Finite Group Databasebeta

← #28599838

Subgroups — #28599838

Order 15104.

1012 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837562C211yesmaximal, characteristic
2#21426586C211yesmaximal, characteristic
3#21424956C211yesmaximal, characteristic, complemented
4#21424953C211yesmaximal, characteristic, complemented
5#21424778C211yesmaximal, characteristic, complemented
6#21424771C211yesmaximal, characteristic, complemented
7#21424730C211yesmaximal, characteristic, complemented
8#21424716C211yesmaximal, characteristic, complemented
9#21424451C211yesmaximal, characteristic, complemented
10#21424437C211yesmaximal, characteristic, complemented
11#21424409C211yesmaximal, characteristic, complemented
12#21424293C211yesmaximal, characteristic, complemented
13#21424034C211yesmaximal, characteristic
14C4×C22⋊(C59⋊C8)C211yesmaximal, characteristic, complemented
15C4×C22⋊Q8×C59C211yesmaximal, characteristic, complemented
16C22×#11745685C2211yescharacteristic
17C22×#11745672C2211yescharacteristic
18C22×#11745671C2211yescharacteristic
19C2×#14273686C2211yescharacteristic
20#16837562C418yescomplemented
21C2×#14273660C2211yescharacteristic
22C2×#14273658C2211yescharacteristic
23C2×#14273651C2211yescharacteristic
24C2×#14273651C2211yescharacteristic
25C2×#14273650C2211yescharacteristic
26C2×#14273650C2211yescharacteristic
27C2×#14273650C2211yescharacteristic
28C2×#14273647C2211yescharacteristic
29C2×#14273647C2211yescharacteristic
30C2×#14273647C2211yescharacteristic
31C2×C22⋊(C59⋊C8)C2211yescharacteristic
32C2×C22⋊(C59⋊C8)C2211yescharacteristic
33C2×C4×C59⋊C8C2211yescharacteristic
34C2×C4×C59⋊C8C2211yescharacteristic
35#16837308C2211yescharacteristic
36#16837308C2211yescharacteristic
37#16837304C2211yescharacteristic
38#16837304C2211yescharacteristic
39#16837281—21no—
40#16837281—21no—
41C4×(C2×D59)⋊C4—21no—
42C4×(C2×D59)⋊C4—21no—
43#16837164C2211yescharacteristic
44#16837164C2211yescharacteristic
45#16837164C2211yescharacteristic
46#16837164C2211yescharacteristic
47#16837157C2211yescharacteristic
48#16837157C2211yescharacteristic
49C2×C22⋊Q8×C59C2211yescharacteristic
50C2×C4×Q8×C59C2211yescharacteristic
51C22×C42×C59C2211yescharacteristic
52C59×#391C2211yescharacteristic
53C59×#389C2211yescharacteristic
54C59×#387—21no—
55C59×#385—21no—
56C59×#380C2211yescharacteristic
57C4×C4⋊C4×C59—21no—
58C4×C4⋊C4×C59C2211yescharacteristic
59C4×C22⋊C4×C59—21no—
60C2×#11745685—22no—
61C2×#11745685—41no—
62C2×#11745685—41no—
63C2×#11745685—41no—
64C2×#11745685—41no—
65C2×#11745685C2×C414yes—
66C22×Dic118C2311yescharacteristic
67C22×D236C2311yescharacteristic
68C22×C22⋊D59—21no—
69C22×C4×D59—21no—
70C2×#11745672—41no—
71C2×#11745672—41no—
72C2×#11745672C2×C414yescomplemented
73C2×#11745671—41no—
