Finite Group Databasebeta

← #28292979

Subgroups — #28292979

Order 13568.

7050 conjugacy classes of subgroups.

The subgroup lattice has 1426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289154C214yesmaximal, complemented
2#20289150C214yesmaximal, complemented
3#20289148C218yesmaximal, complemented
4#20289057C214yesmaximal, complemented
5#20289051C214yesmaximal, complemented
6#20288624C212yesmaximal, complemented
7#20288618C212yesmaximal, complemented
8#20288617C214yesmaximal, complemented
9#20288593C214yesmaximal, complemented
10#20288530C212yesmaximal, complemented
11#20288529C214yesmaximal, complemented
12#20288528C212yesmaximal, complemented
13#20288494C214yesmaximal, complemented
14#20288424C211yesmaximal, characteristic, complemented
15#20288421C212yesmaximal, complemented
16#20288416C214yesmaximal, complemented
17#20288362C214yesmaximal, complemented
18#20288007C212yesmaximal, complemented
19C22×#13133216C211yesmaximal, characteristic, complemented
20C53×#3492C211yesmaximal, characteristic, complemented
21C2×#13133264C2214yes—
22C23×Dic106C2212yes—
23#16811377C2218yescomplemented
24#16811376C2218yescomplemented
25#16811375C2218yescomplemented
26#16811374C2218yescomplemented
27Q8×Dic106C2214yescomplemented
28#16811353C2214yescomplemented
29#16811350C2218yescomplemented
30#16811350C2214yescomplemented
31#16811349C2214yescomplemented
32#16811344C2214yescomplemented
33#16811341C2214yescomplemented
34#16811340C2218yescomplemented
35#16811337C2214yescomplemented
36#16811336C2214yescomplemented
37#16811332C2218yes—
38#16811332C2214yescomplemented
39#16811331C2214yes—
40#16811331C2214yescomplemented
41#16811330C2214yes—
42#16811329C2214yescomplemented
43#16811328C2214yes—
44#16811328C2214yescomplemented
45#16811327C2218yes—
46#16811325C2214yes—
47#16811322C2218yes—
48#16811321C2214yes—
49#16811319C2214yes—
50#16811316C2218yes—
51#16811315C2214yes—
52#16811313C2214yes—
53#16811310C2218yes—
54#16811308C2214yes—
55#16811306C2218yes—
56D4×Dic106C2218yes—
57D4×Dic106C2218yes—
58D4×Dic106C2214yescomplemented
59#16811288C2214yescomplemented
60#16811286C2218yes—
61#16811286C2218yes—
62#16811286C2218yescomplemented
63#16811282C2218yes—
64#16811282C2218yes—
65#16811279C2218yes—
66#16811279C2218yes—
67#16811277C2214yes—
68#16811274C2214yes—
69#16811274C2214yescomplemented
70#16811273C2214yes—
71#16811273C2214yescomplemented
72#16811272C2218yes—
73#16811271C2218yes—
74#16811271C2218yescomplemented
75#16811254C2211yescharacteristic
76#16811254C2214yescomplemented
77#16811253C2218yescomplemented
78#16811253C2214yescomplemented
79#16811252C2214yes—
80#16811252C2218yescomplemented
81#16811251C2212yes—
82#16811251C2214yescomplemented
83#16811250C2214yescomplemented
84#16811246C2214yescomplemented
85#16811245C2214yescomplemented
86#16811241C2218yescomplemented
87#16811240C2214yescomplemented
88#16811239C2218yescomplemented
89#16811238C2214yescomplemented
90#16811232C2218yescomplemented
91#16811230C2218yescomplemented
92#16811222C2214yes—
93#16811220C2214yes—
94#16811218C2214yes—
95#16811217C2218yes—
96#16811215C2218yes—
97#16811204C2211yescharacteristic
98#16811201C2212yes—
99#16811200C2214yes—
100#16811199C2214yes—
101#16811196C2218yescomplemented
102#16811195C2218yes—
103#16811195C2218yes—
104#16811195C2218yescomplemented
105#16811194C2214yes—
106#16811179C2214yescomplemented
107#16811177C2214yescomplemented
108#16811176C2212yes—
109#16811176C2214yescomplemented
110#16811175C2212yes—
111#16811175C2212yes—
112#16811175C2214yescomplemented
113#16811170C2214yescomplemented
114#16811169C2212yes—
115#16811168C2212yes—
116#16811168C2212yes—
117#16811168C2214yescomplemented
118C2×#13133216C2212yes—
119C2×#13133216C2214yes—
120C2×#13133216C2212yes—
121C2×#13133216C2214yes—
122C2×#13133216C2214yes—
123C2×#13133216C2214yes—
124C2×#13133216C2214yes—
125C2×#13133216C2214yescomplemented
126C4⋊Q8×D53C2214yescomplemented
127#16811159C2212yes—
128#16811159C2212yes—
129#16811154C2212yes—
130#16811154C2212yes—
131#16811153C2214yes—
