Finite Group Databasebeta

← #27385987

Subgroups — #27385987

Order 13568.

1704 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811421C211yesmaximal, characteristic
2#20287916C211yesmaximal, characteristic, complemented
3#20283235C211yesmaximal, characteristic, complemented
4C2×#16810597C211yesmaximal, characteristic, complemented
5#20275206C214yesmaximal, complemented
6#20275199C214yesmaximal, complemented
7C2×#16810395C211yesmaximal, characteristic, complemented
8C2×#16810379C211yesmaximal, characteristic, complemented
9C2×C53×#421C211yesmaximal, characteristic, complemented
10C22×#11719945C2211yescharacteristic
11#16811421—22no—
12#16811421—22no—
13#16811421—22no—
14#16811421—22no—
15C2×#13133248C412yescomplemented
16C2×#13133247C2212yes—
17C2×#13133243C412yescomplemented
18C2×#13133242C2212yes—
19C2×#13133237C414yescomplemented
20C22×#11719917C2211yescharacteristic
21#16811104—22no—
22#16811103—22no—
23#16811100C2212yescomplemented
24#16811097C2212yescomplemented
25#16811096—22no—
26C4×#11719945—22no—
27#16811091—22no—
28C2×#13133176C2211yescharacteristic
29C2×#13133176C2211yescharacteristic
30#117×D53—22no—
31#16810633C2212yescomplemented
32#16810629C2212yescomplemented
33#16810625—22no—
34#16810620—22no—
35#16810597—22no—
36#16810597C2214yes—
37C2×#13133132—22no—
38#16810395C2214yescomplemented
39#16810379C2214yescomplemented
40C22×#41×C53C2211yescharacteristic
41C22×M16×C53C2211yescharacteristic
42C2×#117×C53C2211yescharacteristic
43C53×#421—22no—
44C53×#421C2214yes—
45C2×#104×C53—22no—
46C2×#11719945—21no—
47C2×#11719945—21no—
48C2×#11719945—21no—
49C2×#11719945—21no—
50C2×#11719945—21no—
51C2×#11719945—21no—
52C2×#11719945C2×C412yes—
53C2×#11719945C2×C412yes—
54C2×#11719945D412yes—
55C2×#11719945D412yes—
56C2×#11719945D412yes—
57C2×#11719945D412yes—
58C22×Dic106C2311yescharacteristic
59C22×D212C2311yescharacteristic
60C22×C22⋊D53—21no—
61C22×C4×D53—21no—
62#13133248—24no—
63#13133248—24no—
64#13133247—24no—
65#13133247—24no—
66#13133243—24no—
67#13133243—24no—
68#13133242—24no—
69#13133242—24no—
70#13133237—28no—
71#13133237—28no—
72C2×#11719925C2×C414yescomplemented
73C2×#11719923C2×C414yescomplemented
74C2×#11719924C2×C414yescomplemented
75C2×#11719922C2×C414yescomplemented
76C2×#11719917—21no—
77C2×#11719917—21no—
78C2×#11719917—21no—
79C2×#11719917—21no—
80C2×#11719917C2×C412yescomplemented
81C2×#11719917C2312yes—
82C22×#88322C2×C412yescomplemented
83C4×Dic106—24no—
84#13133182—24no—
85C4×D212—24no—
86#13133179—24no—
87C4×C22⋊D53—28no—
88#13133177—28no—
89#13133176—21no—
90#13133176—21no—
91#13133176—21no—
92#13133176—21no—
93#13133176—21no—
94#13133176D412yes—
95#13133176C2312yes—
96#13133176C2312yes—
97#13133175—24no—
98#13133174—24no—
99#13133173—24no—
100C2×C4⋊Dic53—21no—
101C2×C4⋊Dic53—21no—
