Finite Group Databasebeta

← #28293176

Subgroups — #28293176

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#20288824C214yesmaximal, complemented
2#20288816C214yesmaximal, complemented
3#20288811C214yesmaximal, complemented
4#20288805C214yesmaximal, complemented
5#20288732C214yesmaximal, complemented
6#20288726C214yesmaximal, complemented
7#20288708C214yesmaximal, complemented
8#20288700C214yesmaximal, complemented
9#20288573C216yesmaximal, complemented
10#20288521C211yesmaximal, characteristic, complemented
11#20288482C211yesmaximal, characteristic, complemented
12#20288428C216yesmaximal, complemented
13#20288367C211yesmaximal, characteristic, complemented
14#20288363C211yesmaximal, characteristic, complemented
15#20288142C216yesmaximal, complemented
16#20288100C216yesmaximal, complemented
17C4×#13133265C211yesmaximal, characteristic, complemented
18C2×#16811099C211yesmaximal, characteristic, complemented
19C4×2−1+4×C53C211yesmaximal, characteristic, complemented
20C2×#13133265C2211yescharacteristic
21C22×Q8×D53C2211yescharacteristic
22#16811356C22112yescomplemented
23Q8×Dic106C2214yescomplemented
24#16811352C2214yescomplemented
25#16811351C22112yescomplemented
26#16811349C2214yescomplemented
27#16811349C2214yescomplemented
28#16811346C22112yes—
29#16811345C22112yescomplemented
30#16811343C22112yescomplemented
31#16811341C22112yes—
32#16811341C22112yescomplemented
33#16811338C22112yes—
34#16811336C22112yes—
35#16811328C22112yescomplemented
36#16811323C22112yes—
37#16811321C22112yes—
38#16811314C22112yes—
39#16811312C22112yescomplemented
40#16811308C22112yes—
41#16811308C22112yescomplemented
42#16811292C2214yescomplemented
43Q8×D212C2214yes—
44Q8×D212C2214yes—
45Q8×C22⋊D53C2214yes—
46Q8×C22⋊D53C2214yes—
47Q8×C22⋊D53C2214yescomplemented
48#16811285C2214yes—
49#16811285C2214yes—
50#16811284C2214yescomplemented
51#16811280C2214yes—
52#16811280C2214yes—
53#16811280C2214yescomplemented
54#16811251C2216yes—
55#16811245C2216yes—
56#16811245C2216yes—
57#16811244C22112yescomplemented
58#16811238C2216yes—
59#16811238C2216yes—
60#16811238C22112yescomplemented
61#16811235C22112yescomplemented
62#16811231C2216yes—
63#16811231C2216yes—
64#16811231C22112yescomplemented
65#16811224C2216yes—
66#16811224C2216yes—
67#16811215C22112yes—
68#16811215C22112yes—
69#16811206C2214yes—
70#16811206C22112yes—
71#16811201C2216yes—
72#16811199C2216yes—
73#16811194C2216yes—
74#16811180C22112yescomplemented
75#16811177C22112yescomplemented
76#16811176C2216yes—
77#16811169C2216yes—
78#16811157C22112yes—
79#16811157C22112yes—
80#16811157C22112yescomplemented
81#16811155C22112yescomplemented
82#16811153C22124yes—
83#16811151C22112yes—
84#16811151C22112yes—
85#16811135C2216yes—
86#16811130C2216yes—
87#16811105C2214yescomplemented
88#16811104C2216yes—
89#16811101C2211yescharacteristic
90#16811099C2214yes—
91#16811099C2214yes—
92#16811099C2214yes—
93#16811099C2214yes—
94#16811099C2214yescomplemented
