Finite Group Databasebeta

← #14769440

Subgroups — #14769440

Order 2816.

1608 conjugacy classes of subgroups.

The subgroup lattice has 1256 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
3C22×#66901C211yesmaximal, characteristic, complemented
4C2×D11×#104C211yesmaximal, characteristic, complemented
5C4×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
6#13069533C211yesmaximal, characteristic, complemented
7#13069442C211yesmaximal, characteristic, complemented
8#13069057C211yesmaximal, characteristic, complemented
9#13069056C211yesmaximal, characteristic, complemented
10#13068916C211yesmaximal, characteristic, complemented
11#13068915C211yesmaximal, characteristic, complemented
12#13068634C211yesmaximal, characteristic, complemented
13#13068558C211yesmaximal, characteristic, complemented
14#104×Dic11C211yesmaximal, 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
39C22×C4×Dic11C2211yescharacteristic, complemented
40C22×#4318C2211yescharacteristic, complemented
41C2×M16×D11C2211yescharacteristic, complemented
42C2×(C22⋊D11)⋊C4—21no—
43C2×C42×D11C2211yescharacteristic, complemented
44C2×C11×#104C2211yescharacteristic
45C2×C11×#104C2211yescharacteristic
46C2×C11×#104C2211yescharacteristic, complemented
47C2×C11×#104C2211yescharacteristic, complemented
48C11×#407C2211yescharacteristic, complemented
49C4×C11×C22⋊C4C2211yescharacteristic, complemented
50C2×#66901—24no—
51C2×#66901C2211yescharacteristic
52C2×#66901C2211yescharacteristic
53C2×#66901C2211yescharacteristic, complemented
54C2×#66901C2211yescharacteristic, complemented
55C2×#66889C2211yescharacteristic, complemented
56C2×#66889C2211yescharacteristic, complemented
57#10622739C2211yescharacteristic, complemented
58#10622731C2211yescharacteristic, complemented
59M16×Dic11C2211yescharacteristic, complemented
60C22⋊C4×Dic11—21no—
61C4×(C2×D11)⋊C4C2211yescharacteristic, complemented
62C4×Dic11⋊C4C2211yescharacteristic, complemented
63C42×Dic11C2211yescharacteristic, 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#10622279—21no—
72#10622262—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
94C23×Dic11—21no—
95#41×D11—22no—
96#41×D11—22no—
97#41×D11—41no—
98#41×D11—41no—
99C2×#4343C2×C411yescharacteristic, complemented
100C2×Q8×D11C2×C411yescharacteristic, complemented
101C2×#4341—21no—
102C2×#4341C2×C411yescharacteristic, complemented
103C2×D4×D11—21no—
104C2×D4×D11C2×C411yescharacteristic, complemented
105C2×#4339—21no—
106C2×#4339C2311yescharacteristic
107C22×C4×D11—21no—
108C22×C4×D11—21no—
109C22×C4×D11C2311yescharacteristic
110C2×C11×M16C2311yescharacteristic
111C2×C11×M16C2311yescharacteristic
112C2×C11×C22⋊C4—21no—
113C2×C42×C11C2311yescharacteristic
114C2×C42×C11C2311yescharacteristic
115#67006—21no—
116#67006—21no—
117#67006—21no—
118C2×C22⋊Dic11—21no—
119C2×C22⋊Dic11D411yescharacteristic
120#67000—21no—
121#67000C2×C411yescharacteristic, complemented
122#66999—21no—
123#66999—21no—
124#66999C2×C411yescharacteristic, complemented
125#66999C2×C411yescharacteristic, complemented
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, complemented
141#66991C2×C411yescharacteristic, complemented
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#66979C2311yescharacteristic
