Finite Group Databasebeta

← #27386074

Subgroups — #27386074

Order 13568.

1708 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811389C211yesmaximal, characteristic, complemented
2#20288044C211yesmaximal, characteristic
3#20283234C211yesmaximal, characteristic, complemented
4C2×#16810596C211yesmaximal, characteristic, complemented
5#20275239C214yesmaximal, complemented
6#20275234C214yesmaximal, complemented
7C2×#16810380C211yesmaximal, characteristic, complemented
8C2×#16810379C211yesmaximal, characteristic, complemented
9C53×#2896C211yesmaximal, characteristic, complemented
10C22×#11719945C2211yescharacteristic
11#16811389—22no—
12#16811389—22no—
13#16811389—22no—
14#16811389C2214yes—
15C2×#13133225—22no—
16C2×#13133223—22no—
17C22×#11719917C2211yescharacteristic
18C2×M16×D53—22no—
19#16811201—22no—
20#16811197C2212yes—
21#16811194C412yescomplemented
22#16811190C2212yes—
23#16811187C412yescomplemented
24#16811182—22no—
25#16811169C414yescomplemented
26#16811134—22no—
27#16811130—22no—
28C2×#13133176C2211yescharacteristic
29C2×#13133176C2211yescharacteristic
30#16810632C2212yescomplemented
31#16810628C2212yescomplemented
32#16810624—22no—
33#16810619—22no—
34#16810596—22no—
35#16810596C2214yes—
36C2×#13133131—22no—
37#16810380C2214yescomplemented
38#16810379C2214yescomplemented
39C22×#41×C53C2211yescharacteristic
40C22×M16×C53C2211yescharacteristic
41C2×#117×C53C2211yescharacteristic
42C53×#419C2212yescomplemented
43C53×#418C2212yescomplemented
44C53×#417—22no—
45C53×#416—22no—
46C2×#11719945—21no—
47C2×#11719945—21no—
48C2×#11719945—21no—
49C2×#11719945—21no—
50C2×#11719945—21no—
51C2×#11719945—21no—
52C2×#11719945—21no—
53C2×#11719945—21no—
54C2×#11719945C2×C412yes—
55C2×#11719945D412yes—
56C2×#11719945D412yes—
57C2×#11719945C2312yes—
58C22×Dic106C2×C411yescharacteristic
59C22×D212C2×C411yescharacteristic
60C22×C22⋊D53D412yes—
61C22×C4×D53D412yes—
62#13133225—28no—
63#13133225—28no—
64#13133223—28no—
65#13133223—28no—
66C2×#11719917—21no—
67C2×#11719917—21no—
68C2×#11719917—21no—
69C2×#11719917—21no—
70C2×#11719917D412yescomplemented
71C2×#11719917C2312yes—
72C2×#11719912—24no—
73M16×D53—28no—
74M16×D53—28no—
75C22×#88322D412yescomplemented
76C2×C8×D53—24no—
77#13133215C2×C414yescomplemented
78#13133213C2×C414yescomplemented
79#13133206C2×C414yescomplemented
80#13133204C2×C414yescomplemented
81#13133200—24no—
82#13133198—24no—
83#13133196—24no—
84#13133193—24no—
85#13133191—24no—
86#13133189—28no—
87#13133188—24no—
88#13133186—24no—
89#13133185—24no—
90C4×C22⋊D53—28no—
91#13133176—21no—
92#13133176—21no—
93#13133176—21no—
94#13133176—21no—
95#13133176—21no—
96#13133176C2×C412yes—
97#13133176C2312yes—
98#13133176C2312yes—
99C2×C4⋊Dic53—21no—
100C2×C4⋊Dic53—21no—
101C2×C22⋊Dic53—21no—
102C2×C22⋊Dic53—21no—
