Finite Group Databasebeta

← #28752136

Subgroups — #28752136

Order 15104.

2766 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837966C211yesmaximal, characteristic
2#21427271C212yesmaximal, complemented
3#21427233C212yesmaximal, complemented
4#21427159C212yesmaximal, complemented
5#21427134C212yesmaximal, complemented
6#21427112C212yesmaximal, complemented
7#21427077C212yesmaximal, complemented
8#21426991C212yesmaximal, complemented
9#21426916C212yesmaximal, complemented
10#21426908C214yesmaximal, complemented
11#21426785C212yesmaximal, complemented
12#21426752C214yesmaximal, complemented
13#21426602C212yesmaximal, complemented
14#21426587C211yesmaximal, characteristic, complemented
15C59×#2311C211yesmaximal, characteristic, complemented
16C23×D236C2211yescharacteristic
17#16837966C4116yescomplemented
18C2×#14273723C2212yes—
19C2×#14273716C2212yes—
20C2×#14273701C2212yes—
21C2×#14273701C2212yes—
22C2×#14273695C2212yes—
23C2×#14273695C2212yes—
24C2×#14273689C2212yes—
25C2×#14273689C2212yes—
26C2×C4×C22⋊D59C2214yescomplemented
27C2×(C22⋊D59)⋊C4C2214yescomplemented
28C2×#14273686C2211yescharacteristic
29C2×#14273686C2211yescharacteristic, complemented
30C2×C22⋊C4×D59C2214yes—
31C22×C4×Dic59C2211yescharacteristic, complemented
32#16837309C2212yescomplemented
33#16837305C2212yes—
34#16837303C2212yes—
35#16837303C2212yes—
36#16837302C2214yescomplemented
37#16837302C2214yescomplemented
38#16837298C2212yescomplemented
39#16837298C2212yescomplemented
40#16837294C2214yescomplemented
41#16837293C2214yescomplemented
42#16837292C2214yescomplemented
43#16837291C2214yescomplemented
44#16837290C2214yes—
45#16837290C2214yes—
46#16837282C2211yescharacteristic
47#16837282C2211yescharacteristic
48#16837282C2211yescharacteristic, complemented
49#16837282C2211yescharacteristic, complemented
50#16837281C2214yescomplemented
51#16837280C2214yes—
52#16837280C2214yes—
53#16837279C2214yescomplemented
54#16837278C2214yescomplemented
55#16837278C2214yescomplemented
56#16837276C2214yescomplemented
57#16837273C2214yescomplemented
58#16837269C2214yescomplemented
59#16837257C2214yes—
60C4⋊C4×Dic59C2212yescomplemented
61C4⋊C4×Dic59C2212yescomplemented
62#16837253C2214yescomplemented
63C4×(C2×D59)⋊C4C2214yescomplemented
64C4×C22⋊Dic59C2212yes—
65C4×C22⋊Dic59C2212yescomplemented
66#16837249C2214yescomplemented
67C22×#41×C59C2211yescharacteristic
68C2×#117×C59C2211yescharacteristic, complemented
69C22×C4⋊C4×C59C2211yescharacteristic, complemented
70C59×#391C2212yescomplemented
71C59×#390C2212yes—
72C59×#386C2212yes—
73C59×#386C2212yescomplemented
74C59×#380C2212yes—
75C59×#380C2212yescomplemented
