Finite Group Databasebeta

← #28293113

Subgroups — #28293113

Order 13568.

7474 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288553C216yesmaximal, complemented
2#20288550C216yesmaximal, complemented
3#20288547C216yesmaximal, complemented
4#20288543C216yesmaximal, complemented
5#20288409C216yesmaximal, complemented
6#20288407C216yesmaximal, complemented
7#20288401C216yesmaximal, complemented
8#20288398C216yesmaximal, complemented
9#20288127C211yesmaximal, characteristic, complemented
10#20288124C213yesmaximal, complemented
11#20288121C213yesmaximal, complemented
12#543×D53C211yesmaximal, characteristic, complemented
13#534×D53C213yesmaximal, complemented
14C2×#16811095C213yesmaximal, complemented
15C53×#3459C211yesmaximal, characteristic, complemented
16C22×D4×D53C2213yes—
17#16811326C2216yescomplemented
18#16811324C22112yescomplemented
19#16811323C2216yescomplemented
20#16811320C2216yescomplemented
21#16811318C22112yescomplemented
22#16811317C2216yescomplemented
23#16811314C2216yescomplemented
24#16811312C2216yescomplemented
25#16811311C2216yescomplemented
26#16811309C22112yescomplemented
27#16811307C2216yescomplemented
28#16811305C22112yescomplemented
29#16811303C22112yescomplemented
30#16811302C22112yescomplemented
31#16811301C22112yescomplemented
32#16811300C22112yescomplemented
33#16811298C22112yescomplemented
34#16811298C22112yescomplemented
35#16811297C22112yescomplemented
36#16811296C22112yescomplemented
37#16811285C2212yescomplemented
38#16811283C2216yescomplemented
39#16811281C2216yescomplemented
40#16811280C2212yescomplemented
41#16811270C2216yescomplemented
42#16811268C2216yescomplemented
43#16811266C2216yescomplemented
44#16811265C22112yescomplemented
45#16811262C22112yescomplemented
46#16811261C2216yescomplemented
47#16811249C2213yescomplemented
48#16811248C2216yescomplemented
49#16811248C2216yescomplemented
50#16811222C2216yescomplemented
51#16811220C2216yescomplemented
52#16811218C2216yescomplemented
53#16811217C22112yescomplemented
54#16811215C22112yescomplemented
55#16811213C2216yescomplemented
56#16811211C2216yescomplemented
57#16811210C2216yescomplemented
58#16811208C22112yescomplemented
59#16811206C22112yescomplemented
60#16811185C2213yescomplemented
61#16811184C22112yescomplemented
62#16811183C22112yescomplemented
63#16811182C2216yescomplemented
64#16811181C2216yes—
65#16811181C2216yes—
66#16811159C2216yescomplemented
67#16811157C2216yescomplemented
68#16811154C2216yescomplemented
69#16811153C22112yescomplemented
70#16811150C22112yescomplemented
71#16811136C2216yescomplemented
72#16811134C2216yescomplemented
73#16811133C2216yescomplemented
74#16811132C22112yescomplemented
75#16811129C22112yescomplemented
76#123×D53C22112yescomplemented
77C22⋊Q8×D53C2216yescomplemented
78C22⋊Q8×D53C2216yescomplemented
79#121×D53C2216yescomplemented
80#121×D53C2216yescomplemented
81#120×D53C22112yescomplemented
82#16811095C22112yescomplemented
83#16811095C22112yescomplemented
84#16811095C22112yescomplemented
85#16811095C22112yescomplemented
86C2×C4×D212C2213yescomplemented
87C2×D4×Dic53C2213yescomplemented
88C2×#13133179C2213yescomplemented
89C2×C4×C22⋊D53C2213yescomplemented
90C2×C4×C22⋊D53C2213yescomplemented
91C2×#13133177C2213yescomplemented
92C2×#13133177C2213yescomplemented
93C2×#13133175C2213yescomplemented
94C2×#13133174C2213yescomplemented
95C22×#11719921C2211yescharacteristic
96C22×#11719921C2213yescomplemented
97C2×C22⋊C4×D53C2213yes—
98C2×C22⋊C4×D53C2213yescomplemented
99C53×#543C2211yescharacteristic, complemented
100C53×#539C2216yescomplemented
101C53×#538C2216yescomplemented
102C53×#534C2213yescomplemented
103C53×#529C2216yescomplemented
104C53×#525C2216yescomplemented
105C2×C4×D4×C53C2213yescomplemented
106C24×D53C2313yes—
107C24×D53C2311yescharacteristic
108C2×#11719949C2312yescomplemented
109C2×#11719945C2316yescomplemented
110C2×#11719947C2316yescomplemented
111C2×Q8×D53C2312yescomplemented