95C4×#11719949C2214yescomplemented
96C4×#11719945C2216yes—
97C2×Q8×Dic53C2211yescharacteristic
98C2×C4×Dic106C2213yes—
99C2×#13133182C2213yes—
100C4×Q8×D53C2214yescomplemented
101C2×#13133175C2213yes—
102C2×#13133174C2213yes—
103C2×2−1+4×C53C2211yescharacteristic
104C53×#520C2216yes—
105C53×#520C2214yescomplemented
106C53×#519C2211yescharacteristic
107C53×#519C2214yescomplemented
108C4×#41×C53C2216yes—
109C4×#41×C53C2214yescomplemented
110C2×C4×Q8×C53C2211yescharacteristic
111C2×C4×Q8×C53C2214yescomplemented
112#13133265—28no—
113C2×#11719949C2314yes—
114C2×#11719945C2316yes—
115C22×Dic106C2313yes—
116C2×Q8×D53—28no—
117C2×Q8×D53C2314yes—
118C2×Q8×D53C2314yes—
119C2×Q8×D53C2314yes—
120C22×C4×D53C2313yes—
121#13133217C23112yes—
122#13133217C23112yes—
123#13133216C2316yes—
124#13133216C23112yes—
125#13133216C2316yes—
126#13133215C23112yes—
127#13133215C2316yes—
128#13133213C2316yes—
129#13133212C23112yes—
130#13133212C23124yes—
131#13133212C2314yes—
132#13133211C23112yes—
133#13133211C23112yes—
134#13133211C2314yes—
135#13133211C23112yes—
136#13133210C23124yes—
137#13133210C23112yes—
138#13133210C23112yes—
139#13133209C23112yes—
140#13133209C23112yes—
141#13133209C23112yes—
142#13133208C23112yes—
143#13133208C2316yes—
144#13133208C2316yes—
145#13133207C23124yes—
146#13133207C23112yes—
147#13133207C23112yes—
148#13133206C2316yes—
149#13133205C23112yes—
150#13133205C23112yes—
151#13133205C2314yes—
152#13133204C23112yes—
153#13133204C2316yes—
154#13133203C23124yes—
155#13133203C23112yes—
156#13133203C2314yes—
157#13133202C23112yes—
158#13133202C2314yes—
159#13133201C23112yes—
160#13133200C23112yes—
161#13133200C23112yes—
162#13133200C2314yes—
163#13133200C23112yes—
164#13133199C23112yes—
165#13133199C23112yes—
166#13133198C23112yes—
167#13133197C23112yes—
168#13133197C23112yes—
169#13133197C2316yes—
170#13133197C2316yes—
171#13133196C23112yes—
172#13133196C23112yes—
173#13133196C23112yes—
174#13133196C23112yes—
175#13133196C23112yes—
176#13133195C23112yes—
177#13133195C23112yes—
178#13133194C23112yes—
179#13133194C2314yes—
180#13133193C23112yes—
181#13133193C2316yes—
182#13133193C2316yes—
183#13133192C2316yes—
184#13133192C2316yes—
185#13133191C23112yes—
186#13133191C23112yes—
187#13133191C2314yes—
188#13133190C23112yes—
189#13133190C2314yes—
190#13133189C23112yes—
191#13133189C2314yes—
192#13133188C2316yes—
193#13133188C2316yes—
194#13133188C23112yes—
195#13133187C2314yes—
196#13133185C2314yes—
197Q8×Dic53C2314yes—
198Q8×Dic53C2314yes—
199Q8×Dic53C2314yes—
200Q8×Dic53C2314yes—
201C4×Dic106C23124yes—
202C4×Dic106C2316yes—
203C4×Dic106C23112yes—
204C4×Dic106C23112yes—
205C4×Dic106C23112yes—
206C4×Dic106C2316yes—
207C4×Dic106C23112yes—
208#13133182C23112yes—
209#13133182C23112yes—
210#13133182C23112yes—
211C4×D212C23112yes—
212C4×D212C23112yes—
213C4×D212C2316yes—
214C4×D212C2316yes—
215#13133179C23112yes—
216C4×C22⋊D53C23112yes—
217C4×C22⋊D53C23112yes—
218C4×C22⋊D53C23112yes—
219C4×C22⋊D53C23112yes—
