Finite Group Databasebeta

← #28293082

Subgroups — #28293082

Order 13568.

6616 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289217C216yesmaximal, complemented
2#20289137C216yesmaximal, complemented
3#20288983C216yesmaximal, complemented
4#20288971C216yesmaximal, complemented
5#20288824C216yesmaximal, complemented
6#20288814C216yesmaximal, complemented
7#20288783C216yesmaximal, complemented
8#20288777C216yesmaximal, complemented
9#20288627C213yesmaximal, complemented
10#20288616C213yesmaximal, complemented
11#20288594C213yesmaximal, complemented
12#20288584C213yesmaximal, complemented
13#20288011C211yesmaximal, characteristic, complemented
14#20288011C211yesmaximal, characteristic, complemented
15C53×#3444C211yesmaximal, characteristic, complemented
16#16811375C22112yescomplemented
17#16811366C2214yes—
18#16811364C2214yescomplemented
19#16811362C22112yescomplemented
20#16811356C22112yescomplemented
21#16811356C2216yescomplemented
22#16811355C2216yescomplemented
23#16811350C2216yescomplemented
24#16811349C2216yescomplemented
25#16811345C2216yescomplemented
26#16811344C2216yes—
27#16811342C2216yescomplemented
28#16811341C2216yes—
29#16811337C2216yescomplemented
30#16811336C22112yescomplemented
31#16811336C2216yescomplemented
32#16811332C2216yescomplemented
33#16811329C2216yescomplemented
34#16811326C2216yescomplemented
35#16811323C22112yescomplemented
36#16811323C2216yescomplemented
37#16811322C22112yescomplemented
38#16811320C2216yescomplemented
39#16811317C2216yescomplemented
40#16811314C2216yescomplemented
41#16811312C22112yescomplemented
42#16811312C2216yescomplemented
43#16811311C2216yescomplemented
44#16811307C2216yescomplemented
45#16811306C22112yescomplemented
46#16811302C22112yes—
47#16811297C22112yescomplemented
48#16811292C2216yes—
49#16811291C2216yes—
50#16811285C2216yescomplemented
51#16811283C2216yescomplemented
52#16811281C2216yescomplemented
53#16811280C2216yescomplemented
54#16811275C2216yescomplemented
55#16811272C2216yescomplemented
56#16811270C2216yes—
57#16811268C2216yescomplemented
58#16811266C2216yescomplemented
59#16811261C2216yes—
60#16811246C2216yescomplemented
61#16811245C2216yescomplemented
62#16811241C22112yescomplemented
63#16811240C2216yescomplemented
64#16811238C2216yescomplemented
65#16811238C22112yescomplemented
66#16811233C2216yescomplemented
67#16811231C2216yescomplemented
68#16811226C2216yes—
69#16811225C22112yescomplemented
70#16811224C2216yescomplemented
71#16811224C22112yescomplemented
72#16811216C22112yescomplemented
73#16811215C22112yescomplemented
74#16811209C22112yes—
75#16811206C22112yes—
76#16811203C2216yescomplemented
77#16811202C2216yescomplemented
78#16811196C2216yes—
79#16811189C2216yes—
80#16811180C2213yescomplemented
81#16811180C2213yescomplemented
82#16811178C2213yescomplemented
83#16811178C2213yescomplemented
84#16811174C2213yescomplemented
85#16811173C2213yes—
86#16811173C2213yes—
87#16811171C2213yescomplemented
88C4⋊Q8×D53C2213yescomplemented
89#127×D53C2211yescharacteristic, complemented
