Finite Group Databasebeta

← D53×#3548 #28291881

Subgroups — D53×#3548 #28291881

Order 13568.

7810 conjugacy classes of subgroups.

The subgroup lattice has 1016 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289115C211yesmaximal, characteristic, complemented
2#20289114C214yesmaximal, complemented
3#20289113C212yesmaximal, complemented
4#20289112C214yesmaximal, complemented
5#20289111C214yesmaximal, complemented
6#20289110C218yesmaximal, complemented
7#20289109C214yesmaximal, complemented
8#20289108C214yesmaximal, complemented
9#562×D53C214yesmaximal, complemented
10#554×D53C214yesmaximal, complemented
11#550×D53C214yesmaximal, complemented
12#547×D53C214yesmaximal, complemented
13#540×D53C214yesmaximal, complemented
14#537×D53C218yesmaximal, complemented
15#533×D53C211yesmaximal, characteristic, complemented
16#532×D53C212yesmaximal, complemented
17C53×#3548C211yesmaximal, characteristic, complemented
18C2×#41×D53C2214yes—
19C2×#41×D53C2218yes—
20#16811371C2214yescomplemented
21#16811370C22116yescomplemented
22#16811369C22116yescomplemented
23#16811368C22116yescomplemented
24#16811367C2218yescomplemented
25#16811334C2214yescomplemented
26#16811333C2214yescomplemented
27#16811332C2218yescomplemented
28#16811331C2218yescomplemented
29#16811330C2214yescomplemented
30#16811329C2218yescomplemented
31#16811328C2218yescomplemented
32#16811327C22116yescomplemented
33#16811295C2214yescomplemented
34#16811294C2218yescomplemented
35#16811294C2214yescomplemented
36#16811293C2218yescomplemented
37#16811293C2214yescomplemented
38#16811292C2218yescomplemented
39#16811291C22116yescomplemented
40#16811291C2218yescomplemented
41#16811278C2214yescomplemented
42#16811277C2214yescomplemented
43#16811276C2214yescomplemented
44#16811275C2218yescomplemented
45#16811274C2218yescomplemented
46#16811273C2218yescomplemented
47#16811272C2218yescomplemented
48#16811271C22116yescomplemented
49#16811229C2214yescomplemented
50#16811228C2214yescomplemented
51#16811227C2214yescomplemented
52#16811226C2218yescomplemented
53#16811225C22116yescomplemented
54#16811224C2218yescomplemented
55#16811223C22116yescomplemented
56#16811204C2218yescomplemented
57#16811203C2218yescomplemented
58#16811203C22116yescomplemented
59#16811203C2218yescomplemented
60#16811202C2218yescomplemented
61#16811202C22116yescomplemented
62#16811202C2218yescomplemented
63#16811201C2218yescomplemented
64#16811201C2218yescomplemented
65#16811200C22116yescomplemented
66#16811200C22116yescomplemented
67#16811180C2211yescharacteristic, complemented
68#16811179C2212yescomplemented
69#16811178C2212yescomplemented
70#16811177C2214yescomplemented
71#16811176C2212yescomplemented
72#16811175C2214yescomplemented
73#16811174C2212yescomplemented
74#16811173C2212yescomplemented
75#16811172C2214yescomplemented
76#16811171C2212yescomplemented
77#16811170C2214yescomplemented
78#16811170C2214yescomplemented
79#16811169C2214yescomplemented
80#16811168C2214yescomplemented
81#16811168C2214yescomplemented
82C4⋊Q8×D53C2212yes—
83C4⋊Q8×D53C2212yes—
84#127×D53C2214yes—