220C4×C22⋊D53C23124yes—
221C4×C22⋊D53C2314yes—
222C4×C22⋊D53C23112yes—
223#13133176C23124yes—
224#13133176C2316yes—
225#13133175C23112yes—
226#13133175C23112yes—
227#13133175C23112yes—
228#13133174C23124yes—
229#13133174C2316yes—
230#13133174C2316yes—
231#13133174C2316yes—
232#13133174C2316yes—
233#13133174C23112yes—
234C2×C4⋊Dic53C2313yes—
235C2×#11719919C2313yes—
236C2×#11719919C2313yes—
237C4⋊C4×D53C23112yes—
238C2×#11719921C2311yescharacteristic
239C2×#11719921C2313yes—
240C2×C4×Dic53C2313yes—
241C2×C4×Dic53C2316yes—
242C42×D53C23112yes—
2432−1+4×C53—28no—
244C2×#41×C53C2314yes—
245C2×#41×C53C2316yes—
246C22×Q8×C53C2314yes—
247C22×Q8×C53C2311yescharacteristic
248C4×Q8×C53C2314yes—
249C4×Q8×C53C2314yes—
250C4×Q8×C53C2314yes—
251C4×Q8×C53C2314yes—
252C4×Q8×C53C2316yes—
253C4×Q8×C53C23112yes—
254C4×Q8×C53C2316yes—
255C4×D4×C53C2314yes—
256C4×D4×C53C2316yes—
257C4×D4×C53C23112yes—
258C4×D4×C53C2316yes—
259C4×D4×C53C23112yes—
260#117×C53C2316yes—
261#117×C53C23112yes—
262#117×C53C23112yes—
263C2×C4⋊C4×C53C2313yes—
264C2×C4⋊C4×C53C23112yes—
265C2×C42×C53C2313yes—
266C2×C42×C53C23112yes—
267C23×D53C2411yescharacteristic
268#41×C53—216no—
269#41×C53—224no—
270C2×Q8×C53—216no—
271C2×Q8×C53#4118yes—
272C2×Q8×C53C2416yes—
273C2×Q8×C53C2414yes—
274C2×D4×C53C2414yes—
275C2×D4×C53C2416yes—
276C22×C4×C53C24112yes—
277C22×C4×C53C2411yescharacteristic
278C22×C4×C53C2414yes—
279C22×C4×C53C2413yes—
280C22×C4×C53C24112yes—
281C22×C4×C53C2413yes—
282C2×C22⋊D53C2414yes—
283C2×C22⋊D53C2414yes—
284C2×C22⋊D53C2414yes—
285C2×C22⋊D53C24112yes—
286C2×C22⋊D53C2414yes—
287C22×Dic53C2413yes—
288C22×Dic53C2411yescharacteristic
289C22×Dic53C2413yes—
290#11719949—216no—
291Q8×D53—216no—
292Q8×D53—216no—
293Q8×D53—216no—
294#11719945—224no—
295C2×D212C2416yes—
296C2×D212C2414yes—
297C2×D212C2414yes—
298C2×C4×D53—212no—
299C2×C4×D53C24112yes—
300C2×C4×D53C2416yes—
301C2×C4×D53C2416yes—
302C2×C4×D53C2414yes—
303C2×C4×D53C24112yes—
304C2×Dic106—212no—
305C2×Dic106C24112yes—
306C2×Dic106C2416yes—
307C2×Dic106C2414yes—
308C2×Dic106C24112yes—
309C4⋊C4×C53C24112yes—
310C4⋊C4×C53C2416yes—
311C4⋊C4×C53C24112yes—
312C4⋊C4×C53C2416yes—
313C4⋊C4×C53C2414yes—
314C22⋊C4×C53C2414yes—
315C22⋊C4×C53C2414yes—
316C22⋊C4×C53C24112yes—
317C42×C53C2416yes—
318C42×C53C2414yes—
319C42×C53C2416yes—
320C42×C53C24112yes—
321C42×C53C24112yes—
322C22⋊Dic53C2414yes—
323C22⋊Dic53C24112yes—
324C22⋊Dic53C24112yes—
325C22⋊Dic53C24112yes—
326C22⋊Dic53C2414yes—
327#11719921C2411yescharacteristic
328#11719921C2411yescharacteristic
329#11719921C2411yescharacteristic
330#11719921C2411yescharacteristic
331#11719921C2416yes—
332#11719921C2416yes—
333#11719921C2414yes—
334#11719921C24112yes—
335#11719921C24112yes—
336#11719921C24112yes—
337#11719921C2414yes—
338#11719921C2414yes—
339#11719921C2414yes—
340#11719921C24112yes—
341#11719921C2414yes—
342#11719921C2414yes—
343C4⋊Dic53C2416yes—
344C4⋊Dic53C24112yes—
345C4⋊Dic53C2416yes—
346C4⋊Dic53C24112yes—
