Finite Group Databasebeta

← #28292896

Subgroups — #28292896

Order 13568.

6636 conjugacy classes of subgroups.

The subgroup lattice has 1316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289372C218yesmaximal, complemented
2#20289341C214yesmaximal, complemented
3#20289257C214yesmaximal, complemented
4#20289220C212yesmaximal, complemented
5#20289139C212yesmaximal, complemented
6#20288964C211yesmaximal, characteristic, complemented
7#20288937C212yesmaximal, complemented
8#20288699C214yesmaximal, complemented
9#20288686C214yesmaximal, complemented
10#20288667C214yesmaximal, complemented
11#20288640C214yesmaximal, complemented
12#20288640C218yesmaximal, complemented
13#20288634C212yesmaximal, complemented
14#20288610C212yesmaximal, complemented
15#20288430C214yesmaximal, complemented
16#20288412C214yesmaximal, complemented
17#20288007C211yesmaximal, characteristic, complemented
18C2×#16811154C212yesmaximal, complemented
19C53×#3537C211yesmaximal, characteristic, complemented
20#16811376C2218yescomplemented
21#16811376C2214yescomplemented
22#16811373C2214yescomplemented
23#16811368C2218yescomplemented
24#16811362C2214yescomplemented
25#16811359C2218yescomplemented
26#16811359C2214yescomplemented
27#16811350C2214yescomplemented
28#16811343C2214yescomplemented
29#16811342C2218yescomplemented
30#16811340C2218yescomplemented
31#16811337C2218yescomplemented
32#16811335C2214yescomplemented
33#16811332C2218yescomplemented
34#16811332C2214yescomplemented
35#16811328C2214yescomplemented
36#16811320C2218yescomplemented
37#16811320C2214yescomplemented
38#16811318C2218yescomplemented
39#16811316C2218yescomplemented
40#16811316C2218yescomplemented
41#16811316C2218yescomplemented
42#16811313C2218yescomplemented
43#16811313C2214yescomplemented
44#16811312C2214yescomplemented
45#16811310C2218yescomplemented
46#16811310C2218yescomplemented
47#16811310C2218yescomplemented
48#16811310C2218yescomplemented
49#16811309C2218yescomplemented
50#16811304C2218yescomplemented
51#16811304C2218yescomplemented
52#16811304C2218yescomplemented
53#16811304C2218yescomplemented
54#16811304C2218yescomplemented
55#16811304C2218yescomplemented
56#16811304C2214yescomplemented
57#16811304C2214yescomplemented
58D4×Dic106C2214yescomplemented
59#16811279C2214yescomplemented
60#16811279C2214yescomplemented
61#16811273C2214yescomplemented
62#16811273C2218yescomplemented
63#16811267C2214yescomplemented
64#16811267C2218yescomplemented
65#16811267C2218yescomplemented
66#16811267C2214yescomplemented
67#16811267C2218yescomplemented
68#16811252C2214yescomplemented
69#16811249C2214yescomplemented
70#16811241C2218yescomplemented
71#16811240C2218yescomplemented
72#16811240C2218yescomplemented
73#16811240C2214yescomplemented
74#16811240C2214yescomplemented
75#16811236C2212yescomplemented
76#16811235C2212yescomplemented
77#16811230C2218yescomplemented
78#16811230C2218yescomplemented
79#16811227C2218yescomplemented
80#16811227C2212yescomplemented
81#16811218C2218yescomplemented
82#16811218C2214yescomplemented
83#16811218C2218yescomplemented
84#16811218C2218yescomplemented
85#16811218C2214yescomplemented
86#16811216C2218yescomplemented
87#16811211C2214yescomplemented
88#16811208C2218yescomplemented
89#16811208C2218yescomplemented
90#16811208C2218yescomplemented
91#16811208C2218yescomplemented
92#16811202C2214yescomplemented
93#16811200C2214yescomplemented
94#16811194C2212yescomplemented
95#16811176C2211yescharacteristic, complemented
96#16811176C2212yescomplemented
97#16811175C2212yescomplemented
98#16811171C2212yescomplemented
99#16811169C2211yescharacteristic, complemented
100#16811168C2212yescomplemented
101#16811159C2212yescomplemented
102#16811155C2214yescomplemented
103#16811154C2212yescomplemented
104#16811154C2214yescomplemented
105#16811154C2214yescomplemented
106#16811154C2214yescomplemented
107#16811154C2214yescomplemented
108#16811154C2214yescomplemented
109#16811154C2214yescomplemented
110#16811154C2218yescomplemented
111#16811154C2214yescomplemented
112#16811154C2214yescomplemented
