Finite Group Databasebeta

← #27351628

Subgroups — #27351628

Order 13568.

996 conjugacy classes of subgroups.

The subgroup lattice has 952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288764C211yesmaximal, characteristic
2#20283750C211yesmaximal, characteristic, complemented
3#20273290C211yesmaximal, characteristic, complemented
4#20273286C211yesmaximal, characteristic, complemented
5#20273278C211yesmaximal, characteristic, complemented
6#20273269C211yesmaximal, characteristic, complemented
7#20273265C211yesmaximal, characteristic, complemented
8#20273256C211yesmaximal, characteristic, complemented
9#20273251C211yesmaximal, characteristic, complemented
10#20273247C211yesmaximal, characteristic, complemented
11#20273234C211yesmaximal, characteristic, complemented
12#20273217C211yesmaximal, characteristic, complemented
13#20273204C211yesmaximal, characteristic, complemented
14C2×#16810359C211yesmaximal, characteristic, complemented
15C53×#2318C211yesmaximal, characteristic, complemented
16#16811343C411yescharacteristic, complemented
17#16811328—21no—
18#16811313C411yescharacteristic, complemented
19#16811313C411yescharacteristic, complemented
20#16811299—21no—
21#16811299—21no—
22D4×Dic106C411yescharacteristic, complemented
23#16811282C411yescharacteristic, complemented
24#16811282C411yescharacteristic, complemented
25#16811278C411yescharacteristic, complemented
26#16811277C411yescharacteristic, complemented
27#16811267—21no—
28#16811238—21no—
29#16811215—21no—
30#16811215—21no—
31#16811180C2211yescharacteristic
32#16811157C2211yescharacteristic
33#16811134C2211yescharacteristic
34#16811134C2211yescharacteristic
35C2×#13133196C2211yescharacteristic
36C2×#13133196C2211yescharacteristic
37#16811102—21no—
38#16810701—21no—
39#16810695—21no—
40#16810695—21no—
41D4×#88322—21no—
42#16810680C2211yescharacteristic
43#16810676C2211yescharacteristic
44#16810587C2211yescharacteristic
45#16810587C2211yescharacteristic
46C2×C22⋊#88322C2211yescharacteristic
47C2×C22⋊#88322C2211yescharacteristic
48#16810359C2211yescharacteristic
49#16810359C2211yescharacteristic
50#16810359C2211yescharacteristic
51#16810359C2211yescharacteristic
52#16810359C2211yescharacteristic
53#16810359C2211yescharacteristic
54#16810359C2211yescharacteristic
55#16810359C2211yescharacteristic
56#16810359C2211yescharacteristic
57#16810359C2211yescharacteristic
58#16810359C2211yescharacteristic
59#16810359C2211yescharacteristic
60#16810356C2211yescharacteristic
61#16810356C2211yescharacteristic
62#16810356C2211yescharacteristic
63#16810356C2211yescharacteristic
64C2×C4×D4×C53C2211yescharacteristic
65C53×#388—21no—
66C53×#387—21no—
67C53×#386—21no—
68C53×#385—21no—
69C53×#383C2211yescharacteristic
70C53×#382C2211yescharacteristic
71C53×#381C2211yescharacteristic
