Finite Group Databasebeta

← #27395509

Subgroups — #27395509

Order 13568.

900 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20283931C211yesmaximal, characteristic
2#20283159C211yesmaximal, characteristic, complemented
3#20275607C211yesmaximal, characteristic, complemented
4#20275602C211yesmaximal, characteristic, complemented
5#20275425C211yesmaximal, characteristic, complemented
6#20275418C211yesmaximal, characteristic, complemented
7#20275363C211yesmaximal, characteristic, complemented
8#20275363C211yesmaximal, characteristic, complemented
9#20275042C211yesmaximal, characteristic, complemented
10#20275042C211yesmaximal, characteristic, complemented
11#20275018C211yesmaximal, characteristic, complemented
12#20274919C211yesmaximal, characteristic, complemented
13#20274658C211yesmaximal, characteristic, complemented
14#20274496C211yesmaximal, characteristic, complemented
15C53×#2930C211yesmaximal, characteristic, complemented
16C22×#11719945C2211yescharacteristic
17C2×#13133237C2211yescharacteristic
18C2×#13133237C2211yescharacteristic
19C22×#11719917C2211yescharacteristic
20#16810783C411yescharacteristic, complemented
21#16810783C411yescharacteristic, complemented
22#16810778C411yescharacteristic, complemented
23#16810773C411yescharacteristic, complemented
24#16810766C411yescharacteristic, complemented
25#16810766C411yescharacteristic, complemented
26#16810761C411yescharacteristic, complemented
27#16810756C411yescharacteristic, complemented
28C2×#13133152C2211yescharacteristic, complemented
29C2×#13133152C2211yescharacteristic, complemented
30C2×#13133144C2211yescharacteristic, complemented
31C2×#13133144C2211yescharacteristic, complemented
32C2×#13133143C2211yescharacteristic
33C2×#13133143C2211yescharacteristic
34C2×#13133143C2211yescharacteristic
35C2×#13133143C2211yescharacteristic
36#16810617C2211yescharacteristic
37#16810617C2211yescharacteristic
38#16810591—21no—
39#16810591—21no—
40#16810589C2211yescharacteristic
41#16810589C2211yescharacteristic
42#16810589C2211yescharacteristic
43#16810589C2211yescharacteristic
44#16810586—21no—
45#16810586—21no—
46C2×C22⋊#88322C2211yescharacteristic
47C2×#13133127C2211yescharacteristic, complemented
48C2×C8×Dic53C2211yescharacteristic, complemented
49C4×C22⋊Dic53C2211yescharacteristic
50#16810387C2211yescharacteristic, complemented
51#16810387C2211yescharacteristic, complemented
52#16810382C2211yescharacteristic, complemented
53#16810382C2211yescharacteristic, complemented
54#16810377C2211yescharacteristic, complemented
55#16810377C2211yescharacteristic, complemented
56C2×#131×C53C2211yescharacteristic, complemented
57C22×M16×C53C2211yescharacteristic
58C53×#525C2211yescharacteristic
59C53×#436—21no—
60C53×#436—21no—
61C53×#435—21no—
62C53×#435—21no—
63C53×#424C2211yescharacteristic, complemented
64C53×#408C2211yescharacteristic, complemented
65C53×#407C2211yescharacteristic
66C53×#405C2211yescharacteristic, complemented