103C2×C4×Dic53—21no—
104C2×C4×Dic53C2×C412yes—
105#13133141—24no—
106#13133138—24no—
107#13133131—28no—
108C2×#41×C53—21no—
109C2×#41×C53—21no—
110C2×#41×C53—21no—
111C2×#41×C53—21no—
112C2×#41×C53—21no—
113C2×#41×C53—21no—
114C2×#41×C53—21no—
115C2×#41×C53—21no—
116C2×#41×C53—21no—
117C2×#41×C53—21no—
118C2×#41×C53C2×C412yes—
119C2×#41×C53C2×C412yes—
120C22×Q8×C53C2311yescharacteristic
121C22×D4×C53—21no—
122C22×D4×C53C2311yescharacteristic
123C23×C4×C53—21no—
124C23×C4×C53C2311yescharacteristic
125C2×M16×C53—21no—
126C2×M16×C53—21no—
127C2×M16×C53—21no—
128C2×M16×C53—21no—
129C2×M16×C53D412yescomplemented
130C2×M16×C53C2312yes—
131C22×C8×C53D412yescomplemented
132#117×C53—21no—
133#117×C53—21no—
134#117×C53—21no—
135#117×C53C2312yes—
136C2×C4⋊C4×C53—21no—
137C2×C22⋊C4×C53—21no—
138C2×C42×C53—21no—
139#103×C53—24no—
140#102×C53—24no—
141C24×C53—21no—
142C24×C53C2×D411yescharacteristic
143C23×D53C22⋊C412yes—
144#41×C53—22no—
145#41×C53—22no—
146#41×C53—22no—
147#41×C53—22no—
148#41×C53—22no—
149#41×C53—22no—
150#41×C53—22no—
151#41×C53—22no—
152#41×C53—41no—
153#41×C53—41no—
154#41×C53—41no—
155#41×C53—41no—
156#41×C53—41no—
157#41×C53—41no—
158#41×C53—41no—
159#41×C53—41no—
160C2×Q8×C53—21no—
161C2×Q8×C53—21no—
162C2×Q8×C53—21no—
163C2×Q8×C53—21no—
164C2×Q8×C53—21no—
165C2×Q8×C53C22×C412yes—
166C2×D4×C53—22no—
167C2×D4×C53—22no—
168C2×D4×C53—21no—
169C2×D4×C53—21no—
170C2×D4×C53—21no—
171C2×D4×C53—21no—
172C2×D4×C53—21no—
173C2×D4×C53—41no—
174C2×D4×C53—41no—
175C2×D4×C53—41no—
176C2×D4×C53—41no—
177C2×D4×C53C22×C412yes—
178C22×C4×C53—21no—
179C22×C4×C53—22no—
180C22×C4×C53—22no—
181C22×C4×C53—41no—
182C22×C4×C53—41no—
183C22×C4×C53—41no—
184C22×C4×C53—41no—
185C22×C4×C53—41no—
186C22×C4×C53C22×C411yescharacteristic
187C22×C4×C53C22×C411yescharacteristic
188C22×C4×C53C2×D411yescharacteristic
189C22×C4×C53C2×D411yescharacteristic
190C22×C4×C53C2×D411yescharacteristic
191C22×C4×C53C2×D411yescharacteristic
192C22×C4×C53C2×D411yescharacteristic
193C22×C4×C53C2×D411yescharacteristic
194C22×C4×C53C2×D411yescharacteristic
195C22×C4×C53#4111yescharacteristic
196C22×C4×C53#4111yescharacteristic
197C22×C4×C53#4111yescharacteristic
198C22×C4×C53#4111yescharacteristic
199C22×C4×C53C2411yescharacteristic
200C2×C22⋊D53—22no—
201C2×C22⋊D53—22no—
202C2×C22⋊D53—22no—
203C2×C22⋊D53—22no—
204C2×C22⋊D53—28no—
205C2×C22⋊D53C22⋊C414yes—
206C2×C22⋊D53C2×D414yes—
207C22×Dic53—22no—
208C22×Dic53—41no—
209C22×Dic53C22⋊C412yes—
210#11719945—22no—
211#11719945—22no—
212#11719945—22no—
213#11719945—22no—
214#11719945—22no—
215#11719945—22no—
216#11719945—22no—
217#11719945—22no—
218#11719945—22no—
219#11719945—22no—
220#11719945—22no—
221#11719945—22no—
222#11719945—22no—
223#11719945—22no—
224#11719945—22no—
225#11719945—22no—
226C2×D212—21no—
