Finite Group Databasebeta

← #28292386

Subgroups — #28292386

Order 13568.

7190 conjugacy classes of subgroups.

The subgroup lattice has 934 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288826C214yesmaximal, complemented
2#20288816C214yesmaximal, complemented
3#20288726C214yesmaximal, complemented
4#20288715C214yesmaximal, complemented
5#20288560C216yesmaximal, complemented
6#20288521C211yesmaximal, characteristic, complemented
7#20288482C211yesmaximal, characteristic, complemented
8#20288428C216yesmaximal, complemented
9#20288374C211yesmaximal, characteristic, complemented
10#20288370C211yesmaximal, characteristic, complemented
11#20288341C214yesmaximal, complemented
12#20288332C214yesmaximal, complemented
13#20288313C214yesmaximal, complemented
14#20288310C214yesmaximal, complemented
15#20288131C216yesmaximal, complemented
16#20288008C216yesmaximal, complemented
17C4×#13133265C211yesmaximal, characteristic, complemented
18C2×C4×#11719949C211yesmaximal, characteristic, complemented
19C4×2−1+4×C53C211yesmaximal, characteristic, complemented
20C2×#13133265C2211yescharacteristic
21C22×#11719949C2211yescharacteristic
22#16811358C22112yescomplemented
23#16811356C22112yescomplemented
24Q8×Dic106C2214yescomplemented
25#16811352C2214yescomplemented
26#16811349C2214yescomplemented
27#16811349C2214yescomplemented
28#16811346C22112yescomplemented
29#16811345C22112yescomplemented
30#16811341C22112yescomplemented
31#16811338C22112yescomplemented
32#16811336C22112yescomplemented
33#16811336C22112yescomplemented
34#16811323C22112yescomplemented
35#16811321C22112yescomplemented
36#16811321C22112yescomplemented
37#16811317C22112yescomplemented
38#16811314C22112yescomplemented
39#16811308C22112yescomplemented
40#16811295C2214yes—
41#16811295C2214yes—
42#16811294C22112yescomplemented
43#16811292C2214yes—
44#16811292C2214yes—
45#16811292C2214yescomplemented
46Q8×C22⋊D53C2214yescomplemented
47#16811285C2214yes—
48#16811285C2214yes—
49#16811284C2214yes—
50#16811284C2214yes—
51#16811284C2214yescomplemented
52#16811280C2214yescomplemented
53#16811274C22112yescomplemented
54#16811251C2216yes—
55#16811245C22112yescomplemented
56#16811244C22112yescomplemented
57#16811228C22112yescomplemented
58#16811224C22112yescomplemented
59#16811206C22124yes—
60#16811201C2216yes—
61#16811192C2216yes—
62#16811187C2216yes—
63#16811177C2216yescomplemented
64#16811177C2216yescomplemented
65#16811176C2216yes—
66#16811173C22112yescomplemented
67#16811170C2216yescomplemented
68#16811170C2216yescomplemented
69#16811170C22112yescomplemented
70#16811169C2216yes—
71#16811160C2216yescomplemented
72#16811160C2216yescomplemented
73#16811160C22112yescomplemented
74#16811157C22112yescomplemented
75#16811155C2216yescomplemented
76#16811155C2216yescomplemented
