Finite Group Databasebeta

← #28749142

Subgroups — #28749142

Order 15104.

2110 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837954C211yesmaximal, characteristic
2#21427181C211yesmaximal, characteristic
3#21427179C211yesmaximal, characteristic
4#21427177C212yesmaximal
5#21427176C211yesmaximal, characteristic
6#21427174C212yesmaximal
7#21427052C212yesmaximal, complemented
8#21427050C212yesmaximal, complemented
9#21427050C212yesmaximal, complemented
10#21427049C212yesmaximal, complemented
11#21426841C212yesmaximal, complemented
12#21426839C212yesmaximal, complemented
13#21426715C212yesmaximal
14#21426653C212yesmaximal, complemented
15C4×#14273717C212yesmaximal, complemented
16C2×#16837266C211yesmaximal, characteristic
17#21426451C212yesmaximal
18C4×#14273683C211yesmaximal, characteristic
19C59×#2368C211yesmaximal, characteristic
20#16837954C4116yescomplemented
21C2×#14273726C2211yescharacteristic
22C2×#14273725C2211yescharacteristic
23C2×#14273717C2212yes—
24C2×#14273706C2211yescharacteristic
25C2×#14273704C2212yes—
26C2×Q8×Dic59C2211yescharacteristic
27C2×#14273692C2212yes—
28C2×#14273692C2211yescharacteristic
29C2×#14273683C2211yescharacteristic
30C2×#14273683C2212yes—
31C2×#14273683C2211yescharacteristic
32C22×Dic59⋊C4C2212yes—
33C22×C4×Dic59C2211yescharacteristic
34#16837309C2212yes—
35#16837308C2212yes—
36#16837307C2212yes—
37#16837306C2212yes—
38#16837306C2212yes—
39#16837306C2212yes—
40#16837306C2212yes—
41#16837299C2212yes—
42#16837299C2212yes—
43#16837297C2212yes—
44#16837297C2212yes—
45#16837289C2212yes—
46#16837289C2212yes—
47#16837288C2212yes—
48#16837288C2212yes—
49#16837287C2212yes—
50#16837287C2212yes—
51#16837286C2212yes—
52#16837286C2212yes—
53#16837285C2212yes—
54#16837285C2212yes—
55#16837284C2212yes—
56#16837284C2212yes—
57#16837283C2212yes—
58#16837283C2212yes—
59#16837277C2212yes—
60#16837275C2212yes—
61#16837274C2212yes—
62#16837271C2212yes—
63#16837271C2212yes—
64#16837266C2212yes—
65#16837266C2212yes—
66#16837266C2211yescharacteristic
67#16837266C2211yescharacteristic
68#16837266C2212yes—
69#16837266C2212yes—
70#16837266C2211yescharacteristic
71#16837266C2211yescharacteristic
72C4⋊C4×Dic59C2212yes—
73C4⋊C4×Dic59C2212yes—
74C4×Dic59⋊C4C2212yes—
75C4×Dic59⋊C4C2212yes—
76C4×Dic59⋊C4C2212yes—
77C4×Dic59⋊C4C2212yes—
78C4×Dic59⋊C4C2212yes—
79C4×Dic59⋊C4C2212yes—
80C4×Dic59⋊C4C2212yes—
81C4×C4⋊Dic59C2212yes—
82#16837253C2212yes—
83#16837253C2212yes—
84#16837253C2212yes—
85#16837253C2212yes—
86#16837253C2212yes—
87#16837253C2212yes—
88#16837253C2212yes—
