Finite Group Databasebeta

← #27351295

Subgroups — #27351295

Order 13568.

1102 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288758C211yesmaximal, characteristic
2#20283746C211yesmaximal, characteristic, complemented
3#20277073C211yesmaximal, characteristic, complemented
4#20273239C211yesmaximal, characteristic, complemented
5#20273235C211yesmaximal, characteristic, complemented
6#20273233C211yesmaximal, characteristic, complemented
7#20273225C211yesmaximal, characteristic, complemented
8#20273218C211yesmaximal, characteristic, complemented
9#20273217C211yesmaximal, characteristic, complemented
10#20273212C211yesmaximal, characteristic, complemented
11#20273207C211yesmaximal, characteristic, complemented
12#20273205C211yesmaximal, characteristic, complemented
13#20273200C211yesmaximal, characteristic, complemented
14#328×D53C211yesmaximal, characteristic, complemented
15C2×C53×#328C211yesmaximal, characteristic, complemented
16#16811344C411yescharacteristic, complemented
17#16811327—21no—
18#16811308C411yescharacteristic, complemented
19#16811307C411yescharacteristic, complemented
20#16811300—21no—
21#16811299—21no—
22Q8×C22⋊D53C411yescharacteristic, complemented
23#16811284C411yescharacteristic, complemented
24#16811283C411yescharacteristic, complemented
25#16811275C411yescharacteristic, complemented
26#16811274C411yescharacteristic, complemented
27#16811263—21no—
28#16811243—21no—
29#16811220—21no—
30#16811219—21no—
31#16811175C2211yescharacteristic
32#16811159C2211yescharacteristic
33#16811136C2211yescharacteristic
34#16811134C2211yescharacteristic
35C22⋊Q8×D53C2211yescharacteristic
36#16811104—21no—
37C2×C4×C22⋊D53—21no—
38C2×C4×C22⋊D53C2211yescharacteristic
39#16810698—21no—
40#16810697—21no—
41#16810694—21no—
42C8×C22⋊D53—21no—
43#16810677C2211yescharacteristic
44#16810673C2211yescharacteristic
45#16810587C2211yescharacteristic
46#16810585C2211yescharacteristic
47C22⋊C8×D53C2211yescharacteristic
48#16810474—21no—
49#16810474C2211yescharacteristic
50C4×C22⋊Dic53—21no—
51C4×C22⋊Dic53C2211yescharacteristic
52#16810470—21no—
53#16810470C2211yescharacteristic
54#16810468C2211yescharacteristic
55#95×D53C2211yescharacteristic
56#16810361C2211yescharacteristic
57#16810361C2211yescharacteristic
58#16810360C2211yescharacteristic
59#16810360C2211yescharacteristic
60#16810360C2211yescharacteristic
61#16810360C2211yescharacteristic
62#16810359C2211yescharacteristic
63#16810359C2211yescharacteristic
64#16810358C2211yescharacteristic
65#16810358C2211yescharacteristic
66#16810356C2211yescharacteristic
67#16810356C2211yescharacteristic
68C2×C22⋊Q8×C53C2211yescharacteristic
69C2×C22⋊C8×C53C2211yescharacteristic
70C2×#95×C53C2211yescharacteristic
71C53×#328C2211yescharacteristic
72C53×#328C2211yescharacteristic
73C53×#328C2211yescharacteristic
74C53×#328C2211yescharacteristic
75C2×#11719949C2×C411yescharacteristic, complemented
