Finite Group Databasebeta

← #28293029

Subgroups — #28293029

Order 13568.

7254 conjugacy classes of subgroups.

The subgroup lattice has 1202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289299C218yesmaximal, complemented
2#20289182C214yesmaximal, complemented
3#20289083C214yesmaximal, complemented
4#20289036C218yesmaximal, complemented
5#20288718C214yesmaximal, complemented
6#20288667C214yesmaximal, complemented
7#20288640C218yesmaximal, complemented
8#20288616C214yesmaximal, complemented
9#20288610C212yesmaximal, complemented
10#20288601C211yesmaximal, characteristic, complemented
11#20288589C211yesmaximal, characteristic, complemented
12#20288589C214yesmaximal, complemented
13#20288503C212yesmaximal, complemented
14#20288495C211yesmaximal, characteristic, complemented
15#20288371C212yesmaximal, complemented
16#20288355C212yesmaximal, complemented
17#20288010C211yesmaximal, characteristic, complemented
18#20288008C211yesmaximal, characteristic, complemented
19C2×#16811171C211yesmaximal, characteristic, complemented
20C53×#3498C211yesmaximal, characteristic, complemented
21C2×#13133264C2212yescomplemented
22C22×#11719947C2212yescomplemented
23#16811368C22116yescomplemented
24#16811362C22116yescomplemented
25#16811359C2218yescomplemented
26#16811359C2218yescomplemented
27#16811359C2214yescomplemented
28#16811351C2214yescomplemented
29#16811343C2214yescomplemented
30#16811342C2218yescomplemented
31#16811337C2218yescomplemented
32#16811332C2218yescomplemented
33#16811323C2218yescomplemented
34#16811320C2218yescomplemented
35#16811316C22116yescomplemented
36#16811313C2218yescomplemented
37#16811304C22116yescomplemented
38#16811304C22116yescomplemented
39#16811293C2218yescomplemented
40#16811293C2218yescomplemented
41#16811293C2214yescomplemented
42#16811291C2218yescomplemented
43D4×Dic106C2214yescomplemented
44#16811281C2218yescomplemented
45#16811280C2218yescomplemented
46#16811279C2218yescomplemented
47#16811278C2214yescomplemented
48#16811273C2218yescomplemented
49#16811272C2218yescomplemented
50#16811272C2218yescomplemented
51#16811267C2218yescomplemented
52#16811267C2218yescomplemented
53#16811267C22116yescomplemented
54#16811267C2218yescomplemented
55#16811267C2218yescomplemented
56#16811267C2218yescomplemented
57#16811267C2218yescomplemented
58#16811240C2218yescomplemented
59#16811240C2218yescomplemented
60#16811238C2218yescomplemented
61#16811235C2214yescomplemented
62#16811227C2218yescomplemented
63#16811227C2214yescomplemented
64#16811227C2218yescomplemented
65#16811223C22116yescomplemented
66#16811218C22116yescomplemented
67#16811208C22116yescomplemented
68#16811208C22116yescomplemented
69#16811202C2218yescomplemented
70#16811194C2212yes—
71#16811194C2212yescomplemented
72#16811194C2214yescomplemented
73#16811193C2214yescomplemented
74#16811190C2218yescomplemented
75#16811190C2214yescomplemented
76#16811190C2212yescomplemented
77#16811188C2218yescomplemented
78#16811182C2218yescomplemented
79#16811180C2211yescharacteristic, complemented
80#16811180C2214yescomplemented
81#16811178C2212yescomplemented
82#16811177C2212yescomplemented
83#16811176C2211yescharacteristic, complemented
84#16811171C2212yescomplemented
85#16811171C2214yescomplemented
86#16811171C2214yescomplemented
87#16811171C2214yescomplemented
88#16811171C2212yescomplemented
89#16811171C2214yescomplemented
90#16811171C2214yescomplemented
91#16811170C2212yescomplemented
92#16811169C2211yescharacteristic
93#16811169C2214yescomplemented
94C2×#13133217C2211yescharacteristic, complemented
95C4⋊Q8×D53C2212yescomplemented
96#16811160C2212yescomplemented
97#16811155C2212yescomplemented
98#16811155C2214yescomplemented
99#16811154C2214yescomplemented
100#16811154C2218yescomplemented