89C22⋊C4×Dic59C2211yescharacteristic
90C22⋊C4×Dic59C2211yescharacteristic
91C22⋊C4×Dic59C2212yes—
92C22⋊C4×Dic59C2212yes—
93C4×C22⋊Dic59C2211yescharacteristic
94C4×C22⋊Dic59C2212yes—
95#16837247C2212yes—
96C2×C59⋊#95C2212yes—
97C2×C59⋊#95C2211yescharacteristic
98C42×Dic59C2212yes—
99C2×C22⋊Q8×C59C2211yescharacteristic
100C59×#391C2212yes—
101C59×#387C2212yes—
102C59×#387C2212yes—
103C59×#385C2212yes—
104C4×C4⋊C4×C59C2212yes—
105C4×C22⋊C4×C59C2211yescharacteristic
106C4×C22⋊C4×C59C2212yes—
107C2×#95×C59C2211yescharacteristic
108C22×Dic118C2312yes—
109C22×Dic118C2311yescharacteristic
110C23×Dic59C2312yes—
111C23×Dic59C2311yescharacteristic
112C23×Dic59C2311yescharacteristic
113#14273726C2×C418yescomplemented
114#14273725C2×C418yescomplemented
115#14273717C2×C4116yescomplemented
116#14273706C2×C418yes—
117#14273704C2×C4116yes—
118Q8×Dic59C2×C418yescomplemented
119#14273692C2×C4116yescomplemented
120#14273692C2×C418yescomplemented
121#14273683—24no—
122#14273683C2×C4116yes—
123#14273683Q818yescomplemented
124C2×C4⋊Dic59C2312yes—
125C2×C4⋊Dic59C2312yes—
126C2×C4⋊Dic59C2312yes—
127C2×C4⋊Dic59C2311yescharacteristic
128C2×Dic59⋊C4—28no—
129C2×Dic59⋊C4C2312yes—
130C2×Dic59⋊C4C2312yes—
131C2×Dic59⋊C4C2312yes—
132C2×Dic59⋊C4C2312yes—
133C2×Dic59⋊C4C2312yes—
134C2×Dic59⋊C4C2312yes—
135C2×Dic59⋊C4C2312yes—
136C2×Dic59⋊C4C2312yes—
137C2×Dic59⋊C4C2312yes—
138C2×Dic59⋊C4C2312yes—
139C2×Dic59⋊C4C2312yes—
140C2×Dic59⋊C4C2312yes—
141C2×Dic59⋊C4C2312yes—
142C2×Dic59⋊C4C2312yes—
143C2×Dic59⋊C4C2312yes—
144C2×C22⋊Dic59C2311yescharacteristic
145C2×C22⋊Dic59C2312yes—
146C2×C22⋊Dic59C2311yescharacteristic
147C2×C4×Dic59C2×C418yes—
148C2×C4×Dic59C2312yes—
149C2×C4×Dic59C2312yes—
150C2×C4×Dic59C2312yes—
151C2×C4×Dic59C2312yes—
152C2×C4×Dic59C2312yes—
153C2×C4×Dic59C2312yes—
154C2×C4×Dic59C2312yes—
155C2×C4×Dic59C2312yes—
156C2×C4×Dic59C2312yes—
157C2×C4×Dic59C2312yes—
158C2×C4×Dic59C2311yescharacteristic
159C2×C4×Dic59C2311yescharacteristic
160C2×C4×Dic59C2311yescharacteristic
161C2×C4×Dic59C2312yes—
162C2×C4×Dic59C2312yes—
163C2×C4×Dic59C2311yescharacteristic
164C2×C4×Dic59C2312yes—
165C59⋊#95C2312yes—
166C59⋊#95C2312yes—
167C59⋊#95C2311yescharacteristic
168C59⋊#95C2311yescharacteristic
169C59⋊#95C2312yes—
170C59⋊#95C2312yes—
171C59⋊#95C2312yes—
172C59⋊#95C2312yes—
173C59⋊#95C2312yes—
174C59⋊#95C2312yes—
175C59⋊#95C2312yes—
176C59⋊#95C2312yes—
177C59⋊#95C2312yes—
178C59⋊#95C2312yes—
179C59⋊#95C2312yes—
180C59⋊#95C2312yes—
181C59⋊#95C2312yes—
182C59⋊#95C2312yes—
183C59⋊#95C2312yes—
184C59⋊#95C2312yes—
