Finite Group Databasebeta

← #28586486

Subgroups — #28586486

Order 15104.

1598 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837881C211yesmaximal, characteristic
2C2×#16837400C211yesmaximal, characteristic
3C2×#16837395C211yesmaximal, characteristic
4C2×#16837356C211yesmaximal, characteristic, complemented
5#21426450C211yesmaximal, characteristic, complemented
6#21423929C211yesmaximal, characteristic, complemented
7#21423925C211yesmaximal, characteristic, complemented
8#21423923C211yesmaximal, characteristic, complemented
9#21423921C211yesmaximal, characteristic, complemented
10C4×#14273652C211yesmaximal, characteristic, complemented
11#21423915C211yesmaximal, characteristic, complemented
12#102×Dic59C211yesmaximal, characteristic, complemented
13#21423814C211yesmaximal, characteristic, complemented
14#340×D59C211yesmaximal, characteristic, complemented
15C4×#102×C59C211yesmaximal, characteristic, complemented
16C22×#11745687C2211yescharacteristic
17C22×#11745659C2211yescharacteristic
18C22×C8×D59C2211yescharacteristic
19#16837881—24no—
20#16837881C418yescomplemented
21C2×C4×Dic118C2211yescharacteristic
22C2×#14273692C2211yescharacteristic
23C2×D4×Dic59C2211yescharacteristic
24C2×C4×C22⋊D59—21no—
25C2×(C22⋊D59)⋊C4—21no—
26C2×#14273685C2211yescharacteristic
27C2×#14273684C2211yescharacteristic
28C2×#14273683—21no—
29C22×Dic59⋊C4—21no—
30C2×C4⋊C4×D59C2211yescharacteristic
31C2×C4⋊C4×D59C2211yescharacteristic
32#16837400C418yescomplemented
33#16837395C418yescomplemented
34C2×#14273652C2211yescharacteristic
35C2×#14273652C2211yescharacteristic
36C2×#14273650C2211yescharacteristic
37C2×#14273650C2211yescharacteristic
38C2×#14273648C2211yescharacteristic
39C2×#14273648C2211yescharacteristic
40#16837356—24no—
41C2×#14273638C2211yescharacteristic
42C2×#14273637C2211yescharacteristic
43C2×C8×Dic59C2211yescharacteristic
44C4⋊C4×Dic59C2211yescharacteristic
45C4⋊C4×Dic59C2211yescharacteristic
46C4×Dic59⋊C4—21no—
47C4×C4⋊Dic59C2211yescharacteristic
48#16837253—21no—
49C4×(C2×D59)⋊C4—21no—
50#16837249—21no—
51#16837165C2211yescharacteristic
52#16837165C2211yescharacteristic
53#16837164C2211yescharacteristic
54#16837164C2211yescharacteristic
55#16837164C2211yescharacteristic
56#16837164C2211yescharacteristic
57C2×C4×D4×C59C2211yescharacteristic
58C2×#102×C59C2211yescharacteristic
59C2×#102×C59C2211yescharacteristic
60C2×C4×C8×C59C2211yescharacteristic
61C4×C4⋊C4×C59C2211yescharacteristic
62C59×#340C2211yescharacteristic
63C59×#340C2211yescharacteristic
64C2×#11745687—22no—
65C2×#11745687—22no—
66C2×#11745687—22no—
67C2×#11745687C2×C414yes—
68C2×#11745687C2×C414yes—