101#16811153C2214yescomplemented
102#16811152C2214yescomplemented
103#16811151C2214yescomplemented
104C2×#13133204C2212yescomplemented
105C2×#13133204C2214yescomplemented
106#16811135C2211yescharacteristic, complemented
107#16811133C2214yescomplemented
108#16811132C2214yescomplemented
109#16811130C2211yescharacteristic
110#16811130C2212yescomplemented
111#16811129C2218yescomplemented
112C2×#13133198C2218yescomplemented
113C2×#13133188C2214yescomplemented
114#16811102C2218yescomplemented
115#16811100C2212yescomplemented
116#16811098C2212yescomplemented
117#16811098C2218yescomplemented
118#41×Dic53C2212yescomplemented
119C4×#11719945C2214yescomplemented
120C4×#11719945C2211yescharacteristic, complemented
121C4×#11719947C2214yescomplemented
122C2×D4×Dic53C2214yescomplemented
123C2×C42×D53C2211yescharacteristic, complemented
124C2×H(5,𝔽2)×C53C2212yes—
125C53×#550C2214yescomplemented
126D42×C53C2218yes—
127D42×C53C2214yescomplemented
128C53×#535C2212yes—
129C53×#535C2214yescomplemented
130C53×#532C2211yescharacteristic
131C53×#532C2212yescomplemented
132C2×#127×C53C2211yescharacteristic
133C2×#127×C53C2212yescomplemented
134C4×#41×C53C2211yescharacteristic
135#13133264—48no—
136C2×#11719945C2311yescharacteristic
137C2×#11719945C2314yes—
138C2×#11719945C2314yes—
139C2×#11719947—48no—
140C2×#11719947C2318yes—
141C2×#11719947C2314yes—
142C2×#11719947C2318yes—
143C2×#11719947C2314yes—
144C2×#11719947C2318yes—
145C2×#11719947C2318yes—
146C22×Dic106C2312yes—
147C22×Dic106C2314yes—
148C2×Q8×D53C2314yes—
149C22×C22⋊D53C2314yes—
150C23×Dic53C2314yes—
151C22×C4×D53C2311yescharacteristic
152C22×C4×D53C2312yes—
153#13133217C2314yes—
154#13133217C2312yes—
155#13133217C2312yes—
156#13133217C2312yes—
157#13133216C2318yes—
158#13133216C2312yes—
159#13133215C2314yes—
160#13133215C2314yes—
161#13133215C2311yescharacteristic
162#13133213C2314yes—
163#13133213C23116yes—
164#13133213C2311yescharacteristic
165#13133212C2314yes—
166#13133210C2314yes—
167#13133210C23116yes—
168#13133210C23116yes—
169#13133210C23116yes—
170#13133210C2318yes—
171#13133209C2318yes—
172#13133209C2312yes—
173#13133208C2314yes—
174#13133208C2312yes—
175#13133207C23116yes—
176#13133207C2314yes—
177#13133206C2311yescharacteristic
178#13133204C2314yes—
179#13133204C2314yes—
180#13133204C2314yes—
181#13133204C2318yes—
182#13133204C23116yes—
183#13133204C2318yes—
184#13133204C2314yes—
185#13133204C23116yes—
186#13133204C2311yescharacteristic
187#13133204C2314yes—
188#13133204C2314yes—
189#13133203C23116yes—
190#13133203C2314yes—
191#13133202C2314yes—
192#13133201C2312yes—
193#13133200C23116yes—
194#13133199C23116yes—
195#13133199C2318yes—
196#13133199C2314yes—
197#13133198C2318yes—
198#13133198C23116yes—
199#13133198C23116yes—
200#13133198C23116yes—
201#13133198C23116yes—
202#13133198C23116yes—
203#13133198C23116yes—
204#13133198C2318yes—
205#13133198C2312yes—
206#13133198C2314yes—
207#13133197C2312yes—
208#13133197C2314yes—
209#13133196C2318yes—
210#13133196C2314yes—
211#13133196C2318yes—
212#13133196C2318yes—
213#13133196C23116yes—
214#13133195C2314yes—
215#13133194C23116yes—
216#13133194C23116yes—
217#13133194C2314yes—
218#13133194C23116yes—
219#13133193C2312yes—
220#13133193C2314yes—
221#13133192C2312yes—
222#13133190C23116yes—
223#13133190C2314yes—
224#13133189C2314yes—
225#13133189C23116yes—
226#13133189C23116yes—
227#13133189C23116yes—
228#13133189C23116yes—
229#13133189C23116yes—
230#13133189C23116yes—
231#13133188C2312yes—
232#13133188C2314yes—
233#13133188C2318yes—
234#13133188C2318yes—
235#13133188C23116yes—
236#13133188C2318yes—
237#13133188C2318yes—
238#13133188C2318yes—
239#13133188C2318yes—
240#13133188C2318yes—
241#13133188C2314yes—
242#13133187C2312yes—
243#13133186C2318yes—
