Finite Group Databasebeta

← #14769445

Subgroups — #14769445

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#13082099C211yesmaximal, characteristic
2M16×C22⋊D11C211yesmaximal, characteristic, complemented
3C22×#66889C211yesmaximal, characteristic, complemented
4C2×D11×#104C211yesmaximal, characteristic, complemented
5C4×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
6#13069533C211yesmaximal, characteristic, complemented
7#13069442C211yesmaximal, characteristic, complemented
8#13069060C211yesmaximal, characteristic, complemented
9#13069058C211yesmaximal, characteristic, complemented
10#13068917C211yesmaximal, characteristic, complemented
11#13068635C211yesmaximal, characteristic, complemented
12#13068561C211yesmaximal, characteristic, complemented
13#13068558C211yesmaximal, characteristic, complemented
14#13068420C211yesmaximal, characteristic, complemented
15C11×#1871C211yesmaximal, characteristic, complemented
16C2×#41×D11C2211yescharacteristic
17C22×#4339C2211yescharacteristic
18C22×C11×M16C2211yescharacteristic, complemented
19C11×#525C2211yescharacteristic
20#10623363C2211yescharacteristic
21C2×C4×C22⋊D11C2211yescharacteristic
22C22×C4×Dic11C2211yescharacteristic, complemented
23C2×M16×D11C2211yescharacteristic, complemented
24#10623186—21no—
25#10623185—21no—
26#10623164C411yescharacteristic, complemented
27#10623163C411yescharacteristic, complemented
28#10623162C411yescharacteristic, complemented
29#10623161C411yescharacteristic, complemented
30#10623143C411yescharacteristic, complemented
31#10623140C411yescharacteristic, complemented
32#10623130C411yescharacteristic, complemented
33#10623129C411yescharacteristic, complemented
34#10623122—21no—
35#10623121—21no—
36#10623079—21no—
37#10623078—21no—
38#10623078—21no—
39C4×D4×D11—21no—
40#10623055C2211yescharacteristic
41#10623053C2211yescharacteristic
42C2×(C22⋊D11)⋊C4—21no—
43C2×C42×D11C2211yescharacteristic, complemented
44C2×C11×#104C2211yescharacteristic, complemented
45C2×C11×#104C2211yescharacteristic, complemented
46C4×C11×C22⋊C4C2211yescharacteristic, complemented
47C2×#66901C2211yescharacteristic, complemented
48C2×#66901C2211yescharacteristic, complemented
49#10622820C2211yescharacteristic, complemented
50C2×#66889—24no—
51C2×#66889C2211yescharacteristic
52C2×#66889C2211yescharacteristic
53C2×#66889C2211yescharacteristic, complemented
54C2×#66889C2211yescharacteristic, complemented
55#10622741—21no—
56#10622740—21no—
57#10622739C2211yescharacteristic, complemented
58#10622731C2211yescharacteristic, complemented
59M16×Dic11C2211yescharacteristic, complemented
60#10622724—21no—
61C8×C22⋊D11—21no—
62C22⋊C4×Dic11—21no—
63C4×(C2×D11)⋊C4C2211yescharacteristic, complemented
64C4×Dic11⋊C4C2211yescharacteristic, complemented
65C42×Dic11C2211yescharacteristic, complemented
66C2×#66869C2211yescharacteristic
67C2×#66869C2211yescharacteristic
68C2×#66869C2211yescharacteristic, complemented
69C2×#66869C2211yescharacteristic, complemented
70D11×#104—24no—
71#10622279—21no—
72#10622262—21no—
73C11×#339C2211yescharacteristic, complemented
74C11×#339C2211yescharacteristic, complemented
75#10622170C2211yescharacteristic, complemented
76#10622170C2211yescharacteristic, complemented
