Finite Group Databasebeta

← #28293268

Subgroups — #28293268

Order 13568.

7082 conjugacy classes of subgroups.

The subgroup lattice has 1346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288827C212yesmaximal, complemented
2#20288801C212yesmaximal, complemented
3#20288786C216yesmaximal, complemented
4#20288765C216yesmaximal, complemented
5#20288733C212yesmaximal, complemented
6#20288711C212yesmaximal, complemented
7#20288677C216yesmaximal, complemented
8#20288658C216yesmaximal, complemented
9#20288628C213yesmaximal, complemented
10#20288613C213yesmaximal, complemented
11#20288508C211yesmaximal, characteristic, complemented
12#20288470C213yesmaximal, complemented
13#20288453C213yesmaximal, complemented
14#20288396C211yesmaximal, characteristic, complemented
15#20288385C211yesmaximal, characteristic, complemented
16#20288149C213yesmaximal, complemented
17#20288138C213yesmaximal, complemented
18#20288107C213yesmaximal, complemented
19C2×#16811247C213yesmaximal, complemented
20#20287926C211yesmaximal, characteristic, complemented
21#20287921C211yesmaximal, characteristic, complemented
22#20287914C211yesmaximal, characteristic, complemented
23C53×#3503C211yesmaximal, characteristic, complemented
24C2×#13133264C2211yescharacteristic
25C2×#13133263C2211yescharacteristic
26C2×#41×D53C2211yescharacteristic
27#16811358C2216yescomplemented
28#16811358C2216yescomplemented
29#16811347C2216yescomplemented
30#16811347C2216yescomplemented
31#16811346C2216yescomplemented
32#16811346C2216yescomplemented
33#16811339C2216yescomplemented
34#16811339C2216yescomplemented
35#16811334C2216yescomplemented
36#16811334C2216yescomplemented
37#16811326C2216yescomplemented
38#16811326C2216yescomplemented
39#16811321C22112yescomplemented
40#16811315C22112yescomplemented
41#16811311C2216yescomplemented
42#16811311C2216yescomplemented
43#16811300C22112yescomplemented
44#16811300C22112yescomplemented
45#16811300C22112yescomplemented
46#16811300C22112yescomplemented
47#16811295C2212yes—
48Q8×D212C2212yescomplemented
49#16811285C2212yes—
50#16811285C2212yescomplemented
51#16811285C2212yescomplemented
52#16811285C2212yescomplemented
53#16811284C22112yescomplemented
54#16811277C2216yescomplemented
55#16811276C2216yescomplemented
56#16811276C2216yescomplemented
57#16811268C2216yes—
58#16811268C2216yescomplemented
59#16811268C2216yescomplemented
60#16811268C2216yescomplemented
61#16811264C22112yescomplemented
62D4×D212C2216yes—
63#16811247C2216yescomplemented
64#16811247C2216yescomplemented
65#16811247C2216yescomplemented
66#16811247C2213yescomplemented
67#16811247C2216yescomplemented
68#16811247C2216yescomplemented
69#16811247C2216yescomplemented
70#16811247C2216yescomplemented
71#16811247C2216yescomplemented
72#16811247C2213yescomplemented
73#16811247C2211yescharacteristic, complemented
74#16811247C2213yescomplemented
75#16811247C2216yescomplemented
76#16811236C2216yescomplemented
77#16811236C2213yescomplemented
78#16811236C2213yescomplemented
79#16811229C2216yescomplemented
80#16811229C2213yescomplemented
81#16811229C2213yescomplemented
82#16811222C2216yescomplemented
83#16811222C2216yescomplemented
84#16811222C22112yescomplemented
85#16811213C22112yescomplemented
86#16811213C2216yescomplemented
87#16811213C2216yescomplemented
88#16811204C2213yes—
89#16811204C2213yescomplemented
90#16811199C2213yescomplemented
91#16811199C2213yescomplemented
92#16811192C2213yes—
93#16811192C2213yescomplemented
94#16811178C2216yescomplemented
95#16811178C2216yescomplemented
96#16811174C2216yescomplemented
97#16811174C2216yescomplemented
98#16811173C2213yescomplemented
99#16811160C2216yescomplemented
100#16811160C2216yescomplemented
101#16811160C2216yescomplemented
102#16811160C2216yescomplemented
103#16811159C22112yescomplemented
104#16811158C2216yescomplemented
105#16811158C2216yescomplemented
106#16811158C2216yescomplemented
107#16811158C2216yescomplemented
108C2×#13133212C2216yescomplemented
109C2×#13133206C2216yescomplemented
110C2×#13133205C2213yescomplemented
111#16811136C22112yescomplemented
112#16811135C2213yes—
113#16811135C2213yescomplemented
114C2×#13133202C2216yescomplemented
115C2×#13133197C2213yescomplemented
116C2×#13133193C2216yescomplemented
117C2×#13133192C2213yes—
