Finite Group Databasebeta

← #28291924

Subgroups — #28291924

Order 13568.

7270 conjugacy classes of subgroups.

The subgroup lattice has 1124 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289144C214yesmaximal, complemented
2#20289120C211yesmaximal, characteristic, complemented
3#20289115C212yesmaximal, complemented
4#20289100C214yesmaximal, complemented
5#20289090C214yesmaximal, complemented
6#20289073C214yesmaximal, complemented
7#20289060C212yesmaximal, complemented
8#20289049C212yesmaximal, complemented
9#20289027C218yesmaximal, complemented
10#20288856C214yesmaximal, complemented
11#20288342C212yesmaximal, complemented
12#20288324C212yesmaximal, complemented
13#20288276C214yesmaximal, complemented
14D4×#11719949C214yesmaximal, complemented
15#20288135C218yesmaximal, complemented
16#20288047C214yesmaximal, complemented
17#20288012C212yesmaximal, complemented
18#532×D53C211yesmaximal, characteristic, complemented
19C53×#3550C211yesmaximal, characteristic, complemented
20C22×#11719949C2214yescomplemented
21C2×#41×D53C2212yescomplemented
22#16811372C2218yescomplemented
23#16811371C2218yescomplemented
24#16811369C22116yescomplemented
25#16811365C2214yescomplemented
26#16811364C22116yescomplemented
27#16811363C2218yescomplemented
28#16811339C2218yescomplemented
29#16811339C2212yescomplemented
30#16811339C2218yescomplemented
31#16811338C2214yescomplemented
32#16811333C2214yescomplemented
33#16811333C2214yescomplemented
34#16811323C2218yescomplemented
35#16811317C2218yescomplemented
36#16811314C2218yescomplemented
37#16811307C2218yescomplemented
38#16811301C2218yescomplemented
39#16811298C22116yescomplemented
40#16811295C2218yescomplemented
41#16811295C2214yescomplemented
42#16811295C2214yescomplemented
43#16811284C2218yescomplemented
44#16811276C2218yescomplemented
45#16811276C2214yescomplemented
46#16811276C2214yescomplemented
47#16811266C2218yescomplemented
48#16811266C2218yescomplemented
49#16811264C22116yescomplemented
50#16811264C2218yescomplemented
51D4×D212C2218yescomplemented
52D4×D212C2214yescomplemented
53#16811258C2212yescomplemented
54#16811250C2218yescomplemented
55#16811245C2218yescomplemented
56#16811243C22116yescomplemented
57#16811228C2218yescomplemented
58#16811225C22116yescomplemented
59#16811224C2218yescomplemented
60#16811212C22116yescomplemented
61#16811207C22116yescomplemented
62#16811203C2218yescomplemented
63#16811203C2218yescomplemented
64#16811203C2218yescomplemented
65#16811198C2218yescomplemented
66#16811197C2214yescomplemented
67#16811192C2214yescomplemented
68#16811191C2218yescomplemented
69#16811191C2218yescomplemented
70#16811189C2218yescomplemented
71#16811187C2214yescomplemented
72#16811184C2218yescomplemented
73#16811184C2218yescomplemented
74#16811178C2212yescomplemented
75#16811178C2212yescomplemented
76#16811174C2212yes—
77#16811174C2212yescomplemented
78#16811174C2218yescomplemented
79#16811174C2211yescharacteristic, complemented
80#16811174C2218yescomplemented
81#16811173C2212yescomplemented
82#16811173C2211yescharacteristic, complemented
83#16811172C2218yescomplemented
84#16811172C2212yescomplemented
85#16811171C2211yescharacteristic
86#16811170C2214yescomplemented
87#16811169C2212yescomplemented
88#16811168C2214yescomplemented
89C4⋊Q8×D53C2211yescharacteristic, complemented
90#127×D53C2211yescharacteristic
91#16811160C2214yescomplemented
92#16811160C2214yescomplemented
93#16811159C2214yescomplemented
94#16811159C2214yescomplemented
