Finite Group Databasebeta

← #27352241

Subgroups — #27352241

Order 13568.

942 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288676C211yesmaximal, characteristic
2#20283366C211yesmaximal, characteristic, complemented
3#20273349C211yesmaximal, characteristic, complemented
4#20273347C211yesmaximal, characteristic, complemented
5#20273344C211yesmaximal, characteristic, complemented
6#20273338C211yesmaximal, characteristic, complemented
7#20273336C211yesmaximal, characteristic, complemented
8#20273333C211yesmaximal, characteristic, complemented
9#20273325C211yesmaximal, characteristic, complemented
10#20273320C211yesmaximal, characteristic, complemented
11#20273314C211yesmaximal, characteristic, complemented
12#20273312C211yesmaximal, characteristic, complemented
13#20273301C211yesmaximal, characteristic, complemented
14C2×#16810362C211yesmaximal, characteristic, complemented
15C53×#2970C211yesmaximal, characteristic, complemented
16#16811358C411yescharacteristic
17#16811346C411yescharacteristic
18#16811336—21no—
19#16811297—21no—
20#16811297—21no—
21D4×Dic106C411yescharacteristic
22#16811282C411yescharacteristic
23#16811282C411yescharacteristic
24#16811269C411yescharacteristic
25#16811269C411yescharacteristic
26#16811261—21no—
27D4×D212C411yescharacteristic
28#16811245—21no—
29#16811206—21no—
30#16811206—21no—
31#16811173C2211yescharacteristic
32#16811157C2211yescharacteristic
33#16811157C2211yescharacteristic
34#16811157C2211yescharacteristic
35C2×#13133205C2211yescharacteristic
36C2×#13133205C2211yescharacteristic
37#16811095—21no—
38#16810684—21no—
39#16810684—21no—
40#16810680C2211yescharacteristic, complemented
41#16810680C2211yescharacteristic, complemented
42#16810680C2211yescharacteristic, complemented
43#16810680C2211yescharacteristic, complemented
44#16810650—21no—
45#16810590—21no—
46C4×#11719917C2211yescharacteristic, complemented
47C2×#13133128C2211yescharacteristic, complemented
48#16810364C2211yescharacteristic, complemented
49#16810364C2211yescharacteristic, complemented
50#16810364C2211yescharacteristic, complemented
51#16810364C2211yescharacteristic, complemented
52#16810362C2211yescharacteristic
53#16810362C2211yescharacteristic
54#16810362C2211yescharacteristic
55#16810362C2211yescharacteristic
56#16810362C2211yescharacteristic, complemented
57#16810362C2211yescharacteristic, complemented
58#16810362C2211yescharacteristic, complemented
59#16810362C2211yescharacteristic, complemented
60#16810362C2211yescharacteristic, complemented
61#16810362C2211yescharacteristic, complemented
62#16810362C2211yescharacteristic, complemented
63#16810362C2211yescharacteristic, complemented
64C4×#41×C53C2211yescharacteristic
65C53×#446—21no—
66C53×#435—21no—
67C53×#435—21no—
68C8×D4×C53—21no—
69C53×#432C2211yescharacteristic, complemented
70C53×#432C2211yescharacteristic, complemented
71C53×#432C2211yescharacteristic, complemented
72C4×M16×C53C2211yescharacteristic, complemented
