Finite Group Databasebeta

← #28291942

Subgroups — #28291942

Order 13568.

6518 conjugacy classes of subgroups.

The subgroup lattice has 1798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289211C214yesmaximal, complemented
2#20289209C211yesmaximal, characteristic, complemented
3#20289196C214yesmaximal, complemented
4#20289179C214yesmaximal, complemented
5#20289171C211yesmaximal, characteristic, complemented
6#20289168C212yesmaximal, complemented
7#20289148C214yesmaximal, complemented
8#20289125C212yesmaximal, complemented
9#20289111C211yesmaximal, characteristic, complemented
10#20289001C214yesmaximal, complemented
11#20288993C214yesmaximal, complemented
12#20288863C211yesmaximal, characteristic, complemented
13#20288861C212yesmaximal, complemented
14#20288859C211yesmaximal, characteristic, complemented
15#20288329C214yesmaximal, complemented
16#20288309C214yesmaximal, complemented
17#20288294C214yesmaximal, complemented
18#20288147C214yesmaximal, complemented
19#20288145C214yesmaximal, complemented
20#20288101C214yesmaximal, complemented
21#20288009C212yesmaximal, complemented
22C2×#16811179C211yesmaximal, characteristic, complemented
23C53×#3553C211yesmaximal, characteristic, complemented
24C53⋊#564C2211yescharacteristic, complemented
25C53⋊#564C2212yescomplemented
26#16811377C2214yes—
27#16811377C2212yescomplemented
28#16811377C2212yescomplemented
29#16811377C2214yescomplemented
30#16811376C2214yescomplemented
31#16811375C2214yes—
32#16811375C2214yescomplemented
33#16811374C2214yes—
34#16811374C2214yescomplemented
35#16811373C2212yescomplemented
36#16811372C2214yes—
37#16811371C2214yes—
38#16811371C2211yescharacteristic, complemented
39#16811370C2214yes—
40#16811369C2214yes—
41#16811368C2214yes—
42#16811367C2212yescomplemented
43#16811357C2214yescomplemented
44#16811357C2214yescomplemented
45#16811356C2214yescomplemented
46#16811353C2214yescomplemented
47#16811351C2214yescomplemented
48#16811350C2214yescomplemented
49#16811350C2214yescomplemented
50#16811350C2214yescomplemented
51#16811350C2214yescomplemented
52#16811345C2214yes—
53#16811341C2214yescomplemented
54#16811340C2214yes—
55#16811340C2214yescomplemented
56#16811340C2214yescomplemented
57#16811340C2214yescomplemented
58#16811332C2214yes—
59#16811332C2214yes—
60#16811328C2214yes—
61#16811328C2214yescomplemented
62#16811327C2214yes—
63#16811327C2214yes—
64#16811327C2214yescomplemented
65#16811327C2214yescomplemented
66#16811322C2214yes—
67#16811322C2214yes—
68#16811321C2214yes—
69#16811316C2214yes—
70#16811316C2214yes—
71#16811312C2214yescomplemented
72#16811306C2214yes—
73#16811306C2214yescomplemented
74#16811305C2214yes—
75#16811305C2214yescomplemented
76#16811291C2214yescomplemented
77D4×Dic106C2214yes—
78#16811286C2214yes—
79#16811286C2214yescomplemented
80#16811286C2214yescomplemented
81#16811283C2214yes—
82#16811282C2214yes—
83#16811282C2214yes—
84#16811279C2214yes—
85#16811274C2214yes—
86#16811271C2214yes—
87#16811271C2214yescomplemented
88#16811253C2214yescomplemented
89#16811252C2214yescomplemented
90#16811245C2214yes—
91#16811244C2214yes—
92#16811243C2214yes—
93#16811243C2214yes—
94#16811243C2214yes—
95#16811243C2214yes—
96#16811241C2214yes—
97#16811241C2214yescomplemented
98#16811239C2214yes—
99#16811239C2214yes—
100#16811239C2214yes—
101#16811239C2214yescomplemented
102#16811232C2214yes—
103#16811232C2214yes—
104#16811232C2214yes—
105#16811232C2214yes—
106#16811232C2214yescomplemented
107#16811232C2214yescomplemented
108#16811231C2214yescomplemented
109#16811230C2214yescomplemented
110#16811230C2214yescomplemented
111#16811225C2214yes—
112#16811225C2214yes—
113#16811221C2214yes—
114#16811221C2214yescomplemented
115#16811220C2214yes—
116#16811220C2214yes—
117#16811217C2214yes—
118#16811217C2214yes—
119#16811215C2214yes—
120#16811215C2214yescomplemented
121#16811214C2214yes—
122#16811214C2214yescomplemented
123#16811213C2214yes—
124#16811210C2214yes—
125#16811206C2214yes—
126#16811206C2214yes—
127#16811203C2214yes—
128#16811200C2214yes—
129#16811198C2214yes—
130#16811196C2214yescomplemented
131#16811195C2214yes—
132#16811195C2214yescomplemented
133#16811179C2212yes—
134#16811179C2211yescharacteristic
135#16811179C2211yescharacteristic
136#16811179C2211yescharacteristic
137#16811179C2211yescharacteristic
138#16811179C2214yes—
139#16811179C2214yes—
140#16811179C2212yes—
141#16811179C2212yes—
142#16811179C2214yescomplemented
143#16811179C2214yescomplemented
144#16811178C2214yescomplemented
145#16811177C2212yes—
146#16811175C2212yes—
147#16811175C2214yes—
148#16811175C2214yescomplemented
149#16811175C2214yescomplemented
150#16811175C2214yescomplemented
151#16811172C2212yes—
152#16811170C2212yes—
153#16811168C2212yes—
154#16811168C2214yes—
155C2×#13133216C2212yes—
156#16811159C2214yes—
157#16811159C2214yes—
158#16811158C2212yes—
159#16811158C2214yes—
160#16811158C2214yes—
161#16811158C2214yescomplemented
162#16811157C2212yes—
163#16811156C2214yes—
164#16811156C2214yes—
165#16811156C2214yes—
166#16811156C2214yes—
167#16811156C2214yescomplemented
168#16811156C2214yescomplemented