72C53×#380C2211yescharacteristic
73C4×C22⋊C4×C53C2211yescharacteristic
74C2×#95×C53C2211yescharacteristic
75C2×#11719945C2×C411yescharacteristic
76C2×#11719945C2×C411yescharacteristic, complemented
77C2×#11719947—21no—
78C22×Dic106C2×C411yescharacteristic
79C22×Dic106C2×C411yescharacteristic, complemented
80C2×#11719917—21no—
81C2×#11719917—21no—
82C22×#88322—21no—
83C22×#88322—21no—
84#13133217C2×C411yescharacteristic, complemented
85#13133217C2×C411yescharacteristic, complemented
86#13133216—21no—
87#13133211—21no—
88#13133210—21no—
89#13133210—21no—
90#13133210—21no—
91#13133210—21no—
92#13133209—21no—
93#13133209C2×C411yescharacteristic, complemented
94#13133207—21no—
95#13133207—21no—
96#13133205C2×C411yescharacteristic, complemented
97#13133204—21no—
98#13133203—21no—
99#13133203—21no—
100#13133201—21no—
101#13133201—21no—
102#13133200—21no—
103#13133200—21no—
104#13133200—21no—
105#13133199—21no—
106#13133199—21no—
107#13133198—21no—
108#13133198—21no—
109#13133197—21no—
110#13133196—21no—
111#13133196—21no—
112#13133196—21no—
113#13133196—21no—
114#13133196—21no—
115#13133196C2×C411yescharacteristic
116#13133196C2×C411yescharacteristic
117#13133196C2×C411yescharacteristic
118#13133196C2×C411yescharacteristic, complemented
119#13133196C2×C411yescharacteristic, complemented
120#13133196C2×C411yescharacteristic, complemented
121#13133196C2311yescharacteristic
122#13133196C2311yescharacteristic
123#13133196C2311yescharacteristic
124#13133195—21no—
125#13133195—21no—
126#13133194—21no—
127#13133194—21no—
128#13133191C2×C411yescharacteristic
129#13133191C2×C411yescharacteristic, complemented
130#13133191C2311yescharacteristic
131#13133189—21no—
132#13133189—21no—
133#13133188—21no—
134#13133186—21no—
135#13133186—21no—
136C4×Dic106—21no—
137C4×Dic106C2×C411yescharacteristic, complemented
138C4×Dic106C2×C411yescharacteristic, complemented
139C4×Dic106C2×C411yescharacteristic, complemented
140#13133182—21no—
141C4×D212C2×C411yescharacteristic, complemented
142D4×Dic53—21no—
143C4×C22⋊D53—21no—
144C4×C22⋊D53—21no—
145C4×C22⋊D53—21no—
146C4×C22⋊D53—21no—
147C4×C22⋊D53—21no—
148#13133177—21no—
149#13133177—21no—
150#13133176—21no—
151#13133176C2×C411yescharacteristic
152#13133176C2×C411yescharacteristic, complemented
153#13133174—21no—
154#13133173—21no—
155#13133173—21no—
156C2×C4⋊Dic53C2×C411yescharacteristic
157C2×C4⋊Dic53C2×C411yescharacteristic, complemented
158C2×#11719919—21no—
159C2×#11719919—21no—
160C4⋊C4×D53—21no—
161C2×C22⋊Dic53—21no—
162C2×C22⋊Dic53—21no—
163C4⋊#88322—21no—
164C4⋊#88322—21no—
165C22⋊#88322—21no—
166C22⋊#88322—21no—
167C22⋊#88322—21no—
168C22⋊#88322—21no—
169C22⋊#88322C2311yescharacteristic
170C22⋊#88322C2311yescharacteristic
171C22⋊#88322C2311yescharacteristic
172C22⋊#88322C2311yescharacteristic
