Finite Group Databasebeta

← #27400579

Subgroups — #27400579

Order 13568.

1148 conjugacy classes of subgroups.

The subgroup lattice has 1048 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288273C211yesmaximal, characteristic
2#20277160C211yesmaximal, characteristic, complemented
3#20275695C211yesmaximal, characteristic, complemented
4#20275659C211yesmaximal, characteristic, complemented
5#20275161C211yesmaximal, characteristic, complemented
6#20275156C211yesmaximal, characteristic, complemented
7#20275017C211yesmaximal, characteristic, complemented
8#20275017C211yesmaximal, characteristic, complemented
9#20274812C211yesmaximal, characteristic, complemented
10#20274812C211yesmaximal, characteristic, complemented
11#20274732C211yesmaximal, characteristic, complemented
12#20274528C211yesmaximal, characteristic, complemented
13#20274426C211yesmaximal, characteristic, complemented
14C2×#16810384C211yesmaximal, characteristic, complemented
15D4×M16×C53C211yesmaximal, characteristic, complemented
16#16811343C411yescharacteristic, complemented
17#16811338C411yescharacteristic, complemented
18#16811330C411yescharacteristic, complemented
19#16811319C411yescharacteristic, complemented
20#16811319C411yescharacteristic, complemented
21#16811313C411yescharacteristic, complemented
22#16811313C411yescharacteristic, complemented
23#16811308—21no—
24#16811299—21no—
25#16811299—21no—
26#16811277C411yescharacteristic, complemented
27#16811267—21no—
28#16811180C2211yescharacteristic
29#16811155—21no—
30#16811153—21no—
31#16811153—21no—
32#16811134C2211yescharacteristic
33#16811134C2211yescharacteristic
34C4×#11719945C2211yescharacteristic
35C4×#11719947—21no—
36C2×#13133176C2211yescharacteristic
37C2×#13133176C2211yescharacteristic
38C2×#13133176C2211yescharacteristic
39C22×C4×Dic53C2211yescharacteristic
40C2×#13133143C2211yescharacteristic
41C2×#13133143C2211yescharacteristic
42C2×#13133143C2211yescharacteristic
43C2×#13133143C2211yescharacteristic
44#16810516—21no—
45#16810509—21no—
46#16810503—21no—
47#16810498—21no—
48C4×C4⋊Dic53C2211yescharacteristic
49C4×C22⋊Dic53C2211yescharacteristic
50C4×C22⋊Dic53C2211yescharacteristic
51#16810469C2211yescharacteristic
52#16810384C2211yescharacteristic
53#16810384C2211yescharacteristic
54#16810384C2211yescharacteristic
55#16810384C2211yescharacteristic
56#16810384C2211yescharacteristic
57#16810384C2211yescharacteristic
58#16810384C2211yescharacteristic
59#16810384C2211yescharacteristic
60#16810384C2211yescharacteristic
61#16810384C2211yescharacteristic
62#16810384C2211yescharacteristic
63#16810384C2211yescharacteristic
64C22×M16×C53C2211yescharacteristic
65C22×M16×C53C2211yescharacteristic
66C2×C4×D4×C53C2211yescharacteristic
67C53×#436—21no—
68C53×#435—21no—
69C53×#435—21no—
70C8×D4×C53—21no—
71C53×#423C2211yescharacteristic
72C53×#407C2211yescharacteristic
73C53×#407C2211yescharacteristic
74C4×M16×C53C2211yescharacteristic
75C2×#11719945C2311yescharacteristic
76C2×#11719947—21no—
77C23×Dic53—21no—
78#13133217C2×C411yescharacteristic, complemented
79#13133217C2×C411yescharacteristic, complemented
80#13133212—21no—
81#13133212—21no—
82#13133210—21no—
83#13133210—21no—
84#13133210—21no—
