Finite Group Databasebeta

← #28268994

Subgroups — #28268994

Order 13568.

2126 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#20288554C211yesmaximal, characteristic, complemented
2#20286811C214yesmaximal, complemented
3#20286691C214yesmaximal, complemented
4#20286266C214yesmaximal, complemented
5#20286241C214yesmaximal, complemented
6#20285742C212yesmaximal, complemented
7#20285536C211yesmaximal, characteristic, complemented
8#20285517C211yesmaximal, characteristic, complemented
9#20285496C212yesmaximal, complemented
10#20284853C212yesmaximal, complemented
11#20283975C211yesmaximal, characteristic, complemented
12#20283967C211yesmaximal, characteristic, complemented
13#20283933C212yesmaximal, complemented
14#20283744C211yesmaximal, characteristic, complemented
15C2×C53×#547C211yesmaximal, characteristic, complemented
16C2×#13133247C2212yescomplemented
17C2×#13133242C2212yescomplemented
18C2×#13133237C2214yescomplemented
19#16811322—22no—
20#16811319C2212yescomplemented
21#16811313C2212yescomplemented
22#16811302—22no—
23#16811282C2212yescomplemented
24#16811269C2212yescomplemented
25#16811220—21no—
26#16811211—21no—
27#16811182—21no—
28#16811157C2212yes—
29#16811134C2212yes—
30C2×#13133196C2211yescharacteristic
31C2×#13133191C2211yescharacteristic
32#16811096—21no—
33#16811015C2214yescomplemented
34#16810991C2214yescomplemented
35#16810961C2214yescomplemented
36#16810956C2212yescomplemented
37#16810953C2212yescomplemented
38#16810951C2212yescomplemented
39#16810936C2212yes—
40#16810923C2214yescomplemented
41#16810879C2214yescomplemented
42#16810871C2214yescomplemented
43#16810862C2214yescomplemented
44#16810854C2214yescomplemented
45#16810838C2214yescomplemented
46#16810830C2214yescomplemented
47#16810825C2214yescomplemented
48#16810785C2214yescomplemented
49#16810785C2214yescomplemented
50#16810783C2214yescomplemented
51#16810779C2212yescomplemented
52#16810779C2212yescomplemented
53#16810778C2212yescomplemented
54#16810774C2212yescomplemented
55#16810773C2212yescomplemented
56#16810768C2214yescomplemented
57#16810768C2214yescomplemented
58#16810762C2212yes—
59#16810762C2212yes—
60#16810757C2212yes—
61#16810733C2214yescomplemented
62#16810723C2214yescomplemented
63#16810695C2214yescomplemented
64#16810695C2214yescomplemented
65#16810680C2212yescomplemented
66#16810624C2212yescomplemented
67#16810624C2212yescomplemented
68#16810619C2214yescomplemented
69#16810587C2211yescharacteristic
70#16810587C2211yescharacteristic
71C2×C22⋊#88322C2212yescomplemented
72C22×#41×C53C2211yescharacteristic
73C22×#41×C53C2211yescharacteristic, complemented
74C53×#547—22no—
75C53×#547—22no—
76C53×#547C2214yes—
77C53×#547C2214yescomplemented
