Finite Group Databasebeta

← #14769459

Subgroups — #14769459

Order 2816.

1494 conjugacy classes of subgroups.

The subgroup lattice has 1244 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×C22⋊D11C211yesmaximal, characteristic
2M16×C22⋊D11C211yesmaximal, characteristic, complemented
3C2×D11×#104C211yesmaximal, characteristic, complemented
4#13071053C211yesmaximal, characteristic, complemented
5#13069533C211yesmaximal, characteristic, complemented
6#13069446C211yesmaximal, characteristic, complemented
7#13069064C211yesmaximal, characteristic, complemented
8#13069056C211yesmaximal, characteristic, complemented
9#13068918C211yesmaximal, characteristic, complemented
10#13068915C211yesmaximal, characteristic, complemented
11#13068634C211yesmaximal, characteristic, complemented
12#13068560C211yesmaximal, characteristic, complemented
13#13068558C211yesmaximal, characteristic, complemented
14#13068428C211yesmaximal, characteristic, complemented
15C2×C11×#421C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C2×#41×D11C2211yescharacteristic
18C22×C11×M16C2211yescharacteristic, complemented
19C2×C11×#117C2211yescharacteristic, complemented
20#10623365C411yescharacteristic, complemented
21#10623363—21no—
22#10623363C2211yescharacteristic
23#10623362C411yescharacteristic, complemented
24#10623360—21no—
25#10623360C411yescharacteristic, complemented
26#10623359—21no—
27#10623359C2211yescharacteristic
28#41×Dic11C2211yescharacteristic
29#10623355—21no—
30#10623355C411yescharacteristic, complemented
31#10623348C411yescharacteristic, complemented
32Q8×C22⋊D11C411yescharacteristic, complemented
33#10623337—21no—
34#10623337C411yescharacteristic, complemented
35D4×C22⋊D11—21no—
36D4×C22⋊D11C411yescharacteristic, complemented
37#10623322—21no—
38#10623322C2211yescharacteristic
39C2×C4×C22⋊D11—21no—
40C2×C4×C22⋊D11C2211yescharacteristic
41C2×M16×D11C2211yescharacteristic, complemented
42C2×C42×D11C2211yescharacteristic, complemented
43C11×#421—24no—
44C2×C11×#104C2211yescharacteristic
45C2×C11×#104C2211yescharacteristic
46C2×C11×#104C2211yescharacteristic, complemented
47C2×C11×#104C2211yescharacteristic, complemented
48C2×#66901C2211yescharacteristic
49C2×#66901C2211yescharacteristic
50C2×#66901C2211yescharacteristic, complemented
51C2×#66901C2211yescharacteristic, complemented
52C4×C22⋊Dic11C2211yescharacteristic, complemented
53#10622820C2211yescharacteristic, complemented
54C2×#66889C2211yescharacteristic, complemented
55C2×#66889C2211yescharacteristic, complemented
56#10622741—21no—
57#10622740—21no—
58#10622739C2211yescharacteristic, complemented
59#10622731C2211yescharacteristic, complemented
60M16×Dic11C2211yescharacteristic, complemented
61#10622724—21no—
62C8×C22⋊D11—21no—
63#10622602—21no—
64#10622591—21no—
65#10622569—21no—
66#10622557—21no—
67C4×(C2×D11)⋊C4C2211yescharacteristic, complemented
68#10622545C2211yescharacteristic, complemented
69C4×Dic11⋊C4C2211yescharacteristic, complemented
70C2×#66869C2211yescharacteristic, complemented
71C2×#66869C2211yescharacteristic, complemented
72D11×#104—24no—
73#10622193C2211yescharacteristic, complemented
74#10622193C2211yescharacteristic, complemented
75#10622161C2211yescharacteristic, complemented
76#10622161C2211yescharacteristic, complemented
77C2×C11×#41—21no—
78C2×C11×#41—21no—
79C2×C11×#41—22no—
80C2×C11×#41—22no—
81C2×C11×#41—41no—
82C2×C11×#41—41no—
83C2×C11×#41C2×C411yescharacteristic, complemented
84C2×C11×#41C2×C411yescharacteristic, complemented
85C2×C11×#41C2311yescharacteristic
86C2×C11×#41C2311yescharacteristic
87C22×Q8×C11C2×C411yescharacteristic, complemented
88C22×D4×C11—21no—
