Finite Group Databasebeta

← #28606061

Subgroups — #28606061

Order 15104.

888 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21432613C211yesmaximal, characteristic
2#21432542C211yesmaximal, characteristic
3#21424806C211yesmaximal, characteristic, complemented
4#21424799C211yesmaximal, characteristic, complemented
5#21424744C211yesmaximal, characteristic, complemented
6#21424744C211yesmaximal, characteristic, complemented
7#21424370C211yesmaximal, characteristic, complemented
8#21424370C211yesmaximal, characteristic, complemented
9#21424195C211yesmaximal, characteristic, complemented
10#21424136C211yesmaximal, characteristic, complemented
11#21424039C211yesmaximal, characteristic
12#21423942C211yesmaximal, characteristic, complemented
13#21423935C211yesmaximal, characteristic, complemented
14#21423882C211yesmaximal, characteristic, complemented
15C59×#2924C211yesmaximal, characteristic, complemented
16C22×#11745685C2211yescharacteristic
17C2×#14273733C2211yescharacteristic
18C2×#14273733C2211yescharacteristic
19C22×#11745664C2211yescharacteristic
20C2×#14273662C2211yescharacteristic, complemented
21C2×#14273662C2211yescharacteristic, complemented
22C2×#14273653C2211yescharacteristic
23C2×#14273653C2211yescharacteristic
24C2×#14273653C2211yescharacteristic
25C2×#14273653C2211yescharacteristic
26#16837410C411yescharacteristic, complemented
27#16837410C411yescharacteristic, complemented
28#16837406C411yescharacteristic, complemented
29#16837406C411yescharacteristic, complemented
30#16837401C411yescharacteristic, complemented
31#16837401C411yescharacteristic, complemented
32#16837401C411yescharacteristic, complemented
33#16837401C411yescharacteristic, complemented
34#16837396C2211yescharacteristic
35#16837396C2211yescharacteristic
36#16837396C2211yescharacteristic
37#16837396C2211yescharacteristic
38#16837368C2211yescharacteristic
39#16837368C2211yescharacteristic
40#16837367—21no—
41#16837367—21no—
42#16837366C2211yescharacteristic
43#16837364—21no—
44C22⋊C8×D59—21no—
45C2×#14273637C2211yescharacteristic, complemented
46C2×C8×Dic59C2211yescharacteristic, complemented
47C4×C22⋊Dic59C2211yescharacteristic
48#16837166C2211yescharacteristic, complemented
49#16837166C2211yescharacteristic, complemented
50#16837161C2211yescharacteristic, complemented
51#16837161C2211yescharacteristic, complemented
52#16837161C2211yescharacteristic, complemented
53#16837161C2211yescharacteristic, complemented
54#16837156C2211yescharacteristic, complemented
55#16837156C2211yescharacteristic, complemented
56C2×#117×C59C2211yescharacteristic
57C59×#433—21no—
58C59×#433—21no—
59C59×#432—21no—
60C59×#431—21no—
61C59×#424C2211yescharacteristic, complemented
62C59×#424C2211yescharacteristic, complemented
