Finite Group Databasebeta

← #27351698

Subgroups — #27351698

Order 13568.

1004 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288450C211yesmaximal, characteristic
2#20283373C211yesmaximal, characteristic, complemented
3#20273290C211yesmaximal, characteristic, complemented
4#20273274C211yesmaximal, characteristic, complemented
5#20273269C211yesmaximal, characteristic, complemented
6#20273261C211yesmaximal, characteristic, complemented
7#20273251C211yesmaximal, characteristic, complemented
8#20273243C211yesmaximal, characteristic, complemented
9#20273238C211yesmaximal, characteristic, complemented
10#20273222C211yesmaximal, characteristic, complemented
11#20273217C211yesmaximal, characteristic, complemented
12#20273209C211yesmaximal, characteristic, complemented
13#20273199C211yesmaximal, characteristic, complemented
14C2×#16810356C211yesmaximal, characteristic, complemented
15C53×#2343C211yesmaximal, characteristic, complemented
16#16811336—21no—
17#16811321—21no—
18#16811317—21no—
19#16811297—21no—
20#16811297—21no—
21#16811274—21no—
22#16811263—21no—
23#16811263—21no—
24#16811251C411yescharacteristic, complemented
25#16811244C411yescharacteristic, complemented
26#16811244C411yescharacteristic, complemented
27#16811228C411yescharacteristic, complemented
28#16811228C411yescharacteristic, complemented
29#16811192C411yescharacteristic, complemented
30#16811173C2211yescharacteristic
31#16811173C2211yescharacteristic
32#16811157C2211yescharacteristic
33#16811157C2211yescharacteristic
34#16811134C2211yescharacteristic
35C2×#13133191C2211yescharacteristic
36#16811103C411yescharacteristic, complemented
37#16811097C411yescharacteristic, complemented
38#16810684—21no—
39#16810684—21no—
40#16810680C2211yescharacteristic, complemented
41#16810680C2211yescharacteristic, complemented
42#16810676C2211yescharacteristic, complemented
43#16810676C2211yescharacteristic, complemented
44#16810650—21no—
45#16810587C2211yescharacteristic
46C2×C22⋊#88322C2211yescharacteristic
47#16810579—21no—
48#16810359C2211yescharacteristic, complemented
49#16810359C2211yescharacteristic, complemented
50#16810359C2211yescharacteristic, complemented
51#16810359C2211yescharacteristic, complemented
52#16810356C2211yescharacteristic
53#16810356C2211yescharacteristic
54#16810356C2211yescharacteristic
55#16810356C2211yescharacteristic
56#16810356C2211yescharacteristic
57#16810356C2211yescharacteristic
58#16810356C2211yescharacteristic
59#16810356C2211yescharacteristic
60#16810356C2211yescharacteristic, complemented
61#16810356C2211yescharacteristic, complemented
62#16810356C2211yescharacteristic, complemented
63#16810356C2211yescharacteristic, complemented
64C2×#117×C53C2211yescharacteristic
65C53×#387—21no—
66C53×#387—21no—
67C53×#385—21no—
68C53×#383C2211yescharacteristic, complemented
69C53×#382C2211yescharacteristic, complemented
70C53×#381C2211yescharacteristic
71C4×C4⋊C4×C53C2211yescharacteristic, complemented
72C4×C22⋊C4×C53—21no—