102C4⋊C4×D53—24no—
103C2×C22⋊Dic53—21no—
104C2×C22⋊Dic53D412yes—
105C22⋊C4×D53—24no—
106C2×C4×Dic53—21no—
107C2×C4×Dic53—21no—
108C42×D53—24no—
109#13133142—24no—
110#13133139—24no—
111#13133132—28no—
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×C53—21no—
119C2×#41×C53—21no—
120C2×#41×C53—21no—
121C2×#41×C53—21no—
122C2×#41×C53C2×C412yescomplemented
123C2×#41×C53C2312yes—
124C22×Q8×C53C2×C411yescharacteristic, complemented
125C22×D4×C53—21no—
126C22×D4×C53C2×C411yescharacteristic, complemented
127C23×C4×C53—21no—
128C23×C4×C53C2311yescharacteristic
129C2×M16×C53—21no—
130C2×M16×C53—21no—
131C2×M16×C53—21no—
132C2×M16×C53—21no—
133C2×M16×C53—21no—
134C2×M16×C53C2312yes—
135C22×C8×C53—21no—
136#117×C53—21no—
137#117×C53—21no—
138#117×C53D412yes—
139#117×C53C2312yes—
140C2×C4⋊C4×C53—21no—
141C2×C22⋊C4×C53—21no—
142C2×C42×C53D412yes—
143#104×C53—28no—
144C24×C53—21no—
145C24×C53C2×D411yescharacteristic
146C23×D53—21no—
147#41×C53—22no—
148#41×C53—22no—
149#41×C53—22no—
150#41×C53—22no—
151#41×C53—22no—
152#41×C53—22no—
153#41×C53—22no—
154#41×C53—22no—
155#41×C53—41no—
156#41×C53—41no—
157#41×C53—41no—
158#41×C53—41no—
159#41×C53—41no—
160#41×C53—41no—
161#41×C53—41no—
162#41×C53—41no—
163C2×Q8×C53—21no—
164C2×Q8×C53—21no—
165C2×Q8×C53—21no—
166C2×Q8×C53—21no—
167C2×Q8×C53—21no—
168C2×Q8×C53C22×C412yes—
169C2×D4×C53—22no—
170C2×D4×C53—22no—
171C2×D4×C53—21no—
172C2×D4×C53—21no—
173C2×D4×C53—21no—
174C2×D4×C53—21no—
175C2×D4×C53—21no—
176C2×D4×C53—41no—
177C2×D4×C53—41no—
178C2×D4×C53—41no—
179C2×D4×C53—41no—
180C2×D4×C53C22×C412yes—
181C22×C4×C53—21no—
182C22×C4×C53—22no—
183C22×C4×C53—22no—
184C22×C4×C53—22no—
185C22×C4×C53—41no—
186C22×C4×C53—41no—
187C22×C4×C53—41no—
188C22×C4×C53—41no—
189C22×C4×C53C22×C411yescharacteristic
190C22×C4×C53C22×C411yescharacteristic
191C22×C4×C53C2×D411yescharacteristic
192C22×C4×C53C2×D411yescharacteristic
193C22×C4×C53C2×D411yescharacteristic
194C22×C4×C53C2×D411yescharacteristic
195C22×C4×C53C2×D411yescharacteristic
196C22×C4×C53C2×D411yescharacteristic
197C22×C4×C53C2×D411yescharacteristic
198C22×C4×C53#4111yescharacteristic
199C22×C4×C53#4111yescharacteristic
200C22×C4×C53#4111yescharacteristic
201C22×C4×C53#4111yescharacteristic
202C22×C4×C53C2411yescharacteristic
203C2×C22⋊D53—22no—
204C2×C22⋊D53—22no—
205C2×C22⋊D53—22no—
206C2×C22⋊D53—22no—
207C2×C22⋊D53—22no—
208C2×C22⋊D53—22no—
209C22×Dic53—21no—
210C22×Dic53—22no—
211C22×Dic53—41no—
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#11719945C22⋊C414yes—
225#11719945C22⋊C414yes—
226#11719945C22⋊C414yes—
227#11719945C22⋊C414yes—
228C2×D212—21no—
229C2×D212—21no—
230C2×D212—21no—
231C2×D212C22×C412yes—
232C2×D212C2×D412yes—
233C2×D212C2×D412yes—
234C2×C4×D53—22no—
235C2×C4×D53—22no—
236C2×C4×D53—22no—
