Finite Group Databasebeta

← #14769460

Subgroups — #14769460

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
1D4×#4339C211yesmaximal, characteristic
2D4×#4318C211yesmaximal, characteristic, complemented
3C2×#10622618C211yesmaximal, characteristic, complemented
4C22×#66869C211yesmaximal, characteristic, complemented
5#13069534C211yesmaximal, characteristic, complemented
6#13069448C211yesmaximal, characteristic, complemented
7#13069064C211yesmaximal, characteristic, complemented
8#13069059C211yesmaximal, characteristic, complemented
9#13068916C211yesmaximal, characteristic, complemented
10#13068916C211yesmaximal, characteristic, complemented
11#13068637C211yesmaximal, characteristic, complemented
12#13068561C211yesmaximal, characteristic, complemented
13#13068561C211yesmaximal, characteristic, complemented
14#13068427C211yesmaximal, characteristic, complemented
15C11×#2290C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C22×#4339C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×C11×#117C2211yescharacteristic, complemented
20C22×C42×C11C2211yescharacteristic, complemented
21D4×C22⋊D11—21no—
22#10623322C2211yescharacteristic
23#10623322C2211yescharacteristic
24C22×#4318C2211yescharacteristic, complemented
25C22×#4318C2211yescharacteristic, complemented
26#10623084C411yescharacteristic, complemented
27#10623083C411yescharacteristic, complemented
28#10623083C411yescharacteristic, complemented
29#10623082C411yescharacteristic, complemented
30#10623081C411yescharacteristic, complemented
31#10623081C411yescharacteristic, complemented
32D4×D44C411yescharacteristic, complemented
33#10623079—21no—
34#10623078—21no—
35#10623078—21no—
36C4×D4×D11—21no—
37D4×Dic22C411yescharacteristic, complemented
38#10623038—21no—
39#10623021—21no—
40#10623021—21no—
41#10623008C2211yescharacteristic
42C4×#4339C2211yescharacteristic
43C11×#388—21no—
44C11×#387—21no—
45C11×#386—21no—
46C11×#385—21no—
47C4×C11×C4⋊C4C2211yescharacteristic, complemented
48C4×C11×C22⋊C4C2211yescharacteristic, complemented
49C4×C11×C22⋊C4C2211yescharacteristic, complemented
50C11×#376C2211yescharacteristic, complemented
51#10622820C2211yescharacteristic, complemented
52#10622820C2211yescharacteristic, complemented
53#10622625—21no—
54#10622624—21no—
55#10622624—21no—
56D4×C11⋊C8—21no—
57#10622618—24no—
58C2×#66869—24no—
59C2×#66869C2211yescharacteristic
60C2×#66869C2211yescharacteristic
61C2×#66869C2211yescharacteristic
62C2×#66869C2211yescharacteristic
63C2×#66869C2211yescharacteristic, complemented
64C2×#66869C2211yescharacteristic, complemented
65C2×#66869C2211yescharacteristic, complemented
66C2×#66869C2211yescharacteristic, complemented
67C2×#66869C2211yescharacteristic, complemented
68C2×#66869C2211yescharacteristic, complemented
69C2×#66869C2211yescharacteristic, complemented
70C2×#66869C2211yescharacteristic, complemented
71#10622537C2211yescharacteristic, complemented
72C4×#4318C2211yescharacteristic, complemented
73#10622161C2211yescharacteristic, complemented
74#10622161C2211yescharacteristic, complemented
75#10622161C2211yescharacteristic, complemented
76#10622161C2211yescharacteristic, complemented
77C22×D4×C11D411yescharacteristic
78C23×C4×C11—21no—
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C22×C22⋊D11—21no—
82C22×C22⋊D11—21no—
83C2×D4×D11—21no—
84C2×#4339—21no—
85C2×#4339—21no—
86C2×#4339—21no—
87C2×#4339—21no—
88C2×#4339—22no—
89C2×#4339—22no—
90C2×#4339—22no—
91C2×#4339—22no—
92C2×#4339—41no—
