Finite Group Databasebeta

← #27386005

Subgroups — #27386005

Order 13568.

1704 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
1C2×#16811421C211yesmaximal, characteristic
2#20287918C211yesmaximal, characteristic, complemented
3C2×#16810639C211yesmaximal, characteristic, complemented
4C2×#16810596C211yesmaximal, characteristic, complemented
5#20275214C218yesmaximal, complemented
6C2×#16810394C211yesmaximal, characteristic, complemented
7#20274424C211yesmaximal, characteristic, complemented
8C2×C53×#421C211yesmaximal, characteristic, complemented
9C22×#11719945C2211yescharacteristic
10#16811421—22no—
11#16811421—22no—
12#16811421C414yescomplemented
13#16811421C2214yes—
14C2×#13133248—21no—
15C2×#13133247C412yescomplemented
16C2×#13133243—21no—
17C2×#13133242C412yescomplemented
18C2×#13133237—22no—
19C22×#11719917C2211yescharacteristic
20#16811106—22no—
21#16811106—22no—
22#16811101—21no—
23#16811098—22no—
24#16811098—21no—
25#41×Dic53—22no—
26#41×Dic53C2214yescomplemented
27C2×#13133176—22no—
28C2×#13133176C2211yescharacteristic
29C2×#13133176C2211yescharacteristic
30#16810639—22no—
31#16810639—22no—
32C2×#13133143C2214yescomplemented
33#16810596—22no—
34#16810596C2214yescomplemented
35C2×#13133131—22no—
36#16810394C2214yescomplemented
37#16810382C2214yescomplemented
38C22×#41×C53C2211yescharacteristic
39C22×M16×C53C2211yescharacteristic
40C2×#117×C53C2211yescharacteristic
41C53×#421—22no—
42C53×#421C2214yescomplemented
43C2×#104×C53—22no—
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×#11719945—21no—
54C2×#11719945C2×C412yescomplemented
55C2×#11719945C2312yes—
56C22×Dic106C2×C411yescharacteristic, complemented
57C22×D212C2×C411yescharacteristic, complemented
58C22×C22⋊D53—21no—
59C22×C4×D53—21no—
60#13133248—24no—
61#13133248—24no—
62#13133247—24no—
63#13133247C2×C418yescomplemented
64#13133243—24no—
65#13133243—24no—
66#13133242—24no—
67#13133242C2×C418yescomplemented
68#13133237—28no—
69#13133237—28no—
70C2×#11719925—22no—
71C2×#11719923—22no—
72C2×#11719924—22no—
73C2×#11719922—22no—
74C2×#11719917—21no—
75C2×#11719917—21no—
76C2×#11719917—21no—
77C2×#11719917C2×C412yescomplemented
78C2×#11719917C2×C412yescomplemented
79C2×#11719917C2312yes—
80C22×#88322—21no—
81Q8×Dic53—24no—
82Q8×Dic53—24no—
83D4×Dic53—24no—
84D4×Dic53—28no—
85D4×Dic53—28no—
86D4×Dic53—24no—
87#13133176—24no—
88#13133176—24no—
89#13133176—24no—
90#13133176—21no—
91#13133176—21no—
92#13133176—21no—
93#13133176—21no—
94#13133176D412yes—
95#13133176D412yes—
96#13133176D412yes—
97#13133176C2312yes—
98C2×C4⋊Dic53—24no—
99C2×C4⋊Dic53—21no—
100C2×C4⋊Dic53—21no—
101C2×C22⋊Dic53—24no—
102C2×C22⋊Dic53—21no—
103C2×C22⋊Dic53D412yes—
104C2×C4×Dic53—24no—
105C2×C4×Dic53—21no—
106C2×C4×Dic53C2312yes—
107#13133143—28no—
108#13133131—28no—
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×C53C2×C412yes—
116C2×#41×C53C2×C412yes—
117C2×#41×C53D412yes—
118C2×#41×C53D412yes—
119C2×#41×C53D412yes—
120C2×#41×C53C2312yes—
121C22×Q8×C53D411yescharacteristic
122C22×D4×C53—21no—
123C22×D4×C53D411yescharacteristic
