Finite Group Databasebeta

← #27351636

Subgroups — #27351636

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#20277348C211yesmaximal, characteristic, complemented
3#20273293C211yesmaximal, characteristic, complemented
4#20273288C211yesmaximal, characteristic, complemented
5#20273280C211yesmaximal, characteristic, complemented
6#20273272C211yesmaximal, characteristic, complemented
7#20273267C211yesmaximal, characteristic, complemented
8#20273259C211yesmaximal, characteristic, complemented
9#20273254C211yesmaximal, characteristic, complemented
10#20273249C211yesmaximal, characteristic, complemented
11#20273236C211yesmaximal, characteristic, complemented
12#20273220C211yesmaximal, characteristic, complemented
13#20273207C211yesmaximal, characteristic, complemented
14C2×#16810361C211yesmaximal, characteristic, complemented
15C53×#2974C211yesmaximal, 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#16810516—21no—
39#16810509—21no—
40#16810503—21no—
41#16810498—21no—
42#16810491C2211yescharacteristic
43#16810489C2211yescharacteristic
44#16810486C2211yescharacteristic
45#16810483C2211yescharacteristic
46C4×C22⋊Dic53C2211yescharacteristic
47C2×#13133124C2211yescharacteristic
48#16810361C2211yescharacteristic
49#16810361C2211yescharacteristic
50#16810361C2211yescharacteristic
51#16810361C2211yescharacteristic
52#16810361C2211yescharacteristic
53#16810361C2211yescharacteristic
54#16810361C2211yescharacteristic
55#16810361C2211yescharacteristic
56#16810361C2211yescharacteristic
57#16810361C2211yescharacteristic
58#16810361C2211yescharacteristic
59#16810361C2211yescharacteristic
60#16810358C2211yescharacteristic
61#16810358C2211yescharacteristic
62#16810358C2211yescharacteristic
63#16810358C2211yescharacteristic
64C2×C4×D4×C53C2211yescharacteristic
65C53×#436—21no—
66C53×#435—21no—
67C53×#435—21no—
68C8×D4×C53—21no—
69C53×#432C2211yescharacteristic
70C53×#431C2211yescharacteristic
71C53×#407C2211yescharacteristic
72C53×#407C2211yescharacteristic
73C2×C22⋊C8×C53C2211yescharacteristic
74C2×C22⋊C8×C53C2211yescharacteristic
75C2×#11719945C2×C411yescharacteristic
76C2×#11719945C2×C411yescharacteristic, complemented
77C2×#11719947—21no—
78C22×Dic106C2×C411yescharacteristic
79C22×Dic106C2×C411yescharacteristic, complemented
80C23×Dic53—21no—
81#13133217C2×C411yescharacteristic, complemented
82#13133217C2×C411yescharacteristic, complemented
83#13133216—21no—
84#13133211—21no—
85#13133210—21no—
86#13133210—21no—
87#13133210—21no—
88#13133210—21no—
89#13133209—21no—
90#13133209C2×C411yescharacteristic, complemented
91#13133207—21no—
92#13133207—21no—
93#13133205C2×C411yescharacteristic, complemented
94#13133204—21no—
95#13133203—21no—
96#13133203—21no—
97#13133201—21no—
98#13133201—21no—
99#13133200—21no—
100#13133200—21no—
101#13133200—21no—
102#13133199—21no—
103#13133199—21no—
104#13133198—21no—
105#13133198—21no—
106#13133197—21no—
107#13133196—21no—
108#13133196—21no—
109#13133196—21no—
110#13133196—21no—
111#13133196—21no—
112#13133196C2×C411yescharacteristic
113#13133196C2×C411yescharacteristic
114#13133196C2×C411yescharacteristic
115#13133196C2×C411yescharacteristic, complemented
116#13133196C2×C411yescharacteristic, complemented
117#13133196C2×C411yescharacteristic, complemented
118#13133196C2311yescharacteristic
119#13133196C2311yescharacteristic
120#13133196C2311yescharacteristic
121#13133195—21no—
122#13133195—21no—
123#13133194—21no—
124#13133194—21no—
125#13133191C2×C411yescharacteristic
