Finite Group Databasebeta

← C2×#20284914 #28252339

Subgroups — C2×#20284914 #28252339

Order 13568.

2198 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811228C211yesmaximal, characteristic, complemented
2#20284914C2116yesmaximal, direct product factor
3C2×#16810941C211yesmaximal, characteristic, complemented
4C2×#16810936C211yesmaximal, characteristic, complemented
5C2×#16810930C211yesmaximal, characteristic, complemented
6C2×#16810923C211yesmaximal, characteristic, complemented
7C2×#16810823C211yesmaximal, characteristic, complemented
8C2×#16810818C211yesmaximal, characteristic, complemented
9C2×#16810768C211yesmaximal, characteristic, complemented
10C2×#16810768C211yesmaximal, characteristic, complemented
11C2×#16810733C211yesmaximal, characteristic, complemented
12C2×#16810721C211yesmaximal, characteristic, complemented
13C2×C4×#11719924C211yesmaximal, characteristic, complemented
14C2×C4×#11719922C211yesmaximal, characteristic, complemented
15C2×#16810684C211yesmaximal, characteristic, complemented
16C2×C53×#520C211yesmaximal, characteristic, complemented
17C22×#11719924C2211yescharacteristic
18C22×#11719924C2211yescharacteristic
19C22×#11719922C2211yescharacteristic
20C22×#11719922C2211yescharacteristic
21#16811228—24no—
22#16811228C2218yescomplemented
23C2×#13133214C2211yescharacteristic
24C2×#13133209C2211yescharacteristic
25C2×#13133202—21no—
26C2×#13133202—21no—
27C2×#13133191C2211yescharacteristic
28C2×#13133191C2211yescharacteristic
29C2×#13133190—21no—
30C2×#13133190—21no—
31C2×C4×D212C2211yescharacteristic
32C2×C4×D212C2211yescharacteristic
33#16810941C2218yescomplemented
34#16810936C2218yescomplemented
35#16810930C2218yescomplemented
36#16810923C2218yescomplemented
37#16810823C2218yescomplemented
38#16810818C2218yescomplemented
39#16810768C2218yescomplemented
40#16810768C2218yescomplemented
41#16810733C2218yescomplemented
42#16810721C2218yescomplemented
43C4×#11719924C2218yescomplemented
44C4×#11719922C2218yescomplemented
45#16810684C2218yescomplemented
46C2×#13133150C2211yescharacteristic
47C2×#13133150C2211yescharacteristic
48C2×#13133148C2211yescharacteristic
49C2×#13133148C2211yescharacteristic
50C2×C4⋊#88322C2211yescharacteristic
51C2×C4⋊#88322C2211yescharacteristic
52C2×#13133141C2211yescharacteristic
53C2×#13133141C2211yescharacteristic
54C2×#13133138C2211yescharacteristic
55C2×#13133138C2211yescharacteristic
56C2×#13133137C2211yescharacteristic
57C2×#13133137C2211yescharacteristic
58C2×#13133137C2211yescharacteristic
59C2×#13133137C2211yescharacteristic
60C2×C22⋊#88322C2211yescharacteristic
61C2×C22⋊#88322C2211yescharacteristic
62C2×#13133128C2211yescharacteristic
