Finite Group Databasebeta

← #27352347

Subgroups — #27352347

Order 13568.

898 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288637C211yesmaximal, characteristic
2#20283729C211yesmaximal, characteristic, complemented
3#20273347C211yesmaximal, characteristic, complemented
4#20273344C211yesmaximal, characteristic, complemented
5#20273341C211yesmaximal, characteristic, complemented
6#20273336C211yesmaximal, characteristic, complemented
7#20273333C211yesmaximal, characteristic, complemented
8#20273327C211yesmaximal, characteristic, complemented
9#20273325C211yesmaximal, characteristic, complemented
10#20273323C211yesmaximal, characteristic, complemented
11#20273320C211yesmaximal, characteristic, complemented
12#20273304C211yesmaximal, characteristic, complemented
13#20273301C211yesmaximal, characteristic, complemented
14C2×#16810364C211yesmaximal, characteristic, complemented
15C53×#2970C211yesmaximal, characteristic, complemented
16#16811323—21no—
17#16811323—21no—
18#16811322—21no—
19#16811322—21no—
20#16811322—21no—
21#16811322—21no—
22#16811314—21no—
23#16811314—21no—
24#16811235C411yescharacteristic
25#16811235C411yescharacteristic
26#16811228C411yescharacteristic
27#16811228C411yescharacteristic
28#16811201C411yescharacteristic
29#16811201C411yescharacteristic
30#16811173C2211yescharacteristic
31#16811157C2211yescharacteristic
32#16811157C2211yescharacteristic
33#16811157C2211yescharacteristic
34#16811157C2211yescharacteristic
35C2×#13133209C2211yescharacteristic
36#16811103C411yescharacteristic
37#16811103C411yescharacteristic
38#16810754—21no—
39#16810695—21no—
40#16810695—21no—
41D4×#88322—21no—
42#16810680C2211yescharacteristic
43#16810680C2211yescharacteristic
44#16810680C2211yescharacteristic
45C4×#11719917C2211yescharacteristic
46C2×#13133128C2211yescharacteristic
47C2×#13133128C2211yescharacteristic
48#16810364C2211yescharacteristic
49#16810364C2211yescharacteristic
50#16810364C2211yescharacteristic
51#16810364C2211yescharacteristic
52#16810364C2211yescharacteristic
53#16810364C2211yescharacteristic
54#16810364C2211yescharacteristic
55#16810364C2211yescharacteristic
56#16810362C2211yescharacteristic
57#16810362C2211yescharacteristic
58#16810362C2211yescharacteristic
59#16810362C2211yescharacteristic
60#16810362C2211yescharacteristic
61#16810362C2211yescharacteristic
62#16810362C2211yescharacteristic
63#16810362C2211yescharacteristic
64C4×#41×C53C2211yescharacteristic
65C53×#446—21no—
66C53×#435—21no—
67C53×#435—21no—
68C8×D4×C53—21no—
69C53×#432C2211yescharacteristic
70C53×#432C2211yescharacteristic
71C53×#432C2211yescharacteristic
72C4×M16×C53C2211yescharacteristic
73C2×#97×C53C2211yescharacteristic
74C2×#97×C53C2211yescharacteristic
75C2×#11719945C2×C411yescharacteristic
76C2×#11719945C2×C411yescharacteristic
77C2×#11719917—21no—
78C22×#88322—21no—
79C22×#88322—21no—
80#13133217C2×C411yescharacteristic
81#13133214C2×C411yescharacteristic
82#13133211—21no—