132#16811153C2214yes—
133#16811150C2214yes—
134#16811150C2214yes—
135#16811134C2212yes—
136#16811134C2214yes—
137#16811129C2214yes—
138#16811129C2214yes—
139#16811129C2218yes—
140#16811106C2212yes—
141#16811104C2212yes—
142#16811103C2212yes—
143#16811102C2218yes—
144#16811100C2214yes—
145#41×Dic53C2212yes—
146#16811091C2212yes—
147C4×#11719947C2214yes—
148C4×#11719947C2214yes—
149C22×C4⋊Dic53C2211yescharacteristic
150C22×#11719919C2212yes—
151C22×C4×Dic53C2211yescharacteristic
152C53×#554C2214yes—
153C53×#553C2214yes—
154C53×#552C2214yes—
155C53×#547C2214yes—
156C53×#544C2211yescharacteristic
157C53×#539C2214yes—
158C53×#537C2211yescharacteristic
159C53×#525C2212yes—
160C53×#525C2214yes—
161C53×#520C2212yes—
162C22×C4⋊C4×C53C2211yescharacteristic
163#13133264—416no—
164C2×#11719945C2312yes—
165C2×#11719945C2314yes—
166C2×#11719945C2318yes—
167C2×#11719947C2314yes—
168C2×#11719947C2314yes—
169C2×#11719947C2318yes—
170C2×#11719947C2318yes—
171C22×Dic106—48no—
172C22×Dic106C2314yes—
173C22×Dic106C2314yes—
174C22×Dic106C2318yes—
175C22×Dic106C2314yes—
176C22×Dic106C2318yes—
177C22×Dic106C2314yes—
178C2×Q8×D53C2318yes—
179C23×Dic53C2311yescharacteristic
180C23×Dic53C2311yescharacteristic
181C23×Dic53C2312yes—
182#13133217C2314yes—
183#13133217C2318yes—
184#13133216C2318yes—
185#13133216C2318yes—
186#13133216C2314yes—
187#13133216C2314yes—
188#13133216C2314yes—
189#13133216C2314yes—
190#13133216C2318yes—
191#13133216C2318yes—
192#13133216C2318yes—
193#13133216C2318yes—
194#13133216C2314yes—
195#13133216C2314yes—
196#13133216C2318yes—
197#13133216C2312yes—
198#13133216C2314yes—
199#13133216C2314yes—
200#13133216C2318yes—
201#13133216C2314yes—
202#13133216C2318yes—
203#13133216C2314yes—
204#13133216C2312yes—
205#13133215C2318yes—
206#13133215C2318yes—
207#13133215C2312yes—
208#13133213C2312yes—
209#13133212C2318yes—
210#13133212C2318yes—
211#13133212C2318yes—
212#13133212C2314yes—
213#13133212C2314yes—
214#13133211C2318yes—
215#13133210C2318yes—
216#13133210C2318yes—
217#13133210C2318yes—
218#13133210C2314yes—
219#13133210C2314yes—
220#13133209C2318yes—
221#13133209C2314yes—
222#13133208C2314yes—
223#13133208C2318yes—
224#13133208C2314yes—
225#13133208C2318yes—
226#13133208C2312yes—
227#13133208C2312yes—
228#13133207C2318yes—
229#13133207C2318yes—
230#13133207C2318yes—
231#13133207C2318yes—
232#13133207C2318yes—
233#13133207C2318yes—
234#13133207C2314yes—
235#13133207C2314yes—
236#13133206C2312yes—
237#13133205C2318yes—
238#13133204C2318yes—
239#13133204C2312yes—
240#13133203C2318yes—
241#13133203C2318yes—
242#13133203C2318yes—
243#13133203C2318yes—
244#13133203C2314yes—
245#13133203C2314yes—
246#13133202C2318yes—
247#13133202C2318yes—
248#13133201C2318yes—
249#13133201C2318yes—
250#13133201C2314yes—
251#13133201C2314yes—
252#13133200C2318yes—
253#13133200C2318yes—
254#13133200C2314yes—
255#13133199C2318yes—
256#13133199C2318yes—
257#13133198C2318yes—
258#13133198C2318yes—
259#13133198C2314yes—
260#13133198C2314yes—
261#13133197C2318yes—
262#13133197C2318yes—
263#13133197C2318yes—
264#13133197C2314yes—
265#13133196C2318yes—
266#13133196C2318yes—
267#13133196C2318yes—
268#13133196C2314yes—
269#13133196C2314yes—
270#13133196C2312yes—
271#13133196C2314yes—
272#13133196C2312yes—
273#13133195C2318yes—
274#13133195C2318yes—
275#13133195C2318yes—
276#13133195C2318yes—
277#13133195C2318yes—
278#13133195C2318yes—
279#13133195C2318yes—
280#13133194C2318yes—
281#13133194C2318yes—
282#13133194C2318yes—
283#13133194C2318yes—
284#13133194C2318yes—
285#13133194C2318yes—
286#13133194C2314yes—
287#13133194C2314yes—
288#13133194C2318yes—
289#13133194C2318yes—
290#13133194C2314yes—
291#13133194C2318yes—
292#13133194C2314yes—
293#13133193C2318yes—
294#13133193C2314yes—
295#13133192C2314yes—
296#13133191C2312yes—
297#13133191C2314yes—
298#13133191C2314yes—
299#13133191C2314yes—
300#13133191C2312yes—
301#13133190C2318yes—
302#13133189C2314yes—
303#13133189C2318yes—
304#13133189C2314yes—
305#13133189C2314yes—
306#13133189C2318yes—
