Finite Group Databasebeta

← #28293159

Subgroups — #28293159

Order 13568.

7106 conjugacy classes of subgroups.

The subgroup lattice has 1000 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288786C218yesmaximal, complemented
2#20288765C218yesmaximal, complemented
3#20288694C218yesmaximal, complemented
4#20288658C218yesmaximal, complemented
5#20288582C212yesmaximal, complemented
6#20288556C214yesmaximal, complemented
7#20288479C211yesmaximal, characteristic, complemented
8#20288425C212yesmaximal, complemented
9#20288414C214yesmaximal, complemented
10#20288360C212yesmaximal, complemented
11#20288149C212yesmaximal, complemented
12#20288127C214yesmaximal, complemented
13#20288107C212yesmaximal, complemented
14C2×#16811222C214yesmaximal, complemented
15#20287919C212yesmaximal, complemented
16C2×#16811102C211yesmaximal, characteristic, complemented
17C53×#3501C211yesmaximal, characteristic, complemented
18C2×#13133262C2212yes—
19C22×#11719947C2211yescharacteristic
20#16811358C2214yescomplemented
21#16811352C2214yescomplemented
22#16811347C2214yescomplemented
23#16811346C2218yescomplemented
24#16811334C2214yescomplemented
25#16811334C2218yescomplemented
26#16811326C2218yescomplemented
27#16811321C2218yescomplemented
28#16811321C22116yescomplemented
29#16811315C22116yescomplemented
30#16811315C2218yescomplemented
31#16811315C22116yescomplemented
32#16811311C2218yescomplemented
33#16811311C2218yescomplemented
34#16811300C22116yescomplemented
35#16811300C22116yescomplemented
36#16811300C22116yescomplemented
37#16811284C2218yescomplemented
38#16811277C2218yescomplemented
39#16811277C2218yescomplemented
40#16811277C2214yescomplemented
41#16811276C2218yescomplemented
42#16811268C2218yescomplemented
43#16811268C2218yescomplemented
44#16811268C2218yescomplemented
45#16811264C2218yescomplemented
46D4×D212C2214yescomplemented
47#16811247C2214yescomplemented
48#16811247C2214yescomplemented
49#16811247C2218yescomplemented
50#16811236C2218yescomplemented
51#16811236C2214yescomplemented
52#16811229C2214yescomplemented
53#16811222C22116yescomplemented
54#16811222C2218yescomplemented
55#16811222C2214yescomplemented
56#16811222C2218yescomplemented
57#16811222C22116yescomplemented
58#16811222C2218yescomplemented
59#16811222C2214yescomplemented
60#16811222C22116yescomplemented
61#16811213C22116yescomplemented
62#16811213C2214yescomplemented
63#16811213C2214yescomplemented
64#16811204C2212yes—
65#16811199C2214yescomplemented
66#16811185C2214yes—
67#16811185C2218yescomplemented
68#16811178C2218yescomplemented
69#16811173C2212yes—
70#16811160C2218yescomplemented
71#16811160C2218yescomplemented
72#16811159C22116yescomplemented
73#16811159C2218yescomplemented
74#16811159C2218yescomplemented
75#16811158C2218yescomplemented
76C2×#13133212C2218yescomplemented
77C2×#13133208C2218yescomplemented
78#16811136C2218yescomplemented
79#16811136C22116yescomplemented
80#16811135C2214yescomplemented
81C2×#13133202C2218yescomplemented
82C2×#13133201C2218yescomplemented
83C2×#13133193C2218yescomplemented
84C2×#13133191C2214yes—
85#16811103C2214yescomplemented
86#16811102C2218yescomplemented
87#16811102C2218yescomplemented
