Finite Group Databasebeta

← #28605065

Subgroups — #28605065

Order 15104.

1174 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838110C211yesmaximal, characteristic
2C2×#16837470C211yesmaximal, characteristic
3#21427021C211yesmaximal, characteristic
4#21425067C211yesmaximal, characteristic, complemented
5#21425046C211yesmaximal, characteristic, complemented
6#21424526C211yesmaximal, characteristic, complemented
7#21424520C211yesmaximal, characteristic, complemented
8#21424405C211yesmaximal, characteristic, complemented
9#21424187C211yesmaximal, characteristic, complemented
10#21424181C211yesmaximal, characteristic, complemented
11#21424109C211yesmaximal, characteristic, complemented
12#21423928C211yesmaximal, characteristic, complemented
13#21423814C211yesmaximal, characteristic, complemented
14C2×#16837164C211yesmaximal, characteristic, complemented
15C59×#1872C211yesmaximal, characteristic, complemented
16C22×#11745659C2211yescharacteristic
17C23×C59⋊C8C2211yescharacteristic
18#16838110—24no—
19#16838110C418yescomplemented
20C2×#14273726C2211yescharacteristic
21C2×#14273717—21no—
22C2×#14273707—21no—
23C2×#14273704—21no—
24C2×#14273703C2211yescharacteristic
25C2×Q8×Dic59C2211yescharacteristic
26C2×C4×C22⋊D59C2211yescharacteristic
27C2×(C22⋊D59)⋊C4—21no—
28C2×#14273685C2211yescharacteristic
29C22×C4⋊Dic59C2211yescharacteristic
30C2×C4⋊C4×D59C2211yescharacteristic
31#16837470—24no—
32C2×Dic59⋊C8C2211yescharacteristic
33C2×#14273651C2211yescharacteristic
34C2×#14273651C2211yescharacteristic
35C2×(C2×D59)⋊C8C2211yescharacteristic
36C2×#14273637C2211yescharacteristic
37#16837292—21no—
38#16837283—21no—
39#16837281—21no—
40#16837267C2211yescharacteristic
41#16837262C2211yescharacteristic
42#16837259C2211yescharacteristic
43C4⋊C4×Dic59C2211yescharacteristic
44C4×C22⋊Dic59—21no—
45#16837165C2211yescharacteristic
46#16837165C2211yescharacteristic
47#16837165C2211yescharacteristic
48#16837165C2211yescharacteristic
49#16837164C2211yescharacteristic
50#16837164C2211yescharacteristic
51#16837164C2211yescharacteristic
52#16837164C2211yescharacteristic
53#16837164C2211yescharacteristic
54#16837164C2211yescharacteristic
55C2×C22⋊Q8×C59C2211yescharacteristic
56C22×C4⋊C4×C59C2211yescharacteristic
57C2×#103×C59C2211yescharacteristic
58C2×#103×C59C2211yescharacteristic
59C2×C22⋊C8×C59C2211yescharacteristic
60C59×#340C2211yescharacteristic
61C59×#340C2211yescharacteristic
62C22×Dic118—21no—
63C22×C22⋊D59D411yescharacteristic
64C23×Dic59—21no—
65C22×C4×D59—21no—
66C22×C4×D59C2311yescharacteristic
67C2×#11745659—22no—
68C2×#11745659—22no—
69C2×#11745659—41no—
70C22×C59⋊C8—22no—
71C22×C59⋊C8—22no—
72C22×C59⋊C8—41no—
73C22×C59⋊C8C2311yescharacteristic
