Finite Group Databasebeta

← #28292827

Subgroups — #28292827

Order 13568.

6670 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289343C216yesmaximal, complemented
2#20289333C216yesmaximal, complemented
3#20289271C216yesmaximal, complemented
4#20289261C216yesmaximal, complemented
5#20288783C2112yesmaximal, complemented
6#20288769C2112yesmaximal, complemented
7#20288416C216yesmaximal, complemented
8#20288398C216yesmaximal, complemented
9#20288011C211yesmaximal, characteristic, complemented
10C22×#13133211C211yesmaximal, characteristic, complemented
11C53×#3444C211yesmaximal, characteristic, complemented
12#16811375C22112yescomplemented
13#16811372C22112yescomplemented
14#16811364C2214yescomplemented
15#16811360C2214yescomplemented
16#16811345C22112yescomplemented
17#16811341C22112yescomplemented
18#16811332C22112yescomplemented
19#16811327C22112yescomplemented
20#16811322C22112yescomplemented
21#16811322C22112yescomplemented
22#16811317C22112yescomplemented
23#16811316C22112yescomplemented
24#16811314C22112yescomplemented
25#16811310C22112yescomplemented
26#16811306C22112yescomplemented
27#16811306C22112yescomplemented
28#16811302C22112yescomplemented
29#16811302C22112yescomplemented
30#16811300C22112yescomplemented
31#16811297C22112yescomplemented
32#16811297C22112yescomplemented
33#16811296C22112yescomplemented
34#16811272C22112yescomplemented
35#16811271C22112yescomplemented
36#16811268C22112yescomplemented
37#16811265C22112yescomplemented
38#16811262C22112yescomplemented
39#16811261C22112yescomplemented
40#16811252C2216yescomplemented
41#16811248C2216yescomplemented
42#16811245C22112yescomplemented
43#16811237C22112yescomplemented
44#16811232C22112yescomplemented
45#16811231C22112yescomplemented
46#16811222C2216yescomplemented
47#16811221C22112yescomplemented
48#16811218C2216yescomplemented
49#16811215C22112yescomplemented
50#16811215C22112yescomplemented
51#16811213C2216yes—
52#16811210C2216yes—
53#16811207C22112yescomplemented
54#16811206C22112yes—
55#16811206C22112yescomplemented
56#16811200C2216yescomplemented
57#16811181C2216yescomplemented
58#16811180C2213yescomplemented
59#16811173C2213yescomplemented
60#16811157C2216yescomplemented
61#16811157C2216yescomplemented
62#16811157C22112yescomplemented
63#16811156C22112yescomplemented
64C2×#13133211C2216yescomplemented
65C2×#13133211C2216yescomplemented
66C2×#13133211C2216yescomplemented
67C2×#13133211C2216yescomplemented
68C2×#13133211C2214yescomplemented
69#126×D53C2214yescomplemented
70#16811134C2216yescomplemented
71#16811129C22112yescomplemented
72#120×D53C2214yes—
73#16811102C22112yescomplemented
74#16811095C22112yescomplemented
75C4×#11719945C2216yescomplemented
76C22×#11719919C2213yescomplemented