347C4⋊Dic53C24112yes—
348C4⋊Dic53C24112yes—
349C4⋊Dic53C2414yes—
350#11719919C24112yes—
351#11719919C2416yes—
352#11719919C2416yes—
353#11719919C2416yes—
354#11719919C2416yes—
355#11719919C2414yes—
356#11719919C24112yes—
357#11719919C24112yes—
358#11719919C2414yes—
359#11719919C24112yes—
360#11719919C24112yes—
361#11719919C24112yes—
362#11719919C2414yes—
363#11719919C2414yes—
364C4×Dic53C2414yes—
365C4×Dic53C24112yes—
366C4×Dic53C24112yes—
367C4×Dic53C2416yes—
368C4×Dic53C2416yes—
369C4×Dic53C24124yes—
370C23×C53C2514yes—
371C23×C53C2511yescharacteristic
372C22×D53—22no—
373C22×D53—41no—
374C22×D53—41no—
375C22×D53C2514yes—
376C22×D53C2511yescharacteristic
377C22×D53C2511yescharacteristic
378Q8×C53—212no—
379Q8×C53C2×#41116yes—
380D4×C53—28no—
381D4×C53—212no—
382C2×C4×C53—224no—
383C2×C4×C53—44no—
384C2×C4×C53—412no—
385C2×C4×C53—41no—
386C2×C4×C53—43no—
387C2×C4×C53C2×#41112yes—
388C2×C4×C53C2514yes—
389C2×C4×C53C2514yes—
390C2×C4×C53C2511yescharacteristic
391C2×C4×C53C2516yes—
392C2×C4×C53C2511yescharacteristic
393C2×C4×C53C2514yes—
394C2×C4×C53C2516yes—
395C22⋊D53—28no—
396C22⋊D53—44no—
397C22⋊D53—412no—
398C22⋊D53—44no—
399C22⋊D53—44no—
400C2×Dic53—26no—
401C2×Dic53—41no—
402C2×Dic53—43no—
403C2×Dic53C2516yes—
404C2×Dic53C2511yescharacteristic
405C2×Dic53C2514yes—
406C2×Dic53C2514yes—
407C2×Dic53C2516yes—
408C2×Dic53C2514yes—
409C2×Dic53C2511yescharacteristic
410D212—212no—
411D212—44no—
412D212—44no—
413C4×D53—212no—
414C4×D53—212no—
415C4×D53—224no—
416C4×D53—44no—
417C4×D53—412no—
418Dic106—224no—
419Dic106—212no—
420Dic106—44no—
421Dic106—412no—
422#62850—531nomaximal, Sylow
423C22×C53—21no—
424C22×C53—21no—
425C22×C53—24no—
426C22×C53—24no—
427C22×C53—24no—
428C22×C53C22×#4112yes—
429C22×C53C2611yescharacteristic
430C2×D53—21no—
431C2×D53—21no—
432C2×D53—24no—
433C2×D53—24no—
434C2×D53—24no—
435C2×D53—21no—
436C2×D53—21no—
437C2×D53—21no—
438C2×D53—21no—
439C2×D53—44no—
440C4×C53—24no—
441C4×C53—24no—
442C4×C53—24no—
443C4×C53—21no—
444C4×C53—26no—
445C4×C53—21no—
446C4×C53C22×#41112yes—
447Dic53—26no—
448Dic53—24no—
449Dic53—21no—
450Dic53—24no—
451Dic53—26no—
452Dic53—24no—
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#3486—531no—
468#3461—536no—
469#3455—536no—
470C4×2−1+4—531no—
471C4×2−1+4D5311yescharacteristic, complemented
472C2×#519—531no—
473C2×C53—22no—
474C2×C53—44no—
475C2×C53C23×#4111yescharacteristic
476C2×C532−1+611yescharacteristic
477C2×C532−1+611yescharacteristic
478D53—44no—
479D53—41no—
480D53—41no—
481C2×2−1+4—531no—
482C2×2−1+4C2×D5311yescharacteristic
483C23×Q8—531no—
484#559—5312no—
485Q82—534no—
486#557—534no—
487#557—534no—
488#557—5312no—
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×Q8—534no—
509D4×Q8—534no—
510#548—534no—
511#548—534no—
512#548—534no—
513#548—534no—
514#548—534no—
515#548—534no—
516#544—536no—
517#542—536no—
518#542—536no—
519#542—536no—
520#542—536no—
521#542—5312no—
522#542—5312no—
523#541—536no—
524#541—536no—