74C22×C59⋊C8C2311yescharacteristic
75#14273726—22no—
76#14273726C2×C414yescomplemented
77#14273717—28no—
78#14273707—28no—
79#14273704—28no—
80#14273703—22no—
81#14273703C2×C414yescomplemented
82Q8×Dic59—22no—
83Q8×Dic59C2×C414yescomplemented
84C4×C22⋊D59C2×C414yes—
85C4×C22⋊D59D414yes—
86(C22⋊D59)⋊C4—28no—
87#14273685—22no—
88#14273685—41no—
89C2×C4⋊Dic59—21no—
90C2×C4⋊Dic59—22no—
91C2×C4⋊Dic59—21no—
92C2×C4⋊Dic59C2×C414yes—
93C2×C4⋊Dic59C2311yescharacteristic
94C2×C4⋊Dic59C2311yescharacteristic
95C2×C4⋊Dic59C2311yescharacteristic
96C2×C4⋊Dic59C2311yescharacteristic
97C2×Dic59⋊C4—21no—
98C2×Dic59⋊C4—21no—
99C2×Dic59⋊C4—21no—
100C2×Dic59⋊C4D411yescharacteristic
101C4⋊C4×D59—22no—
102C4⋊C4×D59C2×C414yescomplemented
103C2×C22⋊Dic59—21no—
104C2×C22⋊Dic59D411yescharacteristic
105C2×(C2×D59)⋊C4—21no—
106C2×(C2×D59)⋊C4—21no—
107C2×(C2×D59)⋊C4—21no—
108C2×(C2×D59)⋊C4D411yescharacteristic
109C2×C4×Dic59—21no—
110C2×C4×Dic59—21no—
111C2×C4×Dic59—21no—
112C2×C4×Dic59C2311yescharacteristic
113Dic59⋊C8—22no—
114#14273651—22no—
115#14273651—41no—
116(C2×D59)⋊C8—22no—
117#14273637—22no—
118C59⋊#95—21no—
119C59⋊#95—21no—
120C59⋊#95—21no—
121C59⋊#95—21no—
122C59⋊#95—21no—
123C22×Q8×C59C2311yescharacteristic
124C23×C4×C59—21no—
125C23×C4×C59C2311yescharacteristic
126C22×C8×C59C2311yescharacteristic
127C22×C8×C59C2311yescharacteristic
128C22⋊Q8×C59—22no—
129C22⋊Q8×C59C2×C414yes—
130C2×C4⋊C4×C59—21no—
131C2×C4⋊C4×C59—22no—
132C2×C4⋊C4×C59—21no—
133C2×C4⋊C4×C59—41no—
134C2×C4⋊C4×C59C2311yescharacteristic
135C2×C4⋊C4×C59C2311yescharacteristic
136C2×C4⋊C4×C59C2311yescharacteristic
137C2×C22⋊C4×C59—21no—
138#103×C59—22no—
139#103×C59—41no—
140C22⋊C8×C59—22no—
141C24×C59C2×D411yescharacteristic
142C23×D59C2×D411yescharacteristic
143C2×Q8×C59—21no—
144C2×Q8×C59—21no—
145C2×Q8×C59—21no—
146C2×Q8×C59—21no—
147C2×Q8×C59—21no—
148C2×Q8×C59C22×C412yes—
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—42no—
158C22×C4×C59—42no—
159C22×C4×C59—81no—
160C22×C4×C59C22×C412yes—
161C22×C4×C59C2×D411yescharacteristic
162C22×C4×C59C2×D412yes—
163C22×C4×C59C2411yescharacteristic
164C2×C22⋊D59—22no—
165C2×C22⋊D59—22no—
166C2×C22⋊D59C22⋊C414yes—
167C22×Dic59—21no—
168C22×Dic59—21no—
169C22×Dic59—24no—
170C22×Dic59—21no—
171C22×Dic59—21no—
172C22×Dic59—81no—
173C22×Dic59—81no—
174C22×Dic59C2×D411yescharacteristic
175C22×Dic59C2×D411yescharacteristic
176C22×Dic59C2×D411yescharacteristic
177C2×C4×D59—21no—
178C2×C4×D59—21no—
179C2×C4×D59—21no—
180C2×C4×D59—21no—
181C2×C4×D59—24no—
182C2×C4×D59—81no—
183C2×C4×D59—81no—
184C2×C4×D59C22×C412yes—
185C2×C4×D59C2×D412yes—
186C2×Dic118—24no—
187C2×Dic118—81no—
188C2×Dic118—81no—
189C2×C8×C59—21no—
190C2×C8×C59—21no—
191C2×C8×C59—21no—