63C2×C4×#88322C2211yescharacteristic
64C22×#41×C53C2211yescharacteristic
65C53×#520—24no—
66C53×#520C2218yescomplemented
67C2×C4×Q8×C53C2211yescharacteristic
68C2×C4×Q8×C53C2211yescharacteristic
69C2×C4×D4×C53—21no—
70C2×C4×D4×C53—21no—
71C2×C4×D4×C53C2211yescharacteristic
72C2×C4×D4×C53C2211yescharacteristic
73C2×#117×C53—21no—
74C2×#117×C53C2211yescharacteristic
75C22×C4⋊C4×C53—21no—
76C22×C4⋊C4×C53C2211yescharacteristic
77C22×D212—21no—
78C22×D212—21no—
79C22×D212C2311yescharacteristic
80C22×D212C2311yescharacteristic
81C22×C22⋊D53—21no—
82C22×C22⋊D53—21no—
83C22×C4×D53—21no—
84C22×C4×D53—21no—
85C2×#11719924—24no—
86C2×#11719924—24no—
87C2×#11719924C2314yes—
88C2×#11719924C2314yes—
89C2×#11719922—24no—
90C2×#11719922—24no—
91C2×#11719922C2314yes—
92C2×#11719922C2314yes—
93C22×#88322C2311yescharacteristic
94C22×#88322C2311yescharacteristic
95C22×#88322C2311yescharacteristic
96C22×#88322C2311yescharacteristic
97#13133214—22no—
98#13133214C2314yes—
99#13133209—22no—
100#13133209C2314yes—
101#13133202—28no—
102#13133202—28no—
103#13133191—22no—
104#13133191—22no—
105#13133191C2314yes—
106#13133191C2314yes—
107#13133190—28no—
108#13133190—28no—
109C4×D212—22no—
110C4×D212—22no—
111C4×D212C2314yes—
112C4×D212C2314yes—
113C2×C4⋊Dic53C2311yescharacteristic
114C2×C4⋊Dic53C2311yescharacteristic
115C2×#11719919—21no—
116C2×#11719919—21no—
117C2×#11719921—21no—
118C2×#11719921—21no—
119C2×#11719921—21no—
120C2×#11719921—21no—
121#13133150C2314yes—
122#13133150C2314yes—
123#13133148C2314yes—
124#13133148C2314yes—
125C4⋊#88322C2314yes—
126C4⋊#88322C2314yes—
127#13133141C2314yes—
128#13133141C2314yes—
129#13133138C2314yes—
130#13133138C2314yes—
131#13133137C2314yes—
132#13133137C2314yes—
133#13133137C2314yes—
134#13133137C2314yes—
135C22⋊#88322C2314yes—
136C22⋊#88322C2314yes—
137#13133128C2314yes—
138C4×#88322C2314yes—
139C2×#41×C53—24no—
140C2×#41×C53—24no—
141C2×#41×C53—22no—
142C2×#41×C53C2314yes—
143C22×Q8×C53C2311yescharacteristic
144C22×D4×C53—21no—
145C22×D4×C53C2311yescharacteristic
146C23×C4×C53—21no—
147C23×C4×C53—21no—
148C23×C4×C53—21no—
149C23×C4×C53—21no—
150C23×C4×C53C2311yescharacteristic
151C4×Q8×C53—22no—
152C4×Q8×C53—22no—
153C4×Q8×C53C2314yes—
154C4×Q8×C53C2314yes—
155C4×D4×C53—28no—
156C4×D4×C53—28no—
157C4×D4×C53—22no—
158C4×D4×C53—22no—
159C4×D4×C53C2314yes—
160C4×D4×C53C2314yes—
161#117×C53—28no—
162#117×C53D414yes—
163#117×C53C2314yes—
164C2×C4⋊C4×C53—28no—
165C2×C4⋊C4×C53—21no—
166C2×C4⋊C4×C53—21no—
167C2×C4⋊C4×C53—21no—
168C2×C4⋊C4×C53—22no—
169C2×C4⋊C4×C53D411yescharacteristic
170C2×C4⋊C4×C53D411yescharacteristic
171C2×C4⋊C4×C53C2311yescharacteristic
