Finite Group Databasebeta

← #27351753

Subgroups — #27351753

Order 13568.

944 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288467C211yesmaximal, characteristic
2#20283373C211yesmaximal, characteristic, complemented
3#20273290C211yesmaximal, characteristic, complemented
4#20273278C211yesmaximal, characteristic, complemented
5#20273269C211yesmaximal, characteristic
6#20273265C211yesmaximal, characteristic, complemented
7#20273251C211yesmaximal, characteristic, complemented
8#20273247C211yesmaximal, characteristic, complemented
9#20273238C211yesmaximal, characteristic, complemented
10#20273226C211yesmaximal, characteristic, complemented
11#20273217C211yesmaximal, characteristic
12#20273213C211yesmaximal, characteristic, complemented
13#20273199C211yesmaximal, characteristic, complemented
14C2×#16810359C211yesmaximal, characteristic, complemented
15C53×#2343C211yesmaximal, characteristic, complemented
16#16811341—21no—
17#16811328—21no—
18#16811312—21no—
19#16811308—21no—
20#16811306—21no—
21#16811306—21no—
22#16811299—21no—
23#16811299—21no—
24#16811251C411yescharacteristic, complemented
25#16811244C411yescharacteristic, complemented
26#16811244C411yescharacteristic, complemented
27#16811235C411yescharacteristic, complemented
28#16811235C411yescharacteristic, complemented
29#16811199C411yescharacteristic, complemented
30#16811180C2211yescharacteristic
31#16811180C2211yescharacteristic
32#16811157C2211yescharacteristic
33#16811157C2211yescharacteristic
34#16811134C2211yescharacteristic
35C2×#13133196C2211yescharacteristic
36#16811103C411yescharacteristic, complemented
37#16811100C411yescharacteristic, complemented
38#16810684—21no—
39#16810684—21no—
40#16810680C2211yescharacteristic
41#16810680C2211yescharacteristic
42#16810676C2211yescharacteristic
43#16810676C2211yescharacteristic
44#16810650—21no—
45#16810587C2211yescharacteristic
46C2×C22⋊#88322C2211yescharacteristic
47#16810579—21no—
48#16810359C2211yescharacteristic
49#16810359C2211yescharacteristic
50#16810359C2211yescharacteristic
51#16810359C2211yescharacteristic
52#16810359C2211yescharacteristic
53#16810359C2211yescharacteristic
54#16810359C2211yescharacteristic
55#16810359C2211yescharacteristic
56#16810359C2211yescharacteristic
57#16810359C2211yescharacteristic
58#16810359C2211yescharacteristic
59#16810359C2211yescharacteristic
60#16810356C2211yescharacteristic
61#16810356C2211yescharacteristic
62#16810356C2211yescharacteristic
63#16810356C2211yescharacteristic
64C2×#117×C53C2211yescharacteristic
65C53×#387—21no—
66C53×#387—21no—
67C53×#385—21no—
68C53×#383C2211yescharacteristic
69C53×#382C2211yescharacteristic
70C53×#381C2211yescharacteristic
71C4×C4⋊C4×C53C2211yescharacteristic
72C4×C22⋊C4×C53—21no—
73C53×#376C2211yescharacteristic
