Finite Group Databasebeta

← #28253652

Subgroups — #28253652

Order 13568.

3178 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811437C211yesmaximal, characteristic, complemented
2C2×#16811433C212yesmaximal, complemented
3C2×#16811424C211yesmaximal, characteristic, complemented
4#20288507C212yesmaximal, complemented
5#20285209C211yesmaximal, characteristic, complemented
6#20285205C212yesmaximal, complemented
7#20285195C212yesmaximal, complemented
8#20285188C214yesmaximal, complemented
9#20285187C212yesmaximal, complemented
10#20285180C214yesmaximal, complemented
11#20285177C212yesmaximal, complemented
12#20285142C212yesmaximal, complemented
13#20285139C211yesmaximal, characteristic, complemented
14C2×#16811006C211yesmaximal, characteristic, complemented
15#495×D53C212yesmaximal, complemented
16#20283137C211yesmaximal, characteristic, complemented
17C53×#3155C211yesmaximal, characteristic, complemented
18C2×#13133264C2212yes—
19C2×#13133262C2212yes—
20#16811437—28no—
21#16811433—216no—
22#16811424—28no—
23C2×#13133250C2212yescomplemented
24C2×#13133247C2212yescomplemented
25C2×#13133246C2214yescomplemented
26C2×#13133246C2214yescomplemented
27C2×#13133243C2212yes—
28C2×#13133241C2214yes—
29C2×#13133241C2214yescomplemented
30C2×#13133239C2211yescharacteristic
31C2×#13133237C2212yescomplemented
32C2×#13133236C2212yes—
33C2×#13133236C2214yescomplemented
34C2×#13133236C2212yescomplemented
35C22×Dic212C2211yescharacteristic, complemented
36C2×Q16×D53C2212yescomplemented
37C22×#11719923C2212yescomplemented
38C2×SD16×D53C2214yescomplemented
39C2×D8×D53C2212yes—
40C2×#13133225C2211yescharacteristic
41C2×#13133223C2211yescharacteristic
42#16811279—24no—
43#16811270—24no—
44#16811260—28no—
45#16811199C2212yescomplemented
46#16811193C2214yescomplemented
47#16811186C2214yescomplemented
48#16811171C2214yescomplemented
49#16811169C2212yescomplemented
50C2×#13133204C2212yescomplemented
51#124×D53C2214yescomplemented
52#16811091C2211yescharacteristic
53#16811018C2214yescomplemented
54#16811017C2214yescomplemented
55#16811014C2214yescomplemented
56#16811011C2214yescomplemented
57#16811010C2214yescomplemented
58#16811008C2211yescharacteristic, complemented
59#16811007C2212yescomplemented
60#16811006C2212yescomplemented
61#16811006C2212yescomplemented
62#16811006C2212yescomplemented
63#16811006C2212yescomplemented
64#16811006C2211yescharacteristic, complemented
65#16811006C2214yescomplemented
66#16811005C2214yescomplemented
67#16811004C2214yescomplemented
68#16811004C2212yescomplemented
69#16811003C2212yescomplemented
70#16811001C2211yescharacteristic, complemented
71#16810998C2211yescharacteristic, complemented
72#16810995C2214yescomplemented
73#16810994C2212yescomplemented
74#16810580C2212yescomplemented
75#16810579C2211yescharacteristic, complemented
76#16810577C2212yescomplemented
77#16810575C2212yescomplemented
