Finite Group Databasebeta

← #27389946

Subgroups — #27389946

Order 13568.

1320 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811390C211yesmaximal, characteristic, complemented
2#20283933C211yesmaximal, characteristic
3C2×#16810742C211yesmaximal, characteristic, complemented
4C2×#16810737C211yesmaximal, characteristic, complemented
5#20283414C211yesmaximal, characteristic, complemented
6#20275040C211yesmaximal, characteristic, complemented
7#20275040C211yesmaximal, characteristic, complemented
8#20275015C211yesmaximal, characteristic, complemented
9#20274988C211yesmaximal, characteristic, complemented
10#20274988C211yesmaximal, characteristic, complemented
11#20274919C211yesmaximal, characteristic, complemented
12#20274560C211yesmaximal, characteristic, complemented
13#20274553C211yesmaximal, characteristic, complemented
14#20274499C211yesmaximal, characteristic, complemented
15C53×#1789C211yesmaximal, characteristic, complemented
16C2×#13133237C2211yescharacteristic
17C2×#13133237C2211yescharacteristic
18#16811390—24no—
19#16811390—24no—
20C2×#13133225C2211yescharacteristic, complemented
21C2×#13133224—21no—
22C2×#13133224—21no—
23C2×#13133224C2211yescharacteristic
24C2×#13133224C2211yescharacteristic
25C2×#13133224C2211yescharacteristic
26C2×#13133224C2211yescharacteristic
27C22×#11719917—21no—
28C22×#11719917—21no—
29C22×#11719917C2211yescharacteristic
30C22×#11719917C2211yescharacteristic
31#16811134C2211yescharacteristic
32#16810785C411yescharacteristic, complemented
33#16810785C411yescharacteristic, complemented
34#16810779C411yescharacteristic, complemented
35#16810774C411yescharacteristic, complemented
36#16810768C411yescharacteristic, complemented
37#16810768C411yescharacteristic, complemented
38#16810762C411yescharacteristic, complemented
39#16810757C411yescharacteristic, complemented
40#16810742—24no—
41#16810737—24no—
42#16810698—21no—
43#16810698—21no—
44#16810697—21no—
45#16810697—21no—
46C2×#13133152C2211yescharacteristic, complemented
47C2×#13133152C2211yescharacteristic, complemented
48#16810651C2211yescharacteristic, complemented
49C2×#13133145C2211yescharacteristic, complemented
50C2×#13133145C2211yescharacteristic, complemented
51#16810619C2211yescharacteristic
52#16810619C2211yescharacteristic
53#16810591C2211yescharacteristic, complemented
54C2×C22⋊#88322C2211yescharacteristic
55#16810581C2211yescharacteristic, complemented
56C2×#13133128C2211yescharacteristic, complemented
57C2×C4×#88322C2211yescharacteristic, complemented
58#16810387C2211yescharacteristic, complemented
59#16810387C2211yescharacteristic, complemented
60#16810383C2211yescharacteristic, complemented
61#16810383C2211yescharacteristic, complemented
62#16810378C2211yescharacteristic, complemented
63#16810378C2211yescharacteristic, complemented
64C22×#41×C53C2211yescharacteristic
65C2×#104×C53C2211yescharacteristic
66C2×#104×C53C2211yescharacteristic
67C2×#104×C53C2211yescharacteristic
68C2×#104×C53C2211yescharacteristic
69C53×#407C2211yescharacteristic