76C2×#11719945—21no—
77C2×#11719945C2×C411yescharacteristic, complemented
78C2×Q8×D53C2×C411yescharacteristic, complemented
79C22×C22⋊D53D411yescharacteristic
80C22×C4×D53—21no—
81C22×C4×D53C2311yescharacteristic
82C2×#11719917—21no—
83C2×#11719912—21no—
84C2×C8×D53—21no—
85#13133216C2×C411yescharacteristic, complemented
86#13133215—21no—
87#13133215C2×C411yescharacteristic, complemented
88#13133212—21no—
89#13133212—21no—
90#13133212—21no—
91#13133210—21no—
92#13133210—21no—
93#13133208C2×C411yescharacteristic, complemented
94#13133207—21no—
95#13133207—21no—
96#13133207—21no—
97#13133206—21no—
98#13133206C2×C411yescharacteristic, complemented
99#13133203—21no—
100#13133203—21no—
101#13133202—21no—
102#13133202—21no—
103#13133202—21no—
104#13133201—21no—
105#13133200—21no—
106#13133200—21no—
107#13133200—21no—
108#13133199—21no—
109#13133199—21no—
110#13133197C2×C411yescharacteristic, complemented
111#13133196—21no—
112#13133196C2×C411yescharacteristic, complemented
113#13133196C2311yescharacteristic
114#13133195—21no—
115#13133195—21no—
116#13133195—21no—
117#13133194—21no—
118#13133194—21no—
119#13133193—21no—
120#13133193—21no—
121#13133193C2×C411yescharacteristic, complemented
122#13133193C2×C411yescharacteristic, complemented
123#13133192C2×C411yescharacteristic, complemented
124#13133191—21no—
125#13133191C2×C411yescharacteristic, complemented
126#13133191C2311yescharacteristic
127#13133190—21no—
128#13133190—21no—
129#13133187—21no—
130#13133186—21no—
131Q8×Dic53C2×C411yescharacteristic, complemented
132Q8×Dic53C2×C411yescharacteristic, complemented
133#13133182—21no—
134#13133182—21no—
135#13133182C2×C411yescharacteristic, complemented
136#13133179—21no—
137#13133179—21no—
138#13133179C2×C411yescharacteristic, complemented
139C4×C22⋊D53—28no—
140C4×C22⋊D53—21no—
141C4×C22⋊D53—21no—
142C4×C22⋊D53—21no—
143C4×C22⋊D53—21no—
144C4×C22⋊D53C2×C411yescharacteristic
145C4×C22⋊D53C2×C411yescharacteristic
146C4×C22⋊D53C2×C411yescharacteristic
147C4×C22⋊D53C2×C411yescharacteristic
148C4×C22⋊D53D411yescharacteristic
149C4×C22⋊D53D411yescharacteristic
150C4×C22⋊D53D411yescharacteristic
151C4×C22⋊D53D411yescharacteristic
152#13133177—21no—
153#13133177—21no—
154#13133176—21no—
155#13133176C2×C411yescharacteristic, complemented
156#13133175—21no—
157#13133175—21no—
158#13133175C2×C411yescharacteristic, complemented
159#13133173—21no—
160C2×#11719919—21no—
161C2×#11719919D411yescharacteristic
162C4⋊C4×D53—21no—
163C4⋊C4×D53—21no—
164C4⋊C4×D53C2×C411yescharacteristic, complemented
165C2×C22⋊Dic53—21no—
166C2×C22⋊Dic53D411yescharacteristic
167C2×#11719921—21no—
168C2×#11719921D411yescharacteristic
169C22⋊C4×D53—21no—
170C2×C4×Dic53—21no—
171C2×C4×Dic53—21no—
172C2×C4×Dic53—21no—
173C2×C4×Dic53—21no—
174C2×C4×Dic53C2311yescharacteristic
175#13133146—21no—
176#13133146—21no—
177C22⋊#88322—21no—
