Finite Group Databasebeta

← #28637326

Subgroups — #28637326

Order 15104.

988 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837715C211yesmaximal, characteristic, complemented
2C2×D4×C59⋊C8C211yesmaximal, characteristic, complemented
3#21427536C211yesmaximal, characteristic
4#21425587C211yesmaximal, characteristic, complemented
5#21425522C211yesmaximal, characteristic, complemented
6#21425481C211yesmaximal, characteristic, complemented
7#21425278C211yesmaximal, characteristic, complemented
8#21424826C211yesmaximal, characteristic, complemented
9#21424778C211yesmaximal, characteristic, complemented
10#21424522C211yesmaximal, characteristic, complemented
11#21424522C211yesmaximal, characteristic, complemented
12#21424283C211yesmaximal, characteristic, complemented
13#21424123C211yesmaximal, characteristic, complemented
14C2×#16837164C211yesmaximal, characteristic, complemented
15C59×#2486C211yesmaximal, characteristic, complemented
16C23×C59⋊C8C2211yescharacteristic
17C23×C59⋊C8C2211yescharacteristic
18C2×#14273701C2211yescharacteristic
19C2×#14273701C2211yescharacteristic
20C2×#14273699—21no—
21C22×C4⋊Dic59C2211yescharacteristic
22#16837715—24no—
23D4×C59⋊C8—24no—
24C2×#14273660C2211yescharacteristic
25C2×#14273660C2211yescharacteristic
26C2×#14273660C2211yescharacteristic
27C2×#14273660C2211yescharacteristic
28C2×C4⋊(C59⋊C8)C2211yescharacteristic
29C2×#14273647C2211yescharacteristic
30C2×#14273647C2211yescharacteristic
31C2×#14273647C2211yescharacteristic
32C2×#14273647C2211yescharacteristic
33C2×C22⋊(C59⋊C8)C2211yescharacteristic
34C2×C22⋊(C59⋊C8)C2211yescharacteristic
35C2×C4×C59⋊C8C2211yescharacteristic
36#16837324—21no—
37#16837318—21no—
38#16837304C2211yescharacteristic
39#16837300C2211yescharacteristic
40#16837279—21no—
41#16837262C2211yescharacteristic
42#16837164C2211yescharacteristic
43#16837164C2211yescharacteristic
44#16837164C2211yescharacteristic
45#16837164C2211yescharacteristic
46#16837164C2211yescharacteristic
47#16837164C2211yescharacteristic
48#16837164C2211yescharacteristic
49#16837164C2211yescharacteristic
50C2×#123×C59—21no—
51C2×C4×D4×C59C2211yescharacteristic
52C22×C4⋊C4×C59C2211yescharacteristic
53C59×#398—21no—
54C59×#397—21no—
55C59×#389C2211yescharacteristic
56C59×#389C2211yescharacteristic
57C59×#381—21no—
58C59×#380C2211yescharacteristic
59C59×#380C2211yescharacteristic
60C59×#380C2211yescharacteristic
61C22×D236C2311yescharacteristic
62C22×C22⋊D59—21no—
63C22×C22⋊D59—21no—
64C23×Dic59—21no—
65C22×C59⋊C8—22no—
66C22×C59⋊C8—22no—
67C22×C59⋊C8—22no—
68C22×C59⋊C8—22no—
69C22×C59⋊C8—41no—
70C22×C59⋊C8—41no—
71C22×C59⋊C8C2311yescharacteristic
72C22×C59⋊C8C2311yescharacteristic
73C22×C59⋊C8C2311yescharacteristic
74C22×C59⋊C8C2311yescharacteristic
75#14273701—22no—
76#14273701—22no—
77#14273701—22no—
78#14273701—41no—
79#14273699—44no—
80C2×C4⋊Dic59—22no—
81C2×C4⋊Dic59—21no—
82C2×C4⋊Dic59—41no—
83C2×C4⋊Dic59C2311yescharacteristic
84C2×C4⋊Dic59C2311yescharacteristic
85C2×C4⋊Dic59C2311yescharacteristic
86C2×Dic59⋊C4—21no—
87C2×C22⋊Dic59—21no—
88C2×(C2×D59)⋊C4—21no—
89C2×(C2×D59)⋊C4—21no—
90C2×(C2×D59)⋊C4—21no—
91C2×(C2×D59)⋊C4—21no—
