Finite Group Databasebeta

← #28291932

Subgroups — #28291932

Order 13568.

6518 conjugacy classes of subgroups.

The subgroup lattice has 2068 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289221C211yesmaximal, characteristic, complemented
2#20289217C212yesmaximal, complemented
3#20289208C211yesmaximal, characteristic, complemented
4#20289202C212yesmaximal, complemented
5#20289195C212yesmaximal, complemented
6#20289185C212yesmaximal, complemented
7#20289178C212yesmaximal, complemented
8#20289162C214yesmaximal, complemented
9#20289149C214yesmaximal, complemented
10#20289123C212yesmaximal, complemented
11#20289109C211yesmaximal, characteristic, complemented
12#20289007C214yesmaximal, complemented
13#20288999C214yesmaximal, complemented
14#20288861C214yesmaximal, complemented
15#20288329C214yesmaximal, complemented
16#20288311C212yesmaximal, complemented
17#20288307C212yesmaximal, complemented
18#20288297C212yesmaximal, complemented
19#20288294C212yesmaximal, complemented
20#20288145C214yesmaximal, complemented
21#20288141C214yesmaximal, complemented
22#20288106C211yesmaximal, characteristic, complemented
23#20288102C212yesmaximal, complemented
24#20288099C211yesmaximal, characteristic, complemented
25#20288009C212yesmaximal, complemented
26#533×D53C211yesmaximal, characteristic, complemented
27C53×#3557C211yesmaximal, characteristic, complemented
28C53⋊#564C2214yescomplemented
29#16811377C2214yes—
30#16811375C2214yes—
31#16811375C2214yescomplemented
32#16811375C2214yescomplemented
33#16811375C2214yescomplemented
34#16811374C2214yes—
35#16811374C2214yescomplemented
36#16811372C2214yes—
37#16811372C2214yescomplemented
38#16811370C2214yes—
39#16811370C2214yescomplemented
40#16811369C2214yes—
41#16811369C2214yes—
42#16811367C2214yes—
43#16811358C2212yescomplemented
44#16811356C2212yescomplemented
45#16811356C2212yescomplemented
46#16811355C2212yescomplemented
47#16811355C2212yescomplemented
48Q8×Dic106C2212yescomplemented
49#16811353C2212yescomplemented
50#16811351C2212yescomplemented
51#16811351C2212yescomplemented
52#16811350C2212yescomplemented
53#16811350C2212yescomplemented
54#16811350C2214yescomplemented
55#16811349C2212yescomplemented
56#16811349C2212yescomplemented
57#16811348C2212yescomplemented
58#16811346C2212yescomplemented
59#16811345C2214yes—
60#16811345C2212yescomplemented
61#16811345C2212yescomplemented
62#16811342C2212yescomplemented
63#16811342C2212yescomplemented
64#16811340C2214yes—
65#16811340C2214yescomplemented
66#16811333C2214yes—
67#16811333C2212yescomplemented
68#16811332C2212yescomplemented
69#16811332C2212yescomplemented
70#16811329C2214yes—
71#16811329C2214yes—
72#16811329C2212yescomplemented
73#16811329C2212yescomplemented
74#16811328C2214yes—
75#16811327C2214yes—
76#16811327C2214yes—
77#16811324C2214yes—
78#16811324C2214yes—
79#16811323C2214yes—
80#16811318C2214yes—
81#16811318C2214yes—
82#16811317C2214yes—
83#16811312C2214yescomplemented
84#16811306C2214yes—
85#16811306C2214yescomplemented
86#16811305C2214yes—
87#16811305C2214yescomplemented
88#16811294C2212yescomplemented
89#16811293C2212yescomplemented
90D4×Dic106C2212yescomplemented
91#16811288C2214yes—
92#16811288C2212yescomplemented
93#16811286C2214yes—
94#16811286C2214yescomplemented
95#16811283C2214yes—
96#16811283C2214yes—
97#16811282C2214yes—
98#16811281C2214yes—
99#16811274C2214yes—
100#16811271C2214yes—
101#16811271C2214yescomplemented
102#16811252C2214yescomplemented
103#16811250C2214yescomplemented
104#16811247C2212yes—
105#16811246C2212yes—
106#16811245C2212yes—
107#16811244C2212yes—
108#16811243C2214yes—
109#16811243C2214yescomplemented
110#16811242C2212yes—
111#16811241C2214yes—
112#16811241C2214yes—
113#16811240C2212yes—
114#16811238C2212yes—
115#16811238C2214yes—
116#16811237C2214yes—
117#16811237C2214yescomplemented
118#16811236C2211yescharacteristic
119#16811235C2211yescharacteristic
120#16811235C2214yescomplemented
121#16811234C2211yescharacteristic
122#16811233C2212yes—
123#16811232C2214yescomplemented
124#16811232C2214yescomplemented
125#16811231C2212yes—
126#16811231C2214yescomplemented
127#16811230C2214yes—
128#16811230C2214yes—
129#16811230C2214yescomplemented
130#16811230C2214yescomplemented
131#16811229C2211yescharacteristic
132#16811228C2211yescharacteristic
133#16811227C2211yescharacteristic
134#16811226C2212yes—
135#16811224C2212yes—
136#16811221C2214yes—
137#16811220C2214yescomplemented
138#16811219C2214yes—
139#16811219C2214yes—
140#16811219C2214yescomplemented
141#16811216C2214yes—
142#16811216C2214yes—
143#16811216C2214yescomplemented
144#16811215C2214yes—
145#16811215C2214yescomplemented
146#16811214C2214yes—
147#16811212C2214yes—
148#16811209C2214yes—
149#16811207C2214yes—
150#16811205C2214yes—
151#16811202C2214yes—
152#16811200C2214yes—
153#16811196C2214yescomplemented
154#16811195C2214yes—
155#16811195C2214yescomplemented
156#16811193C2214yes—
157#16811180C2211yescharacteristic
158#16811179C2212yes—
159#16811179C2212yes—
160#16811179C2211yescharacteristic
161#16811179C2211yescharacteristic
162#16811179C2214yescomplemented
163#16811179C2214yescomplemented
164#16811178C2212yes—
165#16811178C2212yes—
166#16811178C2214yescomplemented
167#16811177C2212yes—
168#16811177C2212yes—
169#16811177C2212yes—
170#16811176C2211yescharacteristic
171#16811176C2211yescharacteristic
172#16811175C2212yes—
173#16811175C2212yes—
174#16811175C2212yes—
175#16811175C2214yescomplemented
176#16811175C2214yescomplemented
177#16811175C2214yescomplemented
178#16811174C2211yescharacteristic
179#16811172C2212yes—
180#16811172C2212yes—
181#16811171C2211yescharacteristic
182#16811170C2212yes—
183#16811168C2212yes—
184C4⋊Q8×D53C2212yes—
185#16811159C2214yes—
186#16811159C2214yescomplemented
187#16811158C2212yes—
188#16811158C2214yes—
189#16811157C2212yes—
190#16811156C2214yes—
191#16811156C2214yes—
192#16811156C2214yes—
193#16811156C2214yes—