74C2×#95×C53C2211yescharacteristic
75C2×#11719945C2×C411yescharacteristic
76C22×Dic106C2×C411yescharacteristic
77C2×#11719917—21no—
78C22×#88322—21no—
79#13133217C2×C411yescharacteristic, complemented
80#13133217C2×C411yescharacteristic, complemented
81#13133217C2×C411yescharacteristic, complemented
82#13133217C2×C411yescharacteristic, complemented
83#13133216—21no—
84#13133212—21no—
85#13133212—21no—
86#13133211—21no—
87#13133211—21no—
88#13133210—21no—
89#13133210—21no—
90#13133210—21no—
91#13133210—21no—
92#13133209—21no—
93#13133209—21no—
94#13133209C2×C411yescharacteristic, complemented
95#13133209C2×C411yescharacteristic, complemented
96#13133208—21no—
97#13133207—21no—
98#13133207—21no—
99#13133207—21no—
100#13133207—21no—
101#13133205C2×C411yescharacteristic, complemented
102#13133205C2×C411yescharacteristic, complemented
103#13133203—21no—
104#13133203—21no—
105#13133201—21no—
106#13133201—21no—
107#13133200—21no—
108#13133200—21no—
109#13133200—21no—
110#13133199—21no—
111#13133199—21no—
112#13133197—21no—
113#13133197—21no—
114#13133196—21no—
115#13133196—21no—
116#13133196—21no—
117#13133196—21no—
118#13133196C2×C411yescharacteristic
119#13133196C2×C411yescharacteristic
120#13133196C2×C411yescharacteristic
121#13133196C2311yescharacteristic
122#13133196C2311yescharacteristic
123#13133196C2311yescharacteristic
124#13133195—21no—
125#13133195—21no—
126#13133194—21no—
127#13133194—21no—
128#13133191C2×C411yescharacteristic
129#13133191C2311yescharacteristic
130#13133186—21no—
131C4×Dic106—21no—
132C4×Dic106—21no—
133C4×Dic106C2×C411yescharacteristic, complemented
134C4×Dic106C2×C411yescharacteristic, complemented
135C4×Dic106C2×C411yescharacteristic, complemented
136C4×Dic106C2×C411yescharacteristic, complemented
137C4×Dic106C2×C411yescharacteristic, complemented
138C4×Dic106C2×C411yescharacteristic, complemented
139#13133182—21no—
140#13133182—21no—
141C4×D212C2×C411yescharacteristic, complemented
142C4×D212C2×C411yescharacteristic, complemented
143C4×C22⋊D53—21no—
144C4×C22⋊D53—21no—
145C4×C22⋊D53—21no—
146C4×C22⋊D53—21no—
147#13133177—21no—
148#13133177—21no—
149#13133176—21no—
150#13133176—21no—
151#13133176C2×C411yescharacteristic
152#13133175—21no—
153#13133174—21no—
154#13133174—21no—
155#13133173—21no—
156#13133173—21no—
157C2×C4⋊Dic53C2×C411yescharacteristic
158C2×#11719919—21no—
159C4⋊C4×D53—21no—
160C2×C22⋊Dic53—21no—
161C4⋊#88322—21no—
162C4⋊#88322—21no—
163C4⋊#88322—21no—
164C4⋊#88322—21no—
165C22⋊#88322—21no—
166C22⋊#88322—21no—
167C22⋊#88322C2311yescharacteristic
168C22⋊#88322C2311yescharacteristic
169C22⋊#88322C2311yescharacteristic
170C22⋊#88322C2311yescharacteristic
171#13133128—21no—
172#13133128—21no—
173C4×#88322—21no—
174C4×#88322—21no—
175C23×C4×C53—21no—
176C23×C4×C53C2311yescharacteristic
