Finite Group Databasebeta

← #27399581

Subgroups — #27399581

Order 13568.

1478 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811278C211yesmaximal, characteristic
2C2×#16810695C211yesmaximal, characteristic, complemented
3C2×#16810622C211yesmaximal, characteristic, complemented
4C2×#16810617C211yesmaximal, characteristic, complemented
5#20275638C211yesmaximal, characteristic, complemented
6#20275534C211yesmaximal, characteristic, complemented
7#20275146C211yesmaximal, characteristic, complemented
8#20275136C211yesmaximal, characteristic, complemented
9#20275027C211yesmaximal, characteristic, complemented
10#20275022C211yesmaximal, characteristic, complemented
11#20274722C211yesmaximal, characteristic, complemented
12#20274653C211yesmaximal, characteristic, complemented
13#20274653C211yesmaximal, characteristic, complemented
14#20274543C211yesmaximal, characteristic, complemented
15C53×#2352C211yesmaximal, characteristic, complemented
16C22×#11719945C2211yescharacteristic
17C22×#11719945C2211yescharacteristic
18C22×#11719917C2211yescharacteristic
19C23×#88322C2211yescharacteristic
20#16811278—24no—
21#16811278C418yescomplemented
22C2×#13133217C2211yescharacteristic
23C2×#13133199—21no—
24C2×#13133199—21no—
25C2×#13133196C2211yescharacteristic
26C2×#13133196C2211yescharacteristic
27C2×#13133188—21no—
28C2×C4×D212C2211yescharacteristic
29C2×C4⋊C4×D53—21no—
30#16810695—24no—
31C2×C4⋊#88322C2211yescharacteristic
32#16810622—24no—
33#16810617—24no—
34C2×#13133140C2211yescharacteristic
35C2×#13133140C2211yescharacteristic
36C2×#13133140C2211yescharacteristic
37C2×#13133140C2211yescharacteristic
38C2×#13133140C2211yescharacteristic
39C2×#13133140C2211yescharacteristic
40C2×#13133140C2211yescharacteristic
41C2×#13133140C2211yescharacteristic
42C2×#13133137C2211yescharacteristic
43C2×#13133137C2211yescharacteristic
44C2×#13133137C2211yescharacteristic
45C2×#13133137C2211yescharacteristic
46C2×C22⋊#88322C2211yescharacteristic
47C2×C22⋊#88322C2211yescharacteristic
48C2×#13133128C2211yescharacteristic
49#16810385C2211yescharacteristic
50#16810385C2211yescharacteristic
51#16810385C2211yescharacteristic
52#16810385C2211yescharacteristic
53C2×C4×D4×C53C2211yescharacteristic
54C2×#117×C53C2211yescharacteristic
55C22×C4⋊C4×C53C2211yescharacteristic
56C53×#388—21no—
57C53×#387—21no—
58C53×#386—21no—
59C53×#382C2211yescharacteristic
60C53×#380C2211yescharacteristic
61C53×#380C2211yescharacteristic
62C4×C4⋊C4×C53C2211yescharacteristic
63C4×C22⋊C4×C53—21no—
64C2×#11719945—22no—
65C2×#11719945—22no—
66C2×#11719945—22no—
67C2×#11719945—22no—
68C2×#11719945—22no—
69C2×#11719945—22no—
