Finite Group Databasebeta

← #27401464

Subgroups — #27401464

Order 13568.

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#20283232C211yesmaximal, characteristic
2#20283161C211yesmaximal, characteristic
3#20275425C211yesmaximal, characteristic, complemented
4#20275418C211yesmaximal, characteristic, complemented
5#20275363C211yesmaximal, characteristic, complemented
6#20275363C211yesmaximal, characteristic, complemented
7#20274989C211yesmaximal, characteristic, complemented
8#20274989C211yesmaximal, characteristic, complemented
9#20274814C211yesmaximal, characteristic, complemented
10#20274755C211yesmaximal, characteristic, complemented
11#20274658C211yesmaximal, characteristic
12#20274561C211yesmaximal, characteristic, complemented
13#20274554C211yesmaximal, characteristic, complemented
14#20274501C211yesmaximal, characteristic, complemented
15C53×#2924C211yesmaximal, characteristic, complemented
16C22×#11719945C2211yescharacteristic
17C2×#13133223C2211yescharacteristic
18C2×#13133223C2211yescharacteristic
19C22×#11719917C2211yescharacteristic
20C2×#13133152C2211yescharacteristic, complemented
21C2×#13133152C2211yescharacteristic, complemented
22C2×#13133143C2211yescharacteristic
23C2×#13133143C2211yescharacteristic
24C2×#13133143C2211yescharacteristic
25C2×#13133143C2211yescharacteristic
26#16810631C411yescharacteristic, complemented
27#16810631C411yescharacteristic, complemented
28#16810627C411yescharacteristic, complemented
29#16810627C411yescharacteristic, complemented
30#16810622C411yescharacteristic, complemented
31#16810622C411yescharacteristic, complemented
32#16810622C411yescharacteristic, complemented
33#16810622C411yescharacteristic, complemented
34#16810617C2211yescharacteristic
35#16810617C2211yescharacteristic
36#16810617C2211yescharacteristic
37#16810617C2211yescharacteristic
38#16810589C2211yescharacteristic
39#16810589C2211yescharacteristic
40#16810588—21no—
41#16810588—21no—
42#16810587C2211yescharacteristic
43#16810585—21no—
44C22⋊C8×D53—21no—
45C2×#13133127C2211yescharacteristic, complemented
46C2×C8×Dic53C2211yescharacteristic, complemented
47C4×C22⋊Dic53C2211yescharacteristic
48#16810387C2211yescharacteristic, complemented
49#16810387C2211yescharacteristic, complemented
50#16810382C2211yescharacteristic, complemented
51#16810382C2211yescharacteristic, complemented
52#16810382C2211yescharacteristic, complemented
53#16810382C2211yescharacteristic, complemented
54#16810377C2211yescharacteristic, complemented
55#16810377C2211yescharacteristic, complemented
56C2×#117×C53C2211yescharacteristic
57C53×#433—21no—
58C53×#433—21no—
59C53×#432—21no—
60C53×#431—21no—
61C53×#424C2211yescharacteristic, complemented
62C53×#424C2211yescharacteristic, complemented
63C53×#407C2211yescharacteristic
