Finite Group Databasebeta

← #27351017

Subgroups — #27351017

Order 13568.

958 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288279C211yesmaximal, characteristic
2#20283381C211yesmaximal, characteristic, complemented
3#20273189C211yesmaximal, characteristic, complemented
4#20273181C211yesmaximal, characteristic, complemented
5#20273176C211yesmaximal, characteristic, complemented
6#20273159C211yesmaximal, characteristic, complemented
7#20273155C211yesmaximal, characteristic, complemented
8#20273150C211yesmaximal, characteristic, complemented
9#20273137C211yesmaximal, characteristic, complemented
10#20273129C211yesmaximal, characteristic, complemented
11#20273124C211yesmaximal, characteristic, complemented
12#20273107C211yesmaximal, characteristic, complemented
13#20273103C211yesmaximal, characteristic, complemented
14#20273098C211yesmaximal, characteristic, complemented
15C53×#2965C211yesmaximal, characteristic, complemented
16#16811346C411yescharacteristic
17#16811338C411yescharacteristic
18#16811333C411yescharacteristic
19#16811323—21no—
20#16811314—21no—
21#16811313C411yescharacteristic
22#16811313C411yescharacteristic
23#16811302—21no—
24#16811302—21no—
25#16811278C411yescharacteristic
26#16811269C411yescharacteristic
27#16811269C411yescharacteristic
28#16811180C2211yescharacteristic
29#16811157C2211yescharacteristic
30#16811157C2211yescharacteristic
31#16811151—21no—
32#16811151—21no—
33#16811130—21no—
34C4×#11719945C2211yescharacteristic
35C4×#11719945C2211yescharacteristic
36C2×C4×D212C2211yescharacteristic
37#117×D53—21no—
38#16810684—21no—
39#16810684—21no—
40#16810680C2211yescharacteristic
41#16810680C2211yescharacteristic, complemented
42#16810676C2211yescharacteristic
43#16810676C2211yescharacteristic, complemented
44#16810647C2211yescharacteristic, complemented
45C2×C4⋊#88322C2211yescharacteristic, complemented
46#16810590—21no—
47#16810579—21no—
48#16810355C2211yescharacteristic, complemented
49#16810355C2211yescharacteristic, complemented
50#16810355C2211yescharacteristic, complemented
51#16810355C2211yescharacteristic, complemented
52#16810355C2211yescharacteristic, complemented
53#16810355C2211yescharacteristic, complemented
54#16810355C2211yescharacteristic, complemented
55#16810355C2211yescharacteristic, complemented
56#16810352C2211yescharacteristic
57#16810352C2211yescharacteristic
58#16810352C2211yescharacteristic
59#16810352C2211yescharacteristic
60#16810352C2211yescharacteristic
61#16810352C2211yescharacteristic
62#16810352C2211yescharacteristic
63#16810352C2211yescharacteristic
64C4×#41×C53C2211yescharacteristic
65C53×#446—21no—
66C53×#436—21no—
67C53×#435—21no—
68C53×#435—21no—
69C53×#431C2211yescharacteristic
70C53×#431C2211yescharacteristic, complemented
