Finite Group Databasebeta

← #28735643

Subgroups — #28735643

Order 15104.

984 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21432383C211yesmaximal, characteristic
2#21425533C211yesmaximal, characteristic, complemented
3#21425532C211yesmaximal, characteristic, complemented
4#21425522C211yesmaximal, characteristic, complemented
5#21425299C211yesmaximal, characteristic, complemented
6#21425296C211yesmaximal, characteristic, complemented
7#21425292C211yesmaximal, characteristic, complemented
8#21425292C211yesmaximal, characteristic, complemented
9#21425289C211yesmaximal, characteristic, complemented
10#21425289C211yesmaximal, characteristic, complemented
11#21425104C211yesmaximal, characteristic, complemented
12#21425104C211yesmaximal, characteristic, complemented
13#21425104C211yesmaximal, characteristic, complemented
14#21424006C211yesmaximal, characteristic
15C59×#2848C211yesmaximal, characteristic
16C22×#11745672C2211yescharacteristic, complemented
17C2×#14273706C2211yescharacteristic
18C2×#14273706C2211yescharacteristic
19C2×#14273706C2211yescharacteristic
20C2×#14273660C2211yescharacteristic, complemented
21C2×#14273658C2211yescharacteristic, complemented
22C2×#14273658C2211yescharacteristic, complemented
23C2×#14273651C2211yescharacteristic, complemented
24C2×#14273651C2211yescharacteristic, complemented
25C2×#14273651C2211yescharacteristic, complemented
26C2×#14273650C2211yescharacteristic, complemented
27C2×#14273650C2211yescharacteristic, complemented
28C2×#14273650C2211yescharacteristic, complemented
29C2×C22⋊(C59⋊C8)C2211yescharacteristic
30C2×C22⋊(C59⋊C8)C2211yescharacteristic
31C2×C22⋊(C59⋊C8)C2211yescharacteristic
32C2×C22⋊(C59⋊C8)C2211yescharacteristic
33C2×C22⋊(C59⋊C8)C2211yescharacteristic
34C2×C22⋊(C59⋊C8)C2211yescharacteristic
35#16837275—21no—
36#16837275—21no—
37#16837275—21no—
38#16837262C2211yescharacteristic
39#16837262C2211yescharacteristic
40#16837262C2211yescharacteristic
41#16837258—21no—
42#16837164C2211yescharacteristic, complemented
43#16837164C2211yescharacteristic, complemented
44#16837164C2211yescharacteristic, complemented
45#16837164C2211yescharacteristic, complemented
46#16837164C2211yescharacteristic, complemented
47#16837164C2211yescharacteristic, complemented
48C24×C4×C59C2211yescharacteristic
49C2×C22⋊Q8×C59C2211yescharacteristic
50C2×C22⋊Q8×C59C2211yescharacteristic
51C2×C22⋊Q8×C59C2211yescharacteristic
52C59×#385—21no—
53C59×#385—21no—
54C59×#385—21no—
55C59×#380C2211yescharacteristic
56C59×#380C2211yescharacteristic
57C59×#380C2211yescharacteristic
58C59×#379—21no—
59C22×Dic118C2311yescharacteristic
60C2×#11745672—41no—
61C2×#11745672—41no—
62C2×#11745672—41no—
63C22×C59⋊C8C2311yescharacteristic
64C22×C59⋊C8C2311yescharacteristic
65C22×C59⋊C8C2311yescharacteristic
66C22×C59⋊C8C2311yescharacteristic