70C2×#11719945—41no—
71C2×#11719945—41no—
72C2×#11719945—41no—
73C2×#11719945—41no—
74C2×#11719945C2×C414yes—
75C2×#11719945C2×C414yescomplemented
76C22×Dic106C2311yescharacteristic
77C22×Dic106C2311yescharacteristic
78C22×D212C2311yescharacteristic
79C22×C22⋊D53—21no—
80C22×C22⋊D53—21no—
81C22×C4×D53—21no—
82C22×C4×D53—21no—
83C22×C4×D53—21no—
84C2×#11719917—22no—
85C2×#11719917—22no—
86C2×#11719917—41no—
87C22×#88322—22no—
88C22×#88322—22no—
89C22×#88322—41no—
90C22×#88322C2311yescharacteristic
91C22×#88322C2311yescharacteristic
92C22×#88322C2311yescharacteristic
93C22×#88322C2311yescharacteristic
94#13133217—22no—
95#13133217C2×C414yescomplemented
96#13133199—28no—
97#13133199—28no—
98#13133196—22no—
99#13133196—22no—
100#13133196C2×C414yes—
101#13133196C2×C414yescomplemented
102#13133188—28no—
103C4×D212—22no—
104C4×D212C2×C414yescomplemented
105C2×C4⋊Dic53—21no—
106C2×C4⋊Dic53—21no—
107C2×C4⋊Dic53C2311yescharacteristic
108C2×#11719919—21no—
109C2×#11719919—21no—
110C4⋊C4×D53—28no—
111C2×C22⋊Dic53—21no—
112C2×C22⋊Dic53—21no—
113C2×#11719921—21no—
114C4⋊#88322—22no—
115#13133140—22no—
116#13133140—22no—
117#13133140—22no—
118#13133140—22no—
119#13133140—41no—
120#13133140—41no—
121#13133140—41no—
122#13133140—41no—
123#13133137—22no—
124#13133137—22no—
125#13133137—22no—
126#13133137D414yescomplemented
127C22⋊#88322—22no—
128C22⋊#88322—22no—
129#13133128—22no—
130C22×D4×C53D411yescharacteristic
131C23×C4×C53—21no—
132C23×C4×C53C2311yescharacteristic
133C23×C4×C53C2311yescharacteristic
134C4×D4×C53C2×C414yes—
135C4×D4×C53D414yes—
136#117×C53—22no—
137#117×C53—41no—
138C2×C4⋊C4×C53—21no—
139C2×C4⋊C4×C53—22no—
140C2×C4⋊C4×C53—41no—
141C2×C4⋊C4×C53D411yescharacteristic
142C2×C4⋊C4×C53C2311yescharacteristic
143C2×C4⋊C4×C53C2311yescharacteristic
144C2×C4⋊C4×C53C2311yescharacteristic
145C2×C4⋊C4×C53C2311yescharacteristic
146C2×C22⋊C4×C53—21no—
147C2×C22⋊C4×C53—21no—
148C2×C22⋊C4×C53—21no—
149C2×C22⋊C4×C53D411yescharacteristic
150C2×C22⋊C4×C53D411yescharacteristic
151C2×C42×C53—21no—
152C2×C42×C53—21no—
153C2×C42×C53C2311yescharacteristic
154#95×C53—21no—
155#95×C53—21no—
156#95×C53—21no—
157#95×C53—21no—
158#95×C53—21no—
159C24×C53C2×D411yescharacteristic
160C24×C53C2×D411yescharacteristic
161C23×D53—21no—
162C2×D4×C53—41no—
163C2×D4×C53—41no—
164C2×D4×C53C22⋊C414yes—
165C22×C4×C53—21no—
166C22×C4×C53—21no—
167C22×C4×C53—21no—
168C22×C4×C53—21no—
169C22×C4×C53—21no—
170C22×C4×C53—21no—
171C22×C4×C53—21no—
172C22×C4×C53—21no—
173C22×C4×C53—21no—
174C22×C4×C53—21no—
175C22×C4×C53—21no—
176C22×C4×C53—21no—
177C22×C4×C53—42no—
178C22×C4×C53—42no—
179C22×C4×C53—81no—
180C22×C4×C53C22×C412yes—
