Finite Group Databasebeta

← #28598951

Subgroups — #28598951

Order 15104.

1122 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊C8×D59C211yesmaximal, characteristic
2#21426478C211yesmaximal, characteristic
3#21426475C211yesmaximal, characteristic
4#21424298C211yesmaximal, characteristic, complemented
5#21424297C211yesmaximal, characteristic, complemented
6#21424296C211yesmaximal, characteristic, complemented
7#21424295C211yesmaximal, characteristic, complemented
8#21424294C211yesmaximal, characteristic, complemented
9#21424293C211yesmaximal, characteristic, complemented
10#21424292C211yesmaximal, characteristic, complemented
11#21424124C211yesmaximal, characteristic, complemented
12#21424122C211yesmaximal, characteristic, complemented
13#21424120C211yesmaximal, characteristic, complemented
14#21424118C211yesmaximal, characteristic, complemented
15C59×#1854C211yesmaximal, characteristic, complemented
16C23×C4×D59C2211yescharacteristic
17C22×C8×D59C2211yescharacteristic
18C22×C8×D59C2211yescharacteristic
19C2×#14273686C2211yescharacteristic
20C2×#14273685C2211yescharacteristic
21C2×#14273685C2211yescharacteristic
22C2×#14273661C2211yescharacteristic, complemented
23C2×#14273660C2211yescharacteristic, complemented
24C2×#14273660C2211yescharacteristic, complemented
25C2×#14273659C2211yescharacteristic, complemented
26C2×#14273658C2211yescharacteristic, complemented
27C2×#14273658C2211yescharacteristic, complemented
28C2×C22⋊(C59⋊C8)C2211yescharacteristic
29C2×(C2×D59)⋊C8C2211yescharacteristic
30C2×(C2×D59)⋊C8C2211yescharacteristic
31C22⋊C8×D59C418yescomplemented
32#16837264—21no—
33#16837263—21no—
34#16837262C2211yescharacteristic
35#16837259C2211yescharacteristic
36#16837259C2211yescharacteristic
37#16837259C2211yescharacteristic
38#16837259C2211yescharacteristic
39#16837259C2211yescharacteristic
40#16837259C2211yescharacteristic
41#16837257—21no—
42#16837257—21no—
43C22⋊C4×Dic59—21no—
44C4×(C2×D59)⋊C4—21no—
45C4×(C2×D59)⋊C4—21no—
46#16837249—21no—
47#16837165C2211yescharacteristic, complemented
48#16837165C2211yescharacteristic, complemented
49#16837164C2211yescharacteristic, complemented
50#16837164C2211yescharacteristic, complemented
51#16837164C2211yescharacteristic, complemented
52#16837164C2211yescharacteristic, complemented
53C2×#117×C59C2211yescharacteristic
54C2×#107×C59C2211yescharacteristic, complemented
55C2×#106×C59C2211yescharacteristic, complemented
56C2×C22⋊C8×C59C2211yescharacteristic
57C59×#380C2211yescharacteristic
58C59×#340C2211yescharacteristic, complemented
59C59×#340C2211yescharacteristic, complemented
60C24×D59D411yescharacteristic
61C23×Dic59D411yescharacteristic
62C22×C4×D59—41no—
63C22×C4×D59—41no—
64C22×C4×D59—41no—
65C22×C4×D59—41no—
66C22×C4×D59C2×C414yes—
67C22×C4×D59D411yescharacteristic
68C22×C4×D59D411yescharacteristic
69C22×C4×D59Q814yes—
