complemented
11#548×D59C218yesmaximal, complemented
12#537×D59C216yesmaximal, complemented
13#532×D59C216yesmaximal, complemented
14C2×C4×Q8×D59C211yesmaximal, characteristic, complemented
15C59×#3497C211yesmaximal, characteristic, complemented
16C2×#14273775C2212yescomplemented
17C2×#14273775C2218yescomplemented
18C2×#14273774C2218yescomplemented
19C2×#14273774C22112yescomplemented
202−1+4×D59—232no—
21C2×#41×D59C2218yes—
22C2×#41×D59C22112yes—
23C22×Q8×D59C2218yes—
24C22×Q8×D59C2211yescharacteristic
25#16838074C2214yescomplemented
26#16838073C22112yescomplemented
27#16838072C22112yescomplemented
28#16838071C2218yescomplemented
29#16838070C22124yescomplemented
30Q8×D236C2214yescomplemented
31D4×Dic118C22112yescomplemented
32#16838067C22112yescomplemented
33Q8×C22⋊D59C2218yescomplemented
34#16838065C22124yescomplemented
35#16838064C2218yescomplemented
36#16838063C2218yescomplemented
37#16838062C22124yescomplemented
38#16838061C22124yescomplemented
39#16838060C22124yescomplemented
40#16838059C2218yescomplemented
41#16838058C22124yescomplemented
42#16837983C2216yescomplemented
43#16837982C22124yescomplemented
44#16837981C22124yescomplemented
45#16837980C22112yescomplemented
46#16837979C22124yescomplemented
47#16837953C2216yescomplemented
48#16837952C2216yescomplemented
49#16837951C22112yescomplemented
50#16837950C2216yescomplemented
51#16837949C22112yescomplemented
52#16837949C22112yescomplemented
53#16837948C22112yescomplemented
54#16837947C22112yescomplemented
55#16837947C22112yescomplemented
56C4⋊Q8×D59C2216yes—
57#127×D59C2216yes—
58#124×D59C22112yes—
59C22⋊Q8×D59C22124yes—
60#121×D59C22124yes—
61#121×D59C2214yes—
62#121×D59C22112yes—
63C2×Q8×Dic59C2211yescharacteristic, complemented
64C2×C4×Dic118C2213yescomplemented
65C2×#14273692C2213yescomplemented
66C4×Q8×D59C2214yes—
67C4×Q8×D59C2214yes—
68C4×Q8×D59C2214yescomplemented
69C4×Q8×D59C2214yescomplemented
70C4×D4×D59C22112yes—
71C4×D4×D59C22112yes—
72C2×C4⋊C4×D59C2213yes—
73C2×C42×D59C2213yes—
74C2×2−1+4×C59C2212yescomplemented
75C59×#550C2214yescomplemented
76D4×Q8×C59C2214yescomplemented
77C59×#548C2218yescomplemented
78C59×#537C2216yescomplemented
79C59×#532C2216yescomplemented
80C2×C4×Q8×C59C2211yescharacteristic, complemented
81#14273775—216no—
82#14273775—264no—
83#14273774—264no—
84#14273774—296no—
85C2×#11745689C23112yes—
86C2×#11745689C2318yes—
87C2×#11745685C23112yes—
88C2×#11745685C23124yes—
89C2×#11745685C23124yes—
90C2×#11745687C23124yes—
91C2×#11745687C23112yes—
92C2×#11745687C23124yes—
93#41×D59—264no—
94#41×D59—296no—
95C22×Dic118C23124yes—
96C22×Dic118C2313yes—
97C2×Q8×D59—264no—
98C2×Q8×D59D4116yescomplemented
99C2×Q8×D59C23112yes—