178C22⋊#88322C2311yescharacteristic
179C22⋊#88322C2311yescharacteristic
180#13133129—21no—
181#13133129—21no—
182#13133127—21no—
183C8×Dic53—21no—
184#13133124—21no—
185#13133124—21no—
186#13133124C2311yescharacteristic
187#13133124C2311yescharacteristic
188C22×Q8×C53C2×C411yescharacteristic, complemented
189C23×C4×C53—21no—
190C23×C4×C53C2311yescharacteristic
191C22×C8×C53—21no—
192C22⋊Q8×C53—21no—
193C22⋊Q8×C53—21no—
194C22⋊Q8×C53C2×C411yescharacteristic, complemented
195C22⋊Q8×C53C2×C411yescharacteristic, complemented
196C22⋊Q8×C53C2311yescharacteristic
197C22⋊Q8×C53C2311yescharacteristic
198C2×C4⋊C4×C53—21no—
199C2×C4⋊C4×C53C2×C411yescharacteristic, complemented
200C2×C22⋊C4×C53—21no—
201C22⋊C8×C53—21no—
202C22⋊C8×C53C2311yescharacteristic
203C22⋊C8×C53C2311yescharacteristic
204#95×C53—21no—
205#95×C53C2311yescharacteristic
206#95×C53C2311yescharacteristic
207C24×C53C2×D411yescharacteristic
208C23×D53C2×D411yescharacteristic
209C2×Q8×C53—21no—
210C2×Q8×C53—81no—
211C2×Q8×C53C22×C411yescharacteristic
212C2×Q8×C53C22×C411yescharacteristic
213C22×C4×C53—21no—
214C22×C4×C53—21no—
215C22×C4×C53—21no—
216C22×C4×C53—24no—
217C22×C4×C53—21no—
218C22×C4×C53—81no—
219C22×C4×C53—81no—
220C22×C4×C53—81no—
221C22×C4×C53C22×C411yescharacteristic
222C22×C4×C53C22×C411yescharacteristic
223C22×C4×C53C2×D411yescharacteristic
224C22×C4×C53C2×D411yescharacteristic
225C22×C4×C53C2×D411yescharacteristic
226C22×C4×C53C2411yescharacteristic
227C2×C22⋊D53—24no—
228C2×C22⋊D53—21no—
229C2×C22⋊D53—21no—
230C2×C22⋊D53—21no—
231C2×C22⋊D53C22⋊C411yescharacteristic
232C2×C22⋊D53C22⋊C411yescharacteristic
233C2×C22⋊D53C22⋊C411yescharacteristic
234C2×C22⋊D53C22⋊C411yescharacteristic
235C22×Dic53—21no—
236C22×Dic53—21no—
237C22×Dic53C2×D411yescharacteristic
238C22×Dic53C2×D411yescharacteristic
239C22×Dic53C2×D411yescharacteristic
240#11719949—81no—
241Q8×D53—81no—
242#11719945—44no—
243#11719945—81no—
244C2×D212—21no—
245C2×D212—21no—
246C2×D212C22×C411yescharacteristic
247C2×C4×D53—21no—
248C2×C4×D53—21no—
249C2×C4×D53—24no—
250C2×C4×D53—21no—
251C2×C4×D53—21no—
252C2×C4×D53—21no—
253C2×C4×D53—81no—
254C2×C4×D53—81no—
255C2×C4×D53—81no—
256C2×C4×D53C22×C411yescharacteristic
257C2×C4×D53C22×C411yescharacteristic
258C2×C4×D53C2×D411yescharacteristic
259C2×C4×D53C2×D411yescharacteristic
260C2×Dic106—21no—
261C2×Dic106—21no—
262C2×Dic106C22×C411yescharacteristic
263C2×C8×C53—21no—
264C2×C8×C53—21no—
265C2×C8×C53—81no—
266C4⋊C4×C53—21no—
267C4⋊C4×C53—21no—
268C4⋊C4×C53—21no—
269C4⋊C4×C53—21no—
270C4⋊C4×C53—21no—
271C4⋊C4×C53C22×C411yescharacteristic
272C4⋊C4×C53C22×C411yescharacteristic
273C22⋊C4×C53—21no—
274C22⋊C4×C53—21no—
275C22⋊C4×C53—21no—
276C22⋊C4×C53—21no—
277C22⋊Dic53—24no—
278C22⋊Dic53—21no—
279C22⋊Dic53—21no—
280C22⋊Dic53—21no—
281C22⋊Dic53C22⋊C411yescharacteristic
282C22⋊Dic53C22⋊C411yescharacteristic
