Finite Group Databasebeta

← #27437213

Subgroups — #27437213

Order 13568.

1108 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810964C211yesmaximal, characteristic, complemented
2C2×#16810879C211yesmaximal, characteristic, complemented
3#20278166C211yesmaximal, characteristic
4#20276050C211yesmaximal, characteristic, complemented
5#20275915C211yesmaximal, characteristic, complemented
6#20275863C211yesmaximal, characteristic, complemented
7#20275723C211yesmaximal, characteristic, complemented
8#20275056C211yesmaximal, characteristic, complemented
9#20275023C211yesmaximal, characteristic, complemented
10#20275022C211yesmaximal, characteristic, complemented
11#20275013C211yesmaximal, characteristic
12#20274983C211yesmaximal, characteristic, complemented
13#20274908C211yesmaximal, characteristic, complemented
14#20274436C211yesmaximal, characteristic, complemented
15C2×C53×#552C211yesmaximal, characteristic
16C22×#11719925C2211yescharacteristic
17C22×#11719917C2211yescharacteristic
18C2×#13133196C2211yescharacteristic
19C2×#13133196C2211yescharacteristic
20C22×C4⋊Dic53C2211yescharacteristic
21#16810964—24no—
22#16810879—24no—
23C2×#13133150C2211yescharacteristic
24C2×#13133148C2211yescharacteristic
25C2×#13133148C2211yescharacteristic
26C2×#13133141C2211yescharacteristic
27C2×#13133141C2211yescharacteristic
28C2×#13133141C2211yescharacteristic
29C2×#13133140C2211yescharacteristic
30C2×#13133140C2211yescharacteristic
31C2×#13133140C2211yescharacteristic
32C2×C22⋊#88322C2211yescharacteristic
33C2×C22⋊#88322C2211yescharacteristic
34C2×C22⋊#88322C2211yescharacteristic
35#16810556—21no—
36#16810546—21no—
37#16810529C2211yescharacteristic
38#16810521C2211yescharacteristic
39#16810503—21no—
40#16810483C2211yescharacteristic
41#16810481—21no—
42#16810385C2211yescharacteristic
43#16810385C2211yescharacteristic
44#16810385C2211yescharacteristic
45#16810385C2211yescharacteristic
46#16810385C2211yescharacteristic
47#16810385C2211yescharacteristic
48#16810378C2211yescharacteristic
49#16810378C2211yescharacteristic
50C53×#552—24no—
51C53×#552—24no—
52C2×#126×C53—21no—
53C2×#125×C53—21no—
54C2×#125×C53C2211yescharacteristic
55C2×#123×C53—21no—
56C2×C22⋊Q8×C53C2211yescharacteristic
57C2×C22⋊Q8×C53C2211yescharacteristic
58C2×C4×Q8×C53C2211yescharacteristic
59C2×C4×D4×C53C2211yescharacteristic
60C2×#117×C53—21no—
61C2×#117×C53C2211yescharacteristic
62C22×C4⋊C4×C53C2211yescharacteristic
63C22×Dic106C2311yescharacteristic
64C23×Dic53—21no—
65C2×#11719925—22no—
66C2×#11719925—22no—
67C2×#11719925—41no—
68C2×#11719917—22no—
69C2×#11719917—22no—
70C2×#11719917—41no—
71C22×#88322C2311yescharacteristic
72C22×#88322C2311yescharacteristic