77#16811153C2214yes—
78#16811153C22112yes—
79#16811151C22112yescomplemented
80#16811151C22112yescomplemented
81#16811135C2216yes—
82#16811132C22112yes—
83#16811132C22112yes—
84#16811130C2216yes—
85#16811105C2214yescomplemented
86#16811104C2216yes—
87#16811101C2211yescharacteristic
88#16811099C2214yescomplemented
89C4×#11719949C2214yes—
90C4×#11719949C2214yes—
91C4×#11719949C2214yes—
92C4×#11719949C2214yes—
93C4×#11719949C2214yescomplemented
94C4×#11719945C2216yes—
95C4×#11719945C22112yescomplemented
96C4×#11719945C22112yescomplemented
97C2×Q8×Dic53C2211yescharacteristic
98C4×Q8×D53C2214yescomplemented
99C2×C4×D212C2213yes—
100C2×#13133179C2213yes—
101C2×#13133175C2213yes—
102C2×C42×D53C2213yes—
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×#11719949—28no—
114C2×#11719949C2314yes—
115C2×#11719949C2314yes—
116C2×#11719949C2314yes—
117C2×#11719945C2316yes—
118C2×#11719945C23112yes—
119C2×#11719945C23112yes—
120C2×Q8×D53C2314yes—
121C22×D212C2313yes—
122C22×C4×D53C2313yes—
123C22×C4×D53C2313yes—
124C22×C4×D53C2313yes—
125#13133217C23112yes—
126#13133216C2316yes—
127#13133216C2316yes—
128#13133216C23112yes—
129#13133215C2316yes—
130#13133214C23112yes—
131#13133213C23112yes—
132#13133213C2316yes—
133#13133212C23124yes—
134#13133212C23112yes—
135#13133212C2314yes—
136#13133211C23124yes—
137#13133210C23112yes—
138#13133210C2314yes—
139#13133209C23112yes—
140#13133208C23112yes—
141#13133208C2316yes—
142#13133208C2316yes—
143#13133207C23112yes—
144#13133207C2314yes—
145#13133206C23112yes—
146#13133206C2316yes—
147#13133205C23112yes—
148#13133205C23124yes—
149#13133204C2316yes—
150#13133203C23112yes—
151#13133203C23124yes—
152#13133203C2314yes—
153#13133202C23124yes—
154#13133202C23112yes—
155#13133202C23112yes—
156#13133201C2314yes—
157#13133200C23124yes—
158#13133199C23112yes—
159#13133199C23112yes—
160#13133198C2314yes—
161#13133197C2316yes—
162#13133197C2316yes—
163#13133196C23112yes—
164#13133195C23112yes—
165#13133195C23112yes—
166#13133194C2314yes—
167#13133194C23112yes—
168#13133193C2316yes—
169#13133193C2316yes—
170#13133193C23112yes—
171#13133192C23112yes—
172#13133192C23112yes—
173#13133192C2316yes—
174#13133192C2316yes—
175#13133191C23112yes—
176#13133191C23112yes—
177#13133191C23112yes—
178#13133191C23124yes—
179#13133190C23112yes—
180#13133190C23124yes—
181#13133190C23112yes—
182#13133189C2314yes—
183#13133189C23112yes—
184#13133188C23112yes—
185#13133188C2316yes—
186#13133188C2316yes—
187#13133187C23112yes—
188#13133185C23112yes—
189Q8×Dic53C2314yes—
190Q8×Dic53C2314yes—
191Q8×Dic53C2314yes—
192Q8×Dic53C2314yes—
193C4×Dic106C23112yes—
194C4×Dic106C23112yes—
195C4×Dic106C2316yes—
196C4×Dic106C2316yes—
197C4×Dic106C2314yes—
198C4×Dic106C23112yes—
199#13133182C23112yes—