71C53×#431C2211yescharacteristic, complemented
72C4×M16×C53C2211yescharacteristic
73C4×M16×C53C2211yescharacteristic, complemented
74C2×C4×C8×C53C2211yescharacteristic, complemented
75C2×#11719945C2×C411yescharacteristic
76C2×#11719945C2×C411yescharacteristic
77C22×D212C2×C411yescharacteristic
78C22×C4×D53—21no—
79C2×#11719917—21no—
80C22×#88322—21no—
81#13133217C2×C411yescharacteristic
82#13133217C2×C411yescharacteristic
83#13133212—21no—
84#13133212—21no—
85#13133211—21no—
86#13133211—21no—
87#13133210—21no—
88#13133210—21no—
89#13133209—21no—
90#13133209C2×C411yescharacteristic
91#13133209C2×C411yescharacteristic
92#13133207—21no—
93#13133207—21no—
94#13133205C2×C411yescharacteristic
95#13133205C2×C411yescharacteristic
96#13133203—21no—
97#13133203—21no—
98#13133202—21no—
99#13133202—21no—
100#13133200—21no—
101#13133200—21no—
102#13133199—21no—
103#13133199—21no—
104#13133198—21no—
105#13133198—21no—
106#13133196—21no—
107#13133196C2×C411yescharacteristic
108#13133196C2×C411yescharacteristic
109#13133196C2×C411yescharacteristic
110#13133196C2×C411yescharacteristic
111#13133195—21no—
112#13133195—21no—
113#13133193—21no—
114#13133193—21no—
115#13133191C2×C411yescharacteristic
116#13133191C2×C411yescharacteristic
117#13133190—21no—
118#13133190—21no—
119#13133188—21no—
120#13133188—21no—
121#13133185—21no—
122#13133185—21no—
123C4×Dic106—21no—
124C4×Dic106C2×C411yescharacteristic
125C4×Dic106C2×C411yescharacteristic
126C4×Dic106C2311yescharacteristic
127C4×Dic106C2311yescharacteristic
128C4×D212—21no—
129C4×D212—21no—
130C4×D212C2×C411yescharacteristic
131C4×D212C2×C411yescharacteristic
132C4×D212C2×C411yescharacteristic
133C4×D212C2×C411yescharacteristic
134C4×D212C2311yescharacteristic
135C4×D212C2311yescharacteristic
136C4×C22⋊D53—21no—
137C4×C22⋊D53—21no—
138C4×C22⋊D53—21no—
139C4×C22⋊D53—21no—
140C4×C22⋊D53—21no—
141C4×C22⋊D53—21no—
142#13133176—21no—
143#13133176C2×C411yescharacteristic
144#13133176C2×C411yescharacteristic
145#13133175—21no—
146#13133175—21no—
147#13133174—21no—
148#13133174—21no—
149#13133174—21no—
150#13133174—21no—
151#13133173—21no—
152#13133173—21no—
153C2×C4⋊Dic53C2×C411yescharacteristic
154C4⋊C4×D53—21no—
155C4⋊C4×D53—21no—
156C2×#11719921—21no—
157C22⋊C4×D53—21no—
158C22⋊C4×D53—21no—
159C42×D53—21no—
160C42×D53—21no—
161C4⋊#88322—21no—
162C4⋊#88322—21no—
163C4⋊#88322C2311yescharacteristic
164C4⋊#88322C2311yescharacteristic
165C4⋊#88322C2311yescharacteristic
166C4⋊#88322C2311yescharacteristic
167C22⋊#88322—21no—
168C22⋊#88322—21no—
169C22⋊#88322—21no—
170C22⋊#88322—21no—
171#13133128—21no—
172#13133128—21no—
173C4×#88322—21no—
174C4×#88322—21no—
175C2×#41×C53D411yescharacteristic
176C2×M16×C53—21no—
177C2×M16×C53—21no—
178C22×C8×C53—21no—
179C4×Q8×C53C2×C411yescharacteristic