307#13133189C2318yes—
308#13133189C2314yes—
309#13133188C2314yes—
310#13133186C2314yes—
311Q8×Dic53C2314yes—
312Q8×Dic53C2312yes—
313Q8×Dic53C2312yes—
314C4×Dic106C2318yes—
315C4×Dic106C2318yes—
316C4×Dic106C2314yes—
317C4×Dic106C2318yes—
318C4×Dic106C2314yes—
319C4×Dic106C2314yes—
320#13133182C2318yes—
321#13133182C2318yes—
322#13133182C2314yes—
323#13133182C2314yes—
324#13133182C2318yes—
325#13133182C2312yes—
326#13133182C2314yes—
327#13133182C2312yes—
328C4×D212C2314yes—
329D4×Dic53C2314yes—
330D4×Dic53C2314yes—
331D4×Dic53C2312yes—
332D4×Dic53C2314yes—
333D4×Dic53C2314yes—
334D4×Dic53C2318yes—
335D4×Dic53C2318yes—
336D4×Dic53C2314yes—
337D4×Dic53C2312yes—
338#13133179C2314yes—
339#13133179C2312yes—
340#13133179C2312yes—
341C4×C22⋊D53C2318yes—
342C4×C22⋊D53C2314yes—
343C4×C22⋊D53C2314yes—
344C4×C22⋊D53C2318yes—
345C4×C22⋊D53C2318yes—
346C4×C22⋊D53C2314yes—
347C4×C22⋊D53C2314yes—
348#13133177C2314yes—
349#13133177C2318yes—
350#13133177C2314yes—
351#13133177C2314yes—
352#13133177C2314yes—
353#13133177C2314yes—
354#13133177C2318yes—
355#13133177C2318yes—
356#13133177C2314yes—
357#13133176C2314yes—
358#13133176C2314yes—
359#13133176C2312yes—
360#13133176C2314yes—
361#13133175C2314yes—
362#13133175C2314yes—
363#13133175C2314yes—
364#13133175C2314yes—
365#13133174C2318yes—
366#13133174C2314yes—
367#13133173C2318yes—
368#13133173C2318yes—
369#13133173C2314yes—
370#13133173C2314yes—
371#13133173C2314yes—
372#13133173C2314yes—
373C2×C4⋊Dic53C2314yes—
374C2×C4⋊Dic53C2314yes—
375C2×C4⋊Dic53C2314yes—
376C2×C4⋊Dic53C2312yes—
377C2×C4⋊Dic53C2312yes—
378C2×#11719919C2318yes—
379C2×#11719919C2318yes—
380C2×#11719919C2314yes—
381C2×#11719919C2314yes—
382C2×#11719919C2314yes—
383C2×#11719919C2314yes—
384C4⋊C4×D53C2318yes—
385C4⋊C4×D53C2314yes—
386C4⋊C4×D53C2314yes—
387C2×C4×Dic53C2312yes—
388C2×C4×Dic53C2312yes—
389C2×C4×Dic53C2312yes—
390C2×C4×Dic53C2312yes—
391C2×C4×Dic53C2312yes—
392C2×C4×Dic53C2312yes—
393C2×C4×Dic53C2314yes—
394C42×D53C2314yes—
395C2×#41×C53C2312yes—
396C2×#41×C53C2314yes—
397C23×C4×C53C2311yescharacteristic
398C23×C4×C53C2312yes—
399C4⋊Q8×C53C2314yes—
400#126×C53C2318yes—
401#125×C53C2318yes—
402#125×C53C2314yes—
403#123×C53C2318yes—
404#123×C53C2318yes—
405#123×C53C2314yes—
406C22⋊Q8×C53C2314yes—
407C22⋊Q8×C53C2314yes—
408C22⋊Q8×C53C2318yes—
409C22⋊Q8×C53C2312yes—
410C22⋊Q8×C53C2312yes—
411C22⋊Q8×C53C2314yes—
412#121×C53C2312yes—
413#121×C53C2314yes—
414#121×C53C2314yes—
415#121×C53C2314yes—
416#121×C53C2312yes—
417#120×C53C2314yes—
418C4×Q8×C53C2314yes—
419C4×D4×C53C2314yes—
420C4×D4×C53C2318yes—
421C4×D4×C53C2318yes—
422C4×D4×C53C2314yes—
423C4×D4×C53C2314yes—
424#117×C53C2312yes—
425#117×C53C2314yes—
426#117×C53C2314yes—
427C2×C4⋊C4×C53C2314yes—
428C2×C4⋊C4×C53C2314yes—
429C2×C4⋊C4×C53C2311yescharacteristic
430C2×C4⋊C4×C53C2311yescharacteristic
431C2×C4⋊C4×C53C2312yes—
432C2×C4⋊C4×C53C2314yes—
433C24×C53C2411yescharacteristic
434#41×C53—28no—
435#41×C53—48no—
436C2×Q8×C53C2412yes—
437C2×Q8×C53C2414yes—
438C2×D4×C53C2414yes—
439C2×D4×C53C2414yes—
440C2×D4×C53C2412yes—
441C2×D4×C53C2414yes—
442C2×D4×C53C2414yes—
443C22×C4×C53—24no—
444C22×C4×C53—44no—
445C22×C4×C53C2414yes—
446C22×C4×C53C2412yes—
447C22×C4×C53C2412yes—
448C22×C4×C53C2411yescharacteristic
449C22×C4×C53C2414yes—
450C22×C4×C53C2412yes—
451C22×C4×C53C2414yes—
452C22×C4×C53C2412yes—
453C22×C4×C53C2418yes—
454C22×C4×C53C2411yescharacteristic
455C2×C22⋊D53C2414yes—
456C2×C22⋊D53C2414yes—
457C2×C22⋊D53C2414yes—
458C2×C22⋊D53C2414yes—
459C2×C22⋊D53C2414yes—
460C2×C22⋊D53C2418yes—
461C22×Dic53—24no—
462C22×Dic53—24no—
463C22×Dic53—44no—
464C22×Dic53C2412yes—
465C22×Dic53C2412yes—
466C22×Dic53C2411yescharacteristic
467C22×Dic53C2412yes—
468C22×Dic53C2412yes—
469C22×Dic53C2411yescharacteristic
470C22×Dic53C2414yes—
471C22×Dic53C2414yes—
472C22×Dic53C2414yes—
473C22×Dic53C2414yes—
474C22×Dic53C2414yes—
475C22×Dic53C2418yes—
476C22×Dic53C2411yescharacteristic
477C22×Dic53C2411yescharacteristic
478Q8×D53—416no—
479#11719947—216no—