244#13133186C23116yes—
245#13133186C23116yes—
246#13133185C2312yes—
247#13133185C2314yes—
248Q8×Dic53C2314yes—
249C4×Dic106C2318yes—
250C4×Dic106C2312yes—
251C4×Dic106C2318yes—
252C4×Dic106C2314yes—
253C4×Dic106C2314yes—
254C4×Dic106C2314yes—
255#13133182C2318yes—
256#13133182C2314yes—
257C4×D212C2312yes—
258C4×D212C2314yes—
259C4×D212C2314yes—
260D4×Dic53C2318yes—
261D4×Dic53C2314yes—
262D4×Dic53C2318yes—
263D4×Dic53C2318yes—
264D4×Dic53C2318yes—
265D4×Dic53C2318yes—
266D4×Dic53C2318yes—
267D4×Dic53C23116yes—
268D4×Dic53C23116yes—
269D4×Dic53C2318yes—
270D4×Dic53C2318yes—
271D4×Dic53C2318yes—
272D4×Dic53C2314yes—
273C4×C22⋊D53C2314yes—
274C4×C22⋊D53C2314yes—
275C4×C22⋊D53C2314yes—
276C4×C22⋊D53C2314yes—
277C4×C22⋊D53C2314yes—
278C4×C22⋊D53C2318yes—
279C4×C22⋊D53C23116yes—
280#13133177C23116yes—
281#13133177C2318yes—
282#13133176C2318yes—
283#13133176C2311yescharacteristic
284#13133176C2314yes—
285#13133176C2312yes—
286#13133176C2314yes—
287#13133175C2314yes—
288#13133174C2314yes—
289#13133174C2314yes—
290#13133174C2312yes—
291#13133173C2318yes—
292#13133173C2318yes—
293#13133173C23116yes—
294C2×C4⋊Dic53C2314yes—
295C2×#11719919C23116yes—
296C4⋊C4×D53C2318yes—
297C2×C22⋊Dic53C23116yes—
298C2×C22⋊Dic53C23116yes—
299C2×C22⋊Dic53C2318yes—
300C2×C22⋊Dic53C2318yes—
301C2×C4×Dic53C2312yes—
302C2×C4×Dic53C2311yescharacteristic
303C2×C4×Dic53C2314yes—
304C42×D53C2312yes—
305C42×D53C2312yes—
306C42×D53C2312yes—
307C42×D53C2312yes—
308C42×D53C2312yes—
309H(5,𝔽2)×C53—48no—
310C2×#41×C53C2311yescharacteristic
311C2×#41×C53C2312yes—
312C2×#41×C53C2314yes—
313C2×#41×C53C2314yes—
314C22×D4×C53C2312yes—
315C22×D4×C53C2314yes—
316C22×D4×C53C2314yes—
317C22×D4×C53C2318yes—
318C22×D4×C53C2318yes—
319C22×D4×C53C2314yes—
320C4⋊Q8×C53C2311yescharacteristic
321#127×C53C2314yes—
322#127×C53C2314yes—
323#127×C53C2318yes—
324#127×C53C2312yes—
325#127×C53C2312yes—
326#127×C53C2311yescharacteristic
327#124×C53C2314yes—
328#124×C53C2312yes—
329#121×C53C2314yes—
330#121×C53C2318yes—
331#121×C53C2318yes—
332#121×C53C23116yes—
333#120×C53C2318yes—
334#120×C53C23116yes—
335C4×Q8×C53C2312yes—
336C4×D4×C53C2314yes—
337C4×D4×C53C2314yes—
338C4×D4×C53C2312yes—
339C4×D4×C53C2318yes—
340#117×C53C2311yescharacteristic
341#117×C53C2312yes—
342C2×C42×C53C2311yescharacteristic
343C2×C42×C53C2312yes—
344C24×C53C2414yes—
345C24×C53C2418yes—
346C23×D53C2411yescharacteristic
347#41×C53—24no—
348#41×C53—28no—
349#41×C53—48no—
350#41×C53—48no—
351C2×Q8×C53C2411yescharacteristic
352C2×Q8×C53C2412yes—
353C2×D4×C53—28no—
354C2×D4×C53—48no—
355C2×D4×C53—416no—
356C2×D4×C53—48no—
357C2×D4×C53—48no—
358C2×D4×C53—416no—
359C2×D4×C53C2412yes—
360C2×D4×C53C2411yescharacteristic
361C2×D4×C53C2414yes—
362C2×D4×C53C2418yes—
363C2×D4×C53C2414yes—
364C2×D4×C53C2414yes—
365C2×D4×C53C2414yes—
366C2×D4×C53C2412yes—
367C2×D4×C53C2418yes—
368C2×D4×C53C24116yes—
369C2×D4×C53C2418yes—
370C2×D4×C53C2418yes—
371C22×C4×C53C2412yes—
372C22×C4×C53C2412yes—
373C22×C4×C53C2414yes—
374C22×C4×C53C2414yes—
375C22×C4×C53C2418yes—
376C22×C4×C53C2411yescharacteristic
377C2×C22⋊D53—48no—
378C2×C22⋊D53C2412yes—
379C2×C22⋊D53C2418yes—
380C2×C22⋊D53C24116yes—
381C2×C22⋊D53C2414yes—
382C2×C22⋊D53C2414yes—
383C2×C22⋊D53C2418yes—
384C2×C22⋊D53C24116yes—
385C22×Dic53—48no—
386C22×Dic53C2411yescharacteristic
387C22×Dic53C2414yes—
388C22×Dic53C2412yes—
389C22×Dic53C2418yes—
390C22×Dic53C24116yes—
391C22×Dic53C2418yes—
392C22×Dic53C24116yes—
393Q8×D53—48no—
394#11719947—416no—
395#11719947—416no—
396#11719947—48no—
397#11719947—416no—
398#11719947—48no—
399#11719947—416no—
400#11719945—24no—
401#11719945—48no—
402#11719945—48no—
403C2×D212C2411yescharacteristic
404C2×D212C2414yes—
405C2×C4×D53—24no—
406C2×C4×D53—44no—
407C2×C4×D53C2412yes—
