Finite Group Databasebeta

← #28292487

Subgroups — #28292487

Order 13568.

7856 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288801C212yesmaximal, complemented
2#20288748C216yesmaximal, complemented
3#20288722C212yesmaximal, complemented
4#20288677C216yesmaximal, complemented
5#20288628C213yesmaximal, complemented
6#20288592C213yesmaximal, complemented
7#20288493C211yesmaximal, characteristic, complemented
8#20288453C216yesmaximal, complemented
9#20288385C212yesmaximal, complemented
10#20288342C212yesmaximal, complemented
11#20288326C216yesmaximal, complemented
12#20288315C212yesmaximal, complemented
13D4×#11719949C216yesmaximal, complemented
14#20288138C216yesmaximal, complemented
15#20288012C213yesmaximal, complemented
16C2×#16811174C213yesmaximal, complemented
17#20287921C212yesmaximal, complemented
18C4×#41×D53C211yesmaximal, characteristic, complemented
19C53×#3503C211yesmaximal, characteristic, complemented
20C2×#13133263C2212yes—
21C22×#11719949C2216yescomplemented
22C2×#41×D53C2211yescharacteristic
23#16811358C2216yescomplemented
24#16811358C2216yescomplemented
25#16811347C2216yescomplemented
26#16811339C2216yescomplemented
27#16811339C22112yescomplemented
28#16811334C2216yescomplemented
29#16811326C22112yescomplemented
30#16811326C22112yescomplemented
31#16811321C22112yescomplemented
32#16811300C22124yescomplemented
33#16811295C2212yescomplemented
34#16811295C2212yescomplemented
35#16811295C2216yescomplemented
36#16811295C2216yescomplemented
37#16811295C2214yescomplemented
38#16811285C2214yescomplemented
39#16811284C22112yescomplemented
40#16811276C22112yescomplemented
41#16811276C2216yescomplemented
42#16811268C22112yescomplemented
43#16811264C22112yescomplemented
44#16811264C22112yescomplemented
45#16811264C22124yescomplemented
46D4×D212C2216yescomplemented
47D4×D212C22112yescomplemented
48D4×D212C2216yescomplemented
49#16811247C22112yescomplemented
50#16811247C22112yescomplemented
51#16811229C22112yescomplemented
52#16811229C22112yescomplemented
53#16811213C22124yescomplemented
54#16811204C2216yescomplemented
55#16811192C2216yescomplemented
56#16811192C2216yescomplemented
57#16811178C2211yescharacteristic, complemented
58#16811178C2213yescomplemented
59#16811174C2213yescomplemented
60#16811174C2213yescomplemented
61#16811174C2216yescomplemented
62#16811174C2216yescomplemented
63#16811174C2216yescomplemented
64#16811174C2216yescomplemented
65#16811174C22112yescomplemented
66#16811174C2216yescomplemented
67#16811174C2216yescomplemented
68#16811174C2216yescomplemented
69#16811173C2213yescomplemented
70C2×#13133214C2213yescomplemented
71#16811160C2216yescomplemented
72#16811160C2216yescomplemented
73#16811159C2216yescomplemented
74#16811159C2216yescomplemented
75#16811158C2216yescomplemented
76#16811158C2216yescomplemented
77#16811158C22112yescomplemented
78C2×#13133206C2216yescomplemented
79#16811136C2216yescomplemented
80#16811136C2216yescomplemented
81#16811136C22124yescomplemented
82#16811135C2216yescomplemented
83C2×#13133192C2216yescomplemented
84C2×#13133192C2216yescomplemented
85#16811105C2214yescomplemented
86#16811104C2216yescomplemented
87#16811097C2216yescomplemented
88#16811095C22112yescomplemented
89#41×Dic53C2211yescharacteristic
90C4×#11719949C2216yescomplemented
91C4×#11719949C2216yescomplemented
