Finite Group Databasebeta

← #28604918

Subgroups — #28604918

Order 15104.

1162 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×#16838087C211yesmaximal, characteristic
2C2×(C22⋊D59)⋊C8C211yesmaximal, characteristic
3#21427027C211yesmaximal, characteristic
4#21425059C211yesmaximal, characteristic, complemented
5#21425052C211yesmaximal, characteristic, complemented
6#21424518C211yesmaximal, characteristic, complemented
7#21424517C211yesmaximal, characteristic, complemented
8#21424407C211yesmaximal, characteristic, complemented
9#21424401C211yesmaximal, characteristic, complemented
10#21424189C211yesmaximal, characteristic, complemented
11#21424110C211yesmaximal, characteristic, complemented
12#21423915C211yesmaximal, characteristic, complemented
13#21423811C211yesmaximal, characteristic, complemented
14C2×#16837164C211yesmaximal, characteristic, complemented
15C59×#1823C211yesmaximal, characteristic, complemented
16C23×C59⋊C8C2211yescharacteristic
17C22×C8×D59C2211yescharacteristic
18#16838087—24no—
19#16838087C418yescomplemented
20C2×#14273722—21no—
21C2×#14273718C2211yescharacteristic
22C2×#14273717—21no—
23C2×#14273710—21no—
24C2×#14273707C2211yescharacteristic
25C2×#14273706C2211yescharacteristic
26C2×#14273692C2211yescharacteristic
27C2×C4×C22⋊D59C2211yescharacteristic
28C2×#14273686—21no—
29C2×#14273685C2211yescharacteristic
30C2×#14273685C2211yescharacteristic
31C22×C4⋊Dic59C2211yescharacteristic
32(C22⋊D59)⋊C8—24no—
33C2×Dic59⋊C8C2211yescharacteristic
34C2×#14273652C2211yescharacteristic
35C2×#14273652C2211yescharacteristic
36C2×#14273650C2211yescharacteristic
37C2×#14273650C2211yescharacteristic
38C2×(C2×D59)⋊C8C2211yescharacteristic
39C2×C8×Dic59C2211yescharacteristic
40#16837294—21no—
41#16837289—21no—
42#16837279—21no—
43#16837267C2211yescharacteristic
44#16837259C2211yescharacteristic
45C4⋊C4×Dic59C2211yescharacteristic
46C22⋊C4×Dic59—21no—
47#16837165C2211yescharacteristic
48#16837165C2211yescharacteristic
49#16837164C2211yescharacteristic
50#16837164C2211yescharacteristic
51#16837164C2211yescharacteristic
52#16837164C2211yescharacteristic
53#16837164C2211yescharacteristic
54#16837164C2211yescharacteristic
55C22×C4⋊C4×C59C2211yescharacteristic
56C2×C22⋊C8×C59C2211yescharacteristic
57C59×#380C2211yescharacteristic
58C59×#340C2211yescharacteristic
59C59×#340C2211yescharacteristic
60C59×#340C2211yescharacteristic
61C59×#340C2211yescharacteristic
62C22×Dic118C2311yescharacteristic
63C22×C22⋊D59D411yescharacteristic
64C23×Dic59—21no—
65C22×C4×D59C2311yescharacteristic
66C22×C59⋊C8—22no—
67C22×C59⋊C8—22no—
68C22×C59⋊C8—41no—
69C22×C59⋊C8C2311yescharacteristic
70C22×C59⋊C8C2311yescharacteristic
71C2×C8×D59—22no—
72C2×C8×D59—22no—
73C2×C8×D59—41no—