113#16811154C2214yescomplemented
114#16811153C2214yescomplemented
115#16811153C2218yescomplemented
116#16811150C2214yescomplemented
117C2×#13133210C2214yescomplemented
118C2×#13133208C2212yescomplemented
119#125×D53C2212yescomplemented
120C2×#13133204C2212yescomplemented
121C2×#13133204C2212yescomplemented
122#16811134C2211yescharacteristic, complemented
123#16811129C2214yescomplemented
124#16811129C2218yescomplemented
125C2×#13133198C2218yescomplemented
126C2×#13133198C2214yescomplemented
127C2×#13133196C2212yescomplemented
128#16811102C2214yescomplemented
129#16811102C2218yescomplemented
130#16811100C2212yescomplemented
131#16811098C2212yescomplemented
132#16811098C2218yescomplemented
133#41×Dic53C2211yescharacteristic, complemented
134#16811091C2211yescharacteristic, complemented
135C4×#11719947C2214yescomplemented
136C2×#13133182C2212yescomplemented
137C2×D4×Dic53C2214yescomplemented
138C2×D4×Dic53C2212yescomplemented
139C2×#13133173C2214yescomplemented
140C22×C4×Dic53C2211yescharacteristic, complemented
141C53×#560C2214yes—
142C53×#553C2214yes—
143D42×C53C2214yes—
144D42×C53C2214yes—
145C53×#540C2212yes—
146C53×#538C2214yes—
147C53×#535C2212yes—
148C53×#534C2214yes—
149C53×#525C2211yescharacteristic
150C2×#121×C53C2212yes—
151C2×#11719945C2311yescharacteristic
152C2×#11719947C2314yes—
153C2×#11719947C2318yes—
154C2×#11719947C2314yes—
155C22×Dic106C2312yes—
156C22×Dic106C2312yes—
157C23×Dic53C2312yes—
158C23×Dic53C2314yes—
159#13133217C2312yes—
160#13133216C2314yes—
161#13133216C2318yes—
162#13133216C2318yes—
163#13133216C2312yes—
164#13133215C2314yes—
165#13133215C2311yescharacteristic
166#13133213C2311yescharacteristic
167#13133212C2318yes—
168#13133212C2314yes—
169#13133210C2314yes—
170#13133210C2318yes—
171#13133210C2318yes—
172#13133210C2318yes—
173#13133210C2318yes—
174#13133210C2318yes—
175#13133210C2318yes—
176#13133210C2318yes—
177#13133210C2318yes—
178#13133210C2318yes—
179#13133210C2318yes—
180#13133210C2318yes—
181#13133210C2318yes—
182#13133210C2318yes—
183#13133210C2318yes—
184#13133209C2318yes—
185#13133209C2312yes—
186#13133208C2314yes—
187#13133208C2312yes—
188#13133208C2318yes—
189#13133208C2314yes—
190#13133208C2314yes—
191#13133208C2314yes—
192#13133207C2318yes—
193#13133207C2318yes—
194#13133207C2318yes—
195#13133207C2318yes—
196#13133207C2318yes—
197#13133207C2318yes—
198#13133207C2314yes—
199#13133206C2311yescharacteristic
200#13133204C2314yes—
201#13133204C2314yes—
202#13133204C2318yes—
203#13133204C2318yes—
204#13133204C2318yes—
205#13133204C2311yescharacteristic
206#13133204C2314yes—
207#13133204C2318yes—
208#13133204C2314yes—
209#13133204C2314yes—
210#13133204C2314yes—
211#13133203C2318yes—
212#13133203C2318yes—
213#13133203C2314yes—
214#13133201C2314yes—
215#13133200C2312yes—
216#13133199C2318yes—
217#13133199C2318yes—
218#13133199C2318yes—
219#13133198C2318yes—
220#13133198C2318yes—
221#13133198C2318yes—
222#13133198C2318yes—
223#13133198C2318yes—
224#13133198C2318yes—
225#13133198C2318yes—
226#13133198C2318yes—
227#13133198C2314yes—
228#13133198C2314yes—
229#13133198C2318yes—
230#13133198C2318yes—
231#13133198C2318yes—
232#13133198C2318yes—
233#13133198C2318yes—
234#13133198C2314yes—
235#13133198C2318yes—
236#13133198C2318yes—
237#13133197C2314yes—
238#13133196C2314yes—
239#13133196C2314yes—
240#13133196C2318yes—
241#13133196C2318yes—
242#13133196C2318yes—
243#13133196C2314yes—
244#13133196C2314yes—
245#13133196C2314yes—
246#13133196C2312yes—
247#13133195C2318yes—
248#13133194C2318yes—
249#13133194C2318yes—
250#13133194C2318yes—
251#13133194C2318yes—
252#13133194C2318yes—
253#13133194C2318yes—
254#13133194C2318yes—
255#13133194C2314yes—
256#13133194C2318yes—
257#13133194C2318yes—
258#13133194C2318yes—
259#13133194C2318yes—
260#13133194C2314yes—
261#13133191C2312yes—
262#13133190C2318yes—
263#13133189C2318yes—
264#13133189C2314yes—
265#13133189C2318yes—
266#13133189C2318yes—
267#13133189C2318yes—
268#13133189C2318yes—
269#13133189C2318yes—
270#13133189C2314yes—
271#13133188C2314yes—
272#13133188C2318yes—
