Finite Group Databasebeta

← #27351134

Subgroups — #27351134

Order 13568.

936 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288330C211yesmaximal, characteristic
2#20283359C211yesmaximal, characteristic, complemented
3#20273187C211yesmaximal, characteristic, complemented
4#20273178C211yesmaximal, characteristic, complemented
5#20273173C211yesmaximal, characteristic, complemented
6#20273161C211yesmaximal, characteristic, complemented
7#20273147C211yesmaximal, characteristic, complemented
8#20273143C211yesmaximal, characteristic, complemented
9#20273126C211yesmaximal, characteristic, complemented
10#20273121C211yesmaximal, characteristic, complemented
11#20273117C211yesmaximal, characteristic, complemented
12#20273109C211yesmaximal, characteristic, complemented
13#20273100C211yesmaximal, characteristic, complemented
14C2×#16810353C211yesmaximal, characteristic, complemented
15C53×#2990C211yesmaximal, characteristic, complemented
16#16811351C411yescharacteristic
17#16811346C411yescharacteristic
18#16811341—21no—
19#16811313C411yescharacteristic
20#16811313C411yescharacteristic
21#16811306—21no—
22#16811306—21no—
23D4×Dic106C411yescharacteristic
24#16811282C411yescharacteristic
25#16811282C411yescharacteristic
26#16811277C411yescharacteristic
27#16811272—21no—
28#16811180C2211yescharacteristic
29#16811177—21no—
30#16811157C2211yescharacteristic
31#16811157C2211yescharacteristic
32#16811153—21no—
33#16811153—21no—
34C4×#11719945C2211yescharacteristic
35C4×#11719947—21no—
36C2×C4×Dic106C2211yescharacteristic
37C2×C4×Dic106C2211yescharacteristic
38#16810684—21no—
39#16810684—21no—
40#16810676C2211yescharacteristic
41#16810676C2211yescharacteristic
42#16810676C2211yescharacteristic
43#16810676C2211yescharacteristic
44#16810650—21no—
45#16810590—21no—
46C4×#11719917C2211yescharacteristic
47C2×C4×#88322C2211yescharacteristic
48#16810353C2211yescharacteristic
49#16810353C2211yescharacteristic
50#16810353C2211yescharacteristic
51#16810353C2211yescharacteristic
52#16810353C2211yescharacteristic
53#16810353C2211yescharacteristic
54#16810353C2211yescharacteristic
55#16810353C2211yescharacteristic
56#16810353C2211yescharacteristic
57#16810353C2211yescharacteristic
58#16810353C2211yescharacteristic
59#16810353C2211yescharacteristic
60#16810350C2211yescharacteristic
61#16810350C2211yescharacteristic
62#16810350C2211yescharacteristic
63#16810350C2211yescharacteristic
64C4×#41×C53C2211yescharacteristic
65C53×#446—21no—
66C53×#435—21no—
67C53×#435—21no—
68C8×D4×C53—21no—
69C53×#432C2211yescharacteristic
70C53×#432C2211yescharacteristic
71C53×#431C2211yescharacteristic
72C53×#423C2211yescharacteristic
73C2×C4⋊C8×C53C2211yescharacteristic
74C2×C4⋊C8×C53C2211yescharacteristic
75C2×#11719945C2×C411yescharacteristic
76C2×#11719947—21no—
77C22×Dic106C2×C411yescharacteristic
78C22×Dic106C2×C411yescharacteristic