73C2×#97×C53C2211yescharacteristic, complemented
74C2×#97×C53C2211yescharacteristic, complemented
75C2×#11719945C2×C411yescharacteristic
76C2×#11719945C2×C411yescharacteristic
77C22×Dic106C2×C411yescharacteristic
78C22×Dic106C2×C411yescharacteristic
79C22×D212C2×C411yescharacteristic
80C22×D212C2×C411yescharacteristic
81C2×D4×D53—21no—
82C2×#11719917—21no—
83C22×#88322—21no—
84#13133217C2×C411yescharacteristic
85#13133216—21no—
86#13133214C2×C411yescharacteristic
87#13133212—21no—
88#13133212—21no—
89#13133211—21no—
90#13133211—21no—
91#13133211—21no—
92#13133209C2311yescharacteristic
93#13133206—21no—
94#13133205—21no—
95#13133205—21no—
96#13133205—21no—
97#13133205—21no—
98#13133205C2×C411yescharacteristic
99#13133205C2×C411yescharacteristic
100#13133205C2×C411yescharacteristic
101#13133205C2×C411yescharacteristic
102#13133205C2311yescharacteristic
103#13133205C2311yescharacteristic
104#13133205C2311yescharacteristic
105#13133203—21no—
106#13133203—21no—
107#13133202—21no—
108#13133202—21no—
109#13133202—21no—
110#13133202—21no—
111#13133200—21no—
112#13133200—21no—
113#13133200—21no—
114#13133196C2×C411yescharacteristic
115#13133196C2×C411yescharacteristic
116#13133196C2×C411yescharacteristic
117#13133195—21no—
118#13133195—21no—
119#13133194—21no—
120#13133194—21no—
121#13133193—21no—
122#13133192—21no—
123#13133191—21no—
124#13133191—21no—
125#13133191C2×C411yescharacteristic
126#13133191C2×C411yescharacteristic
127#13133191C2×C411yescharacteristic
128#13133190—21no—
129#13133190—21no—
130#13133189—21no—
131#13133189—21no—
132#13133187—21no—
133#13133187—21no—
134#13133185—21no—
135#13133185—21no—
136C4×Dic106C2×C411yescharacteristic
137C4×Dic106C2×C411yescharacteristic
138C4×Dic106C2×C411yescharacteristic
139C4×D212—21no—
140C4×D212—21no—
141C4×D212C2×C411yescharacteristic
142C4×D212C2×C411yescharacteristic
143C4×D212C2×C411yescharacteristic
144D4×Dic53—21no—
145#13133179—21no—
146C4×C22⋊D53—21no—
147C4×C22⋊D53—21no—
148C4×C22⋊D53—21no—
149#13133177—21no—
150#13133177—21no—
151#13133175—21no—
152#13133174—21no—
153#13133174—21no—
154#13133174—21no—
155C2×#11719921—21no—
156C2×#11719921—21no—
157C2×#11719921—21no—
158C2×#11719921—21no—
159C22⋊C4×D53—21no—
160C22⋊C4×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—
170#13133128C2311yescharacteristic
171#13133128C2311yescharacteristic
172#13133128C2311yescharacteristic
173#13133128C2311yescharacteristic
174C4×#88322—21no—
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—
196C22⋊C8×C53—21no—
197C22⋊C8×C53—21no—
198C22⋊C8×C53—21no—
199#97×C53—21no—
200#97×C53—21no—
201#97×C53C2311yescharacteristic
202#97×C53C2311yescharacteristic
203#97×C53C2311yescharacteristic
204#97×C53C2311yescharacteristic
205C4×C8×C53—21no—
206C23×D53—21no—
207C23×D53—21no—
208#41×C53—42no—
209C2×Q8×C53C22⋊C411yescharacteristic
210C2×D4×C53C22⋊C411yescharacteristic
211C2×D4×C53C22⋊C411yescharacteristic
212C2×D4×C53C22⋊C411yescharacteristic
213C22×C4×C53C22×C411yescharacteristic
