Finite Group Databasebeta

← #27401451

Subgroups — #27401451

Order 13568.

906 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#20283372C211yesmaximal, characteristic, complemented
2#416×D53C211yesmaximal, characteristic
3#20283163C211yesmaximal, characteristic
4#20275421C211yesmaximal, characteristic, complemented
5#20275366C211yesmaximal, characteristic, complemented
6#20275360C211yesmaximal, characteristic, complemented
7#20274991C211yesmaximal, characteristic, complemented
8#20274989C211yesmaximal, characteristic, complemented
9#20274813C211yesmaximal, characteristic, complemented
10#20274752C211yesmaximal, characteristic, complemented
11#20274657C211yesmaximal, characteristic
12#20274552C211yesmaximal, characteristic, complemented
13#20274551C211yesmaximal, characteristic, complemented
14C8×#11719921C211yesmaximal, characteristic, complemented
15C53×#1937C211yesmaximal, characteristic, complemented
16C2×#41×D53C2211yescharacteristic
17C2×#13133225C2211yescharacteristic
18C2×#13133223C2211yescharacteristic
19C22×C8×D53C2211yescharacteristic
20#117×D53C2211yescharacteristic
21#16810683—21no—
22#16810683—21no—
23#16810679—21no—
24#16810675—21no—
25C2×#13133152C2211yescharacteristic, complemented
26C2×#13133152C2211yescharacteristic, complemented
27#16810650C2211yescharacteristic, complemented
28C2×#13133145C2211yescharacteristic
29C2×#13133144C2211yescharacteristic
30C2×#13133143C2211yescharacteristic
31#16810620C2211yescharacteristic
32#16810619C2211yescharacteristic
33#16810618C411yescharacteristic, complemented
34#16810618C411yescharacteristic, complemented
35#16810617C2211yescharacteristic
36#16810616C411yescharacteristic, complemented
37#16810616C411yescharacteristic, complemented
38#103×D53C411yescharacteristic, complemented
39#103×D53C411yescharacteristic, complemented
40#102×D53C411yescharacteristic, complemented
41#102×D53C411yescharacteristic, complemented
42#16810590C2211yescharacteristic
43#16810588—21no—
44#16810588—21no—
45#16810586C2211yescharacteristic
46#16810586C2211yescharacteristic
47#16810585—21no—
48C2×#13133129C2211yescharacteristic
49C22⋊C8×D53—21no—
50#16810581C2211yescharacteristic, complemented
51#16810578C2211yescharacteristic, complemented
52C2×C8×Dic53C2211yescharacteristic, complemented
53C4×#11719921C2211yescharacteristic
54#16810388C2211yescharacteristic, complemented
55#16810384C2211yescharacteristic, complemented
56#16810383C2211yescharacteristic, complemented
57#16810382C2211yescharacteristic, complemented
58#16810378C2211yescharacteristic, complemented
59#16810377C2211yescharacteristic, complemented
60C53×#424C2211yescharacteristic, complemented
61C2×#104×C53C2211yescharacteristic
62C53×#416C2211yescharacteristic
63C53×#408C2211yescharacteristic
64C2×C4×C8×C53C2211yescharacteristic, complemented
65C53×#341C2211yescharacteristic, complemented
66C53×#339C2211yescharacteristic, complemented
67C2×#11719949C2×C411yescharacteristic
68C2×#11719945—21no—
69C2×#11719945C2311yescharacteristic
70C2×#11719947—21no—
71C2×#11719947C2×C411yescharacteristic
72#41×D53—22no—
73#41×D53—22no—
74#41×D53—41no—
75#41×D53—41no—