73C22×#88322C2311yescharacteristic
74C22×#88322C2311yescharacteristic
75#13133196—22no—
76#13133196—22no—
77#13133196—22no—
78#13133196—41no—
79C2×C4⋊Dic53—21no—
80C2×C4⋊Dic53—22no—
81C2×C4⋊Dic53—41no—
82C2×C4⋊Dic53C2311yescharacteristic
83C2×C4⋊Dic53C2311yescharacteristic
84C2×C4⋊Dic53C2311yescharacteristic
85C2×#11719919—21no—
86C2×#11719919—21no—
87C2×#11719919—21no—
88C2×C22⋊Dic53—21no—
89C2×C22⋊Dic53—21no—
90C2×C22⋊Dic53—21no—
91#13133150—22no—
92#13133148—22no—
93#13133148—22no—
94#13133141—22no—
95#13133141—22no—
96#13133141—41no—
97#13133140—22no—
98#13133140—22no—
99#13133140—22no—
100C22⋊#88322—22no—
101C22⋊#88322—22no—
102C22⋊#88322—41no—
103#13133124—21no—
104#13133124—21no—
105#13133124—21no—
106#13133124—21no—
107C22×Q8×C53C2311yescharacteristic
108C22×D4×C53D411yescharacteristic
109C23×C4×C53—21no—
110C23×C4×C53C2311yescharacteristic
111C23×C4×C53C2311yescharacteristic
112#126×C53—28no—
113#125×C53—28no—
114#125×C53—22no—
115#125×C53—22no—
116#123×C53—28no—
117C22⋊Q8×C53—22no—
118C22⋊Q8×C53—22no—
119C22⋊Q8×C53—22no—
120C22⋊Q8×C53D414yes—
121C4×Q8×C53—22no—
122C4×Q8×C53—22no—
123C4×D4×C53—22no—
124C4×D4×C53—22no—
125#117×C53—28no—
126#117×C53—22no—
127#117×C53D414yes—
128C2×C4⋊C4×C53—22no—
129C2×C4⋊C4×C53—22no—
130C2×C4⋊C4×C53—21no—
131C2×C4⋊C4×C53—21no—
132C2×C4⋊C4×C53—21no—
133C2×C4⋊C4×C53—21no—
134C2×C4⋊C4×C53—21no—
135C2×C4⋊C4×C53—21no—
136C2×C4⋊C4×C53D411yescharacteristic
137C2×C4⋊C4×C53C2311yescharacteristic
138C2×C4⋊C4×C53C2311yescharacteristic
139C2×C4⋊C4×C53C2311yescharacteristic
140C2×C22⋊C4×C53—21no—
141C2×C22⋊C4×C53—21no—
142C2×C22⋊C4×C53—21no—
143C2×C22⋊C4×C53D411yescharacteristic
144C2×C22⋊C4×C53D411yescharacteristic
145C2×C42×C53—21no—
146C2×C42×C53—21no—
147C2×C42×C53C2311yescharacteristic
148C24×C53C2×D411yescharacteristic
149C24×C53C2×D411yescharacteristic
150C2×Q8×C53—21no—
151C2×Q8×C53—21no—
152C2×Q8×C53—21no—
153C2×Q8×C53—21no—
154C2×Q8×C53—21no—
155C2×Q8×C53C2×D412yes—
156C2×D4×C53—22no—
157C2×D4×C53—22no—
158C2×D4×C53—41no—
159C22×C4×C53—21no—
160C22×C4×C53—21no—
161C22×C4×C53—21no—
162C22×C4×C53—21no—
163C22×C4×C53—24no—
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×C53—21no—
171C22×C4×C53—21no—
172C22×C4×C53—21no—
173C22×C4×C53—21no—
174C22×C4×C53—42no—
175C22×C4×C53—42no—
176C22×C4×C53C2×D411yescharacteristic
177C22×C4×C53C2×D411yescharacteristic
178C22×C4×C53C2×D411yescharacteristic
179C22×C4×C53C2×D411yescharacteristic
180C22×C4×C53C2×D412yes—
181C22×C4×C53C2×D412yes—
182C22×C4×C53C2411yescharacteristic
183C22×Dic53—21no—
184C22×Dic53—21no—
185C22×Dic53—21no—
186C22×Dic53—21no—
187C22×Dic53—42no—
188C22×Dic53—42no—
189C22×Dic53—81no—
190C2×Dic106—21no—