200C4×D212C23112yes—
201C4×D212C23112yes—
202C4×D212C23112yes—
203C4×D212C23112yes—
204C4×D212C23112yes—
205C4×D212C2316yes—
206C4×D212C2316yes—
207C4×D212C23112yes—
208#13133179C23112yes—
209#13133179C23112yes—
210#13133179C23112yes—
211C4×C22⋊D53C23112yes—
212C4×C22⋊D53C23112yes—
213C4×C22⋊D53C23112yes—
214C4×C22⋊D53C23112yes—
215C4×C22⋊D53C23112yes—
216C4×C22⋊D53C23112yes—
217C4×C22⋊D53C2314yes—
218C4×C22⋊D53C23112yes—
219C4×C22⋊D53C2314yes—
220C4×C22⋊D53C23112yes—
221#13133176C23112yes—
222#13133176C2316yes—
223#13133176C2314yes—
224#13133175C23112yes—
225#13133175C23112yes—
226#13133175C23112yes—
227#13133174C23112yes—
228#13133174C23112yes—
229#13133174C23112yes—
230#13133174C2314yes—
231#13133174C23112yes—
232C2×C4⋊Dic53C2313yes—
233C4⋊C4×D53C23112yes—
234C2×#11719921C2316yes—
235C2×C4×Dic53C2311yescharacteristic
236C2×C4×Dic53C2313yes—
237C2×C4×Dic53C2313yes—
238C42×D53C2316yes—
239C42×D53C2316yes—
240C42×D53C2316yes—
241C42×D53C2316yes—
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×C53C23112yes—
256C4×D4×C53C2314yes—
257C4×D4×C53C2316yes—
258C4×D4×C53C23112yes—
259C4×D4×C53C2316yes—
260#117×C53C2316yes—
261#117×C53C23112yes—
262#117×C53C23112yes—
263C2×C4⋊C4×C53C23112yes—
264C2×C4⋊C4×C53C2313yes—
265C2×C42×C53C2313yes—
266C2×C42×C53C23112yes—
267C23×D53C2413yes—
268#41×C53—216no—
269#41×C53—224no—
270C2×Q8×C53—216no—
271C2×Q8×C53#4118yescomplemented
272C2×Q8×C53C2416yes—
273C2×Q8×C53C2414yes—
274C2×D4×C53C2414yes—
275C2×D4×C53C2416yes—
276C22×C4×C53C2411yescharacteristic
277C22×C4×C53C2414yes—
278C22×C4×C53C24112yes—
279C22×C4×C53C2413yes—
280C22×C4×C53C24112yes—
281C22×C4×C53C2413yes—
282C2×C22⋊D53C2414yes—
283C2×C22⋊D53C2414yes—
284C2×C22⋊D53C24112yes—
285C2×C22⋊D53C24112yes—
286C2×C22⋊D53C24112yes—
287C22×Dic53C2411yescharacteristic
288C22×Dic53C2411yescharacteristic
289C22×Dic53C2413yes—
290#11719949—216no—
291#11719949—216no—
292#11719949—216no—
293Q8×D53—216no—
294#11719945—224no—
295#11719945—424no—
296#11719945—424no—
297C2×D212—212no—
298C2×D212C24112yes—
299C2×D212C2416yes—
300C2×D212C24112yes—
301C2×D212C24112yes—
302C2×C4×D53—212no—
303C2×C4×D53—46no—
304C2×C4×D53—46no—
305C2×C4×D53C2414yes—
306C2×C4×D53C2416yes—
307C2×C4×D53C2416yes—
308C2×C4×D53C2416yes—
309C2×C4×D53C2416yes—
310C2×C4×D53C24112yes—
311C2×C4×D53C2416yes—
312C2×C4×D53C2416yes—
313C2×C4×D53C24112yes—
314C2×Dic106C2416yes—
315C2×Dic106C2414yes—
316C2×Dic106C24112yes—
317C4⋊C4×C53C24112yes—
318C4⋊C4×C53C2416yes—
319C4⋊C4×C53C24112yes—
320C4⋊C4×C53C2416yes—
321C4⋊C4×C53C2414yes—
322C22⋊C4×C53C2414yes—
323C22⋊C4×C53C2414yes—
324C22⋊C4×C53C24112yes—
325C42×C53C2416yes—
326C42×C53C2414yes—
327C42×C53C2416yes—
328C42×C53C24112yes—
329C42×C53C24112yes—
330C22⋊Dic53C2414yes—
331C22⋊Dic53C2414yes—
332C22⋊Dic53C2414yes—