273#13133188C2318yes—
274#13133188C2318yes—
275#13133186C2312yes—
276#13133186C2318yes—
277#13133186C2318yes—
278Q8×Dic53C2312yes—
279C4×Dic106C2314yes—
280C4×Dic106C2318yes—
281C4×Dic106C2318yes—
282C4×Dic106C2314yes—
283#13133182C2314yes—
284#13133182C2314yes—
285#13133182C2312yes—
286#13133182C2314yes—
287#13133182C2318yes—
288#13133182C2314yes—
289#13133182C2314yes—
290#13133182C2314yes—
291D4×Dic53C2314yes—
292D4×Dic53C2318yes—
293D4×Dic53C2318yes—
294D4×Dic53C2318yes—
295D4×Dic53C2314yes—
296D4×Dic53C2318yes—
297D4×Dic53C2318yes—
298D4×Dic53C2312yes—
299D4×Dic53C2318yes—
300D4×Dic53C2314yes—
301D4×Dic53C2314yes—
302D4×Dic53C2318yes—
303D4×Dic53C2318yes—
304D4×Dic53C2318yes—
305D4×Dic53C2318yes—
306D4×Dic53C2314yes—
307D4×Dic53C2314yes—
308D4×Dic53C2318yes—
309D4×Dic53C2314yes—
310#13133179C2312yes—
311C4×C22⋊D53C2314yes—
312C4×C22⋊D53C2318yes—
313C4×C22⋊D53C2314yes—
314C4×C22⋊D53C2318yes—
315C4×C22⋊D53C2318yes—
316#13133177C2318yes—
317#13133177C2314yes—
318#13133177C2318yes—
319#13133177C2314yes—
320#13133177C2314yes—
321#13133176C2318yes—
322#13133176C2318yes—
323#13133176C2312yes—
324#13133176C2312yes—
325#13133176C2311yescharacteristic
326#13133175C2314yes—
327#13133174C2318yes—
328#13133174C2312yes—
329#13133173C2314yes—
330#13133173C2318yes—
331#13133173C2318yes—
332#13133173C2314yes—
333#13133173C2318yes—
334#13133173C2318yes—
335#13133173C2318yes—
336#13133173C2318yes—
337#13133173C2318yes—
338#13133173C2318yes—
339C2×C4⋊Dic53C2312yes—
340C2×C4⋊Dic53C2314yes—
341C2×#11719919C2318yes—
342C2×#11719919C2318yes—
343C2×#11719919C2314yes—
344C2×#11719919C2314yes—
345C2×#11719919C2314yes—
346C4⋊C4×D53C2318yes—
347C4⋊C4×D53C2314yes—
348C2×C22⋊Dic53C2314yes—
349C2×C22⋊Dic53C2314yes—
350C2×C22⋊Dic53C2314yes—
351C2×C22⋊Dic53C2318yes—
352C2×C22⋊Dic53C2318yes—
353C2×C22⋊Dic53C2318yes—
354C2×C22⋊Dic53C2318yes—
355C2×C22⋊Dic53C2314yes—
356C2×C4×Dic53C2312yes—
357C2×C4×Dic53C2312yes—
358C2×C4×Dic53C2312yes—
359C2×C4×Dic53C2311yescharacteristic
360C2×C4×Dic53C2312yes—
361C2×C4×Dic53C2312yes—
362C2×C4×Dic53C2311yescharacteristic
363C2×C4×Dic53C2314yes—
364C2×C4×Dic53C2312yes—
365C42×D53C2312yes—
366C2×#41×C53C2311yescharacteristic
367C22×D4×C53C2314yes—
368C22×D4×C53C2312yes—
369C22×D4×C53C2318yes—
370C22×D4×C53C2312yes—
371C23×C4×C53C2311yescharacteristic
372#127×C53C2314yes—
373#127×C53C2312yes—
374#126×C53C2318yes—
375#125×C53C2312yes—
376#124×C53C2314yes—
377#123×C53C2312yes—
378#123×C53C2318yes—
379#123×C53C2318yes—
380C22⋊Q8×C53C2312yes—
381#121×C53C2314yes—
382#121×C53C2318yes—
383#121×C53C2314yes—
384#121×C53C2314yes—
385#121×C53C2314yes—
386#121×C53C2314yes—
387#121×C53C2312yes—
388#121×C53C2318yes—
389#121×C53C2318yes—
390#120×C53C2312yes—
391#120×C53C2314yes—
392#120×C53C2318yes—
393#120×C53C2314yes—
394#120×C53C2318yes—
395C4×D4×C53C2314yes—
396C4×D4×C53C2318yes—
397C4×D4×C53C2314yes—
398#117×C53C2311yescharacteristic
399#117×C53C2312yes—
400C2×C4⋊C4×C53C2312yes—
401C2×C22⋊C4×C53C2314yes—
402C24×C53C2411yescharacteristic
403C24×C53C2414yes—
404C24×C53C2414yes—
405#41×C53—42no—
406C2×Q8×C53C2411yescharacteristic
407C2×D4×C53—44no—
408C2×D4×C53—44no—
409C2×D4×C53—48no—
410C2×D4×C53—416no—
411C2×D4×C53C2414yes—
412C2×D4×C53C2418yes—
413C2×D4×C53C2414yes—
414C2×D4×C53C2411yescharacteristic
415C2×D4×C53C2412yes—
416C2×D4×C53C2414yes—
417C2×D4×C53C2418yes—
418C2×D4×C53C2418yes—
419C2×D4×C53C2414yes—
420C2×D4×C53C2418yes—
421C22×C4×C53—42no—
422C22×C4×C53C2412yes—
423C22×C4×C53C2412yes—
424C22×C4×C53C2411yescharacteristic
425C22×C4×C53C2412yes—
426C22×C4×C53C2414yes—
427C22×C4×C53C2418yes—
428C22×C4×C53C2411yescharacteristic
429C2×C22⋊D53C2414yes—
430C2×C22⋊D53C2412yes—
431C2×C22⋊D53C2418yes—
432C2×C22⋊D53C2418yes—
433C2×C22⋊D53C2414yes—
434C22×Dic53—44no—
435C22×Dic53—48no—
436C22×Dic53C2412yes—
437C22×Dic53C2412yes—
438C22×Dic53C2414yes—
439C22×Dic53C2412yes—
440C22×Dic53C2412yes—
441C22×Dic53C2412yes—
442C22×Dic53C2412yes—
443C22×Dic53C2414yes—
444C22×Dic53C2414yes—
445C22×Dic53C2418yes—
446C22×Dic53C2418yes—
447C22×Dic53C2414yes—
