Finite Group Databasebeta

← #28293064

Subgroups — #28293064

Order 13568.

6518 conjugacy classes of subgroups.

The subgroup lattice has 1380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289363C214yesmaximal, complemented
2#20289350C214yesmaximal, complemented
3#20289192C214yesmaximal, complemented
4#20289093C214yesmaximal, complemented
5#20288993C218yesmaximal, complemented
6#20288730C214yesmaximal, complemented
7#20288699C218yesmaximal, complemented
8#20288681C214yesmaximal, complemented
9#20288635C211yesmaximal, characteristic, complemented
10#20288624C212yesmaximal, complemented
11#20288617C214yesmaximal, complemented
12#20288593C214yesmaximal, complemented
13#20288541C211yesmaximal, characteristic, complemented
14#20288539C211yesmaximal, characteristic, complemented
15#20288528C212yesmaximal, complemented
16#20288434C212yesmaximal, complemented
17#20288428C212yesmaximal, complemented
18#20288010C211yesmaximal, characteristic, complemented
19#20288008C211yesmaximal, characteristic, complemented
20C2×#16811179C211yesmaximal, characteristic, complemented
21C53×#3512C211yesmaximal, characteristic, complemented
22#16811377C2218yes—
23#16811375C2218yes—
24#16811370C2218yes—
25#16811368C2218yes—
26Q8×Dic106C2214yescomplemented
27#16811350C2214yescomplemented
28#16811350C2218yescomplemented
29#16811349C2214yescomplemented
30#16811349C2214yescomplemented
31#16811346C2214yes—
32#16811344C2214yes—
33#16811344C2214yes—
34#16811344C2214yescomplemented
35#16811343C2218yescomplemented
36#16811341C2214yes—
37#16811340C2218yes—
38#16811340C2218yescomplemented
39#16811340C2218yescomplemented
40#16811338C2214yes—
41#16811337C2214yes—
42#16811337C2214yes—
43#16811337C2214yescomplemented
44#16811336C2214yes—
45#16811332C2218yes—
46#16811332C2218yes—
47#16811332C2214yescomplemented
48#16811332C2214yescomplemented
49#16811331C2214yescomplemented
50#16811329C2214yescomplemented
51#16811328C2218yes—
52#16811325C2214yes—
53#16811325C2214yes—
54#16811323C2214yes—
55#16811321C2214yes—
56#16811319C2214yescomplemented
57#16811316C2218yes—
58#16811316C2218yes—
59#16811315C2214yes—
60#16811315C2214yes—
61#16811314C2214yes—
62#16811313C2214yescomplemented
63#16811312C2218yescomplemented
64#16811310C2218yescomplemented
65#16811310C2218yescomplemented
66#16811308C2214yes—
67#16811306C2218yes—
68D4×Dic106C2218yes—
69D4×Dic106C2214yescomplemented
70#16811282C2218yes—
71#16811279C2218yes—
72#16811279C2218yescomplemented
73#16811273C2214yescomplemented
74#16811271C2218yes—
75#16811254C2212yes—
76#16811254C2214yescomplemented
77#16811253C2214yescomplemented
78#16811251C2212yes—
79#16811251C2214yescomplemented
80#16811251C2214yescomplemented
81#16811246C2214yescomplemented
82#16811244C2218yes—
83#16811241C2218yes—
84#16811241C2218yescomplemented
85#16811241C2218yescomplemented
86#16811240C2218yescomplemented
87#16811240C2214yescomplemented
88#16811239C2218yes—
89#16811236C2218yescomplemented
90#16811234C2212yescomplemented
91#16811232C2218yes—
92#16811230C2218yescomplemented
93#16811230C2218yescomplemented
94#16811227C2212yescomplemented
95#16811215C2218yes—
96#16811214C2218yes—
97#16811210C2218yes—
98#16811206C2218yes—
99#16811201C2212yes—
100#16811200C2218yes—
101#16811195C2218yes—
102#16811180C2211yescharacteristic
103#16811180C2212yescomplemented
104#16811179C2214yes—
105#16811179C2214yes—
106#16811179C2214yes—
107#16811179C2214yes—
108#16811179C2212yescomplemented
109#16811178C2212yes—
110#16811177C2212yes—
111#16811176C2211yescharacteristic
112#16811176C2214yescomplemented
113#16811175C2214yescomplemented
114#16811171C2212yes—
115#16811170C2212yes—
116#16811169C2211yescharacteristic
117#16811168C2214yescomplemented
118C2×#13133216C2212yes—
119C2×#13133216C2214yescomplemented
120#16811160C2212yes—
121#16811155C2212yes—
122#16811155C2214yes—
123#16811154C2214yes—
124#16811154C2218yes—
125#16811153C2214yes—
126#16811153C2218yes—
127#16811152C2212yes—