214C22×C4×C53C22×C411yescharacteristic
215C22×C4×C53C22×C411yescharacteristic
216C22×C4×C53C2×D411yescharacteristic
217C22×C4×C53C2×D411yescharacteristic
218C22×C4×C53C2×D411yescharacteristic
219C22×C4×C53C2×D411yescharacteristic
220C22×C4×C53C2×D411yescharacteristic
221C22×C4×C53C2×D411yescharacteristic
222C2×C22⋊D53—21no—
223C2×C22⋊D53—21no—
224C2×C22⋊D53—21no—
225C2×C22⋊D53—21no—
226C2×C22⋊D53—21no—
227C22×Dic53—21no—
228C22×Dic53—21no—
229D4×D53—44no—
230#11719945—81no—
231#11719945—81no—
232C2×D212—21no—
233C2×D212—21no—
234C2×D212—21no—
235C2×D212—21no—
236C2×D212—81no—
237C2×D212—81no—
238C2×D212C22×C411yescharacteristic
239C2×D212C22×C411yescharacteristic
240C2×D212C22×C411yescharacteristic
241C2×C4×D53—21no—
242C2×C4×D53—21no—
243C2×C4×D53—21no—
244C2×C4×D53—21no—
245C2×C4×D53—21no—
246C2×Dic106—21no—
247C2×Dic106—21no—
248C2×Dic106—81no—
249C2×Dic106—81no—
250C2×Dic106C22×C411yescharacteristic
251C2×Dic106C22×C411yescharacteristic
252C2×Dic106C22×C411yescharacteristic
253M16×C53—42no—
254C2×C8×C53—21no—
255C2×C8×C53—21no—
256C2×C8×C53—21no—
257C2×C8×C53—21no—
258C2×C8×C53—42no—
259C2×C8×C53—42no—
260C4⋊C4×C53C22⋊C411yescharacteristic
261C4⋊C4×C53C22⋊C411yescharacteristic
262C4⋊C4×C53C22⋊C411yescharacteristic
263C4⋊C4×C53C22⋊C411yescharacteristic
264C4⋊C4×C53C22⋊C411yescharacteristic
265C4⋊C4×C53C22⋊C411yescharacteristic
266C22⋊C4×C53C22⋊C411yescharacteristic
267C22⋊C4×C53C22⋊C411yescharacteristic
268C22⋊C4×C53C22⋊C411yescharacteristic
269C22⋊C4×C53C22⋊C411yescharacteristic
270C22⋊C4×C53C22⋊C411yescharacteristic
271C22⋊C4×C53C22⋊C411yescharacteristic
272C42×C53C22×C411yescharacteristic
273C42×C53C22×C411yescharacteristic
274C42×C53C22×C411yescharacteristic
275C42×C53C2×D411yescharacteristic
276C42×C53C2×D411yescharacteristic
277C42×C53C2×D411yescharacteristic
278C42×C53C2×D411yescharacteristic
279C42×C53C2×D411yescharacteristic
280C42×C53C2×D411yescharacteristic
281C42×C53C2411yescharacteristic
282C22⋊Dic53—21no—
283C22⋊Dic53—21no—
284C22⋊Dic53—21no—
285#11719921—21no—
286#11719921—21no—
287#11719921—21no—
288#11719921—21no—
289#11719921—21no—
290#11719921—21no—
291#11719921—21no—
292#11719921—21no—
293#11719921—21no—
294#11719921—21no—
295#11719921—21no—
296#11719921—21no—
297#11719921—21no—
298#11719921—21no—
299#11719921—21no—
300#11719921—21no—
301#11719921—21no—
302#11719921—21no—
303#11719921—21no—
304#11719921—21no—
305C4⋊Dic53—21no—
306C4⋊Dic53—21no—
307C4⋊Dic53C22×C411yescharacteristic
308C4⋊Dic53C22×C411yescharacteristic
309#11719919—21no—
310#11719919—21no—
311#11719919—21no—
312#11719919—21no—
313#11719919—21no—
314#11719919—21no—
315#11719919—21no—
316#11719919—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—
330C22×D53—21no—
331C22×D53—21no—
332C22×D53—42no—
333C22×D53—42no—
334C22×D53—81no—
335C22×D53—81no—
336C22×D53—81no—
337C22×D53—81no—
338Q8×C53—41no—
339D4×C53—22no—
340D4×C53—22no—
341D4×C53—41no—
342C2×C4×C53—22no—
