Finite Group Databasebeta

← #28291938

Subgroups — #28291938

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#20289223C211yesmaximal, characteristic, complemented
2#20289220C211yesmaximal, characteristic, complemented
3#20289214C212yesmaximal, complemented
4#20289208C211yesmaximal, characteristic, complemented
5#20289201C212yesmaximal, complemented
6#20289193C212yesmaximal, complemented
7#20289184C212yesmaximal, complemented
8#20289176C212yesmaximal, complemented
9#20289165C214yesmaximal, complemented
10#20289148C214yesmaximal, complemented
11#20289123C212yesmaximal, complemented
12#20289109C211yesmaximal, characteristic, complemented
13#20289003C214yesmaximal, complemented
14#20288995C214yesmaximal, complemented
15#20288860C214yesmaximal, complemented
16#20288328C214yesmaximal, complemented
17#20288312C212yesmaximal, complemented
18#20288308C212yesmaximal, complemented
19#41×Dic106C212yesmaximal, complemented
20#20288293C212yesmaximal, complemented
21#20288144C214yesmaximal, complemented
22#20288140C214yesmaximal, complemented
23#20288105C211yesmaximal, characteristic, complemented
24#20288103C212yesmaximal, complemented
25#20288007C212yesmaximal, complemented
26C2×#16811176C211yesmaximal, characteristic, complemented
27C53×#3455C211yesmaximal, characteristic, complemented
28C53⋊#564C2214yescomplemented
29#16811377C2214yescomplemented
30#16811376C2214yes—
31#16811376C2214yescomplemented
32#16811375C2214yes—
33#16811375C2214yes—
34#16811375C2214yescomplemented
35#16811375C2214yescomplemented
36#16811374C2214yescomplemented
37#16811374C2214yescomplemented
38#16811373C2214yes—
39#16811370C2214yes—
40#16811370C2214yescomplemented
41#16811368C2214yes—
42#16811368C2214yes—
43#16811367C2214yes—
44#16811359C2212yescomplemented
45#16811358C2212yescomplemented
46#16811356C2212yescomplemented
47#16811356C2212yescomplemented
48#16811355C2212yescomplemented
49#16811355C2212yescomplemented
50Q8×Dic106C2212yescomplemented
51#16811353C2212yescomplemented
52#16811352C2212yescomplemented
53#16811351C2212yescomplemented
54#16811350C2212yescomplemented
55#16811350C2212yescomplemented
56#16811350C2214yescomplemented
57#16811349C2212yescomplemented
58#16811349C2212yescomplemented
59#16811348C2212yescomplemented
60#16811348C2212yescomplemented
61#16811347C2212yescomplemented
62#16811345C2212yescomplemented
63#16811345C2212yescomplemented
64#16811343C2212yescomplemented
65#16811342C2214yes—
66#16811342C2212yescomplemented
67#16811342C2212yescomplemented
68#16811340C2214yes—
69#16811340C2214yescomplemented
70#16811334C2212yescomplemented
71#16811332C2214yes—
72#16811332C2214yes—
73#16811332C2212yescomplemented
74#16811332C2212yescomplemented
75#16811331C2214yes—
76#16811330C2214yes—
77#16811330C2212yescomplemented
78#16811329C2212yescomplemented
79#16811329C2212yescomplemented
80#16811327C2214yes—
81#16811327C2214yes—
82#16811325C2214yes—
83#16811322C2214yes—
84#16811322C2214yes—
85#16811319C2214yes—
86#16811316C2214yes—
87#16811316C2214yes—
88#16811315C2214yescomplemented
89#16811311C2214yescomplemented
90#16811310C2214yes—
91#16811310C2214yescomplemented
92#16811309C2214yes—
93#16811309C2214yescomplemented
94#16811294C2212yescomplemented
95#16811293C2212yescomplemented
96D4×Dic106C2214yes—
97D4×Dic106C2212yescomplemented
98#16811288C2212yescomplemented
99#16811286C2214yes—
100#16811286C2214yescomplemented
101#16811282C2214yes—
102#16811281C2214yes—
103#16811279C2214yes—
104#16811279C2214yes—
105#16811273C2214yes—
106#16811271C2214yes—
107#16811271C2214yescomplemented
108#16811253C2214yescomplemented
109#16811252C2214yescomplemented
110#16811246C2212yes—
111#16811246C2212yes—
112#16811244C2212yes—
113#16811244C2212yes—
114#16811242C2214yes—
115#16811241C2214yes—
116#16811241C2214yescomplemented
117#16811240C2212yes—
118#16811240C2212yes—
119#16811240C2214yes—
120#16811239C2214yes—
121#16811239C2214yescomplemented
122#16811237C2214yes—
123#16811237C2214yes—
124#16811236C2214yescomplemented
125#16811235C2211yescharacteristic
126#16811235C2211yescharacteristic
127#16811233C2212yes—
128#16811233C2212yes—
129#16811233C2214yescomplemented
130#16811232C2214yescomplemented
131#16811232C2214yescomplemented
132#16811230C2214yes—
133#16811230C2214yes—
134#16811230C2214yescomplemented
135#16811230C2214yescomplemented
136#16811228C2211yescharacteristic
137#16811228C2211yescharacteristic
138#16811226C2212yes—
139#16811226C2212yes—
140#16811222C2214yescomplemented
141#16811220C2214yes—
142#16811218C2214yes—
143#16811217C2214yes—
144#16811217C2214yes—
145#16811217C2214yes—
146#16811217C2214yescomplemented
147#16811216C2214yes—
148#16811216C2214yescomplemented
149#16811214C2214yes—
150#16811214C2214yescomplemented
151#16811211C2214yes—
152#16811208C2214yes—
153#16811208C2214yes—
154#16811202C2214yes—
155#16811200C2214yes—
156#16811196C2214yescomplemented
157#16811195C2214yes—
158#16811195C2214yescomplemented
159#16811193C2214yes—
160#16811180C2211yescharacteristic
161#16811180C2214yescomplemented
162#16811177C2214yescomplemented
163#16811177C2214yescomplemented
164#16811177C2214yescomplemented
165#16811176C2212yes—
166#16811176C2211yescharacteristic
167#16811176C2212yes—
168#16811176C2211yescharacteristic
169#16811176C2212yes—
170#16811176C2212yes—
171#16811176C2212yes—
172#16811176C2212yes—
173#16811176C2211yescharacteristic