67C2×#11719945—21no—
68C2×#11719945—21no—
69C2×#11719945—41no—
70C2×#11719945—41no—
71C2×#11719945—41no—
72C2×#11719945—41no—
73C2×#11719945C2×C411yescharacteristic
74C2×#11719945C2×C411yescharacteristic
75C2×#11719945C2311yescharacteristic
76C2×#11719945C2311yescharacteristic
77C22×Dic106C2×C411yescharacteristic
78C22×D212C2×C411yescharacteristic
79C22×C22⋊D53—21no—
80C22×C4×D53—21no—
81#13133237—41no—
82#13133237—41no—
83#13133237—41no—
84#13133237—41no—
85C2×#11719925C2×C411yescharacteristic
86C2×#11719925C2×C411yescharacteristic
87C2×#11719923C2×C411yescharacteristic
88C2×#11719923C2×C411yescharacteristic
89C2×#11719924C2×C411yescharacteristic
90C2×#11719924C2×C411yescharacteristic
91C2×#11719922C2×C411yescharacteristic
92C2×#11719922C2×C411yescharacteristic
93C2×#11719917—21no—
94C2×#11719917—41no—
95C2×#11719917—41no—
96C2×#11719917C2311yescharacteristic
97C2×#11719917C2311yescharacteristic
98C22×#88322—21no—
99C22×#88322C2311yescharacteristic
100C22×#88322C2311yescharacteristic
101C2×C22⋊Dic53—21no—
102C2×C4×Dic53C2311yescharacteristic
103C2×C4×Dic53C2311yescharacteristic
104#13133152—41no—
105#13133152—41no—
106#13133144—41no—
107#13133144—41no—
108#13133143—41no—
109#13133143—41no—
110#13133143—41no—
111#13133143—41no—
112#13133140C2×C411yescharacteristic
113#13133140C2×C411yescharacteristic
114#13133140C2×C411yescharacteristic
115#13133140C2×C411yescharacteristic
116#13133137C2×C411yescharacteristic
117#13133137C2×C411yescharacteristic
118#13133137C2×C411yescharacteristic
119#13133137C2×C411yescharacteristic
120C22⋊#88322C2×C411yescharacteristic
121C22⋊#88322C2×C411yescharacteristic
122C22⋊#88322C2×C411yescharacteristic
123C22⋊#88322C2×C411yescharacteristic
124#13133129—21no—
125#13133129—21no—
126#13133129—21no—
127#13133129—21no—
128#13133129—21no—
129#13133129—21no—
130#13133129—21no—
131#13133129—21no—
132#13133127—41no—
133C8×Dic53—41no—
134#13133124—21no—
135C2×#41×C53C2311yescharacteristic
136C23×C4×C53C2311yescharacteristic
137#131×C53—41no—
138#131×C53—41no—
139C2×M16×C53—21no—
140C2×M16×C53—41no—
141C2×M16×C53—41no—
142C2×M16×C53D411yescharacteristic
143C2×M16×C53D411yescharacteristic
144C2×M16×C53D411yescharacteristic
145C2×M16×C53D411yescharacteristic
146C2×M16×C53C2311yescharacteristic
147C2×M16×C53C2311yescharacteristic
148C22×C8×C53—21no—
149C22×C8×C53C2311yescharacteristic
150C22×C8×C53C2311yescharacteristic
151#123×C53—21no—
152C22⋊Q8×C53C2×C411yescharacteristic
153C22⋊Q8×C53C2×C411yescharacteristic
154#121×C53C2×C411yescharacteristic
155#121×C53C2×C411yescharacteristic
156#120×C53—21no—
157C4×D4×C53—21no—
158C4×D4×C53—21no—
159#117×C53C2311yescharacteristic
160C4⋊C8×C53—21no—
161C4⋊C8×C53—21no—
162C22⋊C8×C53—21no—
163C22⋊C8×C53—21no—
164C22⋊C8×C53—21no—
165C22⋊C8×C53—21no—
166#97×C53—21no—
167C4×C8×C53—21no—
168C24×C53#4111yescharacteristic
169C23×D53—21no—
170#41×C53—21no—
171#41×C53—21no—
172#41×C53—21no—