77C2×C11×#41C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C22×C22⋊D11—21no—
80C22×C22⋊D11D411yescharacteristic
81C23×Dic11—21no—
82#41×D11—22no—
83#41×D11—22no—
84#41×D11—41no—
85#41×D11—41no—
86C2×#4343C2×C411yescharacteristic, complemented
87C2×Q8×D11C2×C411yescharacteristic, complemented
88C2×#4341—21no—
89C2×#4341C2×C411yescharacteristic, complemented
90C2×D4×D11—21no—
91C2×D4×D11—21no—
92C2×D4×D11C2×C411yescharacteristic, complemented
93C2×#4339—21no—
94C2×#4339—21no—
95C2×#4339—21no—
96C2×#4339—22no—
97C2×#4339—22no—
98C2×#4339—41no—
99C2×#4339—41no—
100C2×#4339C2×C411yescharacteristic, complemented
101C2×#4339C2×C411yescharacteristic, complemented
102C2×#4339C2311yescharacteristic
103C2×#4339C2311yescharacteristic
104C22×D44C2×C411yescharacteristic, complemented
105C22×C4×D11—21no—
106C22×C4×D11—21no—
107C22×C4×D11—21no—
108C22×C4×D11C2311yescharacteristic
109C22×Dic22C2×C411yescharacteristic, complemented
110C2×C11×M16—21no—
111C2×C11×M16—22no—
112C2×C11×M16—41no—
113C2×C11×M16C2311yescharacteristic
114C2×C11×M16C2311yescharacteristic
115C22×C8×C11—21no—
116C11×#123—21no—
117C11×C22⋊Q8C2×C411yescharacteristic, complemented
118C11×C22⋊Q8C2×C411yescharacteristic, complemented
119C11×#121C2×C411yescharacteristic, complemented
120C11×#121C2×C411yescharacteristic, complemented
121C11×#120—21no—
122C4×D4×C11—21no—
123C4×D4×C11—21no—
124C11×#117C2311yescharacteristic
125C2×C11×C22⋊C4—21no—
126C2×C42×C11C2311yescharacteristic
127C2×C42×C11C2311yescharacteristic
128C2×C22⋊Dic11D411yescharacteristic
129#67000C2×C411yescharacteristic, complemented
130#66997C2×C411yescharacteristic, complemented
131#66993—21no—
132#66993C2×C411yescharacteristic, complemented
133#66992—21no—
134#66992—21no—
135#66992—21no—
136#66992—21no—
137#66991—21no—
138#66990—21no—
139#66990—21no—
140#66989C2×C411yescharacteristic, complemented
141D4×Dic11—21no—
142C4×C22⋊D11—21no—
143C4×C22⋊D11—21no—
144C4×C22⋊D11C2×C411yescharacteristic
145C4×C22⋊D11C2×C411yescharacteristic
146C4×C22⋊D11C2×C411yescharacteristic
147C4×C22⋊D11C2×C411yescharacteristic
148C4×C22⋊D11D411yescharacteristic
149C4×C22⋊D11D411yescharacteristic
150C4×C22⋊D11D411yescharacteristic
151C4×C22⋊D11D411yescharacteristic
152C2×(C2×D11)⋊C4—21no—
153C2×(C2×D11)⋊C4D411yescharacteristic
154C2×Dic11⋊C4—21no—
155C2×Dic11⋊C4D411yescharacteristic
156C2×C4×Dic11—21no—
157C2×C4×Dic11—22no—
158C2×C4×Dic11—21no—
159C2×C4×Dic11—21no—
160C2×C4×Dic11—21no—
161C2×C4×Dic11—41no—
162C2×C4×Dic11C2311yescharacteristic
163C2×C4×Dic11C2311yescharacteristic
164C2×C4×Dic11C2311yescharacteristic
165C2×#4318C2311yescharacteristic
166C2×#4318C2311yescharacteristic
167M16×D11—22no—
168M16×D11—41no—
169C2×#4313—21no—
170C2×C8×D11—21no—
171#66950C2×C411yescharacteristic, complemented
172#66950C2×C411yescharacteristic, complemented
173#66949—21no—
174#66949—21no—
175#66948—21no—
176#66948C2×C411yescharacteristic, complemented
177#66948C2×C411yescharacteristic, complemented
178#66947—21no—
179#66947—21no—
180#66946—21no—
181#66946C2×C411yescharacteristic, complemented
182#66946C2×C411yescharacteristic, complemented
183C4⋊C4×D11—21no—
184#66941—21no—
185#66940C2×C411yescharacteristic, complemented
186#66940C2×C411yescharacteristic, complemented