77C22×#11719921C2213yes—
78C53×#533C2213yescomplemented
79C53×#532C2213yescomplemented
80C53×#529C2216yescomplemented
81C53×#529C2216yescomplemented
82C53×#525C2216yescomplemented
83C4×#41×C53C2216yescomplemented
84C22×C42×C53C2211yescharacteristic, complemented
85C24×D53C2311yescharacteristic
86C2×#11719945C2316yes—
87C2×#11719947C23112yes—
88C2×D4×D53C23112yes—
89C23×Dic53C2313yes—
90#13133217C2313yescomplemented
91#13133216C23112yescomplemented
92#13133215C23112yescomplemented
93#13133214C2311yescharacteristic, complemented
94#13133212C23112yes—
95#13133212C23112yes—
96#13133212C23112yes—
97#13133212C23112yescomplemented
98#13133211C23112yes—
99#13133211C23112yes—
100#13133211C23112yes—
101#13133211C2314yes—
102#13133211C2314yes—
103#13133211C2314yes—
104#13133211C2314yes—
105#13133211C23112yes—
106#13133211C23112yes—
107#13133211C23112yescomplemented
108#13133211C2314yescomplemented
109#13133211C2314yescomplemented
110#13133210C23112yescomplemented
111#13133210C23112yescomplemented
112#13133209C23112yescomplemented
113#13133209C2316yescomplemented
114#13133208C23112yescomplemented
115#13133207C23112yescomplemented
116#13133207C23112yescomplemented
117#13133207C23112yescomplemented
118#13133207C23112yescomplemented
119#13133206C23112yes—
120#13133205C23112yes—
121#13133205C2316yescomplemented
122#13133203C23112yes—
123#13133203C23112yes—
124#13133202C23112yes—
125#13133202C23112yes—
126#13133202C23112yes—
127#13133202C23112yescomplemented
128#13133201C23112yes—
129#13133201C23112yes—
130#13133200C23112yes—
131#13133200C23112yes—
132#13133200C23112yescomplemented
133#13133199C23112yes—
134#13133199C23112yescomplemented
135#13133198C23112yes—
136#13133198C23112yescomplemented
137#13133197C23112yes—
138#13133196C2316yes—
139#13133196C2316yes—
140#13133196C23112yescomplemented
141#13133195C23112yes—
142#13133195C23112yes—
143#13133195C23112yescomplemented
144#13133195C23112yescomplemented
145#13133194C23112yes—
146#13133194C23112yes—
147#13133194C23112yescomplemented
148#13133194C23112yescomplemented
149#13133193C23112yes—
150#13133193C23112yescomplemented
151#13133192C23112yes—
152#13133191C2316yes—
153#13133191C23112yes—
154#13133191C2316yes—
155#13133190C23112yes—
156#13133190C23112yescomplemented
157#13133189C23112yes—
158#13133189C23112yes—
159#13133189C23112yes—
160#13133189C23112yescomplemented
161#13133187C23112yes—
162#13133187C23112yes—
163#13133186C2314yes—
164#13133185C23112yes—
165#13133185C23112yes—
166C4×Dic106C2316yescomplemented
167C4×Dic106C23112yescomplemented
168C4×Dic106C2316yescomplemented
169#13133182C23112yescomplemented
170C4×D212C23112yes—
171C4×D212C2316yescomplemented
172C4×D212C2316yescomplemented
173D4×Dic53C23112yes—
174D4×Dic53C23112yes—