283C22⋊Dic53C22⋊C411yescharacteristic
284C22⋊Dic53C22⋊C411yescharacteristic
285#11719921—24no—
286#11719921—21no—
287#11719921—21no—
288#11719921—21no—
289#11719921—21no—
290#11719921—21no—
291#11719921—21no—
292#11719921—21no—
293#11719921—21no—
294#11719921—21no—
295#11719921—21no—
296#11719921C22⋊C411yescharacteristic
297#11719921C22⋊C411yescharacteristic
298#11719921C22⋊C411yescharacteristic
299#11719921C22⋊C411yescharacteristic
300C4⋊Dic53—21no—
301C4⋊Dic53—21no—
302C4⋊Dic53—21no—
303C4⋊Dic53—21no—
304C4⋊Dic53C22×C411yescharacteristic
305C4⋊Dic53C22×C411yescharacteristic
306#11719919—24no—
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#11719919C22⋊C411yescharacteristic
318#11719919C22⋊C411yescharacteristic
319#11719919C22⋊C411yescharacteristic
320#11719919C22⋊C411yescharacteristic
321C4×Dic53—24no—
322C4×Dic53—21no—
323C4×Dic53—21no—
324C4×Dic53—21no—
325C4×Dic53—21no—
326C4×Dic53—21no—
327C4×Dic53—81no—
328C4×Dic53—81no—
329C4×Dic53—81no—
330C4×Dic53C22×C411yescharacteristic
331C4×Dic53C22×C411yescharacteristic
332C4×Dic53C2×D411yescharacteristic
333C4×Dic53C2×D411yescharacteristic
334#11719917—81no—
335C2×#88322—21no—
336C2×#88322—21no—
337#11719912—81no—
338C8×D53—81no—
339C23×C53—21no—
340C23×C53—21no—
341C23×C53—22no—
342C23×C53—41no—
343C23×C53C2×C22⋊C411yescharacteristic
344C23×C53C2×C22⋊C411yescharacteristic
345C23×C53C22×D411yescharacteristic
346C22×D53—21no—
347C22×D53—21no—
348C22×D53—22no—
349C22×D53—21no—
350C22×D53—41no—
351C22×D53C2×C22⋊C411yescharacteristic
352C22×D53C2×C22⋊C411yescharacteristic
353Q8×C53—41no—
354Q8×C53—41no—
355Q8×C53—81no—
356C2×C4×C53—22no—
357C2×C4×C53—22no—
358C2×C4×C53—21no—
359C2×C4×C53—21no—
360C2×C4×C53—21no—
361C2×C4×C53—21no—
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—42no—
373C2×C4×C53—81no—
374C2×C4×C53—84no—
375C2×C4×C53C2×C22⋊C411yescharacteristic
376C2×C4×C53C2×C22⋊C411yescharacteristic
377C2×C4×C53C23×C411yescharacteristic
378C2×C4×C53C22×D411yescharacteristic
379C22⋊D53—22no—
380C22⋊D53—22no—
381C22⋊D53—22no—
382C22⋊D53—41no—
383C22⋊D53—41no—
384C22⋊D53—42no—
385C22⋊D53—81no—
386C22⋊D53#10414yes—
387C2×Dic53—21no—
388C2×Dic53—21no—
389C2×Dic53—22no—
390C2×Dic53—22no—
391C2×Dic53—22no—
392C2×Dic53—21no—
393C2×Dic53—21no—
394C2×Dic53—21no—
395C2×Dic53—41no—
396C2×Dic53—41no—
397C2×Dic53—41no—
398C2×Dic53—41no—
399C2×Dic53—41no—
400C2×Dic53C2×C22⋊C411yescharacteristic
401C2×Dic53C2×C22⋊C411yescharacteristic
402C2×Dic53C2×C22⋊C411yescharacteristic
403C2×Dic53C2×C22⋊C411yescharacteristic
404C2×Dic53C2×C22⋊C411yescharacteristic
405C2×Dic53C2×C22⋊C411yescharacteristic
406D212—41no—
407D212—42no—
408D212—81no—
409C4×D53—41no—
410C4×D53—41no—
411C4×D53—41no—
412C4×D53—41no—
413C4×D53—42no—
414C4×D53—42no—
415C4×D53—81no—
416C4×D53—81no—
417C4×D53—81no—
418C4×D53—84no—
419Dic106—42no—
420Dic106—41no—
421Dic106—81no—
422C8×C53—41no—
423C8×C53—41no—
