Finite Group Databasebeta

← #28292705

Subgroups — #28292705

Order 13568.

7220 conjugacy classes of subgroups.

The subgroup lattice has 1352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288827C212yesmaximal, complemented
2#20288812C211yesmaximal, characteristic, complemented
3#20288801C211yesmaximal, characteristic, complemented
4#20288786C216yesmaximal, complemented
5#20288765C213yesmaximal, complemented
6#20288748C213yesmaximal, complemented
7#20288733C211yesmaximal, characteristic, complemented
8#20288722C211yesmaximal, characteristic, complemented
9#20288711C212yesmaximal, complemented
10#20288694C213yesmaximal, complemented
11#20288677C213yesmaximal, complemented
12#20288658C216yesmaximal, complemented
13#20288310C213yesmaximal, complemented
14#20288282C216yesmaximal, complemented
15#20288282C213yesmaximal, complemented
16#41×D212C211yesmaximal, characteristic, complemented
17#41×D212C212yesmaximal, complemented
18#20288107C216yesmaximal, complemented
19#20288012C213yesmaximal, complemented
20C2×#16811160C213yesmaximal, complemented
21#20287914C212yesmaximal, complemented
22C4×#41×D53C211yesmaximal, characteristic, complemented
23Q8×#41×C53C211yesmaximal, characteristic, complemented
24C2×#41×D53C2211yescharacteristic
25C2×#41×D53C2212yes—
26#16811358C2213yescomplemented
27#16811358C2216yescomplemented
28#16811352C2213yescomplemented
29#16811347C2216yescomplemented
30#16811347C2213yescomplemented
31#16811346C2216yescomplemented
32#16811346C2213yescomplemented
33#16811339C2216yescomplemented
34#16811339C2213yescomplemented
35#16811334C2213yescomplemented
36#16811334C2216yescomplemented
37#16811326C2216yescomplemented
38#16811326C2216yescomplemented
39#16811326C2216yescomplemented
40#16811321C22112yescomplemented
41#16811321C2216yescomplemented
42#16811315C22112yescomplemented
43#16811315C2216yescomplemented
44#16811311C2216yescomplemented
45#16811311C2216yescomplemented
46#16811311C2216yescomplemented
47#16811300C22112yescomplemented
48#16811300C22112yescomplemented
49#16811300C22112yescomplemented
50#16811295C2211yescharacteristic, complemented
51#16811295C2213yescomplemented
52#16811295C2212yescomplemented
53Q8×D212C2212yescomplemented
54Q8×D212C2211yescharacteristic, complemented
55#16811285C2212yescomplemented
56#16811285C2212yescomplemented
57#16811285C2212yescomplemented
58#16811284C2216yescomplemented
59#16811277C2216yescomplemented
60#16811277C2213yescomplemented
61#16811276C2216yescomplemented
62#16811276C2213yescomplemented
63#16811268C2216yescomplemented
64#16811268C2216yescomplemented
65#16811268C2216yescomplemented
66#16811264C22112yescomplemented
67#16811264C2216yescomplemented
68D4×D212C2216yescomplemented
69D4×D212C2213yescomplemented
70#16811247C2216yescomplemented
71#16811247C2216yescomplemented
72#16811247C2216yescomplemented
73#16811247C2216yescomplemented
74#16811236C2216yescomplemented
75#16811236C2216yescomplemented
76#16811229C2216yescomplemented
77#16811229C2216yescomplemented
78#16811222C22112yescomplemented
79#16811222C22112yescomplemented
80#16811213C22112yescomplemented
81#16811213C22112yescomplemented
82#16811178C2213yescomplemented
83#16811178C2213yescomplemented
84#16811174C2213yescomplemented
85#16811174C2213yescomplemented
86#16811173C2213yescomplemented
87#16811173C2216yescomplemented
88#16811160C2213yes—
89#16811160C2211yescharacteristic
90#16811160C2213yescomplemented
91#16811160C2216yescomplemented
92#16811160C2216yescomplemented
93#16811160C22112yescomplemented
94#16811160C2213yescomplemented
95#16811160C2216yescomplemented
96#16811160C22112yescomplemented
97#16811160C2213yescomplemented
98#16811160C2213yescomplemented
99#16811160C2216yescomplemented
100#16811160C2216yescomplemented
101#16811160C2213yescomplemented
102#16811160C2213yescomplemented
103#16811159C2216yescomplemented
104#16811159C2216yescomplemented
105#16811158C2216yescomplemented
106#16811158C2216yescomplemented
107C2×#13133212C2216yescomplemented
108C2×#13133208C2213yescomplemented
109C2×#13133206C2213yescomplemented
110#16811136C2216yescomplemented
111#16811136C2216yescomplemented
112#16811135C2216yescomplemented
113#16811135C2216yescomplemented
114#16811135C2216yescomplemented
115C2×#13133202C2216yescomplemented
116C2×#13133193C2213yescomplemented