85#13133210—21no—
86#13133209C2×C411yescharacteristic, complemented
87#13133209C2×C411yescharacteristic, complemented
88#13133208—21no—
89#13133207—21no—
90#13133207—21no—
91#13133204—21no—
92#13133203—21no—
93#13133203—21no—
94#13133201—21no—
95#13133201—21no—
96#13133200—21no—
97#13133200—21no—
98#13133199—21no—
99#13133199—21no—
100#13133198—21no—
101#13133198—21no—
102#13133197—21no—
103#13133196—21no—
104#13133196—21no—
105#13133196C2×C411yescharacteristic
106#13133196C2×C411yescharacteristic
107#13133196C2×C411yescharacteristic, complemented
108#13133196C2×C411yescharacteristic, complemented
109#13133194—21no—
110#13133194—21no—
111#13133191C2×C411yescharacteristic
112#13133191C2×C411yescharacteristic
113#13133191C2×C411yescharacteristic, complemented
114#13133191C2×C411yescharacteristic, complemented
115#13133189—21no—
116#13133189—21no—
117#13133188—21no—
118#13133186—21no—
119#13133186—21no—
120C4×Dic106—21no—
121C4×Dic106—21no—
122C4×Dic106C2×C411yescharacteristic, complemented
123C4×Dic106C2×C411yescharacteristic, complemented
124#13133182—21no—
125C4×D212C2×C411yescharacteristic, complemented
126C4×D212C2×C411yescharacteristic, complemented
127D4×Dic53—21no—
128C4×C22⋊D53—21no—
129C4×C22⋊D53—21no—
130C4×C22⋊D53—21no—
131C4×C22⋊D53—21no—
132C4×C22⋊D53—21no—
133C4×C22⋊D53—21no—
134#13133177—21no—
135#13133177—21no—
136#13133176—22no—
137#13133176—21no—
138#13133176—21no—
139#13133176—21no—
140#13133176—21no—
141#13133176—41no—
142#13133176C2×C411yescharacteristic
143#13133176C2×C411yescharacteristic
144#13133176C2×C411yescharacteristic, complemented
145#13133176C2×C411yescharacteristic, complemented
146#13133176C2311yescharacteristic
147#13133176C2311yescharacteristic
148#13133176C2311yescharacteristic
149#13133175—21no—
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
157C2×C4⋊Dic53C2×C411yescharacteristic, complemented
158C2×C4⋊Dic53C2×C411yescharacteristic, complemented
159C2×C22⋊Dic53—21no—
160C2×C22⋊Dic53—21no—
161C2×C22⋊Dic53—21no—
162C2×C22⋊Dic53—21no—
163C2×C22⋊Dic53—21no—
164C2×C4×Dic53—21no—
165C2×C4×Dic53—21no—
166C2×C4×Dic53—21no—
167C2×C4×Dic53—22no—
168C2×C4×Dic53—41no—
169C2×C4×Dic53C2311yescharacteristic
170C2×C4×Dic53C2311yescharacteristic
171C2×C4×Dic53C2311yescharacteristic
172C2×C4×Dic53C2311yescharacteristic
173C42×D53—21no—
174#13133143—22no—
175#13133143—22no—
176#13133143—41no—
177#13133143—41no—
178#13133124—21no—
179#13133124—21no—
180#13133124—21no—
181#13133124—21no—
182#13133124—21no—
183C22×D4×C53D411yescharacteristic
184C23×C4×C53C2311yescharacteristic
185C23×C4×C53C2311yescharacteristic
186C2×M16×C53—22no—
187C2×M16×C53—22no—
188C2×M16×C53—21no—
189C2×M16×C53—21no—
190C2×M16×C53—41no—
191C2×M16×C53—41no—
192C2×M16×C53C2311yescharacteristic
193C2×M16×C53C2311yescharacteristic
194C2×M16×C53C2311yescharacteristic
195C2×M16×C53C2311yescharacteristic
196C22×C8×C53—21no—
197C22×C8×C53—21no—
198C4×D4×C53C2×C411yescharacteristic
199C4×D4×C53C2×C411yescharacteristic
200C4×D4×C53C2×C411yescharacteristic
201C4×D4×C53C2×C411yescharacteristic
202C4×D4×C53D411yescharacteristic
203C4×D4×C53D411yescharacteristic
204C4×D4×C53D411yescharacteristic
205C4×D4×C53D411yescharacteristic
