Finite Group Databasebeta

← #28293319

Subgroups — #28293319

Order 13568.

6854 conjugacy classes of subgroups.

The subgroup lattice has 1326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288806C212yesmaximal, complemented
2#20288802C212yesmaximal, complemented
3#20288772C216yesmaximal, complemented
4#20288768C216yesmaximal, complemented
5#20288701C212yesmaximal, complemented
6#20288697C212yesmaximal, complemented
7#20288684C216yesmaximal, complemented
8#20288680C216yesmaximal, complemented
9#20288636C213yesmaximal, complemented
10#20288600C213yesmaximal, complemented
11#20288537C211yesmaximal, characteristic, complemented
12#20288496C211yesmaximal, characteristic, complemented
13#20288469C213yesmaximal, complemented
14#20288461C213yesmaximal, complemented
15#20288395C211yesmaximal, characteristic, complemented
16#20288143C213yesmaximal, complemented
17#20288139C213yesmaximal, complemented
18#20288103C213yesmaximal, complemented
19C2×#16811233C213yesmaximal, complemented
202−1+4×Dic53C211yesmaximal, characteristic, complemented
21#20287926C211yesmaximal, characteristic, complemented
22#20287918C211yesmaximal, characteristic, complemented
23C53×#3489C211yesmaximal, characteristic, complemented
24C2×#13133264C2211yescharacteristic
25#16811352C2212yescomplemented
26#16811349C2212yescomplemented
27#16811348C2216yescomplemented
28#16811348C2216yescomplemented
29#16811344C2216yes—
30#16811343C2216yes—
31#16811342C2216yescomplemented
32#16811342C2216yescomplemented
33#16811332C2216yescomplemented
34#16811331C2216yescomplemented
35#16811330C2216yescomplemented
36#16811330C2216yescomplemented
37#16811325C22112yescomplemented
38#16811325C2216yescomplemented
39#16811320C2216yescomplemented
40#16811316C22112yescomplemented
41#16811315C2216yescomplemented
42#16811315C2216yescomplemented
43#16811313C2216yes—
44#16811313C2216yescomplemented
45#16811310C22112yescomplemented
46#16811310C22112yescomplemented
47#16811310C22112yescomplemented
48#16811308C22112yescomplemented
49#16811307C2216yes—
50#16811307C2216yescomplemented
51#16811304C22112yes—
52#16811299C22112yes—
53Q8×C22⋊D53C2212yes—
54Q8×C22⋊D53C2212yescomplemented
55Q8×C22⋊D53C2212yescomplemented
56#16811280C2212yes—
57#16811272C2216yes—
58#16811272C2216yescomplemented
59#16811272C2216yescomplemented
60#16811267C2216yes—
61#16811254C2213yescomplemented
62#16811251C2213yescomplemented
63#16811246C2213yes—
64#16811246C2213yescomplemented
65#16811242C2216yescomplemented
66#16811240C2213yes—
67#16811240C2216yescomplemented
68#16811240C2213yescomplemented
69#16811234C2216yescomplemented
70#16811233C2216yes—
71#16811233C2216yes—
72#16811233C2213yes—
73#16811233C2216yes—
74#16811233C2216yescomplemented
75#16811233C2216yescomplemented
76#16811233C2216yescomplemented
77#16811233C2216yescomplemented
78#16811233C2216yescomplemented
79#16811233C2213yescomplemented
80#16811226C2211yescharacteristic
81#16811226C2213yescomplemented
82#16811218C22112yescomplemented
83#16811217C22112yescomplemented
84#16811217C2216yescomplemented
85#16811217C2216yescomplemented
86#16811208C2216yes—
87#16811208C2216yes—
88#16811201C2213yes—
89#16811197C2213yescomplemented
90#16811194C2213yes—
91#16811194C2213yescomplemented
92#16811178C2216yescomplemented
93#16811176C2213yescomplemented
94#16811175C2216yescomplemented
95#16811175C2216yescomplemented
96#16811175C2216yescomplemented
97#16811169C2213yescomplemented
98C2×#13133215C2213yescomplemented
99#16811159C2216yescomplemented
100#16811155C2216yes—
101#16811155C2216yescomplemented
102#16811154C2216yescomplemented
103#16811154C22112yescomplemented
104#16811154C2216yescomplemented
105#16811153C2216yes—
106#16811153C2216yescomplemented
107#16811152C2216yescomplemented
108#16811150C22112yescomplemented
109C2×#13133210C2216yes—
110C2×#13133210C2216yes—
111C2×#13133208C2213yescomplemented
112C2×#13133208C2216yescomplemented
113C2×#13133207C2216yescomplemented
114#16811134C2213yes—
115C2×#13133196C2213yes—