118#16811105C2211yescharacteristic, complemented
119#16811105C2212yescomplemented
120#16811105C2211yescharacteristic, complemented
121#16811104C2213yescomplemented
122#16811104C2213yescomplemented
123#16811102C2213yescomplemented
124#16811102C2216yescomplemented
125#16811102C2213yescomplemented
126#16811100C2213yescomplemented
127#16811099C2212yescomplemented
128#16811099C2211yescharacteristic, complemented
129#16811099C2211yescharacteristic, complemented
130#16811097C2213yescomplemented
131#16811095C2216yescomplemented
132#16811095C2213yescomplemented
133#16811095C2213yescomplemented
134#41×Dic53C2211yescharacteristic
135C4×#11719949C2212yescomplemented
136C4×#11719945C2213yescomplemented
137#16811091C2213yescomplemented
138#16811091C2213yescomplemented
139#16811091C2213yescomplemented
140C4×#11719947C2216yescomplemented
141C2×#13133182C2213yescomplemented
142C4×Q8×D53C2212yescomplemented
143C2×#13133179C2213yescomplemented
144C4×D4×D53C2216yescomplemented
145C2×#13133174C2213yescomplemented
146#117×D53C2213yescomplemented
147Q82×C53C2212yescomplemented
148C53×#557C2212yescomplemented
149C53×#554C2216yescomplemented
150D4×Q8×C53C2216yescomplemented
151C53×#544C2213yescomplemented
152C53×#544C2213yescomplemented
153C53×#533C2213yescomplemented
154C2×C4⋊Q8×C53C2213yescomplemented
155C53×#520C2211yescharacteristic
156C53×#520C2211yescharacteristic
157C4×#41×C53C2211yescharacteristic
158#13133264—28no—
159#13133263—28no—
160C2×#11719949C2312yes—
161C2×#11719949C2311yescharacteristic
162C2×#11719949C23112yes—
163C2×#11719945C2313yes—
164C2×#11719945C2313yes—
165C2×#11719945C2313yes—
166C2×#11719947C2313yes—
167C2×#11719947C2316yes—
168#41×D53—28no—
169C22×Dic106C2313yes—
170C2×Q8×D53C2311yescharacteristic
171C2×Q8×D53C2312yes—
172C22×D212C2313yes—
173C22×D212C2316yes—
174C2×D4×D53C2316yes—
175C2×D4×D53C2313yes—
176C22×C4×D53C2313yes—
177C22×C4×D53C2316yes—
178#13133217C2316yes—
179#13133217C2313yes—
180#13133214C2316yes—
181#13133214C2313yes—
182#13133212C2316yes—
183#13133212C23112yes—
184#13133212C2316yes—
185#13133212C2316yes—
186#13133212C23112yes—
187#13133212C23112yes—
188#13133212C23112yes—
189#13133212C2316yes—
190#13133212C2316yes—
191#13133212C23112yes—
192#13133212C2316yes—
193#13133212C2316yes—
194#13133212C2312yes—
195#13133208C2316yes—
196#13133208C23112yes—
197#13133208C2316yes—
198#13133208C2316yes—
199#13133208C2316yes—
200#13133206C23112yes—
201#13133206C2316yes—
202#13133206C23112yes—
203#13133206C23112yes—
204#13133206C2316yes—
205#13133206C2316yes—
206#13133206C23112yes—
207#13133206C2312yes—
208#13133205C2316yes—
209#13133205C2316yes—
210#13133205C2316yes—
211#13133205C2316yes—
212#13133205C2313yes—
213#13133205C2316yes—
214#13133205C2311yescharacteristic
215#13133202C23112yes—
216#13133202C23112yes—
217#13133202C2316yes—
218#13133202C2316yes—
219#13133202C23112yes—
220#13133202C23112yes—
221#13133202C2316yes—
222#13133202C2316yes—
223#13133202C2316yes—
224#13133202C23112yes—
225#13133202C2316yes—
226#13133202C2316yes—
227#13133202C2312yes—
228#13133201C2316yes—
229#13133201C23112yes—
230#13133201C23112yes—
231#13133201C2316yes—
232#13133197C2316yes—
233#13133197C2316yes—
234#13133197C2316yes—
235#13133197C2316yes—
236#13133197C2316yes—
237#13133197C2316yes—
238#13133197C2313yes—
239#13133197C2316yes—
240#13133197C2311yescharacteristic
241#13133197C2313yes—
242#13133197C2313yes—
243#13133193C23112yes—
244#13133193C23112yes—
245#13133193C2316yes—
246#13133193C23112yes—
247#13133193C2316yes—
248#13133193C2316yes—
249#13133193C23112yes—
250#13133193C2312yes—
251#13133192C2316yes—
252#13133192C2316yes—
253#13133192C23112yes—
254#13133192C2316yes—
255#13133192C2316yes—
256#13133192C2316yes—
257#13133192C2316yes—
258#13133192C2316yes—
259#13133192C2316yes—
260#13133192C2313yes—
261#13133192C2316yes—
262#13133192C2313yes—
263#13133192C2311yescharacteristic
264#13133192C2313yes—
265#13133192C2316yes—
266#13133192C2316yes—
267#13133191C23112yes—
268#13133191C2316yes—
269#13133191C2316yes—
270#13133191C23112yes—
271#13133187C2316yes—
272#13133187C23112yes—
273#13133187C23112yes—
274#13133187C2316yes—
275Q8×Dic53C23112yes—
276Q8×Dic53C2311yescharacteristic
277Q8×Dic53C2311yescharacteristic
278C4×Dic106C2316yes—
279C4×Dic106C2316yes—