90#16811157C2213yes—
91#16811157C2213yes—
92#16811157C2216yescomplemented
93#16811157C2213yescomplemented
94#16811157C2213yescomplemented
95#16811157C2216yescomplemented
96#16811157C22112yescomplemented
97#16811156C22112yescomplemented
98C2×#13133211C2214yescomplemented
99#126×D53C2214yescomplemented
100#16811134C2213yes—
101#16811134C2213yescomplemented
102#16811134C2216yescomplemented
103#16811105C2216yescomplemented
104#16811102C2216yescomplemented
105#16811099C2216yescomplemented
106#16811095C2216yescomplemented
107C4×#11719945C2213yes—
108C4×#11719945C2216yescomplemented
109C4×#11719945C2213yescomplemented
110C53×#533C2213yescomplemented
111C53×#532C2213yes—
112C53×#529C2216yescomplemented
113C53×#529C2216yescomplemented
114C53×#525C2216yescomplemented
115C4×#41×C53C2216yescomplemented
116C22×C42×C53C2211yescharacteristic, complemented
117C2×#11719949C2316yes—
118C2×#11719945C2316yes—
119C2×#11719945C2313yes—
120C2×#11719945C2313yes—
121C2×#11719947C2316yes—
122C2×Q8×D53C2316yes—
123C2×D4×D53C2316yes—
124#13133217C2313yes—
125#13133217C2313yes—
126#13133216C2316yes—
127#13133216C2316yes—
128#13133216C23112yes—
129#13133215C2316yes—
130#13133214C2311yescharacteristic
131#13133214C2311yescharacteristic
132#13133213C2316yes—
133#13133213C23112yes—
134#13133212C23112yes—
135#13133212C23112yes—
136#13133211C23112yes—
137#13133211C23112yes—
138#13133211C2314yes—
139#13133211C2311yescharacteristic
140#13133211C2311yescharacteristic
141#13133211C2314yes—
142#13133211C2313yes—
143#13133211C2313yes—
144#13133210C23112yes—
145#13133210C23112yes—
146#13133210C23112yes—
147#13133210C23112yes—
148#13133209C2313yes—
149#13133209C2313yes—
150#13133209C23112yes—
151#13133209C2316yes—
152#13133208C2316yes—
153#13133208C23112yes—
154#13133208C2316yes—
155#13133207C23112yes—
156#13133207C23112yes—
157#13133206C2316yes—
158#13133205C2316yes—
159#13133205C23112yes—
160#13133205C2313yes—
161#13133205C2313yes—
162#13133204C2316yes—
163#13133204C23112yes—
164#13133203C23112yes—
165#13133203C23112yes—
166#13133203C23112yes—
167#13133203C23112yes—
168#13133202C23112yes—
169#13133202C23112yes—
170#13133201C23112yes—
171#13133200C23112yes—
172#13133200C2313yes—
173#13133200C23112yes—
174#13133200C2313yes—
175#13133200C2313yes—
176#13133200C2313yes—
177#13133200C23112yes—
178#13133199C23112yes—
179#13133199C23112yes—
180#13133199C23112yes—
181#13133199C23112yes—
182#13133198C23112yes—
183#13133197C2316yes—
184#13133197C2316yes—
185#13133197C23112yes—
186#13133196C2316yes—
187#13133196C23112yes—
188#13133196C2313yes—
189#13133196C2313yes—
190#13133196C2313yes—
191#13133196C2313yes—
192#13133196C2316yes—
193#13133195C23112yes—
194#13133195C23112yes—
195#13133194C23112yes—
196#13133194C23112yes—
197#13133193C2316yes—
198#13133193C2316yes—
199#13133192C2316yes—
200#13133192C2316yes—
201#13133192C23112yes—
202#13133191C23112yes—
203#13133191C2316yes—
204#13133191C2313yes—
205#13133191C2313yes—
206#13133191C2316yes—
207#13133191C2313yes—
208#13133191C2313yes—
209#13133190C23112yes—