175#13133179C23112yes—
176C4×C22⋊D53C23112yes—
177C4×C22⋊D53C23112yes—
178C4×C22⋊D53C23112yes—
179C4×C22⋊D53C23112yescomplemented
180#13133177C23112yes—
181#13133177C23112yes—
182#13133177C23112yes—
183#13133177C23112yescomplemented
184#13133176C2316yes—
185#13133175C23112yes—
186#13133174C23112yes—
187#13133174C23112yescomplemented
188#13133174C23112yescomplemented
189#13133173C23112yes—
190#13133173C23112yescomplemented
191C2×#11719919C2316yes—
192C2×#11719919C2316yes—
193C2×#11719919C2316yes—
194C2×#11719919C2316yes—
195C2×#11719919C2316yes—
196C2×#11719919C2316yes—
197C2×#11719919C23112yescomplemented
198C4⋊C4×D53C23112yescomplemented
199C2×#11719921C2316yes—
200C2×#11719921C2316yes—
201C2×#11719921C23112yes—
202C2×#11719921C2316yes—
203C2×#11719921C2316yes—
204C2×#11719921C2316yes—
205C2×#11719921C2316yes—
206C22⋊C4×D53C23112yes—
207C22⋊C4×D53C23112yes—
208C42×D53C2314yescomplemented
209C2×#41×C53C2316yes—
210C23×C4×C53C2313yes—
211C4⋊Q8×C53C2313yescomplemented
212#127×C53C2311yescharacteristic, complemented
213#126×C53C2314yescomplemented
214#126×C53C2314yescomplemented
215#125×C53C2316yescomplemented
216#124×C53C2316yescomplemented
217#123×C53C23112yes—
218C22⋊Q8×C53C2316yes—
219C22⋊Q8×C53C2316yes—
220#121×C53C2316yes—
221#121×C53C2316yes—
222#120×C53C2314yes—
223C4×Q8×C53C2316yescomplemented
224C4×Q8×C53C2316yescomplemented
225C4×D4×C53C23112yes—
226C4×D4×C53C23112yes—
227C4×D4×C53C2316yescomplemented
228C4×D4×C53C2316yescomplemented
229#117×C53C2316yes—
230#117×C53C23112yescomplemented
231C2×C42×C53C2313yes—
232C2×C42×C53C2313yes—
233C2×C42×C53C2313yes—
234C2×C42×C53C2313yes—
235C2×C42×C53C2314yescomplemented
236C24×C53C2411yescharacteristic
237C23×D53—46no—
238C23×D53C2416yes—
239C23×D53C2414yes—
240#41×C53—412no—
241C2×Q8×C53C2416yes—
242C2×D4×C53C24112yes—
243C2×D4×C53C2416yes—
244C22×C4×C53—46no—
245C22×C4×C53C2413yes—
246C22×C4×C53C2413yes—
247C22×C4×C53C2413yes—
248C22×C4×C53C2413yes—
249C22×C4×C53C2413yes—
250C22×C4×C53C2413yes—
251C22×C4×C53C24112yes—
252C2×C22⋊D53C24112yes—
253C2×C22⋊D53C24112yes—
254C2×C22⋊D53C24112yes—
255C22×Dic53—46no—
256C22×Dic53C2416yes—
257C22×Dic53C2416yes—
258C22×Dic53C2416yes—
259C22×Dic53C24112yes—
260#11719947—424no—
261D4×D53—424no—
262#11719945—412no—
263C2×D212C24112yes—
264C2×D212C2416yes—
265C2×C4×D53C24112yes—
266C2×C4×D53C24112yes—
267C2×C4×D53C24112yes—
268C2×Dic106C24112yes—
269C2×Dic106C2416yes—
270C4⋊C4×C53C2416yes—
271C4⋊C4×C53C2416yes—
272C4⋊C4×C53C24112yes—
273C4⋊C4×C53C24112yes—
274C22⋊C4×C53C24112yes—
275C22⋊C4×C53C24112yes—
276C22⋊C4×C53C24112yes—
277C42×C53C2411yescharacteristic
278C42×C53C2413yes—
279C42×C53C2413yes—
280C42×C53C2413yes—
281C42×C53C2413yes—
282C42×C53C2411yescharacteristic
283C42×C53C2411yescharacteristic
