Finite Group Databasebeta

← #28605016

Subgroups — #28605016

Order 15104.

1130 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838122C211yesmaximal, characteristic
2C2×#16837474C211yesmaximal, characteristic
3#21425068C211yesmaximal, characteristic, complemented
4#21425044C211yesmaximal, characteristic, complemented
5#21424527C211yesmaximal, characteristic, complemented
6#21424517C211yesmaximal, characteristic, complemented
7#21424408C211yesmaximal, characteristic, complemented
8#21424403C211yesmaximal, characteristic, complemented
9#21424188C211yesmaximal, characteristic, complemented
10#21424188C211yesmaximal, characteristic, complemented
11#21424108C211yesmaximal, characteristic, complemented
12#21423929C211yesmaximal, characteristic, complemented
13#21423815C211yesmaximal, characteristic, complemented
14#21423812C211yesmaximal, characteristic, complemented
15C59×#2352C211yesmaximal, characteristic
16C22×#11745664C2211yescharacteristic
17C23×C59⋊C8C2211yescharacteristic
18#16838122—24no—
19#16838122C418yescomplemented
20C2×#14273727C2211yescharacteristic
21C2×#14273720—21no—
22C2×#14273720—21no—
23C2×#14273714—21no—
24C2×#14273706C2211yescharacteristic
25C2×#14273706C2211yescharacteristic
26C2×C4×Dic118C2211yescharacteristic
27C2×#14273692—21no—
28C2×#14273686C2211yescharacteristic
29C2×#14273686C2211yescharacteristic
30#16837474—24no—
31C2×C4⋊(C59⋊C8)C2211yescharacteristic
32C2×#14273650C2211yescharacteristic
33C2×#14273650C2211yescharacteristic
34C2×#14273650C2211yescharacteristic
35C2×#14273650C2211yescharacteristic
36C2×C22⋊(C59⋊C8)C2211yescharacteristic
37C2×C22⋊(C59⋊C8)C2211yescharacteristic
38C2×#14273638C2211yescharacteristic
39#16837164C2211yescharacteristic
40#16837164C2211yescharacteristic
41#16837164C2211yescharacteristic
42#16837164C2211yescharacteristic
43#16837164C2211yescharacteristic
44#16837164C2211yescharacteristic
45#16837164C2211yescharacteristic
46#16837164C2211yescharacteristic
47#16837164C2211yescharacteristic
48#16837164C2211yescharacteristic
49#16837164C2211yescharacteristic
50#16837164C2211yescharacteristic
51C2×C4×D4×C59C2211yescharacteristic
52C2×#117×C59C2211yescharacteristic
53C22×C4⋊C4×C59C2211yescharacteristic
54C59×#388—21no—
55C59×#387—21no—
56C59×#386—21no—
57C59×#382C2211yescharacteristic
58C59×#380C2211yescharacteristic
59C59×#380C2211yescharacteristic
60C4×C4⋊C4×C59C2211yescharacteristic
61C4×C22⋊C4×C59—21no—
62C22×Dic118—21no—
63C22×Dic118C2311yescharacteristic
64C2×#11745664—22no—
65C2×#11745664—22no—
66C2×#11745664—41no—
67C22×C59⋊C8—22no—
68C22×C59⋊C8—22no—
69C22×C59⋊C8—41no—
70C22×C59⋊C8C2311yescharacteristic
71C22×C59⋊C8C2311yescharacteristic
72C22×C59⋊C8C2311yescharacteristic