173#41×C53—21no—
174C2×Q8×C53C22×C411yescharacteristic
175C2×D4×C53—21no—
176C2×D4×C53—21no—
177C2×D4×C53—21no—
178C2×D4×C53C22×C411yescharacteristic
179C22×C4×C53—21no—
180C22×C4×C53—21no—
181C22×C4×C53—21no—
182C22×C4×C53—21no—
183C22×C4×C53—21no—
184C22×C4×C53C22×C411yescharacteristic
185C22×C4×C53C22×C411yescharacteristic
186C22×C4×C53C2×D411yescharacteristic
187C22×C4×C53C2×D411yescharacteristic
188C22×C4×C53#4111yescharacteristic
189C22×C4×C53C2411yescharacteristic
190C2×C22⋊D53—21no—
191C2×C22⋊D53—21no—
192C2×C22⋊D53—21no—
193C2×C22⋊D53—21no—
194C2×C22⋊D53—42no—
195C2×C22⋊D53—42no—
196C22×Dic53—21no—
197C22×Dic53—21no—
198C22×Dic53—21no—
199#11719945—21no—
200#11719945—21no—
201#11719945—21no—
202#11719945—21no—
203#11719945—21no—
204#11719945—21no—
205#11719945—21no—
206#11719945—21no—
207#11719945—41no—
208#11719945—41no—
209#11719945—41no—
210#11719945—41no—
211#11719945—42no—
212#11719945—42no—
213#11719945—42no—
214#11719945—42no—
215C2×D212—21no—
216C2×D212—41no—
217C2×D212—41no—
218C2×D212C22×C411yescharacteristic
219C2×D212C22×C411yescharacteristic
220C2×C4×D53—21no—
221C2×C4×D53—21no—
222C2×C4×D53—21no—
223C2×C4×D53—21no—
224C2×C4×D53—42no—
225C2×C4×D53—42no—
226C2×Dic106—21no—
227C2×Dic106—41no—
228C2×Dic106—41no—
229C2×Dic106C22×C411yescharacteristic
230C2×Dic106C22×C411yescharacteristic
231M16×C53—21no—
232M16×C53—21no—
233M16×C53—21no—
234M16×C53—21no—
235M16×C53—41no—
236M16×C53—41no—
237M16×C53—41no—
238M16×C53—41no—
239M16×C53—42no—
240C2×C8×C53—21no—
241C2×C8×C53—21no—
242C2×C8×C53—21no—
243C2×C8×C53—21no—
244C2×C8×C53—21no—
245C2×C8×C53—21no—
246C2×C8×C53—42no—
247C2×C8×C53C2×D411yescharacteristic
248C2×C8×C53C2×D411yescharacteristic
249C2×C8×C53C2×D411yescharacteristic
250C2×C8×C53C2×D411yescharacteristic
251C4⋊C4×C53—21no—
252C4⋊C4×C53—21no—
253C4⋊C4×C53C22×C411yescharacteristic
254C4⋊C4×C53C22×C411yescharacteristic
255C22⋊C4×C53—21no—
256C22⋊C4×C53—21no—
257C22⋊C4×C53—21no—
258C22⋊C4×C53—21no—
259C22⋊C4×C53—21no—
260C42×C53—21no—
261C22⋊Dic53—42no—
262#11719925—41no—
263#11719925—41no—
264#11719924—41no—
265#11719924—41no—
266#11719923—41no—
267#11719923—41no—
268#11719922—41no—
269#11719922—41no—
270C4×Dic53—21no—
271C4×Dic53—21no—
272C4×Dic53—21no—
273C4×Dic53—21no—
274#11719917—21no—
275#11719917—21no—
276#11719917—21no—
277#11719917—21no—
278#11719917—42no—
279C2×#88322—21no—
280C2×#88322—21no—
281C2×#88322—21no—
282C2×#88322—21no—
283C2×#88322—21no—
284C2×#88322—21no—
285C2×#88322—42no—
286C2×#88322C22×C411yescharacteristic
287C2×#88322C22×C411yescharacteristic
288C2×#88322C22×C411yescharacteristic
289C2×#88322C22×C411yescharacteristic
290C23×C53—21no—
291C23×C53—21no—
292C23×C53—21no—
293C23×C53—41no—
294C23×C53—41no—
295C23×C53C4×D411yescharacteristic
296C23×C53C4×D411yescharacteristic
297C23×C53C2×#4111yescharacteristic
298C22×D53—21no—
299C22×D53—21no—
300C22×D53—42no—
301C22×D53—81no—
302C22×D53—81no—
303Q8×C53—21no—
304Q8×C53—21no—