117C2×#13133192C2213yes—
118#16811105C2212yescomplemented
119#16811105C2212yescomplemented
120#16811102C2216yescomplemented
121#16811102C2216yescomplemented
122#16811099C2212yescomplemented
123#16811099C2212yescomplemented
124#16811095C2216yescomplemented
125#16811095C2216yescomplemented
126#41×Dic53C2211yescharacteristic
127C4×#11719949C2216yescomplemented
128C4×#11719949C2216yescomplemented
129C4×#11719949C2211yescharacteristic, complemented
130C4×#11719949C2211yescharacteristic, complemented
131C4×#11719945C2213yescomplemented
132C4×#11719945C2216yescomplemented
133#16811091C2216yescomplemented
134#16811091C2213yescomplemented
135C4×#11719947C2213yescomplemented
136C4×#11719947C2213yescomplemented
137C4×Q8×D53C2211yescharacteristic, complemented
138C4×Q8×D53C2211yescharacteristic, complemented
139C2×C4×D212C2213yescomplemented
140C2×C4×D212C2216yescomplemented
141C4×D4×D53C2213yescomplemented
142C4×D4×D53C2213yescomplemented
143C2×#13133174C2216yescomplemented
144#117×D53C2213yescomplemented
145#117×D53C2216yescomplemented
146C2×C42×D53C2213yescomplemented
147Q82×C53C2211yescharacteristic, complemented
148C53×#557C2211yescharacteristic, complemented
149C53×#557C2212yescomplemented
150C53×#554C2216yescomplemented
151C53×#554C2213yescomplemented
152D4×Q8×C53C2213yescomplemented
153C53×#533C2213yescomplemented
154C53×#533C2216yescomplemented
155C4×#41×C53C2211yescharacteristic
156C4×#41×C53C2212yes—
157C2×C4×Q8×C53C2213yescomplemented
158C2×#11719949C2311yescharacteristic
159C2×#11719949C2312yes—
160C2×#11719949C2316yes—
161C2×#11719949C2316yes—
162C2×#11719945C2316yes—
163C2×#11719945C2313yes—
164C2×#11719947C2313yes—
165C2×#11719947C2316yes—
166#41×D53—28no—
167#41×D53—216no—
168C2×Q8×D53C2311yescharacteristic
169C2×Q8×D53C2312yes—
170C22×D212C2316yes—
171C22×D212C2313yes—
172C2×D4×D53C2313yes—
173C2×D4×D53C2316yes—
174C22×C4×D53C2313yes—
175C22×C4×D53C2316yes—
176C22×C4×D53C2313yes—
177C22×C4×D53C2313yes—
178#13133217C2313yes—
179#13133217C2316yes—
180#13133214C2313yes—
181#13133214C2316yes—
182#13133212C2316yes—
183#13133212C23112yes—
184#13133212C2316yes—
185#13133212C23112yes—
186#13133212C23112yes—
187#13133212C2316yes—
188#13133212C23112yes—
189#13133212C2316yes—
190#13133212C2312yes—
191#13133212C2316yes—
192#13133212C2316yes—
193#13133212C2316yes—
194#13133212C23112yes—
195#13133208C2316yes—
196#13133208C23112yes—
197#13133208C23112yes—
198#13133208C2313yes—
199#13133208C2313yes—
200#13133208C2311yescharacteristic
201#13133208C2313yes—
202#13133208C2316yes—
203#13133208C2316yes—
204#13133206C2313yes—
205#13133206C23112yes—
206#13133206C2313yes—
207#13133206C23112yes—
208#13133206C2316yes—
209#13133206C2311yescharacteristic
210#13133206C2313yes—
211#13133206C2316yes—
212#13133206C2316yes—
213#13133205C2316yes—
214#13133205C2316yes—
215#13133205C2316yes—
216#13133202C2316yes—
217#13133202C23112yes—
218#13133202C23112yes—
219#13133202C2316yes—
220#13133202C23112yes—
221#13133202C23112yes—
222#13133202C2316yes—
223#13133202C2316yes—
224#13133202C2312yes—
225#13133202C2316yes—
226#13133202C2316yes—
227#13133202C2316yes—
228#13133202C23112yes—
229#13133201C23112yes—
230#13133201C23112yes—
231#13133201C23112yes—
232#13133197C2316yes—
233#13133197C2316yes—
234#13133197C2316yes—
235#13133197C2316yes—
236#13133197C2316yes—
237#13133197C2316yes—
238#13133193C2313yes—
239#13133193C23112yes—
240#13133193C2313yes—
241#13133193C23112yes—
242#13133193C2316yes—
243#13133193C2311yescharacteristic
244#13133193C2313yes—
245#13133193C2316yes—
246#13133193C2316yes—
247#13133192C2316yes—
248#13133192C23112yes—
249#13133192C2313yes—
250#13133192C23112yes—
251#13133192C2316yes—
252#13133192C2316yes—
253#13133192C2316yes—
254#13133192C2316yes—
255#13133192C2316yes—
256#13133192C2316yes—
257#13133192C2313yes—
258#13133192C2311yescharacteristic
259#13133192C2313yes—
260#13133192C2316yes—
261#13133192C2316yes—
262#13133191C23112yes—
263#13133191C2316yes—
264#13133191C2316yes—
265#13133191C23112yes—
266#13133187C23112yes—
267#13133187C23112yes—
268#13133187C23112yes—
269Q8×Dic53C2316yes—
270Q8×Dic53C2316yes—
271Q8×Dic53C2311yescharacteristic
272Q8×Dic53C2311yescharacteristic
273C4×Dic106C2313yes—
274C4×Dic106C2316yes—
275C4×Dic106C2313yes—
276C4×Dic106C2316yes—
277#13133182C2313yes—
278#13133182C2313yes—