63C59×#407C2211yescharacteristic
64C2×C22⋊C8×C59C2211yescharacteristic
65C59×#405C2211yescharacteristic, complemented
66C59×#405C2211yescharacteristic, complemented
67C2×#11745685—21no—
68C2×#11745685—21no—
69C2×#11745685—22no—
70C2×#11745685—22no—
71C2×#11745685—41no—
72C2×#11745685—41no—
73C2×#11745685C2×C411yescharacteristic
74C2×#11745685C2×C411yescharacteristic
75C2×#11745685C2311yescharacteristic
76C2×#11745685C2311yescharacteristic
77C22×Dic118C2×C411yescharacteristic
78C22×D236C2×C411yescharacteristic
79C22×C22⋊D59—21no—
80C22×C4×D59—21no—
81#14273733—22no—
82#14273733—22no—
83#14273733—41no—
84#14273733—41no—
85C2×#11745664—41no—
86C2×#11745664—41no—
87C2×#11745664C2×C411yescharacteristic
88C2×#11745664C2×C411yescharacteristic
89C2×#11745664C2×C411yescharacteristic
90C2×#11745664C2×C411yescharacteristic
91C2×#11745664C2311yescharacteristic
92C2×#11745664C2311yescharacteristic
93C2×#11745659—21no—
94C2×#11745659—21no—
95C22×C59⋊C8C2311yescharacteristic
96C22×C59⋊C8C2311yescharacteristic
97C2×C8×D59—21no—
98C2×C8×D59—21no—
99C2×C22⋊Dic59—21no—
100C2×C4×Dic59C2311yescharacteristic
101C2×C4×Dic59C2311yescharacteristic
102#14273662—41no—
103#14273662—41no—
104#14273653—22no—
105#14273653—22no—
106#14273653—41no—
107#14273653—41no—
108#14273650C2×C411yescharacteristic
109#14273650C2×C411yescharacteristic
110#14273650C2×C411yescharacteristic
111#14273650C2×C411yescharacteristic
112#14273650C2×C411yescharacteristic
113#14273650C2×C411yescharacteristic
114#14273650C2×C411yescharacteristic
115#14273650C2×C411yescharacteristic
116#14273647C2×C411yescharacteristic
117#14273647C2×C411yescharacteristic
118#14273647C2×C411yescharacteristic
119#14273647C2×C411yescharacteristic
120#14273647C2×C411yescharacteristic
121#14273647C2×C411yescharacteristic
122#14273647C2×C411yescharacteristic
123#14273647C2×C411yescharacteristic
124C22⋊(C59⋊C8)—21no—
125C22⋊(C59⋊C8)—21no—
126(C2×D59)⋊C8—21no—
127(C2×D59)⋊C8—21no—
128(C2×D59)⋊C8—21no—
129(C2×D59)⋊C8—21no—
130#14273637—41no—
131C8×Dic59—41no—
132C59⋊#95—21no—
133C23×C4×C59C2311yescharacteristic
134C2×M16×C59C2311yescharacteristic
135C2×M16×C59C2311yescharacteristic
136C22×C8×C59C2311yescharacteristic
137C22×C8×C59C2311yescharacteristic
138#117×C59—21no—
139#117×C59—21no—
140#117×C59C2×C411yescharacteristic
141#117×C59C2×C411yescharacteristic
142#117×C59C2311yescharacteristic
143#117×C59C2311yescharacteristic
144C2×C4⋊C4×C59C2×C411yescharacteristic
145C2×C4⋊C4×C59C2×C411yescharacteristic
146C2×C22⋊C4×C59—21no—
147C2×C42×C59—21no—
148C4⋊C8×C59—21no—
149C4⋊C8×C59—21no—
150C4⋊C8×C59—21no—
151C4⋊C8×C59—21no—
152C22⋊C8×C59—21no—
153C22⋊C8×C59—21no—
154C22⋊C8×C59D411yescharacteristic
155C22⋊C8×C59D411yescharacteristic
156C22⋊C8×C59D411yescharacteristic
157C22⋊C8×C59D411yescharacteristic