185C59⋊#95C2312yes—
186C59⋊#95C2312yes—
187C22×Q8×C59C2311yescharacteristic
188C23×C4×C59C2312yes—
189C23×C4×C59C2311yescharacteristic
190C22⋊Q8×C59C2×C418yes—
191C2×C4⋊C4×C59C2312yes—
192C2×C4⋊C4×C59C2312yes—
193C2×C4⋊C4×C59C2312yes—
194C2×C4⋊C4×C59C2311yescharacteristic
195C2×C22⋊C4×C59C2311yescharacteristic
196C2×C22⋊C4×C59C2312yes—
197C2×C22⋊C4×C59C2311yescharacteristic
198C2×C42×C59C2312yes—
199C2×C42×C59C2312yes—
200C2×C42×C59C2312yes—
201#95×C59C2311yescharacteristic
202#95×C59C2311yescharacteristic
203#95×C59C2312yes—
204#95×C59C2312yes—
205#95×C59C2312yes—
206#95×C59C2312yes—
207#95×C59C2312yes—
208#95×C59C2312yes—
209C24×C59C2411yescharacteristic
210C2×Q8×C59—42no—
211C2×Q8×C59C22×C414yes—
212C22×C4×C59—24no—
213C22×C4×C59—42no—
214C22×C4×C59—42no—
215C22×C4×C59—42no—
216C22×C4×C59C22×C414yes—
217C22×C4×C59C2412yes—
218C22×C4×C59C2412yes—
219C22×C4×C59C2412yes—
220C22×C4×C59C2411yescharacteristic
221C22×C4×C59C2411yescharacteristic
222C22×C4×C59C2412yes—
223C22×C4×C59C2412yes—
224C22×C4×C59C2412yes—
225C22×Dic59—24no—
226C22×Dic59—42no—
227C22×Dic59—42no—
228C22×Dic59—42no—
229C22×Dic59C22×C414yes—
230C22×Dic59C22×C414yes—
231C22×Dic59C2×Q814yes—
232C22×Dic59#4114yes—
233C22×Dic59C2412yes—
234C22×Dic59C2412yes—
235C22×Dic59C2412yes—
236C22×Dic59C2411yescharacteristic
237C22×Dic59C2411yescharacteristic
238C22×Dic59C2412yes—
239C22×Dic59C2412yes—
240C22×Dic59C2412yes—
241C22×Dic59C2411yescharacteristic
242C22×Dic59C2411yescharacteristic
243C2×Dic118—42no—
244C2×Dic118—42no—
245C2×Dic118—42no—
246C2×Dic118C22×C418yes—
247C2×Dic118C22×C414yes—
248C4⋊C4×C59—42no—
249C4⋊C4×C59—42no—
250C4⋊C4×C59C22×C418yes—
251C4⋊C4×C59C22×C414yes—
252C22⋊C4×C59—22no—
253C22⋊C4×C59C22×C418yes—
254C22⋊C4×C59C2×Q814yes—
255C42×C59—42no—
256C42×C59—42no—
257C42×C59—42no—
258C22⋊Dic59—22no—
259C22⋊Dic59C22×C418yes—
260C22⋊Dic59C2×Q814yes—
261C4⋊Dic59—42no—
262C4⋊Dic59—42no—
263C4⋊Dic59C22×C418yes—
264C4⋊Dic59C22×C414yes—
265Dic59⋊C4—24no—
266Dic59⋊C4—24no—
267Dic59⋊C4—24no—
268Dic59⋊C4—24no—
269Dic59⋊C4—24no—
270Dic59⋊C4—42no—
271Dic59⋊C4—42no—
272Dic59⋊C4—42no—
273Dic59⋊C4—42no—
274Dic59⋊C4C22×C418yes—
275Dic59⋊C4C22×C418yes—
276Dic59⋊C4C22×C418yes—
277Dic59⋊C4C22×C418yes—
278Dic59⋊C4C22×C418yes—
279Dic59⋊C4C2×Q818yes—
280C4×Dic59—24no—
281C4×Dic59—42no—
282C4×Dic59—42no—
283C4×Dic59—42no—
284C4×Dic59—42no—
285C4×Dic59—42no—
286C4×Dic59—42no—
287C4×Dic59—42no—
288C4×Dic59—42no—
289C4×Dic59—42no—
290C4×Dic59C22×C414yes—
291C4×Dic59C22×C414yes—
292C4×Dic59C22×C414yes—
293C4×Dic59C22×C414yes—