74#14273722—28no—
75#14273718—22no—
76#14273718C2×C414yescomplemented
77#14273717—28no—
78#14273710—28no—
79#14273707—22no—
80#14273707C2×C414yescomplemented
81#14273706—22no—
82#14273706C2×C414yes—
83#14273692—22no—
84#14273692C2×C414yescomplemented
85C4×C22⋊D59C2×C414yes—
86C4×C22⋊D59D414yes—
87#14273686—28no—
88#14273685—22no—
89#14273685—22no—
90#14273685—41no—
91#14273685C2×C414yescomplemented
92C2×C4⋊Dic59—21no—
93C2×C4⋊Dic59—21no—
94C2×C4⋊Dic59—22no—
95C2×C4⋊Dic59—21no—
96C2×C4⋊Dic59—41no—
97C2×C4⋊Dic59C2311yescharacteristic
98C2×C4⋊Dic59C2311yescharacteristic
99C2×C4⋊Dic59C2311yescharacteristic
100C2×Dic59⋊C4—21no—
101C2×Dic59⋊C4—21no—
102C2×Dic59⋊C4—21no—
103C2×Dic59⋊C4D411yescharacteristic
104C2×C22⋊Dic59—21no—
105C2×C22⋊Dic59D411yescharacteristic
106C2×(C2×D59)⋊C4—21no—
107C2×(C2×D59)⋊C4—21no—
108C2×(C2×D59)⋊C4—21no—
109C2×(C2×D59)⋊C4—21no—
110C2×(C2×D59)⋊C4D411yescharacteristic
111C2×C4×Dic59—21no—
112C2×C4×Dic59—21no—
113C2×C4×Dic59—21no—
114C2×C4×Dic59—21no—
115C2×C4×Dic59C2311yescharacteristic
116Dic59⋊C8—22no—
117#14273652—22no—
118#14273652—41no—
119#14273650—22no—
120#14273650—41no—
121(C2×D59)⋊C8—22no—
122C8×Dic59—22no—
123C59⋊#95—21no—
124C59⋊#95—21no—
125C59⋊#95—21no—
126C59⋊#95—21no—
127C23×C4×C59—21no—
128C23×C4×C59C2311yescharacteristic
129C22×C8×C59C2311yescharacteristic
130C22×C8×C59C2311yescharacteristic
131C2×C4⋊C4×C59—21no—
132C2×C4⋊C4×C59—22no—
133C2×C4⋊C4×C59C2×C414yes—
134C2×C4⋊C4×C59C2311yescharacteristic
135C2×C4⋊C4×C59C2311yescharacteristic
136C2×C4⋊C4×C59C2311yescharacteristic
137C2×C4⋊C4×C59C2311yescharacteristic
138C2×C22⋊C4×C59—21no—
139C22⋊C8×C59—22no—
140#95×C59—21no—
141C24×C59C2×D411yescharacteristic
142C23×D59C2×D411yescharacteristic
143C22×C4×C59—21no—
144C22×C4×C59—21no—
145C22×C4×C59—21no—
146C22×C4×C59—21no—
147C22×C4×C59—24no—
148C22×C4×C59—21no—
149C22×C4×C59—21no—
150C22×C4×C59—21no—
151C22×C4×C59—21no—
152C22×C4×C59—42no—
153C22×C4×C59—42no—
154C22×C4×C59C22×C412yes—
155C22×C4×C59C2×D411yescharacteristic
156C22×C4×C59C2×D412yes—
157C22×C4×C59C2411yescharacteristic
158C2×C22⋊D59—22no—
159C2×C22⋊D59—22no—
160C2×C22⋊D59C22⋊C414yes—
161C22×Dic59—21no—
162C22×Dic59—21no—
163C22×Dic59—21no—
164C22×Dic59—21no—
165C22×Dic59—42no—
166C22×Dic59—42no—
167C22×Dic59—81no—
168C22×Dic59C2×D411yescharacteristic
169C22×Dic59C2×D411yescharacteristic
170C22×Dic59C2×D411yescharacteristic
171C2×C4×D59—21no—
172C2×C4×D59—21no—
173C2×C4×D59—21no—
174C2×C4×D59—21no—
175C2×C4×D59C22×C412yes—
176C2×C4×D59C2×D412yes—
177C2×Dic118—21no—
178C2×Dic118—21no—
179C2×Dic118—21no—
180C2×Dic118—21no—
181C2×Dic118—21no—
182C2×Dic118C22×C412yes—
183C2×C8×C59—21no—
184C2×C8×C59—21no—
185C2×C8×C59—21no—
186C2×C8×C59—21no—
187C2×C8×C59—21no—
