Finite Group Databasebeta

← #27389871

Subgroups — #27389871

Order 13568.

1400 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810762C211yesmaximal, characteristic
2C2×#16810721C211yesmaximal, characteristic, complemented
3C2×C4×#11719924C211yesmaximal, characteristic, complemented
4#20277408C211yesmaximal, characteristic
5#20275070C211yesmaximal, characteristic, complemented
6#20275070C211yesmaximal, characteristic, complemented
7#20275037C211yesmaximal, characteristic
8#20274983C211yesmaximal, characteristic, complemented
9#20274969C211yesmaximal, characteristic, complemented
10#20274914C211yesmaximal, characteristic, complemented
11#20274650C211yesmaximal, characteristic, complemented
12#20274545C211yesmaximal, characteristic, complemented
13C4×#13133141C211yesmaximal, characteristic, complemented
14#20274481C211yesmaximal, characteristic, complemented
15C2×C53×#519C211yesmaximal, characteristic, complemented
16C22×#11719924C2211yescharacteristic
17C22×#11719924C2211yescharacteristic
18C2×#13133191C2211yescharacteristic
19C2×C4×D212C2211yescharacteristic
20#16810762C418yescomplemented
21#16810721—24no—
22C4×#11719924—24no—
23C2×#13133150C2211yescharacteristic
24C2×#13133148C2211yescharacteristic
25C2×#13133141C2211yescharacteristic
26C2×#13133141C2211yescharacteristic
27C2×#13133141C2211yescharacteristic
28C2×#13133141C2211yescharacteristic
29C2×#13133141C2211yescharacteristic
30C2×#13133141C2211yescharacteristic
31C2×#13133137C2211yescharacteristic
32C2×#13133137C2211yescharacteristic
33C2×C22⋊#88322C2211yescharacteristic
34C2×C22⋊#88322C2211yescharacteristic
35C2×#13133128C2211yescharacteristic
36C2×C4×#88322C2211yescharacteristic
37#16810525C2211yescharacteristic
38#16810523—21no—
39#16810521C2211yescharacteristic
40#16810513—21no—
41#16810499—21no—
42#16810494—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×D212C2311yescharacteristic
65C22×C22⋊D53—21no—
66C22×C4×D53—21no—
67C2×#11719924—22no—
68C2×#11719924—22no—
69C2×#11719924—22no—
70C2×#11719924—22no—
71C2×#11719924C2×C414yes—
72C2×#11719924C2×C414yes—
73C22×#88322C2311yescharacteristic
74C22×#88322C2311yescharacteristic
75C22×#88322C2311yescharacteristic
76C22×#88322C2311yescharacteristic
77#13133191—22no—
78#13133191C2×C414yes—
79C4×D212—22no—
80C4×D212—22no—
81C2×C4⋊Dic53C2311yescharacteristic
82C2×C4⋊Dic53C2311yescharacteristic
83C2×C4⋊Dic53C2311yescharacteristic
84C2×#11719919—21no—
85C2×C22⋊Dic53—21no—
86C2×#11719921—21no—
87C2×#11719921—21no—
88C2×#11719921—21no—
89C2×#11719921—21no—
90C2×C4×Dic53—21no—
91#13133150—22no—
92#13133148—22no—
93#13133141—22no—
94#13133141—22no—
95#13133141—22no—
96#13133141—22no—
97#13133141C2×C414yescomplemented
98#13133141C2×C414yescomplemented
99#13133137—22no—
100#13133137—22no—
101C22⋊#88322—22no—
102C22⋊#88322C2×C414yescomplemented
103#13133128—22no—
104C4×#88322—22no—
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×C414yescomplemented
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×C53D414yescomplemented
128C4×Q8×C53D414yescomplemented
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
154C23×D53—21no—
