Finite Group Databasebeta

← #28264126

Subgroups — #28264126

Order 13568.

1776 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288601C211yesmaximal, characteristic, complemented
2#20288534C211yesmaximal, characteristic, complemented
3#20287516C212yesmaximal, complemented
4#20287494C212yesmaximal, complemented
5#20287453C212yesmaximal, complemented
6#20287431C212yesmaximal, complemented
7#20287398C212yesmaximal, complemented
8#20287391C212yesmaximal, complemented
9#20287362C212yesmaximal, complemented
10#20287355C212yesmaximal, complemented
11#20285084C212yesmaximal, complemented
12C2×#16810974C211yesmaximal, characteristic, complemented
13#20284560C212yesmaximal, complemented
14#20284530C211yesmaximal, characteristic, complemented
15#20284263C212yesmaximal
16#20284202C211yesmaximal, characteristic, complemented
17#20283649C211yesmaximal, characteristic, complemented
18#20283561C212yesmaximal, complemented
19C4×#135×C53C211yesmaximal, characteristic
20C2×#13133247C2212yes—
21Q8×Dic106C2212yes—
22#16811352C2212yes—
23#16811351C2212yes—
24#16811351C2212yes—
25#16811343C2212yes—
26#16811343C2212yes—
27#16811330—22no—
28#16811330C2212yes—
29#16811313—22no—
30#16811313—22no—
31D4×Dic106—22no—
32D4×Dic106C2212yes—
33#16811251—22no—
34#16811251C2212yes—
35#16811235—22no—
36#16811194C2212yes—
37#16811180—21no—
38#16811180—21no—
39#16811180—21no—
40#16811180C2211yescharacteristic
41C2×#13133217—21no—
42C2×#13133217C2211yescharacteristic
43C2×#13133217C2211yescharacteristic
44#16811106C2212yes—
45#16811100C2212yes—
46#16810990C2214yes—
47#16810981C2214yes—
48#16810976C2214yes—
49#16810974C2212yes—
50#16810974C2212yes—
51#16810974C2212yes—
52#16810974C2212yes—
53#16810972C2214yes—
54#16810933C2214yes—
55#16810929C2214yes—
56#16810918C2212yes—
57#16810917C2214yes—
58#16810913C2212yes—
59#16810908C2212yes—
60#16810907C2214yes—
61#16810903C2212yes—
62#16810843C2214yes—
63#16810836C2214yes—
64#16810833C2212yes—
65#16810833C2212yes—
66#16810831C2214yes—
67#16810828C2212yes—
68#16810828C2212yes—
69#16810826C2214yes—
70#16810753C2212yes—
71#16810753C2212yes—
72C8×Dic106C2212yes—
73C8×Dic106C2212yes—
74#16810727C2214yes—
75#16810720C2214yes—
76#16810715C2214yes—
77#16810714C2214yes—
78#16810666C2212yes—
79#16810649C2212yes—
80#16810647C2211yescharacteristic
81#16810631C2212yes—
82#16810624C2212yes—
83C2×#13133142C2212yes—
84C2×#13133142C2212yes—
85#16810578C2212yes—
86C2×#135×C53C2211yescharacteristic
87C4×#41×C53C2211yescharacteristic
88C4×#41×C53C2211yescharacteristic
89C4×Q16×C53C2211yescharacteristic
90C4×Q16×C53C2211yescharacteristic
91C4×SD16×C53C2211yescharacteristic
92C4×SD16×C53C2211yescharacteristic
93C4×SD16×C53C2211yescharacteristic
94C4×SD16×C53C2211yescharacteristic
95C4×D8×C53C2211yescharacteristic
