Finite Group Databasebeta

← #104×C22⋊D11 #14769443

Subgroups — #104×C22⋊D11 #14769443

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
2M16×C22⋊D11C211yesmaximal, characteristic, complemented
3C2×D11×#104C211yesmaximal, characteristic, complemented
4C42×C22⋊D11C211yesmaximal, characteristic, complemented
5#13069533C211yesmaximal, characteristic, complemented
6#13069442C211yesmaximal, characteristic, complemented
7#13069059C211yesmaximal, 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#104×Dic11C211yesmaximal, characteristic, complemented
15C22×C11×#104C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C2×#41×D11C2211yescharacteristic
18C22×C11×M16C2211yescharacteristic, complemented
19C22×C42×C11C2211yescharacteristic, 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⋊D11—21no—
41C2×C4×C22⋊D11C2211yescharacteristic
42C2×M16×D11C2211yescharacteristic, complemented
43C2×C42×D11C2211yescharacteristic, complemented
44C2×C11×#104—24no—
45C2×C11×#104C2211yescharacteristic
46C2×C11×#104C2211yescharacteristic
47C2×C11×#104C2211yescharacteristic, complemented
48C2×C11×#104C2211yescharacteristic, complemented
49C2×#66901C2211yescharacteristic
50C2×#66901C2211yescharacteristic
51C2×#66901C2211yescharacteristic, complemented
52C2×#66901C2211yescharacteristic, complemented
53C4×C22⋊Dic11—21no—
54C4×C22⋊Dic11C2211yescharacteristic, complemented
55#10622820C2211yescharacteristic, complemented
56C2×#66889C2211yescharacteristic, complemented
57C2×#66889C2211yescharacteristic, complemented
58#10622741—21no—
59#10622740—21no—
60#10622739C2211yescharacteristic, complemented
61#10622731C2211yescharacteristic, complemented
62M16×Dic11C2211yescharacteristic, complemented
63#10622724—21no—
64C8×C22⋊D11—21no—
65C4×(C2×D11)⋊C4—21no—
66C4×(C2×D11)⋊C4C2211yescharacteristic, complemented
67C4×Dic11⋊C4—21no—
68C4×Dic11⋊C4C2211yescharacteristic, complemented
69C42×Dic11C2211yescharacteristic, 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×C11—21no—
92C23×C4×C11C2311yescharacteristic
93C22×C22⋊D11—21no—
94C22×C22⋊D11D411yescharacteristic
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×M16—21no—
111C2×C11×M16—22no—
112C2×C11×M16—41no—
113C2×C11×M16C2311yescharacteristic
114C2×C11×M16C2311yescharacteristic
115C22×C8×C11—21no—
116C2×C42×C11—22no—
117C2×C42×C11—21no—
118C2×C42×C11—41no—
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, complemented
132#66999C2×C411yescharacteristic, complemented
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, complemented
148#66991C2×C411yescharacteristic, complemented
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—28no—
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⋊D11—21no—
179C4×C22⋊D11C2×C411yescharacteristic
180C4×C22⋊D11C2×C411yescharacteristic
181C4×C22⋊D11C2×C411yescharacteristic
182C4×C22⋊D11C2×C411yescharacteristic
