Finite Group Databasebeta

← #27389953

Subgroups — #27389953

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
1#20283933C211yesmaximal, characteristic
2C2×#16810743C211yesmaximal, characteristic, complemented
3C2×#16810738C211yesmaximal, characteristic, complemented
4#20283418C211yesmaximal, characteristic, complemented
5#20275042C211yesmaximal, characteristic, complemented
6#20275042C211yesmaximal, characteristic, complemented
7#20275017C211yesmaximal, characteristic, complemented
8#20274990C211yesmaximal, characteristic, complemented
9#20274990C211yesmaximal, characteristic, complemented
10#20274920C211yesmaximal, characteristic, complemented
11#20274659C211yesmaximal, characteristic, complemented
12#20274557C211yesmaximal, characteristic, complemented
13#20274550C211yesmaximal, characteristic, complemented
14#20274496C211yesmaximal, characteristic, complemented
15C2×C53×#568C211yesmaximal, characteristic, complemented
16C2×#13133237C2211yescharacteristic
17C2×#13133237C2211yescharacteristic
18C2×#13133223C2211yescharacteristic, complemented
19#16811134C2211yescharacteristic
20#16810785C411yescharacteristic, complemented
21#16810785C411yescharacteristic, complemented
22#16810779C411yescharacteristic, complemented
23#16810774C411yescharacteristic, complemented
24#16810768C411yescharacteristic, complemented
25#16810768C411yescharacteristic, complemented
26#16810762C411yescharacteristic, complemented
27#16810757C411yescharacteristic, complemented
28#16810743—24no—
29#16810738—24no—
30#16810699—21no—
31#16810699—21no—
32#16810692—21no—
33#16810692—21no—
34C2×#13133152C2211yescharacteristic, complemented
35C2×#13133152C2211yescharacteristic, complemented
36#16810649C2211yescharacteristic, complemented
37C2×#13133144C2211yescharacteristic
38C2×#13133144C2211yescharacteristic
39C2×#13133144C2211yescharacteristic
40C2×#13133144C2211yescharacteristic
41C2×#13133143C2211yescharacteristic, complemented
42C2×#13133143C2211yescharacteristic, complemented
43#16810619C2211yescharacteristic
44#16810619C2211yescharacteristic
45#16810589C2211yescharacteristic, complemented
46#16810587C2211yescharacteristic
47C2×C22⋊#88322C2211yescharacteristic
48#16810578C2211yescharacteristic, complemented
49C2×#13133127C2211yescharacteristic, complemented
50C2×C8×Dic53C2211yescharacteristic, complemented
51C4×C22⋊Dic53C2211yescharacteristic
52#16810387C2211yescharacteristic, complemented
53#16810387C2211yescharacteristic, complemented
54#16810384C2211yescharacteristic, complemented
55#16810384C2211yescharacteristic, complemented
56#16810377C2211yescharacteristic, complemented
57#16810377C2211yescharacteristic, complemented
58C22×#41×C53C2211yescharacteristic
59C53×#568—24no—
60C53×#568—24no—
61C2×#131×C53—21no—
62C2×#131×C53—21no—
63C2×#131×C53C2211yescharacteristic
64C2×#131×C53C2211yescharacteristic
65C2×#131×C53C2211yescharacteristic
66C2×#131×C53C2211yescharacteristic
67C22×M16×C53—21no—
68C22×M16×C53—21no—
69C22×M16×C53C2211yescharacteristic
70C22×M16×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#13133223—22no—
85#13133223—22no—
86C2×#11719917C2311yescharacteristic
87C2×#11719917C2311yescharacteristic
88C2×#11719912—21no—
89C22×#88322C2311yescharacteristic
90C22×#88322C2311yescharacteristic
91C2×C8×D53—21no—
92#13133200—21no—
93#13133196C2×C411yescharacteristic
94#13133196C2×C411yescharacteristic
95#13133191C2×C411yescharacteristic
96#13133191C2×C411yescharacteristic
97#13133186—21no—
98C4×C22⋊D53—21no—
99C4×C22⋊D53—21no—
100#13133176C2311yescharacteristic
101C2×C22⋊Dic53—21no—
102C2×C4×Dic53C2311yescharacteristic
103C2×C4×Dic53C2311yescharacteristic