408C2×C4×D53C2412yes—
409C2×C4×D53C2412yes—
410C2×C4×D53C2412yes—
411C2×C4×D53C2414yes—
412C2×C4×D53C2412yes—
413C2×C4×D53C2412yes—
414C2×C4×D53C2412yes—
415C2×C4×D53C2418yes—
416C2×Dic106—28no—
417C2×Dic106—48no—
418C2×Dic106C2414yes—
419C2×Dic106C2414yes—
420C2×Dic106C2414yes—
421C2×Dic106C2411yescharacteristic
422C2×Dic106C2414yes—
423C2×Dic106C2418yes—
424C4⋊C4×C53C2412yes—
425C4⋊C4×C53C2414yes—
426C4⋊C4×C53C2414yes—
427C22⋊C4×C53C2412yes—
428C22⋊C4×C53C2414yes—
429C22⋊C4×C53C24116yes—
430C22⋊C4×C53C2418yes—
431C42×C53C2411yescharacteristic
432C42×C53C2411yescharacteristic
433C42×C53C2412yes—
434C42×C53C2412yes—
435C42×C53C2414yes—
436C22⋊Dic53C2412yes—
437C22⋊Dic53C2414yes—
438C22⋊Dic53C2414yes—
439C22⋊Dic53C2414yes—
440C22⋊Dic53C24116yes—
441C22⋊Dic53C2418yes—
442C22⋊Dic53C24116yes—
443C22⋊Dic53C24116yes—
444C22⋊Dic53C24116yes—
445C22⋊Dic53C24116yes—
446C22⋊Dic53C24116yes—
447C22⋊Dic53C2418yes—
448#11719921C2414yes—
449#11719921C2414yes—
450#11719921C2414yes—
451#11719921C2414yes—
452#11719921C2414yes—
453#11719921C2418yes—
454C4⋊Dic53C2418yes—
455C4⋊Dic53C2418yes—
456C4⋊Dic53C2414yes—
457C4⋊Dic53C2412yes—
458C4⋊Dic53C2414yes—
459C4⋊Dic53C2414yes—
460C4⋊Dic53C2414yes—
461C4⋊Dic53C2418yes—
462#11719919C24116yes—
463#11719919C2414yes—
464#11719919C2418yes—
465#11719919C24116yes—
466#11719919C2414yes—
467#11719919C2418yes—
468#11719919C24116yes—
469#11719919C2414yes—
470#11719919C2414yes—
471#11719919C2414yes—
472C4×Dic53C2411yescharacteristic
473C4×Dic53C2412yes—
474C4×Dic53C2412yes—
475C4×Dic53C2411yescharacteristic
476C4×Dic53C2412yes—
477C4×Dic53C2412yes—
478C4×Dic53C2412yes—
479C4×Dic53C2412yes—
480C4×Dic53C2414yes—
481C4×Dic53C2418yes—
482C4×Dic53C2414yes—
483C4×Dic53C24116yes—
484C23×C53—28no—
485C23×C53—48no—
486C23×C53—48no—
487C23×C53—416no—
488C23×C53C2514yes—
489C23×C53C2518yes—
490C23×C53C2512yes—
491C23×C53C2511yescharacteristic
492C22×D53—22no—
493C22×D53—42no—
494C22×D53C2512yes—
495C22×D53C2512yes—
496Q8×C53—24no—
497Q8×C53—22no—
498D4×C53—28no—
499D4×C53—24no—
500D4×C53—28no—
501D4×C53—28no—
502D4×C53—24no—
503D4×C53—22no—
504D4×C53—216no—
505D4×C53—28no—
506D4×C53—48no—
507D4×C53—48no—
508D4×C53—416no—
509D4×C53—48no—
510C2×C4×C53—28no—
511C2×C4×C53—24no—
512C2×C4×C53—24no—
513C2×C4×C53—28no—
514C2×C4×C53—48no—
515C2×C4×C53H(5,𝔽2)14yes—
516C2×C4×C53C2514yes—
517C2×C4×C53C2514yes—
518C2×C4×C53C2512yes—
519C2×C4×C53C2512yes—
520C2×C4×C53C2511yescharacteristic
521C2×C4×C53C2511yescharacteristic
522C2×C4×C53C2512yes—
523C22⋊D53—24no—
524C22⋊D53—48no—
525C22⋊D53—44no—
526C22⋊D53—44no—
527C22⋊D53—416no—
528C22⋊D53—48no—
529C22⋊D53—416no—
530C2×Dic53—28no—
531C2×Dic53—22no—
532C2×Dic53—48no—
533C2×Dic53—42no—
534C2×Dic53—416no—
535C2×Dic53—416no—
536C2×Dic53—48no—
537C2×Dic53C2512yes—
538C2×Dic53C2518yes—
539C2×Dic53C2512yes—
540C2×Dic53C2514yes—
541C2×Dic53C2518yes—
542C2×Dic53C2512yes—
543C2×Dic53C2512yes—
544D212—22no—
545D212—44no—
546C4×D53—24no—
547C4×D53—24no—
548C4×D53—24no—
549C4×D53—24no—
550C4×D53—24no—
551C4×D53—28no—
552C4×D53—42no—
553C4×D53—42no—
554C4×D53—48no—
555Dic106—28no—
556Dic106—28no—
557Dic106—22no—
558Dic106—28no—
559Dic106—48no—
560Dic106—44no—
561#62836—531nomaximal, Sylow
562C22×C53—22no—
563C22×C53—24no—
564C22×C53—28no—
565C22×C53—22no—
566C22×C53—216no—
567C22×C53—28no—
568C22×C53—24no—
569C22×C53—88no—
570C22×C53—168no—
571C22×C53C2×H(5,𝔽2)12yes—
572C22×C53C2611yescharacteristic
573C2×D53—22no—
574C2×D53—22no—
575C2×D53—22no—
576C2×D53—22no—
577C2×D53—24no—
578C2×D53—44no—
579C4×C53—24no—
580C4×C53—22no—
581C4×C53—24no—
582C4×C53—22no—
583C4×C53C2×H(5,𝔽2)12yes—
584C4×C53C2×H(5,𝔽2)12yes—
585C4×C53#58514yes—
586Dic53—28no—
587Dic53—22no—
588Dic53—22no—
589Dic53—28no—
590Dic53—22no—
591Dic53—24no—