89C22×D4×C11C2×C411yescharacteristic, complemented
90C23×C4×C11—21no—
91C23×C4×C11C2311yescharacteristic
92C22×C22⋊D11—21no—
93C22×C22⋊D11D411yescharacteristic
94#41×D11—22no—
95#41×D11—22no—
96#41×D11—41no—
97#41×D11—41no—
98C2×#4343C2×C411yescharacteristic
99C2×Q8×D11C2×C411yescharacteristic
100C2×#4341—21no—
101C2×#4341C2×C411yescharacteristic
102C2×D4×D11—21no—
103C2×D4×D11C2×C411yescharacteristic
104C2×#4339—21no—
105C2×#4339C2311yescharacteristic
106C22×C4×D11—21no—
107C22×C4×D11—21no—
108C22×C4×D11C2311yescharacteristic
109C2×C11×M16—21no—
110C2×C11×M16—22no—
111C2×C11×M16—41no—
112C2×C11×M16C2311yescharacteristic
113C2×C11×M16C2311yescharacteristic
114C22×C8×C11—21no—
115C11×#117—22no—
116C11×#117—41no—
117C2×C11×C4⋊C4—21no—
118C2×C11×C22⋊C4—21no—
119C2×C42×C11C2311yescharacteristic
120C2×C42×C11C2311yescharacteristic
121#67006—21no—
122#67006—21no—
123#67006—21no—
124C2×C22⋊Dic11—21no—
125C2×C22⋊Dic11—21no—
126C2×C22⋊Dic11D411yescharacteristic
127#67000—21no—
128#67000C2×C411yescharacteristic, complemented
129#66999—21no—
130#66999—21no—
131#66999C2×C411yescharacteristic
132#66999C2×C411yescharacteristic
133Q8×Dic11C2×C411yescharacteristic, complemented
134Q8×Dic11C2×C411yescharacteristic, complemented
135#66997—21no—
136#66997C2×C411yescharacteristic, complemented
137#66993—21no—
138#66993C2×C411yescharacteristic, complemented
139#66992—21no—
140#66992—21no—
141#66992—21no—
142#66992—21no—
143#66992—21no—
144#66992—21no—
145#66991—21no—
146#66991—21no—
147#66991C2×C411yescharacteristic
148#66991C2×C411yescharacteristic
149#66990—21no—
150#66990—21no—
151#66990—21no—
152#66989—21no—
153#66989C2×C411yescharacteristic, complemented
154#66988—21no—
155#66988—21no—
156#66988—21no—
157D4×Dic11—21no—
158D4×Dic11—21no—
159D4×Dic11C2×C411yescharacteristic, complemented
160D4×Dic11C2×C411yescharacteristic, complemented
161#66983—21no—
162#66983—21no—
163#66983C2×C411yescharacteristic, complemented
164#66983C2×C411yescharacteristic, complemented
165#66982—21no—
166#66982—21no—
167#66982—21no—
168C4×C22⋊D11—21no—
169C4×C22⋊D11—21no—
170C4×C22⋊D11—21no—
171C4×C22⋊D11—21no—
172C4×C22⋊D11—21no—
173C4×C22⋊D11—21no—
174C4×C22⋊D11—21no—
175C4×C22⋊D11—21no—
176C4×C22⋊D11—21no—
177C4×C22⋊D11—21no—
178C4×C22⋊D11C2×C411yescharacteristic
179C4×C22⋊D11C2×C411yescharacteristic
180C4×C22⋊D11C2×C411yescharacteristic
181C4×C22⋊D11C2×C411yescharacteristic
182C4×C22⋊D11D411yescharacteristic
183C4×C22⋊D11D411yescharacteristic
184C4×C22⋊D11D411yescharacteristic
185C4×C22⋊D11D411yescharacteristic
186C2×(C2×D11)⋊C4—21no—
187C2×(C2×D11)⋊C4—21no—
188C2×(C2×D11)⋊C4D411yescharacteristic
189#66979—21no—
190#66979C2311yescharacteristic
191#66977—21no—
192#66977—21no—
193#66977C2×C411yescharacteristic, complemented
194#66977C2×C411yescharacteristic, complemented
195C2×Dic11⋊C4—21no—
196C2×Dic11⋊C4—21no—
197C2×Dic11⋊C4D411yescharacteristic
198C2×C4×Dic11—21no—
199C2×C4×Dic11—21no—
200C2×C4×Dic11C2311yescharacteristic
201C2×C4×Dic11C2311yescharacteristic
202C2×C4×Dic11C2311yescharacteristic
203C2×#4318C2311yescharacteristic
204C2×#4318C2311yescharacteristic
205M16×D11—22no—
206M16×D11—41no—
207C2×#4313—21no—
208C2×C8×D11—21no—
209C42×D11—22no—
210C42×D11—41no—
211C11×#104—22no—
212C11×#104—22no—
213C11×#104—22no—
214C11×#104D414yescomplemented
215#66901—22no—
216#66901—22no—
217#66901—41no—
218#66901—41no—
219C11⋊#95—21no—
220C11⋊#95—21no—
221C11⋊#95—21no—
222C11⋊#95—21no—
223C11⋊#95—21no—
224C22⋊(C11⋊C8)—21no—
225C22⋊(C11⋊C8)—21no—
226#66889—22no—
227#66889—41no—
228(C2×D11)⋊C8—21no—
229(C2×D11)⋊C8—21no—
230#66879—21no—
231Dic11⋊C8—21no—
232Dic11⋊C8—21no—
233C8×Dic11—21no—