78M16×Dic53C2211yescharacteristic, complemented
79C2×C8×Dic53C2211yescharacteristic, complemented
80C4×C8×D53C2212yescomplemented
81C2×AGL(1,ℤ/8)×C53C2212yescomplemented
82C2×#135×C53C2211yescharacteristic, complemented
83C22×D8×C53C2211yescharacteristic
84C53×#535C2212yescomplemented
85C53×#496C2214yescomplemented
86C53×#495C2212yescomplemented
87C53×#493C2212yescomplemented
88C53×#405C2211yescharacteristic, complemented
89#13133264—28no—
90#13133264—28no—
91#13133262—28no—
92#13133262—28no—
93C2×#11719945—22no—
94C2×#11719945C2311yescharacteristic
95C2×#11719945C2312yes—
96C2×#11719947—24no—
97C2×#11719947—22no—
98C2×#11719947C2314yes—
99C2×#11719947C2314yes—
100C22×Dic106—22no—
101C22×Dic106C2312yes—
102C2×Q8×D53C2314yes—
103C22×C22⋊D53—24no—
104C2×D4×D53—22no—
105C2×D4×D53C2314yes—
106#13133250—28no—
107#13133247—28no—
108#13133246—216no—
109#13133246—216no—
110#13133243—28no—
111#13133241—216no—
112#13133241—216no—
113#13133239—24no—
114#13133237—28no—
115#13133236—28no—
116#13133236—216no—
117#13133236—28no—
118C2×Dic212—24no—
119C2×Dic212C2314yes—
120C2×Dic212C2312yes—
121C2×Dic212C2312yes—
122C2×Dic212C2311yescharacteristic
123C2×#11719925C2314yes—
124C2×#11719925C2312yes—
125Q16×D53—28no—
126C2×#11719913C2314yes—
127C2×#11719913C2312yes—
128C2×#11719923—28no—
129C2×#11719923C2314yes—
130C2×#11719923C2314yes—
131C2×#11719923C2314yes—
132C2×#11719923C2314yes—
133C2×#11719923C2312yes—
134C2×#11719924C2312yes—
135SD16×D53—216no—
136C2×D424C2311yescharacteristic
137C2×#11719922C2312yes—
138C2×#11719922C2314yes—
139D8×D53—28no—
140#13133225D418yescomplemented
141#13133223D418yescomplemented
142C2×#11719917C2311yescharacteristic
143C2×#11719912C2312yes—
144C2×#11719912C2312yes—
145C22×#88322C2311yescharacteristic
146C2×C8×D53C2312yes—
147C2×C8×D53C2312yes—
148#13133217C2314yes—
149#13133215C2312yes—
150#13133213C2312yes—
151#13133206C2312yes—
152#13133205C2314yes—
153#13133204—24no—
154#13133204C2314yes—
155#13133204C2314yes—
156#13133204C2312yes—
157#13133203—28no—
158#13133201—24no—
159#13133199—28no—
160#13133197—24no—
161#13133194—28no—
162#13133189—28no—
163#13133189—24no—
164#13133188—28no—
165#13133185—28no—
166#13133182D412yes—
167D4×Dic53—28no—
168#13133179D412yes—
169C4×C22⋊D53—24no—
170#13133177D414yes—
171#13133174C2312yes—
172C2×C22⋊Dic53—24no—
173C22⋊C4×D53—28no—
174C2×C4×Dic53C2311yescharacteristic
175C42×D53C2312yes—
176#13133128C2312yes—
177#13133127C2312yes—
178C4×#88322C2312yes—
179C8×Dic53C2311yescharacteristic
180C8×Dic53C2312yes—
181C8×Dic53C2311yescharacteristic
182C8×Dic53C2311yescharacteristic
183C8×Dic53C2311yescharacteristic
184C2×#41×C53C2312yes—
185C22×D4×C53C2312yes—
186AGL(1,ℤ/8)×C53—28no—
187#135×C53—24no—
188C2×Q16×C53C2311yescharacteristic
189C2×SD16×C53C2314yes—
190C2×SD16×C53C2312yes—
191C2×D8×C53—24no—
192C2×D8×C53C2314yes—
193C2×D8×C53C2311yescharacteristic
194C2×D8×C53C2312yes—