188C2×C8×C59—21no—
189C4⋊C4×C59—24no—
190C4⋊C4×C59—21no—
191C4⋊C4×C59—21no—
192C4⋊C4×C59—21no—
193C4⋊C4×C59—21no—
194C4⋊C4×C59—21no—
195C4⋊C4×C59—21no—
196C4⋊C4×C59C22×C412yes—
197C4⋊C4×C59C22×C412yes—
198C22⋊C4×C59—42no—
199C22⋊Dic59—24no—
200C22⋊Dic59C22⋊C414yes—
201(C2×D59)⋊C4—24no—
202(C2×D59)⋊C4—24no—
203(C2×D59)⋊C4—42no—
204(C2×D59)⋊C4—81no—
205(C2×D59)⋊C4C22⋊C414yes—
206C4⋊Dic59—21no—
207C4⋊Dic59—21no—
208C4⋊Dic59—24no—
209C4⋊Dic59—24no—
210C4⋊Dic59—21no—
211C4⋊Dic59—21no—
212C4⋊Dic59—42no—
213C4⋊Dic59C22×C412yes—
214C4⋊Dic59#4112yes—
215Dic59⋊C4—24no—
216Dic59⋊C4—24no—
217Dic59⋊C4—24no—
218Dic59⋊C4C22⋊C414yes—
219C4×Dic59—24no—
220C4×Dic59—24no—
221C4×Dic59—42no—
222C4×Dic59—81no—
223C4×Dic59C22×C412yes—
224C4×Dic59C2×D412yes—
225C2×C59⋊C8—21no—
226C2×C59⋊C8—21no—
227C2×C59⋊C8—21no—
228C2×C59⋊C8—21no—
229C2×C59⋊C8—21no—
230C2×C59⋊C8—44no—
231C2×C59⋊C8#4112yes—
232C8×D59—44no—
233C23×C59—21no—
234C23×C59—21no—
235C23×C59—21no—
236C23×C59—21no—
237C23×C59C2×C22⋊C412yes—
238C23×C59#13512yes—
239C23×C59#13512yes—
240C23×C59C22×D411yescharacteristic
241C22×D59—21no—
242C22×D59—21no—
243C22×D59—21no—
244C22×D59—21no—
245C22×D59—21no—
246C22×D59—21no—
247C22×D59C2×C22⋊C412yes—
248C2×C4×C59—21no—
249C2×C4×C59—21no—
250C2×C4×C59—22no—
251C2×C4×C59—22no—
252C2×C4×C59—22no—
253C2×C4×C59—22no—
254C2×C4×C59—22no—
255C2×C4×C59—22no—
256C2×C4×C59—41no—
257C2×C4×C59—41no—
258C2×C4×C59—41no—
259C2×C4×C59—41no—
260C2×C4×C59—48no—
261C2×C4×C59—41no—
262C2×C4×C59—41no—
263C2×C4×C59—41no—
264C2×C4×C59—41no—
265C2×C4×C59—41no—
266C2×C4×C59—41no—
267C2×C4×C59C2×C22⋊C412yes—
268C2×C4×C59C23×C411yescharacteristic
269C2×C4×C59C22×D411yescharacteristic
270C2×C4×C59C2×#4111yescharacteristic
271C2×C4×C59C2×#4111yescharacteristic
272C2×C4×C59H(5,𝔽2)11yescharacteristic
273C2×C4×C592−1+411yescharacteristic
274C22⋊D59—28no—
275C2×Dic59—21no—
276C2×Dic59—21no—
277C2×Dic59—21no—
278C2×Dic59—21no—
279C2×Dic59—21no—
280C2×Dic59—21no—
281C2×Dic59—22no—
282C2×Dic59—22no—
283C2×Dic59—22no—
284C2×Dic59—41no—
285C2×Dic59—41no—
286C2×Dic59—41no—
287C2×Dic59—41no—
288C2×Dic59—41no—
289C2×Dic59—41no—
290C2×Dic59—41no—
291C2×Dic59—41no—
292C2×Dic59—41no—
293C2×Dic59—84no—
294C2×Dic59C2×C22⋊C412yes—
295C2×Dic59C2×C22⋊C412yes—
296C2×Dic59C2×C22⋊C412yes—
297C4×D59—22no—
298C4×D59—22no—
299C4×D59—22no—
300C4×D59—22no—
301Dic118—22no—
302Dic118—22no—
303Dic118—41no—
304Dic118—41no—
305C8×C59—41no—
306C8×C59—41no—
307C59⋊C8—22no—
308C59⋊C8—41no—
309#22486—591nomaximal, Sylow
310C22×C59—22no—
311C22×C59—22no—
312C22×C59—22no—
313C22×C59—22no—
314C22×C59—22no—
315C22×C59—22no—
316C22×C59#41614yes—
317C22×C59C22×C22⋊C411yescharacteristic
318C22×C59#54611yescharacteristic
319C22×C59#54711yescharacteristic
