Finite Group Databasebeta

← #27401467

Subgroups — #27401467

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#20283375C211yesmaximal, characteristic, complemented
2#20283234C211yesmaximal, characteristic
3#20283164C211yesmaximal, characteristic
4#20275423C211yesmaximal, characteristic, complemented
5#20275416C211yesmaximal, characteristic, complemented
6#20275366C211yesmaximal, characteristic, complemented
7#20275366C211yesmaximal, characteristic, complemented
8#20274988C211yesmaximal, characteristic, complemented
9#20274988C211yesmaximal, characteristic, complemented
10#20274815C211yesmaximal, characteristic, complemented
11#20274755C211yesmaximal, characteristic, complemented
12#20274560C211yesmaximal, characteristic, complemented
13#20274553C211yesmaximal, characteristic, complemented
14#20274499C211yesmaximal, characteristic, complemented
15C53×#1789C211yesmaximal, characteristic
16C2×#13133224C2211yescharacteristic
17C2×#13133224C2211yescharacteristic
18C22×#11719917C2211yescharacteristic
19C2×#13133176C2211yescharacteristic
20#16810681—21no—
21#16810681—21no—
22#16810677—21no—
23#16810673—21no—
24C2×#13133152C2211yescharacteristic, complemented
25C2×#13133152C2211yescharacteristic, complemented
26#16810651C2211yescharacteristic, complemented
27#16810651C2211yescharacteristic, complemented
28#16810632C411yescharacteristic, complemented
29#16810632C411yescharacteristic, complemented
30#16810628C411yescharacteristic, complemented
31#16810628C411yescharacteristic, complemented
32#16810624C411yescharacteristic, complemented
33#16810624C411yescharacteristic, complemented
34#16810624C411yescharacteristic, complemented
35#16810624C411yescharacteristic, complemented
36#16810619C2211yescharacteristic
37#16810619C2211yescharacteristic
38#16810619C2211yescharacteristic
39#16810619C2211yescharacteristic
40#16810590—21no—
41#16810590—21no—
42#16810590C2211yescharacteristic
43#16810590C2211yescharacteristic
44#16810587—21no—
45#16810587C2211yescharacteristic
46C2×C22⋊#88322—21no—
47C2×C22⋊#88322C2211yescharacteristic
48#16810581C2211yescharacteristic, complemented
49#16810581C2211yescharacteristic, complemented
50C2×#13133128C2211yescharacteristic, complemented
51C2×C4×#88322C2211yescharacteristic, complemented
52#16810387C2211yescharacteristic, complemented
53#16810387C2211yescharacteristic, complemented
54#16810383C2211yescharacteristic, complemented
55#16810383C2211yescharacteristic, complemented
56#16810383C2211yescharacteristic, complemented
57#16810383C2211yescharacteristic, complemented
58#16810378C2211yescharacteristic, complemented
59#16810378C2211yescharacteristic, complemented
60C22×#41×C53C2211yescharacteristic
61C2×#104×C53C2211yescharacteristic
62C2×#104×C53C2211yescharacteristic
63C2×#104×C53C2211yescharacteristic
64C2×#104×C53C2211yescharacteristic
65C53×#407C2211yescharacteristic
66C4×C22⋊C4×C53C2211yescharacteristic
67#13133224—22no—
68#13133224—22no—
69#13133224—41no—
70#13133224—41no—
71C2×#11719917—21no—
72C2×#11719917—21no—
73C2×#11719917—41no—
74C2×#11719917—41no—
75C2×#11719917C2×C411yescharacteristic
76C2×#11719917C2×C411yescharacteristic
77C2×#11719917C2×C411yescharacteristic
78C2×#11719917C2×C411yescharacteristic
79C2×#11719917C2311yescharacteristic
80C2×#11719917C2311yescharacteristic
81C22×#88322—21no—
82C22×#88322—21no—
83C22×#88322C2311yescharacteristic
84C22×#88322C2311yescharacteristic
85C22×#88322C2311yescharacteristic
86C22×#88322C2311yescharacteristic
87#13133176—21no—
88#13133176—21no—
89#13133176C2×C411yescharacteristic
90#13133176C2×C411yescharacteristic
91#13133176C2311yescharacteristic
92#13133176C2311yescharacteristic
93C2×C4⋊Dic53C2×C411yescharacteristic
94C2×C4⋊Dic53C2×C411yescharacteristic
95C2×C22⋊Dic53—21no—
96C2×C4×Dic53—21no—
97#13133152—41no—
98#13133152—41no—
99#13133146—21no—
100#13133146—21no—
101#13133146—21no—
102#13133146—21no—
103#13133141C2×C411yescharacteristic
104#13133141C2×C411yescharacteristic
105#13133141C2×C411yescharacteristic
