Finite Group Databasebeta

← C2×#20275095 #27385629

Subgroups — C2×#20275095 #27385629

Order 13568.

1794 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811389C211yesmaximal, characteristic, complemented
2C2×#16811169C211yesmaximal, characteristic
3C2×#16810640C211yesmaximal, characteristic, complemented
4C2×#16810596C211yesmaximal, characteristic, complemented
5#20275095C218yesmaximal, direct product factor
6C2×#16810384C211yesmaximal, characteristic, complemented
7C2×#16810382C211yesmaximal, characteristic, complemented
8C2×C53×#421C211yesmaximal, characteristic, complemented
9C22×#11719945C2211yescharacteristic
10#16811389—22no—
11#16811389—22no—
12#16811389—22no—
13#16811389C2214yescomplemented
14C2×#13133225—22no—
15C2×#13133223—22no—
16C22×#11719917C2211yescharacteristic
17C2×M16×D53—22no—
18#16811169—22no—
19#16811169—22no—
20#16811169C414yescomplemented
21#16811169C2214yes—
22C2×#13133215C411yescharacteristic, complemented
23C2×#13133213C411yescharacteristic, complemented
24C2×#13133206C411yescharacteristic, complemented
25C2×#13133204C411yescharacteristic, complemented
26C2×#13133189—22no—
27C2×C4×C22⋊D53—22no—
28C2×#13133176C2211yescharacteristic
29C22×C4×Dic53C2211yescharacteristic
30#16810640—22no—
31#16810640C2214yescomplemented
32C2×#13133144—22no—
33#16810596—22no—
34#16810596C2214yescomplemented
35C2×#13133131—22no—
36#16810384C2214yescomplemented
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×#11719945C2×C412yes—
53C2×#11719945D412yes—
54C2×#11719945D412yes—
55C2×#11719945C2312yes—
56C22×Dic106C2×C411yescharacteristic
57C22×D212C2×C411yescharacteristic
58C22×C22⋊D53—22no—
59C22×C22⋊D53D412yes—
60C23×Dic53—21no—
61C22×C4×D53D412yes—
62#13133225—28no—
63#13133225—28no—
64#13133223—28no—
65#13133223—28no—
66C2×#11719917—21no—
67C2×#11719917—21no—
68C2×#11719917—21no—
69C2×#11719917D412yescomplemented
70C2×#11719917D412yescomplemented
71C2×#11719917C2312yes—
72C2×#11719912—24no—
73M16×D53—28no—
74M16×D53—28no—
75C22×#88322—21no—
76C2×C8×D53—24no—
77#13133215—22no—
78#13133215C2×C414yescomplemented
79#13133213—22no—
80#13133213C2×C414yescomplemented
81#13133206—22no—
82#13133206C2×C414yescomplemented
83#13133204—22no—
84#13133204C2×C414yescomplemented
85#13133189—28no—
86#13133189—28no—
87C4×C22⋊D53—28no—
88C4×C22⋊D53—28no—
89#13133176—21no—
90#13133176—21no—
91#13133176—21no—
92#13133176C2312yes—
93C2×C4⋊Dic53—21no—
94C2×#11719919—22no—
95C2×C22⋊Dic53—22no—
96C2×C22⋊Dic53—21no—
97C2×#11719921—22no—
98C2×C4×Dic53—21no—
99C2×C4×Dic53—21no—
100C2×C4×Dic53—21no—
101C2×C4×Dic53—21no—
102C2×C4×Dic53C2×C411yescharacteristic
103C2×C4×Dic53C2×C411yescharacteristic
104C2×C4×Dic53C2×C412yes—
105C2×C4×Dic53C2312yes—
106#13133144—28no—
107#13133131—28no—
108C2×#41×C53—21no—
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×C53—21no—
116C2×#41×C53—21no—
117C2×#41×C53—21no—
118C2×#41×C53C2×C412yes—
119C2×#41×C53C2312yes—
120C22×Q8×C53C2×C411yescharacteristic
121C22×D4×C53—21no—
122C22×D4×C53C2×C411yescharacteristic
123C23×C4×C53—21no—
124C23×C4×C53C2311yescharacteristic