116#16811106C2211yescharacteristic
117#16811106C2213yes—
118#16811106C2213yes—
119#16811106C2211yescharacteristic
120#16811106C2211yescharacteristic
121#16811106C2216yescomplemented
122#16811106C2213yescomplemented
123#16811104C2213yescomplemented
124#16811102C2216yescomplemented
125#16811101C2211yescharacteristic
126#16811101C2211yescharacteristic
127#16811101C2212yescomplemented
128#16811101C2213yescomplemented
129#16811100C2213yescomplemented
130#16811099C2212yescomplemented
131#16811098C2213yes—
132#16811098C2213yes—
133#41×Dic53C2211yescharacteristic
134#41×Dic53C2213yes—
135#41×Dic53C2213yes—
136#41×Dic53C2211yescharacteristic
137#41×Dic53C2216yescomplemented
138#41×Dic53C2213yescomplemented
139#16811091C2213yescomplemented
140C4×#11719947C2216yescomplemented
141C2×Q8×Dic53C2212yescomplemented
142C2×Q8×Dic53C2213yescomplemented
143C2×#13133182C2213yescomplemented
144C4×Q8×D53C2212yescomplemented
145C2×#13133176C2213yes—
146C2×#13133176C2213yes—
147C2×2−1+4×C53C2211yescharacteristic
148C22×#41×C53C2211yescharacteristic
149D4×Q8×C53C2212yes—
150C53×#548C2212yes—
151C53×#547C2216yes—
152C53×#546C2216yes—
153C53×#537C2213yes—
154C53×#536C2213yes—
155C53×#525C2213yes—
156C2×C22⋊Q8×C53C2213yes—
157C53×#520C2211yescharacteristic
158#13133264—28no—
159C2×#11719945C2313yes—
160C2×#11719947C2316yes—
161C22×Dic106C2313yes—
162C2×Q8×D53C2312yes—
163#13133217C2316yes—
164#13133216C2316yes—
165#13133216C2313yes—
166#13133216C2313yes—
167#13133215C2316yes—
168#13133215C2316yes—
169#13133215C2316yes—
170#13133215C2313yes—
171#13133215C2316yes—
172#13133213C2311yescharacteristic
173#13133212C2316yes—
174#13133212C23112yes—
175#13133212C2316yes—
176#13133210C23112yes—
177#13133210C23112yes—
178#13133210C23112yes—
179#13133210C2316yes—
180#13133210C2316yes—
181#13133210C2316yes—
182#13133210C23112yes—
183#13133210C23112yes—
184#13133210C2316yes—
185#13133210C2316yes—
186#13133210C23112yes—
187#13133210C23112yes—
188#13133210C2316yes—
189#13133209C2316yes—
190#13133208C2316yes—
191#13133208C2316yes—
192#13133208C23112yes—
193#13133208C2316yes—
194#13133208C23112yes—
195#13133208C2316yes—
196#13133208C2316yes—
197#13133208C2313yes—
198#13133208C2316yes—
199#13133208C23112yes—
200#13133208C2311yescharacteristic
201#13133207C23112yes—
202#13133207C23112yes—
203#13133207C23112yes—
204#13133207C23112yes—
205#13133207C2316yes—
206#13133207C2316yes—
207#13133207C23112yes—
208#13133206C2313yes—
209#13133204C2316yes—
210#13133204C2316yes—
211#13133204C2316yes—
212#13133204C2313yes—
213#13133203C2316yes—
214#13133203C2316yes—
215#13133201C23112yes—
216#13133201C2316yes—
217#13133201C2312yes—
218#13133200C2316yes—
219#13133200C23112yes—
220#13133199C2316yes—
221#13133199C2316yes—
222#13133199C2316yes—
223#13133199C2312yes—
224#13133198C23112yes—
225#13133198C23112yes—
226#13133198C2316yes—
227#13133198C23112yes—
228#13133198C2316yes—
229#13133197C2316yes—
230#13133197C2316yes—
231#13133196C2316yes—
232#13133196C2316yes—
233#13133196C2316yes—
234#13133196C2316yes—
235#13133196C23112yes—
236#13133196C2313yes—
237#13133196C2316yes—
238#13133196C2313yes—
239#13133194C23112yes—
240#13133194C23112yes—
241#13133194C23112yes—
242#13133194C2316yes—
243#13133194C2316yes—
244#13133194C2316yes—
245#13133194C2316yes—
246#13133193C2316yes—
247#13133193C2316yes—
248#13133193C2316yes—
249#13133191C2311yescharacteristic
250#13133191C2313yes—
251#13133189C23112yes—
252#13133189C2316yes—
253#13133189C2316yes—
254#13133189C2316yes—
255#13133189C2312yes—
256#13133188C2316yes—
257#13133188C2316yes—
258#13133188C2312yes—
259#13133186C2316yes—
260Q8×Dic53C2312yes—
261Q8×Dic53C2311yescharacteristic
262Q8×Dic53C2311yescharacteristic
263Q8×Dic53C2316yes—
264Q8×Dic53C2313yes—
265Q8×Dic53C2313yes—
266Q8×Dic53C2316yes—
267Q8×Dic53C2311yescharacteristic
268Q8×Dic53C2311yescharacteristic
269Q8×Dic53C2313yes—
270Q8×Dic53C2316yes—
271Q8×Dic53C2316yes—
272Q8×Dic53C2316yes—
273Q8×Dic53C2313yes—
274Q8×Dic53C2313yes—
275Q8×Dic53C2313yes—