448C22×Dic53C2418yes—
449C22×Dic53C2418yes—
450#11719947—48no—
451#11719947—48no—
452#11719947—416no—
453#11719945—42no—
454C2×D212C2411yescharacteristic
455C2×C4×D53C2412yes—
456C2×C4×D53C2414yes—
457C2×C4×D53C2418yes—
458C2×Dic106—44no—
459C2×Dic106—44no—
460C2×Dic106C2414yes—
461C2×Dic106C2411yescharacteristic
462C2×Dic106C2414yes—
463C2×Dic106C2418yes—
464C2×Dic106C2414yes—
465C2×Dic106C2414yes—
466C4⋊C4×C53C2414yes—
467C4⋊C4×C53C2414yes—
468C4⋊C4×C53C2412yes—
469C4⋊C4×C53C2414yes—
470C4⋊C4×C53C2418yes—
471C22⋊C4×C53C2418yes—
472C22⋊C4×C53C2418yes—
473C22⋊C4×C53C2414yes—
474C22⋊C4×C53C2412yes—
475C22⋊C4×C53C2414yes—
476C22⋊C4×C53C2418yes—
477C22⋊C4×C53C2418yes—
478C22⋊C4×C53C2414yes—
479C42×C53C2412yes—
480C42×C53C2414yes—
481C22⋊Dic53C2418yes—
482C22⋊Dic53C2414yes—
483C22⋊Dic53C2418yes—
484C22⋊Dic53C2418yes—
485C22⋊Dic53C2414yes—
486C22⋊Dic53C2418yes—
487C22⋊Dic53C2418yes—
488C22⋊Dic53C2414yes—
489C22⋊Dic53C2418yes—
490C22⋊Dic53C2414yes—
491C22⋊Dic53C2418yes—
492C22⋊Dic53C2418yes—
493C22⋊Dic53C2418yes—
494C22⋊Dic53C2418yes—
495C22⋊Dic53C2418yes—
496C22⋊Dic53C2418yes—
497C22⋊Dic53C2418yes—
498C22⋊Dic53C2412yes—
499#11719921C2414yes—
500#11719921C2414yes—
501#11719921C2418yes—
502#11719921C2414yes—
503C4⋊Dic53C2414yes—
504C4⋊Dic53C2418yes—
505C4⋊Dic53C2418yes—
506C4⋊Dic53C2414yes—
507C4⋊Dic53C2414yes—
508C4⋊Dic53C2414yes—
509C4⋊Dic53C2418yes—
510C4⋊Dic53C2418yes—
511C4⋊Dic53C2412yes—
512#11719919C2418yes—
513#11719919C2418yes—
514#11719919C2418yes—
515#11719919C2414yes—
516#11719919C2418yes—
517#11719919C2414yes—
518#11719919C2418yes—
519#11719919C2418yes—
520#11719919C2418yes—
521#11719919C2418yes—
522#11719919C2418yes—
523#11719919C2418yes—
524#11719919C2418yes—
525#11719919C2414yes—
526#11719919C2414yes—
527#11719919C2414yes—
528#11719919C2418yes—
529C4×Dic53C2411yescharacteristic
530C4×Dic53C2414yes—
531C4×Dic53C2411yescharacteristic
532C4×Dic53C2412yes—
533C4×Dic53C2412yes—
534C4×Dic53C2412yes—
535C4×Dic53C2411yescharacteristic
536C4×Dic53C2412yes—
537C4×Dic53C2412yes—
538C4×Dic53C2412yes—
539C4×Dic53C2411yescharacteristic
540C4×Dic53C2418yes—
541C4×Dic53C2414yes—
542C4×Dic53C2418yes—
543C4×Dic53C2412yes—
544C4×Dic53C2414yes—
545C4×Dic53C2418yes—
546C4×Dic53C2418yes—
547C23×C53—24no—
548C23×C53—28no—
549C23×C53—41no—
550C23×C53—44no—
551C23×C53—44no—
552C23×C53—44no—
553C23×C53—48no—
554C23×C53C2511yescharacteristic
555C23×C53C2512yes—
556C23×C53C2518yes—
557C23×C53C2512yes—
558C22×D53C2512yes—
559Q8×C53—41no—
560D4×C53—216no—
561D4×C53—28no—
562D4×C53—28no—
563D4×C53—44no—
564D4×C53—44no—
565D4×C53—48no—
566D4×C53—48no—
567D4×C53—48no—
568D4×C53—42no—
569D4×C53—41no—
570C2×C4×C53—24no—
571C2×C4×C53—24no—
572C2×C4×C53—22no—
573C2×C4×C53—41no—
574C2×C4×C53—42no—
575C2×C4×C53—44no—
576C2×C4×C53—48no—
577C2×C4×C53C2512yes—
578C2×C4×C53C2512yes—
579C2×C4×C53C2518yes—
580C2×C4×C53C2514yes—
581C2×C4×C53C2511yescharacteristic
582C2×C4×C53C2511yescharacteristic
583C22⋊D53—28no—
584C22⋊D53—42no—
585C22⋊D53—48no—
586C22⋊D53—44no—
587C22⋊D53—48no—
588C2×Dic53—24no—
589C2×Dic53—28no—
590C2×Dic53—24no—
591C2×Dic53—44no—
592C2×Dic53—44no—
593C2×Dic53—48no—
594C2×Dic53—48no—
595C2×Dic53—44no—
596C2×Dic53—42no—
597C2×Dic53—42no—
598C2×Dic53—48no—
599C2×Dic53—48no—
600C2×Dic53—42no—
601C2×Dic53—42no—
602C2×Dic53C2518yes—
603C2×Dic53C2514yes—
604C2×Dic53C2512yes—
605C2×Dic53C2512yes—
606C2×Dic53C2518yes—
607C2×Dic53C2512yes—
608C2×Dic53C2512yes—
609C2×Dic53C2512yes—
610D212—41no—
611C4×D53—24no—
612C4×D53—48no—
613C4×D53—44no—
614Dic106—28no—
615Dic106—44no—
616Dic106—44no—
617Dic106—41no—
618Dic106—44no—
619Dic106—48no—
620#62829—531nomaximal, Sylow
621C22×C53—22no—
622C22×C53—22no—
623C22×C53—22no—
624C22×C53—28no—
625C22×C53—22no—
626C22×C53—28no—
627C22×C53—28no—
628C22×C53—24no—
629C22×C53—21no—
630C22×C53—44no—
631C22×C53—88no—
632C22×C53—164no—
633C22×C53#58514yes—
634C22×C53C2611yescharacteristic
635C2×D53—22no—
636C2×D53—24no—
637C4×C53—22no—
638C4×C53—22no—
639C4×C53—24no—
640C4×C53—28no—
641C4×C53—21no—
642C4×C53#58512yes—
643Dic53—28no—