177#117×C53C2×C411yescharacteristic
178#117×C53C2×C411yescharacteristic
179#117×C53C2×C411yescharacteristic
180#117×C53C2×C411yescharacteristic
181#117×C53D411yescharacteristic
182#117×C53D411yescharacteristic
183#117×C53D411yescharacteristic
184#117×C53D411yescharacteristic
185C2×C4⋊C4×C53—21no—
186C2×C4⋊C4×C53—21no—
187C2×C4⋊C4×C53D411yescharacteristic
188C2×C4⋊C4×C53D411yescharacteristic
189C2×C22⋊C4×C53—21no—
190C2×C22⋊C4×C53D411yescharacteristic
191C2×C22⋊C4×C53D411yescharacteristic
192C2×C42×C53—21no—
193C2×C42×C53—21no—
194C2×C42×C53C2311yescharacteristic
195C2×C42×C53C2311yescharacteristic
196#95×C53—21no—
197#95×C53—21no—
198#95×C53—21no—
199#95×C53—21no—
200#95×C53—21no—
201#95×C53—21no—
202#95×C53C2311yescharacteristic
203#95×C53C2311yescharacteristic
204#95×C53C2311yescharacteristic
205#95×C53C2311yescharacteristic
206C24×C53C2×D411yescharacteristic
207C22×C4×C53—21no—
208C22×C4×C53—21no—
209C22×C4×C53—21no—
210C22×C4×C53—21no—
211C22×C4×C53—42no—
212C22×C4×C53—42no—
213C22×C4×C53—42no—
214C22×C4×C53—81no—
215C22×C4×C53C22×C411yescharacteristic
216C22×C4×C53C22×C411yescharacteristic
217C22×C4×C53C2×D411yescharacteristic
218C22×C4×C53C2×D411yescharacteristic
219C22×C4×C53C2×D411yescharacteristic
220C22×C4×C53C2×D411yescharacteristic
221C22×C4×C53C2×D411yescharacteristic
222C22×C4×C53C2×D411yescharacteristic
223C22×C4×C53C2×D411yescharacteristic
224C22×C4×C53C2411yescharacteristic
225C2×C22⋊D53—21no—
226C2×C22⋊D53—21no—
227C2×C22⋊D53—21no—
228C22×Dic53—21no—
229C22×Dic53—21no—
230#11719945—42no—
231C2×D212C22×C411yescharacteristic
232C2×C4×D53—21no—
233C2×C4×D53—21no—
234C2×C4×D53—21no—
235C2×Dic106—21no—
236C2×Dic106—21no—
237C2×Dic106—21no—
238C2×Dic106—42no—
239C2×Dic106C22×C411yescharacteristic
240C2×Dic106C22×C411yescharacteristic
241C2×Dic106C22×C411yescharacteristic
242C4⋊C4×C53—42no—
243C4⋊C4×C53—81no—
244C4⋊C4×C53C22⋊C411yescharacteristic
245C4⋊C4×C53C22⋊C411yescharacteristic
246C4⋊C4×C53C22⋊C411yescharacteristic
247C4⋊C4×C53C22⋊C411yescharacteristic
248C4⋊C4×C53C22⋊C411yescharacteristic
249C4⋊C4×C53C22⋊C411yescharacteristic
250C4⋊C4×C53C22⋊C411yescharacteristic
251C4⋊C4×C53C22⋊C411yescharacteristic
252C22⋊C4×C53—42no—
253C22⋊C4×C53C22⋊C411yescharacteristic
254C22⋊C4×C53C22⋊C411yescharacteristic
255C22⋊C4×C53C22⋊C411yescharacteristic
256C22⋊C4×C53C22⋊C411yescharacteristic
257C22⋊C4×C53C22⋊C411yescharacteristic
258C22⋊C4×C53C22⋊C411yescharacteristic
259C22⋊C4×C53C22⋊C411yescharacteristic
260C22⋊C4×C53C22⋊C411yescharacteristic
261C42×C53—42no—
262C42×C53—81no—
263C42×C53C22×C411yescharacteristic
264C42×C53C22×C411yescharacteristic
265C42×C53C22×C411yescharacteristic
266C42×C53C22×C411yescharacteristic
267C42×C53C2×D411yescharacteristic
268C42×C53C2×D411yescharacteristic
269C42×C53C2×D411yescharacteristic