69C2×#11745687C2×C414yes—
70C22×Dic118C2311yescharacteristic
71C22×C22⋊D59—21no—
72C23×Dic59—21no—
73C23×Dic59—21no—
74C22×C4×D59—21no—
75C22×C4×D59—21no—
76C22×C4×D59C2311yescharacteristic
77C2×#11745659—22no—
78C2×#11745659—22no—
79C2×#11745659C2×C414yescomplemented
80C22×C59⋊C8C2311yescharacteristic
81C22×C59⋊C8C2311yescharacteristic
82C2×C8×D59—22no—
83C2×C8×D59—22no—
84C2×C8×D59C2×C414yescomplemented
85C4×Dic118—22no—
86C4×Dic118C2×C414yescomplemented
87#14273692—22no—
88#14273692C2×C414yescomplemented
89D4×Dic59—22no—
90D4×Dic59C2×C414yescomplemented
91C4×C22⋊D59—28no—
92(C22⋊D59)⋊C4—28no—
93#14273685—22no—
94#14273685C2×C414yescomplemented
95#14273684C2×C414yes—
96#14273684D414yes—
97#14273683—28no—
98C2×C4⋊Dic59C2311yescharacteristic
99C2×C4⋊Dic59C2311yescharacteristic
100C2×C4⋊Dic59C2311yescharacteristic
101C2×Dic59⋊C4—21no—
102C2×Dic59⋊C4—21no—
103C2×Dic59⋊C4—21no—
104C2×Dic59⋊C4—21no—
105C2×Dic59⋊C4—28no—
106C2×Dic59⋊C4D411yescharacteristic
107C2×Dic59⋊C4D411yescharacteristic
108C4⋊C4×D59—22no—
109C4⋊C4×D59—22no—
110C4⋊C4×D59C2×C414yes—
111C4⋊C4×D59C2×C414yescomplemented
112C2×C22⋊Dic59—21no—
113C2×(C2×D59)⋊C4—21no—
114C2×(C2×D59)⋊C4D411yescharacteristic
115C2×(C2×D59)⋊C4D411yescharacteristic
116C2×C4×Dic59—21no—
117C2×C4×Dic59—21no—
118C2×C4×Dic59—21no—
119C2×C4×Dic59—21no—
120C2×C4×Dic59—21no—
121C2×C4×Dic59—21no—
122C2×C4×Dic59C2311yescharacteristic
123#14273652C2×C414yescomplemented
124#14273652C2×C414yescomplemented
125#14273650C2×C414yescomplemented
126#14273650C2×C414yescomplemented
127#14273648C2×C414yescomplemented
128#14273648C2×C414yescomplemented
129#14273638—22no—
130#14273637—22no—
131C8×Dic59—22no—
132C59⋊#95—21no—
133C59⋊#95—21no—
134C59⋊#95—21no—
135C22×D4×C59C2311yescharacteristic
136C23×C4×C59—21no—
137C22×C8×C59C2311yescharacteristic
138C22×C8×C59C2311yescharacteristic
139C4×D4×C59—22no—
140C4×D4×C59C2×C414yescomplemented
141C2×C4⋊C4×C59C2311yescharacteristic
142C2×C4⋊C4×C59C2311yescharacteristic
143C2×C4⋊C4×C59C2311yescharacteristic
144C2×C22⋊C4×C59—21no—
145C2×C42×C59—21no—
146C2×C42×C59C2311yescharacteristic
147#102×C59C2×C414yescomplemented
148#102×C59C2×C414yescomplemented
149C4×C8×C59—22no—
150#95×C59—21no—
151C24×C59—21no—
152C23×D59C2×D411yescharacteristic
153C2×D4×C59—21no—
154C2×D4×C59—21no—
155C2×D4×C59—21no—
156C2×D4×C59C22×C412yes—
157C2×D4×C59C22×C412yes—
158C2×D4×C59C22×C412yes—
159C22×C4×C59—21no—
160C22×C4×C59—21no—
161C22×C4×C59—21no—
162C22×C4×C59—24no—
163C22×C4×C59—81no—
164C22×C4×C59—81no—
165C22×C4×C59C2×D411yescharacteristic
166C22×C4×C59C2×D411yescharacteristic
167C22×C4×C59C2411yescharacteristic
168C2×C22⋊D59—24no—