73C53×#376C2211yescharacteristic, complemented
74C2×#95×C53C2211yescharacteristic
75C2×#11719945—21no—
76C2×#11719945—21no—
77C2×#11719945C2×C411yescharacteristic
78C22×D212C2×C411yescharacteristic
79C22×C22⋊D53—21no—
80C2×#11719917—21no—
81C22×#88322—21no—
82#13133217C2×C411yescharacteristic, complemented
83#13133217C2×C411yescharacteristic, complemented
84#13133216—21no—
85#13133214C2×C411yescharacteristic, complemented
86#13133214C2×C411yescharacteristic, complemented
87#13133212—21no—
88#13133212—21no—
89#13133211—21no—
90#13133211—21no—
91#13133209C2×C411yescharacteristic, complemented
92#13133209C2×C411yescharacteristic, complemented
93#13133208—21no—
94#13133205—21no—
95#13133205—21no—
96#13133205C2×C411yescharacteristic, complemented
97#13133205C2×C411yescharacteristic, complemented
98#13133203—21no—
99#13133203—21no—
100#13133202—21no—
101#13133202—21no—
102#13133202—21no—
103#13133202—21no—
104#13133200—21no—
105#13133200—21no—
106#13133200—21no—
107#13133199—21no—
108#13133199—21no—
109#13133196C2×C411yescharacteristic
110#13133196C2311yescharacteristic
111#13133195—21no—
112#13133195—21no—
113#13133194—21no—
114#13133194—21no—
115#13133192—21no—
116#13133192—21no—
117#13133191—21no—
118#13133191—21no—
119#13133191—21no—
120#13133191—21no—
121#13133191C2×C411yescharacteristic
122#13133191C2×C411yescharacteristic
123#13133191C2×C411yescharacteristic
124#13133191C2311yescharacteristic
125#13133191C2311yescharacteristic
126#13133191C2311yescharacteristic
127#13133190—21no—
128#13133190—21no—
129#13133190—21no—
130#13133190—21no—
131#13133187—21no—
132#13133187—21no—
133#13133186—21no—
134C4×Dic106C2×C411yescharacteristic, complemented
135C4×Dic106C2×C411yescharacteristic, complemented
136C4×D212—21no—
137C4×D212—21no—
138C4×D212C2×C411yescharacteristic, complemented
139C4×D212C2×C411yescharacteristic, complemented
140C4×D212C2×C411yescharacteristic, complemented
141C4×D212C2×C411yescharacteristic, complemented
142C4×D212C2×C411yescharacteristic, complemented
143C4×D212C2×C411yescharacteristic, complemented
144#13133179—21no—
145#13133179—21no—
146C4×C22⋊D53—21no—
147C4×C22⋊D53—21no—
148C4×C22⋊D53—21no—
149C4×C22⋊D53—21no—
150#13133177—21no—
151#13133177—21no—
152#13133176C2×C411yescharacteristic
153#13133175—21no—
154#13133174—21no—
155#13133174—21no—
156C2×C4⋊Dic53C2×C411yescharacteristic
157C4⋊C4×D53—21no—
158C2×#11719921—21no—
159C22⋊C4×D53—21no—
160C22⋊C4×D53—21no—
161C4⋊#88322—21no—
162C4⋊#88322—21no—
163C4⋊#88322—21no—
164C4⋊#88322—21no—
165C22⋊#88322—21no—
166C22⋊#88322—21no—
167C22⋊#88322C2311yescharacteristic
168C22⋊#88322C2311yescharacteristic
169C22⋊#88322C2311yescharacteristic
170C22⋊#88322C2311yescharacteristic
171#13133128—21no—
172#13133128—21no—
173C4×#88322—21no—
174C4×#88322—21no—
175C23×C4×C53—21no—
176C23×C4×C53C2311yescharacteristic
177#117×C53C2×C411yescharacteristic
178#117×C53C2×C411yescharacteristic
179#117×C53C2×C411yescharacteristic
180#117×C53C2×C411yescharacteristic
181#117×C53D411yescharacteristic