294C4×Dic59C22×C418yes—
295C4×Dic59C22×C418yes—
296C4×Dic59C2×Q818yes—
297C23×C59—22no—
298C23×C59—22no—
299C23×C59C23×C412yes—
300C23×C59C22×Q812yes—
301C23×C59C2×#4112yes—
302C23×C59C2511yescharacteristic
303Q8×C59—44no—
304C2×C4×C59—22no—
305C2×C4×C59—22no—
306C2×C4×C59—22no—
307C2×C4×C59—22no—
308C2×C4×C59—22no—
309C2×C4×C59—22no—
310C2×C4×C59—22no—
311C2×C4×C59—22no—
312C2×C4×C59—22no—
313C2×C4×C59—22no—
314C2×C4×C59—22no—
315C2×C4×C59—22no—
316C2×C4×C59—22no—
317C2×C4×C59—22no—
318C2×C4×C59—22no—
319C2×C4×C59—22no—
320C2×C4×C59—22no—
321C2×C4×C59—44no—
322C2×C4×C59—84no—
323C2×C4×C59C23×C412yes—
324C2×C4×C59C23×C412yes—
325C2×C4×C59C23×C414yes—
326C2×C4×C59C23×C414yes—
327C2×C4×C59C22×Q814yes—
328C2×Dic59—22no—
329C2×Dic59—22no—
330C2×Dic59—22no—
331C2×Dic59—22no—
332C2×Dic59—22no—
333C2×Dic59—22no—
334C2×Dic59—22no—
335C2×Dic59—22no—
336C2×Dic59—22no—
337C2×Dic59—22no—
338C2×Dic59—22no—
339C2×Dic59—22no—
340C2×Dic59—22no—
341C2×Dic59—22no—
342C2×Dic59—22no—
343C2×Dic59—22no—
344C2×Dic59—22no—
345C2×Dic59—44no—
346C2×Dic59—84no—
347C2×Dic59C4×Q8116yes—
348C2×Dic59C23×C412yes—
349C2×Dic59C23×C412yes—
350C2×Dic59C23×C414yes—
351C2×Dic59C23×C414yes—
352C2×Dic59C23×C412yes—
353C2×Dic59C23×C412yes—
354C2×Dic59C22×Q814yes—
355C2×Dic59C22×Q812yes—
356C2×Dic59C22×Q812yes—
357C2×Dic59C2×#4112yes—
358C2×Dic59C2×#4112yes—
359Dic118—48no—
360Dic118—44no—
361#34215—591nomaximal, Sylow
362C22×C59—22no—
363C22×C59—22no—
364C22×C59—24no—
365C22×C59—24no—
366C22×C59C2×C4×Q814yes—
367C22×C59C24×C411yescharacteristic
368C22×C59C23×Q811yescharacteristic
369C22×C59C22×#4111yescharacteristic
370C22×C59#58512yes—
371C22×C59#58512yes—
372C4×C59—22no—
373C4×C59—24no—
374C4×C59—22no—
375C4×C59—24no—
376C4×C59—24no—
377C4×C59—42no—
378C4×C59—42no—
379C4×C59—42no—
380Dic59—22no—
381Dic59—24no—
382Dic59—24no—
383Dic59—22no—
384Dic59—24no—
385Dic59—42no—
386Dic59—42no—
387Dic59—42no—
388Dic59C2×C4×Q814yes—
389Dic59C2×C4×Q814yes—
390C2×#533—591no—
391#2368—592no—
392#2368—592no—
393#2368—591no—
394#2368—591no—
395#2368—591no—
396#2368D5911yescharacteristic
397#2355—592no—
398#2355—592no—
399#2355—592no—
400#2355—592no—
401#2331—592no—
402#2331—592no—
403#2317—592no—
404C4×#125—592no—
405C4×#125—592no—
406C2×#382—591no—
407#2274—592no—
408C4×#117—591no—
409C2×C59—24no—
410C2×C59C22×C4×Q811yescharacteristic
411C2×C59#342811yescharacteristic
412C2×C59#342811yescharacteristic
413C2×C59#350412yes—
414C2×C59#351012yes—
415#533—5916no—
416C2×C4⋊Q8—591no—
417C2×C4⋊Q8—591no—
418C2×#125—592no—
419C2×C22⋊Q8—591no—