169C2×C22⋊D59—24no—
170C2×C22⋊D59—24no—
171C22×Dic59—21no—
172C22×Dic59—24no—
173C22×Dic59—24no—
174C22×Dic59—24no—
175C22×Dic59—21no—
176C22×Dic59—21no—
177C22×Dic59—21no—
178C22×Dic59—24no—
179C22×Dic59—81no—
180C22×Dic59—81no—
181C22×Dic59C2×D411yescharacteristic
182C22×Dic59C2×D411yescharacteristic
183C22×Dic59C2×D411yescharacteristic
184#11745687—28no—
185#11745687—28no—
186#11745687—28no—
187#11745687C42116yescomplemented
188C2×C4×D59—24no—
189C2×C4×D59—24no—
190C2×C4×D59—81no—
191C2×C4×D59—81no—
192C2×C4×D59—81no—
193C2×C4×D59—81no—
194C2×C4×D59C22×C412yes—
195C2×C4×D59C22×C412yes—
196C2×C4×D59C22×C412yes—
197C2×C4×D59C2×D412yes—
198C2×C4×D59#4112yes—
199C2×C4×D59#4112yes—
200C2×Dic118—21no—
201C2×Dic118—21no—
202C2×Dic118—21no—
203C2×Dic118C22×C412yes—
204C2×Dic118C22×C412yes—
205C2×Dic118C22×C412yes—
206C2×C8×C59—21no—
207C2×C8×C59—21no—
208C2×C8×C59—21no—
209C2×C8×C59—21no—
210C2×C8×C59C22×C412yes—
211C2×C8×C59C22×C412yes—
212C4⋊C4×C59—21no—
213C4⋊C4×C59—21no—
214C4⋊C4×C59—21no—
215C4⋊C4×C59C22×C412yes—
216C4⋊C4×C59C22×C412yes—
217C4⋊C4×C59C22×C412yes—
218C22⋊C4×C59—24no—
219C42×C59—81no—
220C42×C59C22×C412yes—
221C42×C59C2×D412yes—
222C22⋊Dic59—24no—
223(C2×D59)⋊C4—24no—
224(C2×D59)⋊C4C22⋊C414yes—
225(C2×D59)⋊C4C22⋊C414yes—
226C4⋊Dic59—21no—
227C4⋊Dic59—21no—
228C4⋊Dic59—21no—
229C4⋊Dic59C22×C412yes—
230C4⋊Dic59C22×C412yes—
231C4⋊Dic59C22×C412yes—
232Dic59⋊C4—24no—
233Dic59⋊C4—24no—
234Dic59⋊C4—24no—
235Dic59⋊C4—24no—
236Dic59⋊C4C22⋊C414yes—
237Dic59⋊C4C22⋊C414yes—
238C4×Dic59—24no—
239C4×Dic59—24no—
240C4×Dic59—24no—
241C4×Dic59—81no—
242C4×Dic59—81no—
243C4×Dic59—81no—
244C4×Dic59C22×C412yes—
245C4×Dic59C2×D412yes—
246C2×C59⋊C8—21no—
247C2×C59⋊C8—21no—
248C2×C59⋊C8—21no—
249C2×C59⋊C8—21no—
250C2×C59⋊C8C22×C412yes—
251C2×C59⋊C8C22×C412yes—
252#11745659—28no—
253C8×D59—28no—
254C23×C59—22no—
255C23×C59—22no—
256C23×C59—22no—
257C23×C59—41no—
258C23×C59—41no—
259C23×C59—41no—
260C23×C59—41no—
261C23×C59C22×D411yescharacteristic
262C22×D59—21no—
263C22×D59—21no—
264C22×D59—21no—
265C22×D59—21no—
266C22×D59C2×C22⋊C412yes—
267C22×D59C4×D412yes—
268C22×D59C4×D412yes—
269D4×C59—22no—
270D4×C59—22no—
271D4×C59—22no—
272D4×C59C2×C4214yes—
273C2×C4×C59—21no—
274C2×C4×C59—21no—
275C2×C4×C59—21no—
276C2×C4×C59—21no—
277C2×C4×C59—22no—
278C2×C4×C59—22no—
279C2×C4×C59—22no—
280C2×C4×C59—41no—
281C2×C4×C59—41no—
282C2×C4×C59—41no—
283C2×C4×C59—41no—
284C2×C4×C59—41no—
285C2×C4×C59—41no—
286C2×C4×C59—84no—
287C2×C4×C59C2×C22⋊C412yes—
288C2×C4×C59C2×C22⋊C412yes—
289C2×C4×C59C23×C411yescharacteristic
290C2×C4×C59C23×C411yescharacteristic
291C2×C4×C59C23×C411yescharacteristic