333C22⋊Dic53C2414yes—
334C22⋊Dic53C24112yes—
335#11719921C24124yes—
336#11719921C2414yes—
337#11719921C2414yes—
338#11719921C24112yes—
339#11719921C2414yes—
340#11719921C2414yes—
341#11719921C24112yes—
342#11719921C24112yes—
343#11719921C24112yes—
344#11719921C24112yes—
345#11719921C24112yes—
346C4⋊Dic53C2416yes—
347C4⋊Dic53C24112yes—
348C4⋊Dic53C2416yes—
349C4⋊Dic53C2414yes—
350C4⋊Dic53C2414yes—
351C4⋊Dic53C2414yes—
352C4⋊Dic53C24112yes—
353#11719919C24112yes—
354#11719919C2414yes—
355#11719919C2414yes—
356#11719919C2414yes—
357#11719919C2414yes—
358#11719919C2414yes—
359#11719919C2414yes—
360#11719919C24112yes—
361#11719919C24112yes—
362#11719919C24112yes—
363C4×Dic53C2411yescharacteristic
364C4×Dic53C2411yescharacteristic
365C4×Dic53C2411yescharacteristic
366C4×Dic53C2411yescharacteristic
367C4×Dic53C2414yes—
368C4×Dic53C2416yes—
369C4×Dic53C2416yes—
370C4×Dic53C2416yes—
371C4×Dic53C2416yes—
372C4×Dic53C24112yes—
373C4×Dic53C24112yes—
374C23×C53C2514yes—
375C23×C53C2511yescharacteristic
376C22×D53—26no—
377C22×D53—43no—
378C22×D53—43no—
379C22×D53C2514yes—
380C22×D53C2516yes—
381Q8×C53—212no—
382Q8×C53C2×#41116yes—
383D4×C53—28no—
384D4×C53—212no—
385C2×C4×C53—224no—
386C2×C4×C53—22no—
387C2×C4×C53—28no—
388C2×C4×C53—43no—
389C2×C4×C53—412no—
390C2×C4×C53C2×#41112yes—
391C2×C4×C53C2514yes—
392C2×C4×C53C2514yes—
393C2×C4×C53C2511yescharacteristic
394C2×C4×C53C2516yes—
395C2×C4×C53C2514yes—
396C2×C4×C53C2516yes—
397C2×C4×C53C2511yescharacteristic
398C22⋊D53—28no—
399C22⋊D53—28no—
400C22⋊D53—412no—
401C22⋊D53—412no—
402C22⋊D53—412no—
403C2×Dic53—22no—
404C2×Dic53—22no—
405C2×Dic53—43no—
406C2×Dic53C2514yes—
407C2×Dic53C2514yes—
408C2×Dic53C2516yes—
409C2×Dic53C2514yes—
410C2×Dic53C2511yescharacteristic
411C2×Dic53C2511yescharacteristic
412C2×Dic53C2511yescharacteristic
413C2×Dic53C2511yescharacteristic
414D212—224no—
415D212—212no—
416D212—412no—
417D212—412no—
418C4×D53—212no—
419C4×D53—212no—
420C4×D53—224no—
421C4×D53—212no—
422C4×D53—28no—
423C4×D53—212no—
424C4×D53—46no—
425C4×D53—46no—
426C4×D53—412no—
427Dic106—212no—
428Dic106—28no—
429Dic106—412no—
430#62793—531nomaximal, Sylow
431C22×C53—21no—
432C22×C53—21no—
433C22×C53—24no—
434C22×C53—24no—
435C22×C53—24no—
436C22×C53C22×#4112yes—
437C22×C53C2611yescharacteristic
438C2×D53—24no—
439C2×D53—26no—
440C2×D53—26no—
441C2×D53—26no—
442C2×D53—24no—
443C2×D53—24no—
444C2×D53—412no—
445C4×C53—24no—
446C4×C53—24no—
447C4×C53—24no—
448C4×C53—26no—
449C4×C53—21no—
450C4×C53C22×#41112yes—
451C4×C53#58512yes—
452Dic53—24no—
453Dic53—21no—
454Dic53—21no—
455Dic53—24no—
456Dic53—24no—
457Dic53—26no—
458Dic53—21no—
459Dic53#58512yes—
460#3524—534no—
461#3524—534no—
462#3518—534no—
463#3517—534no—
464#3506—536no—
465#3502—531no—
466#3497—531no—
467#3493—536no—