104#13133152—22no—
105#13133152—22no—
106#13133146—21no—
107#13133146—21no—
108#13133144—22no—
109#13133144—22no—
110#13133144—22no—
111#13133144—22no—
112#13133143—22no—
113#13133143—22no—
114#13133141C2×C411yescharacteristic
115#13133141C2×C411yescharacteristic
116#13133141C2×C411yescharacteristic
117#13133141C2×C411yescharacteristic
118#13133138C2×C411yescharacteristic
119#13133138C2×C411yescharacteristic
120#13133138C2×C411yescharacteristic
121#13133138C2×C411yescharacteristic
122C22⋊#88322—21no—
123C22⋊#88322—21no—
124C22⋊#88322C2×C411yescharacteristic
125C22⋊#88322C2×C411yescharacteristic
126C22⋊#88322C2×C411yescharacteristic
127C22⋊#88322C2×C411yescharacteristic
128#13133129—21no—
129#13133129—21no—
130#13133127—22no—
131#13133127—21no—
132C8×Dic53—22no—
133C8×Dic53—21no—
134#13133124—21no—
135C2×#41×C53—22no—
136C2×#41×C53—22no—
137C2×#41×C53—22no—
138C2×#41×C53—22no—
139C2×#41×C53—21no—
140C2×#41×C53—21no—
141C2×#41×C53C2×C411yescharacteristic
142C2×#41×C53C2×C411yescharacteristic
143C2×#41×C53C2311yescharacteristic
144C2×#41×C53C2311yescharacteristic
145C22×Q8×C53C2×C411yescharacteristic
146C22×D4×C53—21no—
147C22×D4×C53C2×C411yescharacteristic
148C23×C4×C53—21no—
149C23×C4×C53C2311yescharacteristic
150#131×C53—28no—
151#131×C53—28no—
152#131×C53—22no—
153#131×C53—22no—
154#131×C53—22no—
155#131×C53—22no—
156#131×C53—22no—
157#131×C53—22no—
158#131×C53D414yescomplemented
159#131×C53D414yescomplemented
160C2×M16×C53—28no—
161C2×M16×C53—28no—
162C2×M16×C53—22no—
163C2×M16×C53—22no—
164C2×M16×C53—21no—
165C2×M16×C53—21no—
166C2×M16×C53—21no—
167C2×M16×C53—21no—
168C2×M16×C53—22no—
169C2×M16×C53—22no—
170C2×M16×C53—21no—
171C2×M16×C53D411yescharacteristic
172C2×M16×C53D411yescharacteristic
173C2×M16×C53D411yescharacteristic
174C2×M16×C53D411yescharacteristic
175C2×M16×C53C2311yescharacteristic
176C2×M16×C53C2311yescharacteristic
177C22×C8×C53—21no—
178C22×C8×C53—21no—
179C22×C8×C53—21no—
180C22×C8×C53—21no—
181C22×C8×C53—21no—
182C22×C8×C53C2311yescharacteristic
183C22×C8×C53C2311yescharacteristic
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×C53C22×C411yescharacteristic
230C22×C4×C53C22×C411yescharacteristic
231C22×C4×C53C2×D411yescharacteristic
232C22×C4×C53C2×D411yescharacteristic
233C22×C4×C53#4111yescharacteristic
234C22×C4×C53C2411yescharacteristic
235C2×C22⋊D53—21no—
236C2×C22⋊D53—21no—
237C2×C22⋊D53—21no—
238C22×Dic53—21no—
239C22×Dic53—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—24no—
248M16×C53—24no—
249M16×C53—24no—
250M16×C53—21no—
251M16×C53—21no—
252M16×C53—22no—
253M16×C53—22no—
254M16×C53—24no—
255M16×C53—24no—
256M16×C53—22no—
257M16×C53—22no—
258M16×C53C2×D412yes—
259M16×C53C2×D412yes—
260C2×C8×C53—24no—
261C2×C8×C53—24no—
262C2×C8×C53—24no—
263C2×C8×C53—21no—
264C2×C8×C53—21no—
265C2×C8×C53—21no—
266C2×C8×C53—21no—
267C2×C8×C53—24no—
268C2×C8×C53—24no—
269C2×C8×C53C2×D411yescharacteristic
270C2×C8×C53C2×D411yescharacteristic
271C2×C8×C53C2×D411yescharacteristic
272C2×C8×C53C2×D411yescharacteristic
273C2×C8×C53C2×D412yes—
274C2×C8×C53C2×D412yes—
275C22⋊Dic53—21no—
276C22⋊Dic53—21no—
277C22⋊Dic53—21no—
278C22⋊Dic53—42no—
279#11719925—22no—
280#11719925—22no—
281#11719924—22no—
282#11719924—22no—
283#11719923—22no—
284#11719923—22no—
285#11719922—22no—
286#11719922—22no—
287#11719921—21no—
288#11719921—21no—
289C4⋊Dic53C22×C411yescharacteristic
290C4⋊Dic53C22×C411yescharacteristic
291#11719919—21no—
292#11719919—21no—
293C4×Dic53—21no—
294C4×Dic53—21no—
295C4×Dic53—21no—
296C4×Dic53—21no—
297C4×Dic53—21no—
298#11719917—21no—
299#11719917—21no—
300#11719917—21no—
301#11719917—21no—
302C2×#88322—21no—