270C42×C53C2×D411yescharacteristic
271C22⋊Dic53—21no—
272C22⋊Dic53—21no—
273C22⋊Dic53—21no—
274C22⋊Dic53—21no—
275C22⋊Dic53—21no—
276C22⋊Dic53—21no—
277C22⋊Dic53—21no—
278#11719921—21no—
279#11719921—21no—
280#11719921—21no—
281#11719921—21no—
282#11719921—21no—
283#11719921—21no—
284#11719921—21no—
285#11719921—21no—
286C4⋊Dic53—21no—
287C4⋊Dic53—21no—
288C4⋊Dic53—21no—
289C4⋊Dic53—21no—
290C4⋊Dic53—21no—
291C4⋊Dic53—21no—
292C4⋊Dic53—21no—
293C4⋊Dic53C22×C411yescharacteristic
294C4⋊Dic53C22×C411yescharacteristic
295C4⋊Dic53C22×C411yescharacteristic
296C4⋊Dic53C22×C411yescharacteristic
297#11719919—21no—
298#11719919—21no—
299#11719919—21no—
300#11719919—21no—
301#11719919—21no—
302#11719919—21no—
303#11719919—21no—
304#11719919—21no—
305#11719919—21no—
306#11719919—21no—
307#11719919—21no—
308#11719919—21no—
309#11719919—21no—
310#11719919—21no—
311#11719919—21no—
312#11719919—21no—
313C4×Dic53—21no—
314C4×Dic53—21no—
315C4×Dic53—21no—
316C4×Dic53—21no—
317C4×Dic53—21no—
318C4×Dic53—21no—
319C4×Dic53—21no—
320#11719917—42no—
321C2×#88322—21no—
322C2×#88322—21no—
323C2×#88322—21no—
324C2×#88322—21no—
325C2×#88322—42no—
326C23×C53—21no—
327C23×C53—21no—
328C23×C53—22no—
329C23×C53—41no—
330C23×C53C2×C22⋊C411yescharacteristic
331C23×C53C2×C22⋊C411yescharacteristic
332C23×C53C22×D411yescharacteristic
333C22×D53—21no—
334C2×C4×C53—21no—
335C2×C4×C53—21no—
336C2×C4×C53—21no—
337C2×C4×C53—21no—
338C2×C4×C53—22no—
339C2×C4×C53—22no—
340C2×C4×C53—22no—
341C2×C4×C53—41no—
342C2×C4×C53—41no—
343C2×C4×C53—41no—
344C2×C4×C53—41no—
345C2×C4×C53—41no—
346C2×C4×C53—41no—
347C2×C4×C53—41no—
348C2×C4×C53—41no—
349C2×C4×C53—41no—
350C2×C4×C53—41no—
351C2×C4×C53—41no—
352C2×C4×C53—41no—
353C2×C4×C53—41no—
354C2×C4×C53—41no—
355C2×C4×C53—41no—
356C2×C4×C53—41no—
357C2×C4×C53—41no—
358C2×C4×C53—84no—
359C2×C4×C53C2×C22⋊C411yescharacteristic
360C2×C4×C53C2×C22⋊C411yescharacteristic
361C2×C4×C53C2×C22⋊C411yescharacteristic
362C2×C4×C53C2×C22⋊C411yescharacteristic
363C2×C4×C53C2×C22⋊C411yescharacteristic
364C2×C4×C53C2×C22⋊C411yescharacteristic
365C2×C4×C53C2×C22⋊C411yescharacteristic
366C2×C4×C53C2×C22⋊C411yescharacteristic
367C2×C4×C53C2×C22⋊C411yescharacteristic
368C2×C4×C53C2×C22⋊C411yescharacteristic
369C2×C4×C53C23×C411yescharacteristic
370C2×C4×C53C22×D411yescharacteristic
371C22⋊D53—41no—
372C22⋊D53—41no—
373C22⋊D53—42no—
374C22⋊D53—81no—
375C2×Dic53—21no—
376C2×Dic53—21no—
377C2×Dic53—21no—
378C2×Dic53—21no—
379C2×Dic53—21no—
380C2×Dic53—21no—
381C2×Dic53—21no—
382C2×Dic53—42no—
383C2×Dic53—81no—
384D212—41no—
385C4×D53—42no—
386C4×D53—81no—
387C4×D53—81no—
388Dic106—42no—
389Dic106—41no—
390Dic106—41no—
391Dic106—41no—
392Dic106—81no—
393Dic106—81no—
394#88322—41no—
395#88322—41no—
396#88322—41no—
397#88322—41no—