67#14273706—41no—
68#14273706—41no—
69#14273706—41no—
70#14273706—41no—
71#14273706—41no—
72#14273706—41no—
73C2×C4⋊Dic59C2311yescharacteristic
74C2×C4⋊Dic59C2311yescharacteristic
75C2×C4⋊Dic59C2311yescharacteristic
76C2×Dic59⋊C4—21no—
77C2×Dic59⋊C4—21no—
78C2×Dic59⋊C4—21no—
79C2×C22⋊Dic59—21no—
80C2×C22⋊Dic59—21no—
81C2×C22⋊Dic59—21no—
82C2×C22⋊Dic59—21no—
83C2×C22⋊Dic59—21no—
84C2×C22⋊Dic59—21no—
85#14273660—41no—
86#14273658—41no—
87#14273658—41no—
88#14273651—41no—
89#14273651—41no—
90#14273651—41no—
91#14273650—41no—
92#14273650—41no—
93#14273650—41no—
94C22⋊(C59⋊C8)—41no—
95C22⋊(C59⋊C8)—41no—
96C22⋊(C59⋊C8)—41no—
97C22⋊(C59⋊C8)—41no—
98C22⋊(C59⋊C8)—41no—
99C22⋊(C59⋊C8)—41no—
100C59⋊#95—21no—
101C59⋊#95—21no—
102C59⋊#95—21no—
103C25×C59D411yescharacteristic
104C22×Q8×C59C2311yescharacteristic
105C23×C4×C59—41no—
106C23×C4×C59—41no—
107C23×C4×C59—41no—
108C23×C4×C59—41no—
109C23×C4×C59—41no—
110C23×C4×C59—41no—
111C23×C4×C59D411yescharacteristic
112C23×C4×C59D411yescharacteristic
113C23×C4×C59D411yescharacteristic
114C23×C4×C59C2311yescharacteristic
115C23×C4×C59C2311yescharacteristic
116C23×C4×C59C2311yescharacteristic
117C22⋊Q8×C59—41no—
118C22⋊Q8×C59—41no—
119C22⋊Q8×C59—41no—
120C22⋊Q8×C59—41no—
121C22⋊Q8×C59—41no—
122C22⋊Q8×C59—41no—
123C2×C4⋊C4×C59—21no—
124C2×C4⋊C4×C59—21no—
125C2×C4⋊C4×C59—21no—
126C2×C4⋊C4×C59C2311yescharacteristic
127C2×C4⋊C4×C59C2311yescharacteristic
128C2×C4⋊C4×C59C2311yescharacteristic
129C2×C22⋊C4×C59—21no—
130C2×C22⋊C4×C59—21no—
131C2×C22⋊C4×C59—21no—
132C2×C22⋊C4×C59—21no—
133C2×C22⋊C4×C59—21no—
134C2×C22⋊C4×C59—21no—
135#95×C59—21no—
136#95×C59—21no—
137#95×C59—21no—
138C24×C59—22no—
139C24×C59—22no—
140C24×C59—22no—
141C24×C59—41no—
142C24×C59—41no—
143C24×C59—41no—
144C24×C59—41no—
145C24×C59C2×D411yescharacteristic
146C24×C59C2×D411yescharacteristic
147C24×C59C2×D411yescharacteristic
148C2×Q8×C59—21no—
149C2×Q8×C59—21no—
150C2×Q8×C59—21no—
151C2×Q8×C59—21no—
152C2×Q8×C59—21no—
153C2×Q8×C59—21no—
154C22×C4×C59—21no—
155C22×C4×C59—21no—
156C22×C4×C59—21no—
157C22×C4×C59—21no—
158C22×C4×C59—21no—
159C22×C4×C59—21no—
160C22×C4×C59—21no—
161C22×C4×C59—21no—
162C22×C4×C59—21no—
163C22×C4×C59—21no—
164C22×C4×C59—21no—
165C22×C4×C59—21no—
166C22×C4×C59—21no—
167C22×C4×C59—21no—
168C22×C4×C59—21no—
169C22×C4×C59—21no—
170C22×C4×C59—21no—
171C22×C4×C59—21no—
172C22×C4×C59—21no—
173C22×C4×C59—21no—
174C22×C4×C59—21no—
175C22×C4×C59—21no—
176C22×C4×C59—41no—
177C22×C4×C59—41no—
178C22×C4×C59—41no—
179C22×C4×C59—41no—
180C22×C4×C59—41no—
181C22×C4×C59—41no—
182C22×C4×C59—41no—
183C22×C4×C59—41no—
184C22×C4×C59—41no—
185C22×C4×C59—44no—
186C22×C4×C59—44no—
187C22×C4×C59—44no—
188C22×C4×C59—44no—
189C22×C4×C59C2×D411yescharacteristic
190C22×C4×C59C2×D411yescharacteristic
191C22×C4×C59C2×D411yescharacteristic