76C24×D59C2312yes—
77C22×D236—42no—
78C22×D236—42no—
79C22×D236C2×C418yescomplemented
80C22×D236C2312yes—
81C22×D236C2312yes—
82C22×C22⋊D59C2314yes—
83C22×C22⋊D59C2314yes—
84C23×Dic59C2311yescharacteristic
85C23×Dic59C2311yescharacteristic
86C22×C4×D59C2314yes—
87C22×C4×D59C2314yes—
88#14273723C2×C4116yescomplemented
89#14273716C2×C4116yescomplemented
90#14273701C2×C4116yescomplemented
91#14273701C2×C4116yescomplemented
92#14273695C2×C4116yescomplemented
93#14273695C2×C4116yescomplemented
94#14273689—44no—
95#14273689—44no—
96C4×C22⋊D59—48no—
97(C22⋊D59)⋊C4—48no—
98#14273686—42no—
99#14273686C2×C418yescomplemented
100C2×C4⋊Dic59C2312yes—
101C2×C4⋊Dic59C2312yes—
102C2×Dic59⋊C4C2314yes—
103C2×Dic59⋊C4C2314yes—
104C2×C22⋊Dic59C2312yes—
105C2×C22⋊Dic59C2312yes—
106C2×C22⋊Dic59C2312yes—
107C2×C22⋊Dic59C2312yes—
108C2×C22⋊Dic59C2311yescharacteristic
109C2×C22⋊Dic59C2311yescharacteristic
110C2×C22⋊Dic59C2312yes—
111C2×(C2×D59)⋊C4C2314yes—
112C2×(C2×D59)⋊C4C2314yes—
113C2×(C2×D59)⋊C4C2314yes—
114C2×(C2×D59)⋊C4C2314yes—
115C2×(C2×D59)⋊C4C2314yes—
116C2×(C2×D59)⋊C4C2314yes—
117C2×(C2×D59)⋊C4C2314yes—
118C2×(C2×D59)⋊C4C2314yes—
119C22⋊C4×D59—48no—
120C2×C4×Dic59—42no—
121C2×C4×Dic59C2312yes—
122C2×C4×Dic59C2312yes—
123C2×C4×Dic59C2312yes—
124C2×C4×Dic59C2314yes—
125C2×C4×Dic59C2314yes—
126C2×C4×Dic59C2312yes—
127C59⋊#95C2314yes—
128C59⋊#95C2312yes—
129C59⋊#95C2312yes—
130C59⋊#95C2312yes—
131C59⋊#95C2312yes—
132C59⋊#95C2314yes—
133C59⋊#95C2314yes—
134C59⋊#95C2314yes—
135C2×#41×C59—42no—
136C2×#41×C59—42no—
137C2×#41×C59C2×C418yescomplemented
138C22×Q8×C59C2311yescharacteristic
139C22×D4×C59C2311yescharacteristic
140C22×D4×C59C2311yescharacteristic
141C22×D4×C59C2311yescharacteristic
142C23×C4×C59C2311yescharacteristic
143C23×C4×C59C2311yescharacteristic
144C23×C4×C59C2311yescharacteristic
145C23×C4×C59C2312yes—
146#117×C59—42no—
147C2×C4⋊C4×C59—42no—
148C2×C4⋊C4×C59C2312yes—
149C2×C4⋊C4×C59C2312yes—
150C2×C4⋊C4×C59C2312yes—
151C2×C22⋊C4×C59C2314yes—
152C2×C22⋊C4×C59C2314yes—
153C2×C22⋊C4×C59C2312yes—
154C2×C42×C59C2312yes—
155#95×C59C2314yes—
156#95×C59C2314yes—
157C24×C59C2411yescharacteristic
158C24×C59C2411yescharacteristic
159C24×C59C2411yescharacteristic
160C23×D59—44no—
161C23×D59—42no—
162C23×D59—42no—
163C23×D59—44no—
164C23×D59C22×C418yes—
165C23×D59C2414yes—
166#41×C59—416no—
167C2×Q8×C59—41no—
168C2×Q8×C59—41no—
169C2×Q8×C59C22×C414yes—
170C2×D4×C59—41no—
171C2×D4×C59—41no—
172C2×D4×C59—41no—
173C2×D4×C59—41no—
174C2×D4×C59—41no—
175C2×D4×C59—41no—
176C2×D4×C59C22×C414yes—
177C2×D4×C59C22×C414yes—
178C2×D4×C59C22×C414yes—
179C22×C4×C59—22no—
180C22×C4×C59—22no—
181C22×C4×C59—22no—