192C2×C8×C59—21no—
193C2×C8×C59—21no—
194C2×C8×C59—21no—
195C4⋊C4×C59—24no—
196C4⋊C4×C59—21no—
197C4⋊C4×C59—21no—
198C4⋊C4×C59—21no—
199C4⋊C4×C59—21no—
200C4⋊C4×C59—42no—
201C4⋊C4×C59C22×C412yes—
202C4⋊C4×C59#4112yes—
203C22⋊C4×C59—24no—
204C22⋊Dic59—42no—
205C22⋊Dic59C22⋊C414yes—
206(C2×D59)⋊C4—24no—
207(C2×D59)⋊C4—42no—
208(C2×D59)⋊C4—81no—
209(C2×D59)⋊C4C22⋊C414yes—
210C4⋊Dic59—24no—
211C4⋊Dic59—21no—
212C4⋊Dic59—21no—
213C4⋊Dic59—24no—
214C4⋊Dic59—21no—
215C4⋊Dic59—21no—
216C4⋊Dic59—21no—
217C4⋊Dic59—21no—
218C4⋊Dic59C22×C412yes—
219C4⋊Dic59C22×C412yes—
220Dic59⋊C4—24no—
221Dic59⋊C4—24no—
222Dic59⋊C4—24no—
223Dic59⋊C4C22⋊C414yes—
224C4×Dic59—24no—
225C4×Dic59—42no—
226C4×Dic59—81no—
227C4×Dic59C22×C412yes—
228C4×Dic59C2×D412yes—
229C2×C59⋊C8—21no—
230C2×C59⋊C8—21no—
231C2×C59⋊C8—21no—
232C2×C59⋊C8—21no—
233C2×C59⋊C8—21no—
234C2×C59⋊C8—44no—
235C2×C59⋊C8#4112yes—
236#11745659—44no—
237C23×C59—21no—
238C23×C59—21no—
239C23×C59—21no—
240C23×C59—21no—
241C23×C59C2×C22⋊C412yes—
242C23×C59#13712yes—
243C23×C59#13712yes—
244C23×C59C22×D411yescharacteristic
245C22×D59—21no—
246C22×D59—21no—
247C22×D59—21no—
248C22×D59—21no—
249C22×D59—21no—
250C22×D59—21no—
251C22×D59C2×C22⋊C412yes—
252Q8×C59—22no—
253Q8×C59—22no—
254Q8×C59—41no—
255Q8×C59—41no—
256C2×C4×C59—21no—
257C2×C4×C59—21no—
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—41no—
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—84no—
275C2×C4×C59C2×C22⋊C412yes—
276C2×C4×C59C23×C411yescharacteristic
277C2×C4×C59C22×D411yescharacteristic
278C2×C4×C59C2×#4111yescharacteristic
279C2×C4×C59C2×#4111yescharacteristic
280C2×C4×C59H(5,𝔽2)11yescharacteristic
281C2×C4×C592−1+411yescharacteristic
282C22⋊D59—28no—
283C2×Dic59—21no—
284C2×Dic59—21no—
285C2×Dic59—21no—
286C2×Dic59—21no—
287C2×Dic59—21no—
288C2×Dic59—21no—
289C2×Dic59—22no—
290C2×Dic59—22no—
291C2×Dic59—41no—
292C2×Dic59—41no—
293C2×Dic59—41no—
294C2×Dic59—41no—
295C2×Dic59—41no—
296C2×Dic59—41no—
297C2×Dic59—41no—
298C2×Dic59—41no—
299C2×Dic59—41no—
300C2×Dic59—41no—
301C2×Dic59—84no—
302C2×Dic59C2×C22⋊C412yes—
303C2×Dic59C2×C22⋊C412yes—
304C2×Dic59C2×C22⋊C412yes—
305C4×D59—22no—
306C4×D59—22no—
307C4×D59—22no—
308C4×D59—22no—
309C4×D59—84no—
310Dic118—84no—
311C8×C59—41no—
312C8×C59—41no—
313C59⋊C8—22no—
314C59⋊C8—41no—
315#22497—591nomaximal, Sylow
316C22×C59—22no—
317C22×C59—22no—
318C22×C59—22no—
319C22×C59—22no—
320C22×C59—22no—
321C22×C59—22no—
322C22×C59#41914yes—
323C22×C59C22×C22⋊C411yescharacteristic
324C22×C59#54611yescharacteristic
325C22×C59#54711yescharacteristic
326C22×C59C2×#13711yescharacteristic
327C22×C59C2×#13711yescharacteristic
328C22×C59#57611yescharacteristic
329C22×C59#57711yescharacteristic
330C2×D59—22no—