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×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×C53C2×C22⋊C411yescharacteristic
359C2×C4×C53C2×C22⋊C411yescharacteristic
360C2×C4×C53C23×C411yescharacteristic
361C2×C4×C53C22×D411yescharacteristic
362C2×C4×C53C22×D411yescharacteristic
363C22⋊D53—42no—
364C22⋊D53—42no—
365C22⋊D53—81no—
366C22⋊D53—81no—
367C22⋊D53—81no—
368C2×Dic53—21no—
369C2×Dic53—21no—
370C2×Dic53—21no—
371C2×Dic53—21no—
372C2×Dic53—21no—
373C2×Dic53—81no—
374C2×Dic53—81no—
375D212—41no—
376D212—41no—
377D212—41no—
378D212—42no—
379D212—81no—
380D212—81no—
381D212—81no—
382C4×D53—42no—
383C4×D53—81no—
384C4×D53—81no—
385C4×D53—81no—
386C4×D53—81no—
387Dic106—41no—
388Dic106—41no—
389Dic106—41no—
390Dic106—81no—
391Dic106—81no—
392C8×C53—22no—
393C8×C53—41no—
394C8×C53—41no—
395C8×C53—41no—
396#88322—41no—
397#88322—41no—
398#88322—41no—
399#88322—41no—
400#17679—531nomaximal, Sylow
401C22×C53—21no—
402C22×C53—21no—
403C22×C53—21no—
404C22×C53—21no—
405C22×C53—21no—
406C22×C53—21no—
407C22×C53—21no—
408C22×C53—21no—
409C22×C53#42112yes—
410C22×C53C22×C22⋊C411yescharacteristic
411C2×D53—41no—
412C2×D53—41no—
413C2×D53—41no—
414C2×D53—41no—
415C2×D53—41no—
416C2×D53—41no—
417C2×D53—41no—
418C2×D53—41no—
419C2×D53—41no—
420C2×D53—162no—
421C2×D53—162no—
422C4×C53—21no—
423C4×C53—21no—
424C4×C53—21no—
425C4×C53—21no—
426C4×C53—21no—
427C4×C53—21no—
428C4×C53—21no—
429C4×C53—21no—
430C4×C53—21no—
431C4×C53—21no—
432C4×C53—21no—
433C4×C53—21no—
434Dic53—41no—
435Dic53—41no—
436Dic53—41no—
437Dic53—41no—
438Dic53—41no—
439#3514—531no—
440#2970D5311yescharacteristic, complemented
441#2923—531no—
442#1536—531no—
443#1535—531no—
444#1535—531no—
445#1533—531no—
446#1532—531no—
447#1532—531no—
448#1530—531no—
449#1529—531no—
450#1527—531no—
451#1527—531no—
452#1524—531no—
453C2×#329—531no—
454C2×C53—22no—
455C2×C53—41no—
456C2×C53—41no—
457C2×C53#288811yescharacteristic
458C2×C53C2×#42111yescharacteristic
459C2×C53#290111yescharacteristic
460D53—81no—
461D53—81no—
462D53—81no—
463#559—531no—
464#556—531no—
465#555—1061no—
466#551—1061no—
467#551—1061no—
468D4×Q8—531no—
469#548—531no—
470#548—531no—
471#546—531no—
472#546—531no—
473#546—1061no—
474D42—531no—
475#542—1061no—
476#538—1061no—
477#538—1061no—
478#532—531no—
479#529—531no—
480#529—531no—
481#529—531no—
482C2×#124—531no—
483C2×#124—531no—
484#518—1061no—
485C4×#41C2×D5311yescharacteristic
486#446—21no—
487#435—21no—
488#435—21no—
489C8×D4—21no—
490#433—1061no—
491#433—1061no—
492#432—531no—
493#432—531no—
494#432—531no—
495#432—531no—
496#432C2×D5311yescharacteristic, complemented
497#432C2×D5311yescharacteristic, complemented
498#432C2×D5311yescharacteristic, complemented
499#424—1061no—
500#408—1061no—
501C4×M16—531no—
502C4×M16C2×D5311yescharacteristic, complemented
503C2×#97—531no—
504C2×#97C2×D5311yescharacteristic, complemented
505C2×#97C2×D5311yescharacteristic, complemented
506#330—531no—
507#330—531no—
508#330—531no—
509#330—531no—