206C2×C4⋊C4×C53D411yescharacteristic
207C2×C22⋊C4×C53D411yescharacteristic
208C2×C22⋊C4×C53D411yescharacteristic
209C2×C42×C53C2311yescharacteristic
210C4⋊C8×C53—21no—
211C4⋊C8×C53—21no—
212C22⋊C8×C53—21no—
213C22⋊C8×C53—21no—
214C22⋊C8×C53—21no—
215C22⋊C8×C53—21no—
216#97×C53—21no—
217C4×C8×C53—21no—
218C24×C53C2×D411yescharacteristic
219C24×C53C2×D411yescharacteristic
220C2×D4×C53—42no—
221C2×D4×C53C22⋊C411yescharacteristic
222C2×D4×C53C22⋊C411yescharacteristic
223C2×D4×C53C22⋊C411yescharacteristic
224C2×D4×C53C22⋊C411yescharacteristic
225C22×C4×C53—21no—
226C22×C4×C53—21no—
227C22×C4×C53—21no—
228C22×C4×C53—21no—
229C22×C4×C53—21no—
230C22×C4×C53—21no—
231C22×C4×C53—21no—
232C22×C4×C53—21no—
233C22×C4×C53C22×C411yescharacteristic
234C22×C4×C53C22×C411yescharacteristic
235C22×C4×C53C22×C411yescharacteristic
236C22×C4×C53C22×C411yescharacteristic
237C22×C4×C53C2×D411yescharacteristic
238C22×C4×C53C2×D411yescharacteristic
239C22×C4×C53C2×D411yescharacteristic
240C22×C4×C53C2×D411yescharacteristic
241C22×C4×C53C2×D411yescharacteristic
242C22×C4×C53C2×D411yescharacteristic
243C22×C4×C53C2×D411yescharacteristic
244C22×C4×C53C2×D411yescharacteristic
245C22×C4×C53C2411yescharacteristic
246C2×C22⋊D53—21no—
247C2×C22⋊D53—21no—
248C2×C22⋊D53—21no—
249C2×C22⋊D53—21no—
250C2×C22⋊D53—21no—
251C22×Dic53—21no—
252C22×Dic53—21no—
253C22×Dic53—21no—
254C22×Dic53—21no—
255C22×Dic53—21no—
256C22×Dic53—21no—
257C22×Dic53—21no—
258C22×Dic53—21no—
259C22×Dic53—42no—
260C22×Dic53—42no—
261C22×Dic53—42no—
262#11719947—44no—
263#11719945—21no—
264#11719945—21no—
265#11719945—21no—
266#11719945—21no—
267C2×D212C22×C411yescharacteristic
268C2×C4×D53—21no—
269C2×C4×D53—21no—
270C2×C4×D53—21no—
271C2×Dic106—21no—
272C2×Dic106—21no—
273C2×Dic106C22×C411yescharacteristic
274M16×C53—21no—
275M16×C53—21no—
276M16×C53—21no—
277M16×C53—21no—
278M16×C53—21no—
279M16×C53—21no—
280M16×C53—21no—
281M16×C53—42no—
282M16×C53—42no—
283M16×C53#4112yescomplemented
284C2×C8×C53—21no—
285C2×C8×C53—21no—
286C2×C8×C53—21no—
287C2×C8×C53—21no—
288C2×C8×C53—42no—
289C2×C8×C53—42no—
290C4⋊C4×C53C22⋊C411yescharacteristic
291C4⋊C4×C53C22⋊C411yescharacteristic
292C4⋊C4×C53C22⋊C411yescharacteristic
293C4⋊C4×C53C22⋊C411yescharacteristic
294C22⋊C4×C53C22⋊C411yescharacteristic
295C22⋊C4×C53C22⋊C411yescharacteristic
296C22⋊C4×C53C22⋊C411yescharacteristic
297C22⋊C4×C53C22⋊C411yescharacteristic
298C22⋊C4×C53C22⋊C411yescharacteristic
299C22⋊C4×C53C22⋊C411yescharacteristic
300C22⋊C4×C53C22⋊C411yescharacteristic
301C22⋊C4×C53C22⋊C411yescharacteristic
302C42×C53C22×C411yescharacteristic
303C42×C53C22×C411yescharacteristic
304C42×C53C2×D411yescharacteristic
305C42×C53C2×D411yescharacteristic
306C22⋊Dic53—21no—
307C22⋊Dic53—21no—
308C22⋊Dic53—21no—
309C22⋊Dic53—21no—
310C22⋊Dic53—21no—
311C22⋊Dic53—21no—
312C22⋊Dic53—21no—
313C22⋊Dic53—21no—
314C22⋊Dic53—21no—
315C22⋊Dic53—21no—
316C22⋊Dic53—21no—
317C22⋊Dic53—42no—
318C22⋊Dic53—42no—
319C22⋊Dic53—42no—
320#11719921—21no—
321#11719921—21no—
322#11719921—21no—
323#11719921—21no—
324#11719921—21no—
325#11719921—21no—
326C4⋊Dic53—21no—
327C4⋊Dic53—21no—
328C4⋊Dic53—21no—
329C4⋊Dic53—21no—
330C4⋊Dic53—21no—
331C4⋊Dic53—21no—