92#14273660—22no—
93#14273660—22no—
94#14273660—22no—
95#14273660—41no—
96C4⋊(C59⋊C8)—22no—
97#14273647—22no—
98#14273647—22no—
99#14273647—22no—
100#14273647—41no—
101C22⋊(C59⋊C8)—22no—
102C22⋊(C59⋊C8)D414yescomplemented
103C4×C59⋊C8—22no—
104C59⋊#95—21no—
105C59⋊#95—21no—
106C22×D4×C59D411yescharacteristic
107C23×C4×C59—21no—
108C23×C4×C59C2311yescharacteristic
109C23×C4×C59C2311yescharacteristic
110#123×C59—44no—
111C4×D4×C59—22no—
112C4×D4×C59—22no—
113C2×C4⋊C4×C59—22no—
114C2×C4⋊C4×C59—22no—
115C2×C4⋊C4×C59—21no—
116C2×C4⋊C4×C59—21no—
117C2×C4⋊C4×C59—21no—
118C2×C4⋊C4×C59D411yescharacteristic
119C2×C4⋊C4×C59C2311yescharacteristic
120C2×C4⋊C4×C59C2311yescharacteristic
121C2×C4⋊C4×C59C2311yescharacteristic
122C2×C4⋊C4×C59C2311yescharacteristic
123C2×C22⋊C4×C59—21no—
124C2×C22⋊C4×C59—21no—
125C2×C22⋊C4×C59—21no—
126C2×C22⋊C4×C59D411yescharacteristic
127C2×C22⋊C4×C59D411yescharacteristic
128C2×C42×C59C2311yescharacteristic
129#95×C59—21no—
130#95×C59—21no—
131#95×C59—21no—
132#95×C59—21no—
133#95×C59—21no—
134C24×C59C2×D411yescharacteristic
135C24×C59C2×D411yescharacteristic
136C23×D59—21no—
137C2×D4×C59—22no—
138C2×D4×C59—22no—
139C2×D4×C59D814yes—
140C22×C4×C59—21no—
141C22×C4×C59—21no—
142C22×C4×C59—21no—
143C22×C4×C59—21no—
144C22×C4×C59—21no—
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×C59—21no—
154C22×C4×C59—42no—
155C22×C4×C59—42no—
156C22×C4×C59—42no—
157C22×C4×C59C2×D411yescharacteristic
158C22×C4×C59C2×D411yescharacteristic
159C22×C4×C59C2×D411yescharacteristic
160C22×C4×C59C2×D412yes—
161C22×C4×C59C2×D411yescharacteristic
162C22×C4×C59#4112yes—
163C22×C4×C59C2411yescharacteristic
164C2×C22⋊D59—42no—
165C2×C22⋊D59—42no—
166C2×C22⋊D59—42no—
167C2×C22⋊D59—42no—
168C2×C22⋊D59—42no—
169C2×C22⋊D59—81no—
170C22×Dic59—21no—
171C22×Dic59—21no—
172C22×Dic59—21no—
173C22×Dic59—42no—
174C22×Dic59—42no—
175C22×Dic59—81no—
176C2×D236—21no—
177C2×D236—21no—
178C2×D236—21no—
179C2×D236—21no—
180C2×D236—21no—
181C2×D236—21no—
182C4⋊C4×C59—22no—
183C4⋊C4×C59—21no—
184C4⋊C4×C59—21no—
185C4⋊C4×C59—21no—
186C4⋊C4×C59—21no—
187C4⋊C4×C59—21no—
188C4⋊C4×C59—21no—
189C4⋊C4×C59—21no—
190C4⋊C4×C59—21no—
191C4⋊C4×C59—42no—
192C4⋊C4×C59—42no—
193C4⋊C4×C59—42no—
194C22⋊C4×C59—22no—
195C22⋊C4×C59—22no—
196C22⋊C4×C59—42no—
197C22⋊C4×C59—42no—
198C22⋊C4×C59—42no—
199C42×C59—21no—
200C42×C59—21no—
201C22⋊Dic59—42no—
202(C2×D59)⋊C4—42no—
203(C2×D59)⋊C4—42no—
204(C2×D59)⋊C4—42no—
205(C2×D59)⋊C4—81no—
206C4⋊Dic59—21no—
207C4⋊Dic59—21no—
208C4⋊Dic59—21no—
209C4⋊Dic59—21no—
210C4⋊Dic59—21no—
211C4⋊Dic59—42no—
212C4⋊Dic59#4112yes—
213Dic59⋊C4—42no—
214C2×C59⋊C8—21no—
215C2×C59⋊C8—21no—
216C2×C59⋊C8—21no—
217C2×C59⋊C8—21no—
218C2×C59⋊C8—21no—
219C2×C59⋊C8—21no—
220C2×C59⋊C8—21no—
221C2×C59⋊C8—21no—
222C2×C59⋊C8—21no—
223C2×C59⋊C8—44no—
224C2×C59⋊C8—44no—
225C2×C59⋊C8C2×D412yes—
226C2×C59⋊C8C2×D412yes—
227C2×C59⋊C8#4112yes—
228C23×C59—21no—
229C23×C59—21no—
230C23×C59—21no—
231C23×C59—21no—
232C23×C59—21no—
233C23×C59—21no—
234C23×C59—21no—
235C23×C59—21no—
236C23×C59—21no—
237C23×C59—21no—
238C23×C59#12112yes—
239C23×C59C2×D812yes—
240C23×C59C2×D812yes—
241C23×C59#13512yes—