182C22×C4×C59—22no—
183C22×C4×C59—22no—
184C22×C4×C59—22no—
185C22×C4×C59—42no—
186C22×C4×C59—44no—
187C22×C4×C59C22×C414yes—
188C22×C4×C59C22×C414yes—
189C22×C4×C59C22×C414yes—
190C22×C4×C59C2414yes—
191C22×C4×C59C2414yes—
192C22×C4×C59C2411yescharacteristic
193C22×C4×C59C2411yescharacteristic
194C22×C4×C59C2411yescharacteristic
195C22×C4×C59C2411yescharacteristic
196C2×C22⋊D59—44no—
197C2×C22⋊D59—44no—
198C2×C22⋊D59—44no—
199C2×C22⋊D59—44no—
200C2×C22⋊D59C22×C4116yes—
201C2×C22⋊D59C22×C4116yes—
202C22×Dic59—24no—
203C22×Dic59—41no—
204C22×Dic59—41no—
205C22×Dic59—42no—
206C22×Dic59C2412yes—
207C22×Dic59C2412yes—
208C22×Dic59C2412yes—
209C22×Dic59C2414yes—
210C22×Dic59C2412yes—
211C2×D236—24no—
212C2×D236—24no—
213C2×D236—416no—
214C2×D236—42no—
215C2×D236—42no—
216C2×D236C22×C418yes—
217C2×D236C22×C418yes—
218C2×C4×D59—28no—
219C2×C4×D59—44no—
220C2×C4×D59—44no—
221C2×C4×D59—44no—
222C2×C4×D59—44no—
223C2×C4×D59—44no—
224C4⋊C4×C59—24no—
225C4⋊C4×C59—24no—
226C4⋊C4×C59—42no—
227C22⋊C4×C59—42no—
228C22⋊C4×C59—44no—
229C22⋊C4×C59—44no—
230C42×C59—42no—
231C22⋊Dic59—24no—
232C22⋊Dic59—24no—
233C22⋊Dic59—42no—
234C22⋊Dic59—42no—
235C22⋊Dic59—41no—
236C22⋊Dic59—41no—
237C22⋊Dic59C22×C418yes—
238(C2×D59)⋊C4—28no—
239(C2×D59)⋊C4—44no—
240(C2×D59)⋊C4—44no—
241(C2×D59)⋊C4—44no—
242(C2×D59)⋊C4—44no—
243(C2×D59)⋊C4—44no—
244(C2×D59)⋊C4C22×C4116yes—
245(C2×D59)⋊C4C22×C4116yes—
246C4⋊Dic59—42no—
247C4⋊Dic59C22×C418yes—
248Dic59⋊C4—28no—
249Dic59⋊C4—44no—
250C4×Dic59—24no—
251C4×Dic59—24no—
252C4×Dic59—42no—
253C4×Dic59—44no—
254C4×Dic59—44no—
255C4×Dic59C22×C418yes—
256C23×C59—22no—
257C23×C59—22no—
258C23×C59—21no—
259C23×C59—22no—
260C23×C59—21no—
261C23×C59—21no—
262C23×C59—21no—
263C23×C59—21no—
264C23×C59—21no—
265C23×C59—22no—
266C23×C59—22no—
267C23×C59—22no—
268C23×C59C23×C412yes—
269C23×C59C23×C412yes—
270C23×C59C23×C412yes—
271C23×C59C2511yescharacteristic
272C22×D59—24no—
273C22×D59—24no—
274C22×D59—24no—
275C22×D59—24no—
276C22×D59—24no—
277C22×D59—24no—
278C22×D59—48no—
279C22×D59—416no—
280C22×D59—84no—
281C22×D59—84no—
282C22×D59—88no—
283C22×D59C23×C418yes—
284Q8×C59—44no—
285D4×C59—44no—
286D4×C59—44no—
287D4×C59—44no—
288C2×C4×C59—21no—
289C2×C4×C59—21no—
290C2×C4×C59—21no—
291C2×C4×C59—21no—
292C2×C4×C59—21no—
293C2×C4×C59—21no—
294C2×C4×C59—28no—
295C2×C4×C59—28no—
296C2×C4×C59—28no—
297C2×C4×C59—24no—
298C2×C4×C59—24no—
299C2×C4×C59—24no—
300C2×C4×C59—24no—
301C2×C4×C59—24no—
302C2×C4×C59—24no—
303C2×C4×C59—84no—
304C2×C4×C59C23×C412yes—
305C2×C4×C59C23×C412yes—
306C2×C4×C59C23×C412yes—
307C2×C4×C59C23×C412yes—
308C2×C4×C59H(5,𝔽2)12yes—
309C2×C4×C59H(5,𝔽2)12yes—