320C22×C59C2×#13511yescharacteristic
321C22×C59C2×#13511yescharacteristic
322C22×C59#57711yescharacteristic
323C22×C59#57811yescharacteristic
324C2×D59—22no—
325C2×D59—22no—
326C2×D59—22no—
327C2×D59—41no—
328C2×D59—41no—
329C2×D59—41no—
330C2×D59—41no—
331C4×C59—22no—
332C4×C59—42no—
333C4×C59—42no—
334C4×C59—81no—
335C4×C59—81no—
336C4×C59C4×#4111yescharacteristic
337C4×C59#52011yescharacteristic
338C4×C59#54611yescharacteristic
339C4×C59#54711yescharacteristic
340Dic59—22no—
341Dic59—22no—
342Dic59—22no—
343Dic59—42no—
344Dic59—42no—
345Dic59—42no—
346Dic59—81no—
347C2×#552—591no—
348C2×C8×D4—591no—
349#2352—591no—
350#1991—591no—
351#1989—591no—
352#1892—591no—
353#1892—591no—
354#1873—591no—
355#1872—591no—
356#1825—591no—
357#1823D5911yescharacteristic, complemented
358#1805—591no—
359C4×#103—591no—
360#1735—591no—
361C2×#340—591no—
362C2×C59—24no—
363C2×C59#233911yescharacteristic
364C2×C59C2×#41611yescharacteristic
365C2×C59#289811yescharacteristic
366C2×C59#329611yescharacteristic
367C2×C59#330011yescharacteristic
368C2×C59#333611yescharacteristic
369C2×C59#333711yescharacteristic
370D59—42no—
371C23×C8—591no—
372C23×C8—591no—
373#552—598no—
374#552—1184no—
375C2×#126—1181no—
376C2×#125—591no—
377C2×#125—1181no—
378C2×#123—1181no—
379C2×C22⋊Q8—591no—
380C2×C22⋊Q8—591no—
381C2×C4×Q8—591no—
382C2×C4×D4—591no—
383C2×#117—591no—
384C2×#117—591no—
385C2×#117—1181no—
386C22×C4⋊C4—591no—
387C22×C4⋊C4C2×D5911yescharacteristic
388C8×D4—1184no—
389C2×C4⋊C8—591no—
390C2×#103—591no—
391C2×#103—591no—
392C2×#103—591no—
393C2×#103—591no—
394C2×C22⋊C8—591no—
395C2×C22⋊C8C2×D5911yescharacteristic
396C2×C4×C8—591no—
397#388—1181no—
398#387—1181no—
399#386—1181no—
400#382—591no—
401#380—591no—
402#380C2×D5911yescharacteristic
403C4×C4⋊C4—591no—
404C4×C22⋊C4—1181no—
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#340C2×D5911yescharacteristic
414#340C2×D5911yescharacteristic
415#340C2×D5911yescharacteristic
416#340C2×D5911yescharacteristic
417C59#2248611yescharacteristic, complemented, Sylow
418C22×Q8—591no—
419C22×D4—591no—
420C23×C4—21no—
421C23×C4—591no—
422C23×C4—1181no—
423C23×C4C22×D5911yescharacteristic
424C22×C8—591no—
425C22×C8—591no—
426C22×C8—1182no—
427C22×C8—1182no—
428C22×C8—1182no—
429C22×C8—1182no—
430C22×C8—2361no—
431C22×C8—2361no—
432C22×C8C22×D5911yescharacteristic
433C22×C8C22×D5911yescharacteristic
434#126—1188no—
435#125—594no—
436#125—1182no—
437#125—1188no—
438#123—1188no—
439C22⋊Q8—594no—
440C22⋊Q8—594no—
441C22⋊Q8—1182no—
442C22⋊Q8—1182no—
443C4×Q8—594no—
444C4×Q8—1182no—
445C4×D4—594no—
446C4×D4—594no—
447#117—594no—
448#117—1188no—
449#117—1182no—
450#117—1182no—
451#117—2361no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—591no—