169#16811154C2214yescomplemented
170#16811152C2212yes—
171#16811151C2214yes—
172#16811150C2214yes—
173#16811150C2214yes—
174#16811150C2214yes—
175#16811150C2214yescomplemented
176#16811150C2214yescomplemented
177C2×#13133209C2211yescharacteristic
178#16811136C2212yes—
179#16811133C2212yes—
180#16811132C2214yes—
181#16811131C2214yes—
182C2×#13133195C2214yes—
183C4×#11719949C2212yes—
184#16811091C2214yes—
185#16811091C2214yescomplemented
186C4×#11719947C2214yes—
187C4×#11719947C2212yes—
188C4×#11719947C2214yes—
189C4×#11719947C2214yes—
190C4×#11719947C2214yescomplemented
191C2×#13133182C2214yes—
192C2×#13133182C2214yescomplemented
193C4×Q8×D53C2214yescomplemented
194C2×#13133175C2212yes—
195C2×C42×D53C2211yescharacteristic
196C53×#564C2211yescharacteristic, complemented
197C53×#563C2212yescomplemented
198C53×#562C2211yescharacteristic, complemented
199C53×#554C2214yes—
200C53×#553C2214yes—
201C53×#552C2214yescomplemented
202C53×#541C2214yescomplemented
203C53×#539C2214yes—
204C53×#539C2214yescomplemented
205C53×#529C2212yes—
206C2×#125×C53C2211yescharacteristic
207C2×#11719949C2312yes—
208C2×#11719945C2314yes—
209C2×#11719945C2314yes—
210C2×#11719947C2314yes—
211C2×#11719947C2314yes—
212C2×#11719947C2312yes—
213C22×Dic106C2314yes—
214C22×Dic106C2314yes—
215C2×Q8×D53C2314yes—
216C22×C4×D53C2311yescharacteristic
217C22×C4×D53C2312yes—
218#13133217C2314yes—
219#13133216C2314yes—
220#13133216C2312yes—
221#13133216C2314yes—
222#13133216C2314yes—
223#13133216C2312yes—
224#13133216C2312yes—
225#13133216C2314yes—
226#13133216C2314yes—
227#13133216C2314yes—
228#13133216C2314yes—
229#13133216C2314yes—
230#13133216C2312yes—
231#13133216C2314yes—
232#13133216C2312yes—
233#13133216C2312yes—
234#13133216C2314yes—
235#13133216C2314yes—
236#13133215C2314yes—
237#13133215C2314yes—
238#13133215C2314yes—
239#13133215C2314yes—
240#13133215C2312yes—
241#13133213C2314yes—
242#13133213C2312yes—
243#13133212C2314yes—
244#13133212C2314yes—
245#13133212C2314yes—
246#13133212C2314yes—
247#13133212C2314yes—
248#13133212C2314yes—
249#13133212C2314yes—
250#13133212C2314yes—
251#13133212C2314yes—
252#13133212C2314yes—
253#13133212C2314yes—
254#13133212C2314yes—
255#13133212C2314yes—
256#13133212C2314yes—
257#13133212C2314yes—
258#13133211C2314yes—
259#13133211C2314yes—
260#13133211C2314yes—
261#13133211C2314yes—
262#13133211C2314yes—
263#13133210C2314yes—
264#13133210C2314yes—
265#13133210C2314yes—
266#13133210C2314yes—
267#13133210C2314yes—
268#13133210C2314yes—
269#13133210C2314yes—
270#13133209C2314yes—
271#13133209C2312yes—
272#13133209C2314yes—
273#13133209C2311yescharacteristic
274#13133209C2311yescharacteristic
275#13133209C2312yes—
276#13133209C2314yes—
277#13133208C2314yes—
278#13133208C2314yes—
279#13133208C2314yes—
280#13133208C2314yes—
281#13133208C2314yes—
282#13133207C2314yes—
283#13133207C2314yes—
284#13133207C2314yes—
285#13133207C2314yes—
286#13133207C2314yes—
287#13133207C2314yes—
288#13133207C2314yes—
289#13133207C2314yes—
290#13133207C2314yes—
291#13133207C2314yes—
292#13133207C2314yes—
293#13133207C2314yes—
294#13133207C2314yes—
295#13133207C2314yes—
296#13133207C2314yes—
297#13133207C2314yes—
298#13133207C2314yes—
299#13133207C2314yes—
300#13133206C2314yes—
301#13133206C2314yes—
302#13133205C2314yes—
303#13133205C2314yes—
304#13133205C2312yes—
305#13133205C2314yes—
306#13133204C2314yes—
307#13133203C2314yes—
308#13133203C2314yes—
309#13133203C2314yes—
310#13133203C2314yes—
311#13133203C2314yes—
312#13133203C2314yes—
313#13133203C2314yes—
314#13133203C2314yes—
315#13133203C2314yes—
316#13133203C2314yes—
317#13133203C2314yes—
318#13133203C2314yes—
319#13133202C2314yes—
320#13133202C2314yes—
321#13133202C2314yes—
322#13133202C2314yes—
323#13133202C2314yes—
324#13133202C2314yes—
325#13133202C2314yes—
326#13133202C2314yes—
327#13133202C2314yes—
328#13133202C2314yes—
329#13133202C2314yes—
330#13133202C2314yes—
331#13133201C2314yes—
332#13133201C2314yes—
333#13133201C2314yes—
334#13133201C2314yes—
335#13133200C2314yes—
336#13133200C2314yes—
337#13133200C2314yes—
338#13133200C2314yes—
339#13133200C2314yes—
340#13133199C2314yes—
341#13133199C2314yes—
342#13133199C2314yes—
343#13133199C2314yes—
344#13133199C2314yes—
345#13133199C2314yes—
346#13133198C2314yes—
347#13133198C2314yes—
348#13133197C2314yes—
349#13133197C2314yes—
350#13133197C2314yes—
351#13133197C2314yes—
352#13133197C2312yes—
353#13133197C2314yes—
354#13133196C2314yes—
355#13133196C2314yes—
356#13133196C2314yes—
357#13133196C2314yes—
358#13133196C2312yes—
359#13133196C2314yes—
360#13133195C2314yes—
361#13133195C2314yes—
362#13133195C2314yes—
363#13133195C2314yes—
364#13133195C2314yes—
365#13133195C2314yes—
366#13133195C2314yes—
367#13133195C2314yes—
368#13133195C2314yes—
369#13133195C2314yes—
370#13133195C2314yes—
371#13133195C2314yes—
372#13133195C2314yes—
373#13133195C2314yes—
374#13133195C2314yes—
375#13133195C2314yes—
376#13133195C2314yes—
377#13133195C2314yes—
378#13133195C2314yes—
379#13133195C2314yes—
380#13133195C2314yes—
381#13133195C2314yes—
382#13133195C2314yes—
383#13133194C2314yes—