234#66869—22no—
235#66869—41no—
236#22434—111nomaximal, Sylow
237C24×C11—21no—
238C24×C11C2×D411yescharacteristic
239C23×D11—21no—
240C23×D11C2×D411yescharacteristic
241C11×#41—21no—
242C11×#41—21no—
243C11×#41—22no—
244C11×#41—22no—
245C11×#41—21no—
246C11×#41—21no—
247C11×#41—21no—
248C11×#41—21no—
249C11×#41—42no—
250C11×#41—42no—
251C11×#41—41no—
252C11×#41—41no—
253C11×#41—42no—
254C11×#41—42no—
255C11×#41C2×D412yes—
256C11×#41#4112yes—
257C2×Q8×C11—21no—
258C2×Q8×C11—22no—
259C2×Q8×C11—41no—
260C2×Q8×C11C22×C411yescharacteristic
261C2×Q8×C11C22×C411yescharacteristic
262C2×D4×C11—21no—
263C2×D4×C11—22no—
264C2×D4×C11—21no—
265C2×D4×C11—21no—
266C2×D4×C11—21no—
267C2×D4×C11—21no—
268C2×D4×C11—41no—
269C2×D4×C11—42no—
270C2×D4×C11—42no—
271C2×D4×C11C22×C411yescharacteristic
272C2×D4×C11C22×C411yescharacteristic
273C22×C4×C11—21no—
274C22×C4×C11—21no—
275C22×C4×C11—21no—
276C22×C4×C11—21no—
277C22×C4×C11—21no—
278C22×C4×C11—21no—
279C22×C4×C11—21no—
280C22×C4×C11—21no—
281C22×C4×C11—21no—
282C22×C4×C11—21no—
283C22×C4×C11—21no—
284C22×C4×C11—42no—
285C22×C4×C11—42no—
286C22×C4×C11C22×C411yescharacteristic
287C22×C4×C11C22×C411yescharacteristic
288C22×C4×C11C2×D411yescharacteristic
289C22×C4×C11C2×D411yescharacteristic
290C22×C4×C11C2×D411yescharacteristic
291C22×C4×C11C2411yescharacteristic
292C2×C22⋊D11—21no—
293C2×C22⋊D11—21no—
294C2×C22⋊D11—21no—
295C2×C22⋊D11—21no—
296C2×C22⋊D11—21no—
297C2×C22⋊D11—21no—
298C2×C22⋊D11—21no—
299C2×C22⋊D11—21no—
300C2×C22⋊D11—21no—
301C2×C22⋊D11—42no—
302C2×C22⋊D11—44no—
303C2×C22⋊D11C22⋊C411yescharacteristic
304C2×C22⋊D11C22⋊C411yescharacteristic
305C2×C22⋊D11C22⋊C411yescharacteristic
306C2×C22⋊D11C22⋊C411yescharacteristic
307C22×Dic11—21no—
308C22×Dic11—21no—
309C22×Dic11—21no—
310C22×Dic11—21no—
311C22×Dic11—21no—
312C22×Dic11C2×D411yescharacteristic
313C22×Dic11C2×D411yescharacteristic
314C22×Dic11C2×D411yescharacteristic
315#4343—22no—
316#4343—41no—
317Q8×D11—22no—
318Q8×D11—41no—
319#4341—22no—
320#4341—41no—
321#4341—42no—
322#4341—42no—
323D4×D11—22no—
324D4×D11—42no—
325D4×D11—42no—
326D4×D11—41no—
327#4339—21no—
328#4339—21no—
329#4339—21no—
330#4339—21no—
331#4339—42no—
332#4339—42no—
333C2×D44—21no—
334C2×D44C22×C411yescharacteristic
335C2×C4×D11—21no—
336C2×C4×D11—21no—
337C2×C4×D11—21no—
338C2×C4×D11—21no—
339C2×C4×D11—21no—
340C2×C4×D11—21no—
341C2×C4×D11—21no—
342C2×C4×D11—42no—
343C2×C4×D11—42no—
344C2×C4×D11—42no—
345C2×C4×D11—42no—
346C2×C4×D11—42no—
347C2×C4×D11C22×C411yescharacteristic
348C2×C4×D11C22×C411yescharacteristic
349C2×C4×D11C2×D411yescharacteristic
350C2×C4×D11C2×D411yescharacteristic
351C2×Dic22—21no—
352C2×Dic22C22×C411yescharacteristic
353C11×M16—21no—
354C11×M16—21no—
355C11×M16—21no—
356C11×M16—42no—
357C11×M16C2×D412yescomplemented
358C2×C8×C11—21no—
359C2×C8×C11—21no—
360C2×C8×C11—42no—
361C11×C4⋊C4—42no—
362C11×C22⋊C4—42no—
363C42×C11—21no—
364C42×C11—21no—
365C42×C11—21no—
366C42×C11C2×D412yescomplemented
367C22⋊Dic11—21no—
368C22⋊Dic11—21no—
369C22⋊Dic11—21no—
370C22⋊Dic11—21no—
371C22⋊Dic11—21no—
372C22⋊Dic11—21no—
373C22⋊Dic11—21no—
374C22⋊Dic11—21no—
375C22⋊Dic11—21no—
376C22⋊Dic11—42no—
377C22⋊Dic11C22⋊C411yescharacteristic
378C22⋊Dic11C22⋊C411yescharacteristic
379C22⋊Dic11C22⋊C411yescharacteristic
380C22⋊Dic11C22⋊C411yescharacteristic
381(C2×D11)⋊C4—21no—
382(C2×D11)⋊C4—21no—
383(C2×D11)⋊C4—21no—
384(C2×D11)⋊C4—21no—
385(C2×D11)⋊C4—21no—
386(C2×D11)⋊C4—21no—
387(C2×D11)⋊C4—42no—
388(C2×D11)⋊C4C22⋊C411yescharacteristic
389(C2×D11)⋊C4C22⋊C411yescharacteristic
390(C2×D11)⋊C4C22⋊C411yescharacteristic
391(C2×D11)⋊C4C22⋊C411yescharacteristic
392C4⋊Dic11—21no—