106#13133141C2×C411yescharacteristic
107#13133141C2×C411yescharacteristic
108#13133141C2×C411yescharacteristic
109#13133141C2×C411yescharacteristic
110#13133141C2×C411yescharacteristic
111#13133138C2×C411yescharacteristic
112#13133138C2×C411yescharacteristic
113#13133138C2×C411yescharacteristic
114#13133138C2×C411yescharacteristic
115#13133138C2×C411yescharacteristic
116#13133138C2×C411yescharacteristic
117#13133138C2×C411yescharacteristic
118#13133138C2×C411yescharacteristic
119C22⋊#88322—21no—
120C22⋊#88322—21no—
121C22⋊#88322—21no—
122C22⋊#88322—21no—
123C22⋊#88322—21no—
124C22⋊#88322—21no—
125C22⋊#88322D411yescharacteristic
126C22⋊#88322D411yescharacteristic
127C22⋊#88322D411yescharacteristic
128C22⋊#88322D411yescharacteristic
129#13133128—41no—
130#13133127—21no—
131#13133127—21no—
132C4×#88322—41no—
133C8×Dic53—21no—
134C8×Dic53—21no—
135C2×#41×C53—21no—
136C2×#41×C53—21no—
137C2×#41×C53—22no—
138C2×#41×C53—22no—
139C2×#41×C53—41no—
140C2×#41×C53—41no—
141C2×#41×C53C2×C411yescharacteristic
142C2×#41×C53C2×C411yescharacteristic
143C2×#41×C53C2311yescharacteristic
144C2×#41×C53C2311yescharacteristic
145C22×Q8×C53C2×C411yescharacteristic
146C22×D4×C53—21no—
147C22×D4×C53C2×C411yescharacteristic
148C23×C4×C53—21no—
149C23×C4×C53C2311yescharacteristic
150C2×M16×C53C2311yescharacteristic
151C2×M16×C53C2311yescharacteristic
152C2×C22⋊C4×C53—21no—
153C2×C42×C53C2311yescharacteristic
154C2×C42×C53C2311yescharacteristic
155#104×C53—22no—
156#104×C53—22no—
157#104×C53—41no—
158#104×C53—41no—
159C22⋊C8×C53—21no—
160C22⋊C8×C53—21no—
161#95×C53—21no—
162C24×C53—21no—
163C24×C53#4111yescharacteristic
164#41×C53—21no—
165#41×C53—21no—
166#41×C53—22no—
167#41×C53—22no—
168#41×C53—21no—
169#41×C53—21no—
170#41×C53—21no—
171#41×C53—21no—
172#41×C53—42no—
173#41×C53—42no—
174#41×C53—41no—
175#41×C53—41no—
176#41×C53—42no—
177#41×C53—42no—
178#41×C53#4112yes—
179#41×C53#4112yes—
180C2×Q8×C53—21no—
181C2×Q8×C53—22no—
182C2×Q8×C53—41no—
183C2×Q8×C53C22×C411yescharacteristic
184C2×Q8×C53C22×C411yescharacteristic
185C2×D4×C53—21no—
186C2×D4×C53—22no—
187C2×D4×C53—21no—
188C2×D4×C53—21no—
189C2×D4×C53—21no—
190C2×D4×C53—21no—
191C2×D4×C53—41no—
192C2×D4×C53—42no—
193C2×D4×C53—42no—
194C2×D4×C53C22×C411yescharacteristic
195C2×D4×C53C22×C411yescharacteristic
196C22×C4×C53—21no—
197C22×C4×C53—21no—
198C22×C4×C53—21no—
199C22×C4×C53—21no—
200C22×C4×C53—21no—
201C22×C4×C53—21no—
202C22×C4×C53—21no—
203C22×C4×C53—21no—
204C22×C4×C53—21no—
205C22×C4×C53—21no—
206C22×C4×C53—21no—
207C22×C4×C53—42no—
208C22×C4×C53—42no—
209C22×C4×C53C22×C411yescharacteristic
210C22×C4×C53C22×C411yescharacteristic
211C22×C4×C53C2×D411yescharacteristic
212C22×C4×C53C2×D411yescharacteristic
213C22×C4×C53#4111yescharacteristic
214C22×C4×C53C2411yescharacteristic
215C22×Dic53—21no—
216C22×Dic53—21no—
217M16×C53—21no—
218M16×C53—21no—
219M16×C53—21no—
220M16×C53—21no—
221C2×C8×C53—21no—
222C2×C8×C53—21no—
223C22⋊C4×C53—42no—
224C42×C53—21no—
225C42×C53—21no—
226C42×C53—21no—
227C42×C53—21no—
228C22⋊Dic53—21no—
229C22⋊Dic53—21no—
230C22⋊Dic53—21no—
231C22⋊Dic53—21no—
232C4⋊Dic53—21no—
233C4⋊Dic53—21no—
234C4⋊Dic53C22×C411yescharacteristic
235C4⋊Dic53C22×C411yescharacteristic
236C4⋊Dic53C22×C411yescharacteristic
237C4⋊Dic53C22×C411yescharacteristic
238C4×Dic53—21no—
239C4×Dic53—21no—
240C4×Dic53—21no—
241C4×Dic53—21no—
242#11719917—21no—
243#11719917—21no—
244#11719917—21no—
245#11719917—21no—
246#11719917—41no—
247#11719917—41no—
248#11719917—41no—
249#11719917—41no—
250#11719917—42no—
251#11719917—42no—
252C2×#88322—21no—
253C2×#88322—21no—
254C2×#88322—21no—
255C2×#88322—21no—
256C2×#88322—21no—
257C2×#88322—21no—
258C2×#88322—21no—
259C2×#88322—21no—
260C2×#88322—21no—
261C2×#88322—21no—
262C2×#88322—42no—
263C2×#88322—42no—
264C2×#88322C22×C411yescharacteristic
265C2×#88322C22×C411yescharacteristic
266C2×#88322C22×C411yescharacteristic
267C2×#88322C22×C411yescharacteristic
268C2×#88322C2×D411yescharacteristic
269C2×#88322C2×D411yescharacteristic