155C2×Q8×C53—24no—
156C2×Q8×C53—28no—
157C2×Q8×C53—28no—
158C2×Q8×C53—24no—
159C2×Q8×C53—28no—
160C2×Q8×C53—28no—
161C2×Q8×C53—24no—
162C2×Q8×C53—21no—
163C2×Q8×C53—21no—
164C2×Q8×C53—21no—
165C2×Q8×C53—21no—
166C2×Q8×C53—21no—
167C2×Q8×C53—21no—
168C2×Q8×C53C22×C412yes—
169C2×Q8×C53C22×C412yes—
170C2×Q8×C53C2×D412yes—
171C2×Q8×C53C2×D412yes—
172C2×Q8×C53#4112yes—
173C2×Q8×C53#4112yes—
174C22×C4×C53—24no—
175C22×C4×C53—24no—
176C22×C4×C53—24no—
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×C53—21no—
185C22×C4×C53C22×C412yes—
186C22×C4×C53C2×D411yescharacteristic
187C22×C4×C53C2×D411yescharacteristic
188C22×C4×C53C2×D411yescharacteristic
189C22×C4×C53C2×D411yescharacteristic
190C22×C4×C53C2×D411yescharacteristic
191C22×C4×C53#4112yes—
192C22×C4×C53C2411yescharacteristic
193C2×C22⋊D53—24no—
194C2×C22⋊D53—81no—
195C2×C22⋊D53—81no—
196C22×Dic53—21no—
197C22×Dic53—21no—
198C22×Dic53—21no—
199C2×D212—21no—
200C2×D212—21no—
201C2×D212—21no—
202C2×D212—21no—
203C2×D212—21no—
204C2×D212C22×C412yes—
205C2×C4×D53—42no—
206C2×C4×D53—81no—
207C2×C4×D53—81no—
208C4⋊C4×C53—24no—
209C4⋊C4×C53—24no—
210C4⋊C4×C53—24no—
211C4⋊C4×C53—24no—
212C4⋊C4×C53—22no—
213C4⋊C4×C53—22no—
214C4⋊C4×C53—21no—
215C4⋊C4×C53—21no—
216C4⋊C4×C53C2×D412yes—
217C4⋊C4×C53C2×D412yes—
218C22⋊C4×C53—24no—
219C22⋊C4×C53—22no—
220C22⋊C4×C53—22no—
221C42×C53—24no—
222C42×C53—24no—
223C42×C53—24no—
224C42×C53—24no—
225C42×C53—24no—
226C42×C53—21no—
227C42×C53—21no—
228C42×C53C2×D412yes—
229C42×C53C2×D412yes—
230C22⋊Dic53—81no—
231#11719924—28no—
232#11719924—28no—
233#11719921—24no—
234#11719921—42no—
235#11719921—81no—
236#11719921—81no—
237C4⋊Dic53—21no—
238C4⋊Dic53—21no—
239C4⋊Dic53—21no—
240C4⋊Dic53—21no—
241C4⋊Dic53—21no—
242C4⋊Dic53C22×C412yes—
243#11719919—81no—
244C4×Dic53—81no—
245C2×#88322—21no—
246C2×#88322—21no—
247C2×#88322—21no—
248C2×#88322—21no—
249C2×#88322—21no—
250C2×#88322—21no—
251C2×#88322—21no—
252C2×#88322—21no—
253C2×#88322—21no—
254C2×#88322—21no—
255C2×#88322C22×C412yes—
256C2×#88322C22×C412yes—
257C23×C53—21no—
258C23×C53—21no—
259C23×C53—21no—
260C23×C53—21no—
261C23×C53—21no—
262C23×C53—21no—
263C23×C53C4×D412yes—
264C23×C53C22×D411yescharacteristic
265C22×D53—22no—
266C22×D53—41no—
267C22×D53—41no—
268C22×D53—41no—
269C22×D53—41no—
270C22×D53—41no—
271C22×D53—41no—
272Q8×C53—216no—
273Q8×C53—22no—
274Q8×C53—22no—
275Q8×C53—22no—
276Q8×C53—22no—
277Q8×C53—22no—
278Q8×C53—22no—
279Q8×C53C4×D414yes—
280Q8×C53C4×D414yes—
281C2×C4×C53—216no—
282C2×C4×C53—22no—
283C2×C4×C53—22no—
284C2×C4×C53—22no—
285C2×C4×C53—22no—
286C2×C4×C53—21no—
287C2×C4×C53—22no—
288C2×C4×C53—22no—
289C2×C4×C53—21no—
290C2×C4×C53—21no—
291C2×C4×C53—21no—
292C2×C4×C53—21no—
293C2×C4×C53—21no—
294C2×C4×C53—22no—
295C2×C4×C53—22no—
296C2×C4×C53—22no—
297C2×C4×C53—22no—
298C2×C4×C53—22no—
299C2×C4×C53—22no—
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—41no—
307C2×C4×C53—41no—
308C2×C4×C53—41no—
309C2×C4×C53—41no—
310C2×C4×C53C4×D412yes—
311C2×C4×C53#12012yes—
312C2×C4×C53#12012yes—
313C2×C4×C53C23×C411yescharacteristic
314C2×C4×C53C22×D411yescharacteristic
315C2×C4×C53C22×D411yescharacteristic