187#66939—21no—
188#66938—21no—
189#66938—21no—
190#66937—21no—
191#66937—21no—
192#66937—21no—
193#66937—21no—
194#66936—21no—
195#66936—21no—
196#66935—21no—
197#66935—21no—
198#66935—21no—
199(C22⋊D11)⋊C4—28no—
200(C22⋊D11)⋊C4—21no—
201(C22⋊D11)⋊C4—21no—
202(C22⋊D11)⋊C4—21no—
203(C22⋊D11)⋊C4—21no—
204C22⋊C4×D11—21no—
205C22⋊C4×D11—21no—
206#66931—21no—
207#66931—21no—
208C4×D44—21no—
209C4×D44—21no—
210#66925—21no—
211C42×D11—21no—
212C42×D11—22no—
213C42×D11—41no—
214C11×#104—22no—
215C11×#104—41no—
216C11×#95—21no—
217#66901—22no—
218#66901—41no—
219C11⋊#95—21no—
220C11⋊#95—21no—
221C22⋊(C11⋊C8)—21no—
222C22⋊(C11⋊C8)—21no—
223#66889—22no—
224#66889—22no—
225#66889—22no—
226#66889D414yescomplemented
227(C2×D11)⋊C8—21no—
228(C2×D11)⋊C8—21no—
229#66879—21no—
230Dic11⋊C8—21no—
231Dic11⋊C8—21no—
232C8×Dic11—21no—
233#66869—22no—
234#66869—22no—
235#66869—41no—
236#66869—41no—
237D4×#104—111nomaximal, Sylow
238C24×C11C2×D411yescharacteristic
239C23×D11—21no—
240C23×D11—21no—
241C23×D11C2×D411yescharacteristic
242C11×#41—21no—
243C11×#41—21no—
244C11×#41—21no—
245C11×#41—21no—
246C2×Q8×C11C22×C411yescharacteristic
247C2×D4×C11—21no—
248C2×D4×C11—21no—
249C2×D4×C11—21no—
250C2×D4×C11C22×C411yescharacteristic
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×C11C22×C411yescharacteristic
259C22×C4×C11C22×C411yescharacteristic
260C22×C4×C11C2×D411yescharacteristic
261C22×C4×C11C2×D411yescharacteristic
262C22×C4×C11C2×D411yescharacteristic
263C22×C4×C11C2411yescharacteristic
264C2×C22⋊D11—24no—
265C2×C22⋊D11—21no—
266C2×C22⋊D11—21no—
267C2×C22⋊D11—21no—
268C2×C22⋊D11—21no—
269C2×C22⋊D11—21no—
270C2×C22⋊D11—21no—
271C2×C22⋊D11—21no—
272C2×C22⋊D11—21no—
273C2×C22⋊D11—42no—
274C2×C22⋊D11—42no—
275C2×C22⋊D11C22⋊C411yescharacteristic
276C2×C22⋊D11C22⋊C411yescharacteristic
277C2×C22⋊D11C22⋊C411yescharacteristic
278C2×C22⋊D11C22⋊C411yescharacteristic
279C22×Dic11—24no—
280C22×Dic11—21no—
281C22×Dic11—21no—
282C22×Dic11—21no—
283C22×Dic11—21no—
284C22×Dic11—42no—
285C22×Dic11—42no—
286C22×Dic11C2×D411yescharacteristic
287C22×Dic11C2×D411yescharacteristic
288C22×Dic11C2×D411yescharacteristic
289#4343—22no—
290#4343—41no—
291Q8×D11—22no—
292Q8×D11—41no—
293#4341—22no—
294#4341—41no—
295#4341—42no—
296#4341—42no—
297D4×D11—22no—
298D4×D11—41no—
299D4×D11—42no—
300D4×D11—42no—
301D4×D11—44no—
302#4339—22no—
303#4339—22no—
304#4339—21no—
305#4339—21no—
306#4339—21no—
307#4339—21no—
308#4339—21no—
309#4339—21no—
310#4339—41no—
311#4339—41no—
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—21no—
321C2×D44—21no—
322C2×D44—21no—
323C2×D44—22no—
324C2×D44—21no—
325C2×D44—41no—
326C2×D44C22×C411yescharacteristic
327C2×D44C22×C411yescharacteristic
328C2×C4×D11—24no—
329C2×C4×D11—21no—
330C2×C4×D11—21no—
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—21no—
341C2×C4×D11—42no—
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—22no—
352C2×Dic22—21no—
353C2×Dic22—21no—
354C2×Dic22—41no—
355C2×Dic22C22×C411yescharacteristic
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—
365C11×C4⋊C4—21no—
366C11×C4⋊C4—21no—
367C11×C4⋊C4C22×C411yescharacteristic
368C11×C4⋊C4C22×C411yescharacteristic
369C11×C22⋊C4—24no—
370C11×C22⋊C4—21no—
371C11×C22⋊C4—21no—