510#329—531no—
511#329—531no—
512#329—531no—
513#329—531no—
514#329—531no—
515#329—531no—
516#329—531no—
517#329—531no—
518#329—531no—
519#329—531no—
520#329—531no—
521#329—531no—
522C53#1767911yescharacteristic, complemented, Sylow
523C2×#41—531no—
524C2×#41—531no—
525C2×#41D21211yescharacteristic
526C22×Q8—531no—
527C22×Q8—531no—
528C22×D4—531no—
529C22×D4—531no—
530C22×D4—1061no—
531C2×M16—21no—
532C2×M16—1061no—
533C22×C8—21no—
534C22×C8—21no—
535C22×C8—1061no—
536C4⋊Q8—531no—
537C4⋊Q8—1061no—
538#127—531no—
539#126—1061no—
540#126—1061no—
541#126—1061no—
542#126—1061no—
543#126—1061no—
544#125—531no—
545#124—531no—
546#124—531no—
547#124—531no—
548#124—531no—
549#124—531no—
550#124—531no—
551#124—531no—
552#124—1061no—
553#124—1061no—
554#124—1061no—
555#124—1061no—
556#124—1061no—
557#124—1061no—
558#124—1061no—
559#123—1061no—
560#123—1061no—
561#123—1061no—
562#123—1061no—
563#123—1061no—
564#123—1061no—
565#123—1061no—
566C22⋊Q8—531no—
567C22⋊Q8—531no—
568C22⋊Q8—531no—
569C22⋊Q8—1061no—
570C22⋊Q8—1061no—
571C22⋊Q8—1061no—
572C22⋊Q8—1061no—
573C22⋊Q8—1061no—
574#121—531no—
575#121—531no—
576#121—531no—
577#121—1061no—
578#121—1061no—
579#121—1061no—
580#121—1061no—
581#121—1061no—
582#121—1061no—
583#121—1061no—
584#120—1061no—
585#120—1061no—
586#120—1061no—
587#120—1061no—
588C4×Q8—531no—
589C4×Q8—531no—
590C4×Q8—531no—
591C4×Q8C4×D5311yescharacteristic
592C4×Q8C22⋊D5311yescharacteristic
593C4×D4—531no—
594C4×D4—531no—
595C4×D4—531no—
596C4×D4—1061no—
597C4×D4—1061no—
598C4×D4—1061no—
599C4×D4—1061no—
600C4×D4—1061no—
601C4×D4—1061no—
602C4×D4—1061no—
603C4×D4—1061no—
604C4×D4—1061no—
605C4×D4C4×D5311yescharacteristic
606C4×D4C4×D5311yescharacteristic
607C4×D4C4×D5311yescharacteristic
608C4×D4C22⋊D5311yescharacteristic
609C4×D4C22⋊D5311yescharacteristic
610C4×D4C22⋊D5311yescharacteristic
611#117—1061no—
612#117—1061no—
613#117—1061no—
614#117—1061no—
615#117D21211yescharacteristic
616#117D21211yescharacteristic
617#117D21211yescharacteristic
618C2×C22⋊C4—1061no—
619C2×C22⋊C4—1061no—
620C2×C22⋊C4—1061no—
621C2×C22⋊C4—1061no—
622C2×C22⋊C4—1061no—
623C2×C22⋊C4—1061no—
624C2×C42C22×D5311yescharacteristic
625C2×C42C22×D5311yescharacteristic
626C2×C42C22×D5311yescharacteristic
627C4⋊C8—21no—
628C4⋊C8—21no—
629C4⋊C8—21no—
630C4⋊C8—1061no—
631C4⋊C8—1061no—
632C4⋊C8—1061no—
633C4⋊C8—1061no—
634C22⋊C8—21no—
635C22⋊C8—21no—
636C22⋊C8—21no—
637C22⋊C8—1061no—
638C22⋊C8—1061no—
639C22⋊C8—1061no—
640C22⋊C8—1061no—
641#97—21no—
642#97—21no—
643#97—531no—
644#97—531no—
645#97—531no—
646#97—531no—
647#97—1061no—
648#97C22×D5311yescharacteristic
649#97C22×D5311yescharacteristic
650#97C22×D5311yescharacteristic
651#97C22×D5311yescharacteristic
652C4×C8—21no—
653C4×C8—1061no—
654C24—1061no—
655C24—1061no—
656#41—42no—
657#41—4241no—
658#41—4241no—
659C2×Q8—531no—
660C2×Q8—531no—
661C2×Q8—531no—
662C2×Q8—1061no—
663C2×Q8—1061no—
664C2×Q8—4241no—
665C2×Q8—4241no—
666C2×Q8#1171992111yescharacteristic
667C2×D4—531no—