95#16811158C2214yescomplemented
96#16811158C2214yescomplemented
97#16811156C22116yescomplemented
98#16811152C2218yescomplemented
99#124×D53C2212yescomplemented
100#16811136C2214yescomplemented
101#16811136C2214yescomplemented
102#16811136C2218yescomplemented
103#16811136C22116yescomplemented
104#16811135C2214yescomplemented
105#16811131C2218yescomplemented
106#16811131C2218yescomplemented
107#121×D53C2214yescomplemented
108C4×#11719949C2214yescomplemented
109C4×#11719949C2214yescomplemented
110C4×#11719949C2218yescomplemented
111#16811091C2214yescomplemented
112C4×D4×D53C2214yescomplemented
113C4×D4×D53C2218yescomplemented
114#117×D53C2214yescomplemented
115C2×C42×D53C2211yescharacteristic, complemented
116C53×#563C2214yescomplemented
117C53×#559C2212yescomplemented
118Q82×C53C2212yescomplemented
119C53×#556C2214yescomplemented
120D4×Q8×C53C2214yescomplemented
121C53×#542C2218yescomplemented
122C53×#536C2214yescomplemented
123C53×#533C2212yescomplemented
124C53×#532C2211yescharacteristic
125C2×#11719949—416no—
126C2×#11719949C2314yes—
127C2×#11719949C2318yes—
128C2×#11719949C2318yes—
129C2×#11719949C2314yes—
130C2×#11719949C2318yes—
131C2×#11719949C2318yes—
132C2×#11719949C2312yes—
133C2×#11719945C2314yes—
134C2×#11719945C2312yes—
135C2×#11719945C2314yes—
136C2×#11719947C2312yes—
137C2×#11719947C2314yes—
138#41×D53—48no—
139C2×Q8×D53C2312yes—
140C22×D212C2318yes—
141C22×D212C2314yes—
142C2×D4×D53C2314yes—
143C2×D4×D53C2318yes—
144C2×D4×D53C2314yes—
145C2×D4×D53C2312yes—
146C22×C4×D53C2311yescharacteristic
147C22×C4×D53C2314yes—
148C22×C4×D53C2312yes—
149C22×C4×D53C2318yes—
150#13133217C2311yescharacteristic
151#13133217C2312yes—
152#13133216C2314yes—
153#13133215C2312yes—
154#13133215C2318yes—
155#13133214C2311yescharacteristic
156#13133214C2318yes—
157#13133214C2318yes—
158#13133214C2312yes—
159#13133213C2312yes—
160#13133213C2314yes—
161#13133213C2318yes—
162#13133212C2318yes—
163#13133212C2318yes—
164#13133211C23116yes—
165#13133210C23116yes—
166#13133209C2318yes—
167#13133208C2314yes—
168#13133208C2314yes—
169#13133207C23116yes—
170#13133206C2314yes—
171#13133206C23116yes—
172#13133206C2312yes—
173#13133206C2318yes—
174#13133206C2318yes—
175#13133206C2314yes—
176#13133205C2314yes—
177#13133205C2312yes—
178#13133205C2318yes—
179#13133204C2312yes—
180#13133203C23116yes—
181#13133203C2318yes—
182#13133202C23116yes—
183#13133202C23116yes—
184#13133202C23116yes—
185#13133202C23116yes—
186#13133202C2318yes—
187#13133202C2318yes—
188#13133201C2318yes—
189#13133200C2318yes—
190#13133200C2318yes—
191#13133199C23116yes—
192#13133199C23116yes—
193#13133197C2314yes—
194#13133197C2314yes—
195#13133195C23116yes—
196#13133195C23116yes—
197#13133195C23116yes—
198#13133193C2314yes—
199#13133193C2318yes—
200#13133193C2318yes—
201#13133193C23116yes—
202#13133193C2314yes—
203#13133192C2314yes—
204#13133192C23116yes—
205#13133192C2318yes—
206#13133192C23116yes—
207#13133192C2314yes—
208#13133192C2318yes—
209#13133192C2318yes—
210#13133192C2314yes—
211#13133192C23116yes—
212#13133192C23116yes—
213#13133192C2314yes—
214#13133192C2314yes—
215#13133191C2318yes—
216#13133191C23116yes—
217#13133191C2314yes—
218#13133191C2314yes—
219#13133191C2314yes—
220#13133190C23116yes—
221#13133190C23116yes—
222#13133190C2318yes—
223#13133190C23116yes—
224#13133190C23116yes—
225#13133190C23116yes—
226#13133189C2318yes—
227#13133188C2314yes—
228#13133188C2318yes—
229#13133187C23116yes—
230#13133187C23116yes—
231#13133187C23116yes—
232#13133187C2318yes—
