Finite Group Databasebeta

← #14769451

Subgroups — #14769451

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
2#13077348C211yesmaximal, characteristic, complemented
3C2×#10622849C211yesmaximal, characteristic, complemented
4C2×D11×#104C211yesmaximal, characteristic, complemented
5#13071062C211yesmaximal, characteristic, complemented
6#13069533C211yesmaximal, characteristic, complemented
7#13069446C211yesmaximal, characteristic, complemented
8#13069062C211yesmaximal, characteristic, complemented
9#13069056C211yesmaximal, characteristic, complemented
10#13068916C211yesmaximal, characteristic, complemented
11#13068915C211yesmaximal, characteristic, complemented
12#13068634C211yesmaximal, characteristic, complemented
13#13068558C211yesmaximal, characteristic, complemented
14#13068428C211yesmaximal, characteristic, complemented
15C11×#1789C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C2×#41×D11C2211yescharacteristic
18#10623365C411yescharacteristic, complemented
19#10623363—21no—
20#10623363C2211yescharacteristic
21#10623362C411yescharacteristic, complemented
22#10623360—21no—
23#10623360C411yescharacteristic, complemented
24#10623359—21no—
25#10623359C2211yescharacteristic
26#41×Dic11C2211yescharacteristic
27#10623355—21no—
28#10623355C411yescharacteristic, complemented
29#10623348C411yescharacteristic, complemented
30Q8×C22⋊D11C411yescharacteristic, complemented
31#10623337—21no—
32#10623337C411yescharacteristic, complemented
33D4×C22⋊D11—21no—
34D4×C22⋊D11C411yescharacteristic, complemented
35#10623322—21no—
36#10623322C2211yescharacteristic
37C2×C4×C22⋊D11—21no—
38C2×C4×C22⋊D11C2211yescharacteristic
39C2×#66979C2211yescharacteristic, complemented
40C22×#4318C2211yescharacteristic, complemented
41C2×M16×D11C2211yescharacteristic, complemented
42C2×C42×D11C2211yescharacteristic, complemented
43C2×C11×#104C2211yescharacteristic
44C2×C11×#104C2211yescharacteristic
45C2×C11×#104C2211yescharacteristic, complemented
46C2×C11×#104C2211yescharacteristic, complemented
47C11×#407C2211yescharacteristic, complemented
48C4×C11×C22⋊C4C2211yescharacteristic, complemented
49#10622849—24no—
50C2×#66901C2211yescharacteristic
51C2×#66901C2211yescharacteristic
52C2×#66901C2211yescharacteristic, complemented
53C2×#66901C2211yescharacteristic, complemented
54C2×#66889C2211yescharacteristic, complemented
55C2×#66889C2211yescharacteristic, complemented
56#10622739C2211yescharacteristic, complemented
57#10622731C2211yescharacteristic, complemented
58M16×Dic11C2211yescharacteristic, complemented
59#10622569—21no—
60#10622558—21no—
61C4×(C2×D11)⋊C4C2211yescharacteristic, complemented
62#10622545C2211yescharacteristic, complemented
63C4×Dic11⋊C4C2211yescharacteristic, complemented
64C2×#66869C2211yescharacteristic, complemented
65C2×#66869C2211yescharacteristic, complemented
66D11×#104—24no—
67#10622343—21no—
68#10622342—21no—
69#10622341—21no—
70(C22⋊D11)⋊C8—21no—
71#10622281—21no—
72#10622268—21no—
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×M16C2311yescharacteristic
110C2×C11×M16C2311yescharacteristic
111C2×C11×C22⋊C4—21no—
112C2×C42×C11C2311yescharacteristic
113C2×C42×C11C2311yescharacteristic
114#67006—21no—
115#67006—21no—
116#67006—21no—
117C2×C22⋊Dic11—21no—
118C2×C22⋊Dic11—21no—
119C2×C22⋊Dic11D411yescharacteristic
120#67000—21no—
121#67000C2×C411yescharacteristic, complemented
122#66999—21no—
123#66999—21no—
124#66999C2×C411yescharacteristic