124C23×C4×C53—21no—
125C23×C4×C53C2311yescharacteristic
126C2×M16×C53—21no—
127C2×M16×C53—21no—
128C2×M16×C53—21no—
129C2×M16×C53—21no—
130C2×M16×C53—21no—
131C2×M16×C53C2312yes—
132C22×C8×C53—21no—
133#117×C53—21no—
134#117×C53—21no—
135#117×C53—21no—
136#117×C53C2312yes—
137C2×C4⋊C4×C53—21no—
138C2×C22⋊C4×C53—21no—
139C2×C42×C53—21no—
140#104×C53—28no—
141C24×C53—21no—
142C24×C53C2×D411yescharacteristic
143C23×D53—21no—
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—22no—
153#41×C53—22no—
154#41×C53—22no—
155#41×C53—22no—
156#41×C53C22⋊C414yes—
157#41×C53C22⋊C414yes—
158#41×C53C22×C414yes—
159#41×C53C2×D414yes—
160C2×Q8×C53—21no—
161C2×Q8×C53—21no—
162C2×Q8×C53—21no—
163C2×Q8×C53C22⋊C412yes—
164C2×Q8×C53C22⋊C412yes—
165C2×Q8×C53C2×D412yes—
166C2×D4×C53—22no—
167C2×D4×C53—22no—
168C2×D4×C53—22no—
169C2×D4×C53—22no—
170C2×D4×C53—22no—
171C2×D4×C53—22no—
172C2×D4×C53—21no—
173C2×D4×C53—21no—
174C2×D4×C53—21no—
175C2×D4×C53C22⋊C412yes—
176C2×D4×C53C22⋊C412yes—
177C2×D4×C53C2×D412yes—
178C22×C4×C53—21no—
179C22×C4×C53—22no—
180C22×C4×C53—22no—
181C22×C4×C53—22no—
182C22×C4×C53—22no—
183C22×C4×C53—22no—
184C22×C4×C53—22no—
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—41no—
203C2×C22⋊D53—41no—
204C2×C22⋊D53—41no—
205C2×C22⋊D53—41no—
206C22×Dic53—21no—
207C22×Dic53—28no—
208C22×Dic53—22no—
209C22×Dic53—22no—
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—41no—
219#11719945—41no—
220#11719945—41no—
221#11719945—41no—
222#11719945—41no—
223#11719945—41no—
224#11719945—41no—
225#11719945—41no—
226C2×D212—21no—
227C2×D212—21no—
228C2×D212—21no—
229C2×D212—21no—
230C2×D212—21no—
231C2×D212C22×C412yes—
232C2×C4×D53—22no—
233C2×C4×D53—22no—
234C2×C4×D53—41no—
235C2×C4×D53—41no—
236C2×C4×D53—41no—
237C2×C4×D53—41no—
238C2×Dic106—21no—
239C2×Dic106—21no—
240C2×Dic106—21no—
241C2×Dic106—21no—
242C2×Dic106—21no—
243C2×Dic106C22×C412yes—
244M16×C53—22no—
245M16×C53—22no—
246M16×C53—41no—
247M16×C53—41no—
248C2×C8×C53—22no—
249C2×C8×C53—41no—
250C2×C8×C53—41no—
251C4⋊C4×C53—22no—
252C4⋊C4×C53—41no—
253C22⋊C4×C53—22no—
254C22⋊C4×C53—41no—
255C42×C53—22no—
256C42×C53—41no—
257C22⋊Dic53—28no—
258C22⋊Dic53—22no—
259C22⋊Dic53—22no—
260C22⋊Dic53—22no—
261C22⋊Dic53C2×D414yes—
262#11719925—28no—
263#11719924—28no—
264#11719923—28no—
265#11719922—28no—
266C4⋊Dic53—28no—
267C4⋊Dic53—22no—
268C4⋊Dic53—22no—
269C4⋊Dic53—22no—
270C4⋊Dic53—22no—
271C4×Dic53—28no—
272C4×Dic53—22no—
273C4×Dic53—22no—
274C4×Dic53—22no—
275C4×Dic53C2×D414yes—
276#11719917—22no—
277#11719917—22no—
278#11719917—22no—
279#11719917C22×C414yes—
280C2×#88322—22no—
281C2×#88322—22no—
282C2×#88322—22no—
283C23×C53—22no—
284C23×C53—22no—
285C23×C53—22no—
286C23×C53—81no—
287C23×C53—82no—
288C23×C53C4×D411yescharacteristic
289C23×C53C4×D411yescharacteristic
290C23×C53#12011yescharacteristic
291C23×C53#12011yescharacteristic
292C23×C53#12111yescharacteristic
293C23×C53#12111yescharacteristic
294C23×C53C22×D411yescharacteristic
295C22×D53—22no—
296C22×D53—41no—
297C22×D53—41no—
298C22×D53—82no—
299Q8×C53—22no—
300Q8×C53—22no—