279#13133182C2316yes—
280#13133182C2316yes—
281C4×D212C2316yes—
282C4×D212C2316yes—
283C4×D212C2316yes—
284C4×D212C2313yes—
285C4×D212C2313yes—
286C4×D212C2316yes—
287C4×D212C2316yes—
288C4×D212C2316yes—
289C4×D212C2313yes—
290C4×D212C2316yes—
291C4×D212C2313yes—
292C4×D212C2312yes—
293C4×D212C2311yescharacteristic
294C4×D212C2316yes—
295C4×D212C2313yes—
296C4×D212C2316yes—
297C4×D212C2316yes—
298C4×D212C2316yes—
299C4×D212C2316yes—
300C4×D212C23112yes—
301D4×Dic53C2313yes—
302D4×Dic53C2313yes—
303#13133179C23112yes—
304#13133179C2316yes—
305#13133179C2316yes—
306#13133179C23112yes—
307#13133179C2313yes—
308#13133179C2313yes—
309#13133179C2316yes—
310#13133179C2316yes—
311C4×C22⋊D53C2316yes—
312C4×C22⋊D53C23112yes—
313C4×C22⋊D53C23112yes—
314C4×C22⋊D53C2316yes—
315#13133177C2316yes—
316#13133177C2316yes—
317#13133177C23112yes—
318#13133177C23112yes—
319#13133176C2313yes—
320#13133175C2316yes—
321#13133175C23112yes—
322#13133175C23112yes—
323#13133175C2313yes—
324#13133175C2316yes—
325#13133175C2316yes—
326#13133175C2316yes—
327#13133175C2313yes—
328#13133174C2316yes—
329#13133174C2316yes—
330#13133174C2312yes—
331#13133174C2316yes—
332#13133174C2316yes—
333#13133174C2316yes—
334#13133174C2316yes—
335#13133174C2316yes—
336#13133174C2316yes—
337#13133173C2316yes—
338#13133173C23112yes—
339C2×C4⋊Dic53C2313yes—
340C2×C4⋊Dic53C2316yes—
341C2×#11719919C2316yes—
342C2×#11719919C2316yes—
343C4⋊C4×D53C2313yes—
344C4⋊C4×D53C2316yes—
345C4⋊C4×D53C2316yes—
346C4⋊C4×D53C2313yes—
347C2×#11719921C2316yes—
348C2×#11719921C2316yes—
349C2×#11719921C2316yes—
350C2×#11719921C2316yes—
351C2×#11719921C2316yes—
352C22⋊C4×D53C2316yes—
353C22⋊C4×D53C23112yes—
354C2×C4×Dic53C2313yes—
355C2×C4×Dic53C2313yes—
356C2×C4×Dic53C2313yes—
357C42×D53C2311yescharacteristic
358C42×D53C2313yes—
359C42×D53C2313yes—
360C42×D53C2313yes—
361C42×D53C2313yes—
362C42×D53C2313yes—
363C42×D53C2313yes—
364C42×D53C2313yes—
365C42×D53C23112yes—
366C2×#41×C53C2311yescharacteristic
367C22×Q8×C53C2313yes—
368C4⋊Q8×C53C2313yes—
369C4⋊Q8×C53C2316yes—
370C4⋊Q8×C53C2316yes—
371C4⋊Q8×C53C2313yes—
372#125×C53C2316yes—
373#125×C53C2316yes—
374#125×C53C2316yes—
375C22⋊Q8×C53C2316yes—
376C22⋊Q8×C53C23112yes—
377C22⋊Q8×C53C23112yes—
378C22⋊Q8×C53C2316yes—
379C4×Q8×C53C2311yescharacteristic
380C4×Q8×C53C2312yes—
381C4×Q8×C53C2312yes—
382C4×Q8×C53C2311yescharacteristic
383C4×Q8×C53C2311yescharacteristic
384C4×Q8×C53C2313yes—
385C4×Q8×C53C2313yes—
386C4×Q8×C53C2316yes—
387C4×Q8×C53C2313yes—
388C4×Q8×C53C2316yes—
389C4×Q8×C53C2316yes—
390C4×D4×C53C2316yes—
391C4×D4×C53C2313yes—
392C4×D4×C53C2313yes—
393C4×D4×C53C2316yes—
394#117×C53C2313yes—
395#117×C53C2316yes—
396C2×C4⋊C4×C53C2313yes—
397C2×C4⋊C4×C53C2316yes—
398C2×C42×C53C2313yes—
399C2×C42×C53C2316yes—
400C23×D53C2413yes—
401C23×D53C2416yes—
402#41×C53#4118yescomplemented
403C2×Q8×C53—46no—
404C2×Q8×C53C2411yescharacteristic
405C2×Q8×C53C2413yes—
406C2×Q8×C53C2416yes—
407C2×Q8×C53C2416yes—
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⋊D53C24112yes—
417C22×Dic53C2413yes—
418C22×Dic53C2416yes—
419C22×Dic53C2413yes—
420C22×Dic53C2413yes—
421#11719949—24no—
422#11719949—28no—
423#11719949—412no—
424#11719949—412no—
425Q8×D53—24no—
426Q8×D53—28no—
427#11719947—212no—
428#11719947—224no—
429D4×D53—212no—
430D4×D53—224no—
431#11719945—212no—
432#11719945—224no—
433C2×D212—46no—
434C2×D212—412no—
435C2×D212C2416yes—
436C2×D212C2413yes—
437C2×D212C2413yes—
438C2×D212C2416yes—
439C2×D212C2412yes—
440C2×D212C2411yescharacteristic
441C2×D212C2416yes—
442C2×D212C24112yes—
443C2×D212C2416yes—
444C2×D212C2416yes—
445C2×D212C2416yes—
446C2×C4×D53—212no—
447C2×C4×D53—224no—
448C2×C4×D53—46no—
449C2×C4×D53—46no—
450C2×C4×D53C2411yescharacteristic
451C2×C4×D53C2411yescharacteristic
452C2×C4×D53C2411yescharacteristic
453C2×C4×D53C2413yes—
454C2×C4×D53C2413yes—
455C2×C4×D53C2413yes—
456C2×C4×D53C2416yes—
457C2×C4×D53C2413yes—
458C2×C4×D53C2413yes—
459C2×C4×D53C2416yes—
460C2×C4×D53C2412yes—
461C2×C4×D53C2416yes—
462C2×C4×D53C2413yes—
463C2×C4×D53C2413yes—
464C2×C4×D53C2413yes—
465C2×C4×D53C2413yes—
466C2×C4×D53C24112yes—
467C2×C4×D53C24112yes—
468C2×Dic106C2413yes—
469C2×Dic106C2416yes—
470C4⋊C4×C53C2411yescharacteristic
471C4⋊C4×C53C2412yes—
472C4⋊C4×C53C2416yes—
473C4⋊C4×C53C2416yes—
474C4⋊C4×C53C2416yes—