227C2×D212—21no—
228C2×D212—21no—
229C2×D212—21no—
230C2×D212C22⋊C412yes—
231C2×D212C22×C412yes—
232C2×C4×D53—22no—
233C2×C4×D53—22no—
234C2×C4×D53—22no—
235C2×C4×D53—22no—
236C2×C4×D53C22⋊C414yes—
237C2×C4×D53C2×D414yes—
238C2×Dic106—21no—
239C2×Dic106—21no—
240C2×Dic106—21no—
241C2×Dic106—21no—
242C2×Dic106C22⋊C412yes—
243C2×Dic106C22×C412yes—
244M16×C53—22no—
245M16×C53—22no—
246M16×C53—22no—
247M16×C53—22no—
248C2×C8×C53—22no—
249C2×C8×C53—22no—
250C2×C8×C53C2×D414yes—
251C4⋊C4×C53—22no—
252C4⋊C4×C53—41no—
253C22⋊C4×C53—22no—
254C22⋊C4×C53—41no—
255C42×C53—22no—
256C42×C53—41no—
257C22⋊Dic53—22no—
258C22⋊Dic53—22no—
259C22⋊Dic53—28no—
260C22⋊Dic53—22no—
261C22⋊Dic53—41no—
262#11719921—28no—
263C4⋊Dic53—22no—
264C4⋊Dic53—22no—
265C4⋊Dic53—22no—
266C4⋊Dic53—41no—
267#11719919—28no—
268C4×Dic53—22no—
269C4×Dic53—22no—
270C4×Dic53—41no—
271C4×Dic53C22×C414yes—
272#11719917—22no—
273#11719917—22no—
274#11719917—22no—
275#11719917—22no—
276C2×#88322—22no—
277C2×#88322—22no—
278C2×#88322C2×D414yes—
279#11719912—216no—
280C8×D53—216no—
281C23×C53—22no—
282C23×C53—41no—
283C23×C53—41no—
284C23×C53—81no—
285C23×C53—82no—
286C23×C53C2×C22⋊C411yescharacteristic
287C23×C53C2×C22⋊C411yescharacteristic
288C23×C53#12111yescharacteristic
289C23×C53#12111yescharacteristic
290C23×C53#12111yescharacteristic
291C23×C53#12111yescharacteristic
292C23×C53C22×D411yescharacteristic
293C22×D53—22no—
294C22×D53—22no—
295C22×D53—82no—
296C22×D53C2×C22⋊C414yes—
297Q8×C53—22no—
298Q8×C53—22no—
299Q8×C53—41no—
300Q8×C53—41no—
301D4×C53—22no—
302D4×C53—22no—
303D4×C53—42no—
304D4×C53—42no—
305D4×C53—42no—
306D4×C53—42no—
307D4×C53—41no—
308D4×C53—41no—
309C2×C4×C53—22no—
310C2×C4×C53—41no—
311C2×C4×C53—41no—
312C2×C4×C53—42no—
313C2×C4×C53—42no—
314C2×C4×C53—42no—
315C2×C4×C53—42no—
316C2×C4×C53—42no—
317C2×C4×C53—82no—
318C2×C4×C53C2×C22⋊C411yescharacteristic
319C2×C4×C53C2×C22⋊C411yescharacteristic
320C2×C4×C53C4×D411yescharacteristic
321C2×C4×C53C4×D411yescharacteristic
322C2×C4×C53C4×D411yescharacteristic
323C2×C4×C53C4×D411yescharacteristic
324C2×C4×C53C4×D411yescharacteristic
325C2×C4×C53C4×D411yescharacteristic
326C2×C4×C53C4×D411yescharacteristic
327C2×C4×C53C4×D411yescharacteristic
328C2×C4×C53#12011yescharacteristic
329C2×C4×C53#12011yescharacteristic
330C2×C4×C53#12011yescharacteristic
331C2×C4×C53#12011yescharacteristic
332C2×C4×C53#12111yescharacteristic
333C2×C4×C53#12111yescharacteristic
334C2×C4×C53#12111yescharacteristic
335C2×C4×C53#12111yescharacteristic
336C2×C4×C53#12311yescharacteristic
337C2×C4×C53#12311yescharacteristic
338C2×C4×C53#12311yescharacteristic
339C2×C4×C53#12311yescharacteristic
340C2×C4×C53C23×C411yescharacteristic
341C2×C4×C53C22×D411yescharacteristic
342C2×C4×C53C22×D411yescharacteristic
