Finite Group Databasebeta

← #27399888

Subgroups — #27399888

Order 13568.

1434 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133248C211yesmaximal, characteristic
2C2×#16810721C211yesmaximal, characteristic, complemented
3C2×C4×#11719924C211yesmaximal, characteristic, complemented
4#20277546C211yesmaximal, characteristic
5#20275585C211yesmaximal, characteristic, complemented
6#20275575C211yesmaximal, characteristic, complemented
7#20275056C211yesmaximal, characteristic, complemented
8#20275056C211yesmaximal, characteristic, complemented
9#20275052C211yesmaximal, characteristic, complemented
10#20275052C211yesmaximal, characteristic, complemented
11#20274746C211yesmaximal, characteristic, complemented
12#20274653C211yesmaximal, characteristic
13#20274650C211yesmaximal, characteristic, complemented
14#20274499C211yesmaximal, characteristic, complemented
15Q8×C22⋊C4×C53C211yesmaximal, characteristic, complemented
16C22×#11719945C2211yescharacteristic
17C2×#13133248—24no—
18C2×#13133248—24no—
19C2×#13133248C418yescomplemented
20C22×#11719925C2211yescharacteristic
21C22×#11719925C2211yescharacteristic
22C22×#11719924C2211yescharacteristic
23C22×#11719924C2211yescharacteristic
24C22×#11719917C2211yescharacteristic
25C2×C4×D212C2211yescharacteristic
26C2×C4×D212C2211yescharacteristic
27#16810721—24no—
28C4×#11719924—24no—
29C2×#13133150C2211yescharacteristic
30C2×#13133148C2211yescharacteristic
31C2×#13133141C2211yescharacteristic
32C2×#13133141C2211yescharacteristic
33C2×#13133141C2211yescharacteristic
34C2×#13133141C2211yescharacteristic
35C2×#13133140C2211yescharacteristic
36C2×#13133140C2211yescharacteristic
37C2×#13133137C2211yescharacteristic
38C2×#13133137C2211yescharacteristic
39C2×C22⋊#88322C2211yescharacteristic
40C2×#13133128C2211yescharacteristic
41C2×C4×#88322C2211yescharacteristic
42#16810529C2211yescharacteristic
43#16810529C2211yescharacteristic
44#16810499—21no—
45#16810499—21no—
46#16810485—21no—
47#16810483C2211yescharacteristic
48#95×D53—21no—
49#16810385C2211yescharacteristic
50#16810385C2211yescharacteristic
51#16810378C2211yescharacteristic
52#16810378C2211yescharacteristic
53C23×Q8×C53C2211yescharacteristic
54C2×C4×Q8×C53C2211yescharacteristic
55C2×C4×Q8×C53C2211yescharacteristic
56C53×#391—21no—
57C53×#391—21no—
58C53×#391C2211yescharacteristic
59C53×#391C2211yescharacteristic
60C53×#380—21no—
61C53×#380C2211yescharacteristic
62C4×C22⋊C4×C53—21no—
63C4×C22⋊C4×C53C2211yescharacteristic
64C2×#11719945—22no—
65C2×#11719945—22no—
66C2×#11719945—22no—
67C2×#11719945—41no—
68C2×#11719945—41no—
69C2×#11719945C2×C414yes—
70C22×Dic106C2311yescharacteristic
71C22×D212C2311yescharacteristic
72C22×C22⋊D53—21no—
73C22×C4×D53—21no—
74C22×C4×D53—21no—
75C22×C4×D53—21no—
76#13133248—232no—
77C2×#11719925—22no—
78C2×#11719925—22no—
79C2×#11719925—22no—
80C2×#11719925—22no—
81C2×#11719925C2×C414yescomplemented
82C2×#11719925C2×C414yescomplemented
83C2×#11719924—22no—