112C2×Q8×D53C2312yescomplemented
113C22×D212C2313yes—
114C22×C22⋊D53C2313yes—
115C22×C22⋊D53C2313yes—
116C2×D4×D53—224no—
117C2×D4×D53C23112yes—
118C2×D4×D53C23112yes—
119C2×D4×D53C2316yescomplemented
120C2×D4×D53C2316yescomplemented
121C23×Dic53C2311yescharacteristic
122C23×Dic53C2313yescomplemented
123C22×C4×D53C2313yes—
124C22×C4×D53C2313yes—
125C22×C4×D53C2313yes—
126C22×C4×D53C2313yescomplemented
127C22×C4×D53C2313yescomplemented
128#13133212C23112yescomplemented
129#13133212C23112yescomplemented
130#13133212C23112yescomplemented
131#13133211C23112yescomplemented
132#13133210C23112yescomplemented
133#13133210C23112yescomplemented
134#13133210C23112yescomplemented
135#13133209C2316yescomplemented
136#13133208C2316yescomplemented
137#13133208C2316yescomplemented
138#13133207C23112yescomplemented
139#13133207C23112yescomplemented
140#13133206C2316yescomplemented
141#13133205C2316yescomplemented
142#13133204C2316yescomplemented
143#13133203C23112yescomplemented
144#13133203C23112yescomplemented
145#13133202C23112yes—
146#13133202C23112yes—
147#13133202C23112yescomplemented
148#13133202C23112yescomplemented
149#13133201C23112yescomplemented
150#13133201C23112yescomplemented
151#13133200C23112yescomplemented
152#13133200C23112yescomplemented
153#13133199C23112yes—
154#13133199C23112yes—
155#13133199C23112yescomplemented
156#13133199C23112yescomplemented
157#13133198C23112yescomplemented
158#13133198C23112yescomplemented
159#13133197C2316yescomplemented
160#13133197C2316yescomplemented
161#13133197C2316yescomplemented
162#13133196C2316yescomplemented
163#13133196C2316yescomplemented
164#13133196C2316yescomplemented
165#13133195C23112yescomplemented
166#13133195C23112yescomplemented
167#13133195C23112yescomplemented
168#13133194C23112yescomplemented
169#13133194C23112yescomplemented
170#13133194C23112yescomplemented
171#13133193C2316yescomplemented
172#13133193C2316yescomplemented
173#13133193C2316yescomplemented
174#13133192C2316yescomplemented
175#13133192C2316yescomplemented
176#13133192C2316yescomplemented
177#13133191C2316yes—
178#13133191C2316yes—
179#13133191C2316yescomplemented
180#13133190C23112yescomplemented
181#13133190C23112yescomplemented
182#13133190C23112yescomplemented
183#13133189C23112yes—
184#13133189C23112yes—
185#13133189C23112yescomplemented
186#13133188C2316yescomplemented
187#13133188C2316yescomplemented
188#13133188C2316yescomplemented
189#13133187C23112yes—
190#13133187C23112yes—
191#13133187C23112yescomplemented
192#13133186C23112yescomplemented
193#13133185C23112yes—
194#13133185C23112yes—
195#13133185C23112yescomplemented
196Q8×Dic53C2312yescomplemented
197C4×Dic106C2316yescomplemented
198#13133182C2316yescomplemented
199C4×D212C2316yes—
200C4×D212C2316yes—
201C4×D212C2316yescomplemented
202C4×D212C2316yescomplemented
203C4×D212C2316yescomplemented
204D4×Dic53C2316yescomplemented
205D4×Dic53C23112yescomplemented
206D4×Dic53C23112yescomplemented
207#13133179C23112yes—
208#13133179C2316yescomplemented
209#13133179C23112yescomplemented
210C4×C22⋊D53C2316yes—
211C4×C22⋊D53C2316yes—
212C4×C22⋊D53C2316yescomplemented
213C4×C22⋊D53C2316yescomplemented
214C4×C22⋊D53C23112yescomplemented
215C4×C22⋊D53C23112yescomplemented
216C4×C22⋊D53C23112yescomplemented
217#13133177C23112yes—
218#13133177C23112yescomplemented
219#13133177C23112yescomplemented
220#13133177C23112yescomplemented
221#13133177C23112yescomplemented
222#13133176C2316yescomplemented
223#13133175C23112yescomplemented
224#13133175C2316yescomplemented
225#13133175C23112yescomplemented
226#13133175C2316yescomplemented
227#13133174C23112yescomplemented
228#13133174C23112yescomplemented
229#13133174C23112yescomplemented
230#13133173C23112yescomplemented
231C2×C4⋊Dic53C2313yescomplemented
232C2×#11719919C2313yescomplemented
233C2×#11719919C2313yescomplemented
234C4⋊C4×D53C2316yescomplemented
235C4⋊C4×D53C2316yescomplemented