85#127×D53C2212yes—
86#125×D53C2212yes—
87#125×D53C2214yes—
88#124×D53C2214yes—
89#123×D53C22116yes—
90C22⋊Q8×D53C2214yes—
91C22⋊Q8×D53C22116yes—
92C22⋊Q8×D53C2218yes—
93#121×D53C22116yes—
94#121×D53C2214yes—
95#121×D53C22116yes—
96#121×D53C2218yes—
97#121×D53C2214yes—
98C4×Q8×D53C2214yes—
99C4×D4×D53C2218yes—
100C4×D4×D53C2214yes—
101C4×D4×D53C2214yes—
102#117×D53C2212yes—
103C2×C4⋊C4×D53C2218yes—
104C2×C42×D53C2211yescharacteristic
105C53×#562C2214yescomplemented
106C53×#554C2214yescomplemented
107C53×#550C2214yescomplemented
108C53×#547C2214yescomplemented
109C53×#540C2214yescomplemented
110C53×#537C2218yescomplemented
111C53×#533C2211yescharacteristic, complemented
112C53×#532C2212yescomplemented
113C2×#11719949C2318yes—
114C2×#11719949C2314yes—
115C2×#11719945C23116yes—
116C2×#11719945C2318yes—
117C2×#11719945C2314yes—
118C2×#11719945C2318yes—
119C2×#11719947C23116yes—
120C2×#11719947C2318yes—
121C2×#11719947C2318yes—
122C2×#11719947C2314yes—
123#41×D53—416no—
124#41×D53—432no—
125C2×Q8×D53C2314yes—
126C2×Q8×D53C2314yes—
127C2×D4×D53C2314yes—
128C2×D4×D53C2314yes—
129C2×D4×D53C2318yes—
130C2×D4×D53C23116yes—
131C2×D4×D53C2314yes—
132C22×C4×D53C2311yescharacteristic
133C22×C4×D53C2312yes—
134C22×C4×D53C2318yes—
135C22×C4×D53C23116yes—
136#13133217C2312yes—
137#13133217C2312yes—
138#13133216C2314yes—
139#13133216C2314yes—
140#13133216C2314yes—
141#13133216C2314yes—
142#13133215C2314yes—
143#13133215C2314yes—
144#13133214C2312yes—
145#13133214C2314yes—
146#13133213C2314yes—
147#13133213C23116yes—
148#13133213C2314yes—
149#13133213C2314yes—
150#13133213C2318yes—
151#13133209C2314yes—
152#13133209C2312yes—
153#13133208C2318yes—
154#13133208C2314yes—
155#13133207C23116yes—
156#13133207C2318yes—
157#13133206C2314yes—
158#13133205C2314yes—
159#13133204C2314yes—
160#13133203C2318yes—
161#13133203C2318yes—
162#13133202C23116yes—
163#13133202C23116yes—
164#13133201C23116yes—
165#13133200C23116yes—
166#13133199C23116yes—
167#13133199C23116yes—
168#13133198C23116yes—
169#13133197C2318yes—
170#13133197C23116yes—
171#13133197C2314yes—
172#13133196C2318yes—
173#13133196C23116yes—
174#13133196C2314yes—
175#13133195C23116yes—
176#13133195C23116yes—
177#13133195C23116yes—
178#13133195C2318yes—
179#13133194C23116yes—
180#13133194C23116yes—
181#13133194C23116yes—
182#13133194C2318yes—
183#13133193C2318yes—
184#13133193C23116yes—
185#13133193C2314yes—
186#13133192C2318yes—
187#13133192C23116yes—
188#13133192C2314yes—
189#13133192C2314yes—
190#13133192C23116yes—
191#13133191C2318yes—
192#13133191C23116yes—
193#13133191C2314yes—
194#13133191C2314yes—
195#13133191C23116yes—
196#13133190C23116yes—
197#13133190C23116yes—
198#13133190C23116yes—
199#13133190C2318yes—
200#13133190C2318yes—
201#13133190C23116yes—
202#13133190C23116yes—
203#13133189C23116yes—
204#13133189C23116yes—
205#13133189C23116yes—
206#13133189C2318yes—
207#13133189C2318yes—
208#13133189C23116yes—
209#13133189C23116yes—
210#13133188C2318yes—
211#13133188C23116yes—
212#13133188C2314yes—
213#13133188C2314yes—
214#13133188C23116yes—
215Q8×Dic53C2314yes—