316C2×C4×C53C2×#4111yescharacteristic
317C2×C4×C53C2×#4111yescharacteristic
318C2×C4×C53C2×#4111yescharacteristic
319C22⋊D53—84no—
320C2×Dic53—22no—
321C2×Dic53—41no—
322C2×Dic53—41no—
323C2×Dic53—41no—
324C2×Dic53—41no—
325C2×Dic53—41no—
326C2×Dic53—41no—
327C2×Dic53—41no—
328C2×Dic53—41no—
329D212—22no—
330D212—22no—
331D212—41no—
332D212—41no—
333C4×D53—84no—
334#88322—22no—
335#88322—22no—
336#88322—41no—
337#88322—41no—
338#21462—531nomaximal, Sylow
339C22×C53—22no—
340C22×C53—22no—
341C22×C53—22no—
342C22×C53—41no—
343C22×C53—41no—
344C22×C53—41no—
345C22×C53—41no—
346C22×C53C2×C4×D411yescharacteristic
347C22×C53C2×#12011yescharacteristic
348C22×C53#52511yescharacteristic
349C22×C53#57711yescharacteristic
350C22×C53#57711yescharacteristic
351C22×C53#57711yescharacteristic
352C22×C53#57811yescharacteristic
353C2×D53—42no—
354C2×D53—42no—
355C2×D53—42no—
356C2×D53—81no—
357C2×D53—81no—
358C2×D53—81no—
359C2×D53—81no—
360C4×C53—22no—
361C4×C53—22no—
362C4×C53—24no—
363C4×C53—24no—
364C4×C53—22no—
365C4×C53—41no—
366C4×C53—42no—
367C4×C53—41no—
368C4×C53—42no—
369C4×C53C2×C4×D411yescharacteristic
370C4×C53C2×C4×D411yescharacteristic
371C4×C53#52511yescharacteristic
372C4×C53#52511yescharacteristic
373Dic53—42no—
374Dic53—81no—
375Dic53—81no—
376C2×#519D5311yescharacteristic, complemented
377C2×#448—531no—
378C2×#440—531no—
379C2×C4×SD16—531no—
380#2324—531no—
381#1880—531no—
382#1880—531no—
383#1875—531no—
384#1865—531no—
385#1863—531no—
386#1854—531no—
387#1787—531no—
388#1763—531no—
389C4×#103—531no—
390#1750—531no—
391C2×C53—42no—
392C2×C53C4×#12011yescharacteristic
393C2×C53#294711yescharacteristic
394C2×C53#294911yescharacteristic
395C2×C53#301011yescharacteristic
396C2×C53#301311yescharacteristic
397C2×C53#312111yescharacteristic
398C2×C53#312611yescharacteristic
399D53—82no—
400C23×Q8C2×D5311yescharacteristic
401C22×SD16—531no—
402C22×SD16—531no—
403C2×#121—531no—
404#519—24no—
405#519—24no—
406C2×C4×Q8—21no—
407C2×C4×Q8—21no—
408C2×C4×Q8C2×D5311yescharacteristic
409C2×C4×Q8C2×D5311yescharacteristic
410C2×C4×Q8C2×D5311yescharacteristic
411C2×C4×Q8C2×D5311yescharacteristic
412C2×C4×D4—531no—
413C2×#117—21no—
414C2×#117—21no—
415C2×#117C2×D5311yescharacteristic
416C2×#117C2×D5311yescharacteristic
417#448—538no—
418#440—1064no—
419C4×SD16—1064no—
420C2×#107—531no—
421C2×#106—531no—
422C2×#103—531no—
423C2×#103—531no—
424C2×#103—531no—
425C2×#103—531no—
426C2×#103—531no—
427C2×#103—531no—
428C2×#102—531no—
429C2×#102—531no—
430C2×C22⋊C8—531no—
431C2×C22⋊C8—531no—
432C2×#97—531no—
433C2×C4×C8—531no—
434#390—531no—
435#390—1061no—
436#389—531no—
437#388—1061no—
438#386—1061no—
439#385—1061no—
440#380—531no—
441C4×C4⋊C4—531no—
442#340—531no—
443#340—531no—
444#340—531no—
445#340—531no—
446#336—531no—
447#336—531no—
448C53#2146211yescharacteristic, complemented, Sylow
449C22×Q8—22no—
450C22×Q8—22no—
451C22×Q8—22no—
452C22×Q8—22no—
453C22×Q8—22no—
454C22×Q8—21no—
455C22×Q8C4×D5314yescomplemented
456C22×Q8C22×D5311yescharacteristic
457C22×Q8C22×D5311yescharacteristic
458C22×D4—531no—
459C22×D4—1061no—
460C23×C4—21no—
461C23×C4—1061no—