237C2×C4×D53—22no—
238C2×C4×D53—22no—
239C2×C4×D53—22no—
240C2×C4×D53—28no—
241C2×Dic106—21no—
242C2×Dic106—21no—
243C2×Dic106—21no—
244C2×Dic106C22×C412yes—
245C2×Dic106C2×D412yes—
246C2×Dic106C2×D412yes—
247M16×C53—22no—
248M16×C53—22no—
249M16×C53—41no—
250M16×C53—41no—
251C2×C8×C53—22no—
252C2×C8×C53—41no—
253C2×C8×C53—41no—
254C4⋊C4×C53—22no—
255C4⋊C4×C53—22no—
256C22⋊C4×C53—22no—
257C22⋊C4×C53—22no—
258C42×C53—22no—
259C42×C53C2×D414yes—
260C22⋊Dic53—22no—
261C22⋊Dic53—22no—
262C22⋊Dic53—41no—
263C22⋊Dic53C2×D414yes—
264#11719925—28no—
265#11719924—28no—
266#11719923—28no—
267#11719922—28no—
268#11719921—28no—
269C4⋊Dic53—22no—
270C4⋊Dic53—22no—
271C4⋊Dic53—22no—
272C4⋊Dic53—41no—
273#11719919—28no—
274C4×Dic53—28no—
275C4×Dic53—22no—
276C4×Dic53—22no—
277C4×Dic53—22no—
278C4×Dic53—41no—
279#11719917—22no—
280#11719917—22no—
281#11719917—22no—
282#11719917—22no—
283C2×#88322—22no—
284C2×#88322—22no—
285C2×#88322C22×C414yes—
286C23×C53—22no—
287C23×C53—41no—
288C23×C53—41no—
289C23×C53—81no—
290C23×C53—82no—
291C23×C53C4×D411yescharacteristic
292C23×C53C4×D411yescharacteristic
293C23×C53#12011yescharacteristic
294C23×C53#12011yescharacteristic
295C23×C53#12111yescharacteristic
296C23×C53#12111yescharacteristic
297C23×C53C22×D411yescharacteristic
298C22×D53—22no—
299C22×D53—22no—
300C22×D53—22no—
301C22×D53—82no—
302Q8×C53—22no—
303Q8×C53—22no—
304Q8×C53—41no—
305Q8×C53—41no—
306D4×C53—22no—
307D4×C53—22no—
308D4×C53—42no—
309D4×C53—42no—
310D4×C53—42no—
311D4×C53—42no—
312D4×C53—41no—
313D4×C53—41no—
314C2×C4×C53—22no—
315C2×C4×C53—24no—
316C2×C4×C53—41no—
317C2×C4×C53—41no—
318C2×C4×C53—42no—
319C2×C4×C53—42no—
320C2×C4×C53—42no—
321C2×C4×C53—42no—
322C2×C4×C53—82no—
323C2×C4×C53C2×C22⋊C411yescharacteristic
324C2×C4×C53C2×C22⋊C411yescharacteristic
325C2×C4×C53C2×C22⋊C411yescharacteristic
326C2×C4×C53C2×C22⋊C411yescharacteristic
327C2×C4×C53C4×D411yescharacteristic
328C2×C4×C53C4×D411yescharacteristic
329C2×C4×C53C4×D411yescharacteristic
330C2×C4×C53C4×D411yescharacteristic
331C2×C4×C53C4×D411yescharacteristic
332C2×C4×C53C4×D411yescharacteristic
333C2×C4×C53#12011yescharacteristic
334C2×C4×C53#12011yescharacteristic
335C2×C4×C53#12111yescharacteristic
336C2×C4×C53#12111yescharacteristic
337C2×C4×C53#12111yescharacteristic
338C2×C4×C53#12111yescharacteristic
339C2×C4×C53#12111yescharacteristic
340C2×C4×C53#12111yescharacteristic
341C2×C4×C53#12311yescharacteristic
342C2×C4×C53#12311yescharacteristic
343C2×C4×C53#12311yescharacteristic
344C2×C4×C53#12311yescharacteristic
345C2×C4×C53C23×C411yescharacteristic
346C2×C4×C53C22×D411yescharacteristic
347C2×C4×C53C22×D411yescharacteristic
348C2×C4×C53C22×D411yescharacteristic
349C2×C4×C53C2×#4111yescharacteristic
350C2×C4×C53C2×#4111yescharacteristic