216C4×Dic106C2318yes—
217C4×Dic106C2314yes—
218#13133182C2318yes—
219#13133182C2314yes—
220C4×D212C2314yes—
221C4×D212C2318yes—
222C4×D212C2314yes—
223D4×Dic53C2314yes—
224D4×Dic53C2318yes—
225D4×Dic53C2314yes—
226#13133179C2314yes—
227#13133179C2314yes—
228#13133179C2318yes—
229C4×C22⋊D53C2318yes—
230C4×C22⋊D53C23116yes—
231C4×C22⋊D53C2318yes—
232#13133177C2318yes—
233#13133177C2318yes—
234#13133177C23116yes—
235#13133176C2312yes—
236#13133175C2314yes—
237#13133174C2314yes—
238#13133173C2314yes—
239C2×C4⋊Dic53C2318yes—
240C2×#11719919C23116yes—
241C4⋊C4×D53C23116yes—
242C4⋊C4×D53C2318yes—
243C4⋊C4×D53C2318yes—
244C4⋊C4×D53C2314yes—
245C4⋊C4×D53C2314yes—
246C4⋊C4×D53C23116yes—
247C4⋊C4×D53C2314yes—
248C4⋊C4×D53C2314yes—
249C4⋊C4×D53C2318yes—
250C22⋊C4×D53C2314yes—
251C22⋊C4×D53C23116yes—
252C22⋊C4×D53C2318yes—
253C22⋊C4×D53C2318yes—
254C2×C4×Dic53C2311yescharacteristic
255C2×C4×Dic53C2312yes—
256C42×D53C2311yescharacteristic
257C42×D53C2312yes—
258C42×D53C2311yescharacteristic
259C42×D53C2311yescharacteristic
260C42×D53C2312yes—
261C42×D53C2311yescharacteristic
262C42×D53C2314yes—
263C2×#41×C53C2318yes—
264C2×#41×C53C2314yes—
265C4⋊Q8×C53C2312yes—
266C4⋊Q8×C53C2312yes—
267#127×C53C2312yes—
268#127×C53C2314yes—
269#125×C53C2312yes—
270#125×C53C2314yes—
271#124×C53C2314yes—
272#123×C53C23116yes—
273C22⋊Q8×C53C2318yes—
274C22⋊Q8×C53C2314yes—
275C22⋊Q8×C53C23116yes—
276#121×C53C2318yes—
277#121×C53C23116yes—
278#121×C53C2314yes—
279#121×C53C2314yes—
280#121×C53C23116yes—
281C4×Q8×C53C2314yes—
282C4×D4×C53C2314yes—
283C4×D4×C53C2314yes—
284C4×D4×C53C2318yes—
285#117×C53C2312yes—
286C2×C4⋊C4×C53C2318yes—
287C2×C42×C53C2311yescharacteristic
288C23×D53C2411yescharacteristic
289C23×D53C2418yes—
290#41×C53—48no—
291#41×C53—416no—
292C2×Q8×C53C2414yes—
293C2×Q8×C53C2414yes—
294C2×D4×C53C2414yes—
295C2×D4×C53C2414yes—
296C2×D4×C53C2418yes—
297C2×D4×C53C24116yes—
298C2×D4×C53C2414yes—
299C22×C4×C53C2411yescharacteristic
300C22×C4×C53C2412yes—
301C22×C4×C53C2418yes—
302C22×C4×C53C24116yes—
303C2×C22⋊D53C2418yes—
304C2×C22⋊D53C2418yes—
305C2×C22⋊D53C2418yes—
306C2×C22⋊D53C2418yes—
307C2×C22⋊D53C24116yes—
308C2×C22⋊D53C2418yes—
309C2×C22⋊D53C24116yes—
310C22×Dic53C2411yescharacteristic
311C22×Dic53C2412yes—
312C22×Dic53C2418yes—
313C22×Dic53C24116yes—
314#11719949—48no—
315#11719949—416no—
316Q8×D53—216no—
317Q8×D53—48no—
318#11719947—416no—
319#11719947—432no—
320#11719947—416no—
321#11719947—48no—
322D4×D53—216no—
323D4×D53—216no—
324D4×D53—416no—
325D4×D53—48no—
326D4×D53—432no—
327#11719945—432no—
328#11719945—416no—
329#11719945—416no—
330#11719945—48no—
331C2×D212C2414yes—
332C2×D212C2414yes—
333C2×D212C2418yes—
334C2×D212C2414yes—
335C2×D212C24116yes—
336C2×C4×D53—232no—
337C2×C4×D53—28no—
338C2×C4×D53—24no—
339C2×C4×D53—432no—
340C2×C4×D53C2411yescharacteristic
341C2×C4×D53C2412yes—
342C2×C4×D53C2411yescharacteristic
343C2×C4×D53C2411yescharacteristic
344C2×C4×D53C2412yes—
345C2×C4×D53C2412yes—
346C2×C4×D53C2418yes—
347C2×C4×D53C2418yes—
348C2×C4×D53C2418yes—
349C2×C4×D53C2418yes—
350C2×C4×D53C24116yes—
351C2×C4×D53C24116yes—