393C4⋊Dic11—21no—
394C4⋊Dic11C22×C411yescharacteristic
395C4⋊Dic11C22×C411yescharacteristic
396Dic11⋊C4—21no—
397Dic11⋊C4—21no—
398Dic11⋊C4—21no—
399Dic11⋊C4—21no—
400Dic11⋊C4—21no—
401Dic11⋊C4—21no—
402Dic11⋊C4—42no—
403Dic11⋊C4C22⋊C411yescharacteristic
404Dic11⋊C4C22⋊C411yescharacteristic
405Dic11⋊C4C22⋊C411yescharacteristic
406Dic11⋊C4C22⋊C411yescharacteristic
407C4×Dic11—21no—
408C4×Dic11—21no—
409C4×Dic11—21no—
410C4×Dic11—21no—
411C4×Dic11—21no—
412C4×Dic11—21no—
413C4×Dic11—21no—
414C4×Dic11—42no—
415C4×Dic11C22×C411yescharacteristic
416C4×Dic11C22×C411yescharacteristic
417C4×Dic11C2×D411yescharacteristic
418C4×Dic11C2×D411yescharacteristic
419#4318—21no—
420#4318—21no—
421#4318—21no—
422#4318—21no—
423C2×C11⋊C8—21no—
424C2×C11⋊C8—21no—
425#4313—42no—
426C8×D11—42no—
427D4×#41—111no—
428D4×M16—111no—
429C2×#421D1111yescharacteristic, complemented
430C22×#104—111no—
431#2290—111no—
432#1980—111no—
433#1963—111no—
434#1897—111no—
435#1896—111no—
436#1871—111no—
437#1871—111no—
438#1806—111no—
439#1789—111no—
440#1789—111no—
441#1759—111no—
442C23×C11—21no—
443C23×C11—21no—
444C23×C11—21no—
445C23×C11—21no—
446C23×C11—41no—
447C23×C11—41no—
448C23×C11—42no—
449C23×C11—42no—
450C23×C11—81no—
451C23×C11C2×C22⋊C411yescharacteristic
452C23×C11C2×C22⋊C411yescharacteristic
453C23×C11C22×D411yescharacteristic
454C22×D11—21no—
455C22×D11—21no—
456C22×D11—22no—
457C22×D11—21no—
458C22×D11—41no—
459C22×D11—42no—
460C22×D11—42no—
461C22×D11—81no—
462C22×D11C2×C22⋊C411yescharacteristic
463C22×D11C2×C22⋊C411yescharacteristic
464Q8×C11—21no—
465Q8×C11—21no—
466Q8×C11—21no—
467Q8×C11—42no—
468Q8×C11C4×D412yes—
469D4×C11—22no—
470D4×C11—22no—
471D4×C11—21no—
472D4×C11—21no—
473D4×C11—21no—
474D4×C11—42no—
475D4×C11—42no—
476D4×C11—42no—
477D4×C11—41no—
478D4×C11—41no—
479D4×C11C4×D412yes—
480C2×C4×C11—21no—
481C2×C4×C11—21no—
482C2×C4×C11—21no—
483C2×C4×C11—21no—
484C2×C4×C11—21no—
485C2×C4×C11—21no—
486C2×C4×C11—21no—
487C2×C4×C11—21no—
488C2×C4×C11—21no—
489C2×C4×C11—22no—
490C2×C4×C11—22no—
491C2×C4×C11—21no—
492C2×C4×C11—21no—
493C2×C4×C11—21no—
494C2×C4×C11—22no—
495C2×C4×C11—42no—
496C2×C4×C11—42no—
497C2×C4×C11—42no—
498C2×C4×C11—41no—
499C2×C4×C11—41no—
500C2×C4×C11—41no—
501C2×C4×C11—41no—
502C2×C4×C11—41no—
503C2×C4×C11—41no—
504C2×C4×C11—41no—
505C2×C4×C11C2×C22⋊C411yescharacteristic
506C2×C4×C11C2×C22⋊C411yescharacteristic
507C2×C4×C11C23×C411yescharacteristic
508C2×C4×C11C22×D411yescharacteristic
509C2×C4×C11C22×D411yescharacteristic
510C2×C4×C11C2×#4111yescharacteristic
511C2×C4×C11H(5,𝔽2)11yescharacteristic
512C2×C4×C11H(5,𝔽2)11yescharacteristic
513C22⋊D11—22no—
514C22⋊D11—22no—
515C22⋊D11—41no—
516C22⋊D11—41no—
517C22⋊D11—42no—
518C22⋊D11—42no—
519C22⋊D11—42no—
520C22⋊D11—42no—
521C22⋊D11—41no—
522C22⋊D11—41no—
523C22⋊D11—42no—
524C22⋊D11—81no—
525C22⋊D11—81no—
526C22⋊D11—81no—
527C2×Dic11—21no—
528C2×Dic11—21no—
529C2×Dic11—22no—
530C2×Dic11—21no—
531C2×Dic11—21no—
532C2×Dic11—21no—
533C2×Dic11—41no—
534C2×Dic11—41no—
535C2×Dic11—42no—
536C2×Dic11—42no—
537C2×Dic11—41no—
538C2×Dic11—41no—
539C2×Dic11—41no—
540C2×Dic11—41no—
541C2×Dic11—41no—
542C2×Dic11—81no—
543C2×Dic11C2×C22⋊C411yescharacteristic
544C2×Dic11C2×C22⋊C411yescharacteristic
545C2×Dic11C2×C22⋊C411yescharacteristic
546C2×Dic11C2×C22⋊C411yescharacteristic
547C2×Dic11C2×C22⋊C411yescharacteristic
548C2×Dic11C2×C22⋊C411yescharacteristic
549D44—21no—
550D44—21no—
551D44—42no—
552C4×D11—21no—
553C4×D11—21no—
554C4×D11—21no—
555C4×D11—21no—
556C4×D11—21no—
557C4×D11—21no—
558C4×D11—21no—
559C4×D11—21no—
560C4×D11—42no—
561C4×D11—42no—
562C4×D11—48no—
563C4×D11—41no—
564C4×D11—41no—