292C2×C4×C59C22×D411yescharacteristic
293C2×C4×C59C2×#4111yescharacteristic
294C2×C4×C59C2×#4111yescharacteristic
295C22⋊D59—216no—
296C2×Dic59—22no—
297C2×Dic59—22no—
298C2×Dic59—22no—
299C2×Dic59—21no—
300C2×Dic59—21no—
301C2×Dic59—21no—
302C2×Dic59—21no—
303C2×Dic59—216no—
304C2×Dic59—22no—
305C2×Dic59—22no—
306C2×Dic59—22no—
307C2×Dic59—41no—
308C2×Dic59—41no—
309C2×Dic59—41no—
310C2×Dic59—41no—
311C2×Dic59—41no—
312C2×Dic59—41no—
313C2×Dic59—84no—
314C2×Dic59C2×C22⋊C412yes—
315C2×Dic59C2×C22⋊C412yes—
316C2×Dic59C2×C22⋊C412yes—
317C2×Dic59C4×D412yes—
318C2×Dic59C4×D412yes—
319C4×D59—84no—
320C4×D59—84no—
321C4×D59C2×C4214yes—
322C4×D59#11714yes—
323C4×D59C4×D414yes—
324C4×D59C4×D414yes—
325Dic118—22no—
326Dic118—22no—
327Dic118—22no—
328Dic118C2×C4214yes—
329C8×C59—22no—
330C8×C59—22no—
331C59⋊C8—22no—
332C59⋊C8—22no—
333#20415—591nomaximal, Sylow
334C22×C59—24no—
335C22×C59—42no—
336C22×C59—42no—
337C22×C59—42no—
338C22×C59—42no—
339C22×C59—42no—
340C22×C59—42no—
341C22×C59C22×C22⋊C411yescharacteristic
342C22×C59C2×C4×D411yescharacteristic
343C22×C59C2×C4×D411yescharacteristic
344C22×C59#57611yescharacteristic
345C22×C59#57711yescharacteristic
346C22×C59#57711yescharacteristic
347C22×C59#57811yescharacteristic
348C2×D59—22no—
349C2×D59—22no—
350C2×D59—22no—
351C2×D59—22no—
352C2×D59—22no—
353C2×D59—22no—
354C2×D59C4×C22⋊C414yes—
355C4×C59—22no—
356C4×C59—22no—
357C4×C59—42no—
358C4×C59—42no—
359C4×C59—42no—
360C4×C59C22×C4211yescharacteristic
361C4×C59C2×#11711yescharacteristic
362C4×C59C2×C4×D411yescharacteristic
363C4×C59C2×C4×D411yescharacteristic
364Dic59—22no—
365Dic59—22no—
366Dic59—24no—
367Dic59—42no—
368Dic59—42no—
369Dic59—42no—
370Dic59C4×C22⋊C414yes—
371C2×#520—591no—
372C2×#417—591no—
373C2×#416—591no—
374C2×#405—591no—
375#2274—591no—
376#1763—591no—
377#1763—591no—
378#1762—591no—
379#1762—591no—
380C4×#103—591no—
381C4×#103—591no—
382C4×#102—591no—
383C4×#102D5911yescharacteristic, complemented
384#1736—591no—
385C2×#340—591no—
386C2×C59—44no—
387C2×C59C2×C4×C22⋊C411yescharacteristic
388C2×C59#289711yescharacteristic
389C2×C59#289811yescharacteristic
390C2×C59#294611yescharacteristic
391C2×C59#294711yescharacteristic
392C2×C59#295111yescharacteristic
393C2×C59#295211yescharacteristic
394D59—24no—
395C22×#41—591no—
396C22×M16—591no—
397C23×C8—591no—
398#520—598no—
399#520—1184no—
400C2×C4×Q8—591no—
401C2×C4×Q8—591no—
402C2×C4×D4—591no—
403C2×C4×D4—1181no—
404C2×C4×D4—1181no—
405C2×C4×D4C2×D5911yescharacteristic
406C2×#117—591no—
407C2×#117—591no—
408C2×#117—1181no—
409C22×C4⋊C4—591no—
410C22×C4⋊C4—591no—
411C22×C4⋊C4—1181no—
412#417—598no—
413#416—598no—