184#66977—21no—
185#66977—21no—
186#66977C2×C411yescharacteristic, complemented
187#66977C2×C411yescharacteristic, complemented
188C2×Dic11⋊C4—21no—
189C2×Dic11⋊C4—21no—
190C2×Dic11⋊C4D411yescharacteristic
191C2×C4×Dic11—21no—
192C2×C4×Dic11—21no—
193C2×C4×Dic11—22no—
194C2×C4×Dic11—21no—
195C2×C4×Dic11—21no—
196C2×C4×Dic11—21no—
197C2×C4×Dic11—41no—
198C2×C4×Dic11C2311yescharacteristic
199C2×C4×Dic11C2311yescharacteristic
200C2×C4×Dic11C2311yescharacteristic
201C2×#4318—21no—
202C2×#4318—22no—
203C2×#4318—41no—
204C2×#4318C2311yescharacteristic
205C2×#4318C2311yescharacteristic
206C22×C11⋊C8—21no—
207M16×D11—22no—
208M16×D11—41no—
209C2×#4313—21no—
210C2×C8×D11—21no—
211(C22⋊D11)⋊C4—28no—
212C42×D11—22no—
213C42×D11—41no—
214C11×#104—22no—
215C11×#104—22no—
216C11×#104—41no—
217C11×#104—41no—
218C11×C22⋊C8—21no—
219C11×C22⋊C8—21no—
220C11×#95—21no—
221#66901—22no—
222#66901—22no—
223#66901—22no—
224#66901D414yescomplemented
225C11⋊#95—21no—
226C11⋊#95—21no—
227#66889—22no—
228#66889—41no—
229(C2×D11)⋊C8—21no—
230(C2×D11)⋊C8—21no—
231#66879—21no—
232Dic11⋊C8—21no—
233Dic11⋊C8—21no—
234C8×Dic11—21no—
235#66869—22no—
236#66869—41no—
237D4×#104—111nomaximal, Sylow
238C24×C11—21no—
239C24×C11C2×D411yescharacteristic
240C23×D11—21no—
241C23×D11C2×D411yescharacteristic
242C11×#41—21no—
243C11×#41—21no—
244C11×#41—22no—
245C11×#41—22no—
246C11×#41—21no—
247C11×#41—21no—
248C11×#41—21no—
249C11×#41—21no—
250C11×#41—42no—
251C11×#41—42no—
252C11×#41—41no—
253C11×#41—41no—
254C11×#41—42no—
255C11×#41—42no—
256C11×#41C2×D412yes—
257C11×#41#4112yes—
258C2×Q8×C11—21no—
259C2×Q8×C11—22no—
260C2×Q8×C11—41no—
261C2×Q8×C11C22×C411yescharacteristic
262C2×Q8×C11C22×C411yescharacteristic
263C2×D4×C11—21no—
264C2×D4×C11—22no—
265C2×D4×C11—21no—
266C2×D4×C11—21no—
267C2×D4×C11—21no—
268C2×D4×C11—21no—
269C2×D4×C11—41no—
270C2×D4×C11—42no—
271C2×D4×C11—42no—
272C2×D4×C11C22×C411yescharacteristic
273C2×D4×C11C22×C411yescharacteristic
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—21no—
285C22×C4×C11—42no—
286C22×C4×C11—42no—
287C22×C4×C11C22×C411yescharacteristic
288C22×C4×C11C22×C411yescharacteristic
289C22×C4×C11C2×D411yescharacteristic
290C22×C4×C11C2×D411yescharacteristic
291C22×C4×C11C2×D411yescharacteristic
292C22×C4×C11C2411yescharacteristic
293C2×C22⋊D11—24no—
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—21no—
302C2×C22⋊D11—21no—
303C2×C22⋊D11—44no—
304C2×C22⋊D11C22⋊C411yescharacteristic
305C2×C22⋊D11C22⋊C411yescharacteristic
306C2×C22⋊D11C22⋊C411yescharacteristic
307C2×C22⋊D11C22⋊C411yescharacteristic
308C22×Dic11—24no—
309C22×Dic11—21no—
310C22×Dic11—21no—
311C22×Dic11—21no—
312C22×Dic11—21no—
313C22×Dic11—21no—
314C22×Dic11—42no—
315C22×Dic11—42no—
316C22×Dic11C2×D411yescharacteristic
317C22×Dic11C2×D411yescharacteristic
318C22×Dic11C2×D411yescharacteristic
319#4343—22no—
320#4343—41no—
321Q8×D11—22no—
322Q8×D11—41no—
323#4341—22no—
324#4341—41no—
325#4341—42no—
326#4341—42no—
327D4×D11—22no—
328D4×D11—42no—
329D4×D11—42no—
330D4×D11—41no—
331#4339—21no—
332#4339—21no—
333#4339—21no—
334#4339—21no—
335#4339—42no—
336#4339—42no—
337C2×D44—21no—
338C2×D44C22×C411yescharacteristic
339C2×C4×D11—24no—
340C2×C4×D11—21no—