174#16811176C2211yescharacteristic
175#16811176C2212yes—
176#16811176C2212yes—
177#16811176C2214yescomplemented
178#16811176C2214yescomplemented
179#16811175C2212yes—
180#16811175C2212yes—
181#16811173C2211yescharacteristic
182#16811169C2212yes—
183#16811169C2212yes—
184#16811168C2212yes—
185#16811168C2212yes—
186C2×#13133216C2212yes—
187#16811159C2212yes—
188#16811159C2212yes—
189#16811157C2214yescomplemented
190#16811155C2214yes—
191#16811155C2214yes—
192#16811155C2214yescomplemented
193#16811154C2212yes—
194#16811154C2212yes—
195#16811153C2214yes—
196#16811153C2214yes—
197#16811153C2214yes—
198#16811153C2214yes—
199#16811153C2214yescomplemented
200#16811153C2214yescomplemented
201#16811151C2214yes—
202#16811151C2214yes—
203#16811151C2214yescomplemented
204#16811151C2214yescomplemented
205#16811150C2214yes—
206#16811150C2214yes—
207C2×#13133208C2212yes—
208#16811134C2212yes—
209#16811129C2214yes—
210#16811129C2214yes—
211C2×#13133194C2212yes—
212C2×#13133194C2212yes—
213#41×Dic53C2212yes—
214#41×Dic53C2212yes—
215C4×#11719945C2212yes—
216C4×#11719945C2214yescomplemented
217#16811091C2212yes—
218#16811091C2212yes—
219C4×#11719947C2214yes—
220C4×#11719947C2214yes—
221C4×#11719947C2214yescomplemented
222C2×C4×Dic106C2212yes—
223C2×C4×Dic106C2212yes—
224C2×C4×Dic106C2214yescomplemented
225C4×Q8×D53C2214yescomplemented
226C2×#13133176C2211yescharacteristic
227C22×C4×Dic53C2211yescharacteristic
228C53×#542C2212yes—
229C53×#542C2212yes—
230C53×#541C2211yescharacteristic
231C53×#541C2211yescharacteristic
232C53×#540C2211yescharacteristic
233C53×#540C2211yescharacteristic
234C53×#539C2214yes—
235C53×#538C2214yes—
236C53×#533C2211yescharacteristic
237C53×#532C2211yescharacteristic
238C53×#529C2214yes—
239C53×#529C2214yes—
240C53×#525C2212yes—
241C4×#41×C53C2212yes—
242C2×#117×C53C2211yescharacteristic
243C2×#11719945C2312yes—
244C2×#11719945C2314yes—
245C2×#11719947C2314yes—
246C2×#11719947C2314yes—
247C2×#11719947C2314yes—
248C22×Dic106C2312yes—
249C22×Dic106C2314yes—
250C22×Dic106C2312yes—
251C2×Q8×D53C2314yes—
252C23×Dic53C2312yes—
253#13133217C2314yes—
254#13133217C2312yes—
255#13133217C2314yes—
256#13133217C2311yescharacteristic
257#13133216C2314yes—
258#13133216C2312yes—
259#13133216C2314yes—
260#13133216C2314yes—
261#13133216C2312yes—
262#13133216C2314yes—
263#13133216C2312yes—
264#13133216C2312yes—
265#13133216C2314yes—
266#13133216C2312yes—
267#13133216C2312yes—
268#13133216C2314yes—
269#13133216C2314yes—
270#13133216C2312yes—
271#13133216C2312yes—
272#13133216C2312yes—
273#13133216C2312yes—
274#13133216C2312yes—
275#13133216C2312yes—
276#13133215C2314yes—
277#13133215C2314yes—
278#13133215C2314yes—
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#13133211C2314yes—
295#13133211C2314yes—
296#13133210C2314yes—
297#13133210C2314yes—
298#13133210C2314yes—
299#13133210C2314yes—
300#13133210C2314yes—
301#13133210C2314yes—
302#13133210C2314yes—
303#13133210C2314yes—
304#13133210C2314yes—
305#13133210C2314yes—
306#13133210C2314yes—
307#13133210C2314yes—
308#13133210C2314yes—
309#13133210C2314yes—
310#13133210C2314yes—
311#13133210C2314yes—
312#13133209C2314yes—
313#13133209C2314yes—
314#13133209C2314yes—
315#13133209C2311yescharacteristic
316#13133209C2311yescharacteristic
317#13133208C2314yes—
318#13133208C2312yes—
319#13133208C2314yes—
320#13133208C2312yes—
321#13133208C2314yes—
322#13133208C2314yes—
323#13133208C2312yes—
324#13133208C2312yes—
325#13133208C2314yes—
326#13133208C2312yes—
327#13133208C2314yes—
328#13133208C2312yes—
329#13133208C2312yes—
330#13133208C2312yes—
331#13133208C2312yes—
332#13133208C2312yes—
333#13133208C2312yes—
334#13133208C2312yes—
335#13133208C2314yes—
336#13133207C2314yes—
337#13133207C2314yes—
338#13133207C2314yes—
339#13133207C2314yes—
340#13133207C2314yes—
341#13133207C2314yes—
342#13133207C2314yes—
343#13133207C2314yes—
344#13133207C2314yes—
345#13133207C2314yes—
346#13133207C2314yes—
347#13133207C2314yes—
348#13133207C2314yes—
349#13133207C2314yes—
350#13133207C2314yes—
351#13133207C2314yes—
352#13133206C2312yes—
353#13133206C2312yes—
354#13133205C2314yes—
355#13133205C2312yes—
356#13133204C2314yes—
357#13133204C2314yes—
358#13133204C2312yes—
359#13133204C2312yes—
360#13133204C2314yes—
361#13133203C2314yes—
362#13133203C2314yes—
363#13133203C2314yes—
364#13133203C2314yes—
365#13133203C2314yes—
366#13133203C2314yes—
367#13133203C2314yes—
368#13133203C2314yes—
369#13133203C2314yes—
370#13133203C2314yes—
371#13133202C2314yes—
372#13133202C2314yes—
373#13133202C2314yes—
374#13133202C2314yes—
375#13133201C2314yes—
376#13133201C2314yes—
377#13133201C2314yes—
378#13133201C2314yes—
379#13133201C2314yes—
380#13133201C2314yes—
381#13133200C2314yes—
382#13133200C2314yes—
383#13133200C2314yes—
384#13133199C2314yes—
385#13133199C2314yes—
386#13133199C2314yes—
387#13133199C2314yes—
388#13133199C2314yes—
389#13133199C2314yes—
390#13133199C2314yes—
391#13133199C2314yes—
392#13133199C2314yes—
393#13133199C2314yes—
394#13133198C2314yes—
395#13133198C2314yes—
396#13133198C2314yes—
397#13133198C2314yes—
398#13133198C2314yes—
399#13133198C2314yes—
400#13133197C2314yes—
401#13133197C2314yes—
402#13133197C2314yes—
403#13133197C2314yes—
404#13133197C2314yes—
405#13133197C2314yes—
406#13133196C2314yes—
407#13133196C2314yes—
408#13133196C2314yes—
409#13133196C2314yes—
410#13133196C2314yes—
411#13133196C2314yes—