74C2×#11745671—41no—
75C2×#11745671C2×C414yescomplemented
76C22×C59⋊C8C2311yescharacteristic
77C22×C59⋊C8C2311yescharacteristic
78C22×C59⋊C8C2311yescharacteristic
79C22×C59⋊C8C2311yescharacteristic
80#14273686—41no—
81#14273686—41no—
82C2×C4⋊Dic59C2311yescharacteristic
83C2×C4⋊Dic59C2311yescharacteristic
84C2×C22⋊Dic59—21no—
85C2×(C2×D59)⋊C4—21no—
86C2×(C2×D59)⋊C4—21no—
87C2×(C2×D59)⋊C4—21no—
88C2×(C2×D59)⋊C4—21no—
89C2×C4×Dic59—21no—
90#14273660—41no—
91#14273658—41no—
92#14273651—41no—
93#14273651—41no—
94#14273650—41no—
95#14273650—41no—
96#14273650C2×C414yescomplemented
97#14273647—41no—
98#14273647—41no—
99#14273647C2×C414yescomplemented
100C22⋊(C59⋊C8)—22no—
101C22⋊(C59⋊C8)C2×C414yes—
102C4×C59⋊C8—41no—
103C4×C59⋊C8—41no—
104C59⋊#95—21no—
105C59⋊#95—21no—
106C59⋊#95—21no—
107C59⋊#95—21no—
108C22×Q8×C59C2311yescharacteristic
109C23×C4×C59D411yescharacteristic
110C23×C4×C59D411yescharacteristic
111C23×C4×C59C2311yescharacteristic
112C22⋊Q8×C59—22no—
113C22⋊Q8×C59C2×C414yes—
114C4×Q8×C59—41no—
115C4×Q8×C59—41no—
116C2×C4⋊C4×C59—21no—
117C2×C4⋊C4×C59—21no—
118C2×C4⋊C4×C59—21no—
119C2×C4⋊C4×C59C2311yescharacteristic
120C2×C4⋊C4×C59C2311yescharacteristic
121C2×C4⋊C4×C59C2311yescharacteristic
122C2×C22⋊C4×C59—21no—
123C2×C22⋊C4×C59—21no—
124C2×C42×C59—21no—
125C2×C42×C59—21no—
126C2×C42×C59—41no—
127C2×C42×C59—41no—
128C2×C42×C59D411yescharacteristic
129C2×C42×C59D411yescharacteristic
130C2×C42×C59C2311yescharacteristic
131C2×C42×C59C2311yescharacteristic
132#95×C59—21no—
133#95×C59—21no—
134#95×C59—21no—
135#95×C59—21no—
136#95×C59—21no—
137C24×C59C2×D411yescharacteristic
138C23×D59—21no—
139C2×Q8×C59—21no—
140C2×Q8×C59—21no—
141C2×Q8×C59—21no—
142C2×Q8×C59—21no—
143C2×Q8×C59—21no—
144C2×Q8×C59C22×C412yes—
145C22×C4×C59—21no—
146C22×C4×C59—21no—
147C22×C4×C59—21no—
148C22×C4×C59—21no—
149C22×C4×C59—21no—
150C22×C4×C59—21no—
151C22×C4×C59—22no—
152C22×C4×C59—22no—
153C22×C4×C59—22no—
154C22×C4×C59—21no—
155C22×C4×C59—21no—
156C22×C4×C59—41no—
157C22×C4×C59—41no—
158C22×C4×C59—41no—
159C22×C4×C59C22×C412yes—
160C22×C4×C59C2×D411yescharacteristic
161C22×C4×C59C2×D411yescharacteristic
162C22×C4×C59C2×D411yescharacteristic
163C22×C4×C59C2×D411yescharacteristic
164C22×C4×C59C2×D411yescharacteristic
165C22×C4×C59#4112yes—
166C22×C4×C59C2411yescharacteristic
167C2×C22⋊D59—24no—
168C2×C22⋊D59—42no—
169C2×C22⋊D59—42no—
170C22×Dic59—21no—
171C22×Dic59—21no—
172C22×Dic59—21no—
173#11745685—44no—
174#11745685—44no—
175#11745685—44no—
176#11745685—44no—
177C2×D236—21no—
178C2×D236—21no—
179C2×D236—21no—
180C2×D236—21no—
181C2×D236—21no—
182C2×D236C22×C412yes—
183C2×C4×D59—24no—
184C2×C4×D59—42no—
185C2×C4×D59—42no—
186C2×Dic118—21no—
187C2×Dic118—21no—
188C2×Dic118—21no—
189C2×Dic118—21no—