305D4×C53—21no—
306D4×C53—21no—
307D4×C53—41no—
308D4×C53—41no—
309D4×C53—81no—
310D4×C53—81no—
311C2×C4×C53—21no—
312C2×C4×C53—21no—
313C2×C4×C53—21no—
314C2×C4×C53—21no—
315C2×C4×C53—21no—
316C2×C4×C53—21no—
317C2×C4×C53—21no—
318C2×C4×C53—21no—
319C2×C4×C53—21no—
320C2×C4×C53—21no—
321C2×C4×C53—21no—
322C2×C4×C53—21no—
323C2×C4×C53—21no—
324C2×C4×C53—41no—
325C2×C4×C53—41no—
326C2×C4×C53C4×D411yescharacteristic
327C2×C4×C53C4×D411yescharacteristic
328C2×C4×C53C23×C411yescharacteristic
329C2×C4×C53C22×D411yescharacteristic
330C2×C4×C53H(5,𝔽2)11yescharacteristic
331C2×C4×C53H(5,𝔽2)11yescharacteristic
332C2×C4×C53H(5,𝔽2)11yescharacteristic
333C2×C4×C53H(5,𝔽2)11yescharacteristic
334C22⋊D53—42no—
335C22⋊D53—42no—
336C22⋊D53—41no—
337C22⋊D53—41no—
338C22⋊D53—41no—
339C22⋊D53—41no—
340C2×Dic53—22no—
341C2×Dic53—21no—
342C2×Dic53—21no—
343C2×Dic53—42no—
344C2×Dic53—41no—
345C2×Dic53—41no—
346C2×Dic53—41no—
347C2×Dic53—41no—
348C2×Dic53—41no—
349D212—21no—
350D212—21no—
351D212—21no—
352D212—21no—
353D212—42no—
354C4×D53—42no—
355C4×D53—42no—
356C4×D53—41no—
357C4×D53—41no—
358C4×D53—41no—
359C4×D53—41no—
360Dic106—21no—
361Dic106—21no—
362Dic106—21no—
363Dic106—21no—
364Dic106—42no—
365C8×C53—21no—
366C8×C53—21no—
367C8×C53—21no—
368C8×C53—21no—
369C8×C53—41no—
370C8×C53—41no—
371#88322—21no—
372#88322—21no—
373#88322—21no—
374#88322—21no—
375#88322—41no—
376#88322—41no—
377#22062—531nomaximal, Sylow
378C22×C53—21no—
379C22×C53—21no—
380C22×C53—21no—
381C22×C53—21no—
382C22×C53—21no—
383C22×C53—21no—
384C22×C53—21no—
385C22×C53—21no—
386C22×C53—41no—
387C22×C53—41no—
388C22×C53—41no—
389C22×C53—81no—
390C22×C53—81no—
391C22×C53C2×C4×D411yescharacteristic
392C22×C53#53811yescharacteristic
393C22×C53#53811yescharacteristic
394C2×D53—41no—
395C2×D53—41no—
396C2×D53—41no—
397C2×D53—41no—
398C2×D53—41no—
399C2×D53—41no—
400C2×D53—84no—
401C4×C53—21no—
402C4×C53—21no—
403C4×C53—41no—
404C4×C53—41no—
405C4×C53—41no—
406C4×C53#51811yescharacteristic
407C4×C53#51811yescharacteristic
408C4×C53#53411yescharacteristic
409C4×C53#53511yescharacteristic
410Dic53—42no—
411Dic53—41no—
412Dic53—41no—
413Dic53—81no—
414#3002—531no—
415#2930D5311yescharacteristic, complemented
416#2879—531no—
417#1975—531no—
418#1974—531no—
419#1938—531no—
420#1937—531no—
421#1929—531no—
422#1929—531no—
423#1876—531no—
424#1876—531no—
425#1871—531no—
426#1855—531no—
427#1789—531no—
428#1753—531no—
429C2×C53—21no—
430C2×C53—21no—
431C2×C53—41no—
432C2×C53—41no—
433C2×C53—81no—
434C2×C53#232111yescharacteristic
435C2×C53#295611yescharacteristic
436C2×C53#295711yescharacteristic
437D53—81no—
438D53—81no—
439C22×#41—531no—
440C2×#135—531no—
441C2×#135—531no—
442C2×#131C2×D5311yescharacteristic, complemented
443C22×M16—531no—
444C22×M16C2×D5311yescharacteristic
445#525C2×D5311yescharacteristic
446#452—531no—
447#452—531no—
448#451—531no—
449#450—531no—
450#449—531no—
451#449—531no—
452#448—531no—