78C2×C4⋊Q8×C53C2211yescharacteristic, complemented
79C2×#123×C53—21no—
80C2×#123×C53—21no—
81C2×C22⋊Q8×C53C2211yescharacteristic
82C2×C22⋊Q8×C53C2211yescharacteristic, complemented
83C2×#121×C53—21no—
84C2×C4×D4×C53C2211yescharacteristic
85C2×C4×D4×C53C2211yescharacteristic, complemented
86C22×C4⋊C4×C53—21no—
87C2×#11719945C2312yes—
88C22×Dic106C2311yescharacteristic
89C22×D212C2311yescharacteristic
90C22×C22⋊D53—21no—
91#13133247—44no—
92#13133242—44no—
93#13133237—48no—
94C2×#11719925C2314yes—
95C2×#11719925C2314yes—
96C2×#11719923C2314yes—
97C2×#11719924C2314yes—
98C2×#11719924C2314yes—
99C2×#11719922C2314yes—
100C2×#11719917C2312yes—
101C2×#11719917C2312yes—
102C22×#88322C2314yes—
103#13133212—22no—
104#13133211—22no—
105#13133210—22no—
106#13133209C2312yes—
107#13133207—22no—
108#13133205C2312yes—
109#13133203—22no—
110#13133202—22no—
111#13133200—22no—
112#13133200—22no—
113#13133199—22no—
114#13133198—22no—
115#13133196—21no—
116#13133196—21no—
117#13133196C2312yes—
118#13133196C2312yes—
119#13133196C2312yes—
120#13133195—22no—
121#13133191—21no—
122#13133191—21no—
123#13133191C2312yes—
124#13133191C2312yes—
125#13133191C2312yes—
126#13133190—22no—
127#13133189—22no—
128#13133189—22no—
129#13133186—22no—
130#13133185—22no—
131C4×Dic106C2312yes—
132C4×D212C2312yes—
133C4×C22⋊D53—22no—
134C4×C22⋊D53—22no—
135C4×C22⋊D53—22no—
136#13133177—22no—
137#13133177—22no—
138#13133176C2312yes—
139#13133174—22no—
140#13133173—22no—
141C2×C4⋊Dic53C2311yescharacteristic
142C2×C4⋊Dic53C2311yescharacteristic
143C2×#11719919—21no—
144C2×C22⋊Dic53—21no—
145C2×#11719921—21no—
146C22⋊C4×D53—22no—
147#13133150C2314yes—
148#13133148C2314yes—
149C4⋊#88322C2314yes—
150#13133141C2314yes—
151#13133141C2314yes—
152#13133141C2314yes—
153#13133141C2314yes—
154#13133140C2314yes—
155#13133138C2314yes—
156#13133138C2314yes—
157#13133137C2314yes—
158C22⋊#88322C2312yes—
159C22⋊#88322C2312yes—
160C22⋊#88322C2312yes—
161C22⋊#88322C2314yes—
162C22⋊#88322C2312yes—
163#13133128C2314yes—
164C2×#41×C53—21no—
165C2×#41×C53—21no—
166C2×#41×C53—22no—
167C2×#41×C53—44no—
168C2×#41×C53—44no—
169C2×#41×C53C2312yes—
170C2×#41×C53C2314yes—
171C2×#41×C53C2312yes—
172C22×Q8×C53C2311yescharacteristic
173C22×Q8×C53C2311yescharacteristic
174C22×D4×C53—21no—
175C22×D4×C53—21no—
176C22×D4×C53D411yescharacteristic
177C22×D4×C53C2311yescharacteristic
178C23×C4×C53—21no—
179C23×C4×C53—21no—
180C23×C4×C53—21no—
181C23×C4×C53C2311yescharacteristic
182C23×C4×C53C2311yescharacteristic
183C4⋊Q8×C53—22no—
184C4⋊Q8×C53C2314yes—
185#123×C53—24no—
186#123×C53—24no—
187#123×C53—24no—
188#123×C53—24no—
189C22⋊Q8×C53—21no—
190C22⋊Q8×C53—21no—
191C22⋊Q8×C53—22no—
192C22⋊Q8×C53C2312yes—