644Dic53—24no—
645Dic53—22no—
646Dic53—22no—
647Dic53—28no—
648Dic53—22no—
649Dic53—22no—
650Dic53—22no—
651#3566—538no—
652#3564—534no—
653#3560—534no—
654#3557—532no—
655#3551—532no—
656#3538—531no—
657#3537D5311yescharacteristic, complemented
658#3536—532no—
659#3516—534no—
660#3515—534no—
661#3514—534no—
662#3513—538no—
663#3513—534no—
664#3512—532no—
665#3510—532no—
666#3493—534no—
667#3491—534no—
668#3444—531no—
669C2×#529—532no—
670C2×C53—24no—
671C2×C53—41no—
672C2×C53—48no—
673C2×C53—42no—
674C2×C53C2×#58512yes—
675C2×C53C2×#58511yescharacteristic
676D53—42no—
677#563—534no—
678#563—534no—
679#563—538no—
680#562—538no—
681#560—534no—
682#560C2×D5314yes—
683#559—538no—
684#559—534no—
685#557—534no—
686#556—538no—
687#556—538no—
688#556—534no—
689#555—534no—
690#555—538no—
691#554—534no—
692#554—538no—
693#554—534no—
694#553—538no—
695#553—538no—
696#553—538no—
697#553—538no—
698#553—538no—
699#553—534no—
700#553C2×D5314yes—
701#552—538no—
702#552—538no—
703#552—538no—
704#552—538no—
705#552—538no—
706#552—534no—
707#552—538no—
708#552—534no—
709#551—534no—
710#551—538no—
711#551—538no—
712#551—538no—
713#551—538no—
714#551—534no—
715#551—538no—
716#551—538no—
717D4×Q8—534no—
718#548—534no—
719#548—534no—
720#547—534no—
721#547—538no—
722#546—538no—
723#546—538no—
724#546—534no—
725#546—534no—
726#546—538no—
727D42C2×D5314yes—
728D42C2×D5314yes—
729#544—534no—
730#543—534no—
731#542—538no—
732#542—534no—
733#542—534no—
734#542—538no—
735#542—538no—
736#541—538no—
737#541—538no—
738#541—532no—
739#541—532no—
740#540—532no—
741#540—538no—
742#540C2×D5312yes—
743#539—538no—
744#539—538no—
745#539—534no—
746#539—534no—
747#539—538no—
748#539—538no—
749#538—538no—
750#538—538no—
751#538—538no—
752#538—538no—
753#538—534no—
754#538C2×D5314yes—
755#537—534no—
756#537—534no—
757#536—532no—
758#535C2×D5312yes—
759#534C2×D5314yes—
760#533—532no—
761#533—531no—
762#533—532no—
763#532—531no—
764#532—532no—
765#532—532no—
766#529—534no—
767#529—532no—
768#529—534no—
769#529—534no—
770#529—534no—
771#529—534no—
772#529—534no—
773#529—534no—
774#529—534no—
775#529—534no—
776#529—532no—
777#529—538no—
778#529—534no—
779#529—534no—
780#529—538no—
781#529—534no—
782C2×#126—534no—
783C2×#125—532no—
784C2×#125—532no—
785C2×#124—532no—
786C2×#124—532no—
787#525—531no—
788#525—534no—
789#525—538no—
790#525C2×D5311yescharacteristic
791C2×#123—534no—
792C2×#123—538no—
793C2×C22⋊Q8—532no—
794C2×#121C2×D5312yes—
795#520—538no—
796#520—534no—
797#519—532no—
798#518—538no—
799#518—532no—
800C4×#41—531no—
801C4×#41—534no—
802C4×#41—531no—
803C2×C4×Q8—532no—
804C2×C4×D4—534no—
805C2×C4×D4—532no—
806C2×#117—534no—
807C22×C42—531no—
808C53#6282911yescharacteristic, complemented, Sylow
809C2×#41—534no—
810C2×#41—538no—
811C2×#41—534no—
812C2×#41—531no—
813C2×#41C22×D5311yescharacteristic
814C22×Q8—532no—
815C22×Q8—532no—
816C22×D4C22×D5314yes—
817C22×D4C22×D5312yes—
818C22×D4C22×D5318yes—
819C22×D4C22×D5312yes—
820C23×C4—534no—
821C23×C4—532no—
822C23×C4C22×D5311yescharacteristic
823C4⋊Q8—531no—
824C4⋊Q8—534no—
825C4⋊Q8—532no—
826C4⋊Q8—534no—
827C4⋊Q8—538no—
828C4⋊Q8—538no—
829C4⋊Q8—532no—
830#127—531no—
831#127C22×D5312yes—
832#127C22×D5314yes—
833#126—534no—
834#126—538no—
835#126—538no—
836#126—538no—
837#126—538no—
838#126—538no—
839#126—534no—
840#126—538no—
841#126—538no—
842#126—538no—
843#126—538no—
844#126—538no—
845#126—538no—
846#126—538no—
847#126—538no—
848#126—538no—
849#126—538no—
850#126C22×D5318yes—
851#125—534no—
852#125—534no—
853#125—534no—
854#125—534no—
855#125—538no—
856#125—534no—
857#125—532no—
858#125—538no—
859#125—538no—
860#125—538no—
861#125—538no—
862#125—538no—
863#125—538no—
864#125—532no—
865#125—538no—
866#125C22×D5312yes—
867#124—531no—
868#124—534no—
869#124—534no—
870#124—534no—
871#124—534no—
872#124—538no—
873#124—534no—
874#124—531no—
875#124—538no—
876#124—534no—
877#124—538no—
878#124—538no—
879#124—534no—
880#124—538no—
881#124—538no—
882#124C22×D5314yes—
883#123—538no—
884#123—534no—
885#123—538no—
886#123—538no—
