Finite Group Databasebeta

← #28599955

Subgroups — #28599955

Order 15104.

1084 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837547C211yesmaximal, characteristic
2C4×#14273701C211yesmaximal, characteristic, complemented
3#21424980C211yesmaximal, characteristic, complemented
4#21424971C211yesmaximal, characteristic, complemented
5#21424796C211yesmaximal, characteristic, complemented
6#21424789C211yesmaximal, characteristic, complemented
7#21424727C211yesmaximal, characteristic, complemented
8#21424713C211yesmaximal, characteristic, complemented
9#21424447C211yesmaximal, characteristic, complemented
10#21424433C211yesmaximal, characteristic, complemented
11#21424418C211yesmaximal, characteristic, complemented
12#21424295C211yesmaximal, characteristic, complemented
13#21424036C211yesmaximal, characteristic, complemented
14#21423858C211yesmaximal, characteristic, complemented
15C59×#2297C211yesmaximal, characteristic, complemented
16C22×#11745671C2211yescharacteristic
17C22×#11745669C2211yescharacteristic
18C2×#14273701C2211yescharacteristic
19C2×C4×D236C2211yescharacteristic
20C2×C4×C22⋊D59—21no—
21#16837547C418yescomplemented
22C2×#14273660C2211yescharacteristic
23C2×#14273658C2211yescharacteristic
24C2×#14273651C2211yescharacteristic
25C2×#14273651C2211yescharacteristic
26C2×#14273651C2211yescharacteristic
27C2×#14273648C2211yescharacteristic
28C2×#14273648C2211yescharacteristic
29C2×#14273648C2211yescharacteristic
30C2×#14273647C2211yescharacteristic
31C2×#14273647C2211yescharacteristic
32C2×C22⋊(C59⋊C8)C2211yescharacteristic
33C2×C22⋊(C59⋊C8)C2211yescharacteristic
34C2×#14273638C2211yescharacteristic
35C2×#14273638C2211yescharacteristic
36#16837304C2211yescharacteristic
37#16837300C2211yescharacteristic
38#16837293—21no—
39#16837281—21no—
40#16837262C2211yescharacteristic
41C4×C4⋊Dic59C2211yescharacteristic
42C4×(C2×D59)⋊C4—21no—
43#16837164C2211yescharacteristic
44#16837164C2211yescharacteristic
45#16837164C2211yescharacteristic
46#16837164C2211yescharacteristic
47#16837157C2211yescharacteristic
48#16837157C2211yescharacteristic
49C22×#41×C59C2211yescharacteristic
50C2×#117×C59C2211yescharacteristic
51C22×C42×C59C2211yescharacteristic
52C59×#391C2211yescharacteristic
53C59×#391C2211yescharacteristic
54C59×#390C2211yescharacteristic
55C59×#390C2211yescharacteristic
56C59×#386—21no—
57C59×#386—21no—
58C4×C22⋊C4×C59—21no—
59C4×C22⋊C4×C59—21no—
60C22×D236C2311yescharacteristic
61C22×C22⋊D59—21no—
62C22×C4×D59—21no—
63C2×#11745671—41no—
64C2×#11745671—41no—
65C2×#11745671C2×C414yescomplemented
66C2×#11745669—41no—
67C2×#11745669—41no—
68C2×#11745669C2×C414yescomplemented
69C22×C59⋊C8C2311yescharacteristic
70C22×C59⋊C8C2311yescharacteristic
71C22×C59⋊C8C2311yescharacteristic
72C22×C59⋊C8C2311yescharacteristic
73#14273701—22no—
74#14273701C2×C414yes—
75C4×D236—41no—
76C4×D236—41no—
77C4×C22⋊D59—44no—