191C2×Dic106—21no—
192C2×Dic106—21no—
193C2×Dic106—21no—
194C2×Dic106—21no—
195C2×Dic106—21no—
196C4⋊C4×C53—24no—
197C4⋊C4×C53—24no—
198C4⋊C4×C53—24no—
199C4⋊C4×C53—24no—
200C4⋊C4×C53—24no—
201C4⋊C4×C53—24no—
202C4⋊C4×C53—22no—
203C4⋊C4×C53—21no—
204C4⋊C4×C53—21no—
205C4⋊C4×C53—21no—
206C4⋊C4×C53C2×D412yes—
207C4⋊C4×C53C2×D412yes—
208C4⋊C4×C53C2×D412yes—
209C22⋊C4×C53—24no—
210C22⋊C4×C53—24no—
211C22⋊C4×C53—24no—
212C22⋊C4×C53—22no—
213C22⋊C4×C53—22no—
214C42×C53—24no—
215C42×C53—24no—
216C42×C53—21no—
217C42×C53—21no—
218C22⋊Dic53—42no—
219C22⋊Dic53—42no—
220C22⋊Dic53—81no—
221#11719925—44no—
222C4⋊Dic53—21no—
223C4⋊Dic53—21no—
224C4⋊Dic53—21no—
225C4⋊Dic53—21no—
226C4⋊Dic53—21no—
227C4⋊Dic53—42no—
228C4⋊Dic53#4112yes—
229#11719919—42no—
230#11719919—42no—
231#11719919—81no—
232#11719917—44no—
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—21no—
243C2×#88322—21no—
244C2×#88322#4112yes—
245C23×C53—21no—
246C23×C53—21no—
247C23×C53—21no—
248C23×C53—21no—
249C23×C53—21no—
250C23×C53—21no—
251C23×C53—21no—
252C23×C53—21no—
253C23×C53—21no—
254C23×C53—21no—
255C23×C53—21no—
256C23×C53—21no—
257C23×C53#12012yes—
258C23×C53#13712yes—
259C23×C53C22×D411yescharacteristic
260Q8×C53—22no—
261Q8×C53—22no—
262Q8×C53—41no—
263Q8×C53—41no—
264D4×C53—44no—
265C2×C4×C53—21no—
266C2×C4×C53—21no—
267C2×C4×C53—22no—
268C2×C4×C53—22no—
269C2×C4×C53—22no—
270C2×C4×C53—22no—
271C2×C4×C53—22no—
272C2×C4×C53—22no—
273C2×C4×C53—21no—
274C2×C4×C53—22no—
275C2×C4×C53—22no—
276C2×C4×C53—21no—
277C2×C4×C53—21no—
278C2×C4×C53—21no—
279C2×C4×C53—21no—
280C2×C4×C53—21no—
281C2×C4×C53—21no—
282C2×C4×C53—21no—
283C2×C4×C53—21no—
284C2×C4×C53—48no—
285C2×C4×C53—41no—
286C2×C4×C53—41no—
287C2×C4×C53—41no—
288C2×C4×C53—41no—
289C2×C4×C53—41no—
290C2×C4×C53—41no—
291C2×C4×C53—41no—
292C2×C4×C53—41no—
293C2×C4×C53—41no—
294C2×C4×C53—41no—
295C2×C4×C53—41no—
296C2×C4×C53—41no—
297C2×C4×C53#12012yes—
298C2×C4×C53C22×D411yescharacteristic
299C2×C4×C53C22×D411yescharacteristic
300C2×C4×C53C2×#4111yescharacteristic
301C2×C4×C53C2×#4111yescharacteristic
302C2×C4×C53H(5,𝔽2)11yescharacteristic
303C2×C4×C532−1+411yescharacteristic
304C2×Dic53—22no—
305C2×Dic53—41no—
306C2×Dic53—41no—
307C2×Dic53—41no—
308C2×Dic53—41no—
309C2×Dic53—41no—
310C2×Dic53—41no—
311C2×Dic53—41no—
312C2×Dic53—41no—
313C2×Dic53—41no—
314C2×Dic53—41no—
315C2×Dic53—41no—
316C2×Dic53—84no—
317Dic106—41no—
318Dic106—41no—
319Dic106—41no—
320Dic106—41no—
321#88322—22no—
322#88322—41no—
323#88322—41no—
324#88322—41no—
325#25562—531nomaximal, Sylow
326C22×C53—22no—
327C22×C53—22no—
328C22×C53—22no—
329C22×C53—22no—
330C22×C53—22no—
331C22×C53—22no—
332C22×C53—41no—
333C22×C53—41no—
