Finite Group Databasebeta

← #27389886

Subgroups — #27389886

Order 13568.

1344 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810779C211yesmaximal, characteristic
2C2×#16810728C211yesmaximal, characteristic, complemented
3C2×C4×#11719925C211yesmaximal, characteristic, complemented
4#20277397C211yesmaximal, characteristic
5#20275056C211yesmaximal, characteristic, complemented
6#20275056C211yesmaximal, characteristic, complemented
7#20275027C211yesmaximal, characteristic
8#20274983C211yesmaximal, characteristic, complemented
9#20274969C211yesmaximal, characteristic, complemented
10#20274914C211yesmaximal, characteristic
11#20274650C211yesmaximal, characteristic
12#20274545C211yesmaximal, characteristic, complemented
13C4×#13133141C211yesmaximal, characteristic, complemented
14#20274481C211yesmaximal, characteristic
15C2×C53×#519C211yesmaximal, characteristic
16C22×#11719925C2211yescharacteristic
17C22×#11719925C2211yescharacteristic
18C2×#13133196C2211yescharacteristic
19C2×C4×Dic106C2211yescharacteristic
20#16810779C418yescomplemented
21#16810728—24no—
22C4×#11719925—24no—
23C2×#13133150C2211yescharacteristic
24C2×#13133148C2211yescharacteristic
25C2×#13133141C2211yescharacteristic
26C2×#13133141C2211yescharacteristic
27C2×#13133141C2211yescharacteristic
28C2×#13133141C2211yescharacteristic
29C2×#13133141C2211yescharacteristic
30C2×#13133141C2211yescharacteristic
31C2×#13133140C2211yescharacteristic
32C2×#13133140C2211yescharacteristic
33C2×C22⋊#88322C2211yescharacteristic
34C2×C22⋊#88322C2211yescharacteristic
35C2×#13133128C2211yescharacteristic
36C2×C4×#88322C2211yescharacteristic
37#16810529C2211yescharacteristic
38#16810521C2211yescharacteristic
39#16810518—21no—
40#16810517—21no—
41#16810511—21no—
42#16810504—21no—
43#16810483C2211yescharacteristic
44C4×C4⋊Dic53C2211yescharacteristic
45#16810385C2211yescharacteristic
46#16810385C2211yescharacteristic
47#16810385C2211yescharacteristic
48#16810385C2211yescharacteristic
49#16810378C2211yescharacteristic
50#16810378C2211yescharacteristic
51C23×Q8×C53C2211yescharacteristic
52C53×#519—24no—
53C53×#519—24no—
54C2×C4×Q8×C53—21no—
55C2×C4×Q8×C53—21no—
56C2×C4×Q8×C53C2211yescharacteristic
57C2×C4×Q8×C53C2211yescharacteristic
58C2×C4×Q8×C53C2211yescharacteristic
59C2×C4×Q8×C53C2211yescharacteristic
60C2×#117×C53—21no—
61C2×#117×C53—21no—
62C2×#117×C53C2211yescharacteristic
63C2×#117×C53C2211yescharacteristic
64C22×Dic106C2311yescharacteristic
65C2×#11719925—22no—
66C2×#11719925—22no—
67C2×#11719925—22no—
68C2×#11719925—22no—
69C2×#11719925C2×C414yes—
70C2×#11719925C2×C414yes—
71C22×#88322C2311yescharacteristic
72C22×#88322C2311yescharacteristic