592Dic53—22no—
593#3562—538no—
594#3554—534no—
595#3546—534no—
596#3542—538no—
597#3517—534no—
598#3514—534no—
599#3513—538no—
600#3511—534no—
601#3510—532no—
602#3509—531no—
603#3508—531no—
604#3508—534no—
605#3500—532no—
606#3499—531no—
607#3498D5311yescharacteristic, complemented
608#3487—532no—
609#3485—532no—
610#3444—531no—
611#3444—531no—
612C2×#532—531no—
613C2×C53—22no—
614C2×C53—48no—
615C2×C53—44no—
616C2×C53—42no—
617C2×C53C22×H(5,𝔽2)11yescharacteristic
618C2×C53C2×#58512yes—
619D53—42no—
620D53—42no—
621C2×2−1+4—532no—
622C2×H(5,𝔽2)C2×D5312yes—
623C22×#41—532no—
624#562—5316no—
625#560—5316no—
626#559—538no—
627#559—538no—
628#559—534no—
629#557—534no—
630#556—538no—
631#556—534no—
632#555—538no—
633#554—538no—
634#553—5316no—
635#553—538no—
636#553—538no—
637#552—538no—
638#551—5316no—
639#551—5316no—
640#550—538no—
641#550—538no—
642#550—534no—
643#550—538no—
644#550C2×D5314yescomplemented
645D4×Q8—534no—
646#548—538no—
647#548—538no—
648#548—538no—
649#547—538no—
650#547—538no—
651#547—538no—
652#547—534no—
653#546—538no—
654#546—538no—
655#546—538no—
656#546—5316no—
657#546—538no—
658#546—538no—
659#546—538no—
660D42C2×D5318yes—
661D42C2×D5314yescomplemented
662#542—538no—
663#542—538no—
664#542—538no—
665#541—534no—
666#540—538no—
667#540—538no—
668#540—534no—
669#540—5316no—
670#539—5316no—
671#538—5316no—
672#538—5316no—
673#537—538no—
674#536—532no—
675#536—532no—
676#536—534no—
677#536—534no—
678#535—532no—
679#535—534no—
680#535—538no—
681#535—538no—
682#535C2×D5312yes—
683#535C2×D5314yescomplemented
684#534—538no—
685#533—532no—
686#533—532no—
687#533—531no—
688#533—531no—
689#533—534no—
690#532—531no—
691#532—534no—
692#532—534no—
693#532—534no—
694#532—534no—
695#532—534no—
696#532—532no—
697#532—532no—
698#532—534no—
699#532—532no—
700#532C2×D5311yescharacteristic
701#532C2×D5312yescomplemented
702C2×C4⋊Q8—532no—
703C2×C4⋊Q8—531no—
704C2×#127C2×D5311yescharacteristic
705C2×#127C2×D5312yescomplemented
706#529—534no—
707#529—534no—
708#529—538no—
709#529—532no—
710#529—534no—
711#529—532no—
712#529—534no—
713#529—534no—
714C2×#124—532no—
715C2×#124—534no—
716#525—531no—
717#525—532no—
718#525—534no—
719#525—538no—
720#525—534no—
721#525—531no—
722C2×#123—538no—
723C2×#121—534no—
724#520—538no—
725#519—532no—
726#518—532no—
727#518—538no—
728C4×#41—532no—
729C4×#41—534no—
730C4×#41—531no—
731C4×#41—534no—
732C4×#41C2×D5311yescharacteristic
733C2×C4×D4—534no—
734C22×C42—531no—
735C53#6283611yescharacteristic, complemented, Sylow
7362−1+4—2128no—
737H(5,𝔽2)—48no—
738C2×#41—534no—
739C2×#41—538no—
740C2×#41—538no—
741C2×#41—538no—
742C2×#41—538no—
743C2×#41—534no—
744C2×#41—531no—
745C2×#41—534no—
746C2×#41—534no—
747C2×#41—2128no—
748C2×#41C22×D5312yes—
749C2×#41C22×D5311yescharacteristic
750C2×#41C22×D5314yes—
751C2×#41C22×D5314yes—
752C22×Q8—534no—
753C22×Q8—532no—
754C22×Q8—534no—
755C22×D4—534no—
756C22×D4C22×D5312yes—
757C22×D4C22×D5314yes—
758C22×D4C22×D5318yes—
759C22×D4C22×D5318yes—
760C22×D4C22×D5314yes—
761C22×D4C22×D5314yes—
762C23×C4—534no—
763C23×C4—531no—
764C23×C4—532no—
765C4⋊Q8—534no—
766C4⋊Q8—531no—
767C4⋊Q8—534no—
768C4⋊Q8—538no—
769C4⋊Q8—532no—
770C4⋊Q8—532no—
771C4⋊Q8—532no—
772C4⋊Q8—534no—
773C4⋊Q8—532no—
774C4⋊Q8C22×D5311yescharacteristic
775#127—531no—
776#127—534no—
777#127—5316no—
778#127C22×D5312yes—
779#127C22×D5312yes—
780#127C22×D5314yes—
781#127C22×D5311yescharacteristic
782#127C22×D5314yes—
783#127C22×D5318yes—
784#126—534no—
785#126—538no—
786#126—534no—
787#126—5316no—
788#126—5316no—
789#126—5316no—
790#125—532no—
791#125—534no—
792#125—534no—
793#125—5316no—
794#125—532no—
795#125—538no—
796#124—531no—
797#124—531no—
798#124—534no—
799#124—534no—
800#124—538no—
801#124—534no—
802#124—534no—
