Finite Group Databasebeta

← #28293170

Subgroups — #28293170

Order 13568.

6846 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288825C214yesmaximal, complemented
2#20288817C214yesmaximal, complemented
3#20288806C214yesmaximal, complemented
4#20288802C214yesmaximal, complemented
5#20288727C214yesmaximal, complemented
6#20288723C214yesmaximal, complemented
7#20288709C214yesmaximal, complemented
8#20288701C214yesmaximal, complemented
9#20288579C216yesmaximal, complemented
10#20288521C211yesmaximal, characteristic, complemented
11#20288482C211yesmaximal, characteristic, complemented
12#20288432C216yesmaximal, complemented
13#20288366C211yesmaximal, characteristic, complemented
14#20288139C216yesmaximal, complemented
15#20288103C216yesmaximal, complemented
162−1+4×Dic53C211yesmaximal, characteristic, complemented
17#20287924C211yesmaximal, characteristic, complemented
18C2×#16811101C211yesmaximal, characteristic, complemented
19C53×#3486C211yesmaximal, characteristic, complemented
20C2×#13133265C2211yescharacteristic
21#16811355C22112yescomplemented
22Q8×Dic106C2214yescomplemented
23#16811352C2214yescomplemented
24#16811349C2214yescomplemented
25#16811349C2214yescomplemented
26#16811348C22112yescomplemented
27#16811347C22112yescomplemented
28#16811344C22112yes—
29#16811344C22112yescomplemented
30#16811343C22112yes—
31#16811342C22112yescomplemented
32#16811338C22112yes—
33#16811337C22112yes—
34#16811331C22112yescomplemented
35#16811320C22112yes—
36#16811319C22112yes—
37#16811315C22112yescomplemented
38#16811313C22112yes—
39#16811307C22112yes—
40#16811307C22112yescomplemented
41#16811292C2214yescomplemented
42Q8×C22⋊D53C2214yes—
43Q8×C22⋊D53C2214yes—
44Q8×C22⋊D53C2214yescomplemented
45#16811284C2214yes—
46#16811284C2214yes—
47#16811284C2214yescomplemented
48#16811280C2214yescomplemented
49#16811251C2216yes—
50#16811246C2216yes—
51#16811246C2216yes—
52#16811246C22112yescomplemented
53#16811242C22112yescomplemented
54#16811240C2216yes—
55#16811240C2216yes—
56#16811234C22112yescomplemented
57#16811233C2216yes—
58#16811233C2216yes—
59#16811233C22112yescomplemented
60#16811226C2216yes—
61#16811226C2216yes—
62#16811217C22112yes—
63#16811217C22112yes—
64#16811208C2214yes—
65#16811208C22112yes—
66#16811201C2216yes—
67#16811197C2216yes—
68#16811178C22112yescomplemented
69#16811176C2216yes—
70#16811175C22112yescomplemented
71#16811169C2216yes—
72#16811159C22112yescomplemented
73#16811155C22112yes—
74#16811155C22112yes—
75#16811153C22112yes—
76#16811153C22112yes—
77#16811152C22112yescomplemented
78#16811150C22124yes—
79#16811134C2216yes—
80#16811106C2216yes—
81#16811106C2214yescomplemented