233#13133187C2318yes—
234#13133187C2318yes—
235#13133185C2318yes—
236#13133185C2318yes—
237Q8×Dic53C2314yes—
238Q8×Dic53C2314yes—
239#13133182C2314yes—
240#13133182C2314yes—
241C4×D212C2318yes—
242C4×D212C2318yes—
243C4×D212C2318yes—
244C4×D212C2318yes—
245C4×D212C2314yes—
246C4×D212C2314yes—
247C4×D212C23116yes—
248C4×D212C2314yes—
249D4×Dic53C2314yes—
250#13133179C2318yes—
251#13133179C2314yes—
252#13133179C2314yes—
253#13133179C2314yes—
254#13133179C2314yes—
255#13133179C2314yes—
256#13133179C2318yes—
257#13133179C23116yes—
258C4×C22⋊D53C23116yes—
259C4×C22⋊D53C2318yes—
260#13133177C23116yes—
261#13133177C2318yes—
262#13133177C2318yes—
263#13133177C2318yes—
264#13133176C2314yes—
265#13133175C23116yes—
266#13133175C2318yes—
267#13133175C2318yes—
268#13133175C2314yes—
269#13133175C2314yes—
270#13133175C2318yes—
271#13133174C2318yes—
272#13133174C2318yes—
273#13133173C2318yes—
274C4⋊C4×D53C2314yes—
275C4⋊C4×D53C2318yes—
276C4⋊C4×D53C2318yes—
277C22⋊C4×D53C23116yes—
278C22⋊C4×D53C2318yes—
279C22⋊C4×D53C2318yes—
280C2×C4×Dic53C2312yes—
281C2×C4×Dic53C2311yescharacteristic
282C42×D53C2312yes—
283C42×D53C2311yescharacteristic
284C42×D53C2311yescharacteristic
285C42×D53C2311yescharacteristic
286C42×D53C2311yescharacteristic
287C42×D53C2312yes—
288C42×D53C2318yes—
289C42×D53C2318yes—
290C2×#41×C53C2312yes—
291C22×Q8×C53C2314yes—
292C4⋊Q8×C53C2312yes—
293C4⋊Q8×C53C2312yes—
294C4⋊Q8×C53C2318yes—
295C4⋊Q8×C53C2311yescharacteristic
296C4⋊Q8×C53C2318yes—
297#127×C53C2311yescharacteristic
298#126×C53C23116yes—
299#125×C53C2314yes—
300#124×C53C2318yes—
301#124×C53C2312yes—
302#124×C53C2318yes—
303#123×C53C2318yes—
304#123×C53C2318yes—
305C22⋊Q8×C53C2318yes—
306C22⋊Q8×C53C23116yes—
307C22⋊Q8×C53C2314yes—
308C22⋊Q8×C53C2314yes—
309#121×C53C2314yes—
310C4×Q8×C53C2314yes—
311C4×Q8×C53C2314yes—
312C4×Q8×C53C2318yes—
313C4×D4×C53C2314yes—
314C4×D4×C53C2318yes—
315#117×C53C2314yes—
316#117×C53C2314yes—
317C2×C42×C53C2311yescharacteristic
318C23×D53C2414yes—
319C23×D53C2411yescharacteristic
320C23×D53C2418yes—
321#41×C53—44no—
322C2×Q8×C53—48no—
323C2×Q8×C53C2414yes—
324C2×Q8×C53C2414yes—
325C2×Q8×C53C2418yes—
326C2×Q8×C53C2412yes—
327C2×D4×C53C2414yes—
328C2×D4×C53C2414yes—
329C2×D4×C53C2412yes—
330C22×C4×C53C2412yes—
331C22×C4×C53C2411yescharacteristic
332C22×C4×C53C2414yes—
333C22×C4×C53C2418yes—
334C2×C22⋊D53C2418yes—
335C2×C22⋊D53C24116yes—
336C2×C22⋊D53C2418yes—
337C2×C22⋊D53C2414yes—
338C2×C22⋊D53C2414yes—
339C2×C22⋊D53C2414yes—
340C22×Dic53C2411yescharacteristic
341C22×Dic53C2414yes—
342C22×Dic53C2412yes—
343#11719949—216no—
344#11719949—44no—
345#11719949—416no—
346#11719949—416no—
347#11719949—416no—
348#11719949—48no—
349#11719949—416no—
350Q8×D53—44no—
351#11719947—44no—
352#11719947—48no—
353D4×D53—48no—
354D4×D53—416no—
355D4×D53—44no—
356D4×D53—48no—
357#11719945—48no—
358#11719945—44no—
359#11719945—48no—
360C2×D212—48no—
361C2×D212—416no—
362C2×D212C2414yes—
363C2×D212C2414yes—
364C2×D212C2418yes—
365C2×D212C2414yes—
366C2×D212C2414yes—
367C2×D212C2418yes—
368C2×D212C24116yes—
369C2×D212C2418yes—
370C2×D212C24116yes—
371C2×D212C2414yes—
372C2×D212C2412yes—
373C2×C4×D53—24no—
374C2×C4×D53—216no—
375C2×C4×D53—416no—
376C2×C4×D53—44no—
377C2×C4×D53C2412yes—
378C2×C4×D53C2412yes—
379C2×C4×D53C2414yes—
380C2×C4×D53C2411yescharacteristic
381C2×C4×D53C2411yescharacteristic
382C2×C4×D53C2411yescharacteristic
383C2×C4×D53C2418yes—
384C2×C4×D53C2418yes—
385C2×C4×D53C2414yes—
386C2×C4×D53C2414yes—
