Finite Group Databasebeta

← #28264713

Subgroups — #28264713

Order 13568.

1750 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#11719945C211yesmaximal, characteristic
2C2×#16811351C211yesmaximal, characteristic, complemented
3#20287684C214yesmaximal, complemented
4#20287662C214yesmaximal, complemented
5#20287649C212yesmaximal, complemented
6#20287638C212yesmaximal, complemented
7#20287607C212yesmaximal, complemented
8#20287592C212yesmaximal, complemented
9#20285267C212yesmaximal, complemented
10#20285261C211yesmaximal, characteristic, complemented
11#20284538C212yesmaximal
12#20284531C211yesmaximal, characteristic
13#20284522C211yesmaximal, characteristic, complemented
14#20284522C212yesmaximal, complemented
15C4×#13133250C211yesmaximal, characteristic
16C4×#13133250C212yesmaximal
17Q8×M16×C53C211yesmaximal, characteristic, complemented
18C2×#13133250C2211yescharacteristic
19Q8×Dic106C2211yescharacteristic
20#16811351—21no—
21#16811351—21no—
22#16811351—22no—
23#16811351C2212yes—
24#16811351C2212yes—
25#16811351C2214yes—
26#16811351C2211yescharacteristic
27#16811351C2212yes—
28#16811333C2211yescharacteristic
29#16811333C2212yes—
30#16811328—21no—
31#16811328—22no—
32Q8×D212C2211yescharacteristic
33Q8×C22⋊D53—21no—
34#16811180C2211yescharacteristic
35#16811180C2212yes—
36#16811177—21no—
37#16811177—22no—
38C2×#13133217C2211yescharacteristic
39C2×#13133215—21no—
40C2×#13133209C2212yes—
41C2×#13133207—22no—
42C4×#11719945C2211yescharacteristic
43C4×#11719945C2212yes—
44C2×C4×Dic106C2212yes—
45C2×C4×Dic106C2211yescharacteristic
46C2×#13133182—21no—
47C4×Q8×D53—21no—
48#16811032C2214yes—
49#16811032C2214yes—
50#16811032C2214yes—
51#16811028C2212yes—
52#16811025C2214yes—
53#16811025C2214yes—
54#16811021C2212yes—
55#16810931C2214yes—
56#16810931C2214yes—
57#16810931C2214yes—
58#16810931C2214yes—
59#16810931C2214yes—
60#16810924C2214yes—
61#16810924C2214yes—
62#16810919C2212yes—
63#16810919C2214yes—
64#16810919C2212yes—
65#16810914C2212yes—
66#16810909C2212yes—
67#16810909C2214yes—
68#16810909C2212yes—
69#16810904C2212yes—
70#16810731C2214yes—
71#16810731C2212yes—
72#16810725C2214yes—
73#16810725C2212yes—
74C4×Dic212C2212yes—
75C4×Dic212C2214yes—
76C4×#11719913C2212yes—
77C4×#11719913C2214yes—
78#16810665C2212yes—
79#16810665C2212yes—
80#16810665C2211yescharacteristic
81#16810665C2212yes—
82#16810665C2212yes—
83#16810633C2211yescharacteristic
84#16810633C2212yes—
85#16810625C2212yes—
86#16810625C2211yescharacteristic
87C2×C4×Q8×C53C2211yescharacteristic
88C53×#446C2212yes—
89C53×#446C2214yes—
90C8×Q8×C53C2212yes—
91C53×#423C2211yescharacteristic
92C53×#423C2212yes—
93C4×M16×C53C2211yescharacteristic
94C4×M16×C53C2212yes—