79C2×#11719917—21no—
80C22×#88322—21no—
81#13133217C2×C411yescharacteristic
82#13133217C2×C411yescharacteristic
83#13133216—21no—
84#13133215—21no—
85#13133212—21no—
86#13133212—21no—
87#13133211—21no—
88#13133211—21no—
89#13133210—21no—
90#13133210—21no—
91#13133209—21no—
92#13133209C2×C411yescharacteristic
93#13133209C2×C411yescharacteristic
94#13133207—21no—
95#13133207—21no—
96#13133207—21no—
97#13133207—21no—
98#13133205C2×C411yescharacteristic
99#13133205C2×C411yescharacteristic
100#13133203—21no—
101#13133203—21no—
102#13133201—21no—
103#13133201—21no—
104#13133200—21no—
105#13133200—21no—
106#13133198—21no—
107#13133198—21no—
108#13133197—21no—
109#13133196—21no—
110#13133196C2×C411yescharacteristic
111#13133196C2×C411yescharacteristic
112#13133196C2×C411yescharacteristic
113#13133196C2×C411yescharacteristic
114#13133195—21no—
115#13133195—21no—
116#13133194—21no—
117#13133194—21no—
118#13133193—21no—
119#13133191C2×C411yescharacteristic
120#13133191C2×C411yescharacteristic
121#13133189—21no—
122#13133189—21no—
123C4×Dic106—21no—
124C4×Dic106—21no—
125C4×Dic106—21no—
126C4×Dic106—21no—
127C4×Dic106—21no—
128C4×Dic106C2×C411yescharacteristic
129C4×Dic106C2×C411yescharacteristic
130C4×Dic106C2×C411yescharacteristic
131C4×Dic106C2×C411yescharacteristic
132C4×Dic106C2×C411yescharacteristic
133C4×Dic106C2311yescharacteristic
134C4×Dic106C2311yescharacteristic
135C4×Dic106C2311yescharacteristic
136#13133182—21no—
137C4×D212C2×C411yescharacteristic
138C4×D212C2311yescharacteristic
139D4×Dic53—21no—
140C4×C22⋊D53—21no—
141C4×C22⋊D53—21no—
142C4×C22⋊D53—21no—
143C4×C22⋊D53—21no—
144#13133177—21no—
145#13133177—21no—
146#13133176—21no—
147#13133176C2×C411yescharacteristic
148#13133175—21no—
149#13133174—21no—
150#13133174—21no—
151#13133174—21no—
152#13133173—21no—
153#13133173—21no—
154C2×C4⋊Dic53C2×C411yescharacteristic
155C2×C4⋊Dic53C2×C411yescharacteristic
156C2×#11719919—21no—
157C2×#11719919—21no—
158C2×C4×Dic53—21no—
159C2×C4×Dic53—21no—
160C42×D53—21no—
161C4⋊#88322—21no—
162C4⋊#88322—21no—
163C4⋊#88322—21no—
164C4⋊#88322—21no—
165C22⋊#88322—21no—
166C22⋊#88322—21no—
167C22⋊#88322—21no—
168C22⋊#88322—21no—
169#13133128—21no—
170C4×#88322—21no—
171C4×#88322C2311yescharacteristic
172C4×#88322C2311yescharacteristic
173C4×#88322C2311yescharacteristic
174C4×#88322C2311yescharacteristic
175C2×#41×C53D411yescharacteristic
176C2×M16×C53—21no—
177C22×C8×C53—21no—
178C22×C8×C53—21no—
179C4×Q8×C53C2×C411yescharacteristic
180C4×Q8×C53D411yescharacteristic
181C4×D4×C53C2×C411yescharacteristic
182C4×D4×C53C2×C411yescharacteristic
183C4×D4×C53C2×C411yescharacteristic
184C4×D4×C53D411yescharacteristic
185C4×D4×C53D411yescharacteristic
186C4×D4×C53D411yescharacteristic
187#117×C53D411yescharacteristic
188#117×C53D411yescharacteristic
189#117×C53D411yescharacteristic
190C2×C42×C53C2311yescharacteristic