341C2×C4×D11—21no—
342C2×C4×D11—21no—
343C2×C4×D11—21no—
344C2×C4×D11—21no—
345C2×C4×D11—21no—
346C2×C4×D11—21no—
347C2×C4×D11—42no—
348C2×C4×D11—42no—
349C2×C4×D11—42no—
350C2×C4×D11—42no—
351C2×C4×D11C22×C411yescharacteristic
352C2×C4×D11C22×C411yescharacteristic
353C2×C4×D11C2×D411yescharacteristic
354C2×C4×D11C2×D411yescharacteristic
355C2×Dic22—21no—
356C2×Dic22C22×C411yescharacteristic
357C11×M16—21no—
358C11×M16—21no—
359C11×M16—21no—
360C11×M16—21no—
361C2×C8×C11—21no—
362C2×C8×C11—21no—
363C11×C22⋊C4—24no—
364C42×C11—21no—
365C42×C11—21no—
366C42×C11—21no—
367C42×C11—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—21no—
377C22⋊Dic11C22⋊C411yescharacteristic
378C22⋊Dic11C22⋊C411yescharacteristic
379C22⋊Dic11C22⋊C411yescharacteristic
380C22⋊Dic11C22⋊C411yescharacteristic
381(C2×D11)⋊C4—24no—
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—21no—
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—24no—
397Dic11⋊C4—21no—
398Dic11⋊C4—21no—
399Dic11⋊C4—21no—
400Dic11⋊C4—21no—
401Dic11⋊C4—21no—
402Dic11⋊C4—21no—
403Dic11⋊C4C22⋊C411yescharacteristic
404Dic11⋊C4C22⋊C411yescharacteristic
405Dic11⋊C4C22⋊C411yescharacteristic
406Dic11⋊C4C22⋊C411yescharacteristic
407C4×Dic11—24no—
408C4×Dic11—21no—
409C4×Dic11—21no—
410C4×Dic11—21no—
411C4×Dic11—21no—
412C4×Dic11—21no—
413C4×Dic11—21no—
414C4×Dic11—42no—
415C4×Dic11—42no—
416C4×Dic11—42no—
417C4×Dic11C22×C411yescharacteristic
418C4×Dic11C22×C411yescharacteristic
419C4×Dic11C2×D411yescharacteristic
420C4×Dic11C2×D411yescharacteristic
421C4×Dic11C2×D412yescomplemented
422#4318—21no—
423#4318—21no—
424#4318—21no—
425#4318—42no—
426#4318C2×D412yescomplemented
427C2×C11⋊C8—21no—
428C2×C11⋊C8—21no—
429C2×C11⋊C8—42no—
430#4313—42no—
431C8×D11—42no—
432D4×#41—111no—
433D4×M16—111no—
434C22×#104—111no—
435C22×#104—111no—
436C42×D4—111no—
437#1980—111no—
438#1962—111no—
439#1896—111no—
440#1896—111no—
441#1871—111no—
442#1871—111no—
443#1806—111no—
444#1789—111no—
445#1789D1111yescharacteristic, complemented
446C4×#104—111no—
447C23×C11—21no—
448C23×C11—21no—
449C23×C11—21no—
450C23×C11—22no—
451C23×C11—21no—
452C23×C11—41no—
453C23×C11—42no—
454C23×C11—42no—
455C23×C11—81no—
456C23×C11C2×C22⋊C411yescharacteristic
457C23×C11C2×C22⋊C411yescharacteristic
458C23×C11C22×D411yescharacteristic
459C22×D11—21no—
460C22×D11—21no—
461C22×D11—22no—
462C22×D11—21no—
463C22×D11—41no—
464C22×D11—42no—
465C22×D11—42no—
466C22×D11—81no—
467C22×D11C2×C22⋊C411yescharacteristic
468C22×D11C2×C22⋊C411yescharacteristic
469Q8×C11—21no—
470Q8×C11—21no—
471Q8×C11—21no—
472Q8×C11—42no—
473Q8×C11C4×D412yescomplemented
474D4×C11—22no—
475D4×C11—22no—
476D4×C11—21no—
477D4×C11—21no—
478D4×C11—21no—
479D4×C11—42no—
480D4×C11—42no—
481D4×C11—42no—
482D4×C11—41no—
483D4×C11—41no—
484D4×C11C4×D412yescomplemented
485C2×C4×C11—21no—
486C2×C4×C11—21no—
487C2×C4×C11—21no—
488C2×C4×C11—21no—
489C2×C4×C11—21no—
490C2×C4×C11—21no—
491C2×C4×C11—21no—
492C2×C4×C11—21no—
493C2×C4×C11—21no—
494C2×C4×C11—22no—
495C2×C4×C11—22no—
496C2×C4×C11—21no—
497C2×C4×C11—21no—
498C2×C4×C11—22no—
499C2×C4×C11—22no—
500C2×C4×C11—21no—
501C2×C4×C11—42no—
502C2×C4×C11—42no—
503C2×C4×C11—42no—
504C2×C4×C11—41no—
505C2×C4×C11—41no—
506C2×C4×C11—41no—