887#123—538no—
888#123—538no—
889#123—538no—
890#123—538no—
891#123—538no—
892#123—538no—
893#123—538no—
894#123—538no—
895#123—534no—
896#123—534no—
897#123—538no—
898#123—538no—
899#123—538no—
900#123—538no—
901#123—532no—
902#123—534no—
903#123—538no—
904#123—538no—
905#123—538no—
906#123C22×D5312yes—
907#123C22×D5318yes—
908#123C22×D5318yes—
909C22⋊Q8—534no—
910C22⋊Q8—534no—
911C22⋊Q8—534no—
912C22⋊Q8—534no—
913C22⋊Q8—532no—
914C22⋊Q8—534no—
915C22⋊Q8—538no—
916C22⋊Q8—538no—
917C22⋊Q8—538no—
918C22⋊Q8—534no—
919C22⋊Q8—538no—
920C22⋊Q8—534no—
921C22⋊Q8—534no—
922C22⋊Q8—538no—
923C22⋊Q8—538no—
924C22⋊Q8—538no—
925C22⋊Q8—538no—
926C22⋊Q8—538no—
927C22⋊Q8—538no—
928C22⋊Q8—538no—
929C22⋊Q8—538no—
930C22⋊Q8—538no—
931C22⋊Q8—538no—
932C22⋊Q8—538no—
933C22⋊Q8C22×D5312yes—
934#121—534no—
935#121—534no—
936#121—538no—
937#121—538no—
938#121—538no—
939#121—534no—
940#121—538no—
941#121—538no—
942#121—538no—
943#121—538no—
944#121—538no—
945#121—538no—
946#121—532no—
947#121—538no—
948#121C22×D5314yes—
949#121C22×D5314yes—
950#121C22×D5314yes—
951#121C22×D5314yes—
952#121C22×D5312yes—
953#121C22×D5318yes—
954#121C22×D5314yes—
955#121C22×D5318yes—
956#121C22×D5318yes—
957#120—532no—
958#120—538no—
959#120—538no—
960#120C22×D5312yes—
961#120C22×D5318yes—
962#120C22×D5314yes—
963#120C22×D5318yes—
964#120C22×D5314yes—
965C4×Q8—532no—
966C4×Q8—534no—
967C4×Q8—534no—
968C4×Q8—534no—
969C4×Q8—534no—
970C4×Q8—534no—
971C4×Q8—532no—
972C4×Q8—534no—
973C4×Q8—538no—
974C4×Q8—534no—
975C4×Q8—538no—
976C4×Q8—534no—
977C4×Q8—538no—
978C4×D4—538no—
979C4×D4—534no—
980C4×D4—534no—
981C4×D4—538no—
982C4×D4—538no—
983C4×D4—534no—
984C4×D4—534no—
985C4×D4—538no—
986C4×D4—534no—
987C4×D4—534no—
988C4×D4—532no—
989C4×D4—538no—
990C4×D4—538no—
991C4×D4—538no—
992C4×D4—538no—
993C4×D4—538no—
994C4×D4—538no—
995C4×D4—534no—
996C4×D4—538no—
997C4×D4—534no—
998C4×D4—534no—
999C4×D4—538no—
1000C4×D4—538no—
1001C4×D4—538no—
1002C4×D4—532no—
1003C4×D4—534no—
1004C4×D4—534no—
1005C4×D4—534no—
1006C4×D4—538no—
1007C4×D4—538no—
1008C4×D4C22×D5314yes—
1009C4×D4C22×D5318yes—
1010C4×D4C22×D5314yes—
1011#117—532no—
1012#117—531no—
1013#117—538no—
1014#117—538no—
1015#117—532no—
1016#117—534no—
1017#117—538no—
1018#117—538no—
1019#117—538no—
1020#117—538no—
1021#117—534no—
1022#117—534no—
1023#117—538no—
1024#117—538no—
1025#117—538no—
1026#117—538no—
1027#117—532no—
1028#117—538no—
1029#117C22×D5311yescharacteristic
1030#117C22×D5312yes—
1031C2×C4⋊C4—534no—
1032C2×C4⋊C4—534no—
1033C2×C4⋊C4—532no—
1034C2×C4⋊C4—534no—
1035C2×C4⋊C4—534no—
1036C2×C4⋊C4—538no—
1037C2×C4⋊C4—538no—
1038C2×C4⋊C4—534no—
1039C2×C4⋊C4—538no—
1040C2×C4⋊C4C22×D5312yes—
1041C2×C22⋊C4—534no—
1042C2×C22⋊C4—534no—
1043C2×C22⋊C4—534no—
1044C2×C22⋊C4—534no—
1045C2×C22⋊C4—538no—
1046C2×C22⋊C4—538no—
1047C2×C22⋊C4—538no—
1048C2×C22⋊C4—538no—
1049C2×C22⋊C4C22×D5314yes—
1050C2×C42—532no—
1051C2×C42—534no—
1052C2×C42—532no—
1053C2×C42—532no—
1054C2×C42—532no—
1055C2×C42—531no—
1056C2×C42—532no—
1057C2×C42—532no—
1058C2×C42—531no—
1059C2×C42—532no—
1060C24C23×D5311yescharacteristic
1061C24C23×D5314yes—
1062C24C23×D5314yes—
1063#41—42no—
1064#41—2122no—
1065#41—2128no—
1066#41—21216no—
1067#41—2128no—
1068C2×Q8—534no—
1069C2×Q8—531no—
1070C2×Q8—538no—
1071C2×Q8—534no—
1072C2×Q8—534no—
1073C2×Q8—534no—
1074C2×Q8—2124no—
1075C2×Q8—2124no—
1076C2×Q8C23×D5311yescharacteristic
1077C2×D4—44no—
1078C2×D4—44no—
1079C2×D4—48no—
1080C2×D4—416no—
1081C2×D4—534no—
1082C2×D4—538no—
1083C2×D4—538no—
1084C2×D4—534no—
1085C2×D4—532no—
1086C2×D4—531no—
1087C2×D4C23×D5318yes—
1088C2×D4C23×D5314yes—
1089C2×D4C23×D5314yes—
1090C2×D4C23×D5311yescharacteristic
1091C2×D4C23×D5312yes—
1092C2×D4C23×D5314yes—
1093C2×D4C23×D5318yes—
1094C2×D4C23×D5318yes—
1095C2×D4C23×D5314yes—
1096C2×D4C23×D5318yes—
1097C22×C4—42no—
1098C22×C4—532no—
1099C22×C4—532no—
1100C22×C4—534no—
1101C22×C4—532no—
1102C22×C4—532no—
1103C22×C4—532no—
1104C22×C4—532no—
1105C22×C4—534no—
1106C22×C4—534no—
1107C22×C4—538no—
1108C22×C4—538no—
1109C22×C4—534no—
1110C22×C4—538no—