412#13133196C2312yes—
413#13133196C2312yes—
414#13133195C2314yes—
415#13133195C2314yes—
416#13133195C2314yes—
417#13133195C2314yes—
418#13133195C2314yes—
419#13133195C2314yes—
420#13133195C2314yes—
421#13133195C2314yes—
422#13133195C2314yes—
423#13133195C2314yes—
424#13133194C2312yes—
425#13133194C2314yes—
426#13133194C2312yes—
427#13133194C2314yes—
428#13133194C2312yes—
429#13133194C2314yes—
430#13133194C2314yes—
431#13133194C2314yes—
432#13133194C2312yes—
433#13133194C2314yes—
434#13133194C2314yes—
435#13133194C2314yes—
436#13133194C2314yes—
437#13133194C2314yes—
438#13133194C2314yes—
439#13133194C2314yes—
440#13133194C2314yes—
441#13133194C2314yes—
442#13133194C2314yes—
443#13133194C2312yes—
444#13133194C2312yes—
445#13133194C2312yes—
446#13133194C2312yes—
447#13133194C2314yes—
448#13133194C2312yes—
449#13133194C2312yes—
450#13133194C2312yes—
451#13133194C2312yes—
452#13133194C2312yes—
453#13133194C2312yes—
454#13133194C2312yes—
455#13133194C2312yes—
456#13133194C2314yes—
457#13133194C2314yes—
458#13133193C2314yes—
459#13133193C2314yes—
460#13133193C2314yes—
461#13133191C2314yes—
462#13133191C2314yes—
463#13133191C2312yes—
464#13133191C2312yes—
465#13133190C2314yes—
466#13133190C2314yes—
467#13133190C2314yes—
468#13133190C2314yes—
469#13133189C2314yes—
470#13133189C2314yes—
471#13133189C2314yes—
472#13133189C2314yes—
473#13133189C2314yes—
474#13133189C2314yes—
475#13133189C2314yes—
476#13133189C2314yes—
477#13133189C2314yes—
478#13133189C2314yes—
479#13133188C2314yes—
480#13133188C2314yes—
481#13133188C2314yes—
482#13133186C2314yes—
483Q8×Dic53C2314yes—
484Q8×Dic53C2312yes—
485Q8×Dic53C2312yes—
486Q8×Dic53C2312yes—
487Q8×Dic53C2312yes—
488C4×Dic106C2314yes—
489C4×Dic106C2314yes—
490C4×Dic106C2312yes—
491C4×Dic106C2314yes—
492C4×Dic106C2312yes—
493C4×Dic106C2312yes—
494C4×Dic106C2312yes—
495C4×Dic106C2314yes—
496C4×Dic106C2314yes—
497C4×Dic106C2312yes—
498C4×Dic106C2312yes—
499C4×Dic106C2312yes—
500C4×Dic106C2312yes—
501C4×Dic106C2312yes—
502C4×Dic106C2314yes—
503C4×Dic106C2314yes—
504C4×Dic106C2312yes—
505C4×Dic106C2312yes—
506C4×Dic106C2312yes—
507C4×Dic106C2312yes—
508C4×Dic106C2312yes—
509C4×Dic106C2312yes—
510C4×Dic106C2312yes—
511C4×Dic106C2312yes—
512C4×Dic106C2314yes—
513C4×Dic106C2314yes—
514C4×Dic106C2314yes—
515C4×Dic106C2312yes—
516#13133182C2314yes—
517#13133182C2314yes—
518#13133182C2314yes—
519#13133182C2314yes—
520#13133182C2314yes—
521#13133182C2312yes—
522#13133182C2312yes—
523#13133182C2314yes—
524#13133182C2312yes—
525#13133182C2312yes—
526C4×D212C2314yes—
527C4×D212C2312yes—
528C4×D212C2312yes—
529C4×D212C2314yes—
530D4×Dic53C2314yes—
531D4×Dic53C2314yes—
532D4×Dic53C2314yes—
533D4×Dic53C2314yes—
534D4×Dic53C2314yes—
535D4×Dic53C2312yes—
536D4×Dic53C2312yes—
537D4×Dic53C2312yes—
538D4×Dic53C2314yes—
539D4×Dic53C2312yes—
540D4×Dic53C2314yes—
541#13133179C2312yes—
542#13133179C2312yes—
543#13133179C2312yes—
544#13133179C2312yes—
545C4×C22⋊D53C2314yes—
546C4×C22⋊D53C2314yes—
547C4×C22⋊D53C2314yes—
548C4×C22⋊D53C2314yes—
549C4×C22⋊D53C2314yes—
550C4×C22⋊D53C2314yes—
551C4×C22⋊D53C2314yes—
552C4×C22⋊D53C2314yes—
553C4×C22⋊D53C2314yes—
554C4×C22⋊D53C2314yes—
555#13133177C2314yes—
556#13133177C2314yes—
557#13133177C2314yes—
558#13133177C2314yes—
559#13133177C2314yes—
560#13133177C2314yes—
561#13133177C2314yes—
562#13133177C2314yes—
563#13133177C2314yes—
564#13133177C2314yes—
565#13133176C2314yes—
566#13133176C2311yescharacteristic
567#13133176C2312yes—
568#13133176C2311yescharacteristic
569#13133176C2311yescharacteristic
570#13133176C2312yes—
571#13133176C2311yescharacteristic
572#13133176C2312yes—
573#13133176C2314yes—
574#13133176C2314yes—
575#13133175C2314yes—
576#13133175C2314yes—
577#13133175C2314yes—
578#13133174C2314yes—
579#13133174C2314yes—
580#13133174C2314yes—
581#13133174C2314yes—
582#13133174C2314yes—
583#13133173C2314yes—
584#13133173C2314yes—
585#13133173C2314yes—
586#13133173C2314yes—
587#13133173C2314yes—
588#13133173C2314yes—
589C2×C4⋊Dic53C2314yes—
590C2×C4⋊Dic53C2312yes—
591C2×C4⋊Dic53C2312yes—
592C2×C4⋊Dic53C2312yes—
593C2×#11719919C2314yes—
594C2×#11719919C2314yes—
595C2×#11719919C2312yes—
596C2×#11719919C2312yes—
597C2×#11719919C2312yes—
598C2×#11719919C2312yes—
599C4⋊C4×D53C2314yes—
600C4⋊C4×D53C2314yes—
601C4⋊C4×D53C2314yes—
602C2×C22⋊Dic53C2311yescharacteristic
603C2×C22⋊Dic53C2311yescharacteristic
604C2×C4×Dic53C2312yes—
605C2×C4×Dic53C2311yescharacteristic
606C2×C4×Dic53C2312yes—
607C2×C4×Dic53C2311yescharacteristic
608C2×C4×Dic53C2311yescharacteristic
609C2×C4×Dic53C2311yescharacteristic
610C2×C4×Dic53C2311yescharacteristic
611C2×C4×Dic53C2312yes—
612C2×C4×Dic53C2311yescharacteristic
613C2×C4×Dic53C2312yes—
614C2×C4×Dic53C2314yes—
615C2×C4×Dic53C2314yes—
616C42×D53C2314yes—
617C42×D53C2314yes—
618C42×D53C2314yes—
619C2×#41×C53C2312yes—
620C23×C4×C53C2311yescharacteristic
621C4⋊Q8×C53C2312yes—
622C4⋊Q8×C53C2311yescharacteristic
623#127×C53C2311yescharacteristic
624#126×C53C2314yes—
625#126×C53C2314yes—
626#126×C53C2314yes—
627#126×C53C2314yes—
628#125×C53C2314yes—
629#125×C53C2314yes—
630#125×C53C2311yescharacteristic
631#125×C53C2311yescharacteristic
632#124×C53C2314yes—
633#124×C53C2314yes—
634#124×C53C2312yes—
635#123×C53C2314yes—
636#123×C53C2314yes—
637#123×C53C2314yes—
638#123×C53C2314yes—
639#123×C53C2314yes—
640C22⋊Q8×C53C2314yes—