301Q8×C53—22no—
302Q8×C53C2×C22⋊C414yes—
303D4×C53—24no—
304D4×C53—24no—
305D4×C53—24no—
306D4×C53—24no—
307D4×C53—22no—
308D4×C53—22no—
309D4×C53—22no—
310D4×C53C2×C22⋊C414yes—
311C2×C4×C53—22no—
312C2×C4×C53—22no—
313C2×C4×C53—22no—
314C2×C4×C53—24no—
315C2×C4×C53—24no—
316C2×C4×C53—24no—
317C2×C4×C53—24no—
318C2×C4×C53—42no—
319C2×C4×C53—82no—
320C2×C4×C53C2×C22⋊C411yescharacteristic
321C2×C4×C53C2×C22⋊C411yescharacteristic
322C2×C4×C53C2×C22⋊C411yescharacteristic
323C2×C4×C53C2×C22⋊C411yescharacteristic
324C2×C4×C53C4×D411yescharacteristic
325C2×C4×C53C4×D411yescharacteristic
326C2×C4×C53C4×D411yescharacteristic
327C2×C4×C53C4×D411yescharacteristic
328C2×C4×C53C4×D411yescharacteristic
329C2×C4×C53C4×D411yescharacteristic
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#12111yescharacteristic
337C2×C4×C53#12111yescharacteristic
338C2×C4×C53#12311yescharacteristic
339C2×C4×C53#12311yescharacteristic
340C2×C4×C53#12311yescharacteristic
341C2×C4×C53#12311yescharacteristic
342C2×C4×C53C23×C411yescharacteristic
343C2×C4×C53C22×D411yescharacteristic
344C2×C4×C53C22×D411yescharacteristic
345C2×C4×C53C22×D411yescharacteristic
346C2×C4×C53C2×#4111yescharacteristic
347C2×C4×C53C2×#4111yescharacteristic
348C22⋊D53—42no—
349C22⋊D53—42no—
350C22⋊D53—42no—
351C22⋊D53—42no—
352C2×Dic53—22no—
353C2×Dic53—24no—
354C2×Dic53—24no—
355C2×Dic53—41no—
356C2×Dic53—41no—
357C2×Dic53—82no—
358C2×Dic53—82no—
359C2×Dic53—88no—
360D212—22no—
361D212—22no—
362D212—41no—
363D212—41no—
364C4×D53—42no—
365C4×D53—42no—
366C4×D53—42no—
367C4×D53—42no—
368Dic106—22no—
369Dic106—22no—
370Dic106—41no—
371Dic106—41no—
372C8×C53—42no—
373#88322—24no—
374#21000—531nomaximal, Sylow
375C22×C53—24no—
376C22×C53—41no—
377C22×C53—41no—
378C22×C53—41no—
379C22×C53—41no—
380C22×C53—41no—
381C22×C53—41no—
382C22×C53—41no—
383C22×C53—44no—
384C22×C53—82no—
385C22×C53—82no—
386C22×C53#38611yescharacteristic
387C22×C53#38611yescharacteristic
388C22×C53#38611yescharacteristic
389C22×C53#38611yescharacteristic
390C22×C53C2×C4×D411yescharacteristic
391C22×C53C2×#12011yescharacteristic
392C22×C53C2×#12111yescharacteristic
393C2×D53—42no—
394C2×D53—82no—
395C2×D53—82no—
396C2×D53—82no—
397C4×C53—24no—
398C4×C53—82no—
399C4×C53#38611yescharacteristic
400C4×C53#38611yescharacteristic
401C4×C53#38611yescharacteristic
402C4×C53#38611yescharacteristic
403C4×C53C22×C22⋊C411yescharacteristic
404C4×C53C2×C4×D411yescharacteristic
405C4×C53C2×#12111yescharacteristic
406C4×C53C2×#12311yescharacteristic
407Dic53—44no—
408Dic53—44no—
409Dic53—42no—
410C2×#575—531no—
411#3428—531no—
412C2×#421—531no—
413C2×#421D5311yescharacteristic, complemented
414C2×#410—531no—
415#1906—538no—
416C2×#344—531no—
417#1733—531no—
418C2×C53—21no—
419C2×C53—21no—
420C2×C53—21no—
421C2×C53—21no—
422C2×C53—21no—
423C2×C53—21no—
424C2×C53—21no—
425C2×C53—44no—
426C2×C53C2×#38611yescharacteristic
427D53—82no—
428C22×#41—531no—
429C22×#41C2×D5311yescharacteristic
430#575—534no—
431#575—534no—
432#575—1062no—
433#575—1062no—
434C2×#137—532no—
435C2×#137—1061no—