210#13133190C23112yes—
211#13133190C23112yes—
212#13133190C23112yes—
213#13133189C23112yes—
214#13133189C23112yes—
215#13133188C2316yes—
216#13133188C23112yes—
217#13133188C2316yes—
218#13133188C23112yes—
219#13133187C23112yes—
220#13133186C2313yes—
221#13133186C2314yes—
222#13133186C2311yescharacteristic
223#13133185C23112yes—
224Q8×Dic53C2316yes—
225Q8×Dic53C2316yes—
226C4×Dic106C2316yes—
227C4×Dic106C23112yes—
228C4×Dic106C2313yes—
229C4×Dic106C2313yes—
230C4×Dic106C2313yes—
231C4×Dic106C2313yes—
232C4×Dic106C2316yes—
233#13133182C2316yes—
234#13133182C2316yes—
235#13133182C23112yes—
236C4×D212C2313yes—
237C4×D212C2316yes—
238C4×D212C2313yes—
239C4×D212C2313yes—
240C4×D212C2313yes—
241C4×D212C23112yes—
242C4×D212C2316yes—
243D4×Dic53C2316yes—
244D4×Dic53C2316yes—
245#13133179C2316yes—
246#13133179C2316yes—
247#13133179C23112yes—
248C4×C22⋊D53C2313yes—
249C4×C22⋊D53C2313yes—
250C4×C22⋊D53C2313yes—
251C4×C22⋊D53C2313yes—
252C4×C22⋊D53C23112yes—
253C4×C22⋊D53C2313yes—
254C4×C22⋊D53C2313yes—
255C4×C22⋊D53C2313yes—
256C4×C22⋊D53C23112yes—
257C4×C22⋊D53C23112yes—
258C4×C22⋊D53C2313yes—
259C4×C22⋊D53C23112yes—
260#13133177C23112yes—
261#13133177C23112yes—
262#13133176C2316yes—
263#13133176C2313yes—
264#13133176C2313yes—
265#13133175C23112yes—
266#13133175C2316yes—
267#13133175C2316yes—
268#13133174C23112yes—
269#13133174C23112yes—
270#13133174C23112yes—
271#13133174C2313yes—
272#13133174C2313yes—
273#13133174C2313yes—
274#13133174C2313yes—
275#13133173C23112yes—
276C2×#11719919C23112yes—
277C4⋊C4×D53C23112yes—
278C4⋊C4×D53C2316yes—
279C4⋊C4×D53C2316yes—
280C2×#11719921C23112yes—
281C22⋊C4×D53C23112yes—
282C42×D53C2311yescharacteristic
283C42×D53C2313yes—
284C42×D53C2314yes—
285C2×#41×C53C2316yes—
286C23×C4×C53C2313yes—
287C4⋊Q8×C53C2313yes—
288#127×C53C2311yescharacteristic
289#126×C53C2314yes—
290#126×C53C2314yes—
291#125×C53C2316yes—
292#124×C53C2316yes—
293#123×C53C23112yes—
294C22⋊Q8×C53C2316yes—
295C22⋊Q8×C53C2316yes—
296#121×C53C2316yes—
297#121×C53C2316yes—
298#120×C53C2314yes—
299C4×Q8×C53C2316yes—
300C4×Q8×C53C2316yes—
301C4×D4×C53C2316yes—
302C4×D4×C53C23112yes—
303C4×D4×C53C23112yes—
304C4×D4×C53C2316yes—
305#117×C53C23112yes—
306#117×C53C2316yes—
307C2×C42×C53C2313yes—
308C2×C42×C53C2313yes—
309C2×C42×C53C2313yes—
310C2×C42×C53C2313yes—
311C2×C42×C53C2314yes—
312C24×C53C2411yescharacteristic
313C23×D53C2414yes—
314#41×C53—412no—
315C2×Q8×C53C2416yes—
316C2×D4×C53C2416yes—
317C2×D4×C53C24112yes—
318C22×C4×C53—46no—
319C22×C4×C53C2413yes—
320C22×C4×C53C2413yes—
321C22×C4×C53C2413yes—
322C22×C4×C53C2413yes—
323C22×C4×C53C2413yes—
324C22×C4×C53C2413yes—
325C22×C4×C53C24112yes—
326C2×C22⋊D53C24112yes—
327C2×C22⋊D53C24112yes—
328C2×C22⋊D53C2413yes—
329C2×C22⋊D53C24112yes—
330C2×C22⋊D53C2413yes—
331C2×C22⋊D53C2413yes—
332C2×C22⋊D53C2413yes—
333C22×Dic53C24112yes—
334#11719949—412no—
335Q8×D53—412no—
336#11719947—412no—
337D4×D53—412no—
338#11719945—412no—
339#11719945—46no—
340#11719945—46no—
341C2×D212C2416yes—
342C2×D212C24112yes—
343C2×D212C2413yes—
344C2×D212C2413yes—