480#11719947—216no—
481#11719947—416no—
482#11719947—416no—
483#11719945—28no—
484#11719945—416no—
485#11719945—48no—
486C2×D212C2412yes—
487C2×D212C2414yes—
488C2×C4×D53C2414yes—
489C2×C4×D53C2414yes—
490C2×C4×D53C2414yes—
491C2×C4×D53C2418yes—
492C2×C4×D53C2418yes—
493C2×Dic106—216no—
494C2×Dic106—48no—
495C2×Dic106—416no—
496C2×Dic106—48no—
497C2×Dic106—416no—
498C2×Dic106—48no—
499C2×Dic106C2412yes—
500C2×Dic106C2414yes—
501C2×Dic106C2418yes—
502C2×Dic106C2414yes—
503C2×Dic106C2418yes—
504C2×Dic106C2418yes—
505C2×Dic106C2414yes—
506C2×Dic106C2418yes—
507C2×Dic106C2418yes—
508C4⋊C4×C53C2414yes—
509C4⋊C4×C53C2414yes—
510C4⋊C4×C53C2418yes—
511C4⋊C4×C53C2412yes—
512C4⋊C4×C53C2418yes—
513C4⋊C4×C53C2412yes—
514C4⋊C4×C53C2414yes—
515C4⋊C4×C53C2414yes—
516C4⋊C4×C53C2414yes—
517C4⋊C4×C53C2418yes—
518C4⋊C4×C53C2414yes—
519C22⋊C4×C53C2414yes—
520C22⋊C4×C53C2414yes—
521C22⋊C4×C53C2418yes—
522C22⋊C4×C53C2414yes—
523C22⋊C4×C53C2418yes—
524C22⋊C4×C53C2414yes—
525C22⋊C4×C53C2414yes—
526C42×C53C2418yes—
527C42×C53C2414yes—
528C22⋊Dic53C2414yes—
529C22⋊Dic53C2414yes—
530C22⋊Dic53C2418yes—
531C22⋊Dic53C2414yes—
532C22⋊Dic53C2414yes—
533C22⋊Dic53C2414yes—
534C22⋊Dic53C2418yes—
535C22⋊Dic53C2414yes—
536C22⋊Dic53C2414yes—
537#11719921C2418yes—
538#11719921C2414yes—
539#11719921C2414yes—
540#11719921C2418yes—
541#11719921C2414yes—
542#11719921C2414yes—
543#11719921C2414yes—
544#11719921C2414yes—
545#11719921C2418yes—
546#11719921C2418yes—
547C4⋊Dic53C2412yes—
548C4⋊Dic53C2414yes—
549C4⋊Dic53C2418yes—
550C4⋊Dic53C2414yes—
551C4⋊Dic53C2418yes—
552C4⋊Dic53C2418yes—
553C4⋊Dic53C2412yes—
554C4⋊Dic53C2414yes—
555C4⋊Dic53C2414yes—
556C4⋊Dic53C2414yes—
557C4⋊Dic53C2414yes—
558C4⋊Dic53C2414yes—
559C4⋊Dic53C2414yes—
560#11719919C2414yes—
561#11719919C2418yes—
562#11719919C2418yes—
563#11719919C2418yes—
564#11719919C2418yes—
565#11719919C2418yes—
566#11719919C2418yes—
567#11719919C2418yes—
568#11719919C2418yes—
569#11719919C2414yes—
570#11719919C2414yes—
571#11719919C2414yes—
572#11719919C2414yes—
573#11719919C2414yes—
574#11719919C2414yes—
575#11719919C2414yes—
576#11719919C2418yes—
577#11719919C2418yes—
578#11719919C2414yes—
579#11719919C2414yes—
580C4×Dic53C2412yes—
581C4×Dic53C2414yes—
582C4×Dic53C2414yes—
583C4×Dic53C2412yes—
584C4×Dic53C2412yes—
585C4×Dic53C2412yes—
586C4×Dic53C2412yes—
587C4×Dic53C2412yes—
588C4×Dic53C2412yes—
589C4×Dic53C2412yes—
590C4×Dic53C2414yes—
591C4×Dic53C2414yes—
592C4×Dic53C2414yes—
593C4×Dic53C2418yes—
594C4×Dic53C2418yes—
595C4×Dic53C2418yes—
596C23×C53—22no—
597C23×C53—22no—
598C23×C53—22no—
599C23×C53C2514yes—
600C23×C53C2511yescharacteristic
601C23×C53C2511yescharacteristic
602C23×C53C2511yescharacteristic
603C22×D53C2514yes—
604Q8×C53—24no—
605Q8×C53—44no—
606D4×C53—28no—
607D4×C53—28no—
608D4×C53—28no—
609D4×C53—24no—
610D4×C53—44no—
611C2×C4×C53—28no—
612C2×C4×C53—22no—
613C2×C4×C53—24no—
614C2×C4×C53—24no—
615C2×C4×C53—28no—
616C2×C4×C53—42no—
617C2×C4×C53—44no—
618C2×C4×C53—42no—
619C2×C4×C53—48no—
620C2×C4×C532−1+414yescomplemented
621C2×C4×C53C2514yes—
622C2×C4×C53C2514yes—
623C2×C4×C53C2514yes—
624C2×C4×C53C2514yes—
625C2×C4×C53C2512yes—
626C2×C4×C53C2514yes—
627C2×C4×C53C2512yes—
628C22⋊D53—28no—
629C22⋊D53—28no—
630C22⋊D53—28no—
631C22⋊D53—28no—
632C22⋊D53—28no—
633C22⋊D53—48no—
634C2×Dic53—28no—
635C2×Dic53—22no—
636C2×Dic53—22no—
637C2×Dic53—24no—
638C2×Dic53—24no—
639C2×Dic53—28no—
640C2×Dic53—28no—
641C2×Dic53—24no—
642C2×Dic53—24no—
643C2×Dic53—44no—
644C2×Dic53—44no—
645C2×Dic53—48no—
646C2×Dic53H(5,𝔽2)14yes—
647C2×Dic532−1+414yescomplemented
648C2×Dic53C2512yes—
649C2×Dic53C2514yes—
650C2×Dic53C2518yes—
651C2×Dic53C2514yes—
652C2×Dic53C2514yes—
653C2×Dic53C2512yes—
654C2×Dic53C2512yes—
655C2×Dic53C2512yes—
656D212—24no—
657D212—44no—
658C4×D53—28no—
659C4×D53—28no—
660C4×D53—28no—
661C4×D53—48no—
662C4×D53—48no—
663Dic106—24no—
664Dic106—216no—
665Dic106—216no—
666Dic106—28no—
667Dic106—28no—
668Dic106—48no—
669Dic106—48no—
670Dic106—44no—
671Dic106—48no—
672#62833—531nomaximal, Sylow