372C11×C22⋊C4—21no—
373C11×C22⋊C4—21no—
374C11×C22⋊C4—21no—
375C42×C11—21no—
376C42×C11—21no—
377C42×C11—21no—
378C42×C11—21no—
379C42×C11—21no—
380C22⋊Dic11—21no—
381C22⋊Dic11—21no—
382C22⋊Dic11C22⋊C411yescharacteristic
383C22⋊Dic11C22⋊C411yescharacteristic
384C22⋊Dic11C22⋊C411yescharacteristic
385C22⋊Dic11C22⋊C411yescharacteristic
386(C2×D11)⋊C4—24no—
387(C2×D11)⋊C4—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)⋊C4C22⋊C411yescharacteristic
396(C2×D11)⋊C4C22⋊C411yescharacteristic
397(C2×D11)⋊C4C22⋊C411yescharacteristic
398(C2×D11)⋊C4C22⋊C411yescharacteristic
399C4⋊Dic11—21no—
400C4⋊Dic11—21no—
401Dic11⋊C4—24no—
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—42no—
417C4×Dic11—42no—
418C4×Dic11—42no—
419C4×Dic11C22×C411yescharacteristic
420C4×Dic11C22×C411yescharacteristic
421C4×Dic11C2×D411yescharacteristic
422C4×Dic11C2×D411yescharacteristic
423C4×Dic11C2×D412yescomplemented
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×#104—111no—
436C42×D4—111no—
437#1980—111no—
438#1962—111no—
439#1896—111no—
440#1896—111no—
441#1871—111no—
442#1871D1111yescharacteristic, complemented
443#1806—111no—
444#1789—111no—
445#1789—111no—
446C4×#104—111no—
447C23×C11—21no—
448C23×C11—21no—
449C23×C11—22no—
450C23×C11—21no—
451C23×C11—41no—
452C23×C11C2×C22⋊C411yescharacteristic
453C23×C11C2×C22⋊C411yescharacteristic
454C23×C11C22×D411yescharacteristic
455C22×D11—21no—
456C22×D11—21no—
457C22×D11—21no—
458C22×D11—22no—
459C22×D11—21no—
460C22×D11—41no—
461C22×D11—42no—
462C22×D11—42no—
463C22×D11—42no—
464C22×D11—42no—
465C22×D11—81no—
466C22×D11—81no—
467C22×D11C2×C22⋊C411yescharacteristic
468C22×D11C2×C22⋊C411yescharacteristic
469Q8×C11—21no—
470Q8×C11—21no—
471D4×C11—21no—
472D4×C11—21no—
473D4×C11—41no—
474D4×C11—41no—
475D4×C11—42no—
476D4×C11—81no—
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—22no—
488C2×C4×C11—22no—
489C2×C4×C11—21no—
490C2×C4×C11—21no—
491C2×C4×C11—21no—
492C2×C4×C11—41no—
493C2×C4×C11—41no—
494C2×C4×C11—41no—
495C2×C4×C11—41no—
496C2×C4×C11—41no—
497C2×C4×C11—41no—
498C2×C4×C11C2×C22⋊C411yescharacteristic
499C2×C4×C11C2×C22⋊C411yescharacteristic
500C2×C4×C11C23×C411yescharacteristic
501C2×C4×C11C22×D411yescharacteristic
502C2×C4×C11C22×D411yescharacteristic
503C2×C4×C11C2×#4111yescharacteristic
504C2×C4×C11H(5,𝔽2)11yescharacteristic
505C2×C4×C11H(5,𝔽2)11yescharacteristic
506C22⋊D11—22no—
507C22⋊D11—22no—
508C22⋊D11—22no—
509C22⋊D11—22no—
510C22⋊D11—22no—
511C22⋊D11—42no—
512C22⋊D11—42no—
513C22⋊D11—42no—
514C22⋊D11—42no—
515C22⋊D11—41no—
516C22⋊D11—41no—
517C22⋊D11—42no—
518C22⋊D11—81no—
519C22⋊D11#10414yescomplemented
520C2×Dic11—22no—
521C2×Dic11—22no—
522C2×Dic11—21no—
523C2×Dic11—22no—
524C2×Dic11—21no—
525C2×Dic11—21no—
526C2×Dic11—22no—
527C2×Dic11—22no—
528C2×Dic11—21no—
529C2×Dic11—41no—
530C2×Dic11—42no—
531C2×Dic11—42no—
532C2×Dic11—48no—
533C2×Dic11—41no—
534C2×Dic11—41no—
535C2×Dic11C2×C22⋊C411yescharacteristic
536C2×Dic11C2×C22⋊C411yescharacteristic
537C2×Dic11C2×C22⋊C411yescharacteristic
538C2×Dic11C2×C22⋊C411yescharacteristic
539C2×Dic11C2×C22⋊C411yescharacteristic
540C2×Dic11C2×C22⋊C411yescharacteristic
541D44—21no—
542D44—21no—
543D44—21no—
544D44—42no—
545D44—42no—
546D44—42no—
