Finite Group Databasebeta

← #28293264

Subgroups — #28293264

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#20288825C212yesmaximal, complemented
2#20288791C212yesmaximal, complemented
3#20288768C216yesmaximal, complemented
4#20288751C216yesmaximal, complemented
5#20288723C212yesmaximal, complemented
6#20288697C212yesmaximal, complemented
7#20288663C216yesmaximal, complemented
8#20288656C216yesmaximal, complemented
9#20288622C213yesmaximal, complemented
10#20288609C213yesmaximal, complemented
11#20288534C211yesmaximal, characteristic, complemented
12#20288464C213yesmaximal, complemented
13#20288447C213yesmaximal, complemented
14#20288388C211yesmaximal, characteristic, complemented
15#20288377C211yesmaximal, characteristic, complemented
16#20288139C213yesmaximal, complemented
17#20288128C213yesmaximal, complemented
18#20288104C213yesmaximal, complemented
19C2×#16811242C213yesmaximal, complemented
202−1+4×Dic53C211yesmaximal, characteristic, complemented
21H(5,𝔽2)×Dic53C211yesmaximal, characteristic, complemented
22#20287914C211yesmaximal, characteristic, complemented
23C53×#3500C211yesmaximal, characteristic, complemented
24C2×#41×D53C2211yescharacteristic
25#16811355C2216yescomplemented
26#16811355C2216yescomplemented
27Q8×Dic106C2212yescomplemented
28#16811352C2212yescomplemented
29#16811344C2216yescomplemented
30#16811343C2216yescomplemented
31#16811342C2216yescomplemented
32#16811342C2216yescomplemented
33#16811338C2216yescomplemented
34#16811337C2216yescomplemented
35#16811331C2216yescomplemented
36#16811330C2216yescomplemented
37#16811330C2216yescomplemented
38#16811325C22112yescomplemented
39#16811325C2216yescomplemented
40#16811320C2216yescomplemented
41#16811315C2216yescomplemented
42#16811310C22112yescomplemented
43#16811307C2216yescomplemented
44#16811304C22112yescomplemented
45#16811299C22112yescomplemented
46#16811299C22112yescomplemented
47#16811296C22112yescomplemented
48#16811292C2212yes—
49D4×Dic106C2216yescomplemented
50Q8×C22⋊D53C2212yescomplemented
51#16811284C2212yescomplemented
52#16811280C2212yes—
53#16811279C22112yescomplemented
54#16811277C2216yescomplemented
55#16811273C2216yescomplemented
56#16811272C2216yescomplemented
57#16811267C2216yes—
58#16811261C2216yescomplemented
59#16811260C22112yescomplemented
60D4×C22⋊D53C2216yes—
61#16811251C2213yescomplemented
62#16811251C2213yescomplemented
63#16811246C2216yescomplemented
64#16811242C2216yescomplemented
65#16811242C2216yescomplemented
66#16811242C2213yescomplemented
67#16811242C2216yescomplemented
68#16811242C2216yescomplemented
69#16811242C2216yescomplemented
70#16811242C2216yescomplemented
71#16811242C2216yescomplemented
72#16811242C2213yescomplemented
73#16811242C2211yescharacteristic, complemented
74#16811242C2213yescomplemented
75#16811240C2216yescomplemented
76#16811234C2213yescomplemented
77#16811234C2213yescomplemented
78#16811233C2216yescomplemented
79#16811227C2213yescomplemented
80#16811227C2213yescomplemented
81#16811226C2216yescomplemented
82#16811218C2216yescomplemented
83#16811218C2216yescomplemented
84#16811217C22112yescomplemented
85#16811210C2216yescomplemented
86#16811210C2216yescomplemented
87#16811208C22112yescomplemented
88#16811201C2213yes—
89#16811201C2213yescomplemented
90#16811197C2213yescomplemented
91#16811190C2213yes—
92#16811180C2213yescomplemented
93#16811178C2216yescomplemented
94#16811175C2216yescomplemented
95#16811171C2216yescomplemented
96#16811168C2216yescomplemented
97C2×#13133217C2213yescomplemented
98#16811159C2216yescomplemented
99#16811154C2216yescomplemented
100#16811153C2216yescomplemented
101#16811153C2216yescomplemented
102#16811153C2216yescomplemented
103#16811153C2216yescomplemented
104#16811152C2216yescomplemented
105#16811152C2216yescomplemented
106#16811150C22112yescomplemented
107C2×#13133210C2216yescomplemented
108C2×#13133203C2216yescomplemented
109#16811130C2213yes—
110#16811130C2213yescomplemented
111#16811129C22112yescomplemented
112C2×#13133201C2216yescomplemented
113C2×#13133194C2216yescomplemented
114C2×#13133193C2213yescomplemented
115C2×#13133188C2213yes—
116#16811106C2211yescharacteristic
