Finite Group Databasebeta

← #27404435

Subgroups — #27404435

Order 13568.

1174 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810768C211yesmaximal, characteristic
2C2×#16810733C211yesmaximal, characteristic, complemented
3C2×#16810619C211yesmaximal, characteristic, complemented
4#20277751C211yesmaximal, characteristic, complemented
5#20275599C211yesmaximal, characteristic, complemented
6#20275408C211yesmaximal, characteristic, complemented
7#20275346C211yesmaximal, characteristic, complemented
8#20275141C211yesmaximal, characteristic, complemented
9#20275063C211yesmaximal, characteristic, complemented
10#20275052C211yesmaximal, characteristic, complemented
11#20274962C211yesmaximal, characteristic, complemented
12#20274912C211yesmaximal, characteristic, complemented
13#20274540C211yesmaximal, characteristic, complemented
14#20274493C211yesmaximal, characteristic, complemented
15C53×#2339C211yesmaximal, characteristic, complemented
16C22×#11719924C2211yescharacteristic
17C22×#11719922C2211yescharacteristic
18C23×#88322C2211yescharacteristic
19C2×#13133191C2211yescharacteristic
20C2×C4×D212C2211yescharacteristic
21C2×#13133176C2211yescharacteristic
22#16810768C418yescomplemented
23#16810733—24no—
24C2×#13133150C2211yescharacteristic
25C2×#13133148C2211yescharacteristic
26#16810619—24no—
27C2×#13133141C2211yescharacteristic
28C2×#13133141C2211yescharacteristic
29C2×#13133141C2211yescharacteristic
30C2×#13133138C2211yescharacteristic
31C2×#13133138C2211yescharacteristic
32C2×#13133138C2211yescharacteristic
33C2×#13133137C2211yescharacteristic
34C2×#13133137C2211yescharacteristic
35C2×C22⋊#88322C2211yescharacteristic
36C2×#13133128C2211yescharacteristic
37C2×#13133128C2211yescharacteristic
38#16810525C2211yescharacteristic
39#16810523—21no—
40#16810521C2211yescharacteristic
41#16810512—21no—
42#16810499—21no—
43C4×C4⋊Dic53C2211yescharacteristic
44#16810470—21no—
45#16810385C2211yescharacteristic
46#16810385C2211yescharacteristic
47#16810385C2211yescharacteristic
48#16810385C2211yescharacteristic
49#16810378C2211yescharacteristic
50#16810378C2211yescharacteristic
51C22×#41×C53C2211yescharacteristic
52C2×C4×D4×C53C2211yescharacteristic
53C2×C4×D4×C53C2211yescharacteristic
54C53×#391C2211yescharacteristic
55C53×#391C2211yescharacteristic
56C53×#386—21no—
57C53×#386—21no—
58C53×#381—21no—
59C53×#380C2211yescharacteristic
60C4×C22⋊C4×C53C2211yescharacteristic
61C2×#95×C53—21no—
62C22×D212C2311yescharacteristic
63C22×C22⋊D53—21no—
64C22×C4×D53—21no—
65C2×#11719924—41no—
66C2×#11719924—41no—
67C2×#11719924C2×C414yescomplemented
68C2×#11719922—22no—
69C2×#11719922—22no—
70C2×#11719922C2×C414yes—
71C22×#88322—22no—
72C22×#88322—22no—
73C22×#88322—41no—
74C22×#88322C2311yescharacteristic
75C22×#88322C2311yescharacteristic
76C22×#88322C2311yescharacteristic
77C22×#88322C2311yescharacteristic
78#13133191—22no—
79#13133191C2×C414yescomplemented