83#13133211—21no—
84#13133211—21no—
85#13133211—21no—
86#13133210—21no—
87#13133210—21no—
88#13133210—21no—
89#13133210—21no—
90#13133209—21no—
91#13133209—21no—
92#13133209C2×C411yescharacteristic
93#13133209C2×C411yescharacteristic
94#13133209C2311yescharacteristic
95#13133209C2311yescharacteristic
96#13133207—21no—
97#13133207—21no—
98#13133207—21no—
99#13133207—21no—
100#13133205C2311yescharacteristic
101#13133205C2311yescharacteristic
102#13133202—21no—
103#13133202—21no—
104#13133202—21no—
105#13133202—21no—
106#13133200—21no—
107#13133200—21no—
108#13133200—21no—
109#13133200—21no—
110#13133196C2×C411yescharacteristic
111#13133196C2×C411yescharacteristic
112#13133196C2×C411yescharacteristic
113#13133196C2×C411yescharacteristic
114#13133193—21no—
115#13133193—21no—
116#13133191—21no—
117#13133191—21no—
118#13133191C2×C411yescharacteristic
119#13133191C2×C411yescharacteristic
120#13133191C2×C411yescharacteristic
121#13133191C2×C411yescharacteristic
122#13133190—21no—
123#13133190—21no—
124#13133190—21no—
125#13133190—21no—
126#13133189—21no—
127#13133189—21no—
128#13133189—21no—
129#13133189—21no—
130#13133188—21no—
131#13133188—21no—
132C4×Dic106C2×C411yescharacteristic
133C4×Dic106C2×C411yescharacteristic
134C4×Dic106C2×C411yescharacteristic
135C4×Dic106C2×C411yescharacteristic
136C4×D212—21no—
137C4×D212—21no—
138C4×D212C2×C411yescharacteristic
139C4×D212C2×C411yescharacteristic
140C4×D212C2×C411yescharacteristic
141C4×D212C2×C411yescharacteristic
142C4×C22⋊D53—21no—
143C4×C22⋊D53—21no—
144C4×C22⋊D53—21no—
145C4×C22⋊D53—21no—
146#13133177—21no—
147#13133177—21no—
148#13133177—21no—
149#13133177—21no—
150#13133175—21no—
151#13133175—21no—
152#13133174—21no—
153#13133174—21no—
154#13133174—21no—
155#13133174—21no—
156C2×C4⋊Dic53C2×C411yescharacteristic
157C2×C4⋊Dic53C2×C411yescharacteristic
158C2×#11719919—21no—
159C2×#11719919—21no—
160C4⋊C4×D53—21no—
161C4⋊C4×D53—21no—
162C4⋊#88322—21no—
163C4⋊#88322—21no—
164C4⋊#88322—21no—
165C22⋊#88322—21no—
166C22⋊#88322—21no—
167C22⋊#88322—21no—
168#13133128—21no—
169#13133128—21no—
170#13133128C2311yescharacteristic
171#13133128C2311yescharacteristic
172#13133128C2311yescharacteristic
173#13133128C2311yescharacteristic
174C4×#88322—21no—
175C2×#41×C53C2×C411yescharacteristic
176C2×M16×C53—21no—
177C22×C8×C53—21no—
178C22×C8×C53—21no—
179C4×Q8×C53D411yescharacteristic
180C4×Q8×C53D411yescharacteristic
181C4×D4×C53D411yescharacteristic
182C4×D4×C53D411yescharacteristic
183C4×D4×C53D411yescharacteristic
184C4×D4×C53D411yescharacteristic
185C4×D4×C53D411yescharacteristic
186C4×D4×C53D411yescharacteristic
187#117×C53C2×C411yescharacteristic
188#117×C53C2×C411yescharacteristic
189#117×C53C2×C411yescharacteristic
190C2×C42×C53C2311yescharacteristic
191C2×C42×C53C2311yescharacteristic
192C2×C42×C53C2311yescharacteristic
193C4⋊C8×C53—21no—
194C4⋊C8×C53—21no—
195C4⋊C8×C53—21no—
196C22⋊C8×C53—21no—
197C22⋊C8×C53—21no—
198C22⋊C8×C53—21no—
199#97×C53—21no—