284C42×C53C2411yescharacteristic
285C42×C53C24112yes—
286C22⋊Dic53C24112yes—
287C22⋊Dic53C24112yes—
288C22⋊Dic53C24112yes—
289#11719921C24112yes—
290#11719921C24112yes—
291#11719921C24112yes—
292#11719921C24112yes—
293#11719921C24112yes—
294#11719921C24112yes—
295#11719921C24112yes—
296#11719921C24112yes—
297#11719921C24112yes—
298#11719921C24112yes—
299C4⋊Dic53C24112yes—
300C4⋊Dic53C24112yes—
301C4⋊Dic53C2416yes—
302C4⋊Dic53C2416yes—
303#11719919C24112yes—
304#11719919C24112yes—
305#11719919C24112yes—
306#11719919C24112yes—
307#11719919C24112yes—
308#11719919C24112yes—
309#11719919C24112yes—
310#11719919C24112yes—
311#11719919C24112yes—
312#11719919C24112yes—
313C4×Dic53C24112yes—
314C4×Dic53C24112yes—
315C4×Dic53C24112yes—
316C23×C53—26no—
317C23×C53C2514yes—
318C23×C53C2513yes—
319C22×D53—212no—
320C22×D53—46no—
321C22×D53—46no—
322C22×D53—412no—
323C22×D53—88no—
324C22×D53C2514yes—
325C22×D53C2514yes—
326Q8×C53—46no—
327D4×C53—224no—
328D4×C53—46no—
329C2×C4×C53—26no—
330C2×C4×C53—26no—
331C2×C4×C53—43no—
332C2×C4×C53—43no—
333C2×C4×C53—43no—
334C2×C4×C53—43no—
335C2×C4×C53—412no—
336C2×C4×C53C2513yes—
337C2×C4×C53C25112yes—
338C2×C4×C53C2513yes—
339C2×C4×C53C2513yes—
340C2×C4×C53C2513yes—
341C22⋊D53—224no—
342C22⋊D53—412no—
343C22⋊D53—412no—
344C2×Dic53—212no—
345C2×Dic53—412no—
346C2×Dic53—46no—
347C2×Dic53—46no—
348C2×Dic53C25112yes—
349C2×Dic53C25112yes—
350D212—46no—
351D212—412no—
352C4×D53—412no—
353C4×D53—412no—
354C4×D53—412no—
355Dic106—46no—
356Dic106—412no—
357#62826—531nomaximal, Sylow
358C22×C53—28no—
359C22×C53—23no—
360C22×C53—23no—
361C22×C53—212no—
362C22×C53#58516yes—
363C22×C53C2611yescharacteristic
364C2×D53—212no—
365C2×D53—212no—
366C2×D53—812no—
367C2×D53—164no—
368C4×C53—23no—
369C4×C53—212no—
370C4×C53—23no—
371C4×C53—23no—
372C4×C53—23no—
373Dic53—212no—
374Dic53—212no—
375#3564—536no—
376#3564—536no—
377#3560—536no—
378#3560—536no—
379#3521—5312no—
380#3521—5312no—
381#3492—536no—
382#3490—536no—
383#3444—531no—
384#3444D5311yescharacteristic, complemented
385C22×#126—531no—
386C2×C53—26no—
387C2×C53—44no—
388C2×C53C2×#58513yes—
389D53—44no—
390D53—44no—
391#563—5312no—
392#563—5312no—
393#560—534no—
394#560—534no—
395#556—5312no—
396#556—5312no—
397#554—5312no—
398#554—5312no—
399#553—5312no—
400#553—5312no—
401#553—5312no—
402#553—5312no—
403#552—5312no—
404#552—5312no—
405#552—5312no—
406#552—5312no—
407#551—5312no—
408#551—5312no—
409#551—5312no—
410#551—5312no—
411#551—5312no—
412#551—5312no—
413#547—5312no—
414#547—5312no—
415#546—5312no—
416#546—5312no—
417#546—5312no—
418#546—5312no—
419#544—536no—
420#543—536no—
421#542—5312no—
422#542—5312no—
423#541—5312no—
424#541—5312no—
425#539—5312no—
426#539—536no—
427#539—536no—