192C22×C4×C59C2411yescharacteristic
193C22×Dic59—21no—
194C22×Dic59—21no—
195C22×Dic59—21no—
196C22×Dic59—21no—
197C2×Dic118—21no—
198C2×Dic118—21no—
199C2×Dic118—21no—
200C2×Dic118—21no—
201C2×Dic118—21no—
202C2×Dic118—21no—
203C4⋊C4×C59—21no—
204C4⋊C4×C59—21no—
205C4⋊C4×C59—21no—
206C4⋊C4×C59—21no—
207C4⋊C4×C59—21no—
208C4⋊C4×C59—21no—
209C4⋊C4×C59—42no—
210C4⋊C4×C59—42no—
211C4⋊C4×C59—42no—
212C22⋊C4×C59—42no—
213C22⋊C4×C59—42no—
214C22⋊C4×C59—42no—
215C22⋊C4×C59—42no—
216C22⋊C4×C59—42no—
217C22⋊C4×C59—42no—
218C22⋊Dic59—42no—
219C22⋊Dic59—42no—
220C22⋊Dic59—42no—
221C22⋊Dic59—42no—
222C22⋊Dic59—42no—
223C22⋊Dic59—42no—
224#11745672—44no—
225C4⋊Dic59—21no—
226C4⋊Dic59—21no—
227C4⋊Dic59—21no—
228C4⋊Dic59—21no—
229C4⋊Dic59—21no—
230C4⋊Dic59—21no—
231Dic59⋊C4—42no—
232Dic59⋊C4—42no—
233Dic59⋊C4—42no—
234C2×C59⋊C8—21no—
235C2×C59⋊C8—21no—
236C2×C59⋊C8—21no—
237C2×C59⋊C8—21no—
238C2×C59⋊C8—21no—
239C2×C59⋊C8—21no—
240C2×C59⋊C8—21no—
241C2×C59⋊C8—21no—
242C2×C59⋊C8—21no—
243C2×C59⋊C8—21no—
244C2×C59⋊C8—21no—
245C2×C59⋊C8—21no—
246C23×C59—21no—
247C23×C59—21no—
248C23×C59—21no—
249C23×C59—21no—
250C23×C59—21no—
251C23×C59—21no—
252C23×C59—21no—
253C23×C59—21no—
254C23×C59—21no—
255C23×C59—21no—
256C23×C59—21no—
257C23×C59—21no—
258C23×C59—21no—
259C23×C59—21no—
260C23×C59—21no—
261C23×C59—21no—
262C23×C59—21no—
263C23×C59—21no—
264C23×C59—44no—
265C23×C59—44no—
266C23×C59—44no—
267C23×C59—44no—
268C23×C59—44no—
269C23×C59—44no—
270C23×C59—44no—
271C23×C59#13512yes—
272C23×C59#13712yes—
273C23×C59#13712yes—
274C23×C59C22×D411yescharacteristic
275Q8×C59—41no—
276Q8×C59—41no—
277Q8×C59—41no—
278Q8×C59—41no—
279C2×C4×C59—21no—
280C2×C4×C59—21no—
281C2×C4×C59—21no—
282C2×C4×C59—21no—
283C2×C4×C59—21no—
284C2×C4×C59—21no—
285C2×C4×C59—21no—
286C2×C4×C59—21no—
287C2×C4×C59—21no—
288C2×C4×C59—44no—
289C2×C4×C59—44no—
290C2×C4×C59—44no—
291C2×C4×C59—41no—
292C2×C4×C59—41no—
293C2×C4×C59—41no—
294C2×C4×C59—41no—
295C2×C4×C59—41no—
296C2×C4×C59—41no—
297C2×C4×C59—41no—
298C2×C4×C59—41no—
299C2×C4×C59—41no—
300C2×C4×C59—41no—
301C2×C4×C59—41no—
302C2×C4×C59—41no—
303C2×C4×C59—41no—
304C2×C4×C59—41no—
305C2×C4×C59—41no—
306C2×C4×C59—41no—
307C2×C4×C59—41no—
308C2×C4×C59—41no—
309C2×C4×C59—41no—
310C2×C4×C59—41no—
311C2×C4×C59—41no—
312C2×C4×C59—41no—
313C2×C4×C59—41no—
314C2×C4×C59—41no—
315C2×C4×C59H(5,𝔽2)11yescharacteristic
316C2×C4×C59H(5,𝔽2)11yescharacteristic
317C2×C4×C59H(5,𝔽2)11yescharacteristic
318C2×C4×C59H(5,𝔽2)11yescharacteristic
319C2×C4×C59H(5,𝔽2)11yescharacteristic
320C2×C4×C59H(5,𝔽2)11yescharacteristic
321C2×Dic59—41no—
322C2×Dic59—41no—
323C2×Dic59—41no—
324C2×Dic59—41no—
325C2×Dic59—41no—
326C2×Dic59—41no—
327C2×Dic59—41no—
328C2×Dic59—41no—
329C2×Dic59—41no—
330C2×Dic59—41no—
331C2×Dic59—41no—
332C2×Dic59—41no—
333Dic118—41no—
334Dic118—41no—
335Dic118—41no—