195C2×D8×C53C2312yes—
196C2×M16×C53C2311yescharacteristic
197C22×C8×C53C2311yescharacteristic
198#127×C53C2314yes—
199#124×C53C2314yes—
200#121×C53—24no—
201#120×C53—24no—
202#117×C53C2311yescharacteristic
203#97×C53C2312yes—
204C4×C8×C53C2312yes—
205C24×C53—22no—
206C23×D53—24no—
207#41×C53—24no—
208#41×C53—24no—
209C2×Q8×C53C2412yes—
210C2×D4×C53—22no—
211C2×D4×C53—24no—
212C2×D4×C53—24no—
213C2×D4×C53—22no—
214C2×D4×C53—28no—
215C2×D4×C53C2414yes—
216C2×D4×C53C2412yes—
217C22×C4×C53—22no—
218C22×C4×C53C2411yescharacteristic
219C2×C22⋊D53—22no—
220C2×C22⋊D53—24no—
221C2×C22⋊D53—24no—
222C2×C22⋊D53—24no—
223C2×C22⋊D53—24no—
224C2×C22⋊D53—416no—
225C2×C22⋊D53C2×D412yes—
226C22×Dic53—22no—
227C22×Dic53—24no—
228C22×Dic53—24no—
229C22×Dic53C2×D412yes—
230Q8×D53—28no—
231Q8×D53—28no—
232#11719947—28no—
233#11719947—28no—
234#11719947—28no—
235#11719947—28no—
236#11719947—416no—
237#11719947—48no—
238D4×D53—28no—
239D4×D53—28no—
240D4×D53—48no—
241#11719945—24no—
242#11719945—24no—
243#11719945—48no—
244#11719945C2×D414yes—
245#11719945C2×D414yes—
246C2×D212C2×D411yescharacteristic
247C2×D212C2412yes—
248C2×C4×D53—24no—
249C2×C4×D53—22no—
250C2×C4×D53C2×D414yes—
251C2×C4×D53C2412yes—
252C2×Dic106—24no—
253C2×Dic106—24no—
254C2×Dic106—22no—
255C2×Dic106—24no—
256C2×Dic106—48no—
257C2×Dic106C2×D411yescharacteristic
258C2×Dic106C2414yes—
259C2×Dic106C2412yes—
260Q16×C53—22no—
261SD16×C53—24no—
262SD16×C53—28no—
263D8×C53—24no—
264D8×C53—24no—
265D8×C53—22no—
266D8×C53—28no—
267M16×C53C2×D414yes—
268C2×C8×C53C2×D414yes—
269C2×C8×C53C2411yescharacteristic
270C2×C8×C53C2412yes—
271C2×C8×C53C2411yescharacteristic
272C4⋊C4×C53C2×D412yes—
273C22⋊C4×C53—28no—
274C22⋊C4×C53C2×D412yes—
275C42×C53C2412yes—
276C22⋊Dic53—28no—
277C22⋊Dic53—28no—
278C22⋊Dic53—24no—
279#11719925—28no—
280#11719925—24no—
281#11719924—24no—
282#11719923—28no—
283#11719923—28no—
284#11719923—24no—
285#11719923—28no—
286#11719923—28no—
287#11719922—28no—
288#11719922—24no—
289#11719921—28no—
290#11719921—24no—
291#11719921C2×D414yes—
292C4⋊Dic53—28no—
293#11719919—24no—
294#11719919C2×D414yes—
295C4×Dic53C2×D414yes—
296C4×Dic53C2×D412yes—
297C4×Dic53C2411yescharacteristic
298C4×Dic53C2411yescharacteristic
299#11719917C2×D414yes—
300C2×#88322C2×D414yes—
301C2×#88322C2411yescharacteristic
302C2×#88322C2411yescharacteristic
303C2×#88322C2412yes—
304Dic212—24no—
305Dic212—24no—
306Dic212—22no—
307Dic212—28no—
308D424—22no—
309#11719913—28no—
310#11719913—24no—
311#11719912C2×D418yes—
312#11719912C2×D418yes—
313C8×D53C2×D418yes—
314C8×D53C2×D418yes—
315C23×C53—22no—
316C23×C53—24no—
317C23×C53—44no—
318C23×C53—84no—
319C23×C53C22×D411yescharacteristic
320C22×D53—22no—
321C22×D53—48no—
322C22×D53—88no—
323C22×D53C22×D412yes—
324Q8×C53—22no—
325Q8×C53—22no—
326D4×C53—24no—
327D4×C53—24no—
328D4×C53—22no—
329D4×C53—22no—
330D4×C53—44no—
331D4×C53—44no—
332D4×C53—88no—