384#13133194C2314yes—
385#13133194C2314yes—
386#13133194C2314yes—
387#13133194C2314yes—
388#13133194C2314yes—
389#13133194C2314yes—
390#13133194C2314yes—
391#13133194C2314yes—
392#13133194C2314yes—
393#13133194C2314yes—
394#13133194C2314yes—
395#13133194C2314yes—
396#13133193C2314yes—
397#13133193C2314yes—
398#13133193C2312yes—
399#13133192C2314yes—
400#13133192C2314yes—
401#13133192C2312yes—
402#13133192C2314yes—
403#13133191C2314yes—
404#13133191C2314yes—
405#13133191C2312yes—
406#13133191C2314yes—
407#13133190C2314yes—
408#13133190C2314yes—
409#13133190C2314yes—
410#13133190C2314yes—
411#13133190C2314yes—
412#13133190C2314yes—
413#13133190C2314yes—
414#13133189C2314yes—
415#13133189C2314yes—
416#13133189C2314yes—
417#13133189C2314yes—
418#13133189C2314yes—
419#13133189C2314yes—
420#13133189C2314yes—
421#13133188C2312yes—
422#13133187C2314yes—
423#13133185C2314yes—
424Q8×Dic53C2314yes—
425Q8×Dic53C2312yes—
426C4×Dic106C2314yes—
427C4×Dic106C2314yes—
428C4×Dic106C2314yes—
429C4×Dic106C2314yes—
430C4×Dic106C2314yes—
431C4×Dic106C2314yes—
432C4×Dic106C2314yes—
433C4×Dic106C2312yes—
434#13133182C2314yes—
435#13133182C2314yes—
436#13133182C2314yes—
437#13133182C2314yes—
438#13133182C2314yes—
439#13133182C2314yes—
440#13133182C2314yes—
441#13133182C2314yes—
442#13133182C2314yes—
443#13133182C2314yes—
444#13133182C2314yes—
445#13133182C2314yes—
446#13133182C2314yes—
447#13133182C2314yes—
448#13133182C2314yes—
449#13133182C2314yes—
450#13133182C2314yes—
451#13133182C2314yes—
452#13133182C2314yes—
453#13133182C2314yes—
454#13133182C2314yes—
455#13133182C2312yes—
456C4×D212C2314yes—
457C4×D212C2312yes—
458D4×Dic53C2314yes—
459D4×Dic53C2314yes—
460D4×Dic53C2314yes—
461D4×Dic53C2312yes—
462D4×Dic53C2314yes—
463#13133179C2314yes—
464#13133179C2314yes—
465#13133179C2314yes—
466#13133179C2314yes—
467#13133179C2314yes—
468#13133179C2312yes—
469C4×C22⋊D53C2314yes—
470C4×C22⋊D53C2314yes—
471C4×C22⋊D53C2314yes—
472C4×C22⋊D53C2314yes—
473C4×C22⋊D53C2314yes—
474C4×C22⋊D53C2314yes—
475C4×C22⋊D53C2314yes—
476C4×C22⋊D53C2314yes—
477C4×C22⋊D53C2314yes—
478#13133177C2314yes—
479#13133177C2314yes—
480#13133177C2314yes—
481#13133177C2314yes—
482#13133177C2314yes—
483#13133177C2314yes—
484#13133177C2314yes—
485#13133177C2314yes—
486#13133177C2314yes—
487#13133177C2314yes—
488#13133177C2314yes—
489#13133177C2314yes—
490#13133177C2314yes—
491#13133177C2314yes—
492#13133177C2314yes—
493#13133175C2314yes—
494#13133175C2312yes—
495#13133175C2314yes—
496#13133175C2312yes—
497#13133175C2312yes—
498#13133175C2314yes—
499#13133175C2312yes—
500#13133175C2312yes—
501#13133175C2314yes—
502#13133175C2314yes—
503#13133175C2314yes—
504#13133175C2312yes—
505#13133175C2314yes—
506#13133174C2314yes—
507#13133174C2314yes—
508#13133174C2314yes—
509#13133174C2314yes—
510#13133173C2314yes—
511#13133173C2314yes—
512#13133173C2314yes—
513#13133173C2314yes—
514#13133173C2314yes—
515#13133173C2314yes—
516#13133173C2314yes—
517C2×C4⋊Dic53C2312yes—
518C2×#11719919C2314yes—
519C2×#11719919C2314yes—
520C2×#11719919C2314yes—
521C2×#11719919C2314yes—
522C4⋊C4×D53C2314yes—
523C4⋊C4×D53C2314yes—
524C4⋊C4×D53C2314yes—
525C2×#11719921C2314yes—
526C2×C4×Dic53C2312yes—
527C2×C4×Dic53C2311yescharacteristic
528C2×C4×Dic53C2314yes—
529C2×C4×Dic53C2314yes—
530C2×C4×Dic53C2314yes—
531C2×C4×Dic53C2314yes—
532C42×D53C2312yes—
533C42×D53C2311yescharacteristic
534C42×D53C2311yescharacteristic
535C42×D53C2311yescharacteristic
536C42×D53C2312yes—
537C42×D53C2311yescharacteristic
538C42×D53C2314yes—
539C42×D53C2314yes—
540C42×D53C2314yes—
541C4⋊Q8×C53C2314yes—
542#126×C53C2314yes—
543#126×C53C2314yes—
544#126×C53C2314yes—
545#126×C53C2314yes—
546#126×C53C2314yes—
547#125×C53C2314yes—
548#125×C53C2312yes—
549#125×C53C2314yes—
550#125×C53C2311yescharacteristic
551#125×C53C2311yescharacteristic
552#125×C53C2312yes—
553#125×C53C2314yes—
554#125×C53C2314yes—
555#125×C53C2314yes—
556#125×C53C2314yes—
557#124×C53C2312yes—
558#123×C53C2314yes—
559#123×C53C2314yes—
560#123×C53C2314yes—
561#123×C53C2314yes—
562#123×C53C2314yes—
563C22⋊Q8×C53C2314yes—
564C22⋊Q8×C53C2314yes—
565C22⋊Q8×C53C2314yes—
566C22⋊Q8×C53C2314yes—
567C22⋊Q8×C53C2312yes—
568C22⋊Q8×C53C2314yes—
569C22⋊Q8×C53C2314yes—
570#121×C53C2314yes—
571#121×C53C2314yes—
572#121×C53C2312yes—
573C4×Q8×C53C2312yes—
574C4×Q8×C53C2314yes—
575C4×D4×C53C2314yes—
576C4×D4×C53C2314yes—
577C4×D4×C53C2314yes—
578C4×D4×C53C2312yes—
579C4×D4×C53C2314yes—
580#117×C53C2314yes—
581#117×C53C2314yes—
582C2×C4⋊C4×C53C2314yes—
583C2×C4⋊C4×C53C2312yes—
584C2×C4⋊C4×C53C2314yes—
585C2×C42×C53C2311yescharacteristic
586C23×D53C2411yescharacteristic
587C2×Q8×C53C2414yes—
588C2×Q8×C53C2412yes—
589C2×D4×C53C2414yes—
590C2×D4×C53C2414yes—
591C2×D4×C53C2412yes—
592C22×C4×C53C2411yescharacteristic
593C22×C4×C53C2412yes—
594C22×C4×C53C2414yes—
595C22×C4×C53C2414yes—
596C22×C4×C53C2414yes—
597C22×C4×C53C2414yes—
598C2×C22⋊D53C2414yes—
599C2×C22⋊D53C2414yes—
600C2×C22⋊D53C2414yes—
601C2×C22⋊D53C2414yes—
602C2×C22⋊D53C2414yes—
603C2×C22⋊D53C2414yes—
604C2×C22⋊D53C2414yes—
605C22×Dic53C2414yes—
606C22×Dic53C2412yes—