242C23×C59C22×D411yescharacteristic
243C22×D59—41no—
244C22×D59—41no—
245C22×D59—41no—
246C22×D59—41no—
247C22×D59—41no—
248C22×D59—41no—
249C22×D59—41no—
250D4×C59—28no—
251C2×C4×C59—21no—
252C2×C4×C59—21no—
253C2×C4×C59—21no—
254C2×C4×C59—21no—
255C2×C4×C59—22no—
256C2×C4×C59—22no—
257C2×C4×C59—22no—
258C2×C4×C59—22no—
259C2×C4×C59—21no—
260C2×C4×C59—21no—
261C2×C4×C59—21no—
262C2×C4×C59—21no—
263C2×C4×C59—21no—
264C2×C4×C59—21no—
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—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×C59—84no—
282C2×C4×C59#12112yes—
283C2×C4×C59C2×D812yes—
284C2×C4×C59C22×D411yescharacteristic
285C2×C4×C59C2×#4111yescharacteristic
286C2×C4×C59C2×#4111yescharacteristic
287C2×C4×C59C2×#4111yescharacteristic
288C2×C4×C59H(5,𝔽2)11yescharacteristic
289C2×C4×C592−1+411yescharacteristic
290C22⋊D59—84no—
291C22⋊D59—84no—
292C2×Dic59—22no—
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—
302D236—41no—
303D236—41no—
304D236—41no—
305D236—41no—
306C59⋊C8—22no—
307C59⋊C8—22no—
308C59⋊C8—22no—
309C59⋊C8—41no—
310#25232—591nomaximal, Sylow
311C22×C59—22no—
312C22×C59—22no—
313C22×C59—22no—
314C22×C59—22no—
315C22×C59—22no—
316C22×C59—22no—
317C22×C59—22no—
318C22×C59—22no—
319C22×C59—22no—
320C22×C59—41no—
321C22×C59—41no—
322C22×C59—41no—
323C22×C59—41no—
324C22×C59#46614yes—
325C22×C59C2×#12111yescharacteristic
326C22×C59#54611yescharacteristic
327C22×C59#54711yescharacteristic
328C22×C59C22×D811yescharacteristic
329C22×C59C2×#13511yescharacteristic
330C22×C59#57711yescharacteristic
331C22×C59#57811yescharacteristic
332C2×D59—81no—
333C2×D59—81no—
334C2×D59—81no—
335C2×D59—81no—
336C2×D59—81no—
337C2×D59—81no—
338C2×D59—81no—
339C4×C59—22no—
340C4×C59—22no—
341C4×C59—41no—
342C4×C59—41no—
343C4×C59—81no—
344C4×C59—81no—
345C4×C59—81no—
346C4×C59—81no—
347C4×C59#52911yescharacteristic
348C4×C59#53911yescharacteristic
349C4×C59#54611yescharacteristic
350C4×C59#54711yescharacteristic
351Dic59—42no—
352Dic59—81no—
353Dic59—81no—
354C2×#480—591no—
355C2×C8×D4—591no—
356#2486D5911yescharacteristic, complemented
357#2416—591no—
358#2086—591no—
359#2075—591no—
360#2067—591no—
361#2033—591no—
362#1942—591no—
363#1934—591no—
364#1893—591no—
365#1893—591no—
366#1852—591no—
367#1808—591no—
368C2×#340—591no—
369C2×C59—24no—
370C2×C59—42no—
371C2×C59#242511yescharacteristic
372C2×C59C2×#46611yescharacteristic
373C2×C59#306311yescharacteristic
374C2×C59#329411yescharacteristic
375C2×C59#330011yescharacteristic
376C2×C59#333411yescharacteristic
377C2×C59#333711yescharacteristic
378D59—161no—
379C23×C8—591no—
380C23×C8—591no—
381C2×#123—21no—
382C2×#121—591no—
383C2×#121—591no—
384C2×#121—1181no—
385C2×C4×D4C2×D5911yescharacteristic
386C22×C4⋊C4—591no—
387C22×C4⋊C4C2×D5911yescharacteristic
388#480—1184no—
389C8×D4—1184no—
390C2×#107—591no—
391C2×#107—591no—
392C2×#107—591no—
393C2×#107—591no—
394C2×C4⋊C8—591no—
395C2×#102—591no—
396C2×#102—591no—
397C2×#102—591no—
398C2×#102—591no—
399C2×C22⋊C8—591no—
400C2×C22⋊C8—591no—
401C2×C4×C8—591no—
402#398—21no—
403#397—21no—
404#396—1181no—
405#394—1181no—
406#390—591no—
407#389—591no—
408#389C2×D5911yescharacteristic