280C4×Dic106C2313yes—
281C4×Dic106C2313yes—
282#13133182C2316yes—
283#13133182C2313yes—
284#13133182C2316yes—
285#13133182C2316yes—
286#13133182C2311yescharacteristic
287#13133182C2313yes—
288#13133182C2313yes—
289#13133182C2313yes—
290#13133182C2313yes—
291C4×D212C2316yes—
292C4×D212C2316yes—
293C4×D212C2316yes—
294C4×D212C2316yes—
295C4×D212C2313yes—
296C4×D212C2316yes—
297C4×D212C2316yes—
298C4×D212C2316yes—
299C4×D212C2316yes—
300C4×D212C2313yes—
301D4×Dic53C2313yes—
302D4×Dic53C2313yes—
303#13133179C23112yes—
304#13133179C23112yes—
305#13133179C23112yes—
306#13133179C2316yes—
307#13133179C2313yes—
308#13133179C2316yes—
309#13133179C2316yes—
310#13133179C2311yescharacteristic
311#13133179C2313yes—
312#13133179C2313yes—
313#13133179C2313yes—
314#13133179C2313yes—
315C4×C22⋊D53C23112yes—
316C4×C22⋊D53C2316yes—
317C4×C22⋊D53C23112yes—
318C4×C22⋊D53C2316yes—
319#13133177C2316yes—
320#13133177C2316yes—
321#13133177C2316yes—
322#13133177C2316yes—
323#13133177C2316yes—
324#13133177C2316yes—
325#13133176C2313yes—
326#13133175C23112yes—
327#13133175C23112yes—
328#13133175C23112yes—
329#13133175C2313yes—
330#13133175C2316yes—
331#13133175C2316yes—
332#13133175C2313yes—
333#13133174C2313yes—
334#13133174C2311yescharacteristic
335#13133174C2313yes—
336#13133174C2313yes—
337#13133174C2313yes—
338#13133174C2313yes—
339#13133174C2313yes—
340#13133174C2313yes—
341#13133174C2316yes—
342#13133174C2316yes—
343#13133173C23112yes—
344#13133173C2316yes—
345C2×C4⋊Dic53C2316yes—
346C2×#11719919C2313yes—
347C2×#11719919C2313yes—
348C2×#11719919C2316yes—
349C4⋊C4×D53C2316yes—
350C4⋊C4×D53C2313yes—
351C4⋊C4×D53C2316yes—
352C4⋊C4×D53C2313yes—
353C2×#11719921C2316yes—
354C2×#11719921C2316yes—
355C2×#11719921C2316yes—
356C2×#11719921C2316yes—
357C2×#11719921C2313yes—
358C2×#11719921C2313yes—
359C2×#11719921C2316yes—
360C22⋊C4×D53C2316yes—
361C22⋊C4×D53C23112yes—
362C2×C4×Dic53C2313yes—
363C2×C4×Dic53C2316yes—
364C42×D53C2316yes—
365C42×D53C2316yes—
366C42×D53C2316yes—
367C2×#41×C53C2311yescharacteristic
368C22×Q8×C53C2316yes—
369C4⋊Q8×C53C2316yes—
370C4⋊Q8×C53C2316yes—
371C4⋊Q8×C53C2313yes—
372C4⋊Q8×C53C2316yes—
373C4⋊Q8×C53C2316yes—
374C4⋊Q8×C53C2311yescharacteristic
375C4⋊Q8×C53C2316yes—
376#125×C53C2316yes—
377#125×C53C2313yes—
378#125×C53C2313yes—
379#125×C53C2316yes—
380C22⋊Q8×C53C23112yes—
381C22⋊Q8×C53C2316yes—
382C22⋊Q8×C53C2316yes—
383C22⋊Q8×C53C23112yes—
384C4×Q8×C53C2312yes—
385C4×Q8×C53C2311yescharacteristic
386C4×Q8×C53C2311yescharacteristic
387C4×Q8×C53C2312yes—
388C4×Q8×C53C2316yes—
389C4×Q8×C53C2316yes—
390C4×D4×C53C2316yes—
391C4×D4×C53C2313yes—
392C4×D4×C53C2313yes—
393C4×D4×C53C2316yes—
394#117×C53C2313yes—
395#117×C53C2313yes—
396#117×C53C2313yes—
397C2×C4⋊C4×C53C2313yes—
398C2×C4⋊C4×C53C2313yes—
399C2×C4⋊C4×C53C2316yes—
400C2×C42×C53C2313yes—
401C23×D53C2413yes—
402C23×D53C2416yes—
403#41×C53#4118yescomplemented
404C2×Q8×C53—86no—
405C2×Q8×C53C2412yes—
406C2×Q8×C53C2416yes—
407C2×Q8×C53C24112yes—
408C2×Q8×C53C2411yescharacteristic
409C2×D4×C53C2413yes—
410C22×C4×C53C2413yes—
411C22×C4×C53C2413yes—
412C22×C4×C53C2416yes—
413C22×C4×C53C2416yes—
414C22×C4×C53C2413yes—
415C2×C22⋊D53C2416yes—
416C2×C22⋊D53C2416yes—
417C2×C22⋊D53C2416yes—
418C22×Dic53C2416yes—
419C22×Dic53C2413yes—
420C22×Dic53C2413yes—
421C22×Dic53C2413yes—
422#11719949—24no—
423#11719949—28no—
424#11719949—812no—
425Q8×D53—24no—
426Q8×D53—28no—
427#11719947—212no—
428#11719947—224no—
429D4×D53—212no—
430D4×D53—224no—
431#11719945—212no—
432#11719945—212no—
433#11719945—212no—
434C2×D212—212no—
435C2×D212—86no—
436C2×D212C2413yes—
437C2×D212C2411yescharacteristic
438C2×D212C2416yes—
439C2×D212C2413yes—
440C2×D212C2416yes—
441C2×D212C2416yes—
442C2×D212C24112yes—
443C2×D212C2412yes—
444C2×D212C2416yes—
445C2×D212C2416yes—
446C2×D212C2416yes—
447C2×C4×D53—212no—
448C2×C4×D53—86no—
449C2×C4×D53C2413yes—
450C2×C4×D53C2416yes—
451C2×C4×D53C2416yes—
452C2×C4×D53C2413yes—
453C2×C4×D53C2411yescharacteristic
454C2×C4×D53C2413yes—
455C2×C4×D53C2412yes—
456C2×C4×D53C2416yes—
457C2×C4×D53C2416yes—
458C2×C4×D53C2416yes—
459C2×C4×D53C2416yes—
460C2×C4×D53C2416yes—
461C2×C4×D53C24112yes—
462C2×Dic106—212no—
463C2×Dic106C2413yes—
464C2×Dic106C2411yescharacteristic
465C2×Dic106C2416yes—
466C2×Dic106C2413yes—
