Finite Group Databasebeta

← #28557630

Subgroups — #28557630

Order 15104.

870 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21437982C211yesmaximal, characteristic
2#21433221C211yesmaximal, characteristic
3#21422827C211yesmaximal, characteristic, complemented
4#21422824C211yesmaximal, characteristic, complemented
5#21422821C211yesmaximal, characteristic, complemented
6#21422807C211yesmaximal, characteristic, complemented
7#21422804C211yesmaximal, characteristic, complemented
8#21422797C211yesmaximal, characteristic, complemented
9#21422794C211yesmaximal, characteristic, complemented
10#21422787C211yesmaximal, characteristic, complemented
11#21422784C211yesmaximal, characteristic, complemented
12#21422754C211yesmaximal, characteristic, complemented
13#21422751C211yesmaximal, characteristic, complemented
14C2×#16837150C211yesmaximal, characteristic, complemented
15C59×#2990C211yesmaximal, characteristic
16#16838130—21no—
17#16838130—21no—
18#16838122—21no—
19#16838122—21no—
20#16838092—21no—
21#16838092—21no—
22#16838092—21no—
23#16838092—21no—
24#16838014C412yes—
25#16838014C412yes—
26#16837973C412yes—
27#16837959C2211yescharacteristic
28#16837959C2211yescharacteristic
29#16837959C2211yescharacteristic
30#16837959C2211yescharacteristic
31#16837959C2211yescharacteristic
32C2×#14273727C2211yescharacteristic
33#16837879C412yes—
34#16837533—21no—
35#16837474—21no—
36#16837474—21no—
37D4×C59⋊C8—21no—
38#16837459C2211yescharacteristic
39#16837459C2211yescharacteristic
40#16837455C2211yescharacteristic
41#16837426C2211yescharacteristic
42C2×C4⋊(C59⋊C8)C2211yescharacteristic
43C2×C4⋊(C59⋊C8)C2211yescharacteristic
44#16837150C2211yescharacteristic
45#16837150C2211yescharacteristic
46#16837150C2211yescharacteristic
47#16837150C2211yescharacteristic
48#16837150C2211yescharacteristic
49#16837150C2211yescharacteristic
50#16837150C2211yescharacteristic
51#16837150C2211yescharacteristic
52#16837149C2211yescharacteristic
53#16837149C2211yescharacteristic
54#16837149C2211yescharacteristic
55#16837149C2211yescharacteristic
56#16837147C2211yescharacteristic
57#16837147C2211yescharacteristic
58#16837147C2211yescharacteristic
59#16837147C2211yescharacteristic
60C4×#41×C59C2211yescharacteristic
61C59×#446—21no—
62C59×#435—21no—
63C59×#435—21no—
64C8×D4×C59—21no—
65C59×#432C2211yescharacteristic
66C59×#432C2211yescharacteristic
67C59×#431C2211yescharacteristic
68C59×#423C2211yescharacteristic
69C2×C4⋊C8×C59C2211yescharacteristic
70C2×C4⋊C8×C59C2211yescharacteristic
71C22×Dic118C2×C412yes—
72C2×#11745664—21no—
73C22×C59⋊C8—21no—
74C22×C59⋊C8—21no—
75#14273727—21no—
76#14273727—21no—
77#14273727C2×C412yes—
78#14273727C2311yescharacteristic
79#14273727C2311yescharacteristic
80#14273727C2311yescharacteristic
81#14273727C2311yescharacteristic
82#14273725—22no—
83#14273720—22no—
84#14273720—22no—
85#14273720—22no—
86#14273720—22no—
87#14273719—21no—
88#14273719—21no—