310C22⋊D59—416no—
311C22⋊D59—416no—
312C2×Dic59—22no—
313C2×Dic59—24no—
314C2×Dic59—22no—
315C2×Dic59—24no—
316C2×Dic59—22no—
317C2×Dic59—22no—
318C2×Dic59—22no—
319C2×Dic59—22no—
320C2×Dic59—22no—
321C2×Dic59—22no—
322C2×Dic59—22no—
323C2×Dic59—22no—
324C2×Dic59—22no—
325C2×Dic59—44no—
326C2×Dic59—44no—
327C2×Dic59C23×C418yes—
328C2×Dic59H(5,𝔽2)14yes—
329D236—216no—
330D236—48no—
331C4×D59—88no—
332C4×D59—88no—
333#34411—591nomaximal, Sylow
334C22×C59—22no—
335C22×C59—22no—
336C22×C59—22no—
337C22×C59—24no—
338C22×C59—24no—
339C22×C59—24no—
340C22×C59—41no—
341C22×C59—41no—
342C22×C59—41no—
343C22×C59—41no—
344C22×C59—41no—
345C22×C59—41no—
346C22×C59—42no—
347C22×C59—42no—
348C22×C59—42no—
349C22×C59C24×C411yescharacteristic
350C22×C59C2×H(5,𝔽2)12yes—
351C22×C59C2×H(5,𝔽2)11yescharacteristic
352C22×C59C2×H(5,𝔽2)11yescharacteristic
353C22×C59#58512yes—
354C2×D59—28no—
355C2×D59—28no—
356C2×D59—28no—
357C2×D59—44no—
358C2×D59—44no—
359C2×D59—44no—
360C2×D59—44no—
361C2×D59—816no—
362C4×C59—22no—
363C4×C59—22no—
364C4×C59—22no—
365C4×C59—44no—
366C4×C59—44no—
367C4×C59#51814yes—
368Dic59—28no—
369Dic59—24no—
370Dic59—42no—
371Dic59—42no—
372Dic59—42no—
373C2×#535—591no—
374#2380—592no—
375#2375—592no—
376#2366—592no—
377#2363—592no—
378#2361—592no—
379#2358—592no—
380#2347—592no—
381D4×C22⋊C4—592no—
382#2337—594no—
383#2324—592no—
384#2321—594no—
385#2311D5911yescharacteristic, complemented
386C4×#121—592no—
387#2297—591no—
388C2×C59—42no—
389C2×C59—42no—
390C2×C59—42no—
391C2×C59C2×#51811yescharacteristic
392C2×C59C4×H(5,𝔽2)12yes—
393C2×C59#353711yescharacteristic
394C2×C59#354011yescharacteristic
395C2×C59#354612yes—
396D59—48no—
397C22×#41C2×D5911yescharacteristic
398C23×D4—591no—
399#535—5916no—
400C2×#127—592no—
401C2×#124—592no—
402C2×#121—592no—
403C2×#121—592no—
404C2×#120—592no—
405C2×#120—592no—
406C2×C4×D4—594no—
407C2×C4×D4—592no—
408C2×C4×D4—592no—
409C2×C4×D4—594no—
410C2×#117—591no—
411C2×#117—591no—
412C2×#117C2×D5911yescharacteristic, complemented
413C22×C4⋊C4C2×D5911yescharacteristic, complemented
414C22×C22⋊C4—594no—
415C22×C42—591no—
416#391—592no—
417#391C2×D5912yescomplemented
418#390—592no—
419#390—592no—
420#390—592no—
421#390—594no—
422#390—594no—
423#390C2×D5912yes—
424#389—592no—
425#389—592no—
426#388—594no—
427#388—594no—
428#388—594no—
429#388—594no—
430#388—594no—
431#388—594no—
432#386—591no—
433#386—591no—
434#386—591no—
435#386—591no—
436#386—594no—
437#386—594no—
438#386—594no—
439#386—594no—
440#386—594no—
441#386—594no—
442#386C2×D5912yes—
443#386C2×D5912yescomplemented
444#385—594no—
445#385—594no—
446#383—594no—
447#380C2×D5912yes—