128#16811152C2212yes—
129#16811152C2214yescomplemented
130#16811151C2214yes—
131C2×#13133209C2211yescharacteristic
132C2×#13133209C2212yescomplemented
133#125×D53C2212yescomplemented
134#16811135C2211yescharacteristic
135#16811133C2214yes—
136#16811132C2214yes—
137#16811130C2211yescharacteristic
138#16811130C2212yes—
139C2×#13133195C2214yes—
140#16811106C2212yes—
141#16811106C2212yes—
142#16811104C2212yes—
143#16811102C2218yescomplemented
144#16811100C2218yescomplemented
145#41×Dic53C2212yes—
146C4×#11719945C2211yescharacteristic
147C4×#11719945C2214yes—
148C4×#11719947C2214yes—
149C2×#13133182C2214yes—
150C2×#13133175C2212yes—
151C2×C42×D53C2211yescharacteristic
152C53×#553C2218yes—
153C53×#553C2214yescomplemented
154C53×#552C2214yescomplemented
155C53×#541C2212yescomplemented
156C53×#540C2212yescomplemented
157C53×#537C2212yes—
158C53×#532C2211yescharacteristic
159C53×#529C2214yescomplemented
160C2×#125×C53C2211yescharacteristic
161C53×#520C2212yes—
162C4×#41×C53C2211yescharacteristic
163C2×#11719945C2311yescharacteristic
164C2×#11719945C2314yes—
165C2×#11719947C2318yes—
166C2×#11719947C2314yes—
167C22×Dic106C2314yes—
168C22×Dic106C2318yes—
169C22×C4×D53C2311yescharacteristic
170C22×C4×D53C2312yes—
171#13133217C2318yes—
172#13133217C2314yes—
173#13133217C2312yes—
174#13133216C2318yes—
175#13133216C2314yes—
176#13133216C2318yes—
177#13133216C2314yes—
178#13133216C2318yes—
179#13133216C2314yes—
180#13133216C2314yes—
181#13133216C2318yes—
182#13133216C2318yes—
183#13133216C2314yes—
184#13133216C2314yes—
185#13133216C2314yes—
186#13133216C2312yes—
187#13133215C2311yescharacteristic
188#13133213C2311yescharacteristic
189#13133212C2318yes—
190#13133212C2318yes—
191#13133212C2318yes—
192#13133212C2318yes—
193#13133212C2318yes—
194#13133212C2318yes—
195#13133212C2314yes—
196#13133211C2318yes—
197#13133210C2314yes—
198#13133210C2318yes—
199#13133210C2318yes—
200#13133210C2318yes—
201#13133210C2318yes—
202#13133210C2318yes—
203#13133210C2314yes—
204#13133210C2314yes—
205#13133209C2318yes—
206#13133209C2318yes—
207#13133209C2314yes—
208#13133209C2314yes—
209#13133209C2311yescharacteristic
210#13133209C2312yes—
211#13133209C2312yes—
212#13133209C2311yescharacteristic
213#13133208C2314yes—
214#13133208C2318yes—
215#13133208C2318yes—
216#13133208C2318yes—
217#13133208C2314yes—
218#13133208C2314yes—
219#13133208C2314yes—
220#13133208C2312yes—
221#13133207C2318yes—
222#13133207C2318yes—
223#13133207C2318yes—
224#13133207C2314yes—
225#13133207C2318yes—
226#13133207C2318yes—
227#13133206C2311yescharacteristic
228#13133205C2318yes—
229#13133204C2318yes—
230#13133204C2318yes—
231#13133204C2314yes—
232#13133204C2311yescharacteristic
233#13133203C2318yes—
234#13133203C2318yes—
235#13133203C2314yes—
236#13133203C2318yes—
237#13133203C2318yes—
238#13133203C2318yes—
239#13133203C2318yes—
240#13133202C2318yes—
241#13133202C2314yes—
242#13133201C2318yes—
243#13133201C2318yes—
244#13133201C2312yes—
245#13133200C2318yes—
246#13133199C2318yes—
247#13133199C2318yes—
248#13133199C2314yes—
249#13133199C2314yes—
250#13133199C2314yes—
251#13133198C2318yes—
252#13133198C2318yes—
253#13133198C2314yes—
254#13133198C2312yes—
255#13133197C2318yes—
256#13133197C2318yes—
257#13133197C2312yes—
258#13133197C2314yes—
259#13133196C2318yes—
260#13133196C2318yes—
261#13133196C2318yes—
262#13133196C2318yes—
263#13133196C2314yes—
264#13133196C2314yes—
265#13133195C2318yes—
266#13133195C2318yes—
267#13133195C2318yes—
268#13133195C2318yes—
269#13133195C2318yes—
270#13133195C2318yes—
271#13133195C2314yes—
272#13133194C2318yes—
273#13133194C2318yes—
274#13133194C2318yes—
275#13133194C2318yes—
276#13133194C2314yes—
277#13133194C2318yes—
278#13133194C2318yes—
279#13133194C2318yes—
280#13133194C2318yes—
281#13133194C2318yes—
282#13133193C2312yes—
283#13133193C2314yes—
284#13133193C2312yes—
285#13133193C2312yes—
286#13133192C2312yes—
287#13133191C2318yes—
288#13133191C2314yes—
289#13133190C2318yes—