73C22×#88322C2311yescharacteristic
74C22×#88322C2311yescharacteristic
75#13133196—22no—
76#13133196C2×C414yes—
77C4×Dic106—22no—
78C4×Dic106—22no—
79C2×C4⋊Dic53C2311yescharacteristic
80C2×C4⋊Dic53C2311yescharacteristic
81C2×C4⋊Dic53C2311yescharacteristic
82C2×#11719919—21no—
83C2×#11719919—21no—
84C2×#11719919—21no—
85C2×C22⋊Dic53—21no—
86C2×C22⋊Dic53—21no—
87C2×C4×Dic53—21no—
88C2×C4×Dic53—21no—
89#13133150—22no—
90#13133148—22no—
91#13133141—22no—
92#13133141—22no—
93#13133141—22no—
94#13133141—22no—
95#13133141C2×C414yes—
96#13133141C2×C414yes—
97#13133140—22no—
98#13133140—22no—
99C22⋊#88322—22no—
100C22⋊#88322C2×C414yes—
101#13133128—22no—
102C4×#88322—22no—
103#13133124—21no—
104#13133124—21no—
105#13133124—21no—
106#13133124—21no—
107#13133124—21no—
108C22×Q8×C53—22no—
109C22×Q8×C53—22no—
110C22×Q8×C53—22no—
111C22×Q8×C53—22no—
112C22×Q8×C53—21no—
113C22×Q8×C53—22no—
114C22×Q8×C53C2×C414yes—
115C22×Q8×C53C2311yescharacteristic
116C22×Q8×C53C2311yescharacteristic
117C23×C4×C53—21no—
118C23×C4×C53C2311yescharacteristic
119C4×Q8×C53—28no—
120C4×Q8×C53—28no—
121C4×Q8×C53—22no—
122C4×Q8×C53—22no—
123C4×Q8×C53—22no—
124C4×Q8×C53—22no—
125C4×Q8×C53—22no—
126C4×Q8×C53—22no—
127C4×Q8×C53D414yes—
128C4×Q8×C53D414yes—
129#117×C53—28no—
130#117×C53—28no—
131#117×C53—22no—
132#117×C53—22no—
133#117×C53—22no—
134#117×C53—22no—
135C2×C4⋊C4×C53—21no—
136C2×C4⋊C4×C53—21no—
137C2×C4⋊C4×C53—21no—
138C2×C4⋊C4×C53—21no—
139C2×C4⋊C4×C53D411yescharacteristic
140C2×C4⋊C4×C53D411yescharacteristic
141C2×C4⋊C4×C53C2311yescharacteristic
142C2×C4⋊C4×C53C2311yescharacteristic
143C2×C22⋊C4×C53—21no—
144C2×C22⋊C4×C53D411yescharacteristic
145C2×C22⋊C4×C53D411yescharacteristic
146C2×C42×C53—21no—
147C2×C42×C53—21no—
148C2×C42×C53—21no—
149C2×C42×C53—21no—
150C2×C42×C53—21no—
151C2×C42×C53C2311yescharacteristic
152C2×C42×C53C2311yescharacteristic
153C24×C53C2×D411yescharacteristic
154C2×Q8×C53—24no—
155C2×Q8×C53—28no—
156C2×Q8×C53—28no—
157C2×Q8×C53—24no—
158C2×Q8×C53—28no—
159C2×Q8×C53—28no—
160C2×Q8×C53—24no—
161C2×Q8×C53—21no—
162C2×Q8×C53—21no—
163C2×Q8×C53—21no—
164C2×Q8×C53—21no—
165C2×Q8×C53—21no—
166C2×Q8×C53—21no—
167C2×Q8×C53C22×C412yes—
168C2×Q8×C53C22×C412yes—
169C2×Q8×C53C2×D412yes—
170C2×Q8×C53C2×D412yes—
171C2×Q8×C53#4112yes—
172C2×Q8×C53#4112yes—
173C22×C4×C53—24no—
174C22×C4×C53—24no—
175C22×C4×C53—24no—
176C22×C4×C53—21no—
177C22×C4×C53—21no—
178C22×C4×C53—21no—
179C22×C4×C53—21no—
180C22×C4×C53—21no—
181C22×C4×C53—21no—
182C22×C4×C53—21no—
183C22×C4×C53—21no—
184C22×C4×C53C22×C412yes—
185C22×C4×C53C2×D411yescharacteristic
186C22×C4×C53C2×D411yescharacteristic
187C22×C4×C53C2×D411yescharacteristic