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⋊C4—2361no—
466C2×C4⋊C4C4×D5914yes—
467C2×C4⋊C4C22×D5911yescharacteristic
468C2×C4⋊C4C22×D5911yescharacteristic
469C2×C4⋊C4C22×D5911yescharacteristic
470C2×C4⋊C4C22×D5911yescharacteristic
471C2×C22⋊C4—21no—
472C2×C22⋊C4—591no—
473C2×C22⋊C4—591no—
474C2×C22⋊C4—1181no—
475C2×C22⋊C4—1181no—
476C2×C22⋊C4—1181no—
477C2×C22⋊C4—1181no—
478C2×C22⋊C4—1181no—
479C2×C42—591no—
480C2×C42—1181no—
481C2×C42—1181no—
482C2×C42—1181no—
483C2×C42—1181no—
484C4⋊C8—1182no—
485#103—1182no—
486#103—1182no—
487#103—2361no—
488#103—2361no—
489C22⋊C8—22no—
490C22⋊C8—1182no—
491C4×C8—1182no—
492#95—21no—
493#95—1181no—
494#95—1181no—
495#95—1181no—
496#95—1181no—
497C24—591no—
498C24D4×D5911yescharacteristic
499C2×Q8—592no—
500C2×Q8—1181no—
501C2×Q8—1181no—
502C2×Q8—1181no—
503C2×Q8—1181no—
504C2×Q8—1181no—
505C2×D4—594no—
506C2×D4—1182no—
507C2×D4—1182no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—24no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—591no—
520C22×C4—591no—
521C22×C4—591no—
522C22×C4—592no—
523C22×C4—592no—
524C22×C4—1181no—
525C22×C4—1181no—
526C22×C4—1181no—
527C22×C4—1181no—
528C22×C4—1181no—
529C22×C4—1181no—
530C22×C4—1181no—
531C22×C4—1181no—
532C22×C4—4721no—
533C22×C4—2362no—
534C22×C4—2362no—
535C22×C4C2×C4×D5912yes—
536C22×C4D4×D5911yescharacteristic
537C22×C4D4×D5912yes—
538C22×C4C23×D5911yescharacteristic
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—592no—
546C2×C8—1181no—
547C2×C8—1181no—
548C2×C8—1181no—
549C2×C8—1181no—
550C2×C8—1181no—
551C2×C8—2364no—
552C2×C8—2364no—
553C4⋊C4—24no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—594no—
561C4⋊C4—592no—
562C4⋊C4—592no—
563C4⋊C4—1184no—
564C4⋊C4—1184no—
565C4⋊C4—1184no—
566C4⋊C4—1184no—
567C4⋊C4—1184no—
568C4⋊C4—1181no—
569C4⋊C4—1181no—
570C4⋊C4—1181no—
571C4⋊C4—1181no—
572C4⋊C4—2362no—
573C4⋊C4C2×C4×D5912yes—
574C4⋊C4C2×C4×D5912yes—
575C22⋊C4—42no—
576C22⋊C4—594no—
577C22⋊C4—594no—
578C22⋊C4—1184no—
579C22⋊C4—1184no—
580C22⋊C4—1184no—
581C22⋊C4—4721no—
582C22⋊C4—2362no—
583C42—592no—
584C42—592no—
585C42—1184no—
586C42—1184no—
587C42—4721no—
588C42—2362no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—592no—
594C23—1181no—
595C23—1181no—
596C23—1181no—
597C23—1181no—
598C23—1181no—
599C23—1181no—
600C23C22⋊C4×D5912yes—
601C23#1427374612yes—
602C23#1427374812yes—
603C23C2×D4×D5911yescharacteristic
604Q8—1182no—
605Q8—1182no—
606Q8—2361no—
607Q8—2361no—
608D4—1188no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—48no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—592no—
629C2×C4—592no—
630C2×C4—592no—
631C2×C4—1181no—
632C2×C4—1181no—
633C2×C4—1181no—
634C2×C4—1181no—
635C2×C4—1181no—