641C22⋊Q8×C53C2314yes—
642C22⋊Q8×C53C2312yes—
643C22⋊Q8×C53C2312yes—
644C22⋊Q8×C53C2314yes—
645#121×C53C2314yes—
646#121×C53C2314yes—
647#121×C53C2312yes—
648#121×C53C2312yes—
649#121×C53C2314yes—
650#120×C53C2314yes—
651C4×Q8×C53C2312yes—
652C4×Q8×C53C2312yes—
653C4×Q8×C53C2314yes—
654C4×D4×C53C2314yes—
655C4×D4×C53C2314yes—
656C4×D4×C53C2312yes—
657C4×D4×C53C2312yes—
658C4×D4×C53C2314yes—
659C4×D4×C53C2314yes—
660C4×D4×C53C2314yes—
661#117×C53C2312yes—
662#117×C53C2312yes—
663#117×C53C2311yescharacteristic
664#117×C53C2311yescharacteristic
665#117×C53C2311yescharacteristic
666#117×C53C2311yescharacteristic
667#117×C53C2312yes—
668#117×C53C2314yes—
669C2×C4⋊C4×C53C2312yes—
670C2×C22⋊C4×C53C2312yes—
671C2×C42×C53C2311yescharacteristic
672C2×C42×C53C2311yescharacteristic
673C2×C42×C53C2314yes—
674C24×C53C2411yescharacteristic
675#41×C53—28no—
676C2×Q8×C53C2412yes—
677C2×Q8×C53C2414yes—
678C2×D4×C53C2414yes—
679C2×D4×C53C2412yes—
680C2×D4×C53C2414yes—
681C2×D4×C53C2414yes—
682C2×D4×C53C2414yes—
683C22×C4×C53—24no—
684C22×C4×C53C2414yes—
685C22×C4×C53C2411yescharacteristic
686C22×C4×C53C2411yescharacteristic
687C22×C4×C53C2411yescharacteristic
688C22×C4×C53C2411yescharacteristic
689C22×C4×C53C2411yescharacteristic
690C22×C4×C53C2412yes—
691C22×C4×C53C2412yes—
692C22×C4×C53C2414yes—
693C22×C4×C53C2414yes—
694C22×C4×C53C2411yescharacteristic
695C2×C22⋊D53C2414yes—
696C2×C22⋊D53C2414yes—
697C2×C22⋊D53C2414yes—
698C2×C22⋊D53C2414yes—
699C2×C22⋊D53C2414yes—
700C2×C22⋊D53C2414yes—
701C2×C22⋊D53C2414yes—
702C22×Dic53—44no—
703C22×Dic53C2412yes—
704C22×Dic53C2412yes—
705C22×Dic53C2412yes—
706C22×Dic53C2414yes—
707C22×Dic53C2412yes—
708C22×Dic53C2412yes—
709C22×Dic53C2412yes—
710C22×Dic53C2412yes—
711C22×Dic53C2412yes—
712C22×Dic53C2414yes—
713C22×Dic53C2414yes—
714C22×Dic53C2414yes—
715Q8×D53—48no—
716#11719947—48no—
717#11719947—48no—
718#11719947—48no—
719#11719945—28no—
720#11719945—48no—
721C2×D212C2412yes—
722C2×D212C2414yes—
723C2×C4×D53C2414yes—
724C2×C4×D53C2414yes—
725C2×C4×D53C2414yes—
726C2×C4×D53C2414yes—
727C2×C4×D53C2414yes—
728C2×C4×D53C2414yes—
729C2×C4×D53C2414yes—
730C2×Dic106—44no—
731C2×Dic106—48no—
732C2×Dic106—44no—
733C2×Dic106C2412yes—
734C2×Dic106C2412yes—
735C2×Dic106C2414yes—
736C2×Dic106C2412yes—
737C2×Dic106C2412yes—
738C2×Dic106C2412yes—
739C2×Dic106C2414yes—
740C2×Dic106C2414yes—
741C2×Dic106C2412yes—
742C2×Dic106C2412yes—
743C2×Dic106C2414yes—
744C2×Dic106C2412yes—
745C2×Dic106C2414yes—
746C2×Dic106C2412yes—
747C4⋊C4×C53C2412yes—
748C4⋊C4×C53C2412yes—
749C4⋊C4×C53C2412yes—
750C4⋊C4×C53C2412yes—
751C4⋊C4×C53C2412yes—
752C4⋊C4×C53C2412yes—
753C4⋊C4×C53C2414yes—
754C4⋊C4×C53C2414yes—
755C4⋊C4×C53C2414yes—
756C4⋊C4×C53C2414yes—
757C4⋊C4×C53C2414yes—
758C4⋊C4×C53C2414yes—
759C4⋊C4×C53C2414yes—
760C4⋊C4×C53C2414yes—
761C22⋊C4×C53C2412yes—
762C22⋊C4×C53C2412yes—
763C22⋊C4×C53C2412yes—
764C22⋊C4×C53C2412yes—
765C22⋊C4×C53C2414yes—
766C22⋊C4×C53C2414yes—
767C22⋊C4×C53C2414yes—
768C22⋊C4×C53C2414yes—
769C22⋊C4×C53C2414yes—
770C22⋊C4×C53C2414yes—
771C22⋊C4×C53C2414yes—
772C22⋊C4×C53C2414yes—
773C22⋊C4×C53C2414yes—
774C42×C53C2412yes—
775C42×C53C2412yes—
776C42×C53C2414yes—
777C42×C53C2411yescharacteristic
778C42×C53C2411yescharacteristic
779C42×C53C2411yescharacteristic
780C42×C53C2411yescharacteristic
781C42×C53C2414yes—
782C42×C53C2414yes—
783C22⋊Dic53C2411yescharacteristic
784C22⋊Dic53C2412yes—
785C22⋊Dic53C2411yescharacteristic
786C22⋊Dic53C2412yes—
787C22⋊Dic53C2411yescharacteristic
788C22⋊Dic53C2411yescharacteristic
789C22⋊Dic53C2414yes—
790C22⋊Dic53C2414yes—
791C22⋊Dic53C2414yes—
792C22⋊Dic53C2414yes—
793C22⋊Dic53C2414yes—
794C22⋊Dic53C2414yes—
795C22⋊Dic53C2414yes—
796C22⋊Dic53C2414yes—
797C22⋊Dic53C2414yes—
798C22⋊Dic53C2414yes—
799C22⋊Dic53C2414yes—
800#11719921C2414yes—
801#11719921C2414yes—
802#11719921C2414yes—
803#11719921C2414yes—
804#11719921C2414yes—
805#11719921C2414yes—
806#11719921C2414yes—
807#11719921C2414yes—
808#11719921C2414yes—
809#11719921C2414yes—
810#11719921C2414yes—
811#11719921C2414yes—
812#11719921C2414yes—
813#11719921C2414yes—
814C4⋊Dic53C2412yes—
815C4⋊Dic53C2414yes—
816C4⋊Dic53C2414yes—
817C4⋊Dic53C2412yes—
818C4⋊Dic53C2412yes—
819C4⋊Dic53C2412yes—
820C4⋊Dic53C2412yes—
821C4⋊Dic53C2412yes—
822C4⋊Dic53C2412yes—
823C4⋊Dic53C2412yes—
824C4⋊Dic53C2412yes—
825C4⋊Dic53C2414yes—
826C4⋊Dic53C2412yes—
827C4⋊Dic53C2412yes—
828C4⋊Dic53C2412yes—
829C4⋊Dic53C2414yes—
830C4⋊Dic53C2414yes—
831C4⋊Dic53C2412yes—
832C4⋊Dic53C2412yes—
833C4⋊Dic53C2414yes—
834C4⋊Dic53C2414yes—
835C4⋊Dic53C2414yes—
836C4⋊Dic53C2414yes—
837C4⋊Dic53C2414yes—
838#11719919C2412yes—
839#11719919C2412yes—
840#11719919C2414yes—
841#11719919C2414yes—
842#11719919C2414yes—
843#11719919C2414yes—
844#11719919C2412yes—
845#11719919C2412yes—
846#11719919C2412yes—
847#11719919C2412yes—
848#11719919C2412yes—
849#11719919C2412yes—
850#11719919C2412yes—
851#11719919C2414yes—
852#11719919C2412yes—
853#11719919C2414yes—
854#11719919C2414yes—
855#11719919C2412yes—
856#11719919C2414yes—
857#11719919C2412yes—
858#11719919C2412yes—
859#11719919C2412yes—
860#11719919C2412yes—
861#11719919C2412yes—
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×Dic53C2414yes—
879C4×Dic53C2414yes—
880C4×Dic53C2414yes—
881C4×Dic53C2414yes—
882C4×Dic53C2414yes—
883C4×Dic53C2414yes—
884C4×Dic53C2414yes—
885C4×Dic53C2411yescharacteristic