467C4⋊C4×C53C2413yes—
468C4⋊C4×C53C2413yes—
469C4⋊C4×C53C2416yes—
470C4⋊C4×C53C2416yes—
471C4⋊C4×C53C2416yes—
472C4⋊C4×C53C24112yes—
473C4⋊C4×C53C2411yescharacteristic
474C4⋊C4×C53C2411yescharacteristic
475C4⋊C4×C53C2413yes—
476C4⋊C4×C53C2413yes—
477C4⋊C4×C53C2412yes—
478C4⋊C4×C53C2416yes—
479C4⋊C4×C53C2416yes—
480C4⋊C4×C53C2416yes—
481C4⋊C4×C53C2416yes—
482C22⋊C4×C53C2416yes—
483C22⋊C4×C53C2416yes—
484C22⋊C4×C53C2416yes—
485C42×C53C2411yescharacteristic
486C42×C53C2413yes—
487C42×C53C2413yes—
488C42×C53C2413yes—
489C42×C53C2416yes—
490C42×C53C2416yes—
491C22⋊Dic53C2416yes—
492#11719921C2413yes—
493#11719921C2413yes—
494#11719921C2416yes—
495#11719921C24112yes—
496#11719921C2411yescharacteristic
497#11719921C2411yescharacteristic
498#11719921C2416yes—
499#11719921C2416yes—
500#11719921C2416yes—
501#11719921C2416yes—
502#11719921C2416yes—
503#11719921C2413yes—
504#11719921C2413yes—
505#11719921C2413yes—
506#11719921C2413yes—
507#11719921C24112yes—
508#11719921C24112yes—
509#11719921C24112yes—
510#11719921C24112yes—
511#11719921C2412yes—
512#11719921C2416yes—
513#11719921C2416yes—
514#11719921C2416yes—
515#11719921C2416yes—
516#11719921C2416yes—
517#11719921C2412yes—
518#11719921C2412yes—
519#11719921C2412yes—
520#11719921C2412yes—
521C4⋊Dic53C2413yes—
522C4⋊Dic53C2413yes—
523C4⋊Dic53C2416yes—
524C4⋊Dic53C24112yes—
525C4⋊Dic53C2416yes—
526C4⋊Dic53C2416yes—
527C4⋊Dic53C2412yes—
528C4⋊Dic53C2416yes—
529C4⋊Dic53C2416yes—
530#11719919C2413yes—
531#11719919C2413yes—
532#11719919C2416yes—
533#11719919C24112yes—
534#11719919C2411yescharacteristic
535#11719919C2411yescharacteristic
536#11719919C2416yes—
537#11719919C2413yes—
538#11719919C2413yes—
539#11719919C2413yes—
540#11719919C2413yes—
541#11719919C2416yes—
542#11719919C2412yes—
543C4×Dic53C2412yes—
544C4×Dic53C2413yes—
545C4×Dic53C2413yes—
546C4×Dic53C2413yes—
547C4×Dic53C2416yes—
548C4×Dic53C2416yes—
549C4×Dic53C2416yes—
550C4×Dic53C2416yes—
551C4×Dic53C2416yes—
552C4×Dic53C2411yescharacteristic
553C4×Dic53C24112yes—
554C23×C53C2513yes—
555C22×D53—26no—
556C22×D53—212no—
557C22×D53—46no—
558C22×D53—43no—
559C22×D53—43no—
560C22×D53—46no—
561C22×D53C2512yes—
562C22×D53C2513yes—
563C22×D53C2516yes—
564C22×D53C2511yescharacteristic
565Q8×C53—412no—
566Q8×C53—46no—
567Q8×C53—42no—
568Q8×C53C2×#4114yes—
569D4×C53C2×#41112yes—
570C2×C4×C53—46no—
571C2×C4×C53—46no—
572C2×C4×C53—43no—
573C2×C4×C53—43no—
574C2×C4×C53C2×#41112yes—
575C2×C4×C53C2516yes—
576C2×C4×C53C2512yes—
577C2×C4×C53C2513yes—
578C2×C4×C53C2513yes—
579C2×C4×C53C2516yes—
580C2×C4×C53C2512yes—
581C2×C4×C53C2511yescharacteristic
582C2×C4×C53C2511yescharacteristic
583C2×C4×C53C2511yescharacteristic
584C2×C4×C53C2513yes—
585C22⋊D53—212no—
586C22⋊D53—212no—
587C22⋊D53—212no—
588C2×Dic53—212no—
589C2×Dic53—26no—
590C2×Dic53—43no—
591C2×Dic53—43no—
592C2×Dic53C2516yes—
593C2×Dic53C2513yes—
594C2×Dic53C2512yes—
595C2×Dic53C2513yes—
596C2×Dic53C2511yescharacteristic
597C2×Dic53C2511yescharacteristic
598C2×Dic53C2513yes—
599C2×Dic53C2511yescharacteristic
600D212—26no—
601D212—212no—
602D212—22no—
603D212—26no—
604D212—46no—
605D212—412no—
606D212—42no—
607D212—46no—
608D212—46no—
609D212—46no—
610D212—46no—
611C4×D53—22no—
612C4×D53—26no—
613C4×D53—26no—
614C4×D53—26no—
615C4×D53—212no—
616C4×D53—212no—
617C4×D53—46no—
618C4×D53—412no—
619C4×D53—46no—
620C4×D53—46no—
621C4×D53—42no—
622C4×D53—46no—
623C4×D53—46no—
624Dic106—26no—
625Dic106—212no—
626Dic106—22no—
627Dic106—26no—
628#62857—531nomaximal, Sylow
629C22×C53—23no—
630C22×C53—23no—
631C22×C53C22×#4116yes—
632C22×C53C2611yescharacteristic
633C2×D53—21no—
634C2×D53—22no—
635C2×D53—23no—
636C2×D53—26no—
637C2×D53—22no—
638C2×D53—26no—
639C2×D53—23no—
640C2×D53—21no—
641C2×D53—23no—
642C2×D53—22no—
643C2×D53—26no—
644C2×D53—21no—
645C2×D53—86no—
646C2×D53—812no—
647C4×C53—26no—
648C4×C53—23no—
649C4×C53—26no—
650C4×C53—21no—
651C4×C53—22no—
652C4×C53—23no—
653C4×C53—22no—
654C4×C53—21no—
655C4×C53C22×#4112yes—
656C4×C53C22×#4116yes—
657Dic53—26no—
658Dic53—23no—
659Dic53—22no—
660Dic53—21no—
661Dic53—23no—
662Dic53—21no—
663Dic53—23no—
664Dic53—21no—
665#3524—532no—
666#3522—532no—
667#3521—536no—
668#3520—536no—
669#3518—532no—
670#3516—532no—
671#3514—536no—
672#3513—536no—
673#3511—533no—