236C4⋊C4×D53C2316yescomplemented
237C4⋊C4×D53C2316yescomplemented
238C2×C22⋊Dic53C2313yes—
239C2×C22⋊Dic53C2313yescomplemented
240C2×#11719921C2313yes—
241C2×#11719921C2313yes—
242C2×#11719921C2313yes—
243C2×#11719921C2313yes—
244C2×#11719921C2313yes—
245C2×#11719921C2313yes—
246C2×#11719921C23112yescomplemented
247C2×#11719921C23112yescomplemented
248C2×#11719921C2313yescomplemented
249C2×#11719921C2313yescomplemented
250C22⋊C4×D53C23112yes—
251C22⋊C4×D53C23112yes—
252C22⋊C4×D53C23112yescomplemented
253C22⋊C4×D53C23112yescomplemented
254C22⋊C4×D53C23112yescomplemented
255C22⋊C4×D53C23112yescomplemented
256C2×C4×Dic53C2313yescomplemented
257C2×C4×Dic53C2313yescomplemented
258C2×C4×Dic53C2313yescomplemented
259C2×#41×C53C2312yescomplemented
260C22×D4×C53C2313yes—
261C23×C4×C53C2311yescharacteristic
262C23×C4×C53C2313yescomplemented
263#126×C53C23112yescomplemented
264#125×C53C2316yescomplemented
265#124×C53C2316yescomplemented
266#123×C53C23112yescomplemented
267#123×C53C23112yescomplemented
268C22⋊Q8×C53C2316yescomplemented
269C22⋊Q8×C53C2316yescomplemented
270C22⋊Q8×C53C2316yescomplemented
271#121×C53C2316yes—
272#121×C53C2316yes—
273#121×C53C2316yescomplemented
274#120×C53C23112yescomplemented
275C4×Q8×C53C2312yescomplemented
276C4×D4×C53C2316yescomplemented
277C4×D4×C53C23112yescomplemented
278C4×D4×C53C23112yescomplemented
279#117×C53C2316yescomplemented
280C2×C4⋊C4×C53C2313yescomplemented
281C2×C22⋊C4×C53C2313yes—
282C2×C22⋊C4×C53C2313yescomplemented
283C2×C42×C53C2313yescomplemented
284C24×C53C2413yes—
285C24×C53C2411yescharacteristic
286C23×D53—212no—
287C23×D53—81no—
288C23×D53—81no—
289C23×D53—83no—
290C23×D53—83no—
291C23×D53#4118yescomplemented
292C23×D53C24112yes—
293C23×D53C2413yes—
294C23×D53C2413yes—
295C23×D53C2413yes—
296#41×C53—82no—
297C2×Q8×C53C2412yes—
298C2×Q8×C53C2412yes—
299C2×D4×C53—212no—
300C2×D4×C53C24112yes—
301C2×D4×C53C2416yes—
302C2×D4×C53C2416yes—
303C22×C4×C53—81no—
304C22×C4×C53—83no—
305C22×C4×C53C2413yes—
306C22×C4×C53C2413yes—
307C22×C4×C53C2413yes—
308C22×C4×C53C2413yes—
309C22×C4×C53C2413yes—
310C22×C4×C53C2416yes—
311C22×C4×C53C2416yes—
312C2×C22⋊D53—212no—
313C2×C22⋊D53—212no—
314C2×C22⋊D53C2416yes—
315C2×C22⋊D53C24112yes—
316C2×C22⋊D53C2416yes—
317C2×C22⋊D53C24112yes—
318C2×C22⋊D53C24112yes—
319C22×Dic53—81no—
320C22×Dic53—83no—
321C22×Dic53C2413yes—
322C22×Dic53C2413yes—
323C22×Dic53C2413yes—
324C22×Dic53C2413yes—
325C22×Dic53C2413yes—
326C22×Dic53C24112yes—
327#11719949—82no—
328Q8×D53—82no—
329Q8×D53—82no—
330#11719947—86no—
331D4×D53—248no—
332D4×D53—248no—
333D4×D53—86no—
334D4×D53—86no—
335#11719945—86no—
336C2×D212—212no—
337C2×D212C2416yes—
338C2×D212C2416yes—
339C2×D212C2416yes—
340C2×D212C2416yes—
341C2×C4×D53—212no—
342C2×C4×D53—83no—
343C2×C4×D53—83no—
344C2×C4×D53—83no—
345C2×C4×D53—83no—
346C2×C4×D53C24112yes—
347C2×C4×D53C2416yes—
348C2×C4×D53C2416yes—
349C2×C4×D53C2416yes—
350C2×C4×D53C2416yes—
351C2×C4×D53C24112yes—
352C2×C4×D53C2416yes—
353C2×C4×D53C2416yes—
354C2×Dic106C2416yes—
355C2×Dic106C2416yes—
356C4⋊C4×C53C24112yes—
357C4⋊C4×C53C2416yes—
358C4⋊C4×C53C2416yes—
359C4⋊C4×C53C2416yes—
360C4⋊C4×C53C2416yes—
361C22⋊C4×C53C24112yes—
362C22⋊C4×C53C24112yes—
363C22⋊C4×C53C24112yes—
364C22⋊C4×C53C24112yes—
365C42×C53C2416yes—
366C42×C53C2416yes—
367C22⋊Dic53C24112yes—
368C22⋊Dic53C2416yes—
369C22⋊Dic53C2416yes—
370C22⋊Dic53C24112yes—
371C22⋊Dic53C24112yes—
372#11719921C24112yes—
373#11719921C24112yes—
374#11719921C2413yes—
375#11719921C2416yes—
376#11719921C24112yes—
377#11719921C24112yes—
378#11719921C24112yes—
379#11719921C24112yes—
380#11719921C2413yes—
381#11719921C2413yes—
382#11719921C2411yescharacteristic
383#11719921C24112yes—
384#11719921C2416yes—
385#11719921C2416yes—
386C4⋊Dic53C2416yes—
387C4⋊Dic53C2416yes—
388C4⋊Dic53C2416yes—
389C4⋊Dic53C2416yes—
390C4⋊Dic53C2416yes—
391C4⋊Dic53C2416yes—
392#11719919C24112yes—
393#11719919C24112yes—