82#16811105C2214yescomplemented
83#16811103C2216yes—
84#16811101C2211yescharacteristic
85#16811101C2214yes—
86#16811101C2214yes—
87#16811101C2214yes—
88#16811101C2214yes—
89#16811101C2214yescomplemented
90#16811099C2214yescomplemented
91#41×Dic53C2216yes—
92#41×Dic53C2214yescomplemented
93C4×#11719949C2214yescomplemented
94#16811091C2216yes—
95C2×Q8×Dic53C2211yescharacteristic
96C2×Q8×Dic53C2213yes—
97C2×Q8×Dic53C2213yes—
98C2×Q8×Dic53C2211yescharacteristic
99C2×Q8×Dic53C2214yescomplemented
100C4×Q8×D53C2214yescomplemented
101C2×#13133176C2213yes—
102C2×#13133176C2213yes—
103C2×2−1+4×C53C2211yescharacteristic
104C23×Q8×C53C2211yescharacteristic
105D4×Q8×C53C2214yes—
106D4×Q8×C53C2214yes—
107C53×#548C2214yes—
108C53×#548C2214yes—
109C53×#536C2216yes—
110C53×#525C2216yes—
111C53×#519C2211yescharacteristic
112#13133265—28no—
113C2×#11719949C2314yes—
114C2×#11719945C2316yes—
115C2×Q8×D53C2314yes—
116#13133217C23112yes—
117#13133216C2316yes—
118#13133216C23112yes—
119#13133216C2316yes—
120#13133215C23112yes—
121#13133215C2316yes—
122#13133213C2316yes—
123#13133212C23124yes—
124#13133212C23112yes—
125#13133212C23112yes—
126#13133210C23112yes—
127#13133210C23124yes—
128#13133210C23112yes—
129#13133210C23112yes—
130#13133210C23112yes—
131#13133210C2314yes—
132#13133210C2314yes—
133#13133209C23112yes—
134#13133208C23112yes—
135#13133208C2316yes—
136#13133208C23112yes—
137#13133208C2316yes—
138#13133208C23112yes—
139#13133207C23124yes—
140#13133207C23112yes—
141#13133207C23112yes—
142#13133206C23112yes—
143#13133206C2316yes—
144#13133204C2316yes—
145#13133204C23112yes—
146#13133204C2314yes—
147#13133203C23124yes—
148#13133203C23112yes—
149#13133203C2314yes—
150#13133201C23112yes—
151#13133201C23112yes—
152#13133200C23112yes—
153#13133199C23112yes—
154#13133199C23112yes—
155#13133199C23112yes—
156#13133199C2314yes—
157#13133198C23112yes—
158#13133198C2314yes—
159#13133197C23112yes—
160#13133197C23112yes—
161#13133196C23112yes—
162#13133196C2316yes—
163#13133196C2316yes—
164#13133194C23112yes—
165#13133194C23112yes—
166#13133194C23112yes—
167#13133194C2314yes—
168#13133193C23112yes—
169#13133193C23112yes—
170#13133193C23112yes—
171#13133191C2316yes—
172#13133191C2316yes—
173#13133191C23112yes—
174#13133189C23112yes—
175#13133189C23112yes—
176#13133189C2314yes—
177#13133189C2314yes—
178#13133188C23112yes—
179#13133188C23112yes—
180#13133188C2314yes—
181#13133186C2314yes—
182Q8×Dic53C2314yes—
183Q8×Dic53C2314yes—
184Q8×Dic53C2314yes—
185Q8×Dic53C2314yes—
186Q8×Dic53C23112yes—
187Q8×Dic53C23112yes—
188Q8×Dic53C23112yes—
189Q8×Dic53C2314yes—
190Q8×Dic53C2314yes—
191Q8×Dic53C23112yes—
192Q8×Dic53C23112yes—
193Q8×Dic53C2316yes—