468#3487—531no—
469#3487—531no—
470#3483—534no—
471#3482—534no—
472#3480—534no—
473#3480—534no—
474#3460—536no—
475#3444—536no—
476C4×2−1+4—531no—
477C4×2−1+4D5311yescharacteristic, complemented
478C2×C4×#41—531no—
479C2×C53—22no—
480C2×C53—44no—
481C2×C53C23×#4111yescharacteristic
482C2×C53C2×#58511yescharacteristic
483C2×C53C2×#58511yescharacteristic
484D53—44no—
485D53—46no—
486C2×2−1+4—531no—
487C2×2−1+4C2×D5311yescharacteristic
488C22×#41—531no—
489#559—5312no—
490#559—5312no—
491Q82—534no—
492#557—534no—
493#557—534no—
494#557—534no—
495#556—5312no—
496#556—5312no—
497#556—5312no—
498#555—5312no—
499#555—5312no—
500#555—5312no—
501#553—5312no—
502#553—5312no—
503#553—5312no—
504#553—5312no—
505#552—5312no—
506#552—5312no—
507#550—534no—
508#550—534no—
509#550—534no—
510#550—534no—
511#550—534no—
512#550—5312no—
513D4×Q8—534no—
514#548—534no—
515#548—534no—
516#548—534no—
517#548—534no—
518#548—534no—
519#548—534no—
520#547—5312no—
521#544—536no—
522#542—5312no—
523#542—5312no—
524#540—5312no—
525#540—5312no—
526#538—5324no—
527#537—536no—
528#535—536no—
529#535—536no—
530#533—536no—
531#533—536no—
532#533—536no—
533#532—536no—
534#532—536no—
535#532—536no—
536#532—5312no—
537#532—5312no—
538#529—536no—
539#529—536no—
540#529—5312no—
541#529—534no—
542#529—5312no—
543#529—536no—
544#529—536no—
545#529—5312no—
546#529—5312no—
547#529—5312no—
548#525—536no—
549#525—5312no—
550#525—5312no—
551#525—536no—
552#520—534no—
553#520—536no—
554#520C2×D5316yes—
555#520C2×D5314yescomplemented
556#519—531no—
557#519—534no—
558#519C2×D5311yescharacteristic
559#519C2×D5314yescomplemented
560C4×#41—534no—
561C4×#41—534no—
562C4×#41—534no—
563C4×#41—534no—
564C4×#41—534no—
565C4×#41—536no—
566C4×#41—5312no—
567C4×#41—5312no—
568C4×#41C2×D5316yes—
569C4×#41C2×D5314yescomplemented
570C2×C4×Q8—531no—
571C2×C4×Q8—534no—
572C2×C4×Q8C2×D5311yescharacteristic
573C2×C4×Q8C2×D5314yescomplemented
574C2×C4×D4—533no—
575C2×C4×D4—533no—
576C2×#117—533no—
577C22×C42—533no—
578C53#6279311yescharacteristic, complemented, Sylow
5792−1+4—28no—
5802−1+4—1068no—
581C2×#41—534no—
582C2×#41—534no—
583C2×#41—534no—
584C2×#41—536no—
585C2×#41—5312no—
586C2×#41—5312no—
587C2×#41—1068no—
588C2×#41C22×D5316yes—
589C2×#41C22×D5314yes—
590C22×Q8—534no—
591C22×Q8C22×D5314yes—
592C22×Q8C22×D5311yescharacteristic
593C22×D4—533no—
594C23×C4—533no—
595C23×C4—533no—
596C23×C4—533no—
597C4⋊Q8—536no—
598C4⋊Q8—536no—
599C4⋊Q8—536no—
600C4⋊Q8—5312no—
601C4⋊Q8—5312no—
602#127—536no—
603#127—5312no—
604#127—5312no—
605#126—534no—
606#126—5312no—
607#126—5324no—
608#126—534no—
609#126—5312no—
610#126—5324no—
611#125—534no—
612#125—5312no—
613#125—536no—
614#125—536no—
615#125—5312no—
616#125—5312no—
617#124—536no—
618#124—5312no—
619#124—536no—
620#124—534no—