70C4×C22⋊C4×C53C2211yescharacteristic
71C2×#11719945C2311yescharacteristic
72#13133237—22no—
73#13133237—22no—
74#13133237—22no—
75#13133237—22no—
76C2×#11719925C2×C411yescharacteristic
77C2×#11719925C2×C411yescharacteristic
78C2×#11719923C2×C411yescharacteristic
79C2×#11719923C2×C411yescharacteristic
80C2×#11719924C2×C411yescharacteristic
81C2×#11719924C2×C411yescharacteristic
82C2×#11719922C2×C411yescharacteristic
83C2×#11719922C2×C411yescharacteristic
84#13133225—22no—
85#13133225—22no—
86#13133224—28no—
87#13133224—28no—
88#13133224—22no—
89#13133224—22no—
90#13133224—22no—
91#13133224—22no—
92#13133224—22no—
93#13133224—22no—
94#13133224D414yescomplemented
95#13133224D414yescomplemented
96C2×#11719917—28no—
97C2×#11719917—28no—
98C2×#11719917—22no—
99C2×#11719917—22no—
100C2×#11719917—21no—
101C2×#11719917—21no—
102C2×#11719917—21no—
103C2×#11719917—21no—
104C2×#11719917—22no—
105C2×#11719917—22no—
106C2×#11719917—21no—
107C2×#11719917D411yescharacteristic
108C2×#11719917D411yescharacteristic
109C2×#11719917D411yescharacteristic
110C2×#11719917D411yescharacteristic
111C2×#11719917C2311yescharacteristic
112C2×#11719917C2311yescharacteristic
113C2×#11719912—21no—
114C22×#88322—21no—
115C22×#88322—21no—
116C22×#88322—21no—
117C22×#88322—21no—
118C22×#88322—21no—
119C22×#88322C2311yescharacteristic
120C22×#88322C2311yescharacteristic
121C22×#88322C2311yescharacteristic
122C22×#88322C2311yescharacteristic
123C2×C8×D53—21no—
124#13133200—21no—
125#13133196C2×C411yescharacteristic
126#13133196C2×C411yescharacteristic
127#13133191C2×C411yescharacteristic
128#13133191C2×C411yescharacteristic
129#13133186—21no—
130C4×C22⋊D53—21no—
131C4×C22⋊D53—21no—
132#13133176C2311yescharacteristic
133#13133152—22no—
134#13133152—22no—
135#13133146—21no—
136#13133146—21no—
137#13133145—22no—
138#13133145—22no—
139#13133141C2×C411yescharacteristic
140#13133141C2×C411yescharacteristic
141#13133141C2×C411yescharacteristic
142#13133141C2×C411yescharacteristic
143#13133138C2×C411yescharacteristic
144#13133138C2×C411yescharacteristic
145#13133138C2×C411yescharacteristic
146#13133138C2×C411yescharacteristic
147C22⋊#88322C2×C411yescharacteristic
148C22⋊#88322C2×C411yescharacteristic
149C22⋊#88322C2×C411yescharacteristic
150C22⋊#88322C2×C411yescharacteristic
151#13133129—21no—
152#13133129—21no—
153#13133128—22no—
154#13133127—21no—
155C4×#88322—22no—
156C8×Dic53—21no—
157C2×#41×C53—22no—
158C2×#41×C53—22no—
159C2×#41×C53—22no—
160C2×#41×C53—22no—
161C2×#41×C53—21no—
162C2×#41×C53—21no—
163C2×#41×C53C2×C411yescharacteristic
164C2×#41×C53C2×C411yescharacteristic
165C2×#41×C53C2311yescharacteristic
166C2×#41×C53C2311yescharacteristic
167C22×Q8×C53C2×C411yescharacteristic
168C22×D4×C53—21no—
169C22×D4×C53C2×C411yescharacteristic
170C23×C4×C53—21no—
171C23×C4×C53C2311yescharacteristic
172C2×M16×C53C2311yescharacteristic
173C2×M16×C53C2311yescharacteristic
174C2×C22⋊C4×C53—21no—
175C2×C42×C53C2311yescharacteristic
176C2×C42×C53C2311yescharacteristic
177#104×C53—22no—
178#104×C53—22no—