290#13133190C2314yes—
291#13133189C2318yes—
292#13133189C2314yes—
293#13133189C2318yes—
294#13133189C2318yes—
295#13133189C2318yes—
296#13133189C2318yes—
297#13133188C2314yes—
298#13133188C2312yes—
299#13133188C2312yes—
300#13133188C2312yes—
301#13133188C2314yes—
302#13133187C2312yes—
303#13133185C2312yes—
304#13133185C2314yes—
305Q8×Dic53C2314yes—
306Q8×Dic53C2314yes—
307Q8×Dic53C2312yes—
308Q8×Dic53C2312yes—
309C4×Dic106C2318yes—
310C4×Dic106C2318yes—
311C4×Dic106C2314yes—
312C4×Dic106C2312yes—
313C4×Dic106C2314yes—
314C4×Dic106C2318yes—
315C4×Dic106C2318yes—
316C4×Dic106C2314yes—
317#13133182C2318yes—
318#13133182C2318yes—
319#13133182C2314yes—
320#13133182C2318yes—
321#13133182C2318yes—
322#13133182C2314yes—
323#13133182C2318yes—
324#13133182C2318yes—
325#13133182C2318yes—
326C4×D212C2314yes—
327C4×D212C2312yes—
328C4×D212C2314yes—
329D4×Dic53C2312yes—
330D4×Dic53C2314yes—
331D4×Dic53C2318yes—
332D4×Dic53C2314yes—
333D4×Dic53C2318yes—
334D4×Dic53C2314yes—
335D4×Dic53C2318yes—
336D4×Dic53C2312yes—
337D4×Dic53C2314yes—
338D4×Dic53C2314yes—
339#13133179C2314yes—
340C4×C22⋊D53C2314yes—
341C4×C22⋊D53C2318yes—
342C4×C22⋊D53C2318yes—
343C4×C22⋊D53C2314yes—
344C4×C22⋊D53C2314yes—
345C4×C22⋊D53C2314yes—
346C4×C22⋊D53C2314yes—
347C4×C22⋊D53C2314yes—
348C4×C22⋊D53C2314yes—
349#13133177C2314yes—
350#13133177C2318yes—
351#13133177C2314yes—
352#13133177C2318yes—
353#13133176C2318yes—
354#13133176C2314yes—
355#13133176C2314yes—
356#13133176C2314yes—
357#13133176C2311yescharacteristic
358#13133176C2312yes—
359#13133176C2314yes—
360#13133175C2314yes—
361#13133175C2314yes—
362#13133175C2314yes—
363#13133175C2314yes—
364#13133175C2314yes—
365#13133175C2314yes—
366#13133174C2314yes—
367#13133174C2314yes—
368#13133174C2318yes—
369#13133174C2312yes—
370#13133173C2318yes—
371#13133173C2318yes—
372#13133173C2318yes—
373#13133173C2318yes—
374#13133173C2314yes—
375#13133173C2314yes—
376C2×C4⋊Dic53C2314yes—
377C2×C4⋊Dic53C2314yes—
378C2×C4⋊Dic53C2312yes—
379C2×#11719919C2318yes—
380C2×#11719919C2318yes—
381C2×#11719919C2314yes—
382C2×#11719919C2314yes—
383C4⋊C4×D53C2318yes—
384C4⋊C4×D53C2314yes—
385C2×#11719921C2314yes—
386C2×C4×Dic53C2312yes—
387C2×C4×Dic53C2311yescharacteristic
388C2×C4×Dic53C2314yes—
389C2×C4×Dic53C2314yes—
390C42×D53C2312yes—
391C42×D53C2312yes—
392C42×D53C2312yes—
393C42×D53C2312yes—
394C42×D53C2312yes—
395C2×#41×C53C2311yescharacteristic
396C2×#41×C53C2312yes—
397C4⋊Q8×C53C2311yescharacteristic
398#127×C53C2311yescharacteristic
399#126×C53C2318yes—
400#126×C53C2318yes—
401#125×C53C2312yes—
402#125×C53C2312yes—
403#125×C53C2314yes—
404#125×C53C2318yes—
405#124×C53C2312yes—
406#123×C53C2318yes—
407#123×C53C2318yes—
408C22⋊Q8×C53C2314yes—
409C22⋊Q8×C53C2314yes—
410#121×C53C2314yes—
411#121×C53C2318yes—
412#121×C53C2318yes—
413#121×C53C2314yes—
414#121×C53C2314yes—
415C4×Q8×C53C2312yes—
416C4×Q8×C53C2314yes—
417C4×D4×C53C2318yes—
418C4×D4×C53C2318yes—
419C4×D4×C53C2314yes—
420C4×D4×C53C2314yes—
421C4×D4×C53C2312yes—
422C4×D4×C53C2314yes—
423#117×C53C2311yescharacteristic
424#117×C53C2312yes—
425#117×C53C2314yes—
426#117×C53C2318yes—
427C2×C4⋊C4×C53C2312yes—
428C2×C4⋊C4×C53C2314yes—
429C2×C4⋊C4×C53C2314yes—
430C2×C42×C53C2311yescharacteristic
431C2×C42×C53C2312yes—
432C23×D53C2411yescharacteristic
433#41×C53—24no—
434#41×C53—28no—
435C2×Q8×C53C2411yescharacteristic
436C2×Q8×C53C2412yes—
437C2×D4×C53C2414yes—
438C2×D4×C53C2412yes—
439C2×D4×C53C2411yescharacteristic
440C2×D4×C53C2412yes—
441C2×D4×C53C2418yes—
442C2×D4×C53C2414yes—
443C22×C4×C53C2412yes—
444C22×C4×C53C2414yes—
445C22×C4×C53C2412yes—
446C22×C4×C53C2414yes—
447C22×C4×C53C2414yes—
448C22×C4×C53C2418yes—
449C22×C4×C53C2411yescharacteristic
450C2×C22⋊D53C2414yes—
451C2×C22⋊D53C2412yes—
452C2×C22⋊D53C2414yes—
453C2×C22⋊D53C2414yes—
454C2×C22⋊D53C2418yes—
455C2×C22⋊D53C2414yes—
456C22×Dic53C2411yescharacteristic
457C22×Dic53C2412yes—
458C22×Dic53C2414yes—
459C22×Dic53C2414yes—