621#124—5312no—
622#124—5324no—
623#124—5312no—
624#124—5324no—
625#123—534no—
626#123—5324no—
627#123—5312no—
628#123—5312no—
629#123—5324no—
630#123—534no—
631#123—5312no—
632#123—5312no—
633C22⋊Q8—536no—
634C22⋊Q8—536no—
635C22⋊Q8—5312no—
636C22⋊Q8—5312no—
637C22⋊Q8—5312no—
638C22⋊Q8—5312no—
639C22⋊Q8—536no—
640C22⋊Q8—536no—
641C22⋊Q8—534no—
642C22⋊Q8—5312no—
643#121—534no—
644#121—5312no—
645#121—536no—
646#121—536no—
647#121—5312no—
648#121—5312no—
649#121—5312no—
650#121—5312no—
651#121—5324no—
652#121—536no—
653#121—536no—
654#121—5312no—
655#121—5312no—
656#121—5312no—
657#121—5312no—
658#121—5324no—
659#120—5312no—
660#120—5312no—
661C4×Q8—534no—
662C4×Q8—534no—
663C4×Q8—534no—
664C4×Q8—534no—
665C4×Q8—5312no—
666C4×Q8—536no—
667C4×Q8—534no—
668C4×Q8—536no—
669C4×Q8—5312no—
670C4×Q8—5312no—
671C4×Q8—5312no—
672C4×Q8C22×D5314yes—
673C4×Q8C22×D5314yes—
674C4×Q8C22×D5316yes—
675C4×Q8C22×D5314yes—
676C4×Q8C22×D53112yes—
677C4×Q8C22×D5316yes—
678C4×Q8C22×D5314yes—
679C4×D4—534no—
680C4×D4—534no—
681C4×D4—5312no—
682C4×D4—5312no—
683C4×D4—5312no—
684C4×D4—5312no—
685C4×D4—5312no—
686C4×D4—5312no—
687C4×D4—5312no—
688C4×D4—5312no—
689C4×D4—5312no—
690C4×D4—5312no—
691C4×D4—5312no—
692C4×D4—5312no—
693C4×D4—5312no—
694C4×D4—536no—
695C4×D4—536no—
696C4×D4—5312no—
697C4×D4—5312no—
698C4×D4—5312no—
699C4×D4—5312no—
700C4×D4C22×D5314yes—
701C4×D4C22×D5316yes—
702C4×D4C22×D53112yes—
703C4×D4C22×D5316yes—
704C4×D4C22×D53112yes—
705#117—534no—
706#117—536no—
707#117—5312no—
708#117—5312no—
709#117—5312no—
710#117—5312no—
711#117—534no—
712#117—5312no—
713#117—5312no—
714#117—5312no—
715#117—5312no—
716#117C22×D5316yes—
717#117C22×D53112yes—
718#117C22×D53112yes—
719C2×C4⋊C4—533no—
720C2×C4⋊C4—5312no—
721C2×C4⋊C4C22×D5313yes—
722C2×C4⋊C4C22×D53112yes—
723C2×C22⋊C4—536no—
724C2×C42—533no—
725C2×C42—533no—
726C2×C42—531no—
727C2×C42—5312no—
728C2×C42—536no—
729C2×C42—536no—
730C2×C42—536no—
731C2×C42—536no—
732C2×C42C22×D5313yes—
733C2×C42C22×D53112yes—
734C24—533no—
735#41—216no—
736#41—224no—
737#41—10616no—
738#41—10616no—
739#41—10616no—
740#41—10624no—
741#41—21224no—
742#41—21224no—
743C2×Q8—216no—
744C2×Q8—536no—
745C2×Q8—534no—
746C2×Q8—5312no—
747C2×Q8—10616no—
748C2×Q8#1171994518yescomplemented
749C2×Q8C23×D5316yes—
750C2×Q8C23×D5314yes—
751C2×D4—534no—
752C2×D4—534no—
753C2×D4—5312no—
754C2×D4—5312no—
755C2×D4—5312no—
756C2×D4—5312no—
757C2×D4—536no—
758C2×D4—5312no—
759C2×D4—5312no—
760C2×D4—10612no—
761C2×D4C23×D5314yes—
762C2×D4C23×D5316yes—
763C22×C4—531no—
764C22×C4—531no—
765C22×C4—533no—
766C22×C4—536no—
767C22×C4—536no—
768C22×C4—536no—
769C22×C4—5312no—
770C22×C4—534no—
771C22×C4—536no—
772C22×C4—536no—
773C22×C4—536no—
774C22×C4—5312no—
775C22×C4—10612no—
776C22×C4—2126no—
777C22×C4—2126no—