333C2×C4×C53—22no—
334C2×C4×C53—44no—
335C2×C4×C53C22×D414yes—
336C2×C4×C53C22×D411yescharacteristic
337C2×C4×C53C22×D412yes—
338C2×C4×C53C22×D412yes—
339C2×C4×C53C2511yescharacteristic
340C22⋊D53—44no—
341C22⋊D53—48no—
342C22⋊D53—48no—
343C22⋊D53—48no—
344C22⋊D53—84no—
345C22⋊D53#12718yes—
346C2×Dic53—24no—
347C2×Dic53—22no—
348C2×Dic53—42no—
349C2×Dic53—44no—
350C2×Dic53—48no—
351C2×Dic53—48no—
352C2×Dic53C22×D412yes—
353C2×Dic53C22×D412yes—
354C2×Dic53C22×D412yes—
355D212—22no—
356D212—22no—
357D212#12714yes—
358C4×D53—44no—
359C4×D53—48no—
360C4×D53—44no—
361C4×D53C22×D414yes—
362C4×D53C22×D414yes—
363Dic106—24no—
364Dic106—24no—
365Dic106—22no—
366Dic106—22no—
367Dic106—44no—
368Dic106—48no—
369Dic106#12714yes—
370C8×C53C22×D412yes—
371C8×C53C22×D414yes—
372C8×C53C22×D412yes—
373#88322C22×D412yes—
374#88322C22×D414yes—
375#88322C22×D412yes—
376#60649—531nomaximal, Sylow
377C22×C53—22no—
378C22×C53—44no—
379C22×C53—48no—
380C22×C53—42no—
381C22×C53—44no—
382C22×C53—164no—
383C22×C53C2×#12712yes—
384C22×C53C23×D411yescharacteristic
385C2×D53—24no—
386C2×D53—44no—
387C2×D53—42no—
388C2×D53—168no—
389C2×D53C2×#12714yes—
390C4×C53—24no—
391C4×C53—42no—
392C4×C53C2×#12712yes—
393C4×C53C23×D411yescharacteristic
394C4×C53C23×D411yescharacteristic
395Dic53—22no—
396Dic53—22no—
397Dic53—44no—
398Dic53—42no—
399Dic53C2×#12714yes—
400C2×#578—531no—
401C2×#577—532no—
402C2×#576—531no—
403#3500—532no—
404#3156—532no—
405#3156—531no—
406#3155—532no—
407#3155D5311yescharacteristic, complemented
408#3154—534no—
409#3154—532no—
410#3153—534no—
411#3153—532no—
412#3147—532no—
413#3147—531no—
414C2×#495—532no—
415C2×#495—531no—
416C4×#131—531no—
417C2×C53—22no—
418C2×C53—84no—
419C2×C53—82no—
420C2×C53C22×#12711yescharacteristic
421C2×C53#358412yes—
422D53—24no—
423D53—82no—
424C2×2−1+4—532no—
425C2×H(5,𝔽2)—532no—
426#578—1068no—
427#577—10616no—
428#576—1068no—
429C2×#137—532no—
430C2×#137—534no—
431C2×#137—534no—
432C2×#137—532no—
433C2×AGL(1,ℤ/8)—532no—
434C2×AGL(1,ℤ/8)—534no—
435C2×AGL(1,ℤ/8)—534no—
436C2×AGL(1,ℤ/8)C2×D5312yescomplemented
437C2×#135—532no—
438C2×#135—534no—
439C2×#135—532no—
440C2×#135—532no—
441C2×#135—531no—
442C2×#135C2×D5311yescharacteristic, complemented
443C22×Q16—532no—
444C22×Q16—531no—
445C22×SD16—532no—
446C22×SD16—534no—
447C22×D8—532no—
448C22×D8C2×D5311yescharacteristic
449C2×#131—531no—
450C2×#131—531no—
451#548—1064no—
452#546—1068no—
453#546—1064no—
454#536—534no—
455#536—532no—
456#535—534no—
457#535C2×D5312yescomplemented
458#532—532no—
459#532—534no—
460C2×#124—532no—
461C2×#124—534no—
462C4×#41—531no—
463#497—534no—
464#497—534no—
465#497—534no—
466#496—534no—
467#496—534no—
468#496C2×D5314yescomplemented
469#495—531no—
470#495—534no—
471#495—532no—
472#495—532no—
473#495—532no—
474#495—532no—
475#495—532no—
476#495—531no—
477#495—534no—
478#495—534no—
479#495—532no—
480#495C2×D5312yescomplemented