93C2×#4339—41no—
94C2×#4339—41no—
95C2×#4339—41no—
96C2×#4339C2×C411yescharacteristic
97C2×#4339C2×C411yescharacteristic
98C2×#4339C2×C411yescharacteristic, complemented
99C2×#4339C2×C411yescharacteristic, complemented
100C2×#4339C2311yescharacteristic
101C2×#4339C2311yescharacteristic
102C2×#4339C2311yescharacteristic
103C22×D44C2×C411yescharacteristic
104C22×D44C2×C411yescharacteristic, complemented
105C22×C4×D11—21no—
106C22×C4×D11—21no—
107C22×Dic22C2×C411yescharacteristic
108C22×Dic22C2×C411yescharacteristic, complemented
109C4×D4×C11C2×C411yescharacteristic
110C4×D4×C11C2×C411yescharacteristic
111C4×D4×C11C2×C411yescharacteristic
112C4×D4×C11C2×C411yescharacteristic
113C4×D4×C11D411yescharacteristic
114C4×D4×C11D411yescharacteristic
115C4×D4×C11D411yescharacteristic
116C4×D4×C11D411yescharacteristic
117C11×#117—22no—
118C11×#117—41no—
119C2×C11×C4⋊C4—21no—
120C2×C11×C4⋊C4—21no—
121C2×C11×C4⋊C4D411yescharacteristic
122C2×C11×C22⋊C4—21no—
123C2×C11×C22⋊C4—21no—
124C2×C11×C22⋊C4—21no—
125C2×C11×C22⋊C4D411yescharacteristic
126C2×C11×C22⋊C4D411yescharacteristic
127C2×C42×C11—22no—
128C2×C42×C11—21no—
129C2×C42×C11—41no—
130C2×C42×C11C2311yescharacteristic
131C2×C42×C11C2311yescharacteristic
132C2×C42×C11C2311yescharacteristic
133C2×C42×C11C2311yescharacteristic
134C2×C42×C11C2311yescharacteristic
135#67006—21no—
136#67006—21no—
137#66993—21no—
138#66992—21no—
139#66992—21no—
140#66991—21no—
141#66990—21no—
142#66990—21no—
143D4×Dic11—21no—
144#66983—21no—
145#66983—21no—
146#66983C2×C411yescharacteristic
147#66983C2×C411yescharacteristic
148#66983C2×C411yescharacteristic, complemented
149#66983C2×C411yescharacteristic, complemented
150#66982—21no—
151#66982—21no—
152C4×C22⋊D11—21no—
153C4×C22⋊D11—21no—
154C4×C22⋊D11—21no—
155C4×C22⋊D11—21no—
156C4×C22⋊D11—21no—
157C4×C22⋊D11—21no—
158#66979C2311yescharacteristic
159#66977C2×C411yescharacteristic
160#66977C2×C411yescharacteristic
161#66977C2×C411yescharacteristic, complemented
162#66977C2×C411yescharacteristic, complemented
163C2×#4318—21no—
164C2×#4318—21no—
165C2×#4318—22no—
166C2×#4318—22no—
167C2×#4318—41no—
168C2×#4318—41no—
169C2×#4318C2311yescharacteristic
170C2×#4318C2311yescharacteristic
171C2×#4318C2311yescharacteristic
172C2×#4318C2311yescharacteristic
173C22×C11⋊C8—21no—
174C22×C11⋊C8—21no—
175#66949—21no—
176#66949—21no—
177#66948—21no—
178#66947—21no—
179#66947—21no—
180#66946—21no—
181C4⋊C4×D11—21no—
182#66941—21no—
183#66938—21no—
184#66938—21no—
185#66937—21no—
186#66937—21no—
187#66937—21no—
188#66937—21no—
189#66936—21no—
190#66936—21no—
191#66935—21no—
192#66935—21no—
193(C22⋊D11)⋊C4—21no—
194(C22⋊D11)⋊C4—21no—
195C22⋊C4×D11—21no—
196C22⋊C4×D11—21no—
197#66931—21no—
198#66931—21no—
199#66928C2×C411yescharacteristic, complemented
200#66928C2×C411yescharacteristic, complemented
201#66927C2×C411yescharacteristic, complemented
202C4×D44—21no—
203C4×D44—21no—
204C4×D44C2×C411yescharacteristic, complemented
205C4×D44C2×C411yescharacteristic, complemented
206#66925—21no—
207C42×D11—21no—
208#66922C2×C411yescharacteristic, complemented
209C4×Dic22C2×C411yescharacteristic, complemented
210C4×Dic22C2×C411yescharacteristic, complemented
211C11×#95—21no—
212C11×#95—21no—
213C11×#95—21no—
214C11×#95—21no—
215C11×#95—21no—
216C22⋊(C11⋊C8)—21no—
217C22⋊(C11⋊C8)—21no—
218C22⋊(C11⋊C8)—21no—
219C22⋊(C11⋊C8)—21no—
220#66869—22no—
221#66869—22no—
222#66869—22no—
223#66869—22no—
224#66869—22no—
225#66869—22no—
226#66869—22no—
227#66869—41no—