387C2×C4×D53C2412yes—
388C2×C4×D53C2412yes—
389C2×C4×D53C2418yes—
390C2×C4×D53C24116yes—
391C2×C4×D53C24116yes—
392C2×C4×D53C2411yescharacteristic
393C2×Dic106C2414yes—
394C2×Dic106C2412yes—
395C2×Dic106C2414yes—
396C4⋊C4×C53C2414yes—
397C4⋊C4×C53C2414yes—
398C4⋊C4×C53C2414yes—
399C4⋊C4×C53C2414yes—
400C4⋊C4×C53C2414yes—
401C4⋊C4×C53C2418yes—
402C4⋊C4×C53C24116yes—
403C4⋊C4×C53C2418yes—
404C22⋊C4×C53C2418yes—
405C22⋊C4×C53C2418yes—
406C22⋊C4×C53C2418yes—
407C22⋊C4×C53C24116yes—
408C42×C53C2412yes—
409C42×C53C2411yescharacteristic
410C42×C53C2411yescharacteristic
411C42×C53C2418yes—
412C42×C53C2418yes—
413C22⋊Dic53C2418yes—
414C22⋊Dic53C2418yes—
415#11719921C2418yes—
416#11719921C2418yes—
417#11719921C2418yes—
418#11719921C24116yes—
419#11719921C2418yes—
420#11719921C2418yes—
421#11719921C2418yes—
422#11719921C2418yes—
423#11719921C24116yes—
424#11719921C2418yes—
425#11719921C2418yes—
426#11719921C2418yes—
427#11719921C24116yes—
428C4⋊Dic53C2414yes—
429C4⋊Dic53C2414yes—
430C4⋊Dic53C2414yes—
431C4⋊Dic53C2418yes—
432C4⋊Dic53C2418yes—
433#11719919C24116yes—
434#11719919C2418yes—
435#11719919C24116yes—
436#11719919C2418yes—
437#11719919C2418yes—
438C4×Dic53C2412yes—
439C4×Dic53C2418yes—
440C4×Dic53C2412yes—
441C4×Dic53C2411yescharacteristic
442C4×Dic53C2412yes—
443C4×Dic53C2412yes—
444C4×Dic53C2412yes—
445C4×Dic53C2411yescharacteristic
446C4×Dic53C2418yes—
447C4×Dic53C2418yes—
448C23×C53C2511yescharacteristic
449C23×C53C2514yes—
450C22×D53—22no—
451C22×D53—28no—
452C22×D53—42no—
453C22×D53—48no—
454C22×D53—48no—
455C22×D53—416no—
456C22×D53C2514yes—
457C22×D53C2511yescharacteristic
458C22×D53C2518yes—
459C22×D53C2511yescharacteristic
460Q8×C53—28no—
461Q8×C53—28no—
462Q8×C53—42no—
463Q8×C53—48no—
464D4×C53—28no—
465D4×C53—42no—
466D4×C53—44no—
467C2×C4×C53—28no—
468C2×C4×C53—22no—
469C2×C4×C53—24no—
470C2×C4×C53—48no—
471C2×C4×C53C2511yescharacteristic
472C2×C4×C53C2512yes—
473C2×C4×C53C2514yes—
474C2×C4×C53C2518yes—
475C2×C4×C53C2518yes—
476C2×C4×C53C2511yescharacteristic
477C2×C4×C53C2512yes—
478C22⋊D53—44no—
479C22⋊D53—44no—
480C22⋊D53—44no—
481C22⋊D53—48no—
482C22⋊D53—416no—
483C22⋊D53—48no—
484C2×Dic53—28no—
485C2×Dic53—22no—
486C2×Dic53—42no—
487C2×Dic53C2511yescharacteristic
488C2×Dic53C2514yes—
489C2×Dic53C2518yes—
490C2×Dic53C2512yes—
491C2×Dic53C2512yes—
492C2×Dic53C2511yescharacteristic
493D212—216no—
494D212—28no—
495D212—28no—
496D212—28no—
497D212—48no—
498D212—416no—
499D212—44no—
500D212—42no—
501D212—44no—
502D212—48no—
503D212—416no—
504C4×D53—22no—
505C4×D53—28no—
506C4×D53—22no—
507C4×D53—28no—
508C4×D53—24no—
509C4×D53—24no—
510C4×D53—216no—
511C4×D53—22no—
512C4×D53—28no—
513C4×D53—216no—
514C4×D53—42no—
515C4×D53—42no—
516C4×D53—416no—
517C4×D53—416no—
518C4×D53—48no—
519C4×D53H(5,𝔽2)14yes—
520Dic106—44no—
521Dic106—44no—
522Dic106—42no—
523#62759—531nomaximal, Sylow
524C22×C53—21no—
525C22×C53—24no—
526C22×C53—22no—
527C22×C53—28no—
528C22×C53C2611yescharacteristic
529C2×D53—22no—
530C2×D53—24no—
531C2×D53—21no—
532C2×D53—28no—
533C2×D53—22no—
534C2×D53—28no—
535C2×D53—28no—
536C2×D53—28no—
537C2×D53—44no—
538C2×D53—88no—
539C2×D53—816no—
540C2×D53C2×H(5,𝔽2)12yes—
541C4×C53—21no—
542C4×C53—24no—
543C4×C53—28no—
544C4×C53—22no—
545C4×C53—28no—
546C4×C53C2×H(5,𝔽2)12yes—
547C4×C53#58514yes—
548Dic53—21no—
549Dic53—24no—
550Dic53—28no—
551Dic53—22no—
552Dic53—22no—
553Dic53C2×H(5,𝔽2)12yes—
554#3551—534no—
555#3550D5311yescharacteristic, complemented
556#3549—531no—
557#3548—532no—