117#16811106C2211yescharacteristic
118#16811106C2212yescomplemented
119#16811106C2213yescomplemented
120#16811106C2213yescomplemented
121#16811106C2216yescomplemented
122#16811105C2211yescharacteristic, complemented
123#16811105C2211yescharacteristic, complemented
124#16811102C2213yescomplemented
125#16811102C2213yescomplemented
126#16811101C2212yescomplemented
127#16811101C2213yescomplemented
128#16811099C2211yescharacteristic, complemented
129#16811099C2211yescharacteristic, complemented
130#16811098C2216yescomplemented
131#16811098C2213yescomplemented
132#16811095C2213yescomplemented
133#16811095C2213yescomplemented
134#41×Dic53C2211yescharacteristic
135#41×Dic53C2216yescomplemented
136#41×Dic53C2212yescomplemented
137#41×Dic53C2213yescomplemented
138#41×Dic53C2213yescomplemented
139C4×#11719945C2213yescomplemented
140#16811091C2213yescomplemented
141C2×Q8×Dic53C2212yescomplemented
142C2×Q8×Dic53C2213yescomplemented
143C2×D4×Dic53C2213yescomplemented
144C2×D4×Dic53C2216yescomplemented
145C2×#13133174C2213yescomplemented
146#117×D53C2213yescomplemented
147C2×2−1+4×C53C2211yescharacteristic
148C2×H(5,𝔽2)×C53C2211yescharacteristic
149C53×#548C2212yescomplemented
150C53×#548C2212yescomplemented
151C53×#546C2216yescomplemented
152C53×#546C2216yescomplemented
153C53×#536C2213yescomplemented
154C53×#535C2213yescomplemented
155C53×#532C2213yescomplemented
156C2×#124×C53C2213yescomplemented
157C4×#41×C53C2211yescharacteristic
158C2×#11719949C2311yescharacteristic
159C2×#11719945C2313yes—
160C2×#11719947C2313yes—
161C2×#11719947C23112yes—
162#41×D53—28no—
163C22×Dic106C2316yes—
164C2×Q8×D53C2311yescharacteristic
165C22×C22⋊D53C2316yes—
166C2×D4×D53C2313yes—
167C23×Dic53C2316yes—
168C22×C4×D53C2313yes—
169#13133217C2316yes—
170#13133217C2316yes—
171#13133217C2313yes—
172#13133217C2316yes—
173#13133217C2311yescharacteristic
174#13133216C2316yes—
175#13133216C2316yes—
176#13133215C2316yes—
177#13133213C2316yes—
178#13133212C2316yes—
179#13133212C2316yes—
180#13133212C2316yes—
181#13133212C2316yes—
182#13133210C2316yes—
183#13133210C23112yes—
184#13133210C23112yes—
185#13133210C23112yes—
186#13133210C23112yes—
187#13133210C2316yes—
188#13133210C2316yes—
189#13133210C23112yes—
190#13133210C2312yes—
191#13133209C2313yes—
192#13133209C2313yes—
193#13133208C2316yes—
194#13133208C23112yes—
195#13133208C2316yes—
196#13133207C2316yes—
197#13133207C2316yes—
198#13133207C2316yes—
199#13133207C2316yes—
200#13133206C2316yes—
201#13133204C2316yes—
202#13133204C23112yes—
203#13133203C2316yes—
204#13133203C23112yes—
205#13133203C23112yes—
206#13133203C2316yes—
207#13133203C2316yes—
208#13133203C23112yes—
209#13133203C2312yes—
210#13133201C2316yes—
211#13133201C23112yes—
212#13133201C23112yes—
213#13133201C2316yes—
214#13133201C2316yes—
215#13133201C23112yes—
216#13133201C2312yes—
217#13133200C23112yes—
218#13133199C23112yes—
219#13133199C23112yes—
220#13133198C2316yes—
221#13133198C2316yes—
222#13133198C2316yes—
223#13133198C2316yes—
224#13133198C2316yes—
225#13133198C2316yes—
226#13133197C23112yes—
227#13133196C2316yes—
228#13133196C2316yes—
229#13133196C2316yes—
230#13133196C2316yes—
231#13133194C23112yes—
232#13133194C2316yes—
233#13133194C23112yes—
234#13133194C23112yes—
235#13133194C23112yes—
236#13133194C2316yes—
237#13133194C2316yes—
238#13133194C23112yes—
239#13133194C2312yes—
240#13133193C2316yes—
241#13133193C2316yes—
242#13133193C2313yes—
243#13133193C2316yes—
244#13133193C2311yescharacteristic
245#13133193C2313yes—
246#13133193C2313yes—
247#13133191C2316yes—
248#13133191C2316yes—
249#13133189C23112yes—
250#13133189C23112yes—
251#13133189C2316yes—
252#13133189C2316yes—
253#13133189C2316yes—
254#13133189C2316yes—
255#13133188C2316yes—
256#13133188C2316yes—
257#13133188C23112yes—
258#13133188C2313yes—
259#13133188C2316yes—
260#13133188C2313yes—
261#13133188C2311yescharacteristic
262#13133188C2313yes—
263#13133186C23112yes—
264#13133185C2316yes—
265#13133185C2316yes—
266Q8×Dic53C2312yes—
267Q8×Dic53C2312yes—
268Q8×Dic53C2316yes—
269Q8×Dic53C2316yes—
270Q8×Dic53C2311yescharacteristic
271Q8×Dic53C2316yes—
272Q8×Dic53C2313yes—
273Q8×Dic53C2316yes—
274Q8×Dic53C2316yes—