193C22⋊Q8×C53C2312yes—
194C22⋊Q8×C53C2314yes—
195#121×C53—24no—
196#121×C53—24no—
197C4×D4×C53—22no—
198C4×D4×C53D412yes—
199C4×D4×C53D412yes—
200C4×D4×C53C2314yes—
201C4×D4×C53C2312yes—
202C4×D4×C53C2312yes—
203C2×C4⋊C4×C53—24no—
204C2×C4⋊C4×C53—24no—
205C2×C4⋊C4×C53—21no—
206C2×C4⋊C4×C53—21no—
207C2×C4⋊C4×C53—21no—
208C2×C4⋊C4×C53—21no—
209C2×C4⋊C4×C53D411yescharacteristic
210C2×C4⋊C4×C53C2311yescharacteristic
211C2×C22⋊C4×C53—21no—
212C2×C22⋊C4×C53—21no—
213C2×C22⋊C4×C53—21no—
214C2×C22⋊C4×C53D411yescharacteristic
215C2×C22⋊C4×C53D411yescharacteristic
216C2×C42×C53C2311yescharacteristic
217C24×C53—21no—
218C24×C53C2×D411yescharacteristic
219C24×C53C2×D411yescharacteristic
220C23×D53—21no—
221#41×C53—28no—
222#41×C53—24no—
223#41×C53—24no—
224#41×C53—42no—
225#41×C53—42no—
226#41×C53—44no—
227#41×C53—44no—
228#41×C53—44no—
229#41×C53—48no—
230C2×Q8×C53—21no—
231C2×Q8×C53—21no—
232C2×Q8×C53—42no—
233C2×Q8×C53—42no—
234C2×Q8×C53C2412yes—
235C2×Q8×C53C2412yes—
236C2×D4×C53—24no—
237C2×D4×C53—22no—
238C2×D4×C53—22no—
239C2×D4×C53—24no—
240C2×D4×C53—21no—
241C2×D4×C53—42no—
242C2×D4×C53—44no—
243C2×D4×C53—44no—
244C2×D4×C53C2×D412yes—
245C2×D4×C53C2×D412yes—
246C2×D4×C53C2412yes—
247C22×C4×C53—21no—
248C22×C4×C53—21no—
249C22×C4×C53—21no—
250C22×C4×C53—24no—
251C22×C4×C53—22no—
252C22×C4×C53—24no—
253C22×C4×C53—22no—
254C22×C4×C53—42no—
255C22×C4×C53—42no—
256C22×C4×C53—44no—
257C22×C4×C53—44no—
258C22×C4×C53—44no—
259C22×C4×C53C2×D411yescharacteristic
260C22×C4×C53C2×D411yescharacteristic
261C22×C4×C53C2×D411yescharacteristic
262C22×C4×C53C2×D411yescharacteristic
263C22×C4×C53C2×D411yescharacteristic
264C22×C4×C53C2×D411yescharacteristic
265C22×C4×C53C2×D412yes—
266C22×C4×C53C2411yescharacteristic
267C22×C4×C53C2411yescharacteristic
268C22×C4×C53C2411yescharacteristic
269C22×C4×C53C2412yes—
270C2×C22⋊D53—22no—
271C2×C22⋊D53—22no—
272C2×C22⋊D53—22no—
273C2×C22⋊D53—22no—
274C2×C22⋊D53—44no—
275C22×Dic53—21no—
276C22×Dic53—21no—
277C22×Dic53—21no—
278#11719945—44no—
279C2×D212—21no—
280C2×D212—42no—
281C2×D212C2412yes—
282C2×C4×D53—22no—
283C2×C4×D53—22no—
284C2×Dic106—21no—
285C2×Dic106—42no—
286C2×Dic106C2412yes—
287C4⋊C4×C53—24no—
288C4⋊C4×C53—22no—
289C4⋊C4×C53—24no—
290C4⋊C4×C53—22no—
291C4⋊C4×C53—24no—
292C4⋊C4×C53—21no—
293C4⋊C4×C53C2×D412yes—
294C4⋊C4×C53C2×D412yes—
295C4⋊C4×C53C2412yes—
296C22⋊C4×C53—22no—
297C22⋊C4×C53—22no—
298C22⋊C4×C53—24no—
299C22⋊C4×C53—24no—
300C22⋊C4×C53C2×D412yes—
301C22⋊C4×C53C2×D412yes—
302C22⋊C4×C53C2×D412yes—
303C22⋊C4×C53C2×D412yes—
304C42×C53C2×D412yes—
305C42×C53C2412yes—
306C22⋊Dic53—22no—
307C22⋊Dic53—22no—
308C22⋊Dic53—22no—
309C22⋊Dic53—22no—
310#11719925—44no—
311#11719925—44no—
312#11719924—44no—