607C22×Dic53C2414yes—
608C22×Dic53C2414yes—
609C22×Dic53C2414yes—
610C22×Dic53C2414yes—
611C22×Dic53C2411yescharacteristic
612#11719949—44no—
613Q8×D53—48no—
614#11719947—216no—
615#11719947—48no—
616#11719947—44no—
617#11719945—48no—
618#11719945—48no—
619C2×D212C2414yes—
620C2×D212C2414yes—
621C2×D212C2414yes—
622C2×D212C2412yes—
623C2×C4×D53—24no—
624C2×C4×D53—44no—
625C2×C4×D53C2414yes—
626C2×C4×D53C2412yes—
627C2×C4×D53C2411yescharacteristic
628C2×C4×D53C2411yescharacteristic
629C2×C4×D53C2411yescharacteristic
630C2×C4×D53C2411yescharacteristic
631C2×C4×D53C2412yes—
632C2×C4×D53C2414yes—
633C2×C4×D53C2412yes—
634C2×C4×D53C2412yes—
635C2×C4×D53C2414yes—
636C2×C4×D53C2414yes—
637C2×C4×D53C2414yes—
638C2×C4×D53C2414yes—
639C2×C4×D53C2414yes—
640C2×Dic106—48no—
641C2×Dic106—48no—
642C2×Dic106C2414yes—
643C2×Dic106C2414yes—
644C2×Dic106C2414yes—
645C2×Dic106C2414yes—
646C2×Dic106C2414yes—
647C2×Dic106C2414yes—
648C2×Dic106C2414yes—
649C2×Dic106C2414yes—
650C2×Dic106C2414yes—
651C2×Dic106C2412yes—
652C4⋊C4×C53C2414yes—
653C4⋊C4×C53C2414yes—
654C4⋊C4×C53C2414yes—
655C4⋊C4×C53C2414yes—
656C4⋊C4×C53C2414yes—
657C4⋊C4×C53C2412yes—
658C4⋊C4×C53C2414yes—
659C4⋊C4×C53C2414yes—
660C4⋊C4×C53C2414yes—
661C4⋊C4×C53C2412yes—
662C4⋊C4×C53C2414yes—
663C4⋊C4×C53C2414yes—
664C4⋊C4×C53C2412yes—
665C4⋊C4×C53C2414yes—
666C4⋊C4×C53C2414yes—
667C4⋊C4×C53C2414yes—
668C4⋊C4×C53C2412yes—
669C4⋊C4×C53C2414yes—
670C4⋊C4×C53C2414yes—
671C22⋊C4×C53C2414yes—
672C22⋊C4×C53C2414yes—
673C22⋊C4×C53C2414yes—
674C22⋊C4×C53C2414yes—
675C22⋊C4×C53C2414yes—
676C22⋊C4×C53C2414yes—
677C22⋊C4×C53C2414yes—
678C22⋊C4×C53C2414yes—
679C22⋊C4×C53C2414yes—
680C42×C53C2411yescharacteristic
681C42×C53C2412yes—
682C42×C53C2411yescharacteristic
683C42×C53C2414yes—
684C42×C53C2414yes—
685C42×C53C2414yes—
686C22⋊Dic53C2414yes—
687C22⋊Dic53C2414yes—
688C22⋊Dic53C2414yes—
689C22⋊Dic53C2414yes—
690C22⋊Dic53C2414yes—
691C22⋊Dic53C2414yes—
692C22⋊Dic53C2414yes—
693#11719921C2414yes—
694#11719921C2414yes—
695#11719921C2414yes—
696#11719921C2414yes—
697#11719921C2414yes—
698#11719921C2414yes—
699#11719921C2414yes—
700#11719921C2414yes—
701#11719921C2414yes—
702#11719921C2414yes—
703#11719921C2414yes—
704#11719921C2414yes—
705#11719921C2414yes—
706#11719921C2414yes—
707#11719921C2414yes—
708#11719921C2414yes—
709#11719921C2414yes—
710#11719921C2414yes—
711#11719921C2414yes—
712#11719921C2414yes—
713#11719921C2414yes—
714#11719921C2414yes—
715C4⋊Dic53C2414yes—
716C4⋊Dic53C2414yes—
717C4⋊Dic53C2414yes—
718C4⋊Dic53C2412yes—
719C4⋊Dic53C2414yes—
720C4⋊Dic53C2412yes—
721C4⋊Dic53C2412yes—
722C4⋊Dic53C2414yes—
723C4⋊Dic53C2414yes—
724C4⋊Dic53C2414yes—
725C4⋊Dic53C2414yes—
726C4⋊Dic53C2412yes—
727C4⋊Dic53C2414yes—
728#11719919C2414yes—
729#11719919C2414yes—
730#11719919C2414yes—
731#11719919C2414yes—
732#11719919C2414yes—
733#11719919C2414yes—
734#11719919C2414yes—
735#11719919C2414yes—
736#11719919C2414yes—
737#11719919C2414yes—
738#11719919C2414yes—
739#11719919C2414yes—
740#11719919C2414yes—
741#11719919C2414yes—
742#11719919C2414yes—
743#11719919C2414yes—
744#11719919C2414yes—
745#11719919C2414yes—
746#11719919C2414yes—
747#11719919C2414yes—
748#11719919C2414yes—
749#11719919C2414yes—
750#11719919C2414yes—
751#11719919C2414yes—
752#11719919C2414yes—
753#11719919C2414yes—
754#11719919C2414yes—
755#11719919C2414yes—
756#11719919C2414yes—
757#11719919C2414yes—
758C4×Dic53C2412yes—
759C4×Dic53C2414yes—
760C4×Dic53C2412yes—
761C4×Dic53C2412yes—
762C4×Dic53C2411yescharacteristic
763C4×Dic53C2412yes—
764C4×Dic53C2412yes—
765C4×Dic53C2411yescharacteristic
766C4×Dic53C2414yes—
767C4×Dic53C2414yes—
768C4×Dic53C2414yes—
769C4×Dic53C2414yes—
770C4×Dic53C2414yes—
771C4×Dic53C2414yes—
772C4×Dic53C2414yes—
773C4×Dic53C2414yes—
774C4×Dic53C2414yes—
775C4×Dic53C2414yes—
776C4×Dic53C2414yes—
777C4×Dic53C2414yes—
778C4×Dic53C2414yes—
779C4×Dic53C2414yes—
780C23×C53C2514yes—
781C23×C53C2511yescharacteristic
782C22×D53—22no—
783C22×D53—42no—
784C22×D53C2514yes—
785C22×D53C2511yescharacteristic
786C22×D53C2511yescharacteristic
787Q8×C53—44no—
788Q8×C53—42no—
789D4×C53—28no—
790D4×C53—44no—
791D4×C53—42no—
792C2×C4×C53—22no—
793C2×C4×C53—44no—
794C2×C4×C53—44no—
795C2×C4×C53—42no—
796C2×C4×C53—44no—
797C2×C4×C53—44no—
798C2×C4×C53C2514yes—
799C2×C4×C53C2514yes—
800C2×C4×C53C2514yes—
801C2×C4×C53C2512yes—
802C2×C4×C53C2514yes—
803C2×C4×C53C2514yes—
804C2×C4×C53C2512yes—
805C2×C4×C53C2511yescharacteristic
806C2×C4×C53C2511yescharacteristic
807C22⋊D53—28no—
808C22⋊D53—28no—
809C22⋊D53—28no—
810C22⋊D53—44no—
811C22⋊D53—44no—
812C22⋊D53—44no—
813C22⋊D53—44no—
814C2×Dic53—28no—
815C2×Dic53—24no—
816C2×Dic53—28no—
817C2×Dic53—44no—
818C2×Dic53—44no—
819C2×Dic53—44no—
820C2×Dic532−1+414yes—
821C2×Dic53C2512yes—
822C2×Dic53C2514yes—
823C2×Dic53C2514yes—
824C2×Dic53C2514yes—
825C2×Dic53C2514yes—
826C2×Dic53C2514yes—
827C2×Dic53C2511yescharacteristic
828C2×Dic53C2511yescharacteristic
829C2×Dic53C2512yes—
830D212—44no—
831D212—44no—
832D212—42no—
833D212—44no—
834C4×D53—22no—
835C4×D53—22no—
836C4×D53—22no—
837C4×D53—22no—
838C4×D53—28no—
839C4×D53—24no—