179#104×C53—22no—
180#104×C53—22no—
181C22⋊C8×C53—21no—
182C22⋊C8×C53—21no—
183#95×C53—21no—
184C24×C53—21no—
185C24×C53#4111yescharacteristic
186#41×C53—24no—
187#41×C53—24no—
188#41×C53—24no—
189#41×C53—24no—
190#41×C53—22no—
191#41×C53—22no—
192#41×C53—22no—
193#41×C53—22no—
194#41×C53—21no—
195#41×C53—21no—
196#41×C53—21no—
197#41×C53—21no—
198#41×C53C2×D412yes—
199#41×C53C2×D412yes—
200#41×C53#4112yes—
201#41×C53#4112yes—
202C2×Q8×C53—22no—
203C2×Q8×C53—22no—
204C2×Q8×C53—21no—
205C2×Q8×C53C22×C411yescharacteristic
206C2×Q8×C53C22×C411yescharacteristic
207C2×D4×C53—24no—
208C2×D4×C53—24no—
209C2×D4×C53—21no—
210C2×D4×C53—21no—
211C2×D4×C53—21no—
212C2×D4×C53—21no—
213C2×D4×C53—22no—
214C2×D4×C53—22no—
215C2×D4×C53—21no—
216C2×D4×C53C22×C411yescharacteristic
217C2×D4×C53C22×C411yescharacteristic
218C22×C4×C53—24no—
219C22×C4×C53—24no—
220C22×C4×C53—21no—
221C22×C4×C53—21no—
222C22×C4×C53—21no—
223C22×C4×C53—21no—
224C22×C4×C53—21no—
225C22×C4×C53—21no—
226C22×C4×C53—21no—
227C22×C4×C53—21no—
228C22×C4×C53—21no—
229C22×C4×C53—21no—
230C22×C4×C53—21no—
231C22×C4×C53C22×C411yescharacteristic
232C22×C4×C53C22×C411yescharacteristic
233C22×C4×C53C2×D411yescharacteristic
234C22×C4×C53C2×D411yescharacteristic
235C22×C4×C53#4111yescharacteristic
236C22×C4×C53C2411yescharacteristic
237C2×C22⋊D53—21no—
238C2×C22⋊D53—21no—
239C2×C22⋊D53—21no—
240#11719945—21no—
241#11719945—21no—
242#11719945—21no—
243#11719945—21no—
244C2×D212C22×C411yescharacteristic
245C2×C4×D53—21no—
246C2×Dic106C22×C411yescharacteristic
247M16×C53—21no—
248M16×C53—21no—
249M16×C53—21no—
250M16×C53—21no—
251C2×C8×C53—21no—
252C2×C8×C53—21no—
253C22⋊C4×C53—42no—
254C42×C53—21no—
255C42×C53—21no—
256C42×C53—21no—
257C42×C53—21no—
258C22⋊Dic53—21no—
259C22⋊Dic53—21no—
260C22⋊Dic53—21no—
261#11719925—22no—
262#11719925—22no—
263#11719924—22no—
264#11719924—22no—
265#11719923—22no—
266#11719923—22no—
267#11719922—22no—
268#11719922—22no—
269#11719921—21no—
270#11719921—21no—
271C4⋊Dic53C22×C411yescharacteristic
272C4⋊Dic53C22×C411yescharacteristic
273#11719919—21no—
274#11719919—21no—
275C4×Dic53—21no—
276#11719917—24no—
277#11719917—24no—
278#11719917—24no—
279#11719917—21no—
280#11719917—21no—
281#11719917—22no—
282#11719917—22no—
283#11719917—24no—
284#11719917—24no—
285#11719917—22no—
286#11719917—22no—
287#11719917C2×D412yes—
288#11719917C2×D412yes—
289C2×#88322—24no—
290C2×#88322—24no—
291C2×#88322—24no—
292C2×#88322—21no—
293C2×#88322—21no—
294C2×#88322—21no—
295C2×#88322—21no—
296C2×#88322—21no—
297C2×#88322—21no—
298C2×#88322—21no—
299C2×#88322—21no—
300C2×#88322—24no—
301C2×#88322—24no—
302C2×#88322C22×C411yescharacteristic
303C2×#88322C22×C411yescharacteristic
304C2×#88322C22×C411yescharacteristic
305C2×#88322C22×C411yescharacteristic
306C2×#88322C2×D411yescharacteristic
307C2×#88322C2×D411yescharacteristic
308C2×#88322C2×D411yescharacteristic
309C2×#88322C2×D412yes—
310C2×#88322C2×D411yescharacteristic
311C2×#88322C2×D412yes—
312#11719912—42no—
313C8×D53—42no—
314C23×C53—24no—