194#16811156C2214yescomplemented
195#16811156C2214yescomplemented
196#16811154C2214yes—
197#16811152C2212yes—
198#16811152C2214yes—
199#16811152C2214yescomplemented
200#16811151C2214yes—
201#16811150C2214yes—
202#16811150C2214yes—
203#16811150C2214yes—
204#16811150C2214yescomplemented
205#16811150C2214yescomplemented
206#125×D53C2212yes—
207#16811136C2212yes—
208#16811133C2212yes—
209#16811132C2214yes—
210#16811131C2214yes—
211C22⋊Q8×D53C2212yes—
212C22⋊Q8×D53C2212yes—
213C4×#11719949C2212yes—
214C4×#11719949C2212yes—
215C4×#11719949C2212yes—
216#16811091C2214yes—
217#16811091C2214yescomplemented
218C4×#11719947C2212yes—
219C4×#11719947C2214yes—
220C4×#11719947C2212yes—
221C4×#11719947C2212yes—
222C4×#11719947C2214yescomplemented
223C2×#13133182C2214yescomplemented
224C4×Q8×D53C2212yes—
225C4×Q8×D53C2212yes—
226C4×Q8×D53C2214yescomplemented
227#117×D53C2211yescharacteristic
228#117×D53C2211yescharacteristic
229C2×C42×D53C2211yescharacteristic
230C53×#563C2214yescomplemented
231C53×#559C2212yescomplemented
232C53×#557C2212yescomplemented
233C53×#556C2212yescomplemented
234C53×#554C2212yescomplemented
235C53×#552C2214yescomplemented
236C53×#542C2212yes—
237C53×#542C2214yes—
238C53×#541C2211yescharacteristic
239C53×#540C2211yescharacteristic
240C53×#539C2214yes—
241C53×#533C2211yescharacteristic
242C53×#529C2212yes—
243C2×#11719949C2312yes—
244C2×#11719945C2314yes—
245C2×#11719945C2314yes—
246C2×#11719947C2312yes—
247C2×#11719947C2314yes—
248C2×#11719947C2314yes—
249C22×Dic106C2314yes—
250C2×Q8×D53C2312yes—
251C2×Q8×D53C2312yes—
252C2×Q8×D53C2314yes—
253C22×C4×D53C2311yescharacteristic
254C22×C4×D53C2312yes—
255#13133217C2312yes—
256#13133217C2314yes—
257#13133217C2311yescharacteristic
258#13133217C2312yes—
259#13133216C2314yes—
260#13133216C2312yes—
261#13133216C2314yes—
262#13133216C2314yes—
263#13133216C2312yes—
264#13133216C2314yes—
265#13133216C2314yes—
266#13133216C2312yes—
267#13133216C2312yes—
268#13133216C2312yes—
269#13133216C2314yes—
270#13133216C2314yes—
271#13133216C2312yes—
272#13133216C2312yes—
273#13133216C2312yes—
274#13133215C2314yes—
275#13133215C2314yes—
276#13133215C2314yes—
277#13133215C2312yes—
278#13133215C2312yes—
279#13133215C2312yes—
280#13133215C2312yes—
281#13133214C2311yescharacteristic
282#13133213C2312yes—
283#13133213C2312yes—
284#13133212C2314yes—
285#13133212C2314yes—
286#13133212C2314yes—
287#13133212C2314yes—
288#13133212C2314yes—
289#13133212C2314yes—
290#13133212C2314yes—
291#13133212C2314yes—
292#13133212C2314yes—
293#13133212C2314yes—
294#13133212C2314yes—
295#13133211C2314yes—
296#13133211C2314yes—
297#13133211C2314yes—
298#13133211C2314yes—
299#13133211C2314yes—
300#13133210C2314yes—
301#13133210C2314yes—
302#13133210C2314yes—
303#13133210C2314yes—
304#13133210C2314yes—
305#13133210C2314yes—
306#13133210C2314yes—
307#13133210C2314yes—
308#13133210C2314yes—
309#13133210C2314yes—
310#13133210C2314yes—
311#13133209C2314yes—
312#13133209C2312yes—
313#13133209C2314yes—
314#13133209C2311yescharacteristic
315#13133209C2312yes—
316#13133209C2314yes—
317#13133209C2311yescharacteristic
318#13133209C2314yes—
319#13133208C2314yes—
320#13133208C2314yes—
321#13133208C2314yes—
322#13133208C2314yes—
323#13133208C2312yes—
324#13133208C2312yes—
325#13133208C2312yes—
326#13133208C2312yes—
327#13133208C2314yes—
328#13133207C2314yes—
329#13133207C2314yes—
330#13133207C2314yes—
331#13133207C2314yes—
332#13133207C2314yes—
333#13133207C2314yes—
334#13133207C2314yes—
335#13133207C2314yes—
336#13133207C2314yes—
337#13133207C2314yes—
338#13133207C2314yes—
339#13133207C2314yes—
340#13133207C2314yes—
341#13133207C2312yes—
342#13133207C2312yes—
343#13133207C2312yes—
344#13133207C2312yes—
345#13133207C2314yes—
346#13133207C2314yes—
347#13133207C2314yes—
348#13133206C2314yes—
349#13133206C2314yes—
350#13133206C2312yes—
351#13133205C2314yes—
352#13133205C2312yes—
353#13133205C2312yes—
354#13133204C2312yes—
355#13133204C2314yes—
356#13133203C2314yes—
357#13133203C2314yes—
358#13133203C2314yes—
359#13133203C2314yes—
360#13133203C2314yes—
361#13133203C2314yes—
362#13133203C2314yes—
363#13133203C2314yes—
364#13133203C2314yes—
365#13133203C2314yes—
366#13133202C2314yes—
367#13133202C2314yes—
368#13133202C2314yes—
369#13133202C2314yes—
370#13133202C2314yes—
371#13133202C2314yes—
372#13133202C2314yes—
373#13133202C2314yes—
374#13133201C2314yes—
375#13133201C2314yes—
376#13133201C2314yes—
377#13133201C2314yes—
378#13133200C2314yes—
379#13133200C2314yes—
380#13133200C2314yes—
381#13133200C2314yes—
382#13133200C2314yes—
383#13133199C2314yes—
384#13133199C2314yes—
385#13133199C2314yes—
386#13133199C2314yes—
387#13133199C2314yes—
388#13133199C2314yes—
389#13133199C2314yes—
390#13133199C2314yes—
391#13133199C2314yes—
392#13133199C2314yes—
393#13133198C2314yes—
394#13133198C2314yes—
395#13133197C2314yes—
396#13133197C2314yes—
397#13133197C2314yes—
398#13133197C2314yes—
399#13133197C2312yes—
400#13133197C2312yes—
401#13133197C2312yes—
402#13133196C2314yes—
403#13133196C2314yes—
404#13133196C2314yes—
405#13133196C2312yes—
406#13133196C2312yes—
407#13133196C2312yes—
408#13133196C2314yes—
409#13133195C2312yes—
410#13133195C2314yes—
411#13133195C2312yes—
412#13133195C2314yes—
413#13133195C2312yes—
414#13133195C2314yes—
415#13133195C2312yes—
416#13133195C2314yes—
417#13133195C2314yes—
418#13133195C2314yes—
419#13133195C2314yes—
420#13133195C2314yes—
421#13133195C2314yes—
422#13133195C2314yes—
423#13133195C2314yes—
424#13133195C2314yes—
425#13133195C2314yes—
426#13133195C2314yes—
427#13133195C2314yes—
428#13133195C2314yes—
429#13133195C2314yes—
430#13133194C2314yes—
431#13133194C2314yes—
432#13133194C2314yes—
433#13133194C2314yes—
434#13133194C2314yes—
435#13133194C2314yes—
436#13133194C2314yes—
437#13133194C2314yes—
438#13133194C2314yes—
439#13133194C2312yes—
440#13133194C2312yes—
441#13133194C2312yes—
442#13133194C2312yes—
443#13133194C2314yes—
444#13133194C2314yes—