276C4×Dic106C2316yes—
277C4×Dic106C2316yes—
278C4×Dic106C2316yes—
279C4×Dic106C2316yes—
280#13133182C23112yes—
281#13133182C23112yes—
282#13133182C2316yes—
283#13133182C2313yes—
284#13133182C2316yes—
285#13133182C2316yes—
286#13133182C2313yes—
287D4×Dic53C2316yes—
288D4×Dic53C2313yes—
289D4×Dic53C2313yes—
290D4×Dic53C23112yes—
291D4×Dic53C23112yes—
292D4×Dic53C2316yes—
293D4×Dic53C2316yes—
294D4×Dic53C2313yes—
295D4×Dic53C2313yes—
296D4×Dic53C2313yes—
297D4×Dic53C2313yes—
298D4×Dic53C2316yes—
299D4×Dic53C2313yes—
300D4×Dic53C2316yes—
301D4×Dic53C2313yes—
302D4×Dic53C2316yes—
303D4×Dic53C2311yescharacteristic
304D4×Dic53C2316yes—
305D4×Dic53C2313yes—
306#13133179C2311yescharacteristic
307#13133179C2313yes—
308C4×C22⋊D53C2316yes—
309C4×C22⋊D53C2316yes—
310C4×C22⋊D53C2316yes—
311C4×C22⋊D53C2316yes—
312C4×C22⋊D53C23112yes—
313#13133177C23112yes—
314#13133177C2316yes—
315#13133177C2316yes—
316#13133176C23112yes—
317#13133176C2313yes—
318#13133176C2316yes—
319#13133176C2316yes—
320#13133176C2313yes—
321#13133176C2311yescharacteristic
322#13133176C2313yes—
323#13133176C2313yes—
324#13133176C2313yes—
325#13133176C2313yes—
326#13133176C2313yes—
327#13133176C2313yes—
328#13133176C2313yes—
329#13133176C2313yes—
330#13133176C2313yes—
331#13133176C2313yes—
332#13133176C2316yes—
333#13133175C23112yes—
334#13133175C2316yes—
335#13133174C2316yes—
336#13133173C23112yes—
337#13133173C23112yes—
338#13133173C23112yes—
339#13133173C23112yes—
340C2×C4⋊Dic53C2316yes—
341C2×C4⋊Dic53C2313yes—
342C2×C4⋊Dic53C2313yes—
343C2×C4⋊Dic53C2316yes—
344C2×C4⋊Dic53C2313yes—
345C2×C4⋊Dic53C2313yes—
346C2×C4⋊Dic53C2313yes—
347C2×C4⋊Dic53C2316yes—
348C2×#11719919C2316yes—
349C2×#11719919C2316yes—
350C2×#11719919C2316yes—
351C2×#11719919C2316yes—
352C2×#11719919C2316yes—
353C4⋊C4×D53C2316yes—
354C2×C22⋊Dic53C2316yes—
355C2×C22⋊Dic53C2316yes—
356C2×C22⋊Dic53C2313yes—
357C2×C22⋊Dic53C2313yes—
358C2×C4×Dic53C2313yes—
359C2×C4×Dic53C2313yes—
360C2×C4×Dic53C2316yes—
361C2×C4×Dic53C2316yes—
362C2×C4×Dic53C2316yes—
363C2×C4×Dic53C2316yes—
364C42×D53C2316yes—
3652−1+4×C53—28no—
366C2×#41×C53—28no—
367C2×#41×C53C2313yes—
368C2×#41×C53C2316yes—
369C2×#41×C53C2311yescharacteristic
370C2×#41×C53C2313yes—
371C2×#41×C53C2313yes—
372C2×#41×C53C2311yescharacteristic
373C22×Q8×C53C2311yescharacteristic
374C22×Q8×C53C2312yes—
375C22×Q8×C53C2313yes—
376C22×D4×C53C2313yes—
377C23×C4×C53C2313yes—
378C4⋊Q8×C53C2316yes—
379#124×C53C2316yes—
380#123×C53C2316yes—
381#123×C53C23112yes—
382C22⋊Q8×C53C2313yes—
383C22⋊Q8×C53C2316yes—
384C22⋊Q8×C53C2316yes—
385C22⋊Q8×C53C2316yes—
386C22⋊Q8×C53C2313yes—
387C22⋊Q8×C53C2316yes—
388#121×C53C2311yescharacteristic
389#121×C53C2313yes—
390#121×C53C23112yes—
391#121×C53C2316yes—
392#120×C53C2316yes—
393C4×Q8×C53C2312yes—
394C4×D4×C53C2316yes—
395C4×D4×C53C2316yes—
396C4×D4×C53C2316yes—
397#117×C53C2313yes—
398C2×C4⋊C4×C53C2313yes—
399C2×C4⋊C4×C53C2316yes—
400C2×C22⋊C4×C53C2316yes—
401C24×C53C2413yes—
402#41×C53—24no—
403#41×C53—212no—
404#41×C53—224no—
405#41×C53—212no—
406#41×C53—212no—
407#41×C53#4118yes—
408C2×Q8×C53—24no—
409C2×Q8×C53—28no—
410C2×Q8×C53—212no—
411C2×Q8×C53C2413yes—
412C2×Q8×C53C2416yes—
413C2×Q8×C53C2413yes—
414C2×Q8×C53C2411yescharacteristic
415C2×D4×C53—212no—
416C2×D4×C53C2416yes—
417C2×D4×C53C2411yescharacteristic
418C2×D4×C53C2416yes—
419C2×D4×C53C2413yes—
420C2×D4×C53C2412yes—
421C2×D4×C53C2416yes—
422C2×D4×C53C2413yes—
423C22×C4×C53—212no—
424C22×C4×C53C2416yes—
425C22×C4×C53C2413yes—
426C22×C4×C53C2416yes—
427C22×C4×C53C2413yes—
428C22×C4×C53C2413yes—
429C22×C4×C53C2411yescharacteristic
430C22×C4×C53C2413yes—
431C22×C4×C53C2416yes—
432C22×C4×C53C2413yes—
433C2×C22⋊D53C2416yes—
434C2×C22⋊D53C2416yes—
435C2×C22⋊D53C2412yes—
436C2×C22⋊D53C2412yes—
437C2×C22⋊D53C2412yes—
438C22×Dic53C2416yes—
439C22×Dic53C2413yes—
440C22×Dic53C2413yes—
441C22×Dic53C2412yes—
442C22×Dic53C2413yes—
443C22×Dic53C2413yes—
444C22×Dic53C2416yes—
445C22×Dic53C2416yes—
446C22×Dic53C2416yes—
