Finite Group Databasebeta

← #28752009

Subgroups — #28752009

Order 15104.

2586 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×#16837913C211yesmaximal, characteristic
2#21427240C214yesmaximal, complemented
3#21427110C212yesmaximal, complemented
4#21427099C212yesmaximal, complemented
5#21427038C212yesmaximal, complemented
6#21427000C212yesmaximal, complemented
7#21426987C211yesmaximal, characteristic, complemented
8#21426979C211yesmaximal, characteristic, complemented
9#21426936C211yesmaximal, characteristic, complemented
10#21426927C211yesmaximal, characteristic, complemented
11#21426789C212yesmaximal, complemented
12#21426778C212yesmaximal, complemented
13#21426751C214yesmaximal, complemented
14#21426736C212yesmaximal, complemented
15#21426725C212yesmaximal, complemented
16C2×#16837262C211yesmaximal, characteristic, complemented
17C59×#2280C211yesmaximal, characteristic, complemented
18C22×#11745685C2211yescharacteristic
19#16837913C4116yescomplemented
20C2×#14273710C2212yes—
21C2×#14273706C2211yescharacteristic
22C2×#14273706C2211yescharacteristic
23C2×#14273701C2211yescharacteristic
24C2×#14273701C2211yescharacteristic
25C2×#14273696C2212yes—
26C2×C4×Dic118C2212yescomplemented
27C2×C4×D236C2212yescomplemented
28C2×C4×C22⋊D59C2212yes—
29C2×C4×C22⋊D59C2212yes—
30C2×(C22⋊D59)⋊C4C2214yes—
31C2×#14273686C2211yescharacteristic
32C22×C4⋊Dic59C2212yes—
33C22×C22⋊Dic59C2212yes—
34#16837308C2212yescomplemented
35#16837304C2212yescomplemented
36#16837302C2214yes—
37#16837302C2214yes—
38#16837300C2212yescomplemented
39#16837300C2212yescomplemented
40#16837299C2214yescomplemented
41#16837297C2214yescomplemented
42#16837296C2214yes—
43#16837296C2214yes—
44#16837294C2214yescomplemented
45#16837292C2214yescomplemented
46#16837290C2214yes—
47#16837290C2214yes—
48#16837289C2214yescomplemented
49#16837283C2214yescomplemented
50#16837279C2214yes—
51#16837278C2214yes—
52#16837278C2214yes—
53#16837276C2214yescomplemented
54#16837274C2214yes—
55#16837273C2214yescomplemented
56#16837269C2212yescomplemented
57#16837266C2212yescomplemented
58#16837264C2212yescomplemented
59#16837262C2211yescharacteristic
60#16837262C2212yes—
61#16837262C2212yes—
62#16837262C2211yescharacteristic
63#16837262C2212yes—
64#16837261C2212yescomplemented
65C4×C4⋊Dic59C2212yescomplemented
66C4×C4⋊Dic59C2212yescomplemented
67#16837253C2212yescomplemented
68C22⋊C4×Dic59C2214yes—
69#16837249C2212yescomplemented
70#16837247C2212yescomplemented
71C2×C59⋊#95C2212yes—
72#95×D59C2212yescomplemented
73C24×C4×C59C2211yescharacteristic
74C2×#117×C59C2212yes—
75C59×#381C2211yescharacteristic
76C59×#381C2211yescharacteristic