270C2×#88322C2×D411yescharacteristic
271C2×#88322C2×D411yescharacteristic
272C23×C53—21no—
273C23×C53—21no—
274C23×C53—21no—
275C23×C53—21no—
276C23×C53—41no—
277C23×C53—41no—
278C23×C53—42no—
279C23×C53—42no—
280C23×C53—81no—
281C23×C53C4×D411yescharacteristic
282C23×C53C4×D411yescharacteristic
283C23×C53C2×#4111yescharacteristic
284Q8×C53—21no—
285Q8×C53—21no—
286Q8×C53—21no—
287Q8×C53—42no—
288Q8×C53#11712yes—
289D4×C53—22no—
290D4×C53—22no—
291D4×C53—21no—
292D4×C53—21no—
293D4×C53—21no—
294D4×C53—42no—
295D4×C53—42no—
296D4×C53—42no—
297D4×C53—41no—
298D4×C53—41no—
299D4×C53#11712yes—
300C2×C4×C53—21no—
301C2×C4×C53—21no—
302C2×C4×C53—21no—
303C2×C4×C53—21no—
304C2×C4×C53—21no—
305C2×C4×C53—21no—
306C2×C4×C53—21no—
307C2×C4×C53—21no—
308C2×C4×C53—21no—
309C2×C4×C53—21no—
310C2×C4×C53—21no—
311C2×C4×C53—22no—
312C2×C4×C53—22no—
313C2×C4×C53—22no—
314C2×C4×C53—21no—
315C2×C4×C53—42no—
316C2×C4×C53—42no—
317C2×C4×C53—42no—
318C2×C4×C53—41no—
319C2×C4×C53—41no—
320C2×C4×C53—41no—
321C2×C4×C53—41no—
322C2×C4×C53—41no—
323C2×C4×C53—41no—
324C2×C4×C53—41no—
325C2×C4×C53C4×D411yescharacteristic
326C2×C4×C53C4×D411yescharacteristic
327C2×C4×C53C23×C411yescharacteristic
328C2×C4×C53C22×D411yescharacteristic
329C2×C4×C53C2×#4111yescharacteristic
330C2×C4×C53C2×#4111yescharacteristic
331C2×C4×C53H(5,𝔽2)11yescharacteristic
332C2×C4×C53H(5,𝔽2)11yescharacteristic
333C2×Dic53—21no—
334C2×Dic53—21no—
335C2×Dic53—21no—
336C2×Dic53—21no—
337C2×Dic53—42no—
338C2×Dic53—81no—
339C8×C53—41no—
340C8×C53—41no—
341#88322—21no—
342#88322—21no—
343#88322—21no—
344#88322—21no—
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—22no—
357C22×C53—21no—
358C22×C53—21no—
359C22×C53—21no—
360C22×C53—21no—
361C22×C53—41no—
362C22×C53—41no—
363C22×C53—41no—
364C22×C53—41no—
365C22×C53—41no—
366C22×C53—81no—
367C22×C53—81no—
368C22×C53—84no—
369C22×C53C2×C4×D411yescharacteristic
370C22×C53#55111yescharacteristic
371C22×C53#55111yescharacteristic
372C4×C53—21no—
373C4×C53—21no—
374C4×C53—22no—
375C4×C53—42no—
376C4×C53—41no—
377C4×C53—81no—
378C4×C53C2×#11711yescharacteristic
379C4×C53#51811yescharacteristic
380C4×C53#54611yescharacteristic
381C4×C53#54611yescharacteristic
382Dic53—41no—
383Dic53—41no—
384Dic53—41no—
385Dic53—41no—
386#2924—531no—
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#1789D5311yescharacteristic
398#1765—531no—
399#1764—531no—
400#1753—531no—
401C2×C53—21no—
402C2×C53—21no—
403C2×C53—41no—
404C2×C53—41no—
405C2×C53—42no—
406C2×C53—81no—
407C2×C53#234211yescharacteristic
408C2×C53#295511yescharacteristic
409C2×C53#295611yescharacteristic
410C22×#41C2×D5311yescharacteristic
411C2×#131—531no—
412C2×#131—531no—
413C22×M16—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#424—531no—
423C2×#104C2×D5311yescharacteristic
424C2×#104C2×D5311yescharacteristic
425C2×#104C2×D5311yescharacteristic
426C2×#104C2×D5311yescharacteristic
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—531no—
447C2×C22⋊C8—1061no—
448#405—531no—
449#405—531no—
450C2×#97—531no—
451C2×C4×C8—531no—
452C4×C22⋊C4C2×D5311yescharacteristic
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—21no—
463C2×#41—21no—
464C2×#41—22no—
465C2×#41—22no—
466C2×#41—41no—
467C2×#41—41no—
468C2×#41C4×D5311yescharacteristic
469C2×#41C4×D5311yescharacteristic
470C2×#41C22×D5311yescharacteristic
471C2×#41C22×D5311yescharacteristic
472C22×Q8C4×D5311yescharacteristic
473C22×D4—21no—
474C22×D4C4×D5311yescharacteristic
475C23×C4—21no—
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—531no—
496C22×C8—531no—
497C22×C8—1061no—
498C22×C8—1061no—
499#117—531no—
500#117—531no—
501#117—531no—
502#117—531no—
503#117—1061no—
504#117—1061no—
505C2×C4⋊C4—531no—
506C2×C4⋊C4—531no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—1061no—
509C2×C42—1061no—
510C2×C42C22×D5311yescharacteristic
511C2×C42C22×D5311yescharacteristic
512#108—2121no—
513#108—2121no—
514C4⋊C8—1061no—
515C4⋊C8—1061no—
516C4⋊C8—1061no—
517C4⋊C8—1061no—