565Dic22—21no—
566Dic22—21no—
567Dic22—42no—
568C8×C11—22no—
569C8×C11—41no—
570C11⋊C8—41no—
571C11⋊C8—41no—
572C22×#41—111no—
573C22×#41C2×D1111yescharacteristic
574C22×M16—111no—
575C22×M16C2×D1111yescharacteristic, complemented
576#550—111no—
577D4×Q8—111no—
578#548—111no—
579#548—111no—
580#547—111no—
581#547—221no—
582#546—111no—
583#546—111no—
584#546—221no—
585#546—221no—
586D42—111no—
587D42—221no—
588#532—111no—
589#532—221no—
590#525—111no—
591#525—111no—
592#525—221no—
593#525—221no—
594C4×#41—111no—
595C2×C4×D4—111no—
596C2×C4×D4—221no—
597C2×#117C2×D1111yescharacteristic, complemented
598C22×C42—111no—
599#436—221no—
600#435—221no—
601#435—221no—
602C8×D4—221no—
603#423—111no—
604#421—24no—
605C2×#104—111no—
606C2×#104—111no—
607C2×#104—111no—
608C2×#104—111no—
609C2×#104—111no—
610C2×#104—111no—
611C2×#104—111no—
612C2×#104—111no—
613C2×#104—224no—
614C2×#104C2×D1111yescharacteristic
615C2×#104C2×D1111yescharacteristic
616C2×#104C2×D1111yescharacteristic, complemented
617C2×#104C2×D1111yescharacteristic, complemented
618#407—111no—
619#407—111no—
620C4×M16—111no—
621#388—221no—
622#387—221no—
623#386—221no—
624#385—221no—
625C4×C4⋊C4—111no—
626C4×C22⋊C4—111no—
627C4×C22⋊C4—111no—
628#376—111no—
629#339—111no—
630#339—111no—
631#339—111no—
632#339—111no—
633C22×C11—21no—
634C22×C11—21no—
635C22×C11—21no—
636C22×C11—21no—
637C22×C11—22no—
638C22×C11—21no—
639C22×C11—21no—
640C22×C11—21no—
641C22×C11—21no—
642C22×C11—41no—
643C22×C11—41no—
644C22×C11—41no—
645C22×C11—41no—
646C22×C11—41no—
647C22×C11—81no—
648C22×C11—81no—
649C22×C11—84no—
650C22×C11C22×C22⋊C411yescharacteristic
651C22×C11D4211yescharacteristic
652C22×C11#54611yescharacteristic
653C2×D11—21no—
654C2×D11—21no—
655C2×D11—21no—
656C2×D11—21no—
657C2×D11—21no—
658C2×D11—42no—
659C2×D11—42no—
660C2×D11—41no—
661C2×D11—41no—
662C2×D11—41no—
663C2×D11—84no—
664C2×D11#42112yescomplemented
665C4×C11—21no—
666C4×C11—21no—
667C4×C11—22no—
668C4×C11—42no—
669C4×C11—41no—
670C4×C11—81no—
671C4×C11C2×C4×D411yescharacteristic
672C4×C11#51811yescharacteristic
673C4×C11D4211yescharacteristic
674C4×C11#54611yescharacteristic
675Dic11—21no—
676Dic11—21no—
677Dic11—21no—
678Dic11—21no—
679Dic11—21no—
680Dic11—21no—
681Dic11—42no—
682Dic11—41no—
683Dic11—41no—
684Dic11—41no—
685Dic11—81no—
686C2×#41—21no—
687C2×#41—21no—
688C2×#41—22no—
689C2×#41—22no—
690C2×#41—41no—
691C2×#41—41no—
692C2×#41—111no—
693C2×#41—111no—
694C2×#41—111no—
695C2×#41—221no—
696C2×#41—221no—
697C2×#41—222no—
698C2×#41—222no—
699C2×#41—441no—
700C2×#41—441no—
701C2×#41C4×D1111yescharacteristic, complemented
702C2×#41C4×D1111yescharacteristic, complemented
703C2×#41C22×D1111yescharacteristic
704C2×#41C22×D1111yescharacteristic
705C22×Q8—111no—
706C22×Q8C4×D1111yescharacteristic, complemented
707C22×D4—21no—
708C22×D4—111no—
709C22×D4—111no—
710C22×D4—221no—
711C22×D4—221no—
712C22×D4C4×D1111yescharacteristic, complemented
713C23×C4—21no—
714C23×C4—111no—
715C23×C4—221no—
716C23×C4—221no—
717C23×C4C22×D1111yescharacteristic
718C2×M16—21no—
719C2×M16—22no—
720C2×M16—41no—
721C2×M16—111no—
722C2×M16—111no—
723C2×M16—221no—
724C2×M16—222no—
725C2×M16—441no—
726C2×M16C22×D1111yescharacteristic
727C2×M16C22×D1111yescharacteristic
728C22×C8—21no—
729C22×C8—221no—
730C4⋊Q8—111no—
731C4⋊Q8—221no—
732#127—111no—
733#127—221no—
734#124—111no—
735#124—111no—
736#124—221no—
737#124—221no—
738#123—221no—
739#123—221no—
740#123—221no—
741#123—221no—
742#123—221no—
743#123—221no—
744C22⋊Q8—111no—
745C22⋊Q8—111no—
746C22⋊Q8—111no—
747C22⋊Q8—111no—
748C22⋊Q8—221no—
749C22⋊Q8—221no—
750C22⋊Q8—221no—
751C22⋊Q8—221no—
752#121—111no—