172C2×C4⋊C4×C53C2311yescharacteristic
173C2×C4⋊C4×C53C2314yes—
174C2×C22⋊C4×C53—21no—
175C2×C22⋊C4×C53—21no—
176C2×C22⋊C4×C53D411yescharacteristic
177C2×C22⋊C4×C53D411yescharacteristic
178C2×C42×C53—21no—
179C2×C42×C53—21no—
180C2×C42×C53C2311yescharacteristic
181C2×C42×C53C2311yescharacteristic
182C24×C53—21no—
183C24×C53C2×D411yescharacteristic
184C23×D53—21no—
185C23×D53—21no—
186#41×C53—216no—
187#41×C53—28no—
188#41×C53—28no—
189C2×Q8×C53—21no—
190C2×Q8×C53—22no—
191C2×Q8×C53#4114yes—
192C2×Q8×C53C2412yes—
193C2×D4×C53—28no—
194C2×D4×C53—24no—
195C2×D4×C53—21no—
196C2×D4×C53—22no—
197C2×D4×C53#4114yes—
198C2×D4×C53C2412yes—
199C22×C4×C53—28no—
200C22×C4×C53—21no—
201C22×C4×C53—24no—
202C22×C4×C53—22no—
203C22×C4×C53—22no—
204C22×C4×C53—21no—
205C22×C4×C53—21no—
206C22×C4×C53—24no—
207C22×C4×C53—24no—
208C22×C4×C53—24no—
209C22×C4×C53—82no—
210C22×C4×C53—82no—
211C22×C4×C53—82no—
212C22×C4×C53C2×D411yescharacteristic
213C22×C4×C53C2×D411yescharacteristic
214C22×C4×C53C2×D411yescharacteristic
215C22×C4×C53C2×D411yescharacteristic
216C22×C4×C53C2×D411yescharacteristic
217C22×C4×C53C2×D412yes—
218C22×C4×C53C2412yes—
219C22×C4×C53C2411yescharacteristic
220C2×C22⋊D53—24no—
221C2×C22⋊D53—24no—
222C2×C22⋊D53—82no—
223C2×C22⋊D53—82no—
224C22×Dic53—21no—
225C22×Dic53—21no—
226C2×D212—22no—
227C2×D212—22no—
228C2×D212—22no—
229C2×D212—22no—
230C2×D212—21no—
231C2×D212—21no—
232C2×D212—24no—
233C2×D212—24no—
234C2×D212—82no—
235C2×D212—82no—
236C2×D212C2412yes—
237C2×D212C2412yes—
238C2×C4×D53—24no—
239C2×C4×D53—24no—
240C2×C4×D53—82no—
241C2×C4×D53—82no—
242C4⋊C4×C53—24no—
243C4⋊C4×C53—24no—
244C4⋊C4×C53—24no—
245C4⋊C4×C53—21no—
246C4⋊C4×C53—21no—
247C4⋊C4×C53C2×D414yes—
248C4⋊C4×C53C2×D414yes—
249C4⋊C4×C53C2412yes—
250C4⋊C4×C53C2412yes—
251C22⋊C4×C53—24no—
252C22⋊C4×C53—24no—
253C22⋊C4×C53C2×D414yes—
254C22⋊C4×C53C2×D414yes—
255C42×C53—24no—
256C42×C53—24no—
257C42×C53C2×D412yes—
258C42×C53C2×D412yes—
259C42×C53C2412yes—
260C42×C53C2412yes—
261#11719924—28no—
262#11719924—28no—
263#11719922—28no—
264#11719922—28no—
265#11719921—24no—
266#11719921—24no—
267#11719921—24no—
268#11719921—24no—
269C4⋊Dic53—21no—
270C4⋊Dic53—21no—
271C4⋊Dic53C2412yes—
272C4⋊Dic53C2412yes—
273#11719919—24no—
274#11719919—24no—
275C2×#88322—22no—
276C2×#88322—22no—
277C2×#88322—22no—
278C2×#88322—22no—
279C2×#88322C2412yes—
280C2×#88322C2412yes—
281C2×#88322C2412yes—
282C2×#88322C2412yes—
283C23×C53—22no—
284C23×C53—24no—
285C23×C53—22no—
286C23×C53—22no—
287C23×C53—22no—
288C23×C53—42no—
289C23×C53—42no—
290C23×C53C22×D412yes—
291C23×C53C22×D411yescharacteristic
292C22×D53—22no—
293C22×D53—22no—