1111C22×C4—538no—
1112C22×C4—532no—
1113C22×C4—534no—
1114C22×C4—538no—
1115C22×C4—2124no—
1116C22×C4—2128no—
1117C22×C4C23×D5312yes—
1118C22×C4C23×D5311yescharacteristic
1119C22×C4C23×D5312yes—
1120C22×C4C23×D5312yes—
1121C22×C4C23×D5311yescharacteristic
1122C22×C4C23×D5314yes—
1123C22×C4C23×D5318yes—
1124C4⋊C4—538no—
1125C4⋊C4—538no—
1126C4⋊C4—534no—
1127C4⋊C4—534no—
1128C4⋊C4—538no—
1129C4⋊C4—538no—
1130C4⋊C4—534no—
1131C4⋊C4—538no—
1132C4⋊C4—538no—
1133C4⋊C4—538no—
1134C4⋊C4—538no—
1135C4⋊C4—538no—
1136C4⋊C4—534no—
1137C4⋊C4—538no—
1138C4⋊C4—538no—
1139C4⋊C4—538no—
1140C4⋊C4—534no—
1141C4⋊C4—538no—
1142C4⋊C4—534no—
1143C4⋊C4—538no—
1144C4⋊C4—538no—
1145C4⋊C4—532no—
1146C4⋊C4—534no—
1147C4⋊C4—534no—
1148C4⋊C4—534no—
1149C4⋊C4—538no—
1150C4⋊C4C23×D5314yes—
1151C4⋊C4C23×D5318yes—
1152C4⋊C4C23×D5314yes—
1153C4⋊C4C23×D5314yes—
1154C4⋊C4C23×D5312yes—
1155C22⋊C4—538no—
1156C22⋊C4—538no—
1157C22⋊C4—534no—
1158C22⋊C4—538no—
1159C22⋊C4—534no—
1160C22⋊C4—538no—
1161C22⋊C4—534no—
1162C22⋊C4—538no—
1163C22⋊C4—534no—
1164C22⋊C4—538no—
1165C22⋊C4—538no—
1166C22⋊C4—538no—
1167C22⋊C4—538no—
1168C22⋊C4—538no—
1169C22⋊C4—538no—
1170C22⋊C4—538no—
1171C22⋊C4—538no—
1172C22⋊C4—532no—
1173C22⋊C4—534no—
1174C22⋊C4—534no—
1175C22⋊C4—538no—
1176C22⋊C4—534no—
1177C22⋊C4C23×D5318yes—
1178C22⋊C4C23×D5318yes—
1179C22⋊C4C23×D5314yes—
1180C22⋊C4C23×D5314yes—
1181C22⋊C4C23×D5318yes—
1182C22⋊C4C23×D5318yes—
1183C22⋊C4C23×D5314yes—
1184C22⋊C4C23×D5312yes—
1185C42—531no—
1186C42—532no—
1187C42—531no—
1188C42—531no—
1189C42—532no—
1190C42—532no—
1191C42—532no—
1192C42—532no—
1193C42—532no—
1194C42—531no—
1195C42—534no—
1196C42—538no—
1197C42—538no—
1198C42—534no—
1199C42—532no—
1200C42—538no—
1201C42—534no—
1202C42—538no—
1203C42C23×D5312yes—
1204C42C23×D5314yes—
1205C23—24no—
1206C23—28no—
1207C23—41no—
1208C23—44no—
1209C23—44no—
1210C23—44no—
1211C23—48no—
1212C23—532no—
1213C23C24×D5312yes—
1214C23C24×D5318yes—
1215C23C24×D5311yescharacteristic
1216C23C24×D5312yes—
1217Q8—41no—
1218Q8—1068no—
1219Q8—2124no—
1220Q8—2124no—
1221Q8—2121no—
1222Q8—2128no—
1223Q8—2124no—
1224D4—216no—
1225D4—28no—
1226D4—28no—
1227D4—44no—
1228D4—44no—
1229D4—48no—
1230D4—48no—
1231D4—48no—
1232D4—41no—
1233D4—42no—
1234D4—1068no—
1235D4—2121no—
1236D4—2122no—
1237D4—2128no—
1238D4—2124no—
1239D4—2128no—
1240C2×C4—24no—
1241C2×C4—22no—
1242C2×C4—24no—
1243C2×C4—41no—
1244C2×C4—42no—
1245C2×C4—44no—
1246C2×C4—48no—
1247C2×C4—532no—
1248C2×C4—532no—
1249C2×C4—532no—
1250C2×C4—534no—
1251C2×C4—538no—
1252C2×C4—532no—
1253C2×C4—532no—
1254C2×C4—538no—
1255C2×C4—1064no—
1256C2×C4—1064no—
1257C2×C4—1068no—
1258C2×C4—1064no—
1259C2×C4—2124no—
1260C2×C4—2128no—
1261C2×C4—2122no—
1262C2×C4—2122no—
1263C2×C4—2128no—
1264C2×C4—2128no—
1265C2×C4—2122no—
1266C2×C4—2122no—
1267C2×C4—2124no—
1268C2×C4—2124no—
1269C2×C4—2124no—
1270C2×C4—2128no—
1271C2×C4—2128no—
1272C2×C4C24×D5312yes—
1273C2×C4C24×D5312yes—
1274C2×C4C24×D5311yescharacteristic
1275C2×C4C24×D5314yes—
1276C2×C4C24×D5318yes—
1277C2×C4C24×D5311yescharacteristic
1278C22—22no—
1279C22—22no—
1280C22—21no—
1281C22—22no—
1282C22—28no—
1283C22—22no—
1284C22—28no—
1285C22—28no—
1286C22—24no—
1287C22—44no—
1288C22—88no—
1289C22—164no—
1290C22—1062no—
1291C22—1064no—
1292C22#1681145814yes—
1293C22C25×D5311yescharacteristic
1294C4—22no—
1295C4—21no—
1296C4—22no—
1297C4—28no—
1298C4—24no—
1299C4—1062no—
1300C4—1062no—
1301C4—1062no—
1302C4—1068no—
1303C4—1062no—
1304C4—1062no—
1305C4—1064no—
1306C4—1068no—
1307C4#1681145812yes—
1308C2—24no—
1309C2—41no—
1310C2—48no—
1311C2—42no—
1312C2—2122no—
1313C2C2×#1681145812yes—
1314C2C2×#1681145811yescharacteristic
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3537C2
hypercenter#3537D53
hypocenterC53#62829
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3537

Complements

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

NH ≅ G/Ntype
1. #20289372C2semidirect
2. #20289341C2semidirect
3. #20289257C2semidirect
4. #20289220C2semidirect
5. #20289139C2semidirect
6. #20288964C2semidirect
7. #20288937C2semidirect