126#13133191C2×C411yescharacteristic, complemented
127#13133191C2311yescharacteristic
128#13133189—21no—
129#13133189—21no—
130#13133188—21no—
131#13133186—21no—
132#13133186—21no—
133C4×Dic106—21no—
134C4×Dic106C2×C411yescharacteristic, complemented
135C4×Dic106C2×C411yescharacteristic, complemented
136C4×Dic106C2×C411yescharacteristic, complemented
137#13133182—21no—
138C4×D212C2×C411yescharacteristic, complemented
139D4×Dic53—21no—
140C4×C22⋊D53—21no—
141C4×C22⋊D53—21no—
142C4×C22⋊D53—21no—
143C4×C22⋊D53—21no—
144C4×C22⋊D53—21no—
145#13133177—21no—
146#13133177—21no—
147#13133176—21no—
148#13133176C2×C411yescharacteristic
149#13133176C2×C411yescharacteristic, complemented
150#13133174—21no—
151#13133173—21no—
152#13133173—21no—
153C2×C4⋊Dic53—21no—
154C2×C4⋊Dic53—21no—
155C2×C4⋊Dic53C2×C411yescharacteristic
156C2×C4⋊Dic53C2×C411yescharacteristic, complemented
157C2×#11719919—21no—
158C2×#11719919—21no—
159C4⋊C4×D53—21no—
160C2×C22⋊Dic53—21no—
161C2×C22⋊Dic53—21no—
162C2×C22⋊Dic53—21no—
163C2×C22⋊Dic53—21no—
164C2×C22⋊Dic53—21no—
165C2×C4×Dic53—21no—
166#13133124—21no—
167#13133124—21no—
168#13133124—21no—
169#13133124—21no—
170#13133124—21no—
171#13133124C2311yescharacteristic
172#13133124C2311yescharacteristic
173#13133124C2311yescharacteristic
174#13133124C2311yescharacteristic
175C22×D4×C53D411yescharacteristic
176C23×C4×C53C2311yescharacteristic
177C23×C4×C53C2311yescharacteristic
178C2×M16×C53—21no—
179C2×M16×C53—21no—
180C22×C8×C53—21no—
181C22×C8×C53—21no—
182C4×D4×C53C2×C411yescharacteristic
183C4×D4×C53C2×C411yescharacteristic
184C4×D4×C53C2×C411yescharacteristic
185C4×D4×C53C2×C411yescharacteristic
186C4×D4×C53D411yescharacteristic
187C4×D4×C53D411yescharacteristic
188C4×D4×C53D411yescharacteristic
189C4×D4×C53D411yescharacteristic
190C2×C4⋊C4×C53D411yescharacteristic
191C2×C22⋊C4×C53D411yescharacteristic
192C2×C22⋊C4×C53D411yescharacteristic
193C2×C42×C53C2311yescharacteristic
194C4⋊C8×C53—21no—
195C4⋊C8×C53—21no—
196C22⋊C8×C53—21no—
197C22⋊C8×C53—21no—
198C22⋊C8×C53—21no—
199C22⋊C8×C53—21no—
200C22⋊C8×C53C2311yescharacteristic
201C22⋊C8×C53C2311yescharacteristic
202C22⋊C8×C53C2311yescharacteristic
203C22⋊C8×C53C2311yescharacteristic
204#97×C53—21no—
205C4×C8×C53—21no—
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—81no—
214C22×C4×C53—81no—
215C22×C4×C53C22×C411yescharacteristic
216C22×C4×C53C22×C411yescharacteristic
217C22×C4×C53C22×C411yescharacteristic
218C22×C4×C53C22×C411yescharacteristic
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×C53C2×D411yescharacteristic
226C22×C4×C53C2×D411yescharacteristic
227C22×C4×C53C2411yescharacteristic
228C2×C22⋊D53—21no—
229C2×C22⋊D53—21no—
230C2×C22⋊D53—21no—
231C2×C22⋊D53—21no—
232C2×C22⋊D53—21no—
233C22×Dic53—21no—
234C22×Dic53—21no—
235C22×Dic53—21no—
236C22×Dic53—21no—
237C22×Dic53—21no—
238C22×Dic53—21no—
239C22×Dic53—21no—
240C22×Dic53—21no—
241C22×Dic53—42no—
242C22×Dic53—81no—
243C22×Dic53—81no—
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
259M16×C53—81no—
260M16×C53—81no—
261C2×C8×C53—21no—
262C2×C8×C53—21no—
263C2×C8×C53—21no—
264C2×C8×C53—21no—
265C2×C8×C53—81no—
266C2×C8×C53—81no—
267C4⋊C4×C53C22⋊C411yescharacteristic
268C4⋊C4×C53C22⋊C411yescharacteristic
269C4⋊C4×C53C22⋊C411yescharacteristic
270C4⋊C4×C53C22⋊C411yescharacteristic
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×C53C22×C411yescharacteristic
280C42×C53C22×C411yescharacteristic
281C42×C53C2×D411yescharacteristic
282C42×C53C2×D411yescharacteristic