200#97×C53—21no—
201#97×C53C2311yescharacteristic
202#97×C53C2311yescharacteristic
203#97×C53C2311yescharacteristic
204#97×C53C2311yescharacteristic
205C4×C8×C53—21no—
206#41×C53—42no—
207C2×Q8×C53C22⋊C411yescharacteristic
208C2×D4×C53C22⋊C411yescharacteristic
209C2×D4×C53C22⋊C411yescharacteristic
210C2×D4×C53C22⋊C411yescharacteristic
211C22×C4×C53C22×C411yescharacteristic
212C22×C4×C53C22×C411yescharacteristic
213C22×C4×C53C22×C411yescharacteristic
214C22×C4×C53C2×D411yescharacteristic
215C22×C4×C53C2×D411yescharacteristic
216C22×C4×C53C2×D411yescharacteristic
217C22×C4×C53C2×D411yescharacteristic
218C22×C4×C53C2×D411yescharacteristic
219C22×C4×C53C2×D411yescharacteristic
220C2×C22⋊D53—21no—
221C2×C22⋊D53—21no—
222C2×C22⋊D53—21no—
223C2×C22⋊D53—21no—
224C2×C22⋊D53—21no—
225C2×C22⋊D53—21no—
226C22×Dic53—21no—
227C22×Dic53—21no—
228#11719945—42no—
229#11719945—42no—
230C2×D212—21no—
231C2×D212—21no—
232C2×D212C22×C411yescharacteristic
233C2×D212C22×C411yescharacteristic
234C2×C4×D53—21no—
235C2×C4×D53—21no—
236C2×C4×D53—21no—
237C2×C4×D53—21no—
238C2×C4×D53—21no—
239C2×C4×D53—21no—
240C2×Dic106C22×C411yescharacteristic
241C2×Dic106C22×C411yescharacteristic
242M16×C53—42no—
243C2×C8×C53—21no—
244C2×C8×C53—21no—
245C2×C8×C53—21no—
246C2×C8×C53—21no—
247C2×C8×C53—42no—
248C2×C8×C53—42no—
249C4⋊C4×C53C22⋊C411yescharacteristic
250C4⋊C4×C53C22⋊C411yescharacteristic
251C4⋊C4×C53C22⋊C411yescharacteristic
252C4⋊C4×C53C22⋊C411yescharacteristic
253C4⋊C4×C53C22⋊C411yescharacteristic
254C4⋊C4×C53C22⋊C411yescharacteristic
255C22⋊C4×C53C22⋊C411yescharacteristic
256C22⋊C4×C53C22⋊C411yescharacteristic
257C22⋊C4×C53C22⋊C411yescharacteristic
258C22⋊C4×C53C22⋊C411yescharacteristic
259C22⋊C4×C53C22⋊C411yescharacteristic
260C22⋊C4×C53C22⋊C411yescharacteristic
261C42×C53C22×C411yescharacteristic
262C42×C53C22×C411yescharacteristic
263C42×C53C22×C411yescharacteristic
264C42×C53C2×D411yescharacteristic
265C42×C53C2×D411yescharacteristic
266C42×C53C2×D411yescharacteristic
267C42×C53C2×D411yescharacteristic
268C42×C53C2×D411yescharacteristic
269C42×C53C2×D411yescharacteristic
270C42×C53C2411yescharacteristic
271C22⋊Dic53—21no—
272C22⋊Dic53—21no—
273C22⋊Dic53—21no—
274C22⋊Dic53—21no—
275#11719921—21no—
276#11719921—21no—
277#11719921—21no—
278#11719921—21no—
279#11719921—21no—
280#11719921—21no—
281#11719921—21no—
282#11719921—21no—
283#11719921—21no—
284#11719921—21no—
285#11719921—21no—
286#11719921—21no—
287C4⋊Dic53—21no—
288C4⋊Dic53—21no—
289C4⋊Dic53—21no—
290C4⋊Dic53—21no—
291C4⋊Dic53C22×C411yescharacteristic
292C4⋊Dic53C22×C411yescharacteristic
293C4⋊Dic53C22×C411yescharacteristic
294C4⋊Dic53C22×C411yescharacteristic
295#11719919—21no—
296#11719919—21no—
297#11719919—21no—
298#11719919—21no—
299#11719919—21no—
300#11719919—21no—
301#11719919—21no—
302#11719919—21no—
303#11719919—21no—
304#11719919—21no—
305#11719919—21no—
306#11719919—21no—
307#11719919—21no—
308#11719919—21no—
309#11719919—21no—