332C4⋊Dic53—42no—
333C4⋊Dic53—42no—
334C4⋊Dic53C22×C411yescharacteristic
335C4⋊Dic53C22×C411yescharacteristic
336C4⋊Dic53C22×C411yescharacteristic
337C4⋊Dic53C22×C411yescharacteristic
338C4⋊Dic53C22×C411yescharacteristic
339C4⋊Dic53C22×C411yescharacteristic
340#11719919—21no—
341#11719919—21no—
342#11719919—21no—
343#11719919—21no—
344#11719919—21no—
345#11719919—21no—
346#11719919—21no—
347#11719919—21no—
348#11719919—21no—
349#11719919—21no—
350C4×Dic53—21no—
351C4×Dic53—21no—
352C4×Dic53—21no—
353C4×Dic53—21no—
354C4×Dic53—21no—
355C4×Dic53—21no—
356C4×Dic53—21no—
357C4×Dic53—21no—
358C4×Dic53—21no—
359C4×Dic53—21no—
360C4×Dic53—21no—
361C4×Dic53—21no—
362C4×Dic53—21no—
363C4×Dic53—21no—
364C4×Dic53—21no—
365C4×Dic53—21no—
366C4×Dic53—42no—
367C4×Dic53#4112yescomplemented
368C23×C53—21no—
369C23×C53—21no—
370C23×C53—22no—
371C23×C53—21no—
372C23×C53—21no—
373C23×C53—41no—
374C23×C53—41no—
375C23×C53—41no—
376C23×C53C2×C22⋊C411yescharacteristic
377C23×C53C2×C22⋊C411yescharacteristic
378C23×C53C2×C22⋊C411yescharacteristic
379C23×C53C2×C22⋊C411yescharacteristic
380C23×C53C22×D411yescharacteristic
381C22×D53—21no—
382D4×C53—22no—
383D4×C53—22no—
384D4×C53—41no—
385D4×C53—41no—
386C2×C4×C53—21no—
387C2×C4×C53—21no—
388C2×C4×C53—21no—
389C2×C4×C53—21no—
390C2×C4×C53—21no—
391C2×C4×C53—21no—
392C2×C4×C53—21no—
393C2×C4×C53—21no—
394C2×C4×C53—21no—
395C2×C4×C53—21no—
396C2×C4×C53—21no—
397C2×C4×C53—21no—
398C2×C4×C53—21no—
399C2×C4×C53—21no—
400C2×C4×C53—21no—
401C2×C4×C53—21no—
402C2×C4×C53—21no—
403C2×C4×C53—21no—
404C2×C4×C53—21no—
405C2×C4×C53—21no—
406C2×C4×C53—41no—
407C2×C4×C53—41no—
408C2×C4×C53C2×C22⋊C411yescharacteristic
409C2×C4×C53C2×C22⋊C411yescharacteristic
410C2×C4×C53C2×C22⋊C411yescharacteristic
411C2×C4×C53C2×C22⋊C411yescharacteristic
412C2×C4×C53C2×C22⋊C411yescharacteristic
413C2×C4×C53C2×C22⋊C411yescharacteristic
414C2×C4×C53C2×C22⋊C411yescharacteristic
415C2×C4×C53C2×C22⋊C411yescharacteristic
416C2×C4×C53C23×C411yescharacteristic
417C2×C4×C53C22×D411yescharacteristic
418C2×C4×C53C2×#4111yescharacteristic
419C2×C4×C53C2×#4111yescharacteristic
420C2×C4×C53H(5,𝔽2)11yescharacteristic
421C2×C4×C532−1+411yescharacteristic
422C22⋊D53—42no—
423C22⋊D53—41no—
424C22⋊D53—41no—
425C22⋊D53—42no—
426C22⋊D53—81no—
427C22⋊D53—81no—
428C2×Dic53—22no—
429C2×Dic53—21no—
430C2×Dic53—21no—
431C2×Dic53—21no—
432C2×Dic53—21no—
433C2×Dic53—21no—
434C2×Dic53—21no—
435C2×Dic53—21no—
436C2×Dic53—22no—
437C2×Dic53—42no—
438C2×Dic53—41no—
439C2×Dic53—41no—
440C2×Dic53—41no—
441C2×Dic53—48no—
442C2×Dic53—41no—
443C2×Dic53—42no—
444C2×Dic53—41no—
445C2×Dic53—41no—
446C2×Dic53—41no—
447C2×Dic53—41no—
448C2×Dic53—41no—
449C2×Dic53—41no—
450C2×Dic53—81no—
451C2×Dic53—81no—
452D212—21no—
453D212—21no—
454C4×D53—42no—
455C4×D53—41no—
456C4×D53—41no—
457C4×D53—81no—
458Dic106—21no—
459Dic106—21no—
460Dic106—42no—
461Dic106—81no—
462C8×C53—22no—
463C8×C53—41no—
464C8×C53—41no—
465C8×C53—41no—
466#22506—531nomaximal, Sylow
467C22×C53—21no—
468C22×C53—21no—
469C22×C53—21no—
470C22×C53—21no—
471C22×C53—21no—
472C22×C53—21no—
473C22×C53—21no—
474C22×C53—21no—
475C22×C53—21no—
476C22×C53—21no—
477C22×C53—21no—
478C22×C53—21no—