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—
292C22⋊Dic53—21no—
293C22⋊Dic53—21no—
294C22⋊Dic53—42no—
295C22⋊Dic53—81no—
296C22⋊Dic53—81no—
297#11719921—21no—
298#11719921—21no—
299#11719921—21no—
300#11719921—21no—
301#11719921—21no—
302#11719921—21no—
303C4⋊Dic53—21no—
304C4⋊Dic53—21no—
305C4⋊Dic53—21no—
306C4⋊Dic53—21no—
307C4⋊Dic53—21no—
308C4⋊Dic53—81no—
309C4⋊Dic53—81no—
310C4⋊Dic53C22×C411yescharacteristic
311C4⋊Dic53C22×C411yescharacteristic
312C4⋊Dic53C22×C411yescharacteristic
313C4⋊Dic53C22×C411yescharacteristic
314#11719919—21no—
315#11719919—21no—
316#11719919—21no—
317#11719919—21no—
318#11719919—21no—
319#11719919—21no—
320#11719919—21no—
321#11719919—21no—
322#11719919—21no—
323#11719919—21no—
324#11719919—21no—
325#11719919—21no—
326#11719919—21no—
327#11719919—21no—
328C4×Dic53—21no—
329C4×Dic53—21no—
330C4×Dic53—21no—
331C4×Dic53—21no—
332C4×Dic53—21no—
333C4×Dic53—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×C53C2×C22⋊C411yescharacteristic
367C2×C4×C53C2×C22⋊C411yescharacteristic
368C2×C4×C53C2×C22⋊C411yescharacteristic
369C2×C4×C53C2×C22⋊C411yescharacteristic
370C2×C4×C53C2×C22⋊C411yescharacteristic
371C2×C4×C53C2×C22⋊C411yescharacteristic
372C2×C4×C53C2×C22⋊C411yescharacteristic
373C2×C4×C53C2×C22⋊C411yescharacteristic
374C2×C4×C53C23×C411yescharacteristic
375C2×C4×C53C22×D411yescharacteristic
376C22⋊D53—42no—
377C22⋊D53—41no—
378C22⋊D53—41no—
379C22⋊D53—42no—
380C22⋊D53—81no—
381C22⋊D53—81no—
382C2×Dic53—21no—
383C2×Dic53—21no—
384C2×Dic53—21no—
385C2×Dic53—21no—
386C2×Dic53—21no—
387C2×Dic53—21no—
388C2×Dic53—21no—
389C2×Dic53—42no—
390C2×Dic53—42no—
391C2×Dic53—41no—
392C2×Dic53—41no—
393C2×Dic53—41no—
394C2×Dic53—41no—
395C2×Dic53—41no—
396C2×Dic53—41no—
397C2×Dic53—41no—
398C2×Dic53—41no—
399C2×Dic53—41no—
400C2×Dic53—41no—
401C2×Dic53—41no—
402C2×Dic53—41no—
403C2×Dic53—81no—
404C2×Dic53—81no—
405C2×Dic53—84no—
406D212—41no—
407C4×D53—42no—
408C4×D53—81no—
409C4×D53—81no—
410Dic106—42no—
411Dic106—41no—
412Dic106—41no—
413Dic106—41no—
414Dic106—81no—
415Dic106—81no—
416C8×C53—41no—
417C8×C53—41no—
418C8×C53—41no—
419C8×C53—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—
455Dic53—41no—
456Dic53—41no—
457Dic53—41no—
458Dic53—41no—
459Dic53—41no—
460Dic53—41no—
461Dic53—41no—
462Dic53—81no—
463Dic53—81no—
464Dic53—81no—
465Dic53—81no—
466#3520—531no—
467#2974D5311yescharacteristic, complemented
468#2318—531no—
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—21no—
515#435—21no—
516#435—21no—
517C8×D4—21no—
518#432C2×D5311yescharacteristic
519#431C2×D5311yescharacteristic
520#407C2×D5311yescharacteristic
521#407C2×D5311yescharacteristic
522C2×C22⋊C8C2×D5311yescharacteristic
523C2×C22⋊C8C2×D5311yescharacteristic
524#388—1061no—
525#387—1061no—
526#386—1061no—
527#385—1061no—
528#383—531no—
529#382—531no—
530#381—531no—
531#380—531no—
532C4×C22⋊C4—531no—
533C2×#95—531no—
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×D4D21211yescharacteristic
557C23×C4—1061no—
558C23×C4C22×D5311yescharacteristic
559C23×C4C22×D5311yescharacteristic
560C2×M16—21no—
561C2×M16—21no—
562C22×C8—21no—
563C22×C8—21no—
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×D4C22⋊D5311yescharacteristic
635C4×D4C22⋊D5311yescharacteristic
636C4×D4C22⋊D5311yescharacteristic
637C4×D4C22⋊D5311yescharacteristic
638#117—531no—
639#117—531no—
640#117—1061no—
641#117—1061no—
642#117—1061no—
643#117—1061no—
644C2×C4⋊C4—531no—
645C2×C4⋊C4—531no—
646C2×C4⋊C4—1061no—
647C2×C4⋊C4—1061no—
648C2×C4⋊C4—1061no—