100C2×Q8×D59C2318yes—
101C2×Q8×D59C23124yes—
102C2×Q8×D59C2314yes—
103C2×Q8×D59C2314yes—
104C2×D4×D59C2318yes—
105C2×D4×D59C23112yes—
106C2×D4×D59C2314yes—
107C2×D4×D59C23112yes—
108C22×C4×D59C2311yescharacteristic
109C22×C4×D59C23124yes—
110C22×C4×D59C2313yes—
111C22×C4×D59C2313yes—
112#14273727C2316yes—
113#14273726C23112yes—
114#14273726C23112yes—
115#14273725C23112yes—
116#14273724C2316yes—
117#14273723C23112yes—
118#14273723C23112yes—
119#14273723C23112yes—
120#14273716C23112yes—
121#14273715C23112yes—
122#14273714C23112yes—
123#14273713C23124yes—
124#14273713C23124yes—
125#14273707C23124yes—
126#14273706C23124yes—
127#14273705C23148yes—
128#14273704C23148yes—
129#14273703C23124yes—
130#14273702C2314yes—
131#14273702C23112yes—
132#14273702C23124yes—
133#14273701C2314yes—
134#14273701C23112yes—
135#14273701C23124yes—
136#14273700C2318yes—
137#14273700C23124yes—
138#14273700C23148yes—
139#14273699C2318yes—
140#14273699C23124yes—
141#14273699C23148yes—
142#14273698C2314yes—
143#14273698C23112yes—
144#14273698C23124yes—
145Q8×Dic59C2314yes—
146Q8×Dic59C2314yes—
147C4×Dic118C23112yes—
148C4×Dic118C23112yes—
149#14273692C23112yes—
150#14273692C23112yes—
151C4×D236C23112yes—
152C4×D236C23112yes—
153D4×Dic59C23112yes—
154D4×Dic59C23112yes—
155#14273689C23112yes—
156#14273689C23112yes—
157C4×C22⋊D59C23124yes—
158C4×C22⋊D59C23124yes—
159(C22⋊D59)⋊C4C23124yes—
160(C22⋊D59)⋊C4C23124yes—
161C2×C4⋊Dic59C2313yes—
162C2×Dic59⋊C4C2316yes—
163C4⋊C4×D59C23112yes—
164C4⋊C4×D59C23112yes—
165C4⋊C4×D59C2314yes—
166C4⋊C4×D59C23112yes—
167C22⋊C4×D59C23124yes—
168C22⋊C4×D59C2318yes—
169C2×C4×Dic59C2313yes—
170C2×C4×Dic59C2313yes—
171C2×C4×Dic59C2313yes—
172C42×D59C2316yes—
173C42×D59C2316yes—
174C42×D59C2316yes—
175C42×D59C2316yes—
1762−1+4×C59—216no—
177C2×#41×C59C23112yes—
178C2×#41×C59C2318yes—
179C22×Q8×C59C2318yes—
180C22×Q8×C59C2311yescharacteristic
181C4⋊Q8×C59C2316yes—
182#127×C59C2316yes—
183#124×C59C23112yes—
184C22⋊Q8×C59C23124yes—
185#121×C59C2314yes—
186#121×C59C23112yes—
187#121×C59C23124yes—
188C4×Q8×C59C2314yes—
189C4×Q8×C59C2314yes—
190C4×D4×C59C23112yes—
191C4×D4×C59C23112yes—
192C2×C4⋊C4×C59C2313yes—
193C2×C42×C59C2313yes—
194C23×D59C2418yes—
195C23×D59C2411yescharacteristic
196#41×C59—232no—
197#41×C59—248no—
198C2×Q8×C59—232no—
199C2×Q8×C59C2×D418yescomplemented
200C2×Q8×C59C24112yes—
201C2×Q8×C59C2414yes—
202C2×D4×C59C2414yes—
203C2×D4×C59C2418yes—
204C2×D4×C59C24112yes—
205C2×D4×C59C24112yes—
206C22×C4×C59C2411yescharacteristic
207C22×C4×C59C24124yes—
208C22×C4×C59C2413yes—
209C22×C4×C59C2413yes—
210C2×C22⋊D59C2418yes—
211C2×C22⋊D59C2418yes—
212C2×C22⋊D59C2418yes—
213C2×C22⋊D59C24124yes—