228#66869—41no—
229#66869—41no—
230#66869—41no—
231#66869D414yescomplemented
232C4⋊(C11⋊C8)—21no—
233C4⋊(C11⋊C8)—21no—
234#66867—21no—
235C4×C11⋊C8—21no—
236#22434—111nomaximal, Sylow
237C24×C11C2×D411yescharacteristic
238C24×C11C2×D411yescharacteristic
239C23×D11—21no—
240C23×D11—21no—
241C2×D4×C11—42no—
242C2×D4×C11C22⋊C411yescharacteristic
243C2×D4×C11C22⋊C411yescharacteristic
244C2×D4×C11C22⋊C411yescharacteristic
245C2×D4×C11C22⋊C411yescharacteristic
246C22×C4×C11—21no—
247C22×C4×C11—21no—
248C22×C4×C11—21no—
249C22×C4×C11—21no—
250C22×C4×C11—21no—
251C22×C4×C11—21no—
252C22×C4×C11—21no—
253C22×C4×C11—21no—
254C22×C4×C11—21no—
255C22×C4×C11—21no—
256C22×C4×C11—21no—
257C22×C4×C11—21no—
258C22×C4×C11—42no—
259C22×C4×C11—42no—
260C22×C4×C11—42no—
261C22×C4×C11C22×C411yescharacteristic
262C22×C4×C11C22×C411yescharacteristic
263C22×C4×C11C22×C411yescharacteristic
264C22×C4×C11C22×C411yescharacteristic
265C22×C4×C11C2×D411yescharacteristic
266C22×C4×C11C2×D411yescharacteristic
267C22×C4×C11C2×D411yescharacteristic
268C22×C4×C11C2×D411yescharacteristic
269C22×C4×C11C2×D411yescharacteristic
270C22×C4×C11C2×D411yescharacteristic
271C22×C4×C11C2×D411yescharacteristic
272C22×C4×C11C2×D411yescharacteristic
273C22×C4×C11C2411yescharacteristic
274C2×C22⋊D11—21no—
275C2×C22⋊D11—21no—
276C2×C22⋊D11—21no—
277C2×C22⋊D11—21no—
278C2×C22⋊D11—21no—
279C2×C22⋊D11—21no—
280C2×C22⋊D11—21no—
281C2×C22⋊D11—21no—
282C2×C22⋊D11—21no—
283C2×C22⋊D11—21no—
284C2×C22⋊D11—21no—
285C2×C22⋊D11—42no—
286C2×C22⋊D11—42no—
287C2×C22⋊D11—42no—
288C2×C22⋊D11—42no—
289C22×Dic11—21no—
290C22×Dic11—21no—
291D4×D11—44no—
292#4339—22no—
293#4339—22no—
294#4339—22no—
295#4339—22no—
296#4339—21no—
297#4339—21no—
298#4339—21no—
299#4339—21no—
300#4339—21no—
301#4339—21no—
302#4339—21no—
303#4339—21no—
304#4339—21no—
305#4339—21no—
306#4339—41no—
307#4339—41no—
308#4339—41no—
309#4339—41no—
310#4339—42no—
311#4339—42no—
312#4339—42no—
313#4339—42no—
314#4339—42no—
315#4339—42no—
316#4339—42no—
317#4339—42no—
318#4339C2×D412yes—
319#4339#4112yes—
320C2×D44—22no—
321C2×D44—22no—
322C2×D44—21no—
323C2×D44—21no—
324C2×D44—21no—
325C2×D44—21no—
326C2×D44—41no—
327C2×D44—41no—
328C2×D44C22×C411yescharacteristic
329C2×D44C22×C411yescharacteristic
330C2×D44C22×C411yescharacteristic
331C2×C4×D11—21no—
332C2×C4×D11—21no—
333C2×C4×D11—21no—
334C2×C4×D11—21no—
335C2×C4×D11—21no—
336C2×C4×D11—21no—
337C2×C4×D11—21no—
338C2×C4×D11—21no—
339C2×C4×D11—21no—
340C2×C4×D11—42no—
341C2×C4×D11—42no—
342C2×C4×D11—42no—
343C2×C4×D11—42no—
344C2×Dic22—22no—
345C2×Dic22—22no—
346C2×Dic22—21no—
347C2×Dic22—21no—
348C2×Dic22—41no—
349C2×Dic22—41no—
350C2×Dic22C22×C411yescharacteristic
351C2×Dic22C22×C411yescharacteristic
352C2×Dic22C22×C411yescharacteristic
353C11×C4⋊C4—42no—
354C11×C4⋊C4—42no—
355C11×C4⋊C4C22⋊C411yescharacteristic
356C11×C4⋊C4C22⋊C411yescharacteristic
357C11×C4⋊C4C22⋊C411yescharacteristic
358C11×C4⋊C4C22⋊C411yescharacteristic
359C11×C22⋊C4—42no—
360C11×C22⋊C4—42no—
361C11×C22⋊C4—42no—
362C11×C22⋊C4C22⋊C411yescharacteristic
363C11×C22⋊C4C22⋊C411yescharacteristic
364C11×C22⋊C4C22⋊C411yescharacteristic
365C11×C22⋊C4C22⋊C411yescharacteristic
366C11×C22⋊C4C22⋊C411yescharacteristic
367C11×C22⋊C4C22⋊C411yescharacteristic
368C11×C22⋊C4C22⋊C411yescharacteristic
369C11×C22⋊C4C22⋊C411yescharacteristic
370C42×C11—21no—
371C42×C11—21no—
372C42×C11—21no—
373C42×C11—21no—
374C42×C11—21no—
375C42×C11—21no—
376C42×C11—21no—
377C42×C11—42no—
378C42×C11C22×C411yescharacteristic