447C22×Dic53C2416yes—
448Q8×D53—28no—
449#11719947—224no—
450#11719945—212no—
451C2×D212C2411yescharacteristic
452C2×C4×D53C2416yes—
453C2×C4×D53C2412yes—
454C2×C4×D53C2416yes—
455C2×Dic106—212no—
456C2×Dic106C2413yes—
457C2×Dic106C2416yes—
458C2×Dic106C2416yes—
459C2×Dic106C2416yes—
460C4⋊C4×C53C2413yes—
461C4⋊C4×C53C2416yes—
462C4⋊C4×C53C2416yes—
463C4⋊C4×C53C24112yes—
464C4⋊C4×C53C2411yescharacteristic
465C4⋊C4×C53C2416yes—
466C22⋊C4×C53C2416yes—
467C22⋊C4×C53C24112yes—
468C22⋊C4×C53C2416yes—
469C22⋊C4×C53C2412yes—
470C22⋊C4×C53C2416yes—
471C22⋊C4×C53C2416yes—
472C42×C53C2416yes—
473C22⋊Dic53C2411yescharacteristic
474C22⋊Dic53C2411yescharacteristic
475C22⋊Dic53C2413yes—
476C22⋊Dic53C2413yes—
477C22⋊Dic53C2416yes—
478C22⋊Dic53C2416yes—
479C22⋊Dic53C24112yes—
480C22⋊Dic53C2413yes—
481C22⋊Dic53C2413yes—
482C22⋊Dic53C2416yes—
483C22⋊Dic53C2413yes—
484C22⋊Dic53C2413yes—
485C22⋊Dic53C2416yes—
486C22⋊Dic53C2416yes—
487C22⋊Dic53C2416yes—
488C22⋊Dic53C2416yes—
489C22⋊Dic53C2412yes—
490C22⋊Dic53C2416yes—
491#11719921C2412yes—
492#11719921C2416yes—
493#11719921C2416yes—
494#11719921C2416yes—
495#11719921C2416yes—
496#11719921C2412yes—
497C4⋊Dic53C2413yes—
498C4⋊Dic53C2413yes—
499C4⋊Dic53C2413yes—
500C4⋊Dic53C2413yes—
501C4⋊Dic53C2411yescharacteristic
502C4⋊Dic53C2411yescharacteristic
503C4⋊Dic53C2416yes—
504C4⋊Dic53C2413yes—
505C4⋊Dic53C24112yes—
506C4⋊Dic53C2416yes—
507C4⋊Dic53C2416yes—
508C4⋊Dic53C24112yes—
509C4⋊Dic53C2413yes—
510C4⋊Dic53C2413yes—
511C4⋊Dic53C2413yes—
512C4⋊Dic53C2413yes—
513C4⋊Dic53C2413yes—
514C4⋊Dic53C2413yes—
515C4⋊Dic53C2411yescharacteristic
516C4⋊Dic53C2416yes—
517C4⋊Dic53C2412yes—
518#11719919C24112yes—
519#11719919C2416yes—
520#11719919C2416yes—
521#11719919C2416yes—
522#11719919C2416yes—
523#11719919C2416yes—
524#11719919C24112yes—
525#11719919C24112yes—
526#11719919C24112yes—
527#11719919C24112yes—
528#11719919C2416yes—
529#11719919C2416yes—
530#11719919C2416yes—
531#11719919C2416yes—
532#11719919C2412yes—
533C4×Dic53C2413yes—
534C4×Dic53C2416yes—
535C4×Dic53C2416yes—
536C4×Dic53C2413yes—
537C4×Dic53C2413yes—
538C4×Dic53C2411yescharacteristic
539C4×Dic53C2413yes—
540C4×Dic53C2411yescharacteristic
541C4×Dic53C2416yes—
542C4×Dic53C24112yes—
543C4×Dic53C2416yes—
544C4×Dic53C2416yes—
545C4×Dic53C24112yes—
546C4×Dic53C2416yes—
547C4×Dic53C2413yes—
548C4×Dic53C2413yes—
549C4×Dic53C2416yes—
550C23×C53—26no—
551C23×C53—43no—
552C23×C53—43no—
553C23×C53C2512yes—
554C23×C53C2513yes—
555C23×C53C2511yescharacteristic
556C23×C53C2513yes—
557C22×D53C2512yes—
558Q8×C53—26no—
559Q8×C53—212no—
560Q8×C53—26no—
561Q8×C53C2×#4114yes—
562D4×C53—212no—
563D4×C53—212no—
564D4×C53—26no—
565D4×C53—22no—
566D4×C53—42no—
567D4×C53—46no—
568D4×C53C2×#41112yes—
569C2×C4×C53—26no—
570C2×C4×C53—212no—
571C2×C4×C53—22no—
572C2×C4×C53—26no—
573C2×C4×C53—26no—
574C2×C4×C53—26no—
575C2×C4×C53—212no—
576C2×C4×C53—46no—
577C2×C4×C53C2×#41112yes—
578C2×C4×C53C2512yes—
579C2×C4×C53C2516yes—
580C2×C4×C53C2511yescharacteristic
581C2×C4×C53C2513yes—
582C2×C4×C53C2516yes—
583C2×C4×C53C2511yescharacteristic
584C2×C4×C53C2513yes—
585C22⋊D53—212no—
586C22⋊D53—42no—
587C22⋊D53—46no—
588C22⋊D53—42no—
589C22⋊D53—42no—
590C2×Dic53—212no—
591C2×Dic53—42no—
592C2×Dic53—46no—
593C2×Dic53—46no—
594C2×Dic53—43no—
595C2×Dic53—43no—
596C2×Dic53—46no—
597C2×Dic53—46no—
598C2×Dic53—43no—
599C2×Dic53—43no—
600C2×Dic53C2516yes—
601C2×Dic53C2512yes—
602C2×Dic53C2513yes—
603C2×Dic53C2513yes—
604C2×Dic53C2516yes—
605C2×Dic53C2513yes—
606C2×Dic53C2511yescharacteristic
607C2×Dic53C2511yescharacteristic
608C2×Dic53C2513yes—
609C2×Dic53C2511yescharacteristic
610C2×Dic53C2511yescharacteristic
611D212—22no—
612C4×D53—212no—
613C4×D53—42no—
614C4×D53—46no—
615Dic106—26no—
616Dic106—212no—
617Dic106—46no—
618Dic106—46no—
619#62861—531nomaximal, Sylow
620C22×C53—23no—
621C22×C53—23no—
622C22×C53—21no—
623C22×C53—22no—
624C22×C53—23no—
625C22×C53—22no—
626C22×C53—23no—
627C22×C53—23no—
628C22×C53—22no—
629C22×C53—21no—