214C2×C22⋊D59C24124yes—
215C22×Dic59C2411yescharacteristic
216C22×Dic59C24124yes—
217C22×Dic59C2413yes—
218C22×Dic59C2413yes—
219#11745689—232no—
220#11745689—248no—
221Q8×D59—232no—
222Q8×D59—248no—
223Q8×D59—296no—
224Q8×D59C2×D4132yes—
225Q8×D59C2×D4132yescomplemented
226#11745687—296no—
227#11745687—248no—
228#11745687—296no—
229D4×D59—232no—
230D4×D59—248no—
231D4×D59—216no—
232D4×D59—424no—
233#11745685—248no—
234#11745685—296no—
235#11745685—296no—
236C2×D236C2414yes—
237C2×D236C2418yes—
238C2×D236C24112yes—
239C2×D236C24112yes—
240C2×C4×D59—296no—
241C2×C4×D59—24no—
242C2×C4×D59—46no—
243C2×C4×D59C2×D4124yes—
244C2×C4×D59C2411yescharacteristic
245C2×C4×D59C2411yescharacteristic
246C2×C4×D59C2411yescharacteristic
247C2×C4×D59C2416yes—
248C2×C4×D59C2418yes—
249C2×C4×D59C24124yes—
250C2×C4×D59C24124yes—
251C2×C4×D59C2416yes—
252C2×C4×D59C2416yes—
253C2×C4×D59C2416yes—
254C2×C4×D59C2411yescharacteristic
255C2×Dic118—296no—
256C2×Dic118C2×D4124yescomplemented
257C2×Dic118C24124yes—
258C2×Dic118C24112yes—
259C2×Dic118C24112yes—
260C4⋊C4×C59C24112yes—
261C4⋊C4×C59C2414yes—
262C4⋊C4×C59C24112yes—
263C22⋊C4×C59C2418yes—
264C22⋊C4×C59C24124yes—
265C42×C59C2416yes—
266C42×C59C2416yes—
267C22⋊Dic59C2418yes—
268C22⋊Dic59C24124yes—
269(C2×D59)⋊C4C2418yes—
270(C2×D59)⋊C4C24124yes—
271(C2×D59)⋊C4C2418yes—
272(C2×D59)⋊C4C24124yes—
273C4⋊Dic59C24112yes—
274C4⋊Dic59C2414yes—
275C4⋊Dic59C24112yes—
276Dic59⋊C4C24124yes—
277Dic59⋊C4C2418yes—
278Dic59⋊C4C24124yes—
279C4×Dic59C2416yes—
280C4×Dic59C2416yes—
281C4×Dic59C2416yes—
282C4×Dic59C2416yes—
283C4×Dic59C2416yes—
284C4×Dic59C2416yes—
285C23×C59C2518yes—
286C23×C59C2511yescharacteristic
287C22×D59—22no—
288C22×D59—22no—
289C22×D59—216no—
290C22×D59—216no—
291C22×D59—216no—
292C22×D59C22×D414yes—
293C22×D59C2518yes—
294C22×D59C2511yescharacteristic
295C22×D59C2511yescharacteristic
296Q8×C59—224no—
297Q8×C59C22×D4116yes—
298D4×C59—216no—
299D4×C59—224no—
300D4×C59—28no—
301D4×C59—412no—
302C2×C4×C59—248no—
303C2×C4×C59—22no—
304C2×C4×C59—43no—
305C2×C4×C59C22×D4112yes—
306C2×C4×C59C2511yescharacteristic
307C2×C4×C59C2516yes—
308C2×C4×C59C2518yes—
309C2×C4×C59C2516yes—
310C2×C4×C59C2511yescharacteristic
311C22⋊D59—216no—
312C22⋊D59—216no—
313C22⋊D59—248no—
314C22⋊D59—216no—
315C22⋊D59—424no—
316C2×Dic59—248no—
317C2×Dic59—22no—
318C2×Dic59—43no—
319C2×Dic59C22×D4112yes—
320C2×Dic59C2511yescharacteristic
321C2×Dic59C2516yes—
322C2×Dic59C2518yes—
323C2×Dic59C2516yes—
324C2×Dic59C2511yescharacteristic
325D236—216no—
326D236—224no—
327D236—28no—
328D236—412no—
329C4×D59—216no—
330C4×D59—22no—
331C4×D59—212no—
332C4×D59—248no—
333C4×D59—22no—
334C4×D59—248no—
335C4×D59—22no—