181C22×C4×C53C22×C412yes—
182C22×C4×C53C2×D411yescharacteristic
183C22×C4×C53C2×D411yescharacteristic
184C22×C4×C53C2×D411yescharacteristic
185C22×C4×C53C2×D411yescharacteristic
186C22×C4×C53C2×D412yes—
187C22×C4×C53C2×D412yes—
188C22×C4×C53C2411yescharacteristic
189C2×C22⋊D53—24no—
190C2×C22⋊D53—24no—
191C2×C22⋊D53—42no—
192C2×C22⋊D53—42no—
193C2×C22⋊D53—42no—
194C2×C22⋊D53—42no—
195C22×Dic53—21no—
196C22×Dic53—21no—
197C22×Dic53—21no—
198#11719945—28no—
199#11719945—28no—
200#11719945—44no—
201#11719945—44no—
202#11719945—44no—
203#11719945—44no—
204#11719945—44no—
205#11719945—44no—
206C2×D212—21no—
207C2×D212—21no—
208C2×D212—21no—
209C2×D212C22×C412yes—
210C2×D212C2×D412yes—
211C2×D212#4112yes—
212C2×C4×D53—24no—
213C2×C4×D53—24no—
214C2×C4×D53—24no—
215C2×C4×D53—42no—
216C2×C4×D53—42no—
217C2×C4×D53—42no—
218C2×C4×D53—42no—
219C2×C4×D53—42no—
220C2×C4×D53—42no—
221C2×Dic106—21no—
222C2×Dic106—21no—
223C2×Dic106—21no—
224C2×Dic106—21no—
225C2×Dic106—21no—
226C2×Dic106—21no—
227C2×Dic106—21no—
228C2×Dic106—21no—
229C2×Dic106—21no—
230C2×Dic106—21no—
231C2×Dic106C22×C412yes—
232C2×Dic106C22×C412yes—
233C4⋊C4×C53—21no—
234C4⋊C4×C53—21no—
235C4⋊C4×C53—21no—
236C4⋊C4×C53—21no—
237C4⋊C4×C53—21no—
238C4⋊C4×C53—21no—
239C4⋊C4×C53—21no—
240C4⋊C4×C53—42no—
241C4⋊C4×C53C22⋊C414yes—
242C4⋊C4×C53C2×D412yes—
243C22⋊C4×C53—42no—
244C22⋊C4×C53—42no—
245C22⋊C4×C53—81no—
246C22⋊C4×C53C22⋊C414yes—
247C22⋊C4×C53C22⋊C414yes—
248C42×C53—42no—
249C42×C53—81no—
250C42×C53C22×C412yes—
251C42×C53C2×D412yes—
252C22⋊Dic53—24no—
253C22⋊Dic53—24no—
254#11719921—24no—
255C4⋊Dic53—24no—
256C4⋊Dic53—24no—
257C4⋊Dic53—21no—
258C4⋊Dic53C22×C412yes—
259#11719919—24no—
260#11719919—24no—
261#11719917—44no—
262C2×#88322—21no—
263C2×#88322—21no—
264C2×#88322—21no—
265C2×#88322—21no—
266C2×#88322—21no—
267C2×#88322—21no—
268C2×#88322—21no—
269C2×#88322—21no—
270C2×#88322—21no—
271C2×#88322—21no—
272C2×#88322—21no—
273C2×#88322—44no—
274C2×#88322C2×D412yes—
275C23×C53—21no—
276C23×C53—21no—
277C23×C53—21no—
278C23×C53—21no—
279C23×C53—21no—
280C23×C53—21no—
281C23×C53—21no—
282C23×C53—21no—
283C23×C53—21no—
284C23×C53—21no—
285C23×C53—21no—
286C23×C53—21no—
287C23×C53C2×C22⋊C412yes—
288C23×C53C2×C22⋊C412yes—
289C23×C53C22×D411yescharacteristic
290C22×D53—22no—
291C22×D53—22no—
292C22×D53—22no—
293C22×D53—41no—
294C22×D53—41no—
295C22×D53—41no—
296C22×D53—41no—
297D4×C53—44no—
298C2×C4×C53—21no—
299C2×C4×C53—21no—
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—22no—
307C2×C4×C53—22no—
308C2×C4×C53—22no—
309C2×C4×C53—22no—
310C2×C4×C53—22no—
311C2×C4×C53—22no—
312C2×C4×C53—22no—
313C2×C4×C53—22no—