409#389C2×D5911yescharacteristic
410#386—1181no—
411#381—21no—
412#380—591no—
413#380C2×D5911yescharacteristic
414#380C2×D5911yescharacteristic
415#380C2×D5911yescharacteristic
416#340—591no—
417#340—591no—
418#340—591no—
419#340—591no—
420#340—591no—
421#340—591no—
422#340—591no—
423#340—591no—
424C59#2523211yescharacteristic, complemented, Sylow
425C22×D4—591no—
426C22×D4—1181no—
427C22×D4—1181no—
428C22×D4C22⋊D5911yescharacteristic
429C23×C4—21no—
430C23×C4—1181no—
431C23×C4C22×D5911yescharacteristic
432C23×C4C22×D5911yescharacteristic
433C22×C8—591no—
434C22×C8—591no—
435C22×C8—591no—
436C22×C8—591no—
437C22×C8—1182no—
438C22×C8—1182no—
439C22×C8—1182no—
440C22×C8—1182no—
441C22×C8—2361no—
442C22×C8—2361no—
443#123—44no—
444#121—1182no—
445#121—1182no—
446#121—1182no—
447#121—2361no—
448#121—2364no—
449C4×D4—22no—
450C4×D4—22no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—591no—
457C2×C4⋊C4—591no—
458C2×C4⋊C4—591no—
459C2×C4⋊C4—1182no—
460C2×C4⋊C4—1181no—
461C2×C4⋊C4—1181no—
462C2×C4⋊C4—2361no—
463C2×C4⋊C4C22⋊D5911yescharacteristic
464C2×C4⋊C4C22×D5911yescharacteristic
465C2×C4⋊C4C22×D5911yescharacteristic
466C2×C4⋊C4C22×D5911yescharacteristic
467C2×C4⋊C4C22×D5911yescharacteristic
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—1181no—
472C2×C22⋊C4—1181no—
473C2×C22⋊C4—1181no—
474C2×C22⋊C4—1181no—
475C2×C22⋊C4—1181no—
476C2×C22⋊C4C22⋊D5911yescharacteristic
477C2×C22⋊C4C22⋊D5911yescharacteristic
478C2×C42C22×D5911yescharacteristic
479#107—1182no—
480#107—1182no—
481#107—1182no—
482#107—2361no—
483C4⋊C8—1182no—
484#102—1182no—
485#102—1182no—
486#102—1182no—
487#102—2361no—
488C22⋊C8—594no—
489C22⋊C8—1182no—
490C4×C8—1182no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95—21no—
496#95—1181no—
497#95—1181no—
498C24—1181no—
499C24C2×C22⋊D5911yescharacteristic
500C24C2×C22⋊D5911yescharacteristic
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—1181no—
504C2×D4—1181no—
505C2×D4—1181no—
506C2×D4—1181no—
507C2×D4—1181no—
508C2×D4—1181no—
509C2×D4—4721no—
510C2×D4—2362no—
511C2×D4—2362no—
512C2×D4—2362no—
513C2×D4—2362no—
514C2×D4—2362no—
515C2×D4#1174566914yes—
516C22×C4—21no—
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—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—1181no—
534C22×C4—1181no—
535C22×C4—1181no—
536C22×C4—4721no—
537C22×C4—2362no—
538C22×C4—2362no—
539C22×C4D4×D5912yes—
540C22×C4#1174568712yes—
541C22×C4C2×C22⋊D5911yescharacteristic
542C22×C4C2×C22⋊D5911yescharacteristic
543C22×C4C2×C22⋊D5911yescharacteristic
544C22×C4C2×C22⋊D5911yescharacteristic
545C22×C4C23×D5911yescharacteristic
546C2×C8—592no—
547C2×C8—592no—
548C2×C8—592no—
549C2×C8—1181no—
550C2×C8—1181no—
551C2×C8—1181no—
552C2×C8—1181no—
553C2×C8—1181no—
554C2×C8—1181no—
555C2×C8—1181no—
556C2×C8—1181no—
557C2×C8—1181no—
558C2×C8—2364no—
559C2×C8—2364no—
560C4⋊C4—22no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—42no—
570C4⋊C4—42no—
571C4⋊C4—42no—
572C4⋊C4—592no—
573C4⋊C4—1181no—
574C4⋊C4—1181no—
575C4⋊C4—1181no—
576C4⋊C4—1181no—
577C4⋊C4—1181no—
578C4⋊C4—2362no—
579C4⋊C4—2362no—
580C22⋊C4—22no—
581C22⋊C4—22no—
582C22⋊C4—42no—