436C2×AGL(1,ℤ/8)—532no—
437C2×AGL(1,ℤ/8)—1061no—
438C2×#135—1062no—
439C22×M16—531no—
440C22×M16C2×D5311yescharacteristic
441#520—1062no—
442#520—1062no—
443#519—1061no—
444#518—1062no—
445#518—1061no—
446C4×#41—534no—
447C4×#41—1062no—
448C2×#117—531no—
449C2×#117—531no—
450C2×#117—1062no—
451C2×#117C2×D5311yescharacteristic
452#421—22no—
453#421—1062no—
454#421—1062no—
455#421C2×D5314yescomplemented
456C2×#104—22no—
457C2×#104—534no—
458#410—534no—
459#410—1062no—
460C2×#99—1062no—
461#344—534no—
462#339—534no—
463C53#2100011yescharacteristic, complemented, Sylow
464C2×#41—21no—
465C2×#41—21no—
466C2×#41—21no—
467C2×#41—21no—
468C2×#41—21no—
469C2×#41—21no—
470C2×#41—532no—
471C2×#41—532no—
472C2×#41—1061no—
473C2×#41—1061no—
474C2×#41—1061no—
475C2×#41—1061no—
476C2×#41—1061no—
477C2×#41—1061no—
478C2×#41—1061no—
479C2×#41—1061no—
480C2×#41—1061no—
481C2×#41—1061no—
482C2×#41C4×D5312yes—
483C2×#41C4×D5312yes—
484C2×#41D21212yes—
485C2×#41C22⋊D5312yes—
486C2×#41C22⋊D5312yes—
487C2×#41C22×D5312yes—
488C22×Q8—531no—
489C22×Q8D21211yescharacteristic
490C22×D4—21no—
491C22×D4—531no—
492C22×D4—1061no—
493C22×D4D21211yescharacteristic
494C23×C4—21no—
495C23×C4—1061no—
496C23×C4C22×D5311yescharacteristic
497#137—538no—
498#137—1064no—
499#137—1064no—
500#137—1064no—
501AGL(1,ℤ/8)—538no—
502AGL(1,ℤ/8)—1064no—
503AGL(1,ℤ/8)—1064no—
504AGL(1,ℤ/8)—1064no—
505#135—1068no—
506#135—1068no—
507C2×Q16—1062no—
508C2×SD16—1062no—
509C2×SD16—1062no—
510C2×D8—1062no—
511C2×M16—21no—
512C2×M16—21no—
513C2×M16—21no—
514C2×M16—21no—
515C2×M16—21no—
516C2×M16—532no—
517C2×M16—532no—
518C2×M16—532no—
519C2×M16—1061no—
520C2×M16—1061no—
521C2×M16—1061no—
522C2×M16C22×D5312yes—
523C22×C8—21no—
524C22×C8—1061no—
525C4×Q8—1064no—
526C4×Q8—1064no—
527C4×D4—1068no—
528C4×D4—1068no—
529C4×D4—1064no—
530C4×D4—1064no—
531#117—21no—
532#117—21no—
533#117—21no—
534#117—532no—
535#117—532no—
536#117—532no—
537#117—532no—
538#117—1064no—
539#117—1064no—
540#117—1064no—
541#117—1061no—
542#117—1061no—
543#117—1061no—
544#117—1061no—
545#117C22×D5312yes—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—1064no—
548C2×C4⋊C4—1061no—
549C2×C4⋊C4—1061no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—532no—
552C2×C22⋊C4—1064no—
553C2×C22⋊C4—1061no—
554C2×C42—21no—
555C2×C42—532no—
556C2×C42—1064no—
557C2×C42—1061no—
558#104—28no—
559#104—1068no—
560#99—1068no—
561C24—21no—
562C24—1061no—
563C24D4×D5311yescharacteristic
564#41—22no—
565#41—22no—
566#41—22no—
567#41—22no—
568#41—22no—
569#41—22no—
570#41—22no—
571#41—22no—
572#41—22no—
573#41—22no—
574#41—22no—
575#41—22no—
576#41—1062no—
577#41—1062no—
578#41—1062no—
579#41—1062no—
580#41—1062no—
581#41—1062no—
582#41—1062no—
583#41—1062no—
584#41—2121no—
585#41—2121no—
586#41—2121no—
587#41—2121no—
588#41—2121no—
589#41—2121no—
590#41—2121no—
591#41—2121no—
592#41#1171992114yes—
593#41#1171992114yes—
594#41C2×C4×D5314yes—
595#41C2×C22⋊D5314yes—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—21no—
599C2×Q8—532no—
600C2×Q8—1061no—
601C2×Q8—1061no—
602C2×Q8—1061no—