84C2×#11719924—22no—
85C2×#11719924C2×C414yes—
86C2×#11719924C2×C414yes—
87C2×#11719924D414yes—
88C2×#11719924D414yes—
89C2×#11719917—22no—
90C2×#11719917—22no—
91C2×#11719917C2×C414yescomplemented
92C22×#88322C2311yescharacteristic
93C22×#88322C2311yescharacteristic
94C22×#88322C2311yescharacteristic
95C22×#88322C2311yescharacteristic
96C4×D212—22no—
97C4×D212—22no—
98C4×D212—41no—
99C4×D212—41no—
100C2×C4⋊Dic53C2311yescharacteristic
101C2×C4⋊Dic53C2311yescharacteristic
102C2×C22⋊Dic53—21no—
103C2×#11719921—21no—
104C2×#11719921—21no—
105#13133150—22no—
106#13133148—22no—
107#13133141—22no—
108#13133141—22no—
109#13133141—41no—
110#13133141—41no—
111#13133140—41no—
112#13133140—41no—
113#13133137—22no—
114#13133137—22no—
115C22⋊#88322—22no—
116#13133128—22no—
117C4×#88322—22no—
118#13133124—21no—
119#13133124—21no—
120#13133124—21no—
121#13133124—21no—
122#13133124—21no—
123C22×Q8×C53—21no—
124C22×Q8×C53—22no—
125C22×Q8×C53—22no—
126C22×Q8×C53—22no—
127C22×Q8×C53—41no—
128C22×Q8×C53—41no—
129C22×Q8×C53C2×C414yescomplemented
130C22×Q8×C53C2311yescharacteristic
131C22×Q8×C53C2311yescharacteristic
132C23×C4×C53—21no—
133C23×C4×C53C2311yescharacteristic
134C4×Q8×C53—22no—
135C4×Q8×C53—22no—
136C4×Q8×C53—41no—
137C4×Q8×C53—41no—
138C2×C4⋊C4×C53—21no—
139C2×C4⋊C4×C53—21no—
140C2×C4⋊C4×C53C2311yescharacteristic
141C2×C4⋊C4×C53C2311yescharacteristic
142C2×C22⋊C4×C53—21no—
143C2×C22⋊C4×C53D411yescharacteristic
144C2×C22⋊C4×C53D411yescharacteristic
145C2×C42×C53—21no—
146C2×C42×C53—21no—
147C2×C42×C53C2311yescharacteristic
148C2×C42×C53C2311yescharacteristic
149#95×C53—21no—
150#95×C53—21no—
151#95×C53—21no—
152#95×C53—21no—
153#95×C53—21no—
154#95×C53D411yescharacteristic
155#95×C53D411yescharacteristic
156C24×C53C2×D411yescharacteristic
157C23×D53—21no—
158C2×Q8×C53—24no—
159C2×Q8×C53—21no—
160C2×Q8×C53—21no—
161C2×Q8×C53—21no—
162C2×Q8×C53—21no—
163C2×Q8×C53—28no—
164C2×Q8×C53—21no—
165C2×Q8×C53—21no—
166C2×Q8×C53—21no—
167C2×Q8×C53—21no—
168C2×Q8×C53—42no—
169C2×Q8×C53—42no—
170C2×Q8×C53—44no—
171C2×Q8×C53—44no—
172C2×Q8×C53—44no—
173C2×Q8×C53C22×C412yes—
174C2×Q8×C53C22×C412yes—
175C2×Q8×C53C2×D412yes—
176C2×Q8×C53C2×D412yes—
177C22×C4×C53—21no—
178C22×C4×C53—21no—
179C22×C4×C53—21no—
180C22×C4×C53—21no—
181C22×C4×C53—21no—
182C22×C4×C53—24no—
183C22×C4×C53—21no—
184C22×C4×C53—21no—
185C22×C4×C53—21no—
186C22×C4×C53—42no—
187C22×C4×C53—42no—
188C22×C4×C53C22×C412yes—
189C22×C4×C53C2×D411yescharacteristic
190C22×C4×C53C2×D411yescharacteristic
191C22×C4×C53C2×D411yescharacteristic
192C22×C4×C53C2×D411yescharacteristic
193C22×C4×C53C2×D411yescharacteristic
194C22×C4×C53#4112yes—
195C22×C4×C53C2411yescharacteristic
196C2×C22⋊D53—24no—
197C2×C22⋊D53—42no—
198C2×C22⋊D53—42no—
199C22×Dic53—21no—
200C22×Dic53—21no—
201C22×Dic53—21no—
202#11719945—28no—
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×D212C2×D412yes—
212C2×C4×D53—24no—
213C2×C4×D53—42no—
214C2×C4×D53—42no—
215C2×C4×D53—42no—