89#14273719—21no—
90#14273719—21no—
91#14273719C2×C412yes—
92#14273717—22no—
93#14273717—22no—
94#14273717—22no—
95#14273717—22no—
96#14273714—22no—
97#14273708—22no—
98#14273708—22no—
99#14273706—21no—
100#14273706—21no—
101#14273706—21no—
102#14273706—21no—
103#14273706—21no—
104#14273706—21no—
105#14273706C2×C412yes—
106#14273706C2×C412yes—
107#14273706C2×C412yes—
108#14273706C2×C412yes—
109C4×Dic118—21no—
110C4×Dic118—21no—
111C4×Dic118—21no—
112C4×Dic118—21no—
113C4×Dic118—21no—
114C4×Dic118—21no—
115C4×Dic118C2×C412yes—
116C4×Dic118C2×C412yes—
117C4×Dic118C2×C412yes—
118C4×Dic118C2×C412yes—
119#14273692—22no—
120#14273692—22no—
121#14273686—21no—
122#14273686—21no—
123#14273686—21no—
124#14273686—21no—
125#14273686C2×C412yes—
126#14273683—22no—
127#14273683—22no—
128C2×C4⋊Dic59—21no—
129C2×C4⋊Dic59—21no—
130C4⋊(C59⋊C8)—21no—
131C4⋊(C59⋊C8)—21no—
132C4⋊(C59⋊C8)—21no—
133C4⋊(C59⋊C8)C2311yescharacteristic
134C4⋊(C59⋊C8)C2311yescharacteristic
135C4⋊(C59⋊C8)C2311yescharacteristic
136C4⋊(C59⋊C8)C2311yescharacteristic
137C22⋊(C59⋊C8)—21no—
138C22⋊(C59⋊C8)—21no—
139C22⋊(C59⋊C8)—21no—
140#14273638—21no—
141#14273638—21no—
142C4×C59⋊C8—21no—
143C2×#41×C59C2×C411yescharacteristic
144C2×M16×C59—21no—
145C22×C8×C59—21no—
146C22×C8×C59—21no—
147C4×Q8×C59D411yescharacteristic
148C4×Q8×C59D411yescharacteristic
149C4×D4×C59D411yescharacteristic
150C4×D4×C59D411yescharacteristic
151C4×D4×C59D411yescharacteristic
152C4×D4×C59D411yescharacteristic
153C4×D4×C59D411yescharacteristic
154C4×D4×C59D411yescharacteristic
155#117×C59C2×C411yescharacteristic
156#117×C59C2×C411yescharacteristic
157#117×C59C2×C411yescharacteristic
158C2×C42×C59C2311yescharacteristic
159C2×C42×C59C2311yescharacteristic
160C2×C42×C59C2311yescharacteristic
161C4⋊C8×C59—21no—
162C4⋊C8×C59—21no—
163C4⋊C8×C59—21no—
164C4⋊C8×C59C2311yescharacteristic
165C4⋊C8×C59C2311yescharacteristic
166C4⋊C8×C59C2311yescharacteristic
167C4⋊C8×C59C2311yescharacteristic
168C22⋊C8×C59—21no—
169C22⋊C8×C59—21no—
170C22⋊C8×C59—21no—
171#97×C59—21no—
172#97×C59—21no—
173C4×C8×C59—21no—
174#41×C59—42no—
175C2×Q8×C59C22⋊C411yescharacteristic
176C2×D4×C59C22⋊C411yescharacteristic
177C2×D4×C59C22⋊C411yescharacteristic
178C2×D4×C59C22⋊C411yescharacteristic
179C22×C4×C59C22×C411yescharacteristic
180C22×C4×C59C22×C411yescharacteristic
181C22×C4×C59C22×C411yescharacteristic
182C22×C4×C59C2×D411yescharacteristic
183C22×C4×C59C2×D411yescharacteristic
184C22×C4×C59C2×D411yescharacteristic
185C22×C4×C59C2×D411yescharacteristic
186C22×C4×C59C2×D411yescharacteristic
187C22×C4×C59C2×D411yescharacteristic
188C22×Dic59—22no—
189C2×Dic118—22no—
190C2×Dic118—21no—
191C2×Dic118—21no—
192C2×Dic118—44no—
193C2×Dic118C22×C412yes—
194C2×Dic118C22×C412yes—
195M16×C59—81no—
196C2×C8×C59—21no—
197C2×C8×C59—21no—
198C2×C8×C59—21no—
199C2×C8×C59—21no—
200C2×C8×C59—81no—
201C2×C8×C59—81no—
202C4⋊C4×C59C22⋊C411yescharacteristic