475C4⋊C4×C53C2413yes—
476C4⋊C4×C53C2416yes—
477C4⋊C4×C53C2416yes—
478C4⋊C4×C53C2413yes—
479C4⋊C4×C53C2413yes—
480C4⋊C4×C53C2416yes—
481C4⋊C4×C53C24112yes—
482C4⋊C4×C53C2416yes—
483C22⋊C4×C53C24112yes—
484C22⋊C4×C53C2416yes—
485C42×C53C2411yescharacteristic
486C42×C53C2412yes—
487C42×C53C2413yes—
488C42×C53C2416yes—
489C42×C53C2413yes—
490C42×C53C2416yes—
491C42×C53C2413yes—
492C42×C53C2416yes—
493C22⋊Dic53C2416yes—
494#11719921C2416yes—
495#11719921C2416yes—
496#11719921C2416yes—
497#11719921C2416yes—
498#11719921C2412yes—
499#11719921C2412yes—
500#11719921C2412yes—
501#11719921C2412yes—
502#11719921C2412yes—
503#11719921C2416yes—
504#11719921C2416yes—
505#11719921C2416yes—
506#11719921C2416yes—
507#11719921C2416yes—
508#11719921C2416yes—
509#11719921C2416yes—
510#11719921C2416yes—
511#11719921C2416yes—
512#11719921C2416yes—
513#11719921C2416yes—
514#11719921C2416yes—
515#11719921C2416yes—
516#11719921C24112yes—
517#11719921C24112yes—
518#11719921C24112yes—
519C4⋊Dic53C2413yes—
520C4⋊Dic53C2413yes—
521C4⋊Dic53C2411yescharacteristic
522C4⋊Dic53C2412yes—
523C4⋊Dic53C2413yes—
524C4⋊Dic53C2416yes—
525C4⋊Dic53C2416yes—
526C4⋊Dic53C2416yes—
527C4⋊Dic53C2416yes—
528C4⋊Dic53C2416yes—
529C4⋊Dic53C24112yes—
530#11719919C2416yes—
531#11719919C2416yes—
532#11719919C2416yes—
533#11719919C2416yes—
534#11719919C2412yes—
535#11719919C2412yes—
536#11719919C2416yes—
537#11719919C2416yes—
538#11719919C2416yes—
539#11719919C2416yes—
540C4×Dic53C2413yes—
541C4×Dic53C2411yescharacteristic
542C4×Dic53C2411yescharacteristic
543C4×Dic53C2411yescharacteristic
544C4×Dic53C2413yes—
545C4×Dic53C2413yes—
546C4×Dic53C2413yes—
547C4×Dic53C2413yes—
548C4×Dic53C2413yes—
549C4×Dic53C2413yes—
550C4×Dic53C2413yes—
551C4×Dic53C2413yes—
552C4×Dic53C24112yes—
553C4×Dic53C24112yes—
554C23×C53C2513yes—
555C22×D53—26no—
556C22×D53—212no—
557C22×D53—26no—
558C22×D53—43no—
559C22×D53—46no—
560C22×D53—46no—
561C22×D53C2513yes—
562C22×D53C2516yes—
563C22×D53C2512yes—
564C22×D53C2511yescharacteristic
565Q8×C53—26no—
566Q8×C53—22no—
567Q8×C53—46no—
568Q8×C53—46no—
569Q8×C53C2×#4114yes—
570D4×C53C2×#41112yes—
571C2×C4×C53—26no—
572C2×C4×C53—43no—
573C2×C4×C53—46no—
574C2×C4×C53—46no—
575C2×C4×C53C2×#41112yes—
576C2×C4×C53C2511yescharacteristic
577C2×C4×C53C2513yes—
578C2×C4×C53C2516yes—
579C2×C4×C53C2513yes—
580C2×C4×C53C2516yes—
581C2×C4×C53C2512yes—
582C2×C4×C53C2512yes—
583C2×C4×C53C2513yes—
584C2×C4×C53C2511yescharacteristic
585C2×C4×C53C2511yescharacteristic
586C22⋊D53—212no—
587C22⋊D53—224no—
588C2×Dic53—26no—
589C2×Dic53—212no—
590C2×Dic53—43no—
591C2×Dic53—43no—
592C2×Dic53C2513yes—
593C2×Dic53C2516yes—
594C2×Dic53C2513yes—
595C2×Dic53C2513yes—
596C2×Dic53C2511yescharacteristic
597C2×Dic53C2511yescharacteristic
598C2×Dic53C2511yescharacteristic
599C2×Dic53C2512yes—
600D212—24no—
601D212—212no—
602D212—26no—
603D212—212no—
604D212—22no—
605D212—26no—
606D212—46no—
607D212—46no—
608D212—46no—
609D212—46no—
610D212—412no—
611C4×D53—22no—
612C4×D53—26no—
613C4×D53—22no—
614C4×D53—24no—
615C4×D53—26no—
616C4×D53—212no—
617C4×D53—26no—
618C4×D53—212no—
619C4×D53—26no—
620C4×D53—212no—
621C4×D53—22no—
622C4×D53—26no—
623C4×D53—43no—
624C4×D53—43no—
625C4×D53—43no—
626C4×D53—43no—
627C4×D53—412no—
628C4×D53—412no—
629Dic106—26no—
630Dic106—212no—
631#62816—531nomaximal, Sylow
632C22×C53—23no—
633C22×C53—23no—
634C22×C53C22×#4116yes—
635C22×C53C2611yescharacteristic
636C2×D53—21no—
637C2×D53—21no—
638C2×D53—22no—
639C2×D53—23no—
640C2×D53—26no—
641C2×D53—23no—
642C2×D53—26no—
643C2×D53—26no—
644C2×D53—23no—
645C2×D53—22no—
646C2×D53—22no—
647C2×D53—412no—
648C2×D53—812no—
649C2×D53#58512yes—
650C4×C53—21no—
651C4×C53—23no—
652C4×C53—26no—
653C4×C53—23no—
654C4×C53—26no—
655C4×C53—22no—
656C4×C53—22no—
657C4×C53C22×#4116yes—
658C4×C53C22×#4112yes—
659C4×C53#58512yes—
660Dic53—23no—
661Dic53—26no—
662Dic53—21no—
663Dic53—22no—
664Dic53—23no—
665Dic53—23no—
666Dic53—21no—
667Dic53—21no—
668#3524—532no—
669#3523—531no—
670#3522—531no—
671#3521—536no—
672#3520—533no—
673#3519—533no—
674#3518—531no—
675#3517—531no—
676#3516—532no—
677#3515—533no—
678#3514—533no—
679#3513—536no—
680#3480—533no—
681Q8×#41D5311yescharacteristic, complemented
682#3475—536no—
683#3475—533no—
684D4×#41—531no—
685D4×#41—532no—
686#3455—536no—
687#3444—533no—