275Q8×Dic53C2311yescharacteristic
276Q8×Dic53C2311yescharacteristic
277Q8×Dic53C2313yes—
278Q8×Dic53C2313yes—
279C4×Dic106C2316yes—
280C4×Dic106C2313yes—
281C4×Dic106C2316yes—
282C4×Dic106C2313yes—
283#13133182C23112yes—
284#13133182C2313yes—
285#13133182C2313yes—
286C4×D212C2313yes—
287C4×D212C2313yes—
288D4×Dic53C2316yes—
289D4×Dic53C2316yes—
290D4×Dic53C2316yes—
291D4×Dic53C23112yes—
292D4×Dic53C23112yes—
293D4×Dic53C23112yes—
294D4×Dic53C2316yes—
295D4×Dic53C2313yes—
296D4×Dic53C2316yes—
297D4×Dic53C2316yes—
298D4×Dic53C2313yes—
299D4×Dic53C2316yes—
300D4×Dic53C2316yes—
301D4×Dic53C2313yes—
302D4×Dic53C2316yes—
303D4×Dic53C2311yescharacteristic
304D4×Dic53C2316yes—
305D4×Dic53C2313yes—
306D4×Dic53C2316yes—
307D4×Dic53C2313yes—
308#13133179C2313yes—
309#13133179C2313yes—
310C4×C22⋊D53C2316yes—
311C4×C22⋊D53C2316yes—
312C4×C22⋊D53C2316yes—
313C4×C22⋊D53C2316yes—
314C4×C22⋊D53C2316yes—
315C4×C22⋊D53C2316yes—
316#13133177C23112yes—
317#13133177C23112yes—
318#13133177C2316yes—
319#13133177C2316yes—
320#13133176C23112yes—
321#13133176C2316yes—
322#13133176C2316yes—
323#13133176C2313yes—
324#13133176C2313yes—
325#13133176C2316yes—
326#13133176C2313yes—
327#13133176C2316yes—
328#13133175C23112yes—
329#13133175C2313yes—
330#13133175C2313yes—
331#13133174C2313yes—
332#13133174C2311yescharacteristic
333#13133174C2313yes—
334#13133174C2313yes—
335#13133174C2313yes—
336#13133174C2313yes—
337#13133174C2313yes—
338#13133174C2313yes—
339#13133173C23112yes—
340#13133173C23112yes—
341#13133173C2316yes—
342C2×C4⋊Dic53C2316yes—
343C2×C4⋊Dic53C2316yes—
344C2×C4⋊Dic53C2316yes—
345C2×C4⋊Dic53C2313yes—
346C2×C4⋊Dic53C2313yes—
347C2×C4⋊Dic53C2316yes—
348C2×#11719919C2316yes—
349C2×#11719919C2313yes—
350C2×#11719919C2313yes—
351C4⋊C4×D53C2313yes—
352C4⋊C4×D53C2313yes—
353C2×C22⋊Dic53C2316yes—
354C2×C22⋊Dic53C23112yes—
355C2×C22⋊Dic53C2316yes—
356C2×#11719921C2316yes—
357C2×#11719921C2313yes—
358C2×#11719921C2313yes—
359C22⋊C4×D53C2316yes—
360C2×C4×Dic53C2313yes—
361C2×C4×Dic53C2316yes—
362C2×C4×Dic53C2316yes—
363C2×C4×Dic53C2316yes—
364C42×D53C2316yes—
3652−1+4×C53—28no—
366H(5,𝔽2)×C53—28no—
367C2×#41×C53C2316yes—
368C2×#41×C53C2312yes—
369C2×#41×C53C2313yes—
370C2×#41×C53C2313yes—
371C2×#41×C53C2311yescharacteristic
372C22×Q8×C53C2312yes—
373C22×Q8×C53C2313yes—
374C22×D4×C53C2316yes—
375C22×D4×C53C2313yes—
376C4⋊Q8×C53C2313yes—
377#127×C53C2313yes—
378#124×C53C2313yes—
379#124×C53C2316yes—
380#124×C53C2316yes—
381#124×C53C2316yes—
382#124×C53C2311yescharacteristic
383#123×C53C23112yes—
384C22⋊Q8×C53C2316yes—
385C22⋊Q8×C53C2316yes—
386#121×C53C2316yes—
387#121×C53C2316yes—
388#121×C53C2316yes—
389#121×C53C2316yes—
390#120×C53C23112yes—
391C4×Q8×C53C2311yescharacteristic
392C4×Q8×C53C2311yescharacteristic
393C4×D4×C53C2316yes—
394C4×D4×C53C2313yes—
395C4×D4×C53C2313yes—
396C4×D4×C53C2316yes—
397#117×C53C2313yes—
398C2×C22⋊C4×C53C2316yes—
399C2×C22⋊C4×C53C2316yes—
400C2×C42×C53C2313yes—
401C24×C53C2416yes—
402C23×D53C2413yes—
403#41×C53—28no—
404#41×C53—224no—
405#41×C53—212no—
406#41×C53—212no—
407#41×C53#4118yescomplemented
408C2×Q8×C53—28no—
409C2×Q8×C53—212no—
410C2×Q8×C53C2416yes—
411C2×Q8×C53C2413yes—
412C2×Q8×C53C2411yescharacteristic
413C2×Q8×C53C2411yescharacteristic
414C2×D4×C53—224no—
415C2×D4×C53—212no—
416C2×D4×C53C2416yes—
417C2×D4×C53C2416yes—
418C2×D4×C53C2416yes—
419C2×D4×C53C2413yes—
420C2×D4×C53C2411yescharacteristic
421C2×D4×C53C2416yes—
422C2×D4×C53C2416yes—
423C2×D4×C53C2413yes—
424C22×C4×C53C2416yes—
425C22×C4×C53C2416yes—
426C22×C4×C53C2416yes—
427C22×C4×C53C2413yes—
428C22×C4×C53C2413yes—
429C22×C4×C53C2413yes—
430C2×C22⋊D53—86no—
431C2×C22⋊D53C2416yes—
432C2×C22⋊D53C2416yes—
433C2×C22⋊D53C24112yes—
434C2×C22⋊D53C2412yes—
435C2×C22⋊D53C2416yes—
436C2×C22⋊D53C2416yes—
437C22×Dic53—86no—
438C22×Dic53C2413yes—
439C22×Dic53C2413yes—
440C22×Dic53C2412yes—
441C22×Dic53C2413yes—
442C22×Dic53C2416yes—
443C22×Dic53C2416yes—
444C22×Dic53C2416yes—
445C22×Dic53C2416yes—
446C22×Dic53C2416yes—
447C22×Dic53C24112yes—
448#11719949—24no—
449Q8×D53—24no—
450#11719947—212no—
451#11719947—812no—
452D4×D53—212no—
453#11719945—212no—
454C2×D212C2413yes—