334C22×C53—41no—
335C22×C53—41no—
336C22×C53—41no—
337C22×C53—41no—
338C22×C53—41no—
339C22×C53—41no—
340C22×C53C2×#12011yescharacteristic
341C22×C53#54611yescharacteristic
342C22×C53#54711yescharacteristic
343C22×C53C2×#13711yescharacteristic
344C22×C53#57511yescharacteristic
345C22×C53#57711yescharacteristic
346C22×C53#57811yescharacteristic
347C4×C53—22no—
348C4×C53—41no—
349C4×C53—42no—
350C4×C53—41no—
351C4×C53—42no—
352C4×C53—42no—
353C4×C53—41no—
354C4×C53—42no—
355C4×C53#53211yescharacteristic
356C4×C53#53711yescharacteristic
357C4×C53#54611yescharacteristic
358C4×C53#54711yescharacteristic
359Dic53—42no—
360Dic53—81no—
361Dic53—81no—
362Dic53—81no—
363C2×#552D5311yescharacteristic
364C2×#485—531no—
365C2×#470—531no—
366#2417—531no—
367#2059—531no—
368#2036—531no—
369#2026—531no—
370#2001—531no—
371#1878—531no—
372#1872—531no—
373#1872—531no—
374#1870—531no—
375#1865—531no—
376#1853—531no—
377#1736—531no—
378C2×C53—42no—
379C2×C53—42no—
380C2×C53#243011yescharacteristic
381C2×C53#300711yescharacteristic
382C2×C53#301311yescharacteristic
383C2×C53#331211yescharacteristic
384C2×C53#332311yescharacteristic
385C2×C53#334411yescharacteristic
386C2×C53#335211yescharacteristic
387C22×Q16—531no—
388C22×M16—531no—
389#552—24no—
390#552—24no—
391C2×#126—21no—
392C2×#125—21no—
393C2×#125C2×D5311yescharacteristic
394C2×#123—21no—
395C2×C22⋊Q8—531no—
396C2×C22⋊Q8—531no—
397C2×C22⋊Q8C2×D5311yescharacteristic
398C2×C22⋊Q8C2×D5311yescharacteristic
399C2×C4×Q8C2×D5311yescharacteristic
400C2×C4×D4C2×D5311yescharacteristic
401C2×#117—21no—
402C2×#117C2×D5311yescharacteristic
403C22×C4⋊C4—531no—
404C22×C4⋊C4C2×D5311yescharacteristic
405#485—1064no—
406#470—1064no—
407C2×#107—531no—
408C2×#106—531no—
409C2×#106—531no—
410C2×#103—531no—
411C2×#103—531no—
412C2×#103—531no—
413C2×#103—531no—
414C2×#103—531no—
415C2×#103—531no—
416C2×C22⋊C8—531no—
417C2×C22⋊C8—531no—
418C2×C22⋊C8—531no—
419#398—1061no—
420#396—1061no—
421#391—531no—
422#389—531no—
423#386—1061no—
424#380—531no—
425#380—1061no—
426#340—531no—
427#340—531no—
428#340—531no—
429#340—531no—
430#340—531no—
431#340—531no—
432#336—531no—
433#336—531no—
434C53#2556211yescharacteristic, complemented, Sylow
435C22×Q8—531no—
436C22×Q8C22×D5311yescharacteristic
437C22×D4C22⋊D5311yescharacteristic
438C23×C4—21no—
439C23×C4—1061no—
440C23×C4C22×D5311yescharacteristic
441C23×C4C22×D5311yescharacteristic
442C2×Q16—1062no—
443C2×Q16—1062no—
444C2×Q16—2121no—
445C2×M16—1062no—
446C2×M16—1062no—
447C2×M16—2121no—
448C22×C8—531no—
449C22×C8—531no—
450C22×C8—531no—
451C22×C8—531no—
452#126—28no—
453#125—28no—
454#125—22no—
455#125—22no—
456#123—28no—
457C22⋊Q8—22no—
458C22⋊Q8—22no—