428#539—5312no—
429#539—5312no—
430#538—5312no—
431#538—536no—
432#538—536no—
433#538—5312no—
434#538—5312no—
435#537—536no—
436#534—536no—
437#533—533no—
438#533C2×D5313yescomplemented
439#532—533no—
440#532C2×D5313yescomplemented
441#529—5312no—
442#529—536no—
443#529—536no—
444#529—5312no—
445#529C2×D5316yescomplemented
446#529C2×D5316yescomplemented
447C2×#126—534no—
448C2×#126—536no—
449C2×#126—536no—
450C2×#126—536no—
451C2×#126—536no—
452C2×#126—534no—
453#525—536no—
454#525—5312no—
455#525C2×D5316yescomplemented
456C2×#120—534no—
457#520—5312no—
458#518—5312no—
459C4×#41—536no—
460C4×#41C2×D5316yescomplemented
461C22×C4⋊C4—533no—
462C22×C22⋊C4—533no—
463C22×C42C2×D5311yescharacteristic, complemented
464C53#6282611yescharacteristic, complemented, Sylow
465C25—531no—
466C2×#41—5312no—
467C2×#41—536no—
468C2×#41C22×D5316yes—
469C22×D4—5312no—
470C23×C4—533no—
471C23×C4C22×D5313yes—
472C4⋊Q8—5312no—
473C4⋊Q8—5312no—
474C4⋊Q8—533no—
475C4⋊Q8C22×D5313yescomplemented
476#127—531no—
477#127C22×D5311yescharacteristic, complemented
478#126—5312no—
479#126—5312no—
480#126—5312no—
481#126—5312no—
482#126—5312no—
483#126—5312no—
484#126—534no—
485#126—534no—
486#126—5312no—
487#126—5312no—
488#126—5312no—
489#126—5312no—
490#126—534no—
491#126—534no—
492#126—534no—
493#126—5312no—
494#126—5312no—
495#126—534no—
496#126C22×D5314yescomplemented
497#126C22×D5314yescomplemented
498#125—5312no—
499#125—5312no—
500#125—5312no—
501#125—5312no—
502#125—5312no—
503#125—536no—
504#125—5312no—
505#125C22×D5316yescomplemented
506#124—5312no—
507#124—5312no—
508#124—5312no—
509#124—536no—
510#124—5312no—
511#124C22×D5316yescomplemented
512#123—5312no—
513#123—5312no—
514#123—5312no—
515#123—5312no—
516#123—5312no—
517#123—5312no—
518#123—5312no—
519#123—5312no—
520#123—5312no—
521#123—5312no—
522#123—5312no—
523#123—5312no—
524#123—5312no—
525#123C22×D53112yes—
526C22⋊Q8—5312no—
527C22⋊Q8—5312no—
528C22⋊Q8—536no—
529C22⋊Q8—536no—
530C22⋊Q8—5312no—
531C22⋊Q8—5312no—
532C22⋊Q8—5312no—
533C22⋊Q8—5312no—
534C22⋊Q8—5312no—
535C22⋊Q8—5312no—
536C22⋊Q8—5312no—
537C22⋊Q8—5312no—
538C22⋊Q8—5312no—
539C22⋊Q8—5312no—
540C22⋊Q8C22×D5316yes—
541C22⋊Q8C22×D5316yes—
542#121—5312no—
543#121—5312no—
544#121—5312no—
545#121—5312no—
546#121—536no—
547#121—536no—
548#121—5312no—
549#121—5312no—
550#121—5312no—
551#121—5312no—
552#121C22×D5316yes—
553#121C22×D5316yes—
554#120—534no—
555#120—5312no—
556#120—5312no—
557#120—5312no—
558#120—5312no—
559#120C22×D5314yes—
560C4×Q8—5312no—
561C4×Q8—536no—
562C4×Q8—536no—
563C4×Q8—5312no—
564C4×Q8C22×D5316yescomplemented
565C4×Q8C22×D5316yescomplemented
566C4×D4—5312no—
567C4×D4—5312no—
568C4×D4—5312no—
569C4×D4—5312no—
570C4×D4—5312no—
571C4×D4—5312no—
572C4×D4—5312no—
