Finite Group Databasebeta

← #27388071

Subgroups — #27388071

Order 13568.

1460 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811421C211yesmaximal, characteristic
2#20283304C211yesmaximal, characteristic, complemented
3C2×#16810639C211yesmaximal, characteristic, complemented
4C2×#16810597C211yesmaximal, characteristic, complemented
5C2×#16810596C211yesmaximal, characteristic, complemented
6#20283133C211yesmaximal, characteristic, complemented
7#20275612C218yesmaximal, complemented
8C2×C53×#421C211yesmaximal, characteristic, complemented
9C22×#11719945C2211yescharacteristic
10#16811421—22no—
11#16811421—22no—
12#16811421—22no—
13#16811421—22no—
14C2×#13133248C412yescomplemented
15C2×#13133247C412yescomplemented
16C2×#13133243C412yescomplemented
17C2×#13133242C412yescomplemented
18C2×#13133237C2214yes—
19C22×#11719917C2211yescharacteristic
20C2×#13133176C2211yescharacteristic
21C2×#13133176C2211yescharacteristic
22#16810666—22no—
23#16810663—22no—
24#16810659C2214yescomplemented
25#16810639—22no—
26#16810639C2214yescomplemented
27C2×#13133143—22no—
28#16810597—22no—
29#16810597C2214yescomplemented
30#16810596—22no—
31#16810596C2214yescomplemented
32C2×#13133132—22no—
33C2×#13133131—22no—
34#16810581C2214yescomplemented
35#16810578—22no—
36M16×Dic53—22no—
37C22×#41×C53C2211yescharacteristic
38C22×M16×C53C2211yescharacteristic
39C2×#117×C53C2211yescharacteristic
40C53×#421—22no—
41C53×#421C2214yescomplemented
42C2×#104×C53—22no—
43C2×#11719945—21no—
44C2×#11719945—21no—
45C2×#11719945—21no—
46C2×#11719945—21no—
47C2×#11719945—21no—
48C2×#11719945—21no—
49C2×#11719945—21no—
50C2×#11719945—21no—
51C2×#11719945—21no—
52C2×#11719945—21no—
53C2×#11719945C2×C412yes—
54C2×#11719945C2312yes—
55C22×Dic106C2×C411yescharacteristic
56C22×D212C2×C411yescharacteristic
57C22×C22⋊D53—21no—
58C22×C4×D53—21no—
59#13133248—24no—
60#13133248—24no—
61#13133247—24no—
62#13133247—24no—
63#13133243—24no—
64#13133243—24no—
65#13133242—24no—
66#13133242—24no—
67#13133237—28no—
68#13133237—28no—
69C2×#11719925C2×C414yescomplemented
70C2×#11719923C2×C414yescomplemented
71C2×#11719924C2×C414yescomplemented
72C2×#11719922C2×C414yescomplemented
73C2×#11719917C2×C412yes—
74C2×#11719917C2×C412yes—
75C2×#11719917D412yes—
76C2×#11719917D412yes—
77C2×#11719917D412yes—
78C2×#11719917D412yes—
79C22×#88322C2312yes—
80#13133176—21no—
81#13133176—21no—
82#13133176—21no—
83#13133176—21no—
84#13133176—21no—
85#13133176D412yes—
86#13133176C2312yes—
87#13133176C2312yes—
88C2×C4⋊Dic53—21no—
89C2×C4⋊Dic53—21no—
90C2×C22⋊Dic53—21no—
91C2×C22⋊Dic53D412yes—
92C2×C4×Dic53—21no—
93C2×C4×Dic53—21no—
94#13133150—24no—
95#13133148—24no—
96#13133143—28no—