70C22×C4×D59C2311yescharacteristic
71C22×C4×D59C2311yescharacteristic
72C22×C59⋊C8C2311yescharacteristic
73C22×C59⋊C8C2311yescharacteristic
74C2×C8×D59—41no—
75C2×C8×D59—41no—
76C2×C8×D59—41no—
77C2×C8×D59—41no—
78C2×C8×D59C2×C414yes—
79C2×C8×D59C2×C414yes—
80#14273686—41no—
81#14273686—41no—
82#14273685—41no—
83#14273685—41no—
84#14273685—41no—
85#14273685—41no—
86C2×C4⋊Dic59C2311yescharacteristic
87C2×C4⋊Dic59C2311yescharacteristic
88C2×C4⋊Dic59C2311yescharacteristic
89C2×C4⋊Dic59C2311yescharacteristic
90C2×C22⋊Dic59—21no—
91C2×C22⋊Dic59—21no—
92C2×(C2×D59)⋊C4—21no—
93C2×(C2×D59)⋊C4—21no—
94C2×(C2×D59)⋊C4—21no—
95C2×(C2×D59)⋊C4—21no—
96C2×(C2×D59)⋊C4—21no—
97C2×(C2×D59)⋊C4—21no—
98C2×(C2×D59)⋊C4—21no—
99C2×(C2×D59)⋊C4—21no—
100C2×C4×Dic59—21no—
101C2×C4×Dic59—21no—
102C2×C4×Dic59—21no—
103#14273661—41no—
104#14273660—41no—
105#14273660—41no—
106#14273659—41no—
107#14273658—41no—
108#14273658—41no—
109C22⋊(C59⋊C8)C2×C414yes—
110(C2×D59)⋊C8C2×C414yes—
111(C2×D59)⋊C8C2×C414yes—
112C59⋊#95—21no—
113C59⋊#95—21no—
114C59⋊#95—21no—
115C59⋊#95—21no—
116C59⋊#95—21no—
117C59⋊#95—21no—
118C59⋊#95—21no—
119C23×C4×C59C2311yescharacteristic
120C22×C8×C59C2311yescharacteristic
121C22×C8×C59C2311yescharacteristic
122#117×C59—41no—
123#117×C59—41no—
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×C42×C59—21no—
131#107×C59—41no—
132#106×C59—41no—
133C22⋊C8×C59C2×C414yes—
134#95×C59—21no—
135C24×C59C2×D411yescharacteristic
136C23×D59—22no—
137C23×D59—22no—
138C23×D59—41no—
139C23×D59—41no—
140C23×D59—41no—
141C23×D59—41no—
142C23×D59C4⋊C414yes—
143C23×D59C2×D411yescharacteristic
144C23×D59C2×D411yescharacteristic
145C22×C4×C59—21no—
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×C59C22×C412yes—
154C22×C4×C59C2×D411yescharacteristic
155C22×C4×C59C2×Q812yes—
156C22×C4×C59C2411yescharacteristic
157C22×Dic59—21no—
158C22×Dic59—21no—
159C22×Dic59—21no—
160C22×Dic59—21no—
161C22×Dic59—41no—
162C22×Dic59—41no—
163C22×Dic59C4⋊C414yes—
164C22×Dic59C2×D411yescharacteristic
165C22×Dic59C2×D411yescharacteristic
166C2×C4×D59—21no—
167C2×C4×D59—21no—
168C2×C4×D59—21no—
169C2×C4×D59—21no—
170C2×C4×D59—21no—
171C2×C4×D59—21no—
172C2×C4×D59—21no—
173C2×C4×D59—21no—
174C2×C4×D59—44no—
175C2×C4×D59—44no—
176C2×C4×D59—44no—
177C2×C4×D59—44no—
178C2×C4×D59—41no—
179C2×C4×D59—41no—
180C2×C4×D59—41no—
181C2×C4×D59—41no—
182C2×C4×D59C4⋊C414yes—
183C2×C4×D59C4⋊C414yes—
184C2×C4×D59C22×C412yes—
185C2×C4×D59C22×C412yes—
186C2×C4×D59C2×Q812yes—
187C2×C4×D59C2×Q812yes—
188C2×C8×C59—21no—
189C2×C8×C59—21no—
190C2×C8×C59—21no—
191C2×C8×C59—21no—
192C2×C8×C59C22×C412yes—
193C2×C8×C59C22×C412yes—
194C4⋊C4×C59—21no—
195C4⋊C4×C59—21no—
196C4⋊C4×C59—21no—
197C4⋊C4×C59—21no—
198C4⋊C4×C59—21no—
199C4⋊C4×C59—21no—
200C4⋊C4×C59—21no—
201C4⋊C4×C59—21no—
202C22⋊C4×C59—42no—
203C22⋊C4×C59—42no—
204C42×C59—42no—
205C22⋊Dic59—42no—