88#16811102C2218yescomplemented
89#16811096C2218yescomplemented
90#16811095C2218yescomplemented
91#16811091C2214yescomplemented
92C4×#11719947C2218yescomplemented
93C2×C4×Dic106C2211yescharacteristic, complemented
94C2×#13133182C2211yescharacteristic, complemented
95C2×D4×Dic53C2211yescharacteristic
96C2×C4×C22⋊D53C2212yescomplemented
97C2×#13133177C2218yescomplemented
98C2×#13133177C2212yescomplemented
99C4×D4×D53C2218yescomplemented
100C2×#13133174C2211yescharacteristic, complemented
101C2×#13133173C2212yescomplemented
102C22×#11719919C2212yescomplemented
103C2×C4⋊C4×D53C2211yescharacteristic, complemented
104C53×#554C2214yescomplemented
105C53×#554C2218yescomplemented
106D4×Q8×C53C2214yescomplemented
107C53×#544C2212yescomplemented
108C53×#543C2214yescomplemented
109C53×#533C2212yescomplemented
110C2×C22⋊Q8×C53C2214yescomplemented
111C53×#518C2212yes—
112C2×C4×D4×C53C2211yescharacteristic
113#13133262—216no—
114C2×#11719949C2318yes—
115C2×#11719945C2314yes—
116C2×#11719947—28no—
117C2×#11719947C2318yes—
118C2×#11719947C2318yes—
119C22×Dic106C2311yescharacteristic
120C22×D212C2314yes—
121C22×C22⋊D53C2312yes—
122C22×C22⋊D53C2318yes—
123C2×D4×D53C2318yes—
124C23×Dic53C2312yes—
125C23×Dic53C2312yes—
126C22×C4×D53C2311yescharacteristic
127C22×C4×D53C2312yes—
128C22×C4×D53C2318yes—
129#13133217C2318yes—
130#13133217C2312yes—
131#13133214C2312yes—
132#13133212C2318yes—
133#13133212C23116yes—
134#13133212C23116yes—
135#13133212C23116yes—
136#13133212C23116yes—
137#13133212C2318yes—
138#13133212C2318yes—
139#13133212C23116yes—
140#13133212C2318yes—
141#13133208C23116yes—
142#13133208C23116yes—
143#13133208C2318yes—
144#13133208C2318yes—
145#13133208C2318yes—
146#13133208C2318yes—
147#13133208C23116yes—
148#13133206C2318yes—
149#13133206C2318yes—
150#13133206C2318yes—
151#13133206C2318yes—
152#13133205C2314yes—
153#13133205C2318yes—
154#13133202C23116yes—
155#13133202C23116yes—
156#13133202C23116yes—
157#13133202C2318yes—
158#13133202C2318yes—
159#13133202C2318yes—
160#13133202C23116yes—
161#13133202C2318yes—
162#13133201C23116yes—
163#13133201C23116yes—
164#13133201C23116yes—
165#13133201C23116yes—
166#13133201C2318yes—
167#13133201C23116yes—
168#13133197C2318yes—
169#13133197C2318yes—
170#13133197C2318yes—
171#13133197C2314yes—
172#13133197C2314yes—
173#13133193C23116yes—
174#13133193C23116yes—
175#13133193C2318yes—
176#13133193C2318yes—
177#13133193C2318yes—
178#13133193C23116yes—
179#13133192C2318yes—
180#13133192C2318yes—
181#13133192C2314yes—
182#13133192C2314yes—
183#13133192C2318yes—
184#13133192C2318yes—
185#13133191C2318yes—
186#13133191C23116yes—
187#13133191C23116yes—
188#13133191C2318yes—
189#13133191C2314yes—
190#13133191C2318yes—
191#13133191C2314yes—
192#13133187C23116yes—
193#13133187C23116yes—
194#13133187C2318yes—
195Q8×Dic53C2318yes—
196Q8×Dic53C2318yes—
197C4×Dic106C2314yes—
198C4×Dic106C2318yes—
199C4×Dic106C2314yes—
200#13133182C2318yes—
201#13133182C2314yes—
202#13133182C2314yes—
203C4×D212C2314yes—
204C4×D212C2318yes—
205C4×D212C2318yes—
206C4×D212C2318yes—
207C4×D212C2314yes—
208D4×Dic53C2318yes—
209#13133179C2318yes—
210#13133179C2318yes—
211#13133179C23116yes—