394#11719919C24112yes—
395#11719919C24112yes—
396#11719919C24112yes—
397#11719919C2416yes—
398#11719919C2416yes—
399C4×Dic53C2416yes—
400C4×Dic53C24112yes—
401C4×Dic53C24112yes—
402C4×Dic53C2416yes—
403C23×C53—26no—
404C23×C53—41no—
405C23×C53—43no—
406C23×C53—41no—
407C23×C53—43no—
408C23×C53C2×#4114yes—
409C23×C53C2516yes—
410C23×C53C2513yes—
411C22×D53—26no—
412C22×D53—224no—
413C22×D53—43no—
414C22×D53—43no—
415C22×D53—43no—
416C22×D53—43no—
417C22×D53—43no—
418C22×D53—43no—
419C22×D53—412no—
420C22×D53—412no—
421C22×D53—88no—
422C22×D53—824no—
423C22×D53C2×#41112yes—
424C22×D53C2×#41112yes—
425C22×D53C2516yes—
426C22×D53C2511yescharacteristic
427C22×D53C2513yes—
428Q8×C53—42no—
429Q8×C53—42no—
430D4×C53—224no—
431D4×C53—46no—
432D4×C53—46no—
433C2×C4×C53—26no—
434C2×C4×C53—43no—
435C2×C4×C53—43no—
436C2×C4×C53—43no—
437C2×C4×C53—46no—
438C2×C4×C53—43no—
439C2×C4×C53—46no—
440C2×C4×C53C2516yes—
441C2×C4×C53C2516yes—
442C2×C4×C53C2513yes—
443C2×C4×C53C2516yes—
444C2×C4×C53C2511yescharacteristic
445C22⋊D53—224no—
446C22⋊D53—212no—
447C22⋊D53—212no—
448C22⋊D53—412no—
449C22⋊D53—412no—
450C2×Dic53—26no—
451C2×Dic53—43no—
452C2×Dic53—43no—
453C2×Dic53—43no—
454C2×Dic53—412no—
455C2×Dic53—43no—
456C2×Dic53C2516yes—
457C2×Dic53C2516yes—
458C2×Dic53C2511yescharacteristic
459C2×Dic53C2513yes—
460C2×Dic53C2516yes—
461D212—212no—
462D212—212no—
463D212—46no—
464D212—46no—
465C4×D53—224no—
466C4×D53—412no—
467C4×D53—46no—
468C4×D53—46no—
469C4×D53—46no—
470C4×D53—46no—
471C4×D53—46no—
472C4×D53—46no—
473Dic106—46no—
474Dic106—46no—
475#62844—531nomaximal, Sylow
476C22×C53—23no—
477C22×C53—23no—
478C22×C53—26no—
479C22×C53—26no—
480C22×C53—26no—
481C22×C53—44no—
482C22×C53—412no—
483C22×C53C22×#4116yes—
484C22×C53C2611yescharacteristic
485C2×D53—21no—
486C2×D53—21no—
487C2×D53—23no—
488C2×D53—23no—
489C2×D53—26no—
490C2×D53—26no—
491C2×D53—26no—
492C2×D53—412no—
493C2×D53—412no—
494C2×D53—412no—
495C2×D53—824no—
496C2×D53C22×#4116yes—
497C2×D53C22×#4112yes—
498C4×C53—26no—
499C4×C53—26no—
500C4×C53—26no—
501C4×C53—23no—
502C4×C53—21no—
503Dic53—26no—
504Dic53—26no—
505Dic53—26no—
506Dic53—21no—
507Dic53—23no—
508#3505—536no—
509#3505—536no—
510#3505—536no—
511#3505—536no—
512#3491—536no—
513#3491—536no—
514#3490—536no—
515#3490—536no—
516#3459—531no—
517#3459—533no—
518#3459—533no—
519#3459D5311yescharacteristic, complemented
520C2×#543—531no—
521C2×#534—533no—
522C2×#518—533no—
523C2×C53—26no—
524C2×C53—46no—
525C2×C53C23×#4111yescharacteristic
526C2×C53H(7,𝔽2)11yescharacteristic
527C2×C53H(7,𝔽2)11yescharacteristic
528D53—26no—
529D53—22no—
530D53—46no—
531C23×D4—533no—
532#553—5312no—
533#553—536no—
534#553—5312no—
535#553—536no—
536#553—536no—
537#553—536no—
538#552—5312no—
539#552—5312no—
540#552—536no—
541#552—536no—
542#552—536no—
543#552—536no—
544#551—5312no—
545#551—5312no—
546#551—5312no—
547#551—5312no—
548#551—5312no—
549#551—5312no—
550#551—5312no—
551#551—5312no—
552#548—532no—
553#548—536no—
554#548—536no—
555#548—532no—
556#546—536no—
557#546—536no—
558#546—5312no—
559#546—536no—
560#546—5312no—
561#546—536no—
562#543—536no—
563#543—536no—
564#543—533no—
565#543C2×D5311yescharacteristic, complemented
566#539—5312no—
567#539—536no—
568#539—536no—
569#539—5312no—
570#539—536no—
571#539C2×D5316yescomplemented
572#538—536no—
573#538—536no—
574#538—5312no—
575#538—5312no—
576#538—536no—
577#538C2×D5316yescomplemented
578#534—536no—
579#534—5312no—
580#534—536no—
581#534—536no—
582#534—5312no—
583#534—533no—
584#534C2×D5313yescomplemented
585#529—5312no—
586#529—536no—
587#529—536no—
588#529—5312no—
589#529—536no—
590#529C2×D5316yescomplemented
591#525—536no—
592#525—536no—
593#525—536no—
594#525—5312no—
595#525—5312no—
596#525C2×D5316yescomplemented
597C2×#123—5312no—
598C2×C22⋊Q8—536no—
599C2×C22⋊Q8—536no—
600C2×#121—536no—
601C2×#121—536no—
602C2×#120—5312no—
603#518—5312no—
604#518—5312no—
605#518—5312no—
606#518—5312no—