336Dic118—41no—
337C59⋊C8—41no—
338C59⋊C8—41no—
339C59⋊C8—41no—
340C59⋊C8—41no—
341#32711—591nomaximal, Sylow
342C22×C59—22no—
343C22×C59—22no—
344C22×C59—22no—
345C22×C59—22no—
346C22×C59—22no—
347C22×C59—22no—
348C22×C59—22no—
349C22×C59—22no—
350C22×C59—22no—
351C22×C59—416no—
352C22×C59—41no—
353C22×C59—41no—
354C22×C59—41no—
355C22×C59—41no—
356C22×C59—41no—
357C22×C59—41no—
358C22×C59—41no—
359C22×C59—41no—
360C22×C59—41no—
361C22×C59—41no—
362C22×C59—41no—
363C22×C59—41no—
364C22×C59#53411yescharacteristic
365C22×C59#53411yescharacteristic
366C22×C59#53411yescharacteristic
367C22×C59C2×#13511yescharacteristic
368C22×C59C2×#13711yescharacteristic
369C22×C59C2×#13711yescharacteristic
370C22×C59#57511yescharacteristic
371C4×C59—41no—
372C4×C59—41no—
373C4×C59—41no—
374C4×C59—81no—
375C4×C59—81no—
376C4×C59—81no—
377C4×C59—81no—
378C4×C59#56011yescharacteristic
379C4×C59#56011yescharacteristic
380C4×C59#56011yescharacteristic
381C4×C59H(3,𝔽4)11yescharacteristic
382Dic59—81no—
383Dic59—81no—
384Dic59—81no—
385Dic59—81no—
386#2848—591no—
387#2848D5911yescharacteristic
388#2077—591no—
389#2077—591no—
390#2075—591no—
391#2036—591no—
392#2036—591no—
393#2035—591no—
394#2035—591no—
395#2035—591no—
396#2035—591no—
397#2001—591no—
398#2001—591no—
399#2001—591no—
400#1779—591no—
401C2×C59—42no—
402C2×C59—42no—
403C2×C59—42no—
404C2×C59#281211yescharacteristic
405C2×C59#319011yescharacteristic
406C2×C59#319011yescharacteristic
407C2×C59#319111yescharacteristic
408C2×C59#319511yescharacteristic
409C2×C59#319611yescharacteristic
410C2×C59#319611yescharacteristic
411C24×C4C2×D5911yescharacteristic
412C22×Q16—591no—
413C2×C22⋊Q8—591no—
414C2×C22⋊Q8—591no—
415C2×C22⋊Q8—591no—
416C2×C22⋊Q8C2×D5911yescharacteristic
417C2×C22⋊Q8C2×D5911yescharacteristic
418C2×C22⋊Q8C2×D5911yescharacteristic
419C2×#107—591no—
420C2×#106—591no—
421C2×#106—591no—
422C2×#103—591no—
423C2×#103—591no—
424C2×#103—591no—
425C2×#103—591no—
426C2×#103—591no—
427C2×#103—591no—
428C2×C22⋊C8—591no—
429C2×C22⋊C8—591no—
430C2×C22⋊C8—591no—
431C2×C22⋊C8—591no—
432C2×C22⋊C8—591no—
433C2×C22⋊C8—591no—
434#385—21no—
435#385—21no—
436#385—21no—
437#385—1181no—
438#385—1181no—
439#385—1181no—
440#380—591no—
441#380—591no—
442#380—591no—
443#380C2×D5911yescharacteristic
444#380C2×D5911yescharacteristic
445#380C2×D5911yescharacteristic
446#379—21no—
447#379—1181no—
448#340—591no—
449#340—591no—
450#340—591no—
451#340—591no—
452#340—591no—
453#340—591no—
454C59#3271111yescharacteristic, complemented, Sylow
455C25C22⋊D5911yescharacteristic
456C22×Q8—591no—
457C22×Q8C22×D5911yescharacteristic
458C23×C4—41no—
459C23×C4—41no—
460C23×C4—41no—
461C23×C4—41no—
462C23×C4—41no—
463C23×C4—41no—
464C23×C4C22⋊D5911yescharacteristic
465C23×C4C22⋊D5911yescharacteristic
466C23×C4C22⋊D5911yescharacteristic