803#124—5316no—
804#124—534no—
805#124—534no—
806#124—538no—
807#124—5316no—
808#124—534no—
809#124—5316no—
810#124C22×D5312yes—
811#124C22×D5314yes—
812#123—532no—
813#123—534no—
814#123—538no—
815#123—538no—
816#123—5316no—
817#123—5316no—
818#123—5316no—
819#123—5316no—
820#123—5316no—
821#123—5316no—
822#123—5316no—
823#123—534no—
824#123—532no—
825#123—534no—
826#123—538no—
827#123—5316no—
828C22⋊Q8—532no—
829C22⋊Q8—534no—
830C22⋊Q8—534no—
831C22⋊Q8—538no—
832C22⋊Q8—538no—
833C22⋊Q8—538no—
834C22⋊Q8—5316no—
835C22⋊Q8—534no—
836C22⋊Q8—532no—
837C22⋊Q8—534no—
838C22⋊Q8—534no—
839C22⋊Q8—5316no—
840C22⋊Q8—5316no—
841C22⋊Q8—5316no—
842#121—538no—
843#121—538no—
844#121—538no—
845#121—538no—
846#121—534no—
847#121—532no—
848#121—534no—
849#121—534no—
850#121—5316no—
851#121—538no—
852#121—538no—
853#121—538no—
854#121—5316no—
855#121—5316no—
856#121—5316no—
857#121—5316no—
858#121—5316no—
859#121—5316no—
860#121—532no—
861#121—534no—
862#121—5316no—
863#121C22×D5314yes—
864#121C22×D5318yes—
865#121C22×D5318yes—
866#121C22×D53116yes—
867#120—538no—
868#120—5316no—
869#120—5316no—
870#120—532no—
871#120—534no—
872#120—532no—
873#120C22×D5318yes—
874#120C22×D53116yes—
875C4×Q8—534no—
876C4×Q8—534no—
877C4×Q8—538no—
878C4×Q8—532no—
879C4×Q8—534no—
880C4×Q8—534no—
881C4×Q8—534no—
882C4×Q8—538no—
883C4×Q8—538no—
884C4×Q8C22×D5312yes—
885C4×D4—538no—
886C4×D4—538no—
887C4×D4—538no—
888C4×D4—538no—
889C4×D4—534no—
890C4×D4—538no—
891C4×D4—534no—
892C4×D4—5316no—
893C4×D4—5316no—
894C4×D4—538no—
895C4×D4—538no—
896C4×D4—538no—
897C4×D4—538no—
898C4×D4—534no—
899C4×D4—534no—
900C4×D4—534no—
901C4×D4—538no—
902C4×D4—534no—
903C4×D4—534no—
904C4×D4—5316no—
905C4×D4—538no—
906C4×D4—5316no—
907C4×D4—534no—
908C4×D4—534no—
909C4×D4—532no—
910C4×D4C22×D5314yes—
911C4×D4C22×D5314yes—
912C4×D4C22×D5312yes—
913C4×D4C22×D5318yes—
914#117—531no—
915#117—534no—
916#117—532no—
917#117—534no—
918#117—538no—
919#117—534no—
920#117—538no—
921#117—538no—
922#117—5316no—
923#117—534no—
924#117—534no—
925#117—532no—
926#117C22×D5311yescharacteristic
927#117C22×D5312yes—
928C2×C4⋊C4—534no—
929C2×C4⋊C4—5316no—
930C2×C4⋊C4—538no—
931C2×C22⋊C4—538no—
932C2×C22⋊C4—538no—
933C2×C22⋊C4—5316no—
934C2×C22⋊C4—5316no—
935C2×C42—532no—
936C2×C42—534no—
937C2×C42—531no—
938C2×C42—532no—
939C2×C42—532no—
940C2×C42—532no—
941C2×C42—532no—
942C2×C42—532no—
943C2×C42C22×D5312yes—
944C2×C42C22×D5311yescharacteristic
945C24—531no—
946C24C23×D5314yes—
947C24C23×D5318yes—
948#41—24no—
949#41—28no—
950#41—48no—
951#41—48no—
952#41—1064no—
953#41—2128no—
954#41—2128no—
955#41—21216no—
956#41—2128no—
957#41—21216no—
958#41—21216no—
959#41—21216no—
960#41—2128no—
961C2×Q8—534no—
962C2×Q8—531no—
963C2×Q8—534no—
964C2×Q8—534no—
965C2×Q8—534no—
966C2×Q8—538no—
967C2×Q8—1068no—
968C2×Q8—2128no—
969C2×Q8—2128no—
970C2×Q8C23×D5312yes—
971C2×Q8C23×D5311yescharacteristic
972C2×D4—28no—
973C2×D4—48no—
974C2×D4—416no—
975C2×D4—48no—
976C2×D4—48no—
977C2×D4—416no—
978C2×D4—532no—
979C2×D4—534no—
980C2×D4—534no—
981C2×D4—538no—
982C2×D4—5316no—
983C2×D4—538no—
984C2×D4—5316no—
985C2×D4—531no—
986C2×D4—534no—
987C2×D4—2128no—
988C2×D4C23×D5318yes—
989C2×D4C23×D5314yes—
990C2×D4C23×D5314yes—
991C2×D4C23×D5314yes—
992C2×D4C23×D5312yes—
993C2×D4C23×D5314yes—
994C2×D4C23×D5312yes—
995C2×D4C23×D5311yescharacteristic
996C2×D4C23×D5318yes—
997C2×D4C23×D53116yes—
998C2×D4C23×D5318yes—
999C2×D4C23×D5318yes—
1000C22×C4—531no—
1001C22×C4—534no—
1002C22×C4—532no—
1003C22×C4—538no—
1004C22×C4—5316no—
1005C22×C4—538no—
1006C22×C4—5316no—
1007C22×C4—532no—
1008C22×C4—532no—
1009C22×C4—532no—
1010C22×C4—532no—
1011C22×C4—534no—
1012C22×C4—532no—
1013C22×C4—532no—
1014C22×C4—532no—
1015C22×C4—538no—
1016C22×C4—1064no—
1017C22×C4—2124no—