96C4×D8×C53C2211yescharacteristic
97C53×#427C2211yescharacteristic
98C53×#416C2211yescharacteristic
99C53×#416C2211yescharacteristic
100C2×C4×C8×C53C2211yescharacteristic
101C22×Dic106—21no—
102C22×Dic106—22no—
103C22×Dic106C2312yes—
104#13133247—28no—
105C2×#11719925C2314yes—
106C2×#11719923C2314yes—
107C2×#11719917C2312yes—
108#13133217—21no—
109#13133217—21no—
110#13133217—21no—
111#13133217—21no—
112#13133217—22no—
113#13133217—22no—
114#13133217—22no—
115#13133217D411yescharacteristic
116#13133217D411yescharacteristic
117#13133217C2312yes—
118#13133217C2312yes—
119#13133217C2312yes—
120#13133217C2312yes—
121#13133216—24no—
122#13133216C2314yes—
123#13133215C2314yes—
124#13133210—24no—
125#13133210—24no—
126#13133209—22no—
127#13133209—22no—
128#13133209—22no—
129#13133209D412yes—
130#13133208—24no—
131#13133208C2314yes—
132#13133207—24no—
133#13133207—24no—
134#13133204C2314yes—
135#13133198—24no—
136#13133196—22no—
137#13133196—22no—
138#13133196—22no—
139#13133196—22no—
140#13133196—22no—
141#13133196—22no—
142#13133196D412yes—
143#13133196D412yes—
144#13133194—24no—
145#13133194—24no—
146#13133194—24no—
147Q8×Dic53C2314yes—
148C4×Dic106—22no—
149C4×Dic106—22no—
150C4×Dic106—22no—
151C4×Dic106—22no—
152C4×Dic106—22no—
153C4×Dic106—22no—
154C4×Dic106C2312yes—
155C4×Dic106C2312yes—
156#13133182C2314yes—
157#13133182C2314yes—
158D4×Dic53—24no—
159D4×Dic53C2314yes—
160#13133176—22no—
161#13133176—22no—
162#13133176—22no—
163#13133176C2312yes—
164#13133173—24no—
165C2×C4⋊Dic53—22no—
166C2×C4⋊Dic53—22no—
167C2×C4⋊Dic53—21no—
168C2×C4⋊Dic53—21no—
169C2×C4⋊Dic53—21no—
170C2×C4⋊Dic53C2312yes—
171#13133150C2314yes—
172#13133148C2314yes—
173C4⋊#88322C2312yes—
174C4⋊#88322C2312yes—
175#13133146C2314yes—
176#13133146C2314yes—
177#13133142C2314yes—
178#13133142C2314yes—
179#13133142C2314yes—
180#13133142C2314yes—
181#13133141C2314yes—
182#13133140C2314yes—
183#13133140C2314yes—
184#13133138C2314yes—
185#13133127C2314yes—
186C8×Dic53C2314yes—
187C2×#41×C53C2311yescharacteristic
188C2×#41×C53C2311yescharacteristic
189#135×C53—24no—
190C2×Q16×C53C2311yescharacteristic
191C2×SD16×C53C2311yescharacteristic
192C2×SD16×C53C2311yescharacteristic
193C2×D8×C53C2311yescharacteristic
194C22×C8×C53C2311yescharacteristic
195C22×C8×C53C2311yescharacteristic
196C4×Q8×C53C2311yescharacteristic
197C4×Q8×C53C2311yescharacteristic
198C4×Q8×C53C2311yescharacteristic
199C4×Q8×C53C2311yescharacteristic
200C4×D4×C53—21no—
201C4×D4×C53—21no—
202C4×D4×C53—21no—
203C4×D4×C53—21no—
204C4×D4×C53C2311yescharacteristic
205C4×D4×C53C2311yescharacteristic
206C4×D4×C53C2311yescharacteristic
207C4×D4×C53C2311yescharacteristic
208#117×C53—21no—
209#117×C53—21no—
210#117×C53C2311yescharacteristic
211#117×C53C2311yescharacteristic
212C2×C42×C53—21no—