460C22×Dic53C2414yes—
461C22×Dic53C2418yes—
462C22×Dic53C2418yes—
463#11719947—416no—
464#11719947—48no—
465#11719945—24no—
466#11719945—48no—
467C2×D212C2411yescharacteristic
468C2×D212C2414yes—
469C2×C4×D53—24no—
470C2×C4×D53—44no—
471C2×C4×D53C2412yes—
472C2×C4×D53C2412yes—
473C2×C4×D53C2412yes—
474C2×C4×D53C2412yes—
475C2×C4×D53C2412yes—
476C2×C4×D53C2412yes—
477C2×C4×D53C2412yes—
478C2×C4×D53C2414yes—
479C2×C4×D53C2418yes—
480C2×Dic106—416no—
481C2×Dic106—48no—
482C2×Dic106C2411yescharacteristic
483C2×Dic106C2418yes—
484C2×Dic106C2414yes—
485C2×Dic106C2418yes—
486C2×Dic106C2418yes—
487C2×Dic106C2414yes—
488C2×Dic106C2418yes—
489C4⋊C4×C53C2412yes—
490C4⋊C4×C53C2414yes—
491C4⋊C4×C53C2418yes—
492C4⋊C4×C53C2414yes—
493C4⋊C4×C53C2418yes—
494C4⋊C4×C53C2418yes—
495C4⋊C4×C53C2414yes—
496C4⋊C4×C53C2418yes—
497C4⋊C4×C53C2414yes—
498C22⋊C4×C53C2414yes—
499C22⋊C4×C53C2412yes—
500C22⋊C4×C53C2414yes—
501C22⋊C4×C53C2418yes—
502C22⋊C4×C53C2418yes—
503C22⋊C4×C53C2414yes—
504C22⋊C4×C53C2418yes—
505C42×C53C2411yescharacteristic
506C42×C53C2412yes—
507C42×C53C2414yes—
508C42×C53C2411yescharacteristic
509C42×C53C2412yes—
510C42×C53C2418yes—
511C22⋊Dic53C2414yes—
512C22⋊Dic53C2414yes—
513C22⋊Dic53C2418yes—
514C22⋊Dic53C2414yes—
515C22⋊Dic53C2414yes—
516C22⋊Dic53C2412yes—
517C22⋊Dic53C2414yes—
518C22⋊Dic53C2414yes—
519C22⋊Dic53C2414yes—
520C22⋊Dic53C2418yes—
521C22⋊Dic53C2418yes—
522#11719921C2418yes—
523#11719921C2418yes—
524#11719921C2414yes—
525#11719921C2418yes—
526#11719921C2414yes—
527#11719921C2414yes—
528#11719921C2414yes—
529#11719921C2414yes—
530#11719921C2414yes—
531#11719921C2414yes—
532#11719921C2418yes—
533C4⋊Dic53C2412yes—
534C4⋊Dic53C2418yes—
535C4⋊Dic53C2414yes—
536C4⋊Dic53C2414yes—
537C4⋊Dic53C2412yes—
538C4⋊Dic53C2418yes—
539C4⋊Dic53C2418yes—
540C4⋊Dic53C2412yes—
541C4⋊Dic53C2414yes—
542C4⋊Dic53C2414yes—
543C4⋊Dic53C2414yes—
544C4⋊Dic53C2414yes—
545C4⋊Dic53C2414yes—
546C4⋊Dic53C2418yes—
547#11719919C2414yes—
548#11719919C2418yes—
549#11719919C2418yes—
550#11719919C2418yes—
551#11719919C2418yes—
552#11719919C2414yes—
553#11719919C2418yes—
554#11719919C2418yes—
555#11719919C2418yes—
556#11719919C2418yes—
557#11719919C2414yes—
558#11719919C2414yes—
559#11719919C2414yes—
560#11719919C2414yes—
561#11719919C2414yes—
562#11719919C2418yes—
563#11719919C2418yes—
564#11719919C2414yes—
565#11719919C2414yes—
566C4×Dic53C2411yescharacteristic
567C4×Dic53C2412yes—
568C4×Dic53C2412yes—
569C4×Dic53C2411yescharacteristic
570C4×Dic53C2412yes—
571C4×Dic53C2412yes—
572C4×Dic53C2412yes—
573C4×Dic53C2414yes—
574C4×Dic53C2412yes—
575C4×Dic53C2418yes—
576C4×Dic53C2414yes—
577C4×Dic53C2414yes—
578C4×Dic53C2418yes—
579C4×Dic53C2414yes—
580C4×Dic53C2418yes—
581C4×Dic53C2418yes—
582C4×Dic53C2418yes—
583C23×C53C2514yes—
584C23×C53C2512yes—
585C23×C53C2511yescharacteristic
586C22×D53—22no—
587C22×D53—42no—
588C22×D53C2512yes—
589C22×D53C2512yes—
590Q8×C53—22no—
591Q8×C53—24no—
592D4×C53—28no—
593D4×C53—24no—
594D4×C53—22no—
595D4×C53—24no—
596D4×C53—48no—
597D4×C53—44no—
598C2×C4×C53—28no—
599C2×C4×C53—24no—
600C2×C4×C53—44no—
601C2×C4×C53—48no—
602C2×C4×C53—42no—
603C2×C4×C53—44no—
604C2×C4×C532−1+414yes—
605C2×C4×C53C2518yes—
606C2×C4×C53C2514yes—
607C2×C4×C53C2512yes—
608C2×C4×C53C2512yes—
609C2×C4×C53C2512yes—
610C2×C4×C53C2514yes—
611C2×C4×C53C2511yescharacteristic
612C2×C4×C53C2511yescharacteristic
613C22⋊D53—24no—
614C22⋊D53—28no—
615C22⋊D53—44no—
616C22⋊D53—48no—
617C22⋊D53—44no—
618C22⋊D53—44no—
619C2×Dic53—22no—
620C2×Dic53—24no—
621C2×Dic53—28no—
622C2×Dic53—28no—
623C2×Dic53—48no—
624C2×Dic53—44no—
625C2×Dic53—48no—
626C2×Dic53C2514yes—
627C2×Dic53C2512yes—
628C2×Dic53C2514yes—
629C2×Dic53C2518yes—
630C2×Dic53C2514yes—
631C2×Dic53C2512yes—
632C2×Dic53C2512yes—
633C2×Dic53C2512yes—
634D212—22no—
635D212—44no—
636C4×D53—24no—
637C4×D53—24no—
638C4×D53—24no—
639C4×D53—24no—
640C4×D53—24no—
641C4×D53—42no—
642C4×D53—42no—
643C4×D53—44no—
644C4×D53—48no—