180C4×Q8×C53D411yescharacteristic
181C4×D4×C53C2×C411yescharacteristic
182C4×D4×C53C2×C411yescharacteristic
183C4×D4×C53C2×C411yescharacteristic
184C4×D4×C53D411yescharacteristic
185C4×D4×C53D411yescharacteristic
186C4×D4×C53D411yescharacteristic
187#117×C53D411yescharacteristic
188#117×C53D411yescharacteristic
189#117×C53D411yescharacteristic
190C2×C42×C53C2311yescharacteristic
191C2×C42×C53C2311yescharacteristic
192C2×C42×C53C2311yescharacteristic
193C4⋊C8×C53—21no—
194C4⋊C8×C53—21no—
195C4⋊C8×C53—21no—
196C22⋊C8×C53—21no—
197C22⋊C8×C53—21no—
198C22⋊C8×C53—21no—
199#97×C53—21no—
200#97×C53—21no—
201C4×C8×C53—21no—
202C4×C8×C53C2311yescharacteristic
203C4×C8×C53C2311yescharacteristic
204C4×C8×C53C2311yescharacteristic
205C4×C8×C53C2311yescharacteristic
206C23×D53—21no—
207#41×C53—41no—
208#41×C53—41no—
209C2×Q8×C53C22⋊C411yescharacteristic
210C2×D4×C53C22⋊C411yescharacteristic
211C2×D4×C53C22⋊C411yescharacteristic
212C2×D4×C53C22⋊C411yescharacteristic
213C22×C4×C53C22×C411yescharacteristic
214C22×C4×C53C22×C411yescharacteristic
215C22×C4×C53C22×C411yescharacteristic
216C22×C4×C53C2×D411yescharacteristic
217C22×C4×C53C2×D411yescharacteristic
218C22×C4×C53C2×D411yescharacteristic
219C22×C4×C53C2×D411yescharacteristic
220C22×C4×C53C2×D411yescharacteristic
221C22×C4×C53C2×D411yescharacteristic
222C2×C22⋊D53—21no—
223C2×C22⋊D53—21no—
224C2×C22⋊D53—21no—
225C2×C22⋊D53—21no—
226C22×Dic53—21no—
227#11719945—22no—
228#11719945—22no—
229#11719945—41no—
230#11719945—41no—
231C2×D212—22no—
232C2×D212—21no—
233C2×D212—41no—
234C2×D212C22×C411yescharacteristic
235C2×D212C22×C411yescharacteristic
236C2×C4×D53—21no—
237C2×C4×D53—21no—
238C2×C4×D53—21no—
239C2×C4×D53—21no—
240C2×C4×D53—21no—
241C2×C4×D53—21no—
242C2×C4×D53—21no—
243C2×C4×D53—21no—
244C2×C4×D53—42no—
245C2×C4×D53—42no—
246C2×Dic106—21no—
247C2×Dic106C22×C411yescharacteristic
248C2×Dic106C22×C411yescharacteristic
249M16×C53—42no—
250M16×C53—42no—
251C2×C8×C53—21no—
252C2×C8×C53—21no—
253C2×C8×C53—21no—
254C2×C8×C53—21no—
255C2×C8×C53—42no—
256C4⋊C4×C53C22⋊C411yescharacteristic
257C4⋊C4×C53C22⋊C411yescharacteristic
258C4⋊C4×C53C22⋊C411yescharacteristic
259C4⋊C4×C53C22⋊C411yescharacteristic
260C4⋊C4×C53C22⋊C411yescharacteristic
261C4⋊C4×C53C22⋊C411yescharacteristic
262C22⋊C4×C53C22⋊C411yescharacteristic
263C22⋊C4×C53C22⋊C411yescharacteristic
264C22⋊C4×C53C22⋊C411yescharacteristic
265C22⋊C4×C53C22⋊C411yescharacteristic
266C22⋊C4×C53C22⋊C411yescharacteristic
267C22⋊C4×C53C22⋊C411yescharacteristic
268C42×C53C22×C411yescharacteristic
269C42×C53C22×C411yescharacteristic
270C42×C53C22×C411yescharacteristic
271C42×C53C2×D411yescharacteristic
272C42×C53C2×D411yescharacteristic
273C42×C53C2×D411yescharacteristic
274C42×C53C2×D411yescharacteristic
275C42×C53C2×D411yescharacteristic
