Finite Group Databasebeta

← #28605046

Subgroups — #28605046

Order 15104.

1122 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838092C211yesmaximal, characteristic
2C2×#16837474C211yesmaximal, characteristic
3#21425064C211yesmaximal, characteristic, complemented
4#21425053C211yesmaximal, characteristic, complemented
5#21424527C211yesmaximal, characteristic, complemented
6#21424517C211yesmaximal, characteristic, complemented
7#21424408C211yesmaximal, characteristic, complemented
8#21424408C211yesmaximal, characteristic, complemented
9#21424188C211yesmaximal, characteristic, complemented
10#21424184C211yesmaximal, characteristic, complemented
11#21424098C211yesmaximal, characteristic, complemented
12#21423929C211yesmaximal, characteristic, complemented
13#21423817C211yesmaximal, characteristic, complemented
14#21423812C211yesmaximal, characteristic, complemented
15C59×#2354C211yesmaximal, characteristic
16C22×#11745664C2211yescharacteristic
17C23×C59⋊C8C2211yescharacteristic
18#16838092—24no—
19#16838092C418yescomplemented
20C2×#14273720—21no—
21C2×#14273719C2211yescharacteristic
22C2×#14273717—21no—
23C2×#14273708—21no—
24C2×#14273706C2211yescharacteristic
25C2×#14273706C2211yescharacteristic
26C2×C4×Dic118C2211yescharacteristic
27C2×#14273686C2211yescharacteristic
28C2×#14273683—21no—
29C22×C4⋊Dic59C2211yescharacteristic
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
53C2×#117×C59C2211yescharacteristic
54C59×#390—21no—
55C59×#388—21no—
56C59×#388—21no—
57C59×#384C2211yescharacteristic
58C59×#380C2211yescharacteristic
59C59×#380C2211yescharacteristic
60C4×C4⋊C4×C59—21no—
61C4×C4⋊C4×C59C2211yescharacteristic
62C22×Dic118C2311yescharacteristic
63C23×Dic59—21no—
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#14273720—28no—
75#14273719—22no—
76#14273719C2×C414yes—
77#14273717—28no—
78#14273708—28no—
79#14273706—22no—
80#14273706—22no—
81#14273706C2×C414yes—
82#14273706C2×C414yes—
83C4×Dic118—22no—
84C4×Dic118C2×C414yes—
85#14273686—22no—
86#14273686C2×C414yes—
87#14273683—28no—
88C2×C4⋊Dic59—21no—
89C2×C4⋊Dic59—22no—
90C2×C4⋊Dic59C2×C414yes—
91C2×C4⋊Dic59C2311yescharacteristic
92C2×C4⋊Dic59C2311yescharacteristic
93C2×C4⋊Dic59C2311yescharacteristic
94C2×Dic59⋊C4—21no—
95C2×Dic59⋊C4—21no—
96C2×Dic59⋊C4—21no—
97C2×Dic59⋊C4—21no—
98C2×Dic59⋊C4—21no—
99C2×C22⋊Dic59—21no—
100C2×C22⋊Dic59—21no—
101C2×C22⋊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×C59C2311yescharacteristic
114C23×C4×C59C2311yescharacteristic
115C4×D4×C59C2×C414yes—
116C4×D4×C59D414yes—
117#117×C59—22no—
118#117×C59—22no—
119#117×C59—41no—
120#117×C59—41no—
121C2×C4⋊C4×C59—21no—
122C2×C4⋊C4×C59—21no—
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×C59—21no—
132C2×C22⋊C4×C59D411yescharacteristic
133C2×C22⋊C4×C59D411yescharacteristic
134C2×C42×C59—21no—
135C2×C42×C59—21no—
136C2×C42×C59—21no—
137C2×C42×C59C2311yescharacteristic
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×C59C22×C412yes—
159C22×C4×C59C22×C412yes—
160C22×C4×C59C2×D411yescharacteristic
161C22×C4×C59C2×D411yescharacteristic
162C22×C4×C59C2×D411yescharacteristic
163C22×C4×C59C2×D411yescharacteristic
164C22×C4×C59C2×D412yes—
165C22×C4×C59C2×D412yes—
166C22×C4×C59C2411yescharacteristic
167C22×Dic59—24no—
168C22×Dic59—21no—