212#13133179C2314yes—
213#13133179C2314yes—
214C4×C22⋊D53C2318yes—
215C4×C22⋊D53C2318yes—
216C4×C22⋊D53C23116yes—
217C4×C22⋊D53C23116yes—
218#13133177C23116yes—
219#13133177C2318yes—
220#13133177C23116yes—
221#13133177C23116yes—
222#13133177C23116yes—
223#13133177C2318yes—
224#13133175C23116yes—
225#13133175C23116yes—
226#13133175C2318yes—
227#13133175C2318yes—
228#13133174C2314yes—
229#13133174C2314yes—
230#13133174C2318yes—
231#13133173C23116yes—
232#13133173C23116yes—
233C2×C4⋊Dic53C2314yes—
234C2×C4⋊Dic53C2318yes—
235C2×C4⋊Dic53C2318yes—
236C2×C4⋊Dic53C2311yescharacteristic
237C2×#11719919C2312yes—
238C2×#11719919C2311yescharacteristic
239C2×#11719919C2312yes—
240C2×#11719919C2312yes—
241C2×#11719919C2318yes—
242C2×#11719919C2318yes—
243C2×#11719919C2311yescharacteristic
244C2×#11719919C2318yes—
245C4⋊C4×D53C2318yes—
246C4⋊C4×D53C2318yes—
247C2×C22⋊Dic53C2312yes—
248C2×#11719921C2318yes—
249C2×#11719921C2318yes—
250C2×#11719921C2318yes—
251C2×#11719921C2311yescharacteristic
252C2×#11719921C2311yescharacteristic
253C2×#11719921C2318yes—
254C22⋊C4×D53C23116yes—
255C2×C4×Dic53C2312yes—
256C2×C4×Dic53C2312yes—
257C2×C4×Dic53C2311yescharacteristic
258C2×C4×Dic53C2318yes—
259C42×D53C2318yes—
260C22×Q8×C53C2314yes—
261C22×D4×C53C2311yescharacteristic
262C23×C4×C53C2312yes—
263C4⋊Q8×C53C2318yes—
264C4⋊Q8×C53C2312yes—
265C4⋊Q8×C53C2312yes—
266#125×C53C2314yes—
267#125×C53C2318yes—
268C22⋊Q8×C53C2318yes—
269C22⋊Q8×C53C2318yes—
270C22⋊Q8×C53C23116yes—
271C22⋊Q8×C53C23116yes—
272C22⋊Q8×C53C2314yes—
273C22⋊Q8×C53C2318yes—
274C22⋊Q8×C53C2314yes—
275C4×Q8×C53C2314yes—
276C4×Q8×C53C2314yes—
277C4×D4×C53C2314yes—
278C4×D4×C53C2318yes—
279C4×D4×C53C2318yes—
280C4×D4×C53C2314yes—
281#117×C53C2314yes—
282C2×C4⋊C4×C53C2311yescharacteristic
283C2×C4⋊C4×C53C2318yes—
284C2×C4⋊C4×C53C2314yes—
285C2×C22⋊C4×C53C2312yes—
286C2×C22⋊C4×C53C2318yes—
287C2×C42×C53C2311yescharacteristic
288C24×C53C2412yes—
289C23×D53C2418yes—
290C23×D53C2411yescharacteristic
291C2×Q8×C53—84no—
292C2×Q8×C53C2414yes—
293C2×Q8×C53C2414yes—
294C2×Q8×C53C2418yes—
295C2×D4×C53#4118yescomplemented
296C2×D4×C53C2414yes—
297C22×C4×C53—82no—
298C22×C4×C53C2411yescharacteristic
299C22×C4×C53C2411yescharacteristic
300C22×C4×C53C2418yes—
301C22×C4×C53C2418yes—
302C22×C4×C53C2412yes—
303C22×C4×C53C2414yes—
304C22×C4×C53C2414yes—
305C22×C4×C53C2411yescharacteristic
306C2×C22⋊D53—28no—
307C2×C22⋊D53—232no—
308C2×C22⋊D53C2418yes—
309C2×C22⋊D53C2418yes—
310C2×C22⋊D53C24116yes—
311C22×Dic53—28no—
312C22×Dic53—82no—
313C22×Dic53C2412yes—
314C22×Dic53C2418yes—
315C22×Dic53C2418yes—
316C22×Dic53C2411yescharacteristic
317C22×Dic53C2411yescharacteristic
318C22×Dic53C2411yescharacteristic
319C22×Dic53C2418yes—
320C22×Dic53C2412yes—
321#11719949—88no—
322#11719947—232no—
323#11719947—232no—
324D4×D53—232no—
325#11719945—216no—
326C2×D212—84no—
327C2×D212C2414yes—
328C2×D212C2414yes—
329C2×D212C2418yes—
330C2×D212C2418yes—
331C2×D212C2418yes—
332C2×D212C2414yes—
333C2×C4×D53—24no—
334C2×C4×D53—88no—
335C2×C4×D53—82no—
336C2×C4×D53C2418yes—
337C2×C4×D53C2414yes—
338C2×C4×D53C2418yes—
339C2×C4×D53C2418yes—
340C2×C4×D53C24116yes—
341C2×C4×D53C2418yes—