206C22⋊Dic59—42no—
207(C2×D59)⋊C4—42no—
208(C2×D59)⋊C4—42no—
209(C2×D59)⋊C4—42no—
210(C2×D59)⋊C4—42no—
211(C2×D59)⋊C4—42no—
212(C2×D59)⋊C4—42no—
213(C2×D59)⋊C4—42no—
214(C2×D59)⋊C4—42no—
215C4⋊Dic59—21no—
216C4⋊Dic59—21no—
217C4⋊Dic59—21no—
218C4⋊Dic59—21no—
219C4⋊Dic59—21no—
220C4⋊Dic59—21no—
221C4⋊Dic59—21no—
222C4⋊Dic59—21no—
223C4×Dic59—42no—
224C4×Dic59—42no—
225C4×Dic59—42no—
226C2×C59⋊C8—21no—
227C2×C59⋊C8—21no—
228C2×C59⋊C8—21no—
229C2×C59⋊C8—21no—
230C2×C59⋊C8C22×C412yes—
231C2×C59⋊C8C22×C412yes—
232C8×D59—44no—
233C8×D59—44no—
234C23×C59—21no—
235C23×C59—21no—
236C23×C59—21no—
237C23×C59—21no—
238C23×C59—21no—
239C23×C59—21no—
240C23×C59C2×C4⋊C412yes—
241C23×C59C22×D411yescharacteristic
242C22×D59—21no—
243C22×D59—21no—
244C22×D59—21no—
245C22×D59—21no—
246C22×D59—21no—
247C22×D59—21no—
248C22×D59—21no—
249C22×D59—21no—
250C22×D59—21no—
251C22×D59—21no—
252C22×D59—28no—
253C22×D59—44no—
254C22×D59—44no—
255C22×D59—44no—
256C22×D59—44no—
257C22×D59—44no—
258C22×D59—44no—
259C22×D59C2×C4⋊C412yes—
260C22×D59C2×C4⋊C412yes—
261C22×D59#13512yes—
262C22×D59#13512yes—
263C2×C4×C59—21no—
264C2×C4×C59—21no—
265C2×C4×C59—22no—
266C2×C4×C59—22no—
267C2×C4×C59—22no—
268C2×C4×C59—22no—
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×C59—41no—
278C2×C4×C59—41no—
279C2×C4×C59—41no—
280C2×C4×C59—41no—
281C2×C4×C59C2×C4⋊C412yes—
282C2×C4×C59C23×C411yescharacteristic
283C2×C4×C59C22×Q811yescharacteristic
284C2×C4×C59H(5,𝔽2)11yescharacteristic
285C2×C4×C59H(5,𝔽2)11yescharacteristic
286C2×C4×C59H(5,𝔽2)11yescharacteristic
287C2×C4×C59H(5,𝔽2)11yescharacteristic
288C2×Dic59—21no—
289C2×Dic59—21no—
290C2×Dic59—21no—
291C2×Dic59—21no—
292C2×Dic59—44no—
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—41no—
302C2×Dic59—41no—
303C2×Dic59—41no—
304C2×Dic59—41no—
305C2×Dic59C2×C4⋊C412yes—
306C2×Dic59C2×C4⋊C412yes—
307C4×D59—22no—
308C4×D59—22no—
309C4×D59—22no—
310C4×D59—22no—
311C4×D59—22no—
312C4×D59—22no—
313C4×D59—22no—
314C4×D59—22no—
315C4×D59—44no—
316C4×D59—44no—
317C8×C59—22no—
318C8×C59—22no—
319C59⋊C8—22no—
320C59⋊C8—22no—
321#21939—591nomaximal, Sylow
322C22×C59—22no—
323C22×C59—22no—
324C22×C59—22no—
325C22×C59—41no—
326C22×C59—41no—
327C22×C59—41no—
328C22×C59—41no—
329C22×C59C22×C4⋊C411yescharacteristic
330C22×C59#53411yescharacteristic
331C22×C59#53411yescharacteristic
332C22×C59C2×#13511yescharacteristic
333C22×C59C2×#13511yescharacteristic
334C22×C59#57511yescharacteristic
335C22×C59#57511yescharacteristic
336C2×D59—22no—
337C2×D59—22no—
338C2×D59—22no—
339C2×D59—22no—
340C2×D59—22no—
341C2×D59—22no—
342C2×D59—22no—
343C2×D59—22no—
344C2×D59—22no—
345C2×D59—416no—
346C2×D59—41no—
347C2×D59—41no—
348C2×D59—41no—
349C2×D59—41no—
350C2×D59#42714yes—
351C4×C59—22no—
352C4×C59—81no—
353C4×C59—81no—
354C4×C59—81no—
355C4×C59—81no—
356C4×C59#51811yescharacteristic