276C42×C53C2×D411yescharacteristic
277C42×C53C2411yescharacteristic
278C22⋊Dic53—21no—
279C22⋊Dic53—21no—
280C22⋊Dic53—21no—
281C22⋊Dic53—21no—
282C22⋊Dic53—21no—
283C22⋊Dic53—21no—
284#11719921—21no—
285#11719921—21no—
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—
296C4⋊Dic53—21no—
297C4⋊Dic53—21no—
298C4⋊Dic53—21no—
299C4⋊Dic53—21no—
300C4⋊Dic53C22×C411yescharacteristic
301C4⋊Dic53C22×C411yescharacteristic
302C4⋊Dic53C22×C411yescharacteristic
303C4⋊Dic53C22×C411yescharacteristic
304#11719919—21no—
305#11719919—21no—
306#11719919—21no—
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—
316C4×Dic53—21no—
317C4×Dic53—21no—
318C4×Dic53—21no—
319C4×Dic53—21no—
320C4×Dic53—21no—
321C4×Dic53—21no—
322#11719917—42no—
323C2×#88322—21no—
324C2×#88322—21no—
325C2×#88322—21no—
326C2×#88322—21no—
327C2×#88322—42no—
328C23×C53C2×C22⋊C411yescharacteristic
329C23×C53C2×C22⋊C411yescharacteristic
330C23×C53C2×C22⋊C411yescharacteristic
331C22×D53—21no—
332C22×D53—21no—
333C22×D53—42no—
334C22×D53—42no—
335C22×D53—81no—
336Q8×C53—41no—
337D4×C53—41no—
338D4×C53—41no—
339D4×C53—41no—
340C2×C4×C53—21no—
341C2×C4×C53—21no—
342C2×C4×C53—21no—
343C2×C4×C53—21no—
344C2×C4×C53—21no—
345C2×C4×C53—21no—
346C2×C4×C53—21no—
347C2×C4×C53—21no—
348C2×C4×C53—21no—
349C2×C4×C53—21no—
350C2×C4×C53—21no—
351C2×C4×C53—21no—
352C2×C4×C53—41no—
353C2×C4×C53—41no—
354C2×C4×C53—41no—
355C2×C4×C53C2×C22⋊C411yescharacteristic
356C2×C4×C53C2×C22⋊C411yescharacteristic
357C2×C4×C53C2×C22⋊C411yescharacteristic
358C2×C4×C53C2×C22⋊C411yescharacteristic
359C2×C4×C53C2×C22⋊C411yescharacteristic
360C2×C4×C53C2×C22⋊C411yescharacteristic
361C2×C4×C53C2×C22⋊C411yescharacteristic
362C2×C4×C53C2×C22⋊C411yescharacteristic
363C2×C4×C53C2×C22⋊C411yescharacteristic
364C2×C4×C53C23×C411yescharacteristic
365C2×C4×C53C22×D411yescharacteristic
366C2×C4×C53C22×D411yescharacteristic
367C22⋊D53—42no—
368C22⋊D53—42no—
369C22⋊D53—81no—
370C22⋊D53—81no—
371C2×Dic53—21no—
372C2×Dic53—21no—
373C2×Dic53—21no—
374C2×Dic53—21no—
375C2×Dic53—21no—
376C2×Dic53—21no—
377C2×Dic53—42no—
378D212—21no—
379D212—21no—
380D212—21no—
381D212—42no—
382D212#13112yes—
383C4×D53—42no—
384C4×D53—42no—
385C4×D53—42no—
386C4×D53—42no—
387C4×D53—41no—
388C4×D53—41no—
389C4×D53—41no—
390C4×D53—41no—
391C4×D53—81no—
392C4×D53—81no—
393Dic106—21no—
394Dic106—21no—
395Dic106—21no—
396Dic106—21no—
397Dic106—81no—
398C8×C53—22no—
399C8×C53—41no—
400C8×C53—41no—
401C8×C53—41no—
402#88322—41no—
403#88322—41no—
404#88322—41no—
405#88322—41no—
406#17513—531nomaximal, Sylow
407C22×C53—21no—
408C22×C53—21no—
409C22×C53—21no—
410C22×C53—21no—
411C22×C53—21no—
412C22×C53—21no—
413C22×C53—21no—
414C22×C53—21no—
415C22×C53—21no—
416C22×C53C22×C22⋊C411yescharacteristic
417C2×D53—22no—