331C2×D59—22no—
332C2×D59—22no—
333C2×D59—41no—
334C2×D59—41no—
335C2×D59—41no—
336C2×D59—41no—
337C4×C59—22no—
338C4×C59—42no—
339C4×C59—42no—
340C4×C59—42no—
341C4×C59—81no—
342C4×C59C4×#4111yescharacteristic
343C4×C59#52011yescharacteristic
344C4×C59#54611yescharacteristic
345C4×C59#54711yescharacteristic
346Dic59—22no—
347Dic59—22no—
348Dic59—22no—
349Dic59—42no—
350Dic59—42no—
351Dic59—81no—
352Dic59—81no—
353C2×#554—591no—
354C2×#435—591no—
355#2352—591no—
356#1993—591no—
357#1988—591no—
358#1894—591no—
359#1892—591no—
360#1873—591no—
361#1872D5911yescharacteristic, complemented
362#1824—591no—
363#1823—591no—
364#1805—591no—
365#1763—591no—
366#1736—591no—
367C2×#340—591no—
368C2×C59—24no—
369C2×C59#233911yescharacteristic
370C2×C59C2×#41911yescharacteristic
371C2×C59#289711yescharacteristic
372C2×C59#331411yescharacteristic
373C2×C59#331611yescharacteristic
374C2×C59#334411yescharacteristic
375C2×C59#334611yescharacteristic
376D59—42no—
377C22×M16—591no—
378C23×C8—591no—
379#554—598no—
380#554—1184no—
381C2×C4⋊Q8—591no—
382C2×#125—1181no—
383C2×C22⋊Q8—591no—
384C2×C22⋊Q8—1181no—
385C2×C22⋊Q8—1181no—
386C2×C22⋊Q8C2×D5911yescharacteristic
387C2×C4×Q8—591no—
388C2×C4×D4—591no—
389C2×C4×D4—1181no—
390C2×#117—591no—
391C22×C4⋊C4—591no—
392C22×C4⋊C4—591no—
393C22×C4⋊C4C2×D5911yescharacteristic
394#435—1184no—
395C2×C4⋊C8—591no—
396C2×#103—591no—
397C2×#103—591no—
398C2×#103C2×D5911yescharacteristic
399C2×#103C2×D5911yescharacteristic
400C2×C22⋊C8—591no—
401C2×C22⋊C8C2×D5911yescharacteristic
402C2×#97—591no—
403#388—1181no—
404#387—1181no—
405#386—1181no—
406#382—591no—
407#380—591no—
408#380—591no—
409C4×C4⋊C4—591no—
410C4×C22⋊C4—1181no—
411#340—591no—
412#340—591no—
413#340—591no—
414#340—591no—
415#340—591no—
416#340—591no—
417#340—591no—
418#340—591no—
419#340—591no—
420#340—591no—
421#340C2×D5911yescharacteristic
422#340C2×D5911yescharacteristic
423C59#2249711yescharacteristic, complemented, Sylow
424C22×Q8—1181no—
425C22×Q8C22×D5911yescharacteristic
426C22×D4—591no—
427C23×C4—21no—
428C23×C4—591no—
429C23×C4—1181no—
430C23×C4—1181no—
431C23×C4C22×D5911yescharacteristic
432C2×M16—1182no—
433C2×M16—1182no—
434C2×M16—2361no—
435C22×C8—591no—
436C22×C8—591no—
437C22×C8—1182no—
438C22×C8—1182no—
439C22×C8—2361no—
440C22×C8C22×D5911yescharacteristic
441C22×C8C22×D5911yescharacteristic
442C4⋊Q8—594no—
443C4⋊Q8—1182no—
444#125—1188no—
445C22⋊Q8—22no—
446C22⋊Q8—594no—
447C22⋊Q8—1188no—
448C22⋊Q8—1188no—
449C22⋊Q8—1182no—
450C22⋊Q8C4×D5914yes—
451C4×Q8—594no—
452C4×Q8—1182no—
453C4×D4—594no—
454C4×D4—594no—
455C4×D4—1188no—
456#117—1182no—
457#117—2361no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—41no—
462C2×C4⋊C4—591no—
463C2×C4⋊C4—594no—