158#97×C59—21no—
159#97×C59—21no—
160C4×C8×C59—21no—
161C4×C8×C59—21no—
162C24×C59#4111yescharacteristic
163C23×D59—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×C59C22×C411yescharacteristic
171C22×C4×C59C22×C411yescharacteristic
172C22×C4×C59C2×D411yescharacteristic
173C22×C4×C59C2×D411yescharacteristic
174C22×C4×C59#4111yescharacteristic
175C22×C4×C59C2411yescharacteristic
176C2×C22⋊D59—21no—
177C2×C22⋊D59—21no—
178C2×C22⋊D59—21no—
179C2×C22⋊D59—21no—
180C2×C22⋊D59—42no—
181C2×C22⋊D59—42no—
182C22×Dic59—21no—
183C22×Dic59—21no—
184C22×Dic59—21no—
185#11745685—21no—
186#11745685—21no—
187#11745685—21no—
188#11745685—21no—
189#11745685—21no—
190#11745685—21no—
191#11745685—22no—
192#11745685—22no—
193#11745685—41no—
194#11745685—41no—
195#11745685—42no—
196#11745685—42no—
197#11745685—42no—
198#11745685—42no—
199#11745685#4112yes—
200#11745685#4112yes—
201C2×D236—22no—
202C2×D236—21no—
203C2×D236—41no—
204C2×D236C22×C411yescharacteristic
205C2×D236C22×C411yescharacteristic
206C2×C4×D59—21no—
207C2×C4×D59—21no—
208C2×C4×D59—21no—
209C2×C4×D59—21no—
210C2×C4×D59—42no—
211C2×C4×D59—42no—
212C2×Dic118—22no—
213C2×Dic118—21no—
214C2×Dic118—41no—
215C2×Dic118C22×C411yescharacteristic
216C2×Dic118C22×C411yescharacteristic
217M16×C59—21no—
218M16×C59—21no—
219M16×C59—21no—
220M16×C59—21no—
221C2×C8×C59—21no—
222C2×C8×C59—21no—
223C2×C8×C59—21no—
224C2×C8×C59—21no—
225C2×C8×C59—21no—
226C2×C8×C59—21no—
227C2×C8×C59C2×D411yescharacteristic
228C2×C8×C59C2×D411yescharacteristic
229C2×C8×C59C2×D411yescharacteristic
230C2×C8×C59C2×D411yescharacteristic
231C4⋊C4×C59—21no—
232C4⋊C4×C59—21no—
233C4⋊C4×C59C22×C411yescharacteristic
234C4⋊C4×C59C22×C411yescharacteristic
235C4⋊C4×C59C22×C411yescharacteristic
236C4⋊C4×C59C22×C411yescharacteristic
237C22⋊C4×C59—21no—
238C22⋊C4×C59—21no—
239C22⋊C4×C59—21no—
240C22⋊C4×C59—21no—
241C42×C59—21no—
242C42×C59—21no—
243C42×C59—21no—
244C42×C59—21no—
245C22⋊Dic59—42no—
246C4×Dic59—21no—
247C4×Dic59—21no—
248C4×Dic59—21no—
249C4×Dic59—21no—
250#11745664—21no—
251#11745664—21no—
252#11745664—21no—
253#11745664—21no—
254#11745664—41no—
255#11745664—41no—
256#11745664—41no—
257#11745664—41no—
258C2×C59⋊C8—21no—
259C2×C59⋊C8—21no—
260C2×C59⋊C8—21no—
261C2×C59⋊C8—21no—
262C2×C59⋊C8—21no—
263C2×C59⋊C8—21no—
264C2×C59⋊C8C22×C411yescharacteristic
265C2×C59⋊C8C22×C411yescharacteristic
266C2×C59⋊C8C22×C411yescharacteristic
267C2×C59⋊C8C22×C411yescharacteristic
268#11745659—42no—
269#11745659—42no—
270C8×D59—42no—
271C8×D59—42no—
272C23×C59—21no—
273C23×C59—21no—
274C23×C59—41no—
275C23×C59—41no—
276C23×C59C4×D411yescharacteristic
277C23×C59C4×D411yescharacteristic
278C23×C59C2×#4111yescharacteristic
279C22×D59—21no—
280C22×D59—21no—
281C22×D59—42no—
282C22×D59—42no—