315C23×C53—21no—
316C23×C53—21no—
317C23×C53—21no—
318C23×C53—21no—
319C23×C53—41no—
320C23×C53—41no—
321C23×C53—81no—
322C23×C53—81no—
323C23×C53C4×D411yescharacteristic
324C23×C53C4×D411yescharacteristic
325C23×C53C2×#4111yescharacteristic
326C22×D53—21no—
327Q8×C53—24no—
328Q8×C53—21no—
329Q8×C53—21no—
330Q8×C53C4×D412yes—
331Q8×C53C4×D412yes—
332D4×C53—24no—
333D4×C53—24no—
334D4×C53—24no—
335D4×C53—22no—
336D4×C53—22no—
337D4×C53—22no—
338D4×C53—22no—
339D4×C53—21no—
340D4×C53—21no—
341D4×C53C4×D412yes—
342D4×C53C4×D412yes—
343C2×C4×C53—24no—
344C2×C4×C53—24no—
345C2×C4×C53—24no—
346C2×C4×C53—21no—
347C2×C4×C53—21no—
348C2×C4×C53—21no—
349C2×C4×C53—21no—
350C2×C4×C53—21no—
351C2×C4×C53—21no—
352C2×C4×C53—21no—
353C2×C4×C53—21no—
354C2×C4×C53—21no—
355C2×C4×C53—22no—
356C2×C4×C53—22no—
357C2×C4×C53—21no—
358C2×C4×C53—21no—
359C2×C4×C53—22no—
360C2×C4×C53—22no—
361C2×C4×C53—21no—
362C2×C4×C53—22no—
363C2×C4×C53—41no—
364C2×C4×C53—41no—
365C2×C4×C53—41no—
366C2×C4×C53—41no—
367C2×C4×C53—41no—
368C2×C4×C53C4×D411yescharacteristic
369C2×C4×C53C4×D411yescharacteristic
370C2×C4×C53C23×C411yescharacteristic
371C2×C4×C53C22×D411yescharacteristic
372C2×C4×C53C22×D411yescharacteristic
373C2×C4×C53C22×D411yescharacteristic
374C2×C4×C53C2×#4111yescharacteristic
375C2×C4×C53C2×#4111yescharacteristic
376C22⋊D53—41no—
377C22⋊D53—41no—
378C22⋊D53—81no—
379C22⋊D53—81no—
380C2×Dic53—21no—
381C2×Dic53—21no—
382C2×Dic53—21no—
383D212—21no—
384D212—21no—
385C4×D53—41no—
386C4×D53—41no—
387Dic106—21no—
388Dic106—21no—
389C8×C53—41no—
390C8×C53—41no—
391#88322—21no—
392#88322—21no—
393#88322—21no—
394#88322—21no—
395#88322—22no—
396#88322—22no—
397#88322—21no—
398#88322—21no—
399#88322#12012yes—
400#88322#12012yes—
401#21468—531nomaximal, Sylow
402C22×C53—21no—
403C22×C53—21no—
404C22×C53—21no—
405C22×C53—21no—
406C22×C53—21no—
407C22×C53—21no—
408C22×C53—21no—
409C22×C53—21no—
410C22×C53—22no—
411C22×C53—22no—
412C22×C53—41no—
413C22×C53—41no—
414C22×C53—41no—
415C22×C53—41no—
416C22×C53—81no—
417C22×C53—81no—
418C22×C53—84no—
419C22×C53C2×C4×D411yescharacteristic
420C22×C53#52511yescharacteristic
421C22×C53#52511yescharacteristic
422C2×D53—41no—
423C2×D53—41no—
424C2×D53—41no—
425C4×C53—21no—
426C4×C53—22no—
427C4×C53—22no—
428C4×C53—21no—
429C4×C53—42no—
430C4×C53—81no—
431C4×C53C2×C4×D411yescharacteristic
432C4×C53C2×C4×D411yescharacteristic
433C4×C53C2×#12011yescharacteristic
434C4×C53#52511yescharacteristic
435Dic53—41no—
436Dic53—41no—
437Dic53—41no—
438C2×#568—531no—
439#3002—531no—
440C2×#444—531no—
441C2×#443—531no—
442#2930—531no—
443#1876—531no—
444#1876—531no—
445#1871—531no—
446#1866—531no—
447#1866—531no—
448#1855—531no—
449#1789D5311yescharacteristic, complemented
450#1765—531no—
451#1764—531no—
452#1753—531no—
453C2×C53—21no—
454C2×C53—21no—
455C2×C53—41no—
456C2×C53—41no—
457C2×C53—42no—
458C2×C53—42no—
459C2×C53C4×#12011yescharacteristic
460C2×C53#295611yescharacteristic
461C2×C53#295711yescharacteristic
462D53—81no—
463C22×#41C2×D5311yescharacteristic