183C4×C22⋊D11D411yescharacteristic
184C4×C22⋊D11D411yescharacteristic
185C4×C22⋊D11D411yescharacteristic
186C4×C22⋊D11D411yescharacteristic
187C2×(C2×D11)⋊C4—21no—
188C2×(C2×D11)⋊C4—21no—
189C2×(C2×D11)⋊C4D411yescharacteristic
190#66979—21no—
191#66979C2311yescharacteristic
192#66977—21no—
193#66977—21no—
194#66977C2×C411yescharacteristic, complemented
195#66977C2×C411yescharacteristic, complemented
196C2×Dic11⋊C4—21no—
197C2×Dic11⋊C4—21no—
198C2×Dic11⋊C4D411yescharacteristic
199C2×C4×Dic11—21no—
200C2×C4×Dic11—21no—
201C2×C4×Dic11—21no—
202C2×C4×Dic11—21no—
203C2×C4×Dic11C2311yescharacteristic
204C2×C4×Dic11C2311yescharacteristic
205C2×C4×Dic11C2311yescharacteristic
206C2×#4318C2311yescharacteristic
207C2×#4318C2311yescharacteristic
208M16×D11—22no—
209M16×D11—41no—
210C2×#4313—21no—
211C2×C8×D11—21no—
212C42×D11—22no—
213C42×D11—41no—
214C11×#104—22no—
215C11×#104—22no—
216C11×#104—22no—
217C11×#104D414yescomplemented
218#66901—22no—
219#66901—22no—
220#66901—41no—
221#66901—41no—
222C11⋊#95—21no—
223C11⋊#95—21no—
224C11⋊#95—21no—
225C22⋊(C11⋊C8)—21no—
226C22⋊(C11⋊C8)—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—24no—
281C22×C4×C11—21no—
282C22×C4×C11—21no—
283C22×C4×C11—21no—
284C22×C4×C11—21no—
285C22×C4×C11—21no—
286C22×C4×C11—42no—
287C22×C4×C11—42no—
288C22×C4×C11—42no—
289C22×C4×C11—42no—
290C22×C4×C11C22×C411yescharacteristic
291C22×C4×C11C22×C411yescharacteristic
292C22×C4×C11C2×D411yescharacteristic
293C22×C4×C11C2×D411yescharacteristic
294C22×C4×C11C2×D411yescharacteristic
295C22×C4×C11C2411yescharacteristic
296C2×C22⋊D11—24no—
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—21no—
304C2×C22⋊D11—21no—
305C2×C22⋊D11—21no—
306C2×C22⋊D11—44no—
307C2×C22⋊D11C22⋊C411yescharacteristic
308C2×C22⋊D11C22⋊C411yescharacteristic
309C2×C22⋊D11C22⋊C411yescharacteristic
310C2×C22⋊D11C22⋊C411yescharacteristic
311C22×Dic11—21no—
312C22×Dic11—21no—
313C22×Dic11—21no—
314C22×Dic11—21no—
315C22×Dic11—21no—
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—42no—
361C11×M16C2×D412yescomplemented
362C2×C8×C11—21no—
363C2×C8×C11—21no—
364C2×C8×C11—42no—
365C42×C11—21no—
366C42×C11—21no—
367C42×C11—21no—
368C42×C11—42no—
369C42×C11C2×D412yescomplemented
370C22⋊Dic11—24no—
371C22⋊Dic11—21no—
372C22⋊Dic11—21no—
373C22⋊Dic11—21no—
374C22⋊Dic11—21no—
375C22⋊Dic11—21no—
376C22⋊Dic11—21no—
377C22⋊Dic11—21no—
378C22⋊Dic11—21no—
379C22⋊Dic11—21no—
380C22⋊Dic11C22⋊C411yescharacteristic
381C22⋊Dic11C22⋊C411yescharacteristic
382C22⋊Dic11C22⋊C411yescharacteristic
383C22⋊Dic11C22⋊C411yescharacteristic
384(C2×D11)⋊C4—24no—
385(C2×D11)⋊C4—21no—
386(C2×D11)⋊C4—21no—
387(C2×D11)⋊C4—21no—
388(C2×D11)⋊C4—21no—
389(C2×D11)⋊C4—21no—
390(C2×D11)⋊C4—21no—
391(C2×D11)⋊C4C22⋊C411yescharacteristic
392(C2×D11)⋊C4C22⋊C411yescharacteristic
393(C2×D11)⋊C4C22⋊C411yescharacteristic