558#3547—534no—
559#3546—534no—
560#3545—534no—
561#3544—532no—
562#3543—532no—
563#3542—538no—
564#3529—534no—
565#3483—532no—
566#3481—532no—
567#3475—534no—
568D4×#41—534no—
569#3460—538no—
570#3449—534no—
571#3444—532no—
572C2×#532—531no—
573C2×C53—41no—
574C2×C53—44no—
575C2×C53C22×H(5,𝔽2)11yescharacteristic
576C2×C53C2×#58512yes—
577D53—22no—
578D53—41no—
579D53—44no—
580D53—48no—
581C22×#41—532no—
582C22×#41—534no—
583#563—538no—
584#563C2×D5314yescomplemented
585#562—538no—
586#562—5316no—
587H(3,𝔽4)—534no—
588#560—5316no—
589#560—538no—
590#559C2×D5312yescomplemented
591Q82C2×D5312yescomplemented
592#556C2×D5314yescomplemented
593#555—538no—
594#555—532no—
595#555—538no—
596#555—534no—
597#554—534no—
598#554—534no—
599#553—538no—
600#553—538no—
601#552—538no—
602#552—538no—
603#551—5316no—
604#551—538no—
605#550—534no—
606#550—538no—
607#550—534no—
608D4×Q8C2×D5314yescomplemented
609#548—538no—
610#547—538no—
611#547—534no—
612#547—534no—
613#546—538no—
614#546—538no—
615#546—5316no—
616#546—538no—
617D42—532no—
618D42—538no—
619D42—534no—
620#544—538no—
621#542—5316no—
622#542—538no—
623#542C2×D5318yescomplemented
624#540—5316no—
625#540—538no—
626#540—538no—
627#538—5316no—
628#538—5316no—
629#537—538no—
630#537—538no—
631#537—538no—
632#536—534no—
633#536—538no—
634#536C2×D5314yescomplemented
635#535—534no—
636#535—538no—
637#535—538no—
638#535—538no—
639#535—534no—
640#534—538no—
641#534—538no—
642#533—532no—
643#533—532no—
644#533C2×D5312yescomplemented
645#532—532no—
646#532—531no—
647#532—532no—
648#532—532no—
649#532—538no—
650#532—538no—
651#532—531no—
652#532—532no—
653#532—538no—
654#532—534no—
655#532—534no—
656#532—531no—
657#532—532no—
658#532C2×D5311yescharacteristic
659C2×C4⋊Q8—531no—
660C2×#127—531no—
661#529—5316no—
662#529—534no—
663#529—534no—
664#529—538no—
665#529—534no—
666#529—534no—
667#529—534no—
668#529—534no—
669C2×#124—532no—
670#525—538no—
671#525—538no—
672#525—534no—
673#525—534no—
674#525—538no—
675#525—5316no—
676#525—534no—
677C2×#121—534no—
678C4×#41—534no—
679C4×#41—534no—
680C4×#41—538no—
681C4×#41—534no—
682C2×C4×D4—534no—
683C2×C4×D4—538no—
684C2×#117—534no—
685C22×C42—531no—
686C53#6275911yescharacteristic, complemented, Sylow
687C2×#41—534no—
688C2×#41—534no—
689C2×#41—538no—
690C2×#41—538no—
691C2×#41—532no—
692C2×#41—538no—
693C2×#41—538no—
694C2×#41—532no—
695C2×#41—534no—
696C2×#41—534no—
697C2×#41—534no—
698C2×#41—532no—
699C2×#41—2128no—
700C2×#41—21216no—
701C2×#41C22×D5312yes—
702C22×Q8—532no—
703C22×Q8C22×D5314yes—
704C22×D4—534no—
705C22×D4—538no—
706C22×D4—534no—
707C22×D4—532no—
708C22×D4—538no—
709C22×D4—534no—
710C23×C4—534no—
711C23×C4—531no—
712C23×C4—538no—
713C23×C4—532no—
714C4⋊Q8—532no—
715C4⋊Q8—538no—
716C4⋊Q8—534no—
717C4⋊Q8—531no—
718C4⋊Q8—532no—
719C4⋊Q8C22×D5311yescharacteristic
720C4⋊Q8C22×D5312yes—
721C4⋊Q8C22×D5312yes—
722C4⋊Q8C22×D5318yes—
723C4⋊Q8C22×D5318yes—
724#127—534no—
725#127—532no—
726#127—538no—
727#127—531no—
728#127—532no—
729#127—538no—
730#127—538no—
731#127C22×D5311yescharacteristic
732#126—538no—
733#126—538no—
734#126—5316no—
735#126—5316no—
736#126C22×D53116yes—
737#125—534no—
738#125—534no—
739#125—5316no—
740#125—538no—
741#125C22×D5314yes—
742#124—532no—
743#124—534no—
744#124—534no—
745#124—538no—
746#124—538no—
747#124—5316no—
748#124—532no—
749#124—538no—
750#124—5316no—
751#124—532no—
752#124—534no—
753#124—538no—
754#124C22×D5312yes—
755#124C22×D5318yes—
756#124C22×D5318yes—
757#123—538no—
