Finite Group Databasebeta

← #28292818

Subgroups — #28292818

Order 13568.

6530 conjugacy classes of subgroups.

The subgroup lattice has 1396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289319C214yesmaximal, complemented
2#20289316C214yesmaximal, complemented
3#20289247C214yesmaximal, complemented
4#20289244C214yesmaximal, complemented
5#20289165C218yesmaximal, complemented
6#20288694C214yesmaximal, complemented
7#20288690C214yesmaximal, complemented
8#20288686C214yesmaximal, complemented
9#20288684C214yesmaximal, complemented
10#20288636C212yesmaximal, complemented
11#20288632C212yesmaximal, complemented
12#20288538C212yesmaximal, complemented
13#20288537C212yesmaximal, complemented
14#20288424C211yesmaximal, characteristic, complemented
15#20288421C212yesmaximal, complemented
16#20288421C214yesmaximal, complemented
17#20288416C214yesmaximal, complemented
18#20288007C212yesmaximal, complemented
19C22×#13133208C211yesmaximal, characteristic, complemented
20C53×#3492C211yesmaximal, characteristic, complemented
21C53⋊#564C2218yescomplemented
22#16811375C2218yescomplemented
23#16811374C2218yescomplemented
24#16811370C2218yescomplemented
25#16811352C2214yescomplemented
26#16811350C2214yescomplemented
27#16811349C2214yescomplemented
28#16811348C2214yescomplemented
29#16811334C2214yescomplemented
30#16811332C2218yes—
31#16811332C2214yescomplemented
32#16811331C2218yes—
33#16811331C2214yes—
34#16811330C2218yes—
35#16811330C2214yes—
36#16811330C2214yescomplemented
37#16811329C2214yescomplemented
38#16811328C2214yes—
39#16811327C2218yes—
40#16811325C2218yes—
41#16811325C2214yes—
42#16811325C2214yescomplemented
43#16811322C2218yes—
44#16811321C2214yes—
45#16811321C2214yescomplemented
46#16811320C2214yescomplemented
47#16811319C2218yes—
48#16811319C2214yes—
49#16811317C2214yescomplemented
50#16811316C2218yes—
51#16811315C2214yes—
52#16811315C2218yes—
53#16811315C2214yescomplemented
54#16811315C2218yescomplemented
55#16811313C2214yes—
56#16811313C2218yes—
57#16811312C2214yescomplemented
58#16811311C2218yescomplemented
59#16811310C2218yes—
60#16811310C2218yescomplemented
61#16811309C2218yescomplemented
62#16811308C2214yes—
63#16811308C2214yescomplemented
64#16811307C2214yescomplemented
65#16811306C2218yes—
66#16811277C2214yes—
67#16811277C2218yes—
68#16811274C2214yes—
69#16811273C2214yes—
70#16811273C2218yes—
71#16811272C2218yes—
72#16811271C2218yes—
73#16811254C2211yescharacteristic
74#16811254C2214yescomplemented
75#16811253C2214yescomplemented
76#16811252C2214yes—
77#16811251C2212yes—
78#16811251C2214yes—
79#16811251C2214yescomplemented
80#16811250C2214yescomplemented
81#16811236C2218yescomplemented
82#16811233C2214yescomplemented
83#16811233C2218yescomplemented
84#16811232C2218yescomplemented
85#16811231C2214yescomplemented
86#16811230C2218yescomplemented
87#16811226C2214yescomplemented
88#16811224C2214yescomplemented
89#16811222C2214yes—
90#16811222C2218yescomplemented
91#16811220C2214yes—
92#16811218C2214yes—
93#16811217C2218yes—
94#16811217C2218yes—
95#16811217C2218yes—
96#16811217C2218yescomplemented
97#16811216C2218yescomplemented
98#16811215C2218yes—
99#16811214C2218yescomplemented
100#16811204C2211yescharacteristic
101#16811201C2212yes—
102#16811201C2214yes—
103#16811200C2214yes—
104#16811178C2214yescomplemented
105#16811176C2212yes—
106#16811176C2214yescomplemented
107#16811175C2212yes—
108#16811175C2212yes—
109#16811169C2212yes—
110#16811168C2212yes—
111#16811168C2212yes—
112#16811160C2214yescomplemented
113#16811159C2212yes—
114#16811159C2212yes—
115#16811159C2214yescomplemented
116#16811155C2214yescomplemented
117#16811154C2212yes—
118#16811154C2212yes—
119#16811154C2214yescomplemented
120#16811153C2214yes—
121#16811153C2214yes—
122#16811150C2214yes—
123#16811150C2214yes—
124C2×#13133208C2212yes—
125C2×#13133208C2212yes—
126C2×#13133208C2214yes—
127C2×#13133208C2214yes—
128C2×#13133208C2214yes—