464C2×#135—531no—
465C2×#135—531no—
466#568—1064no—
467#568—1064no—
468C2×#131—531no—
469C2×#131—531no—
470C2×#131—531no—
471C2×#131—531no—
472C2×#131—531no—
473C2×#131—1061no—
474C2×#131—1061no—
475C22×M16—531no—
476C22×M16—531no—
477C22×M16—1061no—
478C22×M16—1061no—
479#525—531no—
480#452—531no—
481#452—531no—
482#451—531no—
483#450—531no—
484#449—531no—
485#449—531no—
486#448—531no—
487#447—531no—
488#444—1064no—
489#443—1064no—
490#436—1061no—
491#436—1061no—
492#435—1061no—
493#435—1061no—
494C2×#108—531no—
495C2×#108—531no—
496#424—531no—
497C2×#104—531no—
498C2×#104—531no—
499C2×#104C2×D5311yescharacteristic
500C2×#104C2×D5311yescharacteristic
501C2×#104C2×D5311yescharacteristic
502C2×#104C2×D5311yescharacteristic
503#416—531no—
504#416—531no—
505#408—531no—
506#407C2×D5311yescharacteristic
507C2×C22⋊C8—531no—
508#405—531no—
509C2×#97—531no—
510C2×C4×C8—531no—
511C4×C22⋊C4C2×D5311yescharacteristic
512#341—531no—
513#341—531no—
514#339—531no—
515#339—531no—
516#336—531no—
517#336—531no—
518C53#2146811yescharacteristic, complemented, Sylow
519C2×#41—22no—
520C2×#41—22no—
521C2×#41—22no—
522C2×#41—22no—
523C2×#41—21no—
524C2×#41—21no—
525C2×#41—531no—
526C2×#41C4×D5311yescharacteristic
527C2×#41C4×D5311yescharacteristic
528C2×#41C22×D5311yescharacteristic
529C2×#41C22×D5311yescharacteristic
530C22×Q8C4×D5311yescharacteristic
531C22×D4—21no—
532C22×D4C4×D5311yescharacteristic
533C23×C4—21no—
534C23×C4C22×D5311yescharacteristic
535#135—1062no—
536#135—1062no—
537#135—1062no—
538#135—1062no—
539C2×Q16—531no—
540C2×Q16—531no—
541C2×SD16—531no—
542C2×SD16—531no—
543C2×SD16—531no—
544C2×SD16—531no—
545C2×D8—531no—
546C2×D8—531no—
547#131—534no—
548#131—534no—
549#131—1062no—
550#131—1062no—
551#131—1062no—
552#131—1062no—
553#131—1062no—
554#131—1062no—
555#131—1068no—
556#131—1068no—
557#131—1062no—
558#131—1062no—
559C2×M16—531no—
560C2×M16—531no—
561C2×M16—531no—
562C2×M16—531no—
563C2×M16—531no—
564C2×M16—531no—
565C2×M16—1061no—
566C2×M16—1062no—
567C2×M16—1062no—
568C2×M16—1061no—
569C2×M16—1061no—
570C2×M16—1061no—
571C2×M16—1061no—
572C2×M16—1062no—
573C2×M16—1062no—
574C2×M16—1068no—
575C2×M16—1068no—
576C2×M16—1061no—
577C2×M16C22×D5311yescharacteristic
578C2×M16C22×D5311yescharacteristic
579C22×C8—531no—
580C22×C8—531no—
581C22×C8—531no—
582C22×C8—531no—
583C22×C8—1061no—
584C22×C8—1061no—
585C22×C8—1061no—
586C22×C8—1061no—
587C22×C8—1061no—
588C22×C8—1061no—
589#123—1061no—
590C22⋊Q8—531no—
591C22⋊Q8—531no—
592#121—531no—
593#121—531no—
594#120—1061no—
595C4×D4—1061no—
596C4×D4—1061no—
597#117—531no—
598C2×C22⋊C4—21no—
599C2×C42C22×D5311yescharacteristic
600C2×C42C22×D5311yescharacteristic
601#108—1062no—
602#108—1062no—
603C4⋊C8—1061no—
604C4⋊C8—1061no—
605#104—22no—
606#104—22no—
607#104—22no—
608#104—22no—
609#104—1062no—
610#104—1062no—
611#103—531no—
612#103—531no—
613#103—531no—
614#103—531no—
615#102—531no—
616#102—531no—
617#102—531no—
618#102—531no—
619C22⋊C8—21no—
620C22⋊C8—21no—
621C22⋊C8—531no—
622C22⋊C8—531no—
623C22⋊C8—531no—