424#88322—41no—
425#88322—41no—
426#17548—531nomaximal, Sylow
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×C53C2×#10412yes—
437C22×C53C22×C22⋊C411yescharacteristic
438C22×C53#57711yescharacteristic
439C22×C53#57811yescharacteristic
440C2×D53—21no—
441C2×D53—21no—
442C2×D53—21no—
443C2×D53—21no—
444C2×D53—21no—
445C2×D53—42no—
446C2×D53—42no—
447C2×D53—41no—
448C2×D53—41no—
449C2×D53—41no—
450C2×D53C2×#10412yes—
451C4×C53—21no—
452C4×C53—21no—
453C4×C53—21no—
454C4×C53—21no—
455C4×C53—42no—
456C4×C53—42no—
457C4×C53—41no—
458C4×C53—41no—
459C4×C53—41no—
460C4×C53—41no—
461Dic53—21no—
462Dic53—21no—
463Dic53—21no—
464Dic53—21no—
465Dic53—21no—
466Dic53—42no—
467Dic53—42no—
468Dic53—41no—
469Dic53—41no—
470Dic53—41no—
471Dic53C2×#10412yes—
472#3520—531no—
473#2974—531no—
474#2275—531no—
475#1509—531no—
476#1508—531no—
477#1508—531no—
478#1506—531no—
479#1504—531no—
480#1504—531no—
481#1503—531no—
482#1501—531no—
483#1501—531no—
484#1500—531no—
485C2×#328—531no—
486C2×#328D5311yescharacteristic, complemented
487C2×C53—21no—
488C2×C53—21no—
489C2×C53—22no—
490C2×C53—41no—
491C2×C53#288311yescharacteristic
492C2×C53#289811yescharacteristic
493C2×C53C22×#10411yescharacteristic
494D53—22no—
495D53—41no—
496D53—81no—
497#556—531no—
498#554—1061no—
499#552—531no—
500#552—531no—
501#551—1061no—
502#551—1061no—
503D4×Q8—531no—
504#548—531no—
505#548—531no—
506#547—531no—
507#547—531no—
508#546—1061no—
509#542—1061no—
510#539—1061no—
511#539—1061no—
512#533—531no—
513#529—531no—
514#525—531no—
515#525—531no—
516C2×C22⋊Q8—531no—
517C2×C22⋊Q8C2×D5311yescharacteristic
518#520—1061no—
519C2×C4×D4—531no—
520C2×C4×D4—1061no—
521#436—1061no—
522#435—1061no—
523#435—1061no—
524C8×D4—1061no—
525#432—531no—
526#431—531no—
527#407—531no—
528#407—531no—
529C2×C22⋊C8—531no—
530C2×C22⋊C8C2×D5311yescharacteristic
531C4×C4⋊C4—531no—
532C4×C4⋊C4—1061no—
533C4×C22⋊C4—531no—
534C4×C22⋊C4—531no—
535C4×C22⋊C4—1061no—
536C4×C22⋊C4—1061no—
537#376—531no—
538C2×#95—531no—
539C2×#95C2×D5311yescharacteristic
540#328—531no—
541#328—531no—
542#328—531no—
543#328—531no—
544#328—531no—
545#328—531no—
546#328—531no—
547#328—531no—
548#328C2×D5311yescharacteristic
549#328C2×D5311yescharacteristic
550#328C2×D5311yescharacteristic
551#328C2×D5311yescharacteristic
552#327—531no—
553#327—531no—
554#327—531no—
555#327—531no—
556C53#1754811yescharacteristic, complemented, Sylow
557C2×#41—531no—
558C2×#41—531no—
559C2×#41—1061no—
560C22×Q8—531no—
561C22×Q8C4×D5311yescharacteristic, complemented
562C22×D4—531no—
563C23×C4—21no—
564C23×C4—531no—
565C23×C4—1061no—
566C23×C4C22×D5311yescharacteristic
567C2×M16—1061no—
568C2×M16—1061no—
569C22×C8—21no—
570C22×C8—1061no—
571C4⋊Q8—531no—
572C4⋊Q8—531no—
573C4⋊Q8—1061no—
574#126—1061no—
575#126—1061no—
576#126—1061no—
577#126—1061no—
578#126—1061no—
579#125—531no—
580#125—1061no—
581#125—1061no—
582#125—1061no—