97#13133132—28no—
98#13133131—28no—
99#13133127—24no—
100C8×Dic53—24no—
101C2×#41×C53—21no—
102C2×#41×C53—21no—
103C2×#41×C53—21no—
104C2×#41×C53—21no—
105C2×#41×C53—21no—
106C2×#41×C53—21no—
107C2×#41×C53—21no—
108C2×#41×C53—21no—
109C2×#41×C53—21no—
110C2×#41×C53—21no—
111C2×#41×C53C2×C412yes—
112C2×#41×C53C2312yes—
113C22×Q8×C53C2×C411yescharacteristic
114C22×D4×C53—21no—
115C22×D4×C53C2×C411yescharacteristic
116C23×C4×C53—21no—
117C23×C4×C53C2311yescharacteristic
118C2×M16×C53—21no—
119C2×M16×C53—21no—
120C2×M16×C53—21no—
121C2×M16×C53D412yes—
122C2×M16×C53D412yes—
123C2×M16×C53C2312yes—
124C22×C8×C53—21no—
125#117×C53—21no—
126#117×C53—21no—
127#117×C53—21no—
128#117×C53C2312yes—
129C2×C4⋊C4×C53—21no—
130C2×C22⋊C4×C53—21no—
131C2×C42×C53—21no—
132#104×C53—28no—
133C24×C53—21no—
134C24×C53C2×D411yescharacteristic
135C23×D53—21no—
136#41×C53—22no—
137#41×C53—22no—
138#41×C53—22no—
139#41×C53—22no—
140#41×C53—22no—
141#41×C53—22no—
142#41×C53—22no—
143#41×C53—22no—
144#41×C53—41no—
145#41×C53—41no—
146#41×C53—41no—
147#41×C53—41no—
148#41×C53—41no—
149#41×C53—41no—
150#41×C53—41no—
151#41×C53—41no—
152C2×Q8×C53—21no—
153C2×Q8×C53—21no—
154C2×Q8×C53—21no—
155C2×Q8×C53—21no—
156C2×Q8×C53—21no—
157C2×Q8×C53C22×C412yes—
158C2×D4×C53—22no—
159C2×D4×C53—22no—
160C2×D4×C53—21no—
161C2×D4×C53—21no—
162C2×D4×C53—21no—
163C2×D4×C53—21no—
164C2×D4×C53—21no—
165C2×D4×C53—41no—
166C2×D4×C53—41no—
167C2×D4×C53—41no—
168C2×D4×C53—41no—
169C2×D4×C53C22×C412yes—
170C22×C4×C53—21no—
171C22×C4×C53—22no—
172C22×C4×C53—22no—
173C22×C4×C53—41no—
174C22×C4×C53—41no—
175C22×C4×C53—41no—
176C22×C4×C53—41no—
177C22×C4×C53—41no—
178C22×C4×C53C22×C411yescharacteristic
179C22×C4×C53C22×C411yescharacteristic
180C22×C4×C53C2×D411yescharacteristic
181C22×C4×C53C2×D411yescharacteristic
182C22×C4×C53C2×D411yescharacteristic
183C22×C4×C53C2×D411yescharacteristic
184C22×C4×C53C2×D411yescharacteristic
185C22×C4×C53C2×D411yescharacteristic
186C22×C4×C53C2×D411yescharacteristic
187C22×C4×C53#4111yescharacteristic
188C22×C4×C53#4111yescharacteristic
189C22×C4×C53#4111yescharacteristic
190C22×C4×C53#4111yescharacteristic
191C22×C4×C53C2411yescharacteristic
192C2×C22⋊D53—22no—
193C2×C22⋊D53—22no—
194C2×C22⋊D53—41no—
195C2×C22⋊D53—41no—
196C2×C22⋊D53—41no—
197C2×C22⋊D53—41no—
198C22×Dic53—21no—
199C22×Dic53—22no—
200C22×Dic53—41no—
201#11719945—22no—
202#11719945—22no—
203#11719945—22no—
204#11719945—22no—
205#11719945—22no—
206#11719945—22no—
207#11719945—22no—
208#11719945—22no—
209#11719945—41no—
210#11719945—41no—
211#11719945—41no—
212#11719945—41no—
213#11719945—41no—
214#11719945—41no—
215#11719945—41no—
216#11719945—41no—
217C2×D212—21no—
218C2×D212—21no—