294C22×D53—42no—
295C22×D53—42no—
296C22×D53—42no—
297C22×D53—42no—
298C22×D53—42no—
299C22×D53—42no—
300Q8×C53—24no—
301Q8×C53—22no—
302Q8×C53C2×#4114yes—
303D4×C53—216no—
304D4×C53—24no—
305D4×C53—22no—
306D4×C53C2×#4114yes—
307C2×C4×C53—216no—
308C2×C4×C53—22no—
309C2×C4×C53—24no—
310C2×C4×C53—22no—
311C2×C4×C53—22no—
312C2×C4×C53—22no—
313C2×C4×C53—22no—
314C2×C4×C53—22no—
315C2×C4×C53—24no—
316C2×C4×C53—22no—
317C2×C4×C53—22no—
318C2×C4×C53—22no—
319C2×C4×C53—22no—
320C2×C4×C53—42no—
321C2×C4×C53—42no—
322C2×C4×C53—84no—
323C2×C4×C53—84no—
324C2×C4×C53—84no—
325C2×C4×C53C22×D412yes—
326C2×C4×C53C22×D412yes—
327C2×C4×C53C22×D412yes—
328C2×C4×C53C22×D412yes—
329C2×C4×C53C22×D412yes—
330C2×C4×C53C22×D411yescharacteristic
331C2×C4×C53C2×#4112yes—
332C2×C4×C53C2×#4112yes—
333C2×C4×C53C2511yescharacteristic
334C22⋊D53—84no—
335C22⋊D53—84no—
336C2×Dic53—22no—
337C2×Dic53—22no—
338C2×Dic53—42no—
339C2×Dic53—42no—
340D212—22no—
341D212—22no—
342D212—22no—
343D212—22no—
344D212—42no—
345D212—42no—
346D212—84no—
347D212—84no—
348C4×D53—84no—
349C4×D53—84no—
350#88322—22no—
351#88322—22no—
352#88322—22no—
353#88322—22no—
354C2×#3119—531nomaximal, Sylow
355C22×C53—22no—
356C22×C53—24no—
357C22×C53—22no—
358C22×C53—22no—
359C22×C53—44no—
360C22×C53—48no—
361C22×C53—42no—
362C22×C53—42no—
363C22×C53#52512yes—
364C22×C53#57612yes—
365C22×C53#57712yes—
366C22×C53C23×D411yescharacteristic
367C2×D53—42no—
368C2×D53—42no—
369C2×D53—42no—
370C2×D53—42no—
371C2×D53—42no—
372C2×D53—42no—
373C2×D53—84no—
374C2×D53—84no—
375C4×C53—22no—
376C4×C53—24no—
377C4×C53—22no—
378C4×C53—22no—
379C4×C53—22no—
380C4×C53—22no—
381C4×C53—42no—
382C4×C53—42no—
383C4×C53#52512yes—
384C4×C53C22×#4111yescharacteristic
385C4×C53C22×#4111yescharacteristic
386Dic53—42no—
387Dic53—42no—
388C2×#540—531no—
389C2×#520D5311yescharacteristic, complemented
390#3119—5316no—
391C2×#481—531no—
392C2×#480—531no—
393C2×#479—531no—
394C2×#478—531no—
395C2×#460—531no—
396C2×#459—531no—
397C2×#449—531no—
398C2×#449—531no—
399C2×#442—531no—
400C2×#440—531no—
401C2×C4×SD16—531no—
402C2×C4×D8—531no—
403C2×#433—531no—
404C2×C53—42no—
405C2×C53—44no—
406C2×C53#311914yescomplemented
407C2×C53C2×#52511yescharacteristic
408C2×C53C2×#57611yescharacteristic
409C2×C53C2×#57711yescharacteristic
410D53—82no—
411D53—82no—
412C22×#41C2×D5311yescharacteristic
413C22×SD16—531no—
414C22×SD16—531no—
415C22×D8—531no—
416C22×D8—531no—
417#540—538no—
418#540—1064no—
419C2×#127—531no—
420C2×#125—531no—
421C2×#123—1061no—
422C2×#123—1061no—
423C2×#121—531no—
424C2×#121—531no—
425C2×#121—1061no—
426C2×#121—1061no—
427#520—24no—
428#520C2×D5318yescomplemented