213C2×C42×C53—21no—
214C2×C42×C53C2311yescharacteristic
215#107×C53C2311yescharacteristic
216#107×C53C2311yescharacteristic
217#106×C53C2311yescharacteristic
218#106×C53C2311yescharacteristic
219#103×C53C2311yescharacteristic
220#103×C53C2311yescharacteristic
221#103×C53C2311yescharacteristic
222#103×C53C2311yescharacteristic
223#102×C53C2311yescharacteristic
224#102×C53C2311yescharacteristic
225#102×C53C2311yescharacteristic
226#102×C53C2311yescharacteristic
227C4×C8×C53C2311yescharacteristic
228C4×C8×C53C2311yescharacteristic
229C4×C8×C53C2311yescharacteristic
230C4×C8×C53C2311yescharacteristic
231#41×C53—22no—
232#41×C53—22no—
233#41×C53—22no—
234#41×C53#4114yes—
235C2×Q8×C53C2411yescharacteristic
236C2×Q8×C53C2411yescharacteristic
237C2×D4×C53—21no—
238C2×D4×C53—21no—
239C2×D4×C53C2411yescharacteristic
240C2×D4×C53C2411yescharacteristic
241C22×C4×C53—21no—
242C22×C4×C53—21no—
243C22×C4×C53—21no—
244C22×C4×C53—21no—
245C22×C4×C53—21no—
246C22×C4×C53—21no—
247C22×C4×C53C2×D411yescharacteristic
248C22×C4×C53C2×D411yescharacteristic
249C22×C4×C53C2411yescharacteristic
250C22×Dic53—22no—
251C22×Dic53—22no—
252C22×Dic53—24no—
253C2×Dic106—24no—
254C2×Dic106—24no—
255C2×Dic106—22no—
256C2×Dic106—22no—
257C2×Dic106—22no—
258C2×Dic106—24no—
259C2×Dic106—84no—
260C2×Dic106—82no—
261C2×Dic106C2×D412yes—
262C2×Dic106C2×D412yes—
263C2×Dic106C2414yes—
264Q16×C53—22no—
265SD16×C53—22no—
266SD16×C53—22no—
267D8×C53—22no—
268C2×C8×C53—22no—
269C2×C8×C53—22no—
270C2×C8×C53C2411yescharacteristic
271C2×C8×C53C2411yescharacteristic
272C2×C8×C53C2411yescharacteristic
273C2×C8×C53C2411yescharacteristic
274C4⋊C4×C53—21no—
275C4⋊C4×C53—21no—
276C4⋊C4×C53—21no—
277C4⋊C4×C53—21no—
278C4⋊C4×C53C2411yescharacteristic
279C4⋊C4×C53C2411yescharacteristic
280C4⋊C4×C53C2411yescharacteristic
281C4⋊C4×C53C2411yescharacteristic
282C22⋊C4×C53—21no—
283C22⋊C4×C53—21no—
284C22⋊C4×C53—21no—
285C22⋊C4×C53—21no—
286C22⋊C4×C53—21no—
287C22⋊C4×C53—21no—
288C42×C53—21no—
289C42×C53—21no—
290C42×C53—21no—
291C42×C53—21no—
292C42×C53—21no—
293C42×C53—21no—
294C42×C53C2×D411yescharacteristic
295C42×C53C2×D411yescharacteristic
296C42×C53C2411yescharacteristic
297C42×C53C2411yescharacteristic
298C22⋊Dic53—24no—
299C22⋊Dic53—24no—
300C22⋊Dic53—24no—
301C22⋊Dic53C2×D414yes—
302#11719925—28no—
303#11719923—28no—
304C4⋊Dic53—22no—
305C4⋊Dic53—22no—
306C4⋊Dic53—22no—
307C4⋊Dic53—22no—
308C4⋊Dic53—22no—
309C4⋊Dic53—22no—
310C4⋊Dic53—22no—
311C4⋊Dic53—24no—
312C4⋊Dic53—24no—
313C4⋊Dic53C2×D412yes—
314C4⋊Dic53C2×D412yes—
315C4⋊Dic53C2×D412yes—
316C4⋊Dic53C2×D412yes—
317C4⋊Dic53C2414yes—
318#11719919—24no—
319#11719919—24no—
320#11719919—24no—
321#11719919—24no—
322#11719919—24no—
323#11719919—24no—
324#11719919C2×D414yes—
325#11719919C2×D414yes—
326C4×Dic53—24no—