414C2×#103—591no—
415C2×#103—591no—
416C2×#103—591no—
417C2×#103—591no—
418C2×#102—591no—
419C2×#102—591no—
420C2×#102C2×D5911yescharacteristic
421C2×#102C2×D5911yescharacteristic
422#405—1184no—
423C2×#97—591no—
424C2×#97—591no—
425C2×C4×C8—591no—
426C2×C4×C8C2×D5911yescharacteristic
427C4×C4⋊C4—591no—
428C4×C4⋊C4—591no—
429C4×C4⋊C4—591no—
430C4×C4⋊C4—1181no—
431C4×C4⋊C4—1181no—
432C4×C4⋊C4C2×D5911yescharacteristic
433C4×C22⋊C4—1181no—
434C4×C22⋊C4—1181no—
435#340—591no—
436#340—591no—
437#340—591no—
438#340—591no—
439#340—591no—
440#340—591no—
441#340C2×D5911yescharacteristic
442#340C2×D5911yescharacteristic
443C59#2041511yescharacteristic, complemented, Sylow
444C2×#41—594no—
445C2×#41—594no—
446C2×#41—594no—
447C2×#41—1182no—
448C2×#41—1182no—
449C2×#41—1182no—
450C22×Q8—591no—
451C22×D4—1181no—
452C22×D4C22×D5911yescharacteristic
453C23×C4—21no—
454C23×C4—591no—
455C23×C4—1181no—
456C23×C4—1181no—
457C23×C4—1181no—
458C23×C4—1181no—
459C2×M16—594no—
460C2×M16—1182no—
461C2×M16—1182no—
462C22×C8—591no—
463C22×C8—591no—
464C22×C8—594no—
465C22×C8—1182no—
466C22×C8—1182no—
467C22×C8C22×D5911yescharacteristic
468C22×C8C22×D5911yescharacteristic
469C4×Q8—594no—
470C4×Q8—594no—
471C4×Q8—1182no—
472C4×Q8—1182no—
473C4×D4—22no—
474C4×D4—594no—
475C4×D4—1182no—
476C4×D4—1188no—
477C4×D4—1188no—
478C4×D4C4×D5914yescomplemented
479#117—594no—
480#117—594no—
481#117—594no—
482#117—1188no—
483#117—1182no—
484C2×C4⋊C4—591no—
485C2×C4⋊C4—591no—
486C2×C4⋊C4—591no—
487C2×C4⋊C4—591no—
488C2×C4⋊C4—591no—
489C2×C4⋊C4—594no—
490C2×C4⋊C4—594no—
491C2×C4⋊C4—1182no—
492C2×C4⋊C4—1182no—
493C2×C4⋊C4—1188no—
494C2×C4⋊C4—1181no—
495C2×C4⋊C4—1181no—
496C2×C4⋊C4—1181no—
497C2×C4⋊C4—1181no—
498C2×C4⋊C4C22×D5911yescharacteristic
499C2×C4⋊C4C22×D5911yescharacteristic
500C2×C4⋊C4C22×D5911yescharacteristic
501C2×C22⋊C4—21no—
502C2×C22⋊C4—591no—
503C2×C22⋊C4—591no—
504C2×C22⋊C4—1181no—
505C2×C22⋊C4—1181no—
506C2×C42—21no—
507C2×C42—591no—
508C2×C42—1181no—
509C2×C42—1181no—
510C2×C42—1181no—
511C2×C42—1181no—
512C2×C42—1181no—
513C2×C42—1181no—
514C2×C42C22×D5911yescharacteristic
515#103—594no—
516#103—594no—
517#103—594no—
518#103—594no—
519#102—594no—
520#102—594no—
521#102C4×D5914yescomplemented
522#102C4×D5914yescomplemented
523#97—1182no—
524#97—1182no—
525C4×C8—22no—
526C4×C8—1182no—
527#95—21no—
528#95—1181no—
529#95—1181no—
530#95—1181no—
531C24—21no—
532C24—591no—
533#41—5916no—
534#41—1188no—
535#41—1188no—
536#41—1188no—
537C2×Q8—592no—
538C2×Q8—592no—
539C2×Q8—592no—
540C2×Q8—1181no—
541C2×Q8—1181no—
542C2×Q8—1181no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—1184no—
547C2×D4—1184no—