314C2×C4×C53—22no—
315C2×C4×C53—41no—
316C2×C4×C53—41no—
317C2×C4×C53—41no—
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×C53—41no—
326C2×C4×C53—84no—
327C2×C4×C53C2×C22⋊C412yes—
328C2×C4×C53C2×C22⋊C412yes—
329C2×C4×C53C2×C22⋊C412yes—
330C2×C4×C53C2×C22⋊C412yes—
331C2×C4×C53C23×C411yescharacteristic
332C2×C4×C53C22×D411yescharacteristic
333C2×C4×C53C22×D411yescharacteristic
334C2×C4×C53C2×#4111yescharacteristic
335C2×C4×C53H(5,𝔽2)11yescharacteristic
336C2×C4×C53H(5,𝔽2)11yescharacteristic
337C22⋊D53—48no—
338C22⋊D53—48no—
339C2×Dic53—22no—
340C2×Dic53—22no—
341C2×Dic53—22no—
342C2×Dic53—41no—
343C2×Dic53—41no—
344C2×Dic53—41no—
345C2×Dic53—41no—
346C2×Dic53—41no—
347C2×Dic53—41no—
348D212—22no—
349D212—22no—
350D212—22no—
351D212C4×D414yes—
352C4×D53—48no—
353C4×D53—48no—
354C4×D53—48no—
355Dic106—22no—
356Dic106—22no—
357Dic106—22no—
358Dic106—22no—
359Dic106—41no—
360Dic106—41no—
361Dic106—41no—
362Dic106—41no—
363#88322—22no—
364#88322—41no—
365#88322—41no—
366#88322—41no—
367#22420—531nomaximal, Sylow
368C22×C53—22no—
369C22×C53—22no—
370C22×C53—22no—
371C22×C53—22no—
372C22×C53—22no—
373C22×C53—22no—
374C22×C53—41no—
375C22×C53—41no—
376C22×C53—41no—
377C22×C53—41no—
378C22×C53—41no—
379C22×C53—41no—
380C22×C53—41no—
381C22×C53—41no—
382C22×C53C22×C22⋊C411yescharacteristic
383C22×C53D4211yescharacteristic
384C22×C53#54611yescharacteristic
385C22×C53#57511yescharacteristic
386C22×C53#57511yescharacteristic
387C22×C53#57711yescharacteristic
388C22×C53#57811yescharacteristic
389C2×D53—24no—
390C2×D53—42no—
391C2×D53—42no—
392C2×D53—42no—
393C2×D53—42no—
394C2×D53—42no—
395C2×D53—42no—
396C4×C53—22no—
397C4×C53—22no—
398C4×C53—22no—
399C4×C53—22no—
400C4×C53—42no—
401C4×C53—81no—
402C4×C53—81no—
403C4×C53—81no—
404C4×C53C2×C4×D411yescharacteristic
405C4×C53#51811yescharacteristic
406C4×C53D4211yescharacteristic
407C4×C53#54611yescharacteristic
408Dic53—42no—
409Dic53—42no—
410Dic53—42no—
411C2×#547—531no—
412C2×#435—531no—
413C2×#417—531no—
414C2×#416—531no—
415#2352D5311yescharacteristic, complemented
416#1981—531no—
417#1960—531no—
418#1894—531no—
419#1892—531no—
420#1873—531no—
421#1872—531no—
422#1804—531no—
423#1788—531no—
424#1788—531no—
425#1762—531no—
426C2×C53—42no—
427C2×C53—42no—
428C2×C53D4×C22⋊C411yescharacteristic
429C2×C53#289611yescharacteristic
430C2×C53#289811yescharacteristic
431C2×C53#326711yescharacteristic
432C2×C53#326911yescharacteristic
433C2×C53#330711yescharacteristic
434C2×C53#331511yescharacteristic
435D53—44no—
436C22×#41—531no—
437C22×#41—531no—
438C22×M16—531no—
439C23×C8—531no—
440#547—538no—
441#547—1064no—
442C2×C4⋊Q8—531no—