753#121—111no—
754#121—111no—
755#121—111no—
756#121—221no—
757#121—221no—
758#121—221no—
759#121—221no—
760#121—221no—
761#121—221no—
762#121—221no—
763#121—221no—
764#121—221no—
765#121—221no—
766#120—221no—
767#120—221no—
768#120—221no—
769#120—221no—
770#120—221no—
771#120—221no—
772C4×Q8—111no—
773C4×Q8—111no—
774C4×D4—111no—
775C4×D4—111no—
776C4×D4—111no—
777C4×D4—111no—
778C4×D4—111no—
779C4×D4—111no—
780C4×D4—111no—
781C4×D4—111no—
782C4×D4—111no—
783C4×D4—111no—
784C4×D4—221no—
785C4×D4—221no—
786C4×D4—221no—
787C4×D4—221no—
788C4×D4—221no—
789C4×D4—221no—
790C4×D4—221no—
791C4×D4—221no—
792C4×D4—221no—
793C4×D4—221no—
794C4×D4—221no—
795C4×D4—221no—
796#117—22no—
797#117—41no—
798#117—111no—
799#117—221no—
800C2×C4⋊C4—21no—
801C2×C4⋊C4—111no—
802C2×C4⋊C4—221no—
803C2×C4⋊C4—221no—
804C2×C22⋊C4—21no—
805C2×C22⋊C4—111no—
806C2×C22⋊C4—111no—
807C2×C22⋊C4—221no—
808C2×C22⋊C4—221no—
809C2×C22⋊C4—221no—
810C2×C22⋊C4—221no—
811C2×C42—111no—
812C2×C42—111no—
813C2×C42—111no—
814C2×C42—221no—
815C2×C42—222no—
816C2×C42—221no—
817C2×C42—441no—
818C2×C42C22×D1111yescharacteristic
819C2×C42C22×D1111yescharacteristic
820C4⋊C8—221no—
821C4⋊C8—221no—
822#104—22no—
823#104—22no—
824#104—22no—
825#104—222no—
826#104—222no—
827#104—222no—
828#104—222no—
829#104—441no—
830#104—441no—
831#104—441no—
832#104—441no—
833#104C22⋊D1114yescomplemented
834C22⋊C8—221no—
835C22⋊C8—221no—
836C22⋊C8—221no—
837C22⋊C8—221no—
838#97—221no—
839C4×C8—221no—
840#95—221no—
841#95—221no—
842#95—221no—
843#95—221no—
844#95—221no—
845C2×C11—21no—
846C2×C11—21no—
847C2×C11—42no—
848C2×C11—41no—
849C2×C11—41no—
850C2×C11—81no—
851C2×C11D4×C22⋊C411yescharacteristic
852C2×C11C2×#42111yescharacteristic
853C2×C11#290111yescharacteristic
854D11—22no—
855D11—41no—
856D11—81no—
857C24—21no—
858C24—111no—
859C24—221no—
860C24D4×D1111yescharacteristic
861#41—21no—
862#41—21no—
863#41—22no—
864#41—22no—
865#41—21no—
866#41—21no—
867#41—21no—
868#41—21no—
869#41—42no—
870#41—42no—
871#41—41no—
872#41—41no—
873#41—42no—
874#41—42no—
875#41—222no—
876#41—222no—
877#41—221no—
878#41—221no—
879#41—221no—
880#41—221no—
881#41—442no—
882#41—442no—
883#41—441no—
884#41—442no—
885#41—442no—
886#41—441no—
887#41#433912yes—
888#41C2×C22⋊D1112yes—
889C2×Q8—21no—
890C2×Q8—22no—
891C2×Q8—41no—
892C2×Q8—111no—
893C2×Q8—221no—
894C2×Q8—222no—
895C2×Q8—441no—
896C2×Q8C2×C4×D1111yescharacteristic
897C2×Q8C2×C4×D1111yescharacteristic
898C2×D4—21no—
899C2×D4—22no—
900C2×D4—21no—
901C2×D4—21no—
902C2×D4—21no—
903C2×D4—21no—
904C2×D4—41no—
905C2×D4—42no—
906C2×D4—42no—
907C2×D4—111no—
908C2×D4—111no—
909C2×D4—111no—
910C2×D4—111no—
911C2×D4—111no—
912C2×D4—221no—
913C2×D4—221no—
914C2×D4—221no—
915C2×D4—221no—
916C2×D4—222no—
917C2×D4—221no—
918C2×D4—221no—
919C2×D4—221no—
920C2×D4—221no—
921C2×D4—221no—
922C2×D4—221no—
923C2×D4—441no—
924C2×D4—442no—
925C2×D4—442no—
926C2×D4—442no—
927C2×D4—444no—
928C2×D4C2×C4×D1111yescharacteristic
929C2×D4C2×C4×D1111yescharacteristic
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—42no—
942C22×C4—42no—
943C22×C4—111no—
944C22×C4—111no—
945C22×C4—111no—
946C22×C4—111no—
947C22×C4—111no—
948C22×C4—111no—
949C22×C4—111no—
950C22×C4—221no—
951C22×C4—221no—
952C22×C4—221no—
953C22×C4—221no—
954C22×C4—221no—
955C22×C4—221no—
956C22×C4—221no—
957C22×C4—221no—
958C22×C4—221no—
959C22×C4—221no—
960C22×C4—221no—
961C22×C4—221no—
962C22×C4—442no—
963C22×C4—442no—
964C22×C4—442no—
965C22×C4—442no—
966C22×C4—442no—
967C22×C4C2×C4×D1111yescharacteristic
968C22×C4C2×C4×D1111yescharacteristic
969C22×C4D4×D1111yescharacteristic
970C22×C4D4×D1111yescharacteristic
971C22×C4D4×D1111yescharacteristic