668C2×D4—531no—
669C2×D4—531no—
670C2×D4—1061no—
671C2×D4—1061no—
672C2×D4—1061no—
673C2×D4—1061no—
674C2×D4—1061no—
675C2×D4—1061no—
676C2×D4—1061no—
677C2×D4—1061no—
678C2×D4—1061no—
679C2×D4—4241no—
680C2×D4—4241no—
681C2×D4—2124no—
682C2×D4#1171992111yescharacteristic
683C2×D4#1171992111yescharacteristic
684C2×D4#1171992111yescharacteristic
685C22×C4—1061no—
686C22×C4—1061no—
687C22×C4—1061no—
688C22×C4—1061no—
689C22×C4—1061no—
690C22×C4—1061no—
691C22×C4—1061no—
692C22×C4C2×C4×D5311yescharacteristic
693C22×C4C2×C4×D5311yescharacteristic
694C22×C4C2×C4×D5311yescharacteristic
695C22×C4C2×D21211yescharacteristic
696C22×C4C2×D21211yescharacteristic
697C22×C4C2×D21211yescharacteristic
698C22×C4C2×C22⋊D5311yescharacteristic
699C22×C4C2×C22⋊D5311yescharacteristic
700C22×C4C2×C22⋊D5311yescharacteristic
701M16—42no—
702M16—2122no—
703C2×C8—21no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—21no—
707C2×C8—42no—
708C2×C8—42no—
709C2×C8—1061no—
710C2×C8—1061no—
711C2×C8—1061no—
712C2×C8—1061no—
713C2×C8—2122no—
714C4⋊C4—531no—
715C4⋊C4—531no—
716C4⋊C4—1061no—
717C4⋊C4—1061no—
718C4⋊C4—1061no—
719C4⋊C4—1061no—
720C4⋊C4—1061no—
721C4⋊C4—1061no—
722C4⋊C4—1061no—
723C4⋊C4—1061no—
724C4⋊C4—1061no—
725C4⋊C4—1061no—
726C4⋊C4#1171992111yescharacteristic
727C4⋊C4#1171992111yescharacteristic
728C4⋊C4#1171992111yescharacteristic
729C4⋊C4#1171992111yescharacteristic
730C4⋊C4#1171992111yescharacteristic
731C4⋊C4#1171992111yescharacteristic
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—1061no—
748C22⋊C4—1061no—
749C22⋊C4—1061no—
750C22⋊C4—1061no—
751C22⋊C4—1061no—
752C22⋊C4—1061no—
753C22⋊C4—1061no—
754C22⋊C4—1061no—
755C22⋊C4#1171992111yescharacteristic
756C22⋊C4#1171992111yescharacteristic
757C22⋊C4#1171992111yescharacteristic
758C22⋊C4#1171992111yescharacteristic
759C22⋊C4#1171992111yescharacteristic
760C22⋊C4#1171992111yescharacteristic
761C42—1061no—
762C42—1061no—
763C42—1061no—
764C42C2×C4×D5311yescharacteristic
765C42C2×C4×D5311yescharacteristic
766C42C2×C4×D5311yescharacteristic
767C42C2×D21211yescharacteristic
768C42C2×D21211yescharacteristic
769C42C2×D21211yescharacteristic
770C42C2×C22⋊D5311yescharacteristic
771C42C2×C22⋊D5311yescharacteristic
772C42C2×C22⋊D5311yescharacteristic
773C42C23×D5311yescharacteristic
774C23—1061no—
775C23—1061no—
776C23—1061no—
777C23—4241no—
778C23—4241no—
779C23—4241no—
780C23—4241no—
781C23—2122no—
782C23—2122no—
783C23C2×#1171992111yescharacteristic
784C23C2×#1171992111yescharacteristic
785C23C2×#1171992111yescharacteristic
786Q8—41no—
787Q8—4241no—
788Q8—4241no—
789Q8—2121no—
790Q8—2121no—
791Q8—2121no—
792D4—22no—
793D4—22no—
794D4—41no—
795D4—4241no—
796D4—4241no—
797D4—4241no—
798D4—4241no—
799D4—4241no—
800D4—4241no—
801D4—2121no—
802D4—2121no—
803D4—2121no—
804D4—2122no—
805D4—2122no—
806D4—2122no—
807C2×C4—22no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—1061no—
817C2×C4—1061no—
818C2×C4—1061no—
819C2×C4—1061no—
820C2×C4—1061no—