76C2×Q8×D53C2×C411yescharacteristic
77C2×D4×D53—21no—
78C2×D4×D53C2×C411yescharacteristic
79C22×C4×D53—21no—
80C22×C4×D53C2311yescharacteristic
81#13133225—22no—
82#13133225—41no—
83#13133223—22no—
84#13133223—41no—
85C2×#11719917C2311yescharacteristic
86C2×#11719917C2311yescharacteristic
87C2×#11719912—21no—
88C2×#11719912—21no—
89C22×#88322C2311yescharacteristic
90C22×#88322C2311yescharacteristic
91C2×C8×D53—21no—
92C2×C8×D53—21no—
93C2×C8×D53—41no—
94C2×C8×D53—41no—
95C2×C8×D53C2×C411yescharacteristic
96C2×C8×D53C2×C411yescharacteristic
97C2×C8×D53C2×C411yescharacteristic
98C2×C8×D53C2×C411yescharacteristic
99#13133176C2311yescharacteristic
100#13133175C2×C411yescharacteristic
101#13133175C2×C411yescharacteristic
102#13133174—21no—
103#13133173—21no—
104C4⋊C4×D53C2×C411yescharacteristic
105C4⋊C4×D53C2×C411yescharacteristic
106C2×#11719921—21no—
107C22⋊C4×D53—21no—
108C2×C4×Dic53C2311yescharacteristic
109C42×D53—21no—
110#13133152—41no—
111#13133152—41no—
112C4⋊#88322—21no—
113C4⋊#88322—21no—
114#13133145—22no—
115#13133144—41no—
116#13133143—22no—
117#13133142C2×C411yescharacteristic
118#13133142C2×C411yescharacteristic
119#13133141C2×C411yescharacteristic
120#13133141C2×C411yescharacteristic
121#13133140C2×C411yescharacteristic
122#13133140C2×C411yescharacteristic
123#13133139C2×C411yescharacteristic
124#13133139C2×C411yescharacteristic
125#13133138C2×C411yescharacteristic
126#13133138C2×C411yescharacteristic
127#13133137C2×C411yescharacteristic
128#13133137C2×C411yescharacteristic
129C22⋊#88322—21no—
130C22⋊#88322—21no—
131#13133129—21no—
132#13133129—21no—
133#13133129—21no—
134#13133129—21no—
135#13133129D411yescharacteristic
136#13133129D411yescharacteristic
137#13133129D411yescharacteristic
138#13133129D411yescharacteristic
139#13133127—21no—
140#13133127—21no—
141C8×Dic53—21no—
142C8×Dic53—21no—
143C8×Dic53—41no—
144#13133124—21no—
145C2×#41×C53C2311yescharacteristic
146C2×M16×C53C2311yescharacteristic
147C2×M16×C53C2311yescharacteristic
148C22×C8×C53C2311yescharacteristic
149C22×C8×C53C2311yescharacteristic
150#117×C53C2311yescharacteristic
151C2×C42×C53C2311yescharacteristic
152C4⋊C8×C53—21no—
153C4⋊C8×C53—21no—
154#104×C53—41no—
155#103×C53C2×C411yescharacteristic
156#103×C53C2×C411yescharacteristic
157#102×C53C2×C411yescharacteristic
158#102×C53C2×C411yescharacteristic
159C22⋊C8×C53—21no—
160C22⋊C8×C53—21no—
161C4×C8×C53—41no—
162C23×D53—21no—
163C23×D53#4111yescharacteristic
164#41×C53—21no—
165#41×C53—21no—
166#41×C53—21no—
167#41×C53—21no—
168C2×Q8×C53C22×C411yescharacteristic
169C2×D4×C53—21no—
170C2×D4×C53C22×C411yescharacteristic
171C22×C4×C53—21no—
172C22×C4×C53—21no—
173C22×C4×C53C2411yescharacteristic
174C2×C22⋊D53—21no—
175C2×C22⋊D53—21no—
176C2×C22⋊D53—21no—
177C22×Dic53—21no—
178C22×Dic53—21no—
179C22×Dic53#4111yescharacteristic
180#11719949—22no—
181#11719949—41no—
182Q8×D53—22no—
183Q8×D53—41no—
184#11719947—22no—
185#11719947—41no—
186#11719947—42no—
187#11719947—42no—
188D4×D53—22no—
189D4×D53—41no—
190D4×D53—42no—
191D4×D53—42no—
192#11719945—21no—
193#11719945—21no—
194#11719945—42no—
195#11719945—42no—