219C2×D212—21no—
220C2×D212—21no—
221C2×D212—21no—
222C2×D212C22×C412yes—
223C2×C4×D53—22no—
224C2×C4×D53—22no—
225C2×C4×D53—41no—
226C2×C4×D53—41no—
227C2×C4×D53—41no—
228C2×C4×D53—41no—
229C2×Dic106—21no—
230C2×Dic106—21no—
231C2×Dic106—21no—
232C2×Dic106—21no—
233C2×Dic106—21no—
234C2×Dic106C22×C412yes—
235M16×C53—22no—
236M16×C53—22no—
237M16×C53—22no—
238M16×C53C2×D414yes—
239C2×C8×C53—22no—
240C2×C8×C53—22no—
241C2×C8×C53—22no—
242C4⋊C4×C53—22no—
243C4⋊C4×C53—41no—
244C22⋊C4×C53—22no—
245C22⋊C4×C53—41no—
246C42×C53—22no—
247C42×C53—41no—
248C22⋊Dic53—22no—
249C22⋊Dic53—22no—
250C22⋊Dic53—41no—
251C22⋊Dic53C2×D414yes—
252#11719925—28no—
253#11719924—28no—
254#11719923—28no—
255#11719922—28no—
256C4⋊Dic53—22no—
257C4⋊Dic53—22no—
258C4⋊Dic53—22no—
259C4⋊Dic53—41no—
260C4×Dic53—22no—
261C4×Dic53—22no—
262C4×Dic53—22no—
263C4×Dic53—41no—
264#11719917C22⋊C414yes—
265#11719917C22⋊C414yes—
266#11719917C22⋊C414yes—
267#11719917C22⋊C414yes—
268C2×#88322C22×C414yes—
269C2×#88322C2×D414yes—
270C2×#88322C2×D414yes—
271C23×C53—22no—
272C23×C53—41no—
273C23×C53—41no—
274C23×C53—81no—
275C23×C53—82no—
276C23×C53C4×D411yescharacteristic
277C23×C53C4×D411yescharacteristic
278C23×C53#12111yescharacteristic
279C23×C53#12111yescharacteristic
280C23×C53#12711yescharacteristic
281C23×C53#12711yescharacteristic
282C23×C53C22×D411yescharacteristic
283C22×D53—22no—
284C22×D53—41no—
285C22×D53—41no—
286C22×D53—82no—
287Q8×C53—22no—
288Q8×C53—22no—
289Q8×C53—41no—
290Q8×C53—41no—
291D4×C53—22no—
292D4×C53—22no—
293D4×C53—42no—
294D4×C53—42no—
295D4×C53—42no—
296D4×C53—42no—
297D4×C53—41no—
298D4×C53—41no—
299C2×C4×C53—22no—
300C2×C4×C53—41no—
301C2×C4×C53—41no—
302C2×C4×C53—42no—
303C2×C4×C53—42no—
304C2×C4×C53—42no—
305C2×C4×C53—42no—
306C2×C4×C53—42no—
307C2×C4×C53—82no—
308C2×C4×C53C2×C22⋊C411yescharacteristic
309C2×C4×C53C2×C22⋊C411yescharacteristic
310C2×C4×C53C2×C22⋊C411yescharacteristic
311C2×C4×C53C2×C22⋊C411yescharacteristic
312C2×C4×C53C4×D411yescharacteristic
313C2×C4×C53C4×D411yescharacteristic
314C2×C4×C53C4×D411yescharacteristic
315C2×C4×C53C4×D411yescharacteristic
316C2×C4×C53C4×D411yescharacteristic
317C2×C4×C53C4×D411yescharacteristic
318C2×C4×C53#12111yescharacteristic
319C2×C4×C53#12111yescharacteristic
320C2×C4×C53#12111yescharacteristic
321C2×C4×C53#12111yescharacteristic
322C2×C4×C53#12111yescharacteristic
323C2×C4×C53#12111yescharacteristic
324C2×C4×C53#12411yescharacteristic
325C2×C4×C53#12411yescharacteristic
326C2×C4×C53#12411yescharacteristic
327C2×C4×C53#12411yescharacteristic
328C2×C4×C53#12711yescharacteristic
329C2×C4×C53#12711yescharacteristic
330C2×C4×C53C23×C411yescharacteristic