64C2×C22⋊C8×C53C2211yescharacteristic
65C53×#405C2211yescharacteristic, complemented
66C53×#405C2211yescharacteristic, complemented
67C2×#11719945—21no—
68C2×#11719945—21no—
69C2×#11719945—22no—
70C2×#11719945—22no—
71C2×#11719945—41no—
72C2×#11719945—41no—
73C2×#11719945C2×C411yescharacteristic
74C2×#11719945C2×C411yescharacteristic
75C2×#11719945C2311yescharacteristic
76C2×#11719945C2311yescharacteristic
77C22×Dic106C2×C411yescharacteristic
78C22×D212C2×C411yescharacteristic
79C22×C22⋊D53—21no—
80C22×C4×D53—21no—
81#13133223—22no—
82#13133223—22no—
83#13133223—41no—
84#13133223—41no—
85C2×#11719917—41no—
86C2×#11719917—41no—
87C2×#11719917C2×C411yescharacteristic
88C2×#11719917C2×C411yescharacteristic
89C2×#11719917C2×C411yescharacteristic
90C2×#11719917C2×C411yescharacteristic
91C2×#11719917C2311yescharacteristic
92C2×#11719917C2311yescharacteristic
93C2×#11719912—21no—
94C2×#11719912—21no—
95C22×#88322C2311yescharacteristic
96C22×#88322C2311yescharacteristic
97C2×C8×D53—21no—
98C2×C8×D53—21no—
99C2×C22⋊Dic53—21no—
100C2×C4×Dic53C2311yescharacteristic
101C2×C4×Dic53C2311yescharacteristic
102#13133152—41no—
103#13133152—41no—
104#13133143—22no—
105#13133143—22no—
106#13133143—41no—
107#13133143—41no—
108#13133140C2×C411yescharacteristic
109#13133140C2×C411yescharacteristic
110#13133140C2×C411yescharacteristic
111#13133140C2×C411yescharacteristic
112#13133140C2×C411yescharacteristic
113#13133140C2×C411yescharacteristic
114#13133140C2×C411yescharacteristic
115#13133140C2×C411yescharacteristic
116#13133137C2×C411yescharacteristic
117#13133137C2×C411yescharacteristic
118#13133137C2×C411yescharacteristic
119#13133137C2×C411yescharacteristic
120#13133137C2×C411yescharacteristic
121#13133137C2×C411yescharacteristic
122#13133137C2×C411yescharacteristic
123#13133137C2×C411yescharacteristic
124C22⋊#88322—21no—
125C22⋊#88322—21no—
126#13133129—21no—
127#13133129—21no—
128#13133129—21no—
129#13133129—21no—
130#13133127—41no—
131C8×Dic53—41no—
132#13133124—21no—
133C23×C4×C53C2311yescharacteristic
134C2×M16×C53C2311yescharacteristic
135C2×M16×C53C2311yescharacteristic
136C22×C8×C53C2311yescharacteristic
137C22×C8×C53C2311yescharacteristic
138#117×C53—21no—
139#117×C53—21no—
140#117×C53C2×C411yescharacteristic
141#117×C53C2×C411yescharacteristic
142#117×C53C2311yescharacteristic
143#117×C53C2311yescharacteristic
144C2×C4⋊C4×C53C2×C411yescharacteristic
145C2×C4⋊C4×C53C2×C411yescharacteristic
146C2×C22⋊C4×C53—21no—
147C2×C42×C53—21no—
148C4⋊C8×C53—21no—
149C4⋊C8×C53—21no—
150C4⋊C8×C53—21no—
151C4⋊C8×C53—21no—
152C22⋊C8×C53—21no—
153C22⋊C8×C53—21no—
154C22⋊C8×C53D411yescharacteristic
155C22⋊C8×C53D411yescharacteristic
156C22⋊C8×C53D411yescharacteristic
157C22⋊C8×C53D411yescharacteristic
158#97×C53—21no—