445#13133193C2314yes—
446#13133193C2314yes—
447#13133193C2314yes—
448#13133193C2314yes—
449#13133193C2312yes—
450#13133193C2312yes—
451#13133193C2312yes—
452#13133193C2314yes—
453#13133192C2314yes—
454#13133192C2314yes—
455#13133192C2312yes—
456#13133191C2314yes—
457#13133191C2314yes—
458#13133191C2312yes—
459#13133190C2314yes—
460#13133190C2314yes—
461#13133190C2314yes—
462#13133190C2314yes—
463#13133190C2314yes—
464#13133190C2314yes—
465#13133190C2314yes—
466#13133190C2314yes—
467#13133190C2314yes—
468#13133189C2314yes—
469#13133189C2314yes—
470#13133189C2314yes—
471#13133189C2314yes—
472#13133189C2314yes—
473#13133188C2314yes—
474#13133188C2314yes—
475#13133188C2312yes—
476#13133188C2314yes—
477#13133187C2314yes—
478#13133185C2314yes—
479Q8×Dic53C2312yes—
480Q8×Dic53C2312yes—
481Q8×Dic53C2314yes—
482Q8×Dic53C2312yes—
483Q8×Dic53C2312yes—
484Q8×Dic53C2312yes—
485C4×Dic106C2314yes—
486C4×Dic106C2314yes—
487C4×Dic106C2314yes—
488C4×Dic106C2312yes—
489C4×Dic106C2312yes—
490C4×Dic106C2312yes—
491C4×Dic106C2312yes—
492C4×Dic106C2314yes—
493C4×Dic106C2312yes—
494C4×Dic106C2312yes—
495C4×Dic106C2312yes—
496C4×Dic106C2312yes—
497C4×Dic106C2312yes—
498C4×Dic106C2314yes—
499#13133182C2314yes—
500#13133182C2314yes—
501#13133182C2314yes—
502#13133182C2314yes—
503#13133182C2314yes—
504#13133182C2314yes—
505#13133182C2312yes—
506#13133182C2312yes—
507#13133182C2312yes—
508#13133182C2312yes—
509#13133182C2312yes—
510#13133182C2312yes—
511#13133182C2314yes—
512#13133182C2314yes—
513#13133182C2314yes—
514#13133182C2314yes—
515#13133182C2312yes—
516#13133182C2312yes—
517#13133182C2312yes—
518#13133182C2314yes—
519C4×D212C2314yes—
520C4×D212C2314yes—
521C4×D212C2312yes—
522C4×D212C2312yes—
523C4×D212C2314yes—
524C4×D212C2312yes—
525D4×Dic53C2312yes—
526D4×Dic53C2312yes—
527D4×Dic53C2312yes—
528D4×Dic53C2314yes—
529D4×Dic53C2314yes—
530#13133179C2314yes—
531#13133179C2314yes—
532#13133179C2314yes—
533#13133179C2314yes—
534#13133179C2314yes—
535#13133179C2312yes—
536#13133179C2312yes—
537#13133179C2312yes—
538#13133179C2314yes—
539#13133179C2314yes—
540C4×C22⋊D53C2314yes—
541C4×C22⋊D53C2314yes—
542C4×C22⋊D53C2314yes—
543C4×C22⋊D53C2314yes—
544C4×C22⋊D53C2314yes—
545C4×C22⋊D53C2314yes—
546C4×C22⋊D53C2314yes—
547#13133177C2314yes—
548#13133177C2314yes—
549#13133177C2314yes—
550#13133177C2314yes—
551#13133177C2314yes—
552#13133177C2314yes—
553#13133177C2314yes—
554#13133177C2314yes—
555#13133177C2314yes—
556#13133177C2314yes—
557#13133177C2314yes—
558#13133177C2314yes—
559#13133177C2314yes—
560#13133176C2311yescharacteristic
561#13133176C2311yescharacteristic
562#13133175C2314yes—
563#13133175C2312yes—
564#13133175C2312yes—
565#13133175C2312yes—
566#13133175C2312yes—
567#13133175C2314yes—
568#13133175C2314yes—
569#13133175C2314yes—
570#13133175C2314yes—
571#13133174C2314yes—
572#13133174C2314yes—
573#13133174C2314yes—
574#13133174C2314yes—
575#13133174C2312yes—
576#13133174C2311yescharacteristic
577#13133174C2311yescharacteristic
578#13133173C2314yes—
579#13133173C2314yes—
580#13133173C2311yescharacteristic
581#13133173C2311yescharacteristic
582#13133173C2312yes—
583#13133173C2314yes—
584#13133173C2314yes—
585#13133173C2314yes—
586#13133173C2314yes—
587#13133173C2314yes—
588C2×#11719919C2314yes—
589C2×#11719919C2314yes—
590C4⋊C4×D53C2314yes—
591C4⋊C4×D53C2314yes—
592C4⋊C4×D53C2314yes—
593C4⋊C4×D53C2312yes—
594C4⋊C4×D53C2312yes—
595C4⋊C4×D53C2312yes—
596C4⋊C4×D53C2312yes—
597C4⋊C4×D53C2312yes—
598C4⋊C4×D53C2312yes—
599C4⋊C4×D53C2312yes—
600C4⋊C4×D53C2312yes—
601C22⋊C4×D53C2312yes—
602C22⋊C4×D53C2311yescharacteristic
603C22⋊C4×D53C2311yescharacteristic
604C2×C4×Dic53C2312yes—
605C2×C4×Dic53C2311yescharacteristic
606C2×C4×Dic53C2314yes—
607C2×C4×Dic53C2314yes—
608C2×C4×Dic53C2314yes—
609C42×D53C2312yes—
610C42×D53C2311yescharacteristic
611C42×D53C2311yescharacteristic
612C42×D53C2312yes—
613C42×D53C2311yescharacteristic
614C42×D53C2311yescharacteristic
615C42×D53C2311yescharacteristic
616C42×D53C2312yes—
617C42×D53C2311yescharacteristic
618C42×D53C2314yes—
619C42×D53C2314yes—
620C42×D53C2314yes—
621C4⋊Q8×C53C2314yes—
622C4⋊Q8×C53C2312yes—
623C4⋊Q8×C53C2312yes—
624C4⋊Q8×C53C2311yescharacteristic
625#127×C53C2311yescharacteristic
626#126×C53C2314yes—
627#126×C53C2314yes—
628#126×C53C2314yes—
629#126×C53C2314yes—
630#126×C53C2314yes—
631#125×C53C2314yes—
632#125×C53C2312yes—
633#125×C53C2312yes—
634#125×C53C2314yes—
635#125×C53C2311yescharacteristic
636#125×C53C2314yes—
637#125×C53C2311yescharacteristic
638#124×C53C2314yes—
639#124×C53C2312yes—
640#124×C53C2314yes—
641#124×C53C2312yes—
642#123×C53C2314yes—
643#123×C53C2314yes—
644#123×C53C2314yes—
645#123×C53C2314yes—
646#123×C53C2314yes—
647C22⋊Q8×C53C2314yes—
648C22⋊Q8×C53C2314yes—
649C22⋊Q8×C53C2314yes—
650C22⋊Q8×C53C2314yes—
651C22⋊Q8×C53C2312yes—
652C22⋊Q8×C53C2312yes—
653C22⋊Q8×C53C2312yes—
654C22⋊Q8×C53C2314yes—
655#121×C53C2312yes—
656#121×C53C2314yes—
657C4×Q8×C53C2312yes—
658C4×Q8×C53C2312yes—
659C4×Q8×C53C2312yes—
660C4×Q8×C53C2312yes—
661C4×Q8×C53C2314yes—
662C4×Q8×C53C2312yes—
663C4×D4×C53C2314yes—
664C4×D4×C53C2312yes—
665C4×D4×C53C2312yes—
666C4×D4×C53C2314yes—
667C4×D4×C53C2312yes—
668#117×C53C2314yes—
669#117×C53C2314yes—
670#117×C53C2311yescharacteristic
671#117×C53C2311yescharacteristic
672C2×C4⋊C4×C53C2314yes—
673C2×C42×C53C2311yescharacteristic
674C23×D53C2411yescharacteristic
675C2×Q8×C53C2412yes—
676C2×Q8×C53C2412yes—
677C2×Q8×C53C2414yes—
678C2×Q8×C53C2412yes—
679C2×D4×C53C2412yes—
680C2×D4×C53C2414yes—
681C2×D4×C53C2414yes—
682C22×C4×C53C2411yescharacteristic
683C22×C4×C53C2412yes—
684C22×C4×C53C2414yes—
685C22×C4×C53C2414yes—
686C22×C4×C53C2414yes—
687C2×C22⋊D53C2414yes—
688C2×C22⋊D53C2414yes—
689C2×C22⋊D53C2414yes—
690C2×C22⋊D53C2414yes—
691C2×C22⋊D53C2414yes—
692C2×C22⋊D53C2414yes—
693C2×C22⋊D53C2414yes—
694C22×Dic53C2414yes—
695C22×Dic53C2411yescharacteristic
696C22×Dic53C2412yes—