95C2×#11719945C2311yescharacteristic
96C22×Dic106—21no—
97C22×Dic106C2311yescharacteristic
98C2×Q8×D53—21no—
99#13133250Q818yescomplemented
100C2×Dic212C2312yes—
101C2×#11719913C2312yes—
102#13133217—21no—
103#13133217—21no—
104#13133217C2311yescharacteristic
105#13133217C2312yes—
106#13133217C2311yescharacteristic
107#13133217C2312yes—
108#13133217C2312yes—
109#13133217C2312yes—
110#13133216—21no—
111#13133216—22no—
112#13133215—21no—
113#13133215—22no—
114#13133215—22no—
115#13133215—22no—
116#13133215—24no—
117#13133209—22no—
118#13133209—22no—
119#13133209C2312yes—
120#13133209C2312yes—
121#13133209C2314yes—
122#13133209C2312yes—
123#13133209C2314yes—
124#13133207—22no—
125#13133207—22no—
126#13133207—22no—
127#13133207—24no—
128#13133207—24no—
129#13133207—24no—
130#13133207—24no—
131#13133197—21no—
132#13133197—22no—
133#13133196—21no—
134#13133196—22no—
135#13133196—22no—
136#13133196—21no—
137#13133195—22no—
138#13133195—22no—
139#13133195—22no—
140#13133193—21no—
141#13133193—22no—
142Q8×Dic53—21no—
143C4×Dic106—22no—
144C4×Dic106—21no—
145C4×Dic106—22no—
146C4×Dic106—22no—
147C4×Dic106—21no—
148C4×Dic106—21no—
149C4×Dic106—22no—
150C4×Dic106—21no—
151C4×Dic106C2312yes—
152C4×Dic106C2314yes—
153C4×Dic106C2314yes—
154C4×Dic106C2312yes—
155C4×Dic106C2311yescharacteristic
156C4×Dic106C2312yes—
157C4×Dic106C2311yescharacteristic
158C4×Dic106C2312yes—
159#13133182—21no—
160#13133182—22no—
161#13133182—22no—
162#13133182—24no—
163#13133182—22no—
164C4×D212C2311yescharacteristic
165C4×D212C2312yes—
166C4×D212C2311yescharacteristic
167C4×D212C2312yes—
168C4×C22⋊D53—21no—
169C4×C22⋊D53—22no—
170C4×C22⋊D53—22no—
171C4×C22⋊D53—21no—
172#13133176C2311yescharacteristic
173#13133176C2312yes—
174#13133174—22no—
175#13133174—21no—
176C2×C4⋊Dic53—21no—
177C2×C4⋊Dic53C2311yescharacteristic
178C2×C4⋊Dic53C2312yes—
179C2×#11719919—22no—
180C2×#11719919—21no—
181C2×#11719919—22no—
182C2×#11719919—22no—
183C4⋊C4×D53—21no—
184C4⋊C4×D53—22no—
185C2×C4×Dic53—22no—
186C2×C4×Dic53—21no—
187C42×D53—22no—
188C42×D53—21no—
189#13133151C2312yes—
190#13133151C2314yes—
191#13133151C2314yes—
192#13133151C2314yes—
193#13133151C2314yes—
194#13133149C2314yes—
195#13133149C2314yes—
196#13133149C2312yes—
197#13133149C2314yes—
198#13133149C2314yes—
199#13133142C2314yes—
200#13133142C2312yes—
201#13133142C2312yes—
202#13133142C2314yes—
203#13133142C2314yes—
204#13133142C2312yes—
205#13133139C2314yes—
206#13133139C2312yes—
207C22×Q8×C53D411yescharacteristic
208C2×M16×C53C2312yes—
209C2×M16×C53C2311yescharacteristic
210C2×M16×C53C2311yescharacteristic
211C4×Q8×C53D411yescharacteristic
212C4×Q8×C53D411yescharacteristic
213C4×Q8×C53D412yes—
214C4×Q8×C53C2311yescharacteristic