443C2×#123—1061no—
444C2×#123—1061no—
445C2×C22⋊Q8—531no—
446C2×C22⋊Q8—531no—
447C2×#121—1061no—
448C2×C4×D4—531no—
449C2×C4×D4C2×D5311yescharacteristic
450C2×#117C2×D5311yescharacteristic
451C22×C4⋊C4—1061no—
452C22×C4⋊C4C2×D5311yescharacteristic
453#435—1064no—
454C2×C4⋊C8—531no—
455#417—1064no—
456#416—1064no—
457C2×#103—531no—
458C2×#103—531no—
459C2×#103—531no—
460C2×#103—531no—
461C2×#103—531no—
462C2×#103—531no—
463C2×#103—531no—
464C2×#103—531no—
465C2×#102—531no—
466C2×#102—531no—
467C2×#102—531no—
468C2×#102—531no—
469C2×C22⋊C8—531no—
470C2×C22⋊C8—531no—
471C2×#97—531no—
472#388—21no—
473#387—21no—
474#386—21no—
475#382C2×D5311yescharacteristic
476#380C2×D5311yescharacteristic
477#380C2×D5311yescharacteristic
478C4×C4⋊C4C2×D5311yescharacteristic
479C4×C22⋊C4—21no—
480#340—531no—
481#340—531no—
482#340—531no—
483#340—531no—
484C53#2242011yescharacteristic, complemented, Sylow
485C2×#41—534no—
486C2×#41—534no—
487C2×#41—1062no—
488C2×#41—1062no—
489C2×#41—1062no—
490C2×#41—1062no—
491C2×#41—1062no—
492C2×#41—1062no—
493C2×#41—2121no—
494C2×#41—2121no—
495C2×#41—2121no—
496C2×#41—2121no—
497C22×Q8—531no—
498C22×Q8—531no—
499C22×D4—531no—
500C22×D4—1061no—
501C22×D4—1061no—
502C22×D4C22⋊D5311yescharacteristic
503C23×C4—21no—
504C23×C4—1061no—
505C23×C4—1061no—
506C23×C4—1061no—
507C23×C4C22×D5311yescharacteristic
508C23×C4C22×D5311yescharacteristic
509C2×M16—1062no—
510C2×M16—1062no—
511C2×M16—2121no—
512C22×C8—531no—
513C22×C8—531no—
514C22×C8—531no—
515C22×C8—531no—
516C22×C8—1062no—
517C22×C8—1062no—
518C22×C8—2121no—
519C4⋊Q8—534no—
520C4⋊Q8—1062no—
521#123—1068no—
522#123—1068no—
523C22⋊Q8—534no—
524C22⋊Q8—534no—
525C22⋊Q8—1062no—
526C22⋊Q8—1062no—
527#121—1068no—
528C4×D4—534no—
529C4×D4—1062no—
530C4×D4C4×D5314yes—
531C4×D4D21214yes—
532#117—22no—
533#117—41no—
534C2×C4⋊C4—22no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—41no—
537C2×C4⋊C4—531no—
538C2×C4⋊C4—1061no—
539C2×C4⋊C4—1061no—
540C2×C4⋊C4—1061no—
541C2×C4⋊C4—1061no—
542C2×C4⋊C4—1068no—
543C2×C4⋊C4C22⋊D5311yescharacteristic
544C2×C4⋊C4C22×D5311yescharacteristic
545C2×C4⋊C4C22×D5311yescharacteristic
546C2×C4⋊C4C22×D5311yescharacteristic
547C2×C4⋊C4C22×D5311yescharacteristic
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—1061no—
552C2×C22⋊C4—1061no—
553C2×C22⋊C4—1061no—
554C2×C22⋊C4C22⋊D5311yescharacteristic
555C2×C22⋊C4C22⋊D5311yescharacteristic
556C2×C42—21no—
557C2×C42—21no—
558C2×C42C22×D5311yescharacteristic
559C4⋊C8—1062no—
560#103—1062no—
561#103—1062no—
562#103—1062no—
563#103—1062no—
564#103—2121no—
565#103—2121no—
566#103—2121no—
567#103—2121no—
568#102—534no—
569#102—1062no—
570#102—1062no—