583#124—531no—
584#124—1061no—
585#124—1061no—
586#124—1061no—
587#123—1061no—
588#123—1061no—
589#123—1061no—
590#123—1061no—
591#123—1061no—
592#123—1061no—
593#123—1061no—
594#123—1061no—
595#123—1061no—
596C22⋊Q8—21no—
597C22⋊Q8—21no—
598C22⋊Q8—531no—
599C22⋊Q8—531no—
600C22⋊Q8—531no—
601C22⋊Q8—531no—
602C22⋊Q8—531no—
603C22⋊Q8—1061no—
604C22⋊Q8—1061no—
605C22⋊Q8—1061no—
606C22⋊Q8—1061no—
607C22⋊Q8—1061no—
608C22⋊Q8—1061no—
609C22⋊Q8—1061no—
610C22⋊Q8—1061no—
611C22⋊Q8C4×D5311yescharacteristic, complemented
612C22⋊Q8C4×D5311yescharacteristic, complemented
613C22⋊Q8C22×D5311yescharacteristic
614C22⋊Q8C22×D5311yescharacteristic
615#121—531no—
616#121—531no—
617#121—531no—
618#121—1061no—
619#121—1061no—
620#121—1061no—
621#120—1061no—
622#120—1061no—
623C4×Q8—531no—
624C4×Q8—531no—
625C4×Q8—531no—
626C4×Q8—1061no—
627C4×Q8—1061no—
628C4×D4—531no—
629C4×D4—531no—
630C4×D4—531no—
631C4×D4—531no—
632C4×D4—531no—
633C4×D4—531no—
634C4×D4—531no—
635C4×D4—531no—
636C4×D4—531no—
637C4×D4—1061no—
638C4×D4—1061no—
639C4×D4—1061no—
640C4×D4—1061no—
641C4×D4—1061no—
642C4×D4—1061no—
643C4×D4—1068no—
644C4×D4—1061no—
645C4×D4—1061no—
646#117—531no—
647#117—531no—
648#117—1061no—
649#117—1061no—
650#117—1061no—
651#117—1061no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—531no—
654C2×C4⋊C4—531no—
655C2×C4⋊C4—1061no—
656C2×C4⋊C4—1061no—
657C2×C4⋊C4—1061no—
658C2×C4⋊C4C4×D5311yescharacteristic, complemented
659C2×C22⋊C4—21no—
660C2×C22⋊C4—531no—
661C2×C22⋊C4—531no—
662C2×C22⋊C4—1061no—
663C2×C22⋊C4—1061no—
664C2×C22⋊C4—1061no—
665C2×C42—531no—
666C2×C42—1061no—
667C2×C42—1061no—
668C2×C42—1061no—
669C2×C42—1061no—
670C4⋊C8—1061no—
671C4⋊C8—1061no—
672C22⋊C8—21no—
673C22⋊C8—531no—
674C22⋊C8—531no—
675C22⋊C8—1061no—
676C22⋊C8—1061no—
677C22⋊C8—1061no—
678C22⋊C8C22×D5311yescharacteristic
679C22⋊C8C22×D5311yescharacteristic
680#97—1061no—
681C4×C8—1061no—
682#95—21no—
683#95—531no—
684#95—531no—
685#95—1061no—
686#95—1061no—
687#95C22×D5311yescharacteristic
688#95C22×D5311yescharacteristic
689C24—531no—
690C24D4×D5311yescharacteristic
691#41—4241no—
692#41—4241no—
693#41—2124no—
694C2×Q8—21no—
695C2×Q8—81no—
696C2×Q8—531no—
697C2×Q8—1061no—
698C2×Q8—1061no—
699C2×Q8—4241no—
700C2×Q8C2×C4×D5311yescharacteristic
701C2×Q8C2×C4×D5311yescharacteristic
702C2×D4—531no—
703C2×D4—531no—
704C2×D4—531no—
705C2×D4—531no—
706C2×D4—531no—
707C2×D4—1061no—
708C2×D4—1061no—
709C2×D4—1064no—
710C2×D4—1061no—
711C2×D4—1061no—
712C2×D4—1061no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—24no—
717C22×C4—21no—
718C22×C4—81no—
719C22×C4—81no—
720C22×C4—81no—
721C22×C4—531no—
722C22×C4—531no—
723C22×C4—531no—
724C22×C4—531no—
725C22×C4—531no—
726C22×C4—531no—
727C22×C4—531no—
728C22×C4—1061no—
729C22×C4—1061no—
730C22×C4—1061no—
731C22×C4—1064no—
732C22×C4—1061no—
733C22×C4—1061no—
734C22×C4—1061no—
735C22×C4—1061no—