697C22×Dic53C2414yes—
698C22×Dic53C2414yes—
699C22×Dic53C2414yes—
700#11719949—28no—
701Q8×D53—44no—
702Q8×D53—48no—
703Q8×D53—44no—
704#11719947—28no—
705#11719947—48no—
706#11719947—48no—
707#11719945—48no—
708#11719945—48no—
709C2×D212C2414yes—
710C2×D212C2412yes—
711C2×D212C2414yes—
712C2×D212C2414yes—
713C2×C4×D53—24no—
714C2×C4×D53—44no—
715C2×C4×D53C2414yes—
716C2×C4×D53C2411yescharacteristic
717C2×C4×D53C2412yes—
718C2×C4×D53C2411yescharacteristic
719C2×C4×D53C2412yes—
720C2×C4×D53C2411yescharacteristic
721C2×C4×D53C2414yes—
722C2×C4×D53C2412yes—
723C2×C4×D53C2412yes—
724C2×C4×D53C2412yes—
725C2×C4×D53C2412yes—
726C2×C4×D53C2412yes—
727C2×C4×D53C2412yes—
728C2×C4×D53C2414yes—
729C2×C4×D53C2414yes—
730C2×C4×D53C2414yes—
731C2×C4×D53C2414yes—
732C2×C4×D53C2414yes—
733C2×C4×D53C2411yescharacteristic
734C2×Dic106—48no—
735C2×Dic106C2412yes—
736C2×Dic106C2412yes—
737C2×Dic106C2414yes—
738C2×Dic106C2412yes—
739C2×Dic106C2412yes—
740C2×Dic106C2412yes—
741C2×Dic106C2414yes—
742C2×Dic106C2414yes—
743C2×Dic106C2412yes—
744C2×Dic106C2412yes—
745C2×Dic106C2414yes—
746C2×Dic106C2414yes—
747C4⋊C4×C53C2412yes—
748C4⋊C4×C53C2414yes—
749C4⋊C4×C53C2414yes—
750C4⋊C4×C53C2414yes—
751C4⋊C4×C53C2412yes—
752C4⋊C4×C53C2414yes—
753C4⋊C4×C53C2412yes—
754C4⋊C4×C53C2414yes—
755C4⋊C4×C53C2412yes—
756C4⋊C4×C53C2412yes—
757C4⋊C4×C53C2412yes—
758C4⋊C4×C53C2412yes—
759C4⋊C4×C53C2414yes—
760C4⋊C4×C53C2412yes—
761C4⋊C4×C53C2414yes—
762C4⋊C4×C53C2412yes—
763C4⋊C4×C53C2414yes—
764C4⋊C4×C53C2412yes—
765C4⋊C4×C53C2414yes—
766C4⋊C4×C53C2414yes—
767C22⋊C4×C53C2414yes—
768C22⋊C4×C53C2412yes—
769C22⋊C4×C53C2414yes—
770C22⋊C4×C53C2411yescharacteristic
771C22⋊C4×C53C2411yescharacteristic
772C22⋊C4×C53C2414yes—
773C22⋊C4×C53C2414yes—
774C22⋊C4×C53C2414yes—
775C22⋊C4×C53C2414yes—
776C22⋊C4×C53C2414yes—
777C22⋊C4×C53C2414yes—
778C22⋊C4×C53C2414yes—
779C42×C53C2411yescharacteristic
780C42×C53C2412yes—
781C42×C53C2411yescharacteristic
782C42×C53C2414yes—
783C42×C53C2411yescharacteristic
784C42×C53C2412yes—
785C42×C53C2411yescharacteristic
786C42×C53C2414yes—
787C42×C53C2414yes—
788C22⋊Dic53C2411yescharacteristic
789C22⋊Dic53C2411yescharacteristic
790C22⋊Dic53C2412yes—
791C22⋊Dic53C2414yes—
792C22⋊Dic53C2414yes—
793C22⋊Dic53C2414yes—
794C22⋊Dic53C2414yes—
795C22⋊Dic53C2414yes—
796C22⋊Dic53C2414yes—
797C22⋊Dic53C2414yes—
798#11719921C2412yes—
799#11719921C2412yes—
800#11719921C2412yes—
801#11719921C2412yes—
802#11719921C2414yes—
803#11719921C2414yes—
804#11719921C2414yes—
805#11719921C2414yes—
806#11719921C2414yes—
807#11719921C2414yes—
808#11719921C2414yes—
809#11719921C2414yes—
810#11719921C2414yes—
811#11719921C2414yes—
812#11719921C2414yes—
813#11719921C2414yes—
814#11719921C2414yes—
815#11719921C2414yes—
816#11719921C2414yes—
817#11719921C2414yes—
818#11719921C2414yes—
819#11719921C2414yes—
820C4⋊Dic53C2412yes—
821C4⋊Dic53C2412yes—
822C4⋊Dic53C2412yes—
823C4⋊Dic53C2414yes—
824C4⋊Dic53C2412yes—
825C4⋊Dic53C2414yes—
826C4⋊Dic53C2414yes—
827C4⋊Dic53C2412yes—
828C4⋊Dic53C2412yes—
829C4⋊Dic53C2412yes—
830C4⋊Dic53C2412yes—
831C4⋊Dic53C2412yes—
832C4⋊Dic53C2412yes—
833C4⋊Dic53C2414yes—
834C4⋊Dic53C2414yes—
835C4⋊Dic53C2414yes—
836C4⋊Dic53C2414yes—
837C4⋊Dic53C2414yes—
838#11719919C2412yes—
839#11719919C2412yes—
840#11719919C2412yes—
841#11719919C2412yes—
842#11719919C2414yes—
843#11719919C2414yes—
844#11719919C2412yes—
845#11719919C2412yes—
846#11719919C2412yes—
847#11719919C2412yes—
848#11719919C2412yes—
849#11719919C2412yes—
850#11719919C2412yes—
851#11719919C2412yes—
852#11719919C2412yes—
853#11719919C2414yes—
854#11719919C2412yes—
855#11719919C2412yes—
856#11719919C2412yes—
857#11719919C2414yes—
858#11719919C2414yes—
859#11719919C2414yes—
860#11719919C2414yes—
861#11719919C2414yes—
862#11719919C2414yes—
863#11719919C2414yes—
864#11719919C2414yes—
865#11719919C2414yes—
866#11719919C2414yes—
867#11719919C2414yes—
868#11719919C2414yes—
869#11719919C2414yes—
870#11719919C2414yes—
871#11719919C2414yes—
872#11719919C2414yes—
873#11719919C2414yes—
874#11719919C2414yes—
875#11719919C2414yes—
876C4×Dic53C2412yes—
877C4×Dic53C2412yes—
878C4×Dic53C2412yes—
879C4×Dic53C2412yes—
880C4×Dic53C2412yes—
881C4×Dic53C2414yes—
882C4×Dic53C2411yescharacteristic
883C4×Dic53C2412yes—
884C4×Dic53C2412yes—
885C4×Dic53C2411yescharacteristic
886C4×Dic53C2412yes—
887C4×Dic53C2414yes—
888C4×Dic53C2412yes—
889C4×Dic53C2414yes—
890C4×Dic53C2414yes—
891C4×Dic53C2411yescharacteristic
892C4×Dic53C2412yes—
893C4×Dic53C2411yescharacteristic
894C4×Dic53C2414yes—
895C4×Dic53C2414yes—
896C4×Dic53C2414yes—
897C4×Dic53C2414yes—
898C4×Dic53C2414yes—
899C4×Dic53C2414yes—
900C4×Dic53C2414yes—
901C23×C53C2514yes—
902C23×C53C2511yescharacteristic
903C22×D53—22no—
904C22×D53—42no—
905C22×D53C2514yes—
906C22×D53C2511yescharacteristic
907C22×D53C2511yescharacteristic
908Q8×C53—24no—
909Q8×C53—42no—
910Q8×C53—44no—
911Q8×C53—42no—
912D4×C53—24no—
913D4×C53—44no—
914D4×C53—44no—
915C2×C4×C53—22no—
916C2×C4×C53—44no—
917C2×C4×C53—42no—
918C2×C4×C53—44no—
919C2×C4×C53—44no—
920C2×C4×C53C2512yes—
921C2×C4×C53C2514yes—
922C2×C4×C53C2512yes—
923C2×C4×C53C2514yes—
924C2×C4×C53C2512yes—
925C2×C4×C53C2512yes—
926C2×C4×C53C2512yes—
927C2×C4×C53C2512yes—
928C2×C4×C53C2511yescharacteristic
929C2×C4×C53C2514yes—
930C2×C4×C53C2511yescharacteristic
931C22⋊D53—28no—
932C22⋊D53—28no—
933C22⋊D53—44no—
934C22⋊D53—44no—
935C22⋊D53—44no—
936C22⋊D53—44no—
937C22⋊D53—44no—
938C2×Dic53—22no—
939C2×Dic53—28no—
940C2×Dic53—28no—
941C2×Dic53—24no—
942C2×Dic53—44no—
943C2×Dic53—44no—
944C2×Dic53C2512yes—
945C2×Dic53C2512yes—
946C2×Dic53C2514yes—
947C2×Dic53C2514yes—
948C2×Dic53C2512yes—
949C2×Dic53C2512yes—
950C2×Dic53C2512yes—
951C2×Dic53C2514yes—
952C2×Dic53C2511yescharacteristic
953C2×Dic53C2511yescharacteristic
954C2×Dic53C2512yes—
955D212—28no—
956D212—24no—
957D212—44no—
958D212—44no—
959C4×D53—22no—
960C4×D53—22no—
961C4×D53—22no—
962C4×D53—28no—