310#11719919—21no—
311C4×Dic53—21no—
312C4×Dic53—21no—
313C4×Dic53—21no—
314C4×Dic53—21no—
315#11719917—42no—
316C2×#88322—21no—
317C2×#88322—21no—
318C2×#88322—21no—
319C2×#88322—21no—
320C2×#88322—42no—
321C2×#88322—42no—
322C23×C53C2×C22⋊C411yescharacteristic
323C23×C53C2×C22⋊C411yescharacteristic
324C23×C53C2×C22⋊C411yescharacteristic
325C22×D53—21no—
326C22×D53—21no—
327Q8×C53—41no—
328D4×C53—22no—
329D4×C53—22no—
330D4×C53—41no—
331C2×C4×C53—22no—
332C2×C4×C53—41no—
333C2×C4×C53—41no—
334C2×C4×C53—41no—
335C2×C4×C53—41no—
336C2×C4×C53—41no—
337C2×C4×C53—41no—
338C2×C4×C53—41no—
339C2×C4×C53—41no—
340C2×C4×C53C2×C22⋊C411yescharacteristic
341C2×C4×C53C2×C22⋊C411yescharacteristic
342C2×C4×C53C2×C22⋊C411yescharacteristic
343C2×C4×C53C2×C22⋊C411yescharacteristic
344C2×C4×C53C2×C22⋊C411yescharacteristic
345C2×C4×C53C2×C22⋊C411yescharacteristic
346C2×C4×C53C2×C22⋊C411yescharacteristic
347C2×C4×C53C2×C22⋊C411yescharacteristic
348C2×C4×C53C2×C22⋊C411yescharacteristic
349C2×C4×C53C23×C411yescharacteristic
350C2×C4×C53C22×D411yescharacteristic
351C2×C4×C53C22×D411yescharacteristic
352C22⋊D53—42no—
353C22⋊D53—42no—
354C22⋊D53—81no—
355C22⋊D53—81no—
356C22⋊D53—81no—
357C22⋊D53—81no—
358C2×Dic53—21no—
359C2×Dic53—21no—
360C2×Dic53—21no—
361C2×Dic53—21no—
362C2×Dic53—21no—
363C2×Dic53—21no—
364C2×Dic53—81no—
365C2×Dic53—81no—
366D212—41no—
367D212—41no—
368D212—81no—
369D212—81no—
370C4×D53—42no—
371C4×D53—42no—
372C4×D53—81no—
373C4×D53—81no—
374C4×D53—81no—
375C4×D53—81no—
376Dic106—41no—
377Dic106—41no—
378C8×C53—22no—
379C8×C53—41no—
380C8×C53—41no—
381C8×C53—41no—
382#88322—22no—
383#88322—41no—
384#88322—41no—
385#88322—41no—
386#17690—531nomaximal, Sylow
387C22×C53—21no—
388C22×C53—21no—
389C22×C53—21no—
390C22×C53—21no—
391C22×C53—21no—
392C22×C53—21no—
393C22×C53—21no—
394C22×C53—21no—
395C22×C53#41312yes—
396C22×C53C22×C22⋊C411yescharacteristic
397C2×D53—41no—
398C2×D53—41no—
399C2×D53—41no—
400C2×D53—41no—
401C2×D53—41no—
402C2×D53—41no—
403C4×C53—21no—
404C4×C53—21no—
405C4×C53—21no—
406C4×C53—21no—
407C4×C53—21no—
408C4×C53—21no—
409C4×C53—21no—
410C4×C53—21no—
411C4×C53—21no—
412C4×C53—21no—
413C4×C53—21no—
414C4×C53—21no—
415Dic53—41no—
416Dic53—41no—
417Dic53—41no—
418Dic53—41no—
419Dic53—41no—
420Dic53—41no—
421#3512—531no—
422#2970—531no—
423#2970D5311yescharacteristic, complemented
424#1535—531no—
425#1535—531no—
426#1534—531no—
427#1532—531no—
428#1532—531no—
429#1530—531no—
430#1530—531no—
431#1529—531no—
432#1529—531no—
433#1524—531no—
434#1524—531no—
435C2×#330—531no—
436C2×C53—22no—
437C2×C53—41no—
438C2×C53—41no—
439C2×C53C2×#41311yescharacteristic
440C2×C53#290111yescharacteristic
441C2×C53#290111yescharacteristic
442D53—81no—
443D53—81no—
444#553—1061no—
445#553—1061no—
446#553—1061no—
447#553—1061no—
448#553—1061no—
449#553—1061no—
450#552—1061no—
451#552—1061no—
452#541—531no—
453#541—531no—
454#540—531no—
455#540—531no—
456#537—531no—
457#537—531no—
458#532—531no—