573C4×D4—5312no—
574C4×D4—5312no—
575C4×D4—5312no—
576C4×D4—5312no—
577C4×D4—536no—
578C4×D4—536no—
579C4×D4—5312no—
580C4×D4C22×D53112yes—
581C4×D4C22×D53112yes—
582C4×D4C22×D5316yescomplemented
583C4×D4C22×D5316yescomplemented
584#117—536no—
585#117—5312no—
586#117—5312no—
587#117—5312no—
588#117—5312no—
589#117—5312no—
590#117—5312no—
591#117C22×D5316yes—
592#117C22×D53112yescomplemented
593C2×C4⋊C4—536no—
594C2×C4⋊C4—536no—
595C2×C4⋊C4—536no—
596C2×C4⋊C4—536no—
597C2×C4⋊C4—536no—
598C2×C4⋊C4—536no—
599C2×C4⋊C4—5312no—
600C2×C4⋊C4—5312no—
601C2×C22⋊C4—536no—
602C2×C22⋊C4—536no—
603C2×C22⋊C4—536no—
604C2×C22⋊C4—536no—
605C2×C22⋊C4—536no—
606C2×C22⋊C4—536no—
607C2×C22⋊C4—5312no—
608C2×C22⋊C4—5312no—
609C2×C22⋊C4—5312no—
610C2×C42—534no—
611C2×C42C22×D5313yes—
612C2×C42C22×D5313yes—
613C2×C42C22×D5313yes—
614C2×C42C22×D5313yes—
615C2×C42C22×D5314yescomplemented
616C24—536no—
617C24—534no—
618C24—2126no—
619C24C23×D5311yescharacteristic
620#41—412no—
621#41—21212no—
622#41—21224no—
623C2×Q8—5312no—
624C2×Q8—536no—
625C2×Q8C23×D5316yes—
626C2×D4—5312no—
627C2×D4—5312no—
628C2×D4—5312no—
629C2×D4—5312no—
630C2×D4—536no—
631C2×D4—21224no—
632C2×D4C23×D53112yes—
633C2×D4C23×D5316yes—
634C22×C4—46no—
635C22×C4—536no—
636C22×C4—536no—
637C22×C4—536no—
638C22×C4—5312no—
639C22×C4—5312no—
640C22×C4—5312no—
641C22×C4—5312no—
642C22×C4—2126no—
643C22×C4C23×D5313yes—
644C22×C4C23×D5313yes—
645C22×C4C23×D5313yes—
646C22×C4C23×D5313yes—
647C22×C4C23×D5313yes—
648C22×C4C23×D5313yes—
649C22×C4C23×D53112yes—
650C4⋊C4—5312no—
651C4⋊C4—5312no—
652C4⋊C4—5312no—
653C4⋊C4—5312no—
654C4⋊C4—5312no—
655C4⋊C4—5312no—
656C4⋊C4—5312no—
657C4⋊C4—5312no—
658C4⋊C4—5312no—
659C4⋊C4—5312no—
660C4⋊C4—5312no—
661C4⋊C4—5312no—
662C4⋊C4—536no—
663C4⋊C4—536no—
664C4⋊C4C23×D53112yes—
665C4⋊C4C23×D5316yes—
666C4⋊C4C23×D5316yes—
667C4⋊C4C23×D53112yes—
668C22⋊C4—5312no—
669C22⋊C4—5312no—
670C22⋊C4—5312no—
671C22⋊C4—5312no—
672C22⋊C4—5312no—
673C22⋊C4—5312no—
674C22⋊C4—5312no—
675C22⋊C4—5312no—
676C22⋊C4—5312no—
677C22⋊C4—5312no—
678C22⋊C4—5312no—
679C22⋊C4—5312no—
680C22⋊C4—5312no—
681C22⋊C4C23×D53112yes—
682C22⋊C4C23×D53112yes—
683C22⋊C4C23×D53112yes—
684C42—5312no—
685C42—5312no—
686C42—5312no—
687C42C23×D5311yescharacteristic
688C42C23×D5311yescharacteristic
689C42C23×D5313yes—
690C42C23×D5313yes—
691C42C23×D5313yes—
692C42C23×D5313yes—
693C42C23×D5311yescharacteristic
694C42C23×D5311yescharacteristic
695C42C23×D53112yes—
696C23—26no—
697C23—534no—
698C23—534no—
699C23—10612no—
700C23—4248no—
701C23—21212no—
702C23—2126no—
703C23—2126no—
704C23C24×D5314yes—
705C23C24×D5313yes—
706Q8—46no—
707Q8—2126no—
708Q8—21212no—
709D4—224no—
710D4—46no—
711D4—10624no—
712D4—21212no—
713D4—2126no—
714D4—21212no—
715D4—21212no—