420C2×C22⋊Q8—592no—
421C2×C22⋊Q8C2×D5911yescharacteristic
422C2×C4×Q8—591no—
423C2×C4×Q8—591no—
424C2×C4×Q8—592no—
425C2×#117—592no—
426C2×#117—591no—
427C2×#117—591no—
428C22×C4⋊C4—592no—
429C22×C42—591no—
430#391—592no—
431#391—592no—
432#391—592no—
433#391—592no—
434#391—592no—
435#391—592no—
436#391—592no—
437#391C2×D5912yes—
438#389—592no—
439#389—592no—
440#389—592no—
441#389—592no—
442#387—592no—
443#387—592no—
444#387—592no—
445#387—592no—
446#387—592no—
447#387—592no—
448#387—592no—
449#387—592no—
450#387—592no—
451#387—592no—
452#387—592no—
453#387—592no—
454#387—592no—
455#387—592no—
456#387C2×D5912yes—
457#387C2×D5912yes—
458#385—592no—
459#385—592no—
460#385—592no—
461#385C2×D5912yes—
462#384—592no—
463#384—592no—
464#382—591no—
465#382—591no—
466#382—592no—
467#382—592no—
468#382—592no—
469#382—592no—
470#382—591no—
471#382—591no—
472C4×C4⋊C4—592no—
473C4×C4⋊C4—592no—
474C4×C4⋊C4—592no—
475C4×C4⋊C4—592no—
476C4×C4⋊C4—592no—
477C4×C4⋊C4—592no—
478C4×C4⋊C4—592no—
479C4×C4⋊C4—592no—
480C4×C4⋊C4—592no—
481C4×C4⋊C4—592no—
482C4×C4⋊C4—592no—
483C4×C4⋊C4—592no—
484C4×C4⋊C4—592no—
485C4×C4⋊C4—592no—
486C4×C4⋊C4—592no—
487C4×C4⋊C4—592no—
488C4×C4⋊C4—592no—
489C4×C4⋊C4C2×D5912yes—
490C4×C22⋊C4—591no—
491C4×C22⋊C4—592no—
492C4×C22⋊C4—591no—
493C4×C22⋊C4—591no—
494C4×C22⋊C4—592no—
495C4×C22⋊C4—592no—
496C4×C22⋊C4C2×D5911yescharacteristic
497C4×C22⋊C4C2×D5912yes—
498#376—592no—
499C2×#95—592no—
500C2×#95—591no—
501C2×#95C2×D5911yescharacteristic
502C43—592no—
503C59#3421511yescharacteristic, complemented, Sylow
504C22×Q8—592no—
505C22×Q8—591no—
506C22×Q8C22×D5911yescharacteristic
507C23×C4—591no—
508C23×C4—591no—
509C23×C4—592no—
510C23×C4C22×D5912yes—
511C23×C4C22×D5911yescharacteristic
512C4⋊Q8—598no—
513C4⋊Q8—598no—
514#125—5916no—
515C22⋊Q8—598no—
516C22⋊Q8—5916no—
517C22⋊Q8C4×D5918yes—
518C4×Q8—598no—
519C4×Q8—598no—
520C4×Q8—5916no—
521#117—5916no—
522#117—598no—
523#117—1184no—
524C2×C4⋊C4—592no—
525C2×C4⋊C4—592no—
526C2×C4⋊C4—592no—
527C2×C4⋊C4—592no—
528C2×C4⋊C4—592no—
529C2×C4⋊C4—592no—
530C2×C4⋊C4—592no—
531C2×C4⋊C4—591no—
532C2×C4⋊C4—592no—
533C2×C4⋊C4—592no—
534C2×C4⋊C4—592no—
535C2×C4⋊C4—592no—
536C2×C4⋊C4—592no—
537C2×C4⋊C4—592no—
538C2×C4⋊C4—592no—
539C2×C4⋊C4—592no—
540C2×C4⋊C4—592no—
541C2×C4⋊C4—592no—
542C2×C4⋊C4—592no—
543C2×C4⋊C4—1188no—
544C2×C4⋊C4C22×D5912yes—
545C2×C4⋊C4C22×D5912yes—
546C2×C4⋊C4C22×D5912yes—
547C2×C4⋊C4C22×D5911yescharacteristic
548C2×C22⋊C4—592no—
549C2×C22⋊C4—591no—
550C2×C22⋊C4—591no—
551C2×C22⋊C4C22×D5911yescharacteristic
552C2×C22⋊C4C22×D5912yes—