78C2×C4⋊Dic59C2311yescharacteristic
79C2×C4⋊Dic59C2311yescharacteristic
80C2×C4⋊Dic59C2311yescharacteristic
81C2×Dic59⋊C4—21no—
82C2×C22⋊Dic59—21no—
83C2×(C2×D59)⋊C4—21no—
84C2×(C2×D59)⋊C4—21no—
85C2×(C2×D59)⋊C4—21no—
86C2×(C2×D59)⋊C4—21no—
87C2×C4×Dic59—21no—
88#14273660—41no—
89#14273658—41no—
90#14273651—41no—
91#14273651—41no—
92#14273651C2×C414yescomplemented
93#14273648—41no—
94#14273648—41no—
95#14273648C2×C414yescomplemented
96#14273647—41no—
97#14273647—41no—
98C22⋊(C59⋊C8)—22no—
99C22⋊(C59⋊C8)C2×C414yescomplemented
100#14273638—41no—
101#14273638—41no—
102C59⋊#95—21no—
103C59⋊#95—21no—
104C59⋊#95—21no—
105C2×#41×C59—22no—
106C2×#41×C59—41no—
107C2×#41×C59—41no—
108C2×#41×C59—41no—
109C2×#41×C59—41no—
110C2×#41×C59C2×C414yescomplemented
111C22×Q8×C59C2311yescharacteristic
112C22×D4×C59—21no—
113C22×D4×C59C2311yescharacteristic
114C23×C4×C59—21no—
115C23×C4×C59D411yescharacteristic
116C23×C4×C59D411yescharacteristic
117C23×C4×C59C2311yescharacteristic
118#117×C59—41no—
119#117×C59—41no—
120C2×C4⋊C4×C59C2311yescharacteristic
121C2×C4⋊C4×C59C2311yescharacteristic
122C2×C22⋊C4×C59—21no—
123C2×C22⋊C4×C59—21no—
124C2×C22⋊C4×C59—21no—
125C2×C22⋊C4×C59—21no—
126C2×C22⋊C4×C59—21no—
127C2×C42×C59—21no—
128C2×C42×C59—41no—
129C2×C42×C59—41no—
130C2×C42×C59D411yescharacteristic
131C2×C42×C59D411yescharacteristic
132C2×C42×C59C2311yescharacteristic
133C2×C42×C59C2311yescharacteristic
134#95×C59—21no—
135#95×C59—21no—
136#95×C59—21no—
137#95×C59—21no—
138C24×C59—21no—
139C24×C59C2×D411yescharacteristic
140C23×D59—21no—
141#41×C59—44no—
142#41×C59—44no—
143#41×C59—44no—
144#41×C59—44no—
145C2×Q8×C59—21no—
146C2×Q8×C59—21no—
147C2×Q8×C59—21no—
148C2×Q8×C59—21no—
149C2×Q8×C59—21no—
150C2×Q8×C59C22×C412yes—
151C2×D4×C59—24no—
152C2×D4×C59—21no—
153C2×D4×C59—21no—
154C2×D4×C59—21no—
155C2×D4×C59—21no—
156C2×D4×C59—21no—
157C2×D4×C59—42no—
158C2×D4×C59—42no—
159C2×D4×C59C22×C412yes—
160C22×C4×C59—21no—
161C22×C4×C59—21no—
162C22×C4×C59—21no—
163C22×C4×C59—21no—
164C22×C4×C59—21no—
165C22×C4×C59—24no—
166C22×C4×C59—22no—
167C22×C4×C59—21no—
168C22×C4×C59—21no—
169C22×C4×C59—41no—
170C22×C4×C59—41no—
171C22×C4×C59—41no—
172C22×C4×C59—41no—
173C22×C4×C59—41no—
174C22×C4×C59—42no—
175C22×C4×C59—42no—
176C22×C4×C59C22×C412yes—
177C22×C4×C59C2×D411yescharacteristic
178C22×C4×C59C2×D411yescharacteristic
179C22×C4×C59C2×D411yescharacteristic
180C22×C4×C59C2×D411yescharacteristic
181C22×C4×C59C2×D411yescharacteristic
182C22×C4×C59#4112yes—
183C22×C4×C59C2411yescharacteristic
184C2×C22⋊D59—24no—
185C2×C22⋊D59—42no—
186C2×C22⋊D59—42no—
187C22×Dic59—21no—
188C22×Dic59—21no—
189C22×Dic59—21no—
190C2×D236—21no—
191C2×D236—21no—
192C2×D236—21no—
193C2×D236—21no—
194C2×D236—21no—
195C2×D236C22×C412yes—
196C2×C4×D59—42no—
197C2×C4×D59—42no—
198C2×C4×D59—42no—
199C4⋊C4×C59—21no—
200C4⋊C4×C59—21no—
201C4⋊C4×C59—21no—
202C4⋊C4×C59—21no—