194Q8×Dic53C2316yes—
195C4×Dic106C23112yes—
196C4×Dic106C23112yes—
197C4×Dic106C23112yes—
198#13133182C2316yes—
199#13133182C23124yes—
200#13133182C2316yes—
201C4×D212C23112yes—
202D4×Dic53C23112yes—
203D4×Dic53C2314yes—
204D4×Dic53C2316yes—
205D4×Dic53C23112yes—
206D4×Dic53C2316yes—
207#13133179C2316yes—
208#13133179C2316yes—
209C4×C22⋊D53C23112yes—
210C4×C22⋊D53C23112yes—
211C4×C22⋊D53C23112yes—
212C4×C22⋊D53C23112yes—
213#13133177C23124yes—
214#13133177C2314yes—
215#13133177C23112yes—
216#13133176C23112yes—
217#13133176C23112yes—
218#13133176C23112yes—
219#13133176C2316yes—
220#13133176C2316yes—
221#13133176C2316yes—
222#13133176C2316yes—
223#13133176C2316yes—
224#13133176C23112yes—
225#13133175C23124yes—
226#13133175C23112yes—
227#13133174C23112yes—
228#13133173C23124yes—
229C2×C4⋊Dic53C23112yes—
230C2×C4⋊Dic53C2313yes—
231C2×C4⋊Dic53C2313yes—
232C2×C4⋊Dic53C2313yes—
233C2×C4⋊Dic53C2313yes—
234C4⋊C4×D53C23112yes—
235C2×C22⋊Dic53C2311yescharacteristic
236C2×C22⋊Dic53C2313yes—
237C2×C4×Dic53C2313yes—
238C2×C4×Dic53C2316yes—
239C2×C4×Dic53C2313yes—
240C2×C4×Dic53C23112yes—
241C42×D53C23112yes—
2422−1+4×C53—28no—
243C2×#41×C53C2314yes—
244C2×#41×C53C2316yes—
245C22×Q8×C53—28no—
246C22×Q8×C53C2314yes—
247C22×Q8×C53C2314yes—
248C22×Q8×C53C2314yes—
249C22×Q8×C53C2313yes—
250C22×Q8×C53C2311yescharacteristic
251C23×C4×C53C2313yes—
252C4⋊Q8×C53C23112yes—
253#124×C53C23112yes—
254#123×C53C23112yes—
255C22⋊Q8×C53C2316yes—
256C22⋊Q8×C53C2316yes—
257C22⋊Q8×C53C23112yes—
258C22⋊Q8×C53C23112yes—
259#121×C53C2316yes—
260#121×C53C2316yes—
261#120×C53C2314yes—
262C4×Q8×C53C2314yes—
263C4×Q8×C53C2314yes—
264C4×D4×C53C23112yes—
265C4×D4×C53C23112yes—
266#117×C53C2316yes—
267C24×C53C2411yescharacteristic
268#41×C53—216no—
269#41×C53—224no—
270C2×Q8×C53—216no—
271C2×Q8×C53—216no—
272C2×Q8×C53—216no—
273C2×Q8×C53—212no—
274C2×Q8×C53#4118yes—
275C2×Q8×C53C24112yes—
276C2×Q8×C53C2416yes—
277C2×Q8×C53C2414yes—
278C2×D4×C53C2414yes—
279C2×D4×C53C2416yes—
280C2×D4×C53C2414yes—
281C2×D4×C53C2414yes—
282C22×C4×C53—212no—
283C22×C4×C53C2416yes—
284C22×C4×C53C2416yes—
285C22×C4×C53C24112yes—
286C22×C4×C53C2413yes—
287C22×C4×C53C2413yes—
288C2×C22⋊D53C2414yes—
289C2×C22⋊D53C24112yes—
290C2×C22⋊D53C2414yes—
291C2×C22⋊D53C2414yes—
292C2×C22⋊D53C2414yes—
293C22×Dic53C2411yescharacteristic
294C22×Dic53C2413yes—
295C22×Dic53C2411yescharacteristic
296C22×Dic53C2413yes—
297C22×Dic53C2414yes—
298C22×Dic53C24112yes—
299#11719949—216no—
300Q8×D53—216no—
301#11719945—224no—
302C2×D212C2416yes—
303C2×C4×D53C24112yes—
304C2×C4×D53C2414yes—
305C2×C4×D53C24112yes—
306C2×Dic106C2416yes—
307C2×Dic106C24112yes—
308C2×Dic106C2414yes—
