Finite Group Databasebeta

← #28497407

Subgroups — #28497407

Order 15104.

1262 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21426708C211yesmaximal, characteristic
2C2×#16837275C211yesmaximal, characteristic
3C2×#16837169C211yesmaximal, characteristic
4C2×#16837168C211yesmaximal, characteristic
5C2×#16837168C211yesmaximal, characteristic
6#21422319C211yesmaximal, characteristic
7C2×C59×#385C211yesmaximal, characteristic
8C22×Dic59⋊C4—21no—
9C22×C22⋊Dic59C2211yescharacteristic
10C22×C22⋊Dic59C2211yescharacteristic
11C22×C22⋊Dic59C2211yescharacteristic
12C22×C22⋊Dic59C2211yescharacteristic
13#16837275—22no—
14#16837275—21no—
15#16837275—21no—
16#16837275—22no—
17#16837274—21no—
18#16837274—21no—
19#16837260—22no—
20C2×C59⋊#95—21no—
21C2×C59⋊#95—22no—
22#16837169—22no—
23#16837168—22no—
24#16837168C414yescomplemented
25C24×C4×C59C2211yescharacteristic
26C22×C4⋊C4×C59—21no—
27C22×C22⋊C4×C59C2211yescharacteristic
28C22×C22⋊C4×C59C2211yescharacteristic
29C59×#385—22no—
30C59×#385—22no—
31C2×#95×C59—21no—
32C23×Dic59—21no—
33C23×Dic59—21no—
34C23×Dic59D411yescharacteristic
35C23×Dic59D411yescharacteristic
36C23×Dic59D412yes—
37C2×Dic59⋊C4—24no—
38C2×Dic59⋊C4—22no—
39C2×Dic59⋊C4—22no—
40C2×Dic59⋊C4—44no—
41C2×C22⋊Dic59—21no—
42C2×C22⋊Dic59—21no—
43C2×C22⋊Dic59—21no—
44C2×C22⋊Dic59—21no—
45C2×C22⋊Dic59—21no—
46C2×C22⋊Dic59—21no—
47C2×C22⋊Dic59—21no—
48C2×C22⋊Dic59—21no—
49C2×C22⋊Dic59—21no—
50C2×C22⋊Dic59—21no—
51C2×C22⋊Dic59—21no—
52C2×C22⋊Dic59—21no—
53C2×C22⋊Dic59—21no—
54C2×C22⋊Dic59—21no—
55C2×C22⋊Dic59—21no—
56C2×C22⋊Dic59—21no—
57C2×C22⋊Dic59—21no—
58C2×C22⋊Dic59—21no—
59C2×C22⋊Dic59C2×C412yes—
60C2×C22⋊Dic59C2×C412yes—
61C2×C22⋊Dic59D412yes—
62C2×C22⋊Dic59Q812yes—
63C2×C22⋊Dic59Q812yes—
64C2×C22⋊Dic59Q812yes—
65C59⋊#95—24no—
66C59⋊#95—22no—
67C59⋊#95—22no—
68C59⋊#95—44no—
69C25×C59C2311yescharacteristic
70C23×C4×C59—21no—
71C23×C4×C59—21no—
72C23×C4×C59—21no—
73C23×C4×C59—21no—
74C23×C4×C59—21no—
75C23×C4×C59—21no—
76C23×C4×C59—21no—
77C23×C4×C59—44no—
78C23×C4×C59D411yescharacteristic
79C23×C4×C59D412yes—
80C23×C4×C59D411yescharacteristic
81C2×C4⋊C4×C59—24no—
82C2×C4⋊C4×C59—44no—
83C2×C22⋊C4×C59—21no—
84C2×C22⋊C4×C59—21no—
85C2×C22⋊C4×C59—21no—
86C2×C22⋊C4×C59—21no—
87C2×C22⋊C4×C59—21no—
88C2×C22⋊C4×C59—21no—
89C2×C22⋊C4×C59—21no—
90C2×C22⋊C4×C59—21no—
91C2×C22⋊C4×C59—21no—
92C2×C22⋊C4×C59C2×C412yes—
93C2×C22⋊C4×C59D412yes—
94C2×C22⋊C4×C59Q812yes—
95#95×C59—24no—
96C24×C59—42no—
97C24×C59—42no—
98C24×C59C22×C411yescharacteristic
99C24×C59C2×D411yescharacteristic
100C24×C59C2×D411yescharacteristic
101C24×C59C2×D411yescharacteristic
102C24×C59C2×D411yescharacteristic
103C24×C59C2×D411yescharacteristic
104C24×C59C2×D411yescharacteristic
105C24×C59C2×Q811yescharacteristic