80C4×D212—22no—
81C4×D212—41no—
82#13133176—22no—
83#13133176—41no—
84C2×C4⋊Dic53C2311yescharacteristic
85C2×C4⋊Dic53C2311yescharacteristic
86C2×C4⋊Dic53C2311yescharacteristic
87C2×#11719919—21no—
88C2×C22⋊Dic53—21no—
89C2×#11719921—21no—
90C2×#11719921—21no—
91C2×#11719921—21no—
92C2×#11719921—21no—
93C2×C4×Dic53—21no—
94C2×C4×Dic53—21no—
95#13133150—41no—
96#13133148—22no—
97#13133141—22no—
98#13133141—22no—
99#13133141C2×C414yescomplemented
100#13133138—22no—
101#13133138C2×C414yescomplemented
102#13133138D414yescomplemented
103#13133137—22no—
104#13133137—41no—
105C22⋊#88322C2×C414yescomplemented
106#13133128—22no—
107#13133128—41no—
108#13133124—21no—
109#13133124—21no—
110C2×#41×C53—22no—
111C2×#41×C53—22no—
112C2×#41×C53—22no—
113C2×#41×C53—41no—
114C2×#41×C53—41no—
115C2×#41×C53C2×C414yescomplemented
116C22×Q8×C53C2311yescharacteristic
117C22×D4×C53—21no—
118C22×D4×C53C2311yescharacteristic
119C23×C4×C53—21no—
120C23×C4×C53—21no—
121C23×C4×C53—21no—
122C23×C4×C53C2311yescharacteristic
123C4×D4×C53—22no—
124C4×D4×C53—22no—
125C4×D4×C53—41no—
126C4×D4×C53—41no—
127C2×C4⋊C4×C53C2311yescharacteristic
128C2×C4⋊C4×C53C2311yescharacteristic
129C2×C22⋊C4×C53—21no—
130C2×C22⋊C4×C53—21no—
131C2×C22⋊C4×C53—21no—
132C2×C22⋊C4×C53D411yescharacteristic
133C2×C22⋊C4×C53D411yescharacteristic
134C2×C42×C53C2311yescharacteristic
135C2×C42×C53C2311yescharacteristic
136#95×C53—21no—
137#95×C53—21no—
138#95×C53—21no—
139#95×C53—21no—
140#95×C53—21no—
141#95×C53D411yescharacteristic
142#95×C53D411yescharacteristic
143C24×C53—21no—
144C24×C53C2×D411yescharacteristic
145C23×D53—21no—
146#41×C53—28no—
147#41×C53—44no—
148#41×C53—44no—
149#41×C53—44no—
150C2×Q8×C53—21no—
151C2×Q8×C53—21no—
152C2×Q8×C53—21no—
153C2×Q8×C53—21no—
154C2×Q8×C53—21no—
155C2×Q8×C53C22×C412yes—
156C2×D4×C53—24no—
157C2×D4×C53—21no—
158C2×D4×C53—21no—
159C2×D4×C53—21no—
160C2×D4×C53—42no—
161C2×D4×C53—42no—
162C2×D4×C53C22×C412yes—
163C2×D4×C53C2×D412yes—
164C2×D4×C53#4112yes—
165C22×C4×C53—21no—
166C22×C4×C53—21no—
167C22×C4×C53—21no—
168C22×C4×C53—21no—
169C22×C4×C53—21no—
170C22×C4×C53—24no—
171C22×C4×C53—21no—
172C22×C4×C53—21no—
173C22×C4×C53—42no—
174C22×C4×C53—42no—
175C22×C4×C53—42no—
176C22×C4×C53—42no—
177C22×C4×C53—42no—
178C22×C4×C53—42no—
179C22×C4×C53—81no—
180C22×C4×C53—81no—
181C22×C4×C53C22×C412yes—
182C22×C4×C53C2×D411yescharacteristic
183C22×C4×C53C2×D411yescharacteristic
184C22×C4×C53C2×D411yescharacteristic
185C22×C4×C53C2×D411yescharacteristic
186C22×C4×C53C2×D411yescharacteristic
187C22×C4×C53#4112yes—
188C22×C4×C53C2411yescharacteristic
189C2×C22⋊D53—24no—
190C2×C22⋊D53—81no—
191C2×C22⋊D53—81no—
192C22×Dic53—21no—
193C22×Dic53—21no—
194C22×Dic53—21no—
195C2×D212—21no—
196C2×D212—21no—
197C2×D212—21no—
198C2×D212—21no—
199C2×D212—21no—
200C2×D212C22×C412yes—
201C2×C4×D53—42no—
202C2×C4×D53—42no—
203C2×C4×D53—81no—
204C4⋊C4×C53—21no—