303C2×#88322—21no—
304C2×#88322—21no—
305C2×#88322—21no—
306C2×#88322—21no—
307C2×#88322—21no—
308C2×#88322C22×C411yescharacteristic
309C2×#88322C22×C411yescharacteristic
310C2×#88322C22×C411yescharacteristic
311C2×#88322C22×C411yescharacteristic
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×C53C4×D411yescharacteristic
363C2×C4×C53C4×D411yescharacteristic
364C2×C4×C53C23×C411yescharacteristic
365C2×C4×C53C22×D411yescharacteristic
366C2×C4×C53C22×D411yescharacteristic
367C2×C4×C53C22×D411yescharacteristic
368C2×C4×C53C2×#4111yescharacteristic
369C2×C4×C53C2×#4111yescharacteristic
370C22⋊D53—41no—
371C22⋊D53—41no—
372C22⋊D53—81no—
373C22⋊D53—81no—
374C2×Dic53—22no—
375C2×Dic53—21no—
376C2×Dic53—21no—
377C2×Dic53—21no—
378C2×Dic53—41no—
379C2×Dic53—41no—
380C2×Dic53—41no—
381C2×Dic53—41no—
382C2×Dic53—41no—
383D212—21no—
384D212—21no—
385C4×D53—41no—
386C4×D53—41no—
387Dic106—21no—
388Dic106—21no—
389C8×C53—22no—
390C8×C53—22no—
391C8×C53—21no—
392C8×C53—21no—
393C8×C53#12012yes—
394C8×C53#12012yes—
395#88322—21no—
396#88322—21no—
397#88322—21no—
398#88322—21no—
399#88322—41no—
400#88322—41no—
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×C53C2×C4×D411yescharacteristic
430C4×C53C2×C4×D411yescharacteristic
431C4×C53C2×#12011yescharacteristic
432C4×C53#52511yescharacteristic
433Dic53—42no—
434Dic53—41no—
435Dic53—41no—
436Dic53—41no—
437Dic53—81no—
438C2×#568D5311yescharacteristic, complemented
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#1789—531no—
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—24no—
467#568—24no—
468C2×#131—21no—
469C2×#131—21no—
470C2×#131—531no—
471C2×#131C2×D5311yescharacteristic
472C2×#131C2×D5311yescharacteristic
473C2×#131C2×D5311yescharacteristic
474C2×#131C2×D5311yescharacteristic
475C22×M16—21no—
476C22×M16—21no—
477C22×M16C2×D5311yescharacteristic
478C22×M16C2×D5311yescharacteristic
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×#104—531no—
500C2×#104—531no—
501C2×#104—531no—
502C2×#104—531no—
503#416—531no—
504#416—531no—
505#408—531no—
506#407—531no—
507C2×C22⋊C8—531no—
508#405—531no—
509C2×#97—531no—
510C2×C4×C8—531no—
511C4×C22⋊C4—531no—
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—28no—
548#131—28no—
549#131—22no—
550#131—22no—
551#131—22no—
552#131—22no—
553#131—22no—
554#131—22no—
555#131—1062no—
556#131—1062no—
557#131C22⋊D5314yescomplemented
558#131C22⋊D5314yescomplemented
559C2×M16—28no—
560C2×M16—28no—
561C2×M16—21no—
562C2×M16—22no—
563C2×M16—22no—
564C2×M16—21no—
565C2×M16—21no—
566C2×M16—21no—
567C2×M16—21no—
568C2×M16—22no—
569C2×M16—22no—
570C2×M16—531no—
571C2×M16—531no—
572C2×M16—1061no—
573C2×M16C22⋊D5311yescharacteristic
574C2×M16C22⋊D5311yescharacteristic
575C2×M16C22⋊D5311yescharacteristic
576C2×M16C22⋊D5311yescharacteristic
577C2×M16C22×D5311yescharacteristic
578C2×M16C22×D5311yescharacteristic
579C22×C8—21no—
580C22×C8—21no—
581C22×C8—21no—
582C22×C8—21no—
583C22×C8—21no—
584C22×C8—531no—
585C22×C8—531no—
586C22×C8—1061no—
587C22×C8C22×D5311yescharacteristic
588C22×C8C22×D5311yescharacteristic
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—1061no—
599C2×C42—531no—
600C2×C42—531no—
601#108—1062no—
602#108—1062no—
603C4⋊C8—1061no—
604C4⋊C8—1061no—
605#104—1062no—
606#104—1062no—
607#104—1062no—
608#104—1062no—
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—531no—
620C22⋊C8—531no—
621C22⋊C8—531no—
622C22⋊C8—531no—
623C22⋊C8—1061no—
624C22⋊C8—1061no—
625C22⋊C8—1061no—
626C22⋊C8—1061no—
627#97—1062no—
628#97—1061no—
629C4×C8—1062no—
630C4×C8—1061no—
631#95—1061no—
632C24—21no—
633C24#1171994511yescharacteristic