106C24×C59C2×Q811yescharacteristic
107C24×C59C2×Q811yescharacteristic
108C24×C59C2×Q811yescharacteristic
109C24×C59#4111yescharacteristic
110C24×C59#4111yescharacteristic
111C24×C59#4111yescharacteristic
112C24×C59#4111yescharacteristic
113C22×C4×C59—24no—
114C22×C4×C59—24no—
115C22×C4×C59—24no—
116C22×C4×C59—22no—
117C22×C4×C59—22no—
118C22×C4×C59—22no—
119C22×C4×C59—22no—
120C22×C4×C59—22no—
121C22×C4×C59—22no—
122C22×C4×C59—21no—
123C22×C4×C59—21no—
124C22×C4×C59—21no—
125C22×C4×C59—21no—
126C22×C4×C59—21no—
127C22×C4×C59—21no—
128C22×C4×C59—44no—
129C22×C4×C59—44no—
130C22×C4×C59—44no—
131C22×C4×C59—44no—
132C22×C4×C59—42no—
133C22×C4×C59—42no—
134C22×C4×C59—42no—
135C22×C4×C59—42no—
136C22×C4×C59—42no—
137C22×C4×C59—41no—
138C22×C4×C59—41no—
139C22×C4×C59—41no—
140C22×C4×C59—41no—
141C22×C4×C59—42no—
142C22×C4×C59—42no—
143C22×Dic59—22no—
144C22×Dic59—22no—
145C22×Dic59—22no—
146C22×Dic59—22no—
147C22×Dic59—22no—
148C22×Dic59—21no—
149C22×Dic59—21no—
150C22×Dic59—21no—
151C22×Dic59—21no—
152C22×Dic59—22no—
153C22×Dic59—21no—
154C22×Dic59—21no—
155C22×Dic59—42no—
156C22×Dic59—42no—
157C22×Dic59—42no—
158C22×Dic59—42no—
159C22×Dic59—42no—
160C22×Dic59—42no—
161C22×Dic59—42no—
162C22×Dic59—42no—
163C22×Dic59—41no—
164C22×Dic59—41no—
165C22×Dic59C4⋊C414yescomplemented
166C4⋊C4×C59—48no—
167C22⋊C4×C59—22no—
168C22⋊C4×C59—22no—
169C22⋊C4×C59—22no—
170C22⋊C4×C59—41no—
171C22⋊C4×C59—41no—
172C22⋊C4×C59—41no—
173C22⋊C4×C59—41no—
174C22⋊C4×C59C4⋊C414yescomplemented
175C22⋊Dic59—22no—
176C22⋊Dic59—22no—
177C22⋊Dic59—22no—
178C22⋊Dic59—22no—
179C22⋊Dic59—22no—
180C22⋊Dic59—22no—
181C22⋊Dic59—22no—
182C22⋊Dic59—22no—
183C22⋊Dic59—22no—
184C22⋊Dic59—41no—
185C22⋊Dic59—41no—
186C22⋊Dic59—41no—
187C22⋊Dic59—41no—
188C22⋊Dic59—41no—
189C22⋊Dic59—41no—
190C22⋊Dic59C4⋊C414yescomplemented
191Dic59⋊C4—48no—
192Dic59⋊C4—82no—
193Dic59⋊C4—82no—
194C23×C59—22no—
195C23×C59—22no—
196C23×C59—22no—
197C23×C59—22no—
198C23×C59—22no—
199C23×C59—22no—
200C23×C59—41no—
201C23×C59—41no—
202C23×C59—41no—
203C23×C59—41no—
204C23×C59—42no—
205C23×C59—41no—
206C23×C59—41no—
207C23×C59—41no—
208C23×C59—42no—
209C23×C59—42no—
210C23×C59—42no—
211C23×C59—42no—
212C23×C59—42no—
213C23×C59—42no—
214C23×C59—41no—
215C23×C59—42no—
216C23×C59C2×C4⋊C411yescharacteristic
217C23×C59C2×C4⋊C411yescharacteristic
218C23×C59C2×C4⋊C411yescharacteristic
219C23×C59C4×D411yescharacteristic
220C23×C59C4×D411yescharacteristic
221C23×C59C4×D411yescharacteristic
222C23×C59C4×Q811yescharacteristic
223C23×C59#12011yescharacteristic
224C23×C59#12011yescharacteristic
225C23×C59#12011yescharacteristic
226C23×C59#12111yescharacteristic
227C23×C59#12111yescharacteristic
228C23×C59#12111yescharacteristic
229C23×C59C22⋊Q811yescharacteristic
230C23×C59C22⋊Q811yescharacteristic