77C59×#380C2212yes—
78C59×#380C2211yescharacteristic
79C59×#380C2211yescharacteristic
80C59×#379C2212yes—
81C4×C22⋊C4×C59C2211yescharacteristic
82C4×C22⋊C4×C59C2211yescharacteristic
83C4×C22⋊C4×C59C2212yes—
84C2×#11745685—44no—
85C2×#11745685C2×C418yescomplemented
86C22×Dic118C2311yescharacteristic
87C22×D236C2311yescharacteristic
88C22×C22⋊D59C2312yes—
89C22×C22⋊D59C2312yes—
90C22×C22⋊D59C2312yes—
91C23×Dic59C2314yes—
92C22×C4×D59C2314yes—
93C22×C4×D59C2312yes—
94#14273710C2×C4116yescomplemented
95#14273706C2×C418yescomplemented
96#14273706C2×C418yescomplemented
97#14273701C2×C418yes—
98#14273701C2×C418yescomplemented
99#14273696C2×C4116yescomplemented
100C4×Dic118—44no—
101C4×D236—44no—
102C4×C22⋊D59C2×C4116yescomplemented
103C4×C22⋊D59C2×C4116yescomplemented
104(C22⋊D59)⋊C4—48no—
105#14273686C2×C418yescomplemented
106C2×C4⋊Dic59—44no—
107C2×C4⋊Dic59C2312yes—
108C2×C4⋊Dic59C2312yes—
109C2×C4⋊Dic59C2314yes—
110C2×C4⋊Dic59C2311yescharacteristic
111C2×C4⋊Dic59C2311yescharacteristic
112C2×Dic59⋊C4C2314yes—
113C2×Dic59⋊C4C2314yes—
114C2×Dic59⋊C4C2314yes—
115C2×Dic59⋊C4C2312yes—
116C2×Dic59⋊C4C2312yes—
117C2×C22⋊Dic59—44no—
118C2×C22⋊Dic59C2312yes—
119C2×C22⋊Dic59C2314yes—
120C2×C22⋊Dic59C2312yes—
121C2×C22⋊Dic59C2312yes—
122C2×C22⋊Dic59C2312yes—
123C2×C22⋊Dic59C2312yes—
124C2×(C2×D59)⋊C4C2314yes—
125C2×(C2×D59)⋊C4C2314yes—
126C2×(C2×D59)⋊C4C2314yes—
127C2×(C2×D59)⋊C4C2312yes—
128C2×(C2×D59)⋊C4C2312yes—
129C2×C4×Dic59C2314yes—
130C2×C4×Dic59C2314yes—
131C2×C4×Dic59C2314yes—
132C2×C4×Dic59C2312yes—
133C59⋊#95C2312yes—
134C59⋊#95C2314yes—
135C59⋊#95C2312yes—
136C59⋊#95C2314yes—
137C59⋊#95C2314yes—
138C59⋊#95C2314yes—
139C59⋊#95C2314yes—
140C59⋊#95C2314yes—
141C59⋊#95C2314yes—
142C25×C59C2311yescharacteristic
143C23×C4×C59—44no—
144C23×C4×C59C2×C418yescomplemented
145C23×C4×C59C2311yescharacteristic
146C23×C4×C59C2311yescharacteristic
147C23×C4×C59C2311yescharacteristic
148C23×C4×C59C2311yescharacteristic
149C23×C4×C59C2311yescharacteristic
150C23×C4×C59C2311yescharacteristic
151#117×C59—44no—
152C2×C4⋊C4×C59C2312yes—
153C2×C4⋊C4×C59C2312yes—
154C2×C22⋊C4×C59C2312yes—
155C2×C22⋊C4×C59C2312yes—
156C2×C22⋊C4×C59C2312yes—
157C2×C22⋊C4×C59C2312yes—
158C2×C22⋊C4×C59C2312yes—
159C2×C22⋊C4×C59C2312yes—
160C2×C42×C59C2312yes—
161C2×C42×C59C2312yes—
162#95×C59C2311yescharacteristic
163#95×C59C2311yescharacteristic
164#95×C59C2311yescharacteristic
165#95×C59C2311yescharacteristic
166#95×C59C2312yes—
167#95×C59C2312yes—
168C24×C59—22no—
169C24×C59—22no—
170C24×C59—42no—
171C24×C59—42no—
172C24×C59C22×C414yes—
173C24×C59C2411yescharacteristic
174C24×C59C2411yescharacteristic