394(C2×D11)⋊C4C22⋊C411yescharacteristic
395C4⋊Dic11—21no—
396C4⋊Dic11—21no—
397C4⋊Dic11C22×C411yescharacteristic
398C4⋊Dic11C22×C411yescharacteristic
399Dic11⋊C4—24no—
400Dic11⋊C4—21no—
401Dic11⋊C4—21no—
402Dic11⋊C4—21no—
403Dic11⋊C4—21no—
404Dic11⋊C4—21no—
405Dic11⋊C4—21no—
406Dic11⋊C4C22⋊C411yescharacteristic
407Dic11⋊C4C22⋊C411yescharacteristic
408Dic11⋊C4C22⋊C411yescharacteristic
409Dic11⋊C4C22⋊C411yescharacteristic
410C4×Dic11—24no—
411C4×Dic11—21no—
412C4×Dic11—21no—
413C4×Dic11—21no—
414C4×Dic11—21no—
415C4×Dic11—21no—
416C4×Dic11—21no—
417C4×Dic11—21no—
418C4×Dic11—42no—
419C4×Dic11—42no—
420C4×Dic11C22×C411yescharacteristic
421C4×Dic11C22×C411yescharacteristic
422C4×Dic11C2×D411yescharacteristic
423C4×Dic11C2×D411yescharacteristic
424#4318—21no—
425#4318—21no—
426#4318—21no—
427#4318—21no—
428C2×C11⋊C8—21no—
429C2×C11⋊C8—21no—
430#4313—42no—
431C8×D11—42no—
432D4×#41—111no—
433D4×M16—111no—
434C22×#104—111no—
435C22×#104D1111yescharacteristic, complemented
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#1789—111no—
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—22no—
486C2×C4×C11—22no—
487C2×C4×C11—21no—
488C2×C4×C11—22no—
489C2×C4×C11—21no—
490C2×C4×C11—21no—
491C2×C4×C11—21no—
492C2×C4×C11—21no—
493C2×C4×C11—21no—
494C2×C4×C11—21no—
495C2×C4×C11—21no—
496C2×C4×C11—21no—
497C2×C4×C11—22no—
498C2×C4×C11—22no—
499C2×C4×C11—21no—
500C2×C4×C11—21no—
501C2×C4×C11—22no—
502C2×C4×C11—21no—
503C2×C4×C11—42no—
504C2×C4×C11—42no—
505C2×C4×C11—42no—
506C2×C4×C11—48no—
507C2×C4×C11—41no—
508C2×C4×C11—41no—
509C2×C4×C11—41no—
510C2×C4×C11—41no—
511C2×C4×C11C2×C22⋊C411yescharacteristic
512C2×C4×C11C2×C22⋊C411yescharacteristic
513C2×C4×C11C23×C411yescharacteristic
514C2×C4×C11C22×D411yescharacteristic
515C2×C4×C11C22×D411yescharacteristic
516C2×C4×C11C2×#4111yescharacteristic
517C2×C4×C11H(5,𝔽2)11yescharacteristic
518C2×C4×C11H(5,𝔽2)11yescharacteristic
519C22⋊D11—22no—
520C22⋊D11—22no—
521C22⋊D11—22no—
522C22⋊D11—42no—
523C22⋊D11—42no—
524C22⋊D11—41no—
525C22⋊D11—41no—
526C22⋊D11—42no—
527C22⋊D11—42no—
528C22⋊D11—42no—
529C22⋊D11—81no—
530C22⋊D11—81no—
531C22⋊D11—81no—
532C22⋊D11#10414yesdirect product factor
533C2×Dic11—21no—
534C2×Dic11—21no—
535C2×Dic11—22no—
536C2×Dic11—22no—
537C2×Dic11—22no—
538C2×Dic11—21no—
539C2×Dic11—21no—
540C2×Dic11—21no—
541C2×Dic11—41no—
542C2×Dic11—42no—
543C2×Dic11—41no—
544C2×Dic11—41no—
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—42no—
568C4×D11—48no—
569C4×D11—41no—
570C4×D11—41no—
571Dic22—21no—
572Dic22—21no—
573Dic22—42no—
574C8×C11—22no—
575C8×C11—41no—
576C11⋊C8—41no—
577C11⋊C8—41no—
578C22×#41—111no—
579C22×#41C2×D1111yescharacteristic
580C22×M16—111no—
581C22×M16C2×D1111yescharacteristic, complemented
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×C42C2×D1111yescharacteristic, complemented
606#436—221no—
607#435—221no—