129C2×#13133208C2214yes—
130C2×#13133208C2214yes—
131C2×#13133208C2214yescomplemented
132#125×D53C2214yescomplemented
133#16811134C2212yes—
134#16811134C2214yes—
135#16811129C2214yes—
136#16811129C2214yes—
137#16811129C2218yes—
138#16811106C2212yes—
139#16811106C2214yes—
140#16811104C2212yes—
141#16811103C2212yes—
142#16811103C2214yes—
143#16811102C2218yes—
144#41×Dic53C2212yes—
145#16811091C2212yes—
146C4×#11719947C2214yes—
147C4×#11719947C2214yes—
148C22×C4⋊Dic53C2211yescharacteristic
149C22×C4⋊Dic53C2212yes—
150C22×#11719919C2212yes—
151C22×C4×Dic53C2211yescharacteristic
152C53×#554C2214yes—
153C53×#553C2214yes—
154C53×#552C2214yes—
155C53×#547C2214yes—
156C53×#544C2211yescharacteristic
157C53×#539C2214yes—
158C53×#537C2211yescharacteristic
159C53×#525C2212yes—
160C53×#525C2214yes—
161C53×#520C2212yes—
162C22×C4⋊C4×C53C2211yescharacteristic
163C2×#11719945C2312yes—
164C2×#11719945C2314yes—
165C2×#11719947C2314yes—
166C2×#11719947C2314yes—
167C2×#11719947C2318yes—
168C23×Dic53C2311yescharacteristic
169C23×Dic53C2311yescharacteristic
170C23×Dic53C2312yes—
171#13133217C2314yes—
172#13133217C2318yes—
173#13133216C2318yes—
174#13133216C2314yes—
175#13133216C2318yes—
176#13133216C2314yes—
177#13133216C2312yes—
178#13133216C2312yes—
179#13133215C2318yes—
180#13133215C2312yes—
181#13133213C2312yes—
182#13133212C2318yes—
183#13133212C2318yes—
184#13133212C2318yes—
185#13133212C2318yes—
186#13133212C2318yes—
187#13133212C2314yes—
188#13133212C2314yes—
189#13133211C2318yes—
190#13133210C2318yes—
191#13133210C2318yes—
192#13133210C2318yes—
193#13133210C2318yes—
194#13133210C2318yes—
195#13133210C2314yes—
196#13133210C2314yes—
197#13133209C2318yes—
198#13133209C2318yes—
199#13133209C2314yes—
200#13133208C2314yes—
201#13133208C2314yes—
202#13133208C2314yes—
203#13133208C2318yes—
204#13133208C2318yes—
205#13133208C2318yes—
206#13133208C2314yes—
207#13133208C2318yes—
208#13133208C2318yes—
209#13133208C2314yes—
210#13133208C2318yes—
211#13133208C2314yes—
212#13133208C2318yes—
213#13133208C2312yes—
214#13133208C2314yes—
215#13133208C2314yes—
216#13133208C2318yes—
217#13133208C2318yes—
218#13133208C2314yes—
219#13133208C2314yes—
220#13133208C2312yes—
221#13133207C2318yes—
222#13133207C2318yes—
223#13133207C2318yes—
224#13133207C2318yes—
225#13133207C2318yes—
226#13133207C2318yes—
227#13133207C2318yes—
228#13133207C2318yes—
229#13133207C2314yes—
230#13133207C2314yes—
231#13133206C2312yes—
232#13133204C2312yes—
233#13133203C2314yes—
234#13133203C2314yes—
235#13133202C2318yes—
236#13133202C2318yes—
237#13133201C2314yes—
238#13133201C2314yes—
239#13133201C2318yes—
240#13133201C2318yes—
241#13133201C2318yes—
242#13133201C2318yes—
243#13133200C2318yes—
244#13133200C2318yes—
245#13133200C2314yes—
246#13133199C2318yes—
247#13133199C2318yes—
248#13133199C2318yes—
249#13133199C2318yes—
250#13133198C2314yes—
251#13133198C2318yes—
252#13133198C2314yes—
253#13133198C2318yes—
254#13133197C2318yes—
255#13133197C2318yes—
256#13133197C2318yes—
257#13133197C2314yes—
258#13133196C2318yes—
259#13133196C2312yes—
260#13133196C2314yes—
261#13133196C2312yes—
262#13133196C2314yes—
263#13133196C2318yes—
264#13133196C2314yes—
265#13133195C2318yes—
266#13133195C2318yes—
267#13133195C2318yes—
268#13133194C2318yes—
269#13133194C2318yes—
270#13133194C2318yes—
271#13133194C2318yes—
272#13133194C2318yes—
273#13133194C2318yes—
274#13133194C2314yes—
275#13133194C2318yes—
276#13133194C2314yes—
277#13133194C2314yes—
278#13133194C2314yes—
279#13133193C2318yes—
280#13133193C2314yes—
281#13133193C2318yes—
282#13133192C2314yes—
283#13133191C2312yes—
284#13133191C2312yes—
285#13133191C2314yes—
286#13133191C2314yes—
287#13133191C2318yes—
288#13133191C2314yes—
289#13133190C2318yes—
290#13133189C2318yes—
291#13133189C2318yes—
292#13133189C2314yes—
293#13133189C2318yes—
294#13133189C2314yes—
295#13133189C2314yes—
296#13133189C2314yes—
297#13133188C2314yes—