125C2×M16×C53—21no—
126C2×M16×C53—21no—
127C2×M16×C53—21no—
128C2×M16×C53D412yescomplemented
129C2×M16×C53D412yescomplemented
130C2×M16×C53C2312yes—
131C22×C8×C53—21no—
132#117×C53—21no—
133#117×C53—21no—
134#117×C53—21no—
135#117×C53C2312yes—
136C2×C4⋊C4×C53—21no—
137C2×C22⋊C4×C53—21no—
138C2×C42×C53—21no—
139#104×C53—28no—
140C24×C53—21no—
141C24×C53C2×D411yescharacteristic
142C23×D53C22⋊C412yes—
143#41×C53—22no—
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—41no—
152#41×C53—41no—
153#41×C53—41no—
154#41×C53—41no—
155#41×C53—41no—
156#41×C53—41no—
157#41×C53—41no—
158#41×C53—41no—
159C2×Q8×C53—21no—
160C2×Q8×C53—21no—
161C2×Q8×C53—21no—
162C2×Q8×C53—21no—
163C2×Q8×C53—21no—
164C2×Q8×C53C22×C412yes—
165C2×D4×C53—22no—
166C2×D4×C53—22no—
167C2×D4×C53—21no—
168C2×D4×C53—21no—
169C2×D4×C53—21no—
170C2×D4×C53—21no—
171C2×D4×C53—21no—
172C2×D4×C53—41no—
173C2×D4×C53—41no—
174C2×D4×C53—41no—
175C2×D4×C53—41no—
176C2×D4×C53C22×C412yes—
177C22×C4×C53—21no—
178C22×C4×C53—22no—
179C22×C4×C53—22no—
180C22×C4×C53—41no—
181C22×C4×C53—41no—
182C22×C4×C53—41no—
183C22×C4×C53—41no—
184C22×C4×C53—41no—
185C22×C4×C53C22×C411yescharacteristic
186C22×C4×C53C22×C411yescharacteristic
187C22×C4×C53C2×D411yescharacteristic
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×C53#4111yescharacteristic
195C22×C4×C53#4111yescharacteristic
196C22×C4×C53#4111yescharacteristic
197C22×C4×C53#4111yescharacteristic
198C22×C4×C53C2411yescharacteristic
199C2×C22⋊D53—22no—
200C2×C22⋊D53—22no—
201C2×C22⋊D53—22no—
202C2×C22⋊D53—22no—
203C2×C22⋊D53—28no—
204C2×C22⋊D53—48no—
205C2×C22⋊D53C22⋊C414yes—
206C2×C22⋊D53C2×D414yes—
207C22×Dic53—21no—
208C22×Dic53—21no—
209C22×Dic53—22no—
210C22×Dic53—22no—
211C22×Dic53—44no—
212C22×Dic53—41no—
213C22×Dic53C22⋊C412yes—
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#11719945—22no—
225#11719945—22no—
226#11719945—22no—
227#11719945—22no—
228#11719945—22no—
229#11719945—22no—
230C2×D212—21no—
231C2×D212—21no—
232C2×D212—21no—
233C2×D212—21no—
234C2×D212C22⋊C412yes—
235C2×D212C22×C412yes—
236C2×C4×D53—22no—
237C2×C4×D53—22no—
238C2×C4×D53—22no—
239C2×C4×D53—22no—
240C2×C4×D53C22⋊C414yes—
241C2×C4×D53C2×D414yes—
242C2×Dic106—21no—
243C2×Dic106—21no—
244C2×Dic106—21no—
245C2×Dic106—21no—
246C2×Dic106C22⋊C412yes—
247C2×Dic106C22×C412yes—
248M16×C53—22no—
249M16×C53—22no—
250M16×C53—22no—
251M16×C53C2×D414yescomplemented
252C2×C8×C53—22no—
253C2×C8×C53—22no—
254C2×C8×C53—22no—
255C4⋊C4×C53—22no—
256C4⋊C4×C53—41no—
257C22⋊C4×C53—22no—
258C22⋊C4×C53—41no—
259C42×C53—22no—
260C42×C53—41no—
261C22⋊Dic53—28no—
262C22⋊Dic53—22no—
263C22⋊Dic53—41no—
264#11719921—28no—
265C4⋊Dic53—22no—
266C4⋊Dic53—41no—
267#11719919—28no—
268C4×Dic53—22no—
269C4×Dic53—21no—
270C4×Dic53—21no—
271C4×Dic53—22no—
272C4×Dic53—22no—
273C4×Dic53—41no—
274C4×Dic53C22×C412yes—
275C4×Dic53C22×C412yes—
276#11719917—22no—
277#11719917—22no—
278#11719917—22no—
279#11719917C2×D414yescomplemented
280C2×#88322—22no—
281C2×#88322—22no—
282C2×#88322—22no—
283#11719912—216no—
284C8×D53—216no—