182#117×C53D411yescharacteristic
183#117×C53D411yescharacteristic
184#117×C53D411yescharacteristic
185C2×C4⋊C4×C53—21no—
186C2×C4⋊C4×C53—21no—
187C2×C4⋊C4×C53D411yescharacteristic
188C2×C4⋊C4×C53D411yescharacteristic
189C2×C22⋊C4×C53—21no—
190C2×C22⋊C4×C53D411yescharacteristic
191C2×C22⋊C4×C53D411yescharacteristic
192C2×C42×C53—21no—
193C2×C42×C53—21no—
194C2×C42×C53C2311yescharacteristic
195C2×C42×C53C2311yescharacteristic
196#95×C53—21no—
197#95×C53—21no—
198#95×C53—21no—
199#95×C53—21no—
200#95×C53—21no—
201#95×C53—21no—
202#95×C53C2311yescharacteristic
203#95×C53C2311yescharacteristic
204#95×C53C2311yescharacteristic
205#95×C53C2311yescharacteristic
206C24×C53C2×D411yescharacteristic
207C23×D53—21no—
208C22×C4×C53—21no—
209C22×C4×C53—21no—
210C22×C4×C53—21no—
211C22×C4×C53—21no—
212C22×C4×C53—42no—
213C22×C4×C53—42no—
214C22×C4×C53—42no—
215C22×C4×C53—81no—
216C22×C4×C53C22×C411yescharacteristic
217C22×C4×C53C22×C411yescharacteristic
218C22×C4×C53C2×D411yescharacteristic
219C22×C4×C53C2×D411yescharacteristic
220C22×C4×C53C2×D411yescharacteristic
221C22×C4×C53C2×D411yescharacteristic
222C22×C4×C53C2×D411yescharacteristic
223C22×C4×C53C2×D411yescharacteristic
224C22×C4×C53C2×D411yescharacteristic
225C22×C4×C53C2411yescharacteristic
226C2×C22⋊D53—21no—
227C2×C22⋊D53—21no—
228C2×C22⋊D53—21no—
229C2×C22⋊D53—21no—
230C2×C22⋊D53—21no—
231C2×C22⋊D53—21no—
232C2×C22⋊D53—21no—
233C2×C22⋊D53—81no—
234C2×C22⋊D53—81no—
235C22×Dic53—21no—
236#11719945—42no—
237#11719945—81no—
238#11719945—81no—
239#11719945—81no—
240#11719945—81no—
241C2×D212—21no—
242C2×D212—21no—
243C2×D212—21no—
244C2×D212—21no—
245C2×D212—21no—
246C2×D212—42no—
247C2×D212C22×C411yescharacteristic
248C2×D212C22×C411yescharacteristic
249C2×D212C22×C411yescharacteristic
250C2×C4×D53—21no—
251C2×C4×D53—21no—
252C2×C4×D53—21no—
253C2×C4×D53—21no—
254C2×C4×D53—21no—
255C2×C4×D53—21no—
256C2×C4×D53—21no—
257C2×Dic106—21no—
258C2×Dic106—21no—
259C2×Dic106C22×C411yescharacteristic
260C4⋊C4×C53—42no—
261C4⋊C4×C53—81no—
262C4⋊C4×C53C22⋊C411yescharacteristic
263C4⋊C4×C53C22⋊C411yescharacteristic
264C4⋊C4×C53C22⋊C411yescharacteristic
265C4⋊C4×C53C22⋊C411yescharacteristic
266C4⋊C4×C53C22⋊C411yescharacteristic
267C4⋊C4×C53C22⋊C411yescharacteristic
268C4⋊C4×C53C22⋊C411yescharacteristic
269C4⋊C4×C53C22⋊C411yescharacteristic
270C22⋊C4×C53—42no—
271C22⋊C4×C53C22⋊C411yescharacteristic
272C22⋊C4×C53C22⋊C411yescharacteristic
273C22⋊C4×C53C22⋊C411yescharacteristic
274C22⋊C4×C53C22⋊C411yescharacteristic
275C22⋊C4×C53C22⋊C411yescharacteristic
276C22⋊C4×C53C22⋊C411yescharacteristic
277C22⋊C4×C53C22⋊C411yescharacteristic
278C22⋊C4×C53C22⋊C411yescharacteristic
279C42×C53—42no—
280C42×C53—81no—
281C42×C53C22×C411yescharacteristic
282C42×C53C22×C411yescharacteristic
283C42×C53C22×C411yescharacteristic
284C42×C53C22×C411yescharacteristic
285C42×C53C2×D411yescharacteristic
286C42×C53C2×D411yescharacteristic
287C42×C53C2×D411yescharacteristic
288C42×C53C2×D411yescharacteristic