342C2×Dic106—24no—
343C2×Dic106C2414yes—
344C2×Dic106C2414yes—
345C4⋊C4×C53C2418yes—
346C4⋊C4×C53C2414yes—
347C4⋊C4×C53C2414yes—
348C4⋊C4×C53C2418yes—
349C4⋊C4×C53C24116yes—
350C4⋊C4×C53C2414yes—
351C4⋊C4×C53C2414yes—
352C4⋊C4×C53C2418yes—
353C4⋊C4×C53C2414yes—
354C22⋊C4×C53C2418yes—
355C22⋊C4×C53C24116yes—
356C22⋊C4×C53C2418yes—
357C42×C53C2412yes—
358C42×C53C2412yes—
359C42×C53C2418yes—
360C22⋊Dic53C2418yes—
361#11719921C2418yes—
362#11719921C24116yes—
363#11719921C2418yes—
364#11719921C2418yes—
365#11719921C2418yes—
366#11719921C2418yes—
367#11719921C2414yes—
368#11719921C2412yes—
369#11719921C2412yes—
370#11719921C24116yes—
371#11719921C24116yes—
372#11719921C24116yes—
373#11719921C2418yes—
374#11719921C2418yes—
375#11719921C2418yes—
376C4⋊Dic53C2414yes—
377C4⋊Dic53C2414yes—
378C4⋊Dic53C2418yes—
379C4⋊Dic53C2418yes—
380C4⋊Dic53C2418yes—
381C4⋊Dic53C24116yes—
382C4⋊Dic53C24116yes—
383C4⋊Dic53C2414yes—
384#11719919C2418yes—
385#11719919C24116yes—
386#11719919C2412yes—
387#11719919C2412yes—
388#11719919C2418yes—
389#11719919C2414yes—
390#11719919C2414yes—
391#11719919C2418yes—
392#11719919C2414yes—
393#11719919C2418yes—
394C4×Dic53C2414yes—
395C4×Dic53C2418yes—
396C4×Dic53C2418yes—
397C4×Dic53C2418yes—
398C4×Dic53C2418yes—
399C4×Dic53C24116yes—
400C23×C53—42no—
401C23×C53—42no—
402C23×C53C2×#4118yes—
403C23×C53C2511yescharacteristic
404C23×C53C2514yes—
405C22×D53—22no—
406C22×D53—216no—
407C22×D53—41no—
408C22×D53—41no—
409C22×D53—48no—
410C22×D53—48no—
411C22×D53C2512yes—
412C22×D53C2518yes—
413Q8×C53—48no—
414Q8×C53—44no—
415Q8×C53—44no—
416D4×C53C2×#41116yes—
417C2×C4×C53—42no—
418C2×C4×C53—48no—
419C2×C4×C53—44no—
420C2×C4×C53—41no—
421C2×C4×C53—44no—
422C2×C4×C53—48no—
423C2×C4×C53—41no—
424C2×C4×C53C2×#4114yes—
425C2×C4×C53C2518yes—
426C2×C4×C53C2514yes—
427C2×C4×C53C2518yes—
428C2×C4×C53C2511yescharacteristic
429C2×C4×C53C2512yes—
430C2×C4×C53C2511yescharacteristic
431C2×C4×C53C2512yes—
432C22⋊D53—216no—
433C22⋊D53—232no—
434C22⋊D53—216no—
435C2×Dic53—24no—
436C2×Dic53—22no—
437C2×Dic53—216no—
438C2×Dic53—216no—
439C2×Dic53—42no—
440C2×Dic53—48no—
441C2×Dic53—41no—
442C2×Dic53—41no—
443C2×Dic53C2514yes—
444C2×Dic53C2518yes—
445C2×Dic53C2514yes—
446C2×Dic53C2512yes—
447C2×Dic53C2512yes—
448C2×Dic53C2512yes—
449D212—28no—
450D212—44no—
451D212—48no—
452D212—48no—
453D212—44no—
454D212—48no—
455C4×D53—28no—
456C4×D53—216no—
457C4×D53—48no—
458C4×D53—416no—
459C4×D53—48no—
460C4×D53—48no—
461Dic106—28no—
462Dic106—28no—
463#62847—531nomaximal, Sylow
464C22×C53—21no—
465C22×C53—24no—
466C22×C53—21no—
467C22×C53—24no—
468C22×C53—48no—
469C22×C53C22×#4118yes—
470C22×C53C22×#4112yes—
471C22×C53C2611yescharacteristic
472C2×D53—22no—
473C2×D53—28no—
474C2×D53—22no—
475C2×D53—28no—
476C2×D53—28no—
477C2×D53—22no—
478C2×D53—44no—
479C2×D53—816no—
480C4×C53—28no—
481C4×C53—24no—
482C4×C53—21no—
483C4×C53—21no—
484C4×C53—28no—
485C4×C53—22no—
486C4×C53C22×#4114yes—
487Dic53—24no—
488Dic53—28no—
489Dic53—22no—
490Dic53—24no—
491Dic53—22no—
492Dic53—22no—
493#3521—538no—
494#3520—538no—
495#3515—538no—
496#3513—538no—
497#3507—532no—
498#3505—534no—
499#3501D5311yescharacteristic, complemented