821C2×C4—4241no—
822C2×C4—4241no—
823C2×C4—4241no—
824C2×C4—4241no—
825C2×C4—4241no—
826C2×C4—4241no—
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×C4C22×C4×D5311yescharacteristic
838C2×C4C22×C22⋊D5311yescharacteristic
839C2×C4C22×D21211yescharacteristic
840C8—22no—
841C8—41no—
842C8—41no—
843C8—41no—
844C8—2121no—
845C8—2121no—
846C8—2121no—
847C8—2121no—
848C22—21no—
849C22—21no—
850C22—21no—
851C22—21no—
852C22—21no—
853C22—21no—
854C22—21no—
855C22—21no—
856C22—8482no—
857C22—8482no—
858C22—2121no—
859C22—2121no—
860C22—2121no—
861C22—2121no—
862C22—2121no—
863C22—2121no—
864C22—2121no—
865C22—2121no—
866C22—2121no—
867C22#1681063912yes—
868C22C22×#1171992111yescharacteristic
869C4—21no—
870C4—21no—
871C4—21no—
872C4—21no—
873C4—21no—
874C4—21no—
875C4—21no—
876C4—21no—
877C4—21no—
878C4—21no—
879C4—21no—
880C4—21no—
881C4—2121no—
882C4—2121no—
883C4—2121no—
884C4—2121no—
885C4—2121no—
886C2—22no—
887C2—41no—
888C2—41no—
889C2—4241no—
890C2—4241no—
891C2—4241no—
892C2#2028319311yescharacteristic
893C2C2×#1681063911yescharacteristic
894C2#2028326311yescharacteristic
subgroupG/H
centerC22C22×#11719921
commutatorC2×C4×C53C23×C4
FrattiniC42C23×D53
FittingC53×#2970C2
socleC22×C53C22×C22⋊C4
prime radical#20288676C2
cosocleC42×C53C24
hypercenter#2970D53
hypocenterC53#17679
LCSG ▷ C2×C4×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ C4×#41 ◁ #2970

Complements

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

NH ≅ G/Ntype
2. #20283366C2semidirect
3. #20273349C2semidirect
4. #20273347C2semidirect
5. #20273344C2semidirect
6. #20273338C2semidirect
7. #20273336C2semidirect
8. #20273333C2semidirect
9. #20273325C2semidirect
10. #20273320C2semidirect
11. #20273314C2semidirect
12. #20273312C2semidirect
13. #20273301C2semidirect
14. C2×#16810362C2semidirect
15. C53×#2970C2semidirect
40. #16810680C22semidirect
41. #16810680C22semidirect
42. #16810680C22semidirect
43. #16810680C22semidirect
46. C4×#11719917C22semidirect
47. C2×#13133128C22semidirect
48. #16810364C22semidirect
49. #16810364C22semidirect
50. #16810364C22semidirect
51. #16810364C22semidirect
56. #16810362C22semidirect
57. #16810362C22semidirect
58. #16810362C22semidirect
59. #16810362C22semidirect
60. #16810362C22semidirect
61. #16810362C22semidirect
62. #16810362C22semidirect
63. #16810362C22semidirect
69. C53×#432C22semidirect
70. C53×#432C22semidirect
71. C53×#432C22semidirect
72. C4×M16×C53C22semidirect
73. C2×#97×C53C22semidirect
74. C2×#97×C53C22semidirect
440. #2970D53semidirect
496. #432C2×D53semidirect
497. #432C2×D53semidirect
498. #432C2×D53semidirect
502. C4×M16C2×D53semidirect
504. C2×#97C2×D53semidirect
505. C2×#97C2×D53semidirect
522. C53#17679semidirect

Maximal subgroups

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

subgroupindex
#202886762
#202833662
#202733492
#202733472
#202733442
#202733382
#202733362
#202733332
#202733252
#202733202
#202733142
#202733122
#202733012
C2×#168103622
C53×#29702
#1767953