886C4×Dic53C2412yes—
887C4×Dic53C2412yes—
888C4×Dic53C2412yes—
889C4×Dic53C2411yescharacteristic
890C4×Dic53C2412yes—
891C4×Dic53C2412yes—
892C4×Dic53C2412yes—
893C4×Dic53C2411yescharacteristic
894C4×Dic53C2411yescharacteristic
895C4×Dic53C2414yes—
896C4×Dic53C2414yes—
897C4×Dic53C2414yes—
898C4×Dic53C2412yes—
899C4×Dic53C2412yes—
900C4×Dic53C2414yes—
901C23×C53—22no—
902C23×C53—42no—
903C23×C53C2514yes—
904C23×C53C2511yescharacteristic
905C23×C53C2511yescharacteristic
906C23×C53C2511yescharacteristic
907C22×D53C2514yes—
908Q8×C53—24no—
909Q8×C53—44no—
910D4×C53—28no—
911D4×C53—24no—
912D4×C53—44no—
913D4×C53—44no—
914D4×C53—44no—
915C2×C4×C53—22no—
916C2×C4×C53—22no—
917C2×C4×C53—22no—
918C2×C4×C53—22no—
919C2×C4×C53—22no—
920C2×C4×C53—28no—
921C2×C4×C53—44no—
922C2×C4×C53—42no—
923C2×C4×C53—42no—
924C2×C4×C53—44no—
925C2×C4×C532−1+414yes—
926C2×C4×C53C2512yes—
927C2×C4×C53C2512yes—
928C2×C4×C53C2514yes—
929C2×C4×C53C2514yes—
930C2×C4×C53C2512yes—
931C2×C4×C53C2512yes—
932C2×C4×C53C2511yescharacteristic
933C2×C4×C53C2511yescharacteristic
934C2×C4×C53C2514yes—
935C2×C4×C53C2511yescharacteristic
936C2×C4×C53C2511yescharacteristic
937C22⋊D53—28no—
938C22⋊D53—28no—
939C22⋊D53—44no—
940C22⋊D53—44no—
941C22⋊D53—44no—
942C22⋊D53—44no—
943C22⋊D53—44no—
944C2×Dic53—24no—
945C2×Dic53—28no—
946C2×Dic53—24no—
947C2×Dic53—24no—
948C2×Dic53—42no—
949C2×Dic53—44no—
950C2×Dic53—42no—
951C2×Dic53—44no—
952C2×Dic53—44no—
953C2×Dic53—42no—
954C2×Dic53—42no—
955C2×Dic53—42no—
956C2×Dic53C2512yes—
957C2×Dic53C2512yes—
958C2×Dic53C2512yes—
959C2×Dic53C2514yes—
960C2×Dic53C2514yes—
961C2×Dic53C2512yes—
962C2×Dic53C2512yes—
963C2×Dic53C2512yes—
964C2×Dic53C2514yes—
965C2×Dic53C2512yes—
966C2×Dic53C2512yes—
967D212—24no—
968D212—44no—
969C4×D53—28no—
970C4×D53—28no—
971C4×D53—44no—
972C4×D53—44no—
973C4×D53—44no—
974C4×D53—44no—
975C4×D53—44no—
976Dic106—24no—
977Dic106—24no—
978Dic106—24no—
979Dic106—24no—
980Dic106—28no—
981Dic106—24no—
982Dic106—42no—
983Dic106—42no—
984Dic106—44no—
985Dic106—44no—
986Dic106—42no—
987Dic106—42no—
988Dic106—44no—
989Dic106—44no—
990#62761—531nomaximal, Sylow
991C22×C53—22no—
992C22×C53—21no—
993C22×C53—21no—
994C22×C53—24no—
995C22×C53—24no—
996C22×C53—22no—
997C22×C53—22no—
998C22×C53—24no—
999C22×C53—44no—
1000C22×C53C2×2−1+412yes—
1001C22×C53C2611yescharacteristic
1002C2×D53—24no—
1003C2×D53—24no—
1004C2×D53—24no—
1005C4×C53—21no—
1006C4×C53—21no—
1007C4×C53—24no—
1008C4×C53—22no—
1009C4×C53—22no—
1010C4×C53—24no—
1011C4×C53—22no—
1012C4×C53—22no—
1013C4×C53—24no—
1014C4×C53C2×2−1+412yes—
1015C4×C53C2×2−1+412yes—
1016Dic53—24no—
1017Dic53—22no—
1018Dic53—22no—
1019Dic53—24no—
1020Dic53—22no—
1021Dic53—22no—
1022Dic53—22no—
1023Dic53—24no—
1024Dic53—22no—
1025Dic53—22no—
1026Dic53#58514yes—
1027#3557—532no—
1028#3557—531no—
1029#3557—531no—
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#3455D5311yescharacteristic, complemented
1052#3444—532no—
1053C2×#533—531no—
1054C2×C53—22no—
1055C2×C53—44no—
1056C2×C53—41no—
1057C2×C53—41no—
1058C2×C53C22×2−1+411yescharacteristic
1059C2×C53C2×#58512yes—
1060D53—44no—
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#563—534no—
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#559—532no—
1083Q82—532no—
1084Q82—532no—
1085#557—532no—
1086#557—532no—
1087#557—532no—
1088#557—532no—
1089#557—534no—
1090#557—532no—
1091#557—532no—
1092#557—532no—
1093#557—532no—
1094#556—532no—
1095#556—534no—
1096#556—534no—
1097#556—534no—
1098#556—532no—
1099#556—532no—
1100#556—532no—
1101#556—532no—
1102#556—532no—
1103#554—532no—
1104#554—532no—
1105#554—532no—
1106#554—534no—
1107#554—534no—
1108#554—534no—
1109#554—534no—
1110#554—532no—
1111#554—534no—
1112#554—534no—
1113#554—532no—
1114#554—532no—
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#552—534no—
1127#550—532no—
1128#550—532no—
1129D4×Q8—532no—
1130D4×Q8—534no—
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—534no—
1144#542—534no—
1145#542—534no—
1146#542—534no—
1147#542—534no—
1148#542—534no—
1149#542—534no—
1150#542—532no—
1151#542—532no—
1152#542—532no—
1153#542—532no—
1154#542—534no—
1155#542—532no—
1156#542—532no—
1157#542C2×D5312yes—
1158#542C2×D5312yes—
1159#541—534no—
1160#541—534no—
1161#541—534no—
1162#541—534no—
1163#541—534no—
1164#541—534no—
1165#541—534no—
1166#541—532no—
1167#541—532no—
1168#541—534no—
1169#541—531no—
1170#541—531no—
1171#541C2×D5311yescharacteristic
1172#541C2×D5311yescharacteristic
1173#540—532no—
1174#540—532no—
1175#540—531no—
1176#540—531no—
1177#540C2×D5311yescharacteristic
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#538C2×D5314yes—
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—534no—
1205#533—534no—
1206#533—532no—
1207#533—532no—
1208#533—532no—
1209#533—532no—
1210#533—531no—
1211#533—531no—
1212#533—532no—
1213#533—532no—
1214#533—531no—
1215#533—531no—
1216#533—532no—
1217#533—532no—
1218#533—534no—
1219#533—534no—
1220#533—531no—
1221#533—534no—
1222#533C2×D5311yescharacteristic
1223#532—532no—
1224#532—532no—
1225#532—532no—
1226#532—532no—
1227#532—531no—
1228#532C2×D5311yescharacteristic
1229C2×C4⋊Q8—532no—
1230#529—534no—
1231#529—534no—
1232#529—532no—
1233#529—532no—
1234#529—532no—
1235#529—532no—
1236#529—534no—
1237#529—534no—
1238#529—534no—
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#529C2×D5314yes—