630C22×C53—21no—
631C22×C53—86no—
632C22×C53C22×#4116yes—
633C22×C53C2611yescharacteristic
634C2×D53—22no—
635C2×D53—22no—
636C2×D53—22no—
637C4×C53—21no—
638C4×C53—23no—
639C4×C53—26no—
640C4×C53—22no—
641C4×C53—26no—
642C4×C53C22×#4112yes—
643C4×C53C22×#4116yes—
644Dic53—26no—
645Dic53—22no—
646Dic53—23no—
647Dic53—23no—
648Dic53—26no—
649Dic53—21no—
650Dic53—23no—
651Dic53—23no—
652Dic53—21no—
653Dic53—21no—
654Dic53—21no—
655#3523—532no—
656#3523—532no—
657#3521—536no—
658#3521—536no—
659#3516—532no—
660#3516—532no—
661#3515—536no—
662#3515—536no—
663#3512—533no—
664#3509—533no—
665#3504—531no—
666#3499—531no—
667#3495—533no—
668#3495—533no—
669#3489—531no—
670#3489D5311yescharacteristic, complemented
671#3461—533no—
672#3461—533no—
673#3455—533no—
674C2×#541—533no—
675C4×2−1+4—531no—
676C4×2−1+4—531no—
677#3428—531no—
678C2×C53—26no—
679C2×C53—42no—
680C2×C53—43no—
681C2×C53—41no—
682C2×C53C23×#4111yescharacteristic
683C2×C532−1+611yescharacteristic
684C2×C532−1+611yescharacteristic
685D53—42no—
686C2×2−1+4—531no—
687C2×2−1+4C2×D5311yescharacteristic
688C22×#41C2×D5311yescharacteristic
689#557—536no—
690#557—536no—
691#557—532no—
692#557—532no—
693#556—536no—
694#556—536no—
695#556—536no—
696#556—536no—
697#554—536no—
698#554—536no—
699#554—536no—
700#554—536no—
701#553—5312no—
702#553—536no—
703#553—5312no—
704#553—536no—
705#552—5312no—
706#552—5312no—
707#552—5312no—
708#552—536no—
709#552—536no—
710#552—536no—
711#552—536no—
712#552—536no—
713#552—536no—
714#552—5312no—
715#551—5312no—
716#551—5312no—
717D4×Q8—532no—
718D4×Q8—532no—
719D4×Q8—532no—
720D4×Q8C2×D5312yes—
721#548—532no—
722#548C2×D5312yes—
723#547—536no—
724#547—536no—
725#547—536no—
726#547C2×D5316yes—
727#546—536no—
728#546C2×D5316yes—
729#544—533no—
730#544—533no—
731#542—536no—
732#542—533no—
733#542—533no—
734#542—533no—
735#542—533no—
736#542—536no—
737#541—536no—
738#541—533no—
739#541—536no—
740#541—536no—
741#541—536no—
742#541—536no—
743#541—536no—
744#541—536no—
745#541—536no—
746#541—533no—
747#541—536no—
748#540—531no—
749#540—533no—
750#539—536no—
751#539—536no—
752#539—5312no—
753#539—5312no—
754#538—536no—
755#538—536no—
756#537—533no—
757#537C2×D5313yes—
758#536—533no—
759#536—533no—
760#536—533no—
761#536C2×D5313yes—
762#533—536no—
763#533—536no—
764#533—536no—
765#533—536no—
766#533—533no—
767#532—533no—
768C2×C4⋊Q8—533no—
769#529—536no—
770#529—5312no—
771#529—536no—
772#529—536no—
773#529—5312no—
774#529—536no—
775#529—536no—
776#529—536no—
777#529—536no—
778#529—536no—
779C2×#126—536no—
780C2×#126—536no—
781C2×#125—536no—
782C2×#125—533no—
783C2×#125—536no—
784#525—533no—
785#525C2×D5313yes—
786C2×C22⋊Q8—533no—
787C2×C22⋊Q8C2×D5313yes—
788#520—533no—
789#520—533no—
790#520—531no—
791#520—531no—
792#520—531no—
793#520—533no—
794#520—536no—
795#520—536no—
796#520—533no—
797#520C2×D5311yescharacteristic
798#519—531no—
799#519—531no—
800#519—533no—
801#519—532no—
802#519—532no—
803#519—533no—
804#518—533no—
805#518—533no—
806C4×#41—531no—
807C4×#41—533no—
808C4×#41—531no—
809C4×#41—533no—
810C4×#41—533no—
811C4×#41—536no—
812C4×#41—536no—
813C4×#41—533no—
814C2×C4×Q8—533no—
815C2×C4×Q8—532no—
816C2×C4×Q8—532no—
817C2×C4×Q8—533no—
818C2×#117—533no—
819C2×#117—533no—
820C53#6286111yescharacteristic, complemented, Sylow
8212−1+4—28no—
8222−1+4—1068no—
823C2×#41—28no—
824C2×#41—536no—
825C2×#41—533no—
826C2×#41C22×D5313yes—
827C2×#41C22×D5313yes—
828C2×#41C22×D5316yes—
829C2×#41C22×D5313yes—
830C2×#41C22×D5311yescharacteristic
831C2×#41C22×D5311yescharacteristic
832C22×Q8—532no—
833C22×Q8—533no—
834C22×Q8C22×D5313yes—
835C22×Q8C22×D5312yes—
836C22×Q8C22×D5311yescharacteristic
837C22×D4C22×D5313yes—
838C23×C4C22×D5313yes—
839C4⋊Q8—533no—
840C4⋊Q8—536no—
841C4⋊Q8—536no—
842C4⋊Q8—536no—
843C4⋊Q8—536no—
844C4⋊Q8—533no—
845C4⋊Q8—533no—
846C4⋊Q8—536no—
847C4⋊Q8—536no—
848C4⋊Q8C22×D5316yes—
849#127—531no—
850#126—536no—
851#126—5312no—
852#126—536no—
853#126—536no—
854#126—536no—
855#126—5312no—