173#13133128—21no—
174C4×#88322—21no—
175C22×D4×C53D411yescharacteristic
176C23×C4×C53—21no—
177C23×C4×C53C2311yescharacteristic
178C23×C4×C53C2311yescharacteristic
179C4×D4×C53C2×C411yescharacteristic
180C4×D4×C53C2×C411yescharacteristic
181C4×D4×C53C2×C411yescharacteristic
182C4×D4×C53C2×C411yescharacteristic
183C4×D4×C53D411yescharacteristic
184C4×D4×C53D411yescharacteristic
185C4×D4×C53D411yescharacteristic
186C4×D4×C53D411yescharacteristic
187C2×C4⋊C4×C53—21no—
188C2×C4⋊C4×C53—21no—
189C2×C4⋊C4×C53D411yescharacteristic
190C2×C22⋊C4×C53—21no—
191C2×C22⋊C4×C53—21no—
192C2×C22⋊C4×C53—21no—
193C2×C22⋊C4×C53D411yescharacteristic
194C2×C22⋊C4×C53D411yescharacteristic
195C2×C42×C53—21no—
196C2×C42×C53C2311yescharacteristic
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
207C24×C53C2×D411yescharacteristic
208C2×D4×C53—42no—
209C2×D4×C53C22⋊C411yescharacteristic
210C2×D4×C53C22⋊C411yescharacteristic
211C2×D4×C53C22⋊C411yescharacteristic
212C2×D4×C53C22⋊C411yescharacteristic
213C22×C4×C53—21no—
214C22×C4×C53—21no—
215C22×C4×C53—21no—
216C22×C4×C53—21no—
217C22×C4×C53—42no—
218C22×C4×C53—81no—
219C22×C4×C53—81no—
220C22×C4×C53—81no—
221C22×C4×C53—81no—
222C22×C4×C53C22×C411yescharacteristic
223C22×C4×C53C22×C411yescharacteristic
224C22×C4×C53C22×C411yescharacteristic
225C22×C4×C53C22×C411yescharacteristic
226C22×C4×C53C2×D411yescharacteristic
227C22×C4×C53C2×D411yescharacteristic
228C22×C4×C53C2×D411yescharacteristic
229C22×C4×C53C2×D411yescharacteristic
230C22×C4×C53C2×D411yescharacteristic
231C22×C4×C53C2×D411yescharacteristic
232C22×C4×C53C2×D411yescharacteristic
233C22×C4×C53C2×D411yescharacteristic
234C22×C4×C53C2411yescharacteristic
235C2×C22⋊D53—21no—
236C2×C22⋊D53—21no—
237C2×C22⋊D53—21no—
238C2×C22⋊D53—21no—
239C2×C22⋊D53—21no—
240C22×Dic53—21no—
241C22×Dic53—21no—
242C22×Dic53—21no—
243C22×Dic53—21no—
244#11719947—44no—
245#11719945—81no—
246#11719945—81no—
247C2×D212C22×C411yescharacteristic
248C2×C4×D53—21no—
249C2×C4×D53—21no—
250C2×C4×D53—21no—
251C2×Dic106—21no—
252C2×Dic106—21no—
253C2×Dic106—21no—
254C2×Dic106—81no—
255C2×Dic106—81no—
256C2×Dic106C22×C411yescharacteristic
257C2×Dic106C22×C411yescharacteristic
258C2×Dic106C22×C411yescharacteristic
259C4⋊C4×C53—81no—
260C4⋊C4×C53—81no—
261C4⋊C4×C53C22⋊C411yescharacteristic
262C4⋊C4×C53C22⋊C411yescharacteristic
263C4⋊C4×C53C22⋊C411yescharacteristic
264C4⋊C4×C53C22⋊C411yescharacteristic
265C22⋊C4×C53—42no—
266C22⋊C4×C53—81no—
267C22⋊C4×C53—81no—
268C22⋊C4×C53C22⋊C411yescharacteristic
269C22⋊C4×C53C22⋊C411yescharacteristic
270C22⋊C4×C53C22⋊C411yescharacteristic
271C22⋊C4×C53C22⋊C411yescharacteristic
272C22⋊C4×C53C22⋊C411yescharacteristic
273C22⋊C4×C53C22⋊C411yescharacteristic
274C22⋊C4×C53C22⋊C411yescharacteristic
275C22⋊C4×C53C22⋊C411yescharacteristic