716C2×C4—26no—
717C2×C4—26no—
718C2×C4—43no—
719C2×C4—43no—
720C2×C4—43no—
721C2×C4—43no—
722C2×C4—412no—
723C2×C4—5312no—
724C2×C4—5312no—
725C2×C4—10612no—
726C2×C4—21212no—
727C2×C4—21212no—
728C2×C4—21212no—
729C2×C4—2126no—
730C2×C4—2126no—
731C2×C4—21212no—
732C2×C4C24×D5313yes—
733C2×C4C24×D53112yes—
734C2×C4C24×D5313yes—
735C2×C4C24×D5313yes—
736C2×C4C24×D5313yes—
737C22—28no—
738C22—23no—
739C22—23no—
740C22—212no—
741C22—8484no—
742C22—10612no—
743C22—10612no—
744C22—42412no—
745C22#1681145916yes—
746C22C25×D5311yescharacteristic
747C4—23no—
748C4—23no—
749C4—23no—
750C4—23no—
751C4—212no—
752C4—10612no—
753C4—10612no—
754C2—26no—
755C2—44no—
756C2—2124no—
757C2—2124no—
758C2C2×#1681145913yes—
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3444C2
hypercenter#3444D53
hypocenterC53#62826
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3444

Complements

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

NH ≅ G/Ntype
1. #20289343C2semidirect
2. #20289333C2semidirect
3. #20289271C2semidirect
4. #20289261C2semidirect
5. #20288783C2semidirect
6. #20288769C2semidirect
7. #20288416C2semidirect
8. #20288398C2semidirect
9. #20288011C2semidirect
10. C22×#13133211C2semidirect
11. C53×#3444C2semidirect
12. #16811375C22semidirect
13. #16811372C22semidirect
14. #16811364C22semidirect
15. #16811360C22semidirect
16. #16811345C22semidirect
17. #16811341C22semidirect
18. #16811332C22semidirect
19. #16811327C22semidirect
20. #16811322C22semidirect
21. #16811322C22semidirect
22. #16811317C22semidirect
23. #16811316C22semidirect
24. #16811314C22semidirect
25. #16811310C22semidirect
26. #16811306C22semidirect
27. #16811306C22semidirect
28. #16811302C22semidirect
29. #16811302C22semidirect
30. #16811300C22semidirect
31. #16811297C22semidirect
32. #16811297C22semidirect
33. #16811296C22semidirect
34. #16811272C22semidirect
35. #16811271C22semidirect
36. #16811268C22semidirect
37. #16811265C22semidirect
38. #16811262C22semidirect
39. #16811261C22semidirect
40. #16811252C22semidirect
41. #16811248C22semidirect
42. #16811245C22semidirect
43. #16811237C22semidirect
44. #16811232C22semidirect
45. #16811231C22semidirect
46. #16811222C22semidirect
47. #16811221C22semidirect
48. #16811218C22semidirect
49. #16811215C22semidirect
50. #16811215C22semidirect
53. #16811207C22semidirect
55. #16811206C22semidirect
56. #16811200C22semidirect
57. #16811181C22semidirect
58. #16811180C22semidirect
59. #16811173C22semidirect
60. #16811157C22semidirect
61. #16811157C22semidirect
62. #16811157C22semidirect
63. #16811156C22semidirect
64. C2×#13133211C22semidirect
65. C2×#13133211C22semidirect
66. C2×#13133211C22semidirect
67. C2×#13133211C22semidirect
68. C2×#13133211C22semidirect