175C24×C59C2411yescharacteristic
176C23×D59C2412yes—
177C22×C4×C59—24no—
178C22×C4×C59—24no—
179C22×C4×C59—24no—
180C22×C4×C59—416no—
181C22×C4×C59—42no—
182C22×C4×C59—42no—
183C22×C4×C59—42no—
184C22×C4×C59C22×C414yes—
185C22×C4×C59C22×C414yes—
186C22×C4×C59C22×C414yes—
187C22×C4×C59C22×C414yes—
188C22×C4×C59C22×C414yes—
189C22×C4×C59C22×C414yes—
190C22×C4×C59C2412yes—
191C22×C4×C59C2412yes—
192C22×C4×C59C2412yes—
193C22×C4×C59C2412yes—
194C22×C4×C59C2411yescharacteristic
195C22×C4×C59C2411yescharacteristic
196C22×C4×C59C2411yescharacteristic
197C22×C4×C59C2411yescharacteristic
198C2×C22⋊D59—24no—
199C2×C22⋊D59—24no—
200C2×C22⋊D59—44no—
201C2×C22⋊D59—44no—
202C2×C22⋊D59C22×C418yes—
203C2×C22⋊D59C22×C418yes—
204C2×C22⋊D59C22×C418yes—
205C22×Dic59—28no—
206C22×Dic59—44no—
207C22×Dic59—44no—
208C22×Dic59C2414yes—
209C22×Dic59C2414yes—
210C22×Dic59C2412yes—
211C22×Dic59C2412yes—
212C22×Dic59C2412yes—
213#11745685—416no—
214C2×D236—24no—
215C2×D236C22×C414yes—
216C2×C4×D59—44no—
217C2×C4×D59—44no—
218C2×C4×D59—44no—
219C2×C4×D59—44no—
220C2×C4×D59C22×C418yes—
221C2×Dic118—24no—
222C2×Dic118C22×C414yes—
223C4⋊C4×C59—42no—
224C4⋊C4×C59—42no—
225C22⋊C4×C59—24no—
226C22⋊C4×C59—24no—
227C22⋊C4×C59—42no—
228C22⋊C4×C59—42no—
229C22⋊C4×C59—42no—
230C22⋊C4×C59—42no—
231C42×C59—24no—
232C42×C59—24no—
233C22⋊Dic59—42no—
234C22⋊Dic59—44no—
235C22⋊Dic59—42no—
236C22⋊Dic59C22×C418yes—
237C22⋊Dic59C22×C418yes—
238C22⋊Dic59C22×C418yes—
239(C2×D59)⋊C4—44no—
240(C2×D59)⋊C4—44no—
241(C2×D59)⋊C4—44no—
242(C2×D59)⋊C4C22×C418yes—
243(C2×D59)⋊C4C22×C418yes—
244C4⋊Dic59—24no—
245C4⋊Dic59—24no—
246C4⋊Dic59—44no—
247C4⋊Dic59C22×C414yes—
248C4⋊Dic59C22×C414yes—
249Dic59⋊C4—44no—
250Dic59⋊C4—44no—
251Dic59⋊C4—44no—
252Dic59⋊C4C22×C418yes—
253Dic59⋊C4C22×C418yes—
254C4×Dic59—44no—
255C4×Dic59—44no—
256C4×Dic59—44no—
257C4×Dic59C22×C418yes—
258C23×C59—22no—
259C23×C59—22no—
260C23×C59—28no—
261C23×C59—21no—
262C23×C59—21no—
263C23×C59—22no—
264C23×C59—22no—
265C23×C59—21no—
266C23×C59—21no—
267C23×C59—22no—
268C23×C59—22no—
269C23×C59—44no—
270C23×C59—44no—
271C23×C59—48no—
272C23×C59—48no—
273C23×C59C23×C412yes—
274C23×C59C23×C412yes—
275C23×C59C23×C412yes—
276C23×C59H(5,𝔽2)12yes—
277C23×C592−1+412yes—
278C23×C59C2511yescharacteristic
279C22×D59—22no—
280C22×D59—24no—
281C22×D59—22no—
282C22×D59—24no—
283C22×D59C23×C414yes—
284C2×C4×C59—22no—
285C2×C4×C59—22no—
286C2×C4×C59—22no—
287C2×C4×C59—28no—
288C2×C4×C59—28no—
289C2×C4×C59—28no—
290C2×C4×C59—22no—
291C2×C4×C59—22no—
292C2×C4×C59—22no—
293C2×C4×C59—22no—
294C2×C4×C59—22no—
295C2×C4×C59—22no—
296C2×C4×C59—22no—
297C2×C4×C59—22no—
298C2×C4×C59—22no—