758#123—538no—
759#123—538no—
760#123—538no—
761#123—5316no—
762#123—5316no—
763#123—5316no—
764#123—5316no—
765#123—538no—
766#123—5316no—
767#123—5316no—
768#123C22×D5318yes—
769#123C22×D5318yes—
770C22⋊Q8—534no—
771C22⋊Q8—534no—
772C22⋊Q8—538no—
773C22⋊Q8—5316no—
774C22⋊Q8—538no—
775C22⋊Q8—534no—
776C22⋊Q8—534no—
777C22⋊Q8—5316no—
778C22⋊Q8—5316no—
779C22⋊Q8—5316no—
780C22⋊Q8C22×D5314yes—
781C22⋊Q8C22×D5314yes—
782C22⋊Q8C22×D5318yes—
783C22⋊Q8C22×D53116yes—
784#121—538no—
785#121—534no—
786#121—538no—
787#121—534no—
788#121—534no—
789#121—534no—
790#121—538no—
791#121—5316no—
792#121—534no—
793#121—534no—
794#121—534no—
795#121—534no—
796#121—534no—
797#121—538no—
798#121—5316no—
799#121—5316no—
800#121—5316no—
801#121—538no—
802#121—538no—
803#121—5316no—
804#121—538no—
805#121—5316no—
806#121—5316no—
807#121—5316no—
808#121—5316no—
809#121—5316no—
810#121C22×D5314yes—
811#120—538no—
812#120—538no—
813#120—538no—
814#120—538no—
815#120—5316no—
816#120—538no—
817#120—5316no—
818#120—5316no—
819C4×Q8—534no—
820C4×Q8—534no—
821C4×Q8—534no—
822C4×Q8—534no—
823C4×Q8C22×D5314yes—
824C4×Q8C22×D5314yes—
825C4×Q8C22×D5318yes—
826C4×D4—534no—
827C4×D4—538no—
828C4×D4—5316no—
829C4×D4—534no—
830C4×D4—534no—
831C4×D4—534no—
832C4×D4—538no—
833C4×D4—5316no—
834C4×D4—538no—
835C4×D4—534no—
836C4×D4—534no—
837C4×D4—5316no—
838C4×D4—538no—
839C4×D4—538no—
840C4×D4—538no—
841C4×D4—534no—
842C4×D4—538no—
843C4×D4—538no—
844C4×D4—538no—
845C4×D4—534no—
846C4×D4—534no—
847C4×D4—5316no—
848C4×D4—538no—
849C4×D4C22×D5314yes—
850C4×D4C22×D5318yes—
851#117—534no—
852#117—534no—
853#117—538no—
854#117—534no—
855#117—538no—
856#117—538no—
857#117—5316no—
858#117—538no—
859#117—538no—
860#117—538no—
861#117C22×D5314yes—
862#117C22×D5314yes—
863C2×C4⋊C4—538no—
864C2×C4⋊C4—534no—
865C2×C4⋊C4—538no—
866C2×C22⋊C4—538no—
867C2×C22⋊C4—538no—
868C2×C22⋊C4—5316no—
869C2×C42—532no—
870C2×C42—531no—
871C2×C42—538no—
872C2×C42—532no—
873C2×C42—538no—
874C2×C42—531no—
875C2×C42—531no—
876C2×C42—531no—
877C2×C42—531no—
878C2×C42—532no—
879C2×C42C22×D5311yescharacteristic
880C24—534no—
881C24—531no—
882C24—538no—
883#41—44no—
884#41—10616no—
885#41—2128no—
886#41—2128no—
887#41—2124no—
888#41—2124no—
889#41—2128no—
890#41—2124no—
891#41—21216no—
892#41—21216no—
893#41—2128no—
894#41—21216no—
895#41—21216no—
896C2×Q8—48no—
897C2×Q8—534no—
898C2×Q8—532no—
899C2×Q8—534no—
900C2×Q8—2124no—
901C2×Q8C23×D5314yes—
902C2×Q8C23×D5314yes—
903C2×Q8C23×D5318yes—
904C2×Q8C23×D5312yes—
905C2×D4—5316no—
906C2×D4—538no—
907C2×D4—538no—
908C2×D4—534no—
909C2×D4—534no—
910C2×D4—534no—
911C2×D4—534no—
912C2×D4—534no—
913C2×D4—538no—
914C2×D4—534no—
915C2×D4—534no—
916C2×D4—538no—
917C2×D4—5316no—
918C2×D4—538no—
919C2×D4—5316no—
920C2×D4—532no—
921C2×D4—534no—
922C2×D4—2128no—
923C2×D4—21216no—
924C2×D4—2128no—
925C2×D4—21216no—
926C2×D4—2124no—
927C2×D4—2128no—
928C2×D4C23×D5314yes—
929C2×D4C23×D5312yes—
930C2×D4C23×D5314yes—
931C22×C4—531no—
932C22×C4—531no—
933C22×C4—534no—
934C22×C4—532no—
935C22×C4—532no—
936C22×C4—532no—
937C22×C4—531no—
938C22×C4—534no—
939C22×C4—531no—
940C22×C4—531no—
941C22×C4—538no—
942C22×C4—538no—
943C22×C4—534no—
944C22×C4—534no—
945C22×C4—532no—
946C22×C4—532no—
947C22×C4—538no—
948C22×C4—5316no—
949C22×C4—5316no—
950C22×C4—10616no—
951C22×C4—1064no—
952C22×C4—2124no—
953C22×C4—21216no—
954C22×C4C23×D5312yes—
955C22×C4C23×D5311yescharacteristic
956C22×C4C23×D5314yes—
957C22×C4C23×D5318yes—
958C4⋊C4—534no—
959C4⋊C4—534no—