298#13133188C2318yes—
299#13133186C2314yes—
300Q8×Dic53C2312yes—
301Q8×Dic53C2318yes—
302Q8×Dic53C2314yes—
303Q8×Dic53C2312yes—
304C4×Dic106C2318yes—
305C4×Dic106C2318yes—
306C4×Dic106C2314yes—
307C4×Dic106C2314yes—
308C4×Dic106C2314yes—
309#13133182C2314yes—
310#13133182C2312yes—
311#13133182C2318yes—
312#13133182C2312yes—
313#13133182C2314yes—
314#13133182C2314yes—
315C4×D212C2318yes—
316C4×D212C2314yes—
317D4×Dic53C2318yes—
318D4×Dic53C2318yes—
319D4×Dic53C2314yes—
320D4×Dic53C2314yes—
321D4×Dic53C2318yes—
322D4×Dic53C2312yes—
323D4×Dic53C2314yes—
324D4×Dic53C2312yes—
325D4×Dic53C2314yes—
326D4×Dic53C2314yes—
327#13133179C2314yes—
328#13133179C2312yes—
329#13133179C2312yes—
330C4×C22⋊D53C2318yes—
331C4×C22⋊D53C2314yes—
332C4×C22⋊D53C2318yes—
333C4×C22⋊D53C2314yes—
334C4×C22⋊D53C2314yes—
335C4×C22⋊D53C2314yes—
336C4×C22⋊D53C2318yes—
337#13133177C2318yes—
338#13133177C2318yes—
339#13133177C2314yes—
340#13133177C2318yes—
341#13133177C2314yes—
342#13133177C2314yes—
343#13133177C2314yes—
344#13133177C2314yes—
345#13133177C2314yes—
346#13133176C2314yes—
347#13133176C2314yes—
348#13133176C2318yes—
349#13133176C2312yes—
350#13133176C2314yes—
351#13133175C2318yes—
352#13133175C2314yes—
353#13133175C2314yes—
354#13133175C2314yes—
355#13133175C2314yes—
356#13133174C2318yes—
357#13133174C2314yes—
358#13133173C2314yes—
359#13133173C2314yes—
360#13133173C2318yes—
361#13133173C2314yes—
362#13133173C2314yes—
363#13133173C2318yes—
364C2×C4⋊Dic53C2318yes—
365C2×C4⋊Dic53C2314yes—
366C2×C4⋊Dic53C2314yes—
367C2×C4⋊Dic53C2318yes—
368C2×C4⋊Dic53C2314yes—
369C2×C4⋊Dic53C2314yes—
370C2×C4⋊Dic53C2314yes—
371C2×C4⋊Dic53C2312yes—
372C2×C4⋊Dic53C2314yes—
373C2×C4⋊Dic53C2314yes—
374C2×C4⋊Dic53C2312yes—
375C2×#11719919C2318yes—
376C2×#11719919C2318yes—
377C2×#11719919C2314yes—
378C2×#11719919C2314yes—
379C2×#11719919C2314yes—
380C2×#11719919C2314yes—
381C4⋊C4×D53C2318yes—
382C4⋊C4×D53C2318yes—
383C4⋊C4×D53C2314yes—
384C4⋊C4×D53C2314yes—
385C2×C4×Dic53C2312yes—
386C2×C4×Dic53C2312yes—
387C2×C4×Dic53C2312yes—
388C2×C4×Dic53C2312yes—
389C2×C4×Dic53C2312yes—
390C2×C4×Dic53C2312yes—
391C2×C4×Dic53C2314yes—
392C42×D53C2314yes—
393C2×#41×C53C2312yes—
394C2×#41×C53C2314yes—
395C23×C4×C53C2311yescharacteristic
396C23×C4×C53C2312yes—
397C4⋊Q8×C53C2314yes—
398#126×C53C2318yes—
399#125×C53C2318yes—
400#125×C53C2314yes—
401#123×C53C2318yes—
402#123×C53C2314yes—
403#123×C53C2318yes—
404C22⋊Q8×C53C2312yes—
405C22⋊Q8×C53C2314yes—
406C22⋊Q8×C53C2314yes—
407C22⋊Q8×C53C2312yes—
408C22⋊Q8×C53C2314yes—
409C22⋊Q8×C53C2318yes—
410#121×C53C2312yes—
411#121×C53C2314yes—
412#121×C53C2314yes—
413#121×C53C2312yes—
414#121×C53C2314yes—
415#120×C53C2314yes—
416C4×Q8×C53C2314yes—
417C4×D4×C53C2314yes—
418C4×D4×C53C2318yes—
419C4×D4×C53C2318yes—
420C4×D4×C53C2314yes—
421C4×D4×C53C2314yes—
422#117×C53C2312yes—
423#117×C53C2314yes—
424#117×C53C2314yes—
425C2×C4⋊C4×C53C2314yes—
426C2×C4⋊C4×C53C2311yescharacteristic
427C2×C4⋊C4×C53C2311yescharacteristic
428C2×C4⋊C4×C53C2312yes—
429C2×C4⋊C4×C53C2314yes—
430C2×C4⋊C4×C53C2314yes—
431C24×C53C2411yescharacteristic
432#41×C53—28no—
433#41×C53—48no—
434C2×Q8×C53C2412yes—
435C2×Q8×C53C2414yes—
436C2×D4×C53C2414yes—
437C2×D4×C53C2414yes—
438C2×D4×C53C2412yes—
439C2×D4×C53C2414yes—
440C2×D4×C53C2414yes—
441C22×C4×C53—24no—
442C22×C4×C53—44no—
443C22×C4×C53C2414yes—
444C22×C4×C53C2412yes—
445C22×C4×C53C2412yes—
446C22×C4×C53C2411yescharacteristic
447C22×C4×C53C2414yes—
448C22×C4×C53C2412yes—
449C22×C4×C53C2414yes—
450C22×C4×C53C2412yes—
451C22×C4×C53C2418yes—
452C22×C4×C53C2411yescharacteristic
453C2×C22⋊D53C2414yes—
454C2×C22⋊D53C2414yes—
455C2×C22⋊D53C2414yes—
456C2×C22⋊D53C2418yes—
457C2×C22⋊D53C2414yes—
458C2×C22⋊D53C2414yes—
459C22×Dic53—42no—
460C22×Dic53—44no—
461C22×Dic53—42no—
462C22×Dic53C2412yes—
463C22×Dic53C2412yes—
464C22×Dic53C2414yes—
465C22×Dic53C2411yescharacteristic
466C22×Dic53C2412yes—
467C22×Dic53C2411yescharacteristic