8. #20288699C2semidirect
9. #20288686C2semidirect
10. #20288667C2semidirect
11. #20288640C2semidirect
12. #20288640C2semidirect
13. #20288634C2semidirect
14. #20288610C2semidirect
15. #20288430C2semidirect
16. #20288412C2semidirect
17. #20288007C2semidirect
18. C2×#16811154C2semidirect
19. C53×#3537C2semidirect
20. #16811376C22semidirect
21. #16811376C22semidirect
22. #16811373C22semidirect
23. #16811368C22semidirect
24. #16811362C22semidirect
25. #16811359C22semidirect
26. #16811359C22semidirect
27. #16811350C22semidirect
28. #16811343C22semidirect
29. #16811342C22semidirect
30. #16811340C22semidirect
31. #16811337C22semidirect
32. #16811335C22semidirect
33. #16811332C22semidirect
34. #16811332C22semidirect
35. #16811328C22semidirect
36. #16811320C22semidirect
37. #16811320C22semidirect
38. #16811318C22semidirect
39. #16811316C22semidirect
40. #16811316C22semidirect
41. #16811316C22semidirect
42. #16811313C22semidirect
43. #16811313C22semidirect
44. #16811312C22semidirect
45. #16811310C22semidirect
46. #16811310C22semidirect
47. #16811310C22semidirect
48. #16811310C22semidirect
49. #16811309C22semidirect
50. #16811304C22semidirect
51. #16811304C22semidirect
52. #16811304C22semidirect
53. #16811304C22semidirect
54. #16811304C22semidirect
55. #16811304C22semidirect
56. #16811304C22semidirect
57. #16811304C22semidirect
58. D4×Dic106C22semidirect
59. #16811279C22semidirect
60. #16811279C22semidirect
61. #16811273C22semidirect
62. #16811273C22semidirect
63. #16811267C22semidirect
64. #16811267C22semidirect
65. #16811267C22semidirect
66. #16811267C22semidirect
67. #16811267C22semidirect
68. #16811252C22semidirect
69. #16811249C22semidirect
70. #16811241C22semidirect
71. #16811240C22semidirect
72. #16811240C22semidirect
73. #16811240C22semidirect
74. #16811240C22semidirect
75. #16811236C22semidirect
76. #16811235C22semidirect
77. #16811230C22semidirect
78. #16811230C22semidirect
79. #16811227C22semidirect
80. #16811227C22semidirect
81. #16811218C22semidirect
82. #16811218C22semidirect
83. #16811218C22semidirect
84. #16811218C22semidirect
85. #16811218C22semidirect
86. #16811216C22semidirect
87. #16811211C22semidirect
88. #16811208C22semidirect
89. #16811208C22semidirect
90. #16811208C22semidirect
91. #16811208C22semidirect
92. #16811202C22semidirect
93. #16811200C22semidirect
94. #16811194C22semidirect
95. #16811176C22semidirect
96. #16811176C22semidirect
97. #16811175C22semidirect
98. #16811171C22semidirect
99. #16811169C22semidirect
100. #16811168C22semidirect
101. #16811159C22semidirect
102. #16811155C22semidirect
103. #16811154C22semidirect
104. #16811154C22semidirect
105. #16811154C22semidirect
106. #16811154C22semidirect
107. #16811154C22semidirect
108. #16811154C22semidirect
109. #16811154C22semidirect
110. #16811154C22semidirect
111. #16811154C22semidirect
112. #16811154C22semidirect
113. #16811154C22semidirect
114. #16811153C22semidirect
115. #16811153C22semidirect
116. #16811150C22semidirect
117. C2×#13133210C22semidirect
118. C2×#13133208C22semidirect
119. #125×D53C22semidirect
120. C2×#13133204C22semidirect
121. C2×#13133204C22semidirect
122. #16811134C22semidirect
123. #16811129C22semidirect
124. #16811129C22semidirect
125. C2×#13133198C22semidirect
126. C2×#13133198C22semidirect
127. C2×#13133196C22semidirect
128. #16811102C22semidirect
129. #16811102C22semidirect
130. #16811100C22semidirect
131. #16811098C22semidirect
132. #16811098C22semidirect
133. #41×Dic53C22semidirect
134. #16811091C22semidirect
135. C4×#11719947C22semidirect
136. C2×#13133182C22semidirect
137. C2×D4×Dic53C22semidirect
138. C2×D4×Dic53C22semidirect
139. C2×#13133173C22semidirect
140. C22×C4×Dic53C22semidirect
657. #3537D53semidirect
808. C53#62829semidirect

Maximal subgroups

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

subgroupindex
#202893722
#202893412
#202892572
#202892202
#202891392
#202889642
#202889372
#202886992
#202886862
#202886672
#202886402
#202886342
#202886102
#202884302
#202884122
#202880072
C2×#168111542
C53×#35372
#6282953