674#3510—533no—
675#3503D5311yescharacteristic, complemented
676#3500—531no—
677#3495—533no—
678#3494—533no—
679#3489—531no—
680#3488—531no—
681#3461—533no—
682#3460—533no—
683#3455—533no—
684C2×#542—533no—
685C4×2−1+4—531no—
686C4×H(5,𝔽2)—531no—
687#3428—531no—
688C2×C53—26no—
689C2×C53C23×#4111yescharacteristic
690C2×C53H(7,𝔽2)11yescharacteristic
691C2×C532−1+611yescharacteristic
692D53—42no—
693D53—43no—
694D53—46no—
695D53—41no—
696C2×2−1+4—531no—
697C2×H(5,𝔽2)—531no—
698C22×#41—531no—
699#559—536no—
700#559—536no—
701Q82C2×D5312yescomplemented
702#557C2×D5312yescomplemented
703#556—536no—
704#556—536no—
705#556—536no—
706#556—536no—
707#555—536no—
708#555—536no—
709#554—536no—
710#554—536no—
711#554C2×D5316yescomplemented
712#553—536no—
713#553—536no—
714#553—5312no—
715#552—536no—
716#552—536no—
717#552—5312no—
718#551—5312no—
719#551—5312no—
720#551—5312no—
721#551—5312no—
722#550—532no—
723D4×Q8—532no—
724D4×Q8C2×D5316yescomplemented
725#548—5312no—
726#548—532no—
727#548—532no—
728#548—532no—
729#548—532no—
730#547—536no—
731#547—536no—
732#547—536no—
733#546—5312no—
734#546—536no—
735#546—536no—
736#546—536no—
737#546—536no—
738D42—536no—
739#544C2×D5313yescomplemented
740#544C2×D5313yescomplemented
741#542—533no—
742#542—536no—
743#542—536no—
744#542—536no—
745#542—536no—
746#542—536no—
747#542—536no—
748#542—536no—
749#542—531no—
750#542—533no—
751#542—533no—
752#542—536no—
753#542—536no—
754#541—533no—
755#541—533no—
756#541—536no—
757#540—533no—
758#540—533no—
759#540—536no—
760#539—536no—
761#539—536no—
762#539—5312no—
763#538—536no—
764#538—536no—
765#538—5312no—
766#537—533no—
767#537—533no—
768#536—533no—
769#536—533no—
770#535—533no—
771#535—533no—
772#533—536no—
773#533—536no—
774#533C2×D5313yescomplemented
775#532—536no—
776#532—536no—
777#532—533no—
778C2×C4⋊Q8C2×D5313yescomplemented
779#529—536no—
780#529—536no—
781#529—536no—
782#529—536no—
783#529—5312no—
784#529—536no—
785#529—536no—
786#529—536no—
787#529—536no—
788C2×#126—536no—
789C2×#124—536no—
790C2×#124—533no—
791#525—5312no—
792#525—533no—
793#525—533no—
794C2×#123—536no—
795C2×C22⋊Q8—536no—
796C2×C22⋊Q8—533no—
797C2×#121—533no—
798#520—531no—
799#520—531no—
800#520—532no—
801#520—533no—
802#520—533no—
803#520—536no—
804#520—533no—
805#520—533no—
806#520C2×D5311yescharacteristic
807#520C2×D5311yescharacteristic
808#519—531no—
809#519—531no—
810#519—532no—
811#519—533no—
812#518—533no—
813#518—533no—
814#518—536no—
815#518—533no—
816C4×#41—531no—
817C4×#41—532no—
818C4×#41—536no—
819C4×#41—533no—
820C4×#41—533no—
821C4×#41—533no—
822C4×#41—533no—
823C4×#41C2×D5311yescharacteristic
824C2×C4×Q8—532no—
825C2×C4×Q8—533no—
826C2×C4×D4—536no—
827C2×C4×D4—533no—
828C2×#117—533no—
829C2×#117—533no—
830C53#6285711yescharacteristic, complemented, Sylow
8312−1+4—1068no—
832H(5,𝔽2)—1068no—
833C2×#41—532no—
834C2×#41—531no—
835C2×#41—5312no—
836C2×#41—536no—
837C2×#41—533no—
838C2×#41—533no—
839C2×#41—533no—
840C2×#41—533no—
841C2×#41—1068no—
842C2×#41C22×D5311yescharacteristic
843C22×Q8—532no—
844C22×Q8—531no—
845C22×Q8—533no—
846C22×Q8C22×D5316yes—
847C22×D4—536no—
848C22×D4—533no—
849C22×D4—533no—
850C22×D4—536no—
851C23×C4—533no—
852C23×C4—536no—
853C4⋊Q8—533no—
854C4⋊Q8—536no—
855C4⋊Q8C22×D5313yes—
856C4⋊Q8C22×D5316yes—
857C4⋊Q8C22×D5316yes—
858C4⋊Q8C22×D5316yes—
859C4⋊Q8C22×D5316yes—
860C4⋊Q8C22×D5316yes—
861C4⋊Q8C22×D5311yescharacteristic
862#127—533no—
863#127—536no—
864#126—536no—
865#126—5312no—
866#126—5312no—
867#126—5312no—
868#126—536no—
869#126—536no—
870#126—532no—
871#126—536no—
872#126—536no—
873#126—5312no—
874#126—5312no—
875#126—536no—
876#126—536no—
877#125—536no—
878#125—536no—
879#125—536no—
880#125—536no—
881#125—5312no—
882#125C22×D5313yes—
883#125C22×D5313yes—
884#125C22×D5316yes—
885#125C22×D5316yes—
886#124—536no—
887#124—5312no—
888#124—5312no—
889#124—5312no—
890#124—532no—
891#124—536no—
892#124—536no—
893#124—5312no—
894#124—533no—
895#124—536no—
896#124—536no—
897#124—536no—
898#124—536no—
899#124—536no—
900#124—531no—
901#123—536no—
902#123—5312no—
903#123—5312no—
904#123—5312no—
905#123—536no—
906#123—532no—
907#123—536no—
908#123—5312no—
909#123—536no—
910#123—536no—
911#123—536no—
912#123—536no—
913#123—5312no—
914#123—536no—
915#123—536no—