276C42×C53—81no—
277C42×C53C22×C411yescharacteristic
278C42×C53C22×C411yescharacteristic
279C42×C53C2×D411yescharacteristic
280C42×C53C2×D411yescharacteristic
281C22⋊Dic53—21no—
282C22⋊Dic53—21no—
283C22⋊Dic53—21no—
284C22⋊Dic53—21no—
285C22⋊Dic53—21no—
286C22⋊Dic53—21no—
287C22⋊Dic53—21no—
288C22⋊Dic53—21no—
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—
298C4⋊Dic53—21no—
299C4⋊Dic53—21no—
300C4⋊Dic53—21no—
301C4⋊Dic53—21no—
302C4⋊Dic53—21no—
303C4⋊Dic53C22×C411yescharacteristic
304C4⋊Dic53C22×C411yescharacteristic
305C4⋊Dic53C22×C411yescharacteristic
306C4⋊Dic53C22×C411yescharacteristic
307#11719919—21no—
308#11719919—21no—
309#11719919—21no—
310#11719919—21no—
311#11719919—21no—
312#11719919—21no—
313#11719919—21no—
314#11719919—21no—
315#11719919—21no—
316#11719919—21no—
317#11719919—21no—
318#11719919—21no—
319#11719919—21no—
320#11719919—21no—
321C4×Dic53—21no—
322C4×Dic53—21no—
323C4×Dic53—21no—
324C4×Dic53—21no—
325C4×Dic53—21no—
326#11719917—81no—
327#11719917—81no—
328C2×#88322—21no—
329C2×#88322—21no—
330C2×#88322—21no—
331C2×#88322—21no—
332C2×#88322—81no—
333C2×#88322—81no—
334C23×C53—21no—
335C23×C53—21no—
336C23×C53—22no—
337C23×C53—21no—
338C23×C53—21no—
339C23×C53—41no—
340C23×C53—41no—
341C23×C53—41no—
342C23×C53C2×C22⋊C411yescharacteristic
343C23×C53C2×C22⋊C411yescharacteristic
344C23×C53C2×C22⋊C411yescharacteristic
345C23×C53C2×C22⋊C411yescharacteristic
346C23×C53C22×D411yescharacteristic
347C22×D53—21no—
348D4×C53—22no—
349D4×C53—22no—
350D4×C53—41no—
351D4×C53—41no—
352C2×C4×C53—21no—
353C2×C4×C53—21no—
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—41no—
370C2×C4×C53—41no—
371C2×C4×C53—41no—
372C2×C4×C53—41no—
373C2×C4×C53—41no—
374C2×C4×C53—41no—
375C2×C4×C53—41no—
376C2×C4×C53—41no—
377C2×C4×C53—41no—
378C2×C4×C53—84no—
379C2×C4×C53C2×C22⋊C411yescharacteristic
380C2×C4×C53C2×C22⋊C411yescharacteristic
381C2×C4×C53C2×C22⋊C411yescharacteristic
382C2×C4×C53C2×C22⋊C411yescharacteristic
383C2×C4×C53C2×C22⋊C411yescharacteristic
384C2×C4×C53C2×C22⋊C411yescharacteristic
385C2×C4×C53C2×C22⋊C411yescharacteristic
386C2×C4×C53C2×C22⋊C411yescharacteristic
387C2×C4×C53C23×C411yescharacteristic
388C2×C4×C53C22×D411yescharacteristic
389C22⋊D53—42no—
390C22⋊D53—41no—
391C22⋊D53—41no—
392C22⋊D53—42no—
393C22⋊D53—81no—
394C22⋊D53—81no—
395C2×Dic53—21no—
396C2×Dic53—21no—
397C2×Dic53—21no—
398C2×Dic53—21no—
399C2×Dic53—21no—
400C2×Dic53—21no—
401C2×Dic53—21no—
402C2×Dic53—42no—
403C2×Dic53—42no—
404C2×Dic53—81no—
405C2×Dic53—81no—
406D212—41no—
407C4×D53—42no—
408C4×D53—81no—
409C4×D53—81no—
410Dic106—42no—
411Dic106—41no—
412Dic106—41no—
413Dic106—41no—
414Dic106—81no—
415Dic106—81no—
416#88322—41no—
417#88322—41no—
418#88322—41no—
419#88322—41no—
420#17598—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—21no—