453#447—531no—
454#436—21no—
455#436—21no—
456#435—21no—
457#435—21no—
458C2×#108—531no—
459C2×#108—531no—
460#424C2×D5311yescharacteristic, complemented
461C2×#104—531no—
462C2×#104—531no—
463C2×#104—531no—
464C2×#104—531no—
465C2×#104—531no—
466C2×#104—531no—
467#416—531no—
468#416—531no—
469#408—531no—
470#408—531no—
471#408—531no—
472#408—531no—
473#408—1061no—
474#408—1061no—
475#408C2×D5311yescharacteristic, complemented
476#407—1061no—
477#407—1061no—
478#407C2×D5311yescharacteristic
479C2×C22⋊C8—531no—
480#405C2×D5311yescharacteristic, complemented
481C2×#97—531no—
482C2×C4×C8—531no—
483C4×C22⋊C4—531no—
484#341—531no—
485#341—531no—
486#339—531no—
487#339—531no—
488#336—531no—
489#336—531no—
490C53#2206211yescharacteristic, complemented, Sylow
491C2×#41—531no—
492C2×#41—531no—
493C2×#41—531no—
494C2×#41—531no—
495C2×#41—1061no—
496C2×#41—1061no—
497C2×#41—2121no—
498C2×#41—2121no—
499C2×#41—2121no—
500C2×#41—2121no—
501C2×#41C22×D5311yescharacteristic
502C22×Q8—531no—
503C22×D4—531no—
504C22×D4—1061no—
505C23×C4—1061no—
506C23×C4C22×D5311yescharacteristic
507#135—2121no—
508#135—2121no—
509#135—2121no—
510#135—2121no—
511C2×Q16—531no—
512C2×Q16—531no—
513C2×SD16—531no—
514C2×SD16—531no—
515C2×SD16—531no—
516C2×SD16—531no—
517C2×D8—531no—
518C2×D8—531no—
519#131—41no—
520#131—41no—
521C2×M16—21no—
522C2×M16—41no—
523C2×M16—41no—
524C2×M16—531no—
525C2×M16—531no—
526C2×M16—1061no—
527C2×M16—2121no—
528C2×M16—2121no—
529C2×M16C22⋊D5311yescharacteristic
530C2×M16C22⋊D5311yescharacteristic
531C2×M16C22⋊D5311yescharacteristic
532C2×M16C22⋊D5311yescharacteristic
533C2×M16C22×D5311yescharacteristic
534C2×M16C22×D5311yescharacteristic
535C22×C8—21no—
536C22×C8—531no—
537C22×C8—531no—
538C22×C8—1061no—
539C22×C8C22×D5311yescharacteristic
540C22×C8C22×D5311yescharacteristic
541#123—21no—
542C22⋊Q8C4×D5311yescharacteristic
543C22⋊Q8C4×D5311yescharacteristic
544#121C4×D5311yescharacteristic
545#121C4×D5311yescharacteristic
546#120—21no—
547C4×D4—21no—
548C4×D4—21no—
549#117C22×D5311yescharacteristic
550C2×C22⋊C4—1061no—
551C2×C42—531no—
552C2×C42—531no—
553#108—2121no—
554#108—2121no—
555C4⋊C8—21no—
556C4⋊C8—21no—
557#104—2121no—
558#104—2121no—
559#104—2121no—
560#104—2121no—
561#104—2121no—
562#104—2121no—
563#103—531no—
564#103—531no—
565#103—531no—
566#103—531no—
567#102—531no—
568#102—531no—
569#102—531no—
570#102—531no—
571C22⋊C8—21no—
572C22⋊C8—21no—
573C22⋊C8—21no—
574C22⋊C8—21no—
575C22⋊C8—531no—
576C22⋊C8—531no—
577C22⋊C8—531no—
578C22⋊C8—531no—
579C22⋊C8—1061no—
580C22⋊C8—1061no—
581C22⋊C8—1061no—
582C22⋊C8—1061no—
583C22⋊C8—1061no—
584C22⋊C8—1061no—
585C22⋊C8—1061no—
586C22⋊C8—1061no—
587#97—21no—
588#97—2121no—
589C4×C8—21no—
590C4×C8—2121no—
591#95—1061no—
592C24—1061no—
593C24#1171994511yescharacteristic
594#41—21no—
595#41—21no—
596#41—21no—
597#41—21no—
598#41—1061no—
599#41—1061no—
600#41—1061no—
601#41—1061no—
602#41—1061no—
603#41—1061no—
604#41—1061no—