190C2×Dic118—21no—
191C2×Dic118C22×C412yes—
192C4⋊C4×C59—24no—
193C4⋊C4×C59—21no—
194C4⋊C4×C59—21no—
195C4⋊C4×C59—21no—
196C4⋊C4×C59—21no—
197C4⋊C4×C59—21no—
198C4⋊C4×C59—42no—
199C4⋊C4×C59—42no—
200C4⋊C4×C59C22×C412yes—
201C22⋊C4×C59—24no—
202C22⋊C4×C59—42no—
203C42×C59—21no—
204C42×C59—21no—
205C42×C59—21no—
206C42×C59—21no—
207C42×C59—41no—
208C42×C59—41no—
209C42×C59—42no—
210C42×C59—42no—
211C22⋊Dic59—42no—
212#11745672—44no—
213#11745671—44no—
214(C2×D59)⋊C4—42no—
215(C2×D59)⋊C4—42no—
216(C2×D59)⋊C4—42no—
217(C2×D59)⋊C4—42no—
218C4⋊Dic59—21no—
219C4⋊Dic59—21no—
220C4⋊Dic59—21no—
221C4⋊Dic59—21no—
222C4×Dic59—42no—
223C2×C59⋊C8—21no—
224C2×C59⋊C8—21no—
225C2×C59⋊C8—21no—
226C2×C59⋊C8—21no—
227C2×C59⋊C8—21no—
228C2×C59⋊C8—21no—
229C2×C59⋊C8—21no—
230C2×C59⋊C8—21no—
231C2×C59⋊C8—21no—
232C2×C59⋊C8—21no—
233C2×C59⋊C8C22×C412yes—
234C2×C59⋊C8C22×C412yes—
235C23×C59—21no—
236C23×C59—21no—
237C23×C59—21no—
238C23×C59—21no—
239C23×C59—21no—
240C23×C59—21no—
241C23×C59C4×D412yes—
242C23×C59C22×D411yescharacteristic
243C22×D59—22no—
244C22×D59—41no—
245C22×D59—41no—
246C22×D59—41no—
247C22×D59—41no—
248C22×D59—41no—
249C22×D59—41no—
250Q8×C59—22no—
251Q8×C59—22no—
252Q8×C59—41no—
253Q8×C59—41no—
254C2×C4×C59—21no—
255C2×C4×C59—21no—
256C2×C4×C59—21no—
257C2×C4×C59—21no—
258C2×C4×C59—21no—
259C2×C4×C59—21no—
260C2×C4×C59—21no—
261C2×C4×C59—21no—
262C2×C4×C59—22no—
263C2×C4×C59—22no—
264C2×C4×C59—22no—
265C2×C4×C59—22no—
266C2×C4×C59—22no—
267C2×C4×C59—22no—
268C2×C4×C59—21no—
269C2×C4×C59—21no—
270C2×C4×C59—21no—
271C2×C4×C59—44no—
272C2×C4×C59—44no—
273C2×C4×C59—41no—
274C2×C4×C59—41no—
275C2×C4×C59—41no—
276C2×C4×C59—41no—
277C2×C4×C59—41no—
278C2×C4×C59—41no—
279C2×C4×C59—41no—
280C2×C4×C59—41no—
281C2×C4×C59—41no—
282C2×C4×C59—41no—
283C2×C4×C59C4×D412yes—
284C2×C4×C59#13512yes—
285C2×C4×C59#13512yes—
286C2×C4×C59#13712yes—
287C2×C4×C59C23×C411yescharacteristic
288C2×C4×C59C2×#4111yescharacteristic
289C2×C4×C59H(5,𝔽2)11yescharacteristic
290C2×C4×C59H(5,𝔽2)11yescharacteristic
291C2×C4×C59H(5,𝔽2)11yescharacteristic
292C2×C4×C59H(5,𝔽2)11yescharacteristic
293C22⋊D59—48no—
294C2×Dic59—22no—
295C2×Dic59—41no—
296C2×Dic59—41no—
297C2×Dic59—41no—
298C2×Dic59—41no—
299C2×Dic59—41no—
300C2×Dic59—41no—
301C2×Dic59—41no—
302C2×Dic59—41no—
303D236—22no—
304D236—22no—
305D236—41no—
306D236—41no—
307C4×D59—48no—
308Dic118—22no—
309Dic118—22no—
310Dic118—41no—
311Dic118—41no—
312C59⋊C8—22no—
313C59⋊C8—22no—
314C59⋊C8—41no—
315C59⋊C8—41no—
316#22042—591nomaximal, Sylow
317C22×C59—22no—
318C22×C59—22no—
319C22×C59—22no—
320C22×C59—41no—
321C22×C59—41no—
322C22×C59—41no—
323C22×C59—41no—
324C22×C59C2×C4×D411yescharacteristic
325C22×C59#53411yescharacteristic
326C22×C59#53511yescharacteristic