331C2×C4×C53C22×D411yescharacteristic
332C2×C4×C53C22×D411yescharacteristic
333C2×C4×C53C22×D411yescharacteristic
334C2×C4×C53C2×#4111yescharacteristic
335C2×C4×C53C2×#4111yescharacteristic
336C22⋊D53—42no—
337C22⋊D53—42no—
338C22⋊D53—42no—
339C22⋊D53—42no—
340C2×Dic53—22no—
341C2×Dic53—24no—
342C2×Dic53—41no—
343C2×Dic53—41no—
344C2×Dic53—42no—
345C2×Dic53—82no—
346C2×Dic53—82no—
347D212—22no—
348D212—22no—
349D212—41no—
350D212—41no—
351C4×D53—42no—
352C4×D53—42no—
353C4×D53—42no—
354C4×D53—42no—
355Dic106—22no—
356Dic106—22no—
357Dic106—41no—
358Dic106—41no—
359C8×C53—24no—
360#88322C2×C22⋊C418yes—
361#21244—531nomaximal, Sylow
362C22×C53—41no—
363C22×C53—41no—
364C22×C53—41no—
365C22×C53—41no—
366C22×C53—41no—
367C22×C53—41no—
368C22×C53—41no—
369C22×C53—42no—
370C22×C53—82no—
371C22×C53—82no—
372C22×C53—82no—
373C22×C53#39011yescharacteristic
374C22×C53#39011yescharacteristic
375C22×C53#39011yescharacteristic
376C22×C53#39011yescharacteristic
377C22×C53C2×C4×D411yescharacteristic
378C22×C53C2×#12111yescharacteristic
379C22×C53C2×#12711yescharacteristic
380C2×D53—42no—
381C2×D53—82no—
382C2×D53—82no—
383C2×D53—82no—
384C4×C53—42no—
385C4×C53—82no—
386C4×C53#39011yescharacteristic
387C4×C53#39011yescharacteristic
388C4×C53#39011yescharacteristic
389C4×C53#39011yescharacteristic
390C4×C53C22×C22⋊C411yescharacteristic
391C4×C53C2×C4×D411yescharacteristic
392C4×C53C2×#12111yescharacteristic
393C4×C53C2×#12411yescharacteristic
394Dic53—44no—
395Dic53—42no—
396Dic53—82no—
397C2×#575—531no—
398#2911—531no—
399C2×#421—531no—
400C2×#421D5311yescharacteristic, complemented
401C2×#410—531no—
402C2×#410—531no—
403#2873—531no—
404#1976—538no—
405C2×C53—21no—
406C2×C53—21no—
407C2×C53—21no—
408C2×C53—21no—
409C2×C53—21no—
410C2×C53—21no—
411C2×C53—21no—
412C2×C53—82no—
413C2×C53C2×#39011yescharacteristic
414D53—82no—
415C22×#41—531no—
416C22×#41C2×D5311yescharacteristic
417#575—1062no—
418#575—1062no—
419#575—1062no—
420#575—1062no—
421C2×#137—532no—
422C2×#137—532no—
423C2×AGL(1,ℤ/8)—532no—
424C2×AGL(1,ℤ/8)—532no—
425C2×#135—534no—
426C22×M16—531no—
427C22×M16C2×D5311yescharacteristic
428C2×#117—531no—
429C2×#117—531no—
430C2×#117C2×D5311yescharacteristic
431#428—1062no—
432#428—1062no—
433#427—534no—
434#421—22no—
435#421—534no—
436#421—1062no—
437#421C2×D5314yescomplemented
438C2×#104—22no—
439C2×#104—1062no—
440#410—534no—
441#410—534no—
442#410—1062no—
443#410—1062no—
444C2×#99—1062no—
445C2×#99—1062no—
446#405—534no—
447#405—1062no—
448C4×M16—1062no—
449C53#2124411yescharacteristic, complemented, Sylow
450C2×#41—21no—
451C2×#41—21no—
452C2×#41—21no—
453C2×#41—21no—
454C2×#41—21no—
455C2×#41—21no—
456C2×#41—21no—
457C2×#41—21no—