231C23×C59C22⋊Q811yescharacteristic
232C23×C59C22⋊Q811yescharacteristic
233C23×C59C22⋊Q811yescharacteristic
234C23×C59C22⋊Q811yescharacteristic
235C23×C59C22⋊Q811yescharacteristic
236C23×C59C22⋊Q811yescharacteristic
237C23×C59C22⋊Q811yescharacteristic
238C23×C59#12311yescharacteristic
239C23×C59#12311yescharacteristic
240C23×C59#12311yescharacteristic
241C23×C59#12511yescharacteristic
242C23×C59#12511yescharacteristic
243C23×C59#12511yescharacteristic
244C23×C59#12711yescharacteristic
245C23×C59C4⋊Q811yescharacteristic
246C23×C59C4⋊Q811yescharacteristic
247C23×C59C4⋊Q811yescharacteristic
248C23×C59C4⋊Q811yescharacteristic
249C23×C59C4⋊Q811yescharacteristic
250C23×C59C4⋊Q811yescharacteristic
251C2×C4×C59—24no—
252C2×C4×C59—24no—
253C2×C4×C59—24no—
254C2×C4×C59—24no—
255C2×C4×C59—42no—
256C2×C4×C59—44no—
257C2×C4×C59—44no—
258C2×C4×C59—42no—
259C2×C4×C59—42no—
260C2×C4×C59—44no—
261C2×C4×C59—44no—
262C2×C4×C59—42no—
263C2×C4×C59—42no—
264C2×C4×C59—44no—
265C2×C4×C59—42no—
266C2×C4×C59—44no—
267C2×C4×C59—42no—
268C2×C4×C59—42no—
269C2×C4×C59—41no—
270C2×C4×C59—41no—
271C2×C4×C59—42no—
272C2×C4×C59—42no—
273C2×C4×C59—81no—
274C2×C4×C59—81no—
275C2×Dic59—24no—
276C2×Dic59—24no—
277C2×Dic59—42no—
278C2×Dic59—44no—
279C2×Dic59—44no—
280C2×Dic59—42no—
281C2×Dic59—42no—
282C2×Dic59—42no—
283C2×Dic59—44no—
284C2×Dic59—42no—
285C2×Dic59—44no—
286C2×Dic59—42no—
287C2×Dic59—41no—
288C2×Dic59—41no—
289C2×Dic59—42no—
290C2×Dic59—42no—
291C2×Dic59—42no—
292C2×Dic59—82no—
293C2×Dic59—82no—
294C2×Dic59—81no—
295C2×Dic59—81no—
296C2×Dic59—81no—
297C2×Dic59—81no—
298#11344—591nomaximal, Sylow
299C22×C59—22no—
300C22×C59—22no—
301C22×C59—22no—
302C22×C59—22no—
303C22×C59—22no—
304C22×C59—22no—
305C22×C59—22no—
306C22×C59—22no—
307C22×C59—22no—
308C22×C59—22no—
309C22×C59—22no—
310C22×C59—22no—
311C22×C59—21no—
312C22×C59—21no—
313C22×C59—21no—
314C22×C59—21no—
315C22×C59—21no—
316C22×C59—21no—
317C22×C59—21no—
318C22×C59—21no—
319C22×C59—21no—
320C22×C59—21no—
321C22×C59—21no—
322C22×C59—21no—
323C22×C59—41no—
324C22×C59—41no—
325C22×C59—41no—
326C22×C59—41no—
327C22×C59—41no—
328C22×C59—41no—
329C22×C59—41no—
330C22×C59—41no—
331C22×C59—41no—
332C22×C59—41no—
333C22×C59—41no—
334C22×C59—41no—
335C22×C59—41no—
336C22×C59—41no—
337C22×C59—41no—
338C22×C59—41no—
339C22×C59#38411yescharacteristic
340C22×C59#38511yescharacteristic
341C22×C59#38511yescharacteristic
342C22×C59#38511yescharacteristic
343C22×C59#38911yescharacteristic
344C22×C59#38911yescharacteristic
345C22×C59#38911yescharacteristic
346C22×C59#39211yescharacteristic
347C22×C59#39511yescharacteristic
348C22×C59#39511yescharacteristic
349C22×C59#39511yescharacteristic
350C22×C59#39811yescharacteristic
351C22×C59#39811yescharacteristic