205C4⋊C4×C53—21no—
206C4⋊C4×C53—21no—
207C4⋊C4×C53—21no—
208C22⋊C4×C53—41no—
209C22⋊C4×C53—41no—
210C22⋊C4×C53—42no—
211C22⋊C4×C53—42no—
212C22⋊C4×C53—81no—
213C42×C53—21no—
214C42×C53—21no—
215C42×C53—21no—
216C42×C53—21no—
217C22⋊Dic53—42no—
218#11719924—44no—
219#11719922—28no—
220#11719921—24no—
221#11719921—42no—
222#11719921—42no—
223#11719921—81no—
224C4⋊Dic53—21no—
225C4⋊Dic53—21no—
226C4⋊Dic53—21no—
227C4⋊Dic53—21no—
228C4⋊Dic53C22×C412yes—
229C4⋊Dic53C2×D412yes—
230#11719919—81no—
231C4×Dic53—42no—
232C4×Dic53—81no—
233C2×#88322—21no—
234C2×#88322—21no—
235C2×#88322—21no—
236C2×#88322—21no—
237C2×#88322—21no—
238C2×#88322—21no—
239C2×#88322—21no—
240C2×#88322—21no—
241C2×#88322—21no—
242C2×#88322—44no—
243C2×#88322C22×C412yes—
244C2×#88322C22×C412yes—
245C2×#88322C2×D412yes—
246C23×C53—22no—
247C23×C53—21no—
248C23×C53—22no—
249C23×C53—21no—
250C23×C53—22no—
251C23×C53—21no—
252C23×C53—21no—
253C23×C53—21no—
254C23×C53—21no—
255C23×C53—41no—
256C23×C53—41no—
257C23×C53—41no—
258C23×C53—41no—
259C23×C53C4×D412yes—
260C23×C53C22×D411yescharacteristic
261C22×D53—22no—
262C22×D53—41no—
263C22×D53—41no—
264C22×D53—41no—
265C22×D53—41no—
266C22×D53—41no—
267C22×D53—41no—
268Q8×C53—22no—
269Q8×C53—22no—
270Q8×C53—41no—
271Q8×C53—41no—
272D4×C53—22no—
273D4×C53—22no—
274D4×C53—22no—
275D4×C53—48no—
276D4×C53C4×D414yes—
277C2×C4×C53—21no—
278C2×C4×C53—21no—
279C2×C4×C53—22no—
280C2×C4×C53—22no—
281C2×C4×C53—22no—
282C2×C4×C53—22no—
283C2×C4×C53—22no—
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—48no—
297C2×C4×C53—41no—
298C2×C4×C53—41no—
299C2×C4×C53—41no—
300C2×C4×C53—41no—
301C2×C4×C53—41no—
302C2×C4×C53—41no—
303C2×C4×C53—41no—
304C2×C4×C53—41no—
305C2×C4×C53—84no—
306C2×C4×C53—84no—
307C2×C4×C53C4×D412yes—
308C2×C4×C53C23×C411yescharacteristic
309C2×C4×C53C22×D411yescharacteristic
310C2×C4×C53C2×#4111yescharacteristic
311C2×C4×C53C2×#4111yescharacteristic
312C2×C4×C53H(5,𝔽2)11yescharacteristic
313C2×C4×C53H(5,𝔽2)11yescharacteristic
314C22⋊D53—84no—
315C2×Dic53—22no—
316C2×Dic53—22no—
317C2×Dic53—41no—
318C2×Dic53—41no—
319C2×Dic53—41no—
320C2×Dic53—41no—
321C2×Dic53—41no—
322C2×Dic53—41no—
323C2×Dic53—41no—
324D212—22no—
325D212—22no—
326D212—41no—
327D212—41no—
328C4×D53—84no—
329#88322—22no—
330#88322—22no—
331#88322—22no—
332#88322—41no—
333#22860—531nomaximal, Sylow
334C22×C53—22no—
335C22×C53—24no—
336C22×C53—22no—
337C22×C53—22no—
338C22×C53—42no—
339C22×C53—42no—
340C22×C53—41no—
341C22×C53—42no—
342C22×C53—42no—
343C22×C53—41no—
344C22×C53—41no—
345C22×C53—42no—
346C22×C53—42no—
347C22×C53—41no—
348C22×C53C2×C4×D411yescharacteristic
349C22×C53D4211yescharacteristic
350C22×C53#54611yescharacteristic
351C22×C53#57511yescharacteristic
352C22×C53#57511yescharacteristic
353C22×C53#57611yescharacteristic
354C22×C53#57711yescharacteristic
355C2×D53—42no—
356C2×D53—42no—
357C2×D53—42no—
358C2×D53—81no—
359C2×D53—81no—