352C2×C4×D53C2412yes—
353C2×C4×D53C2411yescharacteristic
354C2×Dic106C2418yes—
355C2×Dic106C2414yes—
356C2×Dic106C2414yes—
357C2×Dic106C2418yes—
358C4⋊C4×C53C2414yes—
359C4⋊C4×C53C2414yes—
360C4⋊C4×C53C24116yes—
361C4⋊C4×C53C2414yes—
362C4⋊C4×C53C2414yes—
363C4⋊C4×C53C2418yes—
364C22⋊C4×C53C2414yes—
365C22⋊C4×C53C24116yes—
366C22⋊C4×C53C2418yes—
367C22⋊C4×C53C2418yes—
368C42×C53C2411yescharacteristic
369C42×C53C2412yes—
370C42×C53C2411yescharacteristic
371C42×C53C2414yes—
372C22⋊Dic53C2414yes—
373C22⋊Dic53C24116yes—
374C22⋊Dic53C2418yes—
375C22⋊Dic53C2418yes—
376#11719921C2418yes—
377#11719921C2418yes—
378#11719921C24116yes—
379#11719921C2418yes—
380#11719921C24116yes—
381#11719921C2418yes—
382#11719921C2418yes—
383C4⋊Dic53C2414yes—
384C4⋊Dic53C2414yes—
385C4⋊Dic53C24116yes—
386C4⋊Dic53C2414yes—
387C4⋊Dic53C2414yes—
388C4⋊Dic53C2418yes—
389#11719919C2418yes—
390#11719919C2418yes—
391#11719919C24116yes—
392#11719919C24116yes—
393#11719919C2418yes—
394#11719919C2418yes—
395#11719919C2418yes—
396#11719919C2418yes—
397C4×Dic53C2411yescharacteristic
398C4×Dic53C2412yes—
399C4×Dic53C2412yes—
400C4×Dic53C2412yes—
401C4×Dic53C2412yes—
402C4×Dic53C2411yescharacteristic
403C4×Dic53C2412yes—
404C4×Dic53C2418yes—
405C4×Dic53C2414yes—
406C23×C53C2511yescharacteristic
407C23×C53C2518yes—
408C22×D53—24no—
409C22×D53—216no—
410C22×D53—216no—
411C22×D53—22no—
412C22×D53—216no—
413C22×D53C2511yescharacteristic
414C22×D53C2518yes—
415C22×D53C2511yescharacteristic
416Q8×C53—28no—
417Q8×C53—44no—
418D4×C53—28no—
419D4×C53—28no—
420D4×C53—416no—
421D4×C53—44no—
422D4×C53—48no—
423C2×C4×C53—24no—
424C2×C4×C53—216no—
425C2×C4×C53—22no—
426C2×C4×C53—416no—
427C2×C4×C53C2512yes—
428C2×C4×C53C2518yes—
429C2×C4×C53C2518yes—
430C2×C4×C53C2511yescharacteristic
431C2×C4×C53C2512yes—
432C2×C4×C53C2511yescharacteristic
433C22⋊D53—216no—
434C22⋊D53—216no—
435C22⋊D53—416no—
436C22⋊D53—416no—
437C22⋊D53—48no—
438C22⋊D53—48no—
439C22⋊D53—48no—
440C2×Dic53—24no—
441C2×Dic53—216no—
442C2×Dic53—22no—
443C2×Dic53—416no—
444C2×Dic53C2512yes—
445C2×Dic53C2518yes—
446C2×Dic53C2518yes—
447C2×Dic53C2511yescharacteristic
448C2×Dic53C2512yes—
449C2×Dic53C2511yescharacteristic
450D212—28no—
451D212—28no—
452D212—416no—
453D212—44no—
454D212—48no—
455C4×D53—216no—
456C4×D53—24no—
457C4×D53—216no—
458C4×D53—22no—
459C4×D53—24no—
460C4×D53—216no—
461C4×D53—22no—
462C4×D53—216no—
463C4×D53—24no—
464C4×D53—22no—
465C4×D53—416no—
466C4×D53—416no—
467C4×D53H(5,𝔽2)18yes—
468C4×D532−1+414yes—
469Dic106—28no—
470Dic106—216no—
471Dic106—48no—
472Dic106—44no—
473C2×#3548—531nomaximal, Sylow
474C22×C53—22no—
475C22×C53—28no—
476C22×C53—28no—
477C22×C53—21no—
478C22×C53—28no—
479C22×C53C2611yescharacteristic
480C2×D53—22no—
481C2×D53—28no—
482C2×D53—28no—
483C2×D53—21no—
484C2×D53—28no—
485C2×D53—44no—
486C2×D53—432no—
487C2×D53C2×H(5,𝔽2)14yes—
488C2×D53C2×2−1+412yes—
489C4×C53—28no—
490C4×C53—22no—
491C4×C53—28no—
492C4×C53—21no—
493C4×C53C2×H(5,𝔽2)14yes—
494C4×C53C2×2−1+412yes—
495Dic53—28no—
496Dic53—22no—
497Dic53—28no—
498Dic53—21no—