507C2×C4×C11—41no—
508C2×C4×C11—41no—
509C2×C4×C11—41no—
510C2×C4×C11C2×C22⋊C411yescharacteristic
511C2×C4×C11C2×C22⋊C411yescharacteristic
512C2×C4×C11C23×C411yescharacteristic
513C2×C4×C11C22×D411yescharacteristic
514C2×C4×C11C22×D411yescharacteristic
515C2×C4×C11C2×#4111yescharacteristic
516C2×C4×C11H(5,𝔽2)11yescharacteristic
517C2×C4×C11H(5,𝔽2)11yescharacteristic
518C22⋊D11—22no—
519C22⋊D11—22no—
520C22⋊D11—22no—
521C22⋊D11—42no—
522C22⋊D11—42no—
523C22⋊D11—41no—
524C22⋊D11—41no—
525C22⋊D11—42no—
526C22⋊D11—42no—
527C22⋊D11—42no—
528C22⋊D11—81no—
529C22⋊D11—81no—
530C22⋊D11—81no—
531C22⋊D11#10414yescomplemented
532C2×Dic11—22no—
533C2×Dic11—22no—
534C2×Dic11—22no—
535C2×Dic11—21no—
536C2×Dic11—21no—
537C2×Dic11—22no—
538C2×Dic11—22no—
539C2×Dic11—21no—
540C2×Dic11—21no—
541C2×Dic11—21no—
542C2×Dic11—41no—
543C2×Dic11—42no—
544C2×Dic11—48no—
545C2×Dic11—41no—
546C2×Dic11—41no—
547C2×Dic11—42no—
548C2×Dic11—81no—
549C2×Dic11C2×C22⋊C411yescharacteristic
550C2×Dic11C2×C22⋊C411yescharacteristic
551C2×Dic11C2×C22⋊C411yescharacteristic
552C2×Dic11C2×C22⋊C411yescharacteristic
553C2×Dic11C2×C22⋊C411yescharacteristic
554C2×Dic11C2×C22⋊C411yescharacteristic
555D44—21no—
556D44—21no—
557D44—42no—
558C4×D11—21no—
559C4×D11—21no—
560C4×D11—21no—
561C4×D11—21no—
562C4×D11—21no—
563C4×D11—21no—
564C4×D11—21no—
565C4×D11—21no—
566C4×D11—42no—
567C4×D11—48no—
568C4×D11—42no—
569C4×D11—41no—
570C4×D11—41no—
571Dic22—21no—
572Dic22—21no—
573Dic22—42no—
574C8×C11—41no—
575C8×C11—41no—
576C11⋊C8—22no—
577C11⋊C8—41no—
578C22×#41—111no—
579C22×#41C2×D1111yescharacteristic
580C22×M16—111no—
581C22×M16—111no—
582#550—111no—
583D4×Q8—111no—
584#548—111no—
585#548—111no—
586#547—111no—
587#547—221no—
588#546—111no—
589#546—111no—
590#546—221no—
591#546—221no—
592D42—111no—
593D42—221no—
594#532—111no—
595#532—221no—
596#525—111no—
597#525—111no—
598#525—221no—
599#525—221no—
600C4×#41—111no—
601C2×C4×D4—111no—
602C2×C4×D4—221no—
603C2×C4×D4—221no—
604C22×C42—111no—
605C22×C42—111no—
606#436—221no—
607#435—221no—
608#435—221no—
609C8×D4—221no—
610#423—111no—
611C2×#104—111no—
612C2×#104—111no—
613C2×#104—111no—
614C2×#104—111no—
615C2×#104—111no—
616C2×#104—111no—
617C2×#104—111no—
618C2×#104—111no—
619C2×#104—224no—
620C2×#104—224no—
621C2×#104C2×D1111yescharacteristic
622C2×#104C2×D1111yescharacteristic
623C2×#104C2×D1111yescharacteristic, complemented
624C2×#104C2×D1111yescharacteristic, complemented
625#407—111no—
626#407C2×D1111yescharacteristic, complemented
627C4×M16—111no—
628C4×C4⋊C4—111no—
629C4×C4⋊C4—221no—
630C4×C22⋊C4—111no—
631C4×C22⋊C4—221no—
632C4×C22⋊C4—221no—
633C4×C22⋊C4C2×D1111yescharacteristic, complemented
634C43—111no—
635#339—111no—
636#339—111no—
637#339—111no—
638#339—111no—
639C22×C11—21no—
640C22×C11—21no—
641C22×C11—21no—
642C22×C11—21no—
643C22×C11—21no—
644C22×C11—22no—
645C22×C11—21no—
646C22×C11—21no—
647C22×C11—42no—
648C22×C11—42no—
649C22×C11—41no—
650C22×C11—41no—
651C22×C11—41no—
652C22×C11—41no—
653C22×C11—41no—
654C22×C11—84no—
655C22×C11C2×#10412yescomplemented
656C22×C11C22×C22⋊C411yescharacteristic
657C22×C11D4211yescharacteristic
658C22×C11#54611yescharacteristic
659C2×D11—21no—
660C2×D11—21no—
661C2×D11—21no—
662C2×D11—21no—