547D44—81no—
548D44C4×D412yescomplemented
549C4×D11—21no—
550C4×D11—21no—
551C4×D11—21no—
552C4×D11—21no—
553C4×D11—21no—
554C4×D11—21no—
555C4×D11—22no—
556C4×D11—21no—
557C4×D11—21no—
558C4×D11—22no—
559C4×D11—42no—
560C4×D11—42no—
561C4×D11—42no—
562C4×D11—48no—
563C4×D11—42no—
564C4×D11—41no—
565C4×D11—41no—
566C4×D11—42no—
567C4×D11—81no—
568Dic22—21no—
569Dic22—21no—
570Dic22—21no—
571Dic22—42no—
572Dic22—42no—
573Dic22C4×D412yescomplemented
574C8×C11—22no—
575C8×C11—41no—
576C11⋊C8—41no—
577C11⋊C8—41no—
578C22×#41—111no—
579C22×#41—111no—
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—221no—
598#525—221no—
599#525C2×D1111yescharacteristic
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—111no—
620C2×#104—111no—
621C2×#104—224no—
622C2×#104—224no—
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—221no—
632C4×C22⋊C4—221no—
633C4×C22⋊C4C2×D1111yescharacteristic, complemented
634C43—111no—
635#339—111no—
636#339—111no—
637#339C2×D1111yescharacteristic, complemented
638#339C2×D1111yescharacteristic, complemented
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—41no—
649C22×C11—41no—
650C22×C11—41no—
651C22×C11C2×#10412yescomplemented
652C22×C11C22×C22⋊C411yescharacteristic
653C22×C11D4211yescharacteristic
654C22×C11#54611yescharacteristic
655C2×D11—21no—
656C2×D11—21no—
657C2×D11—21no—
658C2×D11—22no—
659C2×D11—21no—
660C2×D11—21no—
661C2×D11—42no—
662C2×D11—42no—
663C2×D11—41no—
664C2×D11—41no—
665C2×D11—41no—
666C2×D11—41no—
667C2×D11—41no—
668C2×D11—84no—
669C2×D11—84no—
670C2×D11C2×#10412yescomplemented
671C4×C11—21no—
672C4×C11—21no—
673C4×C11—42no—
674C4×C11—42no—
675C4×C11—41no—
676C4×C11—41no—
677C4×C11—41no—
678C4×C11C2×C4×D411yescharacteristic
679C4×C11#51811yescharacteristic
680C4×C11D4211yescharacteristic
681C4×C11#54611yescharacteristic
682Dic11—24no—
683Dic11—22no—
684Dic11—21no—
685Dic11—21no—
686Dic11—21no—
687Dic11—21no—
688Dic11—21no—
689Dic11—42no—
690Dic11—41no—
691Dic11C2×#10412yescomplemented
692C2×#41—111no—
693C2×#41—111no—
694C2×#41—111no—
695C2×#41—111no—
696C2×#41—111no—
697C2×#41—111no—
698C2×#41—221no—
699C2×#41—222no—
700C2×#41—222no—
701C2×#41—221no—
702C2×#41—221no—
703C2×#41—221no—
704C2×#41—222no—
705C2×#41—222no—
706C2×#41—441no—
707C2×#41—441no—
708C2×#41—441no—
709C2×#41—441no—
710C2×#41C22×D1111yescharacteristic
711C22×Q8—111no—
712C22×Q8—111no—
713C22×D4—111no—
714C22×D4—111no—
715C22×D4—111no—
716C22×D4—221no—
717C22×D4—221no—
718C22×D4—221no—
719C23×C4—111no—
720C23×C4—221no—
721C23×C4—221no—
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—21no—
746#123—221no—
747#123—221no—
748#123—221no—
749#123—221no—
750#123—221no—
751C22⋊Q8—111no—
752C22⋊Q8—111no—
753C22⋊Q8—221no—
754C22⋊Q8—221no—
755C22⋊Q8—221no—
756C22⋊Q8—221no—
757C22⋊Q8C4×D1111yescharacteristic, complemented
758C22⋊Q8C4×D1111yescharacteristic, complemented
759#121—111no—
760#121—111no—
761#121—221no—
762#121—221no—
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#121C4×D1111yescharacteristic, complemented
772#121C4×D1111yescharacteristic, complemented
773#120—21no—
774#120—221no—
775#120—221no—
776#120—221no—
777#120—221no—
778#120—221no—
779C4×Q8—111no—
780C4×Q8—111no—
781C4×D4—21no—
782C4×D4—21no—