215C4×Q8×C53C2311yescharacteristic
216C4×Q8×C53C2312yes—
217C2×C4⋊C4×C53D411yescharacteristic
218C2×C4⋊C4×C53D412yes—
219C2×C42×C53C2312yes—
220C2×C42×C53C2311yescharacteristic
221C4⋊C8×C53C2312yes—
222C4⋊C8×C53C2314yes—
223C4⋊C8×C53C2312yes—
224C4⋊C8×C53C2314yes—
225#97×C53C2312yes—
226#97×C53C2314yes—
227C4×C8×C53C2312yes—
228C4×C8×C53C2314yes—
229C2×Q8×C53—42no—
230C2×Q8×C53C2×D411yescharacteristic
231C2×Q8×C53C2×D411yescharacteristic
232C2×Q8×C53C2×D412yes—
233C22×C4×C53C2×D411yescharacteristic
234C22×C4×C53C2×D412yes—
235C22×C4×C53C2×D411yescharacteristic
236C22×C4×C53C2×D412yes—
237C22×C4×C53C2411yescharacteristic
238C2×C22⋊D53—21no—
239C22×Dic53—21no—
240C22×Dic53—21no—
241C22×Dic53—22no—
242Q8×D53—44no—
243#11719945—22no—
244#11719945C2×Q814yes—
245C2×D212C2411yescharacteristic
246C2×C4×D53—21no—
247C2×C4×D53—22no—
248C2×C4×D53—21no—
249C2×C4×D53—22no—
250C2×C4×D53—21no—
251C2×Dic106—21no—
252C2×Dic106—22no—
253C2×Dic106—22no—
254C2×Dic106—22no—
255C2×Dic106—22no—
256C2×Dic106—21no—
257C2×Dic106—22no—
258C2×Dic106—21no—
259C2×Dic106—44no—
260C2×Dic106C2×Q814yescomplemented
261C2×Dic106C2412yes—
262C2×Dic106C2411yescharacteristic
263M16×C53—24no—
264M16×C53—22no—
265M16×C53C2×Q814yescomplemented
266C2×C8×C53C2412yes—
267C2×C8×C53C2414yes—
268C2×C8×C53C2412yes—
269C4⋊C4×C53C2×D411yescharacteristic
270C4⋊C4×C53C2×D412yes—
271C4⋊C4×C53C2×D412yes—
272C4⋊C4×C53C2×D411yescharacteristic
273C4⋊C4×C53C2×D412yes—
274C4⋊C4×C53C2×D412yes—
275C4⋊C4×C53C2×D412yes—
276C42×C53C2×D412yes—
277C42×C53C2×D411yescharacteristic
278C42×C53C2×D412yes—
279C42×C53C2×D411yescharacteristic
280C42×C53C2412yes—
281C42×C53C2411yescharacteristic
282C42×C53C2411yescharacteristic
283C42×C53C2412yes—
284C22⋊Dic53—21no—
285C22⋊Dic53—22no—
286#11719921—21no—
287#11719921—22no—
288#11719921—22no—
289#11719921—21no—
290C4⋊Dic53—22no—
291C4⋊Dic53—21no—
292C4⋊Dic53—22no—
293C4⋊Dic53—22no—
294C4⋊Dic53—21no—
295C4⋊Dic53—22no—
296C4⋊Dic53—22no—
297C4⋊Dic53—21no—
298C4⋊Dic53C2412yes—
299C4⋊Dic53C2414yes—
300C4⋊Dic53C2411yescharacteristic
301C4⋊Dic53C2412yes—
302C4⋊Dic53C2412yes—
303C4⋊Dic53C2411yescharacteristic
304#11719919—22no—
305#11719919—22no—
306#11719919—22no—
307#11719919—24no—
308#11719919—24no—
309#11719919—22no—
310#11719919—22no—
311#11719919—24no—
312#11719919—24no—
313#11719919—24no—
314#11719919—24no—
315#11719919—21no—
316#11719919—22no—
317#11719919—22no—
318#11719919—21no—
319#11719919—22no—
320#11719919—22no—
321#11719919—22no—
322C4×Dic53—22no—
323C4×Dic53—21no—
324C4×Dic53—22no—
325C4×Dic53—21no—
326C4×Dic53—22no—
327C4×Dic53—21no—
328C4×Dic53—24no—
329C4×Dic53—24no—
330C4×Dic53—22no—
331C4×Dic53—22no—
332Dic212C2×Q818yescomplemented