191C2×C42×C53C2311yescharacteristic
192C2×C42×C53C2311yescharacteristic
193C4⋊C8×C53—21no—
194C4⋊C8×C53—21no—
195C4⋊C8×C53—21no—
196C4⋊C8×C53C2311yescharacteristic
197C4⋊C8×C53C2311yescharacteristic
198C4⋊C8×C53C2311yescharacteristic
199C4⋊C8×C53C2311yescharacteristic
200C22⋊C8×C53—21no—
201C22⋊C8×C53—21no—
202C22⋊C8×C53—21no—
203#97×C53—21no—
204#97×C53—21no—
205C4×C8×C53—21no—
206#41×C53—42no—
207C2×Q8×C53C22⋊C411yescharacteristic
208C2×D4×C53C22⋊C411yescharacteristic
209C2×D4×C53C22⋊C411yescharacteristic
210C2×D4×C53C22⋊C411yescharacteristic
211C22×C4×C53C22×C411yescharacteristic
212C22×C4×C53C22×C411yescharacteristic
213C22×C4×C53C22×C411yescharacteristic
214C22×C4×C53C2×D411yescharacteristic
215C22×C4×C53C2×D411yescharacteristic
216C22×C4×C53C2×D411yescharacteristic
217C22×C4×C53C2×D411yescharacteristic
218C22×C4×C53C2×D411yescharacteristic
219C22×C4×C53C2×D411yescharacteristic
220C2×C22⋊D53—21no—
221C2×C22⋊D53—21no—
222C2×C22⋊D53—21no—
223C22×Dic53—21no—
224C22×Dic53—21no—
225C22×Dic53—21no—
226C22×Dic53—21no—
227#11719947—44no—
228#11719945—22no—
229#11719945—41no—
230C2×D212C22×C411yescharacteristic
231C2×C4×D53—21no—
232C2×C4×D53—21no—
233C2×C4×D53—21no—
234C2×Dic106—22no—
235C2×Dic106—22no—
236C2×Dic106—21no—
237C2×Dic106—21no—
238C2×Dic106—21no—
239C2×Dic106—41no—
240C2×Dic106—41no—
241C2×Dic106C22×C411yescharacteristic
242C2×Dic106C22×C411yescharacteristic
243C2×Dic106C22×C411yescharacteristic
244M16×C53—81no—
245C2×C8×C53—21no—
246C2×C8×C53—21no—
247C2×C8×C53—21no—
248C2×C8×C53—21no—
249C2×C8×C53—81no—
250C2×C8×C53—81no—
251C4⋊C4×C53C22⋊C411yescharacteristic
252C4⋊C4×C53C22⋊C411yescharacteristic
253C4⋊C4×C53C22⋊C411yescharacteristic
254C4⋊C4×C53C22⋊C411yescharacteristic
255C4⋊C4×C53C22⋊C411yescharacteristic
256C4⋊C4×C53C22⋊C411yescharacteristic
257C22⋊C4×C53C22⋊C411yescharacteristic
258C22⋊C4×C53C22⋊C411yescharacteristic
259C22⋊C4×C53C22⋊C411yescharacteristic
260C22⋊C4×C53C22⋊C411yescharacteristic
261C22⋊C4×C53C22⋊C411yescharacteristic
262C22⋊C4×C53C22⋊C411yescharacteristic
263C42×C53C22×C411yescharacteristic
264C42×C53C22×C411yescharacteristic
265C42×C53C22×C411yescharacteristic
266C42×C53C2×D411yescharacteristic
267C42×C53C2×D411yescharacteristic
268C42×C53C2×D411yescharacteristic
269C42×C53C2×D411yescharacteristic
270C42×C53C2×D411yescharacteristic
271C42×C53C2×D411yescharacteristic
272C42×C53C2411yescharacteristic
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⋊Dic53C22×C411yescharacteristic
292C4⋊Dic53C22×C411yescharacteristic
293C4⋊Dic53C22×C411yescharacteristic
294C4⋊Dic53C22×C411yescharacteristic
295#11719919—21no—
296#11719919—21no—
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—
311C4×Dic53—21no—
312C4×Dic53—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×C53C2×C22⋊C411yescharacteristic
327C23×C53C2×C22⋊C411yescharacteristic
328C23×C53C2×C22⋊C411yescharacteristic