299C2×C4×C59—22no—
300C2×C4×C59—22no—
301C2×C4×C59—22no—
302C2×C4×C59—44no—
303C2×C4×C59—44no—
304C2×C4×C59—44no—
305C2×C4×C59C23×C412yes—
306C2×C4×C59C23×C412yes—
307C2×C4×C59C23×C412yes—
308C2×C4×C59C23×C412yes—
309C2×C4×C59H(5,𝔽2)14yes—
310C22⋊D59—216no—
311C22⋊D59—48no—
312C22⋊D59—48no—
313C2×Dic59—22no—
314C2×Dic59—24no—
315C2×Dic59—22no—
316C2×Dic59—24no—
317C2×Dic59—24no—
318C2×Dic59—24no—
319C2×Dic59—24no—
320C2×Dic59—24no—
321C2×Dic59—24no—
322C2×Dic59—24no—
323C2×Dic59—88no—
324C2×Dic59C23×C414yes—
325C2×Dic59C23×C414yes—
326C2×Dic59C23×C414yes—
327D236—28no—
328C4×D59—48no—
329C4×D59—88no—
330Dic118—28no—
331#34404—591nomaximal, Sylow
332C22×C59—22no—
333C22×C59—22no—
334C22×C59—24no—
335C22×C59—24no—
336C22×C59—22no—
337C22×C59—22no—
338C22×C59—22no—
339C22×C59—22no—
340C22×C59—22no—
341C22×C59—22no—
342C22×C59—416no—
343C22×C59—42no—
344C22×C59—42no—
345C22×C59—42no—
346C22×C59—42no—
347C22×C59#52014yes—
348C22×C59C24×C411yescharacteristic
349C22×C59C2×H(5,𝔽2)12yes—
350C22×C59C2×H(5,𝔽2)11yescharacteristic
351C22×C59C2×2−1+411yescharacteristic
352C22×C59#58512yes—
353C2×D59—24no—
354C2×D59—24no—
355C2×D59—24no—
356C2×D59—44no—
357C2×D59—44no—
358C4×C59—22no—
359C4×C59—22no—
360C4×C59—22no—
361C4×C59—42no—
362C4×C59—42no—
363C4×C59—42no—
364C4×C59—42no—
365C4×C59#51814yes—
366Dic59—24no—
367Dic59—24no—
368Dic59—24no—
369Dic59—44no—
370Dic59—44no—
371C2×#525—591no—
372#2376—594no—
373#2361—592no—
374#2360—592no—
375#2353—592no—
376#2349—592no—
377#2347—591no—
378#2346—591no—
379#2341—591no—
380#2339—591no—
381#2324—592no—
382#2323—592no—
383#2321—594no—
384#2319—592no—
385#2318—592no—
386#2280D5911yescharacteristic, complemented
387C2×#380—591no—
388C2×C59—24no—
389C2×C59—42no—
390C2×C59—42no—
391C2×C59C2×#51811yescharacteristic
392C2×C59C2×#52011yescharacteristic
393C2×C59#342811yescharacteristic
394C2×C59#354112yes—
395C2×C59#354212yes—
396D59—44no—
397C22×#41—591no—
398C24×C4C2×D5911yescharacteristic
399#525—5916no—
400C2×#123—592no—
401C2×C22⋊Q8—591no—
402C2×C22⋊Q8—591no—
403C2×#121—591no—
404C2×#121—591no—
405C2×#120—592no—
406C2×C4×Q8—592no—
407C2×C4×D4—592no—
408C2×C4×D4—592no—
409C2×C4×D4—594no—
410C2×C4×D4—592no—
411C2×#117—591no—
412C2×#117C2×D5912yes—
413C22×C4⋊C4—592no—
414C22×C22⋊C4—592no—
415#391—592no—
416#390—594no—
417#390—594no—
418#390—592no—
419#389—594no—
420#389—592no—
421#389—592no—
422#389—594no—
423#388—594no—
424#388—594no—
425#388—594no—
426#388—594no—
427#388—594no—
428#388—594no—
429#387—594no—
430#387—594no—
431#386—594no—
432#386—594no—
433#386—594no—
434#385—594no—
435#385—594no—
436#385—594no—
437#383—592no—
438#382—592no—