196#11719945#4112yes—
197#11719945#4112yes—
198C2×D212—21no—
199C2×D212C22×C411yescharacteristic
200C2×C4×D53—21no—
201C2×C4×D53—21no—
202C2×C4×D53—21no—
203C2×C4×D53—21no—
204C2×C4×D53—21no—
205C2×C4×D53—21no—
206C2×C4×D53—21no—
207C2×C4×D53—21no—
208C2×C4×D53—21no—
209C2×C4×D53—42no—
210C2×C4×D53—42no—
211C2×C4×D53C22×C411yescharacteristic
212C2×C4×D53C22×C411yescharacteristic
213C2×C4×D53C2×D411yescharacteristic
214C2×C4×D53C2×D411yescharacteristic
215C2×Dic106—21no—
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×C53C22×C411yescharacteristic
228C2×C8×C53C22×C411yescharacteristic
229C2×C8×C53C2×D411yescharacteristic
230C2×C8×C53C2×D411yescharacteristic
231C4⋊C4×C53C22×C411yescharacteristic
232C4⋊C4×C53C22×C411yescharacteristic
233C22⋊C4×C53—21no—
234C42×C53—21no—
235C42×C53—21no—
236C42×C53—21no—
237C22⋊Dic53—21no—
238#11719921—24no—
239#11719921—21no—
240#11719921—21no—
241C4⋊Dic53C22×C411yescharacteristic
242C4⋊Dic53C22×C411yescharacteristic
243#11719919—21no—
244#11719919—21no—
245C4×Dic53—21no—
246C4×Dic53—21no—
247C4×Dic53—21no—
248C4×Dic53—21no—
249C4×Dic53—21no—
250#11719917—21no—
251#11719917—21no—
252#11719917—21no—
253#11719917—21no—
254C2×#88322—21no—
255C2×#88322—21no—
256C2×#88322—21no—
257C2×#88322—21no—
258C2×#88322—21no—
259C2×#88322—21no—
260C2×#88322C22×C411yescharacteristic
261C2×#88322C22×C411yescharacteristic
262C2×#88322C2×D411yescharacteristic
263C2×#88322C2×D411yescharacteristic
264#11719912—42no—
265#11719912—42no—
266C8×D53—41no—
267C8×D53—41no—
268C8×D53—41no—
269C8×D53—41no—
270C8×D53—42no—
271C8×D53—42no—
272C23×C53—21no—
273C23×C53C2×#4111yescharacteristic
274C22×D53—21no—
275C22×D53—21no—
276C22×D53—21no—
277C22×D53—22no—
278C22×D53—41no—
279C22×D53—42no—
280C22×D53—42no—
281C22×D53—81no—
282C22×D53C4×D411yescharacteristic
283C22×D53C4×D411yescharacteristic
284Q8×C53—21no—
285Q8×C53—21no—
286D4×C53—21no—
287D4×C53—21no—
288D4×C53—41no—
289D4×C53—41no—
290C2×C4×C53—22no—
291C2×C4×C53—21no—
292C2×C4×C53—21no—
293C2×C4×C53—21no—
294C2×C4×C53—41no—
295C2×C4×C53—41no—
296C2×C4×C53—41no—
297C2×C4×C53—41no—
298C2×C4×C53C23×C411yescharacteristic
299C2×C4×C53C22×D411yescharacteristic
300C2×C4×C53C2×#4111yescharacteristic
301C2×C4×C53C2×#4111yescharacteristic
302C2×C4×C53H(5,𝔽2)11yescharacteristic
303C2×C4×C53H(5,𝔽2)11yescharacteristic
304C22⋊D53—22no—
305C22⋊D53—22no—
306C22⋊D53—42no—
307C22⋊D53—42no—
308C2×Dic53—21no—
309C2×Dic53—21no—
310C2×Dic53—21no—
311C2×Dic53—22no—
312C2×Dic53—21no—
313C2×Dic53—21no—
314C2×Dic53—42no—
315C2×Dic53—41no—
316C2×Dic53—41no—
317C2×Dic53C4×D411yescharacteristic
318C2×Dic53C4×D411yescharacteristic
319D212—21no—
320D212—42no—
321D212#11712yes—
322C4×D53—21no—
323C4×D53—21no—
324C4×D53—21no—
325C4×D53—21no—
326C4×D53—21no—
327C4×D53—21no—
328C4×D53—21no—
329C4×D53—21no—
330C4×D53—22no—
331C4×D53—22no—
332C4×D53—42no—
333C4×D53—42no—
334C4×D53—42no—
335C4×D53—81no—
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#22587—531nomaximal, Sylow
352C22×C53—21no—
353C22×C53—21no—
354C22×C53—41no—
355C22×C53—41no—
356C22×C53—41no—
357C22×C53C2×C4×D411yescharacteristic
358C22×C53#55111yescharacteristic