458C2×#41—21no—
459C2×#41—21no—
460C2×#41—532no—
461C2×#41—532no—
462C2×#41—1061no—
463C2×#41—1061no—
464C2×#41—1061no—
465C2×#41—1061no—
466C2×#41—1061no—
467C2×#41—1061no—
468C2×#41—1061no—
469C2×#41—1061no—
470C2×#41—1061no—
471C2×#41—1061no—
472C2×#41C4×D5312yes—
473C2×#41C22×D5312yes—
474C22×Q8—531no—
475C22×Q8C4×D5311yescharacteristic
476C22×D4—21no—
477C22×D4—531no—
478C22×D4—1061no—
479C22×D4C4×D5311yescharacteristic
480C23×C4—21no—
481C23×C4—1061no—
482C23×C4C22×D5311yescharacteristic
483#137—1064no—
484#137—1064no—
485#137—1064no—
486#137—1064no—
487AGL(1,ℤ/8)—1064no—
488AGL(1,ℤ/8)—1064no—
489AGL(1,ℤ/8)—1064no—
490AGL(1,ℤ/8)—1064no—
491#135—1068no—
492#135—1068no—
493C2×Q16—534no—
494C2×SD16—534no—
495C2×SD16—534no—
496C2×D8—534no—
497C2×M16—21no—
498C2×M16—21no—
499C2×M16—21no—
500C2×M16—532no—
501C2×M16—532no—
502C2×M16—532no—
503C2×M16—532no—
504C2×M16—532no—
505C2×M16—532no—
506C2×M16C22⋊D5312yes—
507C2×M16C22⋊D5312yes—
508C2×M16C22×D5312yes—
509C22×C8—21no—
510C22×C8—532no—
511#117—21no—
512#117—21no—
513#117—21no—
514#117—532no—
515#117—532no—
516#117—532no—
517#117—1061no—
518#117—1061no—
519#117—1061no—
520#117—1061no—
521#117—1061no—
522#117C22×D5312yes—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—1061no—
525C2×C4⋊C4—1061no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—532no—
528C2×C22⋊C4—1061no—
529C2×C42—21no—
530C2×C42—1061no—
531C2×C42—1061no—
532#107—1064no—
533#106—1064no—
534#104—28no—
535#104—1068no—
536#99—1068no—
537#99—1068no—
538#97—1064no—
539C4×C8—1064no—
540C24—21no—
541C24—1061no—
542C24D4×D5311yescharacteristic
543#41—22no—
544#41—22no—
545#41—22no—
546#41—22no—
547#41—22no—
548#41—22no—
549#41—22no—
550#41—22no—
551#41—41no—
552#41—41no—
553#41—41no—
554#41—41no—
555#41—41no—
556#41—41no—
557#41—41no—
558#41—41no—
559#41—1062no—
560#41—1062no—
561#41—1062no—
562#41—1062no—
563#41—1062no—
564#41—1062no—
565#41—1062no—
566#41—1062no—
567#41—2121no—
568#41—2121no—
569#41—2121no—
570#41—2121no—
571#41—2121no—
572#41—2121no—
573#41—2121no—
574#41—2121no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—532no—
581C2×Q8—1061no—
582C2×Q8—1061no—
583C2×Q8—1061no—
584C2×Q8—1061no—
585C2×Q8—1061no—
586C2×Q8C2×C4×D5312yes—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—41no—
595C2×D4—41no—
596C2×D4—41no—
597C2×D4—41no—
598C2×D4—532no—
599C2×D4—1062no—
600C2×D4—1062no—
601C2×D4—1061no—
602C2×D4—1061no—
603C2×D4—1061no—
604C2×D4—1061no—
605C2×D4—1061no—
606C2×D4—2121no—
607C2×D4—2121no—
608C2×D4—2121no—
609C2×D4—2121no—
610C2×D4C2×C4×D5312yes—
611C22×C4—21no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—41no—
615C22×C4—41no—
616C22×C4—41no—
617C22×C4—41no—
