Finite Group Databasebeta

← #27386004

Subgroups — #27386004

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#20287916C211yesmaximal, characteristic, complemented
3C2×#16810641C211yesmaximal, characteristic, complemented
4C2×#16810640C211yesmaximal, characteristic, complemented
5#20275213C218yesmaximal, complemented
6C2×#16810393C211yesmaximal, characteristic, complemented
7#20274424C211yesmaximal, characteristic, complemented
8C2×C53×#410C211yesmaximal, characteristic, complemented
9C22×#11719945C2211yescharacteristic
10#16811421—22no—
11#16811421—22no—
12#16811421C414yescomplemented
13#16811421C2214yes—
14C2×#13133248C412yescomplemented
15C2×#13133247—21no—
16C2×#13133243C412yescomplemented
17C2×#13133242—21no—
18C2×#13133237—22no—
19C22×#11719917C2211yescharacteristic
20C22×#11719917C2211yescharacteristic
21#16811104—22no—
22#16811103—22no—
23#16811100—21no—
24#16811097—21no—
25#16811096—22no—
26C4×#11719945—22no—
27#16811091C2214yescomplemented
28C2×#13133176C2211yescharacteristic
29#117×D53—22no—
30#16810641—22no—
31#16810641C2214yescomplemented
32#16810640—22no—
33#16810640—22no—
34C2×#13133145—22no—
35C2×#13133144C2214yescomplemented
36#16810393C2214yescomplemented
37#16810382C2214yescomplemented
38C22×#41×C53C2211yescharacteristic
39C2×#117×C53C2211yescharacteristic
40C2×#117×C53C2211yescharacteristic
41C53×#410—22no—
42C53×#410C2214yescomplemented
43C2×#99×C53—22no—
44C2×#11719945—21no—
45C2×#11719945—21no—
46C2×#11719945—21no—
47C2×#11719945—21no—
48C2×#11719945—21no—
49C2×#11719945—21no—
50C2×#11719945C2×C412yes—
51C2×#11719945C2×C412yes—
52C2×#11719945D412yes—
53C2×#11719945D412yes—
54C2×#11719945D412yes—
55C2×#11719945C2312yes—
56C22×Dic106D411yescharacteristic
57C22×D212D411yescharacteristic
58C22×C22⋊D53—21no—
59C22×C4×D53—21no—
60#13133248—24no—
61#13133248C2×C418yescomplemented
62#13133247—24no—
63#13133247—24no—
64#13133243—24no—
65#13133243C2×C418yescomplemented
66#13133242—24no—
67#13133242—24no—
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×#11719917—21no—
78C2×#11719917—21no—
79C2×#11719917—21no—
80C2×#11719917—21no—
81C2×#11719917—21no—
82C2×#11719917C2×C412yescomplemented
83C2×#11719917C2×C412yescomplemented
84C2×#11719917C2312yes—
85C2×#11719917C2312yes—
86C22×#88322—21no—
87C22×#88322—21no—
88C4×Dic106—24no—
89#13133182—24no—
90C4×D212—24no—
91#13133179—24no—
92C4×C22⋊D53—28no—
93#13133177—28no—
94#13133176—21no—
95#13133176—21no—
96#13133176D412yes—
97#13133176D412yes—
98#13133175—24no—
99#13133174—24no—
100#13133173—24no—
101C2×C4⋊Dic53—21no—
102C4⋊C4×D53—24no—
103C2×C22⋊Dic53—21no—
104C22⋊C4×D53—24no—
105C2×C4×Dic53C2312yes—
106C42×D53—24no—
107#13133145—28no—
108#13133144—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×C53—21no—
116C2×#41×C53—21no—
117C2×#41×C53—21no—
118C2×#41×C53—21no—
119C2×#41×C53C2×C412yescomplemented
120C2×#41×C53C2312yes—
121C22×Q8×C53C2×C411yescharacteristic, complemented
122C22×D4×C53—21no—
123C22×D4×C53C2×C411yescharacteristic, complemented
124C23×C4×C53—21no—
125C23×C4×C53C2311yescharacteristic
126#117×C53—21no—
127#117×C53—21no—
128#117×C53—21no—
129#117×C53—21no—
130#117×C53—21no—
131#117×C53D412yes—
132#117×C53C2312yes—
133#117×C53C2312yes—
134C2×C4⋊C4×C53—21no—
135C2×C4⋊C4×C53—21no—
136C2×C22⋊C4×C53—21no—
137C2×C22⋊C4×C53D412yes—