778C22×C4C23×D53112yes—
779C22×C4C23×D5311yescharacteristic
780C22×C4C23×D5314yes—
781C22×C4C23×D5313yes—
782C22×C4C23×D53112yes—
783C22×C4C23×D5313yes—
784C4⋊C4—536no—
785C4⋊C4—5312no—
786C4⋊C4—5312no—
787C4⋊C4—534no—
788C4⋊C4—534no—
789C4⋊C4—534no—
790C4⋊C4—534no—
791C4⋊C4—536no—
792C4⋊C4—534no—
793C4⋊C4—534no—
794C4⋊C4—534no—
795C4⋊C4—534no—
796C4⋊C4—534no—
797C4⋊C4—5312no—
798C4⋊C4—5312no—
799C4⋊C4—5312no—
800C4⋊C4—5312no—
801C4⋊C4C23×D53112yes—
802C4⋊C4C23×D5316yes—
803C4⋊C4C23×D53112yes—
804C4⋊C4C23×D5316yes—
805C4⋊C4C23×D5314yes—
806C22⋊C4—534no—
807C22⋊C4—534no—
808C22⋊C4—534no—
809C22⋊C4—534no—
810C22⋊C4—5312no—
811C22⋊C4—5324no—
812C22⋊C4—534no—
813C22⋊C4—534no—
814C22⋊C4—5312no—
815C22⋊C4—534no—
816C22⋊C4—534no—
817C22⋊C4—5312no—
818C22⋊C4—5312no—
819C22⋊C4—5312no—
820C22⋊C4—5312no—
821C22⋊C4—5312no—
822C22⋊C4C23×D5314yes—
823C22⋊C4C23×D5314yes—
824C22⋊C4C23×D53112yes—
825C42—531no—
826C42—531no—
827C42—536no—
828C42—536no—
829C42—536no—
830C42—536no—
831C42—5312no—
832C42—5312no—
833C42—531no—
834C42—531no—
835C42—534no—
836C42C23×D5316yes—
837C42C23×D53112yes—
838C42C23×D53112yes—
839C42C23×D5316yes—
840C42C23×D5314yes—
841C23—536no—
842C23—534no—
843C23—1066no—
844C23—2123no—
845C23—2123no—
846C23C24×D5314yes—
847C23C24×D5311yescharacteristic
848Q8—212no—
849Q8—1068no—
850Q8—10612no—
851Q8—21212no—
852Q8C2×#11719945116yes—
853D4—28no—
854D4—212no—
855D4—1068no—
856D4—1068no—
857D4—10624no—
858D4—10612no—
859D4—21212no—
860D4—21212no—
861D4—21212no—
862D4—21212no—
863D4—21212no—
864C2×C4—224no—
865C2×C4—22no—
866C2×C4—28no—
867C2×C4—43no—
868C2×C4—412no—
869C2×C4—531no—
870C2×C4—531no—
871C2×C4—531no—
872C2×C4—531no—
873C2×C4—534no—
874C2×C4—534no—
875C2×C4—536no—
876C2×C4—534no—
877C2×C4—10612no—
878C2×C4—1062no—
879C2×C4—1062no—
880C2×C4—10612no—
881C2×C4—10612no—
882C2×C4—10624no—
883C2×C4—10612no—
884C2×C4—1068no—
885C2×C4—2126no—
886C2×C4—2126no—
887C2×C4—21212no—
888C2×C4—2123no—
889C2×C4C2×#11719945112yes—
890C2×C4C24×D5316yes—
891C2×C4C24×D5311yescharacteristic
892C2×C4C24×D5314yes—
893C2×C4C24×D5314yes—
894C2×C4C24×D5314yes—
895C2×C4C24×D5316yes—
896C2×C4C24×D5311yescharacteristic
897C22—21no—
898C22—21no—
899C22—24no—
900C22—24no—
901C22—24no—
902C22—1064no—
903C22—1066no—
904C22—1066no—
905C22—1064no—
906C22—1066no—
907C22—1064no—
908C22—21212no—
909C22C22×#1171994512yes—
910C22C25×D5311yescharacteristic
911C4—24no—
912C4—26no—
913C4—24no—
914C4—21no—
915C4—24no—
916C4—532no—
917C4—1061no—
918C4—1061no—
919C4—1064no—
920C4—1061no—
921C4—1064no—
922C4—1066no—
923C4—1064no—
924C4C22×#11719945112yes—
925C4#1681146012yes—
926C2—22no—
927C2—44no—
928C2—2126no—
929C2—2124no—
930C2C23×#1171994511yescharacteristic
931C2#585×D5311yescharacteristic
932C2C2×#1681146011yescharacteristic