525#541—5312no—
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#536—536no—
536#533—5312no—
537#533—536no—
538#533—5312no—
539#532—536no—
540#529—5324no—
541#529—5312no—
542#529—5312no—
543#529—5312no—
544#529—5312no—
545#529—5312no—
546#529—5312no—
547#525—536no—
548#525—536no—
549#520—534no—
550#520—536no—
551#520C2×D5316yes—
552#520C2×D5314yescomplemented
553#519—531no—
554#519—534no—
555#519—534no—
556#519—534no—
557#519—534no—
558#519—534no—
559#519C2×D5311yescharacteristic
560#519C2×D5314yescomplemented
561C4×#41—534no—
562C4×#41—536no—
563C4×#41C2×D5316yes—
564C4×#41C2×D5314yescomplemented
565C2×C4×Q8—531no—
566C2×C4×Q8—534no—
567C2×C4×Q8—533no—
568C2×C4×Q8—533no—
569C2×C4×Q8C2×D5311yescharacteristic
570C2×C4×Q8C2×D5314yescomplemented
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—534no—
581C22×Q8—534no—
582C22×Q8—534no—
583C22×Q8—533no—
584C22×Q8—1068no—
585C22×Q8C22×D5314yes—
586C22×Q8C22×D5311yescharacteristic
587C23×C4—533no—
588C4⋊Q8—536no—
589C4⋊Q8—5312no—
590C4⋊Q8—536no—
591C4⋊Q8—536no—
592C4⋊Q8—5312no—
593C4⋊Q8—5312no—
594C4⋊Q8—5312no—
595#127—536no—
596#126—534no—
597#126—5312no—
598#126—5324no—
599#126—5312no—
600#126—5312no—
601#126—5324no—
602#126—534no—
603#126—5312no—
604#126—5312no—
605#126—5312no—
606#125—5312no—
607#125—5312no—
608#125—5324no—
609#125—5312no—
610#125—536no—
611#125—536no—
612#125—5312no—
613#125—5312no—
614#125—5312no—
615#124—536no—
616#124—5312no—
617#124—536no—
618#124—534no—
619#124—5312no—
620#124—5324no—
621#124—534no—
622#124—5312no—
623#124—5312no—
624#123—5312no—
625#123—534no—
626#123—5312no—
627#123—5312no—
628#123—5312no—
629#123—534no—
630#123—5312no—
631#123—5312no—
632#123—5312no—
633#123—5312no—
634C22⋊Q8—536no—
635C22⋊Q8—536no—
636C22⋊Q8—5312no—
637C22⋊Q8—5312no—
638C22⋊Q8—5312no—
639C22⋊Q8—5312no—
640C22⋊Q8—5312no—
641C22⋊Q8—5312no—
642C22⋊Q8—536no—
643C22⋊Q8—536no—
644C22⋊Q8—5312no—
645C22⋊Q8—5312no—
646C22⋊Q8—5312no—
647C22⋊Q8—5312no—
648C22⋊Q8—5312no—
649C22⋊Q8—534no—
650#121—536no—
651#121—536no—
652#121—5312no—
653#121—5312no—
654#121—534no—
655#121—534no—
656#121—5312no—
657#121—5312no—
658#121—536no—
659#121—536no—
660#121—534no—
661#121—5312no—
662#120—534no—
663#120—534no—
664C4×Q8—534no—
665C4×Q8—534no—
666C4×Q8—534no—
667C4×Q8—534no—
668C4×Q8—5312no—
669C4×Q8—5312no—
670C4×Q8—5312no—
671C4×Q8—536no—
672C4×Q8—5312no—
673C4×Q8—5312no—
674C4×Q8—536no—
675C4×Q8—5312no—
676C4×Q8—5312no—
677C4×Q8—5324no—
678C4×Q8C22×D5314yes—
679C4×Q8C22×D5314yes—
680C4×Q8C22×D5316yes—
681C4×Q8C22×D5314yes—
682C4×Q8C22×D53112yes—
683C4×Q8C22×D5316yes—
684C4×Q8C22×D5314yes—
685C4×D4—534no—
686C4×D4—5312no—
687C4×D4—5312no—
688C4×D4—5312no—
689C4×D4—5324no—
690C4×D4—5312no—
691C4×D4—5312no—
692C4×D4—5312no—
693C4×D4—536no—
694C4×D4—536no—
695C4×D4—5312no—
696C4×D4—5312no—
697C4×D4C22×D5314yes—
698C4×D4C22×D5316yes—
699C4×D4C22×D53112yes—
700C4×D4C22×D5316yes—
701C4×D4C22×D53112yes—
702#117—536no—
703#117—5324no—
704#117—5312no—