309C4⋊C4×C53C2416yes—
310C4⋊C4×C53C2416yes—
311C4⋊C4×C53C24112yes—
312C4⋊C4×C53C24112yes—
313C22⋊C4×C53C2414yes—
314C22⋊C4×C53C2414yes—
315C22⋊C4×C53C2414yes—
316C22⋊C4×C53C24112yes—
317C22⋊C4×C53C24112yes—
318C42×C53C24112yes—
319C22⋊Dic53C2411yescharacteristic
320C22⋊Dic53C2416yes—
321C22⋊Dic53C2411yescharacteristic
322C22⋊Dic53C2416yes—
323C22⋊Dic53C2411yescharacteristic
324C22⋊Dic53C2411yescharacteristic
325C22⋊Dic53C24112yes—
326C22⋊Dic53C2414yes—
327C22⋊Dic53C2414yes—
328C22⋊Dic53C24112yes—
329C22⋊Dic53C2414yes—
330C22⋊Dic53C2414yes—
331C22⋊Dic53C2414yes—
332#11719921C2414yes—
333#11719921C24112yes—
334#11719921C24112yes—
335#11719921C24112yes—
336#11719921C24112yes—
337#11719921C2414yes—
338C4⋊Dic53C24112yes—
339C4⋊Dic53C2416yes—
340C4⋊Dic53C24112yes—
341C4⋊Dic53C24112yes—
342C4⋊Dic53C2416yes—
343C4⋊Dic53C2416yes—
344C4⋊Dic53C2416yes—
345C4⋊Dic53C2416yes—
346C4⋊Dic53C24112yes—
347C4⋊Dic53C2416yes—
348C4⋊Dic53C2414yes—
349C4⋊Dic53C2414yes—
350#11719919C24112yes—
351#11719919C24112yes—
352#11719919C24112yes—
353#11719919C2414yes—
354#11719919C24112yes—
355#11719919C2414yes—
356#11719919C24112yes—
357#11719919C24112yes—
358#11719919C2414yes—
359#11719919C2414yes—
360C4×Dic53C2414yes—
361C4×Dic53C2416yes—
362C4×Dic53C24112yes—
363C4×Dic53C2416yes—
364C4×Dic53C2414yes—
365C4×Dic53C24124yes—
366C4×Dic53C24112yes—
367C4×Dic53C24112yes—
368C4×Dic53C2416yes—
369C4×Dic53C2416yes—
370C23×C53—22no—
371C23×C53—41no—
372C23×C53—41no—
373C23×C53C2514yes—
374C23×C53C2511yescharacteristic
375C23×C53C2511yescharacteristic
376C23×C53C2511yescharacteristic
377C22×D53C2514yes—
378Q8×C53—224no—
379Q8×C53—212no—
380Q8×C53C2×#41116yes—
381D4×C53—28no—
382D4×C53—212no—
383D4×C53—44no—
384D4×C53—44no—
385C2×C4×C53—26no—
386C2×C4×C53—212no—
387C2×C4×C53—212no—
388C2×C4×C53—224no—
389C2×C4×C53C2×#41112yes—
390C2×C4×C53C2514yes—
391C2×C4×C53C2514yes—
392C2×C4×C53C2514yes—
393C2×C4×C53C2516yes—
394C2×C4×C53C2516yes—
395C22⋊D53—28no—
396C22⋊D53—44no—
397C22⋊D53—412no—
398C22⋊D53—44no—
399C22⋊D53—44no—
400C2×Dic53—41no—
401C2×Dic53—44no—
402C2×Dic53—43no—
403C2×Dic53—412no—
404C2×Dic53—41no—
405C2×Dic53—43no—
406C2×Dic53C2511yescharacteristic
407C2×Dic53C2514yes—
408C2×Dic53C2514yes—
409C2×Dic53C2516yes—
410C2×Dic53C2514yes—
411C2×Dic53C2511yescharacteristic
412C2×Dic53C2516yes—
413C2×Dic53C2511yescharacteristic
414C2×Dic53C2511yescharacteristic
415D212—212no—
416C4×D53—224no—
417C4×D53—44no—
418C4×D53—412no—
419Dic106—212no—
420Dic106—44no—
421Dic106—412no—
422#62850—531nomaximal, Sylow
423C22×C53—21no—
424C22×C53—21no—
425C22×C53—21no—
426C22×C53—21no—
427C22×C53—24no—
428C22×C53—24no—
429C22×C53—24no—
430C22×C53—21no—