673C22×C53—28no—
674C22×C53—21no—
675C22×C53—21no—
676C22×C53—21no—
677C22×C53—21no—
678C22×C53—21no—
679C22×C53—21no—
680C22×C53—24no—
681C22×C53—24no—
682C22×C53—24no—
683C22×C53C2×H(5,𝔽2)12yes—
684C22×C53C2×2−1+412yes—
685C22×C53C2×2−1+412yes—
686C22×C53C2611yescharacteristic
687C2×D53—24no—
688C2×D53—24no—
689C2×D53—24no—
690C4×C53—24no—
691C4×C53—24no—
692C4×C53—24no—
693C4×C53—24no—
694C4×C53—22no—
695C4×C53—24no—
696C4×C53C2×2−1+414yes—
697Dic53—28no—
698Dic53—24no—
699Dic53—22no—
700Dic53—24no—
701Dic53—24no—
702Dic53—22no—
703Dic53C2×H(5,𝔽2)14yes—
704Dic53C2×2−1+414yes—
705#3552—534no—
706#3552—534no—
707#3552—538no—
708#3544—534no—
709#3544—534no—
710#3511—534no—
711#3511—532no—
712#3511—532no—
713#3509—534no—
714#3503—534no—
715#3503—532no—
716#3503—532no—
717#3499—534no—
718#3492—534no—
719#3492—532no—
720#3492—531no—
721#3492D5311yescharacteristic, complemented
722#3486—534no—
723#3444—532no—
724C22×C4⋊Q8—531no—
725C2×C53—22no—
726C2×C53—22no—
727C2×C53—22no—
728C2×C53—44no—
729C2×C53C22×H(5,𝔽2)11yescharacteristic
730C2×C53C22×2−1+411yescharacteristic
731C2×C53C22×2−1+411yescharacteristic
732D53—44no—
733C2×2−1+4—534no—
734C23×Q8—532no—
735#563—538no—
736#563—538no—
737#563—538no—
738#563—538no—
739Q82—534no—
740Q82—534no—
741#557—538no—
742#557—534no—
743#557—534no—
744#556—538no—
745#556—534no—
746#556—534no—
747#555—534no—
748#555—534no—
749#554—534no—
750#554—538no—
751#554—534no—
752#554—534no—
753#554—534no—
754#554—538no—
755#554—534no—
756#554—534no—
757#554—534no—
758#554C2×D5314yes—
759#553—538no—
760#553—534no—
761#553—534no—
762#553—538no—
763#553—534no—
764#553C2×D5314yes—
765#552—538no—
766#552—534no—
767#552—534no—
768#552—538no—
769#552—534no—
770#552C2×D5314yes—
771D4×Q8—534no—
772D4×Q8—538no—
773D4×Q8—538no—
774D4×Q8—538no—
775D4×Q8—538no—
776D4×Q8—538no—
777D4×Q8—534no—
778#548—538no—
779#548—538no—
780#548—538no—
781#548—538no—
782#547—538no—
783#547—538no—
784#547—538no—
785#547—534no—
786#547—534no—
787#547—534no—
788#547—534no—
789#547—534no—
790#547C2×D5314yes—
791#544—534no—
792#544—538no—
793#544—534no—
794#544—534no—
795#544—538no—
796#544—532no—
797#544—534no—
798#544—531no—
799#544—534no—
800#544C2×D5311yescharacteristic
801#542—538no—
802#542—538no—
803#542—534no—
804#542—534no—
805#542—534no—
806#542—534no—
807#541—538no—
808#541—538no—
809#539—538no—
810#539—534no—
811#539—534no—
812#539—538no—
813#539—534no—
814#539C2×D5314yes—
815#537—532no—
816#537—534no—
817#537—531no—
818#537C2×D5311yescharacteristic
819#536—534no—
820#536—538no—
821#536—538no—
822#536—538no—
823#536—538no—
824#536—534no—
825#533—534no—
826#533—532no—
827#533—532no—
828#533—534no—
829#533—534no—
830#533—532no—
831#533—534no—
832#532—532no—
833#532—532no—
834#532—532no—
835#532—534no—
836#532—534no—
837C2×C4⋊Q8—534no—
838C2×C4⋊Q8—534no—
839C2×C4⋊Q8—534no—
840C2×C4⋊Q8—532no—
841C2×C4⋊Q8—532no—
842C2×C4⋊Q8—534no—
843C2×C4⋊Q8—534no—
844C2×C4⋊Q8—534no—
845C2×C4⋊Q8—534no—
846#529—534no—
847#529—534no—
848#529—532no—
849#529—532no—
850#529—532no—
851#529—532no—
852#529—534no—
853#529—534no—
854#525—532no—
855#525—534no—
856#525—534no—
857#525—534no—
858#525—538no—
859#525C2×D5312yes—
860#525C2×D5314yes—
861#520—532no—
862#520—538no—
863#520—532no—
864#520—532no—
865#520C2×D5312yes—
866#519—534no—
867C4×#41—532no—
868C4×#41—534no—
869C4×#41—534no—
870C4×#41—532no—
871C22×C4⋊C4—532no—
872C22×C4⋊C4—531no—
873C22×C4⋊C4C2×D5311yescharacteristic
874C22×C42—531no—
875C53#6283311yescharacteristic, complemented, Sylow
8762−1+4—21216no—
877C2×#41—534no—
878C2×#41—534no—
879C2×#41—538no—
880C2×#41—538no—
881C2×#41—532no—
882C2×#41—534no—
883C2×#41—538no—
884C2×#41C22×D5312yes—
885C2×#41C22×D5314yes—
886C22×Q8—538no—
887C22×Q8—534no—
888C22×Q8—534no—
889C22×Q8—534no—
890C22×Q8—538no—
891C22×Q8—534no—
892C22×Q8—538no—
893C22×Q8—2128no—
894C23×C4—531no—
895C23×C4—531no—
896C23×C4—532no—
897C23×C4C22×D5311yescharacteristic
898C23×C4C22×D5312yes—
899C4⋊Q8—538no—
900C4⋊Q8—532no—
901C4⋊Q8—538no—