468C22×Dic53C2411yescharacteristic
469C22×Dic53C2412yes—
470C22×Dic53C2411yescharacteristic
471C22×Dic53C2414yes—
472C22×Dic53C2414yes—
473C22×Dic53C2414yes—
474C22×Dic53C2414yes—
475C22×Dic53C2418yes—
476#11719947—48no—
477#11719947—48no—
478#11719947—416no—
479#11719945—28no—
480#11719945—48no—
481C2×D212C2412yes—
482C2×D212C2414yes—
483C2×C4×D53C2414yes—
484C2×C4×D53C2414yes—
485C2×C4×D53C2414yes—
486C2×C4×D53C2418yes—
487C2×C4×D53C2418yes—
488C2×Dic106C2412yes—
489C2×Dic106C2418yes—
490C2×Dic106C2414yes—
491C2×Dic106C2414yes—
492C2×Dic106C2414yes—
493C4⋊C4×C53C2414yes—
494C4⋊C4×C53C2414yes—
495C4⋊C4×C53C2418yes—
496C4⋊C4×C53C2412yes—
497C4⋊C4×C53C2418yes—
498C4⋊C4×C53C2412yes—
499C4⋊C4×C53C2414yes—
500C4⋊C4×C53C2414yes—
501C4⋊C4×C53C2414yes—
502C4⋊C4×C53C2418yes—
503C4⋊C4×C53C2414yes—
504C22⋊C4×C53C2414yes—
505C22⋊C4×C53C2414yes—
506C22⋊C4×C53C2418yes—
507C22⋊C4×C53C2414yes—
508C22⋊C4×C53C2418yes—
509C22⋊C4×C53C2414yes—
510C22⋊C4×C53C2414yes—
511C42×C53C2418yes—
512C42×C53C2414yes—
513C22⋊Dic53C2414yes—
514C22⋊Dic53C2414yes—
515C22⋊Dic53C2414yes—
516C22⋊Dic53C2414yes—
517C22⋊Dic53C2414yes—
518C22⋊Dic53C2414yes—
519C22⋊Dic53C2418yes—
520C22⋊Dic53C2418yes—
521C22⋊Dic53C2414yes—
522#11719921C2414yes—
523#11719921C2414yes—
524#11719921C2414yes—
525#11719921C2418yes—
526#11719921C2414yes—
527#11719921C2414yes—
528#11719921C2414yes—
529#11719921C2418yes—
530#11719921C2418yes—
531#11719921C2418yes—
532C4⋊Dic53C2414yes—
533C4⋊Dic53C2412yes—
534C4⋊Dic53C2414yes—
535C4⋊Dic53C2418yes—
536C4⋊Dic53C2414yes—
537C4⋊Dic53C2418yes—
538C4⋊Dic53C2418yes—
539C4⋊Dic53C2418yes—
540C4⋊Dic53C2418yes—
541C4⋊Dic53C2412yes—
542C4⋊Dic53C2414yes—
543C4⋊Dic53C2414yes—
544C4⋊Dic53C2418yes—
545C4⋊Dic53C2418yes—
546C4⋊Dic53C2414yes—
547C4⋊Dic53C2414yes—
548C4⋊Dic53C2414yes—
549#11719919C2414yes—
550#11719919C2418yes—
551#11719919C2418yes—
552#11719919C2418yes—
553#11719919C2418yes—
554#11719919C2418yes—
555#11719919C2418yes—
556#11719919C2418yes—
557#11719919C2418yes—
558#11719919C2414yes—
559#11719919C2418yes—
560#11719919C2418yes—
561#11719919C2414yes—
562#11719919C2414yes—
563#11719919C2414yes—
564#11719919C2414yes—
565#11719919C2414yes—
566#11719919C2414yes—
567#11719919C2414yes—
568#11719919C2414yes—
569C4×Dic53C2412yes—
570C4×Dic53C2414yes—
571C4×Dic53C2414yes—
572C4×Dic53C2412yes—
573C4×Dic53C2412yes—
574C4×Dic53C2412yes—
575C4×Dic53C2412yes—
576C4×Dic53C2412yes—
577C4×Dic53C2412yes—
578C4×Dic53C2412yes—
579C4×Dic53C2414yes—
580C4×Dic53C2414yes—
581C4×Dic53C2414yes—
582C4×Dic53C2418yes—
583C4×Dic53C2418yes—
584C4×Dic53C2418yes—
585C23×C53—22no—
586C23×C53—22no—
587C23×C53—22no—
588C23×C53C2514yes—
589C23×C53C2511yescharacteristic
590C23×C53C2511yescharacteristic
591C23×C53C2511yescharacteristic
592C22×D53C2514yes—
593Q8×C53—24no—
594Q8×C53—44no—
595D4×C53—28no—
596D4×C53—28no—
597D4×C53—28no—
598D4×C53—24no—
599D4×C53—44no—
600C2×C4×C53—22no—
601C2×C4×C53—28no—
602C2×C4×C53—24no—
603C2×C4×C53—24no—
604C2×C4×C53—28no—
605C2×C4×C53—42no—
606C2×C4×C53—44no—
607C2×C4×C53—42no—
608C2×C4×C53—48no—
609C2×C4×C532−1+414yes—
610C2×C4×C53C2514yes—
611C2×C4×C53C2514yes—
612C2×C4×C53C2514yes—
613C2×C4×C53C2514yes—
614C2×C4×C53C2512yes—
615C2×C4×C53C2514yes—
616C2×C4×C53C2512yes—
617C22⋊D53—28no—
618C22⋊D53—28no—
619C22⋊D53—28no—
620C22⋊D53—44no—
621C22⋊D53—44no—
622C22⋊D53—48no—
623C2×Dic53—24no—
624C2×Dic53—24no—
625C2×Dic53—28no—
626C2×Dic53—44no—
627C2×Dic53—48no—
628C2×Dic53—44no—
629C2×Dic53—41no—
630C2×Dic53—41no—
631C2×Dic53—42no—
632C2×Dic53—42no—
633C2×Dic53—44no—
634C2×Dic53—44no—
635C2×Dic53—41no—
636C2×Dic53—41no—
637C2×Dic53C2514yes—
638C2×Dic53C2514yes—
639C2×Dic53C2512yes—
640C2×Dic53C2512yes—
641C2×Dic53C2518yes—
642C2×Dic53C2514yes—
643C2×Dic53C2512yes—
644C2×Dic53C2512yes—
645D212—24no—
646D212—44no—
647C4×D53—28no—
648C4×D53—48no—
649C4×D53—48no—
650C4×D53—44no—
651C4×D53—44no—
652Dic106—24no—
653Dic106—44no—