203C4⋊C4×C59C22⋊C411yescharacteristic
204C4⋊C4×C59C22⋊C411yescharacteristic
205C4⋊C4×C59C22⋊C411yescharacteristic
206C4⋊C4×C59C22⋊C411yescharacteristic
207C4⋊C4×C59C22⋊C411yescharacteristic
208C22⋊C4×C59C22⋊C411yescharacteristic
209C22⋊C4×C59C22⋊C411yescharacteristic
210C22⋊C4×C59C22⋊C411yescharacteristic
211C22⋊C4×C59C22⋊C411yescharacteristic
212C22⋊C4×C59C22⋊C411yescharacteristic
213C22⋊C4×C59C22⋊C411yescharacteristic
214C42×C59C22×C411yescharacteristic
215C42×C59C22×C411yescharacteristic
216C42×C59C22×C411yescharacteristic
217C42×C59C2×D411yescharacteristic
218C42×C59C2×D411yescharacteristic
219C42×C59C2×D411yescharacteristic
220C42×C59C2×D411yescharacteristic
221C42×C59C2×D411yescharacteristic
222C42×C59C2×D411yescharacteristic
223C42×C59C2411yescharacteristic
224C22⋊Dic59—22no—
225C22⋊Dic59—22no—
226C22⋊Dic59—22no—
227C22⋊Dic59—22no—
228C22⋊Dic59—22no—
229C4⋊Dic59—22no—
230C4⋊Dic59—22no—
231C4⋊Dic59—21no—
232C4⋊Dic59—21no—
233C4⋊Dic59—21no—
234C4⋊Dic59—21no—
235C4⋊Dic59—21no—
236C4⋊Dic59—21no—
237C4⋊Dic59C22×C412yes—
238C4⋊Dic59C22×C412yes—
239Dic59⋊C4—22no—
240Dic59⋊C4—22no—
241Dic59⋊C4—22no—
242Dic59⋊C4—22no—
243Dic59⋊C4—22no—
244Dic59⋊C4—22no—
245Dic59⋊C4—22no—
246Dic59⋊C4—22no—
247Dic59⋊C4—22no—
248Dic59⋊C4—22no—
249C4×Dic59—22no—
250C4×Dic59—22no—
251C4×Dic59—22no—
252C4×Dic59—22no—
253C4×Dic59—22no—
254#11745664—81no—
255C2×C59⋊C8—21no—
256C2×C59⋊C8—21no—
257C2×C59⋊C8—21no—
258C2×C59⋊C8—21no—
259C2×C59⋊C8—81no—
260C2×C59⋊C8—81no—
261C23×C59C2×C22⋊C411yescharacteristic
262C23×C59C2×C22⋊C411yescharacteristic
263C23×C59C2×C22⋊C411yescharacteristic
264Q8×C59—41no—
265D4×C59—22no—
266D4×C59—22no—
267D4×C59—41no—
268C2×C4×C59—22no—
269C2×C4×C59—21no—
270C2×C4×C59—21no—
271C2×C4×C59—21no—
272C2×C4×C59—21no—
273C2×C4×C59—21no—
274C2×C4×C59—21no—
275C2×C4×C59—21no—
276C2×C4×C59—21no—
277C2×C4×C59—21no—
278C2×C4×C59—21no—
279C2×C4×C59—21no—
280C2×C4×C59—21no—
281C2×C4×C59—41no—
282C2×C4×C59—41no—
283C2×C4×C59C2×C22⋊C411yescharacteristic
284C2×C4×C59C2×C22⋊C411yescharacteristic
285C2×C4×C59C2×C22⋊C411yescharacteristic
286C2×C4×C59C2×C22⋊C411yescharacteristic
287C2×C4×C59C2×C22⋊C411yescharacteristic
288C2×C4×C59C2×C22⋊C411yescharacteristic
289C2×C4×C59C2×C22⋊C411yescharacteristic
290C2×C4×C59C2×C22⋊C411yescharacteristic
291C2×C4×C59C2×C22⋊C411yescharacteristic
292C2×C4×C59C23×C411yescharacteristic
293C2×C4×C59C22×D411yescharacteristic
294C2×C4×C59C22×D411yescharacteristic
295C2×Dic59—22no—
296C2×Dic59—22no—
297C2×Dic59—22no—
298C2×Dic59—22no—
299C2×Dic59—44no—
300Dic118—44no—
301Dic118—41no—
302Dic118—41no—
303Dic118—41no—
304Dic118—41no—
305Dic118—42no—
306Dic118—42no—
307C8×C59—41no—
308C8×C59—41no—
309C8×C59—41no—
310C8×C59—41no—
311C59⋊C8—41no—
312C59⋊C8—41no—
313C59⋊C8—41no—
314C59⋊C8—41no—
315#17780—591nomaximal, Sylow
316C22×C59—21no—
317C22×C59—21no—
318C22×C59—21no—
319C22×C59—21no—
320C22×C59—21no—
321C22×C59—21no—
322C22×C59—21no—
323C22×C59—21no—