499Dic53C2×H(5,𝔽2)14yes—
500Dic53C2×2−1+412yes—
501#3548—534no—
502#3548—534no—
503#3548—534no—
504#3548—534no—
505#3548—534no—
506#3548—538no—
507#3548—531no—
508#3548—532no—
509#3548D5311yescharacteristic, direct product factor
510C2×#562—534no—
511C2×#554—534no—
512C2×#550—534no—
513C2×#547—534no—
514C2×#540—534no—
515C2×#537—538no—
516C2×#533—531no—
517C2×#532—532no—
518C2×C53—41no—
519C2×C53—48no—
520C2×C53C22×H(5,𝔽2)12yes—
521C2×C53C22×2−1+411yescharacteristic
522D53—41no—
523D53—48no—
524D53#354814yesdirect product factor
525C22×#41—534no—
526C22×#41—538no—
527#562—534no—
528#562—538no—
529#562—5316no—
530#562—5316no—
531#562—5316no—
532#562C2×D5314yescomplemented
533#554—534no—
534#554—538no—
535#554—5316no—
536#554—538no—
537#554—534no—
538#554—534no—
539#554—538no—
540#554—538no—
541#554C2×D5314yescomplemented
542#550—538no—
543#550—538no—
544#550—534no—
545#550—538no—
546#550—5316no—
547#550—534no—
548#550—538no—
549#550—534no—
550#550C2×D5314yescomplemented
551#547—538no—
552#547—534no—
553#547—5316no—
554#547—538no—
555#547—538no—
556#547—534no—
557#547—534no—
558#547—538no—
559#547C2×D5314yescomplemented
560#540—534no—
561#540—534no—
562#540—5316no—
563#540—5316no—
564#540—538no—
565#540—538no—
566#540—534no—
567#540C2×D5314yescomplemented
568#537—538no—
569#537—538no—
570#537—538no—
571#537—5316no—
572#537—538no—
573#537—5316no—
574#537—5316no—
575#537—538no—
576#537—5316no—
577#537—538no—
578#537—538no—
579#537C2×D5318yescomplemented
580#533—532no—
581#533—532no—
582#533—534no—
583#533—534no—
584#533—532no—
585#533—531no—
586#533C2×D5311yescharacteristic, complemented
587#532—534no—
588#532—532no—
589#532—532no—
590#532—534no—
591#532—534no—
592#532—534no—
593#532—534no—
594#532—534no—
595#532—532no—
596#532C2×D5312yescomplemented
597C2×C4⋊Q8—532no—
598C2×C4⋊Q8—532no—
599C2×#127—532no—
600C2×#127—534no—
601C2×#125—532no—
602C2×#125—534no—
603C2×#124—534no—
604C2×#123—5316no—
605C2×C22⋊Q8—534no—
606C2×C22⋊Q8—538no—
607C2×C22⋊Q8—5316no—
608C2×#121—534no—
609C2×#121—534no—
610C2×#121—5316no—
611C2×#121—538no—
612C2×#121—5316no—
613C2×C4×Q8—534no—
614C2×C4×D4—534no—
615C2×C4×D4—534no—
616C2×C4×D4—538no—
617C2×#117—532no—
618C22×C4⋊C4—538no—
619C22×C42—531no—
620C53C2×#354811yescharacteristic, complemented, Sylow
621C2×#41—534no—
622C2×#41—538no—
623C2×#41—538no—
624C2×#41—534no—
625C2×#41—5316no—
626C2×#41—538no—
627C2×#41—538no—
628C2×#41—534no—
629C2×#41—5316no—
630C2×#41—538no—
631C2×#41—21216no—
632C2×#41—21232no—
633C2×#41C22×D5314yes—
634C2×#41C22×D5318yes—
635C22×Q8—534no—
636C22×Q8—534no—
637C22×D4—534no—
638C22×D4—534no—
639C22×D4—538no—
640C22×D4—5316no—
641C22×D4—534no—
642C23×C4—538no—
643C23×C4—531no—
644C23×C4—532no—
645C23×C4—5316no—
646C4⋊Q8—534no—
647C4⋊Q8—534no—
648C4⋊Q8—534no—
649C4⋊Q8—534no—
650C4⋊Q8—534no—
651C4⋊Q8—534no—
652C4⋊Q8—532no—
653C4⋊Q8—532no—
654C4⋊Q8C22×D5312yes—
655C4⋊Q8C22×D5312yes—
656#127—534no—
657#127—534no—
658#127—534no—
659#127—5316no—
660#127—538no—
661#127—532no—
662#127—534no—
663#127C22×D5312yes—
664#127C22×D5314yes—
665#125—538no—
666#125—534no—