736C22×C4—4241no—
737C22×C4—4241no—
738C22×C4—4241no—
739C22×C4C2×C4×D5311yescharacteristic
740C22×C4C2×C4×D5311yescharacteristic
741C22×C4D4×D5311yescharacteristic
742C22×C4D4×D5311yescharacteristic
743C22×C4D4×D5311yescharacteristic
744C22×C4C23×D5311yescharacteristic
745M16—4241no—
746M16—4241no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—81no—
750C2×C8—1061no—
751C2×C8—1061no—
752C2×C8—4241no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—531no—
759C4⋊C4—531no—
760C4⋊C4—531no—
761C4⋊C4—531no—
762C4⋊C4—531no—
763C4⋊C4—531no—
764C4⋊C4—1061no—
765C4⋊C4—1061no—
766C4⋊C4—1061no—
767C4⋊C4—1061no—
768C4⋊C4—1061no—
769C4⋊C4—1061no—
770C4⋊C4—1061no—
771C4⋊C4—1061no—
772C4⋊C4—1061no—
773C4⋊C4—1061no—
774C4⋊C4—1061no—
775C4⋊C4—1061no—
776C4⋊C4—1064no—
777C4⋊C4—1061no—
778C4⋊C4—1061no—
779C4⋊C4C2×C4×D5311yescharacteristic
780C4⋊C4C2×C4×D5311yescharacteristic
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—531no—
786C22⋊C4—531no—
787C22⋊C4—531no—
788C22⋊C4—531no—
789C22⋊C4—531no—
790C22⋊C4—531no—
791C22⋊C4—531no—
792C22⋊C4—531no—
793C22⋊C4—1061no—
794C22⋊C4—1061no—
795C22⋊C4—1061no—
796C22⋊C4—1061no—
797C22⋊C4—1061no—
798C22⋊C4—1061no—
799C22⋊C4—1061no—
800C22⋊C4—1061no—
801C22⋊C4—1064no—
802C22⋊C4—1064no—
803C22⋊C4—1061no—
804C22⋊C4—1061no—
805C22⋊C4—1061no—
806C22⋊C4—1061no—
807C22⋊C4—1061no—
808C42—531no—
809C42—531no—
810C42—531no—
811C42—531no—
812C42—1061no—
813C42—1061no—
814C42—1061no—
815C42—1061no—
816C42—1064no—
817C42—1061no—
818C42—4241no—
819C42—4241no—
820C42—4241no—
821C23—22no—
822C23—21no—
823C23—21no—
824C23—41no—
825C23—531no—
826C23—531no—
827C23—1062no—
828C23—1061no—
829C23—1061no—
830C23—1061no—
831C23—2121no—
832C23C22⋊C4×D5311yescharacteristic
833C23C22⋊C4×D5311yescharacteristic
834C23C2×D4×D5311yescharacteristic
835Q8—41no—
836Q8—41no—
837Q8—81no—
838Q8—4241no—
839Q8—2121no—
840Q8—2122no—
841D4—534no—
842D4—1062no—
843D4—1062no—
844D4—1062no—
845D4—4241no—
846D4—4241no—
847D4—2121no—
848D4—2122no—
849D4—2122no—
850D4—2121no—
851D4—2121no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
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—42no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—81no—
870C2×C4—84no—
871C2×C4—531no—
872C2×C4—531no—
873C2×C4—531no—
874C2×C4—531no—
875C2×C4—531no—
876C2×C4—531no—
877C2×C4—1062no—
878C2×C4—1061no—
879C2×C4—1061no—
880C2×C4—1062no—
881C2×C4—1062no—
882C2×C4—1061no—
883C2×C4—1061no—
884C2×C4—1061no—
885C2×C4—4241no—
886C2×C4—4241no—
887C2×C4—4241no—
888C2×C4—4244no—
889C2×C4—2121no—
890C2×C4—2121no—
891C2×C4—2121no—
892C2×C4—2121no—
893C2×C4—2122no—
894C2×C4—2122no—
895C2×C4—2121no—
896C2×C4—2121no—
897C2×C4—2121no—
898C2×C4—2121no—
899C2×C4—2121no—
900C2×C4C22⋊C4×D5311yescharacteristic
901C2×C4C22⋊C4×D5311yescharacteristic
902C2×C4C22×C4×D5311yescharacteristic
903C2×C4C2×D4×D5311yescharacteristic
904C8—41no—
905C8—41no—