379C42×C11C22×C411yescharacteristic
380C42×C11C2×D411yescharacteristic
381C42×C11C2×D411yescharacteristic
382C42×C11C2×D412yescomplemented
383C22⋊Dic11—21no—
384C22⋊Dic11—21no—
385C22⋊Dic11—21no—
386C22⋊Dic11—21no—
387C22⋊Dic11—21no—
388(C2×D11)⋊C4—21no—
389(C2×D11)⋊C4—21no—
390(C2×D11)⋊C4—21no—
391(C2×D11)⋊C4—21no—
392(C2×D11)⋊C4—21no—
393(C2×D11)⋊C4—21no—
394(C2×D11)⋊C4—21no—
395(C2×D11)⋊C4—21no—
396(C2×D11)⋊C4—21no—
397(C2×D11)⋊C4—21no—
398C4⋊Dic11—21no—
399C4⋊Dic11—21no—
400C4⋊Dic11C22×C411yescharacteristic
401C4⋊Dic11C22×C411yescharacteristic
402Dic11⋊C4—21no—
403Dic11⋊C4—21no—
404Dic11⋊C4—21no—
405Dic11⋊C4—21no—
406Dic11⋊C4—21no—
407Dic11⋊C4—21no—
408C4×Dic11—21no—
409C4×Dic11—21no—
410C4×Dic11—21no—
411#4318—21no—
412#4318—21no—
413#4318—21no—
414#4318—21no—
415#4318—21no—
416#4318—21no—
417#4318—21no—
418#4318—42no—
419#4318—42no—
420#4318C2×D412yescomplemented
421C2×C11⋊C8—21no—
422C2×C11⋊C8—21no—
423C2×C11⋊C8—21no—
424C2×C11⋊C8—21no—
425C2×C11⋊C8—42no—
426C2×C11⋊C8—42no—
427D4×#41—111no—
428D4×M16—111no—
429C2×#421—111no—
430C22×#104—111no—
431#2290D1111yescharacteristic, complemented
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—22no—
445C23×C11—21no—
446C23×C11—21no—
447C23×C11—41no—
448C23×C11—41no—
449C23×C11—41no—
450C23×C11C2×C22⋊C411yescharacteristic
451C23×C11C2×C22⋊C411yescharacteristic
452C23×C11C2×C22⋊C411yescharacteristic
453C23×C11C2×C22⋊C411yescharacteristic
454C23×C11C22×D411yescharacteristic
455C22×D11—21no—
456C22×D11—21no—
457C22×D11—21no—
458C22×D11—42no—
459C22×D11—42no—
460C22×D11—42no—
461C22×D11—42no—
462C22×D11—81no—
463C22×D11—81no—
464D4×C11—22no—
465D4×C11—22no—
466D4×C11—41no—
467D4×C11—41no—
468C2×C4×C11—21no—
469C2×C4×C11—21no—
470C2×C4×C11—21no—
471C2×C4×C11—21no—
472C2×C4×C11—21no—
473C2×C4×C11—21no—
474C2×C4×C11—21no—
475C2×C4×C11—21no—
476C2×C4×C11—21no—
477C2×C4×C11—21no—
478C2×C4×C11—21no—
479C2×C4×C11—21no—
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—22no—
489C2×C4×C11—22no—
490C2×C4×C11—41no—
491C2×C4×C11—41no—
492C2×C4×C11—41no—
493C2×C4×C11—41no—
494C2×C4×C11—41no—
495C2×C4×C11—48no—
496C2×C4×C11—41no—
497C2×C4×C11—41no—
498C2×C4×C11—41no—
499C2×C4×C11—41no—
500C2×C4×C11—41no—
501C2×C4×C11—41no—
502C2×C4×C11—41no—
503C2×C4×C11C2×C22⋊C411yescharacteristic
504C2×C4×C11C2×C22⋊C411yescharacteristic
505C2×C4×C11C2×C22⋊C411yescharacteristic
506C2×C4×C11C2×C22⋊C411yescharacteristic
507C2×C4×C11C2×C22⋊C411yescharacteristic
508C2×C4×C11C2×C22⋊C411yescharacteristic
509C2×C4×C11C2×C22⋊C411yescharacteristic
510C2×C4×C11C2×C22⋊C411yescharacteristic
511C2×C4×C11C23×C411yescharacteristic
512C2×C4×C11C22×D411yescharacteristic
513C2×C4×C11C22×D411yescharacteristic
514C2×C4×C11C2×#4111yescharacteristic
515C2×C4×C11H(5,𝔽2)11yescharacteristic
516C2×C4×C11H(5,𝔽2)11yescharacteristic
517C22⋊D11—22no—
518C22⋊D11—22no—
519C22⋊D11—42no—
520C22⋊D11—42no—
521C22⋊D11—42no—
522C22⋊D11—42no—
523C22⋊D11—42no—
524C22⋊D11—41no—
525C22⋊D11—41no—
526C22⋊D11—41no—
527C22⋊D11—41no—
528C22⋊D11—42no—
529C22⋊D11—81no—
530C22⋊D11—81no—
531C2×Dic11—21no—
532C2×Dic11—21no—
533C2×Dic11—21no—
534C2×Dic11—21no—
535C2×Dic11—21no—
536C2×Dic11—42no—
537C2×Dic11—42no—
538D44—21no—
539D44—21no—
540D44—21no—
541D44—21no—
542D44—21no—
543D44—42no—
544D44—42no—
545D44—42no—
546D44—81no—
547D44C4×D412yes—
548C4×D11—22no—
549C4×D11—22no—
550C4×D11—42no—
551C4×D11—42no—
552C4×D11—42no—
553C4×D11—42no—
554C4×D11—42no—
555C4×D11—41no—
556C4×D11—41no—
557C4×D11—41no—