418C2×D53—41no—
419C2×D53—41no—
420C2×D53—41no—
421C2×D53—41no—
422C2×D53—41no—
423C2×D53—84no—
424C4×C53—21no—
425C4×C53—21no—
426C4×C53—21no—
427C4×C53—21no—
428C4×C53—21no—
429C4×C53—21no—
430C4×C53—21no—
431C4×C53—21no—
432C4×C53—21no—
433C4×C53—21no—
434C4×C53C2×#13111yescharacteristic
435C4×C53#56811yescharacteristic
436C4×C53#57511yescharacteristic
437C4×C53#57511yescharacteristic
438Dic53—41no—
439Dic53—41no—
440Dic53—41no—
441Dic53—41no—
442Dic53—41no—
443Dic53—41no—
444#3475—531no—
445#2965D5311yescharacteristic, complemented
446#2925—531no—
447#1497—531no—
448#1495—531no—
449#1494—531no—
450#1490—531no—
451#1489—531no—
452#1488—531no—
453#1485—531no—
454#1483—531no—
455#1482—531no—
456#1478—531no—
457#1477—531no—
458#1476—531no—
459C2×C53—41no—
460C2×C53—41no—
461C2×C53—41no—
462C2×C53#288011yescharacteristic
463C2×C53#289611yescharacteristic
464C2×C53#290111yescharacteristic
465D53—42no—
466D53—81no—
467#556—531no—
468#555—531no—
469#554—531no—
470#553—1061no—
471#552—531no—
472#552—531no—
473#552—1061no—
474#551—1061no—
475#551—1061no—
476#547—531no—
477#546—531no—
478#546—531no—
479#533—531no—
480#529—531no—
481#529—531no—
482#529—1061no—
483#529—1061no—
484#525—1061no—
485C4×#41—531no—
486C4×#41—531no—
487C4×#41C2×D5311yescharacteristic
488C2×C4×D4—531no—
489C2×#117—1061no—
490#446—21no—
491#436—21no—
492#435—21no—
493#435—21no—
494#433—1061no—
495#433—1061no—
496#432—531no—
497#432—531no—
498#431—531no—
499#431—531no—
500#431C2×D5311yescharacteristic
501#431C2×D5311yescharacteristic, complemented
502#431C2×D5311yescharacteristic, complemented
503#423—531no—
504C2×C4⋊C8—531no—
505#408—1061no—
506#405—1061no—
507C4×M16C2×D5311yescharacteristic
508C4×M16C2×D5311yescharacteristic, complemented
509C2×C4×C8C2×D5311yescharacteristic, complemented
510Q8⋊C8—531no—
511Q8⋊C8—531no—
512Q8⋊C8—531no—
513Q8⋊C8—531no—
514Q8⋊C8—531no—
515Q8⋊C8—531no—
516Q8⋊C8—531no—
517Q8⋊C8—531no—
518D4⋊C8—531no—
519D4⋊C8—531no—
520D4⋊C8—531no—
521D4⋊C8—531no—
522D4⋊C8—531no—
523D4⋊C8—531no—
524D4⋊C8—531no—
525D4⋊C8—531no—
526C53#1751311yescharacteristic, complemented, Sylow
527C2×#41—531no—
528C2×#41—531no—
529C2×#41D21211yescharacteristic
530C22×D4—531no—
531C23×C4—1061no—
532C2×M16—21no—
533C2×M16—21no—
534C2×M16—1061no—
535C22×C8—21no—
536C22×C8—1061no—
537C4⋊Q8—531no—
538C4⋊Q8—531no—
539#126—1061no—
540#126—1061no—
541#126—1061no—
542#126—1061no—
543#126—1061no—
544#126—1061no—
545#125—531no—
546#125—531no—
547#125—1061no—
548#125—1061no—
549#125—1061no—
550#124—531no—
551#124—531no—
552#124—1061no—
553#124—1061no—
554#123—1061no—
555#123—1061no—
556#123—1061no—
557#123—1061no—
558#123—1061no—
559#123—1061no—
560#123—1061no—
561#123—1061no—
562C22⋊Q8—531no—
563C22⋊Q8—531no—
564C22⋊Q8—531no—
565C22⋊Q8—531no—