345C2×C4×D53C2413yes—
346C2×C4×D53C2413yes—
347C2×C4×D53C2413yes—
348C2×C4×D53C2413yes—
349C2×C4×D53C24112yes—
350C2×C4×D53C24112yes—
351C2×C4×D53C24112yes—
352C2×Dic106C2416yes—
353C2×Dic106C24112yes—
354C2×Dic106C2413yes—
355C2×Dic106C2413yes—
356C4⋊C4×C53C2416yes—
357C4⋊C4×C53C2416yes—
358C4⋊C4×C53C24112yes—
359C4⋊C4×C53C24112yes—
360C22⋊C4×C53C24112yes—
361C22⋊C4×C53C24112yes—
362C22⋊C4×C53C24112yes—
363C42×C53C2411yescharacteristic
364C42×C53C2413yes—
365C42×C53C2413yes—
366C42×C53C2413yes—
367C42×C53C2413yes—
368C42×C53C2411yescharacteristic
369C42×C53C2411yescharacteristic
370C42×C53C2411yescharacteristic
371C42×C53C24112yes—
372C22⋊Dic53C24112yes—
373C22⋊Dic53C24112yes—
374C22⋊Dic53C2413yes—
375C22⋊Dic53C24112yes—
376C22⋊Dic53C2413yes—
377C22⋊Dic53C2413yes—
378C22⋊Dic53C2413yes—
379#11719921C2413yes—
380#11719921C24112yes—
381#11719921C2413yes—
382#11719921C24112yes—
383#11719921C24112yes—
384#11719921C2413yes—
385#11719921C2413yes—
386#11719921C24112yes—
387#11719921C2413yes—
388#11719921C2413yes—
389#11719921C2413yes—
390#11719921C2413yes—
391#11719921C24112yes—
392#11719921C24112yes—
393C4⋊Dic53C2416yes—
394C4⋊Dic53C2416yes—
395C4⋊Dic53C24112yes—
396C4⋊Dic53C24112yes—
397C4⋊Dic53C2413yes—
398C4⋊Dic53C2413yes—
399C4⋊Dic53C2413yes—
400C4⋊Dic53C2413yes—
401#11719919C2413yes—
402#11719919C24112yes—
403#11719919C24112yes—
404#11719919C2413yes—
405#11719919C24112yes—
406#11719919C24112yes—
407#11719919C2413yes—
408#11719919C2413yes—
409#11719919C2413yes—
410#11719919C2413yes—
411#11719919C2413yes—
412#11719919C2413yes—
413#11719919C24112yes—
414#11719919C24112yes—
415C4×Dic53C24112yes—
416C4×Dic53C2413yes—
417C4×Dic53C2413yes—
418C4×Dic53C2413yes—
419C4×Dic53C2413yes—
420C4×Dic53C24112yes—
421C4×Dic53C24112yes—
422C23×C53—43no—
423C23×C53C2514yes—
424C23×C53C2513yes—
425C22×D53—412no—
426C22×D53C2513yes—
427C22×D53C2514yes—
428C22×D53C2511yescharacteristic
429Q8×C53—212no—
430D4×C53—212no—
431D4×C53—412no—
432C2×C4×C53—26no—
433C2×C4×C53—26no—
434C2×C4×C53—26no—
435C2×C4×C53—43no—
436C2×C4×C53—43no—
437C2×C4×C53—43no—
438C2×C4×C53—412no—
439C2×C4×C53C2513yes—
440C2×C4×C53C25112yes—
441C2×C4×C53C2513yes—
442C2×C4×C53C2513yes—
443C2×C4×C53C2513yes—
444C22⋊D53—412no—
445C22⋊D53—43no—
446C22⋊D53—43no—
447C22⋊D53—43no—
448C22⋊D53—43no—
449C22⋊D53—412no—
450C22⋊D53—412no—
451C2×Dic53—412no—
452C2×Dic53C2513yes—
453C2×Dic53C25112yes—
454C2×Dic53C2513yes—
455C2×Dic53C2513yes—
456C2×Dic53C2513yes—
457D212—212no—
458D212—43no—
459D212—43no—
460D212—412no—
461C4×D53—26no—
462C4×D53—26no—
463C4×D53—26no—
464C4×D53—26no—
465C4×D53—412no—
466C4×D53—412no—
467C4×D53—412no—
468Dic106—212no—
469Dic106—43no—
470Dic106—43no—
471Dic106—412no—
472#62839—531nomaximal, Sylow
473C22×C53—212no—
474C22×C53—23no—
475C22×C53—23no—
476C22×C53—23no—
477C22×C53—44no—
478C22×C53C2611yescharacteristic
479C2×D53—23no—
480C2×D53—23no—
481C2×D53—23no—
482C2×D53—23no—
483C2×D53—212no—
484C2×D53—164no—
485C4×C53—23no—
486C4×C53—212no—
487C4×C53—23no—
488C4×C53—23no—
489C4×C53#58516yes—