902C4⋊Q8—532no—
903C4⋊Q8—534no—
904C4⋊Q8—534no—
905C4⋊Q8—538no—
906C4⋊Q8—538no—
907C4⋊Q8—534no—
908C4⋊Q8—534no—
909C4⋊Q8—538no—
910C4⋊Q8—534no—
911C4⋊Q8—534no—
912C4⋊Q8—534no—
913C4⋊Q8—534no—
914C4⋊Q8—538no—
915C4⋊Q8—538no—
916C4⋊Q8—538no—
917C4⋊Q8—538no—
918C4⋊Q8—534no—
919C4⋊Q8—534no—
920C4⋊Q8—532no—
921C4⋊Q8—538no—
922C4⋊Q8—538no—
923C4⋊Q8—534no—
924C4⋊Q8—538no—
925C4⋊Q8C22×D5314yes—
926#127—532no—
927#126—534no—
928#126—534no—
929#126—538no—
930#126—538no—
931#126—538no—
932#126—534no—
933#126—534no—
934#126—538no—
935#126—538no—
936#126—538no—
937#126—538no—
938#126C22×D5318yes—
939#125—534no—
940#125—534no—
941#125—532no—
942#125—532no—
943#125—538no—
944#125—538no—
945#125—534no—
946#125—534no—
947#125—538no—
948#125—538no—
949#125—538no—
950#125—538no—
951#125—538no—
952#125—538no—
953#125—534no—
954#125—538no—
955#125C22×D5314yes—
956#125C22×D5318yes—
957#124—532no—
958#124—532no—
959#124—538no—
960#124—534no—
961#124—534no—
962#124—538no—
963#124—538no—
964#124—538no—
965#124—538no—
966#124—538no—
967#123—534no—
968#123—534no—
969#123—538no—
970#123—538no—
971#123—534no—
972#123—538no—
973#123—538no—
974#123—538no—
975#123—538no—
976#123—534no—
977#123—534no—
978#123—538no—
979#123—538no—
980#123—538no—
981#123—538no—
982#123C22×D5314yes—
983#123C22×D5318yes—
984#123C22×D5318yes—
985C22⋊Q8—534no—
986C22⋊Q8—538no—
987C22⋊Q8—532no—
988C22⋊Q8—532no—
989C22⋊Q8—534no—
990C22⋊Q8—534no—
991C22⋊Q8—534no—
992C22⋊Q8—538no—
993C22⋊Q8—538no—
994C22⋊Q8—538no—
995C22⋊Q8—538no—
996C22⋊Q8—538no—
997C22⋊Q8—538no—
998C22⋊Q8—534no—
999C22⋊Q8—538no—
1000C22⋊Q8—538no—
1001C22⋊Q8—538no—
1002C22⋊Q8—538no—
1003C22⋊Q8—538no—
1004C22⋊Q8—538no—
1005C22⋊Q8—538no—
1006C22⋊Q8—534no—
1007C22⋊Q8—534no—
1008C22⋊Q8—534no—
1009C22⋊Q8—534no—
1010C22⋊Q8—538no—
1011C22⋊Q8—538no—
1012C22⋊Q8—538no—
1013C22⋊Q8—538no—
1014C22⋊Q8—538no—
1015C22⋊Q8—538no—
1016C22⋊Q8—538no—
1017C22⋊Q8—538no—
1018C22⋊Q8—538no—
1019C22⋊Q8C22×D5312yes—
1020C22⋊Q8C22×D5312yes—
1021C22⋊Q8C22×D5314yes—
1022C22⋊Q8C22×D5314yes—
1023C22⋊Q8C22×D5314yes—
1024C22⋊Q8C22×D5318yes—
1025#121—534no—
1026#121—534no—
1027#121—534no—
1028#121—534no—
1029#121—538no—
1030#121—538no—
1031#121—534no—
1032#121—538no—
1033#121—532no—
1034#121—532no—
1035#121—534no—
1036#121—534no—
1037#121—534no—
1038#121—534no—
1039#121—538no—
1040#121C22×D5312yes—
1041#121C22×D5312yes—
1042#121C22×D5314yes—
1043#121C22×D5314yes—
1044#121C22×D5314yes—
1045#120—534no—
1046#120C22×D5314yes—
1047C4×Q8—532no—
1048C4×Q8—532no—
1049C4×Q8—534no—
1050C4×Q8—534no—
1051C4×Q8—532no—
1052C4×Q8—534no—
1053C4×Q8—532no—
1054C4×Q8—538no—
1055C4×Q8—538no—
1056C4×Q8—538no—
1057C4×Q8—534no—
1058C4×Q8—534no—
1059C4×Q8—534no—
1060C4×Q8—538no—
1061C4×Q8—538no—
1062C4×Q8—538no—
1063C4×Q8—534no—
1064C4×Q8C22×D5314yes—
1065C4×D4—534no—
1066C4×D4—534no—
1067C4×D4—534no—
1068C4×D4—534no—
1069C4×D4—532no—
1070C4×D4—532no—
1071C4×D4—538no—
1072C4×D4—538no—
1073C4×D4—534no—
1074C4×D4—534no—
1075C4×D4—534no—
1076C4×D4—534no—
1077C4×D4—534no—
1078C4×D4—538no—
1079C4×D4—538no—
1080C4×D4—538no—
1081C4×D4—532no—
1082C4×D4—532no—
1083C4×D4—534no—
1084C4×D4—534no—
1085C4×D4—534no—
1086C4×D4—534no—
1087C4×D4—534no—
1088C4×D4—534no—
1089C4×D4—534no—
1090C4×D4—538no—
1091C4×D4—538no—
1092C4×D4—538no—
1093C4×D4—534no—
1094C4×D4C22×D5314yes—
1095C4×D4C22×D5314yes—
1096C4×D4C22×D5318yes—
1097C4×D4C22×D5318yes—
1098C4×D4C22×D5314yes—
1099#117—532no—
1100#117—534no—
1101#117—534no—
1102#117—534no—
1103#117—534no—
1104#117—534no—
1105#117—534no—
1106#117—534no—
1107#117—534no—
1108#117—534no—
1109#117—534no—
1110#117—534no—
1111#117—538no—
1112#117—538no—
1113#117—534no—
1114#117—538no—
1115#117C22×D5312yes—
1116#117C22×D5314yes—
1117#117C22×D5314yes—
1118C2×C4⋊C4—534no—
1119C2×C4⋊C4—532no—
1120C2×C4⋊C4—534no—
1121C2×C4⋊C4—532no—
1122C2×C4⋊C4—538no—
1123C2×C4⋊C4—534no—
1124C2×C4⋊C4—534no—
1125C2×C4⋊C4—534no—
1126C2×C4⋊C4—534no—
1127C2×C4⋊C4—538no—
1128C2×C4⋊C4—534no—
1129C2×C4⋊C4—538no—
1130C2×C4⋊C4—534no—
1131C2×C4⋊C4—534no—