159#97×C53—21no—
160C4×C8×C53—21no—
161C4×C8×C53—21no—
162C24×C53#4111yescharacteristic
163C23×D53—21no—
164C22×C4×C53—21no—
165C22×C4×C53—21no—
166C22×C4×C53—21no—
167C22×C4×C53—21no—
168C22×C4×C53—21no—
169C22×C4×C53—21no—
170C22×C4×C53C22×C411yescharacteristic
171C22×C4×C53C22×C411yescharacteristic
172C22×C4×C53C2×D411yescharacteristic
173C22×C4×C53C2×D411yescharacteristic
174C22×C4×C53#4111yescharacteristic
175C22×C4×C53C2411yescharacteristic
176C2×C22⋊D53—21no—
177C2×C22⋊D53—21no—
178C2×C22⋊D53—21no—
179C2×C22⋊D53—21no—
180C2×C22⋊D53—42no—
181C2×C22⋊D53—42no—
182C22×Dic53—21no—
183C22×Dic53—21no—
184C22×Dic53—21no—
185#11719945—21no—
186#11719945—21no—
187#11719945—21no—
188#11719945—21no—
189#11719945—21no—
190#11719945—21no—
191#11719945—22no—
192#11719945—22no—
193#11719945—41no—
194#11719945—41no—
195#11719945—42no—
196#11719945—42no—
197#11719945—42no—
198#11719945—42no—
199#11719945#4112yes—
200#11719945#4112yes—
201C2×D212—22no—
202C2×D212—21no—
203C2×D212—41no—
204C2×D212C22×C411yescharacteristic
205C2×D212C22×C411yescharacteristic
206C2×C4×D53—21no—
207C2×C4×D53—21no—
208C2×C4×D53—21no—
209C2×C4×D53—21no—
210C2×C4×D53—42no—
211C2×C4×D53—42no—
212C2×Dic106—22no—
213C2×Dic106—21no—
214C2×Dic106—41no—
215C2×Dic106C22×C411yescharacteristic
216C2×Dic106C22×C411yescharacteristic
217M16×C53—21no—
218M16×C53—21no—
219M16×C53—21no—
220M16×C53—21no—
221C2×C8×C53—21no—
222C2×C8×C53—21no—
223C2×C8×C53—21no—
224C2×C8×C53—21no—
225C2×C8×C53—21no—
226C2×C8×C53—21no—
227C2×C8×C53C2×D411yescharacteristic
228C2×C8×C53C2×D411yescharacteristic
229C2×C8×C53C2×D411yescharacteristic
230C2×C8×C53C2×D411yescharacteristic
231C4⋊C4×C53—21no—
232C4⋊C4×C53—21no—
233C4⋊C4×C53C22×C411yescharacteristic
234C4⋊C4×C53C22×C411yescharacteristic
235C4⋊C4×C53C22×C411yescharacteristic
236C4⋊C4×C53C22×C411yescharacteristic
237C22⋊C4×C53—21no—
238C22⋊C4×C53—21no—
239C22⋊C4×C53—21no—
240C22⋊C4×C53—21no—
241C42×C53—21no—
242C42×C53—21no—
243C42×C53—21no—
244C42×C53—21no—
245C22⋊Dic53—42no—
246C4×Dic53—21no—
247C4×Dic53—21no—
248C4×Dic53—21no—
249C4×Dic53—21no—
250#11719917—21no—
251#11719917—21no—
252#11719917—21no—
253#11719917—21no—
254#11719917—41no—
255#11719917—41no—
256#11719917—41no—
257#11719917—41no—
258C2×#88322—21no—
259C2×#88322—21no—
260C2×#88322—21no—
261C2×#88322—21no—
262C2×#88322—21no—
263C2×#88322—21no—
264C2×#88322C22×C411yescharacteristic
265C2×#88322C22×C411yescharacteristic
266C2×#88322C22×C411yescharacteristic
267C2×#88322C22×C411yescharacteristic
268#11719912—42no—
269#11719912—42no—
270C8×D53—42no—
271C8×D53—42no—
272C23×C53—21no—
273C23×C53—21no—
274C23×C53—41no—
275C23×C53—41no—
276C23×C53C4×D411yescharacteristic
277C23×C53C4×D411yescharacteristic
278C23×C53C2×#4111yescharacteristic
279C22×D53—21no—