169C22×Dic59—21no—
170C22×Dic59—21no—
171C22×Dic59—21no—
172C22×Dic59—42no—
173C22×Dic59—42no—
174C2×Dic118—21no—
175C2×Dic118—21no—
176C2×Dic118—21no—
177C2×Dic118—21no—
178C2×Dic118—21no—
179C2×Dic118C22×C412yes—
180C4⋊C4×C59—21no—
181C4⋊C4×C59—21no—
182C4⋊C4×C59—21no—
183C4⋊C4×C59—21no—
184C4⋊C4×C59—21no—
185C4⋊C4×C59—21no—
186C4⋊C4×C59—21no—
187C4⋊C4×C59—42no—
188C4⋊C4×C59—81no—
189C4⋊C4×C59C22⋊C414yes—
190C4⋊C4×C59#4112yes—
191C22⋊C4×C59—42no—
192C22⋊C4×C59—42no—
193C22⋊C4×C59—81no—
194C22⋊C4×C59—81no—
195C22⋊C4×C59C22⋊C414yes—
196C22⋊C4×C59C22⋊C414yes—
197C42×C59—42no—
198C42×C59—42no—
199C42×C59—42no—
200C42×C59C22×C412yes—
201C42×C59C2×D412yes—
202C22⋊Dic59—24no—
203C22⋊Dic59—24no—
204C22⋊Dic59—24no—
205C4⋊Dic59—24no—
206C4⋊Dic59—21no—
207C4⋊Dic59—21no—
208C4⋊Dic59—21no—
209C4⋊Dic59C22×C412yes—
210C4⋊Dic59C22×C412yes—
211C4⋊Dic59C22×C412yes—
212Dic59⋊C4—24no—
213Dic59⋊C4—24no—
214Dic59⋊C4—24no—
215Dic59⋊C4—24no—
216Dic59⋊C4—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×C59C2×C22⋊C412yes—
278C2×C4×C59C2×C22⋊C412yes—
279C2×C4×C59C2×C22⋊C412yes—
280C2×C4×C59C2×C22⋊C412yes—
281C2×C4×C59C23×C411yescharacteristic
282C2×C4×C59C22×D411yescharacteristic
283C2×C4×C59C2×#4111yescharacteristic
284C2×C4×C59C2×#4111yescharacteristic
285C2×C4×C59H(5,𝔽2)11yescharacteristic
286C2×C4×C592−1+411yescharacteristic
287C2×Dic59—22no—
288C2×Dic59—22no—
289C2×Dic59—22no—
290C2×Dic59—22no—
291C2×Dic59—48no—
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—41no—
303Dic118—41no—
304C59⋊C8—22no—
305C59⋊C8—41no—
306C59⋊C8—41no—
307C59⋊C8—41no—
308#22496—591nomaximal, Sylow
309C22×C59—22no—
310C22×C59—22no—
311C22×C59—22no—
312C22×C59—22no—
313C22×C59—22no—
314C22×C59—22no—
315C22×C59—41no—
316C22×C59—41no—
317C22×C59—41no—
318C22×C59—41no—
319C22×C59—41no—
320C22×C59—41no—
321C22×C59—41no—
322C22×C59—41no—
323C22×C59C22×C22⋊C411yescharacteristic
324C22×C59#54611yescharacteristic
325C22×C59#54711yescharacteristic
326C22×C59#57511yescharacteristic
327C22×C59#57511yescharacteristic
328C22×C59#57711yescharacteristic
329C22×C59#57811yescharacteristic
330C4×C59—22no—
331C4×C59—22no—
332C4×C59—22no—
333C4×C59—22no—
334C4×C59—42no—
335C4×C59—81no—
336C4×C59—81no—
337C4×C59—81no—
338C4×C59C4×#4111yescharacteristic
339C4×C59#52011yescharacteristic
340C4×C59#54611yescharacteristic
341C4×C59#54711yescharacteristic
342Dic59—42no—
343Dic59—42no—
344Dic59—42no—
345Dic59—42no—
346C2×#552—591no—
347C2×#435—591no—
348#2354D5911yescharacteristic
349#1992—591no—
350#1989—591no—
351#1894—591no—
352#1892—591no—
353#1873—591no—
354#1873—591no—
355#1825—591no—
356#1824—591no—
357#1803—591no—
358#1763—591no—
359#1736—591no—
360#1735—591no—
361C2×C59—42no—
362C2×C59—42no—
363C2×C59#233911yescharacteristic
364C2×C59#289611yescharacteristic
365C2×C59#289811yescharacteristic
366C2×C59#331511yescharacteristic
367C2×C59#331711yescharacteristic
368C2×C59#334811yescharacteristic
369C2×C59#334911yescharacteristic
370C22×M16—591no—
371C23×C8—591no—
372#552—598no—
373#552—1184no—
374C2×#126—1181no—
375C2×#125—591no—
376C2×#125—1181no—
377C2×#123—1181no—
378C2×C22⋊Q8—591no—
379C2×C22⋊Q8—591no—
380C2×C4×Q8—591no—
381C2×C4×D4C2×D5911yescharacteristic
382C2×#117—591no—
383C2×#117—1181no—
384C2×#117C2×D5911yescharacteristic