439#381—592no—
440#381C2×D5911yescharacteristic
441#381C2×D5911yescharacteristic
442#380—592no—
443#380—592no—
444#380—591no—
445#380—591no—
446#380—592no—
447#380—592no—
448#380C2×D5911yescharacteristic
449#380C2×D5911yescharacteristic
450#380C2×D5912yes—
451#379C2×D5912yes—
452C4×C4⋊C4—592no—
453C4×C4⋊C4—592no—
454C4×C4⋊C4—592no—
455C4×C22⋊C4—594no—
456C4×C22⋊C4—592no—
457C4×C22⋊C4C2×D5911yescharacteristic
458C4×C22⋊C4C2×D5911yescharacteristic
459C4×C22⋊C4C2×D5912yes—
460#376—592no—
461C2×#95—592no—
462C2×#95—592no—
463C59#3440411yescharacteristic, complemented, Sylow
464C25C22×D5911yescharacteristic
465C2×#41—598no—
466C2×#41—2364no—
467C22×Q8—591no—
468C22×D4—592no—
469C22×D4—592no—
470C22×D4—592no—
471C22×D4—591no—
472C23×C4—44no—
473C23×C4—592no—
474C23×C4—594no—
475C23×C4—594no—
476C23×C4C4×D5918yescomplemented
477C23×C4C22×D5911yescharacteristic
478C23×C4C22×D5911yescharacteristic
479C23×C4C22×D5911yescharacteristic
480C23×C4C22×D5911yescharacteristic
481C23×C4C22×D5911yescharacteristic
482C23×C4C22×D5911yescharacteristic
483#123—5916no—
484C22⋊Q8—598no—
485C22⋊Q8—598no—
486#121—598no—
487#121—598no—
488#120—5916no—
489C4×Q8—2364no—
490C4×D4—5916no—
491C4×D4—5916no—
492C4×D4—2364no—
493C4×D4—2368no—
494#117—44no—
495#117—598no—
496C2×C4⋊C4—591no—
497C2×C4⋊C4—591no—
498C2×C4⋊C4—592no—
499C2×C4⋊C4—592no—
500C2×C4⋊C4—592no—
501C2×C4⋊C4—592no—
502C2×C4⋊C4—594no—
503C2×C4⋊C4—594no—
504C2×C4⋊C4—594no—
505C2×C4⋊C4—594no—
506C2×C4⋊C4—2364no—
507C2×C4⋊C4C22×D5912yes—
508C2×C4⋊C4C22×D5912yes—
509C2×C22⋊C4—592no—
510C2×C22⋊C4—592no—
511C2×C22⋊C4—592no—
512C2×C22⋊C4—592no—
513C2×C22⋊C4—592no—
514C2×C22⋊C4—592no—
515C2×C22⋊C4—594no—
516C2×C22⋊C4—592no—
517C2×C22⋊C4—594no—
518C2×C22⋊C4—594no—
519C2×C22⋊C4—594no—
520C2×C22⋊C4—2364no—
521C2×C22⋊C4C22×D5912yes—
522C2×C22⋊C4C22×D5912yes—
523C2×C22⋊C4C22×D5912yes—
524C2×C22⋊C4C22×D5912yes—
525C2×C22⋊C4C22×D5912yes—
526C2×C22⋊C4C22×D5912yes—
527C2×C42—592no—
528C2×C42—594no—
529C2×C42—594no—
530C2×C42—594no—
531C2×C42C22×D5912yes—
532C2×C42C22×D5912yes—
533#95—592no—
534#95—592no—
535#95—594no—
536#95—594no—
537#95—594no—
538#95—594no—
539#95—594no—
540#95—594no—
541#95—594no—
542#95C22×D5911yescharacteristic
543#95C22×D5911yescharacteristic
544#95C22×D5911yescharacteristic
545#95C22×D5911yescharacteristic
546#95C22×D5912yes—
547#95C22×D5912yes—
548C24—22no—
549C24—22no—
550C24—42no—
551C24—42no—
552C24—592no—
553C24C2×C4×D5914yes—
554C24C23×D5911yescharacteristic
555C24C23×D5911yescharacteristic
556C24C23×D5911yescharacteristic
557#41—23616no—
558C2×Q8—594no—
559C2×Q8—1184no—
560C2×D4—598no—
561C2×D4—598no—
562C2×D4—598no—
563C2×D4—594no—