464C2×C4⋊C4—591no—
465C2×C4⋊C4—591no—
466C2×C4⋊C4—594no—
467C2×C4⋊C4—591no—
468C2×C4⋊C4—591no—
469C2×C4⋊C4—1182no—
470C2×C4⋊C4—1181no—
471C2×C4⋊C4—1181no—
472C2×C4⋊C4—1181no—
473C2×C4⋊C4—1181no—
474C2×C4⋊C4—1181no—
475C2×C4⋊C4—1182no—
476C2×C4⋊C4C22×D5911yescharacteristic
477C2×C4⋊C4C22×D5911yescharacteristic
478C2×C4⋊C4C22×D5911yescharacteristic
479C2×C22⋊C4—21no—
480C2×C22⋊C4—591no—
481C2×C22⋊C4—591no—
482C2×C22⋊C4—1181no—
483C2×C22⋊C4—1181no—
484C2×C22⋊C4—1181no—
485C2×C22⋊C4—1181no—
486C2×C42—591no—
487C2×C42—1181no—
488C2×C42—1181no—
489C2×C42—1181no—
490C4⋊C8—1182no—
491#103—22no—
492#103—41no—
493#103—1182no—
494#103—2361no—
495C22⋊C8—22no—
496C22⋊C8—1182no—
497#97—1182no—
498#95—1181no—
499#95—1181no—
500#95—1181no—
501#95—1181no—
502#95—1181no—
503C24—591no—
504C24D4×D5911yescharacteristic
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—1184no—
511C2×Q8—4721no—
512C2×Q8—4721no—
513C2×Q8C2×C4×D5912yes—
514C2×D4—594no—
515C2×D4—1182no—
516C2×D4—1182no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—81no—
528C22×C4—591no—
529C22×C4—591no—
530C22×C4—591no—
531C22×C4—592no—
532C22×C4—592no—
533C22×C4—1184no—
534C22×C4—1181no—
535C22×C4—1181no—
536C22×C4—1181no—
537C22×C4—1181no—
538C22×C4—1184no—
539C22×C4—1181no—
540C22×C4—1181no—
541C22×C4—1181no—
542C22×C4—1181no—
543C22×C4—4721no—
544C22×C4—4721no—
545C22×C4—4721no—
546C22×C4—4721no—
547C22×C4C2×C4×D5912yes—
548C22×C4D4×D5911yescharacteristic
549C22×C4D4×D5912yes—
550C22×C4C23×D5911yescharacteristic
551M16—2364no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—592no—
559C2×C8—1181no—
560C2×C8—1181no—
561C2×C8—1181no—
562C2×C8—1181no—
563C2×C8—1181no—
564C2×C8—2364no—
565C4⋊C4—24no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—42no—
571C4⋊C4—594no—
572C4⋊C4—592no—
573C4⋊C4—592no—
574C4⋊C4—1184no—
575C4⋊C4—1184no—
576C4⋊C4—1184no—
577C4⋊C4—1184no—
578C4⋊C4—1184no—
579C4⋊C4—1181no—
580C4⋊C4—1181no—
581C4⋊C4—1181no—
582C4⋊C4—1181no—
583C4⋊C4—1181no—
584C4⋊C4—1181no—
585C4⋊C4C2×C4×D5912yes—
586C4⋊C4#1174568712yes—
587C22⋊C4—24no—
588C22⋊C4—594no—
589C22⋊C4—594no—
590C22⋊C4—1184no—
591C22⋊C4—4721no—
592C22⋊C4—2362no—
593C22⋊C4—2362no—
594C42—592no—
595C42—592no—
596C42—1184no—
597C42—4721no—
598C42—2362no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—592no—
604C23—1181no—
605C23—1181no—
606C23—1181no—
607C23—1181no—
608C23—1181no—
609C23—1181no—
610C23C22⋊C4×D5912yes—
611C23#1427375612yes—
612C23#1427375912yes—
613C23C2×D4×D5911yescharacteristic
614Q8—22no—
615Q8—22no—
616Q8—41no—
617Q8—41no—
618Q8—4724no—
619D4—1188no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
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—592no—
640C2×C4—592no—