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—111no—
792C4×D4—111no—
793C4×D4—221no—
794C4×D4—221no—
795C4×D4—221no—
796C4×D4—221no—
797C4×D4—221no—
798C4×D4—221no—
799C4×D4—221no—
800C4×D4—221no—
801C4×D4—228no—
802C4×D4—221no—
803C4×D4—221no—
804#117—221no—
805#117C22×D1111yescharacteristic
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—221no—
819C2×C42—222no—
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—41no—
833#104—114no—
834#104—222no—
835#104—222no—
836#104—222no—
837#104—222no—
838#104—222no—
839#104—222no—
840#104—441no—
841#104—441no—
842#104—441no—
843C22⋊C8—221no—
844C22⋊C8—221no—
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—41no—
856C2×C11—81no—
857C2×C11D4×C22⋊C411yescharacteristic
858C2×C11C22×#10411yescharacteristic
859C2×C11#290111yescharacteristic
860D11—22no—
861D11—41no—
862D11—42no—
863D11—81no—
864C24—111no—
865C24—221no—
866C24—221no—
867C24D4×D1111yescharacteristic
868#41—21no—
869#41—21no—
870#41—21no—
871#41—21no—
872#41—112no—
873#41—112no—
874#41—222no—
875#41—222no—
876#41—221no—
877#41—221no—
878#41—222no—
879#41—222no—
880#41—221no—
881#41—221no—
882#41—221no—
883#41—221no—
884#41—442no—
885#41—442no—
886#41—441no—
887#41—441no—
888#41—442no—
889#41—442no—
890#41—442no—
891#41—442no—
892#41—441no—
893#41—442no—
894#41—442no—
895#41—441no—
896C2×Q8—111no—
897C2×Q8—111no—
898C2×Q8—221no—
899C2×Q8—222no—
900C2×Q8—221no—
901C2×Q8—222no—
902C2×Q8—441no—
903C2×Q8—441no—
904C2×Q8C2×C4×D1111yescharacteristic
905C2×D4—21no—
906C2×D4—21no—
907C2×D4—21no—
908C2×D4—111no—
909C2×D4—111no—
910C2×D4—111no—
911C2×D4—111no—
912C2×D4—111no—
913C2×D4—111no—
914C2×D4—222no—
915C2×D4—221no—
916C2×D4—221no—
917C2×D4—221no—
918C2×D4—221no—
919C2×D4—221no—
920C2×D4—221no—
921C2×D4—222no—
922C2×D4—224no—
923C2×D4—221no—
924C2×D4—221no—
925C2×D4—221no—
926C2×D4—221no—
927C2×D4—221no—
928C2×D4—221no—
929C2×D4—441no—
930C2×D4—441no—
931C2×D4—444no—
932C2×D4—442no—
933C2×D4—442no—
934C2×D4—442no—
935C2×D4—442no—
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—111no—
945C22×C4—111no—
946C22×C4—111no—
947C22×C4—111no—
948C22×C4—111no—
949C22×C4—111no—
950C22×C4—111no—
951C22×C4—221no—
952C22×C4—221no—
953C22×C4—221no—
954C22×C4—221no—
955C22×C4—224no—
956C22×C4—221no—
957C22×C4—221no—
958C22×C4—221no—
959C22×C4—221no—
960C22×C4—221no—
961C22×C4—221no—
962C22×C4—221no—
963C22×C4—224no—
964C22×C4—221no—
965C22×C4—221no—
966C22×C4—221no—
967C22×C4—221no—
968C22×C4—221no—
969C22×C4—442no—
970C22×C4—442no—
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—42no—
987M16—221no—
988M16—221no—
989M16—221no—
990M16—221no—
991M16—442no—
992M16D4×D1112yescomplemented
993C2×C8—21no—
994C2×C8—21no—
995C2×C8—42no—
996C2×C8—221no—
997C2×C8—221no—
998C2×C8—442no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
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⋊C4C2×C4×D1111yescharacteristic
1013C4⋊C4C2×C4×D1111yescharacteristic
1014C22⋊C4—24no—
1015C22⋊C4—21no—
1016C22⋊C4—21no—
1017C22⋊C4—21no—
1018C22⋊C4—21no—
1019C22⋊C4—21no—
1020C22⋊C4—111no—
1021C22⋊C4—111no—
1022C22⋊C4—111no—
1023C22⋊C4—111no—
1024C22⋊C4—111no—
1025C22⋊C4—111no—
1026C22⋊C4—111no—
1027C22⋊C4—111no—
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—224no—