636C2×C4—1181no—
637C2×C4—1182no—
638C2×C4—1182no—
639C2×C4—1182no—
640C2×C4—1182no—
641C2×C4—1182no—
642C2×C4—1182no—
643C2×C4—1182no—
644C2×C4—4724no—
645C2×C4—2361no—
646C2×C4—2361no—
647C2×C4—2361no—
648C2×C4—2361no—
649C2×C4—2361no—
650C2×C4—2361no—
651C2×C4—2361no—
652C2×C4—2361no—
653C2×C4—2361no—
654C2×C4C22⋊C4×D5912yes—
655C2×C4C22×C4×D5911yescharacteristic
656C2×C4C2×D4×D5911yescharacteristic
657C2×C4#41×D5911yescharacteristic
658C2×C4#41×D5911yescharacteristic
659C2×C4#1427377311yescharacteristic
660C2×C4#1427377411yescharacteristic
661C8—41no—
662C8—41no—
663C8—1182no—
664C8—2361no—
665C22—22no—
666C22—22no—
667C22—22no—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—1182no—
672C22—1182no—
673C22—1182no—
674C22—2361no—
675C22—2361no—
676C22—2361no—
677C22—2361no—
678C22#1683739514yes—
679C22C2×C22⋊C4×D5911yescharacteristic
680C22#1683804411yescharacteristic
681C22#1683805011yescharacteristic
682C22C2×#1427374611yescharacteristic
683C22C2×#1427374811yescharacteristic
684C22#1683821111yescharacteristic
685C22#1683821811yescharacteristic
686C4—22no—
687C4—42no—
688C4—42no—
689C4—81no—
690C4—81no—
691C4—1182no—
692C4—1182no—
693C4—1182no—
694C4—4721no—
695C4—2362no—
696C4—2362no—
697C4—2362no—
698C4#1683787011yescharacteristic
699C4#1683788211yescharacteristic
700C4#1683804411yescharacteristic
701C4#1683805011yescharacteristic
702C2—24no—
703C2—2362no—
704C2#2142692011yescharacteristic
705C2C2×#1683739511yescharacteristic
706C2#2143262811yescharacteristic
707C2#2143592911yescharacteristic
708C2#2143598111yescharacteristic
709C2#2143646211yescharacteristic
710C2#2143647911yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#1823C2
socleC23×C59C22×D4
prime radicalC22×C22⋊D59D4
cosocleC22×C4×C59C24
hypercenter#1823D59
hypocenterC59#22486
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1823

Complements

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

NH ≅ G/Ntype
4. #21425059C2semidirect
5. #21425052C2semidirect
6. #21424518C2semidirect
7. #21424517C2semidirect
8. #21424407C2semidirect
9. #21424401C2semidirect
10. #21424189C2semidirect
11. #21424110C2semidirect
12. #21423915C2semidirect
13. #21423811C2semidirect
14. C2×#16837164C2semidirect
15. C59×#1823C2semidirect
19. #16838087C4semidirect
76. #14273718C2×C4semidirect
80. #14273707C2×C4semidirect
84. #14273692C2×C4semidirect
91. #14273685C2×C4semidirect
357. #1823D59semidirect
417. C59#22486semidirect

Maximal subgroups

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

subgroupindex
C2×#168380872
C2×(C22⋊D59)⋊C82
#214270272
#214250592
#214250522
#214245182
#214245172
#214244072
#214244012
#214241892
#214241102
#214239152
#214238112
C2×#168371642
C59×#18232
#2248659