1018C22×C4—2128no—
1019C22×C4C23×D5312yes—
1020C22×C4C23×D5314yes—
1021C22×C4C23×D5314yes—
1022C22×C4C23×D5312yes—
1023C22×C4C23×D5318yes—
1024C22×C4C23×D5311yescharacteristic
1025C4⋊C4—534no—
1026C4⋊C4—538no—
1027C4⋊C4—538no—
1028C4⋊C4—5316no—
1029C4⋊C4—538no—
1030C4⋊C4—5316no—
1031C4⋊C4—534no—
1032C4⋊C4—534no—
1033C4⋊C4—532no—
1034C4⋊C4—534no—
1035C4⋊C4—534no—
1036C4⋊C4—534no—
1037C4⋊C4—538no—
1038C4⋊C4—538no—
1039C4⋊C4—534no—
1040C4⋊C4—534no—
1041C4⋊C4—534no—
1042C4⋊C4—5316no—
1043C4⋊C4C23×D5314yes—
1044C4⋊C4C23×D5312yes—
1045C4⋊C4C23×D5314yes—
1046C22⋊C4—532no—
1047C22⋊C4—534no—
1048C22⋊C4—534no—
1049C22⋊C4—534no—
1050C22⋊C4—538no—
1051C22⋊C4—5316no—
1052C22⋊C4—5316no—
1053C22⋊C4—5316no—
1054C22⋊C4—5316no—
1055C22⋊C4—5316no—
1056C22⋊C4—5316no—
1057C22⋊C4—538no—
1058C22⋊C4—534no—
1059C22⋊C4—534no—
1060C22⋊C4—534no—
1061C22⋊C4—538no—
1062C22⋊C4—534no—
1063C22⋊C4—534no—
1064C22⋊C4C23×D5312yes—
1065C22⋊C4C23×D53116yes—
1066C22⋊C4C23×D5318yes—
1067C22⋊C4C23×D5314yes—
1068C42—531no—
1069C42—532no—
1070C42—532no—
1071C42—531no—
1072C42—532no—
1073C42—532no—
1074C42—532no—
1075C42—538no—
1076C42—532no—
1077C42—534no—
1078C42—534no—
1079C42—5316no—
1080C42C23×D5311yescharacteristic
1081C42C23×D5311yescharacteristic
1082C42C23×D5312yes—
1083C42C23×D5314yes—
1084C42C23×D5312yes—
1085C23—28no—
1086C23—48no—
1087C23—48no—
1088C23—416no—
1089C23—532no—
1090C23—532no—
1091C23—1062no—
1092C23—2122no—
1093C23C24×D5312yes—
1094C23C24×D5314yes—
1095C23C24×D5318yes—
1096C23C24×D5311yescharacteristic
1097Q8—24no—
1098Q8—22no—
1099Q8—1068no—
1100Q8—1068no—
1101Q8—1062no—
1102Q8—1068no—
1103Q8—2128no—
1104Q8—2124no—
1105D4—24no—
1106D4—28no—
1107D4—28no—
1108D4—28no—
1109D4—22no—
1110D4—24no—
1111D4—216no—
1112D4—28no—
1113D4—48no—
1114D4—48no—
1115D4—48no—
1116D4—416no—
1117D4—1064no—
1118D4—1062no—
1119D4—2124no—
1120D4—21216no—
1121D4—2124no—
1122D4—2124no—
1123D4—2128no—
1124D4—21216no—
1125D4—2128no—
1126C2×C4—24no—
1127C2×C4—28no—
1128C2×C4—24no—
1129C2×C4—28no—
1130C2×C4—48no—
1131C2×C4—532no—
1132C2×C4—532no—
1133C2×C4—538no—
1134C2×C4—532no—
1135C2×C4—534no—
1136C2×C4—532no—
1137C2×C4—538no—
1138C2×C4—1062no—
1139C2×C4—1068no—
1140C2×C4—1064no—
1141C2×C4—1064no—
1142C2×C4—1064no—
1143C2×C4—1064no—
1144C2×C4—1064no—
1145C2×C4—1068no—
1146C2×C4—2122no—
1147C2×C4—2122no—
1148C2×C4—2128no—
1149C2×C4—2122no—
1150C2×C4—21216no—
1151C2×C4—2128no—
1152C2×C4—2128no—
1153C2×C4—21216no—
1154C2×C4#1313326214yes—
1155C2×C4C24×D5314yes—
1156C2×C4C24×D5312yes—
1157C2×C4C24×D5314yes—
1158C2×C4C24×D5312yes—
1159C2×C4C24×D5311yescharacteristic
1160C2×C4C24×D5311yescharacteristic
1161C2×C4C24×D5312yes—
1162C22—22no—
1163C22—24no—
1164C22—22no—
1165C22—28no—
1166C22—24no—
1167C22—216no—
1168C22—28no—
1169C22—88no—
1170C22—168no—
1171C22—1062no—
1172C22—1062no—
1173C22—1062no—
1174C22—1062no—
1175C22—1064no—
1176C22—2124no—
1177C22C2×#1313326212yes—
1178C22C25×D5311yescharacteristic
1179C4—22no—
1180C4—24no—
1181C4—22no—
1182C4—24no—
1183C4—1062no—
1184C4—1062no—
1185C4—1068no—
1186C4—1062no—
1187C4—1064no—
1188C4—1062no—
1189C4—1068no—
1190C4C2×#1313326212yes—
1191C4C2×#1313326212yes—
1192C4#1681145814yes—
1193C2—22no—
1194C2—48no—
1195C2—42no—
1196C2—44no—
1197C2—2122no—
1198C2—2122no—
1199C2C22×#1313326211yescharacteristic
1200C2C2×#1681145812yes—
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3498C2
hypercenter#3498D53
hypocenterC53#62836
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3498

Complements

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

NH ≅ G/Ntype
1. #20289299C2semidirect
2. #20289182C2semidirect
3. #20289083C2semidirect
4. #20289036C2semidirect
5. #20288718C2semidirect
6. #20288667C2semidirect
7. #20288640C2semidirect