663C2×D11—21no—
664C2×D11—42no—
665C2×D11—42no—
666C2×D11—41no—
667C2×D11—41no—
668C2×D11—41no—
669C2×D11—84no—
670C2×D11C2×#10412yescomplemented
671C4×C11—21no—
672C4×C11—21no—
673C4×C11—22no—
674C4×C11—42no—
675C4×C11—42no—
676C4×C11—41no—
677C4×C11C2×C4×D411yescharacteristic
678C4×C11#51811yescharacteristic
679C4×C11D4211yescharacteristic
680C4×C11#54611yescharacteristic
681Dic11—24no—
682Dic11—21no—
683Dic11—21no—
684Dic11—21no—
685Dic11—21no—
686Dic11—21no—
687Dic11—42no—
688Dic11—41no—
689Dic11—41no—
690Dic11—41no—
691Dic11C2×#10412yescomplemented
692C2×#41—21no—
693C2×#41—21no—
694C2×#41—22no—
695C2×#41—22no—
696C2×#41—41no—
697C2×#41—41no—
698C2×#41—111no—
699C2×#41—111no—
700C2×#41—111no—
701C2×#41—221no—
702C2×#41—221no—
703C2×#41—222no—
704C2×#41—222no—
705C2×#41—441no—
706C2×#41—441no—
707C2×#41C4×D1111yescharacteristic, complemented
708C2×#41C4×D1111yescharacteristic, complemented
709C2×#41C22×D1111yescharacteristic
710C2×#41C22×D1111yescharacteristic
711C22×Q8—111no—
712C22×Q8C4×D1111yescharacteristic, complemented
713C22×D4—21no—
714C22×D4—111no—
715C22×D4—111no—
716C22×D4—221no—
717C22×D4—221no—
718C22×D4C4×D1111yescharacteristic, complemented
719C23×C4—21no—
720C23×C4—111no—
721C23×C4—221no—
722C23×C4—221no—
723C23×C4—221no—
724C23×C4C22×D1111yescharacteristic
725C2×M16—111no—
726C2×M16—111no—
727C2×M16—221no—
728C2×M16—221no—
729C2×M16—222no—
730C2×M16—222no—
731C2×M16—441no—
732C2×M16—441no—
733C2×M16C22×D1111yescharacteristic
734C2×M16C22×D1111yescharacteristic
735C22×C8—221no—
736C22×C8—221no—
737C4⋊Q8—111no—
738C4⋊Q8—221no—
739#127—111no—
740#127—221no—
741#124—111no—
742#124—111no—
743#124—221no—
744#124—221no—
745#123—221no—
746#123—221no—
747#123—221no—
748#123—221no—
749#123—221no—
750#123—221no—
751C22⋊Q8—111no—
752C22⋊Q8—111no—
753C22⋊Q8—111no—
754C22⋊Q8—111no—
755C22⋊Q8—221no—
756C22⋊Q8—221no—
757C22⋊Q8—221no—
758C22⋊Q8—221no—
759#121—111no—
760#121—111no—
761#121—111no—
762#121—111no—
763#121—221no—
764#121—221no—
765#121—221no—
766#121—221no—
767#121—221no—
768#121—221no—
769#121—221no—
770#121—221no—
771#121—221no—
772#121—221no—
773#120—221no—
774#120—221no—
775#120—221no—
776#120—221no—
777#120—221no—
778#120—221no—
779C4×Q8—111no—
780C4×Q8—111no—
781C4×D4—111no—
782C4×D4—111no—
783C4×D4—111no—
784C4×D4—111no—
785C4×D4—111no—
786C4×D4—111no—
787C4×D4—111no—
788C4×D4—111no—
789C4×D4—111no—
790C4×D4—111no—
791C4×D4—221no—
792C4×D4—221no—
793C4×D4—228no—
794C4×D4—221no—
795C4×D4—221no—
796C4×D4—221no—
797C4×D4—221no—
798C4×D4—221no—
799C4×D4—221no—
800C4×D4—221no—
801C4×D4—221no—
802C4×D4—221no—
803C4×D4—221no—
804#117—111no—
805#117—221no—
806C2×C4⋊C4—111no—
807C2×C4⋊C4—221no—
808C2×C4⋊C4—221no—
809C2×C22⋊C4—21no—
810C2×C22⋊C4—111no—
811C2×C22⋊C4—111no—
812C2×C22⋊C4—221no—
813C2×C22⋊C4—221no—
814C2×C22⋊C4—221no—
815C2×C42—111no—
816C2×C42—111no—
817C2×C42—111no—
818C2×C42—222no—
819C2×C42—221no—
820C2×C42—222no—
821C2×C42—221no—
822C2×C42—221no—
823C2×C42—221no—
824C2×C42—221no—
825C2×C42—441no—
826C2×C42—441no—
827C2×C42C22×D1111yescharacteristic
828C2×C42C22×D1111yescharacteristic
829C4⋊C8—221no—
830C4⋊C8—221no—
831#104—22no—
832#104—22no—
833#104—41no—
834#104—41no—
835#104—114no—
836#104—222no—
837#104—222no—