429C2×C4×Q8C2×D5311yescharacteristic
430C2×C4×Q8C2×D5311yescharacteristic
431C2×C4×D4—21no—
432C2×C4×D4—21no—
433C2×C4×D4—531no—
434C2×C4×D4—531no—
435C2×C4×D4C2×D5311yescharacteristic
436C2×C4×D4C2×D5311yescharacteristic
437C2×#117—21no—
438C2×#117C2×D5311yescharacteristic
439C22×C4⋊C4—21no—
440C22×C4⋊C4C2×D5311yescharacteristic
441#481—538no—
442#480—538no—
443#479—538no—
444#478—538no—
445#460—538no—
446#459—538no—
447#449—538no—
448#449—538no—
449#442—538no—
450#440—538no—
451C4×SD16—538no—
452C4×D8—538no—
453#433—538no—
454C2×#107—531no—
455C2×#107—531no—
456C2×#106—531no—
457C2×#106—531no—
458C2×C4⋊C8—531no—
459C2×C4⋊C8—531no—
460C2×#103—531no—
461C2×#103—531no—
462C2×#102—531no—
463C2×#102—531no—
464C2×#102—531no—
465C2×#102—531no—
466C2×#102—531no—
467C2×#102—531no—
468C2×C22⋊C8—531no—
469C2×C22⋊C8—531no—
470C2×#97—531no—
471C2×C4×C8—531no—
472C53C2×#311911yescharacteristic, complemented, Sylow
473C2×#41—24no—
474C2×#41—24no—
475C2×#41—22no—
476C2×#41C22×D5314yes—
477C22×Q8C22×D5311yescharacteristic
478C22×D4—21no—
479C22×D4—531no—
480C22×D4—531no—
481C22×D4—1061no—
482C22×D4—1061no—
483C22×D4—1061no—
484C22×D4—1061no—
485C22×D4C22×D5311yescharacteristic
486C23×C4—21no—
487C23×C4—21no—
488C23×C4—21no—
489C23×C4—21no—
490C23×C4—1061no—
491C23×C4—1061no—
492C23×C4C22×D5311yescharacteristic
493C2×SD16—534no—
494C2×SD16—534no—
495C2×SD16—1064no—
496C2×SD16—1064no—
497C2×D8—534no—
498C2×D8—534no—
499C2×D8—1064no—
500C2×D8—1064no—
501C22×C8—531no—
502C22×C8—531no—
503C22×C8—531no—
504C22×C8—531no—
505#127—534no—
506#127—1062no—
507#125—534no—
508#125—1062no—
509#123—1068no—
510#123—1068no—
511#121—534no—
512#121—534no—
513#121—1062no—
514#121—1062no—
515#121—1068no—
516#121—1068no—
517C4×Q8—22no—
518C4×Q8—22no—
519C4×Q8C22×D5314yes—
520C4×Q8C22×D5314yes—
521C4×D4—28no—
522C4×D4—28no—
523C4×D4—22no—
524C4×D4—22no—
525C4×D4—534no—
526C4×D4—534no—
527C4×D4—1062no—
528C4×D4—1062no—
529C4×D4C22×D5314yes—
530C4×D4C22×D5314yes—
531#117—28no—
532#117C22⋊D5314yes—
533#117C22×D5314yes—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—22no—
538C2×C4⋊C4—28no—
539C2×C4⋊C4—531no—
540C2×C4⋊C4—531no—
541C2×C4⋊C4—1061no—
542C2×C4⋊C4—1061no—
543C2×C4⋊C4C22⋊D5311yescharacteristic
544C2×C4⋊C4C22⋊D5311yescharacteristic
545C2×C4⋊C4C22×D5311yescharacteristic
546C2×C4⋊C4C22×D5311yescharacteristic
547C2×C4⋊C4C22×D5314yes—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—1061no—
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
559C2×C42C22×D5311yescharacteristic
560#107—534no—
561#107—534no—
562#106—534no—
563#106—534no—
564C4⋊C8—534no—
565C4⋊C8—534no—
566#103—534no—
567#103—534no—
568#102—534no—