618C22×C4—41no—
619C22×C4—1062no—
620C22×C4—1061no—
621C22×C4—1062no—
622C22×C4—1062no—
623C22×C4—2121no—
624C22×C4—2121no—
625C22×C4—2121no—
626C22×C4—2121no—
627C22×C4—2121no—
628C22×C4C2×C4×D5311yescharacteristic
629C22×C4C2×C4×D5311yescharacteristic
630C22×C4#1171994511yescharacteristic
631C22×C4#1171994511yescharacteristic
632C22×C4D4×D5311yescharacteristic
633C22×C4D4×D5311yescharacteristic
634C22×C4D4×D5311yescharacteristic
635C22×C4D4×D5311yescharacteristic
636C22×C4D4×D5311yescharacteristic
637C22×C4#1171994711yescharacteristic
638C22×C4#1171994711yescharacteristic
639C22×C4C2×C22⋊D5311yescharacteristic
640C22×C4C2×C22⋊D5311yescharacteristic
641C22×C4C23×D5311yescharacteristic
642Q16—1068no—
643SD16—1068no—
644SD16—1068no—
645D8—1068no—
646M16—22no—
647M16—22no—
648M16—22no—
649M16—534no—
650M16—534no—
651M16—534no—
652M16—534no—
653M16C2×C22⋊D5314yes—
654C2×C8—22no—
655C2×C8—22no—
656C2×C8—22no—
657C2×C8—534no—
658C2×C8—534no—
659C2×C8—534no—
660C4⋊C4—22no—
661C4⋊C4—41no—
662C4⋊C4—1062no—
663C4⋊C4—1062no—
664C4⋊C4—1062no—
665C4⋊C4—2121no—
666C22⋊C4—22no—
667C22⋊C4—41no—
668C22⋊C4—534no—
669C22⋊C4—1062no—
670C22⋊C4—1062no—
671C22⋊C4—2121no—
672C42—22no—
673C42—41no—
674C42—1062no—
675C42—1062no—
676C42—1062no—
677C42—2121no—
678C23—22no—
679C23—41no—
680C23—41no—
681C23—81no—
682C23—82no—
683C23—1062no—
684C23—4242no—
685C23—2121no—
686C23—2121no—
687C23#1313317711yescharacteristic
688C23#1313317711yescharacteristic
689C23#1313319011yescharacteristic
690C23#1313319011yescharacteristic
691C23#1313321311yescharacteristic
692C23#1313321311yescharacteristic
693C23C2×D4×D5311yescharacteristic
694Q8—22no—
695Q8—22no—
696Q8—41no—
697Q8—41no—
698Q8—1062no—
699Q8—1062no—
700Q8—2121no—
701Q8—2121no—
702D4—22no—
703D4—22no—
704D4—42no—
705D4—42no—
706D4—42no—
707D4—42no—
708D4—41no—
709D4—41no—
710D4—1062no—
711D4—1062no—
712D4—2122no—
713D4—2122no—
714D4—2122no—
715D4—2122no—
716D4—2121no—
717D4—2121no—
718C2×C4—22no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—82no—
727C2×C4—1062no—
728C2×C4—1064no—
729C2×C4—4242no—
730C2×C4—4242no—
731C2×C4—2122no—
732C2×C4—2121no—
733C2×C4—2121no—
734C2×C4—2122no—
735C2×C4—2122no—
736C2×C4—2122no—
737C2×C4—2122no—
738C2×C4C22⋊C4×D5311yescharacteristic
739C2×C4C22⋊C4×D5311yescharacteristic
740C2×C4C22⋊C4×D5311yescharacteristic
741C2×C4C22⋊C4×D5311yescharacteristic
742C2×C4#1313317711yescharacteristic
743C2×C4#1313317711yescharacteristic
744C2×C4C4×C22⋊D5311yescharacteristic
745C2×C4C4×C22⋊D5311yescharacteristic
746C2×C4C4×C22⋊D5311yescharacteristic
747C2×C4C4×C22⋊D5311yescharacteristic
748C2×C4#1313318911yescharacteristic
749C2×C4#1313318911yescharacteristic