455C2×C4×D53—212no—
456C2×C4×D53C2413yes—
457C2×C4×D53C2413yes—
458C2×C4×D53C2411yescharacteristic
459C2×C4×D53C2413yes—
460C2×C4×D53C2416yes—
461C2×C4×D53C2416yes—
462C2×Dic106—86no—
463C2×Dic106C2413yes—
464C2×Dic106C24112yes—
465C2×Dic106C2412yes—
466C2×Dic106C2416yes—
467C4⋊C4×C53C2413yes—
468C4⋊C4×C53C2413yes—
469C4⋊C4×C53C2416yes—
470C4⋊C4×C53C2416yes—
471C22⋊C4×C53C2416yes—
472C22⋊C4×C53C2416yes—
473C22⋊C4×C53C24112yes—
474C22⋊C4×C53C24112yes—
475C22⋊C4×C53C2416yes—
476C22⋊C4×C53C2412yes—
477C22⋊C4×C53C2412yes—
478C42×C53C2411yescharacteristic
479C42×C53C2413yes—
480C42×C53C2413yes—
481C42×C53C2413yes—
482C22⋊Dic53C2416yes—
483C22⋊Dic53C2416yes—
484C22⋊Dic53C24112yes—
485C22⋊Dic53C2416yes—
486C22⋊Dic53C2416yes—
487C22⋊Dic53C2416yes—
488C22⋊Dic53C24112yes—
489C22⋊Dic53C2416yes—
490C22⋊Dic53C2416yes—
491C22⋊Dic53C2416yes—
492C22⋊Dic53C2412yes—
493C22⋊Dic53C2412yes—
494C22⋊Dic53C2416yes—
495#11719921C2413yes—
496#11719921C2413yes—
497#11719921C2411yescharacteristic
498#11719921C2411yescharacteristic
499#11719921C2416yes—
500#11719921C2413yes—
501#11719921C2413yes—
502#11719921C2413yes—
503#11719921C2413yes—
504#11719921C24112yes—
505#11719921C2416yes—
506#11719921C2416yes—
507#11719921C2412yes—
508C4⋊Dic53C2413yes—
509C4⋊Dic53C2413yes—
510C4⋊Dic53C2413yes—
511C4⋊Dic53C2416yes—
512C4⋊Dic53C2416yes—
513C4⋊Dic53C2413yes—
514C4⋊Dic53C2416yes—
515C4⋊Dic53C2416yes—
516C4⋊Dic53C24112yes—
517C4⋊Dic53C2416yes—
518C4⋊Dic53C24112yes—
519C4⋊Dic53C2411yescharacteristic
520C4⋊Dic53C2412yes—
521C4⋊Dic53C2411yescharacteristic
522C4⋊Dic53C2416yes—
523C4⋊Dic53C2412yes—
524#11719919C2413yes—
525#11719919C2413yes—
526#11719919C2411yescharacteristic
527#11719919C2411yescharacteristic
528#11719919C2416yes—
529#11719919C24112yes—
530#11719919C2413yes—
531#11719919C2413yes—
532#11719919C2413yes—
533#11719919C2413yes—
534#11719919C2416yes—
535#11719919C2416yes—
536#11719919C2416yes—
537#11719919C2416yes—
538#11719919C2416yes—
539#11719919C2412yes—
540#11719919C2416yes—
541C4×Dic53C2413yes—
542C4×Dic53C2416yes—
543C4×Dic53C2416yes—
544C4×Dic53C2411yescharacteristic
545C4×Dic53C2413yes—
546C4×Dic53C2413yes—
547C4×Dic53C2412yes—
548C4×Dic53C2416yes—
549C4×Dic53C2416yes—
550C4×Dic53C24112yes—
551C4×Dic53C2416yes—
552C4×Dic53C2416yes—
553C4×Dic53C2416yes—
554C23×C53—212no—
555C23×C53—46no—
556C23×C53—46no—
557C23×C53C2512yes—
558C23×C53C2516yes—
559C23×C53C2513yes—
560C22×D53—26no—
561C22×D53—43no—
562C22×D53—43no—
563C22×D53C2513yes—
564C22×D53C2511yescharacteristic
565Q8×C53—212no—
566Q8×C53—26no—
567Q8×C53—22no—
568Q8×C53C2×#4114yes—
569D4×C53—212no—
570D4×C53—212no—
571D4×C53—212no—
572D4×C53—26no—
573D4×C53—22no—
574D4×C53—46no—
575D4×C53—46no—
576D4×C53C2×#41112yes—
577C2×C4×C53—212no—
578C2×C4×C53—212no—
579C2×C4×C53—212no—
580C2×C4×C53—43no—
581C2×C4×C53—43no—
582C2×C4×C53C2×#41112yes—
583C2×C4×C53C2511yescharacteristic
584C2×C4×C53C2513yes—
585C2×C4×C53C2511yescharacteristic
586C2×C4×C53C2513yes—
587C2×C4×C53C2512yes—
588C2×C4×C53C2516yes—
589C2×C4×C53C2513yes—
590C2×C4×C53C2511yescharacteristic
591C22⋊D53—212no—
592C22⋊D53—46no—
593C22⋊D53—412no—
594C22⋊D53—46no—
595C22⋊D53—42no—
596C22⋊D53—46no—
597C2×Dic53—26no—
598C2×Dic53—46no—
599C2×Dic53—46no—
600C2×Dic53—46no—
601C2×Dic53—412no—
602C2×Dic53—46no—
603C2×Dic53—43no—
604C2×Dic53—46no—
605C2×Dic53—42no—
606C2×Dic53—43no—
607C2×Dic53C2516yes—
608C2×Dic53C2516yes—
609C2×Dic53C2513yes—
610C2×Dic53C2512yes—
611C2×Dic53C2512yes—
612C2×Dic53C2511yescharacteristic
613C2×Dic53C2513yes—
614C2×Dic53C2513yes—
615C2×Dic53C2511yescharacteristic
616C2×Dic53C2511yescharacteristic
617D212—26no—
618C4×D53—22no—
619C4×D53—26no—
620C4×D53—26no—
621C4×D53—26no—
622C4×D53—46no—
623C4×D53—46no—
624Dic106—26no—
625Dic106—46no—
626Dic106—412no—
627Dic106—42no—
628#62857—531nomaximal, Sylow
629C22×C53—23no—
630C22×C53—23no—
631C22×C53—22no—
632C22×C53—26no—
633C22×C53—22no—
634C22×C53—26no—
635C22×C53—22no—
636C22×C53—26no—
637C22×C53—812no—
638C22×C53C22×#4116yes—
639C22×C53C2611yescharacteristic
640C2×D53—21no—
641C2×D53—23no—
642C2×D53—23no—
643C2×D53—21no—
644C2×D53—23no—
645C2×D53—21no—
646C2×D53—86no—
647C4×C53—22no—