479C22×C53—21no—
480C22×C53—42no—
481C22×C53—42no—
482C22×C53—81no—
483C22×C53—81no—
484C22×C53#42112yes—
485C22×C53C22×C22⋊C411yescharacteristic
486C22×C53#54611yescharacteristic
487C22×C53#54711yescharacteristic
488C2×D53—41no—
489C2×D53—41no—
490C2×D53—41no—
491C4×C53—21no—
492C4×C53—21no—
493C4×C53—21no—
494C4×C53—21no—
495C4×C53—21no—
496C4×C53—21no—
497C4×C53—21no—
498C4×C53—21no—
499C4×C53C4×#4111yescharacteristic
500C4×C53#52011yescharacteristic
501C4×C53#54611yescharacteristic
502C4×C53#54711yescharacteristic
503Dic53—42no—
504Dic53—42no—
505Dic53—41no—
506Dic53—41no—
507Dic53—41no—
508Dic53—41no—
509Dic53—41no—
510Dic53—41no—
511Dic53—41no—
512Dic53—81no—
513Dic53—81no—
514#3475—531no—
515D4×M16D5311yescharacteristic, complemented
516#2290—531no—
517#1995—531no—
518#1986—531no—
519#1897—531no—
520#1896—531no—
521#1871—531no—
522#1871—531no—
523#1826—531no—
524#1826—531no—
525#1806—531no—
526#1759—531no—
527#1733—531no—
528C2×#339—531no—
529C2×C53—21no—
530C2×C53—21no—
531C2×C53—22no—
532C2×C53—41no—
533C2×C53—41no—
534C2×C53—41no—
535C2×C53#233911yescharacteristic
536C2×C53C2×#42111yescharacteristic
537C2×C53#290111yescharacteristic
538D53—81no—
539C22×M16C2×D5311yescharacteristic
540C22×M16C2×D5311yescharacteristic
541#556—531no—
542#555—531no—
543#554—531no—
544#553—531no—
545#553—531no—
546#552—531no—
547#552—531no—
548#552—1061no—
549#551—1061no—
550#551—1061no—
551#547—531no—
552#546—1061no—
553#533—531no—
554#529—1061no—
555#529—1061no—
556#529—1061no—
557#525—531no—
558#525—531no—
559C4×#41—531no—
560C4×#41—1061no—
561C2×C4×D4C2×D5311yescharacteristic
562C2×#117—531no—
563C2×#117—531no—
564C2×#117—531no—
565C22×C42—531no—
566#436—21no—
567#435—21no—
568#435—21no—
569C8×D4—21no—
570#423C2×D5311yescharacteristic
571C2×#104—531no—
572C2×#104—531no—
573C2×#104—531no—
574C2×#104—531no—
575#407C2×D5311yescharacteristic
576#407C2×D5311yescharacteristic
577C4×M16C2×D5311yescharacteristic
578#388—1061no—
579#387—1061no—
580#386—1061no—
581#385—1061no—
582C4×C4⋊C4—531no—
583C4×C22⋊C4—531no—
584C4×C22⋊C4—531no—
585#376—531no—
586#339—531no—
587#339—531no—
588#339—531no—
589#339—531no—
590#339—531no—
591#339—531no—
592#339—531no—
593#339—531no—
594#339—531no—
595#339—531no—
596#339—531no—
597#339—531no—
598C53#2250611yescharacteristic, complemented, Sylow
599C2×#41—531no—
600C2×#41—1061no—
601C22×D4D21211yescharacteristic
602C23×C4—1061no—
603C23×C4C22×D5311yescharacteristic
604C23×C4C22×D5311yescharacteristic
605C2×M16—21no—
606C2×M16—21no—
607C2×M16—22no—
608C2×M16—22no—
609C2×M16—41no—
610C2×M16—41no—
611C2×M16C22×D5311yescharacteristic
612C2×M16C22×D5311yescharacteristic
613C2×M16C22×D5311yescharacteristic
614C2×M16C22×D5311yescharacteristic
615C22×C8—21no—
616C22×C8—21no—
617C4⋊Q8—531no—
618C4⋊Q8—531no—
619#126—1061no—
620#126—1061no—
621#126—1061no—
622#126—1061no—
623#126—1061no—
624#126—1061no—
625#125—531no—
626#125—531no—
627#125—1061no—
628#125—1061no—
629#125—1061no—
630#124—1061no—
631#124—1061no—
632#124—1061no—
633#123—1061no—
634#123—1061no—
635#123—1061no—
636#123—1061no—
637#123—1061no—
638#123—1061no—
639#123—1061no—
640#123—1061no—
641C22⋊Q8—531no—
642C22⋊Q8—531no—
643C22⋊Q8—531no—