8. #20288616C2semidirect
9. #20288610C2semidirect
10. #20288601C2semidirect
11. #20288589C2semidirect
12. #20288589C2semidirect
13. #20288503C2semidirect
14. #20288495C2semidirect
15. #20288371C2semidirect
16. #20288355C2semidirect
17. #20288010C2semidirect
18. #20288008C2semidirect
19. C2×#16811171C2semidirect
20. C53×#3498C2semidirect
21. C2×#13133264C22semidirect
22. C22×#11719947C22semidirect
23. #16811368C22semidirect
24. #16811362C22semidirect
25. #16811359C22semidirect
26. #16811359C22semidirect
27. #16811359C22semidirect
28. #16811351C22semidirect
29. #16811343C22semidirect
30. #16811342C22semidirect
31. #16811337C22semidirect
32. #16811332C22semidirect
33. #16811323C22semidirect
34. #16811320C22semidirect
35. #16811316C22semidirect
36. #16811313C22semidirect
37. #16811304C22semidirect
38. #16811304C22semidirect
39. #16811293C22semidirect
40. #16811293C22semidirect
41. #16811293C22semidirect
42. #16811291C22semidirect
43. D4×Dic106C22semidirect
44. #16811281C22semidirect
45. #16811280C22semidirect
46. #16811279C22semidirect
47. #16811278C22semidirect
48. #16811273C22semidirect
49. #16811272C22semidirect
50. #16811272C22semidirect
51. #16811267C22semidirect
52. #16811267C22semidirect
53. #16811267C22semidirect
54. #16811267C22semidirect
55. #16811267C22semidirect
56. #16811267C22semidirect
57. #16811267C22semidirect
58. #16811240C22semidirect
59. #16811240C22semidirect
60. #16811238C22semidirect
61. #16811235C22semidirect
62. #16811227C22semidirect
63. #16811227C22semidirect
64. #16811227C22semidirect
65. #16811223C22semidirect
66. #16811218C22semidirect
67. #16811208C22semidirect
68. #16811208C22semidirect
69. #16811202C22semidirect
71. #16811194C22semidirect
72. #16811194C22semidirect
73. #16811193C22semidirect
74. #16811190C22semidirect
75. #16811190C22semidirect
76. #16811190C22semidirect
77. #16811188C22semidirect
78. #16811182C22semidirect
79. #16811180C22semidirect
80. #16811180C22semidirect
81. #16811178C22semidirect
82. #16811177C22semidirect
83. #16811176C22semidirect
84. #16811171C22semidirect
85. #16811171C22semidirect
86. #16811171C22semidirect
87. #16811171C22semidirect
88. #16811171C22semidirect
89. #16811171C22semidirect
90. #16811171C22semidirect
91. #16811170C22semidirect
93. #16811169C22semidirect
94. C2×#13133217C22semidirect
95. C4⋊Q8×D53C22semidirect
96. #16811160C22semidirect
97. #16811155C22semidirect
98. #16811155C22semidirect
99. #16811154C22semidirect
100. #16811154C22semidirect
101. #16811153C22semidirect
102. #16811152C22semidirect
103. #16811151C22semidirect
104. C2×#13133204C22semidirect
105. C2×#13133204C22semidirect
106. #16811135C22semidirect
107. #16811133C22semidirect
108. #16811132C22semidirect
110. #16811130C22semidirect
111. #16811129C22semidirect
112. C2×#13133198C22semidirect
113. C2×#13133188C22semidirect
114. #16811102C22semidirect
115. #16811100C22semidirect
116. #16811098C22semidirect
117. #16811098C22semidirect
118. #41×Dic53C22semidirect
119. C4×#11719945C22semidirect
120. C4×#11719945C22semidirect
121. C4×#11719947C22semidirect
122. C2×D4×Dic53C22semidirect
123. C2×C42×D53C22semidirect
125. C53×#550C22semidirect
127. D42×C53C22semidirect
129. C53×#535C22semidirect
131. C53×#532C22semidirect
133. C2×#127×C53C22semidirect
607. #3498D53semidirect
644. #550C2×D53semidirect
661. D42C2×D53semidirect
683. #535C2×D53semidirect
701. #532C2×D53semidirect
705. C2×#127C2×D53semidirect
735. C53#62836semidirect

Maximal subgroups

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

subgroupindex
#202892992
#202891822
#202890832
#202890362
#202887182
#202886672
#202886402
#202886162
#202886102
#202886012
#202885892
#202885032
#202884952
#202883712
#202883552
#202880102
#202880082
C2×#168111712
C53×#34982
#6283653