431C22×C53—21no—
432C22×C53—21no—
433C22×C53—21no—
434C22×C53—44no—
435C22×C53C22×#4112yes—
436C22×C53C2611yescharacteristic
437C2×D53—24no—
438C2×D53—24no—
439C2×D53—24no—
440C4×C53—24no—
441C4×C53—26no—
442C4×C53—24no—
443C4×C53—24no—
444C4×C53C22×#41112yes—
445Dic53—24no—
446Dic53—21no—
447Dic53—24no—
448Dic53—26no—
449Dic53—24no—
450Dic53—21no—
451Dic53—26no—
452Dic53—21no—
453Dic53—21no—
454#3524—534no—
455#3524—534no—
456#3523—534no—
457#3523—534no—
458#3518—534no—
459#3518—534no—
460#3516—534no—
461#3516—534no—
462#3507—536no—
463#3502—531no—
464#3497—531no—
465#3493—536no—
466#3486—531no—
467#3486D5311yescharacteristic, complemented
468#3461—536no—
469#3455—536no—
470C4×2−1+4—531no—
471C4×2−1+4—531no—
472C2×#519—531no—
473C2×C53—22no—
474C2×C53—44no—
475C2×C53—41no—
476C2×C53—41no—
477C2×C53C23×#4111yescharacteristic
478C2×C532−1+611yescharacteristic
479C2×C532−1+611yescharacteristic
480D53—44no—
481C2×2−1+4—531no—
482C2×2−1+4C2×D5311yescharacteristic
483C23×Q8C2×D5311yescharacteristic
484#559—5312no—
485Q82—534no—
486#557—5312no—
487#557—534no—
488#557—534no—
489#557—534no—
490#556—5312no—
491#556—5312no—
492#556—5312no—
493#556—5312no—
494#556—5312no—
495#555—5312no—
496#555—5312no—
497#554—5312no—
498#553—5312no—
499#553—5312no—
500#552—5312no—
501#552—5312no—
502#552—5312no—
503#552—5312no—
504#550—534no—
505D4×Q8—534no—
506D4×Q8—534no—
507D4×Q8—534no—
508D4×Q8C2×D5314yes—
509D4×Q8C2×D5314yes—
510#548—534no—
511#548—534no—
512#548—534no—
513#548—534no—
514#548C2×D5314yes—
515#548C2×D5314yes—
516#544—536no—
517#542—5312no—
518#542—536no—
519#542—536no—
520#542—5312no—
521#542—536no—
522#542—536no—
523#541—5312no—
524#541—536no—
525#541—536no—
526#541—5312no—
527#540—536no—
528#540—536no—
529#539—5312no—
530#539—5312no—
531#538—534no—
532#538—5312no—
533#537—536no—
534#536—536no—
535#536C2×D5316yes—
536#533—5312no—
537#533—5312no—
538#533—536no—
539#532—536no—
540#529—5312no—
541#529—5324no—
542#529—5312no—
543#529—5312no—
544#529—5312no—
545#529—5312no—
546#529—5312no—
547#525—536no—
548#525C2×D5316yes—
549#520—536no—
550#520—534no—
551#520—534no—
552#520—536no—
553#519—534no—
554#519—534no—
555#519—534no—
556#519—534no—
557#519—531no—
558#519—534no—
559#519—534no—
560#519C2×D5311yescharacteristic
561C4×#41—536no—
562C4×#41—534no—
563C4×#41—534no—
564C4×#41—536no—
565C2×C4×Q8—531no—
566C2×C4×Q8—533no—
567C2×C4×Q8—531no—
568C2×C4×Q8—533no—
569C2×C4×Q8—534no—
570C2×C4×Q8—534no—
571C2×#117—533no—
572C2×#117—533no—
573C53#6285011yescharacteristic, complemented, Sylow
5742−1+4—28no—
5752−1+4—1068no—
576C2×#41—534no—
577C2×#41—536no—
578C2×#41C22×D5316yes—
579C2×#41C22×D5314yes—
580C22×Q8—28no—