838#104—222no—
839#104—222no—
840#104—222no—
841#104—441no—
842#104—441no—
843C22⋊C8—21no—
844C22⋊C8—21no—
845C22⋊C8—221no—
846C22⋊C8—221no—
847#97—221no—
848C4×C8—221no—
849#95—21no—
850#95—221no—
851#95—221no—
852C2×C11—21no—
853C2×C11—21no—
854C2×C11—22no—
855C2×C11—42no—
856C2×C11—41no—
857C2×C11—81no—
858C2×C11D4×C22⋊C411yescharacteristic
859C2×C11C22×#10411yescharacteristic
860C2×C11#290111yescharacteristic
861D11—22no—
862D11—41no—
863D11—81no—
864C24—21no—
865C24—111no—
866C24—221no—
867C24D4×D1111yescharacteristic
868#41—21no—
869#41—21no—
870#41—22no—
871#41—22no—
872#41—21no—
873#41—21no—
874#41—21no—
875#41—21no—
876#41—42no—
877#41—42no—
878#41—41no—
879#41—41no—
880#41—42no—
881#41—42no—
882#41—222no—
883#41—222no—
884#41—221no—
885#41—221no—
886#41—221no—
887#41—221no—
888#41—442no—
889#41—442no—
890#41—441no—
891#41—442no—
892#41—442no—
893#41—441no—
894#41D4×D1112yes—
895#41#434112yes—
896C2×Q8—21no—
897C2×Q8—22no—
898C2×Q8—41no—
899C2×Q8—111no—
900C2×Q8—221no—
901C2×Q8—222no—
902C2×Q8—441no—
903C2×Q8C2×C4×D1111yescharacteristic
904C2×Q8C2×C4×D1111yescharacteristic
905C2×D4—21no—
906C2×D4—22no—
907C2×D4—21no—
908C2×D4—21no—
909C2×D4—21no—
910C2×D4—21no—
911C2×D4—41no—
912C2×D4—42no—
913C2×D4—42no—
914C2×D4—111no—
915C2×D4—111no—
916C2×D4—111no—
917C2×D4—111no—
918C2×D4—111no—
919C2×D4—221no—
920C2×D4—221no—
921C2×D4—221no—
922C2×D4—221no—
923C2×D4—224no—
924C2×D4—222no—
925C2×D4—221no—
926C2×D4—221no—
927C2×D4—221no—
928C2×D4—221no—
929C2×D4—221no—
930C2×D4—221no—
931C2×D4—441no—
932C2×D4—442no—
933C2×D4—442no—
934C2×D4—444no—
935C2×D4C2×C4×D1111yescharacteristic
936C2×D4C2×C4×D1111yescharacteristic
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—42no—
949C22×C4—42no—
950C22×C4—111no—
951C22×C4—111no—
952C22×C4—111no—
953C22×C4—111no—
954C22×C4—111no—
955C22×C4—111no—
956C22×C4—111no—
957C22×C4—221no—
958C22×C4—221no—
959C22×C4—224no—
960C22×C4—221no—
961C22×C4—221no—
962C22×C4—221no—
963C22×C4—221no—
964C22×C4—221no—
965C22×C4—221no—
966C22×C4—221no—
967C22×C4—221no—
968C22×C4—224no—
969C22×C4—221no—
970C22×C4—221no—
971C22×C4—442no—
972C22×C4—442no—
973C22×C4—442no—
974C22×C4—442no—
975C22×C4—442no—
976C22×C4—442no—
977C22×C4C2×C4×D1111yescharacteristic
978C22×C4C2×C4×D1111yescharacteristic
979C22×C4D4×D1111yescharacteristic
980C22×C4D4×D1111yescharacteristic
981C22×C4D4×D1111yescharacteristic
982C22×C4C23×D1111yescharacteristic
983M16—21no—
984M16—21no—
985M16—21no—
986M16—21no—
987M16—112no—
988M16—221no—
989M16—221no—
990M16—221no—
991M16—442no—
992M16—442no—
993C2×C8—21no—
994C2×C8—21no—
995C2×C8—221no—
996C2×C8—221no—
997C2×C8—442no—
998C2×C8—442no—
999C4⋊C4—111no—
1000C4⋊C4—111no—
1001C4⋊C4—111no—
1002C4⋊C4—111no—
1003C4⋊C4—111no—
1004C4⋊C4—111no—
1005C4⋊C4—221no—
1006C4⋊C4—221no—
1007C4⋊C4—221no—
1008C4⋊C4—221no—
1009C4⋊C4—221no—
1010C4⋊C4—221no—
1011C4⋊C4—224no—
1012C4⋊C4—221no—
1013C4⋊C4—221no—
1014C22⋊C4—24no—
1015C22⋊C4—111no—
1016C22⋊C4—111no—
1017C22⋊C4—111no—
1018C22⋊C4—111no—
1019C22⋊C4—111no—
1020C22⋊C4—111no—
1021C22⋊C4—111no—
1022C22⋊C4—111no—
1023C22⋊C4—221no—
1024C22⋊C4—221no—
1025C22⋊C4—221no—
1026C22⋊C4—221no—
1027C22⋊C4—224no—
1028C22⋊C4—221no—
1029C22⋊C4—221no—
1030C22⋊C4—221no—
1031C22⋊C4—221no—