566C22⋊Q8—1061no—
567C22⋊Q8—1061no—
568C22⋊Q8—1061no—
569C22⋊Q8—1061no—
570C22⋊Q8—1061no—
571#121—531no—
572#121—531no—
573#121—1061no—
574#121—1061no—
575#121—1061no—
576#121—1061no—
577#120—1061no—
578#120—1061no—
579C4×Q8—531no—
580C4×Q8—531no—
581C4×Q8—531no—
582C4×Q8—531no—
583C4×Q8—1061no—
584C4×Q8C4×D5311yescharacteristic
585C4×Q8C22⋊D5311yescharacteristic
586C4×D4—531no—
587C4×D4—531no—
588C4×D4—531no—
589C4×D4—531no—
590C4×D4—531no—
591C4×D4—531no—
592C4×D4—1061no—
593C4×D4—1061no—
594C4×D4—1061no—
595C4×D4—1061no—
596C4×D4—1061no—
597C4×D4—1061no—
598C4×D4—1061no—
599C4×D4—1061no—
600C4×D4C4×D5311yescharacteristic
601C4×D4C4×D5311yescharacteristic
602C4×D4C4×D5311yescharacteristic
603C4×D4C22⋊D5311yescharacteristic
604C4×D4C22⋊D5311yescharacteristic
605C4×D4C22⋊D5311yescharacteristic
606#117—531no—
607#117—531no—
608#117—1061no—
609#117—1061no—
610#117—1061no—
611#117—1061no—
612#117—1061no—
613#117—1061no—
614#117—1061no—
615#117—1061no—
616#117—1061no—
617#117D21211yescharacteristic
618#117D21211yescharacteristic
619#117D21211yescharacteristic
620C2×C4⋊C4—531no—
621C2×C4⋊C4—1061no—
622C2×C4⋊C4—1061no—
623C2×C22⋊C4—1061no—
624C2×C22⋊C4—1061no—
625C2×C22⋊C4—1061no—
626C2×C42—1061no—
627C2×C42—1061no—
628C2×C42C22×D5311yescharacteristic
629C2×C42C22×D5311yescharacteristic
630C2×C42C22×D5311yescharacteristic
631C4⋊C8—21no—
632C4⋊C8—21no—
633C4⋊C8—21no—
634C4⋊C8—531no—
635C4⋊C8—531no—
636C4⋊C8—531no—
637C4⋊C8—531no—
638C4⋊C8—1061no—
639C4⋊C8—1061no—
640C22⋊C8—21no—
641C22⋊C8—21no—
642C22⋊C8—21no—
643C22⋊C8—1061no—
644C22⋊C8—1061no—
645C22⋊C8—1061no—
646C22⋊C8—1061no—
647#97—21no—
648#97—21no—
649#97—1061no—
650#97—1061no—
651C4×C8—21no—
652C4×C8—1061no—
653C4×C8—1061no—
654C4×C8C22×D5311yescharacteristic
655C4×C8C22×D5311yescharacteristic
656C4×C8C22×D5311yescharacteristic
657C4×C8C22×D5311yescharacteristic
658C24—1061no—
659#41—41no—
660#41—41no—
661#41—1062no—
662#41—1062no—
663#41—2121no—
664#41—2121no—
665C2×Q8—531no—
666C2×Q8—531no—
667C2×Q8—1061no—
668C2×Q8#1171992111yescharacteristic
669C2×D4—531no—
670C2×D4—531no—
671C2×D4—1062no—
672C2×D4—1061no—
673C2×D4—1061no—
674C2×D4—1061no—
675C2×D4—1061no—
676C2×D4—1061no—
677C2×D4—2121no—
678C2×D4#1171992111yescharacteristic
679C2×D4#1171992111yescharacteristic
680C2×D4#1171992111yescharacteristic
681C22×C4—1061no—
682C22×C4—1061no—
683C22×C4—1061no—
684C22×C4—1061no—
685C22×C4—1061no—
686C22×C4—1061no—
687C22×C4—1061no—
688C22×C4—1061no—
689C22×C4—1061no—
690C22×C4—2122no—
691C22×C4—2122no—
692C22×C4C2×C4×D5311yescharacteristic
693C22×C4C2×C4×D5311yescharacteristic
694C22×C4C2×C4×D5311yescharacteristic
695C22×C4C2×D21211yescharacteristic
696C22×C4C2×D21211yescharacteristic
697C22×C4C2×D21211yescharacteristic
698C22×C4C2×C22⋊D5311yescharacteristic