459C22⋊Q8—22no—
460C22⋊Q8—1062no—
461C22⋊Q8—1062no—
462C22⋊Q8—1062no—
463C22⋊Q8—2121no—
464C22⋊Q8C22⋊D5314yes—
465C4×Q8—22no—
466C4×Q8—22no—
467C4×D4—22no—
468C4×D4—22no—
469#117—28no—
470#117—22no—
471#117C22⋊D5314yes—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—531no—
481C2×C4⋊C4—531no—
482C2×C4⋊C4—531no—
483C2×C4⋊C4—1062no—
484C2×C4⋊C4—1061no—
485C2×C4⋊C4—1061no—
486C2×C4⋊C4—1061no—
487C2×C4⋊C4—1061no—
488C2×C4⋊C4—2121no—
489C2×C4⋊C4C22⋊D5311yescharacteristic
490C2×C4⋊C4C22×D5311yescharacteristic
491C2×C4⋊C4C22×D5311yescharacteristic
492C2×C4⋊C4C22×D5311yescharacteristic
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—1061no—
497C2×C22⋊C4—1061no—
498C2×C22⋊C4—1061no—
499C2×C22⋊C4C22⋊D5311yescharacteristic
500C2×C22⋊C4C22⋊D5311yescharacteristic
501C2×C42—21no—
502C2×C42—21no—
503C2×C42C22×D5311yescharacteristic
504#107—1062no—
505#106—1062no—
506#106—1062no—
507#103—1062no—
508#103—1062no—
509#103—1062no—
510#103—1062no—
511#103—1062no—
512#103—2121no—
513C22⋊C8—1062no—
514C22⋊C8—1062no—
515C22⋊C8—2121no—
516#95—1061no—
517#95—1061no—
518#95—1061no—
519#95—1061no—
520C24C2×C22⋊D5311yescharacteristic
521C24C2×C22⋊D5311yescharacteristic
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—1061no—
528C2×Q8—1061no—
529C2×Q8—1061no—
530C2×Q8—1061no—
531C2×Q8—1061no—
532C2×Q8—1061no—
533C2×Q8C2×C22⋊D5312yes—
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—41no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—24no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—1061no—
555C22×C4—1061no—
556C22×C4—1061no—
557C22×C4—1061no—
558C22×C4—4241no—
559C22×C4—2122no—
560C22×C4—2122no—
561C22×C4C2×C22⋊D5311yescharacteristic
562C22×C4C2×C22⋊D5311yescharacteristic
563C22×C4C2×C22⋊D5311yescharacteristic
564C22×C4C2×C22⋊D5311yescharacteristic
565C22×C4C2×C22⋊D5312yes—
566C22×C4C2×C22⋊D5312yes—
567C22×C4C23×D5311yescharacteristic
568Q16—2124no—
569M16—2124no—
570C2×C8—532no—
571C2×C8—1061no—
572C2×C8—1061no—
573C2×C8—1061no—
574C2×C8—1061no—
575C2×C8—1061no—
576C2×C8—1061no—
577C2×C8—1061no—
578C2×C8—1061no—
579C2×C8—1061no—
580C2×C8—1061no—
581C2×C8—1061no—
582C4⋊C4—24no—
583C4⋊C4—24no—
584C4⋊C4—24no—
585C4⋊C4—24no—
586C4⋊C4—24no—
587C4⋊C4—24no—
588C4⋊C4—22no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—532no—
593C4⋊C4—1061no—
594C4⋊C4—1061no—
595C4⋊C4—1061no—
596C4⋊C4—1061no—
597C4⋊C4—1061no—
598C4⋊C4—4241no—
599C4⋊C4—2122no—
600C4⋊C4—2122no—
601C4⋊C4—2122no—
602C4⋊C4C2×C22⋊D5312yes—
603C4⋊C4C2×C22⋊D5312yes—
604C4⋊C4C2×C22⋊D5312yes—
605C22⋊C4—24no—
606C22⋊C4—24no—
607C22⋊C4—24no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—4241no—
611C22⋊C4—2122no—
612C22⋊C4—2122no—
613C42—24no—