467C23×C4C22×D5911yescharacteristic
468C23×C4C22×D5911yescharacteristic
469C23×C4C22×D5911yescharacteristic
470C2×Q16—2361no—
471C2×Q16—2361no—
472C2×Q16—2361no—
473C22×C8—591no—
474C22×C8—591no—
475C22×C8—591no—
476C22×C8—591no—
477C22⋊Q8—41no—
478C22⋊Q8—41no—
479C22⋊Q8—41no—
480C22⋊Q8—41no—
481C22⋊Q8—41no—
482C22⋊Q8—41no—
483C22⋊Q8—2361no—
484C22⋊Q8—2361no—
485C22⋊Q8—2361no—
486C22⋊Q8—2361no—
487C22⋊Q8—2361no—
488C22⋊Q8—2361no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—591no—
493C2×C4⋊C4—591no—
494C2×C4⋊C4—591no—
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—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—1181no—
508C2×C22⋊C4—1181no—
509C2×C22⋊C4—1181no—
510C2×C22⋊C4—1181no—
511C2×C22⋊C4—1181no—
512C2×C22⋊C4—1181no—
513#107—2361no—
514#106—2361no—
515#106—2361no—
516#103—2361no—
517#103—2361no—
518#103—2361no—
519#103—2361no—
520#103—2361no—
521#103—2361no—
522C22⋊C8—2361no—
523C22⋊C8—2361no—
524C22⋊C8—2361no—
525C22⋊C8—2361no—
526C22⋊C8—2361no—
527C22⋊C8—2361no—
528#95—21no—
529#95—21no—
530#95—21no—
531#95—1181no—
532#95—1181no—
533#95—1181no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—41no—
538C24—41no—
539C24—41no—
540C24—41no—
541C24C2×C22⋊D5911yescharacteristic
542C24C2×C22⋊D5911yescharacteristic
543C24C2×C22⋊D5911yescharacteristic
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—1181no—
551C2×Q8—1181no—
552C2×Q8—1181no—
553C2×Q8—1181no—
554C2×Q8—1181no—
555C2×Q8—1181no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—41no—
579C22×C4—41no—
580C22×C4—41no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—41no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—1181no—
592C22×C4—1181no—
593C22×C4—1181no—
594C22×C4—1181no—
595C22×C4C2×C22⋊D5911yescharacteristic
596C22×C4C2×C22⋊D5911yescharacteristic
597C22×C4C2×C22⋊D5911yescharacteristic
598C22×C4C23×D5911yescharacteristic
599Q16—2364no—
600C2×C8—1181no—
601C2×C8—1181no—
602C2×C8—1181no—
603C2×C8—1181no—
604C2×C8—1181no—
605C2×C8—1181no—
606C2×C8—1181no—
607C2×C8—1181no—
608C2×C8—1181no—
609C2×C8—1181no—
610C2×C8—1181no—
611C2×C8—1181no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—42no—
619C4⋊C4—42no—
620C4⋊C4—42no—
621C4⋊C4—1181no—
622C4⋊C4—1181no—
623C4⋊C4—1181no—
624C4⋊C4—1181no—
625C4⋊C4—1181no—
626C4⋊C4—1181no—
627C4⋊C4—2362no—
628C4⋊C4—2362no—
629C4⋊C4—2362no—
630C22⋊C4—42no—
631C22⋊C4—42no—
632C22⋊C4—42no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—2362no—
637C22⋊C4—2362no—
638C22⋊C4—2362no—
639C22⋊C4—2362no—
640C22⋊C4—2362no—
641C22⋊C4—2362no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—44no—
665C23—44no—
666C23—44no—
667C23#1427374712yes—
668C23#1427375712yes—
669C23#1427375812yes—
670C23C22×C22⋊D5911yescharacteristic
671Q8—41no—
672Q8—41no—
673Q8—41no—
674Q8—41no—
675Q8—2361no—
676Q8—2361no—
677Q8—2361no—