289C22⋊Dic53—21no—
290C22⋊Dic53—21no—
291C22⋊Dic53—21no—
292#11719921—21no—
293#11719921—21no—
294#11719921—21no—
295#11719921—21no—
296#11719921—21no—
297#11719921—21no—
298#11719921—21no—
299#11719921—21no—
300#11719921—21no—
301#11719921—21no—
302#11719921—21no—
303#11719921—21no—
304#11719921—21no—
305#11719921—21no—
306#11719921—21no—
307#11719921—21no—
308C4⋊Dic53—21no—
309C4⋊Dic53—21no—
310C4⋊Dic53—21no—
311C4⋊Dic53C22×C411yescharacteristic
312C4⋊Dic53C22×C411yescharacteristic
313C4⋊Dic53C22×C411yescharacteristic
314C4⋊Dic53C22×C411yescharacteristic
315#11719919—21no—
316#11719919—21no—
317#11719919—21no—
318#11719919—21no—
319#11719919—21no—
320#11719919—21no—
321#11719919—21no—
322#11719919—21no—
323C4×Dic53—21no—
324C4×Dic53—21no—
325C4×Dic53—21no—
326#11719917—42no—
327C2×#88322—21no—
328C2×#88322—21no—
329C2×#88322—21no—
330C2×#88322—21no—
331C2×#88322—42no—
332C23×C53—21no—
333C23×C53—21no—
334C23×C53—22no—
335C23×C53—41no—
336C23×C53C2×C22⋊C411yescharacteristic
337C23×C53C2×C22⋊C411yescharacteristic
338C23×C53C22×D411yescharacteristic
339C22×D53—21no—
340C22×D53—21no—
341C22×D53—21no—
342C22×D53—42no—
343C22×D53—81no—
344C22×D53—81no—
345C2×C4×C53—21no—
346C2×C4×C53—21no—
347C2×C4×C53—21no—
348C2×C4×C53—21no—
349C2×C4×C53—22no—
350C2×C4×C53—22no—
351C2×C4×C53—22no—
352C2×C4×C53—41no—
353C2×C4×C53—41no—
354C2×C4×C53—41no—
355C2×C4×C53—41no—
356C2×C4×C53—41no—
357C2×C4×C53—41no—
358C2×C4×C53—41no—
359C2×C4×C53—41no—
360C2×C4×C53—41no—
361C2×C4×C53—41no—
362C2×C4×C53—41no—
363C2×C4×C53—41no—
364C2×C4×C53—41no—
365C2×C4×C53—41no—
366C2×C4×C53—41no—
367C2×C4×C53—41no—
368C2×C4×C53—41no—
369C2×C4×C53—84no—
370C2×C4×C53C2×C22⋊C411yescharacteristic
371C2×C4×C53C2×C22⋊C411yescharacteristic
372C2×C4×C53C2×C22⋊C411yescharacteristic
373C2×C4×C53C2×C22⋊C411yescharacteristic
374C2×C4×C53C2×C22⋊C411yescharacteristic
375C2×C4×C53C2×C22⋊C411yescharacteristic
376C2×C4×C53C2×C22⋊C411yescharacteristic
377C2×C4×C53C2×C22⋊C411yescharacteristic
378C2×C4×C53C2×C22⋊C411yescharacteristic
379C2×C4×C53C2×C22⋊C411yescharacteristic
380C2×C4×C53C23×C411yescharacteristic
381C2×C4×C53C22×D411yescharacteristic
382C22⋊D53—41no—
383C22⋊D53—41no—
384C22⋊D53—41no—
385C22⋊D53—41no—
386C22⋊D53—41no—
387C22⋊D53—41no—
388C22⋊D53—42no—
389C22⋊D53—81no—
390C22⋊D53—81no—
391C22⋊D53—81no—
392C2×Dic53—21no—
393C2×Dic53—21no—
394C2×Dic53—21no—
395C2×Dic53—21no—
396C2×Dic53—21no—
397C2×Dic53—81no—
398D212—41no—
399D212—41no—
400D212—41no—
401D212—42no—
402D212—81no—
403D212—81no—
404D212—81no—
405D212—81no—
406C4×D53—42no—
407C4×D53—81no—
408C4×D53—81no—
409C4×D53—81no—
410C4×D53—81no—
411C4×D53—81no—
412C4×D53—81no—
413Dic106—41no—
414Dic106—81no—
415Dic106—81no—
416#88322—41no—
417#88322—41no—
418#88322—41no—
419#88322—41no—
420#17604—531nomaximal, Sylow
421C22×C53—21no—
422C22×C53—21no—
423C22×C53—21no—
424C22×C53—21no—
425C22×C53—21no—
426C22×C53—21no—
427C22×C53—21no—
428C22×C53—42no—
429C22×C53—42no—
430C22×C53#41012yes—