92C4×#11719949C2214yescomplemented
93C4×#11719949C2211yescharacteristic, complemented
94C4×#11719949C2211yescharacteristic, complemented
95C4×#11719945C2213yescomplemented
96#16811091C2216yescomplemented
97#16811091C2213yescomplemented
98C4×#11719947C2213yescomplemented
99C4×#11719947C2213yescomplemented
100C4×Q8×D53C2211yescharacteristic, complemented
101C4×Q8×D53C2211yescharacteristic, complemented
102C2×#13133179C2216yescomplemented
103C2×#13133179C2216yescomplemented
104C4×D4×D53C22112yescomplemented
105C4×D4×D53C2213yescomplemented
106C4×D4×D53C2213yescomplemented
107#117×D53C2213yescomplemented
108C2×C42×D53C2213yescomplemented
109Q82×C53C2212yescomplemented
110C53×#557C2212yescomplemented
111C53×#554C2216yescomplemented
112D4×Q8×C53C2216yescomplemented
113C53×#544C2216yescomplemented
114C53×#533C2213yescomplemented
115C2×C4⋊Q8×C53C2213yescomplemented
116C53×#520C2212yes—
117C4×#41×C53C2211yescharacteristic
118#13133263—216no—
119C2×#11719949—424no—
120C2×#11719949C2314yes—
121C2×#11719949C2311yescharacteristic
122C2×#11719949C2316yes—
123C2×#11719949C23112yes—
124C2×#11719949C2316yes—
125C2×#11719949C23112yes—
126C2×#11719949C23112yes—
127C2×#11719945C2313yes—
128C2×#11719945C2316yes—
129C2×#11719947C2313yes—
130#41×D53—28no—
131C2×Q8×D53C2311yescharacteristic
132C22×D212C2316yes—
133C22×D212C2316yes—
134C22×D212C23112yes—
135C22×D212C2316yes—
136C2×D4×D53C23112yes—
137C2×D4×D53C2313yes—
138C22×C4×D53C2313yes—
139C22×C4×D53C2313yes—
140C22×C4×D53C2313yes—
141C22×C4×D53C23112yes—
142#13133217C2311yescharacteristic
143#13133214C23112yes—
144#13133214C2316yes—
145#13133214C2316yes—
146#13133214C2313yes—
147#13133214C2316yes—
148#13133212C23112yes—
149#13133212C23124yes—
150#13133212C23112yes—
151#13133208C2316yes—
152#13133208C2312yes—
153#13133206C2316yes—
154#13133206C23124yes—
155#13133206C23112yes—
156#13133206C23112yes—
157#13133206C2316yes—
158#13133206C23112yes—
159#13133205C23112yes—
160#13133205C2316yes—
161#13133202C23112yes—
162#13133202C23124yes—
163#13133202C23124yes—
164#13133202C23124yes—
165#13133202C23112yes—
166#13133201C23112yes—
167#13133197C23112yes—
168#13133197C2312yes—
169#13133197C2316yes—
170#13133193C2316yes—
171#13133193C23124yes—
172#13133193C2312yes—
173#13133192C2316yes—
174#13133192C23124yes—
175#13133192C23124yes—
176#13133192C23112yes—
177#13133192C23112yes—
178#13133192C23112yes—
179#13133192C23112yes—
180#13133192C23112yes—
181#13133192C23112yes—
182#13133192C23112yes—
183#13133192C2316yes—
184#13133192C2316yes—
185#13133192C23112yes—
186#13133192C23112yes—
187#13133192C2316yes—
188#13133191C23124yes—
189#13133191C2316yes—
190#13133191C2316yes—
191#13133187C23124yes—
192#13133187C23112yes—
193#13133187C23124yes—
194Q8×Dic53C2316yes—
195Q8×Dic53C2311yescharacteristic
196Q8×Dic53C2311yescharacteristic
197Q8×Dic53C2312yes—
198C4×Dic106C2313yes—
199C4×Dic106C2313yes—
200#13133182C2313yes—
201#13133182C2313yes—
202#13133182C2312yes—
203#13133182C2316yes—
204C4×D212C23112yes—
205C4×D212C2313yes—
206C4×D212C23112yes—
207C4×D212C23112yes—
208C4×D212C2316yes—
209C4×D212C2313yes—
210C4×D212C23112yes—
211C4×D212C2316yes—
212D4×Dic53C2313yes—
213D4×Dic53C2313yes—
214#13133179C23112yes—
215#13133179C2316yes—
216#13133179C23112yes—
217#13133179C23112yes—
218#13133179C23112yes—
219#13133179C2313yes—
220#13133179C2313yes—