856#126—5312no—
857#126—5312no—
858#126—5312no—
859#126—5312no—
860#126—5312no—
861#126—536no—
862#126—536no—
863#126—536no—
864#126—5312no—
865#126—536no—
866#125—536no—
867#125—536no—
868#125—533no—
869#125—536no—
870#125—5312no—
871#125—5312no—
872#125—5312no—
873#125—5312no—
874#125—5312no—
875#125—5312no—
876#125—536no—
877#125—536no—
878#125—536no—
879#125—536no—
880#125—536no—
881#125—531no—
882#125—5312no—
883#125—5312no—
884#125—536no—
885#124—533no—
886#124—536no—
887#124—533no—
888#124—536no—
889#124—536no—
890#124—536no—
891#124—536no—
892#124C22×D5316yes—
893#123—536no—
894#123—5312no—
895#123—5312no—
896#123—536no—
897#123—5312no—
898#123—536no—
899#123—5312no—
900#123—536no—
901#123—532no—
902#123—532no—
903#123—536no—
904#123—536no—
905#123—536no—
906#123—5312no—
907#123C22×D5316yes—
908#123C22×D53112yes—
909C22⋊Q8—536no—
910C22⋊Q8—536no—
911C22⋊Q8—536no—
912C22⋊Q8—533no—
913C22⋊Q8—536no—
914C22⋊Q8—536no—
915C22⋊Q8—536no—
916C22⋊Q8—533no—
917C22⋊Q8—536no—
918C22⋊Q8—5312no—
919C22⋊Q8—536no—
920C22⋊Q8—536no—
921C22⋊Q8—536no—
922C22⋊Q8—536no—
923C22⋊Q8—536no—
924C22⋊Q8—5312no—
925C22⋊Q8—536no—
926C22⋊Q8—536no—
927C22⋊Q8—5312no—
928C22⋊Q8—5312no—
929C22⋊Q8C22×D5313yes—
930C22⋊Q8C22×D5316yes—
931C22⋊Q8C22×D5316yes—
932C22⋊Q8C22×D5316yes—
933C22⋊Q8C22×D5313yes—
934C22⋊Q8C22×D5316yes—
935#121—532no—
936#121—532no—
937#121—5312no—
938#121—536no—
939#121—536no—
940#121—536no—
941#121—536no—
942#121—536no—
943#121—531no—
944#121—533no—
945#121C22×D5311yescharacteristic
946#121C22×D5313yes—
947#121C22×D53112yes—
948#121C22×D5316yes—
949#120—536no—
950#120C22×D5316yes—
951C4×Q8—531no—
952C4×Q8—531no—
953C4×Q8—536no—
954C4×Q8—533no—
955C4×Q8—536no—
956C4×Q8—536no—
957C4×Q8—532no—
958C4×Q8—536no—
959C4×Q8—533no—
960C4×Q8—536no—
961C4×Q8—533no—
962C4×Q8—533no—
963C4×Q8—531no—
964C4×Q8—531no—
965C4×Q8—533no—
966C4×Q8—533no—
967C4×Q8—536no—
968C4×Q8—533no—
969C4×Q8—536no—
970C4×Q8—536no—
971C4×Q8—533no—
972C4×Q8—5312no—
973C4×Q8—5312no—
974C4×Q8—536no—
975C4×Q8—536no—
976C4×Q8—536no—
977C4×Q8—536no—
978C4×Q8C22×D5312yes—
979C4×D4—533no—
980C4×D4—533no—
981C4×D4—536no—
982C4×D4—531no—
983C4×D4—536no—
984C4×D4—536no—
985C4×D4—533no—
986C4×D4—533no—
987C4×D4—533no—
988C4×D4—533no—
989C4×D4—536no—
990C4×D4—536no—
991C4×D4—533no—
992C4×D4—533no—
993C4×D4—536no—
994C4×D4—533no—
995C4×D4—536no—
996C4×D4—5312no—
997C4×D4—5312no—
998C4×D4—5312no—
999C4×D4—536no—
1000C4×D4—536no—
1001C4×D4—536no—
1002C4×D4—536no—
1003C4×D4—531no—
1004C4×D4—533no—
1005C4×D4—536no—
1006C4×D4—536no—
1007C4×D4—5312no—
1008C4×D4C22×D5316yes—
1009C4×D4C22×D5316yes—
1010C4×D4C22×D5316yes—
1011#117—531no—
1012#117—533no—
1013#117—533no—
1014#117—533no—
1015#117—533no—
1016#117—533no—
1017#117—533no—
1018#117—533no—
1019#117—533no—
1020#117—533no—
1021#117—533no—
1022#117—533no—
1023#117—536no—
1024#117—533no—
1025#117—536no—
1026#117—5312no—
1027#117—536no—
1028#117—536no—
1029#117—5312no—
1030#117—5312no—
1031#117—5312no—
1032#117—5312no—
1033#117—5312no—
1034#117—536no—
1035#117C22×D5313yes—
1036C2×C4⋊C4—533no—
1037C2×C4⋊C4—533no—
1038C2×C4⋊C4—533no—
1039C2×C4⋊C4—533no—
1040C2×C4⋊C4—533no—
1041C2×C4⋊C4—536no—
1042C2×C4⋊C4—536no—
1043C2×C4⋊C4—536no—
1044C2×C4⋊C4—536no—
1045C2×C4⋊C4—536no—
1046C2×C4⋊C4—536no—
1047C2×C4⋊C4—536no—
1048C2×C4⋊C4—536no—
1049C2×C4⋊C4—536no—
1050C2×C4⋊C4C22×D5313yes—
1051C2×C4⋊C4C22×D5316yes—
1052C2×C22⋊C4—533no—
1053C2×C22⋊C4—533no—
1054C2×C22⋊C4—536no—
1055C2×C22⋊C4—536no—
1056C2×C22⋊C4C22×D5316yes—
1057C2×C42—533no—
1058C2×C42—533no—
1059C2×C42—536no—
1060C2×C42—536no—
1061C2×C42—536no—
1062C2×C42—536no—
1063C2×C42—536no—
1064C24C23×D5313yes—
1065#41—24no—
1066#41—212no—
1067#41—224no—
1068#41—212no—
1069#41—212no—
1070#41—10624no—
1071#41—10612no—
1072#41#1171994718yes—
1073C2×Q8—24no—
1074C2×Q8—28no—
1075C2×Q8—212no—
1076C2×Q8—533no—
1077C2×Q8—536no—
1078C2×Q8—536no—
1079C2×Q8—536no—
1080C2×Q8—1068no—
1081C2×Q8—10612no—
1082C2×Q8C23×D5316yes—
1083C2×Q8C23×D5313yes—