688C2×#529—533no—
689#3428—532no—
690C2×C4×#41—531no—
691C2×C53—26no—
692C2×C53C23×#4111yescharacteristic
693C2×C53C2×#58511yescharacteristic
694C2×C53C2×#58511yescharacteristic
695D53—22no—
696D53—43no—
697D53—46no—
698D53—42no—
699C22×#41—531no—
700C22×#41—532no—
701#559—536no—
702#559—533no—
703Q82C2×D5311yescharacteristic, complemented
704#557—533no—
705#557C2×D5312yescomplemented
706#557C2×D5311yescharacteristic, complemented
707#556—533no—
708#556—536no—
709#556—536no—
710#556—533no—
711#555—536no—
712#555—533no—
713#554—533no—
714#554—536no—
715#554C2×D5316yescomplemented
716#554C2×D5313yescomplemented
717#553—536no—
718#553—536no—
719#553—536no—
720#553—5312no—
721#553—536no—
722#552—536no—
723#552—536no—
724#552—536no—
725#552—536no—
726#552—5312no—
727#551—5312no—
728#551—5312no—
729#551—5312no—
730#550—531no—
731#550—532no—
732#550—533no—
733D4×Q8—532no—
734D4×Q8—531no—
735D4×Q8C2×D5313yescomplemented
736#548—536no—
737#548—532no—
738#548—532no—
739#548—532no—
740#547—536no—
741#547—533no—
742#547—533no—
743#547—536no—
744#546—5312no—
745#546—536no—
746#546—536no—
747#546—536no—
748#546—536no—
749D42—536no—
750D42—533no—
751#542—536no—
752#542—536no—
753#542—536no—
754#542—536no—
755#541—536no—
756#541—536no—
757#540—536no—
758#540—536no—
759#539—5312no—
760#539—5312no—
761#538—5312no—
762#538—5312no—
763#533—533no—
764#533—533no—
765#533C2×D5313yescomplemented
766#533C2×D5316yescomplemented
767#532—533no—
768#532—533no—
769#532—533no—
770#532—536no—
771#529—536no—
772#529—536no—
773#529—536no—
774#529—536no—
775#529—531no—
776#529—533no—
777#529—536no—
778#529—536no—
779#529—533no—
780#529—533no—
781#529—533no—
782#529—536no—
783#529—533no—
784#529—533no—
785#529—533no—
786#529—536no—
787#529—536no—
788#529—5312no—
789#529—5312no—
790C2×#126—536no—
791C2×#125—533no—
792C2×#124—533no—
793#525—536no—
794#525—536no—
795#525—536no—
796#525—536no—
797#525—536no—
798C2×#123—536no—
799C2×C22⋊Q8—533no—
800C2×#121—533no—
801#520—532no—
802#520—532no—
803#520—536no—
804#520—536no—
805#519—532no—
806#519—532no—
807#518—536no—
808#518—536no—
809C4×#41—531no—
810C4×#41—531no—
811C4×#41—531no—
812C4×#41—536no—
813C4×#41—536no—
814C4×#41—533no—
815C4×#41—533no—
816C4×#41—533no—
817C4×#41—536no—
818C4×#41—533no—
819C4×#41—536no—
820C4×#41C2×D5311yescharacteristic
821C4×#41C2×D5312yes—
822C2×C4×Q8—531no—
823C2×C4×Q8—531no—
824C2×C4×Q8C2×D5313yescomplemented
825C2×C4×D4—533no—
826C2×C4×D4—533no—
827C2×C4×D4—536no—
828C2×C4×D4—533no—
829C2×#117—533no—
830C2×#117—536no—
831C2×#117—536no—
832C22×C42—533no—
833C53#6281611yescharacteristic, complemented, Sylow
834C2×#41—531no—
835C2×#41—532no—
836C2×#41—536no—
837C2×#41—536no—
838C2×#41—533no—
839C2×#41—536no—
840C2×#41—533no—
841C2×#41—536no—
842C2×#41—1068no—
843C2×#41—10616no—
844C2×#41C22×D5311yescharacteristic
845C22×Q8—531no—
846C22×Q8—532no—
847C22×Q8C22×D5313yes—
848C22×D4—533no—
849C22×D4—536no—
850C22×D4—536no—
851C22×D4—533no—
852C23×C4—536no—
853C23×C4—533no—
854C23×C4—533no—
855C23×C4—533no—
856C4⋊Q8—533no—
857C4⋊Q8—536no—
858C4⋊Q8C22×D5313yes—
859C4⋊Q8C22×D5313yes—
860C4⋊Q8C22×D5316yes—
861C4⋊Q8C22×D5316yes—
862#127—533no—
863#127—536no—
864#126—532no—
865#126—536no—
866#126—536no—
867#126—536no—
868#126—536no—
869#126—536no—
870#126—536no—
871#126—536no—
872#126—5312no—
873#126—5312no—
874#126—5312no—
875#126—5312no—
876#126—5312no—
877#125—531no—
878#125—533no—
879#125—536no—
880#125—536no—
881#125—533no—
882#125—533no—
883#125—536no—
884#125—5312no—
885#125—5312no—
886#125C22×D5316yes—
887#125C22×D5316yes—
888#125C22×D5316yes—
889#124—531no—
890#124—533no—
891#124—536no—
892#124—533no—
893#124—533no—
894#124—536no—
895#124—536no—
896#124—5312no—
897#124—5312no—
898#124—536no—
899#124—536no—
900#124—536no—
901#123—532no—
902#123—536no—
903#123—536no—
904#123—536no—
905#123—536no—
906#123—536no—
907#123—536no—
908#123—536no—
909#123—5312no—
910#123—5312no—
911#123—5312no—
912#123—5312no—
913#123—5312no—
914#123—5312no—
915#123—5312no—
916#123—5312no—
917C22⋊Q8—531no—
918C22⋊Q8—533no—
919C22⋊Q8—536no—
920C22⋊Q8—533no—
921C22⋊Q8—533no—
922C22⋊Q8—536no—
923C22⋊Q8—536no—
924C22⋊Q8—5312no—
925C22⋊Q8—5312no—
926C22⋊Q8—536no—
927C22⋊Q8—536no—
928C22⋊Q8—536no—
929C22⋊Q8—536no—
930C22⋊Q8—536no—
931C22⋊Q8—536no—
932C22⋊Q8C22×D5316yes—