221#13133179C2316yes—
222#13133179C2316yes—
223#13133179C23112yes—
224#13133179C23112yes—
225#13133179C23112yes—
226#13133179C2316yes—
227#13133179C23112yes—
228C4×C22⋊D53C2316yes—
229C4×C22⋊D53C2316yes—
230C4×C22⋊D53C23124yes—
231#13133177C23112yes—
232#13133177C2316yes—
233#13133177C2316yes—
234#13133177C23112yes—
235#13133176C2313yes—
236#13133175C23112yes—
237#13133175C2316yes—
238#13133175C2313yes—
239#13133175C23112yes—
240#13133175C2313yes—
241#13133175C2312yes—
242#13133175C23112yes—
243#13133174C2316yes—
244#13133174C23112yes—
245#13133173C2316yes—
246C4⋊C4×D53C2313yes—
247C4⋊C4×D53C23112yes—
248C4⋊C4×D53C2313yes—
249C2×#11719921C23112yes—
250C2×#11719921C23112yes—
251C22⋊C4×D53C2316yes—
252C22⋊C4×D53C23124yes—
253C2×C4×Dic53C2313yes—
254C2×C4×Dic53C2313yes—
255C2×C4×Dic53C2313yes—
256C42×D53C2311yescharacteristic
257C42×D53C2313yes—
258C42×D53C2313yes—
259C42×D53C2313yes—
260C42×D53C2313yes—
261C42×D53C2313yes—
262C42×D53C2313yes—
263C42×D53C2313yes—
264C42×D53C23112yes—
265C2×#41×C53C2311yescharacteristic
266C22×Q8×C53C2316yes—
267C4⋊Q8×C53C2316yes—
268C4⋊Q8×C53C23112yes—
269C4⋊Q8×C53C2313yes—
270C4⋊Q8×C53C2316yes—
271C4⋊Q8×C53C2316yes—
272C4⋊Q8×C53C2311yescharacteristic
273#125×C53C2316yes—
274#125×C53C23112yes—
275C22⋊Q8×C53C2316yes—
276C22⋊Q8×C53C2316yes—
277C22⋊Q8×C53C23124yes—
278C4×Q8×C53C2314yes—
279C4×Q8×C53C2311yescharacteristic
280C4×Q8×C53C2311yescharacteristic
281C4×Q8×C53C2316yes—
282C4×Q8×C53C2316yes—
283C4×D4×C53C23112yes—
284C4×D4×C53C2313yes—
285C4×D4×C53C2313yes—
286#117×C53C2313yes—
287#117×C53C2316yes—
288C2×C4⋊C4×C53C2316yes—
289C2×C4⋊C4×C53C2316yes—
290C2×C42×C53C2313yes—
291C23×D53C2413yes—
292C23×D53C24112yes—
293#41×C53#4118yescomplemented
294C2×Q8×C53—412no—
295C2×Q8×C53C2412yes—
296C2×Q8×C53C2416yes—
297C2×Q8×C53C24112yes—
298C2×Q8×C53C2411yescharacteristic
299C2×D4×C53C2413yes—
300C22×C4×C53C2413yes—
301C22×C4×C53C2413yes—
302C22×C4×C53C24112yes—
303C22×C4×C53C2413yes—
304C2×C22⋊D53C2416yes—
305C2×C22⋊D53C24112yes—
306C22×Dic53C2413yes—
307C22×Dic53C2413yes—
308C22×Dic53C2413yes—
309#11719949—24no—
310#11719949—216no—
311#11719949—224no—
312#11719949—424no—
313#11719949—424no—
314#11719949—424no—
315#11719949—412no—
316Q8×D53—24no—
317#11719947—212no—
318D4×D53—212no—
319D4×D53—248no—
320#11719945—212no—
321#11719945—224no—
322C2×D212—224no—
323C2×D212—412no—
324C2×D212—412no—
325C2×D212—424no—
326C2×D212C2416yes—
327C2×D212C2416yes—
328C2×D212C24112yes—
329C2×D212C2413yes—
330C2×D212C24112yes—
331C2×D212C2416yes—
332C2×D212C24112yes—
333C2×D212C24112yes—
334C2×D212C24112yes—
335C2×D212C24124yes—
336C2×C4×D53—212no—
337C2×C4×D53—212no—
338C2×C4×D53—424no—
339C2×C4×D53—46no—
340C2×C4×D53C2411yescharacteristic
341C2×C4×D53C2411yescharacteristic
342C2×C4×D53C2413yes—
343C2×C4×D53C2413yes—
344C2×C4×D53C2413yes—
345C2×C4×D53C2413yes—
346C2×C4×D53C2413yes—
347C2×C4×D53C2413yes—
348C2×C4×D53C2413yes—
349C2×C4×D53C24112yes—
350C2×C4×D53C24112yes—
351C2×C4×D53C2413yes—
352C2×C4×D53C2413yes—
353C2×C4×D53C24112yes—
354C2×C4×D53C24124yes—
355C2×C4×D53C2411yescharacteristic
356C2×Dic106C2412yes—
357C2×Dic106C2413yes—
358C4⋊C4×C53C2416yes—
359C4⋊C4×C53C2416yes—
360C4⋊C4×C53C24112yes—
361C4⋊C4×C53C24112yes—
362C4⋊C4×C53C2412yes—
363C4⋊C4×C53C2413yes—
364C4⋊C4×C53C2413yes—
365C4⋊C4×C53C2412yes—
366C4⋊C4×C53C24112yes—