750C2×C4#1313318911yescharacteristic
751C2×C4#1313318911yescharacteristic
752C2×C4#1313319011yescharacteristic
753C2×C4#1313319011yescharacteristic
754C2×C4#1313320311yescharacteristic
755C2×C4#1313320311yescharacteristic
756C2×C4#1313320311yescharacteristic
757C2×C4#1313320311yescharacteristic
758C2×C4#1313321311yescharacteristic
759C2×C4#1313321311yescharacteristic
760C2×C4C22×C4×D5311yescharacteristic
761C2×C4C2×D4×D5311yescharacteristic
762C2×C4C2×D4×D5311yescharacteristic
763C2×C4C22×C22⋊D5311yescharacteristic
764C2×C4C2×#1171994711yescharacteristic
765C2×C4C2×#1171994511yescharacteristic
766C8—24no—
767C8—538no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—42no—
776C22—82no—
777C22—82no—
778C22—82no—
779C22—4242no—
780C22—4242no—
781C22—4242no—
782C22—2122no—
783C22#1681052311yescharacteristic
784C22#1681052311yescharacteristic
785C22#1681052311yescharacteristic
786C22#1681052311yescharacteristic
787C22C2×#1313317711yescharacteristic
788C22C2×#1313319011yescharacteristic
789C22C2×#1313321311yescharacteristic
790C4—42no—
791C4—82no—
792C4—4242no—
793C4—2124no—
794C4—2122no—
795C4#1681052311yescharacteristic
796C4#1681052311yescharacteristic
797C4#1681052311yescharacteristic
798C4#1681052311yescharacteristic
799C4C2×C22⋊C4×D5311yescharacteristic
800C4C2×C4×C22⋊D5311yescharacteristic
801C4C2×#1313318911yescharacteristic
802C4C2×#1313320311yescharacteristic
803C2—21no—
804C2—21no—
805C2—21no—
806C2—21no—
807C2—21no—
808C2—21no—
809C2—21no—
810C2—82no—
811C2—4242no—
812C2C2×#1681052311yescharacteristic
subgroupG/H
centerC4C2×#13133189
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC2×C53×#421C2
socleC2×C53C2×#390
prime radicalC2×#16811421C2
cosocleC22×C4×C53C24
hypercenterC2×#421D53
hypocenterC53#21244
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
2. #20283304C2semidirect
3. C2×#16810639C2semidirect
4. C2×#16810597C2semidirect
5. C2×#16810596C2semidirect
6. #20283133C2semidirect
7. #20275612C2semidirect
8. C2×C53×#421C2semidirect
14. C2×#13133248C4semidirect
15. C2×#13133247C4semidirect
16. C2×#13133243C4semidirect
17. C2×#13133242C4semidirect
24. #16810659C22semidirect
26. #16810639C22semidirect
29. #16810597C22semidirect
31. #16810596C22semidirect
34. #16810581C22semidirect
41. C53×#421C22semidirect
69. C2×#11719925C2×C4semidirect
70. C2×#11719923C2×C4semidirect
71. C2×#11719924C2×C4semidirect
72. C2×#11719922C2×C4semidirect
400. C2×#421D53semidirect
437. #421C2×D53semidirect
449. C53#21244semidirect

Maximal subgroups

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

subgroupindex
C2×#168114212
#202833042
C2×#168106392
C2×#168105972
C2×#168105962
#202831332
#202756122
C2×C53×#4212
#2124453