385C2×#117C2×D5911yescharacteristic
386C22×C4⋊C4—591no—
387#435—1184no—
388C2×C4⋊C8—591no—
389C2×#103—591no—
390C2×#103—591no—
391C2×#103—591no—
392C2×#103—591no—
393C2×C22⋊C8—591no—
394C2×C22⋊C8—591no—
395C2×#97—591no—
396#390—21no—
397#388—21no—
398#388—21no—
399#384C2×D5911yescharacteristic
400#380C2×D5911yescharacteristic
401#380C2×D5911yescharacteristic
402C4×C4⋊C4—21no—
403C4×C4⋊C4C2×D5911yescharacteristic
404#340—591no—
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—
416C59#2249611yescharacteristic, complemented, Sylow
417C22×Q8—591no—
418C22×D4C22⋊D5911yescharacteristic
419C23×C4—1181no—
420C23×C4C22×D5911yescharacteristic
421C23×C4C22×D5911yescharacteristic
422C2×M16—1182no—
423C2×M16—1182no—
424C2×M16—2361no—
425C22×C8—591no—
426C22×C8—591no—
427C22×C8—591no—
428C22×C8—591no—
429C22×C8—1182no—
430C22×C8—1182no—
431C22×C8—2361no—
432#126—1188no—
433#125—594no—
434#125—1188no—
435#125—1182no—
436#123—1188no—
437C22⋊Q8—594no—
438C22⋊Q8—594no—
439C22⋊Q8—1182no—
440C22⋊Q8—1182no—
441C4×Q8—594no—
442C4×Q8—1182no—
443C4×D4C4×D5914yes—
444C4×D4D23614yes—
445#117—22no—
446#117—22no—
447#117—41no—
448#117—41no—
449#117—594no—
450#117—1182no—
451#117—1188no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—594no—
455C2×C4⋊C4—591no—
456C2×C4⋊C4—591no—
457C2×C4⋊C4—591no—
458C2×C4⋊C4—1182no—
459C2×C4⋊C4—1181no—
460C2×C4⋊C4—1181no—
461C2×C4⋊C4—1181no—
462C2×C4⋊C4—1181no—
463C2×C4⋊C4—1181no—
464C2×C4⋊C4—1181no—
465C2×C4⋊C4C22⋊D5911yescharacteristic
466C2×C4⋊C4C22×D5911yescharacteristic
467C2×C4⋊C4C22×D5911yescharacteristic
468C2×C4⋊C4C22×D5911yescharacteristic
469C2×C4⋊C4C22×D5911yescharacteristic
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—1181no—
475C2×C22⋊C4—1181no—
476C2×C22⋊C4—1181no—
477C2×C22⋊C4C22⋊D5911yescharacteristic
478C2×C22⋊C4C22⋊D5911yescharacteristic
479C2×C42—21no—
480C2×C42—21no—
481C2×C42—21no—
482C2×C42—1181no—
483C2×C42—1181no—
484C2×C42C22×D5911yescharacteristic
485C4⋊C8—1182no—
486#103—1182no—
487#103—1182no—
488#103—2361no—
489#103—2361no—
490C22⋊C8—1182no—
491C22⋊C8—1182no—
492#97—1182no—
493#95—21no—
494#95—21no—
495#95—21no—
496C24C2×C22⋊D5911yescharacteristic
497C24C2×C22⋊D5911yescharacteristic
498C2×Q8—592no—
499C2×Q8—1181no—
500C2×Q8—1181no—
501C2×Q8—1181no—
502C2×Q8—1181no—
503C2×Q8—1181no—
504C2×D4—41no—
505C2×D4—41no—
506C2×D4(C2×D59)⋊C414yes—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
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—1184no—
520C22×C4—1181no—
521C22×C4—1181no—
522C22×C4—1181no—
523C22×C4—1181no—
524C22×C4—2362no—
525C22×C4—2362no—
526C22×C4C2×C4×D5912yes—
527C22×C4C2×C4×D5912yes—
528C22×C4C2×D23612yes—
529C22×C4C2×D23612yes—
530C22×C4C2×C22⋊D5911yescharacteristic
531C22×C4C2×C22⋊D5911yescharacteristic
532C22×C4C2×C22⋊D5911yescharacteristic
533C22×C4C2×C22⋊D5911yescharacteristic
534C22×C4C23×D5911yescharacteristic
535M16—2364no—
536C2×C8—592no—
537C2×C8—1181no—
538C2×C8—1181no—
539C2×C8—1181no—
540C2×C8—1181no—
541C2×C8—1181no—
542C2×C8—1181no—
543C2×C8—1181no—
544C2×C8—1181no—
545C2×C8—1181no—
546C2×C8—1181no—
547C2×C8—1181no—
548C2×C8—2364no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—42no—
557C4⋊C4—81no—
558C4⋊C4—592no—
559C4⋊C4—592no—
560C4⋊C4—592no—
561C4⋊C4—1184no—
562C4⋊C4—1184no—
563C4⋊C4—1184no—