624C22⋊C8—531no—
625C22⋊C8—1061no—
626C22⋊C8—1061no—
627#97—1062no—
628#97—1061no—
629C4×C8—1062no—
630C4×C8—1061no—
631#95—21no—
632C24—21no—
633C24#1171994711yescharacteristic
634#41—24no—
635#41—24no—
636#41—24no—
637#41—24no—
638#41—22no—
639#41—22no—
640#41—22no—
641#41—22no—
642#41—21no—
643#41—21no—
644#41—21no—
645#41—21no—
646#41—1061no—
647#41—1061no—
648#41—1061no—
649#41—1061no—
650#41D4×D5312yes—
651#41D4×D5312yes—
652#41#1171994712yes—
653#41#1171994712yes—
654C2×Q8—22no—
655C2×Q8—22no—
656C2×Q8—21no—
657C2×Q8—531no—
658C2×Q8C2×C4×D5311yescharacteristic
659C2×Q8C2×C4×D5311yescharacteristic
660C2×D4—24no—
661C2×D4—24no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—22no—
667C2×D4—22no—
668C2×D4—21no—
669C2×D4—531no—
670C2×D4—1061no—
671C2×D4—1061no—
672C2×D4—1061no—
673C2×D4C2×C4×D5311yescharacteristic
674C2×D4C2×C4×D5311yescharacteristic
675C22×C4—24no—
676C22×C4—24no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—1061no—
689C22×C4C2×C4×D5311yescharacteristic
690C22×C4C2×C4×D5311yescharacteristic
691C22×C4D4×D5311yescharacteristic
692C22×C4D4×D5311yescharacteristic
693C22×C4#1171994711yescharacteristic
694C22×C4C23×D5311yescharacteristic
695Q16—1062no—
696Q16—1062no—
697SD16—1062no—
698SD16—1062no—
699SD16—1062no—
700SD16—1062no—
701D8—1062no—
702D8—1062no—
703M16—21no—
704M16—21no—
705M16—21no—
706M16—21no—
707M16—532no—
708M16—532no—
709M16—1062no—
710M16—1062no—
711M16—1062no—
712M16—1062no—
713M16—1064no—
714M16—1064no—
715M16—1064no—
716M16—1064no—
717M16—1064no—
718M16—1061no—
719M16—1061no—
720M16—2122no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—532no—
724C2×C8—532no—
725C2×C8—531no—
726C2×C8—531no—
727C2×C8—531no—
728C2×C8—531no—
729C2×C8—531no—
730C2×C8—531no—
731C2×C8—531no—
732C2×C8—531no—
733C2×C8—1064no—
734C2×C8—1064no—
735C2×C8—1064no—
736C2×C8—1064no—
737C2×C8—1064no—
738C2×C8—1061no—
739C2×C8—1061no—
740C2×C8—1061no—
741C2×C8—1061no—
742C2×C8—1061no—
743C2×C8—1061no—
744C2×C8—1061no—
745C2×C8—1061no—
746C2×C8—2122no—
747C4⋊C4—531no—
748C4⋊C4—531no—
749C4⋊C4—1061no—
750C4⋊C4—1061no—
751C22⋊C4—42no—
752C22⋊C4—1061no—
753C22⋊C4—1061no—
754C22⋊C4—1061no—
755C22⋊C4—1061no—
756C22⋊C4—1061no—
757C42—21no—
758C42—21no—
759C42—21no—
760C42—21no—
761C42—1061no—
762C23—24no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—41no—
768C23—41no—
769C23—81no—
770C23—81no—
771C23—1061no—
772C23#1313317711yescharacteristic
773C23#1313317711yescharacteristic
774C23C2×#1171994711yescharacteristic
775Q8—24no—
776Q8—21no—
777Q8—21no—
778Q8—1061no—
779Q8—1061no—
780Q8#1313317712yes—
781Q8#1313317712yes—
782D4—24no—
783D4—24no—
784D4—24no—
785D4—22no—
786D4—22no—
787D4—22no—
788D4—22no—
789D4—21no—
790D4—21no—
791D4—1061no—
792D4—1061no—
793D4—4241no—
794D4—4241no—
795D4—2121no—
796D4—2121no—
797D4#1313317712yes—
798D4#1313317712yes—
799C2×C4—24no—
800C2×C4—24no—
801C2×C4—24no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—21no—
818C2×C4—22no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—1061no—