963C4×D53—24no—
964C4×D53—24no—
965C4×D53—28no—
966C4×D53—42no—
967C4×D53—42no—
968C4×D53—44no—
969C4×D53—44no—
970C4×D53—44no—
971C4×D53—44no—
972C4×D53—42no—
973C4×D53—42no—
974C4×D53—44no—
975C4×D53—42no—
976C4×D53—42no—
977C4×D532−1+414yes—
978Dic106—24no—
979Dic106—24no—
980Dic106—28no—
981Dic106—24no—
982Dic106—24no—
983Dic106—24no—
984Dic106—44no—
985Dic106—44no—
986Dic106—44no—
987Dic106—44no—
988Dic106—42no—
989Dic106—42no—
990#62761—531nomaximal, Sylow
991C22×C53—24no—
992C22×C53—21no—
993C22×C53—24no—
994C22×C53—22no—
995C22×C53—24no—
996C22×C53C2611yescharacteristic
997C2×D53—22no—
998C2×D53—21no—
999C2×D53—24no—
1000C2×D53—24no—
1001C2×D53—22no—
1002C2×D53—24no—
1003C2×D53—44no—
1004C2×D53C2×2−1+412yes—
1005C4×C53—21no—
1006C4×C53—24no—
1007C4×C53—22no—
1008C4×C53—24no—
1009C4×C53—22no—
1010C4×C53—22no—
1011C4×C53—22no—
1012C4×C53—24no—
1013C4×C53—22no—
1014C4×C53—22no—
1015C4×C53C2×2−1+412yes—
1016Dic53—24no—
1017Dic53—21no—
1018Dic53—22no—
1019Dic53—22no—
1020Dic53—24no—
1021Dic53—22no—
1022Dic53—22no—
1023Dic53—24no—
1024Dic53—22no—
1025Dic53C2×2−1+412yes—
1026Dic53#58514yes—
1027#3557—531no—
1028#3557—532no—
1029#3557D5311yescharacteristic, complemented
1030#3556—531no—
1031#3555—532no—
1032#3555—532no—
1033#3554—532no—
1034#3554—532no—
1035#3553—534no—
1036#3552—534no—
1037#3550—532no—
1038#3548—531no—
1039#3541—534no—
1040#3541—534no—
1041#3531—534no—
1042#3482—534no—
1043#3480—532no—
1044#3480—532no—
1045Q8×#41—532no—
1046Q8×#41—532no—
1047#3461—534no—
1048#3461—534no—
1049#3455—532no—
1050#3455—531no—
1051#3455—531no—
1052#3444—532no—
1053C2×#533—531no—
1054C2×C53—41no—
1055C2×C53—44no—
1056C2×C53C22×2−1+411yescharacteristic
1057C2×C53C2×#58512yes—
1058D53—22no—
1059D53—44no—
1060D53—41no—
1061#564—534no—
1062#563—534no—
1063#563—534no—
1064#563—534no—
1065#563—534no—
1066#563—534no—
1067#563—534no—
1068#563—534no—
1069#563—534no—
1070#563—534no—
1071#563C2×D5314yescomplemented
1072#562—534no—
1073#562—534no—
1074#562—534no—
1075#562—534no—
1076#562—534no—
1077#559—532no—
1078#559—532no—
1079#559—532no—
1080#559—532no—
1081#559—532no—
1082#559C2×D5312yescomplemented
1083Q82—532no—
1084Q82—532no—
1085#557—532no—
1086#557—532no—
1087#557—532no—
1088#557—534no—
1089#557—532no—
1090#557—532no—
1091#557—532no—
1092#557—532no—
1093#557C2×D5312yescomplemented
1094#556—534no—
1095#556—534no—
1096#556—532no—
1097#556—532no—
1098#556—534no—
1099#556—532no—
1100#556—532no—
1101#556—532no—
1102#556C2×D5312yescomplemented
1103#554—534no—
1104#554—534no—
1105#554—532no—
1106#554—532no—
1107#554—534no—
1108#554—534no—
1109#554—534no—
1110#554—532no—
1111#554—532no—
1112#554—532no—
1113#554—534no—
1114#554C2×D5312yescomplemented
1115#553—534no—
1116#553—534no—
1117#553—534no—
1118#553—534no—
1119#553—534no—
1120#553—534no—
1121#552—534no—
1122#552—534no—
1123#552—534no—
1124#552—534no—
1125#552—534no—
1126#552C2×D5314yescomplemented
1127#550—532no—
1128#550—532no—
1129D4×Q8—534no—
1130D4×Q8—532no—
1131D4×Q8—534no—
1132D4×Q8—534no—
1133D4×Q8—532no—
1134#548—534no—
1135#548—534no—
1136#548—534no—
1137#548—534no—
1138#547—534no—
1139#547—534no—
1140#547—534no—
1141#544—534no—
1142#544—534no—
1143#542—532no—
1144#542—532no—
1145#542—534no—
1146#542—534no—
1147#542—534no—
1148#542—534no—
1149#542—532no—
1150#542—534no—
1151#542—534no—
1152#542—532no—
1153#542—532no—
1154#542—532no—
1155#542—534no—
1156#542—532no—
1157#542C2×D5312yes—
1158#542C2×D5314yes—
1159#541—531no—
1160#541—534no—
1161#541—534no—
1162#541—534no—
1163#541—534no—
1164#541—531no—
1165#541—534no—
1166#541—534no—
1167#541—532no—
1168#541—532no—
1169#541—534no—
1170#541—531no—
1171#541—534no—
1172#541C2×D5311yescharacteristic
1173#540—531no—
1174#540—531no—
1175#540—532no—
1176#540—532no—
1177#540—531no—
1178#540C2×D5311yescharacteristic
1179#539—534no—
1180#539—534no—
1181#539—534no—
1182#539—534no—
1183#539—534no—
1184#539—534no—
1185#539—534no—
1186#539—534no—
1187#539—534no—
1188#539—534no—
1189#539—534no—
1190#539C2×D5314yes—
1191#538—534no—
1192#538—534no—
1193#538—534no—
1194#538—534no—
1195#537—534no—
1196#537—534no—
1197#536—534no—
1198#536—534no—
1199#536—534no—
1200#536—534no—
1201#533—532no—
1202#533—532no—
1203#533—534no—
1204#533—532no—
1205#533—532no—
1206#533—531no—
1207#533—531no—
1208#533—534no—
1209#533—534no—
1210#533—532no—
1211#533—532no—
1212#533—532no—
1213#533—534no—
1214#533—534no—
1215#533—534no—
1216#533—532no—
1217#533—532no—
1218#533—532no—
1219#533—531no—
1220#533—531no—
1221#533—531no—
1222#533C2×D5311yescharacteristic
1223#532—531no—
1224#532—531no—
1225#532—532no—
1226#532—532no—
1227#532—532no—
1228#532—532no—
1229C2×C4⋊Q8—532no—
1230#529—534no—
1231#529—534no—
1232#529—534no—
1233#529—534no—
1234#529—534no—
1235#529—534no—
1236#529—532no—
1237#529—534no—
1238#529—532no—
1239#529—534no—
1240#529—534no—
1241#529—534no—
1242#529—534no—
1243#529—534no—
1244#529—534no—
1245#529—534no—
1246#529—534no—
1247#529—534no—
1248#529—534no—
1249#529—534no—
1250#529—532no—
1251#529C2×D5312yes—
1252C2×#125—532no—
1253#525—534no—
1254#525—532no—
1255#525—532no—
1256#525—534no—
1257C2×C22⋊Q8—532no—
1258C2×C22⋊Q8—532no—
1259C4×#41—532no—
1260C4×#41—532no—
1261C4×#41—532no—
1262C4×#41—534no—
1263C4×#41—532no—
1264C4×#41—532no—
1265C4×#41—532no—
1266C4×#41—534no—
1267C4×#41—534no—
1268C4×#41—534no—
1269C2×C4×Q8—532no—
1270C2×C4×Q8—532no—
1271C2×C4×Q8—534no—
1272C2×C4×Q8—534no—
1273C2×#117—531no—
1274C2×#117—531no—
1275C22×C42—531no—
1276C53#6276111yescharacteristic, complemented, Sylow
1277C2×#41—532no—
1278C2×#41—532no—
1279C2×#41—534no—
1280C2×#41—534no—
1281C2×#41—534no—
1282C2×#41—534no—
1283C22×Q8—532no—
1284C22×Q8—532no—
1285C22×Q8—534no—
1286C22×Q8—534no—
1287C23×C4—531no—
1288C23×C4—532no—
1289C4⋊Q8—532no—
1290C4⋊Q8—532no—
1291C4⋊Q8—532no—
1292C4⋊Q8—532no—
1293C4⋊Q8—534no—
1294C4⋊Q8—534no—
1295C4⋊Q8—534no—
1296C4⋊Q8—532no—
1297C4⋊Q8—532no—
1298C4⋊Q8—532no—