1032C22⋊C4—221no—
1033C22⋊C4—221no—
1034C22⋊C4—221no—
1035C22⋊C4—221no—
1036C22⋊C4—221no—
1037C22⋊C4—221no—
1038C22⋊C4—221no—
1039C42—21no—
1040C42—21no—
1041C42—21no—
1042C42—21no—
1043C42—111no—
1044C42—111no—
1045C42—111no—
1046C42—111no—
1047C42—112no—
1048C42—221no—
1049C42—221no—
1050C42—224no—
1051C42—221no—
1052C42—221no—
1053C42—221no—
1054C42—221no—
1055C42—442no—
1056C42—442no—
1057C42—442no—
1058C11D4×#10411yescharacteristic, complemented, Sylow
1059C23—21no—
1060C23—21no—
1061C23—21no—
1062C23—22no—
1063C23—21no—
1064C23—41no—
1065C23—42no—
1066C23—42no—
1067C23—81no—
1068C23—111no—
1069C23—111no—
1070C23—222no—
1071C23—221no—
1072C23—221no—
1073C23—221no—
1074C23—441no—
1075C23—442no—
1076C23—442no—
1077C23—881no—
1078C23C22⋊C4×D1111yescharacteristic
1079C23C22⋊C4×D1111yescharacteristic
1080C23C2×D4×D1111yescharacteristic
1081Q8—21no—
1082Q8—21no—
1083Q8—21no—
1084Q8—42no—
1085Q8—221no—
1086Q8—221no—
1087Q8—442no—
1088Q8(C22⋊D11)⋊C412yescomplemented
1089D4—22no—
1090D4—22no—
1091D4—21no—
1092D4—21no—
1093D4—21no—
1094D4—42no—
1095D4—42no—
1096D4—42no—
1097D4—41no—
1098D4—41no—
1099D4—114no—
1100D4—222no—
1101D4—222no—
1102D4—222no—
1103D4—221no—
1104D4—221no—
1105D4—442no—
1106D4—442no—
1107D4—442no—
1108D4—442no—
1109D4—442no—
1110D4—441no—
1111D4—441no—
1112D4—442no—
1113D4—881no—
1114D4—881no—
1115D4—881no—
1116D4(C22⋊D11)⋊C412yescomplemented
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—22no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—21no—
1133C2×C4—42no—
1134C2×C4—42no—
1135C2×C4—42no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—111no—
1143C2×C4—111no—
1144C2×C4—111no—
1145C2×C4—111no—
1146C2×C4—111no—
1147C2×C4—111no—
1148C2×C4—222no—
1149C2×C4—222no—
1150C2×C4—222no—
1151C2×C4—222no—
1152C2×C4—221no—
1153C2×C4—221no—
1154C2×C4—221no—
1155C2×C4—221no—
1156C2×C4—221no—
1157C2×C4—221no—
1158C2×C4—221no—
1159C2×C4—221no—
1160C2×C4—221no—
1161C2×C4—221no—
1162C2×C4—222no—
1163C2×C4—221no—
1164C2×C4—221no—
1165C2×C4—221no—
1166C2×C4—442no—
1167C2×C4—442no—
1168C2×C4—448no—
1169C2×C4—442no—
1170C2×C4—441no—
1171C2×C4—442no—
1172C2×C4—448no—
1173C2×C4—441no—
1174C2×C4—441no—
1175C2×C4—441no—
1176C2×C4—441no—
1177C2×C4—881no—
1178C2×C4C22⋊C4×D1111yescharacteristic
1179C2×C4C22⋊C4×D1111yescharacteristic
1180C2×C4C22×C4×D1111yescharacteristic
1181C2×C4C2×D4×D1111yescharacteristic
1182C2×C4C2×D4×D1111yescharacteristic
1183C2×C4C2×#434111yescharacteristic
1184C2×C4#6703711yescharacteristic
1185C2×C4#6703711yescharacteristic
1186C8—41no—
1187C8—41no—
1188C8—222no—
1189C8—441no—
1190C22—21no—
1191C22—21no—
1192C22—21no—
1193C22—21no—
1194C22—21no—
1195C22—22no—
1196C22—21no—
1197C22—21no—
1198C22—42no—
1199C22—42no—
1200C22—41no—
1201C22—41no—
1202C22—41no—
1203C22—41no—
1204C22—41no—
1205C22—84no—
1206C22—112no—
1207C22—221no—
1208C22—221no—
1209C22—221no—
1210C22—221no—
1211C22—221no—
1212C22—442no—
1213C22—442no—
1214C22—441no—
1215C22—441no—
1216C22—441no—
1217C22—884no—
1218C22D11×#10412yescomplemented
1219C22C2×C22⋊C4×D1111yescharacteristic
1220C22#1062312111yescharacteristic
1221C22#1062312211yescharacteristic
1222C4—21no—
1223C4—21no—
1224C4—22no—
1225C4—42no—
1226C4—42no—
1227C4—41no—
1228C4—112no—