351C22⋊D53—24no—
352C22⋊D53—24no—
353C22⋊D53—24no—
354C22⋊D53—24no—
355C2×Dic53—22no—
356C2×Dic53—22no—
357C2×Dic53—22no—
358C2×Dic53—24no—
359C2×Dic53—42no—
360C2×Dic53—82no—
361C2×Dic53—82no—
362D212—22no—
363D212—22no—
364D212—22no—
365D212C2×C22⋊C414yes—
366C4×D53—24no—
367C4×D53—24no—
368C4×D53—24no—
369C4×D53—24no—
370C4×D53—88no—
371Dic106—22no—
372Dic106—22no—
373Dic106—22no—
374Dic106C2×C22⋊C414yes—
375C8×C53—42no—
376#88322—24no—
377#20998—531nomaximal, Sylow
378C22×C53—41no—
379C22×C53—41no—
380C22×C53—41no—
381C22×C53—41no—
382C22×C53—41no—
383C22×C53—41no—
384C22×C53—41no—
385C22×C53—42no—
386C22×C53—82no—
387C22×C53—82no—
388C22×C53—82no—
389C22×C53#38611yescharacteristic
390C22×C53#38611yescharacteristic
391C22×C53#38611yescharacteristic
392C22×C53#38611yescharacteristic
393C22×C53C2×C4×D411yescharacteristic
394C22×C53C2×#12011yescharacteristic
395C22×C53C2×#12111yescharacteristic
396C2×D53—24no—
397C2×D53—44no—
398C2×D53—82no—
399C2×D53—82no—
400C4×C53—44no—
401C4×C53—42no—
402C4×C53#38611yescharacteristic
403C4×C53#38611yescharacteristic
404C4×C53#38611yescharacteristic
405C4×C53#38611yescharacteristic
406C4×C53C22×C22⋊C411yescharacteristic
407C4×C53C2×C4×D411yescharacteristic
408C4×C53C2×#12111yescharacteristic
409C4×C53C2×#12311yescharacteristic
410Dic53—24no—
411Dic53—44no—
412Dic53—82no—
413C2×#575—531no—
414#3428—531no—
415C2×#421D5311yescharacteristic, complemented
416#2896—531no—
417C2×#410—531no—
418#1905—534no—
419#1904—534no—
420C2×#344—531no—
421C2×H(3,ℤ/4)—531no—
422C2×C53—21no—
423C2×C53—21no—
424C2×C53—21no—
425C2×C53—21no—
426C2×C53—21no—
427C2×C53—21no—
428C2×C53—21no—
429C2×C53—82no—
430C2×C53C2×#38611yescharacteristic
431D53—44no—
432C22×#41—531no—
433C22×#41C2×D5311yescharacteristic
434#575—1062no—
435#575—1062no—
436#575—1062no—
437#575—1062no—
438C2×#137—532no—
439C2×#137—532no—
440C2×AGL(1,ℤ/8)—532no—
441C2×AGL(1,ℤ/8)—532no—
442C2×#135—534no—
443C22×M16—531no—
444C22×M16C2×D5311yescharacteristic
445#520—1062no—
446#520—1062no—
447#519—532no—
448#518—532no—
449#518—1062no—
450C4×#41—1062no—
451C4×#41—1062no—
452C2×#117—531no—
453C2×#117—531no—
454C2×#117—1062no—
455C2×#117C2×D5311yescharacteristic
456#421—22no—
457#421C2×D5314yes—
458C2×#104—22no—
459#419—532no—
460#418—532no—
461#417—1062no—
462#416—1062no—
463#410—534no—
464#410—1062no—
465C2×#99—1062no—
466#344—534no—
467H(3,ℤ/4)—534no—
468C53#2099811yescharacteristic, complemented, Sylow
469C2×#41—21no—
470C2×#41—21no—
471C2×#41—21no—
472C2×#41—21no—
473C2×#41—21no—
474C2×#41—21no—
475C2×#41—21no—
476C2×#41—21no—
477C2×#41—21no—
478C2×#41—21no—
479C2×#41—532no—
480C2×#41—532no—
481C2×#41—532no—
482C2×#41—532no—
483C2×#41—532no—
484C2×#41—532no—
485C2×#41—1061no—
486C2×#41—1061no—
487C2×#41—1061no—
488C2×#41—1061no—