481#494—531no—
482#494—532no—
483#493—531no—
484#493C2×D5312yescomplemented
485#492—532no—
486#492—534no—
487#405—531no—
488#405—532no—
489#405—532no—
490#405C2×D5311yescharacteristic, complemented
491C4×M16—531no—
492C4×M16—532no—
493C2×C4×C8—531no—
494C2×C4×C8—532no—
495C53#6064911yescharacteristic, complemented, Sylow
4962−1+4—1068no—
4972−1+4—1068no—
498H(5,𝔽2)—1068no—
499H(5,𝔽2)—1068no—
500C2×#41—531no—
501C2×#41—534no—
502C2×#41—534no—
503C2×#41—532no—
504C2×#41—1062no—
505C2×#41—1064no—
506C2×#41—1062no—
507C2×#41C22×D5312yes—
508C22×Q8—534no—
509C22×Q8—532no—
510C22×Q8—1062no—
511C22×D4—534no—
512C22×D4—1062no—
513C22×D4—1064no—
514C22×D4C22×D5312yes—
515#137—10616no—
516#137—10616no—
517#137—1068no—
518#137—1068no—
519AGL(1,ℤ/8)—28no—
520AGL(1,ℤ/8)—10616no—
521AGL(1,ℤ/8)—10616no—
522AGL(1,ℤ/8)—1068no—
523#135—24no—
524#135—1068no—
525#135—10616no—
526#135—1068no—
527#135—1068no—
528#135—1064no—
529C2×Q16—534no—
530C2×Q16—532no—
531C2×Q16—532no—
532C2×Q16—532no—
533C2×Q16—531no—
534C2×Q16—534no—
535C2×Q16—1068no—
536C2×Q16—1064no—
537C2×Q16C22×D5311yescharacteristic
538C2×SD16—532no—
539C2×SD16—534no—
540C2×SD16—534no—
541C2×SD16—532no—
542C2×SD16—534no—
543C2×SD16—534no—
544C2×SD16—534no—
545C2×SD16—532no—
546C2×SD16—10616no—
547C2×SD16—1068no—
548C2×SD16C22×D5314yes—
549C2×SD16C22×D5312yes—
550C2×D8—24no—
551C2×D8—534no—
552C2×D8—532no—
553C2×D8—531no—
554C2×D8—1068no—
555C2×D8C22×D5312yes—
556C2×D8C22×D5312yes—
557C2×D8C22×D5311yescharacteristic
558C2×D8C22×D5314yes—
559#131—538no—
560#131—538no—
561C2×M16—531no—
562C2×M16—532no—
563C2×M16—532no—
564C2×M16C22×D5311yescharacteristic
565C22×C8—531no—
566C22×C8—532no—
567C22×C8—532no—
568C22×C8C22×D5311yescharacteristic
569C4⋊Q8—532no—
570C4⋊Q8—534no—
571#127—532no—
572#127C22×D5314yes—
573#124—532no—
574#124—534no—
575#124—534no—
576#124—532no—
577#124—534no—
578#124—1068no—
579#124—1064no—
580#124C22×D5314yes—
581#123—1068no—
582#123—1064no—
583C22⋊Q8—1068no—
584C22⋊Q8—1064no—
585#121—24no—
586#121—1068no—
587#121—1068no—
588#121—1064no—
589#120—24no—
590#120—1068no—
591C4×Q8—532no—
592C4×D4—532no—
593C4×D4—534no—
594C4×D4—1064no—
595C4×D4—1068no—
596#117—532no—
597#117C22×D5311yescharacteristic
598C2×C22⋊C4—1068no—
599C2×C22⋊C4—1064no—
600C2×C42—531no—
601C2×C42—532no—
602#97—532no—
603#97—532no—
604#97C22×D5312yes—
605C4×C8—531no—
606C4×C8—531no—
607C4×C8—532no—
608C4×C8—531no—
609C4×C8—531no—
610C4×C8—532no—
611C4×C8C22×D5312yes—
612C24—22no—
613C24—1064no—
614#41—24no—
615#41—24no—
616#41—534no—
617#41—534no—
618#41—1068no—
619#41—1068no—
620#41—1068no—
621#41—1068no—
622#41—1064no—
623#41—1064no—
624#41—2128no—
625#41—21216no—
626#41—2128no—
627C2×Q8—531no—
628C2×Q8—534no—
629C2×Q8—532no—
630C2×Q8—1064no—
631C2×Q8—1068no—
632C2×Q8—1068no—
633C2×Q8—1062no—
634C2×Q8—1064no—
635C2×Q8—1064no—
636C2×Q8—2128no—
637C2×Q8C23×D5312yes—
638C2×D4—22no—