603C2×Q8—1061no—
604C2×Q8—1061no—
605C2×Q8#1171992112yes—
606C2×Q8#1171992112yes—
607C2×Q8C2×D21212yes—
608C2×D4—22no—
609C2×D4—22no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—22no—
613C2×D4—22no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—532no—
618C2×D4—1062no—
619C2×D4—1062no—
620C2×D4—1061no—
621C2×D4—1061no—
622C2×D4—1061no—
623C2×D4—1061no—
624C2×D4—1061no—
625C2×D4—2121no—
626C2×D4—2121no—
627C2×D4—2121no—
628C2×D4—2121no—
629C2×D4#1171992112yes—
630C2×D4#1171992112yes—
631C2×D4C2×D21212yes—
632C22×C4—21no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—41no—
640C22×C4—1068no—
641C22×C4—1062no—
642C22×C4—1062no—
643C22×C4—1061no—
644C22×C4—1062no—
645C22×C4—1062no—
646C22×C4—2121no—
647C22×C4—2121no—
648C22×C4—2121no—
649C22×C4—2121no—
650C22×C4C2×C4×D5311yescharacteristic
651C22×C4C2×C4×D5311yescharacteristic
652C22×C4C2×D21211yescharacteristic
653C22×C4C2×D21211yescharacteristic
654C22×C4D4×D5311yescharacteristic
655C22×C4D4×D5311yescharacteristic
656C22×C4D4×D5311yescharacteristic
657C22×C4#1171994711yescharacteristic
658C22×C4#1171994711yescharacteristic
659C22×C4#1171994711yescharacteristic
660C22×C4#1171994711yescharacteristic
661C22×C4C2×C22⋊D5311yescharacteristic
662C22×C4C2×C22⋊D5311yescharacteristic
663C22×C4C23×D5311yescharacteristic
664Q16—1068no—
665SD16—1068no—
666SD16—1068no—
667D8—1068no—
668M16—22no—
669M16—22no—
670M16—41no—
671M16—41no—
672M16—534no—
673M16—1062no—
674M16—1062no—
675M16—1062no—
676C2×C8—22no—
677C2×C8—41no—
678C2×C8—41no—
679C2×C8—1062no—
680C2×C8—1062no—
681C2×C8—1062no—
682C4⋊C4—22no—
683C4⋊C4—41no—
684C4⋊C4—1068no—
685C4⋊C4—1062no—
686C4⋊C4—1062no—
687C4⋊C4—1062no—
688C4⋊C4—1062no—
689C22⋊C4—22no—
690C22⋊C4—41no—
691C22⋊C4—534no—
692C22⋊C4—1068no—
693C22⋊C4—1062no—
694C22⋊C4—1062no—
695C22⋊C4—1062no—
696C42—22no—
697C42—41no—
698C42—534no—
699C42—1068no—
700C42—1062no—
701C42—1062no—
702C42—1062no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—81no—
707C23—82no—
708C23—1062no—
709C23—4242no—
710C23—2121no—
711C23—2121no—
712C23#1313317711yescharacteristic
713C23#1313317711yescharacteristic
714C23#1313318711yescharacteristic
715C23#1313318711yescharacteristic
716C23#1313318911yescharacteristic
717C23#1313318911yescharacteristic
718C23C2×D4×D5311yescharacteristic
719Q8—22no—
720Q8—22no—
721Q8—22no—
722Q8—1062no—
723Q8—1062no—
724Q8—2121no—
725Q8—2121no—
726Q8C2×#1171992114yes—
727D4—24no—
728D4—24no—
729D4—24no—
730D4—24no—
731D4—22no—
732D4—22no—
733D4—22no—
734D4—1062no—
735D4—1062no—
736D4—2122no—
737D4—2122no—
738D4—2122no—
739D4—2122no—
740D4—2121no—
741D4—2121no—
742D4C2×#1171992114yes—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—42no—
751C2×C4—82no—
752C2×C4—1062no—
753C2×C4—1064no—
754C2×C4—1064no—
755C2×C4—4242no—
756C2×C4—4242no—
757C2×C4—4248no—
758C2×C4—2121no—
759C2×C4—2121no—
760C2×C4—2122no—
761C2×C4—2122no—
762C2×C4—2122no—
763C2×C4—2122no—
764C2×C4C2×#1171992111yescharacteristic
765C2×C4C2×#1171992111yescharacteristic
766C2×C4C2×#1171992111yescharacteristic
767C2×C4C2×#1171992111yescharacteristic