569#102—534no—
570#102—534no—
571#102—534no—
572#102—534no—
573#102—534no—
574C22⋊C8—534no—
575C22⋊C8—534no—
576#97—534no—
577C4×C8—534no—
578C24—21no—
579C24—1061no—
580C24—1061no—
581C24C2×C22⋊D5311yescharacteristic
582#41—216no—
583#41—28no—
584#41—28no—
585C2×Q8—21no—
586C2×Q8—22no—
587C2×Q8#1171994514yes—
588C2×Q8C23×D5312yes—
589C2×D4—28no—
590C2×D4—24no—
591C2×D4—21no—
592C2×D4—22no—
593C2×D4—532no—
594C2×D4—532no—
595C2×D4—1064no—
596C2×D4—1064no—
597C2×D4—1064no—
598C2×D4—1064no—
599C2×D4—1061no—
600C2×D4—1061no—
601C2×D4—1062no—
602C2×D4—1062no—
603C2×D4—1062no—
604C2×D4—1062no—
605C2×D4—4242no—
606C2×D4—4242no—
607C2×D4—4242no—
608C2×D4—4242no—
609C2×D4#1171994514yes—
610C2×D4C23×D5312yes—
611C22×C4—28no—
612C22×C4—21no—
613C22×C4—24no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—24no—
619C22×C4—24no—
620C22×C4—24no—
621C22×C4—82no—
622C22×C4—82no—
623C22×C4—82no—
624C22×C4—1061no—
625C22×C4—1061no—
626C22×C4—1064no—
627C22×C4—1064no—
628C22×C4—4242no—
629C22×C4—4242no—
630C22×C4C2×C22⋊D5312yes—
631C22×C4C2×C22⋊D5311yescharacteristic
632C22×C4C2×C22⋊D5311yescharacteristic
633C22×C4C2×C22⋊D5311yescharacteristic
634C22×C4C2×C22⋊D5311yescharacteristic
635C22×C4C2×C22⋊D5311yescharacteristic
636C22×C4C23×D5312yes—
637C22×C4C23×D5311yescharacteristic
638SD16—1068no—
639SD16—1068no—
640D8—1068no—
641D8—1068no—
642C2×C8—532no—
643C2×C8—532no—
644C2×C8—532no—
645C2×C8—532no—
646C2×C8—1062no—
647C2×C8—1062no—
648C2×C8—1062no—
649C2×C8—1062no—
650C4⋊C4—24no—
651C4⋊C4—24no—
652C4⋊C4—24no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—532no—
656C4⋊C4—532no—
657C4⋊C4—1061no—
658C4⋊C4—1061no—
659C4⋊C4—1064no—
660C4⋊C4—1064no—
661C4⋊C4C2×C22⋊D5314yes—
662C4⋊C4C2×C22⋊D5314yes—
663C4⋊C4C23×D5312yes—
664C4⋊C4C23×D5312yes—
665C22⋊C4—24no—
666C22⋊C4—24no—
667C22⋊C4—1064no—
668C22⋊C4—1064no—
669C22⋊C4—1064no—
670C22⋊C4—1064no—
671C22⋊C4C2×C22⋊D5314yes—
672C22⋊C4C2×C22⋊D5314yes—
673C42—24no—
674C42—24no—
675C42C2×C22⋊D5312yes—
676C42C2×C22⋊D5312yes—
677C42C23×D5312yes—
678C42C23×D5312yes—
679C23—22no—
680C23—24no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—42no—
685C23—42no—
686C23—1062no—
687C23—1062no—
688C23—2122no—
689C23—2122no—
690C23—2122no—
691C23—2122no—
692C23—2122no—
693C23—2122no—
694C23C22×C22⋊D5312yes—
695C23C22×C22⋊D5311yescharacteristic
696Q8—24no—
697Q8—22no—
698Q8C2×#1171994514yes—
699D4—216no—
700D4—24no—
701D4—22no—
702D4—1062no—
703D4—1062no—
704D4—1062no—
705D4—1062no—
706D4—4244no—
707D4—4244no—
708D4—4244no—
709D4—4244no—
710D4—2122no—
711D4—2122no—
712D4C2×#1171994514yes—
713C2×C4—216no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—84no—