313#11719924—44no—
314#11719923—28no—
315#11719922—28no—
316#11719921—22no—
317#11719921—22no—
318#11719921—22no—
319#11719921—22no—
320#11719921—22no—
321#11719921—22no—
322C4⋊Dic53—21no—
323C4⋊Dic53—21no—
324C4⋊Dic53C2412yes—
325C4⋊Dic53C2412yes—
326#11719919—22no—
327#11719919—22no—
328#11719919—22no—
329#11719919—22no—
330#11719919—22no—
331#11719919—22no—
332C4×Dic53—22no—
333C4×Dic53—22no—
334#11719917—42no—
335#11719917—42no—
336C2×#88322—44no—
337C2×#88322C2414yes—
338C2×#88322C2414yes—
339C23×C53—24no—
340C23×C53—22no—
341C23×C53—22no—
342C23×C53—22no—
343C23×C53—41no—
344C23×C53—41no—
345C23×C53—41no—
346C23×C53—41no—
347C23×C53—42no—
348C23×C53—42no—
349C23×C53C22×D411yescharacteristic
350C23×C53C22×D411yescharacteristic
351C23×C53C22×D412yes—
352C23×C53C22×D411yescharacteristic
353C22×D53—22no—
354C22×D53—42no—
355C22×D53—81no—
356C22×D53—81no—
357Q8×C53—22no—
358Q8×C53—24no—
359Q8×C53—22no—
360Q8×C53—42no—
361Q8×C53—42no—
362D4×C53—24no—
363D4×C53—22no—
364D4×C53—42no—
365D4×C53—42no—
366D4×C53—44no—
367D4×C53—48no—
368D4×C53—44no—
369D4×C53H(5,𝔽2)14yes—
370C2×C4×C53—22no—
371C2×C4×C53—22no—
372C2×C4×C53—22no—
373C2×C4×C53—24no—
374C2×C4×C53—22no—
375C2×C4×C53—22no—
376C2×C4×C53—22no—
377C2×C4×C53—22no—
378C2×C4×C53—41no—
379C2×C4×C53—41no—
380C2×C4×C53—41no—
381C2×C4×C53—42no—
382C2×C4×C53—41no—
383C2×C4×C53—41no—
384C2×C4×C53—44no—
385C2×C4×C53—48no—
386C2×C4×C53—44no—
387C2×C4×C53—48no—
388C2×C4×C53—42no—
389C2×C4×C53—42no—
390C2×C4×C53—42no—
391C2×C4×C53C22×D411yescharacteristic
392C2×C4×C53C22×D412yes—
393C2×C4×C53C22×D412yes—
394C2×C4×C53C22×D411yescharacteristic
395C2×C4×C53C22×D412yes—
396C2×C4×C53C22×D411yescharacteristic
397C2×C4×C53C2511yescharacteristic
398C22⋊D53—44no—
399C22⋊D53—44no—
400C22⋊D53—82no—
401C22⋊D53—82no—
402C2×Dic53—22no—
403C2×Dic53—22no—
404C2×Dic53—22no—
405C2×Dic53—42no—
406C2×Dic53—81no—
407C2×Dic53—81no—
408D212—24no—
409D212—81no—
410C4×D53—82no—
411C4×D53—82no—
412Dic106—24no—
413Dic106—81no—
414#88322—24no—
415#88322—24no—
416#61575—531nomaximal, Sylow
417C22×C53—21no—
418C22×C53—21no—
419C22×C53—21no—
420C22×C53—22no—
421C22×C53—21no—
422C22×C53—21no—
423C22×C53—22no—
424C22×C53—21no—
425C22×C53—24no—
426C22×C53—21no—
427C22×C53—21no—
428C22×C53—22no—
429C22×C53—48no—
430C22×C53—42no—
431C22×C53—42no—
432C22×C53—82no—
433C22×C53—82no—
434C22×C53#57512yes—
435C22×C53C23×D411yescharacteristic
436C2×D53—42no—
437C2×D53—42no—
438C2×D53—42no—
439C2×D53—162no—
440C4×C53—22no—
441C4×C53—21no—
442C4×C53—22no—
443C4×C53—21no—
444C4×C53—21no—
445C4×C53—22no—
446C4×C53—42no—
447C4×C53—42no—
448C4×C53—42no—
449C4×C53C2×H(5,𝔽2)12yes—
450Dic53—42no—
451Dic53—42no—
452Dic53—42no—
453#3505—531no—