608#435—221no—
609C8×D4—221no—
610#423—111no—
611C2×#104—24no—
612C2×#104—111no—
613C2×#104—111no—
614C2×#104—111no—
615C2×#104—111no—
616C2×#104—111no—
617C2×#104—111no—
618C2×#104—111no—
619C2×#104—111no—
620C2×#104—224no—
621C2×#104C2×D1111yescharacteristic
622C2×#104C2×D1111yescharacteristic
623C2×#104C2×D1111yescharacteristic, complemented
624C2×#104C2×D1111yescharacteristic, complemented
625#407—111no—
626#407—111no—
627C4×M16—111no—
628C4×C4⋊C4—111no—
629C4×C4⋊C4—221no—
630C4×C22⋊C4—111no—
631C4×C22⋊C4—111no—
632C4×C22⋊C4—221no—
633C4×C22⋊C4—221no—
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—24no—
672C4×C11—21no—
673C4×C11—21no—
674C4×C11—22no—
675C4×C11—42no—
676C4×C11—41no—
677C4×C11C2×C4×D411yescharacteristic
678C4×C11#51811yescharacteristic
679C4×C11D4211yescharacteristic
680C4×C11#54611yescharacteristic
681Dic11—21no—
682Dic11—21no—
683Dic11—21no—
684Dic11—21no—
685Dic11—21no—
686Dic11—42no—
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—21no—
721C23×C4—111no—
722C23×C4—221no—
723C23×C4—221no—
724C23×C4C22×D1111yescharacteristic
725C2×M16—21no—
726C2×M16—22no—
727C2×M16—41no—
728C2×M16—111no—
729C2×M16—111no—
730C2×M16—221no—
731C2×M16—222no—
732C2×M16—441no—
733C2×M16C22×D1111yescharacteristic
734C2×M16C22×D1111yescharacteristic
735C22×C8—21no—
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—221no—
794C4×D4—221no—
795C4×D4—221no—
796C4×D4—221no—
797C4×D4—221no—
798C4×D4—221no—
799C4×D4—228no—
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—111no—
810C2×C22⋊C4—111no—
811C2×C22⋊C4—221no—
812C2×C22⋊C4—221no—
813C2×C22⋊C4—221no—
814C2×C22⋊C4—221no—
815C2×C42—22no—
816C2×C42—21no—
817C2×C42—41no—
818C2×C42—111no—
819C2×C42—111no—
820C2×C42—111no—
821C2×C42—221no—
822C2×C42—221no—
823C2×C42—222no—
824C2×C42—221no—
825C2×C42—221no—
826C2×C42—441no—
827C2×C42C22×D1111yescharacteristic
828C2×C42C22×D1111yescharacteristic
829C4⋊C8—221no—
830C4⋊C8—221no—
831#104—22no—
832#104—22no—
833#104—22no—
834#104—222no—
835#104—222no—
836#104—222no—
837#104—222no—
838#104—441no—
839#104—441no—
840#104—441no—
841#104—441no—
842#104C22⋊D1114yesdirect product factor
843C22⋊C8—221no—
844C22⋊C8—221no—
845C22⋊C8—221no—
846C22⋊C8—221no—
847#97—221no—
848C4×C8—221no—
849#95—221no—
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#41#433912yes—
895#41C2×C22⋊D1112yes—
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—24no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—42no—
950C22×C4—42no—
951C22×C4—42no—
952C22×C4—42no—
953C22×C4—111no—
954C22×C4—111no—
955C22×C4—111no—
956C22×C4—111no—
957C22×C4—111no—
958C22×C4—111no—
959C22×C4—111no—
960C22×C4—221no—
961C22×C4—221no—
962C22×C4—224no—
963C22×C4—221no—
964C22×C4—221no—
965C22×C4—221no—
966C22×C4—221no—
967C22×C4—221no—
968C22×C4—221no—
969C22×C4—221no—
970C22×C4—221no—
971C22×C4—221no—
972C22×C4—221no—