605#41—1061no—
606#41—2121no—
607#41—2121no—
608#41—2121no—
609#41—2121no—
610#41—2122no—
611#41—2122no—
612#41—2122no—
613#41—2122no—
614C2×Q8—531no—
615C2×Q8—531no—
616C2×Q8—1061no—
617C2×Q8—2121no—
618C2×Q8—2121no—
619C2×Q8C2×C4×D5311yescharacteristic
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—531no—
624C2×D4—531no—
625C2×D4—1061no—
626C2×D4—1061no—
627C2×D4—1061no—
628C2×D4—1061no—
629C2×D4—1061no—
630C2×D4—2121no—
631C2×D4—2121no—
632C2×D4—2122no—
633C2×D4—2122no—
634C2×D4C2×C4×D5311yescharacteristic
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—1061no—
641C22×C4—1061no—
642C22×C4—1061no—
643C22×C4—1061no—
644C22×C4—1061no—
645C22×C4—1061no—
646C22×C4—1061no—
647C22×C4—2122no—
648C22×C4—2122no—
649C22×C4C2×C4×D5311yescharacteristic
650C22×C4C2×C4×D5311yescharacteristic
651C22×C4#1171994511yescharacteristic
652C22×C4C2×C22⋊D5311yescharacteristic
653C22×C4C2×C22⋊D5311yescharacteristic
654C22×C4C23×D5311yescharacteristic
655Q16—2121no—
656Q16—2121no—
657SD16—2121no—
658SD16—2121no—
659SD16—2121no—
660SD16—2121no—
661D8—2121no—
662D8—2121no—
663M16—21no—
664M16—21no—
665M16—21no—
666M16—21no—
667M16—41no—
668M16—41no—
669M16—41no—
670M16—41no—
671M16—42no—
672M16—1061no—
673M16—1061no—
674M16—1061no—
675M16—1061no—
676M16—2122no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—42no—
684C2×C8—531no—
685C2×C8—531no—
686C2×C8—531no—
687C2×C8—531no—
688C2×C8—1061no—
689C2×C8—1061no—
690C2×C8—1061no—
691C2×C8—1061no—
692C2×C8—1061no—
693C2×C8—1061no—
694C2×C8—2122no—
695C2×C8C2×C22⋊D5311yescharacteristic
696C2×C8C2×C22⋊D5311yescharacteristic
697C2×C8C2×C22⋊D5311yescharacteristic
698C2×C8C2×C22⋊D5311yescharacteristic
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4C2×C4×D5311yescharacteristic
702C4⋊C4C2×C4×D5311yescharacteristic
703C22⋊C4—21no—
704C22⋊C4—21no—
705C22⋊C4—21no—
706C22⋊C4—21no—
707C22⋊C4—21no—
708C22⋊C4—2122no—
709C42—21no—
710C42—1061no—
711C42—1061no—
712C42—1061no—
713C42—1061no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—41no—
718C23—41no—
719C23—1061no—
720C23—1061no—
721C23—4241no—
722C23—4241no—
723C23—2122no—
724C23C4×C22⋊D5311yescharacteristic
725C23C4×C22⋊D5311yescharacteristic
726C23C2×#1171994511yescharacteristic
727Q8—21no—
728Q8—21no—
729Q8—1061no—
730Q8—1061no—
731Q8—1061no—
732Q8—1061no—
733Q8—2122no—
734D4—21no—
735D4—21no—
736D4—41no—
737D4—41no—
738D4—81no—
739D4—81no—
740D4—1061no—
741D4—1061no—
742D4—1061no—
743D4—1061no—
744D4—2122no—
745D4—2122no—
746D4—2122no—
747D4—2121no—
748D4—2121no—
749D4—2121no—
750D4—2121no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—1062no—
767C2×C4—1061no—
768C2×C4—1061no—
769C2×C4—2122no—
770C2×C4—2122no—
771C2×C4—2121no—
772C2×C4—2121no—
773C2×C4—2121no—
774C2×C4—2121no—
775C2×C4—2122no—
776C2×C4—2121no—
777C2×C4—2121no—
778C2×C4—2121no—
779C2×C4—2121no—
780C2×C4—2121no—
781C2×C4C4×C22⋊D5311yescharacteristic
782C2×C4C4×C22⋊D5311yescharacteristic