648C4×C53—26no—
649C4×C53—21no—
650C4×C53—23no—
651C4×C53—21no—
652C4×C53—23no—
653C4×C53C22×#4116yes—
654C4×C53C22×#4112yes—
655Dic53—23no—
656Dic53—21no—
657Dic53—26no—
658Dic53—26no—
659Dic53—23no—
660Dic53—21no—
661Dic53—22no—
662Dic53—22no—
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#3503—531no—
676#3500D5311yescharacteristic, complemented
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×C53—42no—
690C2×C53—46no—
691C2×C53C23×#4111yescharacteristic
692C2×C53H(7,𝔽2)11yescharacteristic
693C2×C532−1+611yescharacteristic
694D53—43no—
695D53—41no—
696C2×2−1+4C2×D5311yescharacteristic
697C2×H(5,𝔽2)C2×D5311yescharacteristic
698C22×#41—531no—
699#559—536no—
700#559—536no—
701Q82—532no—
702#557—532no—
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#554—536no—
712#553—536no—
713#553—536no—
714#553—5312no—
715#552—5312no—
716#552—536no—
717#552—536no—
718#551—5312no—
719#551—5312no—
720#551—5312no—
721#551—5312no—
722#550—532no—
723D4×Q8—532no—
724D4×Q8—536no—
725#548—532no—
726#548—532no—
727#548—5312no—
728#548C2×D5312yescomplemented
729#548C2×D5312yescomplemented
730#547—536no—
731#547—536no—
732#547—536no—
733#546—536no—
734#546—536no—
735#546—5312no—
736#546C2×D5316yescomplemented
737#546C2×D5316yescomplemented
738D42—536no—
739#544—533no—
740#544—533no—
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—5312no—
761#539—536no—
762#539—536no—
763#538—536no—
764#538—536no—
765#538—5312no—
766#537—533no—
767#537—533no—
768#536—533no—
769#536C2×D5313yescomplemented
770#535—533no—
771#535C2×D5313yescomplemented
772#533—536no—
773#533—536no—
774#533—533no—
775#532—536no—
776#532—536no—
777#532C2×D5313yescomplemented
778C2×C4⋊Q8—533no—
779#529—536no—
780#529—536no—
781#529—5312no—
782#529—536no—
783#529—536no—
784#529—536no—
785#529—536no—
786#529—536no—
787#529—536no—
788C2×#126—536no—
789C2×#124—536no—
790C2×#124C2×D5313yescomplemented
791#525—533no—
792#525—533no—
793#525—5312no—
794C2×#123—536no—
795C2×C22⋊Q8—533no—
796C2×C22⋊Q8—536no—
797C2×#121—533no—
798#520—531no—
799#520—531no—
800#520—533no—
801#520—532no—
802#520—533no—
803#520—536no—
804#520—531no—
805#520—531no—
806#520—533no—
807#520—533no—
808#519—533no—
809#519—532no—
810#519—531no—
811#519—531no—
812#518—533no—
813#518—536no—
814#518—533no—
815#518—533no—
816C4×#41—531no—
817C4×#41—533no—
818C4×#41—532no—
819C4×#41—533no—
820C4×#41—536no—
821C4×#41—533no—
822C4×#41—533no—
823C4×#41C2×D5311yescharacteristic
824C2×C4×Q8—533no—
825C2×C4×Q8—532no—
826C2×C4×D4—533no—
827C2×C4×D4—536no—
828C2×#117—533no—
829C2×#117—533no—
830C53#6285711yescharacteristic, complemented, Sylow
8312−1+4—28no—
832H(5,𝔽2)—28no—
833C2×#41—531no—
834C2×#41—533no—
835C2×#41—5312no—
836C2×#41—533no—
837C2×#41—1068no—
838C2×#41C22×D5313yes—
839C2×#41C22×D5313yes—
840C2×#41C22×D5316yes—
841C2×#41C22×D5312yes—
842C2×#41C22×D5311yescharacteristic
843C22×Q8—531no—
844C22×Q8—536no—
845C22×Q8C22×D5313yes—
846C22×Q8C22×D5312yes—
847C22×D4—536no—
848C22×D4—533no—
849C22×D4C22×D5313yes—
850C22×D4C22×D5316yes—
851C23×C4—536no—
852C23×C4—533no—
853C4⋊Q8—536no—
854C4⋊Q8—536no—
855C4⋊Q8—536no—
856C4⋊Q8—533no—
857C4⋊Q8—536no—
858C4⋊Q8—536no—
859C4⋊Q8—536no—
860C4⋊Q8—531no—
861C4⋊Q8C22×D5313yes—
862#127—536no—
863#127C22×D5313yes—
864#126—536no—
865#126—536no—
866#126—536no—
867#126—536no—
868#126—536no—
869#126—5312no—
870#126—5312no—
871#126—5312no—
872#126—532no—
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—536no—
882#125—536no—
883#125—5312no—
884#125—533no—
885#125—533no—
886#124—536no—
887#124—536no—
888#124—5312no—
889#124—536no—
890#124—5312no—
891#124—5312no—
892#124—5312no—
893#124—532no—
894#124—536no—
895#124—536no—
896#124C22×D5313yes—
897#124C22×D5316yes—
898#124C22×D5316yes—
899#124C22×D5316yes—
900#124C22×D5311yescharacteristic
901#123—536no—
902#123—536no—
903#123—536no—
904#123—536no—
905#123—536no—
906#123—536no—
907#123—5312no—
908#123—536no—
909#123—5312no—
910#123—5312no—
911#123—5312no—
912#123—532no—
913#123—5312no—
914#123—536no—
915#123—536no—
916#123—5312no—
917#123C22×D53112yes—
918C22⋊Q8—533no—
919C22⋊Q8—536no—
920C22⋊Q8—536no—
921C22⋊Q8—536no—
922C22⋊Q8—531no—
923C22⋊Q8—533no—