429C22×C53—21no—
430C22×C53—21no—
431C22×C53—21no—
432C22×C53—21no—
433C22×C53—21no—
434C22×C53—42no—
435C22×C53—42no—
436C22×C53—81no—
437C22×C53—81no—
438C22×C53#42112yes—
439C22×C53C22×C22⋊C411yescharacteristic
440C22×C53#57711yescharacteristic
441C22×C53#57811yescharacteristic
442C2×D53—41no—
443C2×D53—41no—
444C2×D53—41no—
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—81no—
456C4×C53—81no—
457C4×C53—81no—
458C4×C53—81no—
459Dic53—41no—
460Dic53—41no—
461Dic53—41no—
462Dic53—41no—
463Dic53—41no—
464Dic53—41no—
465Dic53—41no—
466#3520—531no—
467#2974—531no—
468#2318D5311yescharacteristic, complemented
469#1521—531no—
470#1520—531no—
471#1518—531no—
472#1516—531no—
473#1515—531no—
474#1513—531no—
475#1512—531no—
476#1511—531no—
477#1508—531no—
478#1504—531no—
479#1501—531no—
480C2×#328—531no—
481C2×C53—21no—
482C2×C53—21no—
483C2×C53—22no—
484C2×C53—41no—
485C2×C53—41no—
486C2×C53—41no—
487C2×C53#288311yescharacteristic
488C2×C53#289811yescharacteristic
489C2×C53C2×#42111yescharacteristic
490D53—81no—
491#556—531no—
492#554—1061no—
493#552—531no—
494#552—531no—
495#551—1061no—
496#551—1061no—
497D4×Q8—531no—
498#548—531no—
499#548—531no—
500#547—531no—
501#547—531no—
502#546—1061no—
503#542—1061no—
504#539—1061no—
505#539—1061no—
506#533—531no—
507#529—531no—
508#525—531no—
509#525—531no—
510C2×C22⋊Q8—531no—
511C2×C22⋊Q8—531no—
512#520—1061no—
513C2×C4×D4C2×D5311yescharacteristic
514#436—1061no—
515#435—1061no—
516#435—1061no—
517C8×D4—1061no—
518#432—531no—
519#431—531no—
520#407—531no—
521#407—531no—
522C2×C22⋊C8—531no—
523C2×C22⋊C8—531no—
524#388—21no—
525#387—21no—
526#386—21no—
527#385—21no—
528#383C2×D5311yescharacteristic
529#382C2×D5311yescharacteristic
530#381C2×D5311yescharacteristic
531#380C2×D5311yescharacteristic
532C4×C22⋊C4C2×D5311yescharacteristic
533C2×#95C2×D5311yescharacteristic
534#328—531no—
535#328—531no—
536#328—531no—
537#328—531no—
538#328—531no—
539#328—531no—
540#328—531no—
541#328—531no—
542#328—531no—
543#328—531no—
544#328—531no—
545#328—531no—
546#327—531no—
547#327—531no—
548#327—531no—
549#327—531no—
550C53#1759811yescharacteristic, complemented, Sylow
551C2×#41—531no—
552C2×#41—531no—
553C2×#41—1061no—
554C22×Q8—531no—
555C22×Q8—531no—
556C22×D4C22⋊D5311yescharacteristic
557C23×C4—21no—
558C23×C4C22×D5311yescharacteristic
559C23×C4C22×D5311yescharacteristic
560C2×M16—1061no—
561C2×M16—1061no—
562C22×C8—1061no—
563C22×C8—1061no—
564C4⋊Q8—531no—
565C4⋊Q8—531no—
566C4⋊Q8—1061no—
567#126—1061no—
568#126—1061no—
569#126—1061no—
570#126—1061no—
571#126—1061no—
572#125—531no—
573#125—1061no—
574#125—1061no—
575#125—1061no—
576#124—531no—
577#124—1061no—
578#124—1061no—
579#124—1061no—
580#123—1061no—
581#123—1061no—
582#123—1061no—
583#123—1061no—
584#123—1061no—
585#123—1061no—