645Dic106—22no—
646Dic106—28no—
647Dic106—216no—
648Dic106—48no—
649Dic106—48no—
650Dic106—48no—
651Dic106—44no—
652#62838—531nomaximal, Sylow
653C22×C53—22no—
654C22×C53—24no—
655C22×C53—22no—
656C22×C53—24no—
657C22×C53—24no—
658C22×C53—24no—
659C22×C53C2×2−1+412yes—
660C22×C53C2611yescharacteristic
661C2×D53—22no—
662C2×D53—22no—
663C2×D53—22no—
664C2×D53—22no—
665C2×D53—24no—
666C2×D53—44no—
667C4×C53—24no—
668C4×C53—22no—
669C4×C53—28no—
670C4×C53—24no—
671C4×C53—22no—
672C4×C53—22no—
673C4×C53C2×2−1+412yes—
674C4×C53C2×2−1+412yes—
675Dic53—22no—
676Dic53—22no—
677Dic53—24no—
678Dic53—28no—
679Dic53—24no—
680Dic53—22no—
681Dic53—24no—
682Dic53#58514yes—
683#3565—534no—
684#3565—534no—
685#3555—534no—
686#3547—534no—
687#3541—538no—
688#3518—534no—
689#3516—538no—
690#3515—534no—
691#3512—531no—
692#3512D5311yescharacteristic, complemented
693#3511—534no—
694#3511—532no—
695#3509—534no—
696#3504—531no—
697#3504—531no—
698#3503—532no—
699#3493—532no—
700#3493—532no—
701#3444—531no—
702#3444—531no—
703C2×#533—531no—
704C2×C53—22no—
705C2×C53—44no—
706C2×C53—42no—
707C2×C53C22×2−1+411yescharacteristic
708C2×C53C2×#58512yes—
709D53—42no—
710D53—42no—
711#563—538no—
712#563—538no—
713#562—538no—
714#562—538no—
715Q82—534no—
716#557—534no—
717#557—538no—
718#557—534no—
719#557—534no—
720#556—538no—
721#556—538no—
722#556—538no—
723#556—534no—
724#556—534no—
725#556—534no—
726#556—534no—
727#556—538no—
728#556—534no—
729#555—534no—
730#555—534no—
731#555—534no—
732#555—534no—
733#555—534no—
734#554—534no—
735#554—534no—
736#554—538no—
737#554—538no—
738#554—534no—
739#554—534no—
740#554—538no—
741#553—538no—
742#553—538no—
743#553—534no—
744#553—534no—
745#553—534no—
746#553—534no—
747#553—534no—
748#553C2×D5318yes—
749#553C2×D5314yescomplemented
750#552—538no—
751#552—538no—
752#552—534no—
753#552—534no—
754#552—534no—
755#552—534no—
756#552—538no—
757#552—538no—
758#552—534no—
759#552C2×D5314yescomplemented
760D4×Q8—538no—
761D4×Q8—534no—
762#548—538no—
763#548—538no—
764#548—538no—
765#547—538no—
766#547—534no—
767#544—534no—
768#544—532no—
769#544—534no—
770#544—534no—
771#544—532no—
772#544—534no—
773#542—538no—
774#542—538no—
775#542—538no—
776#542—538no—
777#542—534no—
778#542—534no—
779#542—538no—
780#542—538no—
781#541—532no—
782#541—538no—
783#541—538no—
784#541—538no—
785#541—538no—
786#541C2×D5312yescomplemented
787#540—532no—
788#540C2×D5312yescomplemented
789#539—538no—
790#539—538no—
791#538—538no—
792#538—538no—
793#537—532no—
794#537—538no—
795#537C2×D5312yes—
796#536—538no—
797#533—532no—
798#533—534no—
799#533—534no—
800#533—534no—
801#533—534no—
802#533—532no—
803#533—534no—
804#533—532no—
805#533—531no—
806#533—534no—
807#533—531no—
808#533—532no—
809#532—531no—
810#532—532no—
811#532—534no—
812#532—532no—
813#532C2×D5311yescharacteristic
814C2×C4⋊Q8—532no—
815C2×C4⋊Q8—534no—
816#529—532no—
817#529—532no—
818#529—534no—
819#529—534no—
820#529—538no—
821#529—532no—
822#529—534no—
823#529—534no—
824#529—532no—
825#529—538no—
826#529—534no—
827#529C2×D5314yescomplemented
828C2×#125—532no—
829C2×#125—531no—
830C2×#125—532no—
831C2×#125C2×D5311yescharacteristic
832#525—532no—
833#525—531no—
834#525—534no—
835#525—534no—
836#525—531no—
837C2×C22⋊Q8—534no—
838#520—532no—
839#520—532no—
840#520—538no—
841#520—532no—
842#520C2×D5312yes—
843#519—538no—
844C4×#41—532no—
845C4×#41—534no—
846C4×#41—531no—
847C4×#41—534no—
848C4×#41C2×D5311yescharacteristic
849C2×C4×Q8—534no—
850C2×#117—532no—
851C22×C42—531no—
852C53#6283811yescharacteristic, complemented, Sylow
853C2×#41—534no—
854C2×#41—538no—
855C2×#41—531no—
856C2×#41—534no—
857C2×#41C22×D5312yes—
858C2×#41C22×D5311yescharacteristic
859C22×Q8—534no—
860C22×Q8—538no—
861C23×C4—531no—
862C23×C4—532no—
863C4⋊Q8—531no—
864C4⋊Q8—534no—
865C4⋊Q8—532no—
866C4⋊Q8—534no—
867C4⋊Q8—534no—
868C4⋊Q8—534no—
869C4⋊Q8—538no—
870C4⋊Q8—538no—
871C4⋊Q8—534no—
872C4⋊Q8—534no—
873C4⋊Q8—534no—