454C2×#547D5311yescharacteristic, complemented
455#3315—534no—
456#3307—534no—
457#3269—534no—
458#3267—534no—
459#3218—532no—
460#3195—531no—
461#3193—531no—
462#3190—532no—
463#3114—532no—
464#3007—531no—
465#3006—531no—
466#3002—532no—
467#2973—531no—
468C2×C53—22no—
469C2×C53—41no—
470C2×C53—41no—
471C2×C53—42no—
472C2×C53—44no—
473C2×C53#348411yescharacteristic
474C2×C53C2×#57511yescharacteristic
475C2×C53#358611yescharacteristic
476D53—82no—
477C22×#41C2×D5311yescharacteristic
478C22×#41C2×D5311yescharacteristic, complemented
479C2×#137—532no—
480C2×AGL(1,ℤ/8)—532no—
481C2×#135—534no—
482#553—532no—
483#553—1062no—
484#552—532no—
485#551—1062no—
486#548—532no—
487#547—22no—
488#547—22no—
489#547C2×D5314yes—
490#547C2×D5314yescomplemented
491#546—532no—
492#539—1061no—
493#538—1061no—
494#534—1061no—
495C2×C4⋊Q8C2×D5311yescharacteristic, complemented
496#529—532no—
497#525—532no—
498C2×#123—21no—
499C2×#123—21no—
500C2×C22⋊Q8—531no—
501C2×C22⋊Q8C2×D5311yescharacteristic
502C2×C22⋊Q8C2×D5311yescharacteristic, complemented
503C2×#121—21no—
504C2×#121—531no—
505#518—1061no—
506C2×C4×D4C2×D5311yescharacteristic
507C2×C4×D4C2×D5311yescharacteristic, complemented
508C22×C4⋊C4—21no—
509#497—534no—
510#491—534no—
511#485—534no—
512#484—532no—
513#483—532no—
514#483—532no—
515#480—532no—
516#478—534no—
517#470—534no—
518#468—534no—
519#467—534no—
520#465—534no—
521#463—534no—
522#462—534no—
523#461—534no—
524#452—534no—
525#452—534no—
526#452—534no—
527#451—532no—
528#451—532no—
529#451—532no—
530#450—532no—
531#450—532no—
532#449—534no—
533#449—534no—
534#448—532no—
535#448—532no—
536#447—532no—
537#442—534no—
538#440—534no—
539#435—534no—
540#435—534no—
541#432—532no—
542#417—532no—
543#417—532no—
544#416—534no—
545#407—531no—
546#407—531no—
547C2×C22⋊C8—532no—
548C53#6157511yescharacteristic, complemented, Sylow
549C2×#41—21no—
550C2×#41—21no—
551C2×#41—22no—
552C2×#41—44no—
553C2×#41—44no—
554C2×#41—532no—
555C2×#41C22×D5312yes—
556C2×#41C22×D5314yes—
557C2×#41C22×D5312yes—
558C22×Q8—531no—
559C22×Q8C22×D5311yescharacteristic
560C22×Q8C22×D5311yescharacteristic
561C22×D4—21no—
562C22×D4—21no—
563C22×D4—531no—
564C22×D4—1061no—
565C22×D4C22⋊D5311yescharacteristic
566C22×D4C22×D5311yescharacteristic
567C23×C4—21no—
568C23×C4—21no—
569C23×C4—21no—
570C23×C4C22×D5311yescharacteristic
571C23×C4C22×D5311yescharacteristic
572#137—2124no—
573AGL(1,ℤ/8)—2124no—
574#135—2128no—
575C2×Q16—534no—
576C2×Q16—534no—
577C2×SD16—534no—
578C2×SD16—534no—
579C2×SD16—534no—
580C2×D8—534no—
581C2×M16—532no—
582C2×M16—532no—
583C22×C8—534no—
584C4⋊Q8—22no—
585C4⋊Q8C22×D5314yes—
586#126—1062no—
587#126—1062no—
588#126—1062no—
589#125—532no—
590#125—1062no—