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—42no—
987M16—221no—
988M16—221no—
989M16—221no—
990M16—221no—
991M16—442no—
992M16C2×C22⋊D1112yescomplemented
993C2×C8—21no—
994C2×C8—21no—
995C2×C8—42no—
996C2×C8—221no—
997C2×C8—221no—
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—111no—
1015C22⋊C4—111no—
1016C22⋊C4—111no—
1017C22⋊C4—111no—
1018C22⋊C4—111no—
1019C22⋊C4—111no—
1020C22⋊C4—111no—
1021C22⋊C4—111no—
1022C22⋊C4—221no—
1023C22⋊C4—221no—
1024C22⋊C4—221no—
1025C22⋊C4—221no—
1026C22⋊C4—224no—
1027C22⋊C4—221no—
1028C22⋊C4—221no—
1029C22⋊C4—221no—
1030C22⋊C4—221no—
1031C22⋊C4—221no—
1032C22⋊C4—221no—
1033C22⋊C4—224no—
1034C22⋊C4—221no—
1035C22⋊C4—221no—
1036C22⋊C4—221no—
1037C22⋊C4—221no—
1038C22⋊C4—221no—
1039C42—21no—
1040C42—21no—
1041C42—21no—
1042C42—42no—
1043C42—111no—
1044C42—111no—
1045C42—111no—
1046C42—111no—
1047C42—221no—
1048C42—221no—
1049C42—224no—
1050C42—221no—
1051C42—221no—
1052C42—221no—
1053C42—221no—
1054C42—221no—
1055C42—442no—
1056C42—442no—
1057C42C2×C22⋊D1112yescomplemented
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—
1088Q8C4×C22⋊D1112yescomplemented
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—
1116D4C4×C22⋊D1112yescomplemented
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—22no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—22no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—21no—
1135C2×C4—42no—
1136C2×C4—42no—
1137C2×C4—42no—
1138C2×C4—48no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—111no—
1144C2×C4—111no—
1145C2×C4—111no—
1146C2×C4—111no—
1147C2×C4—111no—
1148C2×C4—111no—
1149C2×C4—222no—
1150C2×C4—221no—
1151C2×C4—221no—
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—222no—
1161C2×C4—222no—
1162C2×C4—221no—
1163C2×C4—221no—
1164C2×C4—221no—
1165C2×C4—442no—
1166C2×C4—442no—
1167C2×C4—448no—
1168C2×C4—442no—
1169C2×C4—441no—
1170C2×C4—442no—
1171C2×C4—441no—
1172C2×C4—441no—
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×#433911yescharacteristic
1182C2×C4C2×D4×D1111yescharacteristic
1183C2×C4#6703711yescharacteristic
1184C2×C4#6703711yescharacteristic
1185C2×C4C22×C22⋊D1111yescharacteristic
1186C8—22no—
1187C8—41no—
1188C8—441no—
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#1062302111yescharacteristic
1221C22D4×C22⋊D1111yescharacteristic
1222C4—24no—
1223C4—21no—
1224C4—21no—
1225C4—22no—
1226C4—42no—
1227C4—41no—
1228C4—112no—
1229C4—221no—
1230C4—221no—
1231C4—221no—
1232C4—221no—
1233C4—221no—
1234C4—442no—
1235C4—442no—
1236C4—441no—
1237C4—441no—
1238C4—441no—
1239C4#1062301711yescharacteristic
1240C4#1062302111yescharacteristic
1241C4C2×C4×C22⋊D1111yescharacteristic
1242C4D4×C22⋊D1111yescharacteristic
1243C2—21no—
1244C2—21no—
1245C2—22no—
1246C2—41no—
1247C2—42no—
1248C2—81no—
1249C2—222no—
1250C2—441no—
1251C2—881no—
1252C2C22⋊C4×C22⋊D1111yescharacteristic