1037C22⋊C4—221no—
1038C22⋊C4—221no—
1039C42—21no—
1040C42—21no—
1041C42—21no—
1042C42—21no—
1043C42—21no—
1044C42—111no—
1045C42—111no—
1046C42—111no—
1047C42—111no—
1048C42—112no—
1049C42—221no—
1050C42—221no—
1051C42—224no—
1052C42—221no—
1053C42—221no—
1054C42—221no—
1055C42—442no—
1056C42—442no—
1057C42—442no—
1058C11D4×#10411yescharacteristic, complemented, Sylow
1059C23—21no—
1060C23—21no—
1061C23—22no—
1062C23—21no—
1063C23—41no—
1064C23—111no—
1065C23—111no—
1066C23—222no—
1067C23—221no—
1068C23—221no—
1069C23—221no—
1070C23—221no—
1071C23—441no—
1072C23—442no—
1073C23—442no—
1074C23—442no—
1075C23—442no—
1076C23—881no—
1077C23—881no—
1078C23C22⋊C4×D1111yescharacteristic
1079C23C22⋊C4×D1111yescharacteristic
1080C23C2×D4×D1111yescharacteristic
1081Q8—21no—
1082Q8—21no—
1083Q8—112no—
1084Q8—221no—
1085Q8—221no—
1086Q8—221no—
1087Q8—442no—
1088Q8—442no—
1089D4—21no—
1090D4—21no—
1091D4—41no—
1092D4—41no—
1093D4—42no—
1094D4—81no—
1095D4—114no—
1096D4—112no—
1097D4—222no—
1098D4—222no—
1099D4—222no—
1100D4—222no—
1101D4—222no—
1102D4—221no—
1103D4—221no—
1104D4—221no—
1105D4—442no—
1106D4—442no—
1107D4—442no—
1108D4—442no—
1109D4—442no—
1110D4—442no—
1111D4—442no—
1112D4—442no—
1113D4—441no—
1114D4—441no—
1115D4—881no—
1116D4—881no—
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—21no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—111no—
1139C2×C4—111no—
1140C2×C4—111no—
1141C2×C4—111no—
1142C2×C4—111no—
1143C2×C4—111no—
1144C2×C4—222no—
1145C2×C4—222no—
1146C2×C4—222no—
1147C2×C4—221no—
1148C2×C4—222no—
1149C2×C4—221no—
1150C2×C4—221no—
1151C2×C4—221no—
1152C2×C4—221no—
1153C2×C4—221no—
1154C2×C4—221no—
1155C2×C4—221no—
1156C2×C4—221no—
1157C2×C4—222no—
1158C2×C4—221no—
1159C2×C4—221no—
1160C2×C4—222no—
1161C2×C4—222no—
1162C2×C4—221no—
1163C2×C4—442no—
1164C2×C4—442no—
1165C2×C4—442no—
1166C2×C4—442no—
1167C2×C4—442no—
1168C2×C4—448no—
1169C2×C4—441no—
1170C2×C4—442no—
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×C4#6703711yescharacteristic
1184C2×C4#41×D1111yescharacteristic
1185C2×C4#6704211yescharacteristic
1186C8—22no—
1187C8—41no—
1188C8—441no—
1189C8—441no—
1190C22—21no—
1191C22—21no—
1192C22—21no—
1193C22—21no—
1194C22—21no—
1195C22—21no—
1196C22—21no—
1197C22—42no—
1198C22—42no—
1199C22—41no—
1200C22—41no—
1201C22—41no—
1202C22—112no—
1203C22—221no—
1204C22—221no—
1205C22—221no—
1206C22—222no—
1207C22—221no—
1208C22—221no—
1209C22—442no—
1210C22—442no—
1211C22—441no—
1212C22—441no—
1213C22—441no—
1214C22—441no—
1215C22—441no—
1216C22—884no—
1217C22—884no—
1218C22D11×#10412yescomplemented
1219C22C2×C22⋊C4×D1111yescharacteristic
1220C22#1062314011yescharacteristic
1221C22#1062314111yescharacteristic
1222C4—21no—
1223C4—21no—
1224C4—42no—
1225C4—42no—
1226C4—41no—
1227C4—41no—
1228C4—41no—
1229C4—112no—
1230C4—224no—
1231C4—221no—
1232C4—221no—
1233C4—222no—
1234C4—221no—
1235C4—221no—
1236C4—221no—
1237C4—442no—
1238C4—441no—
1239C4C4×D4×D1111yescharacteristic
1240C4#1062307611yescharacteristic
1241C4#1062312111yescharacteristic
1242C4#1062318511yescharacteristic
1243C2—21no—
1244C2—21no—
1245C2—22no—
1246C2—41no—
1247C2—81no—
1248C2—222no—
1249C2—441no—
1250C2—442no—
1251C2—881no—
1252C2#1307143411yescharacteristic