591#124—532no—
592#124—1062no—
593#123—24no—
594#123—24no—
595#123—24no—
596#123—24no—
597#123—1062no—
598#123—1062no—
599#123—1062no—
600#123—1062no—
601#123—1062no—
602C22⋊Q8—21no—
603C22⋊Q8—21no—
604C22⋊Q8—22no—
605C22⋊Q8—532no—
606C22⋊Q8—532no—
607C22⋊Q8—532no—
608C22⋊Q8—1061no—
609C22⋊Q8—1061no—
610C22⋊Q8—1062no—
611C22⋊Q8C22×D5312yes—
612C22⋊Q8C22×D5312yes—
613C22⋊Q8C22×D5314yes—
614#121—24no—
615#121—24no—
616#121—532no—
617#121—532no—
618#121—532no—
619#121—1062no—
620#121—1062no—
621#121—1061no—
622#121—1061no—
623#121—1062no—
624#120—1062no—
625#120—1062no—
626C4×Q8—532no—
627C4×D4—22no—
628C4×D4—532no—
629C4×D4—1062no—
630C4×D4—1062no—
631C4×D4—1062no—
632C4×D4—1062no—
633C4×D4—1062no—
634C4×D4C22⋊D5312yes—
635C4×D4C22⋊D5312yes—
636C4×D4C22×D5314yes—
637C4×D4C22×D5312yes—
638C4×D4C22×D5312yes—
639#117—532no—
640#117—1062no—
641#117—1062no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—24no—
647C2×C4⋊C4—24no—
648C2×C4⋊C4—531no—
649C2×C4⋊C4—531no—
650C2×C4⋊C4—1061no—
651C2×C4⋊C4C22⋊D5311yescharacteristic
652C2×C4⋊C4C22×D5311yescharacteristic
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—1061no—
657C2×C22⋊C4—1061no—
658C2×C22⋊C4—1062no—
659C2×C22⋊C4C22⋊D5311yescharacteristic
660C2×C22⋊C4C22⋊D5311yescharacteristic
661C2×C42C22×D5311yescharacteristic
662#107—534no—
663#106—534no—
664C4⋊C8—534no—
665#103—534no—
666#103—534no—
667#103—534no—
668#103—534no—
669#103—534no—
670#102—534no—
671#102—534no—
672#102—534no—
673C22⋊C8—532no—
674C22⋊C8—532no—
675C22⋊C8—534no—
676C22⋊C8—532no—
677C22⋊C8—532no—
678#97—534no—
679C24—21no—
680C24—1061no—
681C24C2×C22⋊D5311yescharacteristic
682C24C2×C22⋊D5311yescharacteristic
683#41—28no—
684#41—24no—
685#41—24no—
686#41—44no—
687#41—42no—
688#41—42no—
689#41—44no—
690#41—44no—
691#41—48no—
692#41—2124no—
693C2×Q8—21no—
694C2×Q8—21no—
695C2×Q8—42no—
696C2×Q8—42no—
697C2×Q8—532no—
698C2×Q8—1061no—
699C2×Q8—2122no—
700C2×Q8C23×D5312yes—
701C2×Q8C23×D5312yes—
702C2×D4—24no—
703C2×D4—22no—
704C2×D4—24no—
705C2×D4—22no—
706C2×D4—21no—
707C2×D4—42no—
708C2×D4—44no—
709C2×D4—44no—
710C2×D4—532no—
711C2×D4—1062no—
712C2×D4—1062no—
713C2×D4—1062no—
714C2×D4—1062no—
715C2×D4—1061no—
716C2×D4—2122no—
717C2×D4—2124no—
718C2×D4C2×C22⋊D5312yes—
719C2×D4C2×C22⋊D5312yes—
720C2×D4C23×D5312yes—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—24no—
725C22×C4—24no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—42no—
729C22×C4—42no—
730C22×C4—44no—
731C22×C4—44no—
732C22×C4—44no—
733C22×C4—1061no—
734C22×C4—1061no—
735C22×C4—1061no—
736C22×C4—1062no—
737C22×C4—1062no—
738C22×C4C2×C22⋊D5311yescharacteristic
739C22×C4C2×C22⋊D5311yescharacteristic
740C22×C4C2×C22⋊D5311yescharacteristic