336C4×D59—46no—
337C4×D59C22×D4124yes—
338C4×D59C22×D4124yes—
339C4×D592−1+414yescomplemented
340Dic118—224no—
341Dic118—248no—
342Dic118C22×D4148yes—
343C2×#3497—591nomaximal, Sylow
344C22×C59—21no—
345C22×C59—21no—
346C22×C59—28no—
347C22×C59—28no—
348C22×C59—28no—
349C22×C59C23×D412yes—
350C22×C59C2611yescharacteristic
351C2×D59—21no—
352C2×D59—21no—
353C2×D59—28no—
354C2×D59—28no—
355C2×D59—28no—
356C2×D59—28no—
357C2×D59—432no—
358C2×D59C23×D412yes—
359C2×D59C23×D412yes—
360C2×D59C2×2−1+412yes—
361C2×D59#58512yes—
362C4×C59—28no—
363C4×C59—21no—
364C4×C59—26no—
365C4×C59C23×D4112yes—
366C4×C59C2×2−1+412yescomplemented
367Dic59—28no—
368Dic59—21no—
369Dic59—26no—
370Dic59C23×D4112yes—
371Dic59C2×2−1+412yescomplemented
372C22×2−1+4—592no—
373#3497—592no—
374#3497—594no—
375#3497—594no—
376#3497—598no—
377#3497—596no—
378#3497—596no—
379#3497—591no—
380#3497D5911yescharacteristic, direct product factor
381C2×#550—594no—
382C2×D4×Q8—594no—
383C2×#548—598no—
384C2×#537—596no—
385C2×#532—596no—
386C22×C4×Q8—591no—
387C2×C59—22no—
388C2×C59—48no—
389C2×C59C24×D411yescharacteristic
390C2×C59C22×2−1+411yescharacteristic
391C2×C59C2×#58511yescharacteristic
392D59—22no—
393D59—48no—
394D59#349714yesdirect product factor
395C2×2−1+4—598no—
396C2×2−1+4—5912no—
397C2×2−1+4—598no—
398C2×2−1+4—592no—
399C2×2−1+4—11832no—
400C2×2−1+4C2×D5912yescomplemented
401C22×#41—5912no—
402C22×#41—598no—
403C23×Q8—591no—
404C23×Q8—598no—
405#550—598no—
406#550—5912no—
407#550—5924no—
408#550—594no—
409#550—5912no—
410#550C2×D5914yescomplemented
411D4×Q8—598no—
412D4×Q8—5912no—
413D4×Q8—5924no—
414D4×Q8—594no—
415D4×Q8—5912no—
416D4×Q8C2×D5914yescomplemented
417#548—598no—
418#548—598no—
419#548—5924no—
420#548—5924no—
421#548—5924no—
422#548—598no—
423#548—5924no—
424#548C2×D5918yescomplemented
425#537—5912no—
426#537—5924no—
427#537—5924no—
428#537—5924no—
429#537—596no—
430#537C2×D5916yescomplemented
431#532—5912no—
432#532—596no—
433#532—596no—
434#532—5912no—
435#532—5912no—
436#532—5912no—
437#532—5912no—
438#532—5912no—
439#532—596no—
440#532C2×D5916yescomplemented
441C2×C4⋊Q8—596no—
442C2×#127—596no—
443C2×#124—5912no—
444C2×C22⋊Q8—5924no—
445C2×#121—594no—
446C2×#121—5912no—
447C2×#121—5924no—
448C2×C4×Q8—591no—
449C2×C4×Q8—594no—
450C2×C4×Q8—594no—
451C2×C4×Q8—594no—
452C2×C4×Q8—594no—
453C2×C4×Q8—593no—
454C2×C4×Q8—593no—
455C2×C4×Q8C2×D5911yescharacteristic, complemented
456C2×C4×D4—5912no—
457C2×C4×D4—5912no—
458C22×C4⋊C4—593no—
459C22×C42—593no—
460C59C2×#349711yescharacteristic, complemented, Sylow
4612−1+4—216no—
4622−1+4—11864no—
4632−1+4—11864no—
4642−1+4—11896no—
4652−1+4—11816no—
466C2×#41—5912no—