138C2×C42×C53—21no—
139C2×C42×C53—21no—
140#99×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—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—
159#41×C53—41no—
160C2×Q8×C53—21no—
161C2×Q8×C53—21no—
162C2×Q8×C53—21no—
163C2×Q8×C53—21no—
164C2×Q8×C53—21no—
165C2×Q8×C53C22×C412yes—
166C2×D4×C53—22no—
167C2×D4×C53—22no—
168C2×D4×C53—21no—
169C2×D4×C53—21no—
170C2×D4×C53—21no—
171C2×D4×C53—21no—
172C2×D4×C53—21no—
173C2×D4×C53—41no—
174C2×D4×C53—41no—
175C2×D4×C53—41no—
176C2×D4×C53—41no—
177C2×D4×C53C22×C412yes—
178C22×C4×C53—21no—
179C22×C4×C53—22no—
180C22×C4×C53—22no—
181C22×C4×C53—22no—
182C22×C4×C53—41no—
183C22×C4×C53—41no—
184C22×C4×C53—41no—
185C22×C4×C53—41no—
186C22×C4×C53—41no—
187C22×C4×C53C22×C411yescharacteristic
188C22×C4×C53C22×C411yescharacteristic
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×C53C2×D411yescharacteristic
196C22×C4×C53#4111yescharacteristic
197C22×C4×C53#4111yescharacteristic
198C22×C4×C53#4111yescharacteristic
199C22×C4×C53#4111yescharacteristic
200C22×C4×C53C2411yescharacteristic
201C2×C22⋊D53—22no—
202C2×C22⋊D53—22no—
203C2×C22⋊D53—22no—
204C2×C22⋊D53—22no—
205C2×C22⋊D53—22no—
206C2×C22⋊D53—22no—
207C22×Dic53—21no—
208C22×Dic53—22no—
209#11719945—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—22no—
219#11719945—22no—
220#11719945—22no—
221#11719945C22⋊C414yes—
222#11719945C22⋊C414yes—
223#11719945C22×C414yes—
224#11719945C2×D414yes—
225C2×D212—21no—
226C2×D212—21no—
227C2×D212—21no—
228C2×D212C22⋊C412yes—
229C2×D212C22⋊C412yes—
230C2×D212C2×D412yes—
231C2×C4×D53—22no—
232C2×C4×D53—22no—
233C2×C4×D53—22no—
234C2×C4×D53—22no—
235C2×C4×D53—22no—
236C2×C4×D53—22no—
237C2×C4×D53—28no—
238C2×Dic106—21no—
239C2×Dic106—21no—
240C2×Dic106—21no—
241C2×Dic106C22⋊C412yes—
242C2×Dic106C22⋊C412yes—
243C2×Dic106C2×D412yes—
244C4⋊C4×C53—22no—
245C4⋊C4×C53—22no—
246C4⋊C4×C53—22no—
247C4⋊C4×C53—41no—
248C22⋊C4×C53—22no—
249C22⋊C4×C53—22no—
250C22⋊C4×C53—41no—
251C22⋊C4×C53C2×D414yes—
252C42×C53—22no—
253C42×C53—22no—
254C42×C53—22no—
255C42×C53—41no—
256C22⋊Dic53—22no—
257C22⋊Dic53—22no—
258#11719925—28no—
259#11719924—28no—
260#11719923—28no—
261#11719922—28no—
262#11719921—28no—
263C4⋊Dic53—22no—
264C4⋊Dic53—22no—
265#11719919—28no—
266C4×Dic53—28no—
267C4×Dic53—22no—
268C4×Dic53C2×D414yes—
269#11719917—22no—
270#11719917—22no—
271#11719917—22no—
272#11719917—22no—
273#11719917—22no—
274#11719917—41no—
275#11719917—41no—
276#11719917C22×C414yes—
277C2×#88322—22no—
278C2×#88322—22no—
279C2×#88322—22no—
280C2×#88322—22no—
281C2×#88322—41no—
282C2×#88322—41no—
283C23×C53—22no—
284C23×C53—41no—
285C23×C53—41no—
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—22no—
297C22×D53—22no—
298C22×D53—82no—
299Q8×C53—22no—
300Q8×C53—22no—
301Q8×C53—41no—
302Q8×C53—41no—
303D4×C53—22no—
304D4×C53—22no—
305D4×C53—42no—
306D4×C53—42no—
307D4×C53—42no—
308D4×C53—42no—
309D4×C53—41no—
310D4×C53—41no—
311C2×C4×C53—22no—
312C2×C4×C53—24no—
313C2×C4×C53—41no—
314C2×C4×C53—41no—
315C2×C4×C53—42no—
316C2×C4×C53—42no—
317C2×C4×C53—42no—
318C2×C4×C53—42no—
319C2×C4×C53—42no—
320C2×C4×C53—82no—
321C2×C4×C53—82no—
322C2×C4×C53C2×C22⋊C411yescharacteristic
323C2×C4×C53C2×C22⋊C411yescharacteristic
324C2×C4×C53C2×C22⋊C411yescharacteristic
325C2×C4×C53C2×C22⋊C411yescharacteristic