357C4×C59#51811yescharacteristic
358C4×C59#54311yescharacteristic
359C4×C59#54311yescharacteristic
360Dic59—22no—
361Dic59—22no—
362Dic59—81no—
363Dic59—81no—
364Dic59—81no—
365Dic59—81no—
366C22×C22⋊C8—591no—
367#2280—591no—
368#2280—591no—
369#1854—591no—
370#1854—591no—
371#1854—591no—
372#1854—591no—
373#1854—591no—
374#1854—591no—
375#1854—591no—
376#1854D5911yescharacteristic, complemented
377#1808—591no—
378#1808—591no—
379#1807—591no—
380#1807—591no—
381C2×C59—42no—
382C2×C59#231511yescharacteristic
383C2×C59C2×#42711yescharacteristic
384C2×C59#291111yescharacteristic
385C2×C59#319111yescharacteristic
386C2×C59#319111yescharacteristic
387C2×C59#319111yescharacteristic
388C2×C59#319111yescharacteristic
389D59—24no—
390D59—42no—
391C24×C4—591no—
392C23×C8—591no—
393C23×C8—591no—
394C2×#117—591no—
395C2×#117—591no—
396C2×#117—591no—
397C2×#117C2×D5911yescharacteristic
398C2×#107—591no—
399C2×#107—591no—
400C2×#107—591no—
401C2×#107C2×D5911yescharacteristic, complemented
402C2×#106—591no—
403C2×#106—591no—
404C2×#106—591no—
405C2×#106C2×D5911yescharacteristic, complemented
406C2×C22⋊C8—591no—
407C2×C22⋊C8—591no—
408C2×C22⋊C8—591no—
409C2×C22⋊C8—598no—
410C2×C22⋊C8C2×D5911yescharacteristic
411#381—1181no—
412#381—1181no—
413#380—591no—
414#380—591no—
415#380—591no—
416#380—591no—
417#380—591no—
418#380—591no—
419#380—591no—
420#380C2×D5911yescharacteristic
421#379—1181no—
422#379—1181no—
423C4×C22⋊C4—1181no—
424C4×C22⋊C4—1181no—
425C4×C22⋊C4—1181no—
426C4×C22⋊C4—1181no—
427#340—591no—
428#340—591no—
429#340—591no—
430#340—591no—
431#340—591no—
432#340—591no—
433#340C2×D5911yescharacteristic, complemented
434#340C2×D5911yescharacteristic, complemented
435C59#2193911yescharacteristic, complemented, Sylow
436C25—591no—
437C23×C4—591no—
438C23×C4—591no—
439C23×C4—591no—
440C23×C4—594no—
441C23×C4—591no—
442C23×C4—591no—
443C23×C4—594no—
444C23×C4—2361no—
445C23×C4—2361no—
446C23×C4—2361no—
447C23×C4—2361no—
448C23×C4C22×D5911yescharacteristic
449C22×C8—591no—
450C22×C8—591no—
451C22×C8—594no—
452C22×C8—594no—
453C22×C8—2361no—
454C22×C8—2361no—
455C22×C8—2361no—
456C22×C8—2361no—
457C22×C8C22×D5911yescharacteristic
458C22×C8C22×D5911yescharacteristic
459#117—41no—
460#117—41no—
461#117—2361no—
462#117—2361no—
463#117—2361no—
464#117—2361no—
465#117—2361no—
466#117—2361no—
467C2×C4⋊C4—591no—
468C2×C4⋊C4—591no—
469C2×C4⋊C4—591no—
470C2×C4⋊C4—591no—
471C2×C4⋊C4C22×D5911yescharacteristic
472C2×C4⋊C4C22×D5911yescharacteristic
473C2×C4⋊C4C22×D5911yescharacteristic
474C2×C4⋊C4C22×D5911yescharacteristic
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—1181no—
478C2×C22⋊C4—1181no—
479C2×C22⋊C4—1181no—
480C2×C22⋊C4—1181no—
481C2×C22⋊C4—1181no—
482C2×C22⋊C4—1181no—
483C2×C22⋊C4—1181no—
484C2×C22⋊C4—1181no—
485C2×C22⋊C4—1181no—
486C2×C22⋊C4—1181no—
487C2×C42—21no—
488C2×C42—1181no—
489C2×C42—1181no—