431C22×C53C22×C22⋊C411yescharacteristic
432C22×C53#57611yescharacteristic
433C22×C53#57711yescharacteristic
434C2×D53—41no—
435C2×D53—41no—
436C2×D53—41no—
437C2×D53—41no—
438C2×D53—41no—
439C2×D53—41no—
440C2×D53—41no—
441C2×D53—41no—
442C2×D53—41no—
443C2×D53—162no—
444C4×C53—21no—
445C4×C53—21no—
446C4×C53—21no—
447C4×C53—21no—
448C4×C53—21no—
449C4×C53—21no—
450C4×C53—21no—
451C4×C53—21no—
452C4×C53—21no—
453C4×C53—21no—
454C4×C53—21no—
455C4×C53—21no—
456C4×C53—42no—
457C4×C53—81no—
458C4×C53—81no—
459C4×C53—81no—
460Dic53—41no—
461Dic53—41no—
462Dic53—41no—
463Dic53—41no—
464Dic53—41no—
465#3494—531no—
466#2924—531no—
467#2343D5311yescharacteristic, complemented
468#1521—531no—
469#1517—531no—
470#1516—531no—
471#1514—531no—
472#1512—531no—
473#1510—531no—
474#1509—531no—
475#1505—531no—
476#1504—531no—
477#1502—531no—
478#1500—531no—
479C2×#327—531no—
480C2×C53—21no—
481C2×C53—21no—
482C2×C53—22no—
483C2×C53—41no—
484C2×C53C2×#41011yescharacteristic
485C2×C53#289711yescharacteristic
486C2×C53#290111yescharacteristic
487D53—81no—
488D53—81no—
489D53—81no—
490#555—1061no—
491#553—1061no—
492#553—1061no—
493#551—1061no—
494#551—1061no—
495#547—1061no—
496#546—1061no—
497#546—1061no—
498#544—531no—
499#542—531no—
500#542—531no—
501#540—531no—
502#540—531no—
503#535—531no—
504#532—531no—
505#532—531no—
506#529—531no—
507#529—531no—
508#525—531no—
509C2×#121—531no—
510#520—531no—
511#518—531no—
512C2×#117C2×D5311yescharacteristic
513#433—1061no—
514#433—1061no—
515#432—531no—
516#432—531no—
517#431—531no—
518#431—531no—
519#424—1061no—
520#407—531no—
521C2×C22⋊C8—531no—
522#405—1061no—
523#387—21no—
524#387—21no—
525#385—21no—
526#383C2×D5311yescharacteristic, complemented
527#382C2×D5311yescharacteristic, complemented
528#381C2×D5311yescharacteristic
529C4×C4⋊C4C2×D5311yescharacteristic, complemented
530C4×C22⋊C4—21no—
531#376C2×D5311yescharacteristic, complemented
532C2×#95C2×D5311yescharacteristic
533#328—531no—
534#328—531no—
535#328—531no—
536#328—531no—
537#327—531no—
538#327—531no—
539#327—531no—
540#327—531no—
541#327—531no—
542#327—531no—
543#327—531no—
544#327—531no—
545#327—531no—
546#327—531no—
547#327—531no—
548#327—531no—
549C53#1760411yescharacteristic, complemented, Sylow
550C2×#41—531no—
551C2×#41—1061no—
552C2×#41—1061no—
553C22×D4—531no—
554C22×D4—1061no—
555C23×C4—21no—
556C23×C4C22×D5311yescharacteristic
557C2×M16—1061no—
558C22×C8—1061no—
559C4⋊Q8—531no—
560C4⋊Q8—531no—
561C4⋊Q8—1061no—
562#127—531no—
563#127—531no—
564#126—1061no—
565#126—1061no—
566#126—1061no—
567#126—1061no—
568#125—531no—
569#125—531no—
570#125—1061no—
571#124—531no—
572#124—531no—
573#124—1061no—
574#124—1061no—
575#124—1061no—
576#124—1061no—
577#123—1061no—
578#123—1061no—
579#123—1061no—
580#123—1061no—
581#123—1061no—
582#123—1061no—
583#123—1061no—
584#123—1061no—
585#123—1061no—
586C22⋊Q8—531no—
587C22⋊Q8—531no—
588C22⋊Q8—1061no—
589C22⋊Q8—1061no—
590C22⋊Q8—1061no—
591C22⋊Q8—1061no—
592#121—531no—
593#121—531no—
594#121—531no—