327C22×C59C2×#13511yescharacteristic
328C22×C59C2×#13511yescharacteristic
329C22×C59C2×#13711yescharacteristic
330C22×C59#57511yescharacteristic
331C2×D59—42no—
332C2×D59—42no—
333C2×D59—42no—
334C2×D59—81no—
335C2×D59—81no—
336C2×D59—81no—
337C2×D59—81no—
338C4×C59—22no—
339C4×C59—22no—
340C4×C59—22no—
341C4×C59—22no—
342C4×C59—42no—
343C4×C59—41no—
344C4×C59—42no—
345C4×C59—81no—
346C4×C59—81no—
347C4×C59#51811yescharacteristic
348C4×C59#51811yescharacteristic
349C4×C59#53811yescharacteristic
350C4×C59#53811yescharacteristic
351Dic59—42no—
352Dic59—81no—
353Dic59—81no—
354C2×#452—591no—
355C4×C22⋊Q8D5911yescharacteristic, complemented
356#2297—591no—
357#1969—591no—
358#1968—591no—
359#1934—591no—
360#1933—591no—
361#1927—591no—
362#1925—591no—
363#1880—591no—
364#1878—591no—
365#1873—591no—
366#1854—591no—
367#1788—591no—
368C4×C22⋊C8—591no—
369C2×C59—42no—
370C2×C59#232111yescharacteristic
371C2×C59C4×#13511yescharacteristic
372C2×C59C4×#13711yescharacteristic
373C2×C59#319011yescharacteristic
374C2×C59#319111yescharacteristic
375C2×C59#321011yescharacteristic
376C2×C59#321211yescharacteristic
377D59—82no—
378C22×#41—591no—
379C22×Q16—591no—
380C22×SD16—591no—
381C2×C22⋊Q8C2×D5911yescharacteristic
382C2×C4×Q8C2×D5911yescharacteristic
383C2×#117—591no—
384C22×C42C2×D5911yescharacteristic
385#452—598no—
386C2×#107—591no—
387C2×#106—591no—
388C2×#103—591no—
389C2×#103—591no—
390C2×#103—591no—
391C2×#103—591no—
392C2×#103—591no—
393C2×#102—591no—
394C2×#102—591no—
395C2×#102—591no—
396C2×C22⋊C8—591no—
397C2×C22⋊C8—591no—
398C2×C4×C8—591no—
399C2×C4×C8—591no—
400#391—591no—
401#391—591no—
402#391C2×D5911yescharacteristic
403#390—591no—
404#390—591no—
405#389C2×D5911yescharacteristic
406#387—21no—
407#386—1181no—
408#386—1181no—
409#385—21no—
410#380C2×D5911yescharacteristic
411C4×C4⋊C4—21no—
412C4×C4⋊C4C2×D5911yescharacteristic
413C4×C22⋊C4—21no—
414C4×C22⋊C4—1181no—
415C4×C22⋊C4—1181no—
416#340—591no—
417#340—591no—
418#340—591no—
419#340—591no—
420#336—591no—
421#336—591no—
422C59#2204211yescharacteristic, complemented, Sylow
423C2×#41—594no—
424C2×#41—1182no—
425C2×#41—2361no—
426C2×#41—2361no—
427C2×#41—2361no—
428C2×#41—2361no—
429C22×Q8—591no—
430C22×Q8C22×D5911yescharacteristic
431C22×D4—591no—
432C22×D4—1181no—
433C23×C4—1181no—
434C23×C4C22⋊D5911yescharacteristic
435C23×C4C22⋊D5911yescharacteristic
436C23×C4C22×D5911yescharacteristic
437C2×Q16—594no—
438C2×Q16—2361no—
439C2×Q16—2361no—
440C2×SD16—594no—
441C2×SD16—2361no—
442C2×SD16—2361no—
443C22×C8—591no—
444C22×C8—591no—
445C22×C8—591no—
446C22×C8—591no—
447C22⋊Q8—22no—
448C22⋊Q8C4×D5914yes—
449C4×Q8—41no—
450C4×Q8—41no—
451#117—2361no—
452#117—2361no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—591no—