654Dic106—44no—
655Dic106—44no—
656Dic106—48no—
657#62825—531nomaximal, Sylow
658C22×C53—28no—
659C22×C53—21no—
660C22×C53—21no—
661C22×C53—21no—
662C22×C53—21no—
663C22×C53—21no—
664C22×C53—21no—
665C22×C53—24no—
666C22×C53—24no—
667C22×C53—24no—
668C22×C53C2×2−1+412yes—
669C22×C53#58512yes—
670C22×C53#58512yes—
671C22×C53C2611yescharacteristic
672C2×D53—24no—
673C2×D53—24no—
674C2×D53—24no—
675C4×C53—22no—
676C4×C53—24no—
677C4×C53—24no—
678C4×C53—24no—
679C4×C53—24no—
680C4×C53—24no—
681C4×C53C2×2−1+414yes—
682Dic53—24no—
683Dic53—24no—
684Dic53—24no—
685Dic53—22no—
686Dic53—22no—
687Dic53—28no—
688Dic53—22no—
689Dic53—22no—
690#3563—534no—
691#3563—534no—
692#3559—534no—
693#3559—534no—
694#3553—538no—
695#3515—534no—
696#3515—534no—
697#3515—534no—
698#3515—534no—
699#3512—532no—
700#3512—532no—
701#3504—532no—
702#3504—532no—
703#3492—534no—
704#3492—532no—
705#3492—534no—
706#3492—531no—
707#3492D5311yescharacteristic, complemented
708#3444—532no—
709C22×#125—531no—
710C2×C53—22no—
711C2×C53—22no—
712C2×C53—22no—
713C2×C53—44no—
714C2×C53C22×2−1+411yescharacteristic
715C2×C53C2×#58511yescharacteristic
716C2×C53C2×#58511yescharacteristic
717D53—44no—
718#564—538no—
719#563—538no—
720#563—538no—
721#562—538no—
722#557—534no—
723#557—534no—
724#557—534no—
725#557—534no—
726#554—534no—
727#554—534no—
728#554—538no—
729#554—538no—
730#554—534no—
731#554—538no—
732#554—534no—
733#554—534no—
734#554—538no—
735#554—534no—
736#554—534no—
737#554C2×D5314yes—
738#553—538no—
739#553—534no—
740#553—538no—
741#553—534no—
742#553—534no—
743#553—538no—
744#553—534no—
745#553—538no—
746#553—534no—
747#553—534no—
748#553—534no—
749#553C2×D5314yes—
750#552—538no—
751#552—538no—
752#552—538no—
753#552—538no—
754#552—534no—
755#552—538no—
756#552—534no—
757#552—534no—
758#552—538no—
759#552—538no—
760#552—534no—
761#552—538no—
762#552—534no—
763#552—534no—
764#552—534no—
765#552C2×D5314yes—
766#547—538no—
767#547—538no—
768#547—538no—
769#547—534no—
770#547—538no—
771#547—534no—
772#547—534no—
773#547C2×D5314yes—
774#544—534no—
775#544—534no—
776#544—534no—
777#544—532no—
778#544—534no—
779#544—534no—
780#544—531no—
781#544—534no—
782#544C2×D5311yescharacteristic
783#541—538no—
784#541—538no—
785#541—538no—
786#541—534no—
787#541—538no—
788#541—534no—
789#540—534no—
790#540—534no—
791#539—538no—
792#539—538no—
793#539—538no—
794#539—538no—
795#539—538no—
796#539—538no—
797#539—534no—
798#539—538no—
799#539—534no—
800#539—538no—
801#539—534no—
802#539C2×D5314yes—
803#537—532no—
804#537—534no—
805#537—534no—
806#537—531no—
807#537C2×D5311yescharacteristic
808#533—534no—
809#533—532no—
810#533—532no—
811#533—532no—
812#533—534no—
813#532—532no—
814#532—532no—
815#532—532no—
816#529—534no—
817#529—534no—
818#529—532no—
819#529—532no—
820#529—534no—
821#529—532no—
822#529—532no—
823#529—534no—
824#529—534no—
825#529—534no—
826#529—534no—
827#529—534no—
828C2×#125—534no—
829C2×#125—532no—
830C2×#125—532no—
831C2×#125—534no—
832C2×#125—534no—
833C2×#125—534no—
834C2×#125—534no—
835C2×#125—534no—
836C2×#125—534no—
837#525—532no—
838#525—534no—
839#525—534no—
840#525—534no—
841#525—538no—
842#525C2×D5312yes—
843#525C2×D5314yes—
844#520—532no—
845#520—534no—
846#520—538no—
847#520—532no—
848#520—534no—
849#520—532no—
850#520C2×D5312yes—
851C4×#41—532no—
852C4×#41—534no—
853C4×#41—534no—
854C4×#41—532no—
855C22×C4⋊C4—532no—
856C22×C4⋊C4—531no—
857C22×C4⋊C4—532no—
858C22×C4⋊C4C2×D5311yescharacteristic
859C22×C42—531no—
860C53#6282511yescharacteristic, complemented, Sylow
861C2×#41—534no—
862C2×#41—534no—
863C2×#41—538no—
864C2×#41—532no—
865C2×#41—534no—
866C2×#41C22×D5312yes—
867C2×#41C22×D5314yes—
868C23×C4—532no—
869C23×C4—531no—
870C23×C4—531no—
871C23×C4C22×D5311yescharacteristic
872C23×C4C22×D5312yes—
873C4⋊Q8—532no—
874C4⋊Q8—538no—
875C4⋊Q8—532no—
876C4⋊Q8—532no—
877C4⋊Q8—534no—
878C4⋊Q8—534no—
879C4⋊Q8—538no—
880C4⋊Q8—538no—