705#117—5312no—
706#117—5312no—
707#117—536no—
708#117—536no—
709#117—536no—
710#117—536no—
711#117—5312no—
712#117—5324no—
713#117C22×D5316yes—
714#117C22×D53112yes—
715#117C22×D53112yes—
716C2×C4⋊C4—533no—
717C2×C4⋊C4—533no—
718C2×C4⋊C4—533no—
719C2×C4⋊C4—5312no—
720C2×C4⋊C4C22×D5313yes—
721C2×C4⋊C4C22×D53112yes—
722C2×C22⋊C4—531no—
723C2×C22⋊C4—533no—
724C2×C42—536no—
725C2×C42—533no—
726C2×C42—5312no—
727C2×C42C22×D5313yes—
728C2×C42C22×D53112yes—
729C24—531no—
730#41—216no—
731#41—224no—
732#41—10616no—
733#41—10624no—
734C2×Q8—216no—
735C2×Q8—5312no—
736C2×Q8—536no—
737C2×Q8—534no—
738C2×Q8—5312no—
739C2×Q8—10616no—
740C2×Q8—10616no—
741C2×Q8—10616no—
742C2×Q8—10612no—
743C2×Q8#1171994518yes—
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×D4—534no—
753C2×D4—534no—
754C2×D4C23×D5314yes—
755C2×D4C23×D5316yes—
756C22×C4—533no—
757C22×C4—531no—
758C22×C4—533no—
759C22×C4—5312no—
760C22×C4—536no—
761C22×C4—536no—
762C22×C4—534no—
763C22×C4—5312no—
764C22×C4—10612no—
765C22×C4C23×D53112yes—
766C22×C4C23×D5313yes—
767C22×C4C23×D5311yescharacteristic
768C22×C4C23×D5314yes—
769C22×C4C23×D53112yes—
770C22×C4C23×D5313yes—
771C4⋊C4—536no—
772C4⋊C4—5312no—
773C4⋊C4—5312no—
774C4⋊C4—536no—
775C4⋊C4—536no—
776C4⋊C4—536no—
777C4⋊C4—536no—
778C4⋊C4—536no—
779C4⋊C4—534no—
780C4⋊C4—5312no—
781C4⋊C4—5312no—
782C4⋊C4—5312no—
783C4⋊C4—5312no—
784C4⋊C4—534no—
785C4⋊C4—5312no—
786C4⋊C4—5312no—
787C4⋊C4—5312no—
788C4⋊C4—5312no—
789C4⋊C4—534no—
790C4⋊C4—534no—
791C4⋊C4—534no—
792C4⋊C4C23×D53112yes—
793C4⋊C4C23×D5316yes—
794C4⋊C4C23×D53112yes—
795C4⋊C4C23×D5316yes—
796C4⋊C4C23×D5314yes—
797C22⋊C4—534no—
798C22⋊C4—5312no—
799C22⋊C4—5312no—
800C22⋊C4—5312no—
801C22⋊C4—534no—
802C22⋊C4—531no—
803C22⋊C4—531no—
804C22⋊C4—536no—
805C22⋊C4—536no—
806C22⋊C4—531no—
807C22⋊C4—531no—
808C22⋊C4—534no—
809C22⋊C4—5312no—
810C22⋊C4—5312no—
811C22⋊C4—5312no—
812C22⋊C4—534no—
813C22⋊C4—534no—
814C22⋊C4—534no—
815C22⋊C4—534no—
816C22⋊C4—5312no—
817C22⋊C4—534no—
818C22⋊C4C23×D5314yes—
819C22⋊C4C23×D5314yes—
820C22⋊C4C23×D53112yes—
821C42—534no—
822C42—5312no—
823C42—5324no—
824C42—5312no—
825C42—536no—
826C42—536no—
827C42C23×D5316yes—
828C42C23×D5316yes—
829C42C23×D5314yes—
830C42C23×D53112yes—
831C42C23×D53112yes—
832C23—531no—
833C23—531no—
834C23—534no—
835C23—1062no—
836C23—2121no—
837C23—2121no—
838C23C24×D5314yes—
839C23C24×D5311yescharacteristic
840Q8—212no—
841Q8—10624no—
842Q8—10612no—
843Q8—21212no—
844Q8—2124no—
845Q8C2×#11719945116yes—
846D4—28no—
847D4—212no—
848D4—1068no—
849D4—10612no—
850D4—2124no—
851D4—2124no—
852D4—21212no—
853D4—2124no—
854D4—2124no—
855D4—2124no—
856C2×C4—224no—
857C2×C4—41no—
858C2×C4—44no—
859C2×C4—43no—
860C2×C4—412no—
861C2×C4—531no—
862C2×C4—534no—
863C2×C4—536no—
864C2×C4—531no—
865C2×C4—536no—
866C2×C4—534no—
867C2×C4—534no—
868C2×C4—1066no—
869C2×C4—10612no—
870C2×C4—10612no—
871C2×C4—10624no—
872C2×C4—2124no—
873C2×C4—21212no—
874C2×C4—2123no—
875C2×C4—2121no—
876C2×C4C2×#11719945112yes—