352C22×C59#39811yescharacteristic
353C22×C59#39911yescharacteristic
354C22×C59B(4,𝔽2)12yes—
355C22×C59#45812yes—
356C4×C59—44no—
357C4×C59—44no—
358C4×C59—81no—
359C4×C59—81no—
360Dic59—44no—
361Dic59—44no—
362Dic59—82no—
363Dic59—81no—
364Dic59—81no—
365#2315—591no—
366C2×#385—591no—
367C2×#385D5911yescharacteristic
368C2×#342—591no—
369C2×#342—591no—
370C2×#342—591no—
371C22⋊#95—591no—
372C2×C59—21no—
373C2×C59—21no—
374C2×C59—21no—
375C2×C59—21no—
376C2×C59—21no—
377C2×C59—21no—
378C2×C59—21no—
379C2×C59—21no—
380C2×C59—21no—
381C2×C59—21no—
382C2×C59—21no—
383C2×C59—21no—
384C2×C59#144411yescharacteristic
385C2×C59#186712yes—
386C2×C59#202111yescharacteristic
387C2×C59#202211yescharacteristic
388C2×C59#206212yes—
389C24×C4C2×D5911yescharacteristic
390C22×C4⋊C4—21no—
391C22×C4⋊C4—1181no—
392C22×C22⋊C4—591no—
393C22×C22⋊C4—591no—
394C22×C22⋊C4—591no—
395C22×C22⋊C4—591no—
396C22×C22⋊C4C2×D5911yescharacteristic
397C22×C22⋊C4C2×D5911yescharacteristic
398#385—22no—
399#385—22no—
400#385—1181no—
401#385—1181no—
402#385—1182no—
403#385—1181no—
404#385—1181no—
405#385—1182no—
406#380—1182no—
407C2×#95—21no—
408C2×#95—1181no—
409C2×#95—1182no—
410#342—594no—
411#342—1182no—
412#342—1182no—
413C59#1134411yescharacteristic, complemented, Sylow
414C25C22×D5911yescharacteristic
415C23×C4—21no—
416C23×C4—21no—
417C23×C4—21no—
418C23×C4—21no—
419C23×C4—21no—
420C23×C4—21no—
421C23×C4—21no—
422C23×C4—44no—
423C23×C4—592no—
424C23×C4—591no—
425C23×C4—591no—
426C23×C4—1181no—
427C23×C4—1181no—
428C23×C4C22⋊D5911yescharacteristic
429C23×C4C22⋊D5911yescharacteristic
430C23×C4C22⋊D5912yes—
431C2×C4⋊C4—24no—
432C2×C4⋊C4—44no—
433C2×C4⋊C4—1182no—
434C2×C4⋊C4—1182no—
435C2×C4⋊C4—1184no—
436C2×C4⋊C4—2364no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—592no—
447C2×C22⋊C4—592no—
448C2×C22⋊C4—592no—
449C2×C22⋊C4—592no—
450C2×C22⋊C4—592no—
451C2×C22⋊C4—592no—
452C2×C22⋊C4—1181no—
453C2×C22⋊C4—1181no—
454C2×C22⋊C4—1181no—
455C2×C22⋊C4—1181no—
456C2×C22⋊C4—1181no—
457C2×C22⋊C4—1181no—
458C2×C22⋊C4—1181no—
459C2×C22⋊C4—1181no—
460C2×C22⋊C4—1181no—
461C2×C22⋊C4—1181no—
462C2×C22⋊C4—1181no—
463C2×C22⋊C4—1181no—
464C2×C22⋊C4—1181no—
465C2×C22⋊C4—1181no—
466C2×C22⋊C4—1181no—
467C2×C22⋊C4—1181no—
468C2×C22⋊C4—1181no—
469C2×C22⋊C4—1181no—
470C2×C22⋊C4Dic11812yes—
471C2×C22⋊C4C4×D5912yes—
472C2×C22⋊C4C22⋊D5912yes—
473#95—24no—
474#95—1184no—
475#95—1182no—
476#95—1182no—
477#95—2364no—
478C24—42no—
479C24—42no—
480C24C2×Dic11811yescharacteristic
481C24C2×C4×D5911yescharacteristic
482C24#1174568511yescharacteristic
483C24#1174568511yescharacteristic
484C24D4×D5911yescharacteristic
485C24D4×D5911yescharacteristic
486C24D4×D5911yescharacteristic
487C24#1174568711yescharacteristic
488C24Q8×D5911yescharacteristic
489C24Q8×D5911yescharacteristic