1229C4—224no—
1230C4—221no—
1231C4—221no—
1232C4—221no—
1233C4—221no—
1234C4—221no—
1235C4—442no—
1236C4—441no—
1237C4—441no—
1238C4—441no—
1239C4C2×(C22⋊D11)⋊C411yescharacteristic
1240C4#1062301711yescharacteristic
1241C4#1062312111yescharacteristic
1242C4#1062312211yescharacteristic
1243C2—21no—
1244C2—21no—
1245C2—22no—
1246C2—41no—
1247C2—42no—
1248C2—81no—
1249C2—222no—
1250C2—441no—
1251C2—881no—
1252C2#1307143211yescharacteristic
1253C2C2×D11×#10411yescharacteristic
1254C2#1307716211yescharacteristic
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
hypocenterC11D4×#104
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. C22×#66901C2semidirect
4. C2×D11×#104C2semidirect
5. C4×(C22⋊D11)⋊C4C2semidirect
6. #13069533C2semidirect
7. #13069442C2semidirect
8. #13069057C2semidirect
9. #13069056C2semidirect
10. #13068916C2semidirect
11. #13068915C2semidirect
12. #13068634C2semidirect
13. #13068558C2semidirect
14. #104×Dic11C2semidirect
15. C11×#1789C2semidirect
18. #10623365C4semidirect
21. #10623362C4semidirect
23. #10623360C4semidirect
28. #10623355C4semidirect
29. #10623348C4semidirect
30. Q8×C22⋊D11C4semidirect
32. #10623337C4semidirect
34. D4×C22⋊D11C4semidirect
39. C22×C4×Dic11C22semidirect
40. C22×#4318C22semidirect
41. C2×M16×D11C22semidirect
43. C2×C42×D11C22semidirect
46. C2×C11×#104C22semidirect
47. C2×C11×#104C22semidirect
48. C11×#407C22semidirect
49. C4×C11×C22⋊C4C22semidirect
53. C2×#66901C22semidirect
54. C2×#66901C22semidirect
55. C2×#66889C22semidirect
56. C2×#66889C22semidirect
57. #10622739C22semidirect
58. #10622731C22semidirect
59. M16×Dic11C22semidirect
61. C4×(C2×D11)⋊C4C22semidirect
62. C4×Dic11⋊C4C22semidirect
63. C42×Dic11C22semidirect
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
99. C2×#4343C2×C4semidirect
100. C2×Q8×D11C2×C4semidirect
102. C2×#4341C2×C4semidirect
104. C2×D4×D11C2×C4semidirect
121. #67000C2×C4semidirect
124. #66999C2×C4semidirect
125. #66999C2×C4semidirect
126. Q8×Dic11C2×C4semidirect
127. Q8×Dic11C2×C4semidirect
129. #66997C2×C4semidirect
131. #66993C2×C4semidirect
140. #66991C2×C4semidirect
141. #66991C2×C4semidirect
146. #66989C2×C4semidirect
152. D4×Dic11C2×C4semidirect
153. D4×Dic11C2×C4semidirect
156. #66983C2×C4semidirect
157. #66983C2×C4semidirect
186. #66977C2×C4semidirect
187. #66977C2×C4semidirect
224. #66901D4semidirect
421. C4×Dic11C2×D4semidirect
426. #4318C2×D4semidirect
445. #1789D11semidirect
473. Q8×C11C4×D4semidirect
484. D4×C11C4×D4semidirect
531. C22⋊D11#104semidirect
623. C2×#104C2×D11semidirect
624. C2×#104C2×D11semidirect
626. #407C2×D11semidirect
633. C4×C22⋊C4C2×D11semidirect
655. C22×C11C2×#104semidirect
670. C2×D11C2×#104semidirect
691. Dic11C2×#104semidirect
707. C2×#41C4×D11semidirect
708. C2×#41C4×D11semidirect
712. C22×Q8C4×D11semidirect
718. C22×D4C4×D11semidirect
1058. C11D4×#104semidirect
1088. Q8(C22⋊D11)⋊C4semidirect
1116. D4(C22⋊D11)⋊C4semidirect
1218. C22D11×#104semidirect

Maximal subgroups

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

subgroupindex
#41×C22⋊D112
#130773482
C22×#669012
C2×D11×#1042
C4×(C22⋊D11)⋊C42
#130695332
#130694422
#130690572
#130690562
#130689162
#130689152
#130686342
#130685582
#104×Dic112
C11×#17892
D4×#10411