825C2×C4—1061no—
826C2×C4—1061no—
827C2×C4—2121no—
828C2×C4—2121no—
829C2×C4#1313317711yescharacteristic
830C2×C4#1313317711yescharacteristic
831C2×C4C22×C4×D5311yescharacteristic
832C2×C4C2×D4×D5311yescharacteristic
833C2×C4C2×D4×D5311yescharacteristic
834C2×C4C2×D4×D5311yescharacteristic
835C2×C4C2×#1171994711yescharacteristic
836C2×C4C2×#1171994711yescharacteristic
837C8—41no—
838C8—41no—
839C8—532no—
840C8—532no—
841C8—1061no—
842C8—1061no—
843C8—1061no—
844C8—1061no—
845C8—1061no—
846C8—1061no—
847C8—1062no—
848C8—1062no—
849C22—21no—
850C22—21no—
851C22—21no—
852C22—21no—
853C22—22no—
854C22—22no—
855C22—21no—
856C22—21no—
857C22—21no—
858C22—21no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—81no—
864C22—81no—
865C22—84no—
866C22—2121no—
867C22—2121no—
868C22—2121no—
869C22C2×#1313317711yescharacteristic
870C22#1681112911yescharacteristic
871C22#1681112911yescharacteristic
872C4—21no—
873C4—22no—
874C4—22no—
875C4—21no—
876C4—42no—
877C4—81no—
878C4—2121no—
879C4—2121no—
880C4—2121no—
881C4C2×#1313317711yescharacteristic
882C4C2×#1313317711yescharacteristic
883C4#120×D5311yescharacteristic
884C4#1681112911yescharacteristic
885C2—21no—
886C2—21no—
887C2—41no—
888C2—41no—
889C2—42no—
890C2—42no—
891C2—4241no—
892C2#2027721411yescharacteristic
893C2#2028362111yescharacteristic
894C2#2028362811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#1789C2
socleC22×C53C2×C4×D4
prime radical#20283933C2
cosocleC22×C4×C53C24
hypercenter#1789D53
hypocenterC53#21468
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1789

Complements

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

NH ≅ G/Ntype
1. C2×#16811390C2semidirect
3. C2×#16810742C2semidirect
4. C2×#16810737C2semidirect
5. #20283414C2semidirect
6. #20275040C2semidirect
7. #20275040C2semidirect
8. #20275015C2semidirect
9. #20274988C2semidirect
10. #20274988C2semidirect
11. #20274919C2semidirect
12. #20274560C2semidirect
13. #20274553C2semidirect
14. #20274499C2semidirect
15. C53×#1789C2semidirect
20. C2×#13133225C22semidirect
32. #16810785C4semidirect
33. #16810785C4semidirect
34. #16810779C4semidirect
35. #16810774C4semidirect
36. #16810768C4semidirect
37. #16810768C4semidirect
38. #16810762C4semidirect
39. #16810757C4semidirect
46. C2×#13133152C22semidirect
47. C2×#13133152C22semidirect
48. #16810651C22semidirect
49. C2×#13133145C22semidirect
50. C2×#13133145C22semidirect
53. #16810591C22semidirect
55. #16810581C22semidirect
56. C2×#13133128C22semidirect
57. C2×C4×#88322C22semidirect
58. #16810387C22semidirect
59. #16810387C22semidirect
60. #16810383C22semidirect
61. #16810383C22semidirect
62. #16810378C22semidirect
63. #16810378C22semidirect
94. #13133224D4semidirect
95. #13133224D4semidirect
449. #1789D53semidirect
518. C53#21468semidirect

Maximal subgroups

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

subgroupindex
C2×#168113902
#202839332
C2×#168107422
C2×#168107372
#202834142
#202750402
#202750152
#202749882
#202749192
#202745602
#202745532
#202744992
C53×#17892
#2146853