188C22×C4×C53C2×D411yescharacteristic
189C22×C4×C53C2×D411yescharacteristic
190C22×C4×C53#4112yes—
191C22×C4×C53C2411yescharacteristic
192C22×Dic53—21no—
193C22×Dic53—21no—
194C22×Dic53—21no—
195C22×Dic53—21no—
196C2×Dic106—21no—
197C2×Dic106—21no—
198C2×Dic106—21no—
199C2×Dic106—21no—
200C2×Dic106—21no—
201C2×Dic106C22×C412yes—
202C4⋊C4×C53—24no—
203C4⋊C4×C53—24no—
204C4⋊C4×C53—24no—
205C4⋊C4×C53—24no—
206C4⋊C4×C53—22no—
207C4⋊C4×C53—22no—
208C4⋊C4×C53—21no—
209C4⋊C4×C53—21no—
210C4⋊C4×C53C2×D412yes—
211C4⋊C4×C53C2×D412yes—
212C22⋊C4×C53—24no—
213C22⋊C4×C53—22no—
214C22⋊C4×C53—22no—
215C42×C53—24no—
216C42×C53—24no—
217C42×C53—24no—
218C42×C53—24no—
219C42×C53—24no—
220C42×C53—21no—
221C42×C53—21no—
222C42×C53C2×D412yes—
223C42×C53C2×D412yes—
224C22⋊Dic53—24no—
225C22⋊Dic53—81no—
226#11719925—28no—
227#11719925—28no—
228C4⋊Dic53—21no—
229C4⋊Dic53—21no—
230C4⋊Dic53—21no—
231C4⋊Dic53—21no—
232C4⋊Dic53—21no—
233C4⋊Dic53C22×C412yes—
234#11719919—24no—
235#11719919—42no—
236#11719919—81no—
237C4×Dic53—42no—
238C4×Dic53—81no—
239C2×#88322—21no—
240C2×#88322—21no—
241C2×#88322—21no—
242C2×#88322—21no—
243C2×#88322—21no—
244C2×#88322—21no—
245C2×#88322—21no—
246C2×#88322—21no—
247C2×#88322—21no—
248C2×#88322—21no—
249C2×#88322C22×C412yes—
250C2×#88322C22×C412yes—
251C23×C53—21no—
252C23×C53—21no—
253C23×C53—21no—
254C23×C53—21no—
255C23×C53—21no—
256C23×C53—21no—
257C23×C53C4×D412yes—
258C23×C53C22×D411yescharacteristic
259Q8×C53—216no—
260Q8×C53—22no—
261Q8×C53—22no—
262Q8×C53—22no—
263Q8×C53—22no—
264Q8×C53—22no—
265Q8×C53—22no—
266Q8×C53C4×D414yes—
267Q8×C53C4×D414yes—
268C2×C4×C53—216no—
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—22no—
282C2×C4×C53—22no—
283C2×C4×C53—22no—
284C2×C4×C53—22no—
285C2×C4×C53—22no—
286C2×C4×C53—22no—
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—41no—
294C2×C4×C53—41no—
295C2×C4×C53—41no—
296C2×C4×C53—41no—
297C2×C4×C53C4×D412yes—
298C2×C4×C53#12012yes—
299C2×C4×C53#12012yes—
300C2×C4×C53C23×C411yescharacteristic
301C2×C4×C53C22×D411yescharacteristic
302C2×C4×C53C22×D411yescharacteristic
303C2×C4×C53C2×#4111yescharacteristic
304C2×C4×C53C2×#4111yescharacteristic
305C2×C4×C53C2×#4111yescharacteristic
306C2×Dic53—22no—
307C2×Dic53—22no—
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—41no—
317C2×Dic53—41no—
318Dic106—22no—
319Dic106—22no—
320Dic106—41no—
321Dic106—41no—
322#88322—22no—
323#88322—22no—
324#88322—41no—
325#88322—41no—
326#21463—531nomaximal, Sylow
327C22×C53—22no—
328C22×C53—22no—
329C22×C53—22no—
330C22×C53—41no—
331C22×C53—41no—
332C22×C53—41no—
333C22×C53—41no—
334C22×C53C2×C4×D411yescharacteristic