595#121—531no—
596#121—531no—
597#121—531no—
598#121—1061no—
599#121—1061no—
600#121—1061no—
601#121—1061no—
602#121—1061no—
603#121—1061no—
604#121—1061no—
605#121—1061no—
606#121—1061no—
607#121—1061no—
608#120—1061no—
609#120—1061no—
610#120—1061no—
611C4×Q8—531no—
612C4×Q8—531no—
613C4×D4—531no—
614C4×D4—531no—
615C4×D4—531no—
616C4×D4—531no—
617C4×D4—531no—
618C4×D4—531no—
619C4×D4—1061no—
620C4×D4—1061no—
621C4×D4—1061no—
622C4×D4—1061no—
623C4×D4—1061no—
624C4×D4—1061no—
625C4×D4—1061no—
626C4×D4—1061no—
627C4×D4—1061no—
628C4×D4—1061no—
629#117—531no—
630#117—1061no—
631#117—1061no—
632#117—1061no—
633#117C4×D5311yescharacteristic
634#117C4×D5311yescharacteristic
635#117C4×D5311yescharacteristic
636#117C4×D5311yescharacteristic
637#117D21211yescharacteristic
638#117D21211yescharacteristic
639#117D21211yescharacteristic
640#117D21211yescharacteristic
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—531no—
644C2×C4⋊C4—1061no—
645C2×C4⋊C4C22⋊D5311yescharacteristic
646C2×C4⋊C4C22⋊D5311yescharacteristic
647C2×C22⋊C4—21no—
648C2×C22⋊C4—1061no—
649C2×C22⋊C4—1061no—
650C2×C22⋊C4—1061no—
651C2×C22⋊C4C22⋊D5311yescharacteristic
652C2×C22⋊C4C22⋊D5311yescharacteristic
653C2×C42—21no—
654C2×C42—21no—
655C2×C42C22×D5311yescharacteristic
656C2×C42C22×D5311yescharacteristic
657C4⋊C8—1061no—
658C4⋊C8—1061no—
659C4⋊C8—1061no—
660C4⋊C8—1061no—
661C22⋊C8—531no—
662C22⋊C8—531no—
663C22⋊C8—531no—
664C22⋊C8—531no—
665C22⋊C8—1061no—
666C22⋊C8—1061no—
667#97—1061no—
668#97—1061no—
669C4×C8—1061no—
670C4×C8—1061no—
671#95—21no—
672#95—21no—
673#95—21no—
674#95—21no—
675#95—21no—
676#95—21no—
677#95C22×D5311yescharacteristic
678#95C22×D5311yescharacteristic
679#95C22×D5311yescharacteristic
680#95C22×D5311yescharacteristic
681C24—1061no—
682C24C2×C22⋊D5311yescharacteristic
683#41—4241no—
684#41—4241no—
685#41—4241no—
686#41—4241no—
687#41—2122no—
688C2×Q8—531no—
689C2×Q8—1061no—
690C2×Q8—1061no—
691C2×D4—531no—
692C2×D4—531no—
693C2×D4—531no—
694C2×D4—1061no—
695C2×D4—1061no—
696C2×D4—1061no—
697C2×D4—1061no—
698C2×D4—1061no—
699C2×D4—1061no—
700C2×D4—1061no—
701C2×D4—1061no—
702C2×D4—1061no—
703C2×D4—1061no—
704C2×D4—1061no—
705C2×D4—1061no—
706C2×D4—4241no—
707C2×D4—4241no—
708C2×D4—2122no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—42no—
714C22×C4—42no—
715C22×C4—42no—
716C22×C4—81no—
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×C4C2×C4×D5311yescharacteristic
726C22×C4C2×C4×D5311yescharacteristic
727C22×C4C2×D21211yescharacteristic
728C22×C4C2×D21211yescharacteristic
729C22×C4C2×C22⋊D5311yescharacteristic
730C22×C4C2×C22⋊D5311yescharacteristic
731C22×C4C2×C22⋊D5311yescharacteristic
732C22×C4C2×C22⋊D5311yescharacteristic
733C22×C4C2×C22⋊D5311yescharacteristic
734C22×C4C23×D5311yescharacteristic
735M16—2122no—
736C2×C8—1061no—
737C2×C8—1061no—
738C2×C8—1061no—
739C2×C8—1061no—
740C2×C8—2122no—
741C4⋊C4—42no—
742C4⋊C4—81no—
743C4⋊C4—531no—
744C4⋊C4—531no—
745C4⋊C4—531no—
746C4⋊C4—531no—
747C4⋊C4—1061no—
748C4⋊C4—1061no—