360C2×D53—81no—
361C2×D53—81no—
362C4×C53—22no—
363C4×C53—42no—
364C4×C53—41no—
365C4×C53—41no—
366C4×C53—41no—
367C4×C53—41no—
368C4×C53—81no—
369C4×C53—81no—
370C4×C53C2×C4×D411yescharacteristic
371C4×C53#51811yescharacteristic
372C4×C53#54611yescharacteristic
373C4×C53#55111yescharacteristic
374Dic53—42no—
375Dic53—42no—
376Dic53—81no—
377C2×#449—531no—
378C2×#442—531no—
379C2×#416—531no—
380#2363—531no—
381#2339D5311yescharacteristic, complemented
382#1973—531no—
383#1935—531no—
384#1927—531no—
385#1893—531no—
386#1879—531no—
387#1877—531no—
388#1862—531no—
389#1854—531no—
390#1762—531no—
391#1752—531no—
392C2×C53—42no—
393C2×C53—44no—
394C2×C53#235811yescharacteristic
395C2×C53#294311yescharacteristic
396C2×C53#294611yescharacteristic
397C2×C53#326711yescharacteristic
398C2×C53#326811yescharacteristic
399C2×C53#330711yescharacteristic
400C2×C53#331911yescharacteristic
401D53—82no—
402C22×#41C2×D5311yescharacteristic
403C22×SD16—531no—
404C22×D8—531no—
405C23×C8—531no—
406C2×#121—531no—
407C2×C4×D4—531no—
408C2×C4×D4C2×D5311yescharacteristic
409C2×C4×D4C2×D5311yescharacteristic
410C2×#117—531no—
411#449—538no—
412#442—1064no—
413C2×#107—531no—
414C2×#106—531no—
415#416—1064no—
416C2×#103—531no—
417C2×#103—531no—
418C2×#103—531no—
419C2×#102—531no—
420C2×#102—531no—
421C2×#102—531no—
422C2×#102—531no—
423C2×#102—531no—
424C2×C22⋊C8—531no—
425C2×#97—531no—
426C2×#97—531no—
427#391C2×D5311yescharacteristic
428#391C2×D5311yescharacteristic
429#390—531no—
430#390—1061no—
431#389—531no—
432#388—1061no—
433#386—21no—
434#386—21no—
435#386—1061no—
436#381—21no—
437#380C2×D5311yescharacteristic
438C4×C4⋊C4—531no—
439C4×C22⋊C4—1061no—
440C4×C22⋊C4C2×D5311yescharacteristic
441C2×#95—21no—
442#340—531no—
443#340—531no—
444#340—531no—
445#340—531no—
446#336—531no—
447#336—531no—
448C53#2286011yescharacteristic, complemented, Sylow
449C2×#41—22no—
450C2×#41—22no—
451C2×#41—22no—
452C2×#41—41no—
453C2×#41—41no—
454C2×#41C4×D5314yescomplemented
455C22×Q8C22×D5311yescharacteristic
456C22×D4—21no—
457C22×D4—531no—
458C22×D4—1061no—
459C22×D4C22×D5311yescharacteristic
460C23×C4—21no—
461C23×C4—21no—
462C23×C4—21no—
463C23×C4—1061no—
464C23×C4C22×D5311yescharacteristic
465C2×SD16—534no—
466C2×SD16—2121no—
467C2×SD16—2121no—
468C2×D8—534no—
469C2×D8—1062no—
470C2×D8—1062no—
471C22×C8—531no—
472C22×C8—531no—
473C22×C8—531no—
474C22×C8—531no—
475C22×C8—1062no—
476C22×C8—1062no—
477C22×C8—2121no—
478#121—534no—
479#121—1062no—
480C4×D4—22no—
481C4×D4—22no—
482C4×D4—41no—
483C4×D4—41no—
484C4×D4—1062no—
485C4×D4—2121no—
486#117—1062no—
487#117—2121no—
488C2×C4⋊C4—531no—
489C2×C4⋊C4—531no—
490C2×C4⋊C4—531no—
491C2×C4⋊C4—1061no—
492C2×C4⋊C4C22×D5311yescharacteristic
493C2×C4⋊C4C22×D5311yescharacteristic
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—1061no—
498C2×C22⋊C4—1061no—
499C2×C22⋊C4—1061no—
500C2×C22⋊C4—1061no—
501C2×C22⋊C4—1061no—