581C22×Q8—534no—
582C22×Q8C22×D5313yes—
583C22×Q8C22×D5314yes—
584C22×Q8C22×D5314yes—
585C22×Q8C22×D5314yes—
586C22×Q8C22×D5311yescharacteristic
587C23×C4C22×D5313yes—
588C4⋊Q8—536no—
589C4⋊Q8—5312no—
590C4⋊Q8—536no—
591C4⋊Q8—536no—
592C4⋊Q8—5312no—
593C4⋊Q8—5312no—
594C4⋊Q8C22×D53112yes—
595#127—536no—
596#126—5312no—
597#126—5312no—
598#126—5324no—
599#126—534no—
600#126—534no—
601#126—5312no—
602#126—5312no—
603#126—5312no—
604#126—5312no—
605#126—5324no—
606#125—5312no—
607#125—5312no—
608#125—5312no—
609#125—5312no—
610#125—5324no—
611#125—5312no—
612#125—536no—
613#125—536no—
614#125—5312no—
615#124—5312no—
616#124—536no—
617#124—534no—
618#124—5312no—
619#124—536no—
620#124—534no—
621#124—5312no—
622#124—5324no—
623#124C22×D53112yes—
624#123—534no—
625#123—5312no—
626#123—5312no—
627#123—534no—
628#123—5312no—
629#123—5312no—
630#123—5312no—
631#123—5312no—
632#123—5312no—
633#123C22×D53112yes—
634C22⋊Q8—5312no—
635C22⋊Q8—5312no—
636C22⋊Q8—5312no—
637C22⋊Q8—536no—
638C22⋊Q8—536no—
639C22⋊Q8—5312no—
640C22⋊Q8—5312no—
641C22⋊Q8—5312no—
642C22⋊Q8—5312no—
643C22⋊Q8—5312no—
644C22⋊Q8—5312no—
645C22⋊Q8—534no—
646C22⋊Q8C22×D5316yes—
647C22⋊Q8C22×D5316yes—
648C22⋊Q8C22×D53112yes—
649C22⋊Q8C22×D53112yes—
650#121—534no—
651#121—534no—
652#121—5312no—
653#121—5312no—
654#121—5312no—
655#121—5312no—
656#121—534no—
657#121—536no—
658#121—536no—
659#121—5312no—
660#121C22×D5316yes—
661#121C22×D5316yes—
662#120—534no—
663#120C22×D5314yes—
664C4×Q8—534no—
665C4×Q8—534no—
666C4×Q8—536no—
667C4×Q8—5312no—
668C4×Q8—5312no—
669C4×Q8—534no—
670C4×Q8—534no—
671C4×Q8—5312no—
672C4×Q8—5312no—
673C4×Q8—534no—
674C4×Q8—5312no—
675C4×Q8—536no—
676C4×Q8—534no—
677C4×Q8—536no—
678C4×Q8—536no—
679C4×Q8—5324no—
680C4×Q8—5312no—
681C4×Q8—5312no—
682C4×Q8—5312no—
683C4×Q8C22×D5314yes—
684C4×Q8C22×D5314yes—
685C4×D4—534no—
686C4×D4—536no—
687C4×D4—5312no—
688C4×D4—536no—
689C4×D4—5312no—
690C4×D4—5312no—
691C4×D4—5312no—
692C4×D4—5312no—
693C4×D4—5312no—
694C4×D4—536no—
695C4×D4—536no—
696C4×D4—534no—
697C4×D4—5312no—
698C4×D4—5324no—
699C4×D4—5312no—
700C4×D4C22×D53112yes—
701C4×D4C22×D53112yes—
702#117—536no—
703#117—536no—
704#117—536no—
705#117—536no—
706#117—5312no—
707#117—5312no—
708#117—536no—
709#117—5312no—
710#117—5312no—
711#117—5312no—
712#117—5324no—
713#117—5324no—
714#117—5312no—
715#117C22×D5316yes—
716C2×C4⋊C4—533no—
717C2×C4⋊C4—533no—
718C2×C4⋊C4—533no—
719C2×C4⋊C4—533no—
720C2×C4⋊C4—5312no—
721C2×C4⋊C4—5312no—
722C2×C22⋊C4—531no—
723C2×C22⋊C4—533no—
724C2×C42—533no—
725C2×C42—536no—
726C2×C42—533no—
727C2×C42—5312no—
728C2×C42—5312no—
729C24C23×D5311yescharacteristic
730#41—216no—
731#41—224no—