448#380C2×D5912yescomplemented
449#379—594no—
450C4×C4⋊C4—592no—
451C4×C4⋊C4—592no—
452C4×C4⋊C4—594no—
453C4×C22⋊C4—592no—
454C4×C22⋊C4—592no—
455C4×C22⋊C4—594no—
456C4×C22⋊C4—594no—
457C59#3441111yescharacteristic, complemented, Sylow
458C25—592no—
459C2×#41—42no—
460C2×#41—42no—
461C2×#41C4×D5918yescomplemented
462C22×Q8C22×D5911yescharacteristic
463C22×D4—594no—
464C22×D4—594no—
465C22×D4—598no—
466C22×D4—592no—
467C22×D4—592no—
468C22×D4—2362no—
469C22×D4—2362no—
470C22×D4C22×D5911yescharacteristic
471C22×D4C22×D5911yescharacteristic
472C22×D4C22×D5911yescharacteristic
473C23×C4—591no—
474C23×C4—591no—
475C23×C4—594no—
476C23×C4—594no—
477C23×C4C22×D5911yescharacteristic
478C23×C4C22×D5911yescharacteristic
479C23×C4C22×D5911yescharacteristic
480C23×C4C22×D5912yes—
481#127—5916no—
482#124—5916no—
483#121—5916no—
484#121—5916no—
485#120—5916no—
486#120—5916no—
487C4×D4—2364no—
488C4×D4—2364no—
489C4×D4—2368no—
490C4×D4—2368no—
491#117—42no—
492#117—598no—
493#117—2362no—
494C2×C4⋊C4—42no—
495C2×C4⋊C4—592no—
496C2×C4⋊C4—594no—
497C2×C4⋊C4—592no—
498C2×C4⋊C4—594no—
499C2×C4⋊C4C22×D5912yes—
500C2×C4⋊C4C22×D5912yes—
501C2×C4⋊C4C22×D5912yes—
502C2×C22⋊C4—592no—
503C2×C22⋊C4—594no—
504C2×C22⋊C4—594no—
505C2×C22⋊C4—592no—
506C2×C22⋊C4—592no—
507C2×C22⋊C4—594no—
508C2×C22⋊C4—591no—
509C2×C22⋊C4—591no—
510C2×C22⋊C4—592no—
511C2×C22⋊C4—592no—
512C2×C22⋊C4—594no—
513C2×C22⋊C4—594no—
514C2×C22⋊C4—594no—
515C2×C22⋊C4—594no—
516C2×C22⋊C4—594no—
517C2×C22⋊C4—2368no—
518C2×C22⋊C4C22×D5914yes—
519C2×C22⋊C4C22×D5912yes—
520C2×C22⋊C4C22×D5914yes—
521C2×C42—592no—
522C2×C42—592no—
523C2×C42—592no—
524C2×C42—594no—
525C2×C42—594no—
526C2×C42—592no—
527C2×C42—2362no—
528C2×C42C22×D5912yes—
529#95—592no—
530#95—592no—
531#95—592no—
532#95—594no—
533#95—594no—
534#95—592no—
535#95—594no—
536#95—594no—
537#95C22×D5914yes—
538#95C22×D5914yes—
539C24—594no—
540C24—598no—
541C24—2364no—
542C24—2362no—
543C24—2362no—
544C24—2364no—
545C24C23×D5911yescharacteristic
546C24C23×D5911yescharacteristic
547C24C23×D5911yescharacteristic
548#41—416no—
549C2×Q8—41no—
550C2×Q8—41no—
551C2×Q8C2×C4×D5914yes—
552C2×D4—41no—
553C2×D4—41no—
554C2×D4—41no—
555C2×D4—41no—
556C2×D4—41no—
557C2×D4—41no—
558C2×D4—5916no—
559C2×D4—5916no—
560C2×D4—598no—
561C2×D4—598no—
562C2×D4—1184no—
563C2×D4—1184no—
564C2×D4—23616no—
565C2×D4—2362no—
566C2×D4—2362no—
567C2×D4—2364no—
568C2×D4—2364no—
569C2×D4—2364no—
570C2×D4—2364no—
571C2×D4C2×C4×D5914yes—
572C2×D4C2×C4×D5914yes—
573C2×D4C2×C4×D5914yes—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—42no—
581C22×C4—44no—
582C22×C4—594no—
583C22×C4—592no—
584C22×C4—592no—