343C2×C4×C53C22×D411yescharacteristic
344C2×C4×C53C2×#4111yescharacteristic
345C2×C4×C53C2×#4111yescharacteristic
346C22⋊D53—24no—
347C22⋊D53—24no—
348C22⋊D53—24no—
349C22⋊D53—24no—
350C22⋊D53—88no—
351C2×Dic53—22no—
352C2×Dic53—22no—
353C2×Dic53—24no—
354C2×Dic53—42no—
355C2×Dic53—82no—
356C2×Dic53—82no—
357C2×Dic53C2×C22⋊C414yes—
358D212—22no—
359D212—22no—
360D212—22no—
361D212—22no—
362C4×D53—24no—
363C4×D53—24no—
364C4×D53—24no—
365C4×D53—24no—
366Dic106—22no—
367Dic106—22no—
368Dic106—22no—
369Dic106—22no—
370C8×C53—24no—
371#88322—24no—
372#21009—531nomaximal, Sylow
373C22×C53—41no—
374C22×C53—41no—
375C22×C53—41no—
376C22×C53—41no—
377C22×C53—41no—
378C22×C53—41no—
379C22×C53—41no—
380C22×C53—44no—
381C22×C53—42no—
382C22×C53—82no—
383C22×C53—82no—
384C22×C53#38611yescharacteristic
385C22×C53#38611yescharacteristic
386C22×C53#38611yescharacteristic
387C22×C53#38611yescharacteristic
388C22×C53C22×C22⋊C411yescharacteristic
389C22×C53C2×#12111yescharacteristic
390C22×C53C2×#12111yescharacteristic
391C2×D53—24no—
392C2×D53—44no—
393C2×D53—44no—
394C2×D53—82no—
395C4×C53—42no—
396C4×C53—82no—
397C4×C53#38611yescharacteristic
398C4×C53#38611yescharacteristic
399C4×C53#38611yescharacteristic
400C4×C53#38611yescharacteristic
401C4×C53C2×C4×D411yescharacteristic
402C4×C53C2×C4×D411yescharacteristic
403C4×C53C2×#12011yescharacteristic
404C4×C53C2×#12311yescharacteristic
405Dic53—24no—
406Dic53—44no—
407Dic53—82no—
408C2×#568—531no—
409#3449—531no—
410#2896—531no—
411#2896D5311yescharacteristic, complemented
412C2×#410—531no—
413#1910—534no—
414#1909—534no—
415C2×H(3,ℤ/4)—531no—
416C2×H(3,ℤ/4)—531no—
417C2×C53—21no—
418C2×C53—21no—
419C2×C53—21no—
420C2×C53—21no—
421C2×C53—21no—
422C2×C53—21no—
423C2×C53—21no—
424C2×C53—82no—
425C2×C53C2×#38611yescharacteristic
426D53—44no—
427C22×#41—531no—
428C22×#41C2×D5311yescharacteristic
429#568—534no—
430#568—1062no—
431#568—1062no—
432#568—1062no—
433C2×#131—1062no—
434C2×#131—1062no—
435C22×M16—531no—
436C22×M16—1062no—
437C22×M16C2×D5311yescharacteristic
438#537—1062no—
439#536—532no—
440#536—532no—
441#535—532no—
442#535—532no—
443#534—1062no—
444#532—534no—
445#525—1062no—
446#525—1062no—
447C2×#117—531no—
448C2×#117—531no—
449C2×#117C2×D5311yescharacteristic
450#419—532no—
451#419C2×D5312yescomplemented
452#418—532no—
453#418C2×D5312yescomplemented
454#417—22no—
455#417—1062no—
456#416—22no—
457#416—1062no—
458#410—534no—
459#410—1062no—
460C2×#99—1062no—
461H(3,ℤ/4)—534no—
462H(3,ℤ/4)—534no—
463C53#2100911yescharacteristic, complemented, Sylow
464C2×#41—21no—
465C2×#41—21no—
466C2×#41—21no—
467C2×#41—21no—
468C2×#41—21no—
469C2×#41—21no—
470C2×#41—21no—
471C2×#41—21no—
472C2×#41—21no—
473C2×#41—21no—
474C2×#41—532no—
475C2×#41—532no—
476C2×#41—532no—
477C2×#41—532no—