329C22×D53—21no—
330Q8×C53—41no—
331D4×C53—22no—
332D4×C53—22no—
333D4×C53—41no—
334C2×C4×C53—22no—
335C2×C4×C53—21no—
336C2×C4×C53—21no—
337C2×C4×C53—21no—
338C2×C4×C53—21no—
339C2×C4×C53—21no—
340C2×C4×C53—21no—
341C2×C4×C53—21no—
342C2×C4×C53—21no—
343C2×C4×C53—21no—
344C2×C4×C53—21no—
345C2×C4×C53—21no—
346C2×C4×C53—21no—
347C2×C4×C53—41no—
348C2×C4×C53—41no—
349C2×C4×C53C2×C22⋊C411yescharacteristic
350C2×C4×C53C2×C22⋊C411yescharacteristic
351C2×C4×C53C2×C22⋊C411yescharacteristic
352C2×C4×C53C2×C22⋊C411yescharacteristic
353C2×C4×C53C2×C22⋊C411yescharacteristic
354C2×C4×C53C2×C22⋊C411yescharacteristic
355C2×C4×C53C2×C22⋊C411yescharacteristic
356C2×C4×C53C2×C22⋊C411yescharacteristic
357C2×C4×C53C2×C22⋊C411yescharacteristic
358C2×C4×C53C23×C411yescharacteristic
359C2×C4×C53C22×D411yescharacteristic
360C2×C4×C53C22×D411yescharacteristic
361C22⋊D53—42no—
362C22⋊D53—42no—
363C22⋊D53—42no—
364C2×Dic53—21no—
365C2×Dic53—21no—
366C2×Dic53—21no—
367C2×Dic53—21no—
368C2×Dic53—21no—
369C2×Dic53—21no—
370C2×Dic53—21no—
371C2×Dic53—42no—
372C2×Dic53—42no—
373C2×Dic53—42no—
374C2×Dic53—42no—
375D212—21no—
376D212—21no—
377C4×D53—42no—
378C4×D53—42no—
379C4×D53—41no—
380C4×D53—41no—
381Dic106—21no—
382Dic106—21no—
383Dic106—21no—
384Dic106—21no—
385Dic106—21no—
386Dic106—42no—
387Dic106—42no—
388Dic106—42no—
389Dic106#13112yes—
390C8×C53—41no—
391C8×C53—41no—
392C8×C53—41no—
393C8×C53—41no—
394#88322—41no—
395#88322—41no—
396#88322—41no—
397#88322—41no—
398#17524—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—21no—
407C22×C53#42112yes—
408C22×C53C22×C22⋊C411yescharacteristic
409C2×D53—41no—
410C2×D53—41no—
411C2×D53—41no—
412C4×C53—21no—
413C4×C53—21no—
414C4×C53—21no—
415C4×C53—21no—
416C4×C53—21no—
417C4×C53—21no—
418C4×C53—21no—
419C4×C53—21no—
420C4×C53—21no—
421C4×C53—21no—
422C4×C53C2×#13111yescharacteristic
423C4×C53#56811yescharacteristic
424C4×C53#57711yescharacteristic
425C4×C53#57811yescharacteristic
426Dic53—22no—
427Dic53—41no—
428Dic53—41no—
429Dic53—41no—
430Dic53—41no—
431Dic53—41no—
432Dic53—41no—
433#3482—531no—
434#2990D5311yescharacteristic, complemented
435#2922—531no—
436#1497—531no—
437#1495—531no—
438#1494—531no—
439#1491—531no—
440#1488—531no—
441#1487—531no—
442#1483—531no—
443#1482—531no—
444#1481—531no—
445#1479—531no—
446#1477—531no—
447C2×Q8⋊C8—531no—
448C2×C53—22no—
449C2×C53—41no—
450C2×C53—41no—
451C2×C53#288011yescharacteristic
452C2×C53#289811yescharacteristic
453C2×C53C2×#42111yescharacteristic
454D53—81no—
455#557—531no—
456#556—531no—
457#556—1061no—
458#552—531no—
459#552—531no—
460#552—1061no—
461#552—1061no—
462D4×Q8—531no—
463#548—531no—
464#548—531no—
465#547—531no—
466#547—1061no—
467#533—531no—
468#533—1061no—
469#529—531no—
470#529—531no—
471#529—1061no—
472#529—1061no—
473C4×#41—531no—
474C4×#41—1061no—
475C4×#41C2×D5311yescharacteristic