367C4⋊C4×C53C24112yes—
368C22⋊C4×C53C24112yes—
369C22⋊C4×C53C2416yes—
370C42×C53C2411yescharacteristic
371C42×C53C2413yes—
372C42×C53C2413yes—
373C42×C53C2413yes—
374C42×C53C24112yes—
375C22⋊Dic53C2416yes—
376#11719921C24112yes—
377#11719921C24124yes—
378#11719921C2416yes—
379#11719921C2416yes—
380#11719921C24112yes—
381#11719921C24112yes—
382#11719921C24124yes—
383#11719921C2414yes—
384#11719921C24112yes—
385#11719921C24112yes—
386#11719921C24112yes—
387#11719921C24112yes—
388C4⋊Dic53C2413yes—
389C4⋊Dic53C2413yes—
390C4⋊Dic53C2412yes—
391C4⋊Dic53C2414yes—
392C4⋊Dic53C2412yes—
393C4⋊Dic53C24112yes—
394#11719919C24112yes—
395#11719919C2416yes—
396#11719919C2416yes—
397#11719919C2414yes—
398C4×Dic53C2413yes—
399C4×Dic53C2411yescharacteristic
400C4×Dic53C2411yescharacteristic
401C4×Dic53C2411yescharacteristic
402C4×Dic53C2414yes—
403C4×Dic53C2413yes—
404C4×Dic53C2413yes—
405C4×Dic53C2413yes—
406C4×Dic53C2413yes—
407C4×Dic53C2413yes—
408C4×Dic53C2413yes—
409C4×Dic53C2413yes—
410C4×Dic53C2413yes—
411C4×Dic53C24112yes—
412C23×C53C2513yes—
413C22×D53—26no—
414C22×D53—224no—
415C22×D53—26no—
416C22×D53—43no—
417C22×D53—412no—
418C22×D53—412no—
419C22×D53C2513yes—
420C22×D53C25112yes—
421C22×D53C2511yescharacteristic
422Q8×C53—212no—
423Q8×C53—24no—
424Q8×C53—412no—
425Q8×C53C2×#4114yescomplemented
426D4×C53C2×#41112yescomplemented
427C2×C4×C53—26no—
428C2×C4×C53—26no—
429C2×C4×C53—412no—
430C2×C4×C53C2×#41112yescomplemented
431C2×C4×C53C25112yes—
432C2×C4×C53C2514yes—
433C2×C4×C53C2513yes—
434C2×C4×C53C2513yes—
435C2×C4×C53C2511yescharacteristic
436C2×C4×C53C2513yes—
437C2×C4×C53C2511yescharacteristic
438C2×C4×C53C2511yescharacteristic
439C22⋊D53—224no—
440C22⋊D53—212no—
441C2×Dic53—26no—
442C2×Dic53—26no—
443C2×Dic53—43no—
444C2×Dic53C2513yes—
445C2×Dic53C2514yes—
446C2×Dic53C2513yes—
447C2×Dic53C2513yes—
448C2×Dic53C2511yescharacteristic
449C2×Dic53C2511yescharacteristic
450C2×Dic53C2511yescharacteristic
451D212—224no—
452D212—212no—
453D212—224no—
454D212—26no—
455D212—212no—
456D212—212no—
457D212—412no—
458D212—412no—
459D212—424no—
460D212—412no—
461C4×D53—26no—
462C4×D53—22no—
463C4×D53—26no—
464C4×D53—26no—
465C4×D53—26no—
466C4×D53—224no—
467C4×D53—26no—
468C4×D53—22no—
469C4×D53—26no—
470C4×D53—26no—
471C4×D53—224no—
472C4×D53—43no—
473C4×D53—43no—
474C4×D53—424no—
475C4×D53—412no—
476C4×D53H(5,𝔽2)14yescomplemented
477Dic106—24no—
478Dic106—26no—
479#62800—531nomaximal, Sylow
480C22×C53—23no—
481C22×C53—23no—
482C22×C53C22×#4116yes—
483C22×C53C2611yescharacteristic
484C2×D53—21no—
485C2×D53—21no—
486C2×D53—23no—
487C2×D53—212no—
488C2×D53—23no—
489C2×D53—212no—
490C2×D53—23no—
491C2×D53—212no—
492C2×D53—412no—
493C2×D53—824no—
494C2×D53C2×H(5,𝔽2)12yes—
495C4×C53—23no—
496C4×C53—212no—
497C4×C53—24no—
498C4×C53—23no—
499C4×C53C22×#4112yes—
500C4×C53C22×#4116yes—
501C4×C53C2×H(5,𝔽2)12yes—
502C4×C53#58512yes—
503Dic53—23no—
504Dic53—24no—
505Dic53—21no—
506Dic53—23no—
507Dic53—23no—
508Dic53—21no—
509Dic53C2×H(5,𝔽2)12yes—
510#3522—532no—
511#3519—536no—
512#3517—532no—
513#3514—536no—
514#3511—533no—
515#3508—533no—
516#3503D5311yescharacteristic, complemented
517#3498—531no—
518#3494—536no—
519#3488—532no—
520#3483—532no—
521#3481—536no—
522#3480—532no—
523D4×#41—536no—
524#3460—536no—
525#3444—533no—
526C2×#532—533no—
527C4×H(5,𝔽2)—532no—
528C2×C4×#41—531no—