1251#529C2×D5314yes—
1252C2×#125—532no—
1253#525—532no—
1254#525—534no—
1255#525—534no—
1256#525C2×D5312yes—
1257C2×C22⋊Q8—532no—
1258C2×C22⋊Q8—532no—
1259C4×#41—532no—
1260C4×#41—532no—
1261C4×#41—534no—
1262C4×#41—534no—
1263C4×#41—534no—
1264C4×#41—532no—
1265C4×#41—532no—
1266C4×#41—532no—
1267C4×#41—534no—
1268C4×#41C2×D5312yes—
1269C2×C4×Q8—534no—
1270C2×C4×Q8—532no—
1271C2×C4×Q8—532no—
1272C2×C4×Q8—534no—
1273C2×#117—531no—
1274C2×#117C2×D5311yescharacteristic
1275C22×C42—531no—
1276C53#6276111yescharacteristic, complemented, Sylow
1277C2×#41—534no—
1278C2×#41—534no—
1279C2×#41—534no—
1280C2×#41—532no—
1281C2×#41—534no—
1282C2×#41C22×D5312yes—
1283C22×Q8—534no—
1284C22×Q8—532no—
1285C22×Q8—532no—
1286C22×Q8—534no—
1287C23×C4—532no—
1288C23×C4C22×D5311yescharacteristic
1289C4⋊Q8—532no—
1290C4⋊Q8—532no—
1291C4⋊Q8—534no—
1292C4⋊Q8—534no—
1293C4⋊Q8—534no—
1294C4⋊Q8—532no—
1295C4⋊Q8—532no—
1296C4⋊Q8—532no—
1297C4⋊Q8—532no—
1298C4⋊Q8—532no—
1299C4⋊Q8—532no—
1300C4⋊Q8—532no—
1301C4⋊Q8—532no—
1302C4⋊Q8—532no—
1303C4⋊Q8—532no—
1304C4⋊Q8—534no—
1305C4⋊Q8—534no—
1306C4⋊Q8—534no—
1307C4⋊Q8—534no—
1308C4⋊Q8—532no—
1309C4⋊Q8—532no—
1310C4⋊Q8—534no—
1311C4⋊Q8—534no—
1312C4⋊Q8—534no—
1313C4⋊Q8—531no—
1314C4⋊Q8—534no—
1315C4⋊Q8—532no—
1316C4⋊Q8—534no—
1317C4⋊Q8C22×D5311yescharacteristic
1318C4⋊Q8C22×D5312yes—
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#126—534no—
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—532no—
1362#125—532no—
1363#125—534no—
1364#125—532no—
1365#125—532no—
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—534no—
1383#125—534no—
1384#125—534no—
1385#125—534no—
1386#125—534no—
1387#125—534no—
1388#125—532no—
1389#125—532no—
1390#125—534no—
1391#125—534no—
1392#125—534no—
1393#125—531no—
1394#125—531no—
1395#125C22×D5314yes—
1396#125C22×D5314yes—
1397#125C22×D5311yescharacteristic
1398#125C22×D5311yescharacteristic
1399#124—532no—
1400#124—532no—
1401#124—532no—
1402#124—534no—
1403#124—534no—
1404#124—534no—
1405#124—532no—
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—534no—
1415#124—534no—
1416#124—534no—
1417#124—532no—
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—534no—
1456C22⋊Q8—534no—
1457C22⋊Q8—534no—
1458C22⋊Q8—532no—
1459C22⋊Q8—532no—
1460C22⋊Q8—534no—
1461C22⋊Q8—534no—
1462C22⋊Q8—534no—
1463C22⋊Q8—534no—
1464C22⋊Q8—534no—
1465C22⋊Q8—534no—
1466C22⋊Q8—534no—
1467C22⋊Q8—534no—
1468C22⋊Q8—534no—
1469C22⋊Q8—534no—
1470C22⋊Q8—534no—
1471C22⋊Q8—534no—
1472C22⋊Q8—534no—
1473C22⋊Q8—534no—
1474C22⋊Q8—534no—
1475C22⋊Q8—534no—
1476C22⋊Q8—534no—
1477C22⋊Q8—534no—
1478C22⋊Q8—534no—
1479C22⋊Q8—534no—
1480C22⋊Q8—534no—
1481C22⋊Q8—534no—
1482C22⋊Q8—532no—
1483C22⋊Q8—532no—
1484C22⋊Q8—532no—
1485C22⋊Q8—532no—
1486C22⋊Q8—532no—
1487C22⋊Q8—532no—
1488C22⋊Q8—532no—
1489C22⋊Q8—532no—
1490C22⋊Q8—532no—
1491C22⋊Q8—532no—
1492C22⋊Q8—532no—
1493C22⋊Q8—532no—
1494C22⋊Q8—532no—
1495C22⋊Q8—532no—
1496C22⋊Q8—532no—
1497C22⋊Q8—532no—
1498C22⋊Q8—534no—
1499C22⋊Q8—534no—
1500C22⋊Q8—534no—
1501C22⋊Q8—534no—
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⋊Q8—534no—
1514C22⋊Q8—534no—
1515C22⋊Q8—534no—
1516C22⋊Q8C22×D5312yes—
1517C22⋊Q8C22×D5312yes—
1518C22⋊Q8C22×D5314yes—
1519C22⋊Q8C22×D5314yes—
1520C22⋊Q8C22×D5314yes—
1521#121—534no—
1522#121—534no—
1523#121—534no—
1524#121—534no—
1525#121—534no—
1526#121—534no—
1527#121—534no—
1528#121—534no—
1529#121—534no—
1530#121—534no—
1531#121—534no—
1532#121—534no—
1533#121—534no—
1534#121—532no—
1535#121—532no—
1536#121—534no—
1537#121—534no—
1538#121—534no—
1539#121—534no—
1540#121—534no—
1541#121—534no—
1542#121C22×D5312yes—
1543#121C22×D5312yes—
1544#121C22×D5314yes—
1545#121C22×D5314yes—
1546#121C22×D5314yes—
1547#120—534no—
1548#120C22×D5314yes—
1549C4×Q8—534no—
1550C4×Q8—532no—
1551C4×Q8—532no—
1552C4×Q8—532no—
1553C4×Q8—532no—
1554C4×Q8—534no—
1555C4×Q8—534no—
1556C4×Q8—534no—
1557C4×Q8—534no—
1558C4×Q8—534no—
1559C4×Q8—532no—
1560C4×Q8—532no—
1561C4×Q8—534no—
1562C4×Q8—532no—
1563C4×Q8—532no—
1564C4×Q8—532no—
1565C4×Q8—532no—
1566C4×Q8—534no—
1567C4×Q8—532no—
1568C4×Q8—532no—
1569C4×Q8—532no—
1570C4×Q8—532no—
1571C4×Q8—534no—
1572C4×Q8—534no—
1573C4×Q8—532no—
1574C4×Q8—532no—
1575C4×Q8—534no—
1576C4×Q8—532no—
1577C4×Q8—532no—
1578C4×Q8—532no—
1579C4×Q8—532no—
1580C4×Q8—532no—
1581C4×Q8—532no—
1582C4×Q8—532no—
1583C4×Q8—532no—
1584C4×Q8—534no—
1585C4×Q8—534no—
1586C4×Q8—534no—
1587C4×Q8—534no—
1588C4×Q8—534no—
1589C4×Q8—534no—
1590C4×Q8—532no—
1591C4×Q8—532no—
1592C4×Q8C22×D5314yes—
1593C4×Q8C22×D5312yes—
1594C4×Q8C22×D5312yes—
1595C4×D4—534no—
1596C4×D4—534no—
1597C4×D4—534no—
1598C4×D4—534no—
1599C4×D4—532no—
1600C4×D4—532no—
1601C4×D4—534no—
1602C4×D4—534no—
1603C4×D4—534no—
1604C4×D4—532no—
1605C4×D4—532no—
1606C4×D4—534no—
1607C4×D4—534no—
1608C4×D4—534no—
1609C4×D4—534no—
1610C4×D4—534no—
1611C4×D4—534no—
1612C4×D4—534no—
1613C4×D4—534no—
1614C4×D4—534no—
1615C4×D4—534no—
1616C4×D4—532no—
1617C4×D4—532no—
1618C4×D4—532no—
1619C4×D4—532no—
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—534no—
1632C4×D4—532no—
1633C4×D4—532no—
1634C4×D4C22×D5314yes—
1635C4×D4C22×D5314yes—
1636C4×D4C22×D5314yes—
1637C4×D4C22×D5314yes—
1638C4×D4C22×D5314yes—
1639C4×D4C22×D5312yes—
1640C4×D4C22×D5312yes—
1641#117—531no—
1642#117—531no—
1643#117—532no—
1644#117—531no—
1645#117—532no—
1646#117—531no—
1647#117—532no—
1648#117—534no—