333#11719913C2×Q818yescomplemented
334C23×C53C22×D411yescharacteristic
335C22×D53—21no—
336Q8×C53—22no—
337Q8×C53—22no—
338Q8×C53—42no—
339C2×C4×C53—22no—
340C2×C4×C53—42no—
341C2×C4×C53—41no—
342C2×C4×C53—42no—
343C2×C4×C53C22×D411yescharacteristic
344C2×C4×C53C22×D412yes—
345C2×C4×C53C22×D412yes—
346C2×C4×C53C22×D411yescharacteristic
347C2×C4×C53C22×D412yes—
348C2×C4×C53C22×D411yescharacteristic
349C2×C4×C53C22×D412yes—
350C2×C4×C53C22×D411yescharacteristic
351C2×C4×C53C22×D411yescharacteristic
352C2×C4×C53C22×Q812yes—
353C2×C4×C532−1+412yes—
354C2×C4×C53C2511yescharacteristic
355C22⋊D53—24no—
356C2×Dic53—24no—
357C2×Dic53—22no—
358C2×Dic53—21no—
359C2×Dic53—21no—
360C2×Dic53—22no—
361C2×Dic53—21no—
362C2×Dic53—22no—
363C2×Dic53—24no—
364C2×Dic53—22no—
365C2×Dic53—44no—
366C2×Dic53—42no—
367D212—21no—
368D212C22×Q812yes—
369C4×D53—24no—
370C4×D53—44no—
371C4×D53—42no—
372C4×D53—82no—
373C4×D53—81no—
374Dic106—24no—
375Dic106—22no—
376Dic106—21no—
377Dic106—44no—
378Dic106—44no—
379Dic106—44no—
380Dic106—42no—
381Dic106—82no—
382Dic106—81no—
383Dic106C22×Q814yes—
384Dic106C22×Q812yes—
385C8×C53—22no—
386C8×C53—24no—
387C8×C53C22×Q814yes—
388#61369—531nomaximal, Sylow
389C22×C53—21no—
390C22×C53—21no—
391C22×C53D4×Q812yes—
392C22×C53C23×D411yescharacteristic
393C2×D53—22no—
394C2×D53—41no—
395C2×D53—41no—
396C4×C53—22no—
397C4×C53—21no—
398C4×C53—22no—
399C4×C53—21no—
400C4×C53—21no—
401C4×C53—22no—
402C4×C53—22no—
403C4×C53D4×Q812yes—
404C4×C53#57512yes—
405C4×C53C23×Q811yescharacteristic
406C4×C53C2×2−1+411yescharacteristic
407Dic53—24no—
408Dic53—22no—
409Dic53—41no—
410Dic53—42no—
411Dic53—42no—
412Dic53—41no—
413Dic53—42no—
414Dic53—44no—
415Q8×#41—531no—
416C2×#557—531no—
417#3390—534no—
418#3388—534no—
419#3387—532no—
420#3386—532no—
421#3383—532no—
422#3381—532no—
423#3166—532no—
424#3165—531no—
425#3080—532no—
426#3079—531no—
427#3078—531no—
428#3078—532no—
429Q8×M16D5311yescharacteristic, complemented
430C4×#137—531no—
431C4×#137—532no—
432C2×C53—22no—
433C2×C53C2×D4×Q811yescharacteristic
434C2×C53C2×#57511yescharacteristic
435C2×C53#358611yescharacteristic
436D53—42no—
437C2×#137—531no—
438Q82—531no—
439#557—532no—
440#557—531no—
441#557—532no—
442#557—534no—
443#557—532no—
444#557—1061no—
445#557—1062no—
446#557—1061no—
447#554—531no—
448#554—532no—
449#554—1061no—
450#554—1062no—
451D4×Q8—531no—
452D4×Q8—1061no—
453#533—531no—
454#533—532no—
455#533—1062no—
456#533—1061no—
457C2×C4⋊Q8—531no—
458C2×C4⋊Q8—1061no—
459C2×#125—532no—
460C2×#125—1062no—
461C4×#41—531no—
462C4×#41—532no—
463C2×C4×Q8—532no—
464C2×C4×Q8—531no—
465C2×C4×Q8—1061no—
466C2×C4×Q8—1061no—
467C2×C4×Q8C2×D5311yescharacteristic