933C22⋊Q8C22×D5316yes—
934C22⋊Q8C22×D53112yes—
935C22⋊Q8C22×D53112yes—
936#121—536no—
937#121—536no—
938#121—5312no—
939#121—5312no—
940#121—531no—
941#121—533no—
942#121—536no—
943#121—536no—
944#121—533no—
945#121—533no—
946#121—536no—
947#121—536no—
948#121—536no—
949#121—536no—
950#121—536no—
951#121—536no—
952#121—536no—
953#121—5312no—
954#121—5312no—
955#120—5312no—
956#120—5312no—
957#120—5312no—
958C4×Q8—531no—
959C4×Q8—531no—
960C4×Q8—536no—
961C4×Q8—536no—
962C4×Q8—533no—
963C4×Q8—533no—
964C4×Q8—536no—
965C4×Q8—536no—
966C4×Q8—533no—
967C4×Q8—533no—
968C4×Q8—536no—
969C4×Q8—536no—
970C4×Q8C22×D5311yescharacteristic
971C4×Q8C22×D5311yescharacteristic
972C4×Q8C22×D5311yescharacteristic
973C4×Q8C22×D5313yes—
974C4×Q8C22×D5316yes—
975C4×Q8C22×D5313yes—
976C4×Q8C22×D5313yes—
977C4×Q8C22×D5316yes—
978C4×Q8C22×D5316yes—
979C4×Q8C22×D5312yes—
980C4×Q8C22×D5312yes—
981C4×D4—533no—
982C4×D4—533no—
983C4×D4—536no—
984C4×D4—536no—
985C4×D4—5312no—
986C4×D4—5312no—
987C4×D4—533no—
988C4×D4—533no—
989C4×D4—536no—
990C4×D4—536no—
991C4×D4—5312no—
992C4×D4—5312no—
993C4×D4—536no—
994C4×D4—536no—
995C4×D4—536no—
996C4×D4—536no—
997C4×D4—5312no—
998C4×D4—5312no—
999C4×D4—531no—
1000C4×D4—532no—
1001C4×D4—536no—
1002C4×D4—533no—
1003C4×D4—533no—
1004C4×D4—533no—
1005C4×D4—536no—
1006C4×D4—536no—
1007C4×D4—536no—
1008C4×D4—536no—
1009C4×D4—533no—
1010C4×D4—536no—
1011C4×D4—536no—
1012C4×D4—536no—
1013C4×D4—533no—
1014C4×D4—536no—
1015C4×D4—536no—
1016C4×D4—536no—
1017C4×D4—536no—
1018C4×D4—5312no—
1019C4×D4C22×D5313yes—
1020C4×D4C22×D5313yes—
1021C4×D4C22×D5316yes—
1022C4×D4C22×D5316yes—
1023#117—533no—
1024#117—533no—
1025#117—533no—
1026#117—536no—
1027#117—536no—
1028#117—536no—
1029#117—536no—
1030#117—5312no—
1031#117—5312no—
1032#117—536no—
1033#117—5312no—
1034#117—536no—
1035#117—532no—
1036#117—536no—
1037#117—536no—
1038#117—536no—
1039#117—536no—
1040#117—536no—
1041#117—536no—
1042#117—536no—
1043#117C22×D5313yes—
1044#117C22×D5316yes—
1045C2×C4⋊C4—536no—
1046C2×C4⋊C4—536no—
1047C2×C4⋊C4—533no—
1048C2×C4⋊C4—536no—
1049C2×C4⋊C4—533no—
1050C2×C4⋊C4—533no—
1051C2×C4⋊C4—536no—
1052C2×C4⋊C4—536no—
1053C2×C4⋊C4C22×D5313yes—
1054C2×C4⋊C4C22×D5316yes—
1055C2×C22⋊C4—536no—
1056C2×C22⋊C4—536no—
1057C2×C22⋊C4—536no—
1058C2×C22⋊C4—536no—
1059C2×C22⋊C4—536no—
1060C2×C22⋊C4—536no—
1061C2×C22⋊C4—5312no—
1062C2×C42—533no—
1063C2×C42—533no—
1064C2×C42—533no—
1065C2×C42—533no—
1066C2×C42—5312no—
1067C2×C42—533no—
1068C2×C42—533no—
1069C2×C42—533no—
1070C2×C42—533no—
1071C2×C42—533no—
1072C2×C42—533no—
1073C2×C42—531no—
1074C2×C42C22×D5316yes—
1075C2×C42C22×D5313yes—
1076C24—533no—
1077C24—536no—
1078#41—1064no—
1079#41—1068no—
1080#41—10612no—
1081#41—10624no—
1082#41—10612no—
1083#41—10624no—
1084#41—21212no—
1085#41—21212no—
1086#41#1171994918yescomplemented
1087C2×Q8—46no—
1088C2×Q8—533no—
1089C2×Q8—536no—
1090C2×Q8—1064no—
1091C2×Q8—1068no—
1092C2×Q8C23×D5313yes—
1093C2×Q8C23×D5311yescharacteristic
1094C2×Q8C23×D5316yes—
1095C2×Q8C23×D5316yes—
1096C2×Q8C23×D5311yescharacteristic
1097C2×D4—536no—
1098C2×D4—5312no—
1099C2×D4—536no—
1100C2×D4—532no—
1101C2×D4—531no—
1102C2×D4—533no—
1103C2×D4—536no—
1104C2×D4—533no—
1105C2×D4—536no—
1106C2×D4—536no—
1107C2×D4—5312no—
1108C2×D4—536no—
1109C2×D4—536no—
1110C2×D4—10624no—
1111C2×D4—10612no—
1112C2×D4—2126no—
1113C2×D4—21212no—
1114C2×D4C23×D5313yes—
1115C22×C4—533no—
1116C22×C4—536no—
1117C22×C4—533no—
1118C22×C4—533no—
1119C22×C4—531no—
1120C22×C4—531no—
1121C22×C4—533no—
1122C22×C4—533no—
1123C22×C4—533no—
1124C22×C4—533no—
1125C22×C4—536no—
1126C22×C4—536no—
1127C22×C4—531no—
1128C22×C4—536no—
1129C22×C4—533no—
1130C22×C4—532no—
1131C22×C4—533no—
1132C22×C4—533no—
1133C22×C4—533no—
1134C22×C4—533no—
1135C22×C4—5312no—
1136C22×C4—5312no—
1137C22×C4—10624no—
1138C22×C4—10612no—
1139C22×C4—2126no—
1140C22×C4—2126no—
1141C22×C4C23×D5313yes—
1142C22×C4C23×D5313yes—
1143C22×C4C23×D5316yes—
1144C22×C4C23×D5316yes—
1145C22×C4C23×D5313yes—
1146C4⋊C4—533no—
1147C4⋊C4—533no—
1148C4⋊C4—532no—
1149C4⋊C4—536no—
1150C4⋊C4—536no—
1151C4⋊C4—532no—
1152C4⋊C4—531no—
1153C4⋊C4—532no—
1154C4⋊C4—533no—
1155C4⋊C4—536no—
1156C4⋊C4—536no—
1157C4⋊C4—536no—
1158C4⋊C4—536no—
1159C4⋊C4—536no—
1160C4⋊C4—536no—
1161C4⋊C4—536no—
1162C4⋊C4—536no—
1163C4⋊C4—536no—