881C4⋊Q8—534no—
882C4⋊Q8—538no—
883C4⋊Q8C22×D5314yes—
884#127—532no—
885#126—534no—
886#126—534no—
887#126—538no—
888#126—538no—
889#126—538no—
890#126—538no—
891#126—538no—
892#126—534no—
893#126—534no—
894#126—538no—
895#126—538no—
896#126—538no—
897#126—538no—
898#126—538no—
899#126—538no—
900#126C22×D5318yes—
901#125—534no—
902#125—534no—
903#125—538no—
904#125—538no—
905#125—534no—
906#125—534no—
907#125—538no—
908#125—534no—
909#125—534no—
910#125—534no—
911#125—534no—
912#125—538no—
913#125—532no—
914#125—532no—
915#125—538no—
916#125—538no—
917#125—538no—
918#125—538no—
919#125—534no—
920#125—534no—
921#125—534no—
922#125—534no—
923#125—538no—
924#125—538no—
925#125—538no—
926#125—538no—
927#125—538no—
928#125—538no—
929#125—538no—
930#125—538no—
931#125—538no—
932#125—534no—
933#125—538no—
934#125—538no—
935#125C22×D5314yes—
936#125C22×D5318yes—
937#124—532no—
938#124—532no—
939#124—534no—
940#124—534no—
941#123—534no—
942#123—534no—
943#123—538no—
944#123—538no—
945#123—534no—
946#123—538no—
947#123—538no—
948#123—538no—
949#123—538no—
950#123—534no—
951#123—534no—
952#123—538no—
953#123—538no—
954#123—538no—
955#123—538no—
956#123—538no—
957#123—538no—
958#123—538no—
959#123—538no—
960#123C22×D5314yes—
961#123C22×D5318yes—
962#123C22×D5318yes—
963C22⋊Q8—534no—
964C22⋊Q8—538no—
965C22⋊Q8—538no—
966C22⋊Q8—532no—
967C22⋊Q8—532no—
968C22⋊Q8—534no—
969C22⋊Q8—534no—
970C22⋊Q8—534no—
971C22⋊Q8—538no—
972C22⋊Q8—538no—
973C22⋊Q8—534no—
974C22⋊Q8—538no—
975C22⋊Q8—538no—
976C22⋊Q8—538no—
977C22⋊Q8—538no—
978C22⋊Q8—538no—
979C22⋊Q8—538no—
980C22⋊Q8—534no—
981C22⋊Q8—534no—
982C22⋊Q8—534no—
983C22⋊Q8—534no—
984C22⋊Q8—538no—
985C22⋊Q8—538no—
986C22⋊Q8—538no—
987C22⋊Q8—538no—
988C22⋊Q8—538no—
989C22⋊Q8—538no—
990C22⋊Q8—538no—
991C22⋊Q8C22×D5312yes—
992C22⋊Q8C22×D5312yes—
993C22⋊Q8C22×D5314yes—
994C22⋊Q8C22×D5314yes—
995C22⋊Q8C22×D5314yes—
996C22⋊Q8C22×D5318yes—
997#121—534no—
998#121—534no—
999#121—534no—
1000#121—534no—
1001#121—538no—
1002#121—538no—
1003#121—534no—
1004#121—538no—
1005#121—538no—
1006#121—532no—
1007#121—532no—
1008#121—534no—
1009#121—534no—
1010#121—534no—
1011#121—538no—
1012#121—534no—
1013#121—538no—
1014#121C22×D5312yes—
1015#121C22×D5312yes—
1016#121C22×D5314yes—
1017#121C22×D5314yes—
1018#121C22×D5314yes—
1019#120—534no—
1020#120C22×D5314yes—
1021C4×Q8—532no—
1022C4×Q8—532no—
1023C4×Q8—534no—
1024C4×Q8—538no—
1025C4×Q8—534no—
1026C4×Q8—534no—
1027C4×Q8—532no—
1028C4×Q8—532no—
1029C4×Q8—534no—
1030C4×Q8—538no—
1031C4×Q8—534no—
1032C4×Q8—534no—
1033C4×Q8—534no—
1034C4×Q8—538no—
1035C4×Q8—538no—
1036C4×Q8C22×D5314yes—
1037C4×D4—534no—
1038C4×D4—534no—
1039C4×D4—534no—
1040C4×D4—534no—
1041C4×D4—532no—
1042C4×D4—532no—
1043C4×D4—538no—
1044C4×D4—538no—
1045C4×D4—538no—
1046C4×D4—534no—
1047C4×D4—534no—
1048C4×D4—534no—
1049C4×D4—534no—
1050C4×D4—534no—
1051C4×D4—538no—
1052C4×D4—538no—
1053C4×D4—538no—
1054C4×D4—532no—
1055C4×D4—532no—
1056C4×D4—534no—
1057C4×D4—534no—
1058C4×D4—534no—
1059C4×D4—534no—
1060C4×D4—534no—
1061C4×D4—534no—
1062C4×D4—534no—
1063C4×D4—538no—
1064C4×D4—538no—
1065C4×D4—538no—
1066C4×D4—538no—
1067C4×D4—534no—
1068C4×D4C22×D5314yes—
1069C4×D4C22×D5314yes—
1070C4×D4C22×D5318yes—
1071C4×D4C22×D5318yes—
1072C4×D4C22×D5314yes—
1073#117—532no—
1074#117—534no—
1075#117—534no—
1076#117—538no—
1077#117—534no—
1078#117—534no—
1079#117—534no—
1080#117—538no—
1081#117—534no—
1082#117—534no—
1083#117—534no—
1084#117—534no—
1085#117—534no—
1086#117—534no—
1087#117—538no—
1088#117—538no—
1089#117—534no—
1090#117—538no—
1091#117C22×D5312yes—
1092#117C22×D5314yes—
1093#117C22×D5314yes—
1094C2×C4⋊C4—532no—
1095C2×C4⋊C4—534no—
1096C2×C4⋊C4—534no—
1097C2×C4⋊C4—534no—
1098C2×C4⋊C4—534no—
1099C2×C4⋊C4—532no—
1100C2×C4⋊C4—538no—
1101C2×C4⋊C4—534no—
1102C2×C4⋊C4—538no—
1103C2×C4⋊C4—534no—
1104C2×C4⋊C4—534no—
1105C2×C4⋊C4—534no—
1106C2×C4⋊C4—534no—
1107C2×C4⋊C4—534no—