283C22×D59—81no—
284C2×C4×C59—21no—
285C2×C4×C59—21no—
286C2×C4×C59—21no—
287C2×C4×C59—21no—
288C2×C4×C59—21no—
289C2×C4×C59—21no—
290C2×C4×C59—21no—
291C2×C4×C59—21no—
292C2×C4×C59—21no—
293C2×C4×C59—21no—
294C2×C4×C59—21no—
295C2×C4×C59—21no—
296C2×C4×C59—21no—
297C2×C4×C59—21no—
298C2×C4×C59—42no—
299C2×C4×C59—81no—
300C2×C4×C59C4×D411yescharacteristic
301C2×C4×C59C4×D411yescharacteristic
302C2×C4×C59C23×C411yescharacteristic
303C2×C4×C59C22×D411yescharacteristic
304C2×C4×C59C2×#4111yescharacteristic
305C2×C4×C59C2×#4111yescharacteristic
306C2×C4×C59H(5,𝔽2)11yescharacteristic
307C2×C4×C59H(5,𝔽2)11yescharacteristic
308C22⋊D59—22no—
309C22⋊D59—22no—
310C22⋊D59—42no—
311C22⋊D59—42no—
312C22⋊D59—41no—
313C22⋊D59—41no—
314C2×Dic59—21no—
315C2×Dic59—22no—
316C2×Dic59—21no—
317C2×Dic59—42no—
318C2×Dic59—41no—
319C2×Dic59—41no—
320C2×Dic59—41no—
321C2×Dic59—41no—
322C2×Dic59—41no—
323D236—21no—
324D236—21no—
325D236—21no—
326D236—42no—
327D236#11712yes—
328C4×D59—22no—
329C4×D59—22no—
330C4×D59—42no—
331C4×D59—42no—
332C4×D59—41no—
333C4×D59—41no—
334Dic118—21no—
335Dic118—21no—
336Dic118—21no—
337Dic118—42no—
338Dic118#11712yes—
339C8×C59—21no—
340C8×C59—21no—
341C8×C59—21no—
342C8×C59—21no—
343C8×C59—41no—
344C8×C59—41no—
345C59⋊C8—21no—
346C59⋊C8—21no—
347C59⋊C8—21no—
348C59⋊C8—21no—
349C59⋊C8—41no—
350C59⋊C8—41no—
351#22588—591nomaximal, Sylow
352C22×C59—21no—
353C22×C59—21no—
354C22×C59—21no—
355C22×C59—21no—
356C22×C59—21no—
357C22×C59—21no—
358C22×C59—21no—
359C22×C59—21no—
360C22×C59—81no—
361C22×C59—81no—
362C22×C59C2×C4×D411yescharacteristic
363C22×C59#55111yescharacteristic
364C22×C59#55111yescharacteristic
365C2×D59—22no—
366C2×D59—41no—
367C2×D59—41no—
368C2×D59—41no—
369C2×D59—41no—
370C2×D59—41no—
371C2×D59—84no—
372C4×C59—21no—
373C4×C59—21no—
374C4×C59—41no—
375C4×C59—41no—
376C4×C59—41no—
377C4×C59—41no—
378C4×C59C2×#11711yescharacteristic
379C4×C59#51811yescharacteristic
380C4×C59#54611yescharacteristic
381C4×C59#54611yescharacteristic
382Dic59—22no—
383Dic59—42no—
384Dic59—41no—
385Dic59—81no—
386#2924D5911yescharacteristic, complemented
387#2896—591no—
388#2880—591no—
389#1938—591no—
390#1937—591no—
391#1929—591no—
392#1929—591no—
393#1866—591no—
394#1866—591no—
395#1826—591no—
396#1811—591no—
397#1789—591no—
398#1765—591no—
399#1764—591no—
400#1753—591no—
401C2×C59—21no—
402C2×C59—21no—
403C2×C59—41no—
404C2×C59—41no—
405C2×C59#234211yescharacteristic
406C2×C59#295511yescharacteristic
407C2×C59#295611yescharacteristic
408D59—42no—
409D59—81no—
410C22×#41—591no—
411C2×#131—591no—
412C2×#131—591no—
413C22×M16—591no—
414C2×#117C2×D5911yescharacteristic
415#433—21no—
416#433—21no—
417#432—21no—
418#431—21no—
419C2×#108—591no—
420C2×#108—591no—
421#424C2×D5911yescharacteristic, complemented