529C2×C53—26no—
530C2×C53C23×#4111yescharacteristic
531C2×C53C22×H(5,𝔽2)11yescharacteristic
532C2×C53C2×#58511yescharacteristic
533D53—22no—
534D53—43no—
535D53—412no—
536C2×H(5,𝔽2)—532no—
537C22×#41—531no—
538C22×#41—536no—
539#559—536no—
540#559—536no—
541Q82C2×D5312yescomplemented
542#557C2×D5312yescomplemented
543#556—536no—
544#555—5312no—
545#555—536no—
546#554—536no—
547#554C2×D5316yescomplemented
548#553—5312no—
549#553—5312no—
550#553—5312no—
551#551—5324no—
552#550—536no—
553#550—532no—
554#550—534no—
555#550—532no—
556#550—536no—
557D4×Q8C2×D5316yescomplemented
558#548—5312no—
559#548—534no—
560#547—5312no—
561#547—536no—
562#546—5324no—
563#546—5312no—
564#546—5312no—
565#546—5312no—
566D42—5312no—
567D42—536no—
568D42—536no—
569#544C2×D5316yescomplemented
570#542—5312no—
571#542—5312no—
572#540—5312no—
573#540—5312no—
574#538—5324no—
575#537—536no—
576#535—536no—
577#535—536no—
578#533—531no—
579#533—533no—
580#533C2×D5313yescomplemented
581#532—533no—
582#532—536no—
583#532—536no—
584#532—536no—
585#532—536no—
586#532—536no—
587#532—536no—
588#532—536no—
589#532—533no—
590#532—5312no—
591#532—533no—
592C2×C4⋊Q8C2×D5313yescomplemented
593C2×#127—533no—
594#529—536no—
595#529—536no—
596#529—5312no—
597#529—536no—
598#529—536no—
599#529—536no—
600#529—536no—
601C2×#124—536no—
602#525—536no—
603#525—536no—
604#525—5324no—
605#525—536no—
606C2×#121—536no—
607C2×#121—536no—
608#520—534no—
609#520—536no—
610#520C2×D5312yes—
611#518—5312no—
612#518—536no—
613C4×#41—531no—
614C4×#41—531no—
615C4×#41—531no—
616C4×#41—534no—
617C4×#41—536no—
618C4×#41—536no—
619C4×#41—533no—
620C4×#41—533no—
621C4×#41—533no—
622C4×#41—536no—
623C4×#41—533no—
624C4×#41C2×D5311yescharacteristic
625C2×C4×Q8—531no—
626C2×C4×Q8—531no—
627C2×C4×D4—533no—
628C2×C4×D4—533no—
629C2×C4×D4—5312no—
630C2×C4×D4—536no—
631C2×C4×D4—536no—
632C2×#117—533no—
633C22×C42—533no—
634C53#6280011yescharacteristic, complemented, Sylow
635H(5,𝔽2)—10616no—
636C2×#41—531no—
637C2×#41—534no—
638C2×#41—536no—
639C2×#41—536no—
640C2×#41—5312no—
641C2×#41—5312no—
642C2×#41—5312no—
643C2×#41—533no—
644C2×#41—533no—
645C2×#41—536no—
646C2×#41—1068no—
647C2×#41—21224no—
648C2×#41C22×D5311yescharacteristic
649C22×Q8—531no—
650C22×Q8C22×D5316yes—
651C22×D4—533no—
652C22×D4—5312no—
653C22×D4—536no—
654C22×D4—536no—
655C22×D4—5312no—
656C22×D4—536no—
657C23×C4—533no—
658C23×C4—533no—
659C23×C4—5312no—
660C23×C4—533no—
661C4⋊Q8—531no—
662C4⋊Q8C22×D5313yes—
663C4⋊Q8C22×D5316yes—
664C4⋊Q8C22×D5316yes—
665C4⋊Q8C22×D5316yes—
666C4⋊Q8C22×D5311yescharacteristic
667C4⋊Q8C22×D53112yes—
668#127—533no—
669#127—536no—
670#127—536no—
671#127—536no—
672#127—5312no—
673#126—5312no—
674#126—5312no—
675#126—5324no—
676#125—532no—
677#125—536no—
678#125C22×D5316yes—
679#125C22×D53112yes—
680#124—536no—
681#124—5312no—
682#124—5312no—
683#124—5312no—
684#124—536no—
685#124—5324no—
686#124—536no—
687#124—5312no—
688#123—5312no—
689#123—5312no—
690#123—5324no—
691#123—5324no—
692#123—5324no—
693#123—5312no—
694C22⋊Q8—532no—
695C22⋊Q8—536no—
696C22⋊Q8—5324no—
697C22⋊Q8—532no—
698C22⋊Q8—536no—
699C22⋊Q8—5312no—
700C22⋊Q8C22×D5316yes—
701C22⋊Q8C22×D5316yes—
702C22⋊Q8C22×D53124yes—
703#121—536no—
704#121—536no—
705#121—5324no—
706#121—536no—
707#121—536no—
708#121—5312no—
709#121—5312no—
710#121—5312no—