1164C4⋊C4—536no—
1165C4⋊C4—536no—
1166C4⋊C4—5312no—
1167C4⋊C4C23×D5313yes—
1168C4⋊C4C23×D5313yes—
1169C4⋊C4C23×D5316yes—
1170C4⋊C4C23×D5316yes—
1171C4⋊C4C23×D5311yescharacteristic
1172C4⋊C4C23×D5312yes—
1173C4⋊C4C23×D5313yes—
1174C4⋊C4C23×D5316yes—
1175C4⋊C4C23×D5316yes—
1176C4⋊C4C23×D5316yes—
1177C4⋊C4C23×D5316yes—
1178C4⋊C4C23×D5316yes—
1179C4⋊C4C23×D53112yes—
1180C22⋊C4—536no—
1181C22⋊C4—532no—
1182C22⋊C4—536no—
1183C22⋊C4—536no—
1184C22⋊C4—532no—
1185C22⋊C4—532no—
1186C22⋊C4—532no—
1187C22⋊C4—532no—
1188C22⋊C4—536no—
1189C22⋊C4—536no—
1190C22⋊C4—536no—
1191C22⋊C4—536no—
1192C22⋊C4—536no—
1193C22⋊C4—536no—
1194C22⋊C4—536no—
1195C22⋊C4—536no—
1196C22⋊C4—536no—
1197C22⋊C4—536no—
1198C22⋊C4—536no—
1199C22⋊C4—536no—
1200C22⋊C4—536no—
1201C22⋊C4—536no—
1202C22⋊C4—536no—
1203C22⋊C4—5312no—
1204C22⋊C4—5312no—
1205C22⋊C4—5312no—
1206C22⋊C4C23×D5316yes—
1207C22⋊C4C23×D53112yes—
1208C42—531no—
1209C42—531no—
1210C42—533no—
1211C42—533no—
1212C42—533no—
1213C42—533no—
1214C42—533no—
1215C42—533no—
1216C42—533no—
1217C42—533no—
1218C42—5312no—
1219C42—5312no—
1220C42—531no—
1221C42—533no—
1222C42C23×D5313yes—
1223C42C23×D5313yes—
1224C42C23×D5316yes—
1225C42C23×D5316yes—
1226C42C23×D5311yescharacteristic
1227C42C23×D5313yes—
1228C42C23×D5316yes—
1229C42C23×D5312yes—
1230C23—531no—
1231C23—532no—
1232C23—536no—
1233C23—533no—
1234C23—1066no—
1235C23—10612no—
1236C23—1066no—
1237C23—2126no—
1238C23—2126no—
1239C23—2123no—
1240C23C24×D5313yes—
1241Q8—22no—
1242Q8—26no—
1243Q8—46no—
1244Q8—46no—
1245Q8—1066no—
1246Q8—10612no—
1247Q8C2×#1171994914yes—
1248D4—1064no—
1249D4—10612no—
1250D4—10624no—
1251D4—10612no—
1252D4—10612no—
1253D4—1066no—
1254D4—1062no—
1255D4—1066no—
1256D4—2126no—
1257D4—2126no—
1258D4—2126no—
1259D4—2126no—
1260D4—21212no—
1261D4C2×#11719949112yes—
1262C2×C4—26no—
1263C2×C4—43no—
1264C2×C4—46no—
1265C2×C4—46no—
1266C2×C4—531no—
1267C2×C4—533no—
1268C2×C4—531no—
1269C2×C4—533no—
1270C2×C4—531no—
1271C2×C4—533no—
1272C2×C4—536no—
1273C2×C4—532no—
1274C2×C4—1062no—
1275C2×C4—1066no—
1276C2×C4—1066no—
1277C2×C4—10612no—
1278C2×C4—1062no—
1279C2×C4—1064no—
1280C2×C4—1066no—
1281C2×C4—10612no—
1282C2×C4—1066no—
1283C2×C4—10612no—
1284C2×C4—10612no—
1285C2×C4—1066no—
1286C2×C4—1062no—
1287C2×C4—1066no—
1288C2×C4—2123no—
1289C2×C4—2123no—
1290C2×C4—2123no—
1291C2×C4—2123no—
1292C2×C4—21212no—
1293C2×C4—21212no—
1294C2×C4—2123no—
1295C2×C4—2123no—
1296C2×C4C2×#11719949112yes—
1297C2×C4C24×D5311yescharacteristic
1298C2×C4C24×D5313yes—
1299C2×C4C24×D5316yes—
1300C2×C4C24×D5313yes—
1301C2×C4C24×D5316yes—
1302C2×C4C24×D5312yes—
1303C2×C4C24×D5312yes—
1304C2×C4C24×D5313yes—
1305C2×C4C24×D5311yescharacteristic
1306C2×C4C24×D5311yescharacteristic
1307C22—23no—
1308C22—23no—
1309C22—532no—
1310C22—1061no—
1311C22—1061no—
1312C22—1062no—
1313C22—1066no—
1314C22—1063no—
1315C22—1066no—
1316C22—1063no—
1317C22—1062no—
1318C22—1063no—
1319C22—1066no—
1320C22—1062no—
1321C22—42412no—
1322C22—21212no—
1323C22C22×#1171994916yes—
1324C22C25×D5311yescharacteristic
1325C4—21no—
1326C4—22no—
1327C4—23no—
1328C4—26no—
1329C4—23no—
1330C4—22no—
1331C4—26no—
1332C4—1061no—
1333C4—1062no—
1334C4—1063no—
1335C4—1066no—
1336C4—1061no—
1337C4—1063no—
1338C4—1061no—
1339C4—1063no—
1340C4C22×#1171994912yes—
1341C4C22×#1171994916yes—
1342C4#1681145912yes—
1343C2—26no—
1344C2—1062no—
1345C2—2122no—
1346C2—2126no—
1347C2—2123no—
1348C2C23×#1171994911yescharacteristic
1349C2#585×D5311yescharacteristic
1350C2C2×#1681145911yescharacteristic
subgroupG/H
centerC2×C4C24×D53
commutator, socle, cosocleC22×C53C26
FrattiniC22C25×D53
FittingQ8×#41×C53C2
hypercenterQ8×#41D53
hypocenterC53#62816
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ Q8×#41

Complements

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

NH ≅ G/Ntype
1. #20288827C2semidirect
2. #20288812C2semidirect
3. #20288801C2semidirect
4. #20288786C2semidirect
5. #20288765C2semidirect
6. #20288748C2semidirect
7. #20288733C2semidirect
8. #20288722C2semidirect
9. #20288711C2semidirect
10. #20288694C2semidirect
11. #20288677C2semidirect
12. #20288658C2semidirect
13. #20288310C2semidirect
14. #20288282C2semidirect
15. #20288282C2semidirect
16. #41×D212C2semidirect
17. #41×D212C2semidirect
18. #20288107C2semidirect
19. #20288012C2semidirect