398#17609—531nomaximal, Sylow
399C22×C53—21no—
400C22×C53—21no—
401C22×C53—21no—
402C22×C53—21no—
403C22×C53—21no—
404C22×C53—21no—
405C22×C53—21no—
406C22×C53—42no—
407C22×C53—42no—
408C22×C53#41012yes—
409C22×C53C22×C22⋊C411yescharacteristic
410C22×C53#57711yescharacteristic
411C22×C53#57811yescharacteristic
412C2×D53—41no—
413C2×D53—41no—
414C2×D53—41no—
415C4×C53—21no—
416C4×C53—21no—
417C4×C53—21no—
418C4×C53—21no—
419C4×C53—21no—
420C4×C53—21no—
421C4×C53—21no—
422C4×C53—21no—
423C4×C53—21no—
424C4×C53—21no—
425C4×C53—21no—
426C4×C53—21no—
427C4×C53—42no—
428C4×C53—81no—
429C4×C53—81no—
430C4×C53—81no—
431Dic53—41no—
432Dic53—41no—
433Dic53—41no—
434Dic53—41no—
435Dic53—41no—
436Dic53—41no—
437Dic53—41no—
438#3495—531no—
439#2924—531no—
440#2343D5311yescharacteristic, complemented
441#1521—531no—
442#1518—531no—
443#1516—531no—
444#1515—531no—
445#1512—531no—
446#1511—531no—
447#1509—531no—
448#1506—531no—
449#1504—531no—
450#1503—531no—
451#1500—531no—
452C2×#328—531no—
453C2×C53—21no—
454C2×C53—21no—
455C2×C53—22no—
456C2×C53—41no—
457C2×C53C2×#41011yescharacteristic
458C2×C53#289811yescharacteristic
459C2×C53#290111yescharacteristic
460D53—81no—
461#556—1061no—
462#554—1061no—
463#552—1061no—
464#552—1061no—
465#552—1061no—
466#552—1061no—
467#551—1061no—
468#551—1061no—
469#544—531no—
470#542—531no—
471#542—531no—
472#541—531no—
473#541—531no—
474#536—531no—
475#533—531no—
476#533—531no—
477#529—531no—
478#529—531no—
479#525—531no—
480C2×C22⋊Q8—531no—
481#520—531no—
482#519—531no—
483C2×#117C2×D5311yescharacteristic
484#433—1061no—
485#433—1061no—
486#432—531no—
487#432—531no—
488#431—531no—
489#431—531no—
490#424—1061no—
491#407—531no—
492C2×C22⋊C8—531no—
493#405—1061no—
494#387—21no—
495#387—21no—
496#385—21no—
497#383C2×D5311yescharacteristic
498#382C2×D5311yescharacteristic
499#381C2×D5311yescharacteristic
500C4×C4⋊C4C2×D5311yescharacteristic
501C4×C22⋊C4—21no—
502#376C2×D5311yescharacteristic
503C2×#95C2×D5311yescharacteristic
504#328—531no—
505#328—531no—
506#328—531no—
507#328—531no—
508#328—531no—
509#328—531no—
510#328—531no—
511#328—531no—
512#328—531no—
513#328—531no—
514#328—531no—
515#328—531no—
516#327—531no—
517#327—531no—
518#327—531no—
519#327—531no—
520C53#1760911yescharacteristic, complemented, Sylow
521C2×#41—531no—
522C22×Q8—531no—
523C23×C4—21no—
524C23×C4C22×D5311yescharacteristic
525C2×M16—1061no—
526C22×C8—1061no—
527C4⋊Q8—531no—
528C4⋊Q8—531no—
529C4⋊Q8—531no—
530C4⋊Q8—531no—
531C4⋊Q8—1061no—
532#126—1061no—
533#126—1061no—
534#126—1061no—
535#126—1061no—
536#126—1061no—
537#126—1061no—
538#126—1061no—
539#126—1061no—
540#125—531no—
541#125—531no—
542#125—1061no—
543#125—1061no—
544#125—1061no—
545#125—1061no—
546#125—1061no—
547#125—1061no—
548#125—1061no—
549#124—531no—
550#124—531no—