711#121—5312no—
712#121—5312no—
713#121—5312no—
714#121—536no—
715#121—536no—
716#121—5324no—
717#121—5312no—
718#121—5312no—
719#121—5312no—
720#121—5324no—
721#120—5312no—
722#120—5324no—
723#120—5324no—
724C4×Q8—531no—
725C4×Q8—531no—
726C4×Q8—532no—
727C4×Q8—536no—
728C4×Q8—533no—
729C4×Q8—533no—
730C4×Q8—532no—
731C4×Q8—536no—
732C4×Q8—533no—
733C4×Q8—533no—
734C4×Q8C22×D5311yescharacteristic
735C4×Q8C22×D5311yescharacteristic
736C4×Q8C22×D5314yes—
737C4×Q8C22×D5316yes—
738C4×Q8C22×D5316yes—
739C4×D4—533no—
740C4×D4—533no—
741C4×D4—536no—
742C4×D4—536no—
743C4×D4—5324no—
744C4×D4—5312no—
745C4×D4—536no—
746C4×D4—536no—
747C4×D4—533no—
748C4×D4—533no—
749C4×D4—5312no—
750C4×D4—5312no—
751C4×D4—5312no—
752C4×D4—5312no—
753C4×D4—5312no—
754C4×D4—536no—
755C4×D4—5312no—
756C4×D4—5312no—
757C4×D4—536no—
758C4×D4—5312no—
759C4×D4—536no—
760C4×D4—536no—
761C4×D4—5312no—
762C4×D4—533no—
763C4×D4—533no—
764C4×D4—5312no—
765C4×D4—5312no—
766C4×D4—5312no—
767C4×D4—5312no—
768C4×D4—536no—
769C4×D4—536no—
770C4×D4C22×D5313yes—
771C4×D4C22×D5313yes—
772C4×D4C22×D53112yes—
773#117—533no—
774#117—533no—
775#117—533no—
776#117—532no—
777#117—5312no—
778#117—5312no—
779#117—536no—
780#117—5312no—
781#117—536no—
782#117—536no—
783#117—5312no—
784#117C22×D5313yes—
785#117C22×D5316yes—
786C2×C4⋊C4—533no—
787C2×C4⋊C4—533no—
788C2×C4⋊C4—5312no—
789C2×C4⋊C4C22×D5316yes—
790C2×C4⋊C4C22×D5316yes—
791C2×C22⋊C4—5312no—
792C2×C22⋊C4—5312no—
793C2×C22⋊C4—536no—
794C2×C22⋊C4—5324no—
795C2×C42—533no—
796C2×C42—533no—
797C2×C42—533no—
798C2×C42—533no—
799C2×C42—533no—
800C2×C42—533no—
801C2×C42—5312no—
802C2×C42—533no—
803C2×C42—533no—
804C2×C42—533no—
805C2×C42—533no—
806C2×C42—531no—
807C2×C42C22×D5313yes—
808C24—533no—
809C24—5312no—
810#41—10624no—
811#41—1064no—
812#41—10616no—
813#41—10612no—
814#41—10612no—
815#41—10624no—
816#41—21224no—
817#41—21224no—
818#41—21212no—
819#41—21224no—
820#41#1171994918yescomplemented
821C2×Q8—412no—
822C2×Q8—533no—
823C2×Q8—532no—
824C2×Q8—1064no—
825C2×Q8C23×D5312yes—
826C2×Q8C23×D5316yes—
827C2×Q8C23×D53112yes—
828C2×Q8C23×D5311yescharacteristic
829C2×D4—536no—
830C2×D4—5312no—
831C2×D4—536no—
832C2×D4—5312no—
833C2×D4—536no—
834C2×D4—533no—
835C2×D4—5312no—
836C2×D4—536no—
837C2×D4—5312no—
838C2×D4—5312no—
839C2×D4—5312no—
840C2×D4—5324no—
841C2×D4—10612no—
842C2×D4—10648no—
843C2×D4—10624no—
844C2×D4—21212no—
845C2×D4—21212no—
846C2×D4—21224no—
847C2×D4C23×D5313yes—
848C22×C4—531no—
849C22×C4—533no—
850C22×C4—533no—
851C22×C4—533no—
852C22×C4—531no—
853C22×C4—531no—
854C22×C4—533no—
855C22×C4—533no—
856C22×C4—533no—
857C22×C4—533no—
858C22×C4—533no—
859C22×C4—533no—
860C22×C4—533no—
861C22×C4—5312no—
862C22×C4—5312no—
863C22×C4—533no—
864C22×C4—533no—
865C22×C4—5312no—
866C22×C4—5324no—
867C22×C4—10612no—
868C22×C4—10612no—
869C22×C4—2126no—
870C22×C4—21224no—
871C22×C4C23×D5313yes—
872C22×C4C23×D5313yes—
873C22×C4C23×D53112yes—
874C22×C4C23×D5313yes—
875C4⋊C4—533no—
876C4⋊C4—5312no—
877C4⋊C4—533no—
878C4⋊C4—536no—
879C4⋊C4—536no—
880C4⋊C4—532no—
881C4⋊C4—534no—
882C4⋊C4—534no—
883C4⋊C4—532no—
884C4⋊C4—5312no—
885C4⋊C4C23×D53112yes—
886C4⋊C4C23×D5313yes—
887C4⋊C4C23×D5313yes—
888C4⋊C4C23×D5316yes—
889C4⋊C4C23×D5316yes—
890C4⋊C4C23×D53112yes—
891C4⋊C4C23×D5312yes—
892C4⋊C4C23×D53112yes—
893C4⋊C4C23×D53112yes—
894C4⋊C4C23×D5312yes—