subgroupG/H
centerC2×C4C24×D53
commutator, socle, cosocleC22×C53C26
FrattiniC22C25×D53
FittingC4×2−1+4×C53C2
hypercenterC4×2−1+4D53
hypocenterC53#62793
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C4×2−1+4

Complements

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

NH ≅ G/Ntype
1. #20288826C2semidirect
2. #20288816C2semidirect
3. #20288726C2semidirect
4. #20288715C2semidirect
5. #20288560C2semidirect
6. #20288521C2semidirect
7. #20288482C2semidirect
8. #20288428C2semidirect
9. #20288374C2semidirect
10. #20288370C2semidirect
11. #20288341C2semidirect
12. #20288332C2semidirect
13. #20288313C2semidirect
14. #20288310C2semidirect
15. #20288131C2semidirect
16. #20288008C2semidirect
17. C4×#13133265C2semidirect
18. C2×C4×#11719949C2semidirect
19. C4×2−1+4×C53C2semidirect
22. #16811358C22semidirect
23. #16811356C22semidirect
24. Q8×Dic106C22semidirect
25. #16811352C22semidirect
26. #16811349C22semidirect
27. #16811349C22semidirect
28. #16811346C22semidirect
29. #16811345C22semidirect
30. #16811341C22semidirect
31. #16811338C22semidirect
32. #16811336C22semidirect
33. #16811336C22semidirect
34. #16811323C22semidirect
35. #16811321C22semidirect
36. #16811321C22semidirect
37. #16811317C22semidirect
38. #16811314C22semidirect
39. #16811308C22semidirect
42. #16811294C22semidirect
45. #16811292C22semidirect
46. Q8×C22⋊D53C22semidirect
51. #16811284C22semidirect
52. #16811280C22semidirect
53. #16811274C22semidirect
55. #16811245C22semidirect
56. #16811244C22semidirect
57. #16811228C22semidirect
58. #16811224C22semidirect
63. #16811177C22semidirect
64. #16811177C22semidirect
66. #16811173C22semidirect
67. #16811170C22semidirect
68. #16811170C22semidirect
69. #16811170C22semidirect
71. #16811160C22semidirect
72. #16811160C22semidirect
73. #16811160C22semidirect
74. #16811157C22semidirect
75. #16811155C22semidirect
76. #16811155C22semidirect
79. #16811151C22semidirect
80. #16811151C22semidirect
85. #16811105C22semidirect
88. #16811099C22semidirect
93. C4×#11719949C22semidirect
95. C4×#11719945C22semidirect
96. C4×#11719945C22semidirect
98. C4×Q8×D53C22semidirect
105. C53×#520C22semidirect
107. C53×#519C22semidirect
109. C4×#41×C53C22semidirect
111. C2×C4×Q8×C53C22semidirect
271. C2×Q8×C53#41semidirect
477. C4×2−1+4D53semidirect
555. #520C2×D53semidirect
559. #519C2×D53semidirect
569. C4×#41C2×D53semidirect
573. C2×C4×Q8C2×D53semidirect
578. C53#62793semidirect
748. C2×Q8#11719945semidirect

Maximal subgroups

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

subgroupindex
#202888262
#202888162
#202887262
#202887152
#202885602
#202885212
#202884822
#202884282
#202883742
#202883702
#202883412
#202883322
#202883132
#202883102
#202881312
#202880082
C4×#131332652
C2×C4×#117199492
C4×2−1+4×C532
#6279353