644C22⋊Q8—531no—
645C22⋊Q8—1061no—
646C22⋊Q8—1061no—
647C22⋊Q8—1061no—
648C22⋊Q8—1061no—
649C22⋊Q8—1061no—
650#121—531no—
651#121—531no—
652#121—531no—
653#121—531no—
654#121—1061no—
655#121—1061no—
656#121—1061no—
657#120—1061no—
658#120—1061no—
659C4×Q8—531no—
660C4×Q8—531no—
661C4×Q8—1061no—
662C4×Q8—1061no—
663C4×Q8—1061no—
664C4×D4—531no—
665C4×D4—531no—
666C4×D4—1061no—
667C4×D4—1061no—
668C4×D4—1061no—
669C4×D4—1061no—
670C4×D4—1061no—
671C4×D4—1061no—
672C4×D4—1061no—
673C4×D4—1061no—
674C4×D4—1061no—
675C4×D4C4×D5311yescharacteristic
676C4×D4C4×D5311yescharacteristic
677C4×D4C4×D5311yescharacteristic
678C4×D4C4×D5311yescharacteristic
679C4×D4C22⋊D5311yescharacteristic
680C4×D4C22⋊D5311yescharacteristic
681C4×D4C22⋊D5311yescharacteristic
682C4×D4C22⋊D5311yescharacteristic
683#117—531no—
684#117—531no—
685#117—531no—
686#117—531no—
687#117—531no—
688#117—531no—
689#117—531no—
690#117—1062no—
691#117—1061no—
692#117—1061no—
693#117—1061no—
694#117—1061no—
695#117—1061no—
696#117—1061no—
697#117—1061no—
698#117—1061no—
699#117—2121no—
700C2×C4⋊C4—531no—
701C2×C4⋊C4—531no—
702C2×C4⋊C4—531no—
703C2×C4⋊C4—531no—
704C2×C4⋊C4—1061no—
705C2×C4⋊C4—1061no—
706C2×C4⋊C4D21211yescharacteristic
707C2×C22⋊C4—1061no—
708C2×C22⋊C4—1061no—
709C2×C22⋊C4—1061no—
710C2×C22⋊C4—1061no—
711C2×C22⋊C4—1061no—
712C2×C22⋊C4D21211yescharacteristic
713C2×C22⋊C4D21211yescharacteristic
714C2×C42—531no—
715C2×C42—531no—
716C2×C42—531no—
717C2×C42—531no—
718C2×C42—1062no—
719C2×C42—1061no—
720C2×C42—1061no—
721C2×C42—1061no—
722C2×C42—1061no—
723C2×C42—2121no—
724C2×C42C22×D5311yescharacteristic
725C4⋊C8—21no—
726C4⋊C8—21no—
727#104—1062no—
728#104—1062no—
729#104—2121no—
730#104—2121no—
731C22⋊C8—21no—
732C22⋊C8—21no—
733C22⋊C8—21no—
734C22⋊C8—21no—
735#97—21no—
736C4×C8—21no—
737#95—1061no—
738#95—1061no—
739#95—1061no—
740#95—1061no—
741#95—1061no—
742C24C2×D21211yescharacteristic
743C24C2×D21211yescharacteristic
744#41—1061no—
745#41—1061no—
746#41—1061no—
747#41—1061no—
748#41—2124no—
749C2×Q8—531no—
750C2×Q8—1061no—
751C2×Q8—1061no—
752C2×D4—42no—
753C2×D4—531no—
754C2×D4—1061no—
755C2×D4—1061no—
756C2×D4—1061no—
757C2×D4—1061no—
758C2×D4—1061no—
759C2×D4#1171992111yescharacteristic
760C2×D4#1171992111yescharacteristic
761C2×D4#1171992111yescharacteristic
762C2×D4#1171992111yescharacteristic
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—1061no—
772C22×C4—1061no—
773C22×C4—1061no—
774C22×C4—1061no—
775C22×C4—1061no—
776C22×C4—1061no—
777C22×C4—1061no—
778C22×C4—1061no—
779C22×C4—1061no—
780C22×C4—1061no—
781C22×C4—1061no—
782C22×C4—2122no—
783C22×C4—2122no—
784C22×C4—2122no—
785C22×C4C2×C4×D5311yescharacteristic
786C22×C4C2×C4×D5311yescharacteristic
787C22×C4C2×C4×D5311yescharacteristic
788C22×C4C2×C4×D5311yescharacteristic
789C22×C4C2×D21211yescharacteristic
790C22×C4C2×D21211yescharacteristic
791C22×C4C2×D21211yescharacteristic
792C22×C4C2×D21211yescharacteristic
793C22×C4C2×C22⋊D5311yescharacteristic
794C22×C4C2×C22⋊D5311yescharacteristic
795C22×C4C2×C22⋊D5311yescharacteristic
796C22×C4C2×C22⋊D5311yescharacteristic
797C22×C4C23×D5311yescharacteristic
798M16—21no—
799M16—21no—
800M16—21no—
801M16—21no—
802M16—21no—
803M16—21no—