749C4⋊C4—1061no—
750C4⋊C4—1061no—
751C4⋊C4—1061no—
752C4⋊C4—1061no—
753C4⋊C4—1061no—
754C4⋊C4—1061no—
755C4⋊C4—1061no—
756C4⋊C4—1061no—
757C4⋊C4—1061no—
758C4⋊C4#1171992111yescharacteristic
759C4⋊C4#1171992111yescharacteristic
760C4⋊C4#1171992111yescharacteristic
761C4⋊C4#1171992111yescharacteristic
762C4⋊C4#1171992111yescharacteristic
763C4⋊C4#1171992111yescharacteristic
764C4⋊C4#1171992111yescharacteristic
765C4⋊C4#1171992111yescharacteristic
766C22⋊C4—42no—
767C22⋊C4—1061no—
768C22⋊C4—1061no—
769C22⋊C4—1061no—
770C22⋊C4—1061no—
771C22⋊C4—1061no—
772C22⋊C4—1061no—
773C22⋊C4—1061no—
774C22⋊C4—1061no—
775C22⋊C4—1061no—
776C22⋊C4—1061no—
777C22⋊C4—1061no—
778C22⋊C4—1061no—
779C22⋊C4—1061no—
780C22⋊C4—1061no—
781C22⋊C4—1061no—
782C22⋊C4—1061no—
783C22⋊C4—1061no—
784C22⋊C4—1061no—
785C22⋊C4—1061no—
786C22⋊C4#1171992111yescharacteristic
787C22⋊C4#1171992111yescharacteristic
788C22⋊C4#1171992111yescharacteristic
789C22⋊C4#1171992111yescharacteristic
790C22⋊C4#1171992111yescharacteristic
791C22⋊C4#1171992111yescharacteristic
792C22⋊C4#1171992111yescharacteristic
793C22⋊C4#1171992111yescharacteristic
794C42—42no—
795C42—81no—
796C42—1061no—
797C42—1061no—
798C42—1061no—
799C42C2×C4×D5311yescharacteristic
800C42C2×C4×D5311yescharacteristic
801C42C2×C4×D5311yescharacteristic
802C42C2×C4×D5311yescharacteristic
803C42C2×D21211yescharacteristic
804C42C2×D21211yescharacteristic
805C42C2×D21211yescharacteristic
806C42C2×D21211yescharacteristic
807C23—22no—
808C23—21no—
809C23—21no—
810C23—41no—
811C23—1061no—
812C23—1061no—
813C23—1061no—
814C23—4241no—
815C23—4241no—
816C23—2122no—
817C23C2×#1171992111yescharacteristic
818C23C2×#1171992111yescharacteristic
819C23C22×C22⋊D5311yescharacteristic
820Q8—4241no—
821Q8—4241no—
822Q8—2121no—
823D4—4241no—
824D4—4241no—
825D4—4241no—
826D4—4241no—
827D4—4241no—
828D4—4241no—
829D4—4241no—
830D4—2121no—
831D4—2121no—
832D4—2121no—
833D4—2122no—
834D4—2122no—
835D4—2121no—
836D4—2121no—
837D4—2121no—
838D4—2121no—
839D4—2121no—
840D4—2121no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—22no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—84no—
866C2×C4—1061no—
867C2×C4—1061no—
868C2×C4—1061no—
869C2×C4—1061no—
870C2×C4—1061no—
871C2×C4—4241no—
872C2×C4—4241no—
873C2×C4—4241no—
874C2×C4—4241no—
875C2×C4—4241no—
876C2×C4—4241no—
877C2×C4—4241no—
878C2×C4—2122no—
879C2×C4C2×#1171992111yescharacteristic
880C2×C4C2×#1171992111yescharacteristic
881C2×C4C2×#1171992111yescharacteristic
882C2×C4C2×#1171992111yescharacteristic
883C2×C4C2×#1171992111yescharacteristic
884C2×C4C2×#1171992111yescharacteristic
885C2×C4C2×#1171992111yescharacteristic
886C2×C4C2×#1171992111yescharacteristic
887C2×C4C2×#1171992111yescharacteristic
888C2×C4C2×#1171992111yescharacteristic
889C2×C4C22×C4×D5311yescharacteristic
890C2×C4C22×D21211yescharacteristic
891C8—2121no—
892C8—2121no—
893C8—2121no—
894C8—2121no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—42no—
903C22—42no—
904C22—8482no—