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#12111yescharacteristic
335C2×C4×C53#12111yescharacteristic
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—
354C2×Dic53—22no—
355C2×Dic53—22no—
356C2×Dic53—22no—
357C2×Dic53—24no—
358C2×Dic53—82no—
359D212—22no—
360D212—22no—
361D212—22no—
362D212C2×C22⋊C414yes—
363C4×D53—24no—
364C4×D53—24no—
365C4×D53—24no—
366C4×D53—24no—
367C4×D53—88no—
368Dic106—22no—
369Dic106—22no—
370Dic106—22no—
371Dic106C2×C22⋊C414yes—
372#88322—24no—
373#88322—42no—
374#21000—531nomaximal, Sylow
375C22×C53—41no—
376C22×C53—41no—
377C22×C53—41no—
378C22×C53—41no—
379C22×C53—41no—
380C22×C53—41no—
381C22×C53—41no—
382C22×C53—42no—
383C22×C53—82no—
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—24no—
394C2×D53—44no—
395C2×D53—82no—
396C2×D53—82no—
397C4×C53—44no—
398C4×C53—42no—
399C4×C53—82no—
400C4×C53#38611yescharacteristic
401C4×C53#38611yescharacteristic
402C4×C53#38611yescharacteristic
403C4×C53#38611yescharacteristic
404C4×C53C22×C22⋊C411yescharacteristic
405C4×C53C2×C4×D411yescharacteristic
406C4×C53C2×#12111yescharacteristic
407C4×C53C2×#12311yescharacteristic
408Dic53—24no—
409Dic53—44no—
410C2×#575—531no—
411#3428—531no—
412C2×#421—531no—
413C2×#421—531no—
414C2×#410D5311yescharacteristic, complemented
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—82no—
426C2×C53C2×#38611yescharacteristic
427D53—44no—
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×M16—531no—
441#520—1062no—
442#520—1062no—
443#519—1061no—
444#518—1061no—
445#518—1062no—
446C4×#41—534no—
447C4×#41—1062no—
448C2×#117—531no—
449C2×#117—1062no—
450C2×#117C2×D5311yescharacteristic
451C2×#117C2×D5311yescharacteristic
452#421—534no—
453#421—1062no—
454#421—1062no—
455#421—1062no—
456C2×#104—534no—
457C2×#104—1062no—
458#410—22no—
459#410C2×D5314yescomplemented
460C2×#99—22no—
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—21no—
471C2×#41—21no—
472C2×#41—21no—
473C2×#41—21no—
474C2×#41—532no—
475C2×#41—532no—
476C2×#41—532no—
477C2×#41—532no—
478C2×#41—532no—
479C2×#41—532no—
480C2×#41—1061no—
481C2×#41—1061no—
482C2×#41—1061no—
483C2×#41—1061no—
484C2×#41—1061no—
485C2×#41—1061no—
486C2×#41C4×D5312yescomplemented
487C2×#41C22×D5312yes—
488C22×Q8—531no—
489C22×Q8C4×D5311yescharacteristic, complemented
490C22×D4—21no—
491C22×D4—531no—
492C22×D4—1061no—
493C22×D4C4×D5311yescharacteristic, complemented
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—532no—
512C2×M16—532no—
513C2×M16—532no—
514C2×M16—532no—
515C2×M16—1061no—
516C2×M16—1061no—
517C2×M16—1061no—
518C2×M16—1061no—
519C2×M16—1061no—
520C2×M16—1061no—
521C2×M16—1061no—
522C2×M16—1061no—
523C22×C8—1061no—
524C22×C8—1061no—
525C4×Q8—1064no—
526C4×Q8—1064no—
527C4×D4—1064no—
528C4×D4—1064no—
529C4×D4—1068no—
530C4×D4—1068no—
531#117—21no—
532#117—21no—
533#117—21no—
534#117—21no—
535#117—21no—
536#117—532no—
537#117—532no—
538#117—1064no—
539#117—1064no—
540#117—1064no—
541#117—1061no—
542#117—1061no—
543#117C22⋊D5312yes—
544#117C22×D5312yes—
545#117C22×D5312yes—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—1064no—
549C2×C4⋊C4—1061no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—1064no—
552C2×C22⋊C4—1061no—
553C2×C22⋊C4C22⋊D5312yes—
554C2×C42—21no—
555C2×C42—21no—
556C2×C42—532no—
557C2×C42—1064no—
558#104—1068no—