840C4×D53—24no—
841C4×D53—28no—
842C4×D53—42no—
843C4×D53—42no—
844C4×D53—44no—
845C4×D53—44no—
846C4×D53—44no—
847C4×D53—44no—
848C4×D53—44no—
849Dic106—28no—
850Dic106—28no—
851Dic106—28no—
852Dic106—28no—
853Dic106—44no—
854Dic106—44no—
855Dic106—44no—
856Dic106—44no—
857Dic106—42no—
858Dic106—44no—
859#62761—531nomaximal, Sylow
860C22×C53—22no—
861C22×C53—24no—
862C22×C53—24no—
863C22×C53—24no—
864C22×C53C2×2−1+412yes—
865C22×C53C2611yescharacteristic
866C2×D53—21no—
867C2×D53—21no—
868C2×D53—24no—
869C2×D53—24no—
870C2×D53—22no—
871C2×D53—22no—
872C2×D53—24no—
873C2×D53—44no—
874C4×C53—24no—
875C4×C53—21no—
876C4×C53—21no—
877C4×C53—24no—
878C4×C53—24no—
879C4×C53—24no—
880C4×C53—22no—
881C4×C53—24no—
882C4×C53—22no—
883Dic53—24no—
884Dic53—24no—
885Dic53—24no—
886Dic53—24no—
887Dic53—22no—
888Dic53—24no—
889Dic53C2×2−1+412yes—
890Dic53C2×2−1+412yes—
891Dic53#58514yes—
892#3557—534no—
893#3556—531no—
894#3555—534no—
895#3554—534no—
896#3553—532no—
897#3553—531no—
898#3553D5311yescharacteristic, complemented
899#3552—534no—
900#3550—532no—
901#3548—531no—
902#3541—534no—
903#3541—534no—
904#3531—531no—
905#3531—532no—
906#3531—531no—
907#3482—534no—
908#3480—534no—
909Q8×#41—534no—
910#3461—534no—
911#3461—534no—
912#3455—534no—
913#3444—532no—
914C2×#533—531no—
915C2×C53—22no—
916C2×C53—44no—
917C2×C53C22×2−1+411yescharacteristic
918C2×C53C2×#58512yes—
919D53—44no—
920D53—41no—
921D53—41no—
922#564—531no—
923#564—532no—
924#564C2×D5311yescharacteristic, complemented
925#563—534no—
926#563—534no—
927#563—534no—
928#563—534no—
929#563—532no—
930#563—532no—
931#563—534no—
932#563—532no—
933#563—534no—
934#563—534no—
935#563—534no—
936#563C2×D5312yescomplemented
937#562—534no—
938#562—531no—
939#562—532no—
940#562—534no—
941#562—534no—
942#562—534no—
943#562C2×D5311yescharacteristic, complemented
944#559—534no—
945#559—534no—
946#559—534no—
947Q82—534no—
948#557—534no—
949#557—534no—
950#557—534no—
951#557—534no—
952#557—534no—
953#556—534no—
954#556—534no—
955#556—534no—
956#556—534no—
957#556—534no—
958#556—534no—
959#554—534no—
960#554—534no—
961#554—534no—
962#554—534no—
963#554—534no—
964#554—534no—
965#554—534no—
966#554—534no—
967#554C2×D5314yes—
968#553—534no—
969#553—534no—
970#553—534no—
971#553—534no—
972#553—534no—
973#553C2×D5314yes—
974#552—534no—
975#552—534no—
976#552—534no—
977#552—534no—
978#552—534no—
979#552C2×D5314yescomplemented
980#550—534no—
981D4×Q8—534no—
982D4×Q8—534no—
983D4×Q8—534no—
984D4×Q8—534no—
985#548—534no—
986#548—534no—
987#548—534no—
988#548—534no—
989#547—534no—
990#547—534no—
991#547—534no—
992#544—534no—
993#544—534no—
994#542—534no—
995#542—534no—
996#542—534no—
997#542—534no—
998#542—534no—
999#542—534no—
1000#542—534no—
1001#542—534no—
1002#542—534no—
1003#542—534no—
1004#542—534no—
1005#542—534no—
1006#541—534no—
1007#541—534no—
1008#541—534no—
1009#541—534no—
1010#541—534no—
1011#541—534no—
1012#541—534no—
1013#541—534no—
1014#541—534no—
1015#541C2×D5314yescomplemented
1016#540—534no—
1017#540—534no—
1018#539—534no—
1019#539—534no—
1020#539—534no—
1021#539—534no—
1022#539—534no—
1023#539—534no—
1024#539—534no—
1025#539—534no—
1026#539—534no—
1027#539—534no—
1028#539C2×D5314yes—
1029#539C2×D5314yescomplemented
1030#538—534no—
1031#538—534no—
1032#538—534no—
1033#538—534no—
1034#537—534no—
1035#537—534no—
1036#536—534no—
1037#536—534no—
1038#536—534no—
1039#536—534no—
1040#533—534no—
1041#533—534no—
1042#533—532no—
1043#533—531no—
1044#533—531no—
1045#533—531no—
1046#533—531no—
1047#533—534no—
1048#533—532no—
1049#533—532no—
1050#533—534no—
1051#533—534no—
1052#533—532no—
1053#533—534no—
1054#533—534no—
1055#533—534no—
1056#533—534no—
1057#533—532no—
1058#532—532no—
1059#532—532no—
1060#532—534no—
1061#532—532no—
1062C2×C4⋊Q8—532no—
1063#529—534no—
1064#529—534no—
1065#529—534no—
1066#529—534no—
1067#529—534no—
1068#529—534no—
1069#529—532no—
1070#529—534no—
1071#529—534no—
1072#529—534no—
1073#529—532no—
1074#529—534no—
1075#529—534no—
1076#529—534no—
1077#529—534no—
1078#529—534no—
1079#529—534no—
1080#529—534no—
1081#529—534no—
1082#529—534no—
1083#529—532no—
1084#529C2×D5312yes—
1085C2×#125—531no—
1086C2×#125C2×D5311yescharacteristic
1087#525—534no—
1088#525—532no—
1089#525—532no—
1090#525—534no—
1091C2×C22⋊Q8—534no—
1092C4×#41—532no—
1093C4×#41—532no—
1094C4×#41—534no—
1095C4×#41—534no—
1096C4×#41—534no—
1097C4×#41—534no—
1098C4×#41—534no—
1099C4×#41—534no—
1100C2×C4×Q8—534no—
1101C2×C4×Q8—534no—
1102C2×C4×Q8—534no—
1103C2×#117—532no—
1104C22×C42—531no—
1105C53#6276111yescharacteristic, complemented, Sylow
1106C2×#41—532no—
1107C2×#41—534no—
1108C2×#41—532no—
1109C2×#41—534no—
1110C2×#41—534no—
1111C2×#41—534no—
1112C22×Q8—534no—
1113C22×Q8—534no—
1114C22×Q8—534no—
1115C23×C4—531no—
1116C23×C4—532no—
1117C4⋊Q8—532no—
1118C4⋊Q8—534no—
1119C4⋊Q8—534no—
1120C4⋊Q8—534no—
1121C4⋊Q8—534no—
1122C4⋊Q8—534no—
1123C4⋊Q8—534no—
1124C4⋊Q8—532no—
1125C4⋊Q8—532no—
1126C4⋊Q8—532no—
1127C4⋊Q8—532no—
1128C4⋊Q8—532no—
1129C4⋊Q8—532no—
1130C4⋊Q8—534no—
1131C4⋊Q8—534no—
1132C4⋊Q8—534no—
1133C4⋊Q8—534no—
1134C4⋊Q8—534no—