490C2×C42—1181no—
491#107—41no—
492#107—2361no—
493#107—2361no—
494#107—2361no—
495#106—41no—
496#106—2361no—
497#106—2361no—
498#106—2361no—
499C22⋊C8—594no—
500C22⋊C8—594no—
501C22⋊C8—594no—
502C22⋊C8C4×D5914yes—
503#95—21no—
504#95—1181no—
505#95—1181no—
506#95—1181no—
507#95—1181no—
508#95—1181no—
509#95—1181no—
510#95—1181no—
511C24—591no—
512C24—591no—
513C24—594no—
514C24—1182no—
515C24—1182no—
516C24—2361no—
517C24—2361no—
518C24—2361no—
519C24—2361no—
520C24D4×D5911yescharacteristic
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—591no—
530C22×C4—591no—
531C22×C4—594no—
532C22×C4—592no—
533C22×C4—592no—
534C22×C4—592no—
535C22×C4—592no—
536C22×C4—594no—
537C22×C4—594no—
538C22×C4—1181no—
539C22×C4—1181no—
540C22×C4—1181no—
541C22×C4—1181no—
542C22×C4—1181no—
543C22×C4—1181no—
544C22×C4—1181no—
545C22×C4—1181no—
546C22×C4—1181no—
547C22×C4—1181no—
548C22×C4—1181no—
549C22×C4—1181no—
550C22×C4—2364no—
551C22×C4—2364no—
552C22×C4—2364no—
553C22×C4—2364no—
554C22×C4—2361no—
555C22×C4—2361no—
556C22×C4—2361no—
557C22×C4—2361no—
558C22×C4—2361no—
559C22×C4—2361no—
560C22×C4C2×C4×D5912yes—
561C22×C4D4×D5911yescharacteristic
562C22×C4Q8×D5912yes—
563C22×C4C23×D5911yescharacteristic
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—592no—
569C2×C8—592no—
570C2×C8—1181no—
571C2×C8—1181no—
572C2×C8—1181no—
573C2×C8—1181no—
574C2×C8—2364no—
575C2×C8—2364no—
576C2×C8C2×C4×D5912yes—
577C2×C8C2×C4×D5912yes—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—1181no—
587C4⋊C4—1181no—
588C4⋊C4—1181no—
589C4⋊C4—1181no—
590C4⋊C4—1181no—
591C4⋊C4—1181no—
592C4⋊C4—1181no—
593C4⋊C4—1181no—
594C22⋊C4—42no—
595C22⋊C4—42no—
596C22⋊C4—2362no—
597C22⋊C4—2362no—
598C22⋊C4—2362no—
599C22⋊C4—2362no—
600C22⋊C4—2362no—
601C22⋊C4—2362no—
602C22⋊C4—2362no—
603C22⋊C4—2362no—
604C22⋊C4—2362no—
605C22⋊C4—2362no—
606C42—42no—
607C42—2362no—
608C42—2362no—
609C42—2362no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—592no—
617C23—592no—
618C23—592no—
619C23—592no—
620C23—1188no—
621C23—1181no—
622C23—1181no—
623C23—1181no—
624C23—1181no—
625C23—1181no—
626C23—1181no—
627C23—1181no—
628C23—1181no—
629C23—1181no—
630C23—1181no—
631C23—2364no—
632C23—2364no—
633C23—2364no—
634C23—2364no—
635C23—2364no—
636C23—2364no—
637C23C4⋊C4×D5912yes—
638C23C2×D4×D5911yescharacteristic
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—592no—
658C2×C4—592no—
659C2×C4—1181no—
660C2×C4—1181no—
661C2×C4—1181no—
662C2×C4—1181no—
663C2×C4—1182no—
664C2×C4—1182no—
665C2×C4—1182no—
666C2×C4—1182no—
667C2×C4—1182no—
668C2×C4—1182no—
669C2×C4—1182no—
670C2×C4—1182no—
671C2×C4—2364no—
672C2×C4—2364no—
673C2×C4—2364no—
674C2×C4—2361no—
675C2×C4—2361no—
676C2×C4—2361no—
677C2×C4—2361no—
678C2×C4—2361no—
679C2×C4—2361no—
680C2×C4—2361no—
681C2×C4—2361no—
682C2×C4—2361no—
683C2×C4—2361no—
684C2×C4—2361no—