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#41#1171994512yes—
651#41#1171994512yes—
652#41C2×C22⋊D5312yes—
653#41C2×C22⋊D5312yes—
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—1061no—
687C22×C4—1061no—
688C22×C4—1061no—
689C22×C4C2×C4×D5311yescharacteristic
690C22×C4C2×C4×D5311yescharacteristic
691C22×C4#1171994511yescharacteristic
692C22×C4C2×C22⋊D5311yescharacteristic
693C22×C4C2×C22⋊D5311yescharacteristic
694C22×C4C23×D5311yescharacteristic
695Q16—1062no—
696Q16—1062no—
697SD16—1062no—
698SD16—1062no—
699SD16—1062no—
700SD16—1062no—
701D8—1062no—
702D8—1062no—
703M16—24no—
704M16—24no—
705M16—24no—
706M16—21no—
707M16—21no—
708M16—22no—
709M16—22no—
710M16—24no—
711M16—24no—
712M16—22no—
713M16—22no—
714M16—1061no—
715M16—1061no—
716M16—1061no—
717M16—1061no—
718M16—2122no—
719M16C2×C22⋊D5312yes—
720M16C2×C22⋊D5312yes—
721C2×C8—24no—
722C2×C8—24no—
723C2×C8—24no—
724C2×C8—21no—
725C2×C8—21no—
726C2×C8—21no—
727C2×C8—21no—
728C2×C8—24no—
729C2×C8—24no—
730C2×C8—531no—
731C2×C8—531no—
732C2×C8—531no—
733C2×C8—531no—
734C2×C8—1061no—
735C2×C8—1061no—
736C2×C8—1061no—
737C2×C8—1061no—
738C2×C8—1061no—
739C2×C8—1061no—
740C2×C8—2122no—
741C2×C8C2×C22⋊D5311yescharacteristic
742C2×C8C2×C22⋊D5311yescharacteristic
743C2×C8C2×C22⋊D5312yes—
744C2×C8C2×C22⋊D5312yes—
745C2×C8C2×C22⋊D5311yescharacteristic
746C2×C8C2×C22⋊D5311yescharacteristic
747C4⋊C4—531no—
748C4⋊C4—531no—
749C4⋊C4—1061no—
750C4⋊C4—1061no—
751C22⋊C4—1061no—
752C22⋊C4—1061no—
753C22⋊C4—1061no—
754C22⋊C4—1061no—
755C22⋊C4—1061no—
756C22⋊C4—2122no—
757C42—1061no—
758C42—1061no—
759C42—1061no—
760C42—1061no—
761C42—1061no—
762C23—24no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—41no—
768C23—41no—
769C23—81no—
770C23—81no—
771C23—1061no—
772C23C4×C22⋊D5311yescharacteristic
773C23C4×C22⋊D5311yescharacteristic
774C23C2×#1171994511yescharacteristic
775Q8—24no—
776Q8—21no—
777Q8—21no—
778Q8—1061no—
779Q8—1061no—
780Q8C4×C22⋊D5312yes—
781Q8C4×C22⋊D5312yes—
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—
797D4C4×C22⋊D5312yes—
798D4C4×C22⋊D5312yes—
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—1062no—
819C2×C4—1061no—
820C2×C4—1061no—
821C2×C4—1061no—
822C2×C4—2121no—
823C2×C4—2121no—
824C2×C4—2121no—
825C2×C4—2121no—
826C2×C4—2121no—
827C2×C4—2121no—
828C2×C4—2121no—
829C2×C4C4×C22⋊D5311yescharacteristic
830C2×C4C4×C22⋊D5311yescharacteristic
831C2×C4C22×C4×D5311yescharacteristic
832C2×C4C22×C22⋊D5311yescharacteristic
833C2×C4C22×C22⋊D5311yescharacteristic
834C2×C4C22×C22⋊D5311yescharacteristic
835C2×C4C2×#1171994511yescharacteristic
836C2×C4C2×#1171994511yescharacteristic
837C8—22no—
838C8—22no—
839C8—21no—
840C8—21no—
841C8—1061no—
842C8—1061no—
843C8—1061no—
844C8—1061no—
845C8—2121no—
846C8—2121no—
847C8#1313318612yes—
848C8#1313318612yes—
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×C4×C22⋊D5311yescharacteristic
870C22#1681113411yescharacteristic
871C22#1681113411yescharacteristic
872C4—21no—
873C4—22no—
874C4—22no—
875C4—21no—
876C4—4241no—
877C4—2122no—
878C4—2121no—
879C4—2121no—
880C4—2121no—
881C4C2×C4×C22⋊D5311yescharacteristic
882C4C2×C4×C22⋊D5311yescharacteristic
883C4C2×#1313318611yescharacteristic
884C4#1681113411yescharacteristic
885C2—21no—
886C2—21no—
887C2—41no—
888C2—41no—
889C2—42no—
890C2—42no—
891C2—4241no—
892C2C4×#1313318611yescharacteristic
893C2#2028362211yescharacteristic
894C2#2028363011yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC2×C53×#568C2
socleC22×C53C2×C4×D4
prime radical#20283933C2
cosocleC22×C4×C53C24
hypercenterC2×#568D53
hypocenterC53#21468
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C22×M16 ◁ C2×#568