564C4⋊C4—1184no—
565C4⋊C4—1184no—
566C4⋊C4—1184no—
567C4⋊C4—1181no—
568C4⋊C4—1181no—
569C4⋊C4—1181no—
570C4⋊C4(C2×D59)⋊C414yes—
571C4⋊C4#1174568712yes—
572C22⋊C4—42no—
573C22⋊C4—42no—
574C22⋊C4—81no—
575C22⋊C4—81no—
576C22⋊C4—1184no—
577C22⋊C4—1184no—
578C22⋊C4—1184no—
579C22⋊C4(C2×D59)⋊C414yes—
580C22⋊C4(C2×D59)⋊C414yes—
581C42—42no—
582C42—42no—
583C42—42no—
584C42—1184no—
585C42—1184no—
586C42C2×C4×D5912yes—
587C42C2×D23612yes—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23C2×(C2×D59)⋊C412yes—
601C23C2×(C2×D59)⋊C412yes—
602C23C22×C22⋊D5911yescharacteristic
603Q8—1182no—
604Q8—1182no—
605Q8—2361no—
606Q8—2361no—
607D4—44no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—41no—
626C2×C4—41no—
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—1182no—
637C2×C4—1182no—
638C2×C4—1182no—
639C2×C4—1182no—
640C2×C4—2368no—
641C2×C4—2361no—
642C2×C4—2361no—
643C2×C4—2361no—
644C2×C4—2361no—
645C2×C4—2361no—
646C2×C4—2361no—
647C2×C4—2361no—
648C2×C4—2361no—
649C2×C4C2×(C2×D59)⋊C412yes—
650C2×C4C2×(C2×D59)⋊C412yes—
651C2×C4C2×(C2×D59)⋊C412yes—
652C2×C4C2×(C2×D59)⋊C412yes—
653C2×C4C22×C4×D5911yescharacteristic
654C2×C4C22×D23611yescharacteristic
655C2×C4#41×D5911yescharacteristic
656C2×C4C2×#1174568711yescharacteristic
657C2×C4#1427377211yescharacteristic
658C2×C4#1427377411yescharacteristic
659C8—1182no—
660C8—2361no—
661C8—2361no—
662C8—2361no—
663C22—22no—
664C22—22no—
665C22—22no—
666C22—22no—
667C22—22no—
668C22—22no—
669C22—41no—
670C22—41no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—41no—
677C22C22×(C2×D59)⋊C411yescharacteristic
678C22#1683804611yescharacteristic
679C22#1683805111yescharacteristic
680C22#1683820011yescharacteristic
681C22#1683820011yescharacteristic
682C22#1683821311yescharacteristic
683C22#1683821711yescharacteristic
684C4—22no—
685C4—22no—
686C4—22no—
687C4—22no—
688C4—42no—
689C4—81no—
690C4—81no—
691C4—81no—
692C4—2362no—
693C4—2362no—
694C4—2362no—
695C4—2362no—
696C4C4×#1174568711yescharacteristic
697C4#1683788111yescharacteristic
698C4#1683804711yescharacteristic
699C4#1683805611yescharacteristic
700C2—42no—
701C2—42no—
702C2#2142692111yescharacteristic
703C2#2143261311yescharacteristic
704C2#2143262611yescharacteristic
705C2#2143619211yescharacteristic
706C2#2143622211yescharacteristic
707C2#2143661111yescharacteristic
708C2#2143662011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#2354C2
socleC23×C59C22×D4
prime radicalC22×D4×C59D4
cosocleC22×C4×C59C24
hypercenter#2354D59
hypocenterC59#22496
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2354

Complements

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

NH ≅ G/Ntype
3. #21425064C2semidirect
4. #21425053C2semidirect
5. #21424527C2semidirect
6. #21424517C2semidirect
7. #21424408C2semidirect
8. #21424408C2semidirect
9. #21424188C2semidirect
10. #21424184C2semidirect
11. #21424098C2semidirect
12. #21423929C2semidirect
13. #21423817C2semidirect
14. #21423812C2semidirect
19. #16838092C4semidirect
416. C59#22496semidirect

Maximal subgroups

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

subgroupindex
C2×#168380922
C2×#168374742
#214250642
#214250532
#214245272
#214245172
#214244082
#214241882
#214241842
#214240982
#214239292
#214238172
#214238122
C59×#23542
#2249659