280C22×D53—21no—
281C22×D53—42no—
282C22×D53—42no—
283C22×D53—81no—
284C2×C4×C53—21no—
285C2×C4×C53—21no—
286C2×C4×C53—21no—
287C2×C4×C53—21no—
288C2×C4×C53—21no—
289C2×C4×C53—21no—
290C2×C4×C53—21no—
291C2×C4×C53—21no—
292C2×C4×C53—21no—
293C2×C4×C53—21no—
294C2×C4×C53—21no—
295C2×C4×C53—21no—
296C2×C4×C53—21no—
297C2×C4×C53—21no—
298C2×C4×C53—42no—
299C2×C4×C53—81no—
300C2×C4×C53C4×D411yescharacteristic
301C2×C4×C53C4×D411yescharacteristic
302C2×C4×C53C23×C411yescharacteristic
303C2×C4×C53C22×D411yescharacteristic
304C2×C4×C53C2×#4111yescharacteristic
305C2×C4×C53C2×#4111yescharacteristic
306C2×C4×C53H(5,𝔽2)11yescharacteristic
307C2×C4×C53H(5,𝔽2)11yescharacteristic
308C22⋊D53—22no—
309C22⋊D53—22no—
310C22⋊D53—42no—
311C22⋊D53—42no—
312C22⋊D53—41no—
313C22⋊D53—41no—
314C2×Dic53—21no—
315C2×Dic53—22no—
316C2×Dic53—21no—
317C2×Dic53—42no—
318C2×Dic53—41no—
319C2×Dic53—41no—
320C2×Dic53—41no—
321C2×Dic53—41no—
322C2×Dic53—41no—
323D212—21no—
324D212—21no—
325D212—21no—
326D212—42no—
327D212#11712yes—
328C4×D53—22no—
329C4×D53—22no—
330C4×D53—42no—
331C4×D53—42no—
332C4×D53—41no—
333C4×D53—41no—
334Dic106—21no—
335Dic106—21no—
336Dic106—21no—
337Dic106—42no—
338Dic106#11712yes—
339C8×C53—21no—
340C8×C53—21no—
341C8×C53—21no—
342C8×C53—21no—
343C8×C53—41no—
344C8×C53—41no—
345#88322—21no—
346#88322—21no—
347#88322—21no—
348#88322—21no—
349#88322—41no—
350#88322—41no—
351#22588—531nomaximal, Sylow
352C22×C53—21no—
353C22×C53—21no—
354C22×C53—21no—
355C22×C53—21no—
356C22×C53—21no—
357C22×C53—21no—
358C22×C53—21no—
359C22×C53—21no—
360C22×C53—81no—
361C22×C53—81no—
362C22×C53C2×C4×D411yescharacteristic
363C22×C53#55111yescharacteristic
364C22×C53#55111yescharacteristic
365C2×D53—22no—
366C2×D53—41no—
367C2×D53—41no—
368C2×D53—41no—
369C2×D53—41no—
370C2×D53—41no—
371C2×D53—84no—
372C4×C53—21no—
373C4×C53—21no—
374C4×C53—41no—
375C4×C53—41no—
376C4×C53—41no—
377C4×C53—41no—
378C4×C53C2×#11711yescharacteristic
379C4×C53#51811yescharacteristic
380C4×C53#54611yescharacteristic
381C4×C53#54611yescharacteristic
382Dic53—22no—
383Dic53—42no—
384Dic53—41no—
385Dic53—81no—
386#2924D5311yescharacteristic, complemented
387#2896—531no—
388#2880—531no—
389#1938—531no—
390#1937—531no—
391#1929—531no—
392#1929—531no—
393#1866—531no—
394#1866—531no—
395#1826—531no—
396#1811—531no—
397#1789—531no—
398#1765—531no—
399#1764—531no—
400#1753—531no—
401C2×C53—21no—
402C2×C53—21no—
403C2×C53—41no—
404C2×C53—41no—
405C2×C53#234211yescharacteristic
406C2×C53#295511yescharacteristic
407C2×C53#295611yescharacteristic
408D53—42no—
409D53—81no—
410C22×#41—531no—
411C2×#131—531no—
412C2×#131—531no—
413C22×M16—531no—
414C2×#117C2×D5311yescharacteristic
415#433—21no—
416#433—21no—
417#432—21no—
418#431—21no—
419C2×#108—531no—
420C2×#108—531no—