1649#117—534no—
1650#117—534no—
1651#117—534no—
1652#117—534no—
1653#117—534no—
1654#117—534no—
1655#117—534no—
1656#117—534no—
1657#117—534no—
1658#117—534no—
1659#117—534no—
1660#117—534no—
1661#117—534no—
1662#117—534no—
1663#117—534no—
1664#117—534no—
1665#117C22×D5312yes—
1666#117C22×D5312yes—
1667#117C22×D5311yescharacteristic
1668#117C22×D5311yescharacteristic
1669#117C22×D5311yescharacteristic
1670#117C22×D5311yescharacteristic
1671#117C22×D5312yes—
1672#117C22×D5314yes—
1673C2×C4⋊C4—532no—
1674C2×C4⋊C4—532no—
1675C2×C4⋊C4—532no—
1676C2×C4⋊C4—532no—
1677C2×C4⋊C4—532no—
1678C2×C4⋊C4—532no—
1679C2×C4⋊C4—532no—
1680C2×C4⋊C4—534no—
1681C2×C4⋊C4—534no—
1682C2×C4⋊C4—534no—
1683C2×C4⋊C4—534no—
1684C2×C4⋊C4—534no—
1685C2×C4⋊C4—534no—
1686C2×C4⋊C4C22×D5312yes—
1687C2×C22⋊C4—531no—
1688C2×C22⋊C4—531no—
1689C2×C22⋊C4C22×D5312yes—
1690C2×C42—532no—
1691C2×C42—532no—
1692C2×C42—534no—
1693C2×C42—534no—
1694C2×C42—531no—
1695C2×C42—532no—
1696C2×C42—531no—
1697C2×C42—531no—
1698C2×C42—531no—
1699C2×C42—531no—
1700C2×C42—532no—
1701C2×C42—531no—
1702C2×C42—534no—
1703C2×C42—534no—
1704C2×C42—534no—
1705C2×C42C22×D5311yescharacteristic
1706C2×C42C22×D5311yescharacteristic
1707C2×C42C22×D5314yes—
1708C24C23×D5311yescharacteristic
1709#41—28no—
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—532no—
1722C2×Q8—532no—
1723C2×Q8—534no—
1724C2×Q8—534no—
1725C2×Q8—532no—
1726C2×Q8—532no—
1727C2×Q8—534no—
1728C2×Q8—534no—
1729C2×Q8—2124no—
1730C2×Q8—2124no—
1731C2×Q8—2128no—
1732C2×Q8—2128no—
1733C2×Q8C23×D5312yes—
1734C2×Q8C23×D5314yes—
1735C2×D4—534no—
1736C2×D4—534no—
1737C2×D4—534no—
1738C2×D4—534no—
1739C2×D4—534no—
1740C2×D4—534no—
1741C2×D4—534no—
1742C2×D4—532no—
1743C2×D4—534no—
1744C2×D4C23×D5314yes—
1745C2×D4C23×D5312yes—
1746C2×D4C23×D5314yes—
1747C2×D4C23×D5314yes—
1748C2×D4C23×D5314yes—
1749C22×C4—24no—
1750C22×C4—532no—
1751C22×C4—532no—
1752C22×C4—532no—
1753C22×C4—534no—
1754C22×C4—532no—
1755C22×C4—532no—
1756C22×C4—532no—
1757C22×C4—532no—
1758C22×C4—532no—
1759C22×C4—534no—
1760C22×C4—534no—
1761C22×C4—534no—
1762C22×C4—534no—
1763C22×C4—534no—
1764C22×C4—534no—
1765C22×C4—534no—
1766C22×C4—534no—
1767C22×C4—534no—
1768C22×C4—534no—
1769C22×C4—2124no—
1770C22×C4C23×D5311yescharacteristic
1771C22×C4C23×D5311yescharacteristic
1772C22×C4C23×D5311yescharacteristic
1773C22×C4C23×D5314yes—
1774C22×C4C23×D5311yescharacteristic
1775C22×C4C23×D5311yescharacteristic
1776C22×C4C23×D5312yes—
1777C22×C4C23×D5312yes—
1778C22×C4C23×D5314yes—
1779C22×C4C23×D5314yes—
1780C22×C4C23×D5311yescharacteristic
1781C4⋊C4—532no—
1782C4⋊C4—532no—
1783C4⋊C4—532no—
1784C4⋊C4—532no—
1785C4⋊C4—532no—
1786C4⋊C4—532no—
1787C4⋊C4—534no—
1788C4⋊C4—534no—
1789C4⋊C4—534no—
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—532no—
1802C4⋊C4—532no—
1803C4⋊C4—532no—
1804C4⋊C4—534no—
1805C4⋊C4—534no—
1806C4⋊C4—534no—
1807C4⋊C4—534no—
1808C4⋊C4—534no—
1809C4⋊C4—534no—
1810C4⋊C4—532no—
1811C4⋊C4—532no—
1812C4⋊C4—534no—
1813C4⋊C4—534no—
1814C4⋊C4—532no—
1815C4⋊C4—532no—
1816C4⋊C4—532no—
1817C4⋊C4—532no—
1818C4⋊C4—532no—
1819C4⋊C4—532no—
1820C4⋊C4—534no—
1821C4⋊C4—534no—
1822C4⋊C4—532no—
1823C4⋊C4—532no—
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⋊C4—534no—
1838C4⋊C4—534no—
1839C4⋊C4—534no—
1840C4⋊C4—534no—
1841C4⋊C4—534no—
1842C4⋊C4—534no—
1843C4⋊C4C23×D5314yes—
1844C4⋊C4C23×D5314yes—
1845C4⋊C4C23×D5314yes—
1846C4⋊C4C23×D5312yes—
1847C4⋊C4C23×D5312yes—
1848C4⋊C4C23×D5312yes—
1849C4⋊C4C23×D5312yes—
1850C4⋊C4C23×D5314yes—
1851C4⋊C4C23×D5314yes—
1852C4⋊C4C23×D5314yes—
1853C4⋊C4C23×D5312yes—
1854C4⋊C4C23×D5312yes—
1855C4⋊C4C23×D5314yes—
1856C4⋊C4C23×D5314yes—
1857C22⋊C4—531no—
1858C22⋊C4—531no—
1859C22⋊C4—532no—
1860C22⋊C4—532no—
1861C22⋊C4—531no—
1862C22⋊C4—531no—
1863C22⋊C4—534no—
1864C22⋊C4—534no—
1865C22⋊C4—534no—
1866C22⋊C4—534no—
1867C22⋊C4—534no—
1868C22⋊C4—534no—
1869C22⋊C4—534no—
1870C22⋊C4—534no—
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⋊C4C23×D5312yes—
1889C22⋊C4C23×D5312yes—
1890C22⋊C4C23×D5312yes—
1891C22⋊C4C23×D5312yes—
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—531no—
1902C42—532no—
1903C42—531no—
1904C42—532no—
1905C42—532no—
1906C42—532no—
1907C42—531no—
1908C42—531no—
1909C42—534no—
1910C42—534no—
1911C42—534no—
1912C42—534no—
1913C42—532no—
1914C42—532no—
1915C42—534no—
1916C42—534no—
1917C42—534no—
1918C42—534no—
1919C42—534no—
1920C42—534no—
1921C42—532no—
1922C42—532no—
1923C42—532no—
1924C42—532no—
1925C42—534no—
1926C42C23×D5314yes—
1927C42C23×D5311yescharacteristic
1928C42C23×D5311yescharacteristic
1929C42C23×D5311yescharacteristic
1930C42C23×D5311yescharacteristic
1931C42C23×D5314yes—
1932C42C23×D5312yes—
1933C42C23×D5314yes—
1934C42C23×D5312yes—
1935C23—22no—
1936C23—42no—
1937C23—534no—
1938C23C24×D5311yescharacteristic
1939C23C24×D5311yescharacteristic
1940C23C24×D5314yes—
1941C23C24×D5311yescharacteristic
1942Q8—24no—
1943Q8—44no—
1944Q8—1064no—
1945Q8—1064no—
1946Q8—1068no—
1947Q8—1064no—
1948Q8—1064no—
1949Q8—1064no—
1950Q8—2122no—
1951Q8—2124no—
1952Q8—2122no—
1953Q8—2124no—
1954Q8—2122no—
1955Q8—2124no—
1956Q8—2122no—
1957Q8—2124no—
1958D4—28no—
1959D4—24no—
1960D4—44no—
1961D4—44no—
1962D4—44no—
1963D4—1068no—
1964D4—1068no—
1965D4—1064no—
1966D4—2124no—
1967D4—2124no—
1968D4—2124no—
1969D4—2124no—
1970D4—2124no—
1971D4—2124no—
1972C2×C4—22no—
1973C2×C4—22no—
1974C2×C4—22no—