551#124—1061no—
552#124—1061no—
553#123—1061no—
554#123—1061no—
555#123—1061no—
556#123—1061no—
557#123—1061no—
558#123—1061no—
559#123—1061no—
560C22⋊Q8—531no—
561C22⋊Q8—531no—
562C22⋊Q8—531no—
563C22⋊Q8—531no—
564C22⋊Q8—531no—
565C22⋊Q8—531no—
566C22⋊Q8—1061no—
567C22⋊Q8—1061no—
568C22⋊Q8—1061no—
569C22⋊Q8—1061no—
570C22⋊Q8—1061no—
571C22⋊Q8—1061no—
572C22⋊Q8—1061no—
573C22⋊Q8—1061no—
574C22⋊Q8—1061no—
575C22⋊Q8—1061no—
576#121—531no—
577#121—531no—
578#120—1061no—
579C4×Q8—531no—
580C4×Q8—531no—
581C4×Q8—531no—
582C4×Q8—531no—
583C4×Q8—531no—
584C4×Q8—531no—
585C4×Q8—1061no—
586C4×Q8—1061no—
587C4×Q8—1061no—
588C4×Q8—1061no—
589C4×D4—531no—
590C4×D4—531no—
591C4×D4—1061no—
592C4×D4—1061no—
593C4×D4—1061no—
594C4×D4—1061no—
595C4×D4—1061no—
596C4×D4—1061no—
597#117—531no—
598#117—1061no—
599#117—1061no—
600#117—1061no—
601#117—1061no—
602#117—1061no—
603#117—1061no—
604#117—1061no—
605#117C4×D5311yescharacteristic
606#117C4×D5311yescharacteristic
607#117C4×D5311yescharacteristic
608#117C4×D5311yescharacteristic
609#117D21211yescharacteristic
610#117D21211yescharacteristic
611#117D21211yescharacteristic
612#117D21211yescharacteristic
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—531no—
616C2×C4⋊C4—1061no—
617C2×C4⋊C4—1061no—
618C2×C4⋊C4C22⋊D5311yescharacteristic
619C2×C4⋊C4C22⋊D5311yescharacteristic
620C2×C22⋊C4—21no—
621C2×C22⋊C4—1061no—
622C2×C22⋊C4C22⋊D5311yescharacteristic
623C2×C22⋊C4C22⋊D5311yescharacteristic
624C2×C42—21no—
625C2×C42—21no—
626C2×C42C22×D5311yescharacteristic
627C2×C42C22×D5311yescharacteristic
628C4⋊C8—1061no—
629C4⋊C8—1061no—
630C4⋊C8—1061no—
631C4⋊C8—1061no—
632C22⋊C8—531no—
633C22⋊C8—531no—
634C22⋊C8—531no—
635C22⋊C8—531no—
636C22⋊C8—1061no—
637C22⋊C8—1061no—
638#97—1061no—
639#97—1061no—
640C4×C8—1061no—
641C4×C8—1061no—
642#95—21no—
643#95—21no—
644#95—21no—
645#95—21no—
646#95—21no—
647#95—21no—
648#95C22×D5311yescharacteristic
649#95C22×D5311yescharacteristic
650#95C22×D5311yescharacteristic
651#95C22×D5311yescharacteristic
652C24C2×C22⋊D5311yescharacteristic
653#41—2122no—
654C2×Q8—531no—
655C2×Q8—531no—
656C2×Q8—531no—
657C2×Q8—1061no—
658C2×Q8—1061no—
659C2×Q8—1061no—
660C2×Q8—2122no—
661C2×D4—531no—
662C2×D4—1061no—
663C2×D4—1061no—
664C2×D4—1061no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—42no—
670C22×C4—42no—
671C22×C4—42no—
672C22×C4—81no—
673C22×C4—1061no—
674C22×C4—1061no—
675C22×C4—1061no—
676C22×C4—1061no—
677C22×C4—1061no—
678C22×C4C2×C4×D5311yescharacteristic
679C22×C4C2×C4×D5311yescharacteristic
680C22×C4C2×D21211yescharacteristic
681C22×C4C2×D21211yescharacteristic
682C22×C4C2×C22⋊D5311yescharacteristic
683C22×C4C2×C22⋊D5311yescharacteristic
684C22×C4C2×C22⋊D5311yescharacteristic
685C22×C4C2×C22⋊D5311yescharacteristic
686C22×C4C2×C22⋊D5311yescharacteristic