1299C4⋊Q8—532no—
1300C4⋊Q8—532no—
1301C4⋊Q8—532no—
1302C4⋊Q8—534no—
1303C4⋊Q8—534no—
1304C4⋊Q8—534no—
1305C4⋊Q8—534no—
1306C4⋊Q8—532no—
1307C4⋊Q8—532no—
1308C4⋊Q8—534no—
1309C4⋊Q8—534no—
1310C4⋊Q8—534no—
1311C4⋊Q8—532no—
1312C4⋊Q8—531no—
1313C4⋊Q8—534no—
1314C4⋊Q8—532no—
1315C4⋊Q8C22×D5312yes—
1316C4⋊Q8C22×D5311yescharacteristic
1317C4⋊Q8C22×D5312yes—
1318C4⋊Q8C22×D5314yes—
1319#127—532no—
1320#127—532no—
1321#127—531no—
1322#127C22×D5311yescharacteristic
1323#126—534no—
1324#126—534no—
1325#126—534no—
1326#126—534no—
1327#126—534no—
1328#126—534no—
1329#126—534no—
1330#126—534no—
1331#126—534no—
1332#126—534no—
1333#126—534no—
1334#126—534no—
1335#126—534no—
1336#126—534no—
1337#126—534no—
1338#126—534no—
1339#126—534no—
1340#126—534no—
1341#126—534no—
1342#126—534no—
1343#126—534no—
1344#126—534no—
1345#126—534no—
1346#126—534no—
1347#126—534no—
1348#126—534no—
1349#126—534no—
1350#126C22×D5314yes—
1351#126C22×D5314yes—
1352#126C22×D5314yes—
1353#126C22×D5314yes—
1354#126C22×D5314yes—
1355#125—532no—
1356#125—532no—
1357#125—532no—
1358#125—532no—
1359#125—532no—
1360#125—532no—
1361#125—534no—
1362#125—534no—
1363#125—534no—
1364#125—534no—
1365#125—534no—
1366#125—534no—
1367#125—534no—
1368#125—534no—
1369#125—534no—
1370#125—534no—
1371#125—534no—
1372#125—534no—
1373#125—534no—
1374#125—534no—
1375#125—534no—
1376#125—534no—
1377#125—534no—
1378#125—534no—
1379#125—534no—
1380#125—534no—
1381#125—534no—
1382#125—532no—
1383#125—532no—
1384#125—532no—
1385#125—532no—
1386#125—534no—
1387#125—534no—
1388#125—534no—
1389#125—534no—
1390#125—531no—
1391#125—531no—
1392#125C22×D5312yes—
1393#125C22×D5312yes—
1394#125C22×D5314yes—
1395#125C22×D5314yes—
1396#125C22×D5314yes—
1397#125C22×D5311yescharacteristic
1398#125C22×D5311yescharacteristic
1399#124—534no—
1400#124—534no—
1401#124—532no—
1402#124—534no—
1403#124—532no—
1404#124—534no—
1405#124—534no—
1406#124—534no—
1407#124—534no—
1408#124—534no—
1409#124—534no—
1410#124—534no—
1411#124—534no—
1412#124—534no—
1413#124—534no—
1414#124—532no—
1415#124—534no—
1416#124—532no—
1417#124C22×D5312yes—
1418#124C22×D5314yes—
1419#124C22×D5314yes—
1420#124C22×D5312yes—
1421#123—534no—
1422#123—534no—
1423#123—534no—
1424#123—534no—
1425#123—534no—
1426#123—534no—
1427#123—534no—
1428#123—534no—
1429#123—534no—
1430#123—534no—
1431#123—534no—
1432#123—534no—
1433#123—534no—
1434#123—534no—
1435#123—534no—
1436#123—534no—
1437#123—534no—
1438#123—534no—
1439#123—534no—
1440#123—534no—
1441#123—534no—
1442#123—534no—
1443#123—534no—
1444#123—534no—
1445#123—534no—
1446#123—534no—
1447#123—534no—
1448#123—534no—
1449#123—534no—
1450#123C22×D5314yes—
1451#123C22×D5314yes—
1452#123C22×D5314yes—
1453#123C22×D5314yes—
1454#123C22×D5314yes—
1455C22⋊Q8—532no—
1456C22⋊Q8—532no—
1457C22⋊Q8—532no—
1458C22⋊Q8—534no—
1459C22⋊Q8—534no—
1460C22⋊Q8—534no—
1461C22⋊Q8—534no—
1462C22⋊Q8—534no—
1463C22⋊Q8—532no—
1464C22⋊Q8—532no—
1465C22⋊Q8—532no—
1466C22⋊Q8—534no—
1467C22⋊Q8—534no—
1468C22⋊Q8—534no—
1469C22⋊Q8—534no—
1470C22⋊Q8—532no—
1471C22⋊Q8—532no—
1472C22⋊Q8—532no—
1473C22⋊Q8—532no—
1474C22⋊Q8—532no—
1475C22⋊Q8—532no—
1476C22⋊Q8—532no—
1477C22⋊Q8—534no—
1478C22⋊Q8—534no—
1479C22⋊Q8—534no—
1480C22⋊Q8—534no—
1481C22⋊Q8—534no—
1482C22⋊Q8—534no—
1483C22⋊Q8—534no—
1484C22⋊Q8—534no—
1485C22⋊Q8—534no—
1486C22⋊Q8—534no—
1487C22⋊Q8—534no—
1488C22⋊Q8—534no—
1489C22⋊Q8—534no—
1490C22⋊Q8—534no—
1491C22⋊Q8—534no—
1492C22⋊Q8—534no—
1493C22⋊Q8—534no—
1494C22⋊Q8—534no—
1495C22⋊Q8—534no—
1496C22⋊Q8—534no—
1497C22⋊Q8—534no—
1498C22⋊Q8—532no—
1499C22⋊Q8—532no—
1500C22⋊Q8—532no—
1501C22⋊Q8—532no—
1502C22⋊Q8—534no—
1503C22⋊Q8—534no—
1504C22⋊Q8—534no—
1505C22⋊Q8—534no—
1506C22⋊Q8—534no—
1507C22⋊Q8—534no—
1508C22⋊Q8—534no—
1509C22⋊Q8—534no—
1510C22⋊Q8—534no—
1511C22⋊Q8—534no—
1512C22⋊Q8—534no—
1513C22⋊Q8C22×D5312yes—
1514C22⋊Q8C22×D5312yes—
1515C22⋊Q8C22×D5312yes—
1516C22⋊Q8C22×D5314yes—
1517C22⋊Q8C22×D5314yes—
1518C22⋊Q8C22×D5314yes—
1519C22⋊Q8C22×D5314yes—
1520C22⋊Q8C22×D5314yes—
1521#121—534no—
1522#121—532no—
1523#121—534no—
1524#121—534no—
1525#121—534no—
1526#121—534no—
1527#121—534no—
1528#121—534no—
1529#121—534no—
1530#121—532no—
1531#121—534no—
1532#121—534no—
1533#121—532no—
1534#121—534no—
1535#121—534no—
1536#121—534no—
1537#121—534no—
1538#121—534no—
1539#121—534no—
1540#121—534no—
1541#121—534no—
1542#121—534no—
1543#121—534no—
1544#121—534no—
1545#121C22×D5312yes—
1546#121C22×D5314yes—
1547#120—534no—
1548#120—534no—
1549C4×Q8—532no—
1550C4×Q8—532no—
1551C4×Q8—534no—
1552C4×Q8—532no—
1553C4×Q8—532no—
1554C4×Q8—532no—
1555C4×Q8—532no—
1556C4×Q8—532no—
1557C4×Q8—534no—
1558C4×Q8—532no—
1559C4×Q8—532no—
1560C4×Q8—532no—
1561C4×Q8—532no—
1562C4×Q8—534no—
1563C4×Q8—534no—
1564C4×Q8—534no—
1565C4×Q8—534no—
1566C4×Q8—534no—
1567C4×Q8—534no—
1568C4×Q8—534no—
1569C4×Q8—534no—
1570C4×Q8—534no—
1571C4×Q8—532no—
1572C4×Q8—534no—
1573C4×Q8—532no—
1574C4×Q8—532no—
1575C4×Q8—532no—
1576C4×Q8—532no—
1577C4×Q8—532no—
1578C4×Q8—532no—
1579C4×Q8—532no—
1580C4×Q8—532no—
1581C4×Q8—534no—
1582C4×Q8—534no—
1583C4×Q8—534no—
1584C4×Q8—534no—
1585C4×Q8—532no—
1586C4×Q8—534no—
1587C4×Q8—532no—
1588C4×Q8—532no—
1589C4×Q8C22×D5312yes—
1590C4×Q8C22×D5312yes—
1591C4×Q8C22×D5314yes—
1592C4×Q8C22×D5312yes—
1593C4×Q8C22×D5312yes—
1594C4×Q8C22×D5312yes—
1595C4×D4—534no—
1596C4×D4—534no—
1597C4×D4—532no—
1598C4×D4—532no—
1599C4×D4—532no—
1600C4×D4—534no—
1601C4×D4—534no—
1602C4×D4—534no—
1603C4×D4—534no—
1604C4×D4—534no—
1605C4×D4—534no—
1606C4×D4—534no—
1607C4×D4—534no—
1608C4×D4—534no—
1609C4×D4—534no—
1610C4×D4—534no—
1611C4×D4—532no—
1612C4×D4—534no—
1613C4×D4—534no—
1614C4×D4—534no—
1615C4×D4—532no—
1616C4×D4—532no—
1617C4×D4—534no—
1618C4×D4—534no—
1619C4×D4—534no—
1620C4×D4—534no—
1621C4×D4—534no—
1622C4×D4—534no—
1623C4×D4—534no—
1624C4×D4—534no—
1625C4×D4—534no—
1626C4×D4—534no—
1627C4×D4—534no—
1628C4×D4—534no—
1629C4×D4—534no—
1630C4×D4—534no—