1132C2×C4⋊C4C22×D5311yescharacteristic
1133C2×C4⋊C4C22×D5311yescharacteristic
1134C2×C4⋊C4C22×D5312yes—
1135C2×C4⋊C4C22×D5314yes—
1136C2×C4⋊C4C22×D5314yes—
1137C2×C4⋊C4C22×D5314yes—
1138C2×C42—534no—
1139C2×C42—532no—
1140C2×C42—532no—
1141C2×C42—532no—
1142C2×C42—532no—
1143C2×C42—532no—
1144C2×C42—532no—
1145C2×C42—534no—
1146C24C23×D5311yescharacteristic
1147#41—28no—
1148#41—48no—
1149#41—10616no—
1150#41—10616no—
1151#41—1068no—
1152#41—2128no—
1153#41—21216no—
1154#41—21216no—
1155#41—21216no—
1156C2×Q8—534no—
1157C2×Q8—532no—
1158C2×Q8—538no—
1159C2×Q8—534no—
1160C2×Q8—538no—
1161C2×Q8—538no—
1162C2×Q8—534no—
1163C2×Q8—538no—
1164C2×Q8—538no—
1165C2×Q8—10616no—
1166C2×Q8—2128no—
1167C2×Q8—2128no—
1168C2×Q8—21216no—
1169C2×Q8—2128no—
1170C2×Q8—21216no—
1171C2×Q8—21216no—
1172C2×Q8C23×D5312yes—
1173C2×Q8C23×D5314yes—
1174C2×D4—534no—
1175C2×D4—534no—
1176C2×D4—534no—
1177C2×D4—534no—
1178C2×D4—534no—
1179C2×D4—538no—
1180C2×D4—532no—
1181C2×D4—534no—
1182C2×D4C23×D5314yes—
1183C2×D4C23×D5312yes—
1184C2×D4C23×D5314yes—
1185C2×D4C23×D5314yes—
1186C2×D4C23×D5314yes—
1187C22×C4—24no—
1188C22×C4—44no—
1189C22×C4—531no—
1190C22×C4—531no—
1191C22×C4—532no—
1192C22×C4—532no—
1193C22×C4—531no—
1194C22×C4—532no—
1195C22×C4—532no—
1196C22×C4—531no—
1197C22×C4—534no—
1198C22×C4—534no—
1199C22×C4—534no—
1200C22×C4—534no—
1201C22×C4—534no—
1202C22×C4—538no—
1203C22×C4—534no—
1204C22×C4—534no—
1205C22×C4—534no—
1206C22×C4—538no—
1207C22×C4—538no—
1208C22×C4—1064no—
1209C22×C4—1064no—
1210C22×C4—2124no—
1211C22×C4C23×D5312yes—
1212C22×C4C23×D5312yes—
1213C22×C4C23×D5311yescharacteristic
1214C22×C4C23×D5314yes—
1215C22×C4C23×D5314yes—
1216C22×C4C23×D5312yes—
1217C22×C4C23×D5314yes—
1218C22×C4C23×D5312yes—
1219C22×C4C23×D5318yes—
1220C22×C4C23×D5311yescharacteristic
1221C4⋊C4—538no—
1222C4⋊C4—534no—
1223C4⋊C4—538no—
1224C4⋊C4—534no—
1225C4⋊C4—534no—
1226C4⋊C4—532no—
1227C4⋊C4—538no—
1228C4⋊C4—538no—
1229C4⋊C4—538no—
1230C4⋊C4—538no—
1231C4⋊C4—538no—
1232C4⋊C4—538no—
1233C4⋊C4—538no—
1234C4⋊C4—538no—
1235C4⋊C4—538no—
1236C4⋊C4—534no—
1237C4⋊C4—532no—
1238C4⋊C4—534no—
1239C4⋊C4—534no—
1240C4⋊C4—534no—
1241C4⋊C4—534no—
1242C4⋊C4—534no—
1243C4⋊C4—534no—
1244C4⋊C4—534no—
1245C4⋊C4—534no—
1246C4⋊C4—534no—
1247C4⋊C4—534no—
1248C4⋊C4—534no—
1249C4⋊C4—534no—
1250C4⋊C4—538no—
1251C4⋊C4—538no—
1252C4⋊C4—534no—
1253C4⋊C4—534no—
1254C4⋊C4C23×D5312yes—
1255C4⋊C4C23×D5314yes—
1256C4⋊C4C23×D5318yes—
1257C4⋊C4C23×D5314yes—
1258C4⋊C4C23×D5318yes—
1259C4⋊C4C23×D5318yes—
1260C4⋊C4C23×D5312yes—
1261C4⋊C4C23×D5314yes—
1262C4⋊C4C23×D5314yes—
1263C4⋊C4C23×D5314yes—
1264C4⋊C4C23×D5314yes—
1265C22⋊C4—534no—
1266C22⋊C4—534no—
1267C22⋊C4—534no—
1268C22⋊C4—538no—
1269C22⋊C4—538no—
1270C22⋊C4—534no—
1271C22⋊C4—534no—
1272C22⋊C4—534no—
1273C22⋊C4—534no—
1274C22⋊C4—538no—
1275C22⋊C4—538no—
1276C22⋊C4—538no—
1277C22⋊C4—538no—
1278C22⋊C4—534no—
1279C22⋊C4—534no—
1280C22⋊C4—534no—
1281C22⋊C4—534no—
1282C22⋊C4—534no—
1283C22⋊C4—534no—
1284C22⋊C4C23×D5314yes—
1285C22⋊C4C23×D5314yes—
1286C22⋊C4C23×D5318yes—
1287C22⋊C4C23×D5314yes—
1288C22⋊C4C23×D5314yes—
1289C22⋊C4C23×D5314yes—
1290C22⋊C4C23×D5318yes—
1291C42—532no—
1292C42—532no—
1293C42—532no—
1294C42—532no—
1295C42—532no—
1296C42—532no—
1297C42—532no—
1298C42—532no—
1299C42—534no—
1300C42—534no—
1301C42—534no—
1302C42—534no—
1303C42—534no—
1304C42—538no—
1305C42—538no—
1306C42—538no—
1307C42C23×D5314yes—
1308C42C23×D5318yes—
1309C23—22no—
1310C23—22no—
1311C23—22no—
1312C23—534no—
1313C23C24×D5314yes—
1314C23C24×D5311yescharacteristic
1315C23C24×D5311yescharacteristic
1316C23C24×D5311yescharacteristic
1317Q8—24no—
1318Q8—44no—
1319Q8—10616no—
1320Q8—10616no—
1321Q8—1068no—
1322Q8—1068no—
1323Q8—1064no—
1324Q8—2128no—
1325Q8—2128no—
1326Q8—2124no—
1327Q8—2128no—
1328D4—28no—
1329D4—28no—
1330D4—28no—
1331D4—24no—
1332D4—44no—
1333D4—1068no—
1334D4—1068no—
1335D4—1068no—
1336D4—1068no—
1337D4—1068no—
1338D4—1064no—
1339D4—2124no—
1340D4—2128no—
1341C2×C4—28no—
1342C2×C4—22no—
1343C2×C4—24no—
1344C2×C4—24no—