467C2×#41—598no—
468C2×#41—5924no—
469C2×#41—5912no—
470C2×#41—5924no—
471C2×#41—5924no—
472C2×#41—5912no—
473C2×#41—5924no—
474C2×#41—11896no—
475C2×#41—11864no—
476C2×#41C22×D59112yes—
477C2×#41C22×D5918yes—
478C22×Q8—5916no—
479C22×Q8—594no—
480C22×Q8—594no—
481C22×Q8—5912no—
482C22×Q8—5924no—
483C22×Q8—598no—
484C22×Q8—593no—
485C22×Q8—5924no—
486C22×Q8—11864no—
487C22×Q8C22×D5918yes—
488C22×Q8C22×D5911yescharacteristic
489C22×D4—594no—
490C22×D4—598no—
491C22×D4—5912no—
492C22×D4—5912no—
493C23×C4—593no—
494C23×C4—5924no—
495C23×C4—591no—
496C23×C4—593no—
497C4⋊Q8—5912no—
498C4⋊Q8—5912no—
499C4⋊Q8—5912no—
500C4⋊Q8—596no—
501C4⋊Q8C22×D5916yes—
502#127—5912no—
503#127—5912no—
504#127—5912no—
505#127—596no—
506#127C22×D5916yes—
507#124—5912no—
508#124—5912no—
509#124—5924no—
510#124—5924no—
511#124—5912no—
512#124C22×D59112yes—
513C22⋊Q8—5924no—
514C22⋊Q8—5924no—
515C22⋊Q8—5948no—
516C22⋊Q8—5924no—
517C22⋊Q8—5948no—
518C22⋊Q8C22×D59124yes—
519#121—594no—
520#121—598no—
521#121—5912no—
522#121—5924no—
523#121—5924no—
524#121—5948no—
525#121—594no—
526#121—5912no—
527#121—5924no—
528#121—594no—
529#121—5912no—
530#121—5924no—
531#121—598no—
532#121—5924no—
533#121—5948no—
534#121C22×D5914yes—
535#121C22×D59112yes—
536#121C22×D59124yes—
537C4×Q8—594no—
538C4×Q8—594no—
539C4×Q8—5912no—
540C4×Q8—5912no—
541C4×Q8—5912no—
542C4×Q8—5912no—
543C4×Q8C22×D5914yes—
544C4×Q8C22×D5914yes—
545C4×D4—5912no—
546C4×D4—5912no—
547C4×D4—5924no—
548C4×D4—5924no—
549C4×D4—5912no—
550C4×D4—5912no—
551C4×D4—5924no—
552C4×D4—5924no—
553C4×D4—5912no—
554C4×D4—5912no—
555C4×D4C22×D59112yes—
556C4×D4C22×D59112yes—
557C2×C4⋊C4—596no—
558C2×C4⋊C4—593no—
559C2×C4⋊C4—5912no—
560C2×C4⋊C4—5912no—
561C2×C4⋊C4—594no—
562C2×C4⋊C4—5912no—
563C2×C4⋊C4C22×D5913yes—
564C2×C22⋊C4—598no—
565C2×C22⋊C4—5924no—
566C2×C42—593no—
567C2×C42—593no—
568C2×C42—593no—
569C2×C42—596no—
570C2×C42—596no—
571C2×C42—596no—
572C2×C42—596no—
573C2×C42C22×D5913yes—
574C24—591no—
575C24—598no—
576#41—232no—
577#41—248no—
578#41—11896no—
579#41—11896no—
580#41—11896no—
581#41—11848no—
582#41—11848no—
583#41—11896no—
584#41—11832no—
585#41—11848no—
586C2×Q8—232no—
587C2×Q8—5932no—
588C2×Q8—5932no—
589C2×Q8—5924no—
590C2×Q8—5912no—
591C2×Q8—5924no—
592C2×Q8—5912no—
593C2×Q8—11896no—
594C2×Q8—11848no—
595C2×Q8—11896no—
596C2×Q8—11832no—
597C2×Q8D4×D5918yescomplemented
598C2×Q8C23×D59112yes—
599C2×Q8C23×D5914yes—
600C2×D4—598no—
601C2×D4—598no—
602C2×D4—598no—
603C2×D4—5924no—
604C2×D4—5924no—
605C2×D4—594no—
606C2×D4—598no—
607C2×D4—5912no—
608C2×D4—5912no—
609C2×D4—11848no—
610C2×D4—11816no—
611C2×D4—11832no—
612C2×D4—23624no—
613C2×D4C23×D5914yes—
614C2×D4C23×D5918yes—