877C2×C4C24×D5316yes—
878C2×C4C24×D5311yescharacteristic
879C2×C4C24×D5311yescharacteristic
880C2×C4C24×D5314yes—
881C2×C4C24×D5314yes—
882C2×C4C24×D5314yes—
883C2×C4C24×D5316yes—
884C22—21no—
885C22—21no—
886C22—24no—
887C22—24no—
888C22—24no—
889C22—1061no—
890C22—1061no—
891C22—1064no—
892C22—1064no—
893C22—1061no—
894C22—1061no—
895C22—1064no—
896C22—1061no—
897C22—1061no—
898C22—2124no—
899C22C22×#1171994512yes—
900C22C25×D5311yescharacteristic
901C4—24no—
902C4—21no—
903C4—21no—
904C4—24no—
905C4—26no—
906C4—24no—
907C4—1064no—
908C4—1066no—
909C4—1066no—
910C4—1064no—
911C4—1064no—
912C4—1061no—
913C4—1061no—
914C4C22×#11719945112yes—
915C2—22no—
916C2—44no—
917C2—2121no—
918C2—2121no—
919C2—2124no—
920C2C23×#1171994511yescharacteristic
921C2#2028952711yescharacteristic
922C2#2028952811yescharacteristic
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC4×2−1+4×C53C2
hypercenterC4×2−1+4D53
hypocenterC53#62850
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ C4×2−1+4

Complements

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

NH ≅ G/Ntype
1. #20288824C2semidirect
2. #20288816C2semidirect
3. #20288811C2semidirect
4. #20288805C2semidirect
5. #20288732C2semidirect
6. #20288726C2semidirect
7. #20288708C2semidirect
8. #20288700C2semidirect
9. #20288573C2semidirect
10. #20288521C2semidirect
11. #20288482C2semidirect
12. #20288428C2semidirect
13. #20288367C2semidirect
14. #20288363C2semidirect
15. #20288142C2semidirect
16. #20288100C2semidirect
17. C4×#13133265C2semidirect
18. C2×#16811099C2semidirect
19. C4×2−1+4×C53C2semidirect
22. #16811356C22semidirect
23. Q8×Dic106C22semidirect
24. #16811352C22semidirect
25. #16811351C22semidirect
26. #16811349C22semidirect
27. #16811349C22semidirect
29. #16811345C22semidirect
30. #16811343C22semidirect
32. #16811341C22semidirect
35. #16811328C22semidirect
39. #16811312C22semidirect
41. #16811308C22semidirect
42. #16811292C22semidirect
47. Q8×C22⋊D53C22semidirect
50. #16811284C22semidirect
53. #16811280C22semidirect
57. #16811244C22semidirect
60. #16811238C22semidirect
61. #16811235C22semidirect
64. #16811231C22semidirect
74. #16811180C22semidirect
75. #16811177C22semidirect
80. #16811157C22semidirect
81. #16811155C22semidirect
87. #16811105C22semidirect
94. #16811099C22semidirect
95. C4×#11719949C22semidirect
100. C4×Q8×D53C22semidirect
105. C53×#520C22semidirect
107. C53×#519C22semidirect
109. C4×#41×C53C22semidirect
111. C2×C4×Q8×C53C22semidirect
471. C4×2−1+4D53semidirect
552. #520C2×D53semidirect
560. #519C2×D53semidirect
564. C4×#41C2×D53semidirect
570. C2×C4×Q8C2×D53semidirect
573. C53#62850semidirect

Maximal subgroups

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

subgroupindex
#202888242
#202888162
#202888112
#202888052
#202887322
#202887262
#202887082
#202887002
#202885732
#202885212
#202884822
#202884282
#202883672
#202883632
#202881422
#202881002
C4×#131332652
C2×#168110992
C4×2−1+4×C532
#6285053