586#123—1061no—
587#123—1061no—
588#123—1061no—
589C22⋊Q8—531no—
590C22⋊Q8—531no—
591C22⋊Q8—531no—
592C22⋊Q8—531no—
593C22⋊Q8—531no—
594C22⋊Q8—531no—
595C22⋊Q8—531no—
596C22⋊Q8—531no—
597C22⋊Q8—531no—
598C22⋊Q8—1061no—
599C22⋊Q8—1061no—
600C22⋊Q8—1061no—
601C22⋊Q8—1061no—
602C22⋊Q8—1061no—
603C22⋊Q8—1061no—
604C22⋊Q8—1061no—
605C22⋊Q8—1061no—
606C22⋊Q8—1061no—
607C22⋊Q8—1061no—
608#121—531no—
609#121—531no—
610#121—531no—
611#121—1061no—
612#121—1061no—
613#121—1061no—
614#120—1061no—
615#120—1061no—
616C4×Q8—531no—
617C4×Q8—531no—
618C4×Q8—531no—
619C4×Q8—1061no—
620C4×Q8—1061no—
621C4×D4—531no—
622C4×D4—1061no—
623C4×D4—1061no—
624C4×D4—1061no—
625C4×D4—1061no—
626C4×D4—1061no—
627C4×D4—1061no—
628C4×D4—1061no—
629C4×D4—1061no—
630C4×D4C4×D5311yescharacteristic
631C4×D4C4×D5311yescharacteristic
632C4×D4C4×D5311yescharacteristic
633C4×D4C4×D5311yescharacteristic
634C4×D4D21211yescharacteristic
635C4×D4D21211yescharacteristic
636C4×D4D21211yescharacteristic
637C4×D4D21211yescharacteristic
638#117—531no—
639#117—531no—
640#117—1061no—
641#117—1061no—
642#117—1061no—
643#117—1061no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—531no—
647C2×C4⋊C4—531no—
648C2×C4⋊C4—1061no—
649C2×C4⋊C4—1061no—
650C2×C4⋊C4—1061no—
651C2×C4⋊C4C22⋊D5311yescharacteristic
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—1061no—
656C2×C22⋊C4—1061no—
657C2×C22⋊C4C22⋊D5311yescharacteristic
658C2×C22⋊C4C22⋊D5311yescharacteristic
659C2×C42—21no—
660C2×C42C22×D5311yescharacteristic
661C4⋊C8—1061no—
662C4⋊C8—1061no—
663C22⋊C8—531no—
664C22⋊C8—531no—
665C22⋊C8—531no—
666C22⋊C8—531no—
667C22⋊C8—1061no—
668C22⋊C8—1061no—
669C22⋊C8—1061no—
670C22⋊C8—1061no—
671#97—1061no—
672C4×C8—1061no—
673#95—21no—
674#95—21no—
675#95—21no—
676#95—21no—
677#95—21no—
678#95C22×D5311yescharacteristic
679#95C22×D5311yescharacteristic
680#95C22×D5311yescharacteristic
681#95C22×D5311yescharacteristic
682C24C2×C22⋊D5311yescharacteristic
683C24C2×C22⋊D5311yescharacteristic
684#41—4241no—
685#41—4241no—
686#41—2124no—
687C2×Q8—531no—
688C2×Q8—531no—
689C2×Q8—531no—
690C2×Q8—1061no—
691C2×Q8—1061no—
692C2×Q8—1061no—
693C2×Q8—4241no—
694C2×Q8—4241no—
695C2×D4—42no—
696C2×D4—531no—
697C2×D4—1061no—
698C2×D4—1061no—
699C2×D4—1061no—
700C2×D4—1061no—
701C2×D4—1061no—
702C2×D4#1171992111yescharacteristic
703C2×D4#1171992111yescharacteristic
704C2×D4#1171992111yescharacteristic
705C2×D4#1171992111yescharacteristic
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—42no—
711C22×C4—81no—
712C22×C4—81no—
713C22×C4—81no—
714C22×C4—81no—
715C22×C4—1061no—
716C22×C4—1061no—
717C22×C4—1061no—
718C22×C4—1061no—
719C22×C4—1061no—
720C22×C4—1061no—
721C22×C4—1061no—
722C22×C4C2×C4×D5311yescharacteristic
723C22×C4C2×C4×D5311yescharacteristic
724C22×C4C2×C4×D5311yescharacteristic