687C22×C4C23×D5311yescharacteristic
688M16—2122no—
689C2×C8—1061no—
690C2×C8—1061no—
691C2×C8—1061no—
692C2×C8—1061no—
693C2×C8—2122no—
694C4⋊C4—42no—
695C4⋊C4—81no—
696C4⋊C4—531no—
697C4⋊C4—531no—
698C4⋊C4—531no—
699C4⋊C4—531no—
700C4⋊C4—1061no—
701C4⋊C4—1061no—
702C4⋊C4—1061no—
703C4⋊C4—1061no—
704C4⋊C4—1061no—
705C4⋊C4—1061no—
706C4⋊C4—1061no—
707C4⋊C4—1061no—
708C4⋊C4—1061no—
709C4⋊C4—1061no—
710C4⋊C4—1061no—
711C4⋊C4—1061no—
712C4⋊C4—1061no—
713C4⋊C4—1061no—
714C4⋊C4—1061no—
715C4⋊C4—1061no—
716C4⋊C4—1061no—
717C4⋊C4—1061no—
718C4⋊C4—1061no—
719C4⋊C4—1061no—
720C4⋊C4—1061no—
721C4⋊C4—1061no—
722C4⋊C4—1061no—
723C4⋊C4#1171992111yescharacteristic
724C4⋊C4#1171992111yescharacteristic
725C4⋊C4#1171992111yescharacteristic
726C4⋊C4#1171992111yescharacteristic
727C4⋊C4#1171992111yescharacteristic
728C4⋊C4#1171992111yescharacteristic
729C4⋊C4#1171992111yescharacteristic
730C4⋊C4#1171992111yescharacteristic
731C22⋊C4—42no—
732C22⋊C4—1061no—
733C22⋊C4—1061no—
734C22⋊C4—1061no—
735C22⋊C4—1061no—
736C22⋊C4—1061no—
737C22⋊C4—1061no—
738C22⋊C4—1061no—
739C22⋊C4—1061no—
740C22⋊C4—1061no—
741C22⋊C4—1061no—
742C22⋊C4—1061no—
743C22⋊C4—1061no—
744C22⋊C4—1061no—
745C22⋊C4—1061no—
746C22⋊C4—1061no—
747C22⋊C4#1171992111yescharacteristic
748C22⋊C4#1171992111yescharacteristic
749C22⋊C4#1171992111yescharacteristic
750C22⋊C4#1171992111yescharacteristic
751C22⋊C4#1171992111yescharacteristic
752C22⋊C4#1171992111yescharacteristic
753C22⋊C4#1171992111yescharacteristic
754C22⋊C4#1171992111yescharacteristic
755C42—42no—
756C42—81no—
757C42—1061no—
758C42—1061no—
759C42—1061no—
760C42—1061no—
761C42—1061no—
762C42—1061no—
763C42—1061no—
764C42C2×C4×D5311yescharacteristic
765C42C2×C4×D5311yescharacteristic
766C42C2×C4×D5311yescharacteristic
767C42C2×C4×D5311yescharacteristic
768C42C2×D21211yescharacteristic
769C42C2×D21211yescharacteristic
770C42C2×D21211yescharacteristic
771C42C2×D21211yescharacteristic
772C23—22no—
773C23—21no—
774C23—21no—
775C23—41no—
776C23—1061no—
777C23C2×#1171992111yescharacteristic
778C23C2×#1171992111yescharacteristic
779C23C22×C22⋊D5311yescharacteristic
780Q8—4241no—
781Q8—4241no—
782Q8—2121no—
783Q8—2121no—
784Q8—2121no—
785Q8—2122no—
786D4—4241no—
787D4—2121no—
788D4—2122no—
789D4—2121no—
790D4—2121no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—22no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—84no—
816C2×C4—1061no—
817C2×C4—1061no—
818C2×C4—1061no—
819C2×C4—1061no—
820C2×C4—1061no—
821C2×C4—1061no—
822C2×C4—1061no—
823C2×C4—4241no—
824C2×C4—4241no—
825C2×C4—4241no—
826C2×C4—2122no—
827C2×C4—2122no—
828C2×C4C2×#1171992111yescharacteristic
829C2×C4C2×#1171992111yescharacteristic
830C2×C4C2×#1171992111yescharacteristic
831C2×C4C2×#1171992111yescharacteristic
832C2×C4C2×#1171992111yescharacteristic