732#41—10616no—
733#41—10624no—
734C2×Q8—216no—
735C2×Q8—216no—
736C2×Q8—216no—
737C2×Q8—212no—
738C2×Q8—536no—
739C2×Q8—534no—
740C2×Q8—5312no—
741C2×Q8—10616no—
742C2×Q8#1171994718yes—
743C2×Q8C23×D53112yes—
744C2×Q8C23×D5316yes—
745C2×Q8C23×D5314yes—
746C2×D4—534no—
747C2×D4—534no—
748C2×D4—534no—
749C2×D4—5312no—
750C2×D4—534no—
751C2×D4—536no—
752C2×D4C23×D5314yes—
753C2×D4C23×D5316yes—
754C2×D4C23×D5314yes—
755C2×D4C23×D5314yes—
756C22×C4—212no—
757C22×C4—531no—
758C22×C4—533no—
759C22×C4—531no—
760C22×C4—533no—
761C22×C4—534no—
762C22×C4—5312no—
763C22×C4—5312no—
764C22×C4—534no—
765C22×C4—5312no—
766C22×C4C23×D5313yes—
767C22×C4C23×D53112yes—
768C22×C4C23×D5316yes—
769C22×C4C23×D5316yes—
770C22×C4C23×D5313yes—
771C4⋊C4—5312no—
772C4⋊C4—536no—
773C4⋊C4—5312no—
774C4⋊C4—5312no—
775C4⋊C4—5312no—
776C4⋊C4—536no—
777C4⋊C4—536no—
778C4⋊C4—536no—
779C4⋊C4—536no—
780C4⋊C4—536no—
781C4⋊C4—534no—
782C4⋊C4—534no—
783C4⋊C4—5312no—
784C4⋊C4—5312no—
785C4⋊C4—5312no—
786C4⋊C4—534no—
787C4⋊C4—5312no—
788C4⋊C4—5312no—
789C4⋊C4—5312no—
790C4⋊C4—534no—
791C4⋊C4—534no—
792C4⋊C4—534no—
793C4⋊C4C23×D5316yes—
794C4⋊C4C23×D5316yes—
795C4⋊C4C23×D53112yes—
796C4⋊C4C23×D53112yes—
797C22⋊C4—531no—
798C22⋊C4—531no—
799C22⋊C4—536no—
800C22⋊C4—536no—
801C22⋊C4—531no—
802C22⋊C4—531no—
803C22⋊C4—534no—
804C22⋊C4—534no—
805C22⋊C4—5312no—
806C22⋊C4—5312no—
807C22⋊C4—534no—
808C22⋊C4—534no—
809C22⋊C4—534no—
810C22⋊C4—534no—
811C22⋊C4—5312no—
812C22⋊C4—5312no—
813C22⋊C4—5312no—
814C22⋊C4—5312no—
815C22⋊C4—534no—
816C22⋊C4C23×D53112yes—
817C22⋊C4C23×D5314yes—
818C22⋊C4C23×D53112yes—
819C22⋊C4C23×D5314yes—
820C22⋊C4C23×D5314yes—
821C42—536no—
822C42—536no—
823C42—534no—
824C42—534no—
825C42—5312no—
826C42—5324no—
827C42—5312no—
828C42—5312no—
829C42—536no—
830C42—536no—
831C42C23×D53112yes—
832C23—22no—
833C23—41no—
834C23—41no—
835C23—534no—
836C23C24×D5311yescharacteristic
837C23C24×D5311yescharacteristic
838C23C24×D5314yes—
839C23C24×D5311yescharacteristic
840Q8—224no—
841Q8—212no—
842Q8—10612no—
843Q8—2124no—
844Q8—21212no—
845Q8C2×#11719947116yes—
846D4—28no—
847D4—212no—
848D4—44no—
849D4—44no—
850D4—1068no—
851D4—10612no—
852D4—2124no—
853D4—2124no—
854D4—21212no—
855D4—2124no—
856C2×C4—26no—
857C2×C4—212no—
858C2×C4—212no—
859C2×C4—224no—
860C2×C4—531no—
861C2×C4—536no—
862C2×C4—531no—
863C2×C4—531no—
864C2×C4—534no—
865C2×C4—536no—
866C2×C4—531no—
867C2×C4—534no—
868C2×C4—534no—
869C2×C4—10624no—
870C2×C4—21212no—
871C2×C4—2124no—
872C2×C4—2121no—
873C2×C4—2123no—
874C2×C4—21212no—
875C2×C4—2124no—
876C2×C4—2121no—
877C2×C4—2123no—
878C2×C4C2×#11719947112yes—
879C2×C4C24×D5316yes—
880C2×C4C24×D5314yes—
881C2×C4C24×D5314yes—