1135C4⋊Q8—534no—
1136C4⋊Q8—534no—
1137C4⋊Q8—534no—
1138C4⋊Q8—534no—
1139C4⋊Q8—534no—
1140C4⋊Q8C22×D5314yes—
1141#127—532no—
1142#127—534no—
1143#126—534no—
1144#126—534no—
1145#126—534no—
1146#126—534no—
1147#126—534no—
1148#126—534no—
1149#126—534no—
1150#126—534no—
1151#126—534no—
1152#126—534no—
1153#126—534no—
1154#126—534no—
1155#126—534no—
1156#126—534no—
1157#126—534no—
1158#126—534no—
1159#126—534no—
1160#126—534no—
1161#126—534no—
1162#126—534no—
1163#126—534no—
1164#126—534no—
1165#126—534no—
1166#126—534no—
1167#126—534no—
1168#126—534no—
1169#126—534no—
1170#126C22×D5314yes—
1171#126C22×D5314yes—
1172#126C22×D5314yes—
1173#126C22×D5314yes—
1174#126C22×D5314yes—
1175#125—534no—
1176#125—534no—
1177#125—534no—
1178#125—534no—
1179#125—534no—
1180#125—534no—
1181#125—534no—
1182#125—534no—
1183#125—534no—
1184#125—534no—
1185#125—534no—
1186#125—534no—
1187#125—534no—
1188#125—534no—
1189#125—534no—
1190#125—534no—
1191#125—534no—
1192#125—534no—
1193#125—534no—
1194#125—534no—
1195#125—534no—
1196#125—534no—
1197#125—534no—
1198#125—534no—
1199#125—532no—
1200#125—531no—
1201#125—531no—
1202#125—532no—
1203#125—534no—
1204#125—534no—
1205#125C22×D5314yes—
1206#125C22×D5312yes—
1207#125C22×D5311yescharacteristic
1208#125C22×D5311yescharacteristic
1209#125C22×D5312yes—
1210#125C22×D5314yes—
1211#125C22×D5314yes—
1212#125C22×D5314yes—
1213#125C22×D5314yes—
1214#125C22×D5314yes—
1215#124—534no—
1216#124—534no—
1217#124—534no—
1218#124—534no—
1219#124—534no—
1220#124—534no—
1221#124—534no—
1222#124—534no—
1223#124—534no—
1224#124—534no—
1225#124—534no—
1226#124—534no—
1227#124—534no—
1228#124—534no—
1229#124—534no—
1230#124—532no—
1231#124—534no—
1232#124—534no—
1233#124—534no—
1234#124C22×D5312yes—
1235#123—534no—
1236#123—534no—
1237#123—534no—
1238#123—534no—
1239#123—534no—
1240#123—534no—
1241#123—534no—
1242#123—534no—
1243#123—534no—
1244#123—534no—
1245#123—534no—
1246#123—534no—
1247#123—534no—
1248#123—534no—
1249#123—534no—
1250#123—534no—
1251#123—534no—
1252#123—534no—
1253#123—534no—
1254#123—534no—
1255#123—534no—
1256#123—534no—
1257#123—534no—
1258#123—534no—
1259#123—534no—
1260#123—534no—
1261#123—534no—
1262#123—534no—
1263#123—534no—
1264#123C22×D5314yes—
1265#123C22×D5314yes—
1266#123C22×D5314yes—
1267#123C22×D5314yes—
1268#123C22×D5314yes—
1269C22⋊Q8—532no—
1270C22⋊Q8—534no—
1271C22⋊Q8—534no—
1272C22⋊Q8—532no—
1273C22⋊Q8—534no—
1274C22⋊Q8—534no—
1275C22⋊Q8—534no—
1276C22⋊Q8—534no—
1277C22⋊Q8—534no—
1278C22⋊Q8—534no—
1279C22⋊Q8—534no—
1280C22⋊Q8—534no—
1281C22⋊Q8—534no—
1282C22⋊Q8—534no—
1283C22⋊Q8—534no—
1284C22⋊Q8—534no—
1285C22⋊Q8—534no—
1286C22⋊Q8—534no—
1287C22⋊Q8—534no—
1288C22⋊Q8—534no—
1289C22⋊Q8—532no—
1290C22⋊Q8—534no—
1291C22⋊Q8—534no—
1292C22⋊Q8—534no—
1293C22⋊Q8—534no—
1294C22⋊Q8—534no—
1295C22⋊Q8—534no—
1296C22⋊Q8—534no—
1297C22⋊Q8—534no—
1298C22⋊Q8—534no—
1299C22⋊Q8—534no—
1300C22⋊Q8—534no—
1301C22⋊Q8—534no—
1302C22⋊Q8—534no—
1303C22⋊Q8—534no—
1304C22⋊Q8—534no—
1305C22⋊Q8—534no—
1306C22⋊Q8—534no—
1307C22⋊Q8—534no—
1308C22⋊Q8—534no—
1309C22⋊Q8—534no—
1310C22⋊Q8—534no—
1311C22⋊Q8—534no—
1312C22⋊Q8—534no—
1313C22⋊Q8—534no—
1314C22⋊Q8—534no—
1315C22⋊Q8—534no—
1316C22⋊Q8—534no—
1317C22⋊Q8—534no—
1318C22⋊Q8—534no—
1319C22⋊Q8—534no—
1320C22⋊Q8C22×D5312yes—
1321C22⋊Q8C22×D5314yes—
1322C22⋊Q8C22×D5314yes—
1323C22⋊Q8C22×D5314yes—
1324C22⋊Q8C22×D5314yes—
1325C22⋊Q8C22×D5314yes—
1326C22⋊Q8C22×D5314yes—
1327#121—534no—
1328#121—532no—
1329#121—534no—
1330#121—534no—
1331#121—534no—
1332#121—534no—
1333#121—534no—
1334#121—534no—
1335#121—532no—
1336#121—534no—
1337#121—534no—
1338#121—534no—
1339#121—532no—
1340#121—534no—
1341#121—534no—
1342#121—534no—
1343#121—534no—
1344#121—534no—
1345#121—534no—
1346#121—534no—
1347#121—534no—
1348#121—534no—
1349#121—534no—
1350#121C22×D5312yes—
1351#121C22×D5314yes—
1352#121C22×D5314yes—
1353#120—534no—
1354#120—534no—
1355C4×Q8—534no—
1356C4×Q8—532no—
1357C4×Q8—534no—
1358C4×Q8—534no—
1359C4×Q8—534no—
1360C4×Q8—534no—
1361C4×Q8—534no—
1362C4×Q8—534no—
1363C4×Q8—534no—
1364C4×Q8—534no—
1365C4×Q8—534no—
1366C4×Q8—534no—
1367C4×Q8—534no—
1368C4×Q8—534no—
1369C4×Q8—534no—
1370C4×Q8—534no—
1371C4×Q8—534no—
1372C4×Q8—534no—
1373C4×Q8—532no—
1374C4×Q8—534no—
1375C4×Q8—534no—
1376C4×Q8—534no—
1377C4×Q8—534no—
1378C4×Q8—534no—
1379C4×Q8—534no—
1380C4×Q8—534no—
1381C4×Q8—534no—
1382C4×Q8—532no—
1383C4×Q8—534no—
1384C4×Q8—534no—
1385C4×Q8—534no—
1386C4×Q8—534no—
1387C4×Q8C22×D5314yes—
1388C4×Q8C22×D5312yes—
1389C4×D4—534no—
1390C4×D4—532no—
1391C4×D4—534no—
1392C4×D4—534no—
1393C4×D4—534no—
1394C4×D4—534no—
1395C4×D4—534no—
1396C4×D4—534no—
1397C4×D4—534no—
1398C4×D4—534no—
1399C4×D4—534no—
1400C4×D4—534no—
1401C4×D4—534no—
1402C4×D4—534no—
1403C4×D4—534no—
1404C4×D4—534no—
1405C4×D4—534no—
1406C4×D4—532no—
1407C4×D4—534no—
1408C4×D4—534no—
1409C4×D4—534no—
1410C4×D4—534no—
1411C4×D4—534no—
1412C4×D4—534no—
1413C4×D4—534no—
1414C4×D4—534no—
1415C4×D4—534no—
1416C4×D4—534no—
1417C4×D4—534no—
1418C4×D4—534no—
1419C4×D4—534no—
1420C4×D4—534no—
1421C4×D4—534no—
1422C4×D4—534no—
1423C4×D4—534no—