874C4⋊Q8—538no—
875C4⋊Q8—538no—
876C4⋊Q8—538no—
877C4⋊Q8—532no—
878C4⋊Q8—534no—
879C4⋊Q8—538no—
880C4⋊Q8C22×D5311yescharacteristic
881#127—531no—
882#127C22×D5311yescharacteristic
883#126—534no—
884#126—538no—
885#126—538no—
886#126—538no—
887#126—538no—
888#126—538no—
889#126—538no—
890#126—534no—
891#126—534no—
892#126—534no—
893#126—538no—
894#126—538no—
895#126—538no—
896#126—538no—
897#126—538no—
898#126—538no—
899#126C22×D5318yes—
900#126C22×D5318yes—
901#125—538no—
902#125—534no—
903#125—534no—
904#125—532no—
905#125—534no—
906#125—538no—
907#125—538no—
908#125—538no—
909#125—534no—
910#125—534no—
911#125—538no—
912#125—538no—
913#125—538no—
914#125—538no—
915#125—531no—
916#125—532no—
917#125—532no—
918#125—534no—
919#125—538no—
920#125—534no—
921#125—531no—
922#125—538no—
923#125C22×D5312yes—
924#125C22×D5312yes—
925#125C22×D5314yes—
926#125C22×D5318yes—
927#124—531no—
928#124—531no—
929#124—534no—
930#124—538no—
931#124—538no—
932#124—534no—
933#124—538no—
934#124—538no—
935#124—538no—
936#124—538no—
937#124—538no—
938#124—538no—
939#124—538no—
940#124C22×D5312yes—
941#123—534no—
942#123—532no—
943#123—538no—
944#123—538no—
945#123—538no—
946#123—534no—
947#123—538no—
948#123—532no—
949#123—534no—
950#123—534no—
951#123—534no—
952#123—538no—
953#123—538no—
954#123—538no—
955#123—538no—
956#123C22×D5318yes—
957#123C22×D5318yes—
958C22⋊Q8—532no—
959C22⋊Q8—532no—
960C22⋊Q8—532no—
961C22⋊Q8—534no—
962C22⋊Q8—534no—
963C22⋊Q8—538no—
964C22⋊Q8—534no—
965C22⋊Q8—538no—
966C22⋊Q8—538no—
967C22⋊Q8—538no—
968C22⋊Q8—538no—
969C22⋊Q8—538no—
970C22⋊Q8—538no—
971C22⋊Q8—538no—
972C22⋊Q8—534no—
973C22⋊Q8—532no—
974C22⋊Q8—534no—
975C22⋊Q8—538no—
976C22⋊Q8—538no—
977C22⋊Q8—538no—
978C22⋊Q8—538no—
979C22⋊Q8—534no—
980C22⋊Q8—538no—
981C22⋊Q8—538no—
982C22⋊Q8—538no—
983C22⋊Q8—538no—
984C22⋊Q8—538no—
985C22⋊Q8—538no—
986C22⋊Q8—538no—
987C22⋊Q8—538no—
988C22⋊Q8—538no—
989C22⋊Q8C22×D5314yes—
990C22⋊Q8C22×D5314yes—
991#121—534no—
992#121—532no—
993#121—532no—
994#121—532no—
995#121—534no—
996#121—538no—
997#121—534no—
998#121—538no—
999#121—538no—
1000#121—538no—
1001#121—538no—
1002#121—534no—
1003#121—538no—
1004#121—532no—
1005#121—534no—
1006#121—538no—
1007#121C22×D5314yes—
1008#121C22×D5318yes—
1009#121C22×D5314yes—
1010#121C22×D5314yes—
1011#121C22×D5318yes—
1012#120—534no—
1013#120—532no—
1014#120—532no—
1015C4×Q8—532no—
1016C4×Q8—532no—
1017C4×Q8—534no—
1018C4×Q8—534no—
1019C4×Q8—538no—
1020C4×Q8—538no—
1021C4×Q8—538no—
1022C4×Q8—538no—
1023C4×Q8—534no—
1024C4×Q8—538no—
1025C4×Q8—538no—
1026C4×Q8—538no—
1027C4×Q8—534no—
1028C4×Q8—534no—
1029C4×Q8—534no—
1030C4×Q8—532no—
1031C4×Q8—534no—
1032C4×Q8—538no—
1033C4×Q8—538no—
1034C4×Q8—538no—
1035C4×Q8—538no—
1036C4×Q8C22×D5312yes—
1037C4×Q8C22×D5314yes—
1038C4×D4—534no—
1039C4×D4—534no—
1040C4×D4—532no—
1041C4×D4—534no—
1042C4×D4—532no—
1043C4×D4—538no—
1044C4×D4—538no—
1045C4×D4—534no—
1046C4×D4—538no—
1047C4×D4—534no—
1048C4×D4—534no—
1049C4×D4—534no—
1050C4×D4—534no—
1051C4×D4—534no—
1052C4×D4—534no—
1053C4×D4—534no—
1054C4×D4—534no—
1055C4×D4—538no—
1056C4×D4—538no—
1057C4×D4—534no—
1058C4×D4—534no—
1059C4×D4—534no—
1060C4×D4—538no—
1061C4×D4—538no—
1062C4×D4—534no—
1063C4×D4—534no—
1064C4×D4—532no—
1065C4×D4C22×D5314yes—
1066C4×D4C22×D5314yes—
1067C4×D4C22×D5312yes—
1068C4×D4C22×D5318yes—
1069C4×D4C22×D5318yes—
1070C4×D4C22×D5314yes—
1071#117—532no—
1072#117—531no—
1073#117—534no—
1074#117—534no—
1075#117—538no—
1076#117—534no—
1077#117—534no—
1078#117—534no—
1079#117—534no—
1080#117—534no—
1081#117—534no—
1082#117—534no—
1083#117—534no—
1084#117—534no—
1085#117—534no—
1086#117—538no—
1087#117—538no—
1088#117—538no—
1089#117—538no—
1090#117—534no—
1091#117—532no—
1092#117—534no—
1093#117—538no—
1094#117C22×D5311yescharacteristic
1095#117C22×D5312yes—
1096#117C22×D5318yes—
1097#117C22×D5314yes—
1098C2×C4⋊C4—532no—
1099C2×C4⋊C4—534no—
1100C2×C4⋊C4—534no—
1101C2×C4⋊C4—538no—
1102C2×C4⋊C4—534no—