699C22×C4C2×C22⋊D5311yescharacteristic
700C22×C4C2×C22⋊D5311yescharacteristic
701M16—42no—
702M16—42no—
703M16—2122no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—21no—
707C2×C8—21no—
708C2×C8—42no—
709C2×C8—1061no—
710C2×C8—1061no—
711C2×C8—1061no—
712C2×C8—1061no—
713C2×C8—2122no—
714C4⋊C4—531no—
715C4⋊C4—531no—
716C4⋊C4—531no—
717C4⋊C4—531no—
718C4⋊C4—1061no—
719C4⋊C4—1061no—
720C4⋊C4—1061no—
721C4⋊C4—1061no—
722C4⋊C4—1061no—
723C4⋊C4—1061no—
724C4⋊C4—1061no—
725C4⋊C4—1061no—
726C4⋊C4—1061no—
727C4⋊C4—1061no—
728C4⋊C4—1061no—
729C4⋊C4—1061no—
730C4⋊C4—1061no—
731C4⋊C4—1061no—
732C4⋊C4—1061no—
733C4⋊C4—1061no—
734C4⋊C4#1171992111yescharacteristic
735C4⋊C4#1171992111yescharacteristic
736C4⋊C4#1171992111yescharacteristic
737C4⋊C4#1171992111yescharacteristic
738C4⋊C4#1171992111yescharacteristic
739C4⋊C4#1171992111yescharacteristic
740C22⋊C4—1061no—
741C22⋊C4—1061no—
742C22⋊C4—1061no—
743C22⋊C4—1061no—
744C22⋊C4—1061no—
745C22⋊C4—1061no—
746C22⋊C4—1061no—
747C22⋊C4—1061no—
748C22⋊C4—1061no—
749C22⋊C4—1061no—
750C22⋊C4—1061no—
751C22⋊C4—1061no—
752C22⋊C4—1061no—
753C22⋊C4—1061no—
754C22⋊C4—1061no—
755C22⋊C4—1061no—
756C22⋊C4—1061no—
757C22⋊C4—1061no—
758C22⋊C4#1171992111yescharacteristic
759C22⋊C4#1171992111yescharacteristic
760C22⋊C4#1171992111yescharacteristic
761C22⋊C4#1171992111yescharacteristic
762C22⋊C4#1171992111yescharacteristic
763C22⋊C4#1171992111yescharacteristic
764C42—1061no—
765C42—1061no—
766C42—1061no—
767C42—1061no—
768C42—1061no—
769C42—1061no—
770C42C2×C4×D5311yescharacteristic
771C42C2×C4×D5311yescharacteristic
772C42C2×C4×D5311yescharacteristic
773C42C2×D21211yescharacteristic
774C42C2×D21211yescharacteristic
775C42C2×D21211yescharacteristic
776C42C2×C22⋊D5311yescharacteristic
777C42C2×C22⋊D5311yescharacteristic
778C42C2×C22⋊D5311yescharacteristic
779C42C23×D5311yescharacteristic
780C23—1061no—
781C23—1061no—
782C23—4241no—
783C23—2122no—
784C23—2122no—
785C23C2×#1171992111yescharacteristic
786C23C2×#1171992111yescharacteristic
787C23C2×#1171992111yescharacteristic
788Q8—41no—
789Q8—1061no—
790Q8—1061no—
791Q8—1061no—
792Q8—1061no—
793Q8—4241no—
794D4—41no—
795D4—41no—
796D4—41no—
797D4—532no—
798D4—1061no—
799D4—1061no—
800D4—1061no—
801D4—4241no—
802D4—4241no—
803D4—2122no—
804D4—2122no—
805D4—2122no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—1061no—
822C2×C4—1061no—
823C2×C4—1061no—
824C2×C4—1061no—
825C2×C4—1061no—
826C2×C4—1061no—
827C2×C4—4241no—
828C2×C4—4241no—
829C2×C4—2122no—
830C2×C4—2122no—
831C2×C4—2122no—
832C2×C4—2122no—
833C2×C4—2122no—
834C2×C4—2121no—
835C2×C4—2121no—
836C2×C4—2121no—
837C2×C4—2121no—
838C2×C4C2×#1171992111yescharacteristic
839C2×C4C2×#1171992111yescharacteristic
840C2×C4C2×#1171992111yescharacteristic
841C2×C4C2×#1171992111yescharacteristic