924C22⋊Q8—533no—
925C22⋊Q8—536no—
926C22⋊Q8—536no—
927C22⋊Q8—536no—
928C22⋊Q8—536no—
929C22⋊Q8—5312no—
930C22⋊Q8—536no—
931C22⋊Q8—5312no—
932C22⋊Q8—5312no—
933C22⋊Q8—5312no—
934C22⋊Q8—5312no—
935C22⋊Q8—532no—
936C22⋊Q8—536no—
937C22⋊Q8—536no—
938C22⋊Q8—5312no—
939C22⋊Q8C22×D5316yes—
940C22⋊Q8C22×D5316yes—
941#121—533no—
942#121—536no—
943#121—536no—
944#121—536no—
945#121—531no—
946#121—536no—
947#121—533no—
948#121—533no—
949#121—5312no—
950#121—536no—
951#121—5312no—
952#121—536no—
953#121—536no—
954#121—5312no—
955#121—536no—
956#121—536no—
957#121C22×D5316yes—
958#121C22×D5316yes—
959#121C22×D5316yes—
960#121C22×D5316yes—
961#120—5312no—
962#120—536no—
963#120—536no—
964#120C22×D53112yes—
965C4×Q8—531no—
966C4×Q8—533no—
967C4×Q8—536no—
968C4×Q8—536no—
969C4×Q8—536no—
970C4×Q8—532no—
971C4×Q8—536no—
972C4×Q8—531no—
973C4×Q8—531no—
974C4×Q8—533no—
975C4×Q8—536no—
976C4×Q8—533no—
977C4×Q8—532no—
978C4×Q8—533no—
979C4×Q8—533no—
980C4×Q8—5312no—
981C4×Q8—533no—
982C4×Q8—533no—
983C4×Q8—536no—
984C4×Q8—536no—
985C4×Q8C22×D5311yescharacteristic
986C4×Q8C22×D5311yescharacteristic
987C4×D4—533no—
988C4×D4—536no—
989C4×D4—533no—
990C4×D4—536no—
991C4×D4—536no—
992C4×D4—536no—
993C4×D4—536no—
994C4×D4—536no—
995C4×D4—5312no—
996C4×D4—533no—
997C4×D4—536no—
998C4×D4—531no—
999C4×D4—536no—
1000C4×D4—533no—
1001C4×D4—536no—
1002C4×D4—536no—
1003C4×D4—533no—
1004C4×D4—536no—
1005C4×D4—5312no—
1006C4×D4—5312no—
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—5312no—
1018C4×D4—5312no—
1019C4×D4—533no—
1020C4×D4—533no—
1021C4×D4C22×D5313yes—
1022C4×D4C22×D5313yes—
1023C4×D4C22×D5316yes—
1024C4×D4C22×D5316yes—
1025#117—533no—
1026#117—533no—
1027#117—536no—
1028#117—536no—
1029#117—533no—
1030#117—536no—
1031#117—5312no—
1032#117—536no—
1033#117—533no—
1034#117—533no—
1035#117—5312no—
1036#117—536no—
1037#117—5312no—
1038#117—5312no—
1039#117—533no—
1040#117—531no—
1041#117—533no—
1042#117—533no—
1043#117—533no—
1044#117—533no—
1045#117—533no—
1046#117—533no—
1047#117C22×D5313yes—
1048C2×C4⋊C4—533no—
1049C2×C4⋊C4—533no—
1050C2×C4⋊C4—533no—
1051C2×C4⋊C4—536no—
1052C2×C4⋊C4—533no—
1053C2×C4⋊C4—536no—
1054C2×C4⋊C4—536no—
1055C2×C4⋊C4—536no—
1056C2×C4⋊C4—536no—
1057C2×C4⋊C4—533no—
1058C2×C4⋊C4—533no—
1059C2×C22⋊C4—536no—
1060C2×C22⋊C4—5312no—
1061C2×C22⋊C4—536no—
1062C2×C22⋊C4—533no—
1063C2×C22⋊C4—533no—
1064C2×C22⋊C4—536no—
1065C2×C22⋊C4—536no—
1066C2×C22⋊C4C22×D5316yes—
1067C2×C22⋊C4C22×D5316yes—
1068C2×C42—533no—
1069C2×C42—536no—
1070C2×C42—536no—
1071C2×C42—536no—
1072C2×C42—536no—
1073C2×C42C22×D5313yes—
1074C24—533no—
1075C24C23×D5316yes—
1076#41—28no—
1077#41—224no—
1078#41—212no—
1079#41—212no—
1080#41—1064no—
1081#41—10612no—
1082#41—10612no—
1083#41—42412no—
1084#41#1171994718yescomplemented
1085C2×Q8—28no—
1086C2×Q8—212no—
1087C2×Q8—533no—
1088C2×Q8—532no—
1089C2×Q8—536no—
1090C2×Q8—5312no—
1091C2×Q8—1064no—
1092C2×Q8—4246no—
1093C2×Q8C23×D5313yes—
1094C2×Q8C23×D5311yescharacteristic
1095C2×Q8C23×D5316yes—
1096C2×Q8C23×D5311yescharacteristic
1097C2×D4—224no—
1098C2×D4—212no—
1099C2×D4—536no—
1100C2×D4—532no—
1101C2×D4—536no—
1102C2×D4—536no—
1103C2×D4—536no—
1104C2×D4—5312no—
1105C2×D4—533no—
1106C2×D4—10612no—
1107C2×D4—4246no—
1108C2×D4C23×D5316yes—
1109C2×D4C23×D5316yes—
1110C2×D4C23×D5313yes—
1111C2×D4C23×D5311yescharacteristic
1112C2×D4C23×D5316yes—
1113C2×D4C23×D5316yes—
1114C2×D4C23×D5316yes—
1115C2×D4C23×D5313yes—
1116C22×C4—533no—
1117C22×C4—533no—
1118C22×C4—532no—
1119C22×C4—536no—
1120C22×C4—533no—
1121C22×C4—536no—
1122C22×C4—536no—
1123C22×C4—536no—
1124C22×C4—536no—
1125C22×C4—5312no—
1126C22×C4—533no—
1127C22×C4—533no—
1128C22×C4—533no—
1129C22×C4—531no—
1130C22×C4—536no—
1131C22×C4—536no—
1132C22×C4—10612no—
1133C22×C4—4246no—
1134C22×C4C23×D5316yes—
1135C22×C4C23×D5316yes—
1136C22×C4C23×D5316yes—
1137C22×C4C23×D5313yes—
1138C22×C4C23×D5313yes—
1139C22×C4C23×D5313yes—
1140C4⋊C4—533no—
1141C4⋊C4—531no—
1142C4⋊C4—533no—
1143C4⋊C4—531no—
1144C4⋊C4—533no—
1145C4⋊C4—536no—
1146C4⋊C4—533no—
1147C4⋊C4—536no—
1148C4⋊C4—536no—
1149C4⋊C4—533no—
1150C4⋊C4—536no—
1151C4⋊C4—5312no—
1152C4⋊C4—536no—
1153C4⋊C4—536no—
1154C4⋊C4—533no—