203C22⋊C4×C59—42no—
204C22⋊C4×C59—42no—
205C22⋊C4×C59—42no—
206C22⋊C4×C59—42no—
207C22⋊C4×C59—42no—
208C42×C59—21no—
209C42×C59—21no—
210C42×C59—21no—
211C42×C59—21no—
212C42×C59—41no—
213C42×C59—41no—
214C42×C59—42no—
215C22⋊Dic59—42no—
216#11745671—44no—
217#11745669—44no—
218(C2×D59)⋊C4—24no—
219(C2×D59)⋊C4—42no—
220(C2×D59)⋊C4—42no—
221(C2×D59)⋊C4—42no—
222C4⋊Dic59—21no—
223C4⋊Dic59—21no—
224C4⋊Dic59—21no—
225C4⋊Dic59—21no—
226C4⋊Dic59—21no—
227C4⋊Dic59C22×C412yes—
228Dic59⋊C4—42no—
229C4×Dic59—42no—
230C2×C59⋊C8—21no—
231C2×C59⋊C8—21no—
232C2×C59⋊C8—21no—
233C2×C59⋊C8—21no—
234C2×C59⋊C8—21no—
235C2×C59⋊C8—21no—
236C2×C59⋊C8—21no—
237C2×C59⋊C8—21no—
238C2×C59⋊C8—21no—
239C2×C59⋊C8—21no—
240C2×C59⋊C8C22×C412yes—
241C2×C59⋊C8C22×C412yes—
242C23×C59—21no—
243C23×C59—21no—
244C23×C59—21no—
245C23×C59—21no—
246C23×C59—21no—
247C23×C59—21no—
248C23×C59—22no—
249C23×C59—41no—
250C23×C59—41no—
251C23×C59—41no—
252C23×C59—41no—
253C23×C59—41no—
254C23×C59—41no—
255C23×C59C4×D412yes—
256C23×C59C22×D411yescharacteristic
257C22×D59—22no—
258C22×D59—41no—
259C22×D59—41no—
260C22×D59—41no—
261C22×D59—41no—
262C22×D59—41no—
263C22×D59—41no—
264Q8×C59—22no—
265Q8×C59—22no—
266Q8×C59—41no—
267Q8×C59—41no—
268D4×C59—22no—
269D4×C59—22no—
270D4×C59—48no—
271D4×C59—41no—
272D4×C59—41no—
273C2×C4×C59—21no—
274C2×C4×C59—21no—
275C2×C4×C59—21no—
276C2×C4×C59—21no—
277C2×C4×C59—22no—
278C2×C4×C59—22no—
279C2×C4×C59—22no—
280C2×C4×C59—22no—
281C2×C4×C59—22no—
282C2×C4×C59—21no—
283C2×C4×C59—21no—
284C2×C4×C59—21no—
285C2×C4×C59—21no—
286C2×C4×C59—21no—
287C2×C4×C59—21no—
288C2×C4×C59—21no—
289C2×C4×C59—21no—
290C2×C4×C59—21no—
291C2×C4×C59—44no—
292C2×C4×C59—48no—
293C2×C4×C59—44no—
294C2×C4×C59—41no—
295C2×C4×C59—41no—
296C2×C4×C59—41no—
297C2×C4×C59—41no—
298C2×C4×C59—41no—
299C2×C4×C59—41no—
300C2×C4×C59—41no—
301C2×C4×C59—41no—
302C2×C4×C59C4×D412yes—
303C2×C4×C59AGL(1,ℤ/8)12yes—
304C2×C4×C59C23×C411yescharacteristic
305C2×C4×C59C2×#4111yescharacteristic
306C2×C4×C59H(5,𝔽2)11yescharacteristic
307C2×C4×C59H(5,𝔽2)11yescharacteristic
308C2×C4×C59H(5,𝔽2)11yescharacteristic
309C2×C4×C59H(5,𝔽2)11yescharacteristic
310C22⋊D59—48no—
311C2×Dic59—22no—
312C2×Dic59—41no—
313C2×Dic59—41no—
314C2×Dic59—41no—
315C2×Dic59—41no—
316C2×Dic59—41no—
317C2×Dic59—41no—
318C2×Dic59—41no—
319C2×Dic59—41no—
320D236—22no—
321D236—22no—
322D236—41no—
323D236—41no—
324C4×D59—84no—
325C59⋊C8—22no—
326C59⋊C8—22no—
327C59⋊C8—41no—
328C59⋊C8—41no—
329#22051—591nomaximal, Sylow
330C22×C59—22no—
331C22×C59—22no—
332C22×C59—22no—
333C22×C59—41no—
334C22×C59—41no—
335C22×C59—41no—
336C22×C59—41no—
337C22×C59—42no—
338C22×C59—42no—
339C22×C59—42no—
340C22×C59—81no—
341C22×C59—81no—
342C22×C59—81no—
343C22×C59—81no—
344C22×C59C2×C4×D411yescharacteristic
345C22×C59#53411yescharacteristic
346C22×C59#53511yescharacteristic
347C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