571#102—1062no—
572C22⋊C8—1062no—
573C22⋊C8—1062no—
574#97—1062no—
575#95—21no—
576#95—21no—
577#95—21no—
578#95—21no—
579#95—21no—
580C24—1061no—
581C24C2×C22⋊D5311yescharacteristic
582C24C2×C22⋊D5311yescharacteristic
583#41—1068no—
584#41—1068no—
585#41—2124no—
586#41—2124no—
587#41—2124no—
588#41—2124no—
589#41—2124no—
590#41—2124no—
591C2×Q8—532no—
592C2×Q8—532no—
593C2×Q8—1061no—
594C2×Q8—1061no—
595C2×Q8—1061no—
596C2×Q8—1061no—
597C2×Q8—1061no—
598C2×Q8—1061no—
599C2×Q8—1061no—
600C2×Q8—1061no—
601C2×Q8—1061no—
602C2×Q8—1061no—
603C2×D4—41no—
604C2×D4—41no—
605C2×D4—532no—
606C2×D4—532no—
607C2×D4—532no—
608C2×D4—1064no—
609C2×D4—1064no—
610C2×D4—1061no—
611C2×D4—1061no—
612C2×D4—1061no—
613C2×D4—2122no—
614C2×D4—2122no—
615C2×D4—2122no—
616C2×D4—2122no—
617C2×D4#1171992114yes—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—42no—
631C22×C4—42no—
632C22×C4—81no—
633C22×C4—1061no—
634C22×C4—1061no—
635C22×C4—1061no—
636C22×C4—1064no—
637C22×C4—1064no—
638C22×C4—1064no—
639C22×C4—2122no—
640C22×C4—2122no—
641C22×C4—2122no—
642C22×C4—2122no—
643C22×C4—2122no—
644C22×C4—2122no—
645C22×C4C2×C4×D5312yes—
646C22×C4C2×C4×D5312yes—
647C22×C4C2×D21212yes—
648C22×C4C2×D21212yes—
649C22×C4C2×C22⋊D5311yescharacteristic
650C22×C4C2×C22⋊D5311yescharacteristic
651C22×C4C2×C22⋊D5311yescharacteristic
652C22×C4C2×C22⋊D5311yescharacteristic
653C22×C4C23×D5311yescharacteristic
654M16—2124no—
655C2×C8—532no—
656C2×C8—1061no—
657C2×C8—1061no—
658C2×C8—1061no—
659C2×C8—1061no—
660C2×C8—1061no—
661C2×C8—1061no—
662C2×C8—1061no—
663C2×C8—1061no—
664C2×C8—1061no—
665C2×C8—1061no—
666C2×C8—1061no—
667C2×C8—2124no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—42no—
676C4⋊C4—532no—
677C4⋊C4—1064no—
678C4⋊C4—1064no—
679C4⋊C4—1064no—
680C4⋊C4—1064no—
681C4⋊C4—1061no—
682C4⋊C4#1171992114yes—
683C4⋊C4D4×D5312yes—
684C22⋊C4—42no—
685C22⋊C4—42no—
686C22⋊C4—81no—
687C22⋊C4—1064no—
688C22⋊C4—1064no—
689C22⋊C4—1064no—
690C22⋊C4#1171992114yes—
691C22⋊C4#1171992114yes—
692C42—42no—
693C42—81no—
694C42C2×C4×D5312yes—
695C42C2×D21212yes—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—1062no—
709C23—1062no—
710C23—1062no—
711C23—2121no—
712C23—2121no—
713C23—2121no—
714C23—2121no—
715C23C2×#1171992112yes—
716C23C2×#1171992112yes—
717C23C22×C22⋊D5311yescharacteristic
718Q8—1062no—
719Q8—1062no—
720Q8—1062no—
721Q8—1062no—
722Q8—2121no—
723Q8—2121no—
724Q8—2121no—
725Q8—2121no—
726D4—44no—
727D4—534no—
728D4—1062no—
729D4—1062no—
730D4—1062no—
731D4—2128no—
732D4—2128no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—84no—
762C2×C4—1062no—
763C2×C4—1062no—
764C2×C4—1062no—