741C22×C4C2×C22⋊D5311yescharacteristic
742C22×C4C2×C22⋊D5311yescharacteristic
743C22×C4C2×C22⋊D5311yescharacteristic
744C22×C4C2×C22⋊D5312yes—
745C22×C4C23×D5311yescharacteristic
746C22×C4C23×D5311yescharacteristic
747C22×C4C23×D5311yescharacteristic
748C22×C4C23×D5312yes—
749Q16—2124no—
750Q16—2124no—
751SD16—1068no—
752SD16—2124no—
753SD16—2124no—
754D8—1068no—
755M16—2122no—
756M16—2122no—
757C2×C8—534no—
758C2×C8—534no—
759C2×C8—2124no—
760C4⋊C4—24no—
761C4⋊C4—24no—
762C4⋊C4—22no—
763C4⋊C4—22no—
764C4⋊C4—24no—
765C4⋊C4—21no—
766C4⋊C4—532no—
767C4⋊C4—532no—
768C4⋊C4—1061no—
769C4⋊C4—1061no—
770C4⋊C4—1062no—
771C4⋊C4—1062no—
772C4⋊C4—1062no—
773C4⋊C4—1062no—
774C4⋊C4—1062no—
775C4⋊C4—1062no—
776C4⋊C4C2×C22⋊D5312yes—
777C4⋊C4C2×C22⋊D5312yes—
778C4⋊C4C23×D5312yes—
779C22⋊C4—22no—
780C22⋊C4—24no—
781C22⋊C4—22no—
782C22⋊C4—24no—
783C22⋊C4—1062no—
784C22⋊C4—1062no—
785C22⋊C4—1062no—
786C22⋊C4—1062no—
787C22⋊C4—1062no—
788C22⋊C4—1062no—
789C22⋊C4—1062no—
790C22⋊C4—1062no—
791C22⋊C4—1062no—
792C22⋊C4—1062no—
793C22⋊C4C2×C22⋊D5312yes—
794C22⋊C4C2×C22⋊D5312yes—
795C22⋊C4C2×C22⋊D5312yes—
796C22⋊C4C2×C22⋊D5312yes—
797C42—1062no—
798C42—1062no—
799C42C2×C22⋊D5312yes—
800C42C23×D5312yes—
801C23—24no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—42no—
810C23—42no—
811C23—1062no—
812C23—4241no—
813C23—4241no—
814C23—2122no—
815C23C22×C22⋊D5311yescharacteristic
816C23C22×C22⋊D5312yes—
817C23C22×C22⋊D5311yescharacteristic
818C23C22×C22⋊D5311yescharacteristic
819Q8—22no—
820Q8—24no—
821Q8—22no—
822Q8—42no—
823Q8—42no—
824Q8—1064no—
825Q8—4241no—
826D4—24no—
827D4—22no—
828D4—42no—
829D4—42no—
830D4—44no—
831D4—48no—
832D4—44no—
833D4—1064no—
834D4—4241no—
835D4—4242no—
836D4—4242no—
837D4—2124no—
838D4—2124no—
839D4#1313326214yes—
840C2×C4—22no—
841C2×C4—24no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—42no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—48no—
855C2×C4—44no—
856C2×C4—44no—
857C2×C4—48no—
858C2×C4—42no—
859C2×C4—42no—
860C2×C4—42no—
861C2×C4—1062no—
862C2×C4—1062no—
863C2×C4—1062no—
864C2×C4—4242no—
865C2×C4—4242no—
866C2×C4—4241no—
867C2×C4—4241no—
868C2×C4—2122no—
869C2×C4C22×C22⋊D5312yes—
870C2×C4C22×C22⋊D5312yes—
871C2×C4C22×C22⋊D5311yescharacteristic
872C2×C4C22×C22⋊D5312yes—
873C2×C4C22×C22⋊D5311yescharacteristic
874C2×C4C22×C22⋊D5311yescharacteristic
875C2×C4C24×D5311yescharacteristic
876C8—1064no—
877C8—1064no—
878C22—21no—
879C22—21no—
880C22—21no—
881C22—22no—
882C22—21no—
883C22—24no—
884C22—21no—
885C22—21no—
886C22—22no—
887C22—21no—
888C22—22no—
889C22—21no—
890C22—48no—
891C22—42no—
892C22—42no—
893C22—82no—
894C22—82no—
895C22—8482no—
896C22—2122no—
897C22—2122no—
898C22—2122no—
899C22#1681142112yes—