804M16—21no—
805M16—42no—
806M16—42no—
807M16#1171994712yescomplemented
808C2×C8—21no—
809C2×C8—21no—
810C2×C8—21no—
811C2×C8—21no—
812C2×C8—42no—
813C2×C8—42no—
814C4⋊C4—531no—
815C4⋊C4—531no—
816C4⋊C4—531no—
817C4⋊C4—531no—
818C4⋊C4—531no—
819C4⋊C4—531no—
820C4⋊C4—1061no—
821C4⋊C4—1061no—
822C4⋊C4—1061no—
823C4⋊C4—1061no—
824C4⋊C4—1061no—
825C4⋊C4—1061no—
826C4⋊C4—1061no—
827C4⋊C4—1061no—
828C4⋊C4—1061no—
829C4⋊C4—1061no—
830C4⋊C4—1061no—
831C4⋊C4—1061no—
832C4⋊C4—1061no—
833C4⋊C4—1061no—
834C4⋊C4—1061no—
835C4⋊C4—1061no—
836C4⋊C4—2122no—
837C4⋊C4—2122no—
838C4⋊C4#1171992111yescharacteristic
839C4⋊C4#1171992111yescharacteristic
840C4⋊C4#1171992111yescharacteristic
841C4⋊C4#1171992111yescharacteristic
842C22⋊C4—1061no—
843C22⋊C4—1061no—
844C22⋊C4—1061no—
845C22⋊C4—1061no—
846C22⋊C4—1061no—
847C22⋊C4—1061no—
848C22⋊C4—1061no—
849C22⋊C4—1061no—
850C22⋊C4—1061no—
851C22⋊C4—1061no—
852C22⋊C4—1061no—
853C22⋊C4—1061no—
854C22⋊C4—1061no—
855C22⋊C4—1061no—
856C22⋊C4—1061no—
857C22⋊C4—1061no—
858C22⋊C4—1061no—
859C22⋊C4—2122no—
860C22⋊C4—2122no—
861C22⋊C4—2122no—
862C22⋊C4#1171992111yescharacteristic
863C22⋊C4#1171992111yescharacteristic
864C22⋊C4#1171992111yescharacteristic
865C22⋊C4#1171992111yescharacteristic
866C22⋊C4#1171992111yescharacteristic
867C22⋊C4#1171992111yescharacteristic
868C22⋊C4#1171992111yescharacteristic
869C22⋊C4#1171992111yescharacteristic
870C42—532no—
871C42—1061no—
872C42—1061no—
873C42—1061no—
874C42—1061no—
875C42—1061no—
876C42—1061no—
877C42—1061no—
878C42—1061no—
879C42—1061no—
880C42—1061no—
881C42—1061no—
882C42—1061no—
883C42—1061no—
884C42—1061no—
885C42—1061no—
886C42—1061no—
887C42—2122no—
888C42C2×C4×D5311yescharacteristic
889C42C2×C4×D5311yescharacteristic
890C42C2×C22⋊D5311yescharacteristic
891C42C2×C22⋊D5311yescharacteristic
892C23—21no—
893C23—21no—
894C23—22no—
895C23—21no—
896C23—21no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—1061no—
901C23C2×#1171992111yescharacteristic
902C23C2×#1171992111yescharacteristic
903C23C2×#1171992111yescharacteristic
904C23C2×#1171992111yescharacteristic
905C23C22×D21211yescharacteristic
906Q8—1061no—
907Q8—1061no—
908Q8—4241no—
909Q8—2122no—
910D4—22no—
911D4—22no—
912D4—41no—
913D4—41no—
914D4—1061no—
915D4—1061no—
916D4—4241no—
917D4—4241no—
918D4—2122no—
919D4—2121no—
920D4—2121no—
921D4—2122no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—21no—
931C2×C4—21no—
932C2×C4—21no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—21no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—1062no—
945C2×C4—1062no—
946C2×C4—1061no—
947C2×C4—1061no—
948C2×C4—1061no—
949C2×C4—1061no—
950C2×C4—1061no—
951C2×C4—1061no—
952C2×C4—1061no—
953C2×C4—4241no—
954C2×C4—4241no—
955C2×C4—4241no—
956C2×C4—2122no—
957C2×C4—2121no—
958C2×C4—2121no—
959C2×C4—2121no—
960C2×C4—2121no—
961C2×C4—2121no—
962C2×C4—2121no—
963C2×C4—2121no—
964C2×C4—2121no—
965C2×C4—2121no—
966C2×C4—2122no—
967C2×C4—2128no—
968C2×C4—2121no—
969C2×C4—2122no—
970C2×C4—2121no—
971C2×C4—2121no—
972C2×C4C2×#1171992111yescharacteristic
973C2×C4C2×#1171992111yescharacteristic
974C2×C4C2×#1171992111yescharacteristic
975C2×C4C2×#1171992111yescharacteristic
976C2×C4C2×#1171992111yescharacteristic