359C22×C53#55111yescharacteristic
360C2×D53—21no—
361C2×D53—21no—
362C2×D53—21no—
363C2×D53—22no—
364C2×D53—21no—
365C2×D53—21no—
366C2×D53—42no—
367C2×D53—42no—
368C2×D53—41no—
369C2×D53—41no—
370C2×D53—84no—
371C2×D53#44312yes—
372C4×C53—42no—
373C4×C53—41no—
374C4×C53—41no—
375C4×C53—41no—
376C4×C53C2×#11711yescharacteristic
377C4×C53#51811yescharacteristic
378C4×C53#54611yescharacteristic
379C4×C53#54611yescharacteristic
380Dic53—22no—
381Dic53—21no—
382Dic53—21no—
383Dic53—42no—
384Dic53—41no—
385Dic53—41no—
386#2924—531no—
387C2×#416—531no—
388#2880—531no—
389#1937—531no—
390#1937D5311yescharacteristic, complemented
391#1929—531no—
392#1929—531no—
393#1866—531no—
394#1866—531no—
395#1826—531no—
396#1810—531no—
397#1789—531no—
398#1764—531no—
399#1764—531no—
400C8×C22⋊C4—531no—
401C2×C53—21no—
402C2×C53—21no—
403C2×C53—81no—
404C2×C53#234211yescharacteristic
405C2×C53C2×#44311yescharacteristic
406C2×C53#295711yescharacteristic
407D53—22no—
408D53—41no—
409D53—42no—
410C22×#41—531no—
411C2×#131—531no—
412C2×#131—531no—
413C23×C8—531no—
414C2×#117—531no—
415#433—1061no—
416#433—1061no—
417#432—1061no—
418#431—1061no—
419C2×#108—531no—
420C2×#108—531no—
421#424—531no—
422#424C2×D5311yescharacteristic, complemented
423C2×#104—531no—
424C2×#104—531no—
425C2×#104—531no—
426C2×#104C2×D5311yescharacteristic
427#416—531no—
428#416—531no—
429#416—531no—
430#416—531no—
431#416—531no—
432#416—531no—
433#416—531no—
434#416C2×D5311yescharacteristic
435C2×#103—531no—
436C2×#103—531no—
437C2×#102—531no—
438C2×#102—531no—
439#408—531no—
440#408—1061no—
441#408—1061no—
442#408C2×D5311yescharacteristic
443#407—531no—
444#407—531no—
445#407—1061no—
446C2×C22⋊C8—531no—
447C2×C22⋊C8—1061no—
448#405—531no—
449#405—531no—
450C2×C4×C8—531no—
451C2×C4×C8C2×D5311yescharacteristic, complemented
452C4×C22⋊C4—531no—
453#341—531no—
454#341C2×D5311yescharacteristic, complemented
455#339—531no—
456#339—531no—
457#339—531no—
458#339C2×D5311yescharacteristic, complemented
459#336—531no—
460#336—531no—
461C53#2258711yescharacteristic, complemented, Sylow
462C2×#41—531no—
463C2×#41—531no—
464C2×#41—531no—
465C2×#41—1061no—
466C2×#41—1061no—
467C2×#41—1062no—
468C2×#41—1062no—
469C2×#41—2121no—
470C2×#41—2121no—
471C2×#41C22×D5311yescharacteristic
472C22×Q8—531no—
473C22×D4—531no—
474C22×D4—1061no—
475C23×C4—531no—
476C23×C4—1061no—
477#131—1062no—
478#131—1062no—
479#131—2121no—
480#131—2121no—
481C2×M16—531no—
482C2×M16—531no—
483C2×M16—1061no—
484C2×M16—1061no—
485C2×M16C22×D5311yescharacteristic
486C2×M16C22×D5311yescharacteristic
487C22×C8—531no—
488C22×C8—531no—
489C22×C8—531no—
490C22×C8—531no—
491C22×C8—531no—
492C22×C8—531no—
493C22×C8—1061no—
494C22×C8—1061no—
495C22×C8—2121no—
496C22×C8—2121no—
497C22×C8C22×D5311yescharacteristic
498C22×C8C22×D5311yescharacteristic
499#117—531no—
500#117—531no—
501#117—531no—
502#117—1061no—
503#117—1061no—
504#117C22×D5311yescharacteristic
505C2×C4⋊C4—531no—
506C2×C4⋊C4—531no—
507C2×C22⋊C4—1061no—
508C2×C22⋊C4—1061no—
509C2×C42—531no—
510C2×C42—1061no—
511C2×C42C22×D5311yescharacteristic
512#108—2121no—
513#108—2121no—
514C4⋊C8—21no—