1631C4×D4—532no—
1632C4×D4—534no—
1633C4×D4—534no—
1634C4×D4—532no—
1635C4×D4—532no—
1636C4×D4C22×D5314yes—
1637C4×D4C22×D5312yes—
1638C4×D4C22×D5314yes—
1639C4×D4C22×D5312yes—
1640C4×D4C22×D5312yes—
1641#117—531no—
1642#117—531no—
1643#117—532no—
1644#117—532no—
1645#117—532no—
1646#117—532no—
1647#117—534no—
1648#117—534no—
1649#117—534no—
1650#117—534no—
1651#117—534no—
1652#117—531no—
1653#117—531no—
1654#117—532no—
1655#117—534no—
1656#117—534no—
1657#117—534no—
1658#117—534no—
1659#117—534no—
1660#117—534no—
1661#117—534no—
1662#117—531no—
1663#117—531no—
1664#117—532no—
1665#117—534no—
1666#117—534no—
1667#117—534no—
1668#117—534no—
1669#117C22×D5311yescharacteristic
1670#117C22×D5311yescharacteristic
1671#117C22×D5314yes—
1672#117C22×D5314yes—
1673C2×C4⋊C4—534no—
1674C2×C4⋊C4—534no—
1675C2×C4⋊C4—532no—
1676C2×C4⋊C4—532no—
1677C2×C4⋊C4—532no—
1678C2×C4⋊C4—532no—
1679C2×C4⋊C4—532no—
1680C2×C4⋊C4—532no—
1681C2×C4⋊C4—532no—
1682C2×C4⋊C4—532no—
1683C2×C4⋊C4—534no—
1684C2×C4⋊C4—534no—
1685C2×C4⋊C4—534no—
1686C2×C4⋊C4C22×D5314yes—
1687C2×C22⋊C4—531no—
1688C2×C22⋊C4—531no—
1689C2×C22⋊C4—532no—
1690C2×C42—534no—
1691C2×C42—534no—
1692C2×C42—534no—
1693C2×C42—532no—
1694C2×C42—531no—
1695C2×C42—531no—
1696C2×C42—531no—
1697C2×C42—532no—
1698C2×C42—532no—
1699C2×C42—534no—
1700C2×C42—534no—
1701C2×C42—534no—
1702C2×C42—531no—
1703C2×C42—531no—
1704C2×C42—531no—
1705C2×C42—531no—
1706C2×C42—532no—
1707C2×C42C22×D5311yescharacteristic
1708C24—531no—
1709#41—1068no—
1710#41—1068no—
1711#41—2128no—
1712#41—2128no—
1713#41—2128no—
1714#41—2128no—
1715C2×Q8—532no—
1716C2×Q8—532no—
1717C2×Q8—532no—
1718C2×Q8—534no—
1719C2×Q8—532no—
1720C2×Q8—532no—
1721C2×Q8—534no—
1722C2×Q8—534no—
1723C2×Q8—532no—
1724C2×Q8—532no—
1725C2×Q8—534no—
1726C2×Q8—534no—
1727C2×Q8—2128no—
1728C2×Q8—2124no—
1729C2×Q8—2124no—
1730C2×Q8—2128no—
1731C2×Q8C23×D5312yes—
1732C2×Q8C23×D5312yes—
1733C2×Q8C23×D5314yes—
1734C2×Q8C23×D5312yes—
1735C2×D4—534no—
1736C2×D4—534no—
1737C2×D4—534no—
1738C2×D4—534no—
1739C2×D4—534no—
1740C2×D4—534no—
1741C2×D4—534no—
1742C2×D4—534no—
1743C2×D4—532no—
1744C2×D4—534no—
1745C2×D4—534no—
1746C2×D4C23×D5312yes—
1747C2×D4C23×D5314yes—
1748C2×D4C23×D5314yes—
1749C22×C4—531no—
1750C22×C4—534no—
1751C22×C4—531no—
1752C22×C4—532no—
1753C22×C4—534no—
1754C22×C4—534no—
1755C22×C4—534no—
1756C22×C4—534no—
1757C22×C4—531no—
1758C22×C4—532no—
1759C22×C4—531no—
1760C22×C4—531no—
1761C22×C4—532no—
1762C22×C4—534no—
1763C22×C4—532no—
1764C22×C4—532no—
1765C22×C4—532no—
1766C22×C4—532no—
1767C22×C4—532no—
1768C22×C4—532no—
1769C22×C4—534no—
1770C22×C4—534no—
1771C22×C4—534no—
1772C22×C4—534no—
1773C22×C4—534no—
1774C22×C4—1064no—
1775C22×C4—2124no—
1776C22×C4C23×D5311yescharacteristic
1777C22×C4C23×D5312yes—
1778C22×C4C23×D5314yes—
1779C22×C4C23×D5314yes—
1780C22×C4C23×D5314yes—
1781C4⋊C4—532no—
1782C4⋊C4—532no—
1783C4⋊C4—532no—
1784C4⋊C4—532no—
1785C4⋊C4—534no—
1786C4⋊C4—534no—
1787C4⋊C4—532no—
1788C4⋊C4—532no—
1789C4⋊C4—532no—
1790C4⋊C4—532no—
1791C4⋊C4—532no—
1792C4⋊C4—532no—
1793C4⋊C4—532no—
1794C4⋊C4—532no—
1795C4⋊C4—532no—
1796C4⋊C4—532no—
1797C4⋊C4—532no—
1798C4⋊C4—532no—
1799C4⋊C4—532no—
1800C4⋊C4—532no—
1801C4⋊C4—534no—
1802C4⋊C4—534no—
1803C4⋊C4—534no—
1804C4⋊C4—534no—
1805C4⋊C4—534no—
1806C4⋊C4—534no—
1807C4⋊C4—534no—
1808C4⋊C4—534no—
1809C4⋊C4—532no—
1810C4⋊C4—532no—
1811C4⋊C4—532no—
1812C4⋊C4—532no—
1813C4⋊C4—532no—
1814C4⋊C4—532no—
1815C4⋊C4—534no—
1816C4⋊C4—534no—
1817C4⋊C4—532no—
1818C4⋊C4—532no—
1819C4⋊C4—534no—
1820C4⋊C4—534no—
1821C4⋊C4—534no—
1822C4⋊C4—534no—
1823C4⋊C4—534no—
1824C4⋊C4—534no—
1825C4⋊C4—534no—
1826C4⋊C4—534no—
1827C4⋊C4—534no—
1828C4⋊C4—534no—
1829C4⋊C4—534no—
1830C4⋊C4—534no—
1831C4⋊C4—534no—
1832C4⋊C4—534no—
1833C4⋊C4—534no—
1834C4⋊C4—534no—
1835C4⋊C4—534no—
1836C4⋊C4—534no—
1837C4⋊C4C23×D5312yes—
1838C4⋊C4C23×D5312yes—
1839C4⋊C4C23×D5314yes—
1840C4⋊C4C23×D5312yes—
1841C4⋊C4C23×D5312yes—
1842C4⋊C4C23×D5312yes—
1843C4⋊C4C23×D5312yes—
1844C4⋊C4C23×D5314yes—
1845C4⋊C4C23×D5312yes—
1846C4⋊C4C23×D5312yes—
1847C4⋊C4C23×D5314yes—
1848C4⋊C4C23×D5314yes—
1849C4⋊C4C23×D5312yes—
1850C4⋊C4C23×D5312yes—
1851C4⋊C4C23×D5314yes—
1852C4⋊C4C23×D5314yes—
1853C4⋊C4C23×D5314yes—
1854C4⋊C4C23×D5314yes—
1855C4⋊C4C23×D5314yes—
1856C4⋊C4C23×D5314yes—
1857C22⋊C4—531no—
1858C22⋊C4—531no—
1859C22⋊C4—532no—
1860C22⋊C4—534no—
1861C22⋊C4—534no—
1862C22⋊C4—534no—
1863C22⋊C4—534no—
1864C22⋊C4—534no—
1865C22⋊C4—534no—
1866C22⋊C4—534no—
1867C22⋊C4—532no—
1868C22⋊C4—532no—
1869C22⋊C4—532no—
1870C22⋊C4—532no—
1871C22⋊C4—534no—
1872C22⋊C4—534no—
1873C22⋊C4—534no—
1874C22⋊C4—534no—
1875C22⋊C4—534no—
1876C22⋊C4—534no—
1877C22⋊C4—534no—
1878C22⋊C4—534no—
1879C22⋊C4—534no—
1880C22⋊C4—534no—
1881C22⋊C4—534no—
1882C22⋊C4—534no—
1883C22⋊C4—534no—
1884C22⋊C4—534no—
1885C22⋊C4—534no—
1886C22⋊C4—534no—
1887C22⋊C4—534no—
1888C22⋊C4—534no—
1889C22⋊C4C23×D5312yes—
1890C22⋊C4C23×D5311yescharacteristic
1891C22⋊C4C23×D5311yescharacteristic
1892C22⋊C4C23×D5314yes—
1893C22⋊C4C23×D5314yes—
1894C22⋊C4C23×D5314yes—
1895C22⋊C4C23×D5314yes—
1896C22⋊C4C23×D5314yes—
1897C22⋊C4C23×D5314yes—
1898C22⋊C4C23×D5314yes—
1899C22⋊C4C23×D5314yes—
1900C22⋊C4C23×D5314yes—
1901C42—532no—
1902C42—532no—
1903C42—532no—
1904C42—534no—
1905C42—534no—
1906C42—532no—
1907C42—532no—
1908C42—532no—
1909C42—532no—
1910C42—531no—
1911C42—532no—
1912C42—532no—
1913C42—531no—
1914C42—534no—
1915C42—534no—
1916C42—534no—
1917C42—531no—
1918C42—531no—
1919C42—532no—
1920C42—534no—
1921C42—534no—
1922C42—534no—
1923C42—534no—
1924C42—534no—
1925C42—534no—
1926C42C23×D5311yescharacteristic
1927C42C23×D5312yes—
1928C42C23×D5311yescharacteristic
1929C42C23×D5314yes—
1930C42C23×D5311yescharacteristic
1931C42C23×D5312yes—
1932C42C23×D5314yes—
1933C42C23×D5311yescharacteristic
1934C42C23×D5314yes—
1935C23—531no—
1936C23—531no—
1937C23—534no—
1938C23—1062no—
1939C23—2122no—
1940C23C24×D5311yescharacteristic
1941C23C24×D5314yes—