558C4×D11—41no—
559C4×D11—81no—
560Dic22—21no—
561Dic22—21no—
562Dic22—21no—
563Dic22—21no—
564Dic22—21no—
565Dic22—42no—
566Dic22—42no—
567Dic22C4×D412yes—
568C11⋊C8—22no—
569C11⋊C8—41no—
570C11⋊C8—41no—
571C11⋊C8—41no—
572C22×#41—111no—
573C22×#41—111no—
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—221no—
596C2×C4×D4C2×D1111yescharacteristic
597C2×#117C2×D1111yescharacteristic, complemented
598C22×C42C2×D1111yescharacteristic, complemented
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—111no—
614C2×#104—111no—
615C2×#104—111no—
616C2×#104—111no—
617C2×#104—224no—
618#407—111no—
619#407—111no—
620C4×M16—111no—
621#388—21no—
622#387—21no—
623#386—21no—
624#385—21no—
625C4×C4⋊C4C2×D1111yescharacteristic, complemented
626C4×C22⋊C4C2×D1111yescharacteristic, complemented
627C4×C22⋊C4C2×D1111yescharacteristic, complemented
628#376C2×D1111yescharacteristic, complemented
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—21no—
638C22×C11—21no—
639C22×C11—21no—
640C22×C11—21no—
641C22×C11—21no—
642C22×C11—21no—
643C22×C11—21no—
644C22×C11—21no—
645C22×C11—21no—
646C22×C11—42no—
647C22×C11—42no—
648C22×C11—81no—
649C22×C11—81no—
650C22×C11#42112yescomplemented
651C22×C11C22×C22⋊C411yescharacteristic
652C22×C11D4211yescharacteristic
653C22×C11#54611yescharacteristic
654C2×D11—22no—
655C2×D11—41no—
656C2×D11—41no—
657C2×D11—41no—
658C2×D11—41no—
659C2×D11—41no—
660C2×D11—41no—
661C2×D11—41no—
662C2×D11—41no—
663C2×D11—84no—
664C2×D11—84no—
665C4×C11—21no—
666C4×C11—21no—
667C4×C11—21no—
668C4×C11—21no—
669C4×C11—21no—
670C4×C11—21no—
671C4×C11—21no—
672C4×C11—21no—
673C4×C11—42no—
674C4×C11—42no—
675C4×C11—81no—
676C4×C11—81no—
677C4×C11C2×C4×D411yescharacteristic
678C4×C11#51811yescharacteristic
679C4×C11D4211yescharacteristic
680C4×C11#54611yescharacteristic
681Dic11—22no—
682Dic11—41no—
683Dic11—41no—
684Dic11—41no—
685Dic11—41no—
686C2×#41—111no—
687C2×#41—111no—
688C2×#41—111no—
689C2×#41—111no—
690C2×#41—111no—
691C2×#41—111no—
692C2×#41—111no—
693C2×#41—222no—
694C2×#41—222no—
695C2×#41—222no—
696C2×#41—222no—
697C2×#41—221no—
698C2×#41—221no—
699C2×#41—221no—
700C2×#41—221no—
701C2×#41—441no—
702C2×#41—441no—
703C2×#41—441no—
704C2×#41—441no—
705C22×Q8—111no—
706C22×Q8—111no—
707C22×D4—111no—
708C22×D4—111no—
709C22×D4—221no—
710C22×D4—221no—
711C22×D4—221no—
712C22×D4C22⋊D1111yescharacteristic
713C23×C4—21no—
714C23×C4—221no—
715C23×C4—221no—
716C23×C4C22×D1111yescharacteristic
717C23×C4C22×D1111yescharacteristic
718C2×M16—111no—
719C2×M16—111no—
720C2×M16—111no—
721C2×M16—111no—
722C2×M16—221no—
723C2×M16—221no—
724C2×M16—222no—
725C2×M16—222no—
726C2×M16—441no—
727C2×M16—441no—
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—221no—
777C4×D4—221no—
778C4×D4—221no—
779C4×D4—221no—
780C4×D4—221no—
781C4×D4—221no—
782C4×D4—221no—
783C4×D4—221no—
784C4×D4—221no—
785C4×D4—221no—
786C4×D4—221no—
787C4×D4—221no—
788C4×D4C4×D1111yescharacteristic
789C4×D4C4×D1111yescharacteristic
790C4×D4C4×D1111yescharacteristic
791C4×D4C4×D1111yescharacteristic
792C4×D4D4411yescharacteristic
793C4×D4D4411yescharacteristic
794C4×D4D4411yescharacteristic
795C4×D4D4411yescharacteristic
796#117—22no—
797#117—41no—
798#117—111no—
799#117—221no—
800C2×C4⋊C4—21no—
801C2×C4⋊C4—21no—
802C2×C4⋊C4—221no—
803C2×C4⋊C4C22⋊D1111yescharacteristic
804C2×C22⋊C4—21no—
805C2×C22⋊C4—21no—
806C2×C22⋊C4—21no—
807C2×C22⋊C4—221no—
808C2×C22⋊C4—221no—
809C2×C22⋊C4C22⋊D1111yescharacteristic
810C2×C22⋊C4C22⋊D1111yescharacteristic