421#424C2×D5311yescharacteristic, complemented
422#424C2×D5311yescharacteristic, complemented
423C2×#104—531no—
424C2×#104—531no—
425C2×#104—531no—
426C2×#104—531no—
427#419—531no—
428#419—531no—
429#418—531no—
430#418—531no—
431#417—531no—
432#417—531no—
433#417—531no—
434#417—531no—
435#416—531no—
436#416—531no—
437#416—531no—
438#416—531no—
439#408—531no—
440#408—531no—
441#408—1061no—
442#408—1061no—
443#407—531no—
444#407—1061no—
445#407C2×D5311yescharacteristic
446C2×C22⋊C8—1061no—
447C2×C22⋊C8C2×D5311yescharacteristic
448#405C2×D5311yescharacteristic, complemented
449#405C2×D5311yescharacteristic, complemented
450C2×#97—531no—
451C2×C4×C8—531no—
452C4×C22⋊C4—531no—
453#341—531no—
454#341—531no—
455#339—531no—
456#339—531no—
457#339—531no—
458#339—531no—
459#336—531no—
460#336—531no—
461C53#2258811yescharacteristic, complemented, Sylow
462C2×#41—531no—
463C2×#41—531no—
464C2×#41—531no—
465C2×#41—531no—
466C2×#41—1062no—
467C2×#41—1062no—
468C2×#41—1061no—
469C2×#41—1061no—
470C2×#41—2121no—
471C2×#41—2121no—
472C22×Q8—531no—
473C22×D4—531no—
474C22×D4—1061no—
475C23×C4—1061no—
476C23×C4C22×D5311yescharacteristic
477#131—1062no—
478#131—1062no—
479#131—2121no—
480#131—2121no—
481C2×M16—531no—
482C2×M16—531no—
483C2×M16—531no—
484C2×M16—531no—
485C2×M16—531no—
486C2×M16—531no—
487C2×M16—1061no—
488C2×M16—1061no—
489C2×M16—2121no—
490C2×M16—2121no—
491C2×M16C22×D5311yescharacteristic
492C2×M16C22×D5311yescharacteristic
493C22×C8—531no—
494C22×C8—531no—
495C22×C8—1061no—
496C22×C8—1061no—
497C22×C8C22×D5311yescharacteristic
498C22×C8C22×D5311yescharacteristic
499#117—21no—
500#117—21no—
501#117C4×D5311yescharacteristic
502#117C4×D5311yescharacteristic
503#117C22×D5311yescharacteristic
504#117C22×D5311yescharacteristic
505C2×C4⋊C4C4×D5311yescharacteristic
506C2×C4⋊C4C4×D5311yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—1061no—
509C2×C42—21no—
510C2×C42—531no—
511C2×C42—531no—
512#108—2121no—
513#108—2121no—
514C4⋊C8—21no—
515C4⋊C8—21no—
516C4⋊C8—21no—
517C4⋊C8—21no—
518#104—1062no—
519#104—1062no—
520#104—2121no—
521#104—2121no—
522#103—531no—
523#103—531no—
524#103—531no—
525#103—531no—
526#103—531no—
527#103—531no—
528#103—531no—
529#103—531no—
530#102—531no—
531#102—531no—
532#102—531no—
533#102—531no—
534#102—531no—
535#102—531no—
536#102—531no—
537#102—531no—
538C22⋊C8—21no—
539C22⋊C8—21no—
540C22⋊C8—1061no—
541C22⋊C8—1061no—
542C22⋊C8—1061no—
543C22⋊C8—1061no—
544C22⋊C8—1061no—
545C22⋊C8—1061no—
546C22⋊C8C22⋊D5311yescharacteristic
547C22⋊C8C22⋊D5311yescharacteristic
548C22⋊C8C22⋊D5311yescharacteristic
549C22⋊C8C22⋊D5311yescharacteristic
550#97—21no—
551#97—21no—
552#97—2121no—
553C4×C8—21no—
554C4×C8—21no—
555C4×C8—2121no—
556#95—1061no—
557C24—1061no—
558C24#1171994511yescharacteristic