972C22×C4C23×D1111yescharacteristic
973M16—21no—
974M16—21no—
975M16—21no—
976M16—42no—
977M16—221no—
978M16—221no—
979M16—221no—
980M16—221no—
981M16—442no—
982M16C2×C22⋊D1112yescomplemented
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—42no—
986C2×C8—221no—
987C2×C8—221no—
988C2×C8—442no—
989C4⋊C4—42no—
990C4⋊C4—111no—
991C4⋊C4—111no—
992C4⋊C4—111no—
993C4⋊C4—111no—
994C4⋊C4—111no—
995C4⋊C4—111no—
996C4⋊C4—221no—
997C4⋊C4—221no—
998C4⋊C4—221no—
999C4⋊C4—221no—
1000C4⋊C4—221no—
1001C4⋊C4—221no—
1002C4⋊C4—221no—
1003C4⋊C4—221no—
1004C4⋊C4—442no—
1005C22⋊C4—42no—
1006C22⋊C4—111no—
1007C22⋊C4—111no—
1008C22⋊C4—111no—
1009C22⋊C4—111no—
1010C22⋊C4—111no—
1011C22⋊C4—111no—
1012C22⋊C4—111no—
1013C22⋊C4—111no—
1014C22⋊C4—221no—
1015C22⋊C4—221no—
1016C22⋊C4—221no—
1017C22⋊C4—221no—
1018C22⋊C4—221no—
1019C22⋊C4—221no—
1020C22⋊C4—221no—
1021C22⋊C4—221no—
1022C22⋊C4—221no—
1023C22⋊C4—221no—
1024C22⋊C4—221no—
1025C22⋊C4—221no—
1026C22⋊C4—221no—
1027C22⋊C4—221no—
1028C22⋊C4—221no—
1029C22⋊C4—442no—
1030C22⋊C4—442no—
1031C42—21no—
1032C42—21no—
1033C42—21no—
1034C42—111no—
1035C42—111no—
1036C42—111no—
1037C42—111no—
1038C42—221no—
1039C42—221no—
1040C42—221no—
1041C42—221no—
1042C42—221no—
1043C42—221no—
1044C42—221no—
1045C42—442no—
1046C42C2×C22⋊D1112yescomplemented
1047C11#2243411yescharacteristic, complemented, Sylow
1048C23—21no—
1049C23—21no—
1050C23—21no—
1051C23—21no—
1052C23—41no—
1053C23—41no—
1054C23—42no—
1055C23—42no—
1056C23—81no—
1057C23—111no—
1058C23—111no—
1059C23—222no—
1060C23—221no—
1061C23—221no—
1062C23—221no—
1063C23—441no—
1064C23—442no—
1065C23—442no—
1066C23—881no—
1067C23C22⋊C4×D1111yescharacteristic
1068C23C22⋊C4×D1111yescharacteristic
1069C23C2×D4×D1111yescharacteristic
1070Q8—21no—
1071Q8—21no—
1072Q8—21no—
1073Q8—42no—
1074Q8—221no—
1075Q8—221no—
1076Q8—442no—
1077Q8C4×C22⋊D1112yes—
1078D4—22no—
1079D4—22no—
1080D4—21no—
1081D4—21no—
1082D4—21no—
1083D4—42no—
1084D4—42no—
1085D4—42no—
1086D4—41no—
1087D4—41no—
1088D4—222no—
1089D4—222no—
1090D4—221no—
1091D4—221no—
1092D4—442no—
1093D4—441no—
1094D4—441no—
1095D4—442no—
1096D4—442no—
1097D4—442no—
1098D4—442no—
1099D4—442no—
1100D4—441no—
1101D4—441no—
1102D4—881no—
1103D4—881no—
1104D4—881no—
1105D4C4×C22⋊D1112yes—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—22no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—22no—
1119C2×C4—21no—
1120C2×C4—22no—
1121C2×C4—42no—
1122C2×C4—42no—
1123C2×C4—42no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—111no—
1132C2×C4—111no—
1133C2×C4—111no—
1134C2×C4—111no—
1135C2×C4—111no—
1136C2×C4—111no—
1137C2×C4—221no—
1138C2×C4—221no—
1139C2×C4—221no—
1140C2×C4—221no—
1141C2×C4—221no—
1142C2×C4—221no—
1143C2×C4—221no—
1144C2×C4—221no—
1145C2×C4—221no—
1146C2×C4—221no—
1147C2×C4—222no—
1148C2×C4—221no—
1149C2×C4—221no—
1150C2×C4—221no—
1151C2×C4—442no—
1152C2×C4—442no—
1153C2×C4—448no—
1154C2×C4—441no—
1155C2×C4—441no—
1156C2×C4—442no—
1157C2×C4—442no—
1158C2×C4—441no—
1159C2×C4—441no—
1160C2×C4—441no—
1161C2×C4—441no—
1162C2×C4—441no—
1163C2×C4—441no—
1164C2×C4—441no—
1165C2×C4—881no—
1166C2×C4C22⋊C4×D1111yescharacteristic
1167C2×C4C22⋊C4×D1111yescharacteristic
1168C2×C4C22×C4×D1111yescharacteristic
1169C2×C4C2×#433911yescharacteristic
1170C2×C4C2×D4×D1111yescharacteristic
1171C2×C4#6703711yescharacteristic
1172C2×C4#6703711yescharacteristic
1173C2×C4C22×C22⋊D1111yescharacteristic
1174C8—22no—
1175C8—41no—
1176C8—441no—
1177C8—441no—
1178C22—21no—
1179C22—21no—
1180C22—21no—
1181C22—21no—
1182C22—22no—
1183C22—21no—
1184C22—21no—
1185C22—21no—
1186C22—21no—
1187C22—41no—
1188C22—41no—
1189C22—41no—