489C2×#41—1061no—
490C2×#41—1061no—
491C2×#41C4×D5312yescomplemented
492C2×#41C22×D5312yes—
493C22×Q8—531no—
494C22×Q8C4×D5311yescharacteristic, complemented
495C22×D4—21no—
496C22×D4—531no—
497C22×D4—1061no—
498C22×D4C4×D5311yescharacteristic, complemented
499C23×C4—21no—
500C23×C4—1061no—
501C23×C4C22×D5311yescharacteristic
502#137—1064no—
503#137—1064no—
504#137—1064no—
505#137—1064no—
506AGL(1,ℤ/8)—1064no—
507AGL(1,ℤ/8)—1064no—
508AGL(1,ℤ/8)—1064no—
509AGL(1,ℤ/8)—1064no—
510#135—1068no—
511#135—1068no—
512C2×Q16—534no—
513C2×SD16—534no—
514C2×SD16—534no—
515C2×D8—534no—
516C2×M16—21no—
517C2×M16—21no—
518C2×M16—21no—
519C2×M16—21no—
520C2×M16—21no—
521C2×M16—532no—
522C2×M16—532no—
523C2×M16—1061no—
524C2×M16—1061no—
525C2×M16—1061no—
526C2×M16—1061no—
527C2×M16C22×D5312yes—
528C22×C8—21no—
529C22×C8—532no—
530C4×Q8—1064no—
531C4×Q8—1064no—
532C4×D4—1068no—
533C4×D4—1064no—
534C4×D4—1068no—
535C4×D4—1064no—
536#117—21no—
537#117—21no—
538#117—532no—
539#117—532no—
540#117—532no—
541#117—1064no—
542#117—1064no—
543#117—1064no—
544#117—1061no—
545#117—1061no—
546#117—1061no—
547#117—1061no—
548#117—1061no—
549#117C22⋊D5312yes—
550#117C22×D5312yes—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—1064no—
553C2×C4⋊C4—1061no—
554C2×C4⋊C4—1061no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—532no—
557C2×C22⋊C4—1064no—
558C2×C22⋊C4—1061no—
559C2×C42—1064no—
560C2×C42—1061no—
561C2×C42—1061no—
562C2×C42C22⋊D5312yes—
563#104—28no—
564#103—1064no—
565#102—1064no—
566#99—1068no—
567C24—21no—
568C24—1061no—
569C24D4×D5311yescharacteristic
570#41—22no—
571#41—22no—
572#41—22no—
573#41—22no—
574#41—22no—
575#41—22no—
576#41—22no—
577#41—22no—
578#41—41no—
579#41—41no—
580#41—41no—
581#41—41no—
582#41—41no—
583#41—41no—
584#41—41no—
585#41—41no—
586#41—534no—
587#41—534no—
588#41—534no—
589#41—534no—
590#41—1062no—
591#41—1062no—
592#41—1062no—
593#41—1062no—
594#41—1062no—
595#41—1062no—
596#41—1062no—
597#41—1062no—
598#41—1062no—
599#41—1062no—
600#41—1062no—
601#41—1062no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—532no—
608C2×Q8—532no—
609C2×Q8—532no—
610C2×Q8—1061no—
611C2×Q8—1061no—
612C2×Q8—1061no—
613C2×Q8C2×C4×D5312yes—
614C2×D4—22no—
615C2×D4—22no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—41no—
622C2×D4—41no—
623C2×D4—41no—
624C2×D4—41no—
625C2×D4—532no—
626C2×D4—532no—
627C2×D4—532no—
628C2×D4—1062no—
629C2×D4—1062no—
630C2×D4—1062no—
631C2×D4—1062no—
632C2×D4—1062no—
633C2×D4—1062no—
634C2×D4—1061no—
635C2×D4—1061no—
636C2×D4—1061no—
637C2×D4C2×C4×D5312yes—
638C22×C4—21no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—41no—
643C22×C4—41no—
644C22×C4—41no—
645C22×C4—41no—
646C22×C4—1068no—
647C22×C4—1061no—
648C22×C4—1062no—
649C22×C4—1062no—
650C22×C4—1062no—
651C22×C4—1062no—