490Dic53—212no—
491Dic53—23no—
492Dic53—23no—
493Dic53—23no—
494Dic53—23no—
495#3557—536no—
496#3551—536no—
497#3540—536no—
498#3539—536no—
499#3524—536no—
500#3524—536no—
501#3521—536no—
502#3521—536no—
503#3511—533no—
504#3511—533no—
505#3509—533no—
506#3508—533no—
507#3444—531no—
508#3444—531no—
509#3444D5311yescharacteristic, complemented
510C2×C53—44no—
511C2×C53—43no—
512C2×C53C2×#58513yes—
513D53—43no—
514D53—44no—
515D53—41no—
516#563—5312no—
517H(3,𝔽4)—534no—
518#560—534no—
519#560—5312no—
520#559—536no—
521#559—536no—
522#559—5312no—
523#557—536no—
524#557—536no—
525#556—536no—
526#556—536no—
527#556—536no—
528#556—536no—
529#555—536no—
530#555—536no—
531#555—5312no—
532#554—536no—
533#554—536no—
534#553—536no—
535#553—536no—
536#553—5312no—
537#553—536no—
538#553—5312no—
539#553—536no—
540#552—536no—
541#552—536no—
542#552—536no—
543#552—5312no—
544#552—536no—
545#552—5312no—
546#551—5312no—
547#551—5312no—
548#550—536no—
549#550—536no—
550#548—536no—
551#548—536no—
552#548—536no—
553#548—536no—
554#547—536no—
555#547—536no—
556#546—536no—
557#546—536no—
558#546—536no—
559#546—536no—
560#542—5312no—
561#542—536no—
562#542—536no—
563#542—536no—
564#542—536no—
565#542—5312no—
566#541—536no—
567#541—536no—
568#540—5312no—
569#540—536no—
570#540—536no—
571#540—5312no—
572#539—5312no—
573#539—5312no—
574#538—5312no—
575#538—5312no—
576#537—536no—
577#537—536no—
578#536—536no—
579#535—536no—
580#533—533no—
581#533—533no—
582#533—533no—
583#533—533no—
584#533C2×D5313yescomplemented
585#532—533no—
586#532—533no—
587#532—533no—
588#532—533no—
589#532C2×D5313yes—
590C2×C4⋊Q8—533no—
591C2×#127—531no—
592#529—5312no—
593#529—533no—
594#529—533no—
595#529—536no—
596#529—533no—
597#529—533no—
598#529—536no—
599#529—5312no—
600#529C2×D5316yescomplemented
601#529C2×D5316yescomplemented
602C2×#126—534no—
603C2×#126—534no—
604#525—533no—
605#525—533no—
606#525—536no—
607#525C2×D5316yescomplemented
608#520—536no—
609#520—536no—
610#519—536no—
611#518—536no—
612C4×#41—533no—
613C4×#41—533no—
614C4×#41—536no—
615C4×#41C2×D5316yescomplemented
616C22×C42C2×D5311yescharacteristic, complemented
617C53#6283911yescharacteristic, complemented, Sylow
618C2×#41—536no—
619C2×#41—536no—
620C2×#41—533no—
621C2×#41—533no—
622C2×#41—536no—
623C2×#41C22×D5316yes—
624C22×Q8—536no—
625C22×D4—536no—
626C23×C4C22×D5313yes—
627C4⋊Q8—536no—
628C4⋊Q8—536no—
629C4⋊Q8—536no—
630C4⋊Q8—5312no—
631C4⋊Q8—533no—
632C4⋊Q8—533no—
633C4⋊Q8C22×D5313yes—
634#127—536no—
635#127—5312no—
636#127—531no—
637#127—531no—
638#127C22×D5311yescharacteristic
639#126—5312no—
640#126—5312no—
641#126—5312no—
642#126—5312no—
643#126—5312no—
644#126—5312no—
645#126—531no—
646#126—531no—
647#126—534no—
648#126—5312no—
649#126—5312no—
650#126—533no—
651#126—533no—
652#126—534no—
653#126C22×D5314yes—
654#126C22×D5314yes—
655#125—5312no—
656#125—536no—
657#125—536no—
658#125—5312no—
659#125—5312no—
660#125—533no—
661#125—533no—
662#125—536no—
663#125—5312no—
664#125C22×D5316yes—
665#124—536no—
666#124—536no—