564C2×D4—1184no—
565C2×D4—1184no—
566C2×D4—1184no—
567C2×D4—2364no—
568C2×D4—2364no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—24no—
572C22×C4—416no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—592no—
577C22×C4—592no—
578C22×C4—592no—
579C22×C4—598no—
580C22×C4—594no—
581C22×C4—594no—
582C22×C4—1188no—
583C22×C4—2364no—
584C22×C4—2364no—
585C22×C4—2364no—
586C22×C4—2364no—
587C22×C4—2364no—
588C22×C4—2364no—
589C22×C4C2×C4×D5914yes—
590C22×C4C2×C4×D5914yes—
591C22×C4C2×C4×D5914yes—
592C22×C4C2×C4×D5914yes—
593C22×C4C2×C4×D5914yes—
594C22×C4C2×C4×D5914yes—
595C22×C4C23×D5912yes—
596C22×C4C23×D5912yes—
597C22×C4C23×D5912yes—
598C22×C4C23×D5912yes—
599C22×C4C23×D5911yescharacteristic
600C22×C4C23×D5911yescharacteristic
601C22×C4C23×D5911yescharacteristic
602C22×C4C23×D5911yescharacteristic
603C4⋊C4—42no—
604C4⋊C4—42no—
605C4⋊C4—594no—
606C4⋊C4—594no—
607C4⋊C4—598no—
608C4⋊C4—598no—
609C4⋊C4—1184no—
610C4⋊C4—1184no—
611C4⋊C4—2364no—
612C4⋊C4—2364no—
613C4⋊C4—2364no—
614C4⋊C4—2364no—
615C22⋊C4—24no—
616C22⋊C4—24no—
617C22⋊C4—42no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4—42no—
621C22⋊C4—598no—
622C22⋊C4—598no—
623C22⋊C4—598no—
624C22⋊C4—598no—
625C22⋊C4—598no—
626C22⋊C4—2364no—
627C22⋊C4—2364no—
628C22⋊C4—2364no—
629C22⋊C4—2362no—
630C22⋊C4—2364no—
631C22⋊C4—2362no—
632C42—24no—
633C42—24no—
634C42—598no—
635C42—2364no—
636C42—2364no—
637C42—2364no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—22no—
647C23—22no—
648C23—28no—
649C23—44no—
650C23—44no—
651C23—48no—
652C23—48no—
653C23—594no—
654C23—1184no—
655C23—1182no—
656C23—1182no—
657C23—1184no—
658C23C22×C4×D5912yes—
659C23C22×C4×D5912yes—
660C23C22×C4×D5912yes—
661C23#1427377312yes—
662C23#1427377412yes—
663C23C24×D5911yescharacteristic
664Q8—1188no—
665D4—11816no—
666D4—1188no—
667D4—2368no—
668D4—2368no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—28no—
673C2×C4—28no—
674C2×C4—28no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4—594no—
691C2×C4—594no—
692C2×C4—594no—
693C2×C4—1184no—
694C2×C4—1182no—
695C2×C4—1182no—
696C2×C4—1184no—
697C2×C4—1184no—
698C2×C4—1184no—
699C2×C4—1184no—
700C2×C4—1184no—
701C2×C4—1184no—
702C2×C4—1184no—
703C2×C4—4728no—
704C2×C4—4728no—
705C2×C4—2368no—
706C2×C4C22×C4×D5912yes—
707C2×C4C22×C4×D5912yes—
708C2×C4C22×C4×D5912yes—
709C2×C4C22×C4×D5912yes—
710C2×C4#1427377214yes—
711C22—22no—
712C22—22no—
713C22—24no—
714C22—24no—
715C22—22no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—416no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—1184no—
727C22—1184no—
728C22—1184no—
729C22—2364no—
730C22—2364no—
731C22#1683788214yes—