607C2×C4×D4—533no—
608C2×C4×D4—533no—
609C2×C4×D4—533no—
610C2×C4×D4—533no—
611C2×C4×D4—533no—
612C2×C4×D4—533no—
613C2×C4×D4—533no—
614C2×C4×D4C2×D5313yescomplemented
615C2×#117—533no—
616C2×#117—533no—
617C22×C22⋊C4—531no—
618C22×C22⋊C4—533no—
619C22×C22⋊C4—533no—
620C22×C22⋊C4—533no—
621C53#6284411yescharacteristic, complemented, Sylow
622C25—531no—
623C25—533no—
624C2×#41—532no—
625C2×#41—536no—
626C2×#41—536no—
627C2×#41C22×D5312yescomplemented
628C22×Q8—532no—
629C22×Q8—532no—
630C22×D4—533no—
631C22×D4—533no—
632C22×D4—5312no—
633C22×D4—5312no—
634C22×D4—536no—
635C22×D4—536no—
636C22×D4—533no—
637C22×D4—10624no—
638C22×D4C22×D5313yes—
639C23×C4—531no—
640C23×C4—533no—
641C23×C4—533no—
642C23×C4—533no—
643C23×C4—533no—
644C23×C4—533no—
645C23×C4—533no—
646C23×C4C22×D5311yescharacteristic
647C23×C4C22×D5313yescomplemented
648#126—5312no—
649#126—5312no—
650#126—5312no—
651#126—5312no—
652#126—5312no—
653#126—5312no—
654#126—5312no—
655#126C22×D53112yescomplemented
656#125—5312no—
657#125—5312no—
658#125—536no—
659#125—536no—
660#125—536no—
661#125C22×D5316yescomplemented
662#124—536no—
663#124—536no—
664#124—5312no—
665#124—5312no—
666#124—536no—
667#124C22×D5316yescomplemented
668#123—5312no—
669#123—5312no—
670#123—5312no—
671#123—5312no—
672#123—5312no—
673#123—5312no—
674#123—5312no—
675#123—5312no—
676#123—5312no—
677#123—5312no—
678#123—5312no—
679#123—5312no—
680#123—5312no—
681#123—5312no—
682#123C22×D53112yescomplemented
683#123C22×D53112yescomplemented
684C22⋊Q8—536no—
685C22⋊Q8—536no—
686C22⋊Q8—536no—
687C22⋊Q8—536no—
688C22⋊Q8—536no—
689C22⋊Q8—536no—
690C22⋊Q8—5312no—
691C22⋊Q8—5312no—
692C22⋊Q8—536no—
693C22⋊Q8—536no—
694C22⋊Q8—5312no—
695C22⋊Q8—536no—
696C22⋊Q8—5312no—
697C22⋊Q8—5312no—
698C22⋊Q8—5312no—
699C22⋊Q8C22×D5316yescomplemented
700C22⋊Q8C22×D5316yescomplemented
701C22⋊Q8C22×D5316yescomplemented
702#121—5312no—
703#121—5312no—
704#121—536no—
705#121—536no—
706#121—536no—
707#121—5312no—
708#121—536no—
709#121—536no—
710#121—536no—
711#121—536no—
712#121—536no—
713#121—536no—
714#121—5312no—
715#121—5312no—
716#121—5312no—
717#121C22×D5316yes—
718#121C22×D5316yes—
719#121C22×D5316yescomplemented
720#120—5312no—
721#120—5312no—
722#120—5312no—
723#120—5312no—
724#120—5312no—
725#120—5312no—
726#120—5312no—
727#120C22×D53112yescomplemented
728C4×Q8—532no—
729C4×Q8—536no—
730C4×Q8—536no—
731C4×Q8C22×D5312yescomplemented
732C4×D4—5312no—
733C4×D4—5312no—
734C4×D4—536no—
735C4×D4—5312no—
736C4×D4—5312no—
737C4×D4—536no—
738C4×D4—536no—
739C4×D4—536no—
740C4×D4—536no—
741C4×D4—5312no—
742C4×D4—5312no—
743C4×D4—5312no—
744C4×D4—536no—
745C4×D4—5312no—
746C4×D4—5312no—
747C4×D4—5312no—
748C4×D4—5312no—
749C4×D4—5312no—
750C4×D4—536no—
751C4×D4—536no—
752C4×D4—536no—
753C4×D4—536no—
754C4×D4—536no—
755C4×D4C22×D53112yescomplemented
756C4×D4C22×D53112yescomplemented
757C4×D4C22×D5316yescomplemented
758#117—536no—
759#117—5312no—
760#117—5312no—
761#117—536no—
762#117—536no—
763#117—5312no—
764#117—5312no—
765#117—5312no—
766#117—5312no—
767#117C22×D5316yescomplemented
768C2×C4⋊C4—533no—
769C2×C4⋊C4—533no—
770C2×C4⋊C4—533no—
771C2×C4⋊C4—536no—
772C2×C4⋊C4—536no—
773C2×C4⋊C4—536no—
774C2×C4⋊C4—536no—
775C2×C4⋊C4C22×D5313yescomplemented
776C2×C22⋊C4—533no—
777C2×C22⋊C4—533no—
778C2×C22⋊C4—533no—
779C2×C22⋊C4—533no—
780C2×C22⋊C4—533no—
781C2×C22⋊C4—533no—
782C2×C22⋊C4—533no—
783C2×C22⋊C4—533no—
784C2×C22⋊C4—533no—
785C2×C22⋊C4—533no—
786C2×C22⋊C4—5312no—
787C2×C22⋊C4—5312no—
788C2×C22⋊C4—5312no—
789C2×C22⋊C4—5312no—
790C2×C22⋊C4—5312no—
791C2×C22⋊C4—5312no—
792C2×C22⋊C4—5312no—
793C2×C22⋊C4—5312no—
794C2×C22⋊C4C22×D5313yes—
795C2×C22⋊C4C22×D5313yescomplemented
796C2×C42—533no—
797C2×C42—533no—
798C2×C42—533no—
799C2×C42C22×D5313yescomplemented
800C24—538no—
801C24—533no—
802C24—533no—
803C24—5312no—
804C24—533no—
805C24—10612no—
806C24—4243no—
807C24—4241no—
808C24—4243no—
809C24—4241no—