20. C2×#16811160C2semidirect
21. #20287914C2semidirect
22. C4×#41×D53C2semidirect
23. Q8×#41×C53C2semidirect
26. #16811358C22semidirect
27. #16811358C22semidirect
28. #16811352C22semidirect
29. #16811347C22semidirect
30. #16811347C22semidirect
31. #16811346C22semidirect
32. #16811346C22semidirect
33. #16811339C22semidirect
34. #16811339C22semidirect
35. #16811334C22semidirect
36. #16811334C22semidirect
37. #16811326C22semidirect
38. #16811326C22semidirect
39. #16811326C22semidirect
40. #16811321C22semidirect
41. #16811321C22semidirect
42. #16811315C22semidirect
43. #16811315C22semidirect
44. #16811311C22semidirect
45. #16811311C22semidirect
46. #16811311C22semidirect
47. #16811300C22semidirect
48. #16811300C22semidirect
49. #16811300C22semidirect
50. #16811295C22semidirect
51. #16811295C22semidirect
52. #16811295C22semidirect
53. Q8×D212C22semidirect
54. Q8×D212C22semidirect
55. #16811285C22semidirect
56. #16811285C22semidirect
57. #16811285C22semidirect
58. #16811284C22semidirect
59. #16811277C22semidirect
60. #16811277C22semidirect
61. #16811276C22semidirect
62. #16811276C22semidirect
63. #16811268C22semidirect
64. #16811268C22semidirect
65. #16811268C22semidirect
66. #16811264C22semidirect
67. #16811264C22semidirect
68. D4×D212C22semidirect
69. D4×D212C22semidirect
70. #16811247C22semidirect
71. #16811247C22semidirect
72. #16811247C22semidirect
73. #16811247C22semidirect
74. #16811236C22semidirect
75. #16811236C22semidirect
76. #16811229C22semidirect
77. #16811229C22semidirect
78. #16811222C22semidirect
79. #16811222C22semidirect
80. #16811213C22semidirect
81. #16811213C22semidirect
82. #16811178C22semidirect
83. #16811178C22semidirect
84. #16811174C22semidirect
85. #16811174C22semidirect
86. #16811173C22semidirect
87. #16811173C22semidirect
90. #16811160C22semidirect
91. #16811160C22semidirect
92. #16811160C22semidirect
93. #16811160C22semidirect
94. #16811160C22semidirect
95. #16811160C22semidirect
96. #16811160C22semidirect
97. #16811160C22semidirect
98. #16811160C22semidirect
99. #16811160C22semidirect
100. #16811160C22semidirect
101. #16811160C22semidirect
102. #16811160C22semidirect
103. #16811159C22semidirect
104. #16811159C22semidirect
105. #16811158C22semidirect
106. #16811158C22semidirect
107. C2×#13133212C22semidirect
108. C2×#13133208C22semidirect
109. C2×#13133206C22semidirect
110. #16811136C22semidirect
111. #16811136C22semidirect
112. #16811135C22semidirect
113. #16811135C22semidirect
114. #16811135C22semidirect
115. C2×#13133202C22semidirect
116. C2×#13133193C22semidirect
118. #16811105C22semidirect
119. #16811105C22semidirect
120. #16811102C22semidirect
121. #16811102C22semidirect
122. #16811099C22semidirect
123. #16811099C22semidirect
124. #16811095C22semidirect
125. #16811095C22semidirect
127. C4×#11719949C22semidirect
128. C4×#11719949C22semidirect
129. C4×#11719949C22semidirect
130. C4×#11719949C22semidirect
131. C4×#11719945C22semidirect
132. C4×#11719945C22semidirect
133. #16811091C22semidirect
134. #16811091C22semidirect
135. C4×#11719947C22semidirect
136. C4×#11719947C22semidirect
137. C4×Q8×D53C22semidirect
138. C4×Q8×D53C22semidirect
139. C2×C4×D212C22semidirect
140. C2×C4×D212C22semidirect
141. C4×D4×D53C22semidirect
142. C4×D4×D53C22semidirect
143. C2×#13133174C22semidirect
144. #117×D53C22semidirect
145. #117×D53C22semidirect
146. C2×C42×D53C22semidirect
147. Q82×C53C22semidirect
148. C53×#557C22semidirect
149. C53×#557C22semidirect
150. C53×#554C22semidirect
151. C53×#554C22semidirect
152. D4×Q8×C53C22semidirect
153. C53×#533C22semidirect
154. C53×#533C22semidirect
157. C2×C4×Q8×C53C22semidirect
402. #41×C53#41semidirect
681. Q8×#41D53semidirect
703. Q82C2×D53semidirect
705. #557C2×D53semidirect
706. #557C2×D53semidirect
715. #554C2×D53semidirect
716. #554C2×D53semidirect
735. D4×Q8C2×D53semidirect
765. #533C2×D53semidirect
766. #533C2×D53semidirect
824. C2×C4×Q8C2×D53semidirect
833. C53#62816semidirect
1086. #41#11719949semidirect

Maximal subgroups

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

subgroupindex
#202888272
#202888122
#202888012
#202887862
#202887652
#202887482
#202887332
#202887222
#202887112
#202886942
#202886772
#202886582
#202883102
#202882822
#41×D2122
#202881072
#202880122
C2×#168111602
#202879142
C4×#41×D532
Q8×#41×C532
#6281653