1084C2×Q8C23×D5313yes—
1085C2×Q8C23×D5311yescharacteristic
1086C2×D4—212no—
1087C2×D4—536no—
1088C2×D4—532no—
1089C2×D4—536no—
1090C2×D4—532no—
1091C2×D4—532no—
1092C2×D4—531no—
1093C2×D4C23×D5316yes—
1094C2×D4C23×D5316yes—
1095C2×D4C23×D5313yes—
1096C2×D4C23×D5311yescharacteristic
1097C2×D4C23×D5316yes—
1098C2×D4C23×D5312yes—
1099C2×D4C23×D5313yes—
1100C22×C4—212no—
1101C22×C4—536no—
1102C22×C4—533no—
1103C22×C4—533no—
1104C22×C4—532no—
1105C22×C4—533no—
1106C22×C4—533no—
1107C22×C4—536no—
1108C22×C4—536no—
1109C22×C4—536no—
1110C22×C4—536no—
1111C22×C4—536no—
1112C22×C4—532no—
1113C22×C4—536no—
1114C22×C4C23×D5313yes—
1115C22×C4C23×D5316yes—
1116C22×C4C23×D5316yes—
1117C22×C4C23×D5313yes—
1118C22×C4C23×D5313yes—
1119C22×C4C23×D5313yes—
1120C22×C4C23×D5311yescharacteristic
1121C22×C4C23×D5316yes—
1122C22×C4C23×D5313yes—
1123C4⋊C4—533no—
1124C4⋊C4—533no—
1125C4⋊C4—533no—
1126C4⋊C4—533no—
1127C4⋊C4—531no—
1128C4⋊C4—531no—
1129C4⋊C4—533no—
1130C4⋊C4—536no—
1131C4⋊C4—536no—
1132C4⋊C4—5312no—
1133C4⋊C4—536no—
1134C4⋊C4—5312no—
1135C4⋊C4—536no—
1136C4⋊C4—536no—
1137C4⋊C4—536no—
1138C4⋊C4—536no—
1139C4⋊C4—536no—
1140C4⋊C4—533no—
1141C4⋊C4—533no—
1142C4⋊C4—533no—
1143C4⋊C4—533no—
1144C4⋊C4—533no—
1145C4⋊C4—533no—
1146C4⋊C4—5312no—
1147C4⋊C4—5312no—
1148C4⋊C4—5312no—
1149C4⋊C4—5312no—
1150C4⋊C4—5312no—
1151C4⋊C4—531no—
1152C4⋊C4—536no—
1153C4⋊C4—536no—
1154C4⋊C4—536no—
1155C4⋊C4—536no—
1156C4⋊C4—536no—
1157C4⋊C4—532no—
1158C4⋊C4—532no—
1159C4⋊C4C23×D5316yes—
1160C4⋊C4C23×D5313yes—
1161C4⋊C4C23×D5316yes—
1162C4⋊C4C23×D53112yes—
1163C4⋊C4C23×D5311yescharacteristic
1164C4⋊C4C23×D5316yes—
1165C22⋊C4—531no—
1166C22⋊C4—531no—
1167C22⋊C4—533no—
1168C22⋊C4—533no—
1169C22⋊C4—536no—
1170C22⋊C4—536no—
1171C22⋊C4—533no—
1172C22⋊C4—533no—
1173C22⋊C4—536no—
1174C22⋊C4—533no—
1175C22⋊C4—533no—
1176C22⋊C4—5312no—
1177C22⋊C4—536no—
1178C22⋊C4—536no—
1179C22⋊C4—532no—
1180C22⋊C4—536no—
1181C22⋊C4—536no—
1182C22⋊C4—536no—
1183C22⋊C4—536no—
1184C22⋊C4—532no—
1185C22⋊C4—536no—
1186C22⋊C4—536no—
1187C22⋊C4—532no—
1188C22⋊C4—536no—
1189C22⋊C4C23×D5316yes—
1190C22⋊C4C23×D53112yes—
1191C22⋊C4C23×D5316yes—
1192C22⋊C4C23×D5316yes—
1193C22⋊C4C23×D5316yes—
1194C22⋊C4C23×D5312yes—
1195C42—531no—
1196C42—533no—
1197C42—533no—
1198C42—533no—
1199C42—533no—
1200C42—531no—
1201C42—536no—
1202C42—536no—
1203C42—536no—
1204C42—536no—
1205C42—5312no—
1206C42—5312no—
1207C42—536no—
1208C42—536no—
1209C42—533no—
1210C42—533no—
1211C42—536no—
1212C42C23×D5316yes—
1213C23—26no—
1214C23—43no—
1215C23—43no—
1216C23—532no—
1217C23C24×D5311yescharacteristic
1218C23C24×D5313yes—
1219C23C24×D5312yes—
1220C23C24×D5313yes—
1221Q8—212no—
1222Q8—26no—
1223Q8—26no—
1224Q8—10612no—
1225Q8—1066no—
1226Q8—2126no—
1227Q8—2126no—
1228Q8C2×#1171994714yes—
1229D4—212no—
1230D4—212no—
1231D4—26no—
1232D4—22no—
1233D4—42no—
1234D4—46no—
1235D4—10612no—
1236D4—1062no—
1237D4—2122no—
1238D4—2126no—
1239D4—2122no—
1240D4—2122no—
1241D4C2×#11719947112yes—
1242C2×C4—26no—
1243C2×C4—212no—
1244C2×C4—22no—
1245C2×C4—26no—
1246C2×C4—26no—
1247C2×C4—26no—
1248C2×C4—212no—
1249C2×C4—46no—
1250C2×C4—531no—
1251C2×C4—533no—
1252C2×C4—533no—
1253C2×C4—531no—
1254C2×C4—532no—
1255C2×C4—533no—
1256C2×C4—533no—
1257C2×C4—536no—
1258C2×C4—536no—
1259C2×C4—531no—
1260C2×C4—531no—
1261C2×C4—10612no—
1262C2×C4—10612no—
1263C2×C4—2122no—
1264C2×C4—2126no—
1265C2×C4—2123no—
1266C2×C4—2126no—
1267C2×C4—2126no—
1268C2×C4—2123no—
1269C2×C4—2126no—
1270C2×C4—2123no—
1271C2×C4—2126no—
1272C2×C4—2122no—
1273C2×C4—2123no—
1274C2×C4C2×#11719947112yes—
1275C2×C4C24×D5316yes—
1276C2×C4C24×D5313yes—
1277C2×C4C24×D5312yes—
1278C2×C4C24×D5316yes—
1279C2×C4C24×D5311yescharacteristic
1280C2×C4C24×D5311yescharacteristic
1281C2×C4C24×D5313yes—
1282C22—23no—
1283C22—23no—
1284C22—21no—
1285C22—22no—
1286C22—23no—
1287C22—22no—
1288C22—23no—
1289C22—21no—
1290C22—23no—
1291C22—22no—
1292C22—21no—
1293C22—86no—
1294C22—1062no—
1295C22—1062no—
1296C22—1062no—
1297C22C22×#1171994716yes—