960C4⋊C4—5316no—
961C4⋊C4—538no—
962C4⋊C4—5316no—
963C4⋊C4—534no—
964C4⋊C4—538no—
965C4⋊C4—538no—
966C4⋊C4—538no—
967C4⋊C4—538no—
968C4⋊C4C23×D5314yes—
969C4⋊C4C23×D5314yes—
970C4⋊C4C23×D5314yes—
971C4⋊C4C23×D5318yes—
972C4⋊C4C23×D5318yes—
973C4⋊C4C23×D53116yes—
974C4⋊C4C23×D5314yes—
975C4⋊C4C23×D5314yes—
976C22⋊C4—538no—
977C22⋊C4—538no—
978C22⋊C4—538no—
979C22⋊C4—538no—
980C22⋊C4—538no—
981C22⋊C4—5316no—
982C22⋊C4—538no—
983C22⋊C4—538no—
984C22⋊C4—538no—
985C22⋊C4—5316no—
986C22⋊C4—538no—
987C22⋊C4—538no—
988C22⋊C4—538no—
989C22⋊C4—538no—
990C22⋊C4—5316no—
991C22⋊C4C23×D5318yes—
992C22⋊C4C23×D53116yes—
993C22⋊C4C23×D5318yes—
994C22⋊C4C23×D5318yes—
995C42—532no—
996C42—531no—
997C42—538no—
998C42—532no—
999C42—532no—
1000C42—532no—
1001C42—532no—
1002C42—531no—
1003C42—538no—
1004C42—538no—
1005C42C23×D5312yes—
1006C42C23×D5311yescharacteristic
1007C42C23×D5311yescharacteristic
1008C42C23×D5318yes—
1009C42C23×D5318yes—
1010C23—531no—
1011C23—538no—
1012C23—531no—
1013C23—534no—
1014C23—1068no—
1015C23—1062no—
1016C23—2128no—
1017C23—2128no—
1018C23—21216no—
1019C23—2122no—
1020C23C24×D5314yes—
1021C23C24×D5311yescharacteristic
1022Q8—28no—
1023Q8—28no—
1024Q8—48no—
1025Q8—42no—
1026Q8—2122no—
1027Q8—2124no—
1028Q8—2124no—
1029D4—28no—
1030D4—42no—
1031D4—44no—
1032D4—10616no—
1033D4—1068no—
1034D4—1068no—
1035D4—1068no—
1036D4—2122no—
1037D4—2124no—
1038D4—2128no—
1039D4—21216no—
1040D4—2124no—
1041D4—2128no—
1042D4—21216no—
1043D4—2128no—
1044D4—21216no—
1045D4—2124no—
1046D4—2124no—
1047D4—2124no—
1048D4—2128no—
1049C2×C4—28no—
1050C2×C4—22no—
1051C2×C4—24no—
1052C2×C4—48no—
1053C2×C4—531no—
1054C2×C4—534no—
1055C2×C4—532no—
1056C2×C4—538no—
1057C2×C4—532no—
1058C2×C4—531no—
1059C2×C4—534no—
1060C2×C4—1062no—
1061C2×C4—1068no—
1062C2×C4—10616no—
1063C2×C4—1062no—
1064C2×C4—1068no—
1065C2×C4—1068no—
1066C2×C4—1062no—
1067C2×C4—1068no—
1068C2×C4—1062no—
1069C2×C4—1064no—
1070C2×C4—1064no—
1071C2×C4—10616no—
1072C2×C4—2122no—
1073C2×C4—2122no—
1074C2×C4—21216no—
1075C2×C4—2128no—
1076C2×C4—21216no—
1077C2×C4—2122no—
1078C2×C4C24×D5312yes—
1079C2×C4C24×D5311yescharacteristic
1080C2×C4C24×D5314yes—
1081C2×C4C24×D5318yes—
1082C2×C4C24×D5318yes—
1083C2×C4C24×D5311yescharacteristic
1084C2×C4C24×D5312yes—
1085C22—24no—
1086C22—21no—
1087C22—22no—
1088C22—28no—
1089C22—532no—
1090C22—1062no—
1091C22—1064no—
1092C22—1061no—
1093C22—1068no—
1094C22—1062no—
1095C22—1068no—
1096C22—1068no—
1097C22—1068no—
1098C22—4248no—
1099C22—42416no—
1100C22—2124no—
1101C22C25×D5311yescharacteristic
1102C4—21no—
1103C4—24no—
1104C4—28no—
1105C4—22no—
1106C4—28no—
1107C4—532no—
1108C4—1064no—
1109C4—1061no—
1110C4—1062no—
1111C4—1062no—
1112C4—1068no—
1113C4H(5,𝔽2)×D5312yes—
1114C4#1681146014yes—
1115C2—44no—
1116C2—41no—
1117C2—1062no—
1118C2—2128no—
1119C2—2124no—
1120C2—2121no—
1121C2C2×H(5,𝔽2)×D5311yescharacteristic
1122C2C2×#1681146012yes—
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3550C2
hypercenter#3550D53
hypocenterC53#62759
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3550

Complements

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

NH ≅ G/Ntype
1. #20289144C2semidirect
2. #20289120C2semidirect
3. #20289115C2semidirect
4. #20289100C2semidirect
5. #20289090C2semidirect
6. #20289073C2semidirect
7. #20289060C2semidirect
8. #20289049C2semidirect
9. #20289027C2semidirect
10. #20288856C2semidirect
11. #20288342C2semidirect
12. #20288324C2semidirect
13. #20288276C2semidirect
14. D4×#11719949C2semidirect