732C22C23×C4×D5911yescharacteristic
733C22C2×#1427377212yes—
734C22C2×#1427377311yescharacteristic
735C22C2×#1427377411yescharacteristic
736C22#1683823812yes—
737C4—22no—
738C4—22no—
739C4—22no—
740C4—42no—
741C4—42no—
742C4—42no—
743C4—42no—
744C4—1184no—
745C4—1184no—
746C4—1184no—
747C4—2364no—
748C4—2364no—
749C4#1683787514yes—
750C2—24no—
751C2—42no—
752C2—42no—
753C2—2364no—
754C2C2×#1683787511yescharacteristic
755C2C2×#1683788211yescharacteristic
756C2#2143729711yescharacteristic
757C2#2143838912yes—
758C2#2143841212yes—
subgroupG/H
center, FrattiniC23C24×D59
commutatorC22×C59C24×C4
FittingC59×#2280C2
socle, cosocleC23×C59C25
prime radicalC2×#16837913C2
hypercenter#2280D59
hypocenterC59#34404
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ #2280

Complements

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

NH ≅ G/Ntype
2. #21427240C2semidirect
3. #21427110C2semidirect
4. #21427099C2semidirect
5. #21427038C2semidirect
6. #21427000C2semidirect
7. #21426987C2semidirect
8. #21426979C2semidirect
9. #21426936C2semidirect
10. #21426927C2semidirect
11. #21426789C2semidirect
12. #21426778C2semidirect
13. #21426751C2semidirect
14. #21426736C2semidirect
15. #21426725C2semidirect
16. C2×#16837262C2semidirect
17. C59×#2280C2semidirect
19. #16837913C4semidirect
26. C2×C4×Dic118C22semidirect
27. C2×C4×D236C22semidirect
34. #16837308C22semidirect
35. #16837304C22semidirect
38. #16837300C22semidirect
39. #16837300C22semidirect
40. #16837299C22semidirect
41. #16837297C22semidirect
44. #16837294C22semidirect
45. #16837292C22semidirect
48. #16837289C22semidirect
49. #16837283C22semidirect
53. #16837276C22semidirect
55. #16837273C22semidirect
56. #16837269C22semidirect
57. #16837266C22semidirect
58. #16837264C22semidirect
64. #16837261C22semidirect
65. C4×C4⋊Dic59C22semidirect
66. C4×C4⋊Dic59C22semidirect
67. #16837253C22semidirect
69. #16837249C22semidirect
70. #16837247C22semidirect
72. #95×D59C22semidirect
85. C2×#11745685C2×C4semidirect
94. #14273710C2×C4semidirect
95. #14273706C2×C4semidirect
96. #14273706C2×C4semidirect
98. #14273701C2×C4semidirect
99. #14273696C2×C4semidirect
102. C4×C22⋊D59C2×C4semidirect
103. C4×C22⋊D59C2×C4semidirect
105. #14273686C2×C4semidirect
144. C23×C4×C59C2×C4semidirect
386. #2280D59semidirect
463. C59#34404semidirect
476. C23×C4C4×D59semidirect

Maximal subgroups

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

subgroupindex
C2×#168379132
#214272402
#214271102
#214270992
#214270382
#214270002
#214269872
#214269792
#214269362
#214269272
#214267892
#214267782
#214267512
#214267362
#214267252
C2×#168372622
C59×#22802
#3440459