811C2×C42—22no—
812C2×C42—21no—
813C2×C42—41no—
814C2×C42—221no—
815C2×C42C22×D1111yescharacteristic
816C2×C42C22×D1111yescharacteristic
817C2×C42C22×D1111yescharacteristic
818C2×C42C22×D1111yescharacteristic
819C2×C42C22×D1111yescharacteristic
820C4⋊C8—221no—
821C4⋊C8—221no—
822#104—114no—
823#104—222no—
824#104—222no—
825#104—222no—
826#104—222no—
827#104—222no—
828#104—222no—
829#104—222no—
830#104—441no—
831#104—441no—
832#104—441no—
833#104—441no—
834C22⋊C8—221no—
835C22⋊C8—221no—
836C22⋊C8—221no—
837C22⋊C8—221no—
838#97—221no—
839C4×C8—221no—
840#95—21no—
841#95—21no—
842#95—21no—
843#95—21no—
844#95—21no—
845C2×C11—21no—
846C2×C11—21no—
847C2×C11—22no—
848C2×C11—41no—
849C2×C11—41no—
850C2×C11—41no—
851C2×C11D4×C22⋊C411yescharacteristic
852C2×C11C2×#42111yescharacteristic
853C2×C11#290111yescharacteristic
854D11—42no—
855D11—81no—
856D11—81no—
857C24—221no—
858C24—221no—
859C24C2×C22⋊D1111yescharacteristic
860C24C2×C22⋊D1111yescharacteristic
861#41—112no—
862#41—112no—
863#41—222no—
864#41—222no—
865#41—222no—
866#41—222no—
867#41—221no—
868#41—221no—
869#41—221no—
870#41—221no—
871#41—221no—
872#41—221no—
873#41—221no—
874#41—221no—
875#41—221no—
876#41—221no—
877#41—442no—
878#41—442no—
879#41—442no—
880#41—442no—
881#41—441no—
882#41—441no—
883#41—441no—
884#41—441no—
885#41—442no—
886#41—442no—
887#41—442no—
888#41—442no—
889C2×Q8—111no—
890C2×Q8—111no—
891C2×Q8—111no—
892C2×Q8—222no—
893C2×Q8—222no—
894C2×Q8—221no—
895C2×Q8—221no—
896C2×Q8—441no—
897C2×Q8—441no—
898C2×D4—42no—
899C2×D4—111no—
900C2×D4—111no—
901C2×D4—111no—
902C2×D4—222no—
903C2×D4—222no—
904C2×D4—221no—
905C2×D4—221no—
906C2×D4—221no—
907C2×D4—221no—
908C2×D4—221no—
909C2×D4—221no—
910C2×D4—221no—
911C2×D4—221no—
912C2×D4—221no—
913C2×D4—221no—
914C2×D4—221no—
915C2×D4—221no—
916C2×D4—221no—
917C2×D4—221no—
918C2×D4—221no—
919C2×D4—441no—
920C2×D4—441no—
921C2×D4—444no—
922C2×D4—442no—
923C2×D4—442no—
924C2×D4—442no—
925C2×D4—442no—
926C2×D4(C2×D11)⋊C411yescharacteristic
927C2×D4(C2×D11)⋊C411yescharacteristic
928C2×D4(C2×D11)⋊C411yescharacteristic
929C2×D4(C2×D11)⋊C411yescharacteristic
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—21no—
942C22×C4—42no—
943C22×C4—42no—
944C22×C4—42no—
945C22×C4—221no—
946C22×C4—221no—
947C22×C4—221no—
948C22×C4—221no—
949C22×C4—221no—
950C22×C4—221no—
951C22×C4—221no—
952C22×C4—221no—
953C22×C4—221no—
954C22×C4—221no—
955C22×C4—221no—
956C22×C4—442no—
957C22×C4—442no—
958C22×C4—442no—
959C22×C4—442no—
960C22×C4C2×C4×D1111yescharacteristic
961C22×C4C2×C4×D1111yescharacteristic
962C22×C4C2×C4×D1111yescharacteristic
963C22×C4C2×C4×D1111yescharacteristic
964C22×C4C2×D4411yescharacteristic
965C22×C4C2×D4411yescharacteristic
966C22×C4C2×D4411yescharacteristic
967C22×C4C2×D4411yescharacteristic
968C22×C4C2×C22⋊D1111yescharacteristic
969C22×C4C2×C22⋊D1111yescharacteristic
970C22×C4C2×C22⋊D1111yescharacteristic
971C22×C4C2×C22⋊D1111yescharacteristic
972C22×C4C23×D1111yescharacteristic
973M16—112no—
974M16—221no—
975M16—221no—
976M16—221no—
977M16—221no—
978M16—221no—
979M16—221no—
980M16—221no—
981M16—442no—
982M16—442no—
983C2×C8—221no—
984C2×C8—221no—
985C2×C8—221no—
986C2×C8—221no—
987C2×C8—442no—
988C2×C8—442no—
989C4⋊C4—42no—
990C4⋊C4—42no—
991C4⋊C4—111no—
992C4⋊C4—111no—
993C4⋊C4—221no—
994C4⋊C4—221no—
995C4⋊C4—221no—
996C4⋊C4—221no—
997C4⋊C4—221no—
998C4⋊C4—221no—
999C4⋊C4—221no—
1000C4⋊C4—221no—
1001C4⋊C4(C2×D11)⋊C411yescharacteristic
1002C4⋊C4(C2×D11)⋊C411yescharacteristic