478C2×#41—1061no—
479C2×#41—1061no—
480C2×#41—1061no—
481C2×#41—1061no—
482C2×#41—1061no—
483C2×#41—1061no—
484C2×#41—1061no—
485C2×#41—1061no—
486C2×#41C4×D5312yes—
487C2×#41C4×D5312yes—
488C22×Q8—531no—
489C22×Q8C22×D5311yescharacteristic
490C22×D4—21no—
491C22×D4—532no—
492C22×D4—531no—
493C22×D4C22×D5311yescharacteristic
494C23×C4—21no—
495C23×C4—532no—
496C23×C4C22×D5311yescharacteristic
497#131—1068no—
498#131—1068no—
499#131—1068no—
500#131—1068no—
501C2×M16—21no—
502C2×M16—21no—
503C2×M16—21no—
504C2×M16—21no—
505C2×M16—532no—
506C2×M16—532no—
507C2×M16—1064no—
508C2×M16—1068no—
509C2×M16—1068no—
510C2×M16—1061no—
511C2×M16—1061no—
512C2×M16—1061no—
513C2×M16—1061no—
514C2×M16C22⋊D5312yescomplemented
515C2×M16C22×D5312yes—
516C22×C8—532no—
517C22×C8—1064no—
518C22×C8C22⋊D5312yescomplemented
519C4⋊Q8—534no—
520#127—534no—
521#124—534no—
522#124—534no—
523#123—1064no—
524#123—1064no—
525C22⋊Q8—1064no—
526C22⋊Q8—1064no—
527#121—1064no—
528#121—1064no—
529#121—1068no—
530#120—1064no—
531#120—1064no—
532C4×D4—1068no—
533#117—21no—
534#117—21no—
535#117—21no—
536#117—532no—
537#117—532no—
538#117—532no—
539#117—1061no—
540#117—1061no—
541#117—1061no—
542#117—1061no—
543#117—1061no—
544#117C22×D5312yes—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—1061no—
547C2×C4⋊C4—1061no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—1061no—
550C2×C22⋊C4—1061no—
551C2×C42—21no—
552C2×C42—532no—
553C2×C42—1061no—
554#103—24no—
555#103—1064no—
556#102—24no—
557#102—1064no—
558#99—1068no—
559C24—21no—
560C24—532no—
561C24D4×D5311yescharacteristic
562#41—22no—
563#41—22no—
564#41—22no—
565#41—22no—
566#41—22no—
567#41—22no—
568#41—22no—
569#41—22no—
570#41—41no—
571#41—41no—
572#41—41no—
573#41—41no—
574#41—41no—
575#41—41no—
576#41—41no—
577#41—41no—
578#41—1062no—
579#41—1062no—
580#41—1062no—
581#41—1062no—
582#41—1062no—
583#41—1062no—
584#41—1062no—
585#41—1062no—
586#41—1062no—
587#41—1062no—
588#41—1062no—
589#41—1062no—
590#41—1062no—
591#41—1062no—
592#41—1062no—
593#41—1062no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—21no—
599C2×Q8—532no—
600C2×Q8—532no—
601C2×Q8—1061no—
602C2×Q8—1061no—
603C2×Q8—1061no—
604C2×Q8—1061no—
605C2×Q8C2×C4×D5312yes—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—41no—
614C2×D4—41no—
615C2×D4—41no—
616C2×D4—41no—
617C2×D4—534no—
618C2×D4—534no—
619C2×D4—532no—
620C2×D4—532no—
621C2×D4—1062no—
622C2×D4—1062no—
623C2×D4—1062no—
624C2×D4—1062no—
625C2×D4—1068no—
626C2×D4—1061no—
627C2×D4—1061no—
628C2×D4—1061no—
629C2×D4—1061no—
630C2×D4C2×C4×D5312yes—
631C22×C4—21no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—41no—
635C22×C4—41no—
636C22×C4—41no—
637C22×C4—41no—
638C22×C4—41no—
639C22×C4—532no—
640C22×C4—534no—
641C22×C4—534no—
642C22×C4—1062no—
643C22×C4—1062no—