490C24Q8×D5911yescharacteristic
491C24#1174568911yescharacteristic
492C24C2×C22⋊D5911yescharacteristic
493C24C2×C22⋊D5911yescharacteristic
494C24C2×C22⋊D5911yescharacteristic
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—44no—
511C22×C4—44no—
512C22×C4—44no—
513C22×C4—44no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—41no—
520C22×C4—41no—
521C22×C4—41no—
522C22×C4—41no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—594no—
526C22×C4—1182no—
527C22×C4—1182no—
528C22×C4—1182no—
529C22×C4—1182no—
530C22×C4—1182no—
531C22×C4—1181no—
532C22×C4—1181no—
533C22×C4—1181no—
534C22×C4—1181no—
535C22×C4—1181no—
536C22×C4—1181no—
537C22×C4—1182no—
538C22×C4—2362no—
539C22×C4—2362no—
540C22×C4—2361no—
541C22×C4—2361no—
542C22×C4—2362no—
543C22×C4—2362no—
544C22×C4—2362no—
545C22×C4—2362no—
546C22×C4—2362no—
547C22×C4—2362no—
548C4⋊C4—48no—
549C4⋊C4—4722no—
550C4⋊C4—4722no—
551C4⋊C4—2368no—
552C22⋊C4—22no—
553C22⋊C4—22no—
554C22⋊C4—22no—
555C22⋊C4—41no—
556C22⋊C4—41no—
557C22⋊C4—41no—
558C22⋊C4—41no—
559C22⋊C4—594no—
560C22⋊C4—1182no—
561C22⋊C4—1182no—
562C22⋊C4—1182no—
563C22⋊C4—1182no—
564C22⋊C4—1182no—
565C22⋊C4—1182no—
566C22⋊C4—1182no—
567C22⋊C4—1182no—
568C22⋊C4—1182no—
569C22⋊C4—2361no—
570C22⋊C4—2361no—
571C22⋊C4—2361no—
572C22⋊C4—2361no—
573C22⋊C4—2361no—
574C22⋊C4—2361no—
575C22⋊C4Dic59⋊C414yescomplemented
576C23—22no—
577C23—22no—
578C23—22no—
579C23—22no—
580C23—22no—
581C23—22no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—42no—
587C23—42no—
588C23—42no—
589C23—42no—
590C23—41no—
591C23—41no—
592C23—42no—
593C23—42no—
594C23—42no—
595C23—42no—
596C23—41no—
597C23—41no—
598C23C4⋊C4×D5911yescharacteristic
599C23C4⋊C4×D5911yescharacteristic
600C23C2×Dic59⋊C411yescharacteristic
601C23C4×C22⋊D5911yescharacteristic
602C23C4×C22⋊D5911yescharacteristic
603C23#1427368911yescharacteristic
604C23#1427369211yescharacteristic
605C23#1427369511yescharacteristic
606C23#1427369511yescharacteristic
607C23#1427369611yescharacteristic
608C23#1427369811yescharacteristic
609C23#1427369911yescharacteristic
610C23#1427369911yescharacteristic
611C23#1427370311yescharacteristic
612C23#1427370311yescharacteristic
613C23#1427370311yescharacteristic
614C23#1427370511yescharacteristic
615C23#1427370511yescharacteristic
616C23#1427370511yescharacteristic
617C23#1427370511yescharacteristic
618C23#1427370611yescharacteristic
619C23#1427370611yescharacteristic
620C23#1427371011yescharacteristic
621C23#1427371211yescharacteristic
622C23#1427371211yescharacteristic
623C23#1427371711yescharacteristic
624C23#1427371711yescharacteristic
625C23#1427371811yescharacteristic
626C23#1427372311yescharacteristic
627C23#1427372511yescharacteristic
628C23#1427372511yescharacteristic
629C23#1427372511yescharacteristic