639C2×D4—24no—
640C2×D4—24no—
641C2×D4—22no—
642C2×D4—28no—
643C2×D4—532no—
644C2×D4—531no—
645C2×D4—532no—
646C2×D4—1068no—
647C2×D4—1068no—
648C2×D4—1064no—
649C2×D4—1064no—
650C2×D4—1064no—
651C2×D4—1064no—
652C2×D4—1062no—
653C2×D4—2128no—
654C2×D4—21216no—
655C2×D4C23×D5314yes—
656C2×D4C23×D5312yes—
657C22×C4—22no—
658C22×C4—532no—
659C22×C4—532no—
660C22×C4—534no—
661C22×C4—1064no—
662C22×C4—1064no—
663C22×C4—1064no—
664C22×C4—1062no—
665C22×C4—1062no—
666C22×C4C23×D5311yescharacteristic
667Q16—22no—
668Q16—1068no—
669Q16—1064no—
670Q16—1064no—
671Q16—1064no—
672Q16—1062no—
673Q16—1068no—
674SD16—28no—
675SD16—24no—
676SD16—1068no—
677SD16—1068no—
678SD16—1064no—
679SD16—1068no—
680SD16—1068no—
681SD16—1064no—
682SD16—1068no—
683SD16—1064no—
684D8—24no—
685D8—24no—
686D8—22no—
687D8—28no—
688D8—1068no—
689D8—1064no—
690D8—1062no—
691M16—534no—
692M16—538no—
693M16—538no—
694M16D4×D5314yes—
695C2×C8—534no—
696C2×C8—531no—
697C2×C8—531no—
698C2×C8—532no—
699C2×C8—538no—
700C2×C8—538no—
701C2×C8D4×D5314yes—
702C2×C8C23×D5311yescharacteristic
703C2×C8C23×D5311yescharacteristic
704C2×C8C23×D5312yes—
705C4⋊C4—534no—
706C4⋊C4—1064no—
707C4⋊C4—1068no—
708C4⋊C4D4×D5312yes—
709C22⋊C4—28no—
710C22⋊C4—534no—
711C22⋊C4—1064no—
712C22⋊C4—1068no—
713C22⋊C4—1068no—
714C22⋊C4—1064no—
715C22⋊C4—1068no—
716C22⋊C4D4×D5312yes—
717C42—534no—
718C42—532no—
719C42—531no—
720C42—531no—
721C42C23×D5312yes—
722C23—24no—
723C23—22no—
724C23—44no—
725C23—84no—
726C23—532no—
727C23—1062no—
728C23—4248no—
729C23—2128no—
730C23C2×D4×D5311yescharacteristic
731Q8—22no—
732Q8—22no—
733Q8—534no—
734Q8—1064no—
735Q8—1062no—
736Q8—1064no—
737Q8—1062no—
738Q8—2128no—
739Q8—2124no—
740D4—24no—
741D4—22no—
742D4—24no—
743D4—22no—
744D4—44no—
745D4—44no—
746D4—88no—
747D4—538no—
748D4—534no—
749D4—1062no—
750D4—1062no—
751D4—4244no—
752D4—2128no—
753D4—2128no—
754D4—2128no—
755D4—2124no—
756C2×C4—22no—
757C2×C4—44no—
758C2×C4—532no—
759C2×C4—534no—
760C2×C4—534no—
761C2×C4—532no—
762C2×C4—532no—
763C2×C4—1064no—
764C2×C4—1062no—
765C2×C4—2124no—
766C2×C4—2128no—
767C2×C4—2128no—
768C2×C4—2128no—
769C2×C4—2122no—
770C2×C4—2124no—
771C2×C4—2124no—
772C2×C4C2×D4×D5314yes—
773C2×C4C2×D4×D5311yescharacteristic
774C2×C4C2×D4×D5312yes—
775C2×C4C2×D4×D5312yes—
776C2×C4C24×D5311yescharacteristic
777C8—532no—
778C8—534no—
779C8—532no—
780C8C2×D4×D5312yes—
781C8C2×D4×D5314yes—
782C8C2×D4×D5312yes—
783C22—22no—
784C22—44no—
785C22—48no—
786C22—42no—
787C22—44no—
788C22—164no—
789C22—534no—
790C22—8488no—
791C22—1064no—
792C22—2124no—
793C22—2122no—
794C22#127×D5312yes—
795C22C22×D4×D5311yescharacteristic
796C4—24no—
797C4—42no—
798C4—534no—
799C4—1062no—
800C4—1062no—
801C4—2122no—
802C4—2124no—
803C4#127×D5312yes—
804C4C22×D4×D5311yescharacteristic
805C4C22×D4×D5311yescharacteristic
806C2—22no—
807C2—84no—
808C2—82no—
809C2—1064no—
810C2—4242no—
811C2C2×#127×D5311yescharacteristic