644C22×C4—1062no—
645C22×C4—1062no—
646C22×C4—1062no—
647C22×C4—2121no—
648C22×C4C2×C4×D5311yescharacteristic
649C22×C4C2×C4×D5311yescharacteristic
650C22×C4#1171994511yescharacteristic
651C22×C4#1171994511yescharacteristic
652C22×C4D4×D5311yescharacteristic
653C22×C4D4×D5311yescharacteristic
654C22×C4D4×D5311yescharacteristic
655C22×C4D4×D5311yescharacteristic
656C22×C4D4×D5311yescharacteristic
657C22×C4#1171994711yescharacteristic
658C22×C4#1171994711yescharacteristic
659C22×C4C2×C22⋊D5311yescharacteristic
660C22×C4C2×C22⋊D5311yescharacteristic
661C22×C4C23×D5311yescharacteristic
662M16—22no—
663M16—22no—
664M16—22no—
665M16—22no—
666M16—10616no—
667M16—1062no—
668M16—1062no—
669M16—1062no—
670M16—1062no—
671C2×C8—22no—
672C2×C8—22no—
673C2×C8—534no—
674C2×C8—10616no—
675C2×C8—1062no—
676C2×C8—1062no—
677C2×C8C2×C22⋊D5314yes—
678C4⋊C4—22no—
679C4⋊C4—41no—
680C4⋊C4—1068no—
681C4⋊C4—1062no—
682C4⋊C4—1062no—
683C4⋊C4—1062no—
684C4⋊C4—2121no—
685C22⋊C4—22no—
686C22⋊C4—41no—
687C22⋊C4—1068no—
688C22⋊C4—1068no—
689C22⋊C4—1062no—
690C22⋊C4—1062no—
691C22⋊C4—1062no—
692C22⋊C4—2121no—
693C42—22no—
694C42—41no—
695C42—534no—
696C42—1062no—
697C42—1062no—
698C42—2121no—
699C23—22no—
700C23—41no—
701C23—41no—
702C23—81no—
703C23—82no—
704C23—534no—
705C23—1062no—
706C23—1062no—
707C23—4242no—
708C23C22⋊C4×D5311yescharacteristic
709C23C22⋊C4×D5311yescharacteristic
710C23#1313318811yescharacteristic
711C23#1313318811yescharacteristic
712C23#1313319011yescharacteristic
713C23#1313319011yescharacteristic
714C23C2×D4×D5311yescharacteristic
715Q8—22no—
716Q8—22no—
717Q8—41no—
718Q8—41no—
719Q8—1062no—
720Q8—1062no—
721Q8—1062no—
722Q8—1062no—
723D4—22no—
724D4—22no—
725D4—42no—
726D4—42no—
727D4—42no—
728D4—42no—
729D4—41no—
730D4—41no—
731D4—1064no—
732D4—1064no—
733D4—1064no—
734D4—1064no—
735D4—1062no—
736D4—1062no—
737D4—1062no—
738D4—1062no—
739D4—4248no—
740C2×C4—22no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—82no—
749C2×C4—534no—
750C2×C4—1062no—
751C2×C4—1062no—
752C2×C4—1064no—
753C2×C4—1064no—
754C2×C4—1064no—
755C2×C4—1064no—
756C2×C4—1064no—
757C2×C4—4242no—
758C2×C4—4242no—
759C2×C4—2122no—
760C2×C4C22⋊C4×D5311yescharacteristic
761C2×C4C22⋊C4×D5311yescharacteristic
762C2×C4#1313317711yescharacteristic
763C2×C4#1313317711yescharacteristic
764C2×C4#1313317711yescharacteristic
765C2×C4#1313317711yescharacteristic
766C2×C4C4×C22⋊D5311yescharacteristic
767C2×C4C4×C22⋊D5311yescharacteristic
768C2×C4C4×C22⋊D5311yescharacteristic
769C2×C4C4×C22⋊D5311yescharacteristic
770C2×C4#1313318511yescharacteristic
771C2×C4#1313318511yescharacteristic
772C2×C4#1313318511yescharacteristic
773C2×C4#1313318511yescharacteristic
774C2×C4#1313318811yescharacteristic
775C2×C4#1313318811yescharacteristic
776C2×C4#1313319011yescharacteristic