725C22×C4C2×C4×D5311yescharacteristic
726C22×C4C2×D21211yescharacteristic
727C22×C4C2×D21211yescharacteristic
728C22×C4C2×D21211yescharacteristic
729C22×C4C2×D21211yescharacteristic
730C22×C4C2×C22⋊D5311yescharacteristic
731C22×C4C2×C22⋊D5311yescharacteristic
732C22×C4C2×C22⋊D5311yescharacteristic
733C22×C4C2×C22⋊D5311yescharacteristic
734C22×C4C23×D5311yescharacteristic
735M16—4241no—
736M16—4241no—
737C2×C8—1061no—
738C2×C8—1061no—
739C2×C8—1061no—
740C2×C8—1061no—
741C2×C8—4241no—
742C2×C8—4241no—
743C4⋊C4—81no—
744C4⋊C4—81no—
745C4⋊C4—531no—
746C4⋊C4—531no—
747C4⋊C4—531no—
748C4⋊C4—531no—
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—1061no—
759C4⋊C4—1061no—
760C4⋊C4—1061no—
761C4⋊C4—1061no—
762C4⋊C4—1061no—
763C4⋊C4—1061no—
764C4⋊C4—1061no—
765C4⋊C4—1061no—
766C4⋊C4—1061no—
767C4⋊C4—1061no—
768C4⋊C4#1171992111yescharacteristic
769C4⋊C4#1171992111yescharacteristic
770C4⋊C4#1171992111yescharacteristic
771C4⋊C4#1171992111yescharacteristic
772C22⋊C4—42no—
773C22⋊C4—81no—
774C22⋊C4—81no—
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—1061no—
787C22⋊C4—1061no—
788C22⋊C4—1061no—
789C22⋊C4—1061no—
790C22⋊C4—1061no—
791C22⋊C4—1061no—
792C22⋊C4#1171992111yescharacteristic
793C22⋊C4#1171992111yescharacteristic
794C22⋊C4#1171992111yescharacteristic
795C22⋊C4#1171992111yescharacteristic
796C22⋊C4#1171992111yescharacteristic
797C22⋊C4#1171992111yescharacteristic
798C22⋊C4#1171992111yescharacteristic
799C22⋊C4#1171992111yescharacteristic
800C42—81no—
801C42—1061no—
802C42—1061no—
803C42—1061no—
804C42—1061no—
805C42—1061no—
806C42C2×C4×D5311yescharacteristic
807C42C2×C4×D5311yescharacteristic
808C42C2×D21211yescharacteristic
809C42C2×D21211yescharacteristic
810C23—22no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—1061no—
819C23C2×#1171992111yescharacteristic
820C23C2×#1171992111yescharacteristic
821C23C2×#1171992111yescharacteristic
822C23C2×#1171992111yescharacteristic
823C23C22×C22⋊D5311yescharacteristic
824Q8—4241no—
825Q8—4241no—
826Q8—2121no—
827Q8—2121no—
828Q8—2121no—
829Q8—2122no—
830D4—22no—
831D4—22no—
832D4—41no—
833D4—41no—
834D4—4241no—
835D4—4241no—
836D4—2121no—
837D4—2122no—
838D4—2122no—
839D4—2121no—
840D4—2121no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
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—41no—
866C2×C4—41no—
867C2×C4—84no—
868C2×C4—1061no—
869C2×C4—1061no—
870C2×C4—1061no—
871C2×C4—1061no—
872C2×C4—1061no—
873C2×C4—1061no—
874C2×C4—1061no—
875C2×C4—4241no—
876C2×C4—4241no—
877C2×C4—4241no—
878C2×C4—4241no—
879C2×C4—2122no—
880C2×C4—2122no—
881C2×C4—2122no—
882C2×C4C2×#1171992111yescharacteristic
883C2×C4C2×#1171992111yescharacteristic
884C2×C4C2×#1171992111yescharacteristic
885C2×C4C2×#1171992111yescharacteristic
886C2×C4C2×#1171992111yescharacteristic