667#125—5316no—
668#125—538no—
669#125—532no—
670#125—534no—
671#125C22×D5312yes—
672#125C22×D5314yes—
673#124—534no—
674#124—534no—
675#124—538no—
676#124—538no—
677#124—534no—
678#124C22×D5314yes—
679#123—5316no—
680#123—5316no—
681#123—5316no—
682#123—5316no—
683#123—5316no—
684#123—5316no—
685#123—5316no—
686#123C22×D53116yes—
687C22⋊Q8—534no—
688C22⋊Q8—538no—
689C22⋊Q8—5316no—
690C22⋊Q8—534no—
691C22⋊Q8—538no—
692C22⋊Q8—5316no—
693C22⋊Q8—538no—
694C22⋊Q8—534no—
695C22⋊Q8—5316no—
696C22⋊Q8—538no—
697C22⋊Q8—5316no—
698C22⋊Q8—5316no—
699C22⋊Q8—5316no—
700C22⋊Q8—538no—
701C22⋊Q8—5316no—
702C22⋊Q8—5316no—
703C22⋊Q8—5316no—
704C22⋊Q8C22×D5314yes—
705C22⋊Q8C22×D5318yes—
706C22⋊Q8C22×D53116yes—
707#121—534no—
708#121—538no—
709#121—534no—
710#121—538no—
711#121—5316no—
712#121—5316no—
713#121—5316no—
714#121—538no—
715#121—5316no—
716#121—5316no—
717#121—5316no—
718#121—5316no—
719#121—534no—
720#121—534no—
721#121—5316no—
722#121—538no—
723#121—5316no—
724#121—534no—
725#121—534no—
726#121—5316no—
727#121—538no—
728#121—5316no—
729#121—538no—
730#121—538no—
731#121—5316no—
732#121—5316no—
733#121—5316no—
734#121—5316no—
735#121—5316no—
736#121C22×D5314yes—
737#121C22×D5314yes—
738#121C22×D53116yes—
739#121C22×D5318yes—
740#121C22×D53116yes—
741C4×Q8—534no—
742C4×Q8—538no—
743C4×Q8—534no—
744C4×Q8—538no—
745C4×Q8—534no—
746C4×Q8C22×D5314yes—
747C4×D4—534no—
748C4×D4—534no—
749C4×D4—538no—
750C4×D4—538no—
751C4×D4—538no—
752C4×D4—5316no—
753C4×D4—534no—
754C4×D4—534no—
755C4×D4—538no—
756C4×D4—538no—
757C4×D4—538no—
758C4×D4—5316no—
759C4×D4—534no—
760C4×D4—534no—
761C4×D4—538no—
762C4×D4C22×D5314yes—
763C4×D4C22×D5314yes—
764C4×D4C22×D5318yes—
765#117—532no—
766#117—534no—
767#117—534no—
768#117—534no—
769#117C22×D5312yes—
770C2×C4⋊C4—5316no—
771C2×C4⋊C4—538no—
772C2×C4⋊C4—534no—
773C2×C4⋊C4—534no—
774C2×C4⋊C4—5316no—
775C2×C4⋊C4—5316no—
776C2×C4⋊C4—538no—
777C2×C4⋊C4—538no—
778C2×C4⋊C4—534no—
779C2×C4⋊C4—534no—
780C2×C4⋊C4—538no—
781C2×C4⋊C4C22×D5318yes—
782C2×C22⋊C4—534no—
783C2×C22⋊C4—5316no—
784C2×C22⋊C4—538no—
785C2×C22⋊C4—538no—
786C2×C42—532no—
787C2×C42—531no—
788C2×C42—534no—
789C2×C42—531no—
790C2×C42—532no—
791C2×C42—531no—
792C2×C42—531no—
793C2×C42—532no—
794C2×C42—531no—
795C2×C42C22×D5311yescharacteristic
796C24—531no—
797C24—538no—
798#41—48no—
799#41—416no—
800#41—21216no—
801#41—2128no—
802#41—21216no—
803#41—21232no—
804#41—21216no—
805#41—2128no—
806#41—2128no—
807#41—21216no—
808#41—21232no—
809#41—21216no—
810C2×Q8—538no—
811C2×Q8—534no—
812C2×Q8—538no—
813C2×Q8—534no—
814C2×Q8—10616no—
815C2×Q8—2128no—
816C2×Q8C23×D5314yes—
817C2×Q8C23×D5314yes—
818C2×D4—538no—
819C2×D4—538no—
820C2×D4—538no—
821C2×D4—538no—
822C2×D4—5316no—
823C2×D4—5316no—
824C2×D4—538no—
825C2×D4—534no—
826C2×D4—534no—
827C2×D4—538no—
828C2×D4—5316no—
829C2×D4—534no—
830C2×D4—10616no—
831C2×D4—10616no—
832C2×D4—21216no—
833C2×D4—2128no—
834C2×D4—21232no—
835C2×D4C23×D5314yes—
836C2×D4C23×D5314yes—
837C2×D4C23×D5318yes—
838C2×D4C23×D53116yes—
839C2×D4C23×D5314yes—
840C22×C4—531no—
841C22×C4—532no—
842C22×C4—531no—