476C2×C4×Q8—531no—
477C2×C4×Q8—531no—
478#446—21no—
479#435—21no—
480#435—21no—
481C8×D4—21no—
482#433—1061no—
483#433—1061no—
484#432C2×D5311yescharacteristic
485#432C2×D5311yescharacteristic
486#431—531no—
487#431—531no—
488#431—531no—
489#431—531no—
490#431C2×D5311yescharacteristic
491#424—1061no—
492#423C2×D5311yescharacteristic
493C2×C4⋊C8C2×D5311yescharacteristic
494C2×C4⋊C8C2×D5311yescharacteristic
495#408—1061no—
496C4×M16—531no—
497C2×C4×C8—531no—
498Q8⋊C8—531no—
499Q8⋊C8—531no—
500Q8⋊C8—531no—
501Q8⋊C8—531no—
502Q8⋊C8—531no—
503Q8⋊C8—531no—
504Q8⋊C8—531no—
505Q8⋊C8—531no—
506Q8⋊C8—531no—
507Q8⋊C8—531no—
508Q8⋊C8—531no—
509Q8⋊C8—531no—
510D4⋊C8—531no—
511D4⋊C8—531no—
512D4⋊C8—531no—
513D4⋊C8—531no—
514C53#1752411yescharacteristic, complemented, Sylow
515C2×#41—531no—
516C2×#41—1061no—
517C2×#41D21211yescharacteristic
518C22×Q8—531no—
519C22×Q8—531no—
520C2×M16—21no—
521C2×M16—1061no—
522C22×C8—21no—
523C22×C8—21no—
524C22×C8—1061no—
525C4⋊Q8—531no—
526C4⋊Q8—531no—
527C4⋊Q8—1061no—
528C4⋊Q8—1061no—
529#126—1061no—
530#126—1061no—
531#126—1061no—
532#126—1061no—
533#126—1061no—
534#126—1061no—
535#125—531no—
536#125—531no—
537#125—1061no—
538#125—1061no—
539#125—1061no—
540#125—1061no—
541#125—1061no—
542#124—531no—
543#124—531no—
544#124—1061no—
545#124—1061no—
546#123—1061no—
547#123—1061no—
548#123—1061no—
549#123—1061no—
550#123—1061no—
551#123—1061no—
552C22⋊Q8—531no—
553C22⋊Q8—531no—
554C22⋊Q8—531no—
555C22⋊Q8—531no—
556C22⋊Q8—1061no—
557C22⋊Q8—1061no—
558C22⋊Q8—1061no—
559C22⋊Q8—1061no—
560C22⋊Q8—1061no—
561C22⋊Q8—1061no—
562C22⋊Q8—1061no—
563#121—531no—
564#121—531no—
565#121—1061no—
566#121—1061no—
567C4×Q8—531no—
568C4×Q8—531no—
569C4×Q8—531no—
570C4×Q8—531no—
571C4×Q8—531no—
572C4×Q8—531no—
573C4×Q8—531no—
574C4×Q8—531no—
575C4×Q8—1061no—
576C4×Q8—1061no—
577C4×Q8—1061no—
578C4×Q8—1061no—
579C4×Q8—1061no—
580C4×Q8—1061no—
581C4×Q8C4×D5311yescharacteristic
582C4×Q8C22⋊D5311yescharacteristic
583C4×D4—531no—
584C4×D4—531no—
585C4×D4—1061no—
586C4×D4—1061no—
587C4×D4—1061no—
588C4×D4—1061no—
589C4×D4—1061no—
590C4×D4—1061no—
591C4×D4—1061no—
592C4×D4C4×D5311yescharacteristic
593C4×D4C4×D5311yescharacteristic
594C4×D4C4×D5311yescharacteristic
595C4×D4C22⋊D5311yescharacteristic
596C4×D4C22⋊D5311yescharacteristic
597C4×D4C22⋊D5311yescharacteristic
598#117—531no—
599#117—1061no—
600#117—1061no—
601#117—1061no—
602#117—1061no—
603#117—1061no—
604#117—1061no—
605#117—1061no—
606#117D21211yescharacteristic
607#117D21211yescharacteristic
608#117D21211yescharacteristic
609C2×C4⋊C4—531no—
610C2×C4⋊C4—531no—
611C2×C4⋊C4—1061no—
612C2×C4⋊C4—1061no—
613C2×C42—1061no—
614C2×C42—1061no—
615C2×C42—1061no—
616C2×C42C22×D5311yescharacteristic
617C2×C42C22×D5311yescharacteristic
618C2×C42C22×D5311yescharacteristic
619C4⋊C8—21no—
620C4⋊C8—21no—
621C4⋊C8—21no—
622C4⋊C8—1061no—
623C4⋊C8—1061no—