585C22×C4—592no—
586C22×C4—592no—
587C22×C4—1188no—
588C22×C4—1184no—
589C22×C4—2364no—
590C22×C4—2364no—
591C22×C4—2364no—
592C22×C4—2364no—
593C22×C4—2364no—
594C22×C4—2361no—
595C22×C4—2361no—
596C22×C4—2362no—
597C22×C4C2×C4×D5914yes—
598C22×C4C2×C4×D5914yes—
599C22×C4C2×C4×D5914yes—
600C22×C4C23×D5914yes—
601C22×C4C23×D5914yes—
602C22×C4C23×D5911yescharacteristic
603C22×C4C23×D5911yescharacteristic
604C22×C4C23×D5911yescharacteristic
605C22×C4C23×D5911yescharacteristic
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—42no—
609C4⋊C4—598no—
610C4⋊C4—1188no—
611C4⋊C4—2362no—
612C4⋊C4—2364no—
613C22⋊C4—44no—
614C22⋊C4—42no—
615C22⋊C4—44no—
616C22⋊C4—598no—
617C22⋊C4—5916no—
618C22⋊C4—5916no—
619C22⋊C4—1188no—
620C22⋊C4—1184no—
621C22⋊C4—1184no—
622C22⋊C4—2364no—
623C22⋊C4—2364no—
624C22⋊C4—2364no—
625C22⋊C4—2364no—
626C22⋊C4—2364no—
627C22⋊C4—2361no—
628C22⋊C4—2361no—
629C22⋊C4—2362no—
630C22⋊C4—2362no—
631C42—42no—
632C42—598no—
633C42—1184no—
634C42—1184no—
635C42—2362no—
636C42—2364no—
637C42—2364no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—598no—
651C23—1184no—
652C23—1184no—
653C23—1184no—
654C23—1184no—
655C23—1184no—
656C23—1184no—
657C23—4724no—
658C23—4724no—
659C23—4728no—
660C23—2368no—
661C23—23616no—
662C23C22×C4×D5912yes—
663C23C22×C4×D5912yes—
664C23C22×C4×D5912yes—
665C23C24×D5911yescharacteristic
666Q8—44no—
667D4—44no—
668D4—44no—
669D4—44no—
670D4—11816no—
671D4—2368no—
672D4—23616no—
673D4—23616no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—28no—
681C2×C4—28no—
682C2×C4—28no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—84no—
690C2×C4—598no—
691C2×C4—594no—
692C2×C4—1184no—
693C2×C4—1182no—
694C2×C4—1182no—
695C2×C4—1184no—
696C2×C4—1182no—
697C2×C4—1182no—
698C2×C4—1182no—
699C2×C4—1182no—
700C2×C4—1182no—
701C2×C4—1182no—
702C2×C4—1182no—
703C2×C4—1182no—
704C2×C4—1182no—
705C2×C4—4728no—
706C2×C4—4728no—
707C2×C4—2364no—
708C2×C4—2364no—
709C2×C4C22×C4×D5912yes—
710C2×C4C22×C4×D5912yes—
711C2×C4C22×C4×D5912yes—
712C2×C4C22×C4×D5912yes—
713C2×C4#1427377212yes—
714C2×C4#1427377212yes—
715C22—22no—
716C22—22no—
717C22—22no—
718C22—24no—
719C22—24no—
720C22—24no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—42no—
728C22—42no—
729C22—42no—
730C22—1188no—
731C22—1188no—
732C22—1188no—
733C22—47216no—
734C22—2364no—
735C22—2364no—
736C22—2364no—
737C22—2364no—
738C22C23×C4×D5911yescharacteristic
739C22H(5,𝔽2)×D5912yes—
740C22C2×#1427377211yescharacteristic
741C22C2×#1427377211yescharacteristic
742C22#1683823912yes—
743C4—22no—
744C4—22no—
745C4—22no—
746C4—44no—
747C4—44no—
748C4—1188no—
749C4—1184no—