548C2×D4—1184no—
549C2×D4C2×C4×D5912yes—
550C2×D4C2×C4×D5912yes—
551C2×D4C2×C4×D5912yes—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—24no—
556C22×C4—81no—
557C22×C4—81no—
558C22×C4—591no—
559C22×C4—592no—
560C22×C4—592no—
561C22×C4—592no—
562C22×C4—592no—
563C22×C4—592no—
564C22×C4—592no—
565C22×C4—591no—
566C22×C4—591no—
567C22×C4—1184no—
568C22×C4—1184no—
569C22×C4—1184no—
570C22×C4—1184no—
571C22×C4—1184no—
572C22×C4—1184no—
573C22×C4—1181no—
574C22×C4—1181no—
575C22×C4—1181no—
576C22×C4—1181no—
577C22×C4—4721no—
578C22×C4—4721no—
579C22×C4—4721no—
580C22×C4—4721no—
581C22×C4—4721no—
582C22×C4—4721no—
583C22×C4D4×D5911yescharacteristic
584C22×C4D4×D5911yescharacteristic
585C22×C4C23×D5911yescharacteristic
586M16—1188no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—592no—
592C2×C8—592no—
593C2×C8—1188no—
594C2×C8—1181no—
595C2×C8—1181no—
596C2×C8—1181no—
597C2×C8—1181no—
598C2×C8C2×C4×D5912yes—
599C2×C8C2×C4×D5912yes—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—594no—
604C4⋊C4—594no—
605C4⋊C4—592no—
606C4⋊C4—592no—
607C4⋊C4—592no—
608C4⋊C4—1184no—
609C4⋊C4—1184no—
610C4⋊C4—1184no—
611C4⋊C4—1184no—
612C4⋊C4—1181no—
613C4⋊C4—1181no—
614C4⋊C4—1181no—
615C4⋊C4C2×C4×D5912yes—
616C4⋊C4C2×C4×D5912yes—
617C4⋊C4C2×C4×D5912yes—
618C22⋊C4—24no—
619C22⋊C4—594no—
620C22⋊C4—594no—
621C22⋊C4—1184no—
622C22⋊C4—1184no—
623C42—81no—
624C42—592no—
625C42—592no—
626C42—1184no—
627C42—1184no—
628C42—1184no—
629C42—4721no—
630C42—4721no—
631C42—4721no—
632C42C2×C4×D5912yes—
633C42D4×D5912yes—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—592no—
642C23—592no—
643C23—592no—
644C23—1181no—
645C23—1181no—
646C23—1181no—
647C23—1181no—
648C23C2×D4×D5911yescharacteristic
649Q8—594no—
650Q8—1182no—
651Q8—1182no—
652Q8—1182no—
653D4—22no—
654D4—22no—
655D4—22no—
656D4—11816no—
657D4C42×D5914yes—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—84no—
672C2×C4—592no—
673C2×C4—592no—
674C2×C4—592no—
675C2×C4—594no—
676C2×C4—594no—
677C2×C4—594no—
678C2×C4—594no—
679C2×C4—592no—
680C2×C4—592no—
681C2×C4—11816no—
682C2×C4—1181no—
683C2×C4—1181no—
684C2×C4—1181no—
685C2×C4—1181no—
686C2×C4—1182no—
687C2×C4—1182no—
688C2×C4—1182no—
689C2×C4—1182no—
690C2×C4—1182no—
691C2×C4—1182no—
692C2×C4—4724no—
693C2×C4—4724no—
694C2×C4—4724no—
695C2×C4—2361no—
696C2×C4—2361no—
697C2×C4—2361no—
698C2×C4—2361no—
699C2×C4—2361no—
700C2×C4—2361no—
701C2×C4C22⋊C4×D5912yes—
702C2×C4C22⋊C4×D5912yes—
703C2×C4C22×C4×D5911yescharacteristic
704C2×C4C22×C4×D5911yescharacteristic
705C2×C4C22×C4×D5911yescharacteristic
706C2×C4C2×D4×D5911yescharacteristic
707C2×C4#41×D5911yescharacteristic