905C22—2121no—
906C22—2121no—
907C22—2121no—
908C22—2121no—
909C22—2121no—
910C22—2121no—
911C22—2121no—
912C22—2121no—
913C22—2121no—
914C22#1681059612yes—
915C22C22×#1171992111yescharacteristic
916C22#1681142611yescharacteristic
917C22#1681143111yescharacteristic
918C4—21no—
919C4—21no—
920C4—21no—
921C4—21no—
922C4—21no—
923C4—21no—
924C4—21no—
925C4—21no—
926C4—21no—
927C4—21no—
928C4—21no—
929C4—21no—
930C4—42no—
931C4—81no—
932C4—81no—
933C4—81no—
934C4—2121no—
935C4—2121no—
936C4—2121no—
937C4—2121no—
938C4—2121no—
939C2—21no—
940C2—21no—
941C2—22no—
942C2—41no—
943C2—4241no—
944C2—4241no—
945C2—4241no—
946C2C2×#1681059611yescharacteristic
947C2#2028323811yescharacteristic
948C2#2028326311yescharacteristic
subgroupG/H
centerC22C22×#11719921
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#2343C2
socleC22×C53C22×C22⋊C4
prime radical#20288450C2
cosocleC22×C4×C53C24
hypercenter#2343D53
hypocenterC53#17604
LCSG ▷ C2×C4×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ C2×#117 ◁ #2343

Complements

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

NH ≅ G/Ntype
2. #20283373C2semidirect
3. #20273290C2semidirect
4. #20273274C2semidirect
5. #20273269C2semidirect
6. #20273261C2semidirect
7. #20273251C2semidirect
8. #20273243C2semidirect
9. #20273238C2semidirect
10. #20273222C2semidirect
11. #20273217C2semidirect
12. #20273209C2semidirect
13. #20273199C2semidirect
14. C2×#16810356C2semidirect
15. C53×#2343C2semidirect
24. #16811251C4semidirect
25. #16811244C4semidirect
26. #16811244C4semidirect
27. #16811228C4semidirect
28. #16811228C4semidirect
29. #16811192C4semidirect
36. #16811103C4semidirect
37. #16811097C4semidirect
40. #16810680C22semidirect
41. #16810680C22semidirect
42. #16810676C22semidirect
43. #16810676C22semidirect
48. #16810359C22semidirect
49. #16810359C22semidirect
50. #16810359C22semidirect
51. #16810359C22semidirect
60. #16810356C22semidirect
61. #16810356C22semidirect
62. #16810356C22semidirect
63. #16810356C22semidirect
68. C53×#383C22semidirect
69. C53×#382C22semidirect
71. C4×C4⋊C4×C53C22semidirect
73. C53×#376C22semidirect
82. #13133217C2×C4semidirect
83. #13133217C2×C4semidirect
85. #13133214C2×C4semidirect
86. #13133214C2×C4semidirect
91. #13133209C2×C4semidirect
92. #13133209C2×C4semidirect
96. #13133205C2×C4semidirect
97. #13133205C2×C4semidirect
134. C4×Dic106C2×C4semidirect
135. C4×Dic106C2×C4semidirect
138. C4×D212C2×C4semidirect
139. C4×D212C2×C4semidirect
140. C4×D212C2×C4semidirect
141. C4×D212C2×C4semidirect
142. C4×D212C2×C4semidirect
143. C4×D212C2×C4semidirect
467. #2343D53semidirect
526. #383C2×D53semidirect
527. #382C2×D53semidirect
529. C4×C4⋊C4C2×D53semidirect
531. #376C2×D53semidirect
549. C53#17604semidirect

Maximal subgroups

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

subgroupindex
#202884502
#202833732
#202732902
#202732742
#202732692
#202732612
#202732512
#202732432
#202732382
#202732222
#202732172
#202732092
#202731992
C2×#168103562
C53×#23432
#1760453