916#123—5312no—
917#123—5312no—
918C22⋊Q8—536no—
919C22⋊Q8—5312no—
920C22⋊Q8—5312no—
921C22⋊Q8—5312no—
922C22⋊Q8—532no—
923C22⋊Q8—536no—
924C22⋊Q8—536no—
925C22⋊Q8—5312no—
926C22⋊Q8—533no—
927C22⋊Q8—536no—
928C22⋊Q8—536no—
929C22⋊Q8—536no—
930C22⋊Q8—531no—
931C22⋊Q8—533no—
932C22⋊Q8—533no—
933C22⋊Q8—536no—
934C22⋊Q8—536no—
935C22⋊Q8—536no—
936C22⋊Q8—536no—
937C22⋊Q8C22×D53112yes—
938C22⋊Q8C22×D53112yes—
939C22⋊Q8C22×D5316yes—
940C22⋊Q8C22×D5316yes—
941#121—5312no—
942#121—5312no—
943#121—536no—
944#121—536no—
945#121—533no—
946#121—536no—
947#121—536no—
948#121—536no—
949#121—531no—
950#121—536no—
951#121—533no—
952#121—533no—
953#121—536no—
954#121—536no—
955#121—536no—
956#121—536no—
957#121—536no—
958#121—536no—
959#121—536no—
960#121—5312no—
961#120—5312no—
962#120—5312no—
963#120—536no—
964#120—536no—
965C4×Q8—531no—
966C4×Q8—531no—
967C4×Q8—5312no—
968C4×Q8—536no—
969C4×Q8—533no—
970C4×Q8—536no—
971C4×Q8—536no—
972C4×Q8—531no—
973C4×Q8—533no—
974C4×Q8—533no—
975C4×Q8—533no—
976C4×Q8—533no—
977C4×Q8—536no—
978C4×Q8—536no—
979C4×Q8—533no—
980C4×Q8—533no—
981C4×Q8C22×D5312yes—
982C4×Q8C22×D5312yes—
983C4×Q8C22×D5311yescharacteristic
984C4×Q8C22×D5311yescharacteristic
985C4×Q8C22×D5316yes—
986C4×Q8C22×D5316yes—
987C4×D4—533no—
988C4×D4—533no—
989C4×D4—5312no—
990C4×D4—536no—
991C4×D4—536no—
992C4×D4—5312no—
993C4×D4—536no—
994C4×D4—533no—
995C4×D4—536no—
996C4×D4—536no—
997C4×D4—531no—
998C4×D4—533no—
999C4×D4—533no—
1000C4×D4—533no—
1001C4×D4—533no—
1002C4×D4—5312no—
1003C4×D4—5312no—
1004C4×D4—5312no—
1005C4×D4—536no—
1006C4×D4—536no—
1007C4×D4—536no—
1008C4×D4—536no—
1009C4×D4—536no—
1010C4×D4—536no—
1011C4×D4—536no—
1012C4×D4—536no—
1013C4×D4—533no—
1014C4×D4—533no—
1015C4×D4—536no—
1016C4×D4—536no—
1017C4×D4—536no—
1018C4×D4—536no—
1019C4×D4—536no—
1020C4×D4—536no—
1021C4×D4C22×D5316yes—
1022C4×D4C22×D5316yes—
1023C4×D4C22×D5313yes—
1024C4×D4C22×D5313yes—
1025#117—533no—
1026#117—533no—
1027#117—533no—
1028#117—536no—
1029#117—536no—
1030#117—5312no—
1031#117—5312no—
1032#117—5312no—
1033#117—536no—
1034#117—5312no—
1035#117—533no—
1036#117—531no—
1037#117—533no—
1038#117—533no—
1039#117—533no—
1040#117—533no—
1041#117—533no—
1042#117—533no—
1043#117—536no—
1044#117—536no—
1045#117C22×D5313yes—
1046#117C22×D5313yes—
1047#117C22×D5313yes—
1048C2×C4⋊C4—533no—
1049C2×C4⋊C4—533no—
1050C2×C4⋊C4—536no—
1051C2×C4⋊C4—536no—
1052C2×C4⋊C4—533no—
1053C2×C4⋊C4—533no—
1054C2×C4⋊C4—536no—
1055C2×C4⋊C4—536no—
1056C2×C4⋊C4C22×D5313yes—
1057C2×C4⋊C4C22×D5313yes—
1058C2×C4⋊C4C22×D5316yes—
1059C2×C22⋊C4—533no—
1060C2×C22⋊C4—533no—
1061C2×C22⋊C4—536no—
1062C2×C22⋊C4—536no—
1063C2×C22⋊C4—536no—
1064C2×C22⋊C4—536no—
1065C2×C22⋊C4—536no—
1066C2×C22⋊C4—536no—
1067C2×C22⋊C4—5312no—
1068C2×C42—533no—
1069C2×C42—536no—
1070C2×C42—536no—
1071C2×C42—536no—
1072C2×C42—536no—
1073C2×C42C22×D5313yes—
1074C24—533no—
1075C24—536no—
1076#41—1064no—
1077#41—1068no—
1078#41—10612no—
1079#41—10624no—
1080#41—10612no—
1081#41—10612no—
1082#41—10612no—
1083#41—42412no—
1084#41#1171994918yescomplemented
1085C2×Q8—86no—
1086C2×Q8—533no—
1087C2×Q8—536no—
1088C2×Q8—533no—
1089C2×Q8—531no—
1090C2×Q8—1064no—
1091C2×Q8—1068no—
1092C2×Q8—10612no—
1093C2×Q8C23×D53112yes—
1094C2×Q8C23×D5312yes—
1095C2×Q8C23×D5316yes—
1096C2×Q8C23×D5311yescharacteristic
1097C2×D4—536no—
1098C2×D4—536no—
1099C2×D4—536no—
1100C2×D4—533no—
1101C2×D4—536no—
1102C2×D4—533no—
1103C2×D4—531no—
1104C2×D4—532no—
1105C2×D4—536no—
1106C2×D4—536no—
1107C2×D4—536no—
1108C2×D4—536no—
1109C2×D4—536no—
1110C2×D4—5312no—
1111C2×D4—10612no—
1112C2×D4—10624no—
1113C2×D4—10612no—
1114C2×D4—4246no—
1115C2×D4C23×D5313yes—
1116C22×C4—536no—
1117C22×C4—533no—
1118C22×C4—533no—
1119C22×C4—533no—
1120C22×C4—533no—
1121C22×C4—536no—
1122C22×C4—536no—
1123C22×C4—533no—
1124C22×C4—533no—
1125C22×C4—531no—
1126C22×C4—532no—
1127C22×C4—536no—
1128C22×C4—536no—
1129C22×C4—536no—
1130C22×C4—536no—
1131C22×C4—536no—
1132C22×C4—5312no—
1133C22×C4—10612no—
1134C22×C4—4246no—
1135C22×C4C23×D5316yes—
1136C22×C4C23×D5313yes—
1137C22×C4C23×D5313yes—
1138C22×C4C23×D5316yes—
1139C22×C4C23×D5313yes—
1140C4⋊C4—533no—
1141C4⋊C4—531no—
1142C4⋊C4—533no—
1143C4⋊C4—531no—
1144C4⋊C4—533no—
1145C4⋊C4—536no—
1146C4⋊C4—536no—
1147C4⋊C4—5312no—
1148C4⋊C4—536no—