583C22⋊C4—42no—
584C22⋊C4—42no—
585C22⋊C4—4721no—
586C22⋊C4—2362no—
587C22⋊C4—2362no—
588C22⋊C4—2362no—
589C22⋊C4—2362no—
590C42—21no—
591C42—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—2361no—
603C23—2361no—
604C23—2361no—
605C23—2361no—
606C23—2361no—
607C23—2361no—
608C23—2361no—
609C23#1427369912yes—
610C23C2×#1174566912yes—
611C23C2×#1174566912yes—
612C23#1427374712yes—
613C23C22×C22⋊D5911yescharacteristic
614D4—28no—
615D4—4724no—
616D4—4724no—
617D4—2361no—
618D4—2361no—
619D4—2361no—
620D4—2361no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—84no—
652C2×C4—1182no—
653C2×C4—4724no—
654C2×C4—2361no—
655C2×C4—2361no—
656C2×C4—2361no—
657C2×C4—2361no—
658C2×C4—2361no—
659C2×C4—2361no—
660C2×C4—2361no—
661C2×C4—2361no—
662C2×C4#1427369912yes—
663C2×C4C2×#1174566912yes—
664C2×C4C2×D4×D5911yescharacteristic
665C2×C4#41×D5911yescharacteristic
666C2×C4#41×D5911yescharacteristic
667C2×C4C2×#1174568711yescharacteristic
668C2×C4#1427377311yescharacteristic
669C2×C4#1427377411yescharacteristic
670C8—1182no—
671C8—1182no—
672C8—1182no—
673C8—2361no—
674C22—22no—
675C22—22no—
676C22—22no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—41no—
684C22—41no—
685C22—41no—
686C22—41no—
687C22—4721no—
688C22—4721no—
689C22—4721no—
690C22—4721no—
691C22—4721no—
692C22—4721no—
693C22—4721no—
694C22#1683763614yes—
695C22C2×#1427369911yescharacteristic
696C22#1683804011yescharacteristic
697C22#1683805111yescharacteristic
698C22C22×#1174566911yescharacteristic
699C22C2×#1427374711yescharacteristic
700C22#1683821011yescharacteristic
701C22#1683821711yescharacteristic
702C4—22no—
703C4—22no—
704C4—41no—
705C4—41no—
706C4—81no—
707C4—81no—
708C4—81no—
709C4—81no—
710C4—4721no—
711C4—4721no—
712C4—2362no—
713C4#1683792911yescharacteristic
714C4#1683799611yescharacteristic
715C4#1683804411yescharacteristic
716C4#1683805011yescharacteristic
717C2—24no—
718C2—42no—
719C2—9441no—
720C2#2142765111yescharacteristic
721C2C2×#1683763611yescharacteristic
722C2#2143378311yescharacteristic
723C2#2143590311yescharacteristic
724C2#2143597711yescharacteristic
725C2#2143643911yescharacteristic
726C2#2143647511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC59×#2486C2
socleC23×C59C22×D4
prime radical#21427536C2
hypercenter#2486D59
hypocenterC59#25232
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2486

Complements

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

NH ≅ G/Ntype
1. C2×#16837715C2semidirect
2. C2×D4×C59⋊C8C2semidirect
4. #21425587C2semidirect
5. #21425522C2semidirect
6. #21425481C2semidirect
7. #21425278C2semidirect
8. #21424826C2semidirect
9. #21424778C2semidirect
10. #21424522C2semidirect
11. #21424522C2semidirect
12. #21424283C2semidirect
13. #21424123C2semidirect
14. C2×#16837164C2semidirect
15. C59×#2486C2semidirect
102. C22⋊(C59⋊C8)D4semidirect
356. #2486D59semidirect
424. C59#25232semidirect

Maximal subgroups

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

subgroupindex
C2×#168377152
C2×D4×C59⋊C82
#214275362
#214255872
#214255222
#214254812
#214252782
#214248262
#214247782
#214245222
#214242832
#214241232
C2×#168371642
C59×#24862
#2523259