1103C2×C4⋊C4—538no—
1104C2×C4⋊C4—534no—
1105C2×C4⋊C4—538no—
1106C2×C4⋊C4—534no—
1107C2×C4⋊C4C22×D5312yes—
1108C2×C4⋊C4C22×D5314yes—
1109C2×C4⋊C4C22×D5314yes—
1110C2×C22⋊C4—534no—
1111C2×C42—534no—
1112C2×C42—532no—
1113C2×C42—534no—
1114C2×C42—531no—
1115C2×C42—532no—
1116C2×C42—532no—
1117C2×C42—532no—
1118C2×C42—532no—
1119C2×C42—532no—
1120C2×C42C22×D5312yes—
1121C2×C42C22×D5311yescharacteristic
1122C24—531no—
1123#41—28no—
1124#41—24no—
1125#41—1064no—
1126#41—2128no—
1127#41—2128no—
1128#41—21216no—
1129C2×Q8—531no—
1130C2×Q8—538no—
1131C2×Q8—534no—
1132C2×Q8—538no—
1133C2×Q8—534no—
1134C2×Q8—538no—
1135C2×Q8—538no—
1136C2×Q8—2128no—
1137C2×Q8—21216no—
1138C2×Q8C23×D5312yes—
1139C2×Q8C23×D5311yescharacteristic
1140C2×D4—532no—
1141C2×D4—534no—
1142C2×D4—534no—
1143C2×D4—534no—
1144C2×D4—534no—
1145C2×D4—538no—
1146C2×D4—531no—
1147C2×D4—534no—
1148C2×D4C23×D5314yes—
1149C2×D4C23×D5312yes—
1150C2×D4C23×D5312yes—
1151C2×D4C23×D5311yescharacteristic
1152C2×D4C23×D5318yes—
1153C2×D4C23×D5314yes—
1154C22×C4—531no—
1155C22×C4—532no—
1156C22×C4—534no—
1157C22×C4—534no—
1158C22×C4—534no—
1159C22×C4—538no—
1160C22×C4—538no—
1161C22×C4—532no—
1162C22×C4—532no—
1163C22×C4—532no—
1164C22×C4—532no—
1165C22×C4—532no—
1166C22×C4—532no—
1167C22×C4—532no—
1168C22×C4—534no—
1169C22×C4—538no—
1170C22×C4—1064no—
1171C22×C4—2124no—
1172C22×C4C23×D5314yes—
1173C22×C4C23×D5312yes—
1174C22×C4C23×D5312yes—
1175C22×C4C23×D5314yes—
1176C22×C4C23×D5314yes—
1177C22×C4C23×D5318yes—
1178C22×C4C23×D5311yescharacteristic
1179C4⋊C4—532no—
1180C4⋊C4—534no—
1181C4⋊C4—534no—
1182C4⋊C4—532no—
1183C4⋊C4—534no—
1184C4⋊C4—538no—
1185C4⋊C4—534no—
1186C4⋊C4—538no—
1187C4⋊C4—538no—
1188C4⋊C4—538no—
1189C4⋊C4—538no—
1190C4⋊C4—538no—
1191C4⋊C4—538no—
1192C4⋊C4—538no—
1193C4⋊C4—538no—
1194C4⋊C4—538no—
1195C4⋊C4—538no—
1196C4⋊C4—532no—
1197C4⋊C4—534no—
1198C4⋊C4—534no—
1199C4⋊C4—534no—
1200C4⋊C4—534no—
1201C4⋊C4—534no—
1202C4⋊C4—534no—
1203C4⋊C4—534no—
1204C4⋊C4—534no—
1205C4⋊C4—534no—
1206C4⋊C4—534no—
1207C4⋊C4—534no—
1208C4⋊C4—534no—
1209C4⋊C4—538no—
1210C4⋊C4—538no—
1211C4⋊C4—538no—
1212C4⋊C4C23×D5314yes—
1213C4⋊C4C23×D5318yes—
1214C4⋊C4C23×D5314yes—
1215C4⋊C4C23×D5312yes—
1216C4⋊C4C23×D5318yes—
1217C4⋊C4C23×D5318yes—
1218C4⋊C4C23×D5314yes—
1219C4⋊C4C23×D5314yes—
1220C4⋊C4C23×D5318yes—
1221C22⋊C4—534no—
1222C22⋊C4—534no—
1223C22⋊C4—538no—
1224C22⋊C4—534no—
1225C22⋊C4—532no—
1226C22⋊C4—534no—
1227C22⋊C4—538no—
1228C22⋊C4—538no—
1229C22⋊C4—534no—
1230C22⋊C4—534no—
1231C22⋊C4—534no—
1232C22⋊C4—538no—
1233C22⋊C4—538no—
1234C22⋊C4—534no—
1235C22⋊C4—534no—
1236C22⋊C4—534no—
1237C22⋊C4—534no—
1238C22⋊C4—534no—
1239C22⋊C4—534no—
1240C22⋊C4—538no—
1241C22⋊C4—538no—
1242C22⋊C4—534no—
1243C22⋊C4C23×D5314yes—
1244C22⋊C4C23×D5318yes—
1245C22⋊C4C23×D5314yes—
1246C22⋊C4C23×D5318yes—
1247C22⋊C4C23×D5312yes—
1248C22⋊C4C23×D5314yes—
1249C22⋊C4C23×D5318yes—
1250C42—531no—
1251C42—532no—
1252C42—532no—
1253C42—531no—
1254C42—532no—
1255C42—532no—
1256C42—532no—
1257C42—534no—
1258C42—538no—
1259C42—538no—
1260C42—534no—
1261C42—534no—
1262C42—532no—
1263C42—534no—
1264C42—538no—
1265C42—538no—
1266C42—538no—
1267C42C23×D5311yescharacteristic
1268C42C23×D5311yescharacteristic
1269C42C23×D5312yes—
1270C42C23×D5314yes—
1271C42C23×D5312yes—
1272C42C23×D5318yes—
1273C23—532no—
1274C23—532no—
1275C23—1062no—
1276C23—2122no—
1277C23C24×D5314yes—
1278C23C24×D5312yes—
1279C23C24×D5311yescharacteristic
1280Q8—22no—
1281Q8—24no—
1282Q8—1068no—
1283Q8—10616no—
1284Q8—1062no—
1285Q8—2128no—
1286Q8—2128no—
1287Q8—2128no—
1288Q8—2124no—
1289D4—28no—
1290D4—24no—
1291D4—22no—
1292D4—24no—
1293D4—48no—
1294D4—44no—
1295D4—1068no—
1296D4—1064no—
1297D4—1062no—
1298D4—2124no—
1299D4—2124no—
1300D4—2124no—
1301D4—2124no—
1302D4—2128no—
1303C2×C4—28no—
1304C2×C4—24no—
1305C2×C4—42no—
1306C2×C4—48no—
1307C2×C4—44no—
1308C2×C4—44no—
1309C2×C4—532no—
1310C2×C4—532no—
1311C2×C4—532no—
1312C2×C4—534no—
1313C2×C4—532no—