765C2×C4—2128no—
766C2×C4—2128no—
767C2×C4—2128no—
768C2×C4—2121no—
769C2×C4—2121no—
770C2×C4—2121no—
771C2×C4—2121no—
772C2×C4—2121no—
773C2×C4—2121no—
774C2×C4C2×#1171992112yes—
775C2×C4C2×#1171992112yes—
776C2×C4C2×#1171992112yes—
777C2×C4C2×#1171992112yes—
778C2×C4C22×C4×D5311yescharacteristic
779C2×C4C2×D4×D5311yescharacteristic
780C2×C4C22×D21211yescharacteristic
781C2×C4#41×D5311yescharacteristic
782C2×C4#1313326211yescharacteristic
783C2×C4#1313326311yescharacteristic
784C8—1062no—
785C8—2121no—
786C8—2121no—
787C8—2121no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—1064no—
803C22—2122no—
804C22—2122no—
805C22—2122no—
806C22—2122no—
807C22—2122no—
808C22—2122no—
809C22C22×#1171992111yescharacteristic
810C22D4×C22⋊D5311yescharacteristic
811C22#1681126111yescharacteristic
812C22#1681142111yescharacteristic
813C22#1681142111yescharacteristic
814C22#1681143411yescharacteristic
815C22#1681143811yescharacteristic
816C4—22no—
817C4—22no—
818C4—22no—
819C4—22no—
820C4—42no—
821C4—81no—
822C4—81no—
823C4—81no—
824C4—2122no—
825C4—2122no—
826C4—2122no—
827C4C4×D4×D5311yescharacteristic
828C4#1681109511yescharacteristic
829C4D4×D21211yescharacteristic
830C4#1681126811yescharacteristic
831C2—42no—
832C2—42no—
833C2—2124no—
834C2D4×#1171992111yescharacteristic
835C2#2028323211yescharacteristic
836C2#2028324511yescharacteristic
837C2#2028623611yescharacteristic
838C2#2028627111yescharacteristic
839C2#2028668511yescharacteristic
840C2#2028680511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#2352C2
socleC23×C53C22×D4
prime radicalC2×#16811278C2
cosocleC22×C4×C53C24
hypercenter#2352D53
hypocenterC53#22420
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2352

Complements

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

NH ≅ G/Ntype
2. C2×#16810695C2semidirect
3. C2×#16810622C2semidirect
4. C2×#16810617C2semidirect
5. #20275638C2semidirect
6. #20275534C2semidirect
7. #20275146C2semidirect
8. #20275136C2semidirect
9. #20275027C2semidirect
10. #20275022C2semidirect
11. #20274722C2semidirect
12. #20274653C2semidirect
13. #20274653C2semidirect
14. #20274543C2semidirect
15. C53×#2352C2semidirect
21. #16811278C4semidirect
75. C2×#11719945C2×C4semidirect
95. #13133217C2×C4semidirect
101. #13133196C2×C4semidirect
104. C4×D212C2×C4semidirect
126. #13133137D4semidirect
415. #2352D53semidirect
484. C53#22420semidirect

Maximal subgroups

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

subgroupindex
C2×#168112782
C2×#168106952
C2×#168106222
C2×#168106172
#202756382
#202755342
#202751462
#202751362
#202750272
#202750222
#202747222
#202746532
#202745432
C53×#23522
#2242053