216C2×C4×D53—42no—
217C2×C4×D53—42no—
218C2×C4×D53—42no—
219C2×C4×D53—81no—
220C2×C4×D53—81no—
221C2×Dic106—21no—
222C2×Dic106—21no—
223C2×Dic106—21no—
224C2×Dic106—21no—
225C2×Dic106—21no—
226C2×Dic106C22×C412yes—
227C4⋊C4×C53—21no—
228C4⋊C4×C53—21no—
229C4⋊C4×C53—21no—
230C4⋊C4×C53—21no—
231C4⋊C4×C53—42no—
232C4⋊C4×C53—42no—
233C22⋊C4×C53—22no—
234C22⋊C4×C53—41no—
235C22⋊C4×C53—42no—
236C42×C53—21no—
237C42×C53—21no—
238C42×C53—21no—
239C42×C53—21no—
240C42×C53—42no—
241C42×C53—42no—
242C22⋊Dic53—81no—
243#11719925—28no—
244#11719925—28no—
245#11719924—28no—
246#11719924C22⋊C4116yescomplemented
247#11719921—42no—
248#11719921—42no—
249C4⋊Dic53—21no—
250C4⋊Dic53—21no—
251C4⋊Dic53—21no—
252C4⋊Dic53—21no—
253#11719917—28no—
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×#88322C22×C412yes—
263C2×#88322C22×C412yes—
264C2×#88322C2×D412yes—
265C2×#88322C2×D412yes—
266C23×C53—21no—
267C23×C53—21no—
268C23×C53—21no—
269C23×C53—21no—
270C23×C53—21no—
271C23×C53—21no—
272C23×C53C4×D412yes—
273C23×C53C22×D411yescharacteristic
274C22×D53—22no—
275C22×D53—22no—
276C22×D53—22no—
277C22×D53—41no—
278C22×D53—41no—
279C22×D53—41no—
280C22×D53—41no—
281Q8×C53—22no—
282Q8×C53—22no—
283Q8×C53—22no—
284Q8×C53—22no—
285Q8×C53—22no—
286Q8×C53—48no—
287Q8×C53—41no—
288Q8×C53—41no—
289Q8×C53C2×C22⋊C414yes—
290C2×C4×C53—22no—
291C2×C4×C53—21no—
292C2×C4×C53—21no—
293C2×C4×C53—21no—
294C2×C4×C53—22no—
295C2×C4×C53—22no—
296C2×C4×C53—21no—
297C2×C4×C53—22no—
298C2×C4×C53—22no—
299C2×C4×C53—22no—
300C2×C4×C53—22no—
301C2×C4×C53—22no—
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—48no—
312C2×C4×C53—41no—
313C2×C4×C53—41no—
314C2×C4×C53—41no—
315C2×C4×C53—41no—
316C2×C4×C53—41no—
317C2×C4×C53—41no—
318C2×C4×C53—41no—
319C2×C4×C53—41no—
320C2×C4×C53C4×D412yes—
321C2×C4×C53#13712yescomplemented
322C2×C4×C53C23×C411yescharacteristic
323C2×C4×C53C22×D411yescharacteristic
324C2×C4×C53C22×D411yescharacteristic
325C2×C4×C53C2×#4111yescharacteristic
326C2×C4×C53H(5,𝔽2)11yescharacteristic
327C2×C4×C53H(5,𝔽2)11yescharacteristic
328C22⋊D53—48no—
329C2×Dic53—22no—
330C2×Dic53—41no—
331C2×Dic53—41no—
332C2×Dic53—41no—
333C2×Dic53—41no—
334C2×Dic53—41no—
335C2×Dic53—41no—
336C2×Dic53—41no—
337C2×Dic53—41no—
338D212—22no—
339D212—22no—
340D212—22no—
341D212C2×C22⋊C414yes—
342C4×D53—48no—
343C4×D53—84no—
344C4×D53—84no—
345Dic106—22no—
346Dic106—22no—
347Dic106—41no—
348Dic106—41no—
349#88322—22no—
350#88322—41no—
351#88322—41no—
352#88322C2×C22⋊C414yes—
353#22444—531nomaximal, Sylow
354C22×C53—22no—
355C22×C53—22no—
356C22×C53—22no—
357C22×C53—41no—
358C22×C53—41no—
359C22×C53—41no—
360C22×C53—41no—
361C22×C53C2×C4×D411yescharacteristic
362C22×C53D4211yescharacteristic
363C22×C53D4211yescharacteristic
364C22×C53C2×#13711yescharacteristic
365C22×C53#57511yescharacteristic
366C22×C53#57711yescharacteristic
367C22×C53#57811yescharacteristic
368C2×D53—24no—
369C2×D53—42no—
370C2×D53—42no—
371C2×D53—42no—
372C2×D53—42no—