833C2×C4C2×#1171992111yescharacteristic
834C2×C4C2×#1171992111yescharacteristic
835C2×C4C2×#1171992111yescharacteristic
836C2×C4C2×#1171992111yescharacteristic
837C2×C4C2×#1171992111yescharacteristic
838C2×C4C22×C4×D5311yescharacteristic
839C2×C4C22×D21211yescharacteristic
840C8—2121no—
841C8—2121no—
842C8—2121no—
843C8—2121no—
844C22—21no—
845C22—21no—
846C22—21no—
847C22—21no—
848C22—21no—
849C22—21no—
850C22—21no—
851C22—42no—
852C22—42no—
853C22—2121no—
854C22—2121no—
855C22—2121no—
856C22#1681059612yes—
857C22C22×#1171992111yescharacteristic
858C22#1681143411yescharacteristic
859C22#1681143811yescharacteristic
860C4—21no—
861C4—21no—
862C4—21no—
863C4—21no—
864C4—21no—
865C4—21no—
866C4—21no—
867C4—21no—
868C4—21no—
869C4—21no—
870C4—21no—
871C4—21no—
872C4—42no—
873C4—81no—
874C4—81no—
875C4—81no—
876C4—2121no—
877C4—2121no—
878C4—2121no—
879C4—2121no—
880C4—2121no—
881C4—2121no—
882C4—2121no—
883C2—21no—
884C2—21no—
885C2—22no—
886C2—41no—
887C2—4241no—
888C2C2×#1681059611yescharacteristic
889C2#2028324511yescharacteristic
890C2#2028326311yescharacteristic
subgroupG/H
centerC22C22×#11719921
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#2343C2
socleC22×C53C22×C22⋊C4
prime radical#16811134C22
cosocleC22×C4×C53C24
hypercenter#2343D53
hypocenterC53#17609
LCSG ▷ C2×C4×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ C2×#117 ◁ #2343

Complements

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

NH ≅ G/Ntype
2. #20283373C2semidirect
3. #20273290C2semidirect
4. #20273278C2semidirect
6. #20273265C2semidirect
7. #20273251C2semidirect
8. #20273247C2semidirect
9. #20273238C2semidirect
10. #20273226C2semidirect
12. #20273213C2semidirect
13. #20273199C2semidirect
14. C2×#16810359C2semidirect
15. C53×#2343C2semidirect
24. #16811251C4semidirect
25. #16811244C4semidirect
26. #16811244C4semidirect
27. #16811235C4semidirect
28. #16811235C4semidirect
29. #16811199C4semidirect
36. #16811103C4semidirect
37. #16811100C4semidirect
79. #13133217C2×C4semidirect
80. #13133217C2×C4semidirect
81. #13133217C2×C4semidirect
82. #13133217C2×C4semidirect
94. #13133209C2×C4semidirect
95. #13133209C2×C4semidirect
101. #13133205C2×C4semidirect
102. #13133205C2×C4semidirect
133. C4×Dic106C2×C4semidirect
134. C4×Dic106C2×C4semidirect
135. C4×Dic106C2×C4semidirect
136. C4×Dic106C2×C4semidirect
137. C4×Dic106C2×C4semidirect
138. C4×Dic106C2×C4semidirect
141. C4×D212C2×C4semidirect
142. C4×D212C2×C4semidirect
440. #2343D53semidirect
520. C53#17609semidirect

Maximal subgroups

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

subgroupindex
#202884672
#202833732
#202732902
#202732782
#202732692
#202732652
#202732512
#202732472
#202732382
#202732262
#202732172
#202732132
#202731992
C2×#168103592
C53×#23432
#1760953