125#66999C2×C411yescharacteristic
126Q8×Dic11C2×C411yescharacteristic, complemented
127Q8×Dic11C2×C411yescharacteristic, complemented
128#66997—21no—
129#66997C2×C411yescharacteristic, complemented
130#66993—21no—
131#66993C2×C411yescharacteristic, complemented
132#66992—21no—
133#66992—21no—
134#66992—21no—
135#66992—21no—
136#66992—21no—
137#66992—21no—
138#66991—21no—
139#66991—21no—
140#66991C2×C411yescharacteristic
141#66991C2×C411yescharacteristic
142#66990—21no—
143#66990—21no—
144#66990—21no—
145#66989—21no—
146#66989C2×C411yescharacteristic, complemented
147#66988—21no—
148#66988—21no—
149#66988—21no—
150D4×Dic11—21no—
151D4×Dic11—21no—
152D4×Dic11C2×C411yescharacteristic, complemented
153D4×Dic11C2×C411yescharacteristic, complemented
154#66983—21no—
155#66983—21no—
156#66983C2×C411yescharacteristic, complemented
157#66983C2×C411yescharacteristic, complemented
158#66982—21no—
159#66982—21no—
160#66982—21no—
161C4×C22⋊D11—21no—
162C4×C22⋊D11—21no—
163C4×C22⋊D11—21no—
164C4×C22⋊D11—21no—
165C4×C22⋊D11—21no—
166C4×C22⋊D11—21no—
167C4×C22⋊D11—21no—
168C4×C22⋊D11—21no—
169C4×C22⋊D11—21no—
170C4×C22⋊D11—21no—
171C4×C22⋊D11C2×C411yescharacteristic
172C4×C22⋊D11C2×C411yescharacteristic
173C4×C22⋊D11C2×C411yescharacteristic
174C4×C22⋊D11C2×C411yescharacteristic
175C4×C22⋊D11D411yescharacteristic
176C4×C22⋊D11D411yescharacteristic
177C4×C22⋊D11D411yescharacteristic
178C4×C22⋊D11D411yescharacteristic
179C2×(C2×D11)⋊C4—21no—
180C2×(C2×D11)⋊C4—21no—
181C2×(C2×D11)⋊C4D411yescharacteristic
182#66979—21no—
183#66979—22no—
184#66979—41no—
185#66979C2311yescharacteristic
186C2×C4⋊Dic11—21no—
187#66977—21no—
188#66977—21no—
189#66977C2×C411yescharacteristic, complemented
190#66977C2×C411yescharacteristic, complemented
191C2×Dic11⋊C4—21no—
192C2×Dic11⋊C4—21no—
193C2×Dic11⋊C4D411yescharacteristic
194C2×C4×Dic11—21no—
195C2×C4×Dic11—21no—
196C2×C4×Dic11C2311yescharacteristic
197C2×C4×Dic11C2311yescharacteristic
198C2×C4×Dic11C2311yescharacteristic
199C2×#4318—21no—
200C2×#4318—22no—
201C2×#4318—41no—
202C2×#4318C2311yescharacteristic
203C2×#4318C2311yescharacteristic
204C22×C11⋊C8—21no—
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—41no—
214C11×#104—41no—
215C11×C22⋊C8—21no—
216C11×C22⋊C8—21no—
217C11×#95—21no—
218#66901—22no—
219#66901—22no—
220#66901—22no—
221#66901D414yescomplemented
222C11⋊#95—21no—
223C11⋊#95—21no—
224C11⋊#95—21no—
225C11⋊#95—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—21no—
357C2×C8×C11—21no—
358C2×C8×C11—21no—
359C11×C22⋊C4—42no—
360C42×C11—21no—
361C42×C11—21no—
362C42×C11—21no—
363C42×C11—21no—
364C22⋊Dic11—21no—
365C22⋊Dic11—21no—
366C22⋊Dic11—21no—
367C22⋊Dic11—21no—
368C22⋊Dic11—21no—
369C22⋊Dic11—21no—
370C22⋊Dic11—21no—
371C22⋊Dic11—21no—
372C22⋊Dic11—21no—
373C22⋊Dic11—42no—
374C22⋊Dic11C22⋊C411yescharacteristic
375C22⋊Dic11C22⋊C411yescharacteristic
376C22⋊Dic11C22⋊C411yescharacteristic
377C22⋊Dic11C22⋊C411yescharacteristic
378(C2×D11)⋊C4—21no—
379(C2×D11)⋊C4—21no—
380(C2×D11)⋊C4—21no—
381(C2×D11)⋊C4—21no—
382(C2×D11)⋊C4—21no—
383(C2×D11)⋊C4—21no—
384(C2×D11)⋊C4—42no—
385(C2×D11)⋊C4C22⋊C411yescharacteristic
386(C2×D11)⋊C4C22⋊C411yescharacteristic
387(C2×D11)⋊C4C22⋊C411yescharacteristic
388(C2×D11)⋊C4C22⋊C411yescharacteristic
389C4⋊Dic11—21no—
390C4⋊Dic11—21no—
391C4⋊Dic11—42no—
392C4⋊Dic11C22×C411yescharacteristic
393C4⋊Dic11C22×C411yescharacteristic
394Dic11⋊C4—21no—
395Dic11⋊C4—21no—