500#3496—531no—
501#3492—532no—
502#3491—534no—
503#3485—532no—
504#3461—532no—
505#3459—534no—
506#3455—532no—
507C2×#539—534no—
508C4×H(5,𝔽2)—532no—
509C2×#520—531no—
510C2×C53—22no—
511C2×C53—28no—
512C2×C53C23×#4111yescharacteristic
513C2×C53H(7,𝔽2)11yescharacteristic
514C2×C532−1+611yescharacteristic
515D53—42no—
516D53—48no—
517C2×H(5,𝔽2)—532no—
518C22×#41—531no—
519#559—534no—
520#557—534no—
521#556—534no—
522#556—538no—
523#554—538no—
524#554—534no—
525#554C2×D5318yescomplemented
526#554C2×D5314yescomplemented
527#553—538no—
528#553—5316no—
529#553—538no—
530#552—538no—
531#552—538no—
532#552—5316no—
533#552—5316no—
534#552—538no—
535#551—5316no—
536#551—5316no—
537#551—5316no—
538D4×Q8C2×D5314yescomplemented
539#548—538no—
540#547—538no—
541#547—538no—
542#547—538no—
543#547—534no—
544#546—538no—
545#546—538no—
546#546—538no—
547#546—538no—
548D42—534no—
549#544C2×D5312yescomplemented
550#543C2×D5314yescomplemented
551#542—534no—
552#542—534no—
553#542—538no—
554#541—534no—
555#541—538no—
556#540—534no—
557#539—534no—
558#539—538no—
559#539—538no—
560#539—538no—
561#539—5316no—
562#539—5316no—
563#539—534no—
564#539—5316no—
565#538—534no—
566#538—534no—
567#538—5316no—
568#537—532no—
569#536—534no—
570#534—538no—
571#534—534no—
572#533—538no—
573#533C2×D5312yescomplemented
574#532—532no—
575#529—538no—
576#529—538no—
577#529—5316no—
578#529—538no—
579#529—538no—
580#529—538no—
581C2×#126—538no—
582C2×#125—538no—
583#525—538no—
584#525—5316no—
585#525—534no—
586C2×#123—538no—
587C2×#123—538no—
588C2×C22⋊Q8—538no—
589C2×C22⋊Q8C2×D5314yescomplemented
590C2×#121—534no—
591#520—538no—
592#520—538no—
593#520—538no—
594#520—534no—
595#518—538no—
596#518—538no—
597#518C2×D5312yes—
598C4×#41—538no—
599C4×#41—534no—
600C2×C4×Q8—531no—
601C2×C4×Q8—531no—
602C2×C4×D4—531no—
603C2×C4×D4—532no—
604C2×C4×D4—538no—
605C2×C4×D4—532no—
606C2×C4×D4—538no—
607C2×C4×D4C2×D5311yescharacteristic
608C2×#117—532no—
609C2×#117—531no—
610C22×C4⋊C4—532no—
611C22×C4⋊C4—531no—
612C53#6284711yescharacteristic, complemented, Sylow
613H(5,𝔽2)—10616no—
614C2×#41—538no—
615C2×#41—538no—
616C2×#41—538no—
617C2×#41—534no—
618C2×#41—1068no—
619C22×Q8—531no—
620C22×Q8C22×D5314yes—
621C22×D4—532no—
622C22×D4—538no—
623C22×D4—538no—
624C22×D4—534no—
625C22×D4C22×D5311yescharacteristic
626C23×C4—532no—
627C23×C4—532no—
628C23×C4—531no—
629C23×C4—532no—
630C23×C4—538no—
631C23×C4C22×D5312yes—
632C4⋊Q8—532no—
633C4⋊Q8—538no—
634C4⋊Q8C22×D5318yes—
635C4⋊Q8C22×D5312yes—
636C4⋊Q8C22×D5312yes—
637#127—532no—
638#126—538no—
639#126—5316no—
640#126—5316no—
641#126—5316no—
642#126—538no—
643#126—5316no—
644#126—538no—
645#126—538no—
646#126—5316no—
647#125—538no—
648#125—5316no—
649#125—5316no—
650#125—5316no—
651#125—538no—
652#125—538no—
653#125—538no—
654#125C22×D5318yes—
655#125C22×D5314yes—
656#124—538no—
657#124—538no—
658#124—538no—
659#124—538no—
660#124—538no—
661#124—534no—
662#123—538no—
663#123—5316no—
664#123—5316no—
665#123—5316no—
666#123—538no—
667#123—5316no—
668#123—538no—
669#123—538no—
670#123—538no—
671#123—5316no—
672#123—5316no—
673#123—5316no—
674#123—5316no—
675#123—5316no—
676C22⋊Q8—538no—
677C22⋊Q8—5316no—