667#124—5312no—
668#124—5312no—
669#124—5312no—
670#124—5312no—
671#124—5312no—
672#124—536no—
673#124—533no—
674#124—533no—
675#124—5312no—
676#124C22×D5316yes—
677#123—5312no—
678#123—5312no—
679#123—533no—
680#123—533no—
681#123—533no—
682#123—533no—
683#123—5312no—
684#123—5312no—
685#123—5312no—
686#123—5312no—
687#123—5312no—
688#123—5312no—
689#123—5312no—
690#123—5312no—
691#123—5312no—
692#123C22×D53112yes—
693C22⋊Q8—536no—
694C22⋊Q8—536no—
695C22⋊Q8—536no—
696C22⋊Q8—533no—
697C22⋊Q8—533no—
698C22⋊Q8—533no—
699C22⋊Q8—533no—
700C22⋊Q8—536no—
701C22⋊Q8—5312no—
702C22⋊Q8—5312no—
703C22⋊Q8—536no—
704C22⋊Q8—536no—
705C22⋊Q8—5312no—
706C22⋊Q8—5312no—
707C22⋊Q8—5312no—
708C22⋊Q8—5312no—
709C22⋊Q8C22×D5316yes—
710C22⋊Q8C22×D5316yes—
711#121—536no—
712#121—536no—
713#121—5312no—
714#121—5312no—
715#121—5312no—
716#121—5312no—
717#121—536no—
718#121—533no—
719#121—533no—
720#121—533no—
721#121—533no—
722#121—536no—
723#121—5312no—
724#121—536no—
725#121—536no—
726#121—5312no—
727#121—5312no—
728#121—5312no—
729#121—5312no—
730#121—5312no—
731#121C22×D5316yes—
732#121C22×D5316yes—
733#120—533no—
734#120—534no—
735#120—531no—
736#120—5312no—
737#120—5312no—
738#120C22×D5314yes—
739C4×Q8—536no—
740C4×Q8—536no—
741C4×Q8—5312no—
742C4×Q8—536no—
743C4×Q8—536no—
744C4×Q8—536no—
745C4×Q8—536no—
746C4×Q8—533no—
747C4×Q8—533no—
748C4×Q8—533no—
749C4×Q8—533no—
750C4×Q8—5312no—
751C4×Q8C22×D5316yes—
752C4×Q8C22×D5316yes—
753C4×D4—536no—
754C4×D4—536no—
755C4×D4—5312no—
756C4×D4—533no—
757C4×D4—533no—
758C4×D4—533no—
759C4×D4—533no—
760C4×D4—533no—
761C4×D4—533no—
762C4×D4—533no—
763C4×D4—533no—
764C4×D4—5312no—
765C4×D4—5312no—
766C4×D4—5312no—
767C4×D4—536no—
768C4×D4—5312no—
769C4×D4—536no—
770C4×D4—5312no—
771C4×D4—5312no—
772C4×D4—536no—
773C4×D4—533no—
774C4×D4—533no—
775C4×D4—536no—
776C4×D4—533no—
777C4×D4—533no—
778C4×D4—5312no—
779C4×D4C22×D5316yes—
780C4×D4C22×D53112yes—
781C4×D4C22×D53112yes—
782C4×D4C22×D5316yes—
783#117—533no—
784#117—533no—
785#117—536no—
786#117—536no—
787#117—5312no—
788#117—536no—
789#117—5312no—
790#117—533no—
791#117—533no—
792#117—533no—
793#117—533no—
794#117—5312no—
795#117—5312no—
796#117—5312no—
797#117C22×D5316yes—
798#117C22×D53112yes—
799C2×C4⋊C4—5312no—
800C2×C4⋊C4—5312no—
801C2×C4⋊C4—536no—
802C2×C4⋊C4—536no—
803C2×C22⋊C4—5312no—
804C2×C22⋊C4—5312no—
805C2×C42—534no—
806C2×C42—531no—
807C2×C42—533no—
808C2×C42C22×D5313yes—
809C2×C42C22×D5313yes—
810C2×C42C22×D5314yes—
811C2×C42C22×D5313yes—
812C2×C42C22×D5313yes—
813C24—534no—
814C24C23×D5311yescharacteristic
815#41—412no—
816#41—2126no—
817#41—2126no—
818#41—21212no—
819#41—21212no—
820#41—21212no—
821C2×Q8—536no—
822C2×Q8—533no—
823C2×Q8—5312no—
824C2×Q8—533no—
825C2×Q8—21212no—
826C2×Q8C23×D5316yes—
827C2×D4—533no—
828C2×D4—5312no—
829C2×D4—533no—
830C2×D4—533no—
831C2×D4—5312no—
832C2×D4—533no—
833C2×D4—5312no—
834C2×D4—536no—
835C2×D4—533no—
836C2×D4—5312no—
837C2×D4—533no—
838C2×D4—21212no—
839C2×D4C23×D5316yes—
840C2×D4C23×D53112yes—
841C22×C4—46no—
842C22×C4—5312no—