810C24C23×D5313yes—
811C24C23×D5311yescharacteristic
812#41—82no—
813#41—4246no—
814#41—4246no—
815#41—4242no—
816C2×Q8—536no—
817C2×Q8—536no—
818C2×Q8—4242no—
819C2×Q8—4242no—
820C2×Q8C23×D5312yes—
821C2×Q8C23×D5312yes—
822C2×D4—212no—
823C2×D4—536no—
824C2×D4—5312no—
825C2×D4—536no—
826C2×D4—5312no—
827C2×D4—5312no—
828C2×D4—536no—
829C2×D4—536no—
830C2×D4—536no—
831C2×D4—536no—
832C2×D4—10612no—
833C2×D4—10648no—
834C2×D4—10648no—
835C2×D4—10612no—
836C2×D4—10612no—
837C2×D4—4246no—
838C2×D4—4246no—
839C2×D4C23×D53112yes—
840C2×D4C23×D5316yes—
841C2×D4C23×D5316yes—
842C22×C4—81no—
843C22×C4—83no—
844C22×C4—533no—
845C22×C4—533no—
846C22×C4—533no—
847C22×C4—533no—
848C22×C4—533no—
849C22×C4—5312no—
850C22×C4—5312no—
851C22×C4—536no—
852C22×C4—536no—
853C22×C4—536no—
854C22×C4—536no—
855C22×C4—536no—
856C22×C4—536no—
857C22×C4—5312no—
858C22×C4—10612no—
859C22×C4—4243no—
860C22×C4—4243no—
861C22×C4—4243no—
862C22×C4—4243no—
863C22×C4—4241no—
864C22×C4—4243no—
865C22×C4C23×D5313yes—
866C22×C4C23×D5313yes—
867C22×C4C23×D5313yes—
868C22×C4C23×D5313yes—
869C22×C4C23×D5313yes—
870C22×C4C23×D5316yes—
871C22×C4C23×D5316yes—
872C4⋊C4—5312no—
873C4⋊C4—536no—
874C4⋊C4—536no—
875C4⋊C4—536no—
876C4⋊C4—536no—
877C4⋊C4—5312no—
878C4⋊C4—5312no—
879C4⋊C4—536no—
880C4⋊C4—536no—
881C4⋊C4—5312no—
882C4⋊C4—5312no—
883C4⋊C4—536no—
884C4⋊C4—536no—
885C4⋊C4C23×D5316yes—
886C4⋊C4C23×D5316yes—
887C4⋊C4C23×D5316yes—
888C4⋊C4C23×D5316yes—
889C4⋊C4C23×D53112yes—
890C22⋊C4—5312no—
891C22⋊C4—536no—
892C22⋊C4—536no—
893C22⋊C4—5312no—
894C22⋊C4—5312no—
895C22⋊C4—536no—
896C22⋊C4—533no—
897C22⋊C4—533no—
898C22⋊C4—5312no—
899C22⋊C4—5312no—
900C22⋊C4—533no—
901C22⋊C4—531no—
902C22⋊C4—5312no—
903C22⋊C4—536no—
904C22⋊C4—536no—
905C22⋊C4—5312no—
906C22⋊C4—5312no—
907C22⋊C4—5312no—
908C22⋊C4—5312no—
909C22⋊C4C23×D53112yes—
910C22⋊C4C23×D53112yes—
911C22⋊C4C23×D53112yes—
912C22⋊C4C23×D53112yes—
913C42—536no—
914C42—536no—
915C42—5312no—
916C42—5312no—
917C42C23×D5316yes—
918C42C23×D5316yes—
919C23—26no—
920C23—41no—
921C23—43no—
922C23—41no—
923C23—43no—
924C23—533no—
925C23—531no—
926C23—5312no—
927C23—5312no—
928C23—536no—
929C23—10624no—
930C23—1066no—
931C23—42424no—
932C23—4248no—
933C23—21212no—
934C23—21212no—
935C23—2123no—
936C23—2123no—
937C23—2123no—
938C23—2123no—
939C23—2123no—
940C23—2123no—
941C23#41×D5314yes—
942C23C24×D5316yes—
943C23C24×D5313yes—
944Q8—42no—
945Q8—42no—
946Q8—2126no—
947Q8—2126no—
948D4—224no—
949D4—46no—
950D4—46no—
951D4—10612no—
952D4—10612no—
953D4—10612no—
954D4—10612no—
955D4—10624no—
956D4—2126no—
957D4—2126no—
958D4—21212no—
959D4—21212no—
960C2×C4—26no—
961C2×C4—43no—
962C2×C4—43no—
963C2×C4—43no—
964C2×C4—46no—
965C2×C4—46no—
966C2×C4—43no—
967C2×C4—531no—
968C2×C4—533no—
969C2×C4—536no—
970C2×C4—536no—
971C2×C4—536no—
972C2×C4—10624no—
973C2×C4—1066no—
974C2×C4—2126no—
975C2×C4—2126no—
976C2×C4—2126no—
977C2×C4—2126no—
978C2×C4—21212no—
979C2×C4—2126no—
980C2×C4—2126no—
981C2×C4—2123no—
982C2×C4—2123no—
983C2×C4—2123no—
984C2×C4—2123no—
985C2×C4—21212no—
986C2×C4C24×D5313yes—
987C2×C4C24×D5316yes—
988C2×C4C24×D5316yes—
989C2×C4C24×D5311yescharacteristic
990C2×C4C24×D5316yes—
991C22—23no—
992C22—23no—
993C22—26no—
994C22—26no—
995C22—26no—
996C22—44no—
997C22—412no—
998C22—536no—
999C22—532no—
1000C22—1061no—
1001C22—1063no—
1002C22—1061no—
1003C22—1063no—
1004C22—1066no—
1005C22—1066no—
1006C22—1066no—
1007C22—42424no—
1008C22—21212no—
1009C22—21212no—
1010C22—21212no—
1011C22C2×#41×D5316yes—
1012C22C25×D5311yescharacteristic
1013C4—26no—
1014C4—21no—
1015C4—23no—
1016C4—26no—
1017C4—26no—
1018C4—1066no—
1019C4—1066no—
1020C4—1061no—
1021C4—1063no—
1022C4—1066no—
1023C2—26no—
1024C2—46no—
1025C2—1066no—
1026C2—1062no—
1027C2—2126no—
1028C2C22×#41×D5311yescharacteristic
1029C2#2028952511yescharacteristic
1030C2#2028952611yescharacteristic
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3459C2
hypercenter#3459D53