327C4×Dic53—24no—
328C4×Dic53—24no—
329C4×Dic53C2414yes—
330#11719917—24no—
331C2×#88322C2414yes—
332C23×C53—21no—
333C23×C53—21no—
334C23×C53C22×D411yescharacteristic
335Q8×C53—21no—
336Q8×C53—21no—
337Q8×C53—21no—
338Q8×C53C2×#4112yes—
339D4×C53—24no—
340D4×C53—21no—
341D4×C53—21no—
342D4×C53—21no—
343D4×C53—42no—
344D4×C53C2×#4112yes—
345C2×C4×C53—21no—
346C2×C4×C53—24no—
347C2×C4×C53—22no—
348C2×C4×C53—22no—
349C2×C4×C53—21no—
350C2×C4×C53—21no—
351C2×C4×C53—21no—
352C2×C4×C53—21no—
353C2×C4×C53—21no—
354C2×C4×C53—42no—
355C2×C4×C53—42no—
356C2×C4×C53—42no—
357C2×C4×C53—42no—
358C2×C4×C53—42no—
359C2×C4×C53C22×D411yescharacteristic
360C2×C4×C53C22×D411yescharacteristic
361C2×C4×C53C22×D411yescharacteristic
362C2×C4×C53C22×D411yescharacteristic
363C2×C4×C53C22×D411yescharacteristic
364C2×C4×C53C2×#4112yes—
365C2×C4×C532−1+412yes—
366C2×C4×C53C2511yescharacteristic
367C2×Dic53—24no—
368C2×Dic53—24no—
369C2×Dic53—44no—
370C2×Dic53—84no—
371C2×Dic53—82no—
372C2×Dic53C22×D414yes—
373C2×Dic53C22×D414yes—
374Dic106—24no—
375Dic106—24no—
376Dic106—24no—
377Dic106—24no—
378Dic106—44no—
379Dic106—44no—
380Dic106—84no—
381Dic106—82no—
382C8×C53—21no—
383C8×C53—21no—
384C8×C53—21no—
385C8×C53—21no—
386#88322—24no—
387#61330—531nomaximal, Sylow
388C22×C53—21no—
389C22×C53—21no—
390C22×C53—22no—
391C22×C53—41no—
392C22×C53—41no—
393C22×C53—41no—
394C22×C53—41no—
395C22×C53—41no—
396C22×C53#54812yes—
397C22×C53C23×D411yescharacteristic
398C4×C53—22no—
399C4×C53—21no—
400C4×C53—21no—
401C4×C53—41no—
402C4×C53—41no—
403C4×C53—41no—
404C4×C53—41no—
405C4×C53—41no—
406C4×C53#54812yes—
407C4×C53#57712yes—
408C4×C53#57812yes—
409C4×C53C22×#4111yescharacteristic
410C4×C53C2×2−1+411yescharacteristic
411Dic53—24no—
412Dic53—24no—
413Dic53—44no—
414Dic53—44no—
415#3509—531no—
416#3503—531no—
417#3374—532no—
418#3372—532no—
419#3369—532no—
420#3367—532no—
421#3364—532no—
422#3363—532no—
423#3360—532no—
424#3359—532no—
425#3137—532no—
426C2×#487—531no—
427#3082—532no—
428#3079—531no—
429#3046—532no—
430#3039—531no—
431#2960—531no—
432#2947—532no—
433C4×#135D5311yescharacteristic
434C2×C53—22no—
435C2×C53—42no—
436C2×C53—81no—
437C2×C53C2×#54811yescharacteristic
438C2×C53C2×#57711yescharacteristic
439C2×C53C2×#57811yescharacteristic
440C2×#137—532no—
441C2×#135C2×D5311yescharacteristic
442Q82—532no—
443#557—532no—
444#557—532no—
445#557—532no—
446#556—532no—
447#556—532no—
448#554—532no—
449#554—1062no—
450#552—1062no—
451#552—1062no—
452D4×Q8—532no—
453D4×Q8—1062no—
454#544—532no—
455#544—1062no—
456#541—1062no—
457#536—532no—
458#533—531no—
459#533—1061no—
460#533—1061no—
461#533—1061no—
462C2×C4⋊Q8—531no—
463C2×C4⋊Q8—531no—
464C2×C4⋊Q8—1061no—
465#520—532no—
466#519—532no—
467C4×#41C2×D5311yescharacteristic
468C4×#41C2×D5311yescharacteristic