1942Q8—24no—
1943Q8—42no—
1944Q8—44no—
1945Q8—42no—
1946Q8—1064no—
1947Q8—1064no—
1948Q8—1068no—
1949Q8—1064no—
1950Q8—1064no—
1951Q8—1064no—
1952Q8—2124no—
1953Q8—2124no—
1954Q8—2124no—
1955Q8—2122no—
1956Q8—2122no—
1957Q8—2124no—
1958D4—24no—
1959D4—44no—
1960D4—44no—
1961D4—1068no—
1962D4—1068no—
1963D4—1068no—
1964D4—1064no—
1965D4—2124no—
1966D4—2124no—
1967D4—2124no—
1968D4—2124no—
1969D4—2124no—
1970D4—2124no—
1971D4—2124no—
1972C2×C4—22no—
1973C2×C4—42no—
1974C2×C4—44no—
1975C2×C4—44no—
1976C2×C4—44no—
1977C2×C4—531no—
1978C2×C4—532no—
1979C2×C4—534no—
1980C2×C4—534no—
1981C2×C4—531no—
1982C2×C4—532no—
1983C2×C4—532no—
1984C2×C4—534no—
1985C2×C4—534no—
1986C2×C4—532no—
1987C2×C4—532no—
1988C2×C4—532no—
1989C2×C4—1062no—
1990C2×C4—1064no—
1991C2×C4—1064no—
1992C2×C4—1068no—
1993C2×C4—1068no—
1994C2×C4—1062no—
1995C2×C4—1062no—
1996C2×C4—1064no—
1997C2×C4—1068no—
1998C2×C4—1068no—
1999C2×C4—1062no—
2000C2×C4—2122no—
2001C2×C4—2122no—
2002C2×C4—2122no—
2003C2×C4—2124no—
2004C2×C4—2122no—
2005C2×C4—2122no—
2006C2×C4—2122no—
2007C2×C4—2124no—
2008C2×C4—2124no—
2009C2×C4—2124no—
2010C2×C4—2124no—
2011C2×C4—2124no—
2012C2×C4—2124no—
2013C2×C4C24×D5312yes—
2014C2×C4C24×D5314yes—
2015C2×C4C24×D5312yes—
2016C2×C4C24×D5314yes—
2017C2×C4C24×D5312yes—
2018C2×C4C24×D5311yescharacteristic
2019C2×C4C24×D5312yes—
2020C2×C4C24×D5314yes—
2021C2×C4C24×D5312yes—
2022C2×C4C24×D5312yes—
2023C2×C4C24×D5311yescharacteristic
2024C22—21no—
2025C22—24no—
2026C22—24no—
2027C22—24no—
2028C22—22no—
2029C22—532no—
2030C22—1062no—
2031C22—1061no—
2032C22—1064no—
2033C22—1064no—
2034C22—1062no—
2035C22—1064no—
2036C22—2124no—
2037C22C25×D5311yescharacteristic
2038C4—21no—
2039C4—24no—
2040C4—22no—
2041C4—22no—
2042C4—24no—
2043C4—22no—
2044C4—24no—
2045C4—22no—
2046C4—22no—
2047C4—22no—
2048C4—532no—
2049C4—534no—
2050C4—1061no—
2051C4—1064no—
2052C4—1062no—
2053C4—1064no—
2054C4—1062no—
2055C4—1062no—
2056C4—1064no—
2057C4—1062no—
2058C4—1062no—
2059C42−1+4×D5312yes—
2060C2—41no—
2061C2—44no—
2062C2—1062no—
2063C2—2121no—
2064C2—2124no—
2065C2C2×2−1+4×D5311yescharacteristic
2066C2#585×D5312yes—
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3557C2
hypercenter#3557D53
hypocenterC53#62761
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3557

Complements

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

NH ≅ G/Ntype
1. #20289221C2semidirect
2. #20289217C2semidirect
3. #20289208C2semidirect
4. #20289202C2semidirect
5. #20289195C2semidirect
6. #20289185C2semidirect
7. #20289178C2semidirect
8. #20289162C2semidirect
9. #20289149C2semidirect
10. #20289123C2semidirect
11. #20289109C2semidirect
12. #20289007C2semidirect
13. #20288999C2semidirect
14. #20288861C2semidirect
15. #20288329C2semidirect
16. #20288311C2semidirect
17. #20288307C2semidirect
18. #20288297C2semidirect
19. #20288294C2semidirect
20. #20288145C2semidirect
21. #20288141C2semidirect
22. #20288106C2semidirect
23. #20288102C2semidirect
24. #20288099C2semidirect
25. #20288009C2semidirect
26. #533×D53C2semidirect
27. C53×#3557C2semidirect
28. C53⋊#564C22semidirect
31. #16811375C22semidirect
32. #16811375C22semidirect
33. #16811375C22semidirect
35. #16811374C22semidirect
37. #16811372C22semidirect
39. #16811370C22semidirect
43. #16811358C22semidirect
44. #16811356C22semidirect
45. #16811356C22semidirect
46. #16811355C22semidirect
47. #16811355C22semidirect
48. Q8×Dic106C22semidirect
49. #16811353C22semidirect
50. #16811351C22semidirect
51. #16811351C22semidirect
52. #16811350C22semidirect
53. #16811350C22semidirect
54. #16811350C22semidirect
55. #16811349C22semidirect
56. #16811349C22semidirect
57. #16811348C22semidirect
58. #16811346C22semidirect
60. #16811345C22semidirect
61. #16811345C22semidirect
62. #16811342C22semidirect
63. #16811342C22semidirect
65. #16811340C22semidirect
67. #16811333C22semidirect
68. #16811332C22semidirect
69. #16811332C22semidirect
72. #16811329C22semidirect
73. #16811329C22semidirect
83. #16811312C22semidirect
85. #16811306C22semidirect
87. #16811305C22semidirect
88. #16811294C22semidirect
89. #16811293C22semidirect
90. D4×Dic106C22semidirect
92. #16811288C22semidirect
94. #16811286C22semidirect
101. #16811271C22semidirect
102. #16811252C22semidirect
103. #16811250C22semidirect
109. #16811243C22semidirect
117. #16811237C22semidirect
120. #16811235C22semidirect
123. #16811232C22semidirect
124. #16811232C22semidirect
126. #16811231C22semidirect
129. #16811230C22semidirect
130. #16811230C22semidirect
137. #16811220C22semidirect
140. #16811219C22semidirect
143. #16811216C22semidirect
145. #16811215C22semidirect
153. #16811196C22semidirect
155. #16811195C22semidirect
162. #16811179C22semidirect
163. #16811179C22semidirect
166. #16811178C22semidirect
175. #16811175C22semidirect
176. #16811175C22semidirect
177. #16811175C22semidirect
186. #16811159C22semidirect
194. #16811156C22semidirect
195. #16811156C22semidirect
199. #16811152C22semidirect
204. #16811150C22semidirect
205. #16811150C22semidirect
217. #16811091C22semidirect
222. C4×#11719947C22semidirect
223. C2×#13133182C22semidirect
226. C4×Q8×D53C22semidirect
230. C53×#563C22semidirect
231. C53×#559C22semidirect
232. C53×#557C22semidirect
233. C53×#556C22semidirect
234. C53×#554C22semidirect
235. C53×#552C22semidirect
1029. #3557D53semidirect
1071. #563C2×D53semidirect
1082. #559C2×D53semidirect
1093. #557C2×D53semidirect
1102. #556C2×D53semidirect
1114. #554C2×D53semidirect
1126. #552C2×D53semidirect
1276. C53#62761semidirect

Maximal subgroups

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

subgroupindex
#202892212
#202892172
#202892082
#202892022
#202891952
#202891852
#202891782
#202891622
#202891492
#202891232
#202891092
#202890072
#202889992
#202888612
#202883292
#202883112
#202883072
#202882972
#202882942
#202881452
#202881412
#202881062
#202881022
#202880992
#202880092
#533×D532
C53×#35572
#6276153