hypocenterC53#62844
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3459

Complements

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

NH ≅ G/Ntype
1. #20288553C2semidirect
2. #20288550C2semidirect
3. #20288547C2semidirect
4. #20288543C2semidirect
5. #20288409C2semidirect
6. #20288407C2semidirect
7. #20288401C2semidirect
8. #20288398C2semidirect
9. #20288127C2semidirect
10. #20288124C2semidirect
11. #20288121C2semidirect
12. #543×D53C2semidirect
13. #534×D53C2semidirect
14. C2×#16811095C2semidirect
15. C53×#3459C2semidirect
17. #16811326C22semidirect
18. #16811324C22semidirect
19. #16811323C22semidirect
20. #16811320C22semidirect
21. #16811318C22semidirect
22. #16811317C22semidirect
23. #16811314C22semidirect
24. #16811312C22semidirect
25. #16811311C22semidirect
26. #16811309C22semidirect
27. #16811307C22semidirect
28. #16811305C22semidirect
29. #16811303C22semidirect
30. #16811302C22semidirect
31. #16811301C22semidirect
32. #16811300C22semidirect
33. #16811298C22semidirect
34. #16811298C22semidirect
35. #16811297C22semidirect
36. #16811296C22semidirect
37. #16811285C22semidirect
38. #16811283C22semidirect
39. #16811281C22semidirect
40. #16811280C22semidirect
41. #16811270C22semidirect
42. #16811268C22semidirect
43. #16811266C22semidirect
44. #16811265C22semidirect
45. #16811262C22semidirect
46. #16811261C22semidirect
47. #16811249C22semidirect
48. #16811248C22semidirect
49. #16811248C22semidirect
50. #16811222C22semidirect
51. #16811220C22semidirect
52. #16811218C22semidirect
53. #16811217C22semidirect
54. #16811215C22semidirect
55. #16811213C22semidirect
56. #16811211C22semidirect
57. #16811210C22semidirect
58. #16811208C22semidirect
59. #16811206C22semidirect
60. #16811185C22semidirect
61. #16811184C22semidirect
62. #16811183C22semidirect
63. #16811182C22semidirect
66. #16811159C22semidirect
67. #16811157C22semidirect
68. #16811154C22semidirect
69. #16811153C22semidirect
70. #16811150C22semidirect
71. #16811136C22semidirect
72. #16811134C22semidirect
73. #16811133C22semidirect
74. #16811132C22semidirect
75. #16811129C22semidirect
76. #123×D53C22semidirect
77. C22⋊Q8×D53C22semidirect
78. C22⋊Q8×D53C22semidirect
79. #121×D53C22semidirect
80. #121×D53C22semidirect
81. #120×D53C22semidirect
82. #16811095C22semidirect
83. #16811095C22semidirect
84. #16811095C22semidirect
85. #16811095C22semidirect
86. C2×C4×D212C22semidirect
87. C2×D4×Dic53C22semidirect
88. C2×#13133179C22semidirect
89. C2×C4×C22⋊D53C22semidirect
90. C2×C4×C22⋊D53C22semidirect
91. C2×#13133177C22semidirect
92. C2×#13133177C22semidirect
93. C2×#13133175C22semidirect
94. C2×#13133174C22semidirect
96. C22×#11719921C22semidirect
98. C2×C22⋊C4×D53C22semidirect
99. C53×#543C22semidirect
100. C53×#539C22semidirect
101. C53×#538C22semidirect
102. C53×#534C22semidirect
103. C53×#529C22semidirect
104. C53×#525C22semidirect
105. C2×C4×D4×C53C22semidirect
108. C2×#11719949C23semidirect
109. C2×#11719945C23semidirect
110. C2×#11719947C23semidirect
111. C2×Q8×D53C23semidirect
112. C2×Q8×D53C23semidirect
119. C2×D4×D53C23semidirect
120. C2×D4×D53C23semidirect
122. C23×Dic53C23semidirect
126. C22×C4×D53C23semidirect
127. C22×C4×D53C23semidirect
128. #13133212C23semidirect
129. #13133212C23semidirect
130. #13133212C23semidirect
131. #13133211C23semidirect
132. #13133210C23semidirect
133. #13133210C23semidirect
134. #13133210C23semidirect
135. #13133209C23semidirect
136. #13133208C23semidirect
137. #13133208C23semidirect
138. #13133207C23semidirect
139. #13133207C23semidirect
140. #13133206C23semidirect
141. #13133205C23semidirect
142. #13133204C23semidirect
143. #13133203C23semidirect
144. #13133203C23semidirect
147. #13133202C23semidirect
148. #13133202C23semidirect
149. #13133201C23semidirect
150. #13133201C23semidirect
151. #13133200C23semidirect
152. #13133200C23semidirect
155. #13133199C23semidirect
156. #13133199C23semidirect