559#104—1068no—
560#99—28no—
561C24—21no—
562C24—1061no—
563C24C2×C22⋊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—41no—
573#41—41no—
574#41—41no—
575#41—41no—
576#41—41no—
577#41—41no—
578#41—41no—
579#41—41no—
580#41—534no—
581#41—534no—
582#41—534no—
583#41—534no—
584#41—1062no—
585#41—1062no—
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—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8—532no—
602C2×Q8—532no—
603C2×Q8—532no—
604C2×Q8—1061no—
605C2×Q8—1061no—
606C2×Q8—1061no—
607C2×Q8C2×C4×D5312yes—
608C2×D4—22no—
609C2×D4—22no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—41no—
616C2×D4—41no—
617C2×D4—41no—
618C2×D4—41no—
619C2×D4—532no—
620C2×D4—532no—
621C2×D4—532no—
622C2×D4—1062no—
623C2×D4—1062no—
624C2×D4—1062no—
625C2×D4—1062no—
626C2×D4—1062no—
627C2×D4—1062no—
628C2×D4—1061no—
629C2×D4—1061no—
630C2×D4—1061no—
631C2×D4C2×C4×D5312yes—
632C22×C4—21no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—41no—
637C22×C4—41no—
638C22×C4—41no—
639C22×C4—41no—
640C22×C4—41no—
641C22×C4—1068no—
642C22×C4—1061no—
643C22×C4—1062no—
644C22×C4—1062no—
645C22×C4—1062no—
646C22×C4—1062no—
647C22×C4—1062no—
648C22×C4—1062no—
649C22×C4—1062no—
650C22×C4C2×C4×D5311yescharacteristic
651C22×C4C2×C4×D5311yescharacteristic
652C22×C4#1171994511yescharacteristic
653C22×C4#1171994511yescharacteristic
654C22×C4D4×D5311yescharacteristic
655C22×C4D4×D5311yescharacteristic
656C22×C4D4×D5311yescharacteristic
657C22×C4D4×D5311yescharacteristic
658C22×C4D4×D5311yescharacteristic
659C22×C4D4×D5311yescharacteristic
660C22×C4#1171994711yescharacteristic
661C22×C4#1171994711yescharacteristic
662C22×C4C2×C22⋊D5311yescharacteristic
663C22×C4C23×D5311yescharacteristic
664Q16—1068no—
665SD16—1068no—
666SD16—1068no—
667D8—1068no—
668M16—534no—
669M16—1062no—
670M16—1062no—
671M16—1062no—
672M16—1062no—
673M16—1062no—
674M16—2121no—
675M16—2121no—
676C2×C8—1062no—
677C2×C8—1062no—
678C2×C8—1062no—
679C2×C8—1062no—
680C2×C8—2121no—
681C2×C8—2121no—
682C4⋊C4—22no—
683C4⋊C4—22no—
684C4⋊C4—22no—
685C4⋊C4—41no—
686C4⋊C4—1068no—
687C4⋊C4—1062no—
688C4⋊C4—1062no—
689C22⋊C4—22no—
690C22⋊C4—22no—
691C22⋊C4—41no—
692C22⋊C4—1068no—
693C22⋊C4—1062no—
694C22⋊C4—1062no—
695C22⋊C4C2×C22⋊D5314yes—
696C42—22no—
697C42—22no—
698C42—22no—
699C42—41no—
700C42—534no—
701C42—1068no—
702C42—1062no—
703C23—22no—
704C23—41no—
705C23—41no—
706C23—81no—
707C23—82no—
708C23—1062no—
709C23—1062no—
710C23—1062no—
711C23—4242no—
712C23C4×C22⋊D5311yescharacteristic
713C23C4×C22⋊D5311yescharacteristic
714C23#1313318511yescharacteristic
715C23#1313318511yescharacteristic
716C23#1313318811yescharacteristic
717C23#1313318811yescharacteristic
718C23C22×C22⋊D5311yescharacteristic
719Q8—22no—
720Q8—22no—
721Q8—41no—
722Q8—41no—
723Q8—534no—
724Q8—1062no—
725Q8—1062no—
726Q8—1062no—
727D4—22no—
728D4—22no—
729D4—42no—
730D4—42no—
731D4—42no—
732D4—42no—
733D4—41no—
734D4—41no—
735D4—534no—
736D4—1064no—
737D4—1064no—
738D4—1064no—
739D4—1064no—
740D4—1062no—
741D4—1062no—
742D4—1062no—
743C2×C4—22no—
744C2×C4—24no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—82no—
753C2×C4—82no—
754C2×C4—1062no—
755C2×C4—1062no—
756C2×C4—1062no—
757C2×C4—1064no—
758C2×C4—1064no—
759C2×C4—1064no—
760C2×C4—1064no—
761C2×C4—1064no—
762C2×C4—4248no—
763C2×C4—4242no—