1108C2×C4⋊C4—538no—
1109C2×C4⋊C4—538no—
1110C2×C4⋊C4—534no—
1111C2×C4⋊C4—538no—
1112C2×C4⋊C4—538no—
1113C2×C4⋊C4—534no—
1114C2×C4⋊C4—534no—
1115C2×C4⋊C4C22×D5311yescharacteristic
1116C2×C4⋊C4C22×D5311yescharacteristic
1117C2×C4⋊C4C22×D5312yes—
1118C2×C4⋊C4C22×D5314yes—
1119C2×C4⋊C4C22×D5314yes—
1120C2×C4⋊C4C22×D5314yes—
1121C2×C42—534no—
1122C2×C42—532no—
1123C2×C42—532no—
1124C2×C42—532no—
1125C2×C42—532no—
1126C2×C42—532no—
1127C2×C42—532no—
1128C2×C42—534no—
1129C24C23×D5311yescharacteristic
1130#41—28no—
1131#41—48no—
1132#41—1068no—
1133#41—2128no—
1134#41—2128no—
1135#41—2128no—
1136#41—21216no—
1137C2×Q8—532no—
1138C2×Q8—534no—
1139C2×Q8—538no—
1140C2×Q8—534no—
1141C2×Q8—534no—
1142C2×Q8C23×D5312yes—
1143C2×Q8C23×D5314yes—
1144C2×D4—534no—
1145C2×D4—534no—
1146C2×D4—534no—
1147C2×D4—538no—
1148C2×D4—534no—
1149C2×D4—534no—
1150C2×D4—532no—
1151C2×D4—534no—
1152C2×D4C23×D5314yes—
1153C2×D4C23×D5312yes—
1154C2×D4C23×D5314yes—
1155C2×D4C23×D5314yes—
1156C2×D4C23×D5314yes—
1157C22×C4—24no—
1158C22×C4—44no—
1159C22×C4—532no—
1160C22×C4—532no—
1161C22×C4—534no—
1162C22×C4—531no—
1163C22×C4—531no—
1164C22×C4—532no—
1165C22×C4—532no—
1166C22×C4—531no—
1167C22×C4—531no—
1168C22×C4—534no—
1169C22×C4—534no—
1170C22×C4—534no—
1171C22×C4—534no—
1172C22×C4—538no—
1173C22×C4—534no—
1174C22×C4—534no—
1175C22×C4—534no—
1176C22×C4—538no—
1177C22×C4—538no—
1178C22×C4—2122no—
1179C22×C4—2124no—
1180C22×C4—2122no—
1181C22×C4C23×D5312yes—
1182C22×C4C23×D5312yes—
1183C22×C4C23×D5311yescharacteristic
1184C22×C4C23×D5314yes—
1185C22×C4C23×D5314yes—
1186C22×C4C23×D5312yes—
1187C22×C4C23×D5314yes—
1188C22×C4C23×D5312yes—
1189C22×C4C23×D5318yes—
1190C22×C4C23×D5311yescharacteristic
1191C4⋊C4—534no—
1192C4⋊C4—534no—
1193C4⋊C4—538no—
1194C4⋊C4—538no—
1195C4⋊C4—538no—
1196C4⋊C4—538no—
1197C4⋊C4—538no—
1198C4⋊C4—538no—
1199C4⋊C4—538no—
1200C4⋊C4—538no—
1201C4⋊C4—538no—
1202C4⋊C4—532no—
1203C4⋊C4—532no—
1204C4⋊C4—534no—
1205C4⋊C4—534no—
1206C4⋊C4—534no—
1207C4⋊C4—534no—
1208C4⋊C4—538no—
1209C4⋊C4—534no—
1210C4⋊C4—538no—
1211C4⋊C4—538no—
1212C4⋊C4—538no—
1213C4⋊C4—538no—
1214C4⋊C4—538no—
1215C4⋊C4—538no—
1216C4⋊C4—538no—
1217C4⋊C4—534no—
1218C4⋊C4—534no—
1219C4⋊C4—534no—
1220C4⋊C4—534no—
1221C4⋊C4—534no—
1222C4⋊C4—534no—
1223C4⋊C4—534no—
1224C4⋊C4—534no—
1225C4⋊C4—534no—
1226C4⋊C4—534no—
1227C4⋊C4—534no—
1228C4⋊C4C23×D5312yes—
1229C4⋊C4C23×D5314yes—
1230C4⋊C4C23×D5314yes—
1231C4⋊C4C23×D5318yes—
1232C4⋊C4C23×D5314yes—
1233C4⋊C4C23×D5318yes—
1234C4⋊C4C23×D5312yes—
1235C4⋊C4C23×D5318yes—
1236C4⋊C4C23×D5314yes—
1237C4⋊C4C23×D5314yes—
1238C4⋊C4C23×D5314yes—
1239C22⋊C4—534no—
1240C22⋊C4—534no—
1241C22⋊C4—534no—
1242C22⋊C4—534no—
1243C22⋊C4—534no—
1244C22⋊C4—534no—
1245C22⋊C4—534no—
1246C22⋊C4—538no—
1247C22⋊C4—538no—
1248C22⋊C4—534no—
1249C22⋊C4—534no—
1250C22⋊C4—534no—
1251C22⋊C4—534no—
1252C22⋊C4—538no—
1253C22⋊C4—538no—
1254C22⋊C4—538no—
1255C22⋊C4—538no—
1256C22⋊C4—534no—
1257C22⋊C4—534no—
1258C22⋊C4C23×D5314yes—
1259C22⋊C4C23×D5314yes—
1260C22⋊C4C23×D5318yes—
1261C22⋊C4C23×D5314yes—
1262C22⋊C4C23×D5314yes—
1263C22⋊C4C23×D5314yes—
1264C22⋊C4C23×D5318yes—
1265C42—532no—
1266C42—532no—
1267C42—532no—
1268C42—532no—
1269C42—532no—
1270C42—532no—
1271C42—532no—
1272C42—532no—
1273C42—534no—
1274C42—534no—
1275C42—534no—
1276C42—534no—
1277C42—534no—
1278C42—538no—
1279C42—538no—
1280C42—538no—
1281C42C23×D5314yes—
1282C42C23×D5318yes—
1283C23—22no—
1284C23—22no—
1285C23—22no—
1286C23—534no—
1287C23C24×D5314yes—
1288C23C24×D5311yescharacteristic
1289C23C24×D5311yescharacteristic
1290C23C24×D5311yescharacteristic
1291Q8—24no—
1292Q8—44no—
1293Q8—1064no—
1294Q8—2124no—
1295Q8—2124no—
1296Q8—2128no—
1297Q8—2124no—
1298D4—28no—
1299D4—28no—
1300D4—28no—
1301D4—24no—
1302D4—44no—
1303D4—1068no—
1304D4—1068no—
1305D4—1068no—
1306D4—1064no—
1307D4—2124no—
1308D4—2124no—
1309D4—2128no—
1310D4—2124no—
1311C2×C4—22no—
1312C2×C4—28no—
1313C2×C4—24no—