649C2×C4⋊C4—1061no—
650C2×C4⋊C4—1061no—
651C2×C4⋊C4D21211yescharacteristic
652C2×C22⋊C4—1061no—
653C2×C22⋊C4—1061no—
654C2×C22⋊C4—1061no—
655C2×C22⋊C4—1061no—
656C2×C22⋊C4—1061no—
657C2×C22⋊C4D21211yescharacteristic
658C2×C22⋊C4D21211yescharacteristic
659C2×C42—1061no—
660C2×C42C22×D5311yescharacteristic
661C4⋊C8—21no—
662C4⋊C8—21no—
663C22⋊C8—21no—
664C22⋊C8—21no—
665C22⋊C8—21no—
666C22⋊C8—21no—
667C22⋊C8C22×D5311yescharacteristic
668C22⋊C8C22×D5311yescharacteristic
669C22⋊C8C22×D5311yescharacteristic
670C22⋊C8C22×D5311yescharacteristic
671#97—21no—
672C4×C8—21no—
673#95—531no—
674#95—531no—
675#95—531no—
676#95—531no—
677#95—1061no—
678#95—1061no—
679#95—1061no—
680#95—1061no—
681#95—1061no—
682C24C2×D21211yescharacteristic
683C24C2×D21211yescharacteristic
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—81no—
707C22×C4—81no—
708C22×C4—1061no—
709C22×C4—1061no—
710C22×C4—1061no—
711C22×C4—1061no—
712C22×C4—1061no—
713C22×C4—1061no—
714C22×C4—1061no—
715C22×C4—1061no—
716C22×C4—1061no—
717C22×C4—1061no—
718C22×C4—1061no—
719C22×C4—4241no—
720C22×C4—4241no—
721C22×C4—2122no—
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—81no—
736M16—81no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—81no—
742C2×C8—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—1061no—
759C4⋊C4—1061no—
760C4⋊C4—1061no—
761C4⋊C4—1061no—
762C4⋊C4—1061no—
763C4⋊C4—1061no—
764C4⋊C4—1061no—
765C4⋊C4—1061no—
766C4⋊C4—4241no—
767C4⋊C4—4241no—
768C4⋊C4#1171992111yescharacteristic
769C4⋊C4#1171992111yescharacteristic
770C4⋊C4#1171992111yescharacteristic
771C4⋊C4#1171992111yescharacteristic
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—1061no—
787C22⋊C4—1061no—
788C22⋊C4—1061no—
789C22⋊C4—4241no—
790C22⋊C4—4241no—
791C22⋊C4—2122no—
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—1061no—
801C42—1061no—
802C42—1061no—
803C42—1061no—
804C42—1061no—
805C42—4241no—
806C42C2×C4×D5311yescharacteristic
807C42C2×C4×D5311yescharacteristic
808C42C2×C22⋊D5311yescharacteristic
809C42C2×C22⋊D5311yescharacteristic
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×D21211yescharacteristic
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—1061no—
856C2×C4—1061no—
857C2×C4—1061no—
858C2×C4—1061no—
859C2×C4—1061no—
860C2×C4—1061no—
861C2×C4—1061no—
862C2×C4—4241no—
863C2×C4—4241no—
864C2×C4—4244no—
865C2×C4—4241no—
866C2×C4—4241no—
867C2×C4—2122no—
868C2×C4—2121no—
869C2×C4—2121no—
870C2×C4—2121no—
871C2×C4—2121no—
872C2×C4—2121no—
873C2×C4—2121no—
874C2×C4—2121no—
875C2×C4—2121no—
876C2×C4—2121no—
877C2×C4—2121no—
878C2×C4—2121no—
879C2×C4—2121no—
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×C22⋊D5311yescharacteristic
892C8—41no—
893C8—41no—
894C8—41no—
895C8—41no—
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#1681063912yes—
917C22C22×#1171992111yescharacteristic
918C22#1681143511yescharacteristic
919C22#1681144011yescharacteristic
920C4—21no—
921C4—21no—
922C4—21no—
923C4—21no—
924C4—21no—
925C4—21no—
926C4—21no—
927C4—21no—
928C4—21no—
929C4—21no—
930C4—4241no—
931C4—4241no—
932C4—4241no—
933C4—4241no—
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#2028324911yescharacteristic
950C2C2×#1681063911yescharacteristic
subgroupG/H
centerC22C22×#11719921
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#2974C2
socleC22×C53C22×C22⋊C4
prime radical#20288764C2
cosocleC22×C4×C53C24
hypercenter#2974D53
hypocenterC53#17598
LCSG ▷ C2×C4×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2974