641C2×C4—592no—
642C2×C4—1181no—
643C2×C4—1181no—
644C2×C4—1181no—
645C2×C4—1181no—
646C2×C4—1181no—
647C2×C4—1181no—
648C2×C4—1182no—
649C2×C4—1182no—
650C2×C4—1182no—
651C2×C4—1182no—
652C2×C4—1182no—
653C2×C4—1182no—
654C2×C4—4724no—
655C2×C4—4724no—
656C2×C4—2361no—
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×C4—2361no—
666C2×C4C22⋊C4×D5912yes—
667C2×C4C22×C4×D5911yescharacteristic
668C2×C4C2×D4×D5911yescharacteristic
669C2×C4#41×D5911yescharacteristic
670C2×C4C2×#1174568711yescharacteristic
671C2×C4#1427377211yescharacteristic
672C2×C4#1427377411yescharacteristic
673C8—41no—
674C8—41no—
675C8—1182no—
676C8—2361no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—1182no—
684C22—1182no—
685C22—1182no—
686C22—2361no—
687C22—2361no—
688C22—2361no—
689C22—2361no—
690C22#1683740914yes—
691C22C2×C22⋊C4×D5911yescharacteristic
692C22#1683803911yescharacteristic
693C22#1683805011yescharacteristic
694C22C2×#1427375611yescharacteristic
695C22C2×#1427375911yescharacteristic
696C22#1683820611yescharacteristic
697C22#1683821111yescharacteristic
698C4—22no—
699C4—42no—
700C4—42no—
701C4—42no—
702C4—81no—
703C4—1182no—
704C4—1182no—
705C4—1182no—
706C4—4721no—
707C4—4721no—
708C4—2362no—
709C4—2362no—
710C4C4×#1174568711yescharacteristic
711C4#1683788111yescharacteristic
712C4#1683804111yescharacteristic
713C4#1683805211yescharacteristic
714C2—24no—
715C2—2362no—
716C2#2142692211yescharacteristic
717C2C2×#1683740911yescharacteristic
718C2#2143262011yescharacteristic
719C2#2143618111yescharacteristic
720C2#2143621111yescharacteristic
721C2#2143655511yescharacteristic
722C2#2143658511yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#1872C2
socleC23×C59C22×D4
prime radicalC22×C22⋊D59D4
cosocleC22×C4×C59C24
hypercenter#1872D59
hypocenterC59#22497
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1872

Complements

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

NH ≅ G/Ntype
4. #21425067C2semidirect
5. #21425046C2semidirect
6. #21424526C2semidirect
7. #21424520C2semidirect
8. #21424405C2semidirect
9. #21424187C2semidirect
10. #21424181C2semidirect
11. #21424109C2semidirect
12. #21423928C2semidirect
13. #21423814C2semidirect
14. C2×#16837164C2semidirect
15. C59×#1872C2semidirect
19. #16838110C4semidirect
76. #14273726C2×C4semidirect
81. #14273703C2×C4semidirect
83. Q8×Dic59C2×C4semidirect
102. C4⋊C4×D59C2×C4semidirect
361. #1872D59semidirect
423. C59#22497semidirect

Maximal subgroups

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

subgroupindex
C2×#168381102
C2×#168374702
#214270212
#214250672
#214250462
#214245262
#214245202
#214244052
#214241872
#214241812
#214241092
#214239282
#214238142
C2×#168371642
C59×#18722
#2249759