895C22⋊C4—536no—
896C22⋊C4—5312no—
897C22⋊C4—5312no—
898C22⋊C4—5324no—
899C22⋊C4—5312no—
900C22⋊C4—536no—
901C22⋊C4—536no—
902C22⋊C4—5324no—
903C22⋊C4—534no—
904C22⋊C4—5312no—
905C22⋊C4—5312no—
906C22⋊C4—5312no—
907C22⋊C4—5312no—
908C22⋊C4C23×D53112yes—
909C22⋊C4C23×D5316yes—
910C42—531no—
911C42—533no—
912C42—531no—
913C42—531no—
914C42—533no—
915C42—533no—
916C42—534no—
917C42—533no—
918C42—533no—
919C42—533no—
920C42—533no—
921C42—533no—
922C42—533no—
923C42—5312no—
924C42C23×D5311yescharacteristic
925C42C23×D5313yes—
926C42C23×D5313yes—
927C42C23×D5313yes—
928C42C23×D53112yes—
929C23—531no—
930C23—5312no—
931C23—533no—
932C23—1066no—
933C23—10624no—
934C23—1066no—
935C23—21212no—
936C23—21212no—
937C23—2123no—
938C23C24×D5313yes—
939Q8—212no—
940Q8—24no—
941Q8—412no—
942Q8—1066no—
943Q8—1064no—
944Q8C2×#1171994914yescomplemented
945D4—10624no—
946D4—10624no—
947D4—10612no—
948D4—10624no—
949D4—10612no—
950D4—1066no—
951D4—10612no—
952D4—10612no—
953D4—21212no—
954D4—21212no—
955D4—21224no—
956D4—21212no—
957D4C2×#11719949112yescomplemented
958C2×C4—26no—
959C2×C4—26no—
960C2×C4—412no—
961C2×C4—531no—
962C2×C4—534no—
963C2×C4—531no—
964C2×C4—533no—
965C2×C4—531no—
966C2×C4—533no—
967C2×C4—534no—
968C2×C4—533no—
969C2×C4—1066no—
970C2×C4—10624no—
971C2×C4—1066no—
972C2×C4—1066no—
973C2×C4—1066no—
974C2×C4—1062no—
975C2×C4—1066no—
976C2×C4—1066no—
977C2×C4—1066no—
978C2×C4—10624no—
979C2×C4—1066no—
980C2×C4—1062no—
981C2×C4—1066no—
982C2×C4—2123no—
983C2×C4—2123no—
984C2×C4—21224no—
985C2×C4—21212no—
986C2×C4—2123no—
987C2×C4C2×#11719949112yescomplemented
988C2×C4C24×D5313yes—
989C2×C4C24×D5313yes—
990C2×C4C24×D5314yes—
991C2×C4C24×D53112yes—
992C2×C4C24×D5311yescharacteristic
993C2×C4C24×D5313yes—
994C2×C4C24×D5311yescharacteristic
995C2×C4C24×D5311yescharacteristic
996C22—23no—
997C22—23no—
998C22—532no—
999C22—1061no—
1000C22—1061no—
1001C22—1063no—
1002C22—10612no—
1003C22—1063no—
1004C22—10612no—
1005C22—1063no—
1006C22—10612no—
1007C22—42424no—
1008C22—21212no—
1009C22C22×#1171994916yes—
1010C22C25×D5311yescharacteristic
1011C4—23no—
1012C4—212no—
1013C4—23no—
1014C4—24no—
1015C4—532no—
1016C4—1061no—
1017C4—1064no—
1018C4—1063no—
1019C4—1063no—
1020C4—1061no—
1021C4—1063no—
1022C4C22×#1171994916yes—
1023C4C22×#1171994912yes—
1024C4H(5,𝔽2)×D5312yes—
1025C4#1681146012yes—
1026C2—26no—
1027C2—1062no—
1028C2—21212no—
1029C2—2123no—
1030C2C23×#1171994911yescharacteristic
1031C2C2×H(5,𝔽2)×D5311yescharacteristic
1032C2C2×#1681146011yescharacteristic
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3503C2
hypercenter#3503D53
hypocenterC53#62800
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3503

Complements

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

NH ≅ G/Ntype
1. #20288801C2semidirect
2. #20288748C2semidirect
3. #20288722C2semidirect
4. #20288677C2semidirect
5. #20288628C2semidirect
6. #20288592C2semidirect
7. #20288493C2semidirect
8. #20288453C2semidirect
9. #20288385C2semidirect
10. #20288342C2semidirect
11. #20288326C2semidirect
12. #20288315C2semidirect
13. D4×#11719949C2semidirect
14. #20288138C2semidirect
15. #20288012C2semidirect
16. C2×#16811174C2semidirect
17. #20287921C2semidirect
18. C4×#41×D53C2semidirect
19. C53×#3503C2semidirect
21. C22×#11719949C22semidirect
23. #16811358C22semidirect
24. #16811358C22semidirect