1155C4⋊C4—533no—
1156C4⋊C4—533no—
1157C4⋊C4—533no—
1158C4⋊C4—533no—
1159C4⋊C4—5312no—
1160C4⋊C4—5312no—
1161C4⋊C4—531no—
1162C4⋊C4—532no—
1163C4⋊C4—531no—
1164C4⋊C4—536no—
1165C4⋊C4—536no—
1166C4⋊C4—536no—
1167C4⋊C4—536no—
1168C4⋊C4—532no—
1169C4⋊C4—536no—
1170C4⋊C4—536no—
1171C4⋊C4—536no—
1172C4⋊C4—532no—
1173C4⋊C4C23×D5313yes—
1174C4⋊C4C23×D5313yes—
1175C4⋊C4C23×D5316yes—
1176C4⋊C4C23×D5316yes—
1177C22⋊C4—536no—
1178C22⋊C4—536no—
1179C22⋊C4—536no—
1180C22⋊C4—536no—
1181C22⋊C4—5312no—
1182C22⋊C4—536no—
1183C22⋊C4—5312no—
1184C22⋊C4—536no—
1185C22⋊C4—532no—
1186C22⋊C4—536no—
1187C22⋊C4—536no—
1188C22⋊C4—536no—
1189C22⋊C4—532no—
1190C22⋊C4—533no—
1191C22⋊C4—533no—
1192C22⋊C4—531no—
1193C22⋊C4—531no—
1194C22⋊C4—536no—
1195C22⋊C4—533no—
1196C22⋊C4—533no—
1197C22⋊C4—533no—
1198C22⋊C4—533no—
1199C22⋊C4—5312no—
1200C22⋊C4—536no—
1201C22⋊C4—532no—
1202C22⋊C4—536no—
1203C22⋊C4C23×D5316yes—
1204C22⋊C4C23×D5316yes—
1205C22⋊C4C23×D5316yes—
1206C22⋊C4C23×D53112yes—
1207C22⋊C4C23×D53112yes—
1208C22⋊C4C23×D5312yes—
1209C22⋊C4C23×D5312yes—
1210C42—533no—
1211C42—533no—
1212C42—531no—
1213C42—533no—
1214C42—532no—
1215C42—536no—
1216C42—536no—
1217C42—536no—
1218C42—536no—
1219C42—536no—
1220C42—5312no—
1221C42—536no—
1222C42—536no—
1223C42C23×D5313yes—
1224C42C23×D5311yescharacteristic
1225C42C23×D5313yes—
1226C42C23×D5313yes—
1227C23—212no—
1228C23—46no—
1229C23—46no—
1230C23—531no—
1231C23—533no—
1232C23—1066no—
1233C23—2123no—
1234C23—2123no—
1235C23C24×D5316yes—
1236C23C24×D5312yes—
1237C23C24×D5313yes—
1238Q8—212no—
1239Q8—26no—
1240Q8—22no—
1241Q8—1066no—
1242Q8—2122no—
1243Q8—2126no—
1244Q8—21212no—
1245Q8C2×#1171994714yes—
1246D4—212no—
1247D4—212no—
1248D4—212no—
1249D4—26no—
1250D4—22no—
1251D4—46no—
1252D4—46no—
1253D4—10612no—
1254D4—1066no—
1255D4—2122no—
1256D4—2126no—
1257D4—2126no—
1258D4—21212no—
1259D4—2126no—
1260D4C2×#11719947112yes—
1261C2×C4—212no—
1262C2×C4—212no—
1263C2×C4—212no—
1264C2×C4—43no—
1265C2×C4—43no—
1266C2×C4—533no—
1267C2×C4—531no—
1268C2×C4—532no—
1269C2×C4—533no—
1270C2×C4—531no—
1271C2×C4—532no—
1272C2×C4—533no—
1273C2×C4—536no—
1274C2×C4—536no—
1275C2×C4—531no—
1276C2×C4—1066no—
1277C2×C4—1062no—
1278C2×C4—1066no—
1279C2×C4—1066no—
1280C2×C4—1066no—
1281C2×C4—2126no—
1282C2×C4—2126no—
1283C2×C4—2123no—
1284C2×C4—2126no—
1285C2×C4—2122no—
1286C2×C4—2123no—
1287C2×C4—2126no—
1288C2×C4—2126no—
1289C2×C4—21212no—
1290C2×C4—2126no—
1291C2×C4—2126no—
1292C2×C4C2×#11719947112yes—
1293C2×C4C24×D5316yes—
1294C2×C4C24×D5312yes—
1295C2×C4C24×D5313yes—
1296C2×C4C24×D5313yes—
1297C2×C4C24×D5311yescharacteristic
1298C2×C4C24×D5311yescharacteristic
1299C2×C4C24×D5313yes—
1300C2×C4C24×D5311yescharacteristic
1301C22—23no—
1302C22—23no—
1303C22—22no—
1304C22—26no—
1305C22—22no—
1306C22—26no—
1307C22—22no—
1308C22—26no—
1309C22—812no—
1310C22—1061no—
1311C22—1063no—
1312C22—1063no—
1313C22—1061no—
1314C22—1063no—
1315C22—1061no—
1316C22—4246no—
1317C22C22×#1171994716yes—
1318C22C25×D5311yescharacteristic
1319C4—22no—
1320C4—26no—
1321C4—21no—
1322C4—23no—
1323C4—21no—
1324C4—23no—
1325C4—1061no—
1326C4—1063no—
1327C4—1063no—
1328C4—1061no—
1329C4—1066no—
1330C4—1066no—
1331C4—1063no—
1332C4—1061no—
1333C4—1062no—
1334C4—1062no—
1335C4C22×#1171994716yes—
1336C4C22×#1171994712yes—
1337C2—26no—
1338C2—46no—
1339C2—42no—
1340C2—2121no—
1341C2—2123no—
1342C2C23×#1171994711yescharacteristic
1343C2#2028952611yescharacteristic
1344C2#2028952811yescharacteristic
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3500C2
hypercenter#3500D53
hypocenterC53#62857
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3500

Complements

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

NH ≅ G/Ntype
1. #20288825C2semidirect
2. #20288791C2semidirect
3. #20288768C2semidirect
4. #20288751C2semidirect
5. #20288723C2semidirect
6. #20288697C2semidirect
7. #20288663C2semidirect
8. #20288656C2semidirect
9. #20288622C2semidirect
10. #20288609C2semidirect
11. #20288534C2semidirect
12. #20288464C2semidirect
13. #20288447C2semidirect
14. #20288388C2semidirect
15. #20288377C2semidirect
16. #20288139C2semidirect
17. #20288128C2semidirect
18. #20288104C2semidirect