373C2×D53—42no—
374C2×D53—42no—
375C4×C53—22no—
376C4×C53—24no—
377C4×C53—22no—
378C4×C53—42no—
379C4×C53—41no—
380C4×C53—41no—
381C4×C53—41no—
382C4×C53—81no—
383C4×C53—81no—
384C4×C53C22×C22⋊C411yescharacteristic
385C4×C53#51811yescharacteristic
386C4×C53#54611yescharacteristic
387C4×C53#54611yescharacteristic
388Dic53—42no—
389Dic53—81no—
390Dic53—81no—
391C22×#137—531no—
392C2×#440—531no—
393C2×C4×SD16—531no—
394Q8×C22⋊C4D5311yescharacteristic, complemented
395#2339—531no—
396#1971—531no—
397#1969—531no—
398#1878—531no—
399#1878—531no—
400#1877—531no—
401#1877—531no—
402#1809—531no—
403#1788—531no—
404#1787—531no—
405#1753—531no—
406C2×C53—42no—
407C2×C53D4×C22⋊C411yescharacteristic
408C2×C53C4×#13711yescharacteristic
409C2×C53#294711yescharacteristic
410C2×C53#326611yescharacteristic
411C2×C53#326911yescharacteristic
412C2×C53#327511yescharacteristic
413C2×C53#327611yescharacteristic
414D53—44no—
415C22×#41—531no—
416C23×Q8C2×D5311yescharacteristic
417C2×#137—538no—
418C2×#137—1064no—
419C2×#137—1064no—
420C22×Q16—531no—
421C22×Q16—531no—
422C22×SD16—531no—
423C22×SD16—531no—
424C22×M16—531no—
425C2×C4×Q8C2×D5311yescharacteristic
426C2×C4×Q8C2×D5311yescharacteristic
427C2×C4×D4—531no—
428C2×C4×D4—531no—
429#440—1064no—
430C4×SD16—1064no—
431C2×#107—531no—
432C2×#106—531no—
433C2×#103—531no—
434C2×#103—531no—
435C2×#103—531no—
436C2×#103—531no—
437C2×#103—531no—
438C2×#103—531no—
439C2×#102—531no—
440C2×#102—531no—
441C2×C22⋊C8—531no—
442C2×#97—531no—
443C2×C4×C8—531no—
444#391—21no—
445#391—21no—
446#391—531no—
447#391—531no—
448#391C2×D5311yescharacteristic
449#391C2×D5311yescharacteristic
450#386—1061no—
451#386—1061no—
452#381—1061no—
453#380—21no—
454#380—531no—
455#380C2×D5311yescharacteristic
456C4×C22⋊C4—21no—
457C4×C22⋊C4C2×D5311yescharacteristic
458C2×#95—1061no—
459#340—531no—
460#340—531no—
461#336—531no—
462#336—531no—
463C53#2244411yescharacteristic, complemented, Sylow
464C2×#41—534no—
465C2×#41—1062no—
466C2×#41—1062no—
467C2×#41—1062no—
468C2×#41—2121no—
469C2×#41—2121no—
470C22×Q8—22no—
471C22×Q8—21no—
472C22×Q8—22no—
473C22×Q8—22no—
474C22×Q8—41no—
475C22×Q8—41no—
476C22×Q8—531no—
477C22×Q8C4×D5314yescomplemented
478C22×Q8C22×D5311yescharacteristic
479C22×Q8C22×D5311yescharacteristic
480C22×D4—531no—
481C22×D4—1061no—
482C23×C4—21no—
483C23×C4—1061no—
484C23×C4—1061no—
485C23×C4—1061no—
486C23×C4C22×D5311yescharacteristic
487#137—10632no—
488C2×Q16—534no—
489C2×Q16—534no—
490C2×Q16—1062no—
491C2×Q16—1062no—
492C2×Q16—1062no—
493C2×Q16—1062no—
494C2×SD16—534no—
495C2×SD16—534no—
496C2×SD16—534no—
497C2×SD16—534no—
498C2×SD16—1062no—
499C2×SD16—1062no—
500C2×M16—534no—
501C2×M16—1062no—
502C2×M16—1062no—
503C22×C8—531no—
504C22×C8—531no—
505C22×C8—531no—
506C22×C8—531no—
507C4×Q8—22no—
508C4×Q8—22no—
509C4×Q8—41no—
510C4×Q8—41no—
511C4×D4—1062no—
512C4×D4—1062no—
513C4×D4—2121no—
514C4×D4—2121no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—531no—