25. #16811347C22semidirect
26. #16811339C22semidirect
27. #16811339C22semidirect
28. #16811334C22semidirect
29. #16811326C22semidirect
30. #16811326C22semidirect
31. #16811321C22semidirect
32. #16811300C22semidirect
33. #16811295C22semidirect
34. #16811295C22semidirect
35. #16811295C22semidirect
36. #16811295C22semidirect
37. #16811295C22semidirect
38. #16811285C22semidirect
39. #16811284C22semidirect
40. #16811276C22semidirect
41. #16811276C22semidirect
42. #16811268C22semidirect
43. #16811264C22semidirect
44. #16811264C22semidirect
45. #16811264C22semidirect
46. D4×D212C22semidirect
47. D4×D212C22semidirect
48. D4×D212C22semidirect
49. #16811247C22semidirect
50. #16811247C22semidirect
51. #16811229C22semidirect
52. #16811229C22semidirect
53. #16811213C22semidirect
54. #16811204C22semidirect
55. #16811192C22semidirect
56. #16811192C22semidirect
57. #16811178C22semidirect
58. #16811178C22semidirect
59. #16811174C22semidirect
60. #16811174C22semidirect
61. #16811174C22semidirect
62. #16811174C22semidirect
63. #16811174C22semidirect
64. #16811174C22semidirect
65. #16811174C22semidirect
66. #16811174C22semidirect
67. #16811174C22semidirect
68. #16811174C22semidirect
69. #16811173C22semidirect
70. C2×#13133214C22semidirect
71. #16811160C22semidirect
72. #16811160C22semidirect
73. #16811159C22semidirect
74. #16811159C22semidirect
75. #16811158C22semidirect
76. #16811158C22semidirect
77. #16811158C22semidirect
78. C2×#13133206C22semidirect
79. #16811136C22semidirect
80. #16811136C22semidirect
81. #16811136C22semidirect
82. #16811135C22semidirect
83. C2×#13133192C22semidirect
84. C2×#13133192C22semidirect
85. #16811105C22semidirect
86. #16811104C22semidirect
87. #16811097C22semidirect
88. #16811095C22semidirect
90. C4×#11719949C22semidirect
91. C4×#11719949C22semidirect
92. C4×#11719949C22semidirect
93. C4×#11719949C22semidirect
94. C4×#11719949C22semidirect
95. C4×#11719945C22semidirect
96. #16811091C22semidirect
97. #16811091C22semidirect
98. C4×#11719947C22semidirect
99. C4×#11719947C22semidirect
100. C4×Q8×D53C22semidirect
101. C4×Q8×D53C22semidirect
102. C2×#13133179C22semidirect
103. C2×#13133179C22semidirect
104. C4×D4×D53C22semidirect
105. C4×D4×D53C22semidirect
106. C4×D4×D53C22semidirect
107. #117×D53C22semidirect
108. C2×C42×D53C22semidirect
109. Q82×C53C22semidirect
110. C53×#557C22semidirect
111. C53×#554C22semidirect
112. D4×Q8×C53C22semidirect
113. C53×#544C22semidirect
114. C53×#533C22semidirect
115. C2×C4⋊Q8×C53C22semidirect
293. #41×C53#41semidirect
425. Q8×C53C2×#41semidirect
426. D4×C53C2×#41semidirect
430. C2×C4×C53C2×#41semidirect
476. C4×D53H(5,𝔽2)semidirect
516. #3503D53semidirect
541. Q82C2×D53semidirect
542. #557C2×D53semidirect
547. #554C2×D53semidirect
557. D4×Q8C2×D53semidirect
569. #544C2×D53semidirect
580. #533C2×D53semidirect
592. C2×C4⋊Q8C2×D53semidirect
634. C53#62800semidirect
820. #41#11719949semidirect
944. Q8C2×#11719949semidirect
957. D4C2×#11719949semidirect
987. C2×C4C2×#11719949semidirect

Maximal subgroups

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

subgroupindex
#202888012
#202887482
#202887222
#202886772
#202886282
#202885922
#202884932
#202884532
#202883852
#202883422
#202883262
#202883152
D4×#117199492
#202881382
#202880122
C2×#168111742
#202879212
C4×#41×D532
C53×#35032
#6280053