324C22×C59#41312yes—
325C22×C59C22×C22⋊C411yescharacteristic
326C4×C59—21no—
327C4×C59—21no—
328C4×C59—21no—
329C4×C59—21no—
330C4×C59—21no—
331C4×C59—21no—
332C4×C59—21no—
333C4×C59—21no—
334C4×C59—21no—
335C4×C59—21no—
336C4×C59#57711yescharacteristic
337C4×C59#57711yescharacteristic
338C4×C59#57811yescharacteristic
339C4×C59#57811yescharacteristic
340Dic59—42no—
341Dic59—42no—
342Dic59—42no—
343Dic59—42no—
344#3509—591no—
345#2990—591no—
346#2990D5911yescharacteristic
347#1559—591no—
348#1559—591no—
349#1558—591no—
350#1554—591no—
351#1554—591no—
352#1552—591no—
353#1552—591no—
354#1550—591no—
355#1550—591no—
356#1542—591no—
357#1542—591no—
358C2×#333—591no—
359C2×C59—22no—
360C2×C59—41no—
361C2×C59—41no—
362C2×C59C2×#41311yescharacteristic
363C2×C59#289811yescharacteristic
364C2×C59#289811yescharacteristic
365#557—1181no—
366#557—1181no—
367#556—1181no—
368#556—1181no—
369#552—1181no—
370#552—1181no—
371#552—1181no—
372#552—1181no—
373#541—592no—
374#541—592no—
375#536—592no—
376#533—591no—
377#533—591no—
378#533—591no—
379#533—591no—
380#533—591no—
381C2×C4⋊Q8—591no—
382#519—592no—
383C4×#41C2×D5911yescharacteristic
384#446—21no—
385#446—1181no—
386#435—21no—
387#435—21no—
388#435—1181no—
389#435—1181no—
390C8×D4—21no—
391C8×D4—1181no—
392#432—591no—
393#432—591no—
394#432C2×D5911yescharacteristic
395#432C2×D5911yescharacteristic
396#431—591no—
397#431C2×D5911yescharacteristic
398#423—591no—
399#423C2×D5911yescharacteristic
400C2×C4⋊C8—591no—
401C2×C4⋊C8—591no—
402C2×C4⋊C8C2×D5911yescharacteristic
403C2×C4⋊C8C2×D5911yescharacteristic
404#333—591no—
405#333—591no—
406#333—591no—
407#333—591no—
408#333—591no—
409#333—591no—
410#333—591no—
411#333—591no—
412#332—591no—
413#332—591no—
414#332—591no—
415#332—591no—
416#332—591no—
417#332—591no—
418#332—591no—
419#332—591no—
420C59#1778011yescharacteristic, complemented, Sylow
421C2×#41C4×D5911yescharacteristic
422C22×Q8—592no—
423C2×M16—21no—
424C2×M16—1181no—
425C22×C8—21no—
426C22×C8—21no—
427C22×C8—1181no—
428C22×C8—1181no—
429C4⋊Q8—592no—
430C4⋊Q8—591no—
431C4⋊Q8—591no—
432C4⋊Q8—591no—
433C4⋊Q8—591no—
434C4⋊Q8—1182no—
435C4⋊Q8—1181no—
436C4⋊Q8—1181no—
437#126—1182no—
438#126—1182no—
439#126—1182no—
440#126—1182no—
441#125—592no—
442#125—1182no—
443#125—1182no—
444#125—1182no—
445#125—1182no—
446#125—1181no—
447#125—1181no—
448#125—1181no—
449#125—1181no—
450#124—1182no—
451#123—1182no—
452#123—1182no—
453C22⋊Q8—592no—
454C22⋊Q8—592no—
455C22⋊Q8—592no—
456C22⋊Q8—592no—
457C22⋊Q8—1181no—
458C22⋊Q8—1181no—
459C22⋊Q8—1181no—
460C22⋊Q8—1181no—
461C22⋊Q8—1181no—
462C22⋊Q8—1181no—
463C4×Q8—592no—
464C4×Q8—592no—
465C4×Q8—592no—
466C4×Q8—592no—
467C4×Q8—1182no—
468C4×Q8—1182no—
469C4×Q8—1181no—
470C4×Q8—1181no—
471C4×Q8—1181no—
472C4×Q8—1181no—
473C4×Q8—1181no—
474C4×Q8—1181no—
475C4×Q8D23611yescharacteristic
476C4×Q8C22⋊D5911yescharacteristic
477C4×D4D23611yescharacteristic