335C22×C53C2×#12011yescharacteristic
336C22×C53#52511yescharacteristic
337C22×C53#57711yescharacteristic
338C22×C53#57811yescharacteristic
339C22×C53#57811yescharacteristic
340C22×C53#57811yescharacteristic
341C4×C53—22no—
342C4×C53—22no—
343C4×C53—24no—
344C4×C53—24no—
345C4×C53—22no—
346C4×C53—41no—
347C4×C53—42no—
348C4×C53—41no—
349C4×C53—42no—
350C4×C53C2×C4×D411yescharacteristic
351C4×C53C2×C4×D411yescharacteristic
352C4×C53#52511yescharacteristic
353C4×C53#52511yescharacteristic
354Dic53—42no—
355Dic53—42no—
356Dic53—81no—
357Dic53—81no—
358C2×#519D5311yescharacteristic
359C2×#451—531no—
360C2×#441—531no—
361C2×C4×Q16—531no—
362#2323—531no—
363#1878—531no—
364#1878—531no—
365#1873—531no—
366#1865—531no—
367#1863—531no—
368#1854—531no—
369#1787—531no—
370#1763—531no—
371C4×#103—531no—
372#1750—531no—
373C2×C53—42no—
374C2×C53C4×#12011yescharacteristic
375C2×C53#294711yescharacteristic
376C2×C53#295011yescharacteristic
377C2×C53#301111yescharacteristic
378C2×C53#301311yescharacteristic
379C2×C53#312111yescharacteristic
380C2×C53#312711yescharacteristic
381C23×Q8C2×D5311yescharacteristic
382C22×Q16—531no—
383C22×Q16—531no—
384C2×C22⋊Q8—531no—
385#519—24no—
386#519—24no—
387C2×C4×Q8—21no—
388C2×C4×Q8—21no—
389C2×C4×Q8—531no—
390C2×C4×Q8C2×D5311yescharacteristic
391C2×C4×Q8C2×D5311yescharacteristic
392C2×C4×Q8C2×D5311yescharacteristic
393C2×C4×Q8C2×D5311yescharacteristic
394C2×#117—21no—
395C2×#117—21no—
396C2×#117C2×D5311yescharacteristic
397C2×#117C2×D5311yescharacteristic
398#451—538no—
399#441—1064no—
400C4×Q16—1064no—
401C2×#107—531no—
402C2×#106—531no—
403C2×#103—531no—
404C2×#103—531no—
405C2×#103—531no—
406C2×#103—531no—
407C2×#103—531no—
408C2×#103—531no—
409C2×#103—531no—
410C2×#103—531no—
411C2×C22⋊C8—531no—
412C2×C22⋊C8—531no—
413C2×#97—531no—
414C2×C4×C8—531no—
415#391—531no—
416#389—531no—
417#389—1061no—
418#388—1061no—
419#388—1061no—
420#387—1061no—
421#380—531no—
422C4×C4⋊C4—531no—
423#340—531no—
424#340—531no—
425#340—531no—
426#340—531no—
427#336—531no—
428#336—531no—
429C53#2146311yescharacteristic, complemented, Sylow
430C22×Q8—22no—
431C22×Q8—22no—
432C22×Q8—22no—
433C22×Q8—22no—
434C22×Q8—22no—
435C22×Q8—21no—
436C22×Q8—531no—
437C22×Q8C4×D5314yes—
438C22×Q8C22×D5311yescharacteristic
439C22×Q8C22×D5311yescharacteristic
440C23×C4—21no—
441C23×C4C22×D5311yescharacteristic
442C2×Q16—534no—
443C2×Q16—534no—
444C2×Q16—1062no—
445C2×Q16—1062no—
446C2×Q16—1062no—
447C2×Q16—1062no—
448C22×C8—531no—
449C22×C8—531no—
450C22×C8—531no—
451C22×C8—531no—
452C22⋊Q8—534no—
453C22⋊Q8—1062no—
454C4×Q8—28no—
455C4×Q8—28no—
456C4×Q8—22no—
457C4×Q8—22no—
458C4×Q8—22no—
459C4×Q8—22no—
460C4×Q8—22no—