469#491—534no—
470#489—534no—
471#488—534no—
472#487—534no—
473#487—532no—
474#487—532no—
475#487—532no—
476#487—532no—
477#479—534no—
478#479—534no—
479#477—532no—
480#477—534no—
481#476—532no—
482#475—532no—
483#475—534no—
484#474—532no—
485#464—534no—
486#463—534no—
487#462—534no—
488#462—532no—
489#462—532no—
490#461—534no—
491#461—532no—
492#461—532no—
493#446—532no—
494#446—532no—
495C8×Q8—532no—
496C8×Q8—532no—
497#441—534no—
498#440—534no—
499C4×Q16—534no—
500C4×Q16C2×D5311yescharacteristic
501C4×Q16C2×D5311yescharacteristic
502C4×SD16—534no—
503C4×SD16C2×D5311yescharacteristic
504C4×SD16C2×D5311yescharacteristic
505C4×SD16C2×D5311yescharacteristic
506C4×SD16C2×D5311yescharacteristic
507C4×D8C2×D5311yescharacteristic
508C4×D8C2×D5311yescharacteristic
509#428—532no—
510#427C2×D5311yescharacteristic
511#424—532no—
512#423—531no—
513#419—532no—
514#417—532no—
515#416C2×D5311yescharacteristic
516#416C2×D5311yescharacteristic
517C2×#103—532no—
518C2×#103—532no—
519#405—532no—
520C2×C4×C8C2×D5311yescharacteristic
521C53#6133011yescharacteristic, complemented, Sylow
522C2×#41C22×D5311yescharacteristic
523C2×#41C22×D5311yescharacteristic
524C22×Q8—532no—
525C22×Q8—1062no—
526C22×Q8—1061no—
527#137—1068no—
528#135—24no—
529C2×Q16—534no—
530C2×Q16C22×D5311yescharacteristic
531C2×SD16—534no—
532C2×SD16C22×D5311yescharacteristic
533C2×SD16C22×D5311yescharacteristic
534C2×D8C22×D5311yescharacteristic
535C2×M16—532no—
536C22×C8C22×D5311yescharacteristic
537C22×C8C22×D5311yescharacteristic
538C4⋊Q8—534no—
539C4⋊Q8—534no—
540C4⋊Q8—531no—
541C4⋊Q8—531no—
542C4⋊Q8—532no—
543C4⋊Q8—532no—
544C4⋊Q8—532no—
545C4⋊Q8—532no—
546C4⋊Q8—1062no—
547C4⋊Q8—1062no—
548C4⋊Q8—1062no—
549C4⋊Q8—1064no—
550C4⋊Q8—1061no—
551C4⋊Q8—1061no—
552C4⋊Q8—1061no—
553C4⋊Q8—1061no—
554#126—1064no—
555#126—1064no—
556#125—534no—
557#125—532no—
558#125—1062no—
559#125—1062no—
560#125—1062no—
561#125—1064no—
562#125—1064no—
563#125—1064no—
564#124—534no—
565#123—1064no—
566C22⋊Q8—532no—
567C22⋊Q8—532no—
568C22⋊Q8—1064no—
569C22⋊Q8—1064no—
570C22⋊Q8—1064no—
571C22⋊Q8—1062no—
572C22⋊Q8—1062no—
573C22⋊Q8—1062no—
574C22⋊Q8—1062no—
575C22⋊Q8—1062no—
576C22⋊Q8—1062no—
577C4×Q8—532no—
578C4×Q8—532no—
579C4×Q8—534no—
580C4×Q8—534no—
581C4×Q8—534no—
582C4×Q8—1062no—
583C4×Q8—1062no—
584C4×Q8—1062no—
585C4×Q8—1062no—
586C4×Q8—1062no—
587C4×Q8—1062no—
588C4×Q8C22×D5311yescharacteristic
589C4×Q8C22×D5311yescharacteristic
590C4×Q8C22×D5311yescharacteristic
591C4×Q8C22×D5311yescharacteristic
592C4×D4—21no—
593C4×D4—21no—
594C4×D4—21no—
595C4×D4—21no—
596C4×D4—534no—
597C4×D4—1064no—
598C4×D4C22×D5311yescharacteristic
599C4×D4C22×D5311yescharacteristic
600C4×D4C22×D5311yescharacteristic
601C4×D4C22×D5311yescharacteristic
602#117—21no—
603#117—21no—
604#117—532no—