614C42—24no—
615C42—21no—
616C42—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23#1313318612yes—
630C23#1313324712yes—
631C23C22×C22⋊D5311yescharacteristic
632Q8—22no—
633Q8—22no—
634Q8—41no—
635Q8—41no—
636Q8—2121no—
637Q8—2121no—
638Q8—2121no—
639Q8—2121no—
640D4—44no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—22no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—48no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—1062no—
674C2×C4—4244no—
675C2×C4—2121no—
676C2×C4—2121no—
677C2×C4—2121no—
678C2×C4—2121no—
679C2×C4—2121no—
680C2×C4—2121no—
681C2×C4—2121no—
682C2×C4—2121no—
683C2×C4—2121no—
684C2×C4—2121no—
685C2×C4—2121no—
686C2×C4#1313318612yes—
687C2×C4C22×C22⋊D5311yescharacteristic
688C2×C4C22×C22⋊D5311yescharacteristic
689C2×C4#41×D5311yescharacteristic
690C2×C4#41×D5311yescharacteristic
691C2×C4#1313326311yescharacteristic
692C2×C4#1313326411yescharacteristic
693C8—1062no—
694C8—2121no—
695C8—2121no—
696C8—2121no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22C2×#1313318611yescharacteristic
712C22#1681126111yescharacteristic
713C22#1681127211yescharacteristic
714C22C2×#1313324711yescharacteristic
715C22#1681142111yescharacteristic
716C22#1681143111yescharacteristic
717C22#1681143811yescharacteristic
718C4—22no—
719C4—41no—
720C4—42no—
721C4—41no—
722C4—42no—
723C4—42no—
724C4—41no—
725C4—42no—
726C4—4241no—
727C4—4241no—
728C4—4241no—
729C4—2122no—
730C4#1681116911yescharacteristic
731C4#1681120111yescharacteristic
732C4#1681126111yescharacteristic
733C4#1681127211yescharacteristic
734C2—42no—
735C2—42no—
736C2#2027831911yescharacteristic
737C2#2028397511yescharacteristic
738C2#2028403011yescharacteristic
739C2#2028676011yescharacteristic
740C2#2028692511yescharacteristic
741C2#2028717011yescharacteristic
742C2#2028728411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC22×C4×C53C24
FrattiniC22×C4C23×D53
FittingC2×C53×#552C2
socleC23×C53C22×D4
prime radicalC22×D4×C53D4
hypercenterC2×#552D53
hypocenterC53#25562
LCSG ▷ C22×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
1. C2×#16810964C2semidirect
2. C2×#16810879C2semidirect
4. #20276050C2semidirect
5. #20275915C2semidirect
6. #20275863C2semidirect
7. #20275723C2semidirect
8. #20275056C2semidirect
9. #20275023C2semidirect
10. #20275022C2semidirect
12. #20274983C2semidirect
13. #20274908C2semidirect
14. #20274436C2semidirect
434. C53#25562semidirect

Maximal subgroups

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

subgroupindex
C2×#168109642
C2×#168108792
#202781662
#202760502
#202759152
#202758632
#202757232
#202750562
#202750232
#202750222
#202750132
#202749832
#202749082
#202744362
C2×C53×#5522
#2556253