768C2×C4#1313317711yescharacteristic
769C2×C4#1313317711yescharacteristic
770C2×C4#1313317711yescharacteristic
771C2×C4#1313317711yescharacteristic
772C2×C4#1313317711yescharacteristic
773C2×C4#1313317711yescharacteristic
774C2×C4#1313318711yescharacteristic
775C2×C4#1313318711yescharacteristic
776C2×C4#1313318911yescharacteristic
777C2×C4#1313318911yescharacteristic
778C2×C4#1313318911yescharacteristic
779C2×C4#1313318911yescharacteristic
780C2×C4#1313318911yescharacteristic
781C2×C4#1313318911yescharacteristic
782C2×C4#1313320111yescharacteristic
783C2×C4#1313320111yescharacteristic
784C2×C4#1313320111yescharacteristic
785C2×C4#1313320111yescharacteristic
786C2×C4C22×C4×D5311yescharacteristic
787C2×C4C2×D4×D5311yescharacteristic
788C2×C4C22×C22⋊D5311yescharacteristic
789C2×C4C22×D21211yescharacteristic
790C2×C4C2×#1171994711yescharacteristic
791C2×C4C2×#1171994711yescharacteristic
792C8—42no—
793C8—1064no—
794C22—24no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—44no—
803C22—82no—
804C22—82no—
805C22—4242no—
806C22—4242no—
807C22—4242no—
808C22—2122no—
809C22#1681050011yescharacteristic
810C22#1681050011yescharacteristic
811C22#1681050011yescharacteristic
812C22#1681050011yescharacteristic
813C22C2×#1313317711yescharacteristic
814C22C2×#1313318711yescharacteristic
815C22C2×#1313318911yescharacteristic
816C4—24no—
817C4—82no—
818C4—2124no—
819C4—2124no—
820C4—2122no—
821C4#1681050011yescharacteristic
822C4#1681050011yescharacteristic
823C4#1681050011yescharacteristic
824C4#1681050011yescharacteristic
825C4C22×#1171992111yescharacteristic
826C4C2×#1313317711yescharacteristic
827C4C2×#1313318911yescharacteristic
828C4C2×#1313320111yescharacteristic
829C2—21no—
830C2—21no—
831C2—21no—
832C2—21no—
833C2—21no—
834C2—21no—
835C2—21no—
836C2—44no—
837C2—4242no—
838C2C2×#1681050011yescharacteristic
subgroupG/H
centerC4C2×#13133189
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC2×C53×#421C2
socleC2×C53C2×#386
prime radicalC2×#16811421C2
cosocleC22×C4×C53C24
hypercenterC2×#421D53
hypocenterC53#21000
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. #20287918C2semidirect
3. C2×#16810639C2semidirect
4. C2×#16810596C2semidirect
5. #20275214C2semidirect
6. C2×#16810394C2semidirect
7. #20274424C2semidirect
8. C2×C53×#421C2semidirect
12. #16811421C4semidirect
15. C2×#13133247C4semidirect
17. C2×#13133242C4semidirect
26. #41×Dic53C22semidirect
32. C2×#13133143C22semidirect
34. #16810596C22semidirect
36. #16810394C22semidirect
37. #16810382C22semidirect
42. C53×#421C22semidirect
54. C2×#11719945C2×C4semidirect
56. C22×Dic106C2×C4semidirect
57. C22×D212C2×C4semidirect
63. #13133247C2×C4semidirect
67. #13133242C2×C4semidirect
77. C2×#11719917C2×C4semidirect
78. C2×#11719917C2×C4semidirect
413. C2×#421D53semidirect
455. #421C2×D53semidirect
463. C53#21000semidirect

Maximal subgroups

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

subgroupindex
C2×#168114212
#202879182
C2×#168106392
C2×#168105962
#202752142
C2×#168103942
#202744242
C2×C53×#4212
#2100053