812C2#2028948312yes—
subgroupG/H
centerC22C22×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC53×#3155C2
socleC22×C53C23×D4
hypercenter#3155D53
hypocenterC53#60649
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ #117 ◁ #3155

Complements

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

NH ≅ G/Ntype
1. C2×#16811437C2semidirect
2. C2×#16811433C2semidirect
3. C2×#16811424C2semidirect
4. #20288507C2semidirect
5. #20285209C2semidirect
6. #20285205C2semidirect
7. #20285195C2semidirect
8. #20285188C2semidirect
9. #20285187C2semidirect
10. #20285180C2semidirect
11. #20285177C2semidirect
12. #20285142C2semidirect
13. #20285139C2semidirect
14. C2×#16811006C2semidirect
15. #495×D53C2semidirect
16. #20283137C2semidirect
17. C53×#3155C2semidirect
23. C2×#13133250C22semidirect
24. C2×#13133247C22semidirect
25. C2×#13133246C22semidirect
26. C2×#13133246C22semidirect
29. C2×#13133241C22semidirect
31. C2×#13133237C22semidirect
33. C2×#13133236C22semidirect
34. C2×#13133236C22semidirect
35. C22×Dic212C22semidirect
36. C2×Q16×D53C22semidirect
37. C22×#11719923C22semidirect
38. C2×SD16×D53C22semidirect
45. #16811199C22semidirect
46. #16811193C22semidirect
47. #16811186C22semidirect
48. #16811171C22semidirect
49. #16811169C22semidirect
50. C2×#13133204C22semidirect
51. #124×D53C22semidirect
53. #16811018C22semidirect
54. #16811017C22semidirect
55. #16811014C22semidirect
56. #16811011C22semidirect
57. #16811010C22semidirect
58. #16811008C22semidirect
59. #16811007C22semidirect
60. #16811006C22semidirect
61. #16811006C22semidirect
62. #16811006C22semidirect
63. #16811006C22semidirect
64. #16811006C22semidirect
65. #16811006C22semidirect
66. #16811005C22semidirect
67. #16811004C22semidirect
68. #16811004C22semidirect
69. #16811003C22semidirect
70. #16811001C22semidirect
71. #16810998C22semidirect
72. #16810995C22semidirect
73. #16810994C22semidirect
74. #16810580C22semidirect
75. #16810579C22semidirect
76. #16810577C22semidirect
77. #16810575C22semidirect
78. M16×Dic53C22semidirect
79. C2×C8×Dic53C22semidirect
80. C4×C8×D53C22semidirect
81. C2×AGL(1,ℤ/8)×C53C22semidirect
82. C2×#135×C53C22semidirect
84. C53×#535C22semidirect
85. C53×#496C22semidirect
86. C53×#495C22semidirect
87. C53×#493C22semidirect
88. C53×#405C22semidirect
140. #13133225D4semidirect
141. #13133223D4semidirect
407. #3155D53semidirect
436. C2×AGL(1,ℤ/8)C2×D53semidirect
442. C2×#135C2×D53semidirect
457. #535C2×D53semidirect
468. #496C2×D53semidirect
480. #495C2×D53semidirect
484. #493C2×D53semidirect
490. #405C2×D53semidirect
495. C53#60649semidirect

Maximal subgroups

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

subgroupindex
C2×#168114372
C2×#168114332
C2×#168114242
#202885072
#202852092
#202852052
#202851952
#202851882
#202851872
#202851802
#202851772
#202851422
#202851392
C2×#168110062
#495×D532
#202831372
C53×#31552
#6064953