502C2×C22⋊C4C22⋊D5311yescharacteristic
503C2×C22⋊C4C22⋊D5311yescharacteristic
504C2×C42—1061no—
505C2×C42—1061no—
506C2×C42C22×D5311yescharacteristic
507C2×C42C22×D5311yescharacteristic
508#107—2121no—
509#106—1062no—
510#103—534no—
511#103—1062no—
512#103—1062no—
513#102—534no—
514#102—534no—
515#102—1062no—
516#102—1062no—
517#102—2121no—
518C22⋊C8—534no—
519#97—1062no—
520#97—2121no—
521#95—21no—
522#95—21no—
523#95—21no—
524#95—21no—
525#95—21no—
526#95—1061no—
527#95—1061no—
528#95C22⋊D5311yescharacteristic
529#95C22⋊D5311yescharacteristic
530C24—21no—
531C24—1061no—
532C24C2×C22⋊D5311yescharacteristic
533#41—28no—
534#41—44no—
535#41—44no—
536#41—44no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8C2×C4×D5312yes—
543C2×D4—24no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—42no—
548C2×D4—42no—
549C2×D4—532no—
550C2×D4—1064no—
551C2×D4—1061no—
552C2×D4—1061no—
553C2×D4—1061no—
554C2×D4—1061no—
555C2×D4—1061no—
556C2×D4—4241no—
557C2×D4—4241no—
558C2×D4C2×C4×D5312yes—
559C2×D4D4×D5312yes—
560C2×D4#1171994712yes—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—24no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—81no—
576C22×C4—81no—
577C22×C4—1061no—
578C22×C4—1061no—
579C22×C4—1061no—
580C22×C4—4241no—
581C22×C4—2122no—
582C22×C4—2122no—
583C22×C4C2×C4×D5312yes—
584C22×C4#1171994512yes—
585C22×C4C2×C22⋊D5311yescharacteristic
586C22×C4C2×C22⋊D5311yescharacteristic
587C22×C4C2×C22⋊D5311yescharacteristic
588C22×C4C2×C22⋊D5311yescharacteristic
589C22×C4C2×C22⋊D5311yescharacteristic
590C22×C4C23×D5311yescharacteristic
591SD16—2124no—
592D8—1068no—
593C2×C8—532no—
594C2×C8—532no—
595C2×C8—532no—
596C2×C8—1061no—
597C2×C8—1061no—
598C2×C8—1061no—
599C2×C8—1061no—
600C2×C8—1061no—
601C2×C8—1061no—
602C2×C8—1061no—
603C2×C8—1061no—
604C2×C8—1061no—
605C2×C8—2124no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—532no—
611C4⋊C4—532no—
612C4⋊C4—1061no—
613C4⋊C4—1061no—
614C4⋊C4—1061no—
615C4⋊C4—1061no—
616C4⋊C4—4241no—
617C22⋊C4—41no—
618C22⋊C4—41no—
619C22⋊C4—42no—
620C22⋊C4—42no—
621C22⋊C4—81no—
622C22⋊C4—1064no—
623C22⋊C4—4241no—
624C22⋊C4—2122no—
625C22⋊C4—2122no—
626C22⋊C4—2122no—
627C42—21no—
628C42—21no—
629C42—21no—
630C42—21no—
631C42—4241no—
632C42—2122no—
633C23—22no—
634C23—21no—
635C23—22no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—22no—
641C23—21no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—1062no—
647C23—2121no—
648C23—2121no—
649C23—2121no—
650C23—2121no—
651C23—2121no—
652C23—2121no—
653C23C4×C22⋊D5312yes—
654C23C22×C22⋊D5311yescharacteristic
655Q8—22no—
656Q8—22no—
657Q8—41no—
658Q8—41no—
659D4—22no—
660D4—22no—
661D4—22no—
662D4—48no—
663D4—1062no—
664D4—1062no—
665D4—4244no—
666D4—2121no—
667D4—2121no—
668D4#1313317714yes—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—22no—
678C2×C4—21no—
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—48no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—84no—