73C22×C59⋊C8C2311yescharacteristic
74#14273727—22no—
75#14273727C2×C414yescomplemented
76#14273720—28no—
77#14273720—28no—
78#14273714—28no—
79#14273706—22no—
80#14273706—22no—
81#14273706C2×C414yes—
82#14273706C2×C414yescomplemented
83C4×Dic118—22no—
84C4×Dic118C2×C414yescomplemented
85#14273692—28no—
86#14273686—22no—
87#14273686—22no—
88#14273686C2×C414yes—
89#14273686C2×C414yescomplemented
90C2×C4⋊Dic59—21no—
91C2×C4⋊Dic59C2311yescharacteristic
92C2×C4⋊Dic59C2311yescharacteristic
93C2×C4⋊Dic59C2311yescharacteristic
94C2×Dic59⋊C4—21no—
95C2×Dic59⋊C4—21no—
96C2×Dic59⋊C4—21no—
97C2×C22⋊Dic59—21no—
98C2×C22⋊Dic59—21no—
99C2×C22⋊Dic59—21no—
100C2×C22⋊Dic59—21no—
101C2×C4×Dic59—21no—
102C2×C4×Dic59—21no—
103C2×C4×Dic59—21no—
104C4⋊(C59⋊C8)—22no—
105#14273650—22no—
106#14273650—22no—
107#14273650—41no—
108#14273650—41no—
109C22⋊(C59⋊C8)—22no—
110C22⋊(C59⋊C8)—22no—
111#14273638—22no—
112C22×D4×C59D411yescharacteristic
113C23×C4×C59—21no—
114C23×C4×C59C2311yescharacteristic
115C23×C4×C59C2311yescharacteristic
116C4×D4×C59C2×C414yes—
117C4×D4×C59D414yes—
118#117×C59—22no—
119#117×C59—41no—
120C2×C4⋊C4×C59—22no—
121C2×C4⋊C4×C59—21no—
122C2×C4⋊C4×C59—41no—
123C2×C4⋊C4×C59D411yescharacteristic
124C2×C4⋊C4×C59C2311yescharacteristic
125C2×C4⋊C4×C59C2311yescharacteristic
126C2×C4⋊C4×C59C2311yescharacteristic
127C2×C4⋊C4×C59C2311yescharacteristic
128C2×C22⋊C4×C59—21no—
129C2×C22⋊C4×C59—21no—
130C2×C22⋊C4×C59—21no—
131C2×C22⋊C4×C59D411yescharacteristic
132C2×C22⋊C4×C59D411yescharacteristic
133C2×C42×C59—21no—
134C2×C42×C59—21no—
135C2×C42×C59C2311yescharacteristic
136#95×C59—21no—
137#95×C59—21no—
138#95×C59—21no—
139#95×C59—21no—
140#95×C59—21no—
141C24×C59C2×D411yescharacteristic
142C24×C59C2×D411yescharacteristic
143C2×D4×C59—41no—
144C2×D4×C59—41no—
145C2×D4×C59C22⋊C414yes—
146C22×C4×C59—21no—
147C22×C4×C59—21no—
148C22×C4×C59—21no—
149C22×C4×C59—21no—
150C22×C4×C59—21no—
151C22×C4×C59—21no—
152C22×C4×C59—21no—
153C22×C4×C59—21no—
154C22×C4×C59—21no—
155C22×C4×C59—21no—
156C22×C4×C59—21no—
157C22×C4×C59—21no—
158C22×C4×C59—42no—
159C22×C4×C59—42no—
160C22×C4×C59—81no—
161C22×C4×C59C22×C412yes—
162C22×C4×C59C22×C412yes—
163C22×C4×C59C2×D411yescharacteristic
164C22×C4×C59C2×D411yescharacteristic
165C22×C4×C59C2×D411yescharacteristic
166C22×C4×C59C2×D411yescharacteristic
167C22×C4×C59C2×D412yes—
168C22×C4×C59C2×D412yes—
169C22×C4×C59C2411yescharacteristic
170C22×Dic59—21no—
171C22×Dic59—21no—
172C22×Dic59—21no—
173C22×Dic59—21no—
174C2×Dic118—21no—
175C2×Dic118—21no—
176C2×Dic118—21no—
177C2×Dic118—21no—
178C2×Dic118—24no—
179C2×Dic118—21no—
180C2×Dic118—42no—
181C2×Dic118—42no—
182C2×Dic118C22×C412yes—