605#117—1064no—
606#117—1062no—
607#117—1062no—
608#117—1062no—
609#117C22×D5311yescharacteristic
610#117C22×D5311yescharacteristic
611C2×C4⋊C4—532no—
612C2×C4⋊C4—1062no—
613C2×C4⋊C4—1062no—
614C2×C4⋊C4—1061no—
615C2×C4⋊C4—1061no—
616C2×C4⋊C4—1061no—
617C2×C42—21no—
618C2×C42—21no—
619C2×C42C22×D5311yescharacteristic
620#107—534no—
621#107C22×D5311yescharacteristic
622#107C22×D5311yescharacteristic
623#106—534no—
624#106C22×D5311yescharacteristic
625#106C22×D5311yescharacteristic
626C4⋊C8—534no—
627C4⋊C8—534no—
628C4⋊C8—532no—
629C4⋊C8—532no—
630#103—534no—
631#103—534no—
632#103—534no—
633#103—534no—
634#103—534no—
635#103—534no—
636#103—534no—
637#103C22×D5311yescharacteristic
638#103C22×D5311yescharacteristic
639#103C22×D5311yescharacteristic
640#103C22×D5311yescharacteristic
641#102—534no—
642#102C22×D5311yescharacteristic
643#102C22×D5311yescharacteristic
644#102C22×D5311yescharacteristic
645#102C22×D5311yescharacteristic
646#97—534no—
647C4×C8—534no—
648C4×C8C22×D5311yescharacteristic
649C4×C8C22×D5311yescharacteristic
650C4×C8C22×D5311yescharacteristic
651C4×C8C22×D5311yescharacteristic
652#41—22no—
653#41—22no—
654#41—22no—
655#41#1171994514yes—
656C2×Q8—532no—
657C2×Q8—532no—
658C2×Q8—534no—
659C2×Q8—1064no—
660C2×Q8—1062no—
661C2×Q8—1062no—
662C2×Q8—1062no—
663C2×Q8—1064no—
664C2×Q8—1064no—
665C2×Q8—4242no—
666C2×Q8—4244no—
667C2×Q8C23×D5311yescharacteristic
668C2×Q8C23×D5311yescharacteristic
669C2×D4—21no—
670C2×D4—21no—
671C2×D4C23×D5311yescharacteristic
672C2×D4C23×D5311yescharacteristic
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—1064no—
680C22×C4—1062no—
681C22×C4—1062no—
682C22×C4D4×D5311yescharacteristic
683C22×C4D4×D5311yescharacteristic
684C22×C4C23×D5311yescharacteristic
685Q16—22no—
686Q16—1068no—
687SD16—22no—
688SD16—22no—
689SD16—1068no—
690D8—22no—
691M16—1064no—
692C2×C8—22no—
693C2×C8—22no—
694C2×C8—534no—
695C2×C8C23×D5311yescharacteristic
696C2×C8C23×D5311yescharacteristic
697C2×C8C23×D5311yescharacteristic
698C2×C8C23×D5311yescharacteristic
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—532no—
704C4⋊C4—532no—
705C4⋊C4—532no—
706C4⋊C4—532no—
707C4⋊C4—534no—
708C4⋊C4—534no—
709C4⋊C4—534no—
710C4⋊C4—1064no—
711C4⋊C4—1064no—
712C4⋊C4—1064no—
713C4⋊C4—1064no—
714C4⋊C4—1064no—
715C4⋊C4—1064no—
716C4⋊C4—1064no—
717C4⋊C4—1064no—
718C4⋊C4—1062no—
719C4⋊C4—1062no—
720C4⋊C4—1062no—
721C4⋊C4—1062no—
722C4⋊C4—1062no—
723C4⋊C4—1062no—
724C4⋊C4—1062no—
725C4⋊C4C23×D5311yescharacteristic
726C4⋊C4C23×D5311yescharacteristic
727C4⋊C4C23×D5311yescharacteristic
728C4⋊C4C23×D5311yescharacteristic
729C22⋊C4—21no—
730C22⋊C4—21no—
731C22⋊C4—21no—
732C22⋊C4—21no—
733C22⋊C4—21no—
734C22⋊C4—21no—
735C22⋊C4—534no—
736C22⋊C4—1064no—
737C22⋊C4—1064no—
738C22⋊C4—1064no—
739C42—21no—
740C42—21no—