1424C4×D4—534no—
1425C4×D4—532no—
1426C4×D4C22×D5314yes—
1427C4×D4C22×D5312yes—
1428C4×D4C22×D5314yes—
1429C4×D4C22×D5314yes—
1430C4×D4C22×D5314yes—
1431#117—534no—
1432#117—532no—
1433#117—532no—
1434#117—532no—
1435#117—534no—
1436#117—532no—
1437#117—532no—
1438#117—532no—
1439#117—534no—
1440#117—534no—
1441#117—534no—
1442#117—534no—
1443#117—534no—
1444#117—534no—
1445#117—534no—
1446#117—534no—
1447#117—534no—
1448#117—534no—
1449#117—534no—
1450#117—534no—
1451#117—534no—
1452#117—534no—
1453#117—534no—
1454#117—534no—
1455#117C22×D5314yes—
1456#117C22×D5314yes—
1457C2×C4⋊C4—532no—
1458C2×C4⋊C4—534no—
1459C2×C4⋊C4—534no—
1460C2×C4⋊C4—534no—
1461C2×C4⋊C4—534no—
1462C2×C4⋊C4—534no—
1463C2×C4⋊C4—534no—
1464C2×C4⋊C4—534no—
1465C2×C4⋊C4C22×D5312yes—
1466C2×C4⋊C4C22×D5314yes—
1467C2×C4⋊C4C22×D5314yes—
1468C2×C22⋊C4—534no—
1469C2×C42—534no—
1470C2×C42—532no—
1471C2×C42—534no—
1472C2×C42—534no—
1473C2×C42—534no—
1474C2×C42—531no—
1475C2×C42—534no—
1476C2×C42—534no—
1477C2×C42—534no—
1478C2×C42—531no—
1479C2×C42—532no—
1480C2×C42—531no—
1481C2×C42—531no—
1482C2×C42—532no—
1483C2×C42—531no—
1484C2×C42C22×D5311yescharacteristic
1485C24—531no—
1486#41—10616no—
1487#41—2128no—
1488#41—2128no—
1489#41—2124no—
1490#41—2124no—
1491#41—2128no—
1492C2×Q8—534no—
1493C2×Q8—534no—
1494C2×Q8—534no—
1495C2×Q8—534no—
1496C2×Q8—534no—
1497C2×Q8—534no—
1498C2×Q8—534no—
1499C2×Q8—534no—
1500C2×Q8—534no—
1501C2×Q8—532no—
1502C2×Q8—2128no—
1503C2×Q8—2128no—
1504C2×Q8—2128no—
1505C2×Q8C23×D5312yes—
1506C2×Q8C23×D5314yes—
1507C2×D4—534no—
1508C2×D4—534no—
1509C2×D4—534no—
1510C2×D4—534no—
1511C2×D4—534no—
1512C2×D4—534no—
1513C2×D4—534no—
1514C2×D4—534no—
1515C2×D4—534no—
1516C2×D4—534no—
1517C2×D4—532no—
1518C2×D4C23×D5314yes—
1519C2×D4C23×D5312yes—
1520C2×D4C23×D5314yes—
1521C22×C4—531no—
1522C22×C4—534no—
1523C22×C4—532no—
1524C22×C4—534no—
1525C22×C4—534no—
1526C22×C4—534no—
1527C22×C4—534no—
1528C22×C4—534no—
1529C22×C4—531no—
1530C22×C4—531no—
1531C22×C4—531no—
1532C22×C4—531no—
1533C22×C4—532no—
1534C22×C4—532no—
1535C22×C4—534no—
1536C22×C4—532no—
1537C22×C4—532no—
1538C22×C4—534no—
1539C22×C4—534no—
1540C22×C4—534no—
1541C22×C4—534no—
1542C22×C4—534no—
1543C22×C4—1064no—
1544C22×C4—2124no—
1545C22×C4C23×D5311yescharacteristic
1546C22×C4C23×D5312yes—
1547C22×C4C23×D5314yes—
1548C22×C4C23×D5314yes—
1549C22×C4C23×D5314yes—
1550C22×C4C23×D5314yes—
1551C4⋊C4—534no—
1552C4⋊C4—534no—
1553C4⋊C4—534no—
1554C4⋊C4—534no—
1555C4⋊C4—534no—
1556C4⋊C4—534no—
1557C4⋊C4—532no—
1558C4⋊C4—534no—
1559C4⋊C4—532no—
1560C4⋊C4—534no—
1561C4⋊C4—534no—
1562C4⋊C4—534no—
1563C4⋊C4—534no—
1564C4⋊C4—534no—
1565C4⋊C4—534no—
1566C4⋊C4—534no—
1567C4⋊C4—534no—
1568C4⋊C4—534no—
1569C4⋊C4—534no—
1570C4⋊C4—534no—
1571C4⋊C4—534no—
1572C4⋊C4—534no—
1573C4⋊C4—534no—
1574C4⋊C4—534no—
1575C4⋊C4—534no—
1576C4⋊C4—532no—
1577C4⋊C4—534no—
1578C4⋊C4—534no—
1579C4⋊C4—534no—
1580C4⋊C4—532no—
1581C4⋊C4—534no—
1582C4⋊C4—534no—
1583C4⋊C4—534no—
1584C4⋊C4—534no—
1585C4⋊C4—534no—
1586C4⋊C4—534no—
1587C4⋊C4—534no—
1588C4⋊C4—534no—
1589C4⋊C4—534no—
1590C4⋊C4—534no—
1591C4⋊C4—534no—
1592C4⋊C4—534no—
1593C4⋊C4—534no—
1594C4⋊C4C23×D5314yes—
1595C4⋊C4C23×D5314yes—
1596C4⋊C4C23×D5314yes—
1597C4⋊C4C23×D5312yes—
1598C4⋊C4C23×D5314yes—
1599C4⋊C4C23×D5312yes—
1600C4⋊C4C23×D5314yes—
1601C4⋊C4C23×D5314yes—
1602C4⋊C4C23×D5314yes—
1603C4⋊C4C23×D5314yes—
1604C4⋊C4C23×D5314yes—
1605C4⋊C4C23×D5312yes—
1606C4⋊C4C23×D5314yes—
1607C4⋊C4C23×D5312yes—
1608C4⋊C4C23×D5314yes—
1609C4⋊C4C23×D5314yes—
1610C4⋊C4C23×D5314yes—
1611C4⋊C4C23×D5314yes—
1612C4⋊C4C23×D5314yes—
1613C22⋊C4—534no—
1614C22⋊C4—534no—
1615C22⋊C4—534no—
1616C22⋊C4—534no—
1617C22⋊C4—534no—
1618C22⋊C4—534no—
1619C22⋊C4—534no—
1620C22⋊C4—534no—
1621C22⋊C4—534no—
1622C22⋊C4—534no—
1623C22⋊C4—534no—
1624C22⋊C4—534no—
1625C22⋊C4—534no—
1626C22⋊C4—534no—
1627C22⋊C4—534no—
1628C22⋊C4—534no—
1629C22⋊C4—534no—
1630C22⋊C4—534no—
1631C22⋊C4—534no—
1632C22⋊C4—534no—
1633C22⋊C4—534no—
1634C22⋊C4—534no—
1635C22⋊C4—534no—
1636C22⋊C4—534no—
1637C22⋊C4—534no—
1638C22⋊C4—534no—
1639C22⋊C4—534no—
1640C22⋊C4—534no—
1641C22⋊C4—534no—
1642C22⋊C4C23×D5314yes—
1643C22⋊C4C23×D5314yes—
1644C22⋊C4C23×D5314yes—
1645C22⋊C4C23×D5314yes—
1646C22⋊C4C23×D5314yes—
1647C22⋊C4C23×D5314yes—
1648C22⋊C4C23×D5314yes—
1649C22⋊C4C23×D5314yes—
1650C22⋊C4C23×D5314yes—
1651C42—532no—
1652C42—534no—
1653C42—532no—
1654C42—534no—
1655C42—534no—
1656C42—534no—
1657C42—532no—
1658C42—531no—
1659C42—532no—
1660C42—532no—
1661C42—531no—
1662C42—534no—
1663C42—534no—
1664C42—534no—
1665C42—534no—
1666C42—534no—
1667C42—534no—
1668C42—534no—
1669C42—534no—
1670C42—534no—
1671C42—534no—
1672C42—534no—
1673C42C23×D5311yescharacteristic
1674C42C23×D5312yes—
1675C42C23×D5311yescharacteristic
1676C42C23×D5314yes—
1677C42C23×D5314yes—
1678C42C23×D5314yes—
1679C23—531no—
1680C23—531no—
1681C23—534no—
1682C23—1062no—
1683C23—2122no—
1684C23C24×D5314yes—
1685C23C24×D5311yescharacteristic
1686Q8—44no—
1687Q8—42no—
1688Q8—1068no—
1689Q8—1068no—
1690Q8—1068no—
1691Q8—1068no—
1692Q8—2124no—
1693Q8—2124no—
1694Q8—2124no—
1695Q8—2124no—