1003C4⋊C4(C2×D11)⋊C411yescharacteristic
1004C4⋊C4(C2×D11)⋊C411yescharacteristic
1005C22⋊C4—42no—
1006C22⋊C4—42no—
1007C22⋊C4—42no—
1008C22⋊C4—221no—
1009C22⋊C4—221no—
1010C22⋊C4—221no—
1011C22⋊C4—221no—
1012C22⋊C4—221no—
1013C22⋊C4—221no—
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(C2×D11)⋊C411yescharacteristic
1024C22⋊C4(C2×D11)⋊C411yescharacteristic
1025C22⋊C4(C2×D11)⋊C411yescharacteristic
1026C22⋊C4(C2×D11)⋊C411yescharacteristic
1027C22⋊C4(C2×D11)⋊C411yescharacteristic
1028C22⋊C4(C2×D11)⋊C411yescharacteristic
1029C22⋊C4(C2×D11)⋊C411yescharacteristic
1030C22⋊C4(C2×D11)⋊C411yescharacteristic
1031C42—21no—
1032C42—21no—
1033C42—21no—
1034C42—21no—
1035C42—21no—
1036C42—21no—
1037C42—21no—
1038C42—42no—
1039C42—221no—
1040C42—221no—
1041C42—221no—
1042C42C2×C4×D1111yescharacteristic
1043C42C2×C4×D1111yescharacteristic
1044C42C2×D4411yescharacteristic
1045C42C2×D4411yescharacteristic
1046C42D4×D1112yescomplemented
1047C11#2243411yescharacteristic, complemented, Sylow
1048C23—21no—
1049C23—21no—
1050C23—22no—
1051C23—21no—
1052C23—21no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—221no—
1057C23—221no—
1058C23—221no—
1059C23—442no—
1060C23—442no—
1061C23—442no—
1062C23—442no—
1063C23—881no—
1064C23—881no—
1065C23C2×(C2×D11)⋊C411yescharacteristic
1066C23C2×(C2×D11)⋊C411yescharacteristic
1067C23C2×(C2×D11)⋊C411yescharacteristic
1068C23C2×(C2×D11)⋊C411yescharacteristic
1069C23C22×C22⋊D1111yescharacteristic
1070Q8—112no—
1071Q8—221no—
1072Q8—221no—
1073Q8—221no—
1074Q8—221no—
1075Q8—221no—
1076Q8—442no—
1077Q8—442no—
1078D4—22no—
1079D4—22no—
1080D4—41no—
1081D4—41no—
1082D4—112no—
1083D4—222no—
1084D4—222no—
1085D4—221no—
1086D4—221no—
1087D4—221no—
1088D4—221no—
1089D4—221no—
1090D4—442no—
1091D4—442no—
1092D4—442no—
1093D4—442no—
1094D4—442no—
1095D4—442no—
1096D4—442no—
1097D4—442no—
1098D4—441no—
1099D4—441no—
1100D4—441no—
1101D4—441no—
1102D4—442no—
1103D4—881no—
1104D4—881no—
1105D4—881no—
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—21no—
1116C2×C4—21no—
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—22no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—48no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—221no—
1142C2×C4—222no—
1143C2×C4—222no—
1144C2×C4—221no—
1145C2×C4—221no—
1146C2×C4—221no—
1147C2×C4—221no—
1148C2×C4—442no—
1149C2×C4—442no—
1150C2×C4—442no—
1151C2×C4—442no—
1152C2×C4—442no—
1153C2×C4—442no—
1154C2×C4—442no—
1155C2×C4—441no—
1156C2×C4—441no—
1157C2×C4—441no—
1158C2×C4—441no—
1159C2×C4—881no—
1160C2×C4C2×(C2×D11)⋊C411yescharacteristic
1161C2×C4C2×(C2×D11)⋊C411yescharacteristic
1162C2×C4C2×(C2×D11)⋊C411yescharacteristic
1163C2×C4C2×(C2×D11)⋊C411yescharacteristic
1164C2×C4C2×(C2×D11)⋊C411yescharacteristic
1165C2×C4C2×(C2×D11)⋊C411yescharacteristic
1166C2×C4C2×(C2×D11)⋊C411yescharacteristic
1167C2×C4C2×(C2×D11)⋊C411yescharacteristic
1168C2×C4C22×C4×D1111yescharacteristic
1169C2×C4C22×D4411yescharacteristic
1170C2×C4C2×D4×D1111yescharacteristic
1171C2×C4#6703711yescharacteristic
1172C2×C4#41×D1111yescharacteristic
1173C2×C4#6704211yescharacteristic
1174C8—222no—
1175C8—441no—
1176C8—441no—
1177C8—441no—
1178C22—21no—
1179C22—21no—
1180C22—21no—
1181C22—21no—
1182C22—21no—
1183C22—21no—
1184C22—21no—
1185C22—21no—
1186C22—21no—
1187C22—21no—
1188C22—21no—
1189C22—21no—
1190C22—21no—
1191C22—42no—
1192C22—42no—
1193C22—81no—
1194C22—81no—
1195C22—222no—
1196C22—441no—
1197C22—441no—
1198C22—441no—
1199C22—441no—
1200C22—441no—