559#41—532no—
560#41—532no—
561#41—1062no—
562#41—1062no—
563#41—1061no—
564#41—1061no—
565#41—1061no—
566#41—1061no—
567#41—1061no—
568#41—1061no—
569#41—2122no—
570#41—2122no—
571#41—2121no—
572#41—2121no—
573#41—2122no—
574#41—2122no—
575C2×Q8—531no—
576C2×Q8—531no—
577C2×Q8—1062no—
578C2×Q8—1061no—
579C2×Q8—2121no—
580C2×D4—531no—
581C2×D4—531no—
582C2×D4—1062no—
583C2×D4—1061no—
584C2×D4—1061no—
585C2×D4—1061no—
586C2×D4—1061no—
587C2×D4—1061no—
588C2×D4—2121no—
589C2×D4—2122no—
590C2×D4—2122no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—1061no—
598C22×C4—1061no—
599C22×C4—1061no—
600C22×C4—1061no—
601C22×C4—1061no—
602C22×C4—1061no—
603C22×C4—1061no—
604C22×C4—2122no—
605C22×C4—2122no—
606C22×C4C2×C4×D5311yescharacteristic
607C22×C4C2×C4×D5311yescharacteristic
608C22×C4#1171994511yescharacteristic
609C22×C4C2×C22⋊D5311yescharacteristic
610C22×C4C2×C22⋊D5311yescharacteristic
611C22×C4C23×D5311yescharacteristic
612M16—21no—
613M16—21no—
614M16—21no—
615M16—21no—
616M16—1061no—
617M16—1061no—
618M16—1061no—
619M16—1061no—
620M16—2122no—
621M16—2122no—
622M16—2121no—
623M16—2121no—
624M16—2121no—
625M16—2121no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—531no—
633C2×C8—531no—
634C2×C8—531no—
635C2×C8—531no—
636C2×C8—1061no—
637C2×C8—1061no—
638C2×C8—1061no—
639C2×C8—1061no—
640C2×C8—1061no—
641C2×C8—1061no—
642C2×C8—2122no—
643C2×C8—2122no—
644C2×C8C2×C22⋊D5311yescharacteristic
645C2×C8C2×C22⋊D5311yescharacteristic
646C2×C8C2×C22⋊D5311yescharacteristic
647C2×C8C2×C22⋊D5311yescharacteristic
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4C2×C4×D5311yescharacteristic
651C4⋊C4C2×C4×D5311yescharacteristic
652C4⋊C4C2×C4×D5311yescharacteristic
653C4⋊C4C2×C4×D5311yescharacteristic
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—2122no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—21no—
663C42—1061no—
664C42—1061no—
665C42—1061no—
666C42—1061no—
667C23—21no—
668C23—21no—
669C23—41no—
670C23—41no—
671C23—1061no—
672C23—1061no—
673C23—4241no—
674C23—2122no—
675C23—2122no—
676C23C4×C22⋊D5311yescharacteristic
677C23C4×C22⋊D5311yescharacteristic
678C23C2×#1171994511yescharacteristic
679Q8—532no—
680Q8—1061no—
681Q8—1061no—
682Q8—1061no—
683Q8—2122no—
684D4—532no—
685D4—1062no—
686D4—1062no—
687D4—1061no—
688D4—1061no—
689D4—1061no—
690D4—2122no—
691D4—2122no—
692D4—2122no—
693D4—2121no—
694D4—2121no—
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—1061no—
712C2×C4—1062no—
713C2×C4—1062no—
714C2×C4—1062no—
715C2×C4—1061no—
716C2×C4—2122no—
717C2×C4—2122no—
718C2×C4—2122no—
719C2×C4—2121no—
720C2×C4—2121no—
721C2×C4—2121no—
722C2×C4—2121no—
723C2×C4—2121no—
724C2×C4—2121no—
725C2×C4—2121no—
726C2×C4C4×C22⋊D5311yescharacteristic
727C2×C4C4×C22⋊D5311yescharacteristic