843C22×C4—532no—
844C22×C4—538no—
845C22×C4—5316no—
846C22×C4—531no—
847C22×C4—532no—
848C22×C4—531no—
849C22×C4—531no—
850C22×C4—532no—
851C22×C4—532no—
852C22×C4—538no—
853C22×C4—538no—
854C22×C4—538no—
855C22×C4—538no—
856C22×C4—5316no—
857C22×C4—5316no—
858C22×C4—1064no—
859C22×C4—10632no—
860C22×C4—1068no—
861C22×C4—21232no—
862C22×C4C23×D5311yescharacteristic
863C22×C4C23×D5312yes—
864C22×C4C23×D5318yes—
865C22×C4C23×D53116yes—
866C4⋊C4—538no—
867C4⋊C4—534no—
868C4⋊C4—538no—
869C4⋊C4—534no—
870C4⋊C4—5316no—
871C4⋊C4—5316no—
872C4⋊C4—5316no—
873C4⋊C4—538no—
874C4⋊C4—534no—
875C4⋊C4—538no—
876C4⋊C4—534no—
877C4⋊C4—538no—
878C4⋊C4—538no—
879C4⋊C4—538no—
880C4⋊C4C23×D5314yes—
881C4⋊C4C23×D5314yes—
882C4⋊C4C23×D53116yes—
883C4⋊C4C23×D5314yes—
884C4⋊C4C23×D5314yes—
885C4⋊C4C23×D5318yes—
886C22⋊C4—534no—
887C22⋊C4—5316no—
888C22⋊C4—538no—
889C22⋊C4—538no—
890C22⋊C4—538no—
891C22⋊C4—5316no—
892C22⋊C4—5316no—
893C22⋊C4—538no—
894C22⋊C4—538no—
895C22⋊C4—538no—
896C22⋊C4—538no—
897C22⋊C4C23×D5314yes—
898C22⋊C4C23×D53116yes—
899C22⋊C4C23×D5318yes—
900C22⋊C4C23×D5318yes—
901C42—531no—
902C42—532no—
903C42—532no—
904C42—532no—
905C42—532no—
906C42—532no—
907C42—531no—
908C42—538no—
909C42—534no—
910C42C23×D5311yescharacteristic
911C42C23×D5312yes—
912C42C23×D5311yescharacteristic
913C42C23×D5314yes—
914C23—531no—
915C23—531no—
916C23—538no—
917C23—1064no—
918C23—10616no—
919C23—1062no—
920C23—10616no—
921C23—10616no—
922C23C24×D5311yescharacteristic
923C23C24×D5318yes—
924Q8—28no—
925Q8—44no—
926Q8—10616no—
927Q8—1068no—
928Q8—2128no—
929Q8—2124no—
930D4—28no—
931D4—28no—
932D4—48no—
933D4—44no—
934D4—416no—
935D4—10616no—
936D4—10616no—
937D4—1068no—
938D4—1068no—
939D4—2128no—
940D4—2124no—
941D4—21216no—
942D4—2128no—
943D4—2128no—
944D4—2128no—
945D4—21216no—
946D4—21216no—
947C2×C4—216no—
948C2×C4—24no—
949C2×C4—22no—
950C2×C4—416no—
951C2×C4—531no—
952C2×C4—532no—
953C2×C4—538no—
954C2×C4—534no—
955C2×C4—531no—
956C2×C4—532no—
957C2×C4—538no—
958C2×C4—538no—
959C2×C4—1062no—
960C2×C4—10616no—
961C2×C4—1064no—
962C2×C4—1062no—
963C2×C4—10616no—
964C2×C4—1064no—
965C2×C4—10616no—
966C2×C4—1062no—
967C2×C4—10616no—
968C2×C4—1064no—
969C2×C4—10616no—
970C2×C4—1064no—
971C2×C4—1062no—
972C2×C4—21216no—
973C2×C4—21216no—
974C2×C4—21216no—
975C2×C4C24×D5311yescharacteristic
976C2×C4C24×D5312yes—
977C2×C4C24×D5318yes—
978C2×C4C24×D5318yes—
979C2×C4C24×D5312yes—
980C2×C4C24×D5311yescharacteristic
981C22—22no—
982C22—28no—
983C22—28no—
984C22—21no—
985C22—28no—
986C22—534no—
987C22—532no—
988C22—1062no—
989C22—1068no—
990C22—1068no—
991C22—1061no—
992C22—1068no—
993C22—2124no—
994C22—21232no—
995C22C25×D5311yescharacteristic
996C4—28no—
997C4—22no—
998C4—28no—
999C4—21no—
1000C4—534no—
1001C4—532no—
1002C4—1068no—
1003C4—1062no—
1004C4—1068no—
1005C4—1061no—
1006C4H(5,𝔽2)×D5314yes—
1007C42−1+4×D5312yes—
1008C2—41no—
1009C2—48no—
1010C2—534no—
1011C2—2121no—
1012C2—2128no—
1013C2C2×H(5,𝔽2)×D5312yes—
1014C2C2×2−1+4×D5311yescharacteristic
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3548C2
hypercenter#3548D53