843C22×C4—533no—
844C22×C4—533no—
845C22×C4—533no—
846C22×C4—533no—
847C22×C4—5312no—
848C22×C4—5312no—
849C22×C4—5312no—
850C22×C4C23×D5313yes—
851C22×C4C23×D5313yes—
852C22×C4C23×D5313yes—
853C22×C4C23×D5313yes—
854C22×C4C23×D5313yes—
855C22×C4C23×D5313yes—
856C22×C4C23×D53112yes—
857C4⋊C4—533no—
858C4⋊C4—533no—
859C4⋊C4—5312no—
860C4⋊C4—5312no—
861C4⋊C4—536no—
862C4⋊C4—536no—
863C4⋊C4—5312no—
864C4⋊C4—5312no—
865C4⋊C4—5312no—
866C4⋊C4—533no—
867C4⋊C4—533no—
868C4⋊C4—533no—
869C4⋊C4—533no—
870C4⋊C4—533no—
871C4⋊C4—533no—
872C4⋊C4—533no—
873C4⋊C4—533no—
874C4⋊C4—5312no—
875C4⋊C4—533no—
876C4⋊C4—533no—
877C4⋊C4—5312no—
878C4⋊C4—5312no—
879C4⋊C4C23×D5316yes—
880C4⋊C4C23×D5316yes—
881C4⋊C4C23×D53112yes—
882C4⋊C4C23×D53112yes—
883C22⋊C4—5312no—
884C22⋊C4—533no—
885C22⋊C4—533no—
886C22⋊C4—5312no—
887C22⋊C4—5312no—
888C22⋊C4—533no—
889C22⋊C4—533no—
890C22⋊C4—533no—
891C22⋊C4—533no—
892C22⋊C4—5312no—
893C22⋊C4—5312no—
894C22⋊C4—5312no—
895C22⋊C4—533no—
896C22⋊C4—533no—
897C22⋊C4—5312no—
898C22⋊C4—533no—
899C22⋊C4—533no—
900C22⋊C4—533no—
901C22⋊C4—533no—
902C22⋊C4—5312no—
903C22⋊C4—5312no—
904C22⋊C4C23×D53112yes—
905C22⋊C4C23×D53112yes—
906C22⋊C4C23×D53112yes—
907C42—5312no—
908C42—533no—
909C42—533no—
910C42—533no—
911C42—533no—
912C42—5312no—
913C42—5312no—
914C42C23×D5311yescharacteristic
915C42C23×D5311yescharacteristic
916C42C23×D5311yescharacteristic
917C42C23×D5313yes—
918C42C23×D5313yes—
919C42C23×D5313yes—
920C42C23×D5313yes—
921C42C23×D5311yescharacteristic
922C42C23×D53112yes—
923C23—43no—
924C23—531no—
925C23—534no—
926C23—533no—
927C23—21212no—
928C23C24×D5313yes—
929C23C24×D5314yes—
930Q8—212no—
931Q8—10612no—
932Q8—21212no—
933Q8—2123no—
934Q8—2123no—
935D4—212no—
936D4—412no—
937D4—10612no—
938D4—2123no—
939D4—2123no—
940D4—21212no—
941D4—21212no—
942D4—2123no—
943D4—2123no—
944D4—2123no—
945D4—2123no—
946D4—21212no—
947D4—21212no—
948C2×C4—26no—
949C2×C4—26no—
950C2×C4—26no—
951C2×C4—43no—
952C2×C4—43no—
953C2×C4—43no—
954C2×C4—412no—
955C2×C4—533no—
956C2×C4—533no—
957C2×C4—5312no—
958C2×C4—533no—
959C2×C4—533no—
960C2×C4—1066no—
961C2×C4—1066no—
962C2×C4—1066no—
963C2×C4—1066no—
964C2×C4—21212no—
965C2×C4—21212no—
966C2×C4—21212no—
967C2×C4—21212no—
968C2×C4C24×D5313yes—
969C2×C4C24×D53112yes—
970C2×C4C24×D5313yes—
971C2×C4C24×D5313yes—
972C2×C4C24×D5313yes—
973C22—23no—
974C22—23no—
975C22—23no—
976C22—212no—
977C22—44no—
978C22—8484no—
979C22—1063no—
980C22—1063no—
981C22—1063no—
982C22—1063no—
983C22—10612no—
984C22C25×D5311yescharacteristic
985C4—23no—
986C4—23no—
987C4—23no—
988C4—212no—
989C4—1063no—
990C4—1063no—
991C4—1063no—
992C4—1063no—
993C4—10612no—
994C4#1681145916yes—
995C2—43no—
996C2—44no—
997C2—2121no—
998C2—2124no—
999C2—2123no—
1000C2C2×#1681145913yes—
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3444C2
hypercenter#3444D53
hypocenterC53#62839
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3444

Complements

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

NH ≅ G/Ntype
1. #20289217C2semidirect
2. #20289137C2semidirect