462C23×C4C22×D5311yescharacteristic
463C2×SD16—534no—
464C2×SD16—534no—
465C2×SD16—1062no—
466C2×SD16—1062no—
467C2×SD16—1062no—
468C2×SD16—1062no—
469C22×C8—531no—
470C22×C8—531no—
471C22×C8—531no—
472C22×C8—531no—
473#121—534no—
474#121—1062no—
475C4×Q8—28no—
476C4×Q8—28no—
477C4×Q8—22no—
478C4×Q8—22no—
479C4×Q8—22no—
480C4×Q8—22no—
481C4×Q8—22no—
482C4×Q8—22no—
483C4×Q8C22⋊D5314yescomplemented
484C4×Q8C22⋊D5314yescomplemented
485C4×D4—1062no—
486C4×D4—1062no—
487#117—28no—
488#117—28no—
489#117—22no—
490#117—22no—
491#117—22no—
492#117—22no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—531no—
498C2×C4⋊C4—531no—
499C2×C4⋊C4—531no—
500C2×C4⋊C4—1061no—
501C2×C4⋊C4C22⋊D5311yescharacteristic
502C2×C4⋊C4C22⋊D5311yescharacteristic
503C2×C4⋊C4C22×D5311yescharacteristic
504C2×C4⋊C4C22×D5311yescharacteristic
505C2×C22⋊C4—21no—
506C2×C22⋊C4—1061no—
507C2×C22⋊C4—1061no—
508C2×C22⋊C4—1061no—
509C2×C22⋊C4—1061no—
510C2×C22⋊C4—1061no—
511C2×C22⋊C4C22⋊D5311yescharacteristic
512C2×C22⋊C4C22⋊D5311yescharacteristic
513C2×C42—21no—
514C2×C42—21no—
515C2×C42—21no—
516C2×C42—21no—
517C2×C42—21no—
518C2×C42—1061no—
519C2×C42C22×D5311yescharacteristic
520C2×C42C22×D5311yescharacteristic
521#107—1062no—
522#106—1062no—
523#103—534no—
524#103—534no—
525#103—1062no—
526#103—1062no—
527#103—1062no—
528#103—1062no—
529#102—1062no—
530#102—1062no—
531C22⋊C8—534no—
532C22⋊C8—1062no—
533#97—1062no—
534C4×C8—1062no—
535#95—1061no—
536#95—1061no—
537#95—1061no—
538C24—1061no—
539C24C2×C22⋊D5311yescharacteristic
540C2×Q8—24no—
541C2×Q8—28no—
542C2×Q8—28no—
543C2×Q8—24no—
544C2×Q8—28no—
545C2×Q8—28no—
546C2×Q8—24no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8C2×C4×D5312yes—
554C2×Q8C2×C4×D5312yes—
555C2×Q8#1171994512yes—
556C2×Q8#1171994512yes—
557C2×Q8C2×C22⋊D5312yes—
558C2×Q8C2×C22⋊D5312yes—
559C2×D4—532no—
560C2×D4—1064no—
561C2×D4—1061no—
562C2×D4—1061no—
563C2×D4—1061no—
564C2×D4—1061no—
565C2×D4—1061no—
566C2×D4—4241no—
567C2×D4—4241no—
568C22×C4—24no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—1061no—
580C22×C4—1061no—
581C22×C4—1061no—
582C22×C4—4241no—
583C22×C4—4241no—
584C22×C4—2122no—
585C22×C4C2×C4×D5312yes—
586C22×C4#1171994512yes—
587C22×C4C2×C22⋊D5311yescharacteristic
588C22×C4C2×C22⋊D5311yescharacteristic
589C22×C4C2×C22⋊D5311yescharacteristic
590C22×C4C2×C22⋊D5311yescharacteristic
591C22×C4C2×C22⋊D5311yescharacteristic
592C22×C4C23×D5311yescharacteristic
593SD16—1068no—
594SD16—1068no—
595C2×C8—532no—
596C2×C8—532no—
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—1061no—
606C2×C8—1061no—
607C4⋊C4—24no—
608C4⋊C4—24no—
609C4⋊C4—24no—
610C4⋊C4—24no—
611C4⋊C4—22no—
612C4⋊C4—22no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—532no—
616C4⋊C4—1061no—
617C4⋊C4—1061no—
618C4⋊C4—1061no—
619C4⋊C4—1061no—
620C4⋊C4—1061no—
621C4⋊C4—4241no—
622C4⋊C4C2×C22⋊D5312yes—
623C4⋊C4C2×C22⋊D5312yes—
624C22⋊C4—24no—
625C22⋊C4—22no—
626C22⋊C4—22no—
627C22⋊C4—1064no—
628C22⋊C4—4241no—
629C22⋊C4—4241no—
630C22⋊C4—4241no—
631C22⋊C4—2122no—
632C42—24no—
633C42—24no—
634C42—24no—
635C42—24no—
636C42—24no—
637C42—21no—
638C42—21no—
639C42—4241no—