678Q8—2361no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4—44no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—2361no—
716C2×C4—2361no—
717C2×C4—2361no—
718C2×C4—2361no—
719C2×C4—2361no—
720C2×C4—2361no—
721C2×C4—2361no—
722C2×C4—2361no—
723C2×C4—2361no—
724C2×C4—2361no—
725C2×C4—2361no—
726C2×C4—2361no—
727C2×C4#1427377211yescharacteristic
728C2×C4#1427377211yescharacteristic
729C2×C4#1427377211yescharacteristic
730C2×C4#1427377211yescharacteristic
731C2×C4#1427377211yescharacteristic
732C2×C4#1427377211yescharacteristic
733C8—2361no—
734C8—2361no—
735C8—2361no—
736C8—2361no—
737C22—22no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—416no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22#1683796111yescharacteristic
760C22#1683796111yescharacteristic
761C22#1683796111yescharacteristic
762C22C2×#1427374711yescharacteristic
763C22C2×#1427375711yescharacteristic
764C22C2×#1427375811yescharacteristic
765C22#1683820011yescharacteristic
766C4—41no—
767C4—41no—
768C4—41no—
769C4—81no—
770C4—81no—
771C4—81no—
772C4—81no—
773C4—4721no—
774C4—4721no—
775C4—4721no—
776C4—4721no—
777C4#1683814111yescharacteristic
778C4#1683814111yescharacteristic
779C4#1683814111yescharacteristic
780C4#1683814511yescharacteristic
781C2—42no—
782C2—42no—
783C2—42no—
784C2#2143209111yescharacteristic
785C2#2143487311yescharacteristic
786C2#2143487711yescharacteristic
787C2#2143488411yescharacteristic
788C2#2143491711yescharacteristic
789C2#2143492211yescharacteristic
790C2#2143492611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC59×#2848C2
socleC23×C59C22×D4
prime radicalC25×C59D4
hypercenter#2848D59
hypocenterC59#32711
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C24×C4 ◁ #2848

Complements

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

NH ≅ G/Ntype
2. #21425533C2semidirect
3. #21425532C2semidirect
4. #21425522C2semidirect
5. #21425299C2semidirect
6. #21425296C2semidirect
7. #21425292C2semidirect
8. #21425292C2semidirect
9. #21425289C2semidirect
10. #21425289C2semidirect
11. #21425104C2semidirect
12. #21425104C2semidirect
13. #21425104C2semidirect
16. C22×#11745672C22semidirect
20. C2×#14273660C22semidirect
21. C2×#14273658C22semidirect
22. C2×#14273658C22semidirect
23. C2×#14273651C22semidirect
24. C2×#14273651C22semidirect
25. C2×#14273651C22semidirect
26. C2×#14273650C22semidirect
27. C2×#14273650C22semidirect
28. C2×#14273650C22semidirect
42. #16837164C22semidirect
43. #16837164C22semidirect
44. #16837164C22semidirect
45. #16837164C22semidirect
46. #16837164C22semidirect
47. #16837164C22semidirect
454. C59#32711semidirect

Maximal subgroups

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

subgroupindex
#214323832
#214255332
#214255322
#214255222
#214252992
#214252962
#214252922
#214252892
#214251042
#214240062
C59×#28482
#3271159