3. #20288983C2semidirect
4. #20288971C2semidirect
5. #20288824C2semidirect
6. #20288814C2semidirect
7. #20288783C2semidirect
8. #20288777C2semidirect
9. #20288627C2semidirect
10. #20288616C2semidirect
11. #20288594C2semidirect
12. #20288584C2semidirect
13. #20288011C2semidirect
14. #20288011C2semidirect
15. C53×#3444C2semidirect
16. #16811375C22semidirect
18. #16811364C22semidirect
19. #16811362C22semidirect
20. #16811356C22semidirect
21. #16811356C22semidirect
22. #16811355C22semidirect
23. #16811350C22semidirect
24. #16811349C22semidirect
25. #16811345C22semidirect
27. #16811342C22semidirect
29. #16811337C22semidirect
30. #16811336C22semidirect
31. #16811336C22semidirect
32. #16811332C22semidirect
33. #16811329C22semidirect
34. #16811326C22semidirect
35. #16811323C22semidirect
36. #16811323C22semidirect
37. #16811322C22semidirect
38. #16811320C22semidirect
39. #16811317C22semidirect
40. #16811314C22semidirect
41. #16811312C22semidirect
42. #16811312C22semidirect
43. #16811311C22semidirect
44. #16811307C22semidirect
45. #16811306C22semidirect
47. #16811297C22semidirect
50. #16811285C22semidirect
51. #16811283C22semidirect
52. #16811281C22semidirect
53. #16811280C22semidirect
54. #16811275C22semidirect
55. #16811272C22semidirect
57. #16811268C22semidirect
58. #16811266C22semidirect
60. #16811246C22semidirect
61. #16811245C22semidirect
62. #16811241C22semidirect
63. #16811240C22semidirect
64. #16811238C22semidirect
65. #16811238C22semidirect
66. #16811233C22semidirect
67. #16811231C22semidirect
69. #16811225C22semidirect
70. #16811224C22semidirect
71. #16811224C22semidirect
72. #16811216C22semidirect
73. #16811215C22semidirect
76. #16811203C22semidirect
77. #16811202C22semidirect
80. #16811180C22semidirect
81. #16811180C22semidirect
82. #16811178C22semidirect
83. #16811178C22semidirect
84. #16811174C22semidirect
87. #16811171C22semidirect
88. C4⋊Q8×D53C22semidirect
89. #127×D53C22semidirect
92. #16811157C22semidirect
93. #16811157C22semidirect
94. #16811157C22semidirect
95. #16811157C22semidirect
96. #16811157C22semidirect
97. #16811156C22semidirect
98. C2×#13133211C22semidirect
99. #126×D53C22semidirect
101. #16811134C22semidirect
102. #16811134C22semidirect
103. #16811105C22semidirect
104. #16811102C22semidirect
105. #16811099C22semidirect
106. #16811095C22semidirect
108. C4×#11719945C22semidirect
109. C4×#11719945C22semidirect
110. C53×#533C22semidirect
112. C53×#529C22semidirect
113. C53×#529C22semidirect
114. C53×#525C22semidirect
115. C4×#41×C53C22semidirect
116. C22×C42×C53C22semidirect
509. #3444D53semidirect
584. #533C2×D53semidirect
600. #529C2×D53semidirect
601. #529C2×D53semidirect
607. #525C2×D53semidirect
615. C4×#41C2×D53semidirect
616. C22×C42C2×D53semidirect
617. C53#62839semidirect

Maximal subgroups

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

subgroupindex
#202892172
#202891372
#202889832
#202889712
#202888242
#202888142
#202887832
#202887772
#202886272
#202886162
#202885942
#202885842
#202880112
C53×#34442
#6283953