1149C4⋊C4—533no—
1150C4⋊C4—533no—
1151C4⋊C4—533no—
1152C4⋊C4—533no—
1153C4⋊C4—533no—
1154C4⋊C4—5312no—
1155C4⋊C4—532no—
1156C4⋊C4—536no—
1157C4⋊C4—536no—
1158C4⋊C4—536no—
1159C4⋊C4—532no—
1160C4⋊C4—536no—
1161C4⋊C4—536no—
1162C4⋊C4C23×D5316yes—
1163C4⋊C4C23×D5316yes—
1164C4⋊C4C23×D5313yes—
1165C4⋊C4C23×D5313yes—
1166C4⋊C4C23×D5313yes—
1167C4⋊C4C23×D5313yes—
1168C4⋊C4C23×D5316yes—
1169C4⋊C4C23×D53112yes—
1170C4⋊C4C23×D5316yes—
1171C4⋊C4C23×D5316yes—
1172C4⋊C4C23×D5311yescharacteristic
1173C4⋊C4C23×D5311yescharacteristic
1174C4⋊C4C23×D5316yes—
1175C4⋊C4C23×D5316yes—
1176C4⋊C4C23×D5312yes—
1177C22⋊C4—536no—
1178C22⋊C4—533no—
1179C22⋊C4—533no—
1180C22⋊C4—531no—
1181C22⋊C4—531no—
1182C22⋊C4—536no—
1183C22⋊C4—536no—
1184C22⋊C4—5312no—
1185C22⋊C4—536no—
1186C22⋊C4—536no—
1187C22⋊C4—536no—
1188C22⋊C4—536no—
1189C22⋊C4—533no—
1190C22⋊C4—533no—
1191C22⋊C4—533no—
1192C22⋊C4—533no—
1193C22⋊C4—5312no—
1194C22⋊C4—5312no—
1195C22⋊C4—5312no—
1196C22⋊C4—5312no—
1197C22⋊C4—532no—
1198C22⋊C4—536no—
1199C22⋊C4—536no—
1200C22⋊C4—536no—
1201C22⋊C4—532no—
1202C22⋊C4—536no—
1203C22⋊C4—536no—
1204C22⋊C4—532no—
1205C22⋊C4—532no—
1206C22⋊C4—532no—
1207C22⋊C4C23×D5316yes—
1208C22⋊C4C23×D5316yes—
1209C22⋊C4C23×D5316yes—
1210C42—531no—
1211C42—533no—
1212C42—533no—
1213C42—533no—
1214C42—532no—
1215C42—536no—
1216C42—536no—
1217C42—536no—
1218C42—536no—
1219C42—5312no—
1220C42—536no—
1221C42C23×D5313yes—
1222C42C23×D5316yes—
1223C42C23×D5316yes—
1224C42C23×D5311yescharacteristic
1225C42C23×D5313yes—
1226C42C23×D5313yes—
1227C23—531no—
1228C23—536no—
1229C23—533no—
1230C23—532no—
1231C23—1066no—
1232C23—10612no—
1233C23—2126no—
1234C23—2123no—
1235C23—2123no—
1236C23—2126no—
1237C23C24×D5313yes—
1238Q8—46no—
1239Q8—412no—
1240Q8—42no—
1241Q8—10612no—
1242Q8—1066no—
1243Q8—1066no—
1244Q8—1062no—
1245Q8C2×#1171994914yes—
1246D4—10612no—
1247D4—10612no—
1248D4—10612no—
1249D4—10612no—
1250D4—1066no—
1251D4—1066no—
1252D4—1062no—
1253D4—2126no—
1254D4—2122no—
1255D4—2126no—
1256D4—2126no—
1257D4—21212no—
1258D4—2126no—
1259D4—2126no—
1260D4C2×#11719949112yes—
1261C2×C4—46no—
1262C2×C4—43no—
1263C2×C4—46no—
1264C2×C4—43no—
1265C2×C4—533no—
1266C2×C4—531no—
1267C2×C4—533no—
1268C2×C4—531no—
1269C2×C4—536no—
1270C2×C4—533no—
1271C2×C4—532no—
1272C2×C4—531no—
1273C2×C4—1066no—
1274C2×C4—10612no—
1275C2×C4—1062no—
1276C2×C4—1066no—
1277C2×C4—1066no—
1278C2×C4—1066no—
1279C2×C4—10612no—
1280C2×C4—10612no—
1281C2×C4—2126no—
1282C2×C4—2126no—
1283C2×C4—2122no—
1284C2×C4—2126no—
1285C2×C4—21212no—
1286C2×C4—2126no—
1287C2×C4—2126no—
1288C2×C4—2123no—
1289C2×C4—2123no—
1290C2×C4C2×#11719949112yes—
1291C2×C4C24×D5312yes—
1292C2×C4C24×D5316yes—
1293C2×C4C24×D5313yes—
1294C2×C4C24×D5313yes—
1295C2×C4C24×D5312yes—
1296C2×C4C24×D5316yes—
1297C2×C4C24×D5311yescharacteristic
1298C2×C4C24×D5311yescharacteristic
1299C2×C4C24×D5311yescharacteristic
1300C2×C4C24×D5313yes—
1301C22—23no—
1302C22—23no—
1303C22—1061no—
1304C22—1062no—
1305C22—1063no—
1306C22—1066no—
1307C22—1062no—
1308C22—1066no—
1309C22—1063no—
1310C22—1061no—
1311C22—1063no—
1312C22—1062no—
1313C22—1066no—
1314C22—1061no—
1315C22—4246no—
1316C22—42412no—
1317C22C22×#1171994916yes—
1318C22C25×D5311yescharacteristic
1319C4—21no—
1320C4—26no—
1321C4—26no—
1322C4—23no—
1323C4—21no—
1324C4—23no—
1325C4—22no—
1326C4—22no—
1327C4—1061no—
1328C4—1062no—
1329C4—1063no—
1330C4—1066no—
1331C4—1061no—
1332C4—1063no—
1333C4—1063no—
1334C4—1061no—
1335C4C22×#1171994916yes—
1336C4C22×#1171994912yes—
1337C2—26no—
1338C2—2121no—
1339C2—2126no—
1340C2—2123no—
1341C2—2122no—
1342C2C23×#1171994911yescharacteristic
1343C2#2028952511yescharacteristic
1344C2#2028952711yescharacteristic
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3503C2
hypercenter#3503D53
hypocenterC53#62857
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3503

Complements

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

NH ≅ G/Ntype
1. #20288827C2semidirect
2. #20288801C2semidirect
3. #20288786C2semidirect
4. #20288765C2semidirect
5. #20288733C2semidirect
6. #20288711C2semidirect
7. #20288677C2semidirect
8. #20288658C2semidirect
9. #20288628C2semidirect
10. #20288613C2semidirect
11. #20288508C2semidirect
12. #20288470C2semidirect
13. #20288453C2semidirect