624C4⋊C8—1061no—
625C4⋊C8—1061no—
626C4⋊C8C22×D5311yescharacteristic
627C4⋊C8C22×D5311yescharacteristic
628C4⋊C8C22×D5311yescharacteristic
629C4⋊C8C22×D5311yescharacteristic
630C22⋊C8—21no—
631C22⋊C8—21no—
632C22⋊C8—21no—
633C22⋊C8—1061no—
634C22⋊C8—1061no—
635C22⋊C8—1061no—
636C22⋊C8—1061no—
637#97—21no—
638#97—21no—
639#97—1061no—
640C4×C8—21no—
641C4×C8—531no—
642C4×C8—531no—
643C4×C8—531no—
644C4×C8—531no—
645C4×C8—1061no—
646#41—42no—
647#41—1062no—
648#41—2121no—
649#41—2124no—
650C2×Q8—531no—
651C2×Q8—531no—
652C2×Q8—531no—
653C2×Q8—1062no—
654C2×Q8—1062no—
655C2×Q8—1061no—
656C2×Q8—1061no—
657C2×Q8—1061no—
658C2×Q8—2121no—
659C2×Q8—2121no—
660C2×Q8#1171992111yescharacteristic
661C2×D4—531no—
662C2×D4—1061no—
663C2×D4—1061no—
664C2×D4—1061no—
665C2×D4#1171992111yescharacteristic
666C2×D4#1171992111yescharacteristic
667C2×D4#1171992111yescharacteristic
668C22×C4—1061no—
669C22×C4—1061no—
670C22×C4—1061no—
671C22×C4—1061no—
672C22×C4—1061no—
673C22×C4—1061no—
674C22×C4—1061no—
675C22×C4C2×C4×D5311yescharacteristic
676C22×C4C2×C4×D5311yescharacteristic
677C22×C4C2×C4×D5311yescharacteristic
678C22×C4C2×D21211yescharacteristic
679C22×C4C2×D21211yescharacteristic
680C22×C4C2×D21211yescharacteristic
681C22×C4C2×C22⋊D5311yescharacteristic
682C22×C4C2×C22⋊D5311yescharacteristic
683C22×C4C2×C22⋊D5311yescharacteristic
684M16—81no—
685M16—2122no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—81no—
691C2×C8—81no—
692C2×C8—1061no—
693C2×C8—1061no—
694C2×C8—1061no—
695C2×C8—1061no—
696C2×C8—2122no—
697C4⋊C4—531no—
698C4⋊C4—531no—
699C4⋊C4—531no—
700C4⋊C4—531no—
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#1171992111yescharacteristic
723C4⋊C4#1171992111yescharacteristic
724C4⋊C4#1171992111yescharacteristic
725C4⋊C4#1171992111yescharacteristic
726C4⋊C4#1171992111yescharacteristic
727C4⋊C4#1171992111yescharacteristic
728C22⋊C4—1061no—
729C22⋊C4—1061no—
730C22⋊C4—1061no—
731C22⋊C4—1061no—
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#1171992111yescharacteristic
742C22⋊C4#1171992111yescharacteristic
743C22⋊C4#1171992111yescharacteristic
744C22⋊C4#1171992111yescharacteristic
745C22⋊C4#1171992111yescharacteristic
746C22⋊C4#1171992111yescharacteristic
747C42—1061no—
748C42—1061no—
749C42—1061no—
750C42—1061no—
751C42—1061no—
752C42—1061no—
753C42—1061no—
754C42—1061no—
755C42—1061no—
756C42C2×C4×D5311yescharacteristic
757C42C2×C4×D5311yescharacteristic
758C42C2×C4×D5311yescharacteristic
759C42C2×D21211yescharacteristic
760C42C2×D21211yescharacteristic
761C42C2×D21211yescharacteristic
762C42C2×C22⋊D5311yescharacteristic
763C42C2×C22⋊D5311yescharacteristic
764C42C2×C22⋊D5311yescharacteristic
765C42C23×D5311yescharacteristic
766C23—1061no—
767C23C2×#1171992111yescharacteristic
768C23C2×#1171992111yescharacteristic
769C23C2×#1171992111yescharacteristic
770Q8—41no—
771Q8—532no—
772Q8—1061no—