1314C2×C4—534no—
1315C2×C4—538no—
1316C2×C4—534no—
1317C2×C4—1064no—
1318C2×C4—1064no—
1319C2×C4—1064no—
1320C2×C4—1068no—
1321C2×C4—1068no—
1322C2×C4—1062no—
1323C2×C4—1064no—
1324C2×C4—1064no—
1325C2×C4—1064no—
1326C2×C4—2122no—
1327C2×C4—2122no—
1328C2×C4—2124no—
1329C2×C4—2128no—
1330C2×C4—2124no—
1331C2×C4—2128no—
1332C2×C4—2128no—
1333C2×C4#1313326414yes—
1334C2×C4C24×D5312yes—
1335C2×C4C24×D5314yes—
1336C2×C4C24×D5312yes—
1337C2×C4C24×D5318yes—
1338C2×C4C24×D5312yes—
1339C2×C4C24×D5314yes—
1340C2×C4C24×D5311yescharacteristic
1341C2×C4C24×D5311yescharacteristic
1342C22—22no—
1343C22—24no—
1344C22—22no—
1345C22—24no—
1346C22—24no—
1347C22—24no—
1348C22—1062no—
1349C22—1062no—
1350C22—1062no—
1351C22—1062no—
1352C22—1064no—
1353C22—2124no—
1354C22C2×#1313326412yes—
1355C22C25×D5311yescharacteristic
1356C4—24no—
1357C4—22no—
1358C4—22no—
1359C4—24no—
1360C4—28no—
1361C4—22no—
1362C4—534no—
1363C4—1062no—
1364C4—1062no—
1365C4—1064no—
1366C4—1062no—
1367C4—1064no—
1368C4—1064no—
1369C4—1068no—
1370C4C2×#1313326412yes—
1371C4C2×#1313326412yes—
1372C2—22no—
1373C2—44no—
1374C2—42no—
1375C2—2122no—
1376C2—2122no—
1377C2C22×#1313326411yescharacteristic
1378C2#585×D5312yes—
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3512C2
hypercenter#3512D53
hypocenterC53#62838
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3512

Complements

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

NH ≅ G/Ntype
1. #20289363C2semidirect
2. #20289350C2semidirect
3. #20289192C2semidirect
4. #20289093C2semidirect
5. #20288993C2semidirect
6. #20288730C2semidirect
7. #20288699C2semidirect
8. #20288681C2semidirect
9. #20288635C2semidirect
10. #20288624C2semidirect
11. #20288617C2semidirect
12. #20288593C2semidirect
13. #20288541C2semidirect
14. #20288539C2semidirect
15. #20288528C2semidirect
16. #20288434C2semidirect
17. #20288428C2semidirect
18. #20288010C2semidirect
19. #20288008C2semidirect
20. C2×#16811179C2semidirect
21. C53×#3512C2semidirect
26. Q8×Dic106C22semidirect
27. #16811350C22semidirect
28. #16811350C22semidirect
29. #16811349C22semidirect
30. #16811349C22semidirect
34. #16811344C22semidirect
35. #16811343C22semidirect
38. #16811340C22semidirect
39. #16811340C22semidirect
43. #16811337C22semidirect
47. #16811332C22semidirect
48. #16811332C22semidirect
49. #16811331C22semidirect
50. #16811329C22semidirect
56. #16811319C22semidirect
62. #16811313C22semidirect
63. #16811312C22semidirect
64. #16811310C22semidirect
65. #16811310C22semidirect
69. D4×Dic106C22semidirect
72. #16811279C22semidirect
73. #16811273C22semidirect
76. #16811254C22semidirect
77. #16811253C22semidirect
79. #16811251C22semidirect
80. #16811251C22semidirect
81. #16811246C22semidirect
84. #16811241C22semidirect
85. #16811241C22semidirect
86. #16811240C22semidirect
87. #16811240C22semidirect
89. #16811236C22semidirect
90. #16811234C22semidirect
92. #16811230C22semidirect
93. #16811230C22semidirect
94. #16811227C22semidirect
103. #16811180C22semidirect
108. #16811179C22semidirect
112. #16811176C22semidirect
113. #16811175C22semidirect
117. #16811168C22semidirect
119. C2×#13133216C22semidirect
129. #16811152C22semidirect
132. C2×#13133209C22semidirect
133. #125×D53C22semidirect
143. #16811102C22semidirect
144. #16811100C22semidirect
153. C53×#553C22semidirect
154. C53×#552C22semidirect
155. C53×#541C22semidirect
156. C53×#540C22semidirect
159. C53×#529C22semidirect
692. #3512D53semidirect
749. #553C2×D53semidirect
759. #552C2×D53semidirect
786. #541C2×D53semidirect
788. #540C2×D53semidirect
827. #529C2×D53semidirect
852. C53#62838semidirect

Maximal subgroups

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

subgroupindex
#202893632
#202893502
#202891922
#202890932
#202889932
#202887302
#202886992
#202886812
#202886352
#202886242
#202886172
#202885932
#202885412
#202885392
#202885282
#202884342
#202884282
#202880102
#202880082
C2×#168111792
C53×#35122
#6283853