1201C22—441no—
1202C22—441no—
1203C22—441no—
1204C22—884no—
1205C22—884no—
1206C22#1062261812yescomplemented
1207C22C22×(C2×D11)⋊C411yescharacteristic
1208C22D4×C22⋊D1111yescharacteristic
1209C22#1062336011yescharacteristic
1210C4—21no—
1211C4—21no—
1212C4—21no—
1213C4—21no—
1214C4—21no—
1215C4—21no—
1216C4—21no—
1217C4—21no—
1218C4—42no—
1219C4—42no—
1220C4—81no—
1221C4—81no—
1222C4—222no—
1223C4—441no—
1224C4—441no—
1225C4—441no—
1226C4—441no—
1227C4C4×D4×D1111yescharacteristic
1228C4#1062307611yescharacteristic
1229C4D4×D4411yescharacteristic
1230C4#1062308511yescharacteristic
1231C2—21no—
1232C2—21no—
1233C2—22no—
1234C2—41no—
1235C2—41no—
1236C2—41no—
1237C2—442no—
1238C2—881no—
1239C2—881no—
1240C2D4×(C2×D11)⋊C411yescharacteristic
1241C2C2×#1062261811yescharacteristic
1242C2#1307716411yescharacteristic
subgroupG/H
centerC2×C4C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2290C2
socleC22×C11C22×C22⋊C4
prime radicalD4×#4339C2
cosocleC22×C4×C11C24
hypercenter#2290D11
hypocenterC11#22434
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C4×D4 ◁ #2290

Complements

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

NH ≅ G/Ntype
2. D4×#4318C2semidirect
3. C2×#10622618C2semidirect
4. C22×#66869C2semidirect
5. #13069534C2semidirect
6. #13069448C2semidirect
7. #13069064C2semidirect
8. #13069059C2semidirect
9. #13068916C2semidirect
10. #13068916C2semidirect
11. #13068637C2semidirect
12. #13068561C2semidirect
13. #13068561C2semidirect
14. #13068427C2semidirect
15. C11×#2290C2semidirect
19. C2×C11×#117C22semidirect
20. C22×C42×C11C22semidirect
24. C22×#4318C22semidirect
25. C22×#4318C22semidirect
26. #10623084C4semidirect
27. #10623083C4semidirect
28. #10623083C4semidirect
29. #10623082C4semidirect
30. #10623081C4semidirect
31. #10623081C4semidirect
32. D4×D44C4semidirect
37. D4×Dic22C4semidirect
47. C4×C11×C4⋊C4C22semidirect
48. C4×C11×C22⋊C4C22semidirect
49. C4×C11×C22⋊C4C22semidirect
50. C11×#376C22semidirect
51. #10622820C22semidirect
52. #10622820C22semidirect
63. C2×#66869C22semidirect
64. C2×#66869C22semidirect
65. C2×#66869C22semidirect
66. C2×#66869C22semidirect
67. C2×#66869C22semidirect
68. C2×#66869C22semidirect
69. C2×#66869C22semidirect
70. C2×#66869C22semidirect
71. #10622537C22semidirect
72. C4×#4318C22semidirect
73. #10622161C22semidirect
74. #10622161C22semidirect
75. #10622161C22semidirect
76. #10622161C22semidirect
98. C2×#4339C2×C4semidirect
99. C2×#4339C2×C4semidirect
104. C22×D44C2×C4semidirect
108. C22×Dic22C2×C4semidirect
148. #66983C2×C4semidirect
149. #66983C2×C4semidirect
161. #66977C2×C4semidirect
162. #66977C2×C4semidirect
199. #66928C2×C4semidirect
200. #66928C2×C4semidirect
201. #66927C2×C4semidirect
204. C4×D44C2×C4semidirect
205. C4×D44C2×C4semidirect
208. #66922C2×C4semidirect
209. C4×Dic22C2×C4semidirect
210. C4×Dic22C2×C4semidirect
231. #66869D4semidirect
382. C42×C11C2×D4semidirect
420. #4318C2×D4semidirect
431. #2290D11semidirect
597. C2×#117C2×D11semidirect
598. C22×C42C2×D11semidirect
625. C4×C4⋊C4C2×D11semidirect
626. C4×C22⋊C4C2×D11semidirect
627. C4×C22⋊C4C2×D11semidirect
628. #376C2×D11semidirect
650. C22×C11#421semidirect
1046. C42D4×D11semidirect
1047. C11#22434semidirect
1206. C22#10622618semidirect

Maximal subgroups

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

subgroupindex
D4×#43392
D4×#43182
C2×#106226182
C22×#668692
#130695342
#130694482
#130690642
#130690592
#130689162
#130686372
#130685612
#130684272
C11×#22902
#2243411