422#424C2×D5911yescharacteristic, complemented
423C2×#104—591no—
424C2×#104—591no—
425C2×#104—591no—
426C2×#104—591no—
427#419—591no—
428#419—591no—
429#418—591no—
430#418—591no—
431#417—591no—
432#417—591no—
433#417—591no—
434#417—591no—
435#416—591no—
436#416—591no—
437#416—591no—
438#416—591no—
439#408—591no—
440#408—591no—
441#408—1181no—
442#408—1181no—
443#407—591no—
444#407—1181no—
445#407C2×D5911yescharacteristic
446C2×C22⋊C8—1181no—
447C2×C22⋊C8C2×D5911yescharacteristic
448#405C2×D5911yescharacteristic, complemented
449#405C2×D5911yescharacteristic, complemented
450C2×#97—591no—
451C2×C4×C8—591no—
452C4×C22⋊C4—591no—
453#341—591no—
454#341—591no—
455#339—591no—
456#339—591no—
457#339—591no—
458#339—591no—
459#336—591no—
460#336—591no—
461C59#2258811yescharacteristic, complemented, Sylow
462C2×#41—591no—
463C2×#41—591no—
464C2×#41—591no—
465C2×#41—591no—
466C2×#41—1182no—
467C2×#41—1182no—
468C2×#41—1181no—
469C2×#41—1181no—
470C2×#41—2361no—
471C2×#41—2361no—
472C22×Q8—591no—
473C22×D4—591no—
474C22×D4—1181no—
475C23×C4—1181no—
476C23×C4C22×D5911yescharacteristic
477#131—1182no—
478#131—1182no—
479#131—2361no—
480#131—2361no—
481C2×M16—591no—
482C2×M16—591no—
483C2×M16—591no—
484C2×M16—591no—
485C2×M16—591no—
486C2×M16—591no—
487C2×M16—1181no—
488C2×M16—1181no—
489C2×M16—2361no—
490C2×M16—2361no—
491C2×M16C22×D5911yescharacteristic
492C2×M16C22×D5911yescharacteristic
493C22×C8—591no—
494C22×C8—591no—
495C22×C8—1181no—
496C22×C8—1181no—
497C22×C8C22×D5911yescharacteristic
498C22×C8C22×D5911yescharacteristic
499#117—21no—
500#117—21no—
501#117C4×D5911yescharacteristic
502#117C4×D5911yescharacteristic
503#117C22×D5911yescharacteristic
504#117C22×D5911yescharacteristic
505C2×C4⋊C4C4×D5911yescharacteristic
506C2×C4⋊C4C4×D5911yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—1181no—
509C2×C42—21no—
510C2×C42—591no—
511C2×C42—591no—
512#108—2361no—
513#108—2361no—
514C4⋊C8—21no—
515C4⋊C8—21no—
516C4⋊C8—21no—
517C4⋊C8—21no—
518#104—1182no—
519#104—1182no—
520#104—2361no—
521#104—2361no—
522#103—591no—
523#103—591no—
524#103—591no—
525#103—591no—
526#103—591no—
527#103—591no—
528#103—591no—
529#103—591no—
530#102—591no—
531#102—591no—
532#102—591no—
533#102—591no—
534#102—591no—
535#102—591no—
536#102—591no—
537#102—591no—
538C22⋊C8—21no—
539C22⋊C8—21no—
540C22⋊C8—1181no—
541C22⋊C8—1181no—
542C22⋊C8—1181no—
543C22⋊C8—1181no—
544C22⋊C8—1181no—
545C22⋊C8—1181no—
546C22⋊C8C22⋊D5911yescharacteristic
547C22⋊C8C22⋊D5911yescharacteristic
548C22⋊C8C22⋊D5911yescharacteristic
549C22⋊C8C22⋊D5911yescharacteristic
550#97—21no—
551#97—21no—
552#97—2361no—
553C4×C8—21no—
554C4×C8—21no—
555C4×C8—2361no—
556#95—1181no—
557C24—1181no—
558C24#1174568511yescharacteristic
559#41—592no—
560#41—592no—