977C2×C4C2×#1171992111yescharacteristic
978C2×C4C2×#1171992111yescharacteristic
979C2×C4C2×#1171992111yescharacteristic
980C2×C4C22×C4×D5311yescharacteristic
981C2×C4C22×C22⋊D5311yescharacteristic
982C2×C4#41×D5311yescharacteristic
983C2×C4C2×#1171994711yescharacteristic
984C2×C4#1313326211yescharacteristic
985C2×C4#1313326411yescharacteristic
986C8—22no—
987C8—41no—
988C8—41no—
989C8—41no—
990C22—21no—
991C22—21no—
992C22—21no—
993C22—21no—
994C22—21no—
995C22—21no—
996C22—21no—
997C22—21no—
998C22—21no—
999C22—21no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—42no—
1004C22—42no—
1005C22—81no—
1006C22—81no—
1007C22—2121no—
1008C22—2121no—
1009C22—2121no—
1010C22#1681063912yes—
1011C22C22×#1171992111yescharacteristic
1012C22#1681126811yescharacteristic
1013C22#1681127711yescharacteristic
1014C4—21no—
1015C4—21no—
1016C4—21no—
1017C4—21no—
1018C4—21no—
1019C4—21no—
1020C4—21no—
1021C4—21no—
1022C4—4241no—
1023C4—4241no—
1024C4—2122no—
1025C4—2122no—
1026C4—2121no—
1027C4—2121no—
1028C4—2121no—
1029C4—2121no—
1030C4—2121no—
1031C4—2121no—
1032C4—2121no—
1033C4C4×#1171994711yescharacteristic
1034C4#1681110211yescharacteristic
1035C4#1681126711yescharacteristic
1036C4#1681127211yescharacteristic
1037C2—21no—
1038C2—21no—
1039C2—22no—
1040C2—41no—
1041C2—41no—
1042C2—41no—
1043C2—4241no—
1044C2#2027754011yescharacteristic
1045C2C2×#1681063911yescharacteristic
1046C2#2028326011yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingD4×M16×C53C2
socleC22×C53C22×C22⋊C4
prime radical#20288273C2
cosocleC22×C4×C53C24
hypercenterD4×M16D53
hypocenterC53#22506
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C2×C4×D4 ◁ D4×M16

Complements

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

NH ≅ G/Ntype
2. #20277160C2semidirect
3. #20275695C2semidirect
4. #20275659C2semidirect
5. #20275161C2semidirect
6. #20275156C2semidirect
7. #20275017C2semidirect
8. #20275017C2semidirect
9. #20274812C2semidirect
10. #20274812C2semidirect
11. #20274732C2semidirect
12. #20274528C2semidirect
13. #20274426C2semidirect
14. C2×#16810384C2semidirect
15. D4×M16×C53C2semidirect
16. #16811343C4semidirect
17. #16811338C4semidirect
18. #16811330C4semidirect
19. #16811319C4semidirect
20. #16811319C4semidirect
21. #16811313C4semidirect
22. #16811313C4semidirect
26. #16811277C4semidirect
78. #13133217C2×C4semidirect
79. #13133217C2×C4semidirect
86. #13133209C2×C4semidirect
87. #13133209C2×C4semidirect
107. #13133196C2×C4semidirect
108. #13133196C2×C4semidirect
113. #13133191C2×C4semidirect
114. #13133191C2×C4semidirect
122. C4×Dic106C2×C4semidirect
123. C4×Dic106C2×C4semidirect
125. C4×D212C2×C4semidirect
126. C4×D212C2×C4semidirect
144. #13133176C2×C4semidirect
145. #13133176C2×C4semidirect
157. C2×C4⋊Dic53C2×C4semidirect
158. C2×C4⋊Dic53C2×C4semidirect
283. M16×C53#41semidirect
367. C4×Dic53#41semidirect
515. D4×M16D53semidirect
598. C53#22506semidirect
807. M16#11719947semidirect

Maximal subgroups

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

subgroupindex
#202882732
#202771602
#202756952
#202756592
#202751612
#202751562
#202750172
#202748122
#202747322
#202745282
#202744262
C2×#168103842
D4×M16×C532
#2250653