1253C2C2×D11×#10411yescharacteristic
1254C2#1307716211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1871C2
socleC22×C11C22×C22⋊C4
prime radical#13082099C2
cosocleC22×C4×C11C24
hypercenter#1871D11
hypocenterC11D4×#104
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1871

Complements

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

NH ≅ G/Ntype
2. M16×C22⋊D11C2semidirect
3. C22×#66889C2semidirect
4. C2×D11×#104C2semidirect
5. C4×(C22⋊D11)⋊C4C2semidirect
6. #13069533C2semidirect
7. #13069442C2semidirect
8. #13069060C2semidirect
9. #13069058C2semidirect
10. #13068917C2semidirect
11. #13068635C2semidirect
12. #13068561C2semidirect
13. #13068558C2semidirect
14. #13068420C2semidirect
15. C11×#1871C2semidirect
18. C22×C11×M16C22semidirect
22. C22×C4×Dic11C22semidirect
23. C2×M16×D11C22semidirect
26. #10623164C4semidirect
27. #10623163C4semidirect
28. #10623162C4semidirect
29. #10623161C4semidirect
30. #10623143C4semidirect
31. #10623140C4semidirect
32. #10623130C4semidirect
33. #10623129C4semidirect
43. C2×C42×D11C22semidirect
44. C2×C11×#104C22semidirect
45. C2×C11×#104C22semidirect
46. C4×C11×C22⋊C4C22semidirect
47. C2×#66901C22semidirect
48. C2×#66901C22semidirect
49. #10622820C22semidirect
53. C2×#66889C22semidirect
54. C2×#66889C22semidirect
57. #10622739C22semidirect
58. #10622731C22semidirect
59. M16×Dic11C22semidirect
63. C4×(C2×D11)⋊C4C22semidirect
64. C4×Dic11⋊C4C22semidirect
65. C42×Dic11C22semidirect
68. C2×#66869C22semidirect
69. C2×#66869C22semidirect
73. C11×#339C22semidirect
74. C11×#339C22semidirect
75. #10622170C22semidirect
76. #10622170C22semidirect
86. C2×#4343C2×C4semidirect
87. C2×Q8×D11C2×C4semidirect
89. C2×#4341C2×C4semidirect
92. C2×D4×D11C2×C4semidirect
100. C2×#4339C2×C4semidirect
101. C2×#4339C2×C4semidirect
104. C22×D44C2×C4semidirect
109. C22×Dic22C2×C4semidirect
117. C11×C22⋊Q8C2×C4semidirect
118. C11×C22⋊Q8C2×C4semidirect
119. C11×#121C2×C4semidirect
120. C11×#121C2×C4semidirect
129. #67000C2×C4semidirect
130. #66997C2×C4semidirect
132. #66993C2×C4semidirect
140. #66989C2×C4semidirect
171. #66950C2×C4semidirect
172. #66950C2×C4semidirect
176. #66948C2×C4semidirect
177. #66948C2×C4semidirect
181. #66946C2×C4semidirect
182. #66946C2×C4semidirect
185. #66940C2×C4semidirect
186. #66940C2×C4semidirect
226. #66889D4semidirect
361. C11×M16C2×D4semidirect
423. C4×Dic11C2×D4semidirect
442. #1871D11semidirect
519. C22⋊D11#104semidirect
548. D44C4×D4semidirect
573. Dic22C4×D4semidirect
581. C22×M16C2×D11semidirect
623. C2×#104C2×D11semidirect
624. C2×#104C2×D11semidirect
633. C4×C22⋊C4C2×D11semidirect
637. #339C2×D11semidirect
638. #339C2×D11semidirect
651. C22×C11C2×#104semidirect
670. C2×D11C2×#104semidirect
691. Dic11C2×#104semidirect
757. C22⋊Q8C4×D11semidirect
758. C22⋊Q8C4×D11semidirect
771. #121C4×D11semidirect
772. #121C4×D11semidirect
992. M16D4×D11semidirect
1058. C11D4×#104semidirect
1218. C22D11×#104semidirect

Maximal subgroups

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

subgroupindex
#130820992
M16×C22⋊D112
C22×#668892
C2×D11×#1042
C4×(C22⋊D11)⋊C42
#130695332
#130694422
#130690602
#130690582
#130689172
#130686352
#130685612
#130685582
#130684202
C11×#18712
D4×#10411