561#41—1182no—
562#41—1182no—
563#41—1181no—
564#41—1181no—
565#41—1181no—
566#41—1181no—
567#41—1181no—
568#41—1181no—
569#41—2362no—
570#41—2362no—
571#41—2361no—
572#41—2361no—
573#41—2362no—
574#41—2362no—
575C2×Q8—591no—
576C2×Q8—591no—
577C2×Q8—1182no—
578C2×Q8—1181no—
579C2×Q8—2361no—
580C2×D4—591no—
581C2×D4—591no—
582C2×D4—1182no—
583C2×D4—1181no—
584C2×D4—1181no—
585C2×D4—1181no—
586C2×D4—1181no—
587C2×D4—1181no—
588C2×D4—2361no—
589C2×D4—2362no—
590C2×D4—2362no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—1181no—
598C22×C4—1181no—
599C22×C4—1181no—
600C22×C4—1181no—
601C22×C4—1181no—
602C22×C4—1181no—
603C22×C4—1181no—
604C22×C4—2362no—
605C22×C4—2362no—
606C22×C4C2×C4×D5911yescharacteristic
607C22×C4C2×C4×D5911yescharacteristic
608C22×C4#1174568511yescharacteristic
609C22×C4C2×C22⋊D5911yescharacteristic
610C22×C4C2×C22⋊D5911yescharacteristic
611C22×C4C23×D5911yescharacteristic
612M16—21no—
613M16—21no—
614M16—21no—
615M16—21no—
616M16—1181no—
617M16—1181no—
618M16—1181no—
619M16—1181no—
620M16—2362no—
621M16—2362no—
622M16—2361no—
623M16—2361no—
624M16—2361no—
625M16—2361no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—591no—
633C2×C8—591no—
634C2×C8—591no—
635C2×C8—591no—
636C2×C8—1181no—
637C2×C8—1181no—
638C2×C8—1181no—
639C2×C8—1181no—
640C2×C8—1181no—
641C2×C8—1181no—
642C2×C8—2362no—
643C2×C8—2362no—
644C2×C8C2×C22⋊D5911yescharacteristic
645C2×C8C2×C22⋊D5911yescharacteristic
646C2×C8C2×C22⋊D5911yescharacteristic
647C2×C8C2×C22⋊D5911yescharacteristic
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4C2×C4×D5911yescharacteristic
651C4⋊C4C2×C4×D5911yescharacteristic
652C4⋊C4C2×C4×D5911yescharacteristic
653C4⋊C4C2×C4×D5911yescharacteristic
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—2362no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—21no—
663C42—1181no—
664C42—1181no—
665C42—1181no—
666C42—1181no—
667C23—21no—
668C23—21no—
669C23—41no—
670C23—41no—
671C23—1181no—
672C23—1181no—
673C23—4721no—
674C23—2362no—
675C23—2362no—
676C23C4×C22⋊D5911yescharacteristic
677C23C4×C22⋊D5911yescharacteristic
678C23C2×#1174568511yescharacteristic
679Q8—592no—
680Q8—1181no—
681Q8—1181no—
682Q8—1181no—
683Q8—2362no—
684D4—592no—
685D4—1182no—
686D4—1182no—
687D4—1181no—
688D4—1181no—
689D4—1181no—
690D4—2362no—
691D4—2362no—
692D4—2362no—
693D4—2361no—
694D4—2361no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—42no—
710C2×C4—81no—
711C2×C4—1181no—
712C2×C4—1182no—
713C2×C4—1182no—
714C2×C4—1182no—
715C2×C4—1181no—
716C2×C4—2362no—
717C2×C4—2362no—
718C2×C4—2362no—
719C2×C4—2361no—
720C2×C4—2361no—
721C2×C4—2361no—
722C2×C4—2361no—
723C2×C4—2361no—
724C2×C4—2361no—
725C2×C4—2361no—
726C2×C4C4×C22⋊D5911yescharacteristic
727C2×C4C4×C22⋊D5911yescharacteristic