728C2×C4C22×C4×D5311yescharacteristic
729C2×C4C22×C22⋊D5311yescharacteristic
730C2×C4#41×D5311yescharacteristic
731C2×C4#41×D5311yescharacteristic
732C2×C4#1313326311yescharacteristic
733C2×C4#1313326311yescharacteristic
734C8—21no—
735C8—21no—
736C8—21no—
737C8—21no—
738C8—41no—
739C8—41no—
740C8—1061no—
741C8—1061no—
742C8—1061no—
743C8—1061no—
744C8—2121no—
745C8—2121no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—81no—
755C22—81no—
756C22—1062no—
757C22—4244no—
758C22—2121no—
759C22—2121no—
760C22—2121no—
761C22—2121no—
762C22—2121no—
763C22C2×C4×C22⋊D5311yescharacteristic
764C22#1681129711yescharacteristic
765C22#1681129711yescharacteristic
766C4—21no—
767C4—21no—
768C4—41no—
769C4—41no—
770C4—41no—
771C4—41no—
772C4—1062no—
773C4—4241no—
774C4—2122no—
775C4—2121no—
776C4#117×D5311yescharacteristic
777C4#1681109711yescharacteristic
778C4#1681126111yescharacteristic
779C4#1681126111yescharacteristic
780C2—21no—
781C2—21no—
782C2—41no—
783C2—41no—
784C2—4241no—
785C2—2122no—
786C2#2027756511yescharacteristic
787C2#2028361611yescharacteristic
788C2#2028362211yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#2924C2
socleC22×C53C2×C4×D4
prime radicalC22×#11719945C22
cosocleC22×C4×C53C24
hypercenter#2924D53
hypocenterC53#22588
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ #2924

Complements

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

NH ≅ G/Ntype
3. #20275425C2semidirect
4. #20275418C2semidirect
5. #20275363C2semidirect
6. #20275363C2semidirect
7. #20274989C2semidirect
8. #20274989C2semidirect
9. #20274814C2semidirect
10. #20274755C2semidirect
12. #20274561C2semidirect
13. #20274554C2semidirect
14. #20274501C2semidirect
15. C53×#2924C2semidirect
20. C2×#13133152C22semidirect
21. C2×#13133152C22semidirect
26. #16810631C4semidirect
27. #16810631C4semidirect
28. #16810627C4semidirect
29. #16810627C4semidirect
30. #16810622C4semidirect
31. #16810622C4semidirect
32. #16810622C4semidirect
33. #16810622C4semidirect
45. C2×#13133127C22semidirect
46. C2×C8×Dic53C22semidirect
48. #16810387C22semidirect
49. #16810387C22semidirect
50. #16810382C22semidirect
51. #16810382C22semidirect
52. #16810382C22semidirect
53. #16810382C22semidirect
54. #16810377C22semidirect
55. #16810377C22semidirect
61. C53×#424C22semidirect
62. C53×#424C22semidirect
65. C53×#405C22semidirect
66. C53×#405C22semidirect
386. #2924D53semidirect
421. #424C2×D53semidirect
422. #424C2×D53semidirect
448. #405C2×D53semidirect
449. #405C2×D53semidirect
461. C53#22588semidirect

Maximal subgroups

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

subgroupindex
#202832322
#202831612
#202754252
#202754182
#202753632
#202749892
#202748142
#202747552
#202746582
#202745612
#202745542
#202745012
C53×#29242
#2258853