459#529—531no—
460#529—531no—
461#529—531no—
462#529—531no—
463C2×#125—531no—
464#520—531no—
465#520—531no—
466C4×#41C2×D5311yescharacteristic
467#446—21no—
468#446—1061no—
469#435—21no—
470#435—21no—
471#435—1061no—
472#435—1061no—
473C8×D4—21no—
474C8×D4—1061no—
475#432—531no—
476#432—531no—
477#432—531no—
478#432C2×D5311yescharacteristic
479#432C2×D5311yescharacteristic
480#432C2×D5311yescharacteristic
481C4×M16—531no—
482C4×M16C2×D5311yescharacteristic
483C2×#97—531no—
484C2×#97—531no—
485C2×#97C2×D5311yescharacteristic
486C2×#97C2×D5311yescharacteristic
487#330—531no—
488#330—531no—
489#330—531no—
490#330—531no—
491#330—531no—
492#330—531no—
493#330—531no—
494#330—531no—
495#329—531no—
496#329—531no—
497#329—531no—
498#329—531no—
499#329—531no—
500#329—531no—
501#329—531no—
502#329—531no—
503C53#1769011yescharacteristic, complemented, Sylow
504C2×#41—531no—
505C2×#41—531no—
506C2×#41C4×D5311yescharacteristic
507C2×M16—21no—
508C2×M16—1061no—
509C22×C8—21no—
510C22×C8—21no—
511C22×C8—1061no—
512C22×C8—1061no—
513C4⋊Q8—531no—
514#127—531no—
515#126—1061no—
516#126—1061no—
517#126—1061no—
518#126—1061no—
519#126—1061no—
520#126—1061no—
521#126—1061no—
522#126—1061no—
523#125—531no—
524#125—531no—
525#125—531no—
526#125—531no—
527#125—1061no—
528#125—1061no—
529#125—1061no—
530#125—1061no—
531#125—1061no—
532#125—1061no—
533#124—531no—
534#124—531no—
535#123—1061no—
536#123—1061no—
537#123—1061no—
538#123—1061no—
539#123—1061no—
540#123—1061no—
541#123—1061no—
542#123—1061no—
543C22⋊Q8—531no—
544C22⋊Q8—531no—
545C22⋊Q8—531no—
546C22⋊Q8—531no—
547C22⋊Q8—1061no—
548C22⋊Q8—1061no—
549#121—531no—
550#121—531no—
551#121—531no—
552#121—531no—
553#121—1061no—
554#121—1061no—
555#121—1061no—
556#121—1061no—
557#121—1061no—
558#121—1061no—
559#121—1061no—
560#121—1061no—
561#121—1061no—
562#121—1061no—
563#121—1061no—
564#121—1061no—
565C4×Q8—531no—
566C4×Q8—531no—
567C4×Q8—531no—
568C4×Q8—531no—
569C4×Q8D21211yescharacteristic
570C4×Q8C22⋊D5311yescharacteristic
571C4×D4—531no—
572C4×D4—531no—
573C4×D4—531no—
574C4×D4—531no—
575C4×D4—1061no—
576C4×D4—1061no—
577C4×D4—1061no—
578C4×D4—1061no—
579C4×D4—1061no—
580C4×D4—1061no—
581C4×D4—1061no—
582C4×D4—1061no—
583C4×D4—1061no—
584C4×D4—1061no—
585C4×D4D21211yescharacteristic
586C4×D4D21211yescharacteristic
587C4×D4D21211yescharacteristic
588C4×D4C22⋊D5311yescharacteristic
589C4×D4C22⋊D5311yescharacteristic
590C4×D4C22⋊D5311yescharacteristic
591#117—1061no—
592#117—1061no—
593#117—1061no—
594#117—1061no—
595#117—1061no—
596#117—1061no—
597#117C4×D5311yescharacteristic
598#117C4×D5311yescharacteristic
599#117C4×D5311yescharacteristic
600C2×C4⋊C4—531no—
601C2×C4⋊C4—531no—
602C2×C4⋊C4—1061no—
603C2×C4⋊C4—1061no—
604C2×C4⋊C4—1061no—
605C2×C4⋊C4—1061no—
606C2×C42C22×D5311yescharacteristic
607C2×C42C22×D5311yescharacteristic
608C2×C42C22×D5311yescharacteristic
609C4⋊C8—21no—
610C4⋊C8—21no—
611C4⋊C8—21no—
612C4⋊C8—1061no—
613C4⋊C8—1061no—
614C4⋊C8—1061no—