285C23×C53—22no—
286C23×C53—42no—
287C23×C53—44no—
288C23×C53—41no—
289C23×C53—41no—
290C23×C53C2×C22⋊C411yescharacteristic
291C23×C53C2×C22⋊C411yescharacteristic
292C23×C53#12111yescharacteristic
293C23×C53#12111yescharacteristic
294C23×C53#12111yescharacteristic
295C23×C53#12111yescharacteristic
296C23×C53C22×D411yescharacteristic
297C22×D53—22no—
298C22×D53—22no—
299C22×D53—44no—
300C22×D53C2×C22⋊C414yes—
301Q8×C53—22no—
302Q8×C53—22no—
303Q8×C53—41no—
304Q8×C53—41no—
305D4×C53—22no—
306D4×C53—22no—
307D4×C53—42no—
308D4×C53—42no—
309D4×C53—42no—
310D4×C53—42no—
311D4×C53—41no—
312D4×C53—41no—
313C2×C4×C53—22no—
314C2×C4×C53—41no—
315C2×C4×C53—41no—
316C2×C4×C53—42no—
317C2×C4×C53—42no—
318C2×C4×C53—42no—
319C2×C4×C53—42no—
320C2×C4×C53—42no—
321C2×C4×C53—82no—
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×C53C4×D411yescharacteristic
331C2×C4×C53C4×D411yescharacteristic
332C2×C4×C53#12011yescharacteristic
333C2×C4×C53#12011yescharacteristic
334C2×C4×C53#12011yescharacteristic
335C2×C4×C53#12011yescharacteristic
336C2×C4×C53#12111yescharacteristic
337C2×C4×C53#12111yescharacteristic
338C2×C4×C53#12111yescharacteristic
339C2×C4×C53#12111yescharacteristic
340C2×C4×C53#12311yescharacteristic
341C2×C4×C53#12311yescharacteristic
342C2×C4×C53#12311yescharacteristic
343C2×C4×C53#12311yescharacteristic
344C2×C4×C53C23×C411yescharacteristic
345C2×C4×C53C22×D411yescharacteristic
346C2×C4×C53C22×D411yescharacteristic
347C2×C4×C53C22×D411yescharacteristic
348C2×C4×C53C2×#4111yescharacteristic
349C2×C4×C53C2×#4111yescharacteristic
350C22⋊D53—24no—
351C22⋊D53—24no—
352C22⋊D53—24no—
353C22⋊D53—24no—
354C22⋊D53—416no—
355C2×Dic53—24no—
356C2×Dic53—22no—
357C2×Dic53—22no—
358C2×Dic53—22no—
359C2×Dic53—22no—
360C2×Dic53—44no—
361C2×Dic53—44no—
362C2×Dic53—42no—
363C2×Dic53—42no—
364C2×Dic53—82no—
365C2×Dic53C2×C22⋊C414yes—
366D212—22no—
367D212—22no—
368D212—22no—
369D212—22no—
370C4×D53—24no—
371C4×D53—24no—
372C4×D53—24no—
373C4×D53—24no—
374Dic106—22no—
375Dic106—22no—
376Dic106—22no—
377Dic106—22no—
378C8×C53—24no—
379#88322—24no—
380C2×#1884—531nomaximal, Sylow
381C22×C53—22no—
382C22×C53—22no—
383C22×C53—22no—
384C22×C53—41no—
385C22×C53—41no—
386C22×C53—41no—
387C22×C53—41no—
388C22×C53—44no—
389C22×C53—42no—
390C22×C53—82no—
391C22×C53—82no—
392C22×C53#38611yescharacteristic
393C22×C53#38611yescharacteristic
394C22×C53#38611yescharacteristic
395C22×C53#38611yescharacteristic
396C22×C53C22×C22⋊C411yescharacteristic
397C22×C53C2×#12111yescharacteristic
398C22×C53C2×#12111yescharacteristic
399C2×D53—24no—
400C2×D53—44no—
401C2×D53—44no—
402C2×D53—82no—
403C4×C53—42no—
404C4×C53—82no—
405C4×C53#38611yescharacteristic
406C4×C53#38611yescharacteristic
407C4×C53#38611yescharacteristic
408C4×C53#38611yescharacteristic
409C4×C53C2×C4×D411yescharacteristic
410C4×C53C2×C4×D411yescharacteristic
411C4×C53C2×#12011yescharacteristic
412C4×C53C2×#12311yescharacteristic
413Dic53—24no—
414Dic53—24no—
415Dic53—42no—
416Dic53—82no—
417C2×#568—531no—
418C2×#532—531no—
419C2×#421—531no—