468#501—534no—
469#501—534no—
470#501—534no—
471#500—532no—
472#499—534no—
473#499—534no—
474#498—532no—
475#479—534no—
476#479—534no—
477#479—534no—
478#479—534no—
479#479—534no—
480#478—534no—
481#478—534no—
482#477—532no—
483#477—534no—
484#477—532no—
485#476—532no—
486#475—532no—
487#475—534no—
488#475—532no—
489#474—532no—
490#446C2×D5312yes—
491#446C2×D5314yes—
492C8×Q8C2×D5312yes—
493#441—534no—
494#441—532no—
495#440—534no—
496#440—532no—
497C4×Q16—532no—
498C4×Q16—534no—
499C4×SD16—532no—
500C4×SD16—534no—
501#428—532no—
502#428—532no—
503#428—532no—
504#428—532no—
505#428—531no—
506#423C2×D5311yescharacteristic
507#423C2×D5312yes—
508#419—532no—
509#419—531no—
510#417—532no—
511#417—531no—
512C4×M16C2×D5311yescharacteristic
513C4×M16C2×D5312yes—
514C53#6136911yescharacteristic, complemented, Sylow
515C2×#41—531no—
516C22×Q8—531no—
517C22×Q8—1061no—
518C22×Q8—1061no—
519C22×Q8D21211yescharacteristic
520#137—538no—
521C2×Q16—532no—
522C2×SD16—532no—
523C2×M16C22×D5311yescharacteristic
524C2×M16C22×D5312yes—
525C2×M16C22×D5311yescharacteristic
526C4⋊Q8—532no—
527C4⋊Q8—532no—
528C4⋊Q8—531no—
529C4⋊Q8—532no—
530C4⋊Q8—532no—
531C4⋊Q8—531no—
532C4⋊Q8—1062no—
533C4⋊Q8—1062no—
534C4⋊Q8—1064no—
535C4⋊Q8—1061no—
536C4⋊Q8—1062no—
537C4⋊Q8—1061no—
538C4⋊Q8—1062no—
539C4⋊Q8—1061no—
540C4⋊Q8—1061no—
541#125—534no—
542#125—534no—
543#125—532no—
544#125—532no—
545#125—532no—
546#125—1064no—
547#125—1064no—
548#125—1064no—
549#125—1064no—
550#125—1062no—
551#125—1062no—
552#125—1062no—
553#125—1062no—
554#125—1062no—
555C22⋊Q8—1061no—
556C22⋊Q8—1062no—
557C22⋊Q8—1061no—
558C22⋊Q8—1062no—
559C22⋊Q8—1062no—
560C22⋊Q8—1061no—
561C22⋊Q8—1061no—
562C22⋊Q8—1062no—
563C22⋊Q8—1062no—
564C22⋊Q8—1062no—
565C22⋊Q8—1062no—
566C4×Q8—532no—
567C4×Q8—534no—
568C4×Q8—534no—
569C4×Q8—532no—
570C4×Q8—532no—
571C4×Q8—531no—
572C4×Q8—531no—
573C4×Q8—532no—
574C4×Q8—1061no—
575C4×Q8—1061no—
576C4×Q8—1062no—
577C4×Q8—1062no—
578C4×Q8—1064no—
579C4×Q8—1062no—
580C4×Q8—1062no—
581C4×Q8—1062no—
582C4×Q8—1061no—
583C4×Q8—1061no—
584C4×Q8—1062no—
585C4×Q8—1061no—
586C4×Q8—1062no—
587C4×Q8—1061no—
588C4×Q8D21211yescharacteristic
589C4×Q8D21212yes—
590C4×Q8D21211yescharacteristic
591C4×Q8C22×D5311yescharacteristic
592C4×Q8C22×D5311yescharacteristic
593C4×Q8C22×D5312yes—
594C4×D4—531no—
595C4×D4—532no—
596C4×D4—532no—
597C4×D4—531no—
598C4×D4—1061no—
599C4×D4—1062no—
600C4×D4—1062no—
601C4×D4—1061no—
602#117—531no—
603#117—532no—
604#117—1062no—
605#117—1061no—
606C2×C4⋊C4—531no—
607C2×C4⋊C4—532no—
608C2×C4⋊C4—1061no—
609C2×C4⋊C4—1062no—
610C2×C4⋊C4—1062no—
611C2×C4⋊C4—1062no—
612C2×C4⋊C4—1061no—
613C2×C4⋊C4—1061no—
614C2×C4⋊C4—1062no—
615C2×C4⋊C4D21211yescharacteristic