615C22⋊C8—21no—
616C22⋊C8—21no—
617C22⋊C8—21no—
618C22⋊C8—1061no—
619C22⋊C8—1061no—
620C22⋊C8—1061no—
621#97—21no—
622#97—21no—
623#97—531no—
624#97—531no—
625#97—531no—
626#97—531no—
627#97—1061no—
628#97—1061no—
629#97C22×D5311yescharacteristic
630#97C22×D5311yescharacteristic
631#97C22×D5311yescharacteristic
632#97C22×D5311yescharacteristic
633C4×C8—21no—
634C4×C8—1061no—
635#41—42no—
636#41—2122no—
637#41—2122no—
638C2×Q8—531no—
639C2×Q8—531no—
640C2×Q8#1171992111yescharacteristic
641C2×D4—531no—
642C2×D4—531no—
643C2×D4—1061no—
644C2×D4—1061no—
645C2×D4—1061no—
646C2×D4—1061no—
647C2×D4—1061no—
648C2×D4—1061no—
649C2×D4—1061no—
650C2×D4—1061no—
651C2×D4#1171992111yescharacteristic
652C2×D4#1171992111yescharacteristic
653C2×D4#1171992111yescharacteristic
654C22×C4—1061no—
655C22×C4—1061no—
656C22×C4—1061no—
657C22×C4—1061no—
658C22×C4—1061no—
659C22×C4—1061no—
660C22×C4—1061no—
661C22×C4—1061no—
662C22×C4C2×C4×D5311yescharacteristic
663C22×C4C2×C4×D5311yescharacteristic
664C22×C4C2×C4×D5311yescharacteristic
665C22×C4C2×D21211yescharacteristic
666C22×C4C2×D21211yescharacteristic
667C22×C4C2×D21211yescharacteristic
668C22×C4C2×C22⋊D5311yescharacteristic
669C22×C4C2×C22⋊D5311yescharacteristic
670C22×C4C2×C22⋊D5311yescharacteristic
671M16—42no—
672M16—2122no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—42no—
678C2×C8—42no—
679C2×C8—1061no—
680C2×C8—1061no—
681C2×C8—1061no—
682C2×C8—1061no—
683C2×C8—2122no—
684C2×C8—2122no—
685C4⋊C4—531no—
686C4⋊C4—531no—
687C4⋊C4—531no—
688C4⋊C4—531no—
689C4⋊C4—1061no—
690C4⋊C4—1061no—
691C4⋊C4—1061no—
692C4⋊C4—1061no—
693C4⋊C4—1061no—
694C4⋊C4—1061no—
695C4⋊C4—1061no—
696C4⋊C4—1061no—
697C4⋊C4—1061no—
698C4⋊C4—1061no—
699C4⋊C4—1061no—
700C4⋊C4—1061no—
701C4⋊C4—1061no—
702C4⋊C4—1061no—
703C4⋊C4—1061no—
704C4⋊C4—1061no—
705C4⋊C4—1061no—
706C4⋊C4—1061no—
707C4⋊C4—1061no—
708C4⋊C4—1061no—
709C4⋊C4#1171992111yescharacteristic
710C4⋊C4#1171992111yescharacteristic
711C4⋊C4#1171992111yescharacteristic
712C4⋊C4#1171992111yescharacteristic
713C4⋊C4#1171992111yescharacteristic
714C4⋊C4#1171992111yescharacteristic
715C22⋊C4—1061no—
716C22⋊C4—1061no—
717C22⋊C4—1061no—
718C22⋊C4—1061no—
719C22⋊C4—1061no—
720C22⋊C4—1061no—
721C22⋊C4—1061no—
722C22⋊C4—1061no—
723C22⋊C4—1061no—
724C22⋊C4—1061no—
725C22⋊C4—1061no—
726C22⋊C4—1061no—
727C22⋊C4—1061no—
728C22⋊C4—1061no—
729C22⋊C4—1061no—
730C22⋊C4—1061no—
731C22⋊C4#1171992111yescharacteristic
732C22⋊C4#1171992111yescharacteristic
733C22⋊C4#1171992111yescharacteristic
734C22⋊C4#1171992111yescharacteristic
735C22⋊C4#1171992111yescharacteristic
736C22⋊C4#1171992111yescharacteristic
737C42—1061no—
738C42—1061no—
739C42—1061no—
740C42—1061no—
741C42C2×C4×D5311yescharacteristic
742C42C2×C4×D5311yescharacteristic
743C42C2×C4×D5311yescharacteristic
744C42C2×D21211yescharacteristic
745C42C2×D21211yescharacteristic
746C42C2×D21211yescharacteristic
747C42C2×C22⋊D5311yescharacteristic
748C42C2×C22⋊D5311yescharacteristic