777C2×C4#1313319011yescharacteristic
778C2×C4#1313319911yescharacteristic
779C2×C4#1313319911yescharacteristic
780C2×C4#1313319911yescharacteristic
781C2×C4#1313319911yescharacteristic
782C2×C4C22×C4×D5311yescharacteristic
783C2×C4C2×D4×D5311yescharacteristic
784C2×C4C2×D4×D5311yescharacteristic
785C2×C4C22×C22⋊D5311yescharacteristic
786C2×C4C2×#1171994711yescharacteristic
787C2×C4C2×#1171994511yescharacteristic
788C8—24no—
789C8—1064no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—44no—
798C22—42no—
799C22—82no—
800C22—82no—
801C22—1064no—
802C22—4242no—
803C22—2124no—
804C22—2124no—
805C22#1681049911yescharacteristic
806C22#1681049911yescharacteristic
807C22#1681049911yescharacteristic
808C22#1681049911yescharacteristic
809C22C2×C22⋊C4×D5311yescharacteristic
810C22C2×#1313318811yescharacteristic
811C22C2×#1313319011yescharacteristic
812C4—42no—
813C4—82no—
814C4—1064no—
815C4—4242no—
816C4—2124no—
817C4#1681049911yescharacteristic
818C4#1681049911yescharacteristic
819C4#1681049911yescharacteristic
820C4#1681049911yescharacteristic
821C4C2×#1313317711yescharacteristic
822C4C2×C4×C22⋊D5311yescharacteristic
823C4C2×#1313318511yescharacteristic
824C4C2×#1313319911yescharacteristic
825C2—21no—
826C2—21no—
827C2—21no—
828C2—21no—
829C2—21no—
830C2—21no—
831C2—21no—
832C2—82no—
833C2—2124no—
834C2C2×#1681049911yescharacteristic
subgroupG/H
centerC4#16810499
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#2896C2
socleC2×C53C2×#386
prime radical#20288044C2
cosocleC22×C4×C53C24
hypercenter#2896D53
hypocenterC53#21009
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C4 ◁ C23×C4 ◁ #2896

Complements

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

NH ≅ G/Ntype
1. C2×#16811389C2semidirect
3. #20283234C2semidirect
4. C2×#16810596C2semidirect
5. #20275239C2semidirect
6. #20275234C2semidirect
7. C2×#16810380C2semidirect
8. C2×#16810379C2semidirect
9. C53×#2896C2semidirect
21. #16811194C4semidirect
23. #16811187C4semidirect
25. #16811169C4semidirect
30. #16810632C22semidirect
31. #16810628C22semidirect
37. #16810380C22semidirect
38. #16810379C22semidirect
42. C53×#419C22semidirect
43. C53×#418C22semidirect
70. C2×#11719917D4semidirect
75. C22×#88322D4semidirect
77. #13133215C2×C4semidirect
78. #13133213C2×C4semidirect
79. #13133206C2×C4semidirect
80. #13133204C2×C4semidirect
129. C2×M16×C53D4semidirect
131. C22×C8×C53D4semidirect
411. #2896D53semidirect
451. #419C2×D53semidirect
453. #418C2×D53semidirect
463. C53#21009semidirect
514. C2×M16C22⋊D53semidirect
518. C22×C8C22⋊D53semidirect

Maximal subgroups

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

subgroupindex
C2×#168113892
#202880442
#202832342
C2×#168105962
#202752392
#202752342
C2×#168103802
C2×#168103792
C53×#28962
#2100953