420C2×#421D5311yescharacteristic, complemented
421C2×#410—531no—
422#1884—538no—
423C2×#339—531no—
424C2×#339—531no—
425C2×C53—21no—
426C2×C53—21no—
427C2×C53—21no—
428C2×C53—21no—
429C2×C53—21no—
430C2×C53—21no—
431C2×C53—82no—
432C2×C53#188412yescomplemented
433C2×C53C2×#38611yescharacteristic
434D53—44no—
435C22×#41—531no—
436C22×#41C2×D5311yescharacteristic
437#568—534no—
438#568—1062no—
439#568—1062no—
440#568—1062no—
441C2×#131—1062no—
442C2×#131—1062no—
443C22×M16—531no—
444C22×M16—1062no—
445C22×M16C2×D5311yescharacteristic
446#532—534no—
447#532—534no—
448#532—1062no—
449#532—1062no—
450C2×C4⋊Q8—531no—
451C2×#127—531no—
452C2×#124—531no—
453C2×#124—531no—
454C2×#121—1062no—
455C2×C4×D4—1062no—
456C2×#117—531no—
457C2×#117C2×D5311yescharacteristic
458C22×C42—531no—
459#421—22no—
460#421—534no—
461#421—1062no—
462#421C2×D5314yescomplemented
463C2×#104—22no—
464C2×#104—1062no—
465#410—534no—
466#410—1062no—
467C2×#99—1062no—
468#339—534no—
469#339—534no—
470C53C2×#188411yescharacteristic, complemented, Sylow
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—21no—
480C2×#41—21no—
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×#41—1061no—
492C2×#41—1061no—
493C2×#41C4×D5312yes—
494C2×#41C22×D5312yes—
495C22×Q8—531no—
496C22×Q8C4×D5311yescharacteristic
497C22×D4—21no—
498C22×D4—532no—
499C22×D4—531no—
500C22×D4—1062no—
501C22×D4C4×D5311yescharacteristic
502C23×C4—21no—
503C23×C4—532no—
504C23×C4—1061no—
505C23×C4C22×D5311yescharacteristic
506#131—1068no—
507#131—1068no—
508#131—1068no—
509#131—1068no—
510C2×M16—21no—
511C2×M16—21no—
512C2×M16—21no—
513C2×M16—532no—
514C2×M16—532no—
515C2×M16—532no—
516C2×M16—1064no—
517C2×M16—1068no—
518C2×M16—1068no—
519C2×M16—1061no—
520C2×M16—1061no—
521C2×M16—1061no—
522C2×M16C22⋊D5312yescomplemented
523C2×M16C22⋊D5312yescomplemented
524C2×M16C22×D5312yes—
525C22×C8—21no—
526C22×C8—1064no—
527C22×C8—1061no—
528C4⋊Q8—534no—
529C4⋊Q8—1062no—
530#127—534no—
531#127—1062no—
532#124—534no—
533#124—534no—
534#124—1062no—
535#124—1062no—
536#121—1068no—
537#121—1068no—
538C4×D4—1068no—
539C4×D4—1068no—
540#117—21no—
541#117—21no—
542#117—21no—
543#117—532no—
544#117—1061no—
545#117—1061no—
546#117—1061no—
547#117C22×D5312yes—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—1062no—
550C2×C4⋊C4—1061no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—1062no—
553C2×C22⋊C4—1062no—
554C2×C22⋊C4—1061no—
555C2×C42—21no—
556C2×C42—531no—
557C2×C42—531no—
558C2×C42—532no—
559C2×C42—532no—
560C2×C42—1061no—
561C2×C42—1061no—
562C2×C42—1061no—
563C2×C42—1061no—
564#104—28no—
565#104—1068no—
566#99—1068no—
567C24—21no—
568C24—532no—
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—1062no—
587#41—1062no—
588#41—1062no—
589#41—1062no—
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—1061no—
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—534no—
626C2×D4—534no—
627C2×D4—532no—
628C2×D4—532no—
629C2×D4—1062no—
630C2×D4—1062no—
631C2×D4—1062no—
632C2×D4—1062no—
633C2×D4—1068no—
634C2×D4—1061no—
635C2×D4—1061no—
636C2×D4—1061no—