457C2×C4⋊C4—591no—
458C2×C4⋊C4C22×D5911yescharacteristic
459C2×C4⋊C4C22×D5911yescharacteristic
460C2×C4⋊C4C22×D5911yescharacteristic
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—1181no—
464C2×C22⋊C4—1181no—
465C2×C22⋊C4—1181no—
466C2×C22⋊C4—1181no—
467C2×C22⋊C4—1181no—
468C2×C42—21no—
469C2×C42—21no—
470C2×C42—41no—
471C2×C42—41no—
472C2×C42—1181no—
473C2×C42C22⋊D5911yescharacteristic
474C2×C42C22⋊D5911yescharacteristic
475C2×C42C22×D5911yescharacteristic
476C2×C42C22×D5911yescharacteristic
477#107—2361no—
478#106—2361no—
479#103—594no—
480#103—2361no—
481#103—2361no—
482#103—2361no—
483#103—2361no—
484#102—594no—
485#102—2361no—
486#102—2361no—
487C22⋊C8—594no—
488C22⋊C8—1182no—
489C4×C8—2361no—
490C4×C8—2361no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95—21no—
496#95—1181no—
497#95—1181no—
498#95—1181no—
499#95—1181no—
500C24—1181no—
501C24C2×C22⋊D5911yescharacteristic
502#41—2364no—
503#41—2364no—
504#41—2364no—
505#41—2364no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—592no—
512C2×Q8—1181no—
513C2×Q8—1181no—
514C2×Q8—1181no—
515C2×Q8—1181no—
516C2×Q8—1181no—
517C2×Q8C2×C4×D5912yes—
518C2×D4—592no—
519C2×D4—1184no—
520C2×D4—1181no—
521C2×D4—1181no—
522C2×D4—1181no—
523C2×D4—1181no—
524C2×D4—1181no—
525C2×D4—2362no—
526C2×D4—2362no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—41no—
539C22×C4—41no—
540C22×C4—41no—
541C22×C4—1181no—
542C22×C4—1184no—
543C22×C4—1181no—
544C22×C4—1181no—
545C22×C4—2362no—
546C22×C4—2362no—
547C22×C4C2×C4×D5912yes—
548C22×C4#1174568512yes—
549C22×C4C2×C22⋊D5911yescharacteristic
550C22×C4C2×C22⋊D5911yescharacteristic
551C22×C4C2×C22⋊D5911yescharacteristic
552C22×C4C2×C22⋊D5911yescharacteristic
553C22×C4C2×C22⋊D5911yescharacteristic
554C22×C4C23×D5911yescharacteristic
555Q16—2364no—
556SD16—2364no—
557C2×C8—592no—
558C2×C8—592no—
559C2×C8—1181no—
560C2×C8—1181no—
561C2×C8—1181no—
562C2×C8—1181no—
563C2×C8—1181no—
564C2×C8—1181no—
565C2×C8—1181no—
566C2×C8—1181no—
567C2×C8—1181no—
568C2×C8—1181no—
569C4⋊C4—24no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—42no—
576C4⋊C4—42no—
577C4⋊C4—1181no—
578C4⋊C4—1181no—
579C4⋊C4—1181no—
580C4⋊C4—1181no—
581C4⋊C4C2×C4×D5912yes—
582C22⋊C4—24no—
583C22⋊C4—42no—
584C22⋊C4—2362no—
585C22⋊C4—2362no—
586C22⋊C4—2362no—
587C22⋊C4—2362no—
588C22⋊C4—2362no—
589C42—21no—
590C42—21no—
591C42—21no—
592C42—21no—
593C42—41no—
594C42—41no—
595C42—42no—
596C42—42no—
597C42—2362no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—1182no—
605C23—2361no—
606C23—2361no—
607C23—2361no—
608C23—2361no—
609C23—2361no—
610C23—2361no—
611C23C4×C22⋊D5912yes—
612C23C22×C22⋊D5911yescharacteristic
613Q8—22no—
614Q8—22no—
615Q8—41no—
616Q8—41no—
617Q8—1182no—
618Q8—1182no—
619Q8—2361no—
620Q8—2361no—