652C22×C4—1062no—
653C22×C4—1062no—
654C22×C4—1062no—
655C22×C4—2121no—
656C22×C4C2×C4×D5311yescharacteristic
657C22×C4C2×C4×D5311yescharacteristic
658C22×C4#1171994511yescharacteristic
659C22×C4#1171994511yescharacteristic
660C22×C4D4×D5311yescharacteristic
661C22×C4D4×D5311yescharacteristic
662C22×C4D4×D5311yescharacteristic
663C22×C4D4×D5311yescharacteristic
664C22×C4D4×D5311yescharacteristic
665C22×C4#1171994711yescharacteristic
666C22×C4#1171994711yescharacteristic
667C22×C4C2×C22⋊D5311yescharacteristic
668C22×C4C2×C22⋊D5311yescharacteristic
669C22×C4C23×D5311yescharacteristic
670Q16—1068no—
671SD16—1068no—
672SD16—1068no—
673D8—1068no—
674M16—22no—
675M16—22no—
676M16—41no—
677M16—41no—
678M16—1062no—
679M16—1062no—
680M16—1062no—
681M16—1062no—
682C2×C8—22no—
683C2×C8—41no—
684C2×C8—41no—
685C2×C8—534no—
686C2×C8—1062no—
687C2×C8—1062no—
688C4⋊C4—22no—
689C4⋊C4—22no—
690C4⋊C4—1068no—
691C4⋊C4—1062no—
692C4⋊C4—1062no—
693C4⋊C4—1062no—
694C4⋊C4—2121no—
695C22⋊C4—22no—
696C22⋊C4—22no—
697C22⋊C4—534no—
698C22⋊C4—1068no—
699C22⋊C4—1062no—
700C22⋊C4—1062no—
701C22⋊C4—2121no—
702C42—22no—
703C42—1068no—
704C42—1062no—
705C42—1062no—
706C42—1062no—
707C42—2121no—
708C42C2×C22⋊D5314yes—
709C23—22no—
710C23—41no—
711C23—41no—
712C23—81no—
713C23—82no—
714C23—1062no—
715C23—1062no—
716C23—1062no—
717C23—4242no—
718C23#1313317711yescharacteristic
719C23#1313317711yescharacteristic
720C23#1313318511yescharacteristic
721C23#1313318511yescharacteristic
722C23#1313319011yescharacteristic
723C23#1313319011yescharacteristic
724C23C2×D4×D5311yescharacteristic
725Q8—22no—
726Q8—22no—
727Q8—41no—
728Q8—41no—
729Q8—534no—
730Q8—1062no—
731Q8—1062no—
732Q8—1062no—
733D4—22no—
734D4—22no—
735D4—42no—
736D4—42no—
737D4—42no—
738D4—42no—
739D4—41no—
740D4—41no—
741D4—534no—
742D4—1064no—
743D4—1064no—
744D4—1064no—
745D4—1064no—
746D4—1062no—
747D4—1062no—
748D4—1062no—
749C2×C4—22no—
750C2×C4—24no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—82no—
758C2×C4—1062no—
759C2×C4—1062no—
760C2×C4—1062no—
761C2×C4—1064no—
762C2×C4—1064no—
763C2×C4—1064no—
764C2×C4—1064no—
765C2×C4—1064no—
766C2×C4—4248no—
767C2×C4—4242no—
768C2×C4—4242no—
769C2×C4—2122no—
770C2×C4C22⋊C4×D5311yescharacteristic
771C2×C4C22⋊C4×D5311yescharacteristic
772C2×C4C22⋊C4×D5311yescharacteristic
773C2×C4C22⋊C4×D5311yescharacteristic
774C2×C4#1313317711yescharacteristic
775C2×C4#1313317711yescharacteristic
776C2×C4C4×C22⋊D5311yescharacteristic
777C2×C4C4×C22⋊D5311yescharacteristic
778C2×C4C4×C22⋊D5311yescharacteristic
779C2×C4C4×C22⋊D5311yescharacteristic
780C2×C4#1313318511yescharacteristic
781C2×C4#1313318511yescharacteristic
782C2×C4#1313318811yescharacteristic
783C2×C4#1313318811yescharacteristic
784C2×C4#1313318811yescharacteristic