708C2×C4#41×D5911yescharacteristic
709C8—22no—
710C8—22no—
711C8—1182no—
712C8—1182no—
713C22—24no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—594no—
721C22—1182no—
722C22—1182no—
723C22—1182no—
724C22—1182no—
725C22—1182no—
726C22—1182no—
727C22C2×C22⋊C4×D5911yescharacteristic
728C22C4×D4×D5911yescharacteristic
729C22C4×D4×D5911yescharacteristic
730C22#1683820311yescharacteristic
731C22#1683820811yescharacteristic
732C22#1683820911yescharacteristic
733C22#1683821611yescharacteristic
734C4—22no—
735C4—22no—
736C4—42no—
737C4—42no—
738C4—42no—
739C4—594no—
740C4—1182no—
741C4—1182no—
742C4—1184no—
743C4—2362no—
744C4—2362no—
745C4—2362no—
746C4C2×C42×D5911yescharacteristic
747C4#117×D5911yescharacteristic
748C4C4×D4×D5911yescharacteristic
749C4C4×D4×D5911yescharacteristic
750C2—44no—
751C2—1184no—
752C2C4×C22⋊C4×D5911yescharacteristic
753C2#2143261711yescharacteristic
754C2#2143262511yescharacteristic
755C2#2143292111yescharacteristic
756C2#2143293211yescharacteristic
757C2#2143296611yescharacteristic
758C2#2143297411yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutatorC4×C59C22×C42
FrattiniC22×C4C23×D59
FittingC4×#102×C59C2
socleC23×C59C22×D4
prime radicalC22×#11745687C22
cosocleC22×C4×C59C24
hypercenterC4×#102D59
hypocenterC59#20415
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
4. C2×#16837356C2semidirect
5. #21426450C2semidirect
6. #21423929C2semidirect
7. #21423925C2semidirect
8. #21423923C2semidirect
9. #21423921C2semidirect
10. C4×#14273652C2semidirect
11. #21423915C2semidirect
12. #102×Dic59C2semidirect
13. #21423814C2semidirect
14. #340×D59C2semidirect
15. C4×#102×C59C2semidirect
20. #16837881C4semidirect
32. #16837400C4semidirect
33. #16837395C4semidirect
79. C2×#11745659C2×C4semidirect
84. C2×C8×D59C2×C4semidirect
86. C4×Dic118C2×C4semidirect
88. #14273692C2×C4semidirect
90. D4×Dic59C2×C4semidirect
94. #14273685C2×C4semidirect
111. C4⋊C4×D59C2×C4semidirect
123. #14273652C2×C4semidirect
124. #14273652C2×C4semidirect
125. #14273650C2×C4semidirect
126. #14273650C2×C4semidirect
127. #14273648C2×C4semidirect
128. #14273648C2×C4semidirect
140. C4×D4×C59C2×C4semidirect
147. #102×C59C2×C4semidirect
148. #102×C59C2×C4semidirect
187. #11745687C42semidirect
383. C4×#102D59semidirect
443. C59#20415semidirect
478. C4×D4C4×D59semidirect
521. #102C4×D59semidirect
522. #102C4×D59semidirect

Maximal subgroups

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

subgroupindex
C2×#168378812
C2×#168374002
C2×#168373952
C2×#168373562
#214264502
#214239292
#214239252
#214239232
#214239212
C4×#142736522
#214239152
#102×Dic592
#214238142
#340×D592
C4×#102×C592
#2041559