183C4⋊C4×C59—21no—
184C4⋊C4×C59—21no—
185C4⋊C4×C59—21no—
186C4⋊C4×C59—21no—
187C4⋊C4×C59—21no—
188C4⋊C4×C59—21no—
189C4⋊C4×C59—21no—
190C4⋊C4×C59—42no—
191C4⋊C4×C59C22⋊C414yes—
192C4⋊C4×C59#4112yes—
193C22⋊C4×C59—42no—
194C22⋊C4×C59—42no—
195C22⋊C4×C59—81no—
196C22⋊C4×C59C22⋊C414yes—
197C22⋊C4×C59C22⋊C414yes—
198C42×C59—42no—
199C42×C59—81no—
200C42×C59C22×C412yes—
201C42×C59C2×D412yes—
202C22⋊Dic59—24no—
203C22⋊Dic59—24no—
204C22⋊Dic59—24no—
205C22⋊Dic59—24no—
206C4⋊Dic59—24no—
207C4⋊Dic59—21no—
208C4⋊Dic59—21no—
209C4⋊Dic59—21no—
210C4⋊Dic59C22×C412yes—
211C4⋊Dic59C22×C412yes—
212C4⋊Dic59C22×C412yes—
213Dic59⋊C4—24no—
214Dic59⋊C4—24no—
215Dic59⋊C4—24no—
216C4×Dic59—24no—
217C4×Dic59—24no—
218C4×Dic59—24no—
219#11745664—44no—
220C2×C59⋊C8—21no—
221C2×C59⋊C8—21no—
222C2×C59⋊C8—21no—
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—44no—
232C2×C59⋊C8#4112yes—
233C23×C59—21no—
234C23×C59—21no—
235C23×C59—21no—
236C23×C59—21no—
237C23×C59—21no—
238C23×C59—21no—
239C23×C59—21no—
240C23×C59—21no—
241C23×C59—21no—
242C23×C59—21no—
243C23×C59—21no—
244C23×C59—21no—
245C23×C59C2×C22⋊C412yes—
246C23×C59C2×C22⋊C412yes—
247C23×C59C22×D411yescharacteristic
248D4×C59—44no—
249C2×C4×C59—21no—
250C2×C4×C59—21no—
251C2×C4×C59—21no—
252C2×C4×C59—21no—
253C2×C4×C59—21no—
254C2×C4×C59—21no—
255C2×C4×C59—21no—
256C2×C4×C59—21no—
257C2×C4×C59—22no—
258C2×C4×C59—22no—
259C2×C4×C59—22no—
260C2×C4×C59—22no—
261C2×C4×C59—22no—
262C2×C4×C59—22no—
263C2×C4×C59—22no—
264C2×C4×C59—22no—
265C2×C4×C59—22no—
266C2×C4×C59—41no—
267C2×C4×C59—41no—
268C2×C4×C59—41no—
269C2×C4×C59—41no—
270C2×C4×C59—41no—
271C2×C4×C59—41no—
272C2×C4×C59—41no—
273C2×C4×C59—41no—
274C2×C4×C59—41no—
275C2×C4×C59—41no—
276C2×C4×C59—41no—
277C2×C4×C59—84no—
278C2×C4×C59C2×C22⋊C412yes—
279C2×C4×C59C2×C22⋊C412yes—
280C2×C4×C59C2×C22⋊C412yes—
281C2×C4×C59C2×C22⋊C412yes—
282C2×C4×C59C23×C411yescharacteristic
283C2×C4×C59C22×D411yescharacteristic
284C2×C4×C59C2×#4111yescharacteristic
285C2×C4×C59C2×#4111yescharacteristic
286C2×C4×C59H(5,𝔽2)11yescharacteristic
287C2×C4×C592−1+411yescharacteristic
288C2×Dic59—22no—
289C2×Dic59—22no—
290C2×Dic59—22no—
291C2×Dic59—22no—
292C2×Dic59—41no—
293C2×Dic59—41no—
294C2×Dic59—41no—
295C2×Dic59—41no—
296C2×Dic59—41no—
297C2×Dic59—41no—
298C2×Dic59—41no—
299C2×Dic59—41no—
300Dic118—22no—
301Dic118—22no—
302Dic118—48no—
303Dic118—41no—
304Dic118—41no—
305C59⋊C8—22no—
306C59⋊C8—41no—
307C59⋊C8—41no—
308C59⋊C8—41no—
309#22494—591nomaximal, Sylow
310C22×C59—22no—
311C22×C59—22no—
312C22×C59—22no—
313C22×C59—22no—
314C22×C59—22no—
315C22×C59—22no—
316C22×C59—41no—
317C22×C59—41no—
318C22×C59—41no—
319C22×C59—41no—
320C22×C59—41no—
321C22×C59—41no—