14. #20288396C2semidirect
15. #20288385C2semidirect
16. #20288149C2semidirect
17. #20288138C2semidirect
18. #20288107C2semidirect
19. C2×#16811247C2semidirect
20. #20287926C2semidirect
21. #20287921C2semidirect
22. #20287914C2semidirect
23. C53×#3503C2semidirect
27. #16811358C22semidirect
28. #16811358C22semidirect
29. #16811347C22semidirect
30. #16811347C22semidirect
31. #16811346C22semidirect
32. #16811346C22semidirect
33. #16811339C22semidirect
34. #16811339C22semidirect
35. #16811334C22semidirect
36. #16811334C22semidirect
37. #16811326C22semidirect
38. #16811326C22semidirect
39. #16811321C22semidirect
40. #16811315C22semidirect
41. #16811311C22semidirect
42. #16811311C22semidirect
43. #16811300C22semidirect
44. #16811300C22semidirect
45. #16811300C22semidirect
46. #16811300C22semidirect
48. Q8×D212C22semidirect
50. #16811285C22semidirect
51. #16811285C22semidirect
52. #16811285C22semidirect
53. #16811284C22semidirect
54. #16811277C22semidirect
55. #16811276C22semidirect
56. #16811276C22semidirect
58. #16811268C22semidirect
59. #16811268C22semidirect
60. #16811268C22semidirect
61. #16811264C22semidirect
63. #16811247C22semidirect
64. #16811247C22semidirect
65. #16811247C22semidirect
66. #16811247C22semidirect
67. #16811247C22semidirect
68. #16811247C22semidirect
69. #16811247C22semidirect
70. #16811247C22semidirect
71. #16811247C22semidirect
72. #16811247C22semidirect
73. #16811247C22semidirect
74. #16811247C22semidirect
75. #16811247C22semidirect
76. #16811236C22semidirect
77. #16811236C22semidirect
78. #16811236C22semidirect
79. #16811229C22semidirect
80. #16811229C22semidirect
81. #16811229C22semidirect
82. #16811222C22semidirect
83. #16811222C22semidirect
84. #16811222C22semidirect
85. #16811213C22semidirect
86. #16811213C22semidirect
87. #16811213C22semidirect
89. #16811204C22semidirect
90. #16811199C22semidirect
91. #16811199C22semidirect
93. #16811192C22semidirect
94. #16811178C22semidirect
95. #16811178C22semidirect
96. #16811174C22semidirect
97. #16811174C22semidirect
98. #16811173C22semidirect
99. #16811160C22semidirect
100. #16811160C22semidirect
101. #16811160C22semidirect
102. #16811160C22semidirect
103. #16811159C22semidirect
104. #16811158C22semidirect
105. #16811158C22semidirect
106. #16811158C22semidirect
107. #16811158C22semidirect
108. C2×#13133212C22semidirect
109. C2×#13133206C22semidirect
110. C2×#13133205C22semidirect
111. #16811136C22semidirect
113. #16811135C22semidirect
114. C2×#13133202C22semidirect
115. C2×#13133197C22semidirect
116. C2×#13133193C22semidirect
118. #16811105C22semidirect
119. #16811105C22semidirect
120. #16811105C22semidirect
121. #16811104C22semidirect
122. #16811104C22semidirect
123. #16811102C22semidirect
124. #16811102C22semidirect
125. #16811102C22semidirect
126. #16811100C22semidirect
127. #16811099C22semidirect
128. #16811099C22semidirect
129. #16811099C22semidirect
130. #16811097C22semidirect
131. #16811095C22semidirect
132. #16811095C22semidirect
133. #16811095C22semidirect
135. C4×#11719949C22semidirect
136. C4×#11719945C22semidirect
137. #16811091C22semidirect
138. #16811091C22semidirect
139. #16811091C22semidirect
140. C4×#11719947C22semidirect
141. C2×#13133182C22semidirect
142. C4×Q8×D53C22semidirect
143. C2×#13133179C22semidirect
144. C4×D4×D53C22semidirect
145. C2×#13133174C22semidirect
146. #117×D53C22semidirect
147. Q82×C53C22semidirect
148. C53×#557C22semidirect
149. C53×#554C22semidirect
150. D4×Q8×C53C22semidirect
151. C53×#544C22semidirect
152. C53×#544C22semidirect
153. C53×#533C22semidirect
154. C2×C4⋊Q8×C53C22semidirect
403. #41×C53#41semidirect
675. #3503D53semidirect
701. Q82C2×D53semidirect
702. #557C2×D53semidirect
711. #554C2×D53semidirect
724. D4×Q8C2×D53semidirect
739. #544C2×D53semidirect
740. #544C2×D53semidirect
774. #533C2×D53semidirect
778. C2×C4⋊Q8C2×D53semidirect
830. C53#62857semidirect
1084. #41#11719949semidirect

Maximal subgroups

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

subgroupindex
#202888272
#202888012
#202887862
#202887652
#202887332
#202887112
#202886772
#202886582
#202886282
#202886132
#202885082
#202884702
#202884532
#202883962
#202883852
#202881492
#202881382
#202881072
C2×#168112472
#202879262
#202879212
#202879142
C53×#35032
#6285753