750C4—2362no—
751C4—2362no—
752C4—2362no—
753C4#1683787514yes—
754C2—42no—
755C2—42no—
756C2—42no—
757C2—2368no—
758C2C2×#1683787511yescharacteristic
759C2#2143730212yes—
760C2#2143832911yescharacteristic
761C2#2143837311yescharacteristic
762C2#2143845812yes—
subgroupG/H
center, FrattiniC23C24×D59
commutatorC22×C59C24×C4
FittingC59×#2311C2
socle, cosocleC23×C59C25
prime radicalC2×#16837966C2
hypercenter#2311D59
hypocenterC59#34411
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ #2311

Complements

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

NH ≅ G/Ntype
2. #21427271C2semidirect
3. #21427233C2semidirect
4. #21427159C2semidirect
5. #21427134C2semidirect
6. #21427112C2semidirect
7. #21427077C2semidirect
8. #21426991C2semidirect
9. #21426916C2semidirect
10. #21426908C2semidirect
11. #21426785C2semidirect
12. #21426752C2semidirect
13. #21426602C2semidirect
14. #21426587C2semidirect
15. C59×#2311C2semidirect
17. #16837966C4semidirect
26. C2×C4×C22⋊D59C22semidirect
27. C2×(C22⋊D59)⋊C4C22semidirect
29. C2×#14273686C22semidirect
31. C22×C4×Dic59C22semidirect
32. #16837309C22semidirect
36. #16837302C22semidirect
37. #16837302C22semidirect
38. #16837298C22semidirect
39. #16837298C22semidirect
40. #16837294C22semidirect
41. #16837293C22semidirect
42. #16837292C22semidirect
43. #16837291C22semidirect
48. #16837282C22semidirect
49. #16837282C22semidirect
50. #16837281C22semidirect
53. #16837279C22semidirect
54. #16837278C22semidirect
55. #16837278C22semidirect
56. #16837276C22semidirect
57. #16837273C22semidirect
58. #16837269C22semidirect
60. C4⋊C4×Dic59C22semidirect
61. C4⋊C4×Dic59C22semidirect
62. #16837253C22semidirect
63. C4×(C2×D59)⋊C4C22semidirect
65. C4×C22⋊Dic59C22semidirect
66. #16837249C22semidirect
68. C2×#117×C59C22semidirect
69. C22×C4⋊C4×C59C22semidirect
70. C59×#391C22semidirect
73. C59×#386C22semidirect
75. C59×#380C22semidirect
79. C22×D236C2×C4semidirect
88. #14273723C2×C4semidirect
89. #14273716C2×C4semidirect
90. #14273701C2×C4semidirect
91. #14273701C2×C4semidirect
92. #14273695C2×C4semidirect
93. #14273695C2×C4semidirect
99. #14273686C2×C4semidirect
137. C2×#41×C59C2×C4semidirect
385. #2311D59semidirect
412. C2×#117C2×D59semidirect
413. C22×C4⋊C4C2×D59semidirect
417. #391C2×D59semidirect
443. #386C2×D59semidirect
448. #380C2×D59semidirect
457. C59#34411semidirect
461. C2×#41C4×D59semidirect

Maximal subgroups

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

subgroupindex
C2×#168379662
#214272712
#214272332
#214271592
#214271342
#214271122
#214270772
#214269912
#214269162
#214269082
#214267852
#214267522
#214266022
#214265872
C59×#23112
#3441159