322C22×C59—41no—
323C22×C59—41no—
324C22×C59C22×C22⋊C411yescharacteristic
325C22×C59#54611yescharacteristic
326C22×C59#54711yescharacteristic
327C22×C59#57511yescharacteristic
328C22×C59#57511yescharacteristic
329C22×C59#57711yescharacteristic
330C22×C59#57811yescharacteristic
331C4×C59—22no—
332C4×C59—22no—
333C4×C59—22no—
334C4×C59—22no—
335C4×C59—42no—
336C4×C59—81no—
337C4×C59—81no—
338C4×C59—81no—
339C4×C59C4×#4111yescharacteristic
340C4×C59#52011yescharacteristic
341C4×C59#54611yescharacteristic
342C4×C59#54711yescharacteristic
343Dic59—42no—
344Dic59—42no—
345Dic59—42no—
346Dic59—42no—
347C2×#556—591no—
348C2×#435—591no—
349#2352D5911yescharacteristic
350#1993—591no—
351#1987—591no—
352#1894—591no—
353#1892—591no—
354#1873—591no—
355#1872—591no—
356#1825—591no—
357#1825—591no—
358#1805—591no—
359#1763—591no—
360#1736—591no—
361#1735—591no—
362C2×C59—42no—
363C2×C59—42no—
364C2×C59#233911yescharacteristic
365C2×C59#289611yescharacteristic
366C2×C59#289811yescharacteristic
367C2×C59#331111yescharacteristic
368C2×C59#331311yescharacteristic
369C2×C59#334911yescharacteristic
370C2×C59#335011yescharacteristic
371C22×M16—591no—
372C23×C8—591no—
373#556—598no—
374#556—1184no—
375C2×C4⋊Q8—591no—
376C2×#126—1181no—
377C2×#126—1181no—
378C2×#124—1181no—
379C2×C22⋊Q8—591no—
380C2×C22⋊Q8—591no—
381C2×C4×Q8—591no—
382C2×C4×Q8—1181no—
383C2×C4×D4C2×D5911yescharacteristic
384C2×#117—591no—
385C2×#117—591no—
386C2×#117C2×D5911yescharacteristic
387C22×C4⋊C4C2×D5911yescharacteristic
388#435—1184no—
389C2×C4⋊C8—591no—
390C2×#103—591no—
391C2×#103—591no—
392C2×#103—591no—
393C2×#103—591no—
394C2×C22⋊C8—591no—
395C2×C22⋊C8—591no—
396C2×#97—591no—
397#388—21no—
398#387—21no—
399#386—21no—
400#382C2×D5911yescharacteristic
401#380C2×D5911yescharacteristic
402#380C2×D5911yescharacteristic
403C4×C4⋊C4C2×D5911yescharacteristic
404C4×C22⋊C4—21no—
405#340—591no—
406#340—591no—
407#340—591no—
408#340—591no—
409#340—591no—
410#340—591no—
411#340—591no—
412#340—591no—
413#340—591no—
414#340—591no—
415#340—591no—
416#340—591no—
417C59#2249411yescharacteristic, complemented, Sylow
418C22×Q8—591no—
419C22×Q8—1181no—
420C22×D4C22⋊D5911yescharacteristic
421C23×C4—21no—
422C23×C4C22×D5911yescharacteristic
423C23×C4C22×D5911yescharacteristic
424C2×M16—1182no—
425C2×M16—1182no—
426C2×M16—2361no—
427C22×C8—591no—
428C22×C8—591no—
429C22×C8—591no—
430C22×C8—591no—
431C22×C8—1182no—
432C22×C8—1182no—
433C22×C8—2361no—
434C4⋊Q8—594no—
435C4⋊Q8—1182no—
436#126—1188no—
437#126—1188no—
438#124—1188no—
439C22⋊Q8—594no—
440C22⋊Q8—594no—
441C22⋊Q8—1182no—
442C22⋊Q8—1182no—
443C4×Q8—594no—
444C4×Q8—1188no—
445C4×Q8—1182no—
446C4×D4C4×D5914yes—
447C4×D4D23614yes—