685C2×C4—2361no—
686C2×C4C4⋊C4×D5912yes—
687C2×C4C22×C4×D5911yescharacteristic
688C2×C4C2×Q8×D5911yescharacteristic
689C2×C4#1427377211yescharacteristic
690C2×C4#1427377211yescharacteristic
691C2×C4#1427377311yescharacteristic
692C2×C4#1427377311yescharacteristic
693C8—22no—
694C8—22no—
695C8—1182no—
696C8—1182no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—594no—
705C22—1182no—
706C22—1182no—
707C22—1182no—
708C22—1182no—
709C22—1182no—
710C22—1182no—
711C22—1182no—
712C22—1182no—
713C22—1182no—
714C22—23616no—
715C22—2361no—
716C22—2361no—
717C22—2361no—
718C22—2361no—
719C22C2×C4⋊C4×D5911yescharacteristic
720C22#1683796211yescharacteristic
721C22#1683796311yescharacteristic
722C22#135×D5911yescharacteristic
723C22#135×D5911yescharacteristic
724C22#1683819811yescharacteristic
725C22#1683820111yescharacteristic
726C4—22no—
727C4—81no—
728C4—81no—
729C4—81no—
730C4—81no—
731C4—1182no—
732C4—1182no—
733C4—4721no—
734C4—4721no—
735C4—4721no—
736C4—4721no—
737C4#1683787411yescharacteristic
738C4#1683787411yescharacteristic
739C4#1683802711yescharacteristic
740C4#1683802711yescharacteristic
741C2—42no—
742C2—1184no—
743C2—2362no—
744C2#2142670711yescharacteristic
745C2#427×D5911yescharacteristic
746C2#2143268311yescharacteristic
747C2#2143488611yescharacteristic
748C2#2143488711yescharacteristic
749C2#2143488811yescharacteristic
750C2#2143489111yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#1854C2
socleC23×C59C22×D4
prime radicalC24×D59D4
cosocleC22×C4×C59C24
hypercenter#1854D59
hypocenterC59#21939
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1854

Complements

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

NH ≅ G/Ntype
4. #21424298C2semidirect
5. #21424297C2semidirect
6. #21424296C2semidirect
7. #21424295C2semidirect
8. #21424294C2semidirect
9. #21424293C2semidirect
10. #21424292C2semidirect
11. #21424124C2semidirect
12. #21424122C2semidirect
13. #21424120C2semidirect
14. #21424118C2semidirect
15. C59×#1854C2semidirect
22. C2×#14273661C22semidirect
23. C2×#14273660C22semidirect
24. C2×#14273660C22semidirect
25. C2×#14273659C22semidirect
26. C2×#14273658C22semidirect
27. C2×#14273658C22semidirect
31. C22⋊C8×D59C4semidirect
47. #16837165C22semidirect
48. #16837165C22semidirect
49. #16837164C22semidirect
50. #16837164C22semidirect
51. #16837164C22semidirect
52. #16837164C22semidirect
54. C2×#107×C59C22semidirect
55. C2×#106×C59C22semidirect
58. C59×#340C22semidirect
59. C59×#340C22semidirect
376. #1854D59semidirect
401. C2×#107C2×D59semidirect
405. C2×#106C2×D59semidirect
433. #340C2×D59semidirect
434. #340C2×D59semidirect
435. C59#21939semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊C8×D592
#214264782
#214264752
#214242982
#214242972
#214242962
#214242952
#214242942
#214242932
#214242922
#214241242
#214241222
#214241202
#214241182
C59×#18542
#2193959