157. #13133198C23semidirect
158. #13133198C23semidirect
159. #13133197C23semidirect
160. #13133197C23semidirect
161. #13133197C23semidirect
162. #13133196C23semidirect
163. #13133196C23semidirect
164. #13133196C23semidirect
165. #13133195C23semidirect
166. #13133195C23semidirect
167. #13133195C23semidirect
168. #13133194C23semidirect
169. #13133194C23semidirect
170. #13133194C23semidirect
171. #13133193C23semidirect
172. #13133193C23semidirect
173. #13133193C23semidirect
174. #13133192C23semidirect
175. #13133192C23semidirect
176. #13133192C23semidirect
179. #13133191C23semidirect
180. #13133190C23semidirect
181. #13133190C23semidirect
182. #13133190C23semidirect
185. #13133189C23semidirect
186. #13133188C23semidirect
187. #13133188C23semidirect
188. #13133188C23semidirect
191. #13133187C23semidirect
192. #13133186C23semidirect
195. #13133185C23semidirect
196. Q8×Dic53C23semidirect
197. C4×Dic106C23semidirect
198. #13133182C23semidirect
201. C4×D212C23semidirect
202. C4×D212C23semidirect
203. C4×D212C23semidirect
204. D4×Dic53C23semidirect
205. D4×Dic53C23semidirect
206. D4×Dic53C23semidirect
208. #13133179C23semidirect
209. #13133179C23semidirect
212. C4×C22⋊D53C23semidirect
213. C4×C22⋊D53C23semidirect
214. C4×C22⋊D53C23semidirect
215. C4×C22⋊D53C23semidirect
216. C4×C22⋊D53C23semidirect
218. #13133177C23semidirect
219. #13133177C23semidirect
220. #13133177C23semidirect
221. #13133177C23semidirect
222. #13133176C23semidirect
223. #13133175C23semidirect
224. #13133175C23semidirect
225. #13133175C23semidirect
226. #13133175C23semidirect
227. #13133174C23semidirect
228. #13133174C23semidirect
229. #13133174C23semidirect
230. #13133173C23semidirect
231. C2×C4⋊Dic53C23semidirect
232. C2×#11719919C23semidirect
233. C2×#11719919C23semidirect
234. C4⋊C4×D53C23semidirect
235. C4⋊C4×D53C23semidirect
236. C4⋊C4×D53C23semidirect
237. C4⋊C4×D53C23semidirect
239. C2×C22⋊Dic53C23semidirect
246. C2×#11719921C23semidirect
247. C2×#11719921C23semidirect
248. C2×#11719921C23semidirect
249. C2×#11719921C23semidirect
252. C22⋊C4×D53C23semidirect
253. C22⋊C4×D53C23semidirect
254. C22⋊C4×D53C23semidirect
255. C22⋊C4×D53C23semidirect
256. C2×C4×Dic53C23semidirect
257. C2×C4×Dic53C23semidirect
258. C2×C4×Dic53C23semidirect
259. C2×#41×C53C23semidirect
262. C23×C4×C53C23semidirect
263. #126×C53C23semidirect
264. #125×C53C23semidirect
265. #124×C53C23semidirect
266. #123×C53C23semidirect
267. #123×C53C23semidirect
268. C22⋊Q8×C53C23semidirect
269. C22⋊Q8×C53C23semidirect
270. C22⋊Q8×C53C23semidirect
273. #121×C53C23semidirect
274. #120×C53C23semidirect
275. C4×Q8×C53C23semidirect
276. C4×D4×C53C23semidirect
277. C4×D4×C53C23semidirect
278. C4×D4×C53C23semidirect
279. #117×C53C23semidirect
280. C2×C4⋊C4×C53C23semidirect
282. C2×C22⋊C4×C53C23semidirect
283. C2×C42×C53C23semidirect
291. C23×D53#41semidirect
519. #3459D53semidirect
565. #543C2×D53semidirect
571. #539C2×D53semidirect
577. #538C2×D53semidirect
584. #534C2×D53semidirect
590. #529C2×D53semidirect
596. #525C2×D53semidirect
614. C2×C4×D4C2×D53semidirect
621. C53#62844semidirect
627. C2×#41C22×D53semidirect
647. C23×C4C22×D53semidirect
655. #126C22×D53semidirect
661. #125C22×D53semidirect
667. #124C22×D53semidirect
682. #123C22×D53semidirect
683. #123C22×D53semidirect
699. C22⋊Q8C22×D53semidirect
700. C22⋊Q8C22×D53semidirect
701. C22⋊Q8C22×D53semidirect
719. #121C22×D53semidirect
727. #120C22×D53semidirect
731. C4×Q8C22×D53semidirect
755. C4×D4C22×D53semidirect
756. C4×D4C22×D53semidirect
757. C4×D4C22×D53semidirect
767. #117C22×D53semidirect
775. C2×C4⋊C4C22×D53semidirect
795. C2×C22⋊C4C22×D53semidirect
799. C2×C42C22×D53semidirect

Maximal subgroups

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

subgroupindex
#202885532
#202885502
#202885472
#202885432
#202884092
#202884072
#202884012
#202883982
#202881272
#202881242
#202881212
#543×D532
#534×D532
C2×#168110952
C53×#34592
#6284453