448#117—22no—
449#117—41no—
450#117—594no—
451#117—594no—
452#117—1182no—
453#117—1182no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—41no—
457C2×C4⋊C4—591no—
458C2×C4⋊C4—591no—
459C2×C4⋊C4—591no—
460C2×C4⋊C4—1181no—
461C2×C4⋊C4—1181no—
462C2×C4⋊C4—1181no—
463C2×C4⋊C4—1181no—
464C2×C4⋊C4C22⋊D5911yescharacteristic
465C2×C4⋊C4C22×D5911yescharacteristic
466C2×C4⋊C4C22×D5911yescharacteristic
467C2×C4⋊C4C22×D5911yescharacteristic
468C2×C4⋊C4C22×D5911yescharacteristic
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—1181no—
473C2×C22⋊C4—1181no—
474C2×C22⋊C4—1181no—
475C2×C22⋊C4—1181no—
476C2×C22⋊C4C22⋊D5911yescharacteristic
477C2×C22⋊C4C22⋊D5911yescharacteristic
478C2×C42—21no—
479C2×C42—21no—
480C2×C42—1181no—
481C2×C42—1181no—
482C2×C42—1181no—
483C2×C42C22×D5911yescharacteristic
484C4⋊C8—1182no—
485#103—1182no—
486#103—1182no—
487#103—2361no—
488#103—2361no—
489C22⋊C8—1182no—
490C22⋊C8—1182no—
491#97—1182no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95—21no—
496#95—21no—
497C24C2×C22⋊D5911yescharacteristic
498C24C2×C22⋊D5911yescharacteristic
499C2×Q8—592no—
500C2×Q8—1184no—
501C2×Q8—1181no—
502C2×Q8—1181no—
503C2×Q8—1181no—
504C2×Q8—1181no—
505C2×Q8—1181no—
506C2×Q8—2362no—
507C2×Q8—2362no—
508C2×D4—41no—
509C2×D4—41no—
510C2×D4(C2×D59)⋊C414yes—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—81no—
526C22×C4—1181no—
527C22×C4—1181no—
528C22×C4—1181no—
529C22×C4—1181no—
530C22×C4C2×C4×D5912yes—
531C22×C4C2×C4×D5912yes—
532C22×C4C2×D23612yes—
533C22×C4C2×D23612yes—
534C22×C4C2×C22⋊D5911yescharacteristic
535C22×C4C2×C22⋊D5911yescharacteristic
536C22×C4C2×C22⋊D5911yescharacteristic
537C22×C4C2×C22⋊D5911yescharacteristic
538C22×C4C23×D5911yescharacteristic
539M16—2364no—
540C2×C8—592no—
541C2×C8—1181no—
542C2×C8—1181no—
543C2×C8—1181no—
544C2×C8—1181no—
545C2×C8—1181no—
546C2×C8—1181no—
547C2×C8—1181no—
548C2×C8—1181no—
549C2×C8—1181no—
550C2×C8—1181no—
551C2×C8—1181no—
552C2×C8—2364no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—42no—
561C4⋊C4—592no—
562C4⋊C4—592no—
563C4⋊C4—592no—
564C4⋊C4—1184no—
565C4⋊C4—1184no—
566C4⋊C4—1184no—
567C4⋊C4—1184no—
568C4⋊C4—1181no—
569C4⋊C4—1181no—
570C4⋊C4—1181no—
571C4⋊C4(C2×D59)⋊C414yes—
572C4⋊C4#1174568712yes—
573C22⋊C4—42no—
574C22⋊C4—42no—
575C22⋊C4—81no—
576C22⋊C4—1184no—
577C22⋊C4—1184no—
578C22⋊C4—1184no—
579C22⋊C4—1184no—
580C22⋊C4(C2×D59)⋊C414yes—
581C22⋊C4(C2×D59)⋊C414yes—
582C42—42no—
583C42—81no—
584C42—1184no—
585C42—1184no—
586C42—1184no—
587C42C2×C4×D5912yes—
588C42C2×D23612yes—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23C2×(C2×D59)⋊C412yes—
602C23C2×(C2×D59)⋊C412yes—
603C23C22×C22⋊D5911yescharacteristic
604Q8—1182no—
605Q8—1182no—