900C22C23×C22⋊D5311yescharacteristic
901C4—22no—
902C4—21no—
903C4—21no—
904C4—21no—
905C4—22no—
906C4—22no—
907C4—42no—
908C4—42no—
909C4—42no—
910C4—2122no—
911C4—2122no—
912C4—2122no—
913C4C2×#1313326212yes—
914C2—22no—
915C2—41no—
916C2—41no—
917C2—42no—
918C2—44no—
919C2—4242no—
920C2#2028835011yescharacteristic
921C2C2×#1681142111yescharacteristic
922C2#2028950211yescharacteristic
subgroupG/H
centerC22C23×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#547C2
socleC22×C53C23×D4
hypercenterC2×#547D53
hypocenterC53#61575
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. #20288554C2semidirect
2. #20286811C2semidirect
3. #20286691C2semidirect
4. #20286266C2semidirect
5. #20286241C2semidirect
6. #20285742C2semidirect
7. #20285536C2semidirect
8. #20285517C2semidirect
9. #20285496C2semidirect
10. #20284853C2semidirect
11. #20283975C2semidirect
12. #20283967C2semidirect
13. #20283933C2semidirect
14. #20283744C2semidirect
15. C2×C53×#547C2semidirect
16. C2×#13133247C22semidirect
17. C2×#13133242C22semidirect
18. C2×#13133237C22semidirect
20. #16811319C22semidirect
21. #16811313C22semidirect
23. #16811282C22semidirect
24. #16811269C22semidirect
33. #16811015C22semidirect
34. #16810991C22semidirect
35. #16810961C22semidirect
36. #16810956C22semidirect
37. #16810953C22semidirect
38. #16810951C22semidirect
40. #16810923C22semidirect
41. #16810879C22semidirect
42. #16810871C22semidirect
43. #16810862C22semidirect
44. #16810854C22semidirect
45. #16810838C22semidirect
46. #16810830C22semidirect
47. #16810825C22semidirect
48. #16810785C22semidirect
49. #16810785C22semidirect
50. #16810783C22semidirect
51. #16810779C22semidirect
52. #16810779C22semidirect
53. #16810778C22semidirect
54. #16810774C22semidirect
55. #16810773C22semidirect
56. #16810768C22semidirect
57. #16810768C22semidirect
61. #16810733C22semidirect
62. #16810723C22semidirect
63. #16810695C22semidirect
64. #16810695C22semidirect
65. #16810680C22semidirect
66. #16810624C22semidirect
67. #16810624C22semidirect
68. #16810619C22semidirect
71. C2×C22⋊#88322C22semidirect
73. C22×#41×C53C22semidirect
77. C53×#547C22semidirect
78. C2×C4⋊Q8×C53C22semidirect
82. C2×C22⋊Q8×C53C22semidirect
85. C2×C4×D4×C53C22semidirect
454. C2×#547D53semidirect
478. C22×#41C2×D53semidirect
490. #547C2×D53semidirect
495. C2×C4⋊Q8C2×D53semidirect
502. C2×C22⋊Q8C2×D53semidirect
507. C2×C4×D4C2×D53semidirect
548. C53#61575semidirect

Maximal subgroups

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

subgroupindex
#202885542
#202868112
#202866912
#202862662
#202862412
#202857422
#202855362
#202855172
#202854962
#202848532
#202839752
#202839672
#202839332
#202837442
C2×C53×#5472
#6157553