348C22×C59#57511yescharacteristic
349C22×C59#57511yescharacteristic
350C22×C59#57511yescharacteristic
351C2×D59—42no—
352C2×D59—42no—
353C2×D59—42no—
354C2×D59—81no—
355C2×D59—81no—
356C2×D59—81no—
357C2×D59—81no—
358C4×C59—22no—
359C4×C59—22no—
360C4×C59—42no—
361C4×C59—41no—
362C4×C59—41no—
363C4×C59—41no—
364C4×C59—81no—
365C4×C59—81no—
366C4×C59#51811yescharacteristic
367C4×C59#51811yescharacteristic
368C4×C59#53811yescharacteristic
369C4×C59#53811yescharacteristic
370Dic59—42no—
371Dic59—81no—
372Dic59—81no—
373C2×#449—591no—
374C4×#121—591no—
375#2297D5911yescharacteristic, complemented
376#1973—591no—
377#1972—591no—
378#1936—591no—
379#1935—591no—
380#1927—591no—
381#1925—591no—
382#1879—591no—
383#1877—591no—
384#1875—591no—
385#1854—591no—
386#1788—591no—
387#1749—591no—
388C2×C59—42no—
389C2×C59—82no—
390C2×C59#232111yescharacteristic
391C2×C59#294311yescharacteristic
392C2×C59C4×AGL(1,ℤ/8)11yescharacteristic
393C2×C59#319411yescharacteristic
394C2×C59#319711yescharacteristic
395C2×C59#321411yescharacteristic
396C2×C59#321911yescharacteristic
397D59—82no—
398C22×#41C2×D5911yescharacteristic
399C22×SD16—591no—
400C22×D8—591no—
401C2×#121—591no—
402C2×C4×D4—591no—
403C2×C4×D4—1181no—
404C2×#117C2×D5911yescharacteristic
405C22×C42C2×D5911yescharacteristic
406#449—598no—
407C2×#107—591no—
408C2×#106—591no—
409C2×#103—591no—
410C2×#103—591no—
411C2×#103—591no—
412C2×#102—591no—
413C2×#102—591no—
414C2×#102—591no—
415C2×#102—591no—
416C2×#102—591no—
417C2×C22⋊C8—591no—
418C2×C22⋊C8—591no—
419C2×#97—591no—
420C2×#97—591no—
421#391C2×D5911yescharacteristic
422#391C2×D5911yescharacteristic
423#390—591no—
424#390C2×D5911yescharacteristic
425#390C2×D5911yescharacteristic
426#389—591no—
427#388—1181no—
428#386—21no—
429#386—21no—
430#386—1181no—
431#380—591no—
432C4×C4⋊C4—591no—
433C4×C22⋊C4—21no—
434C4×C22⋊C4—21no—
435C4×C22⋊C4—1181no—
436#340—591no—
437#340—591no—
438#340—591no—
439#340—591no—
440#336—591no—
441#336—591no—
442C59#2205111yescharacteristic, complemented, Sylow
443C2×#41—22no—
444C2×#41—41no—
445C2×#41—41no—
446C2×#41—41no—
447C2×#41—41no—
448C2×#41C4×D5914yescomplemented
449C22×Q8C22×D5911yescharacteristic
450C22×D4—21no—
451C22×D4—591no—
452C22×D4—1181no—
453C22×D4C22×D5911yescharacteristic
454C23×C4—21no—
455C23×C4—1181no—
456C23×C4C22⋊D5911yescharacteristic
457C23×C4C22⋊D5911yescharacteristic
458C23×C4C22×D5911yescharacteristic
459C2×SD16—594no—
460C2×SD16—2361no—
461C2×SD16—2361no—
462C2×D8—594no—
463C2×D8—2361no—
464C2×D8—2361no—
465C22×C8—591no—
466C22×C8—591no—
467C22×C8—591no—
468C22×C8—591no—
469#121—594no—
470#121—1182no—
471C4×D4—2361no—
472C4×D4—2361no—
473C4×D4—2364no—
474#117—41no—
475#117—41no—
476C2×C4⋊C4—591no—
477C2×C4⋊C4—591no—
478C2×C4⋊C4—591no—
479C2×C4⋊C4—1181no—
480C2×C4⋊C4C22×D5911yescharacteristic
481C2×C4⋊C4C22×D5911yescharacteristic