Complements

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

NH ≅ G/Ntype
2. #20277348C2semidirect
3. #20273293C2semidirect
4. #20273288C2semidirect
5. #20273280C2semidirect
6. #20273272C2semidirect
7. #20273267C2semidirect
8. #20273259C2semidirect
9. #20273254C2semidirect
10. #20273249C2semidirect
11. #20273236C2semidirect
12. #20273220C2semidirect
13. #20273207C2semidirect
14. C2×#16810361C2semidirect
15. C53×#2974C2semidirect
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
81. #13133217C2×C4semidirect
82. #13133217C2×C4semidirect
90. #13133209C2×C4semidirect
93. #13133205C2×C4semidirect
115. #13133196C2×C4semidirect
116. #13133196C2×C4semidirect
117. #13133196C2×C4semidirect
126. #13133191C2×C4semidirect
134. C4×Dic106C2×C4semidirect
135. C4×Dic106C2×C4semidirect
136. C4×Dic106C2×C4semidirect
138. C4×D212C2×C4semidirect
149. #13133176C2×C4semidirect
156. C2×C4⋊Dic53C2×C4semidirect
467. #2974D53semidirect
550. C53#17598semidirect

Maximal subgroups

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

subgroupindex
#202887642
#202773482
#202732932
#202732882
#202732802
#202732722
#202732672
#202732592
#202732542
#202732492
#202732362
#202732202
#202732072
C2×#168103612
C53×#29742
#1759853