69. #126×D53C22semidirect
70. #16811134C22semidirect
71. #16811129C22semidirect
73. #16811102C22semidirect
74. #16811095C22semidirect
75. C4×#11719945C22semidirect
76. C22×#11719919C22semidirect
78. C53×#533C22semidirect
79. C53×#532C22semidirect
80. C53×#529C22semidirect
81. C53×#529C22semidirect
82. C53×#525C22semidirect
83. C4×#41×C53C22semidirect
84. C22×C42×C53C22semidirect
90. #13133217C23semidirect
91. #13133216C23semidirect
92. #13133215C23semidirect
93. #13133214C23semidirect
97. #13133212C23semidirect
107. #13133211C23semidirect
108. #13133211C23semidirect
109. #13133211C23semidirect
110. #13133210C23semidirect
111. #13133210C23semidirect
112. #13133209C23semidirect
113. #13133209C23semidirect
114. #13133208C23semidirect
115. #13133207C23semidirect
116. #13133207C23semidirect
117. #13133207C23semidirect
118. #13133207C23semidirect
121. #13133205C23semidirect
127. #13133202C23semidirect
132. #13133200C23semidirect
134. #13133199C23semidirect
136. #13133198C23semidirect
140. #13133196C23semidirect
143. #13133195C23semidirect
144. #13133195C23semidirect
147. #13133194C23semidirect
148. #13133194C23semidirect
150. #13133193C23semidirect
156. #13133190C23semidirect
160. #13133189C23semidirect
166. C4×Dic106C23semidirect
167. C4×Dic106C23semidirect
168. C4×Dic106C23semidirect
169. #13133182C23semidirect
171. C4×D212C23semidirect
172. C4×D212C23semidirect
179. C4×C22⋊D53C23semidirect
183. #13133177C23semidirect
187. #13133174C23semidirect
188. #13133174C23semidirect
190. #13133173C23semidirect
197. C2×#11719919C23semidirect
198. C4⋊C4×D53C23semidirect
208. C42×D53C23semidirect
211. C4⋊Q8×C53C23semidirect
212. #127×C53C23semidirect
213. #126×C53C23semidirect
214. #126×C53C23semidirect
215. #125×C53C23semidirect
216. #124×C53C23semidirect
223. C4×Q8×C53C23semidirect
224. C4×Q8×C53C23semidirect
227. C4×D4×C53C23semidirect
228. C4×D4×C53C23semidirect
230. #117×C53C23semidirect
235. C2×C42×C53C23semidirect
384. #3444D53semidirect
438. #533C2×D53semidirect
440. #532C2×D53semidirect
445. #529C2×D53semidirect
446. #529C2×D53semidirect
455. #525C2×D53semidirect
460. C4×#41C2×D53semidirect
463. C22×C42C2×D53semidirect
464. C53#62826semidirect
475. C4⋊Q8C22×D53semidirect
477. #127C22×D53semidirect
496. #126C22×D53semidirect
497. #126C22×D53semidirect
505. #125C22×D53semidirect
511. #124C22×D53semidirect
564. C4×Q8C22×D53semidirect
565. C4×Q8C22×D53semidirect
582. C4×D4C22×D53semidirect
583. C4×D4C22×D53semidirect
592. #117C22×D53semidirect
615. C2×C42C22×D53semidirect

Maximal subgroups

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

subgroupindex
#202893432
#202893332
#202892712
#202892612
#202887832
#202887692
#202884162
#202883982
#202880112
C22×#131332112
C53×#34442
#6282653