887C2×C4C2×#1171992111yescharacteristic
888C2×C4C2×#1171992111yescharacteristic
889C2×C4C2×#1171992111yescharacteristic
890C2×C4C22×C4×D5311yescharacteristic
891C2×C4C22×D21211yescharacteristic
892C8—2121no—
893C8—2121no—
894C8—2121no—
895C8—2121no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—21no—
903C22—21no—
904C22—21no—
905C22—21no—
906C22—21no—
907C22—21no—
908C22—21no—
909C22—42no—
910C22—42no—
911C22—81no—
912C22—81no—
913C22—2121no—
914C22—2121no—
915C22—2121no—
916C22#1681064112yes—
917C22C22×#1171992111yescharacteristic
918C22#1681143411yescharacteristic
919C22#1681143811yescharacteristic
920C4—21no—
921C4—21no—
922C4—21no—
923C4—21no—
924C4—21no—
925C4—21no—
926C4—21no—
927C4—21no—
928C4—21no—
929C4—21no—
930C4—81no—
931C4—81no—
932C4—81no—
933C4—81no—
934C4—2121no—
935C4—2121no—
936C4—2121no—
937C4—2121no—
938C4—2121no—
939C4—2121no—
940C4—2121no—
941C2—21no—
942C2—21no—
943C2—22no—
944C2—41no—
945C2—41no—
946C2—41no—
947C2—4241no—
948C2#2028317511yescharacteristic
949C2#2028324511yescharacteristic
950C2C2×#1681064111yescharacteristic
subgroupG/H
centerC22C22×#11719921
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#2318C2
socleC22×C53C22×C22⋊C4
prime radical#20288764C2
cosocleC22×C4×C53C24
hypercenter#2318D53
hypocenterC53#17598
LCSG ▷ C2×C4×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2318

Complements

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

NH ≅ G/Ntype
2. #20283750C2semidirect
3. #20273290C2semidirect
4. #20273286C2semidirect
5. #20273278C2semidirect
6. #20273269C2semidirect
7. #20273265C2semidirect
8. #20273256C2semidirect
9. #20273251C2semidirect
10. #20273247C2semidirect
11. #20273234C2semidirect
12. #20273217C2semidirect
13. #20273204C2semidirect
14. C2×#16810359C2semidirect
15. C53×#2318C2semidirect
16. #16811343C4semidirect
18. #16811313C4semidirect
19. #16811313C4semidirect
22. D4×Dic106C4semidirect
23. #16811282C4semidirect
24. #16811282C4semidirect
25. #16811278C4semidirect
26. #16811277C4semidirect
76. C2×#11719945C2×C4semidirect
79. C22×Dic106C2×C4semidirect
84. #13133217C2×C4semidirect
85. #13133217C2×C4semidirect
93. #13133209C2×C4semidirect
96. #13133205C2×C4semidirect
118. #13133196C2×C4semidirect
119. #13133196C2×C4semidirect
120. #13133196C2×C4semidirect
129. #13133191C2×C4semidirect
137. C4×Dic106C2×C4semidirect
138. C4×Dic106C2×C4semidirect
139. C4×Dic106C2×C4semidirect
141. C4×D212C2×C4semidirect
152. #13133176C2×C4semidirect
157. C2×C4⋊Dic53C2×C4semidirect
468. #2318D53semidirect
550. C53#17598semidirect

Maximal subgroups

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

subgroupindex
#202887642
#202837502
#202732902
#202732862
#202732782
#202732692
#202732652
#202732562
#202732512
#202732472
#202732342
#202732172
#202732042
C2×#168103592
C53×#23182
#1759853