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—1181no—
488C2×C22⋊C4—1181no—
489C2×C22⋊C4—1181no—
490C2×C22⋊C4—1181no—
491C2×C22⋊C4—1181no—
492C2×C42—21no—
493C2×C42—41no—
494C2×C42—41no—
495C2×C42—1181no—
496C2×C42C22⋊D5911yescharacteristic
497C2×C42C22⋊D5911yescharacteristic
498C2×C42C22×D5911yescharacteristic
499C2×C42C22×D5911yescharacteristic
500#107—2361no—
501#106—2361no—
502#103—594no—
503#103—2361no—
504#103—2361no—
505#102—594no—
506#102—2361no—
507#102—2361no—
508#102—2361no—
509#102—2361no—
510C22⋊C8—594no—
511C22⋊C8—1182no—
512#97—2361no—
513#97—2361no—
514#95—21no—
515#95—21no—
516#95—21no—
517#95—21no—
518#95—1181no—
519#95—1181no—
520#95—1181no—
521C24—21no—
522C24—1181no—
523C24C2×C22⋊D5911yescharacteristic
524#41—44no—
525#41—44no—
526#41—44no—
527#41—44no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8C2×C4×D5912yes—
534C2×D4—24no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—42no—
541C2×D4—42no—
542C2×D4—592no—
543C2×D4—1184no—
544C2×D4—1181no—
545C2×D4—1181no—
546C2×D4—1181no—
547C2×D4—1181no—
548C2×D4—1181no—
549C2×D4—2362no—
550C2×D4—2362no—
551C2×D4C2×C4×D5912yes—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—24no—
558C22×C4—22no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—41no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4—41no—
565C22×C4—41no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—1181no—
569C22×C4—1181no—
570C22×C4—1181no—
571C22×C4—2362no—
572C22×C4—2362no—
573C22×C4—2362no—
574C22×C4C2×C4×D5912yes—
575C22×C4#1174568512yes—
576C22×C4C2×C22⋊D5911yescharacteristic
577C22×C4C2×C22⋊D5911yescharacteristic
578C22×C4C2×C22⋊D5911yescharacteristic
579C22×C4C2×C22⋊D5911yescharacteristic
580C22×C4C2×C22⋊D5911yescharacteristic
581C22×C4C23×D5911yescharacteristic
582SD16—2364no—
583D8—2364no—
584C2×C8—592no—
585C2×C8—592no—
586C2×C8—1181no—
587C2×C8—1181no—
588C2×C8—1181no—
589C2×C8—1181no—
590C2×C8—1181no—
591C2×C8—1181no—
592C2×C8—1181no—
593C2×C8—1181no—
594C2×C8—1181no—
595C2×C8—1181no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—592no—
601C4⋊C4—1181no—
602C4⋊C4—1181no—
603C4⋊C4—1181no—
604C4⋊C4—1181no—
605C4⋊C4—1181no—
606C4⋊C4—2362no—
607C22⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—42no—
611C22⋊C4—42no—
612C22⋊C4—1184no—
613C22⋊C4—2362no—
614C22⋊C4—2362no—
615C22⋊C4—2362no—
616C22⋊C4—2362no—
617C42—21no—
618C42—21no—
619C42—21no—
620C42—21no—
621C42—41no—
622C42—41no—
623C42—42no—
624C42—2362no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—22no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—1182no—
639C23—2361no—
640C23—2361no—
641C23—2361no—
642C23—2361no—
643C23—2361no—
644C23—2361no—
645C23C4×C22⋊D5912yes—
646C23C22×C22⋊D5911yescharacteristic
647Q8—22no—
648Q8—22no—
649Q8—41no—
650Q8—41no—
651D4—22no—
652D4—22no—
653D4—48no—
654D4—41no—
655D4—41no—
656D4—1182no—
657D4—1182no—
658D4—2368no—
659D4—2361no—