616C2×C4⋊C4D21212yes—
617C2×C42—1062no—
618C2×C42—1061no—
619C2×C42—1062no—
620C2×C42—1061no—
621C2×C42C22×D5312yes—
622C2×C42C22×D5311yescharacteristic
623#107—532no—
624#107—534no—
625#107—534no—
626#107—534no—
627#107—534no—
628#106—534no—
629#106—532no—
630#106—534no—
631#106—534no—
632#106—534no—
633C4⋊C8C22×D5312yes—
634C4⋊C8C22×D5314yes—
635C4⋊C8C22×D5314yes—
636C4⋊C8C22×D5312yes—
637#103—534no—
638#103—532no—
639#103—534no—
640#103—532no—
641#103—532no—
642#103—534no—
643#102—534no—
644#102—532no—
645#97C22×D5312yes—
646#97C22×D5314yes—
647C4×C8C22×D5312yes—
648C4×C8C22×D5314yes—
649#41—534no—
650#41—1062no—
651C2×Q8—42no—
652C2×Q8—534no—
653C2×Q8—532no—
654C2×Q8—531no—
655C2×Q8—1061no—
656C2×Q8—1062no—
657C2×Q8—1061no—
658C2×Q8—1062no—
659C2×Q8—1061no—
660C2×Q8—1062no—
661C2×Q8—1062no—
662C2×Q8—1062no—
663C2×Q8—2124no—
664C2×Q8—2124no—
665C2×Q8C2×D21211yescharacteristic
666C2×Q8C2×D21211yescharacteristic
667C2×Q8C2×D21212yes—
668C2×D4—531no—
669C2×D4—1061no—
670C22×C4—1061no—
671C22×C4—1061no—
672C22×C4—1061no—
673C22×C4—1062no—
674C22×C4—1062no—
675C22×C4—1061no—
676C22×C4—1062no—
677C22×C4—1061no—
678C22×C4C2×D21211yescharacteristic
679C22×C4C2×D21212yes—
680C22×C4C2×D21211yescharacteristic
681C22×C4C2×D21212yes—
682C22×C4C23×D5311yescharacteristic
683Q16—538no—
684SD16—538no—
685M16—22no—
686M16—24no—
687M16Q8×D5314yescomplemented
688C2×C8C23×D5312yes—
689C2×C8C23×D5314yes—
690C2×C8C23×D5312yes—
691C4⋊C4—532no—
692C4⋊C4—534no—
693C4⋊C4—532no—
694C4⋊C4—531no—
695C4⋊C4—531no—
696C4⋊C4—532no—
697C4⋊C4—1061no—
698C4⋊C4—1062no—
699C4⋊C4—1062no—
700C4⋊C4—1062no—
701C4⋊C4—1064no—
702C4⋊C4—1064no—
703C4⋊C4—1062no—
704C4⋊C4—1062no—
705C4⋊C4—1062no—
706C4⋊C4—1062no—
707C4⋊C4—1061no—
708C4⋊C4—1064no—
709C4⋊C4—1064no—
710C4⋊C4—1064no—
711C4⋊C4—1064no—
712C4⋊C4—1062no—
713C4⋊C4—1062no—
714C4⋊C4—1062no—
715C4⋊C4—1061no—
716C4⋊C4—1062no—
717C4⋊C4—1061no—
718C4⋊C4—1062no—
719C4⋊C4—1062no—
720C4⋊C4—1062no—
721C4⋊C4—1062no—
722C4⋊C4—1061no—
723C4⋊C4C2×D21211yescharacteristic
724C4⋊C4C2×D21212yes—
725C4⋊C4C2×D21212yes—
726C4⋊C4C2×D21211yescharacteristic
727C4⋊C4C2×D21212yes—
728C4⋊C4C2×D21212yes—
729C4⋊C4C2×D21212yes—
730C22⋊C4—1061no—
731C22⋊C4—1062no—
732C22⋊C4—1062no—
733C22⋊C4—1061no—
734C22⋊C4—1062no—
735C22⋊C4—1061no—
736C42—1062no—
737C42—1061no—
738C42—1062no—
739C42—1061no—
740C42—1062no—
741C42—1061no—
742C42—1064no—
743C42—1064no—
744C42—1062no—
745C42—1062no—
746C42C2×D21212yes—
747C42C2×D21211yescharacteristic
748C42C2×D21212yes—
749C42C2×D21211yescharacteristic
750C42C23×D5312yes—
751C42C23×D5311yescharacteristic
752C42C23×D5312yes—
753C42C23×D5311yescharacteristic
754C23—1061no—
755C23C22×D21211yescharacteristic