1253C2C2×D11×#10411yescharacteristic
1254C2#1307716011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC22×C11×#104C2
socleC22×C11C22×C22⋊C4
prime radical#41×C22⋊D11C2
cosocleC22×C4×C11C24
hypercenterC22×#104D11
hypocenterC11D4×#104
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×#104

Complements

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

NH ≅ G/Ntype
2. M16×C22⋊D11C2semidirect
3. C2×D11×#104C2semidirect
4. C42×C22⋊D11C2semidirect
5. #13069533C2semidirect
6. #13069442C2semidirect
7. #13069059C2semidirect
8. #13069056C2semidirect
9. #13068918C2semidirect
10. #13068915C2semidirect
11. #13068634C2semidirect
12. #13068560C2semidirect
13. #13068558C2semidirect
14. #104×Dic11C2semidirect
15. C22×C11×#104C2semidirect
18. C22×C11×M16C22semidirect
19. C22×C42×C11C22semidirect
20. #10623365C4semidirect
23. #10623362C4semidirect
25. #10623360C4semidirect
30. #10623355C4semidirect
31. #10623348C4semidirect
32. Q8×C22⋊D11C4semidirect
34. #10623337C4semidirect
36. D4×C22⋊D11C4semidirect
42. C2×M16×D11C22semidirect
43. C2×C42×D11C22semidirect
47. C2×C11×#104C22semidirect
48. C2×C11×#104C22semidirect
51. C2×#66901C22semidirect
52. C2×#66901C22semidirect
54. C4×C22⋊Dic11C22semidirect
55. #10622820C22semidirect
56. C2×#66889C22semidirect
57. C2×#66889C22semidirect
60. #10622739C22semidirect
61. #10622731C22semidirect
62. M16×Dic11C22semidirect
66. C4×(C2×D11)⋊C4C22semidirect
68. C4×Dic11⋊C4C22semidirect
69. C42×Dic11C22semidirect
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
99. C2×#4343C2×C4semidirect
100. C2×Q8×D11C2×C4semidirect
102. C2×#4341C2×C4semidirect
104. C2×D4×D11C2×C4semidirect
128. #67000C2×C4semidirect
131. #66999C2×C4semidirect
132. #66999C2×C4semidirect
133. Q8×Dic11C2×C4semidirect
134. Q8×Dic11C2×C4semidirect
136. #66997C2×C4semidirect
138. #66993C2×C4semidirect
147. #66991C2×C4semidirect
148. #66991C2×C4semidirect
153. #66989C2×C4semidirect
159. D4×Dic11C2×C4semidirect
160. D4×Dic11C2×C4semidirect
163. #66983C2×C4semidirect
164. #66983C2×C4semidirect
194. #66977C2×C4semidirect
195. #66977C2×C4semidirect
217. C11×#104D4semidirect
361. C11×M16C2×D4semidirect
369. C42×C11C2×D4semidirect
435. C22×#104D11semidirect
473. Q8×C11C4×D4semidirect
484. D4×C11C4×D4semidirect
532. C22⋊D11#104direct (N × H)
581. C22×M16C2×D11semidirect
605. C22×C42C2×D11semidirect
623. C2×#104C2×D11semidirect
624. C2×#104C2×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
842. #104C22⋊D11direct (N × H)
992. M16C2×C22⋊D11semidirect
1057. C42C2×C22⋊D11semidirect
1058. C11D4×#104semidirect
1088. Q8C4×C22⋊D11semidirect
1116. D4C4×C22⋊D11semidirect
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
M16×C22⋊D112
C2×D11×#1042
C42×C22⋊D112
#130695332
#130694422
#130690592
#130690562
#130689182
#130689152
#130686342
#130685602
#130685582
#104×Dic112
C22×C11×#1042
D4×#10411