749C42C2×C22⋊D5311yescharacteristic
750C42C23×D5311yescharacteristic
751C23—1061no—
752C23—1061no—
753C23C2×#1171992111yescharacteristic
754C23C2×#1171992111yescharacteristic
755C23C2×#1171992111yescharacteristic
756Q8—41no—
757Q8—2121no—
758Q8—2121no—
759D4—22no—
760D4—22no—
761D4—41no—
762D4—4241no—
763D4—4241no—
764D4—4241no—
765D4—4241no—
766D4—4241no—
767D4—4241no—
768D4—2121no—
769D4—2121no—
770D4—2122no—
771D4—2122no—
772C2×C4—22no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—1061no—
782C2×C4—1061no—
783C2×C4—1061no—
784C2×C4—1061no—
785C2×C4—1061no—
786C2×C4—1061no—
787C2×C4—4241no—
788C2×C4—4241no—
789C2×C4—4241no—
790C2×C4—4241no—
791C2×C4—4241no—
792C2×C4—4241no—
793C2×C4—2122no—
794C2×C4—2122no—
795C2×C4C2×#1171992111yescharacteristic
796C2×C4C2×#1171992111yescharacteristic
797C2×C4C2×#1171992111yescharacteristic
798C2×C4C2×#1171992111yescharacteristic
799C2×C4C2×#1171992111yescharacteristic
800C2×C4C2×#1171992111yescharacteristic
801C2×C4C2×#1171992111yescharacteristic
802C2×C4C2×#1171992111yescharacteristic
803C2×C4C2×#1171992111yescharacteristic
804C2×C4C22×C4×D5311yescharacteristic
805C2×C4C22×C22⋊D5311yescharacteristic
806C2×C4C22×D21211yescharacteristic
807C8—22no—
808C8—41no—
809C8—41no—
810C8—41no—
811C8—1062no—
812C8—2121no—
813C8—2121no—
814C8—2121no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—2121no—
824C22—2121no—
825C22—2121no—
826C22—2121no—
827C22—2121no—
828C22—2121no—
829C22#1681060512yes—
830C22C22×#1171992111yescharacteristic
831C4—21no—
832C4—21no—
833C4—21no—
834C4—21no—
835C4—21no—
836C4—21no—
837C4—21no—
838C4—21no—
839C4—21no—
840C4—21no—
841C4—21no—
842C4—21no—
843C4—2121no—
844C4—2121no—
845C4—2121no—
846C4—2121no—
847C4—2121no—
848C4—2121no—
849C2—22no—
850C2—41no—
851C2—41no—
852C2—4241no—
853C2—4241no—
854C2C2×#1681060511yescharacteristic
855C2#2028326011yescharacteristic
856C2#2028326311yescharacteristic
subgroupG/H
centerC22C22×#11719921
commutatorC2×C4×C53C23×C4
FrattiniC42C23×D53
FittingC53×#2970C2
socleC22×C53C22×C22⋊C4
prime radical#20288637C2
cosocleC42×C53C24
hypercenter#2970D53
hypocenterC53#17690
LCSG ▷ C2×C4×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ C4×#41 ◁ #2970

Complements

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

NH ≅ G/Ntype
2. #20283729C2semidirect
3. #20273347C2semidirect
4. #20273344C2semidirect
5. #20273341C2semidirect
6. #20273336C2semidirect
7. #20273333C2semidirect
8. #20273327C2semidirect
9. #20273325C2semidirect
10. #20273323C2semidirect
11. #20273320C2semidirect
12. #20273304C2semidirect
13. #20273301C2semidirect
14. C2×#16810364C2semidirect
15. C53×#2970C2semidirect
423. #2970D53semidirect
503. C53#17690semidirect

Maximal subgroups

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

subgroupindex
#202886372
#202837292
#202733472
#202733442
#202733412
#202733362
#202733332
#202733272
#202733252
#202733232
#202733202
#202733042
#202733012
C2×#168103642
C53×#29702
#1769053