764C2×C4C22⋊C4×D5311yescharacteristic
765C2×C4C22⋊C4×D5311yescharacteristic
766C2×C4C22⋊C4×D5311yescharacteristic
767C2×C4C22⋊C4×D5311yescharacteristic
768C2×C4#1313317711yescharacteristic
769C2×C4#1313317711yescharacteristic
770C2×C4#1313317711yescharacteristic
771C2×C4#1313317711yescharacteristic
772C2×C4C4×C22⋊D5311yescharacteristic
773C2×C4C4×C22⋊D5311yescharacteristic
774C2×C4#1313318511yescharacteristic
775C2×C4#1313318511yescharacteristic
776C2×C4#1313318811yescharacteristic
777C2×C4#1313318811yescharacteristic
778C2×C4#1313319011yescharacteristic
779C2×C4#1313319011yescharacteristic
780C2×C4#1313319011yescharacteristic
781C2×C4#1313319011yescharacteristic
782C2×C4#1313319911yescharacteristic
783C2×C4#1313319911yescharacteristic
784C2×C4#1313319911yescharacteristic
785C2×C4#1313319911yescharacteristic
786C2×C4C22×C4×D5311yescharacteristic
787C2×C4C2×D4×D5311yescharacteristic
788C2×C4C2×D4×D5311yescharacteristic
789C2×C4C2×D4×D5311yescharacteristic
790C2×C4C2×#1171994711yescharacteristic
791C2×C4C2×#1171994511yescharacteristic
792C8—1064no—
793C8—2122no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—42no—
802C22—82no—
803C22—82no—
804C22—82no—
805C22—1064no—
806C22—4242no—
807C22—4242no—
808C22—2124no—
809C22#1681049911yescharacteristic
810C22#1681049911yescharacteristic
811C22#1681049911yescharacteristic
812C22#1681049911yescharacteristic
813C22C2×C4×C22⋊D5311yescharacteristic
814C22C2×#1313318511yescharacteristic
815C22C2×#1313318811yescharacteristic
816C4—44no—
817C4—42no—
818C4—82no—
819C4—1064no—
820C4—2124no—
821C4#1681049911yescharacteristic
822C4#1681049911yescharacteristic
823C4#1681049911yescharacteristic
824C4#1681049911yescharacteristic
825C4C2×C22⋊C4×D5311yescharacteristic
826C4C2×#1313317711yescharacteristic
827C4C2×#1313319011yescharacteristic
828C4C2×#1313319911yescharacteristic
829C2—21no—
830C2—21no—
831C2—21no—
832C2—21no—
833C2—21no—
834C2—21no—
835C2—21no—
836C2—82no—
837C2—2124no—
838C2C2×#1681049911yescharacteristic
subgroupG/H
centerC4C2×#13133190
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC2×C53×#410C2
socleC2×C53C2×#386
prime radicalC2×#16811421C2
cosocleC22×C4×C53C24
hypercenterC2×#410D53
hypocenterC53#21000
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#410

Complements

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

NH ≅ G/Ntype
2. #20287916C2semidirect
3. C2×#16810641C2semidirect
4. C2×#16810640C2semidirect
5. #20275213C2semidirect
6. C2×#16810393C2semidirect
7. #20274424C2semidirect
8. C2×C53×#410C2semidirect
12. #16811421C4semidirect
14. C2×#13133248C4semidirect
16. C2×#13133243C4semidirect
27. #16811091C22semidirect
31. #16810641C22semidirect
35. C2×#13133144C22semidirect
36. #16810393C22semidirect
37. #16810382C22semidirect
42. C53×#410C22semidirect
61. #13133248C2×C4semidirect
65. #13133243C2×C4semidirect
82. C2×#11719917C2×C4semidirect
83. C2×#11719917C2×C4semidirect
119. C2×#41×C53C2×C4semidirect
121. C22×Q8×C53C2×C4semidirect
123. C22×D4×C53C2×C4semidirect
414. C2×#410D53semidirect
459. #410C2×D53semidirect
463. C53#21000semidirect
486. C2×#41C4×D53semidirect
489. C22×Q8C4×D53semidirect
493. 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
C2×#168106412
C2×#168106402
#202752132
C2×#168103932
#202744242
C2×C53×#4102
#2100053