621D4—1182no—
622D4—1182no—
623D4—2368no—
624D4—2361no—
625D4—2361no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—44no—
644C2×C4—44no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—1182no—
656C2×C4—2368no—
657C2×C4—2361no—
658C2×C4—2361no—
659C2×C4—2361no—
660C2×C4—2361no—
661C2×C4—2361no—
662C2×C4—2361no—
663C2×C4—2361no—
664C2×C4—2361no—
665C2×C4C4×C22⋊D5912yes—
666C2×C4#1427374712yes—
667C2×C4#1427374712yes—
668C2×C4#1427375812yes—
669C2×C4C22×C4×D5911yescharacteristic
670C2×C4C2×#1174568511yescharacteristic
671C2×C4#1427377211yescharacteristic
672C2×C4#1427377211yescharacteristic
673C2×C4#1427377311yescharacteristic
674C2×C4#1427377311yescharacteristic
675C8—1182no—
676C8—1182no—
677C8—2361no—
678C8—2361no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—41no—
686C22—4721no—
687C22—4721no—
688C22—4721no—
689C22—4721no—
690C22—2362no—
691C22—2362no—
692C22—2362no—
693C22C2×C4×C22⋊D5911yescharacteristic
694C22#1683796111yescharacteristic
695C22#1683796611yescharacteristic
696C22C2×#1427374711yescharacteristic
697C22C2×#1427374711yescharacteristic
698C22C2×#1427375811yescharacteristic
699C22#1683820011yescharacteristic
700C4—22no—
701C4—22no—
702C4—22no—
703C4—22no—
704C4—41no—
705C4—42no—
706C4—42no—
707C4—81no—
708C4—81no—
709C4—4721no—
710C4—4721no—
711C4—2362no—
712C4#1683787411yescharacteristic
713C4#1683787411yescharacteristic
714C4#1683798511yescharacteristic
715C4#1683798511yescharacteristic
716C2—42no—
717C2—4722no—
718C2#2142675011yescharacteristic
719C2C4×#1427374711yescharacteristic
720C2C4×#1427375811yescharacteristic
721C2#2143487711yescharacteristic
722C2#2143488411yescharacteristic
723C2#2143504811yescharacteristic
724C2#2143506811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC4×C22⋊Q8×C59C2
socleC23×C59C22×D4
prime radicalC22×#11745685C22
cosocleC22×C4×C59C24
hypercenterC4×C22⋊Q8D59
hypocenterC59#22042
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #21424956C2semidirect
4. #21424953C2semidirect
5. #21424778C2semidirect
6. #21424771C2semidirect
7. #21424730C2semidirect
8. #21424716C2semidirect
9. #21424451C2semidirect
10. #21424437C2semidirect
11. #21424409C2semidirect
12. #21424293C2semidirect
14. C4×C22⋊(C59⋊C8)C2semidirect
15. C4×C22⋊Q8×C59C2semidirect
20. #16837562C4semidirect
72. C2×#11745672C2×C4semidirect
75. C2×#11745671C2×C4semidirect
96. #14273650C2×C4semidirect
99. #14273647C2×C4semidirect
355. C4×C22⋊Q8D59semidirect
422. C59#22042semidirect

Maximal subgroups

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

subgroupindex
C2×#168375622
#214265862
#214249562
#214249532
#214247782
#214247712
#214247302
#214247162
#214244512
#214244372
#214244092
#214242932
#214240342
C4×C22⋊(C59⋊C8)2
C4×C22⋊Q8×C592
#2204259