1298C22C25×D5311yescharacteristic
1299C4—21no—
1300C4—23no—
1301C4—26no—
1302C4—22no—
1303C4—26no—
1304C4—1066no—
1305C4—1061no—
1306C4—1063no—
1307C4—1061no—
1308C4—1066no—
1309C4—1063no—
1310C4—1063no—
1311C4—1061no—
1312C4—1061no—
1313C4—1063no—
1314C4—1062no—
1315C4C22×#1171994716yes—
1316C4C22×#1171994712yes—
1317C2—26no—
1318C2—41no—
1319C2—43no—
1320C2—42no—
1321C2—2122no—
1322C2C23×#1171994711yescharacteristic
1323C2#2028952711yescharacteristic
1324C2#2028952811yescharacteristic
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3489C2
hypercenter#3489D53
hypocenterC53#62861
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3489

Complements

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

NH ≅ G/Ntype
1. #20288806C2semidirect
2. #20288802C2semidirect
3. #20288772C2semidirect
4. #20288768C2semidirect
5. #20288701C2semidirect
6. #20288697C2semidirect
7. #20288684C2semidirect
8. #20288680C2semidirect
9. #20288636C2semidirect
10. #20288600C2semidirect
11. #20288537C2semidirect
12. #20288496C2semidirect
13. #20288469C2semidirect
14. #20288461C2semidirect
15. #20288395C2semidirect
16. #20288143C2semidirect
17. #20288139C2semidirect
18. #20288103C2semidirect
19. C2×#16811233C2semidirect
20. 2−1+4×Dic53C2semidirect
21. #20287926C2semidirect
22. #20287918C2semidirect
23. C53×#3489C2semidirect
25. #16811352C22semidirect
26. #16811349C22semidirect
27. #16811348C22semidirect
28. #16811348C22semidirect
31. #16811342C22semidirect
32. #16811342C22semidirect
33. #16811332C22semidirect
34. #16811331C22semidirect
35. #16811330C22semidirect
36. #16811330C22semidirect
37. #16811325C22semidirect
38. #16811325C22semidirect
39. #16811320C22semidirect
40. #16811316C22semidirect
41. #16811315C22semidirect
42. #16811315C22semidirect
44. #16811313C22semidirect
45. #16811310C22semidirect
46. #16811310C22semidirect
47. #16811310C22semidirect
48. #16811308C22semidirect
50. #16811307C22semidirect
54. Q8×C22⋊D53C22semidirect
55. Q8×C22⋊D53C22semidirect
58. #16811272C22semidirect
59. #16811272C22semidirect
61. #16811254C22semidirect
62. #16811251C22semidirect
64. #16811246C22semidirect
65. #16811242C22semidirect
67. #16811240C22semidirect
68. #16811240C22semidirect
69. #16811234C22semidirect
74. #16811233C22semidirect
75. #16811233C22semidirect
76. #16811233C22semidirect
77. #16811233C22semidirect
78. #16811233C22semidirect
79. #16811233C22semidirect
81. #16811226C22semidirect
82. #16811218C22semidirect
83. #16811217C22semidirect
84. #16811217C22semidirect
85. #16811217C22semidirect
89. #16811197C22semidirect
91. #16811194C22semidirect
92. #16811178C22semidirect
93. #16811176C22semidirect
94. #16811175C22semidirect
95. #16811175C22semidirect
96. #16811175C22semidirect
97. #16811169C22semidirect
98. C2×#13133215C22semidirect
99. #16811159C22semidirect
101. #16811155C22semidirect
102. #16811154C22semidirect
103. #16811154C22semidirect
104. #16811154C22semidirect
106. #16811153C22semidirect
107. #16811152C22semidirect
108. #16811150C22semidirect
111. C2×#13133208C22semidirect
112. C2×#13133208C22semidirect
113. C2×#13133207C22semidirect
121. #16811106C22semidirect
122. #16811106C22semidirect
123. #16811104C22semidirect
124. #16811102C22semidirect
127. #16811101C22semidirect
128. #16811101C22semidirect
129. #16811100C22semidirect
130. #16811099C22semidirect
137. #41×Dic53C22semidirect
138. #41×Dic53C22semidirect
139. #16811091C22semidirect
140. C4×#11719947C22semidirect
141. C2×Q8×Dic53C22semidirect
142. C2×Q8×Dic53C22semidirect
143. C2×#13133182C22semidirect
144. C4×Q8×D53C22semidirect
670. #3489D53semidirect
820. C53#62861semidirect

Maximal subgroups

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

subgroupindex
#202888062
#202888022
#202887722
#202887682
#202887012
#202886972
#202886842
#202886802
#202886362
#202886002
#202885372
#202884962
#202884692
#202884612
#202883952
#202881432
#202881392
#202881032
C2×#168112332
2−1+4×Dic532
#202879262
#202879182
C53×#34892
#6286153