19. C2×#16811242C2semidirect
20. 2−1+4×Dic53C2semidirect
21. H(5,𝔽2)×Dic53C2semidirect
22. #20287914C2semidirect
23. C53×#3500C2semidirect
25. #16811355C22semidirect
26. #16811355C22semidirect
27. Q8×Dic106C22semidirect
28. #16811352C22semidirect
29. #16811344C22semidirect
30. #16811343C22semidirect
31. #16811342C22semidirect
32. #16811342C22semidirect
33. #16811338C22semidirect
34. #16811337C22semidirect
35. #16811331C22semidirect
36. #16811330C22semidirect
37. #16811330C22semidirect
38. #16811325C22semidirect
39. #16811325C22semidirect
40. #16811320C22semidirect
41. #16811315C22semidirect
42. #16811310C22semidirect
43. #16811307C22semidirect
44. #16811304C22semidirect
45. #16811299C22semidirect
46. #16811299C22semidirect
47. #16811296C22semidirect
49. D4×Dic106C22semidirect
50. Q8×C22⋊D53C22semidirect
51. #16811284C22semidirect
53. #16811279C22semidirect
54. #16811277C22semidirect
55. #16811273C22semidirect
56. #16811272C22semidirect
58. #16811261C22semidirect
59. #16811260C22semidirect
61. #16811251C22semidirect
62. #16811251C22semidirect
63. #16811246C22semidirect
64. #16811242C22semidirect
65. #16811242C22semidirect
66. #16811242C22semidirect
67. #16811242C22semidirect
68. #16811242C22semidirect
69. #16811242C22semidirect
70. #16811242C22semidirect
71. #16811242C22semidirect
72. #16811242C22semidirect
73. #16811242C22semidirect
74. #16811242C22semidirect
75. #16811240C22semidirect
76. #16811234C22semidirect
77. #16811234C22semidirect
78. #16811233C22semidirect
79. #16811227C22semidirect
80. #16811227C22semidirect
81. #16811226C22semidirect
82. #16811218C22semidirect
83. #16811218C22semidirect
84. #16811217C22semidirect
85. #16811210C22semidirect
86. #16811210C22semidirect
87. #16811208C22semidirect
89. #16811201C22semidirect
90. #16811197C22semidirect
92. #16811180C22semidirect
93. #16811178C22semidirect
94. #16811175C22semidirect
95. #16811171C22semidirect
96. #16811168C22semidirect
97. C2×#13133217C22semidirect
98. #16811159C22semidirect
99. #16811154C22semidirect
100. #16811153C22semidirect
101. #16811153C22semidirect
102. #16811153C22semidirect
103. #16811153C22semidirect
104. #16811152C22semidirect
105. #16811152C22semidirect
106. #16811150C22semidirect
107. C2×#13133210C22semidirect
108. C2×#13133203C22semidirect
110. #16811130C22semidirect
111. #16811129C22semidirect
112. C2×#13133201C22semidirect
113. C2×#13133194C22semidirect
114. C2×#13133193C22semidirect
118. #16811106C22semidirect
119. #16811106C22semidirect
120. #16811106C22semidirect
121. #16811106C22semidirect
122. #16811105C22semidirect
123. #16811105C22semidirect
124. #16811102C22semidirect
125. #16811102C22semidirect
126. #16811101C22semidirect
127. #16811101C22semidirect
128. #16811099C22semidirect
129. #16811099C22semidirect
130. #16811098C22semidirect
131. #16811098C22semidirect
132. #16811095C22semidirect
133. #16811095C22semidirect
135. #41×Dic53C22semidirect
136. #41×Dic53C22semidirect
137. #41×Dic53C22semidirect
138. #41×Dic53C22semidirect
139. C4×#11719945C22semidirect
140. #16811091C22semidirect
141. C2×Q8×Dic53C22semidirect
142. C2×Q8×Dic53C22semidirect
143. C2×D4×Dic53C22semidirect
144. C2×D4×Dic53C22semidirect
145. C2×#13133174C22semidirect
146. #117×D53C22semidirect
149. C53×#548C22semidirect
150. C53×#548C22semidirect
151. C53×#546C22semidirect
152. C53×#546C22semidirect
153. C53×#536C22semidirect
154. C53×#535C22semidirect
155. C53×#532C22semidirect
156. C2×#124×C53C22semidirect
407. #41×C53#41semidirect
676. #3500D53semidirect
728. #548C2×D53semidirect
729. #548C2×D53semidirect
736. #546C2×D53semidirect
737. #546C2×D53semidirect
769. #536C2×D53semidirect
771. #535C2×D53semidirect
777. #532C2×D53semidirect
790. C2×#124C2×D53semidirect
830. C53#62857semidirect
1084. #41#11719947semidirect

Maximal subgroups

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

subgroupindex
#202888252
#202887912
#202887682
#202887512
#202887232
#202886972
#202886632
#202886562
#202886222
#202886092
#202885342
#202884642
#202884472
#202883882
#202883772
#202881392
#202881282
#202881042
C2×#168112422
2−1+4×Dic532
H(5,𝔽2)×Dic532
#202879142
C53×#35002
#6285753