615C2×D4C23×D59112yes—
616C2×D4C23×D59112yes—
617C22×C4—593no—
618C22×C4—5924no—
619C22×C4—591no—
620C22×C4—596no—
621C22×C4—596no—
622C22×C4—591no—
623C22×C4—5924no—
624C22×C4—593no—
625C22×C4—591no—
626C22×C4—591no—
627C22×C4—591no—
628C22×C4—596no—
629C22×C4—598no—
630C22×C4—5924no—
631C22×C4—5924no—
632C22×C4—596no—
633C22×C4—11896no—
634C22×C4—1184no—
635C22×C4—2366no—
636C22×C4C23×D5911yescharacteristic
637C22×C4C23×D59124yes—
638C22×C4C23×D5913yes—
639C22×C4C23×D5913yes—
640C4⋊C4—5924no—
641C4⋊C4—5912no—
642C4⋊C4—598no—
643C4⋊C4—594no—
644C4⋊C4—5924no—
645C4⋊C4—5912no—
646C4⋊C4C23×D59112yes—
647C4⋊C4C23×D5914yes—
648C4⋊C4C23×D59112yes—
649C22⋊C4—598no—
650C22⋊C4—5924no—
651C22⋊C4—598no—
652C22⋊C4—598no—
653C22⋊C4—5924no—
654C22⋊C4—5924no—
655C22⋊C4C23×D5918yes—
656C22⋊C4C23×D59124yes—
657C42—596no—
658C42—596no—
659C42—596no—
660C42—596no—
661C42—596no—
662C42—596no—
663C42C23×D5916yes—
664C42C23×D5916yes—
665C23—591no—
666C23—594no—
667C23—591no—
668C23—598no—
669C23—1182no—
670C23—1182no—
671C23—11816no—
672C23—11816no—
673C23—11816no—
674C23C24×D5918yes—
675C23C24×D5911yescharacteristic
676Q8—224no—
677Q8—5948no—
678Q8—11848no—
679Q8—11824no—
680Q8C2×D4×D59116yes—
681D4—216no—
682D4—224no—
683D4—28no—
684D4—412no—
685D4—11816no—
686D4—11816no—
687D4—11848no—
688D4—11816no—
689D4—11816no—
690D4—11824no—
691D4—1188no—
692D4—23612no—
693D4—23624no—
694C2×C4—248no—
695C2×C4—22no—
696C2×C4—43no—
697C2×C4—5912no—
698C2×C4—591no—
699C2×C4—596no—
700C2×C4—5924no—
701C2×C4—5924no—
702C2×C4—594no—
703C2×C4—591no—
704C2×C4—596no—
705C2×C4—598no—
706C2×C4—1182no—
707C2×C4—11848no—
708C2×C4—1182no—
709C2×C4—11816no—
710C2×C4—11812no—
711C2×C4—1182no—
712C2×C4—11848no—
713C2×C4—11848no—
714C2×C4—1182no—
715C2×C4—2366no—
716C2×C4—2363no—
717C2×C4C2×D4×D59112yes—
718C2×C4C24×D5911yescharacteristic
719C2×C4C24×D5916yes—
720C2×C4C24×D5918yes—
721C2×C4C24×D5916yes—
722C2×C4C24×D5911yescharacteristic
723C22—21no—
724C22—21no—
725C22—28no—
726C22—28no—
727C22—28no—
728C22—592no—
729C22—592no—
730C22—592no—
731C22—592no—
732C22—1188no—
733C22—1181no—
734C22—1181no—
735C22—1188no—
736C22—1188no—
737C22—1188no—
738C22—23632no—
739C22C22×D4×D5912yes—
740C22C25×D5911yescharacteristic
741C4—28no—
742C4—21no—
743C4—26no—
744C4—5912no—
745C4—592no—
746C4—1188no—
747C4—1181no—
748C4—1186no—
749C4C22×D4×D59112yes—
750C42−1+4×D5912yescomplemented
751C2—22no—
752C2—48no—
753C2—594no—
754C2—1182no—
755C2—2368no—
756C2C23×D4×D5911yescharacteristic
757C2C2×2−1+4×D5911yescharacteristic
758C2#585×D5911yescharacteristic
subgroupG/H
center, FrattiniC22C25×D59
commutator, socle, cosocleC22×C59C26
FittingC59×#3497C2