606Q8—2368no—
607Q8—2361no—
608Q8—2361no—
609D4—44no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—84no—
639C2×C4—1182no—
640C2×C4—1182no—
641C2×C4—1182no—
642C2×C4—1182no—
643C2×C4—2361no—
644C2×C4—2361no—
645C2×C4—2361no—
646C2×C4—2361no—
647C2×C4—2361no—
648C2×C4—2361no—
649C2×C4—2361no—
650C2×C4—2361no—
651C2×C4C2×(C2×D59)⋊C412yes—
652C2×C4C2×(C2×D59)⋊C412yes—
653C2×C4C2×(C2×D59)⋊C412yes—
654C2×C4C2×(C2×D59)⋊C412yes—
655C2×C4C22×C4×D5911yescharacteristic
656C2×C4C22×D23611yescharacteristic
657C2×C4#41×D5911yescharacteristic
658C2×C4C2×#1174568711yescharacteristic
659C2×C4#1427377211yescharacteristic
660C2×C4#1427377411yescharacteristic
661C8—1182no—
662C8—2361no—
663C8—2361no—
664C8—2361no—
665C22—22no—
666C22—22no—
667C22—22no—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—41no—
677C22—41no—
678C22—41no—
679C22C22×(C2×D59)⋊C411yescharacteristic
680C22#1683804611yescharacteristic
681C22#1683805111yescharacteristic
682C22#1683820011yescharacteristic
683C22#1683820011yescharacteristic
684C22#1683821311yescharacteristic
685C22#1683821711yescharacteristic
686C4—22no—
687C4—22no—
688C4—22no—
689C4—22no—
690C4—42no—
691C4—81no—
692C4—81no—
693C4—81no—
694C4—2362no—
695C4—2362no—
696C4—2362no—
697C4—2362no—
698C4C4×#1174568711yescharacteristic
699C4#1683788111yescharacteristic
700C4#1683804711yescharacteristic
701C4#1683805611yescharacteristic
702C2—42no—
703C2—42no—
704C2#2142692111yescharacteristic
705C2#2143261311yescharacteristic
706C2#2143262611yescharacteristic
707C2#2143613211yescharacteristic
708C2#2143616211yescharacteristic
709C2#2143662611yescharacteristic
710C2#2143663511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#2352C2
socleC23×C59C22×D4
prime radicalC22×D4×C59D4
cosocleC22×C4×C59C24
hypercenter#2352D59
hypocenterC59#22494
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2352

Complements

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

NH ≅ G/Ntype
3. #21425068C2semidirect
4. #21425044C2semidirect
5. #21424527C2semidirect
6. #21424517C2semidirect
7. #21424408C2semidirect
8. #21424403C2semidirect
9. #21424188C2semidirect
10. #21424188C2semidirect
11. #21424108C2semidirect
12. #21423929C2semidirect
13. #21423815C2semidirect
14. #21423812C2semidirect
19. #16838122C4semidirect
75. #14273727C2×C4semidirect
82. #14273706C2×C4semidirect
84. C4×Dic118C2×C4semidirect
89. #14273686C2×C4semidirect
417. C59#22494semidirect

Maximal subgroups

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

subgroupindex
C2×#168381222
C2×#168374742
#214250682
#214250442
#214245272
#214245172
#214244082
#214244032
#214241882
#214241082
#214239292
#214238152
#214238122
C59×#23522
#2249459