553C2×C22⋊C4C22×D5911yescharacteristic
554C2×C42—598no—
555C2×C42—592no—
556C2×C42—592no—
557C2×C42—592no—
558C2×C42—591no—
559C2×C42—591no—
560C2×C42—591no—
561C2×C42—591no—
562C2×C42—592no—
563C2×C42—592no—
564C2×C42—592no—
565C2×C42—592no—
566C2×C42—592no—
567C2×C42—592no—
568C2×C42—592no—
569C2×C42—592no—
570C2×C42—592no—
571C2×C42—592no—
572C2×C42C22×D5912yes—
573C2×C42C22×D5912yes—
574C2×C42C22×D5912yes—
575#95—592no—
576#95—592no—
577#95—591no—
578#95—591no—
579#95—592no—
580#95—592no—
581#95—592no—
582#95—592no—
583#95—592no—
584#95—592no—
585#95—592no—
586#95—592no—
587#95—592no—
588#95—592no—
589#95—592no—
590#95—592no—
591#95—592no—
592#95—592no—
593#95—592no—
594#95—592no—
595#95—592no—
596#95—592no—
597#95C22×D5911yescharacteristic
598#95C22×D5911yescharacteristic
599#95C22×D5912yes—
600#95C22×D5912yes—
601#95C22×D5912yes—
602#95C22×D5912yes—
603#95C22×D5912yes—
604#95C22×D5912yes—
605C24C23×D5911yescharacteristic
606C2×Q8—42no—
607C2×Q8—598no—
608C2×Q8—594no—
609C2×Q8—2362no—
610C2×Q8—2362no—
611C2×Q8—2362no—
612C2×Q8C2×C4×D5914yes—
613C22×C4—24no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—594no—
618C22×C4—594no—
619C22×C4—594no—
620C22×C4—591no—
621C22×C4—591no—
622C22×C4—591no—
623C22×C4—592no—
624C22×C4—591no—
625C22×C4—592no—
626C22×C4—592no—
627C22×C4—594no—
628C22×C4—592no—
629C22×C4—592no—
630C22×C4—592no—
631C22×C4—1184no—
632C22×C4—2362no—
633C22×C4—2362no—
634C22×C4—2362no—
635C22×C4C2×C4×D5914yes—
636C22×C4C23×D5912yes—
637C22×C4C23×D5912yes—
638C22×C4C23×D5912yes—
639C22×C4C23×D5911yescharacteristic
640C22×C4C23×D5911yescharacteristic
641C22×C4C23×D5912yes—
642C22×C4C23×D5912yes—
643C22×C4C23×D5912yes—
644C4⋊C4—42no—
645C4⋊C4—42no—
646C4⋊C4—598no—
647C4⋊C4—598no—
648C4⋊C4—598no—
649C4⋊C4—598no—
650C4⋊C4—598no—
651C4⋊C4—598no—
652C4⋊C4—594no—
653C4⋊C4—598no—
654C4⋊C4—1184no—
655C4⋊C4—1184no—
656C4⋊C4—1184no—
657C4⋊C4—1184no—
658C4⋊C4—1184no—
659C4⋊C4—2362no—
660C4⋊C4—2362no—
661C4⋊C4—2362no—
662C4⋊C4—2362no—
663C4⋊C4—2362no—
664C4⋊C4—2362no—
665C4⋊C4C2×C4×D5918yes—
666C4⋊C4C2×C4×D5914yes—
667C22⋊C4—22no—
668C22⋊C4—598no—
669C22⋊C4—594no—
670C22⋊C4—1182no—
671C22⋊C4C2×C4×D5918yes—
672C22⋊C4Q8×D5914yes—
673C42—42no—
674C42—42no—
675C42—42no—
676C42—594no—
677C42—594no—
678C42—594no—
679C42—594no—
680C42—598no—
681C42—598no—
682C42—598no—
683C42—1184no—
684C42—2362no—
685C42—2362no—
686C42—2362no—
687C42—2362no—
688C42—2362no—
689C42—2362no—
690C42—2362no—
691C42—2362no—
692C42—2362no—
693C23—22no—
694C23—22no—
695C23C22×C4×D5912yes—