518C2×C4⋊C4—531no—
519C2×C4⋊C4C22×D5311yescharacteristic
520C2×C4⋊C4C22×D5311yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—1061no—
523C2×C22⋊C4—1061no—
524C2×C22⋊C4—1061no—
525C2×C22⋊C4C22⋊D5311yescharacteristic
526C2×C22⋊C4C22⋊D5311yescharacteristic
527C2×C42—21no—
528C2×C42—21no—
529C2×C42C22×D5311yescharacteristic
530C2×C42C22×D5311yescharacteristic
531#107—1062no—
532#106—1062no—
533#103—1062no—
534#103—1062no—
535#103—2121no—
536#103—2121no—
537#103—2121no—
538#103—2121no—
539#102—1062no—
540#102—1062no—
541C22⋊C8—1062no—
542#97—1062no—
543C4×C8—1062no—
544#95—21no—
545#95—21no—
546#95—21no—
547#95—21no—
548#95—21no—
549#95—1061no—
550#95—1061no—
551#95—1061no—
552#95—1061no—
553#95—1061no—
554#95C22⋊D5311yescharacteristic
555#95C22⋊D5311yescharacteristic
556C24—1061no—
557C24C2×C22⋊D5311yescharacteristic
558#41—1068no—
559#41—2124no—
560#41—2124no—
561#41—2124no—
562C2×Q8—24no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—28no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—42no—
573C2×Q8—42no—
574C2×Q8—44no—
575C2×Q8—44no—
576C2×Q8—44no—
577C2×Q8—532no—
578C2×Q8—1061no—
579C2×Q8—1061no—
580C2×Q8—1061no—
581C2×Q8—1061no—
582C2×Q8—1061no—
583C2×Q8C2×C4×D5312yes—
584C2×Q8C2×C4×D5312yes—
585C2×Q8D4×D5312yes—
586C2×Q8D4×D5312yes—
587C2×D4—532no—
588C2×D4—532no—
589C2×D4—532no—
590C2×D4—1064no—
591C2×D4—1061no—
592C2×D4—1061no—
593C2×D4—1061no—
594C2×D4—2122no—
595C2×D4—2122no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—24no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—1061no—
608C22×C4—1064no—
609C22×C4—1061no—
610C22×C4—1061no—
611C22×C4—4241no—
612C22×C4—4241no—
613C22×C4—2122no—
614C22×C4—2122no—
615C22×C4—2122no—
616C22×C4—2122no—
617C22×C4—2122no—
618C22×C4—2122no—
619C22×C4C2×C4×D5312yes—
620C22×C4#1171994512yes—
621C22×C4C2×C22⋊D5311yescharacteristic
622C22×C4C2×C22⋊D5311yescharacteristic
623C22×C4C2×C22⋊D5311yescharacteristic
624C22×C4C2×C22⋊D5311yescharacteristic
625C22×C4C2×C22⋊D5311yescharacteristic
626C22×C4C23×D5311yescharacteristic
627Q16—1068no—
628Q16—1068no—
629SD16—5316no—
630SD16—1068no—
631M16—1068no—
632C2×C8—532no—
633C2×C8—532no—
634C2×C8—532no—
635C2×C8—532no—
636C2×C8—1061no—
637C2×C8—1061no—
638C2×C8—1061no—
639C2×C8—1061no—
640C2×C8—1061no—
641C2×C8—1061no—
642C2×C8—1061no—
643C2×C8—1061no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—42no—
649C4⋊C4—42no—
650C4⋊C4—1061no—
651C4⋊C4—1061no—
652C4⋊C4—1061no—
653C4⋊C4—1061no—
654C22⋊C4—22no—
655C22⋊C4—41no—
656C22⋊C4—42no—
657C22⋊C4—4241no—
658C22⋊C4—2122no—
659C22⋊C4—2122no—
660C42—21no—
661C42—21no—
662C42—21no—
663C42—21no—
664C42—42no—
665C42—42no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—1062no—
673C23—1062no—
674C23—1062no—
675C23—2121no—
676C23—2121no—
677C23—2121no—
678C23—2121no—
679C23C4×C22⋊D5312yes—
680C23C22×C22⋊D5311yescharacteristic
681Q8—22no—
682Q8—22no—
683Q8—22no—
684Q8—22no—
685Q8—22no—
686Q8—48no—
687Q8—41no—
688Q8—41no—
689Q8—1062no—