906C8—2121no—
907C8—2121no—
908C22—21no—
909C22—21no—
910C22—21no—
911C22—21no—
912C22—21no—
913C22—21no—
914C22—21no—
915C22—42no—
916C22—42no—
917C22—532no—
918C22—1061no—
919C22—1061no—
920C22—1061no—
921C22—1061no—
922C22—1061no—
923C22—2122no—
924C22—2122no—
925C22—2121no—
926C22—2121no—
927C22—2121no—
928C22#104×D5312yes—
929C22C2×C22⋊C4×D5311yescharacteristic
930C22#1681142911yescharacteristic
931C22#1681143611yescharacteristic
932C4—21no—
933C4—21no—
934C4—21no—
935C4—21no—
936C4—42no—
937C4—42no—
938C4—41no—
939C4—41no—
940C4—41no—
941C4—41no—
942C4—532no—
943C4—1061no—
944C4—1061no—
945C4—1061no—
946C4—1061no—
947C4—1061no—
948C4—2122no—
949C4—2122no—
950C4—2121no—
951C4—2121no—
952C4—2121no—
953C2—21no—
954C2—21no—
955C2—22no—
956C2—41no—
957C2—1062no—
958C2—4241no—
959C2—2121no—
960C2#2028317311yescharacteristic
961C2#2028324311yescharacteristic
962C2C2×#104×D5311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC2×C53×#328C2
socleC22×C53C22×C22⋊C4
prime radical#20288758C2
cosocleC22×C4×C53C24
hypercenterC2×#328D53
hypocenterC53#17548
LCSG ▷ C2×C4×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
2. #20283746C2semidirect
3. #20277073C2semidirect
4. #20273239C2semidirect
5. #20273235C2semidirect
6. #20273233C2semidirect
7. #20273225C2semidirect
8. #20273218C2semidirect
9. #20273217C2semidirect
10. #20273212C2semidirect
11. #20273207C2semidirect
12. #20273205C2semidirect
13. #20273200C2semidirect
14. #328×D53C2semidirect
15. C2×C53×#328C2semidirect
16. #16811344C4semidirect
18. #16811308C4semidirect
19. #16811307C4semidirect
22. Q8×C22⋊D53C4semidirect
23. #16811284C4semidirect
24. #16811283C4semidirect
25. #16811275C4semidirect
26. #16811274C4semidirect
75. C2×#11719949C2×C4semidirect
77. C2×#11719945C2×C4semidirect
78. C2×Q8×D53C2×C4semidirect
85. #13133216C2×C4semidirect
87. #13133215C2×C4semidirect
93. #13133208C2×C4semidirect
98. #13133206C2×C4semidirect
110. #13133197C2×C4semidirect
112. #13133196C2×C4semidirect
121. #13133193C2×C4semidirect
122. #13133193C2×C4semidirect
123. #13133192C2×C4semidirect
125. #13133191C2×C4semidirect
131. Q8×Dic53C2×C4semidirect
132. Q8×Dic53C2×C4semidirect
135. #13133182C2×C4semidirect
138. #13133179C2×C4semidirect
155. #13133176C2×C4semidirect
158. #13133175C2×C4semidirect
164. C4⋊C4×D53C2×C4semidirect
188. C22×Q8×C53C2×C4semidirect
194. C22⋊Q8×C53C2×C4semidirect
195. C22⋊Q8×C53C2×C4semidirect
199. C2×C4⋊C4×C53C2×C4semidirect
486. C2×#328D53semidirect
556. C53#17548semidirect
561. C22×Q8C4×D53semidirect
611. C22⋊Q8C4×D53semidirect
612. C22⋊Q8C4×D53semidirect
658. C2×C4⋊C4C4×D53semidirect

Maximal subgroups

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

subgroupindex
#202887582
#202837462
#202770732
#202732392
#202732352
#202732332
#202732252
#202732182
#202732172
#202732122
#202732072
#202732052
#202732002
#328×D532
C2×C53×#3282
#1754853