773Q8—1061no—
774Q8—1061no—
775Q8—1061no—
776Q8—1061no—
777Q8—2122no—
778Q8—2122no—
779Q8—2122no—
780D4—22no—
781D4—22no—
782D4—41no—
783D4—1061no—
784D4—1061no—
785D4—2122no—
786D4—2122no—
787D4—2122no—
788C2×C4—22no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—1061no—
804C2×C4—1061no—
805C2×C4—1061no—
806C2×C4—1061no—
807C2×C4—1061no—
808C2×C4—1061no—
809C2×C4—1061no—
810C2×C4—2122no—
811C2×C4—2122no—
812C2×C4—2122no—
813C2×C4—2122no—
814C2×C4—2122no—
815C2×C4—2122no—
816C2×C4—2121no—
817C2×C4—2121no—
818C2×C4C2×#1171992111yescharacteristic
819C2×C4C2×#1171992111yescharacteristic
820C2×C4C2×#1171992111yescharacteristic
821C2×C4C2×#1171992111yescharacteristic
822C2×C4C2×#1171992111yescharacteristic
823C2×C4C2×#1171992111yescharacteristic
824C2×C4C2×#1171992111yescharacteristic
825C2×C4C2×#1171992111yescharacteristic
826C2×C4C2×#1171992111yescharacteristic
827C2×C4C22×C4×D5311yescharacteristic
828C2×C4C22×C22⋊D5311yescharacteristic
829C2×C4C22×D21211yescharacteristic
830C8—41no—
831C8—41no—
832C8—41no—
833C8—41no—
834C8—2121no—
835C8—2121no—
836C8—2121no—
837C8—2121no—
838C22—21no—
839C22—21no—
840C22—21no—
841C22—21no—
842C22—21no—
843C22—21no—
844C22—21no—
845C22—21no—
846C22—2121no—
847C22—2121no—
848C22—2121no—
849C22#1681063912yes—
850C22C22×#1171992111yescharacteristic
851C4—21no—
852C4—21no—
853C4—21no—
854C4—21no—
855C4—21no—
856C4—21no—
857C4—21no—
858C4—21no—
859C4—21no—
860C4—21no—
861C4—1062no—
862C4—2121no—
863C4—2121no—
864C4—2121no—
865C4—2121no—
866C4—2121no—
867C4—2121no—
868C4#131×D5311yescharacteristic
869C4#1681138811yescharacteristic
870C4#1681143411yescharacteristic
871C4#1681143811yescharacteristic
872C2—22no—
873C2—41no—
874C2—41no—
875C2—4241no—
876C2#2028316211yescharacteristic
877C2#2028324511yescharacteristic
878C2C2×#1681063911yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D53
commutatorC2×C4×C53C23×C4
FrattiniC42C23×D53
FittingC53×#2990C2
socleC22×C53C22×C22⋊C4
prime radical#20288330C2
cosocleC42×C53C24
hypercenter#2990D53
hypocenterC53#17524
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #2990

Complements

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

NH ≅ G/Ntype
2. #20283359C2semidirect
3. #20273187C2semidirect
4. #20273178C2semidirect
5. #20273173C2semidirect
6. #20273161C2semidirect
7. #20273147C2semidirect
8. #20273143C2semidirect
9. #20273126C2semidirect
10. #20273121C2semidirect
11. #20273117C2semidirect
12. #20273109C2semidirect
13. #20273100C2semidirect
14. C2×#16810353C2semidirect
15. C53×#2990C2semidirect
434. #2990D53semidirect
514. C53#17524semidirect

Maximal subgroups

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

subgroupindex
#202883302
#202833592
#202731872
#202731782
#202731732
#202731612
#202731472
#202731432
#202731262
#202731212
#202731172
#202731092
#202731002
C2×#168103532
C53×#29902
#1752453