640C42C2×C22⋊D5312yes—
641C42C2×C22⋊D5312yes—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—1062no—
649C23—2121no—
650C23—2121no—
651C23—2121no—
652C23—2121no—
653C23—2121no—
654C23—2121no—
655C23C4×C22⋊D5312yes—
656C23C22×C22⋊D5311yescharacteristic
657Q8—216no—
658Q8—22no—
659Q8—22no—
660Q8—22no—
661Q8—22no—
662Q8—22no—
663Q8—22no—
664Q8C4×C22⋊D5314yes—
665Q8C4×C22⋊D5314yes—
666D4—1062no—
667D4—1062no—
668D4—4244no—
669D4—2121no—
670D4—2121no—
671C2×C4—216no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—21no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
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×C4—2121no—
710C2×C4C4×C22⋊D5312yes—
711C2×C4#1313318612yes—
712C2×C4#1313318612yes—
713C2×C4C22×C4×D5311yescharacteristic
714C2×C4C22×C22⋊D5311yescharacteristic
715C2×C4C22×C22⋊D5311yescharacteristic
716C2×C4C2×#1171994511yescharacteristic
717C2×C4C2×#1171994511yescharacteristic
718C2×C4C2×#1171994511yescharacteristic
719C8—1062no—
720C8—1062no—
721C8—2121no—
722C8—2121no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—4241no—
731C22—4241no—
732C22—4241no—
733C22—4241no—
734C22—2122no—
735C22—2122no—
736C22—2122no—
737C22C2×C4×C22⋊D5311yescharacteristic
738C22C2×#1313318611yescharacteristic
739C22#1681113411yescharacteristic
740C22#1681143111yescharacteristic
741C22#1681143111yescharacteristic
742C22#1681143111yescharacteristic
743C22#1681143811yescharacteristic
744C4—22no—
745C4—22no—
746C4—24no—
747C4—24no—
748C4—22no—
749C4—41no—
750C4—42no—
751C4—41no—
752C4—42no—
753C4—4241no—
754C4—4241no—
755C4—2122no—
756C4C2×C4×C22⋊D5311yescharacteristic
757C4C2×C4×C22⋊D5311yescharacteristic
758C4#1681113411yescharacteristic
759C4#1681113411yescharacteristic
760C2—42no—
761C2—4242no—
762C2C4×#1313318611yescharacteristic
763C2#2028355811yescharacteristic
764C2#2028357411yescharacteristic
765C2#2028400111yescharacteristic
766C2#2028403011yescharacteristic
767C2#2028494411yescharacteristic
768C2#2028500611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC2×C53×#519C2
socleC23×C53C22×D4
prime radicalC2×#13133191C22
cosocleC22×C4×C53C24
hypercenterC2×#519D53
hypocenterC53#21462
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×#16810721C2semidirect
3. C2×C4×#11719924C2semidirect
5. #20275070C2semidirect
6. #20275070C2semidirect
8. #20274983C2semidirect
9. #20274969C2semidirect
10. #20274914C2semidirect
11. #20274650C2semidirect
12. #20274545C2semidirect
13. C4×#13133141C2semidirect
14. #20274481C2semidirect
15. C2×C53×#519C2semidirect
20. #16810762C4semidirect
97. #13133141C2×C4semidirect
98. #13133141C2×C4semidirect
102. C22⋊#88322C2×C4semidirect
114. C22×Q8×C53C2×C4semidirect
127. C4×Q8×C53D4semidirect
128. C4×Q8×C53D4semidirect
376. C2×#519D53semidirect
448. C53#21462semidirect
455. C22×Q8C4×D53semidirect
483. C4×Q8C22⋊D53semidirect
484. C4×Q8C22⋊D53semidirect

Maximal subgroups

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

subgroupindex
C2×#168107622
C2×#168107212
C2×C4×#117199242
#202774082
#202750702
#202750372
#202749832
#202749692
#202749142
#202746502
#202745452
C4×#131331412
#202744812
C2×C53×#5192
#2146253