728C2×C4C22×C4×D5911yescharacteristic
729C2×C4C22×C22⋊D5911yescharacteristic
730C2×C4#41×D5911yescharacteristic
731C2×C4#41×D5911yescharacteristic
732C2×C4#1427377311yescharacteristic
733C2×C4#1427377311yescharacteristic
734C8—21no—
735C8—21no—
736C8—21no—
737C8—21no—
738C8—41no—
739C8—41no—
740C8—1181no—
741C8—1181no—
742C8—1181no—
743C8—1181no—
744C8—2361no—
745C8—2361no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—81no—
755C22—81no—
756C22—1182no—
757C22—4724no—
758C22—2361no—
759C22—2361no—
760C22—2361no—
761C22—2361no—
762C22—2361no—
763C22C2×C4×C22⋊D5911yescharacteristic
764C22#1683807611yescharacteristic
765C22#1683807611yescharacteristic
766C4—21no—
767C4—21no—
768C4—41no—
769C4—41no—
770C4—41no—
771C4—41no—
772C4—1182no—
773C4—4721no—
774C4—2362no—
775C4—2361no—
776C4#117×D5911yescharacteristic
777C4#1683787611yescharacteristic
778C4#1683804011yescharacteristic
779C4#1683804011yescharacteristic
780C2—21no—
781C2—21no—
782C2—41no—
783C2—41no—
784C2—4721no—
785C2—2362no—
786C2#2142694611yescharacteristic
787C2#2143299711yescharacteristic
788C2#2143300311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#2924C2
socleC22×C59C2×C4×D4
prime radicalC22×#11745685C22
cosocleC22×C4×C59C24
hypercenter#2924D59
hypocenterC59#22588
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ #2924

Complements

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

NH ≅ G/Ntype
3. #21424806C2semidirect
4. #21424799C2semidirect
5. #21424744C2semidirect
6. #21424744C2semidirect
7. #21424370C2semidirect
8. #21424370C2semidirect
9. #21424195C2semidirect
10. #21424136C2semidirect
12. #21423942C2semidirect
13. #21423935C2semidirect
14. #21423882C2semidirect
15. C59×#2924C2semidirect
20. C2×#14273662C22semidirect
21. C2×#14273662C22semidirect
26. #16837410C4semidirect
27. #16837410C4semidirect
28. #16837406C4semidirect
29. #16837406C4semidirect
30. #16837401C4semidirect
31. #16837401C4semidirect
32. #16837401C4semidirect
33. #16837401C4semidirect
45. C2×#14273637C22semidirect
46. C2×C8×Dic59C22semidirect
48. #16837166C22semidirect
49. #16837166C22semidirect
50. #16837161C22semidirect
51. #16837161C22semidirect
52. #16837161C22semidirect
53. #16837161C22semidirect
54. #16837156C22semidirect
55. #16837156C22semidirect
61. C59×#424C22semidirect
62. C59×#424C22semidirect
65. C59×#405C22semidirect
66. C59×#405C22semidirect
386. #2924D59semidirect
421. #424C2×D59semidirect
422. #424C2×D59semidirect
448. #405C2×D59semidirect
449. #405C2×D59semidirect
461. C59#22588semidirect

Maximal subgroups

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

subgroupindex
#214326132
#214325422
#214248062
#214247992
#214247442
#214243702
#214241952
#214241362
#214240392
#214239422
#214239352
#214238822
C59×#29242
#2258859