515C4⋊C8—21no—
516C4⋊C8—1061no—
517C4⋊C8—1061no—
518#104—41no—
519#104—1062no—
520#104—1062no—
521#104—2121no—
522#103—531no—
523#103—531no—
524#103—531no—
525#103—531no—
526#103—531no—
527#103—531no—
528#103C4×D5311yescharacteristic
529#103C4×D5311yescharacteristic
530#102—531no—
531#102—531no—
532#102—531no—
533#102—531no—
534#102—531no—
535#102—531no—
536#102C4×D5311yescharacteristic
537#102C4×D5311yescharacteristic
538C22⋊C8—21no—
539C22⋊C8—21no—
540C22⋊C8—531no—
541C22⋊C8—531no—
542C22⋊C8—531no—
543C22⋊C8—531no—
544C22⋊C8—1061no—
545C22⋊C8—1061no—
546C22⋊C8—1061no—
547C22⋊C8—1061no—
548C22⋊C8—1061no—
549C22⋊C8—1061no—
550#97—1061no—
551#97—1061no—
552C4×C8—41no—
553C4×C8—1061no—
554C4×C8—1061no—
555C4×C8—2121no—
556#95—1061no—
557C24—531no—
558C24—1061no—
559#41—21no—
560#41—21no—
561#41—21no—
562#41—21no—
563#41—532no—
564#41—532no—
565#41—1061no—
566#41—1061no—
567#41—1062no—
568#41—1062no—
569#41—2122no—
570#41—2122no—
571#41—2121no—
572#41—2122no—
573#41—2122no—
574#41—2121no—
575C2×Q8—531no—
576C2×Q8—1061no—
577C2×Q8—1062no—
578C2×Q8—2121no—
579C2×Q8C2×C4×D5311yescharacteristic
580C2×D4—21no—
581C2×D4—531no—
582C2×D4—1061no—
583C2×D4—1061no—
584C2×D4—1062no—
585C2×D4—1061no—
586C2×D4—1061no—
587C2×D4—2121no—
588C2×D4—2122no—
589C2×D4—2122no—
590C2×D4C2×C4×D5311yescharacteristic
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—531no—
594C22×C4—531no—
595C22×C4—531no—
596C22×C4—531no—
597C22×C4—531no—
598C22×C4—1061no—
599C22×C4—1061no—
600C22×C4—1061no—
601C22×C4—1061no—
602C22×C4—1061no—
603C22×C4—1061no—
604C22×C4—1061no—
605C22×C4—1061no—
606C22×C4—1061no—
607C22×C4—1061no—
608C22×C4—1061no—
609C22×C4—2122no—
610C22×C4—2122no—
611C22×C4C23×D5311yescharacteristic
612M16—21no—
613M16—21no—
614M16—21no—
615M16—21no—
616M16—1061no—
617M16—1061no—
618M16—1061no—
619M16—1061no—
620M16—2122no—
621M16—2122no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—531no—
629C2×C8—531no—
630C2×C8—531no—
631C2×C8—531no—
632C2×C8—1061no—
633C2×C8—1061no—
634C2×C8—1061no—
635C2×C8—1061no—
636C2×C8—1061no—
637C2×C8—1061no—
638C2×C8—2121no—
639C2×C8—2121no—
640C2×C8—2121no—
641C2×C8—2121no—
642C2×C8—2122no—
643C2×C8—2122no—
644C2×C8C2×C4×D5311yescharacteristic
645C2×C8C2×C4×D5311yescharacteristic
646C2×C8D4×D5311yescharacteristic
647C2×C8D4×D5311yescharacteristic
648C4⋊C4—531no—
649C4⋊C4—531no—
650C4⋊C4—1061no—
651C4⋊C4—1061no—
652C4⋊C4C2×C4×D5311yescharacteristic
653C4⋊C4C2×C4×D5311yescharacteristic
654C22⋊C4—21no—
655C22⋊C4—1061no—
656C22⋊C4—1061no—
657C22⋊C4—1064no—
658C22⋊C4—1061no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—1061no—
663C42—1061no—
664C42—1061no—
665C42—1061no—
666C42—1061no—
667C23—21no—
668C23—531no—
669C23—531no—
670C23—1062no—
671C23—1061no—
672C23—1061no—
673C23—1061no—
674C23—4241no—
675C23—2121no—
676C23—2122no—
677C23—2122no—
678C23#41×D5311yescharacteristic
679Q8—21no—
680Q8—21no—
681Q8—532no—
682Q8—1061no—
683Q8—2122no—
684D4—21no—
685D4—21no—
686D4—41no—
687D4—41no—
688D4—532no—
689D4—1062no—
690D4—1062no—
691D4—1061no—
692D4—2122no—
693D4—2122no—
694D4—2122no—
695C2×C4—22no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—531no—