396Dic11⋊C4—21no—
397Dic11⋊C4—21no—
398Dic11⋊C4—21no—
399Dic11⋊C4—21no—
400Dic11⋊C4—42no—
401Dic11⋊C4C22⋊C411yescharacteristic
402Dic11⋊C4C22⋊C411yescharacteristic
403Dic11⋊C4C22⋊C411yescharacteristic
404Dic11⋊C4C22⋊C411yescharacteristic
405C4×Dic11—21no—
406C4×Dic11—21no—
407C4×Dic11—21no—
408C4×Dic11—21no—
409C4×Dic11—21no—
410C4×Dic11—21no—
411C4×Dic11—42no—
412C4×Dic11C22×C411yescharacteristic
413C4×Dic11C22×C411yescharacteristic
414C4×Dic11C2×D411yescharacteristic
415C4×Dic11C2×D411yescharacteristic
416C4×Dic11C2×D412yescomplemented
417#4318—21no—
418#4318—21no—
419#4318—21no—
420#4318—42no—
421#4318C2×D412yescomplemented
422C2×C11⋊C8—21no—
423C2×C11⋊C8—21no—
424C2×C11⋊C8—42no—
425#4313—42no—
426C8×D11—42no—
427D4×#41—111no—
428D4×M16—111no—
429C2×#421—111no—
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#1789D1111yescharacteristic, complemented
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—22no—
494C2×C4×C11—21no—
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—21no—
530C2×Dic11—21no—
531C2×Dic11—21no—
532C2×Dic11—22no—
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—41no—
569C8×C11—41no—
570C11⋊C8—22no—
571C11⋊C8—41no—
572C22×#41—111no—
573C22×#41C2×D1111yescharacteristic
574C22×M16—111no—
575C22×M16—111no—
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×#117—111no—
598C22×C42—111no—
599#436—221no—
600#435—221no—
601#435—221no—
602C8×D4—221no—
603#423—111no—
604#421—224no—
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#407C2×D1111yescharacteristic, complemented
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⋊C4C2×D1111yescharacteristic, complemented
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—111no—
719C2×M16—111no—
720C2×M16—221no—
721C2×M16—221no—
722C2×M16—222no—
723C2×M16—222no—
724C2×M16—441no—
725C2×M16—441no—
726C2×M16C22×D1111yescharacteristic
727C2×M16C22×D1111yescharacteristic
728C22×C8—221no—
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—111no—
797#117—221no—
798#117—222no—
799#117—441no—
800C2×C4⋊C4—111no—
801C2×C4⋊C4—221no—
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—222no—
815C2×C42—221no—
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—41no—
825#104—41no—
826#104—114no—
827#104—222no—
828#104—222no—
829#104—222no—
830#104—222no—
831#104—222no—
832#104—441no—
833#104—441no—
834C22⋊C8—21no—
835C22⋊C8—21no—
836C22⋊C8—221no—
837C22⋊C8—221no—
838#97—221no—
839C4×C8—221no—
840#95—21no—
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#41D4×D1112yes—
888#41#434112yes—
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—21no—
977M16—112no—
978M16—221no—
979M16—221no—
980M16—221no—
981M16—442no—
982M16—442no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—221no—
986C2×C8—221no—
987C2×C8—442no—
988C2×C8—442no—
989C4⋊C4—111no—
990C4⋊C4—111no—
991C4⋊C4—111no—
992C4⋊C4—111no—
993C4⋊C4—111no—
994C4⋊C4—111no—
995C4⋊C4—221no—
996C4⋊C4—221no—
997C4⋊C4—221no—
998C4⋊C4—221no—
999C4⋊C4—221no—
1000C4⋊C4—221no—
1001C4⋊C4—221no—
1002C4⋊C4—221no—
1003C4⋊C4—442no—
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—21no—
1035C42—111no—
1036C42—111no—
1037C42—111no—
1038C42—111no—
1039C42—112no—
1040C42—221no—
1041C42—221no—
1042C42—221no—
1043C42—221no—
1044C42—221no—
1045C42—221no—
1046C42—442no—
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—
1077Q8(C22⋊D11)⋊C412yes—
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—