15. #20288135C2semidirect
16. #20288047C2semidirect
17. #20288012C2semidirect
18. #532×D53C2semidirect
19. C53×#3550C2semidirect
20. C22×#11719949C22semidirect
21. C2×#41×D53C22semidirect
22. #16811372C22semidirect
23. #16811371C22semidirect
24. #16811369C22semidirect
25. #16811365C22semidirect
26. #16811364C22semidirect
27. #16811363C22semidirect
28. #16811339C22semidirect
29. #16811339C22semidirect
30. #16811339C22semidirect
31. #16811338C22semidirect
32. #16811333C22semidirect
33. #16811333C22semidirect
34. #16811323C22semidirect
35. #16811317C22semidirect
36. #16811314C22semidirect
37. #16811307C22semidirect
38. #16811301C22semidirect
39. #16811298C22semidirect
40. #16811295C22semidirect
41. #16811295C22semidirect
42. #16811295C22semidirect
43. #16811284C22semidirect
44. #16811276C22semidirect
45. #16811276C22semidirect
46. #16811276C22semidirect
47. #16811266C22semidirect
48. #16811266C22semidirect
49. #16811264C22semidirect
50. #16811264C22semidirect
51. D4×D212C22semidirect
52. D4×D212C22semidirect
53. #16811258C22semidirect
54. #16811250C22semidirect
55. #16811245C22semidirect
56. #16811243C22semidirect
57. #16811228C22semidirect
58. #16811225C22semidirect
59. #16811224C22semidirect
60. #16811212C22semidirect
61. #16811207C22semidirect
62. #16811203C22semidirect
63. #16811203C22semidirect
64. #16811203C22semidirect
65. #16811198C22semidirect
66. #16811197C22semidirect
67. #16811192C22semidirect
68. #16811191C22semidirect
69. #16811191C22semidirect
70. #16811189C22semidirect
71. #16811187C22semidirect
72. #16811184C22semidirect
73. #16811184C22semidirect
74. #16811178C22semidirect
75. #16811178C22semidirect
77. #16811174C22semidirect
78. #16811174C22semidirect
79. #16811174C22semidirect
80. #16811174C22semidirect
81. #16811173C22semidirect
82. #16811173C22semidirect
83. #16811172C22semidirect
84. #16811172C22semidirect
86. #16811170C22semidirect
87. #16811169C22semidirect
88. #16811168C22semidirect
89. C4⋊Q8×D53C22semidirect
91. #16811160C22semidirect
92. #16811160C22semidirect
93. #16811159C22semidirect
94. #16811159C22semidirect
95. #16811158C22semidirect
96. #16811158C22semidirect
97. #16811156C22semidirect
98. #16811152C22semidirect
99. #124×D53C22semidirect
100. #16811136C22semidirect
101. #16811136C22semidirect
102. #16811136C22semidirect
103. #16811136C22semidirect
104. #16811135C22semidirect
105. #16811131C22semidirect
106. #16811131C22semidirect
107. #121×D53C22semidirect
108. C4×#11719949C22semidirect
109. C4×#11719949C22semidirect
110. C4×#11719949C22semidirect
111. #16811091C22semidirect
112. C4×D4×D53C22semidirect
113. C4×D4×D53C22semidirect
114. #117×D53C22semidirect
115. C2×C42×D53C22semidirect
116. C53×#563C22semidirect
117. C53×#559C22semidirect
118. Q82×C53C22semidirect
119. C53×#556C22semidirect
120. D4×Q8×C53C22semidirect
121. C53×#542C22semidirect
122. C53×#536C22semidirect
123. C53×#533C22semidirect
555. #3550D53semidirect
584. #563C2×D53semidirect
590. #559C2×D53semidirect
591. Q82C2×D53semidirect
592. #556C2×D53semidirect
608. D4×Q8C2×D53semidirect
623. #542C2×D53semidirect
634. #536C2×D53semidirect
644. #533C2×D53semidirect
686. C53#62759semidirect

Maximal subgroups

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

subgroupindex
#202891442
#202891202
#202891152
#202891002
#202890902
#202890732
#202890602
#202890492
#202890272
#202888562
#202883422
#202883242
#202882762
D4×#117199492
#202881352
#202880472
#202880122
#532×D532
C53×#35502
#6275953