696C23C2×Q8×D5912yes—
697C23#41×D5912yes—
698C23C24×D5911yescharacteristic
699Q8—44no—
700Q8—2364no—
701Q8—2368no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—44no—
720C2×C4—84no—
721C2×C4—592no—
722C2×C4—592no—
723C2×C4—592no—
724C2×C4—592no—
725C2×C4—592no—
726C2×C4—592no—
727C2×C4—5916no—
728C2×C4—592no—
729C2×C4—592no—
730C2×C4—594no—
731C2×C4—594no—
732C2×C4—594no—
733C2×C4—1182no—
734C2×C4—1182no—
735C2×C4—1182no—
736C2×C4—1182no—
737C2×C4—1182no—
738C2×C4—1182no—
739C2×C4—1182no—
740C2×C4—1182no—
741C2×C4—1182no—
742C2×C4—1182no—
743C2×C4—1182no—
744C2×C4—1182no—
745C2×C4—1182no—
746C2×C4—1182no—
747C2×C4—1182no—
748C2×C4—1182no—
749C2×C4—1182no—
750C2×C4—4724no—
751C2×C4—2364no—
752C2×C4C22×C4×D5912yes—
753C2×C4C22×C4×D5912yes—
754C2×C4C22×C4×D5914yes—
755C2×C4C22×C4×D5914yes—
756C2×C4C2×Q8×D5914yes—
757C22—24no—
758C22—22no—
759C22—22no—
760C22—24no—
761C22C4×Q8×D5914yes—
762C22C23×C4×D5911yescharacteristic
763C22C22×Q8×D5911yescharacteristic
764C22C2×#41×D5911yescharacteristic
765C22#1683823712yes—
766C22#1683823812yes—
767C4—22no—
768C4—22no—
769C4—24no—
770C4—24no—
771C4—24no—
772C4—42no—
773C4—42no—
774C4—42no—
775C4—594no—
776C4—594no—
777C4—1184no—
778C4—1182no—
779C4—1182no—
780C4—1184no—
781C4—1184no—
782C4—2362no—
783C4—2362no—
784C4—2362no—
785C2—24no—
786C2C2×C4×Q8×D5911yescharacteristic
787C2#2143729411yescharacteristic
788C2#2143729511yescharacteristic
789C2#2143791612yes—
790C2#2143798412yes—
subgroupG/H
center, FrattiniC23C24×D59
commutatorC22×C59C24×C4
FittingC59×#2368C2
socle, cosocleC23×C59C25
prime radicalC24×C59C24
hypercenter#2368D59
hypocenterC59#34215
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ #2368

Complements

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

NH ≅ G/Ntype
7. #21427052C2semidirect
8. #21427050C2semidirect
9. #21427050C2semidirect
10. #21427049C2semidirect
11. #21426841C2semidirect
12. #21426839C2semidirect
14. #21426653C2semidirect
15. C4×#14273717C2semidirect
20. #16837954C4semidirect
113. #14273726C2×C4semidirect
114. #14273725C2×C4semidirect
115. #14273717C2×C4semidirect
118. Q8×Dic59C2×C4semidirect
119. #14273692C2×C4semidirect
120. #14273692C2×C4semidirect
123. #14273683Q8semidirect
503. C59#34215semidirect

Maximal subgroups

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

subgroupindex
C2×#168379542
#214271812
#214271792
#214271772
#214271762
#214271742
#214270522
#214270502
#214270492
#214268412
#214268392
#214267152
#214266532
C4×#142737172
C2×#168372662
#214264512
C4×#142736832
C59×#23682
#3421559