660D4—2361no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—44no—
680C2×C4—48no—
681C2×C4—44no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—1182no—
691C2×C4—4724no—
692C2×C4—2361no—
693C2×C4—2361no—
694C2×C4—2361no—
695C2×C4—2361no—
696C2×C4—2361no—
697C2×C4—2361no—
698C2×C4—2361no—
699C2×C4—2361no—
700C2×C4C4×C22⋊D5912yes—
701C2×C4#1427375212yes—
702C2×C4C22×C4×D5911yescharacteristic
703C2×C4C2×#1174568511yescharacteristic
704C2×C4#1427377211yescharacteristic
705C2×C4#1427377211yescharacteristic
706C2×C4#1427377211yescharacteristic
707C2×C4#1427377211yescharacteristic
708C8—1182no—
709C8—1182no—
710C8—2361no—
711C8—2361no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—81no—
723C22—81no—
724C22—81no—
725C22—81no—
726C22—4721no—
727C22—4721no—
728C22—4721no—
729C22—4721no—
730C22—2362no—
731C22—2362no—
732C22—2362no—
733C22C2×C4×C22⋊D5911yescharacteristic
734C22#1683796111yescharacteristic
735C22#1683796911yescharacteristic
736C22C2×#1427375211yescharacteristic
737C22#1683820011yescharacteristic
738C22#1683820011yescharacteristic
739C22#1683820011yescharacteristic
740C4—22no—
741C4—22no—
742C4—41no—
743C4—41no—
744C4—41no—
745C4—42no—
746C4—81no—
747C4—81no—
748C4—4721no—
749C4—4721no—
750C4—2362no—
751C4#1683787511yescharacteristic
752C4#1683787511yescharacteristic
753C4#1683799011yescharacteristic
754C4#1683799011yescharacteristic
755C2—42no—
756C2—82no—
757C2—4722no—
758C2#2142675411yescharacteristic
759C2#2143289411yescharacteristic
760C2C4×#1427375211yescharacteristic
761C2#2143490611yescharacteristic
762C2#2143493311yescharacteristic
763C2#2143509111yescharacteristic
764C2#2143513311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#2297C2
socleC23×C59C22×D4
prime radicalC2×#16837547C2
cosocleC22×C4×C59C24
hypercenter#2297D59
hypocenterC59#22051
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2297

Complements

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

NH ≅ G/Ntype
2. C4×#14273701C2semidirect
3. #21424980C2semidirect
4. #21424971C2semidirect
5. #21424796C2semidirect
6. #21424789C2semidirect
7. #21424727C2semidirect
8. #21424713C2semidirect
9. #21424447C2semidirect
10. #21424433C2semidirect
11. #21424418C2semidirect
12. #21424295C2semidirect
13. #21424036C2semidirect
14. #21423858C2semidirect
15. C59×#2297C2semidirect
21. #16837547C4semidirect
65. C2×#11745671C2×C4semidirect
68. C2×#11745669C2×C4semidirect
92. #14273651C2×C4semidirect
95. #14273648C2×C4semidirect
99. C22⋊(C59⋊C8)C2×C4semidirect
110. C2×#41×C59C2×C4semidirect
375. #2297D59semidirect
442. C59#22051semidirect
448. C2×#41C4×D59semidirect

Maximal subgroups

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

subgroupindex
C2×#168375472
C4×#142737012
#214249802
#214249712
#214247962
#214247892
#214247272
#214247132
#214244472
#214244332
#214244182
#214242952
#214240362
#214238582
C59×#22972
#2205159