hypocenterC53C2×#3548
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3548

Complements

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

NH ≅ G/Ntype
1. #20289115C2semidirect
2. #20289114C2semidirect
3. #20289113C2semidirect
4. #20289112C2semidirect
5. #20289111C2semidirect
6. #20289110C2semidirect
7. #20289109C2semidirect
8. #20289108C2semidirect
9. #562×D53C2semidirect
10. #554×D53C2semidirect
11. #550×D53C2semidirect
12. #547×D53C2semidirect
13. #540×D53C2semidirect
14. #537×D53C2semidirect
15. #533×D53C2semidirect
16. #532×D53C2semidirect
17. C53×#3548C2semidirect
20. #16811371C22semidirect
21. #16811370C22semidirect
22. #16811369C22semidirect
23. #16811368C22semidirect
24. #16811367C22semidirect
25. #16811334C22semidirect
26. #16811333C22semidirect
27. #16811332C22semidirect
28. #16811331C22semidirect
29. #16811330C22semidirect
30. #16811329C22semidirect
31. #16811328C22semidirect
32. #16811327C22semidirect
33. #16811295C22semidirect
34. #16811294C22semidirect
35. #16811294C22semidirect
36. #16811293C22semidirect
37. #16811293C22semidirect
38. #16811292C22semidirect
39. #16811291C22semidirect
40. #16811291C22semidirect
41. #16811278C22semidirect
42. #16811277C22semidirect
43. #16811276C22semidirect
44. #16811275C22semidirect
45. #16811274C22semidirect
46. #16811273C22semidirect
47. #16811272C22semidirect
48. #16811271C22semidirect
49. #16811229C22semidirect
50. #16811228C22semidirect
51. #16811227C22semidirect
52. #16811226C22semidirect
53. #16811225C22semidirect
54. #16811224C22semidirect
55. #16811223C22semidirect
56. #16811204C22semidirect
57. #16811203C22semidirect
58. #16811203C22semidirect
59. #16811203C22semidirect
60. #16811202C22semidirect
61. #16811202C22semidirect
62. #16811202C22semidirect
63. #16811201C22semidirect
64. #16811201C22semidirect
65. #16811200C22semidirect
66. #16811200C22semidirect
67. #16811180C22semidirect
68. #16811179C22semidirect
69. #16811178C22semidirect
70. #16811177C22semidirect
71. #16811176C22semidirect
72. #16811175C22semidirect
73. #16811174C22semidirect
74. #16811173C22semidirect
75. #16811172C22semidirect
76. #16811171C22semidirect
77. #16811170C22semidirect
78. #16811170C22semidirect
79. #16811169C22semidirect
80. #16811168C22semidirect
81. #16811168C22semidirect
105. C53×#562C22semidirect
106. C53×#554C22semidirect
107. C53×#550C22semidirect
108. C53×#547C22semidirect
109. C53×#540C22semidirect
110. C53×#537C22semidirect
111. C53×#533C22semidirect
112. C53×#532C22semidirect
509. #3548D53direct (N × H)
524. D53#3548direct (N × H)
532. #562C2×D53semidirect
541. #554C2×D53semidirect
550. #550C2×D53semidirect
559. #547C2×D53semidirect
567. #540C2×D53semidirect
579. #537C2×D53semidirect
586. #533C2×D53semidirect
596. #532C2×D53semidirect
620. C53C2×#3548semidirect

Maximal subgroups

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

subgroupindex
#202891152
#202891142
#202891132
#202891122
#202891112
#202891102
#202891092
#202891082
#562×D532
#554×D532
#550×D532
#547×D532
#540×D532
#537×D532
#533×D532
#532×D532
C53×#35482
C2×#354853