741C42—21no—
742C42—21no—
743C42—21no—
744C42—21no—
745C42—534no—
746C42—1064no—
747C42—1064no—
748C42—1064no—
749C42D4×D5311yescharacteristic
750C42D4×D5311yescharacteristic
751C42C23×D5311yescharacteristic
752C42C23×D5311yescharacteristic
753C23—21no—
754C23—21no—
755C23C2×D4×D5311yescharacteristic
756Q8—21no—
757Q8—21no—
758Q8—21no—
759Q8—1064no—
760Q8—1064no—
761Q8—1064no—
762Q8—1064no—
763Q8—4242no—
764Q8—4244no—
765Q8—2124no—
766Q8—2124no—
767Q8C2×#1171994512yes—
768D4—24no—
769D4—21no—
770D4—21no—
771D4—21no—
772D4—42no—
773D4C2×#1171994512yes—
774C2×C4—21no—
775C2×C4—24no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—534no—
789C2×C4—534no—
790C2×C4—1064no—
791C2×C4—1064no—
792C2×C4—4244no—
793C2×C4—4242no—
794C2×C4—2124no—
795C2×C4C2×D4×D5311yescharacteristic
796C2×C4C2×D4×D5311yescharacteristic
797C2×C4C2×D4×D5311yescharacteristic
798C2×C4C2×D4×D5311yescharacteristic
799C2×C4C2×D4×D5311yescharacteristic
800C2×C4C2×#1171994512yes—
801C2×C4#1313326412yes—
802C2×C4C24×D5311yescharacteristic
803C8—21no—
804C8—21no—
805C8—21no—
806C8—21no—
807C8—1064no—
808C22—21no—
809C22—21no—
810C22—22no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22#1681128212yes—
817C22C22×D4×D5311yescharacteristic
818C4—22no—
819C4—21no—
820C4—21no—
821C4—41no—
822C4—41no—
823C4—41no—
824C4—41no—
825C4—41no—
826C4—1064no—
827C4—1064no—
828C4—2124no—
829C4—2124no—
830C4#1681128212yes—
831C4#1681143012yes—
832C4#1681143712yes—
833C4C22×#1171994511yescharacteristic
834C4C2×#1313326411yescharacteristic
835C2—22no—
836C2—42no—
837C2—81no—
838C2C2×#1681128211yescharacteristic
839C2C2×#1681143011yescharacteristic
840C2C2×#1681143711yescharacteristic
subgroupG/H
centerC22C22×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC4×#135×C53C2
socleC22×C53C23×D4
prime radicalC2×#135×C53C22
hypercenterC4×#135D53
hypocenterC53#61330
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#135

Complements

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

NH ≅ G/Ntype
1. #20288601C2semidirect
2. #20288534C2semidirect
3. #20287516C2semidirect
4. #20287494C2semidirect
5. #20287453C2semidirect
6. #20287431C2semidirect
7. #20287398C2semidirect
8. #20287391C2semidirect
9. #20287362C2semidirect
10. #20287355C2semidirect
11. #20285084C2semidirect
12. C2×#16810974C2semidirect
13. #20284560C2semidirect
14. #20284530C2semidirect
16. #20284202C2semidirect
17. #20283649C2semidirect
18. #20283561C2semidirect
521. C53#61330semidirect

Maximal subgroups

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

subgroupindex
#202886012
#202885342
#202875162
#202874942
#202874532
#202874312
#202873982
#202873912
#202873622
#202873552
#202850842
C2×#168109742
#202845602
#202845302
#202842632
#202842022
#202836492
#202835612
C4×#135×C532
#6133053