678C22⋊Q8—5316no—
679C22⋊Q8—5316no—
680C22⋊Q8—538no—
681C22⋊Q8—538no—
682C22⋊Q8—534no—
683C22⋊Q8—534no—
684C22⋊Q8—538no—
685C22⋊Q8—538no—
686C22⋊Q8—538no—
687C22⋊Q8C22×D5314yes—
688C22⋊Q8C22×D5318yes—
689C22⋊Q8C22×D5318yes—
690C22⋊Q8C22×D5318yes—
691C22⋊Q8C22×D53116yes—
692C22⋊Q8C22×D5314yes—
693C22⋊Q8C22×D53116yes—
694#121—534no—
695#121—538no—
696#121—538no—
697#121—538no—
698#121—5316no—
699#121—534no—
700#121—5316no—
701#121—538no—
702#121—538no—
703#121—534no—
704#121—534no—
705#121—538no—
706#121—538no—
707#120—538no—
708#120—5316no—
709#120—5316no—
710C4×Q8—538no—
711C4×Q8—538no—
712C4×Q8—538no—
713C4×Q8—534no—
714C4×Q8—534no—
715C4×Q8—534no—
716C4×Q8—534no—
717C4×Q8—538no—
718C4×Q8C22×D5314yes—
719C4×Q8C22×D5314yes—
720C4×D4—538no—
721C4×D4—5316no—
722C4×D4—538no—
723C4×D4—538no—
724C4×D4—5316no—
725C4×D4—534no—
726C4×D4—534no—
727C4×D4—538no—
728C4×D4—5316no—
729C4×D4—538no—
730C4×D4—5316no—
731C4×D4—538no—
732C4×D4—5316no—
733C4×D4—5316no—
734C4×D4—5316no—
735C4×D4—538no—
736C4×D4—538no—
737C4×D4—538no—
738C4×D4—538no—
739C4×D4—534no—
740C4×D4—534no—
741C4×D4C22×D5318yes—
742C4×D4C22×D5314yes—
743C4×D4C22×D5314yes—
744C4×D4C22×D5318yes—
745#117—538no—
746#117—5316no—
747#117—538no—
748#117—5316no—
749#117—5316no—
750#117—5316no—
751#117—534no—
752#117—534no—
753#117—538no—
754#117C22×D5314yes—
755C2×C4⋊C4—531no—
756C2×C4⋊C4—532no—
757C2×C4⋊C4—531no—
758C2×C4⋊C4—532no—
759C2×C4⋊C4—532no—
760C2×C4⋊C4—538no—
761C2×C4⋊C4—538no—
762C2×C4⋊C4—531no—
763C2×C4⋊C4—538no—
764C2×C4⋊C4—534no—
765C2×C4⋊C4—538no—
766C2×C4⋊C4—538no—
767C2×C4⋊C4—538no—
768C2×C4⋊C4—538no—
769C2×C4⋊C4C22×D5311yescharacteristic
770C2×C4⋊C4C22×D5318yes—
771C2×C4⋊C4C22×D5314yes—
772C2×C22⋊C4—532no—
773C2×C22⋊C4—531no—
774C2×C22⋊C4—531no—
775C2×C22⋊C4—538no—
776C2×C22⋊C4—538no—
777C2×C22⋊C4—538no—
778C2×C22⋊C4—538no—
779C2×C22⋊C4—5316no—
780C2×C22⋊C4C22×D5312yes—
781C2×C22⋊C4C22×D5318yes—
782C2×C42—531no—
783C2×C42—532no—
784C2×C42—532no—
785C2×C42—538no—
786C2×C42—538no—
787C2×C42C22×D5311yescharacteristic
788C24—538no—
789C24—531no—
790C24C23×D5312yes—
791#41—10632no—
792#41—10632no—
793#41—10616no—
794#41—4248no—
795C2×Q8—84no—
796C2×Q8—534no—
797C2×Q8—534no—
798C2×Q8—1064no—
799C2×Q8C23×D5314yes—
800C2×Q8C23×D5318yes—
801C2×Q8C23×D5314yes—
802C2×D4—538no—
803C2×D4—5316no—
804C2×D4—538no—
805C2×D4—534no—
806C2×D4—534no—
807C2×D4—538no—
808C2×D4—538no—
809C2×D4—538no—
810C2×D4—534no—
811C2×D4—1068no—
812C2×D4—10632no—
813C2×D4—10632no—
814C2×D4—4244no—
815C2×D4#1171994918yescomplemented
816C2×D4C23×D5314yes—
817C22×C4—82no—
818C22×C4—532no—
819C22×C4—538no—
820C22×C4—538no—
821C22×C4—531no—
822C22×C4—531no—
823C22×C4—538no—
824C22×C4—531no—
825C22×C4—532no—
826C22×C4—538no—
827C22×C4—534no—
828C22×C4—538no—
829C22×C4—538no—
830C22×C4—5316no—
831C22×C4—538no—
832C22×C4—1068no—
833C22×C4—1064no—
834C22×C4—4242no—
835C22×C4—4248no—
836C22×C4—4242no—
837C22×C4C23×D5311yescharacteristic
838C22×C4C23×D5318yes—
839C22×C4C23×D5312yes—
840C22×C4C23×D5311yescharacteristic
841C22×C4C23×D5314yes—
842C22×C4C23×D5318yes—
843C22×C4C23×D5314yes—
844C22×C4C23×D5311yescharacteristic
845C4⋊C4—534no—
846C4⋊C4—532no—
847C4⋊C4—538no—