Complements

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

NH ≅ G/Ntype
2. C2×#16810743C2semidirect
3. C2×#16810738C2semidirect
4. #20283418C2semidirect
5. #20275042C2semidirect
6. #20275042C2semidirect
7. #20275017C2semidirect
8. #20274990C2semidirect
9. #20274990C2semidirect
10. #20274920C2semidirect
11. #20274659C2semidirect
12. #20274557C2semidirect
13. #20274550C2semidirect
14. #20274496C2semidirect
15. C2×C53×#568C2semidirect
18. C2×#13133223C22semidirect
20. #16810785C4semidirect
21. #16810785C4semidirect
22. #16810779C4semidirect
23. #16810774C4semidirect
24. #16810768C4semidirect
25. #16810768C4semidirect
26. #16810762C4semidirect
27. #16810757C4semidirect
34. C2×#13133152C22semidirect
35. C2×#13133152C22semidirect
36. #16810649C22semidirect
41. C2×#13133143C22semidirect
42. C2×#13133143C22semidirect
45. #16810589C22semidirect
48. #16810578C22semidirect
49. C2×#13133127C22semidirect
50. C2×C8×Dic53C22semidirect
52. #16810387C22semidirect
53. #16810387C22semidirect
54. #16810384C22semidirect
55. #16810384C22semidirect
56. #16810377C22semidirect
57. #16810377C22semidirect
158. #131×C53D4semidirect
159. #131×C53D4semidirect
438. C2×#568D53semidirect
518. C53#21468semidirect
557. #131C22⋊D53semidirect
558. #131C22⋊D53semidirect

Maximal subgroups

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

subgroupindex
#202839332
C2×#168107432
C2×#168107382
#202834182
#202750422
#202750172
#202749902
#202749202
#202746592
#202745572
#202745502
#202744962
C2×C53×#5682
#2146853