518#104—22no—
519#104—22no—
520#104—41no—
521#104—41no—
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—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—
552#97—2121no—
553C4×C8—1061no—
554C4×C8—1061no—
555C4×C8—2121no—
556#95—21no—
557C24—21no—
558C24#1171994711yescharacteristic
559#41—21no—
560#41—21no—
561#41—22no—
562#41—22no—
563#41—21no—
564#41—21no—
565#41—21no—
566#41—21no—
567#41—42no—
568#41—42no—
569#41—41no—
570#41—41no—
571#41—42no—
572#41—42no—
573#41#1171994712yes—
574#41#1171994712yes—
575C2×Q8—21no—
576C2×Q8—22no—
577C2×Q8—41no—
578C2×Q8C2×C4×D5311yescharacteristic
579C2×Q8C2×C4×D5311yescharacteristic
580C2×D4—21no—
581C2×D4—22no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—41no—
587C2×D4—42no—
588C2×D4—42no—
589C2×D4C2×C4×D5311yescharacteristic
590C2×D4C2×C4×D5311yescharacteristic
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—1061no—
605C22×C4—1061no—
606C22×C4C2×C4×D5311yescharacteristic
607C22×C4C2×C4×D5311yescharacteristic
608C22×C4D4×D5311yescharacteristic
609C22×C4D4×D5311yescharacteristic
610C22×C4#1171994711yescharacteristic
611C22×C4C23×D5311yescharacteristic
612M16—21no—
613M16—21no—
614M16—21no—
615M16—21no—
616M16—1061no—
617M16—1061no—
618M16—1061no—
619M16—1061no—
620M16—2121no—
621M16—2121no—
622M16—2121no—
623M16—2121no—
624M16—2122no—
625M16—2122no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—531no—
629C2×C8—531no—
630C2×C8—531no—
631C2×C8—531no—
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—1061no—
643C2×C8—1061no—
644C2×C8—1061no—
645C2×C8—1061no—
646C2×C8—2122no—
647C2×C8—2122no—
648C4⋊C4—531no—
649C4⋊C4—531no—
650C4⋊C4—531no—
651C4⋊C4—531no—
652C4⋊C4—1061no—
653C4⋊C4—1061no—
654C22⋊C4—42no—
655C22⋊C4—1061no—
656C22⋊C4—1061no—
657C22⋊C4—1061no—
658C22⋊C4—1061no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—21no—
663C42—1061no—
664C42—1061no—
665C42—1061no—
666C42—1061no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—41no—
672C23—41no—
673C23—42no—
674C23—42no—
675C23—81no—
676C23#1313317711yescharacteristic
677C23#1313317711yescharacteristic
678C23C2×#1171994711yescharacteristic
679Q8—21no—
680Q8—21no—
681Q8—21no—
682Q8—42no—
683Q8#1313317312yes—
684D4—22no—
685D4—22no—
686D4—21no—
687D4—21no—
688D4—21no—
689D4—42no—
690D4—42no—
691D4—42no—
692D4—41no—
693D4—41no—
694D4#1313317312yes—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—22no—
709C2×C4—21no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—1061no—
721C2×C4—1061no—
722C2×C4—1061no—
723C2×C4—1061no—
724C2×C4—4241no—
725C2×C4—2122no—
726C2×C4#1313317711yescharacteristic
727C2×C4#1313317711yescharacteristic
728C2×C4C22×C4×D5311yescharacteristic
729C2×C4C2×D4×D5311yescharacteristic
730C2×C4C2×#1171994711yescharacteristic
731C2×C4C2×#1171994711yescharacteristic
732C2×C4#1313326211yescharacteristic
733C2×C4#1313326211yescharacteristic
734C8—41no—
735C8—41no—
736C8—1061no—
737C8—1061no—
738C8—1061no—
739C8—1061no—
740C8—1061no—
741C8—1061no—
742C8—1061no—
743C8—1061no—
744C8—2121no—
745C8—2121no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—22no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—21no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—81no—
761C22—81no—
762C22—84no—
763C22C2×#1313317711yescharacteristic
764C22#1681130411yescharacteristic
765C22#1681130411yescharacteristic
766C4—21no—
767C4—21no—
768C4—22no—
769C4—42no—
770C4—41no—
771C4—81no—
772C4—2121no—
773C4—2121no—
774C4—2121no—
775C4—2121no—
776C4C2×#1313317311yescharacteristic
777C4#1681109611yescharacteristic
778C4#1681126011yescharacteristic
779C4#1681126011yescharacteristic
780C2—21no—
781C2—21no—
782C2—41no—
783C2—41no—
784C2—42no—
785C2—81no—
786C2#2027756611yescharacteristic
787C2#2028361411yescharacteristic
788C2#2028362111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#1789C2
socleC22×C53C2×C4×D4
prime radicalC22×#41×C53C22
cosocleC22×C4×C53C24
hypercenter#1789D53
hypocenterC53#22588
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1789