785C2×C4#1313318811yescharacteristic
786C2×C4#1313319011yescharacteristic
787C2×C4#1313319011yescharacteristic
788C2×C4#1313319911yescharacteristic
789C2×C4#1313319911yescharacteristic
790C2×C4#1313319911yescharacteristic
791C2×C4#1313319911yescharacteristic
792C2×C4C22×C4×D5311yescharacteristic
793C2×C4C2×D4×D5311yescharacteristic
794C2×C4C2×D4×D5311yescharacteristic
795C2×C4C22×C22⋊D5311yescharacteristic
796C2×C4C2×#1171994711yescharacteristic
797C2×C4C2×#1171994511yescharacteristic
798C8—42no—
799C8—1064no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—42no—
808C22—82no—
809C22—82no—
810C22—82no—
811C22—1064no—
812C22—4242no—
813C22—4242no—
814C22—2124no—
815C22#1681049911yescharacteristic
816C22#1681049911yescharacteristic
817C22#1681049911yescharacteristic
818C22#1681049911yescharacteristic
819C22C2×#1313317711yescharacteristic
820C22C2×#1313318511yescharacteristic
821C22C2×#1313319011yescharacteristic
822C4—44no—
823C4—42no—
824C4—1064no—
825C4—4242no—
826C4—2124no—
827C4#1681049911yescharacteristic
828C4#1681049911yescharacteristic
829C4#1681049911yescharacteristic
830C4#1681049911yescharacteristic
831C4C2×C22⋊C4×D5311yescharacteristic
832C4C2×C4×C22⋊D5311yescharacteristic
833C4C2×#1313318811yescharacteristic
834C4C2×#1313319911yescharacteristic
835C2—21no—
836C2—21no—
837C2—21no—
838C2—21no—
839C2—21no—
840C2—21no—
841C2—21no—
842C2—82no—
843C2—2124no—
844C2C2×#1681049911yescharacteristic
subgroupG/H
centerC4#16810499
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC2×C53×#421C2
socleC2×C53C2×#386
prime radicalC2×#16811421C2
cosocleC22×C4×C53C24
hypercenterC2×#421D53
hypocenterC53#20998
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. #20287916C2semidirect
3. #20283235C2semidirect
4. C2×#16810597C2semidirect
5. #20275206C2semidirect
6. #20275199C2semidirect
7. C2×#16810395C2semidirect
8. C2×#16810379C2semidirect
9. C2×C53×#421C2semidirect
15. C2×#13133248C4semidirect
17. C2×#13133243C4semidirect
19. C2×#13133237C4semidirect
23. #16811100C22semidirect
24. #16811097C22semidirect
31. #16810633C22semidirect
32. #16810629C22semidirect
38. #16810395C22semidirect
39. #16810379C22semidirect
72. C2×#11719925C2×C4semidirect
73. C2×#11719923C2×C4semidirect
74. C2×#11719924C2×C4semidirect
75. C2×#11719922C2×C4semidirect
80. C2×#11719917C2×C4semidirect
82. C22×#88322C2×C4semidirect
122. C2×#41×C53C2×C4semidirect
124. C22×Q8×C53C2×C4semidirect
126. C22×D4×C53C2×C4semidirect
415. C2×#421D53semidirect
468. C53#20998semidirect
491. C2×#41C4×D53semidirect
494. C22×Q8C4×D53semidirect
498. C22×D4C4×D53semidirect

Maximal subgroups

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

subgroupindex
C2×#168114212
#202879162
#202832352
C2×#168105972
#202752062
#202751992
C2×#168103952
C2×#168103792
C2×C53×#4212
#2099853