756Q8—22no—
757Q8—22no—
758Q8—42no—
759Q8—534no—
760Q8—532no—
761Q8—1064no—
762Q8—1062no—
763Q8—1061no—
764Q8—4242no—
765Q8—4241no—
766Q8—2124no—
767Q8—2124no—
768Q8—2124no—
769Q8—2122no—
770D4—532no—
771D4—1064no—
772D4—1061no—
773C2×C4—22no—
774C2×C4—42no—
775C2×C4—41no—
776C2×C4—42no—
777C2×C4—1064no—
778C2×C4—1061no—
779C2×C4—1062no—
780C2×C4—1064no—
781C2×C4—1062no—
782C2×C4—1061no—
783C2×C4—1062no—
784C2×C4—1061no—
785C2×C4—1062no—
786C2×C4—1064no—
787C2×C4—4242no—
788C2×C4—4241no—
789C2×C4—2124no—
790C2×C4—2122no—
791C2×C4—2124no—
792C2×C4—2122no—
793C2×C4C22×D21212yes—
794C2×C4C22×D21212yes—
795C2×C4C22×D21211yescharacteristic
796C2×C4C22×D21211yescharacteristic
797C2×C4C22×D21212yes—
798C2×C4C22×D21212yes—
799C2×C4C22×D21211yescharacteristic
800C2×C4C22×D21211yescharacteristic
801C2×C4C22×D21211yescharacteristic
802C2×C4C2×Q8×D5312yes—
803C2×C4#1313326412yes—
804C2×C4C24×D5311yescharacteristic
805C8—22no—
806C8—24no—
807C8C2×Q8×D5314yes—
808C22—21no—
809C22—21no—
810C22—1062no—
811C22—2121no—
812C22—2121no—
813C22Q8×D21212yes—
814C22C23×D21211yescharacteristic
815C4—21no—
816C4—22no—
817C4—22no—
818C4—22no—
819C4—21no—
820C4—22no—
821C4—21no—
822C4—1062no—
823C4—1064no—
824C4—2122no—
825C4—2121no—
826C4—2124no—
827C4—2122no—
828C4—2121no—
829C4—2122no—
830C4Q8×D21212yes—
831C4#1681142312yes—
832C4C22×Q8×D5311yescharacteristic
833C4C2×#1313326411yescharacteristic
834C2—22no—
835C2—2122no—
836C2C2×Q8×D21211yescharacteristic
837C2C2×#1681142311yescharacteristic
838C2#2028950311yescharacteristic
subgroupG/H
centerC22C23×D212
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingQ8×M16×C53C2
socleC22×C53C23×D4
prime radicalC2×#11719945C23
hypercenterQ8×M16D53
hypocenterC53#61369
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C2×C4×Q8 ◁ Q8×M16

Complements

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

NH ≅ G/Ntype
2. C2×#16811351C2semidirect
3. #20287684C2semidirect
4. #20287662C2semidirect
5. #20287649C2semidirect
6. #20287638C2semidirect
7. #20287607C2semidirect
8. #20287592C2semidirect
9. #20285267C2semidirect
10. #20285261C2semidirect
13. #20284522C2semidirect
14. #20284522C2semidirect
17. Q8×M16×C53C2semidirect
99. #13133250Q8semidirect
260. C2×Dic106C2×Q8semidirect
265. M16×C53C2×Q8semidirect
332. Dic212C2×Q8semidirect
333. #11719913C2×Q8semidirect
429. Q8×M16D53semidirect
514. C53#61369semidirect
687. M16Q8×D53semidirect

Maximal subgroups

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

subgroupindex
Q8×#117199452
C2×#168113512
#202876842
#202876622
#202876492
#202876382
#202876072
#202875922
#202852672
#202852612
#202845382
#202845312
#202845222
C4×#131332502
Q8×M16×C532
#6136953