637C2×D4—1061no—
638C2×D4—2128no—
639C2×D4C2×C4×D5312yes—
640C22×C4—21no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—41no—
644C22×C4—41no—
645C22×C4—41no—
646C22×C4—41no—
647C22×C4—41no—
648C22×C4—532no—
649C22×C4—534no—
650C22×C4—534no—
651C22×C4—1061no—
652C22×C4—1062no—
653C22×C4—1062no—
654C22×C4—1062no—
655C22×C4—1062no—
656C22×C4—1061no—
657C22×C4—1062no—
658C22×C4—1062no—
659C22×C4—2124no—
660C22×C4—2121no—
661C22×C4C2×C4×D5311yescharacteristic
662C22×C4C2×C4×D5311yescharacteristic
663C22×C4#1171994511yescharacteristic
664C22×C4#1171994511yescharacteristic
665C22×C4D4×D5311yescharacteristic
666C22×C4D4×D5311yescharacteristic
667C22×C4D4×D5311yescharacteristic
668C22×C4D4×D5311yescharacteristic
669C22×C4D4×D5311yescharacteristic
670C22×C4#1171994711yescharacteristic
671C22×C4#1171994711yescharacteristic
672C22×C4C2×C22⋊D5311yescharacteristic
673C22×C4C2×C22⋊D5311yescharacteristic
674C22×C4C23×D5311yescharacteristic
675M16—22no—
676M16—22no—
677M16—22no—
678M16—534no—
679M16—10616no—
680M16—1062no—
681M16—1062no—
682M16—1062no—
683M16C2×C22⋊D5314yescomplemented
684C2×C8—22no—
685C2×C8—22no—
686C2×C8—22no—
687C2×C8—10616no—
688C2×C8—1062no—
689C2×C8—1062no—
690C2×C8—1062no—
691C4⋊C4—22no—
692C4⋊C4—41no—
693C4⋊C4—1068no—
694C4⋊C4—1062no—
695C4⋊C4—2121no—
696C22⋊C4—22no—
697C22⋊C4—41no—
698C22⋊C4—1068no—
699C22⋊C4—1068no—
700C22⋊C4—1062no—
701C22⋊C4—2121no—
702C42—22no—
703C42—41no—
704C42—532no—
705C42—532no—
706C42—1062no—
707C42—1061no—
708C42—1061no—
709C42—1062no—
710C42—1062no—
711C42—2121no—
712C23—22no—
713C23—42no—
714C23—44no—
715C23—41no—
716C23—41no—
717C23—534no—
718C23—1062no—
719C23—1062no—
720C23—2124no—
721C23C22⋊C4×D5311yescharacteristic
722C23C22⋊C4×D5311yescharacteristic
723C23#1313318811yescharacteristic
724C23#1313318811yescharacteristic
725C23#1313319011yescharacteristic
726C23#1313319011yescharacteristic
727C23C2×D4×D5311yescharacteristic
728Q8—22no—
729Q8—22no—
730Q8—41no—
731Q8—41no—
732Q8—1062no—
733Q8—1062no—
734Q8—1062no—
735Q8—1062no—
736D4—22no—
737D4—22no—
738D4—42no—
739D4—42no—
740D4—42no—
741D4—42no—
742D4—41no—
743D4—41no—
744D4—1064no—
745D4—1064no—
746D4—1064no—
747D4—1064no—
748D4—1062no—
749D4—1062no—
750D4—1062no—
751D4—1062no—
752D4—21216no—
753C2×C4—22no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—82no—
762C2×C4—534no—
763C2×C4—1064no—
764C2×C4—1062no—
765C2×C4—1062no—
766C2×C4—1062no—
767C2×C4—1064no—
768C2×C4—1064no—
769C2×C4—1064no—
770C2×C4—1064no—
771C2×C4—1062no—
772C2×C4—4242no—
773C2×C4—2124no—
774C2×C4—2124no—
775C2×C4—2122no—
776C2×C4—2122no—
777C2×C4C22⋊C4×D5311yescharacteristic
778C2×C4C22⋊C4×D5311yescharacteristic
779C2×C4#1313317711yescharacteristic
780C2×C4#1313317711yescharacteristic
781C2×C4#1313317711yescharacteristic
782C2×C4#1313317711yescharacteristic
783C2×C4C4×C22⋊D5311yescharacteristic
784C2×C4C4×C22⋊D5311yescharacteristic
785C2×C4C4×C22⋊D5311yescharacteristic
786C2×C4C4×C22⋊D5311yescharacteristic
787C2×C4#1313318511yescharacteristic
788C2×C4#1313318511yescharacteristic
789C2×C4#1313318511yescharacteristic