690Q8—1062no—
691Q8—2121no—
692Q8—2121no—
693Q8C22⋊C4×D5314yes—
694D4—534no—
695D4—1062no—
696D4—1062no—
697D4—1062no—
698D4—2128no—
699C2×C4—22no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—48no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—1062no—
730C2×C4—4244no—
731C2×C4—4244no—
732C2×C4—2128no—
733C2×C4—2121no—
734C2×C4—2121no—
735C2×C4—2121no—
736C2×C4—2121no—
737C2×C4—2121no—
738C2×C4—2121no—
739C2×C4—2121no—
740C2×C4—2121no—
741C2×C4C4×C22⋊D5312yes—
742C2×C4#1313324812yescomplemented
743C2×C4C22×C4×D5311yescharacteristic
744C2×C4C2×D4×D5311yescharacteristic
745C2×C4C2×D4×D5311yescharacteristic
746C2×C4C2×#1171994511yescharacteristic
747C2×C4#1313326211yescharacteristic
748C2×C4#1313326211yescharacteristic
749C8—534no—
750C8—1062no—
751C8—2121no—
752C8—2121no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—1064no—
761C22—2122no—
762C22—2122no—
763C22—2122no—
764C22—2122no—
765C22—2122no—
766C22—2122no—
767C22C2×C4×C22⋊D5311yescharacteristic
768C22D4×C22⋊D5311yescharacteristic
769C22D4×C22⋊D5311yescharacteristic
770C22C2×#1313324811yescharacteristic
771C22#1681142111yescharacteristic
772C22#1681143111yescharacteristic
773C22#1681143811yescharacteristic
774C4—22no—
775C4—22no—
776C4—24no—
777C4—42no—
778C4—41no—
779C4—41no—
780C4—41no—
781C4—81no—
782C4—81no—
783C4—4241no—
784C4—4241no—
785C4—2122no—
786C4C2×C22⋊C4×D5311yescharacteristic
787C4#1681109611yescharacteristic
788C4#1681126311yescharacteristic
789C4#1681126311yescharacteristic
790C2—42no—
791C2—2124no—
792C2C22⋊C4×C22⋊D5311yescharacteristic
793C2C4×#1313324811yescharacteristic
794C2#2028355811yescharacteristic
795C2#2028622611yescharacteristic
796C2#2028627111yescharacteristic
797C2#2028634711yescharacteristic
798C2#2028636111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingQ8×C22⋊C4×C53C2
socleC23×C53C22×D4
prime radicalC22×#11719945C22
cosocleC22×C4×C53C24
hypercenterQ8×C22⋊C4D53
hypocenterC53#22444
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ Q8×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#16810721C2semidirect
3. C2×C4×#11719924C2semidirect
5. #20275585C2semidirect
6. #20275575C2semidirect
7. #20275056C2semidirect
8. #20275056C2semidirect
9. #20275052C2semidirect
10. #20275052C2semidirect
11. #20274746C2semidirect
13. #20274650C2semidirect
14. #20274499C2semidirect
15. Q8×C22⋊C4×C53C2semidirect
19. C2×#13133248C4semidirect
81. C2×#11719925C2×C4semidirect
82. C2×#11719925C2×C4semidirect
91. C2×#11719917C2×C4semidirect
129. C22×Q8×C53C2×C4semidirect
246. #11719924C22⋊C4semidirect
321. C2×C4×C53#137semidirect
394. Q8×C22⋊C4D53semidirect
463. C53#22444semidirect
477. C22×Q8C4×D53semidirect
742. C2×C4#13133248semidirect

Maximal subgroups

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

subgroupindex
C22×#131332482
C2×#168107212
C2×C4×#117199242
#202775462
#202755852
#202755752
#202750562
#202750522
#202747462
#202746532
#202746502
#202744992
Q8×C22⋊C4×C532
#2244453