1975C2×C4—22no—
1976C2×C4—22no—
1977C2×C4—28no—
1978C2×C4—42no—
1979C2×C4—44no—
1980C2×C4—42no—
1981C2×C4—44no—
1982C2×C4—532no—
1983C2×C4—532no—
1984C2×C4—534no—
1985C2×C4—532no—
1986C2×C4—532no—
1987C2×C4—532no—
1988C2×C4—534no—
1989C2×C4—534no—
1990C2×C4—532no—
1991C2×C4—532no—
1992C2×C4—532no—
1993C2×C4—1068no—
1994C2×C4—1064no—
1995C2×C4—1064no—
1996C2×C4—1064no—
1997C2×C4—1068no—
1998C2×C4—1068no—
1999C2×C4—2124no—
2000C2×C4—2124no—
2001C2×C4—2124no—
2002C2×C4—2124no—
2003C2×C4—2124no—
2004C2×C4—2122no—
2005C2×C4—2122no—
2006C2×C4—2122no—
2007C2×C4—2122no—
2008C2×C4—2122no—
2009C2×C4—2124no—
2010C2×C4—2124no—
2011C2×C4—2124no—
2012C2×C4#1313326414yes—
2013C2×C4C24×D5314yes—
2014C2×C4C24×D5311yescharacteristic
2015C2×C4C24×D5311yescharacteristic
2016C2×C4C24×D5312yes—
2017C2×C4C24×D5314yes—
2018C2×C4C24×D5314yes—
2019C2×C4C24×D5312yes—
2020C2×C4C24×D5312yes—
2021C2×C4C24×D5312yes—
2022C2×C4C24×D5311yescharacteristic
2023C2×C4C24×D5311yescharacteristic
2024C22—22no—
2025C22—21no—
2026C22—21no—
2027C22—24no—
2028C22—24no—
2029C22—24no—
2030C22—22no—
2031C22—22no—
2032C22—44no—
2033C22—1064no—
2034C22—1064no—
2035C22—1064no—
2036C22C2×#1313326412yes—
2037C22C25×D5311yescharacteristic
2038C4—21no—
2039C4—21no—
2040C4—24no—
2041C4—22no—
2042C4—22no—
2043C4—24no—
2044C4—22no—
2045C4—24no—
2046C4—22no—
2047C4—534no—
2048C4—1064no—
2049C4—1062no—
2050C4—1062no—
2051C4—1064no—
2052C4—1062no—
2053C4—1062no—
2054C4—1062no—
2055C4—1064no—
2056C4—1062no—
2057C4—1062no—
2058C4C2×#1313326412yes—
2059C4C2×#1313326412yes—
2060C2—22no—
2061C2—41no—
2062C2—41no—
2063C2—44no—
2064C2—2124no—
2065C2C22×#1313326411yescharacteristic
2066C2#585×D5312yes—
subgroupG/H
centerC2×C4C24×D53
commutator, socle, cosocleC22×C53C26
FrattiniC22C25×D53
FittingC53×#3455C2
hypercenter#3455D53
hypocenterC53#62761
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ #3455

Complements

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

NH ≅ G/Ntype
1. #20289223C2semidirect
2. #20289220C2semidirect
3. #20289214C2semidirect
4. #20289208C2semidirect
5. #20289201C2semidirect
6. #20289193C2semidirect
7. #20289184C2semidirect
8. #20289176C2semidirect
9. #20289165C2semidirect
10. #20289148C2semidirect
11. #20289123C2semidirect
12. #20289109C2semidirect
13. #20289003C2semidirect
14. #20288995C2semidirect
15. #20288860C2semidirect
16. #20288328C2semidirect
17. #20288312C2semidirect
18. #20288308C2semidirect
19. #41×Dic106C2semidirect
20. #20288293C2semidirect
21. #20288144C2semidirect
22. #20288140C2semidirect
23. #20288105C2semidirect
24. #20288103C2semidirect
25. #20288007C2semidirect
26. C2×#16811176C2semidirect
27. C53×#3455C2semidirect
28. C53⋊#564C22semidirect
29. #16811377C22semidirect
31. #16811376C22semidirect
34. #16811375C22semidirect
35. #16811375C22semidirect
36. #16811374C22semidirect
37. #16811374C22semidirect
40. #16811370C22semidirect
44. #16811359C22semidirect
45. #16811358C22semidirect
46. #16811356C22semidirect
47. #16811356C22semidirect
48. #16811355C22semidirect
49. #16811355C22semidirect
50. Q8×Dic106C22semidirect
51. #16811353C22semidirect
52. #16811352C22semidirect
53. #16811351C22semidirect
54. #16811350C22semidirect
55. #16811350C22semidirect
56. #16811350C22semidirect
57. #16811349C22semidirect
58. #16811349C22semidirect
59. #16811348C22semidirect
60. #16811348C22semidirect
61. #16811347C22semidirect
62. #16811345C22semidirect
63. #16811345C22semidirect
64. #16811343C22semidirect
66. #16811342C22semidirect
67. #16811342C22semidirect
69. #16811340C22semidirect
70. #16811334C22semidirect
73. #16811332C22semidirect
74. #16811332C22semidirect
77. #16811330C22semidirect
78. #16811329C22semidirect
79. #16811329C22semidirect
88. #16811315C22semidirect
89. #16811311C22semidirect
91. #16811310C22semidirect
93. #16811309C22semidirect
94. #16811294C22semidirect
95. #16811293C22semidirect
97. D4×Dic106C22semidirect
98. #16811288C22semidirect
100. #16811286C22semidirect
107. #16811271C22semidirect
108. #16811253C22semidirect
109. #16811252C22semidirect
116. #16811241C22semidirect
121. #16811239C22semidirect
124. #16811236C22semidirect
129. #16811233C22semidirect
130. #16811232C22semidirect
131. #16811232C22semidirect
134. #16811230C22semidirect
135. #16811230C22semidirect
140. #16811222C22semidirect
146. #16811217C22semidirect
148. #16811216C22semidirect
150. #16811214C22semidirect
156. #16811196C22semidirect
158. #16811195C22semidirect
161. #16811180C22semidirect
162. #16811177C22semidirect
163. #16811177C22semidirect
164. #16811177C22semidirect
177. #16811176C22semidirect
178. #16811176C22semidirect
189. #16811157C22semidirect
192. #16811155C22semidirect
199. #16811153C22semidirect
200. #16811153C22semidirect
203. #16811151C22semidirect
204. #16811151C22semidirect
216. C4×#11719945C22semidirect
221. C4×#11719947C22semidirect
224. C2×C4×Dic106C22semidirect
225. C4×Q8×D53C22semidirect
1051. #3455D53semidirect
1276. C53#62761semidirect

Maximal subgroups

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

subgroupindex
#202892232
#202892202
#202892142
#202892082
#202892012
#202891932
#202891842
#202891762
#202891652
#202891482
#202891232
#202891092
#202890032
#202889952
#202888602
#202883282
#202883122
#202883082
#41×Dic1062
#202882932
#202881442
#202881402
#202881052
#202881032
#202880072
C2×#168111762
C53×#34552
#6276153