698C2×C4—84no—
699C2×C4—1062no—
700C2×C4—1062no—
701C2×C4—4244no—
702C2×C4—2121no—
703C2×C4—2121no—
704C2×C4—2121no—
705C2×C4—2121no—
706C2×C4—2121no—
707C2×C4—2121no—
708C2×C4—2121no—
709C2×C4C4×C22⋊D5312yes—
710C2×C4C22×C4×D5311yescharacteristic
711C2×C4C2×D4×D5311yescharacteristic
712C2×C4C2×#1171994711yescharacteristic
713C2×C4C2×#1171994511yescharacteristic
714C2×C4#1313326211yescharacteristic
715C2×C4#1313326211yescharacteristic
716C8—1062no—
717C8—1062no—
718C8—1062no—
719C8—2121no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—24no—
724C22—41no—
725C22—42no—
726C22—42no—
727C22—41no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22—41no—
732C22—41no—
733C22—42no—
734C22—4241no—
735C22—4241no—
736C22—4241no—
737C22—4241no—
738C22—2122no—
739C22—2122no—
740C22—2122no—
741C22C2×C4×C22⋊D5311yescharacteristic
742C22D4×C22⋊D5311yescharacteristic
743C22#1681126711yescharacteristic
744C22#1681142111yescharacteristic
745C22#1681142111yescharacteristic
746C22#1681142611yescharacteristic
747C22#1681143111yescharacteristic
748C4—22no—
749C4—41no—
750C4—41no—
751C4—41no—
752C4—42no—
753C4—41no—
754C4—81no—
755C4—81no—
756C4—4241no—
757C4—2122no—
758C4—2122no—
759C4C2×#1313317711yescharacteristic
760C4#1681109611yescharacteristic
761C4#1681126311yescharacteristic
762C4#1681129911yescharacteristic
763C2—42no—
764C2—44no—
765C2—4242no—
766C2#2027769411yescharacteristic
767C2#2028351311yescharacteristic
768C2#2028354311yescharacteristic
769C2#2028624111yescharacteristic
770C2#2028625111yescharacteristic
771C2#2028669111yescharacteristic
772C2#2028687111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#2339C2
socleC23×C53C22×D4
prime radicalC2×#16810768C2
cosocleC22×C4×C53C24
hypercenter#2339D53
hypocenterC53#22860
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2339

Complements

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

NH ≅ G/Ntype
2. C2×#16810733C2semidirect
3. C2×#16810619C2semidirect
4. #20277751C2semidirect
5. #20275599C2semidirect
6. #20275408C2semidirect
7. #20275346C2semidirect
8. #20275141C2semidirect
9. #20275063C2semidirect
10. #20275052C2semidirect
11. #20274962C2semidirect
12. #20274912C2semidirect
13. #20274540C2semidirect
14. #20274493C2semidirect
15. C53×#2339C2semidirect
22. #16810768C4semidirect
67. C2×#11719924C2×C4semidirect
79. #13133191C2×C4semidirect
99. #13133141C2×C4semidirect
101. #13133138C2×C4semidirect
102. #13133138D4semidirect
105. C22⋊#88322C2×C4semidirect
115. C2×#41×C53C2×C4semidirect
381. #2339D53semidirect
448. C53#22860semidirect
454. C2×#41C4×D53semidirect

Maximal subgroups

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

subgroupindex
C2×#168107682
C2×#168107332
C2×#168106192
#202777512
#202755992
#202754082
#202753462
#202751412
#202750632
#202750522
#202749622
#202749122
#202745402
#202744932
C53×#23392
#2286053