1696Q8—2124no—
1697Q8—2122no—
1698D4—28no—
1699D4—44no—
1700D4—42no—
1701D4—1068no—
1702D4—1068no—
1703D4—1068no—
1704D4—2124no—
1705D4—2124no—
1706D4—2122no—
1707D4—2124no—
1708D4—2124no—
1709D4—2124no—
1710D4—2124no—
1711D4—2124no—
1712C2×C4—22no—
1713C2×C4—42no—
1714C2×C4—44no—
1715C2×C4—44no—
1716C2×C4—44no—
1717C2×C4—44no—
1718C2×C4—534no—
1719C2×C4—531no—
1720C2×C4—531no—
1721C2×C4—532no—
1722C2×C4—534no—
1723C2×C4—532no—
1724C2×C4—534no—
1725C2×C4—534no—
1726C2×C4—534no—
1727C2×C4—534no—
1728C2×C4—1062no—
1729C2×C4—1062no—
1730C2×C4—1062no—
1731C2×C4—1062no—
1732C2×C4—1064no—
1733C2×C4—1064no—
1734C2×C4—1068no—
1735C2×C4—1068no—
1736C2×C4—1064no—
1737C2×C4—1068no—
1738C2×C4—1068no—
1739C2×C4—2122no—
1740C2×C4—2122no—
1741C2×C4—2124no—
1742C2×C4—2124no—
1743C2×C4—2124no—
1744C2×C4—2124no—
1745C2×C4—2124no—
1746C2×C4—2124no—
1747C2×C4—2124no—
1748C2×C4—2124no—
1749C2×C4C24×D5312yes—
1750C2×C4C24×D5314yes—
1751C2×C4C24×D5314yes—
1752C2×C4C24×D5314yes—
1753C2×C4C24×D5314yes—
1754C2×C4C24×D5311yescharacteristic
1755C2×C4C24×D5311yescharacteristic
1756C2×C4C24×D5314yes—
1757C2×C4C24×D5312yes—
1758C22—22no—
1759C22—24no—
1760C22—24no—
1761C22—24no—
1762C22—1061no—
1763C22—1061no—
1764C22—1064no—
1765C22—1064no—
1766C22—1062no—
1767C22—1062no—
1768C22—1064no—
1769C22—2124no—
1770C222−1+4×D5312yes—
1771C22C25×D5311yescharacteristic
1772C4—21no—
1773C4—21no—
1774C4—24no—
1775C4—22no—
1776C4—24no—
1777C4—24no—
1778C4—24no—
1779C4—22no—
1780C4—24no—
1781C4—532no—
1782C4—532no—
1783C4—534no—
1784C4—1064no—
1785C4—1064no—
1786C4—1062no—
1787C4—1064no—
1788C4—1064no—
1789C4—1064no—
1790C2—22no—
1791C2—44no—
1792C2—2121no—
1793C2—2121no—
1794C2—2124no—
1795C2C2×2−1+4×D5311yescharacteristic
1796C2#585×D5312yes—
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3553C2
hypercenter#3553D53
hypocenterC53#62761
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3553

Complements

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

NH ≅ G/Ntype
1. #20289211C2semidirect
2. #20289209C2semidirect
3. #20289196C2semidirect
4. #20289179C2semidirect
5. #20289171C2semidirect
6. #20289168C2semidirect
7. #20289148C2semidirect
8. #20289125C2semidirect
9. #20289111C2semidirect
10. #20289001C2semidirect
11. #20288993C2semidirect
12. #20288863C2semidirect
13. #20288861C2semidirect
14. #20288859C2semidirect
15. #20288329C2semidirect
16. #20288309C2semidirect
17. #20288294C2semidirect
18. #20288147C2semidirect
19. #20288145C2semidirect
20. #20288101C2semidirect
21. #20288009C2semidirect
22. C2×#16811179C2semidirect
23. C53×#3553C2semidirect
24. C53⋊#564C22semidirect
25. C53⋊#564C22semidirect
27. #16811377C22semidirect
28. #16811377C22semidirect
29. #16811377C22semidirect
30. #16811376C22semidirect
32. #16811375C22semidirect
34. #16811374C22semidirect
35. #16811373C22semidirect
38. #16811371C22semidirect
42. #16811367C22semidirect
43. #16811357C22semidirect
44. #16811357C22semidirect
45. #16811356C22semidirect
46. #16811353C22semidirect
47. #16811351C22semidirect
48. #16811350C22semidirect
49. #16811350C22semidirect
50. #16811350C22semidirect
51. #16811350C22semidirect
53. #16811341C22semidirect
55. #16811340C22semidirect
56. #16811340C22semidirect
57. #16811340C22semidirect
61. #16811328C22semidirect
64. #16811327C22semidirect
65. #16811327C22semidirect
71. #16811312C22semidirect
73. #16811306C22semidirect
75. #16811305C22semidirect
76. #16811291C22semidirect
79. #16811286C22semidirect
80. #16811286C22semidirect
87. #16811271C22semidirect
88. #16811253C22semidirect
89. #16811252C22semidirect
97. #16811241C22semidirect
101. #16811239C22semidirect
106. #16811232C22semidirect
107. #16811232C22semidirect
108. #16811231C22semidirect
109. #16811230C22semidirect
110. #16811230C22semidirect
114. #16811221C22semidirect
120. #16811215C22semidirect
122. #16811214C22semidirect
130. #16811196C22semidirect
132. #16811195C22semidirect
142. #16811179C22semidirect
143. #16811179C22semidirect
144. #16811178C22semidirect
148. #16811175C22semidirect
149. #16811175C22semidirect
150. #16811175C22semidirect
161. #16811158C22semidirect
167. #16811156C22semidirect
168. #16811156C22semidirect
169. #16811154C22semidirect
175. #16811150C22semidirect
176. #16811150C22semidirect
185. #16811091C22semidirect
190. C4×#11719947C22semidirect
192. C2×#13133182C22semidirect
193. C4×Q8×D53C22semidirect
196. C53×#564C22semidirect
197. C53×#563C22semidirect
198. C53×#562C22semidirect
201. C53×#552C22semidirect
202. C53×#541C22semidirect
204. C53×#539C22semidirect
898. #3553D53semidirect
924. #564C2×D53semidirect
936. #563C2×D53semidirect
943. #562C2×D53semidirect
979. #552C2×D53semidirect
1015. #541C2×D53semidirect
1029. #539C2×D53semidirect
1105. C53#62761semidirect

Maximal subgroups

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

subgroupindex
#202892112
#202892092
#202891962
#202891792
#202891712
#202891682
#202891482
#202891252
#202891112
#202890012
#202889932
#202888632
#202888612
#202888592
#202883292
#202883092
#202882942
#202881472
#202881452
#202881012
#202880092
C2×#168111792
C53×#35532
#6276153