848C4⋊C4—532no—
849C4⋊C4—534no—
850C4⋊C4—538no—
851C4⋊C4—534no—
852C4⋊C4—538no—
853C4⋊C4—5316no—
854C4⋊C4—534no—
855C4⋊C4—538no—
856C4⋊C4—538no—
857C4⋊C4—534no—
858C4⋊C4—538no—
859C4⋊C4—5316no—
860C4⋊C4—5316no—
861C4⋊C4—538no—
862C4⋊C4—534no—
863C4⋊C4C23×D5314yes—
864C4⋊C4C23×D5314yes—
865C4⋊C4C23×D5318yes—
866C4⋊C4C23×D5314yes—
867C4⋊C4C23×D5318yes—
868C4⋊C4C23×D53116yes—
869C4⋊C4C23×D5314yes—
870C4⋊C4C23×D5318yes—
871C4⋊C4C23×D5314yes—
872C22⋊C4—538no—
873C22⋊C4—538no—
874C22⋊C4—5316no—
875C22⋊C4—538no—
876C22⋊C4—538no—
877C22⋊C4—538no—
878C22⋊C4—538no—
879C22⋊C4—532no—
880C22⋊C4—534no—
881C22⋊C4—532no—
882C22⋊C4—5316no—
883C22⋊C4—5316no—
884C22⋊C4—5316no—
885C22⋊C4—538no—
886C22⋊C4—538no—
887C22⋊C4—538no—
888C22⋊C4C23×D53116yes—
889C22⋊C4C23×D5318yes—
890C22⋊C4C23×D5318yes—
891C42—534no—
892C42—538no—
893C42—5316no—
894C42—538no—
895C42—538no—
896C42—538no—
897C42C23×D5318yes—
898C42C23×D5312yes—
899C42C23×D5312yes—
900C23—42no—
901C23—42no—
902C23—538no—
903C23—532no—
904C23—10616no—
905C23—1062no—
906C23—2128no—
907C23—2128no—
908C23—2121no—
909C23—2121no—
910C23C2×#1171994918yes—
911C23C24×D5314yes—
912C23C24×D5311yescharacteristic
913Q8—44no—
914Q8—48no—
915Q8—44no—
916Q8—1068no—
917Q8—1068no—
918D4—10632no—
919D4—10616no—
920D4—10616no—
921D4—1068no—
922D4—2128no—
923D4—2124no—
924D4—2124no—
925D4—2128no—
926D4—2128no—
927D4C2×#11719949116yes—
928C2×C4—41no—
929C2×C4—42no—
930C2×C4—44no—
931C2×C4—44no—
932C2×C4—48no—
933C2×C4—48no—
934C2×C4—41no—
935C2×C4—532no—
936C2×C4—534no—
937C2×C4—532no—
938C2×C4—534no—
939C2×C4—538no—
940C2×C4—532no—
941C2×C4—1062no—
942C2×C4—1064no—
943C2×C4—10616no—
944C2×C4—10616no—
945C2×C4—1068no—
946C2×C4—10616no—
947C2×C4—2128no—
948C2×C4—2128no—
949C2×C4—2128no—
950C2×C4—21216no—
951C2×C4—2121no—
952C2×C4—2128no—
953C2×C4—2122no—
954C2×C4—2121no—
955C2×C4C2×#1171994914yes—
956C2×C4C24×D5312yes—
957C2×C4C24×D5318yes—
958C2×C4C24×D5314yes—
959C2×C4C24×D5318yes—
960C2×C4C24×D5311yescharacteristic
961C2×C4C24×D5311yescharacteristic
962C2×C4C24×D5312yes—
963C22—24no—
964C22—21no—
965C22—24no—
966C22—21no—
967C22—48no—
968C22—1062no—
969C22—1068no—
970C22—1062no—
971C22—1068no—
972C22—1068no—
973C22—1062no—
974C22—42416no—
975C22—2124no—
976C22C22×#1171994918yes—
977C22C22×#1171994912yes—
978C22C25×D5311yescharacteristic
979C4—21no—
980C4—21no—
981C4—24no—
982C4—28no—
983C4—28no—
984C4—22no—
985C4—1062no—
986C4—1068no—
987C4—1064no—
988C4—1062no—
989C4—1064no—
990C4—1062no—
991C4C22×#1171994914yes—
992C2—22no—
993C2—28no—
994C2—2128no—
995C2—2122no—
996C2C23×#1171994911yescharacteristic
997C2#2028952511yescharacteristic
998C2#2028952811yescharacteristic
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3501C2
hypercenter#3501D53
hypocenterC53#62847
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3501

Complements

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

NH ≅ G/Ntype
1. #20288786C2semidirect
2. #20288765C2semidirect
3. #20288694C2semidirect
4. #20288658C2semidirect
5. #20288582C2semidirect
6. #20288556C2semidirect
7. #20288479C2semidirect
8. #20288425C2semidirect
9. #20288414C2semidirect
10. #20288360C2semidirect