729C2×C4—84no—
730C2×C4—84no—
731C2×C4—1062no—
732C2×C4—1062no—
733C2×C4—4244no—
734C2×C4—4244no—
735C2×C4—2122no—
736C2×C4—2122no—
737C2×C4C22×C22⋊D5312yes—
738C2×C4C22×C22⋊D5312yes—
739C2×C4C22×C22⋊D5312yes—
740C2×C4C22×C22⋊D5312yes—
741C2×C4C22×C22⋊D5312yes—
742C2×C4C22×C22⋊D5311yescharacteristic
743C2×C4C2×#1171994512yes—
744C2×C4C2×#1171994512yes—
745C2×C4C24×D5311yescharacteristic
746C8—1062no—
747C8—1062no—
748C8—1062no—
749C8—1062no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—24no—
754C22—42no—
755C22—42no—
756C22—44no—
757C22—48no—
758C22—4244no—
759C22—4244no—
760C22—2122no—
761C22—2122no—
762C22—2122no—
763C22—2122no—
764C22—2122no—
765C22—2122no—
766C22#1681113412yes—
767C22#1681142612yes—
768C22#1681143112yes—
769C22C23×C22⋊D5311yescharacteristic
770C4—22no—
771C4—22no—
772C4—22no—
773C4—22no—
774C4—22no—
775C4—24no—
776C4—42no—
777C4—42no—
778C4—2122no—
779C4—2122no—
780C4#1681113412yes—
781C4C22×#1171994511yescharacteristic
782C4C22×#1171994511yescharacteristic
783C2—42no—
784C2—44no—
785C2—4242no—
786C2—4242no—
787C2#2028491414yesdirect product factor
788C2C2×#1681113411yescharacteristic
789C2C2×#1681142611yescharacteristic
790C2C2×#1681143111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#520C2
socleC23×C53C22×D4
hypercenterC2×#520D53
hypocenterC53C2×#3119
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. C2×#16811228C2semidirect
2. #20284914C2direct (N × H)
3. C2×#16810941C2semidirect
4. C2×#16810936C2semidirect
5. C2×#16810930C2semidirect
6. C2×#16810923C2semidirect
7. C2×#16810823C2semidirect
8. C2×#16810818C2semidirect
9. C2×#16810768C2semidirect
10. C2×#16810768C2semidirect
11. C2×#16810733C2semidirect
12. C2×#16810721C2semidirect
13. C2×C4×#11719924C2semidirect
14. C2×C4×#11719922C2semidirect
15. C2×#16810684C2semidirect
16. C2×C53×#520C2semidirect
22. #16811228C22semidirect
33. #16810941C22semidirect
34. #16810936C22semidirect
35. #16810930C22semidirect
36. #16810923C22semidirect
37. #16810823C22semidirect
38. #16810818C22semidirect
39. #16810768C22semidirect
40. #16810768C22semidirect
41. #16810733C22semidirect
42. #16810721C22semidirect
43. C4×#11719924C22semidirect
44. C4×#11719922C22semidirect
45. #16810684C22semidirect
66. C53×#520C22semidirect
389. C2×#520D53semidirect
406. C2×C53#3119semidirect
428. #520C2×D53semidirect
472. C53C2×#3119semidirect
787. C2#20284914direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112282
#202849142
C2×#168109412
C2×#168109362
C2×#168109302
C2×#168109232
C2×#168108232
C2×#168108182
C2×#168107682
C2×#168107332
C2×#168107212
C2×C4×#117199242
C2×C4×#117199222
C2×#168106842
C2×C53×#5202
C2×#311953