1314C2×C4—24no—
1315C2×C4—28no—
1316C2×C4—42no—
1317C2×C4—44no—
1318C2×C4—42no—
1319C2×C4—48no—
1320C2×C4—532no—
1321C2×C4—532no—
1322C2×C4—534no—
1323C2×C4—534no—
1324C2×C4—534no—
1325C2×C4—532no—
1326C2×C4—532no—
1327C2×C4—538no—
1328C2×C4—1064no—
1329C2×C4—1064no—
1330C2×C4—1068no—
1331C2×C4—1068no—
1332C2×C4—2128no—
1333C2×C4—2124no—
1334C2×C4—2124no—
1335C2×C4—2128no—
1336C2×C4—2121no—
1337C2×C4—2122no—
1338C2×C4—2121no—
1339C2×C4—2121no—
1340C2×C4—2122no—
1341C2×C4—2124no—
1342C2×C4—2124no—
1343C2×C4—2121no—
1344C2×C4—2124no—
1345C2×C4—2124no—
1346C2×C4—2128no—
1347C2×C4#1313326414yes—
1348C2×C4C24×D5314yes—
1349C2×C4C24×D5312yes—
1350C2×C4C24×D5314yes—
1351C2×C4C24×D5314yes—
1352C2×C4C24×D5314yes—
1353C2×C4C24×D5314yes—
1354C2×C4C24×D5312yes—
1355C22—28no—
1356C22—21no—
1357C22—21no—
1358C22—21no—
1359C22—21no—
1360C22—21no—
1361C22—21no—
1362C22—24no—
1363C22—24no—
1364C22—24no—
1365C22—1064no—
1366C22—1064no—
1367C22—1064no—
1368C22C2×#1313326412yes—
1369C22#1681145812yes—
1370C22#1681146012yes—
1371C22C25×D5311yescharacteristic
1372C4—22no—
1373C4—24no—
1374C4—24no—
1375C4—24no—
1376C4—24no—
1377C4—24no—
1378C4—1064no—
1379C4—1062no—
1380C4—1062no—
1381C4—1064no—
1382C4—1062no—
1383C4—1068no—
1384C4—1062no—
1385C4—1064no—
1386C4C2×#1313326414yes—
1387C2—22no—
1388C2—22no—
1389C2—22no—
1390C2—44no—
1391C2—2124no—
1392C2C22×#1313326411yescharacteristic
1393C2C2×#1681145811yescharacteristic
1394C2C2×#1681146011yescharacteristic
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3492C2
hypercenter#3492D53
hypocenterC53#62825
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3492

Complements

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

NH ≅ G/Ntype
1. #20289319C2semidirect
2. #20289316C2semidirect
3. #20289247C2semidirect
4. #20289244C2semidirect
5. #20289165C2semidirect
6. #20288694C2semidirect
7. #20288690C2semidirect
8. #20288686C2semidirect
9. #20288684C2semidirect
10. #20288636C2semidirect
11. #20288632C2semidirect
12. #20288538C2semidirect
13. #20288537C2semidirect
14. #20288424C2semidirect
15. #20288421C2semidirect
16. #20288421C2semidirect
17. #20288416C2semidirect
18. #20288007C2semidirect
19. C22×#13133208C2semidirect
20. C53×#3492C2semidirect
21. C53⋊#564C22semidirect
22. #16811375C22semidirect
23. #16811374C22semidirect
24. #16811370C22semidirect
25. #16811352C22semidirect
26. #16811350C22semidirect
27. #16811349C22semidirect
28. #16811348C22semidirect
29. #16811334C22semidirect
31. #16811332C22semidirect
36. #16811330C22semidirect
37. #16811329C22semidirect
42. #16811325C22semidirect
45. #16811321C22semidirect
46. #16811320C22semidirect
49. #16811317C22semidirect
53. #16811315C22semidirect
54. #16811315C22semidirect
57. #16811312C22semidirect
58. #16811311C22semidirect
60. #16811310C22semidirect
61. #16811309C22semidirect
63. #16811308C22semidirect
64. #16811307C22semidirect
74. #16811254C22semidirect
75. #16811253C22semidirect
79. #16811251C22semidirect
80. #16811250C22semidirect
81. #16811236C22semidirect
82. #16811233C22semidirect
83. #16811233C22semidirect
84. #16811232C22semidirect
85. #16811231C22semidirect
86. #16811230C22semidirect
87. #16811226C22semidirect
88. #16811224C22semidirect
90. #16811222C22semidirect
96. #16811217C22semidirect
97. #16811216C22semidirect
99. #16811214C22semidirect
104. #16811178C22semidirect
106. #16811176C22semidirect
112. #16811160C22semidirect
115. #16811159C22semidirect
116. #16811155C22semidirect
119. #16811154C22semidirect
131. C2×#13133208C22semidirect
132. #125×D53C22semidirect
707. #3492D53semidirect
860. C53#62825semidirect

Maximal subgroups

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

subgroupindex
#202893192
#202893162
#202892472
#202892442
#202891652
#202886942
#202886902
#202886862
#202886842
#202886362
#202886322
#202885382
#202885372
#202884242
#202884212
#202884162
#202880072
C22×#131332082
C53×#34922
#6282553