1190C22—41no—
1191C22—41no—
1192C22—81no—
1193C22—81no—
1194C22—84no—
1195C22—112no—
1196C22—221no—
1197C22—221no—
1198C22—221no—
1199C22—221no—
1200C22—221no—
1201C22—442no—
1202C22—442no—
1203C22—441no—
1204C22—441no—
1205C22—441no—
1206C22—884no—
1207C22C2×C22⋊C4×D1111yescharacteristic
1208C22#1062302111yescharacteristic
1209C22D4×C22⋊D1111yescharacteristic
1210C4—21no—
1211C4—21no—
1212C4—22no—
1213C4—42no—
1214C4—41no—
1215C4—81no—
1216C4—221no—
1217C4—221no—
1218C4—221no—
1219C4—221no—
1220C4—221no—
1221C4—221no—
1222C4—442no—
1223C4—441no—
1224C4—441no—
1225C4—441no—
1226C4—881no—
1227C4#1062301711yescharacteristic
1228C4#1062302111yescharacteristic
1229C4C2×C4×C22⋊D1111yescharacteristic
1230C4D4×C22⋊D1111yescharacteristic
1231C2—21no—
1232C2—21no—
1233C2—41no—
1234C2—41no—
1235C2—42no—
1236C2—81no—
1237C2—222no—
1238C2—441no—
1239C2—881no—
1240C2C22⋊C4×C22⋊D1111yescharacteristic
1241C2D11×#42111yescharacteristic
1242C2#1307716211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#421C2
socleC22×C11C22×C22⋊C4
prime radical#41×C22⋊D11C2
cosocleC22×C4×C11C24
hypercenterC2×#421D11
hypocenterC11#22434
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
2. M16×C22⋊D11C2semidirect
3. C2×D11×#104C2semidirect
4. #13071053C2semidirect
5. #13069533C2semidirect
6. #13069446C2semidirect
7. #13069064C2semidirect
8. #13069056C2semidirect
9. #13068918C2semidirect
10. #13068915C2semidirect
11. #13068634C2semidirect
12. #13068560C2semidirect
13. #13068558C2semidirect
14. #13068428C2semidirect
15. C2×C11×#421C2semidirect
18. C22×C11×M16C22semidirect
19. C2×C11×#117C22semidirect
20. #10623365C4semidirect
23. #10623362C4semidirect
25. #10623360C4semidirect
30. #10623355C4semidirect
31. #10623348C4semidirect
32. Q8×C22⋊D11C4semidirect
34. #10623337C4semidirect
36. D4×C22⋊D11C4semidirect
41. C2×M16×D11C22semidirect
42. C2×C42×D11C22semidirect
46. C2×C11×#104C22semidirect
47. C2×C11×#104C22semidirect
50. C2×#66901C22semidirect
51. C2×#66901C22semidirect
52. C4×C22⋊Dic11C22semidirect
53. #10622820C22semidirect
54. C2×#66889C22semidirect
55. C2×#66889C22semidirect
58. #10622739C22semidirect
59. #10622731C22semidirect
60. M16×Dic11C22semidirect
67. C4×(C2×D11)⋊C4C22semidirect
68. #10622545C22semidirect
69. C4×Dic11⋊C4C22semidirect
70. C2×#66869C22semidirect
71. C2×#66869C22semidirect
73. #10622193C22semidirect
74. #10622193C22semidirect
75. #10622161C22semidirect
76. #10622161C22semidirect
83. C2×C11×#41C2×C4semidirect
84. C2×C11×#41C2×C4semidirect
87. C22×Q8×C11C2×C4semidirect
89. C22×D4×C11C2×C4semidirect
128. #67000C2×C4semidirect
133. Q8×Dic11C2×C4semidirect
134. Q8×Dic11C2×C4semidirect
136. #66997C2×C4semidirect
138. #66993C2×C4semidirect
153. #66989C2×C4semidirect
159. D4×Dic11C2×C4semidirect
160. D4×Dic11C2×C4semidirect
163. #66983C2×C4semidirect
164. #66983C2×C4semidirect
193. #66977C2×C4semidirect
194. #66977C2×C4semidirect
214. C11×#104D4semidirect
357. C11×M16C2×D4semidirect
366. C42×C11C2×D4semidirect
429. C2×#421D11semidirect
575. C22×M16C2×D11semidirect
597. C2×#117C2×D11semidirect
616. C2×#104C2×D11semidirect
617. C2×#104C2×D11semidirect
664. C2×D11#421semidirect
701. C2×#41C4×D11semidirect
702. C2×#41C4×D11semidirect
706. C22×Q8C4×D11semidirect
712. C22×D4C4×D11semidirect
833. #104C22⋊D11semidirect
982. M16C2×C22⋊D11semidirect
1046. C42C2×C22⋊D11semidirect
1047. C11#22434semidirect

Maximal subgroups

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

subgroupindex
#41×C22⋊D112
M16×C22⋊D112
C2×D11×#1042
#130710532
#130695332
#130694462
#130690642
#130690562
#130689182
#130689152
#130686342
#130685602
#130685582
#130684282
C2×C11×#4212
#2243411