704C2×C4—531no—
705C2×C4—1061no—
706C2×C4—1061no—
707C2×C4—1061no—
708C2×C4—1062no—
709C2×C4—1061no—
710C2×C4—1061no—
711C2×C4—1061no—
712C2×C4—1061no—
713C2×C4—1061no—
714C2×C4—1061no—
715C2×C4—1062no—
716C2×C4—1061no—
717C2×C4—1061no—
718C2×C4—1062no—
719C2×C4—1061no—
720C2×C4—1061no—
721C2×C4—4241no—
722C2×C4—2122no—
723C2×C4—2122no—
724C2×C4—2122no—
725C2×C4—2122no—
726C2×C4—2121no—
727C2×C4—2121no—
728C2×C4C22×C4×D5311yescharacteristic
729C2×C4C2×D4×D5311yescharacteristic
730C2×C4#41×D5311yescharacteristic
731C2×C4#41×D5311yescharacteristic
732C2×C4#1313326211yescharacteristic
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—41no—
749C22—41no—
750C22—41no—
751C22—532no—
752C22—1061no—
753C22—1061no—
754C22—1061no—
755C22—1062no—
756C22—1061no—
757C22—1061no—
758C22—4244no—
759C22—2122no—
760C22—2122no—
761C22—2121no—
762C22—2121no—
763C22C4×D4×D5311yescharacteristic
764C22#1681129811yescharacteristic
765C22#1681130111yescharacteristic
766C4—42no—
767C4—41no—
768C4—41no—
769C4—41no—
770C4—1061no—
771C4—1061no—
772C4—1062no—
773C4—2122no—
774C4—2121no—
775C4—2121no—
776C4#117×D5311yescharacteristic
777C4#1681109511yescharacteristic
778C4#1681126211yescharacteristic
779C4#1681126611yescharacteristic
780C2—21no—
781C2—21no—
782C2—81no—
783C2—1062no—
784C2—2121no—
785C2—2122no—
786C2#2027756311yescharacteristic
787C2#443×D5311yescharacteristic
788C2#2028362711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#1937C2
socleC22×C53C2×C4×D4
prime radicalC2×#41×D53C22
cosocleC22×C4×C53C24
hypercenter#1937D53
hypocenterC53#22587
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1937

Complements

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

NH ≅ G/Ntype
1. #20283372C2semidirect
4. #20275421C2semidirect
5. #20275366C2semidirect
6. #20275360C2semidirect
7. #20274991C2semidirect
8. #20274989C2semidirect
9. #20274813C2semidirect
10. #20274752C2semidirect
12. #20274552C2semidirect
13. #20274551C2semidirect
14. C8×#11719921C2semidirect
15. C53×#1937C2semidirect
25. C2×#13133152C22semidirect
26. C2×#13133152C22semidirect
27. #16810650C22semidirect
33. #16810618C4semidirect
34. #16810618C4semidirect
36. #16810616C4semidirect
37. #16810616C4semidirect
38. #103×D53C4semidirect
39. #103×D53C4semidirect
40. #102×D53C4semidirect
41. #102×D53C4semidirect
50. #16810581C22semidirect
51. #16810578C22semidirect
52. C2×C8×Dic53C22semidirect
54. #16810388C22semidirect
55. #16810384C22semidirect
56. #16810383C22semidirect
57. #16810382C22semidirect
58. #16810378C22semidirect
59. #16810377C22semidirect
60. C53×#424C22semidirect
64. C2×C4×C8×C53C22semidirect
65. C53×#341C22semidirect
66. C53×#339C22semidirect
390. #1937D53semidirect
422. #424C2×D53semidirect
451. C2×C4×C8C2×D53semidirect
454. #341C2×D53semidirect
458. #339C2×D53semidirect
461. C53#22587semidirect

Maximal subgroups

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

subgroupindex
#202833722
#416×D532
#202831632
#202754212
#202753662
#202753602
#202749912
#202749892
#202748132
#202747522
#202746572
#202745522
#202745512
C8×#117199212
C53×#19372
#2258753