478C4×D4D23611yescharacteristic
479C4×D4D23611yescharacteristic
480C4×D4C22⋊D5911yescharacteristic
481C4×D4C22⋊D5911yescharacteristic
482C4×D4C22⋊D5911yescharacteristic
483#117—592no—
484#117—1181no—
485#117—1181no—
486#117—1181no—
487#117—1181no—
488#117—1182no—
489#117—1182no—
490#117C4×D5911yescharacteristic
491#117C4×D5911yescharacteristic
492#117C4×D5911yescharacteristic
493C2×C4⋊C4—1181no—
494C2×C4⋊C4—1181no—
495C2×C42C22×D5911yescharacteristic
496C2×C42C22×D5911yescharacteristic
497C2×C42C22×D5911yescharacteristic
498C4⋊C8—21no—
499C4⋊C8—21no—
500C4⋊C8—21no—
501C4⋊C8—591no—
502C4⋊C8—591no—
503C4⋊C8—591no—
504C4⋊C8—591no—
505C4⋊C8—1181no—
506C4⋊C8—1181no—
507C4⋊C8—1181no—
508C4⋊C8C22×D5911yescharacteristic
509C4⋊C8C22×D5911yescharacteristic
510C4⋊C8C22×D5911yescharacteristic
511C4⋊C8C22×D5911yescharacteristic
512C22⋊C8—21no—
513C22⋊C8—21no—
514C22⋊C8—21no—
515C22⋊C8—1181no—
516C22⋊C8—1181no—
517C22⋊C8—1181no—
518#97—21no—
519#97—21no—
520#97—1181no—
521#97—1181no—
522C4×C8—21no—
523C4×C8—1181no—
524#41—42no—
525C2×Q8—592no—
526C2×Q8—592no—
527C2×Q8—1182no—
528C2×Q8—1181no—
529C2×Q8—1181no—
530C2×Q8—2364no—
531C2×Q8(C2×D59)⋊C411yescharacteristic
532C2×D4(C2×D59)⋊C411yescharacteristic
533C2×D4(C2×D59)⋊C411yescharacteristic
534C2×D4(C2×D59)⋊C411yescharacteristic
535C22×C4—1182no—
536C22×C4C2×C4×D5911yescharacteristic
537C22×C4C2×C4×D5911yescharacteristic
538C22×C4C2×C4×D5911yescharacteristic
539C22×C4C2×D23611yescharacteristic
540C22×C4C2×D23611yescharacteristic
541C22×C4C2×D23611yescharacteristic
542C22×C4C2×C22⋊D5911yescharacteristic
543C22×C4C2×C22⋊D5911yescharacteristic
544C22×C4C2×C22⋊D5911yescharacteristic
545M16—81no—
546M16—4721no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—81no—
552C2×C8—81no—
553C2×C8—1181no—
554C2×C8—1181no—
555C2×C8—1181no—
556C2×C8—1181no—
557C2×C8—4721no—
558C2×C8—4721no—
559C4⋊C4—592no—
560C4⋊C4—592no—
561C4⋊C4—1182no—
562C4⋊C4—1182no—
563C4⋊C4—1182no—
564C4⋊C4—1182no—
565C4⋊C4—1182no—
566C4⋊C4—1182no—
567C4⋊C4—1182no—
568C4⋊C4—1182no—
569C4⋊C4—1182no—
570C4⋊C4—1182no—
571C4⋊C4—1182no—
572C4⋊C4—1182no—
573C4⋊C4—1181no—
574C4⋊C4—1181no—
575C4⋊C4—1181no—
576C4⋊C4—1181no—
577C4⋊C4—1181no—
578C4⋊C4—1181no—
579C4⋊C4(C2×D59)⋊C411yescharacteristic
580C4⋊C4(C2×D59)⋊C411yescharacteristic
581C4⋊C4(C2×D59)⋊C411yescharacteristic
582C4⋊C4(C2×D59)⋊C411yescharacteristic
583C4⋊C4(C2×D59)⋊C411yescharacteristic
584C4⋊C4(C2×D59)⋊C411yescharacteristic
585C22⋊C4—1182no—
586C22⋊C4—1182no—
587C22⋊C4—1182no—
588C22⋊C4—1182no—
589C22⋊C4—1182no—
590C22⋊C4(C2×D59)⋊C411yescharacteristic
591C22⋊C4(C2×D59)⋊C411yescharacteristic
592C22⋊C4(C2×D59)⋊C411yescharacteristic
593C22⋊C4(C2×D59)⋊C411yescharacteristic
594C22⋊C4(C2×D59)⋊C411yescharacteristic
595C22⋊C4(C2×D59)⋊C411yescharacteristic
596C42—1182no—
597C42—1182no—
598C42—1182no—
599C42—1182no—
600C42—1182no—
601C42C2×C4×D5911yescharacteristic
602C42C2×C4×D5911yescharacteristic