11. #20288149C2semidirect
12. #20288127C2semidirect
13. #20288107C2semidirect
14. C2×#16811222C2semidirect
15. #20287919C2semidirect
16. C2×#16811102C2semidirect
17. C53×#3501C2semidirect
20. #16811358C22semidirect
21. #16811352C22semidirect
22. #16811347C22semidirect
23. #16811346C22semidirect
24. #16811334C22semidirect
25. #16811334C22semidirect
26. #16811326C22semidirect
27. #16811321C22semidirect
28. #16811321C22semidirect
29. #16811315C22semidirect
30. #16811315C22semidirect
31. #16811315C22semidirect
32. #16811311C22semidirect
33. #16811311C22semidirect
34. #16811300C22semidirect
35. #16811300C22semidirect
36. #16811300C22semidirect
37. #16811284C22semidirect
38. #16811277C22semidirect
39. #16811277C22semidirect
40. #16811277C22semidirect
41. #16811276C22semidirect
42. #16811268C22semidirect
43. #16811268C22semidirect
44. #16811268C22semidirect
45. #16811264C22semidirect
46. D4×D212C22semidirect
47. #16811247C22semidirect
48. #16811247C22semidirect
49. #16811247C22semidirect
50. #16811236C22semidirect
51. #16811236C22semidirect
52. #16811229C22semidirect
53. #16811222C22semidirect
54. #16811222C22semidirect
55. #16811222C22semidirect
56. #16811222C22semidirect
57. #16811222C22semidirect
58. #16811222C22semidirect
59. #16811222C22semidirect
60. #16811222C22semidirect
61. #16811213C22semidirect
62. #16811213C22semidirect
63. #16811213C22semidirect
65. #16811199C22semidirect
67. #16811185C22semidirect
68. #16811178C22semidirect
70. #16811160C22semidirect
71. #16811160C22semidirect
72. #16811159C22semidirect
73. #16811159C22semidirect
74. #16811159C22semidirect
75. #16811158C22semidirect
76. C2×#13133212C22semidirect
77. C2×#13133208C22semidirect
78. #16811136C22semidirect
79. #16811136C22semidirect
80. #16811135C22semidirect
81. C2×#13133202C22semidirect
82. C2×#13133201C22semidirect
83. C2×#13133193C22semidirect
85. #16811103C22semidirect
86. #16811102C22semidirect
87. #16811102C22semidirect
88. #16811102C22semidirect
89. #16811096C22semidirect
90. #16811095C22semidirect
91. #16811091C22semidirect
92. C4×#11719947C22semidirect
93. C2×C4×Dic106C22semidirect
94. C2×#13133182C22semidirect
96. C2×C4×C22⋊D53C22semidirect
97. C2×#13133177C22semidirect
98. C2×#13133177C22semidirect
99. C4×D4×D53C22semidirect
100. C2×#13133174C22semidirect
101. C2×#13133173C22semidirect
102. C22×#11719919C22semidirect
103. C2×C4⋊C4×D53C22semidirect
104. C53×#554C22semidirect
105. C53×#554C22semidirect
106. D4×Q8×C53C22semidirect
107. C53×#544C22semidirect
108. C53×#543C22semidirect
109. C53×#533C22semidirect
110. C2×C22⋊Q8×C53C22semidirect
295. C2×D4×C53#41semidirect
499. #3501D53semidirect
525. #554C2×D53semidirect
526. #554C2×D53semidirect
538. D4×Q8C2×D53semidirect
549. #544C2×D53semidirect
550. #543C2×D53semidirect
573. #533C2×D53semidirect
589. C2×C22⋊Q8C2×D53semidirect
612. C53#62847semidirect
815. C2×D4#11719949semidirect

Maximal subgroups

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

subgroupindex
#202887862
#202887652
#202886942
#202886582
#202885822
#202885562
#202884792
#202884252
#202884142
#202883602
#202881492
#202881272
#202881072
C2×#168112222
#202879192
C2×#168111022
C53×#35012
#6284753