461C4×Q8—22no—
462C4×Q8—1062no—
463C4×Q8—1062no—
464C4×Q8C22⋊D5314yes—
465C4×Q8C22⋊D5314yes—
466#117—28no—
467#117—28no—
468#117—22no—
469#117—22no—
470#117—22no—
471#117—22no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—531no—
477C2×C4⋊C4—531no—
478C2×C4⋊C4—531no—
479C2×C4⋊C4—1061no—
480C2×C4⋊C4—1061no—
481C2×C4⋊C4—1061no—
482C2×C4⋊C4C22⋊D5311yescharacteristic
483C2×C4⋊C4C22⋊D5311yescharacteristic
484C2×C4⋊C4C22×D5311yescharacteristic
485C2×C4⋊C4C22×D5311yescharacteristic
486C2×C22⋊C4—21no—
487C2×C22⋊C4—1061no—
488C2×C22⋊C4—1061no—
489C2×C22⋊C4C22⋊D5311yescharacteristic
490C2×C22⋊C4C22⋊D5311yescharacteristic
491C2×C42—21no—
492C2×C42—21no—
493C2×C42—21no—
494C2×C42—21no—
495C2×C42—21no—
496C2×C42—1061no—
497C2×C42—1061no—
498C2×C42C22×D5311yescharacteristic
499C2×C42C22×D5311yescharacteristic
500#107—1062no—
501#106—1062no—
502#103—534no—
503#103—534no—
504#103—1062no—
505#103—1062no—
506#103—1062no—
507#103—1062no—
508#103—1062no—
509#103—1062no—
510C22⋊C8—534no—
511C22⋊C8—1062no—
512#97—1062no—
513C4×C8—1062no—
514#95—1061no—
515#95—1061no—
516#95—1061no—
517#95—1061no—
518#95—1061no—
519C24C2×C22⋊D5311yescharacteristic
520C2×Q8—24no—
521C2×Q8—28no—
522C2×Q8—28no—
523C2×Q8—24no—
524C2×Q8—28no—
525C2×Q8—28no—
526C2×Q8—24no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—532no—
534C2×Q8—1061no—
535C2×Q8—1061no—
536C2×Q8—1061no—
537C2×Q8—1061no—
538C2×Q8—1061no—
539C2×Q8C2×C4×D5312yes—
540C2×Q8C2×C4×D5312yes—
541C2×Q8#1171994512yes—
542C2×Q8#1171994512yes—
543C2×Q8C2×C22⋊D5312yes—
544C2×Q8C2×C22⋊D5312yes—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—1061no—
557C22×C4—1061no—
558C22×C4—1061no—
559C22×C4—1061no—
560C22×C4C2×C4×D5312yes—
561C22×C4#1171994512yes—
562C22×C4C2×C22⋊D5311yescharacteristic
563C22×C4C2×C22⋊D5311yescharacteristic
564C22×C4C2×C22⋊D5311yescharacteristic
565C22×C4C2×C22⋊D5311yescharacteristic
566C22×C4C2×C22⋊D5311yescharacteristic
567C22×C4C23×D5311yescharacteristic
568Q16—1068no—
569Q16—1068no—
570C2×C8—532no—
571C2×C8—532no—
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—22no—
587C4⋊C4—22no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—532no—
591C4⋊C4—1064no—
592C4⋊C4—1061no—
593C4⋊C4—1061no—
594C4⋊C4—1061no—
595C4⋊C4—1061no—
596C4⋊C4—1061no—
597C4⋊C4—4241no—
598C4⋊C4—2122no—
599C4⋊C4C2×C22⋊D5312yes—
600C4⋊C4C2×C22⋊D5312yes—
601C22⋊C4—24no—
602C22⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—1064no—
605C22⋊C4—4241no—
606C42—24no—
607C42—24no—
608C42—24no—
609C42—24no—
610C42—24no—
611C42—21no—
612C42—21no—
613C42—4241no—
614C42—2122no—
615C42C2×C22⋊D5312yes—
616C42C2×C22⋊D5312yes—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23C4×C22⋊D5312yes—