603C42C2×C4×D5911yescharacteristic
604C42C2×D23611yescharacteristic
605C42C2×D23611yescharacteristic
606C42C2×D23611yescharacteristic
607C42C2×C22⋊D5911yescharacteristic
608C42C2×C22⋊D5911yescharacteristic
609C42C2×C22⋊D5911yescharacteristic
610C42C23×D5911yescharacteristic
611C23C2×(C2×D59)⋊C411yescharacteristic
612C23C2×(C2×D59)⋊C411yescharacteristic
613C23C2×(C2×D59)⋊C411yescharacteristic
614Q8—41no—
615Q8—2362no—
616Q8—2362no—
617Q8—2364no—
618Q8—2361no—
619Q8—2361no—
620Q8—2361no—
621Q8—2361no—
622D4—22no—
623D4—22no—
624D4—41no—
625C2×C4—22no—
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—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—1182no—
641C2×C4—1182no—
642C2×C4—1182no—
643C2×C4—1182no—
644C2×C4—2364no—
645C2×C4C2×(C2×D59)⋊C411yescharacteristic
646C2×C4C2×(C2×D59)⋊C411yescharacteristic
647C2×C4C2×(C2×D59)⋊C411yescharacteristic
648C2×C4C2×(C2×D59)⋊C411yescharacteristic
649C2×C4C2×(C2×D59)⋊C411yescharacteristic
650C2×C4C2×(C2×D59)⋊C411yescharacteristic
651C2×C4C2×(C2×D59)⋊C411yescharacteristic
652C2×C4C2×(C2×D59)⋊C411yescharacteristic
653C2×C4C2×(C2×D59)⋊C411yescharacteristic
654C2×C4C22×C4×D5911yescharacteristic
655C2×C4C22×C22⋊D5911yescharacteristic
656C2×C4C22×D23611yescharacteristic
657C8—41no—
658C8—41no—
659C8—41no—
660C8—41no—
661C8—2361no—
662C8—2361no—
663C8—2361no—
664C8—2361no—
665C22—21no—
666C22—21no—
667C22—21no—
668C22—21no—
669C22—21no—
670C22—21no—
671C22—21no—
672C22—21no—
673C22#1683738412yes—
674C22C22×(C2×D59)⋊C411yescharacteristic
675C4—21no—
676C4—21no—
677C4—21no—
678C4—21no—
679C4—21no—
680C4—21no—
681C4—21no—
682C4—21no—
683C4—21no—
684C4—21no—
685C4—2362no—
686C4—2362no—
687C4—2362no—
688C4—2362no—
689C4#1683821311yescharacteristic
690C4#1683821411yescharacteristic
691C4#1683821711yescharacteristic
692C4#1683821911yescharacteristic
693C2—22no—
694C2—41no—
695C2—41no—
696C2C2×#1683738411yescharacteristic
697C2#2143262611yescharacteristic
698C2#2143263011yescharacteristic
subgroupG/H
centerC22C22×(C2×D59)⋊C4
commutatorC2×C4×C59C23×C4
FrattiniC42C23×D59
FittingC59×#2990C2
socleC22×C59C22×C22⋊C4
prime radicalC2×#41×C59C2×C4
cosocleC42×C59C24
hypercenter#2990D59
hypocenterC59#17780
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×#41 ◁ #2990

Complements

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

NH ≅ G/Ntype
3. #21422827C2semidirect
4. #21422824C2semidirect
5. #21422821C2semidirect
6. #21422807C2semidirect
7. #21422804C2semidirect
8. #21422797C2semidirect
9. #21422794C2semidirect
10. #21422787C2semidirect
11. #21422784C2semidirect
12. #21422754C2semidirect
13. #21422751C2semidirect
14. C2×#16837150C2semidirect
420. C59#17780semidirect

Maximal subgroups

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

subgroupindex
#214379822
#214332212
#214228272
#214228242
#214228212
#214228072
#214228042
#214227972
#214227942
#214227872
#214227842
#214227542
#214227512
C2×#168371502
C59×#29902
#1778059