630C23#1427372611yescharacteristic
631C23#1427372611yescharacteristic
632C23#1427372611yescharacteristic
633C2×C4—24no—
634C2×C4—24no—
635C2×C4—24no—
636C2×C4—24no—
637C2×C4—42no—
638C2×C4—44no—
639C2×C4—42no—
640C2×C4—44no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—44no—
645C2×C4—44no—
646C2×C4—44no—
647C2×C4—42no—
648C2×C4—44no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—81no—
656C2×C4—81no—
657C2×C4—1184no—
658C2×C4—1184no—
659C2×C4—4721no—
660C2×C4—4721no—
661C2×C4—4722no—
662C2×C4—4721no—
663C2×C4—4721no—
664C2×C4—4722no—
665C2×C4—2362no—
666C2×C4—2364no—
667C2×C4—2362no—
668C2×C4—2361no—
669C2×C4—2361no—
670C2×C4—2362no—
671C2×C4—2362no—
672C2×C4—2362no—
673C2×C4—2362no—
674C2×C4—2364no—
675C2×C4—2362no—
676C2×C4—2364no—
677C2×C4—2362no—
678C2×C4—2362no—
679C2×C4—2364no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—22no—
684C22—22no—
685C22—22no—
686C22—21no—
687C22—21no—
688C22—21no—
689C22—21no—
690C22—21no—
691C22—21no—
692C22—21no—
693C22—21no—
694C22—21no—
695C22—21no—
696C22—21no—
697C22—21no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22#1683727111yescharacteristic
721C22#1683727311yescharacteristic
722C22#1683727311yescharacteristic
723C22#1683727511yescharacteristic
724C22#1683729711yescharacteristic
725C22#1683729711yescharacteristic
726C22#1683729811yescharacteristic
727C22#1683731011yescharacteristic
728C22#1683732111yescharacteristic
729C22#1683732211yescharacteristic
730C22#1683732211yescharacteristic
731C22#1683733311yescharacteristic
732C22#1683733511yescharacteristic
733C22#1683733511yescharacteristic
734C22#1683733711yescharacteristic
735C22#1683758812yes—
736C22#1683759112yes—
737C4—44no—
738C4—44no—
739C4—81no—
740C4—81no—
741C4—4722no—
742C4—4721no—
743C4—4721no—
744C4—2364no—
745C4—2364no—
746C2—21no—
747C2—21no—
748C2—21no—
749C2—21no—
750C2—21no—
751C2—21no—
752C2—21no—
753C2—21no—
754C2—21no—
755C2—21no—
756C2—21no—
757C2—21no—
758C2#2142235911yescharacteristic
759C2#2142437512yes—
760C2#2142521911yescharacteristic
761C2#2142522411yescharacteristic
762C2#2142544912yes—
subgroupG/H
centerC23#14273695
commutatorC24×C59C22×C4
FrattiniC25C22×D59
FittingC2×C59×#385C2
socleC23×C59#120
prime radical, cosocleC25×C59C23
hypercenterC2×#385D59
hypocenterC59#11344
LCSG ▷ C24×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C25 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
24. #16837168C4semidirect
165. C22×Dic59C4⋊C4semidirect
174. C22⋊C4×C59C4⋊C4semidirect
190. C22⋊Dic59C4⋊C4semidirect
413. C59#11344semidirect
575. C22⋊C4Dic59⋊C4semidirect

Maximal subgroups

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

subgroupindex
#214267082
C2×#168372752
C2×#168371692
C2×#168371682
#214223192
C2×C59×#3852
#1134459