1105D4(C22⋊D11)⋊C412yes—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—22no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—21no—
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—221no—
1148C2×C4—221no—
1149C2×C4—221no—
1150C2×C4—222no—
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×D4×D1111yescharacteristic
1170C2×C4C2×D4×D1111yescharacteristic
1171C2×C4C2×#434111yescharacteristic
1172C2×C4#6703711yescharacteristic
1173C2×C4#6703711yescharacteristic
1174C8—41no—
1175C8—41no—
1176C8—222no—
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#1062312111yescharacteristic
1209C22#1062312211yescharacteristic
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—
1227C4C2×(C22⋊D11)⋊C411yescharacteristic
1228C4#1062301711yescharacteristic
1229C4#1062312111yescharacteristic
1230C4#1062312211yescharacteristic
1231C2—21no—
1232C2—21no—
1233C2—41no—
1234C2—41no—
1235C2—42no—
1236C2—81no—
1237C2—222no—
1238C2—441no—
1239C2—881no—
1240C2#1307143211yescharacteristic
1241C2D11×#42111yescharacteristic
1242C2#1307716011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1789C2
socleC22×C11C22×C22⋊C4
prime radical#41×C22⋊D11C2
cosocleC22×C4×C11C24
hypercenter#1789D11
hypocenterC11#22434
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1789

Complements

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

NH ≅ G/Ntype
2. #13077348C2semidirect
3. C2×#10622849C2semidirect
4. C2×D11×#104C2semidirect
5. #13071062C2semidirect
6. #13069533C2semidirect
7. #13069446C2semidirect
8. #13069062C2semidirect
9. #13069056C2semidirect
10. #13068916C2semidirect
11. #13068915C2semidirect
12. #13068634C2semidirect
13. #13068558C2semidirect
14. #13068428C2semidirect
15. C11×#1789C2semidirect
18. #10623365C4semidirect
21. #10623362C4semidirect
23. #10623360C4semidirect
28. #10623355C4semidirect
29. #10623348C4semidirect
30. Q8×C22⋊D11C4semidirect
32. #10623337C4semidirect
34. D4×C22⋊D11C4semidirect
39. C2×#66979C22semidirect
40. C22×#4318C22semidirect
41. C2×M16×D11C22semidirect
42. C2×C42×D11C22semidirect
45. C2×C11×#104C22semidirect
46. C2×C11×#104C22semidirect
47. C11×#407C22semidirect
48. C4×C11×C22⋊C4C22semidirect
52. C2×#66901C22semidirect
53. C2×#66901C22semidirect
54. C2×#66889C22semidirect
55. C2×#66889C22semidirect
56. #10622739C22semidirect
57. #10622731C22semidirect
58. M16×Dic11C22semidirect
61. C4×(C2×D11)⋊C4C22semidirect
62. #10622545C22semidirect
63. C4×Dic11⋊C4C22semidirect
64. C2×#66869C22semidirect
65. 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
121. #67000C2×C4semidirect
126. Q8×Dic11C2×C4semidirect
127. Q8×Dic11C2×C4semidirect
129. #66997C2×C4semidirect
131. #66993C2×C4semidirect
146. #66989C2×C4semidirect
152. D4×Dic11C2×C4semidirect
153. D4×Dic11C2×C4semidirect
156. #66983C2×C4semidirect
157. #66983C2×C4semidirect
189. #66977C2×C4semidirect
190. #66977C2×C4semidirect
221. #66901D4semidirect
416. C4×Dic11C2×D4semidirect
421. #4318C2×D4semidirect
440. #1789D11semidirect
616. C2×#104C2×D11semidirect
617. C2×#104C2×D11semidirect
619. #407C2×D11semidirect
627. C4×C22⋊C4C2×D11semidirect
664. C2×D11#421semidirect
701. C2×#41C4×D11semidirect
702. C2×#41C4×D11semidirect
706. C22×Q8C4×D11semidirect
712. C22×D4C4×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
#130773482
C2×#106228492
C2×D11×#1042
#130710622
#130695332
#130694462
#130690622
#130690562
#130689162
#130689152
#130686342
#130685582
#130684282
C11×#17892
#2243411