790C2×C4#1313318511yescharacteristic
791C2×C4#1313318811yescharacteristic
792C2×C4#1313318811yescharacteristic
793C2×C4#1313319011yescharacteristic
794C2×C4#1313319011yescharacteristic
795C2×C4#1313319911yescharacteristic
796C2×C4#1313319911yescharacteristic
797C2×C4#1313319911yescharacteristic
798C2×C4#1313319911yescharacteristic
799C2×C4C22×C4×D5311yescharacteristic
800C2×C4C2×D4×D5311yescharacteristic
801C2×C4C2×D4×D5311yescharacteristic
802C2×C4C22×C22⋊D5311yescharacteristic
803C2×C4C2×#1171994711yescharacteristic
804C2×C4C2×#1171994511yescharacteristic
805C8—24no—
806C8—1064no—
807C22—22no—
808C22—22no—
809C22—22no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—44no—
815C22—42no—
816C22—82no—
817C22—82no—
818C22—1064no—
819C22—4242no—
820C22—2124no—
821C22—2124no—
822C22#1681049911yescharacteristic
823C22#1681049911yescharacteristic
824C22#1681049911yescharacteristic
825C22#1681049911yescharacteristic
826C22C2×C22⋊C4×D5311yescharacteristic
827C22C2×#1313318811yescharacteristic
828C22C2×#1313319011yescharacteristic
829C4—42no—
830C4—82no—
831C4—1064no—
832C4—1064no—
833C4—4242no—
834C4—2122no—
835C4#1681049911yescharacteristic
836C4#1681049911yescharacteristic
837C4#1681049911yescharacteristic
838C4#1681049911yescharacteristic
839C4C2×#1313317711yescharacteristic
840C4C2×C4×C22⋊D5311yescharacteristic
841C4C2×#1313318511yescharacteristic
842C4C2×#1313319911yescharacteristic
843C2—21no—
844C2—21no—
845C2—21no—
846C2—21no—
847C2—21no—
848C2—21no—
849C2—82no—
850C2—2124no—
851C2#2027509512yesdirect product factor
852C2C2×#1681049911yescharacteristic
subgroupG/H
centerC2×C4#13133185
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC2×C53×#421C2
socleC22×C53#386
prime radicalC2×#16811169C2
cosocleC22×C4×C53C24
hypercenterC2×#421D53
hypocenterC53C2×#1884
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
1. C2×#16811389C2semidirect
3. C2×#16810640C2semidirect
4. C2×#16810596C2semidirect
5. #20275095C2direct (N × H)
6. C2×#16810384C2semidirect
7. C2×#16810382C2semidirect
8. C2×C53×#421C2semidirect
13. #16811389C22semidirect
20. #16811169C4semidirect
22. C2×#13133215C4semidirect
23. C2×#13133213C4semidirect
24. C2×#13133206C4semidirect
25. C2×#13133204C4semidirect
31. #16810640C22semidirect
34. #16810596C22semidirect
36. #16810384C22semidirect
37. #16810382C22semidirect
42. C53×#421C22semidirect
69. C2×#11719917D4semidirect
70. C2×#11719917D4semidirect
78. #13133215C2×C4semidirect
80. #13133213C2×C4semidirect
82. #13133206C2×C4semidirect
84. #13133204C2×C4semidirect
128. C2×M16×C53D4semidirect
129. C2×M16×C53D4semidirect
251. M16×C53C2×D4semidirect
279. #11719917C2×D4semidirect
420. C2×#421D53semidirect
432. C2×C53#1884semidirect
462. #421C2×D53semidirect
470. C53C2×#1884semidirect
522. C2×M16C22⋊D53semidirect
523. C2×M16C22⋊D53semidirect
683. M16C2×C22⋊D53semidirect
851. C2#20275095direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113892
C2×#168111692
C2×#168106402
C2×#168105962
#202750952
C2×#168103842
C2×#168103822
C2×C53×#4212
C2×#188453