1345C2×C4—28no—
1346C2×C4—42no—
1347C2×C4—44no—
1348C2×C4—42no—
1349C2×C4—48no—
1350C2×C4—534no—
1351C2×C4—534no—
1352C2×C4—532no—
1353C2×C4—532no—
1354C2×C4—534no—
1355C2×C4—534no—
1356C2×C4—532no—
1357C2×C4—532no—
1358C2×C4—534no—
1359C2×C4—538no—
1360C2×C4—1068no—
1361C2×C4—1068no—
1362C2×C4—1064no—
1363C2×C4—1064no—
1364C2×C4—1064no—
1365C2×C4—1064no—
1366C2×C4—1068no—
1367C2×C4—1068no—
1368C2×C4—1062no—
1369C2×C4—1068no—
1370C2×C4—1062no—
1371C2×C4—1068no—
1372C2×C4—2128no—
1373C2×C4—2128no—
1374C2×C4—2124no—
1375C2×C4—2124no—
1376C2×C4—2128no—
1377C2×C4#1313326414yescomplemented
1378C2×C4C24×D5314yes—
1379C2×C4C24×D5312yes—
1380C2×C4C24×D5314yes—
1381C2×C4C24×D5314yes—
1382C2×C4C24×D5314yes—
1383C2×C4C24×D5314yes—
1384C2×C4C24×D5312yes—
1385C22—28no—
1386C22—21no—
1387C22—21no—
1388C22—21no—
1389C22—21no—
1390C22—21no—
1391C22—21no—
1392C22—24no—
1393C22—24no—
1394C22—24no—
1395C22—1064no—
1396C22—1064no—
1397C22—1064no—
1398C22H(5,𝔽2)×D5312yes—
1399C222−1+4×D5312yes—
1400C22C2×#1313326412yes—
1401C22C25×D5311yescharacteristic
1402C4—24no—
1403C4—24no—
1404C4—24no—
1405C4—24no—
1406C4—22no—
1407C4—24no—
1408C4—534no—
1409C4—534no—
1410C4—1062no—
1411C4—1064no—
1412C4—1068no—
1413C4—1062no—
1414C4—1064no—
1415C4—1064no—
1416C4C2×#1313326414yes—
1417C2—22no—
1418C2—22no—
1419C2—22no—
1420C2—44no—
1421C2—2124no—
1422C2C2×H(5,𝔽2)×D5311yescharacteristic
1423C2C2×2−1+4×D5311yescharacteristic
1424C2C22×#1313326411yescharacteristic
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3492C2
hypercenter#3492D53
hypocenterC53#62833
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3492

Complements

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

NH ≅ G/Ntype
1. #20289154C2semidirect
2. #20289150C2semidirect
3. #20289148C2semidirect
4. #20289057C2semidirect
5. #20289051C2semidirect
6. #20288624C2semidirect
7. #20288618C2semidirect
8. #20288617C2semidirect
9. #20288593C2semidirect
10. #20288530C2semidirect
11. #20288529C2semidirect
12. #20288528C2semidirect
13. #20288494C2semidirect
14. #20288424C2semidirect
15. #20288421C2semidirect
16. #20288416C2semidirect
17. #20288362C2semidirect
18. #20288007C2semidirect
19. C22×#13133216C2semidirect
20. C53×#3492C2semidirect
23. #16811377C22semidirect
24. #16811376C22semidirect
25. #16811375C22semidirect
26. #16811374C22semidirect
27. Q8×Dic106C22semidirect
28. #16811353C22semidirect
29. #16811350C22semidirect
30. #16811350C22semidirect
31. #16811349C22semidirect
32. #16811344C22semidirect
33. #16811341C22semidirect
34. #16811340C22semidirect
35. #16811337C22semidirect
36. #16811336C22semidirect
38. #16811332C22semidirect
40. #16811331C22semidirect
42. #16811329C22semidirect
44. #16811328C22semidirect
58. D4×Dic106C22semidirect
59. #16811288C22semidirect
62. #16811286C22semidirect
69. #16811274C22semidirect
71. #16811273C22semidirect
74. #16811271C22semidirect
76. #16811254C22semidirect
77. #16811253C22semidirect
78. #16811253C22semidirect
80. #16811252C22semidirect
82. #16811251C22semidirect
83. #16811250C22semidirect
84. #16811246C22semidirect
85. #16811245C22semidirect
86. #16811241C22semidirect
87. #16811240C22semidirect
88. #16811239C22semidirect
89. #16811238C22semidirect
90. #16811232C22semidirect
91. #16811230C22semidirect
101. #16811196C22semidirect
104. #16811195C22semidirect
106. #16811179C22semidirect
107. #16811177C22semidirect
109. #16811176C22semidirect
112. #16811175C22semidirect
113. #16811170C22semidirect
117. #16811168C22semidirect
125. C2×#13133216C22semidirect
126. C4⋊Q8×D53C22semidirect
620. C2×C4×C532−1+4semidirect
647. C2×Dic532−1+4semidirect
721. #3492D53semidirect
875. C53#62833semidirect
1377. C2×C4#13133264semidirect

Maximal subgroups

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

subgroupindex
#202891542
#202891502
#202891482
#202890572
#202890512
#202886242
#202886182
#202886172
#202885932
#202885302
#202885292
#202885282
#202884942
#202884242
#202884212
#202884162
#202883622
#202880072
C22×#131332162
C53×#34922
#6283353