hypercenter#3497D59
hypocenterC59C2×#3497
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ #3497

Complements

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

NH ≅ G/Ntype
1. C2×2−1+4×D59C2semidirect
2. #21437867C2semidirect
3. #21437866C2semidirect
4. #21437865C2semidirect
5. #21437864C2semidirect
6. #21437863C2semidirect
7. #21437862C2semidirect
8. #21437861C2semidirect
9. #550×D59C2semidirect
10. D4×Q8×D59C2semidirect
11. #548×D59C2semidirect
12. #537×D59C2semidirect
13. #532×D59C2semidirect
14. C2×C4×Q8×D59C2semidirect
15. C59×#3497C2semidirect
16. C2×#14273775C22semidirect
17. C2×#14273775C22semidirect
18. C2×#14273774C22semidirect
19. C2×#14273774C22semidirect
25. #16838074C22semidirect
26. #16838073C22semidirect
27. #16838072C22semidirect
28. #16838071C22semidirect
29. #16838070C22semidirect
30. Q8×D236C22semidirect
31. D4×Dic118C22semidirect
32. #16838067C22semidirect
33. Q8×C22⋊D59C22semidirect
34. #16838065C22semidirect
35. #16838064C22semidirect
36. #16838063C22semidirect
37. #16838062C22semidirect
38. #16838061C22semidirect
39. #16838060C22semidirect
40. #16838059C22semidirect
41. #16838058C22semidirect
42. #16837983C22semidirect
43. #16837982C22semidirect
44. #16837981C22semidirect
45. #16837980C22semidirect
46. #16837979C22semidirect
47. #16837953C22semidirect
48. #16837952C22semidirect
49. #16837951C22semidirect
50. #16837950C22semidirect
51. #16837949C22semidirect
52. #16837949C22semidirect
53. #16837948C22semidirect
54. #16837947C22semidirect
55. #16837947C22semidirect
63. C2×Q8×Dic59C22semidirect
64. C2×C4×Dic118C22semidirect
65. C2×#14273692C22semidirect
68. C4×Q8×D59C22semidirect
69. C4×Q8×D59C22semidirect
74. C2×2−1+4×C59C22semidirect
75. C59×#550C22semidirect
76. D4×Q8×C59C22semidirect
77. C59×#548C22semidirect
78. C59×#537C22semidirect
79. C59×#532C22semidirect
80. C2×C4×Q8×C59C22semidirect
98. C2×Q8×D59D4semidirect
199. C2×Q8×C59C2×D4semidirect
225. Q8×D59C2×D4semidirect
256. C2×Dic118C2×D4semidirect
339. C4×D592−1+4semidirect
366. C4×C59C2×2−1+4semidirect
371. Dic59C2×2−1+4semidirect
380. #3497D59direct (N × H)
394. D59#3497direct (N × H)
400. C2×2−1+4C2×D59semidirect
410. #550C2×D59semidirect
416. D4×Q8C2×D59semidirect
424. #548C2×D59semidirect
430. #537C2×D59semidirect
440. #532C2×D59semidirect
455. C2×C4×Q8C2×D59semidirect
460. C59C2×#3497semidirect
597. C2×Q8D4×D59semidirect
750. C42−1+4×D59semidirect

Maximal subgroups

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

subgroupindex
C2×2−1+4×D592
#214378672
#214378662
#214378652
#214378642
#214378632
#214378622
#214378612
#550×D592
D4×Q8×D592
#548×D592
#537×D592
#532×D592
C2×C4×Q8×D592
C59×#34972
C2×#349759