842C2×C4C2×#1171992111yescharacteristic
843C2×C4C2×#1171992111yescharacteristic
844C2×C4C2×#1171992111yescharacteristic
845C2×C4C2×#1171992111yescharacteristic
846C2×C4C2×#1171992111yescharacteristic
847C2×C4C22×C4×D5311yescharacteristic
848C2×C4C22×C22⋊D5311yescharacteristic
849C2×C4C22×D21211yescharacteristic
850C8—22no—
851C8—41no—
852C8—41no—
853C8—41no—
854C8—2121no—
855C8—2121no—
856C8—2121no—
857C8—2121no—
858C22—21no—
859C22—21no—
860C22—21no—
861C22—21no—
862C22—21no—
863C22—21no—
864C22—21no—
865C22—21no—
866C22—21no—
867C22—1062no—
868C22—4244no—
869C22—2121no—
870C22—2121no—
871C22—2121no—
872C22—2121no—
873C22—2121no—
874C22C22×#1171992111yescharacteristic
875C4—21no—
876C4—21no—
877C4—21no—
878C4—21no—
879C4—21no—
880C4—21no—
881C4—21no—
882C4—21no—
883C4—21no—
884C4—21no—
885C4—2121no—
886C4—2121no—
887C4—2121no—
888C4—2121no—
889C4—2121no—
890C4—2121no—
891C4#131×D5311yescharacteristic
892C4#1681138811yescharacteristic
893C4#1681142311yescharacteristic
894C4#1681142311yescharacteristic
895C2—41no—
896C2—41no—
897C2—41no—
898C2—4241no—
899C2—2122no—
900C2#2028316211yescharacteristic
901C2#2028323511yescharacteristic
902C2#2028326311yescharacteristic
subgroupG/H
centerC2×C4C22×D212
commutatorC2×C4×C53C23×C4
FrattiniC42C23×D53
FittingC53×#2965C2
socleC22×C53C22×C22⋊C4
prime radical#20288279C2
cosocleC42×C53C24
hypercenter#2965D53
hypocenterC53#17513
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #2965

Complements

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

NH ≅ G/Ntype
2. #20283381C2semidirect
3. #20273189C2semidirect
4. #20273181C2semidirect
5. #20273176C2semidirect
6. #20273159C2semidirect
7. #20273155C2semidirect
8. #20273150C2semidirect
9. #20273137C2semidirect
10. #20273129C2semidirect
11. #20273124C2semidirect
12. #20273107C2semidirect
13. #20273103C2semidirect
14. #20273098C2semidirect
15. C53×#2965C2semidirect
41. #16810680C22semidirect
43. #16810676C22semidirect
44. #16810647C22semidirect
45. C2×C4⋊#88322C22semidirect
48. #16810355C22semidirect
49. #16810355C22semidirect
50. #16810355C22semidirect
51. #16810355C22semidirect
52. #16810355C22semidirect
53. #16810355C22semidirect
54. #16810355C22semidirect
55. #16810355C22semidirect
70. C53×#431C22semidirect
71. C53×#431C22semidirect
73. C4×M16×C53C22semidirect
74. C2×C4×C8×C53C22semidirect
445. #2965D53semidirect
501. #431C2×D53semidirect
502. #431C2×D53semidirect
508. C4×M16C2×D53semidirect
509. C2×C4×C8C2×D53semidirect
526. C53#17513semidirect

Maximal subgroups

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

subgroupindex
#202882792
#202833812
#202731892
#202731812
#202731762
#202731592
#202731552
#202731502
#202731372
#202731292
#202731242
#202731072
#202731032
#202730982
C53×#29652
#1751353