Complements

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

NH ≅ G/Ntype
1. #20283375C2semidirect
4. #20275423C2semidirect
5. #20275416C2semidirect
6. #20275366C2semidirect
7. #20275366C2semidirect
8. #20274988C2semidirect
9. #20274988C2semidirect
10. #20274815C2semidirect
11. #20274755C2semidirect
12. #20274560C2semidirect
13. #20274553C2semidirect
14. #20274499C2semidirect
24. C2×#13133152C22semidirect
25. C2×#13133152C22semidirect
26. #16810651C22semidirect
27. #16810651C22semidirect
28. #16810632C4semidirect
29. #16810632C4semidirect
30. #16810628C4semidirect
31. #16810628C4semidirect
32. #16810624C4semidirect
33. #16810624C4semidirect
34. #16810624C4semidirect
35. #16810624C4semidirect
48. #16810581C22semidirect
49. #16810581C22semidirect
50. C2×#13133128C22semidirect
51. C2×C4×#88322C22semidirect
52. #16810387C22semidirect
53. #16810387C22semidirect
54. #16810383C22semidirect
55. #16810383C22semidirect
56. #16810383C22semidirect
57. #16810383C22semidirect
58. #16810378C22semidirect
59. #16810378C22semidirect
461. C53#22588semidirect

Maximal subgroups

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

subgroupindex
#202833752
#202832342
#202831642
#202754232
#202754162
#202753662
#202749882
#202748152
#202747552
#202745602
#202745532
#202744992
C53×#17892
#2258853