624C23C22×C22⋊D5311yescharacteristic
625Q8—216no—
626Q8—22no—
627Q8—22no—
628Q8—22no—
629Q8—22no—
630Q8—22no—
631Q8—22no—
632Q8—1062no—
633Q8—1062no—
634Q8—2121no—
635Q8—2121no—
636Q8C4×C22⋊D5314yes—
637Q8C4×C22⋊D5314yes—
638C2×C4—216no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—21no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—1062no—
668C2×C4—1062no—
669C2×C4—2121no—
670C2×C4—2121no—
671C2×C4—2121no—
672C2×C4—2121no—
673C2×C4—2121no—
674C2×C4—2121no—
675C2×C4—2121no—
676C2×C4—2121no—
677C2×C4—2121no—
678C2×C4—2121no—
679C2×C4C4×C22⋊D5312yes—
680C2×C4#1313318612yes—
681C2×C4#1313318612yes—
682C2×C4C22×C4×D5311yescharacteristic
683C2×C4C22×C22⋊D5311yescharacteristic
684C2×C4C22×C22⋊D5311yescharacteristic
685C2×C4C2×#1171994511yescharacteristic
686C2×C4C2×#1171994511yescharacteristic
687C2×C4C2×#1171994511yescharacteristic
688C8—1062no—
689C8—1062no—
690C8—2121no—
691C8—2121no—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22C2×C4×C22⋊D5311yescharacteristic
700C22C2×#1313318611yescharacteristic
701C22#1681113411yescharacteristic
702C22#1681143111yescharacteristic
703C22#1681143811yescharacteristic
704C22#1681143811yescharacteristic
705C22#1681143811yescharacteristic
706C4—22no—
707C4—22no—
708C4—24no—
709C4—24no—
710C4—22no—
711C4—41no—
712C4—42no—
713C4—41no—
714C4—42no—
715C4—4241no—
716C4—4241no—
717C4—2122no—
718C4—2122no—
719C4C2×C4×C22⋊D5311yescharacteristic
720C4C2×C4×C22⋊D5311yescharacteristic
721C4#1681113411yescharacteristic
722C4#1681113411yescharacteristic
723C2—42no—
724C2C4×#1313318611yescharacteristic
725C2#2028355811yescharacteristic
726C2#2028358111yescharacteristic
727C2#2028401011yescharacteristic
728C2#2028403011yescharacteristic
729C2#2028494411yescharacteristic
730C2#2028501511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC2×C53×#519C2
socleC23×C53C22×D4
prime radicalC24×C53C2×D4
cosocleC22×C4×C53C24
hypercenterC2×#519D53
hypocenterC53#21463
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#519

Complements

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

NH ≅ G/Ntype
2. C2×#16810728C2semidirect
3. C2×C4×#11719925C2semidirect
5. #20275056C2semidirect
6. #20275056C2semidirect
8. #20274983C2semidirect
9. #20274969C2semidirect
12. #20274545C2semidirect
13. C4×#13133141C2semidirect
20. #16810779C4semidirect
429. C53#21463semidirect

Maximal subgroups

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

subgroupindex
C2×#168107792
C2×#168107282
C2×C4×#117199252
#202773972
#202750562
#202750272
#202749832
#202749692
#202749142
#202746502
#202745452
C4×#131331412
#202744812
C2×C53×#5192
#2146353