783C2×C4C22×C4×D5311yescharacteristic
784C2×C4C22×C22⋊D5311yescharacteristic
785C2×C4#1313326211yescharacteristic
786C2×C4#1313326211yescharacteristic
787C2×C4#1313326311yescharacteristic
788C2×C4#1313326311yescharacteristic
789C8—21no—
790C8—21no—
791C8—21no—
792C8—21no—
793C8—41no—
794C8—41no—
795C8—1061no—
796C8—1061no—
797C8—1061no—
798C8—1061no—
799C8—2121no—
800C8—2121no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—21no—
806C22—21no—
807C22—21no—
808C22—21no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—81no—
813C22—81no—
814C22—4244no—
815C22—2121no—
816C22—2121no—
817C22—2121no—
818C22—2121no—
819C22—2121no—
820C22—2121no—
821C22C2×C4×C22⋊D5311yescharacteristic
822C22#1681120611yescharacteristic
823C22#1681120611yescharacteristic
824C4—21no—
825C4—21no—
826C4—41no—
827C4—41no—
828C4—41no—
829C4—4241no—
830C4—2122no—
831C4—2121no—
832C4—2121no—
833C4#1681109511yescharacteristic
834C4#1681109511yescharacteristic
835C4#1681118211yescharacteristic
836C4#1681118711yescharacteristic
837C2—21no—
838C2—21no—
839C2—41no—
840C2—41no—
841C2—81no—
842C2—4241no—
843C2—4241no—
844C2#2027736911yescharacteristic
845C2#2028362211yescharacteristic
846C2#2028363011yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#2930C2
socleC22×C53C2×C4×D4
prime radical#20283931C2
cosocleC22×C4×C53C24
hypercenter#2930D53
hypocenterC53#22062
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C22×M16 ◁ #2930

Complements

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

NH ≅ G/Ntype
2. #20283159C2semidirect
3. #20275607C2semidirect
4. #20275602C2semidirect
5. #20275425C2semidirect
6. #20275418C2semidirect
7. #20275363C2semidirect
8. #20275363C2semidirect
9. #20275042C2semidirect
10. #20275042C2semidirect
11. #20275018C2semidirect
12. #20274919C2semidirect
13. #20274658C2semidirect
14. #20274496C2semidirect
15. C53×#2930C2semidirect
20. #16810783C4semidirect
21. #16810783C4semidirect
22. #16810778C4semidirect
23. #16810773C4semidirect
24. #16810766C4semidirect
25. #16810766C4semidirect
26. #16810761C4semidirect
27. #16810756C4semidirect
28. C2×#13133152C22semidirect
29. C2×#13133152C22semidirect
30. C2×#13133144C22semidirect
31. C2×#13133144C22semidirect
47. C2×#13133127C22semidirect
48. C2×C8×Dic53C22semidirect
50. #16810387C22semidirect
51. #16810387C22semidirect
52. #16810382C22semidirect
53. #16810382C22semidirect
54. #16810377C22semidirect
55. #16810377C22semidirect
56. C2×#131×C53C22semidirect
63. C53×#424C22semidirect
64. C53×#408C22semidirect
66. C53×#405C22semidirect
415. #2930D53semidirect
442. C2×#131C2×D53semidirect
460. #424C2×D53semidirect
475. #408C2×D53semidirect
480. #405C2×D53semidirect
490. C53#22062semidirect

Maximal subgroups

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

subgroupindex
#202839312
#202831592
#202756072
#202756022
#202754252
#202754182
#202753632
#202750422
#202750182
#202749192
#202746582
#202744962
C53×#29302
#2206253