882C2×C4C24×D5314yes—
883C2×C4C24×D5316yes—
884C22—21no—
885C22—21no—
886C22—21no—
887C22—21no—
888C22—24no—
889C22—24no—
890C22—24no—
891C22—21no—
892C22—21no—
893C22—21no—
894C22—21no—
895C22—44no—
896C22—1064no—
897C22—1064no—
898C22—1064no—
899C22C22×#1171994712yes—
900C22C25×D5311yescharacteristic
901C4—24no—
902C4—26no—
903C4—24no—
904C4—24no—
905C4—1064no—
906C4—1061no—
907C4—1066no—
908C4—1061no—
909C4—1064no—
910C4—1061no—
911C4—1066no—
912C4—1064no—
913C4—1061no—
914C4C22×#11719947112yes—
915C2—22no—
916C2—41no—
917C2—41no—
918C2—44no—
919C2—2124no—
920C2C23×#1171994711yescharacteristic
921C2#2028952711yescharacteristic
922C2#2028952711yescharacteristic
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3486C2
hypercenter#3486D53
hypocenterC53#62850
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3486

Complements

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

NH ≅ G/Ntype
1. #20288825C2semidirect
2. #20288817C2semidirect
3. #20288806C2semidirect
4. #20288802C2semidirect
5. #20288727C2semidirect
6. #20288723C2semidirect
7. #20288709C2semidirect
8. #20288701C2semidirect
9. #20288579C2semidirect
10. #20288521C2semidirect
11. #20288482C2semidirect
12. #20288432C2semidirect
13. #20288366C2semidirect
14. #20288139C2semidirect
15. #20288103C2semidirect
16. 2−1+4×Dic53C2semidirect
17. #20287924C2semidirect
18. C2×#16811101C2semidirect
19. C53×#3486C2semidirect
21. #16811355C22semidirect
22. Q8×Dic106C22semidirect
23. #16811352C22semidirect
24. #16811349C22semidirect
25. #16811349C22semidirect
26. #16811348C22semidirect
27. #16811347C22semidirect
29. #16811344C22semidirect
31. #16811342C22semidirect
34. #16811331C22semidirect
37. #16811315C22semidirect
40. #16811307C22semidirect
41. #16811292C22semidirect
44. Q8×C22⋊D53C22semidirect
47. #16811284C22semidirect
48. #16811280C22semidirect
52. #16811246C22semidirect
53. #16811242C22semidirect
56. #16811234C22semidirect
59. #16811233C22semidirect
68. #16811178C22semidirect
70. #16811175C22semidirect
72. #16811159C22semidirect
77. #16811152C22semidirect
81. #16811106C22semidirect
82. #16811105C22semidirect
89. #16811101C22semidirect
90. #16811099C22semidirect
92. #41×Dic53C22semidirect
93. C4×#11719949C22semidirect
99. C2×Q8×Dic53C22semidirect
100. C4×Q8×D53C22semidirect
467. #3486D53semidirect
573. C53#62850semidirect

Maximal subgroups

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

subgroupindex
#202888252
#202888172
#202888062
#202888022
#202887272
#202887232
#202887092
#202887012
#202885792
#202885212
#202884822
#202884322
#202883662
#202881392
#202881032
2−1+4×Dic532
#202879242
C2×#168111012
C53×#34862
#6285053