Finite Group Databasebeta

← #14769461

Subgroups — #14769461

Order 2816.

1494 conjugacy classes of subgroups.

The subgroup lattice has 1244 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082099C211yesmaximal, characteristic
2M16×C22⋊D11C211yesmaximal, characteristic, complemented
3C2×#10622752C211yesmaximal, characteristic, complemented
4C2×D11×#104C211yesmaximal, characteristic, complemented
5#13071062C211yesmaximal, characteristic, complemented
6#13069533C211yesmaximal, characteristic, complemented
7#13069446C211yesmaximal, characteristic, complemented
8#13069065C211yesmaximal, characteristic, complemented
9#13069058C211yesmaximal, characteristic, complemented
10#13068917C211yesmaximal, characteristic, complemented
11#13068635C211yesmaximal, characteristic, complemented
12#13068561C211yesmaximal, characteristic, complemented
13#13068558C211yesmaximal, characteristic, complemented
14#13068425C211yesmaximal, characteristic, complemented
15C11×#1871C211yesmaximal, characteristic, complemented
16C2×#41×D11C2211yescharacteristic
17C22×#4339C2211yescharacteristic
18C22×C11×M16C2211yescharacteristic, complemented
19C11×#525C2211yescharacteristic
20#10623363C2211yescharacteristic
21C2×C4×C22⋊D11C2211yescharacteristic
22C2×#66979C2211yescharacteristic, 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×C42×D11C2211yescharacteristic, complemented
43C2×C11×#104C2211yescharacteristic, complemented
44C2×C11×#104C2211yescharacteristic, complemented
45C4×C11×C22⋊C4C2211yescharacteristic, complemented
46C2×#66901C2211yescharacteristic, complemented
47C2×#66901C2211yescharacteristic, complemented
48#10622820C2211yescharacteristic, complemented
49#10622752—24no—
50C2×#66889C2211yescharacteristic
51C2×#66889C2211yescharacteristic
52C2×#66889C2211yescharacteristic, complemented
53C2×#66889C2211yescharacteristic, complemented
54#10622741—21no—
55#10622740—21no—
56#10622739C2211yescharacteristic, complemented
57#10622731C2211yescharacteristic, complemented
58M16×Dic11C2211yescharacteristic, complemented
59#10622724—21no—
60C8×C22⋊D11—21no—
61#10622569—21no—
62#10622558—21no—
63C4×(C2×D11)⋊C4C2211yescharacteristic, complemented
64#10622545C2211yescharacteristic, complemented
65C4×Dic11⋊C4C2211yescharacteristic, complemented
66C2×#66869C2211yescharacteristic
67C2×#66869C2211yescharacteristic
68C2×#66869C2211yescharacteristic, complemented
69C2×#66869C2211yescharacteristic, complemented
70D11×#104—24no—
71#10622281—21no—
72#10622268—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
81#41×D11—22no—
82#41×D11—22no—
83#41×D11—41no—
84#41×D11—41no—
85C2×#4343C2×C411yescharacteristic
86C2×Q8×D11C2×C411yescharacteristic
87C2×#4341—21no—
88C2×#4341C2×C411yescharacteristic
89C2×D4×D11—21no—
90C2×D4×D11—21no—
91C2×D4×D11C2×C411yescharacteristic
92C2×#4339—21no—
93C2×#4339—21no—
94C2×#4339—21no—
95C2×#4339—22no—
96C2×#4339—22no—
97C2×#4339—41no—
98C2×#4339—41no—
99C2×#4339C2×C411yescharacteristic, complemented
100C2×#4339C2×C411yescharacteristic, complemented
101C2×#4339C2311yescharacteristic
102C2×#4339C2311yescharacteristic
103C22×D44C2×C411yescharacteristic, complemented
104C22×C4×D11—21no—
105C22×C4×D11—21no—
106C22×C4×D11—21no—
107C22×C4×D11C2311yescharacteristic
108C22×Dic22C2×C411yescharacteristic, complemented
109C2×C11×M16—21no—
110C2×C11×M16—22no—
111C2×C11×M16—41no—
112C2×C11×M16C2311yescharacteristic
113C2×C11×M16C2311yescharacteristic
114C22×C8×C11—21no—
115C11×#123—21no—
116C11×C22⋊Q8C2×C411yescharacteristic, complemented
117C11×C22⋊Q8C2×C411yescharacteristic, complemented
118C11×#121C2×C411yescharacteristic, complemented
119C11×#121C2×C411yescharacteristic, complemented
120C11×#120—21no—
121C4×D4×C11—21no—
122C4×D4×C11—21no—
123C11×#117C2311yescharacteristic
124C2×C11×C22⋊C4—21no—
125C2×C42×C11C2311yescharacteristic
126C2×C42×C11C2311yescharacteristic
127C2×C22⋊Dic11—21no—
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
154#66979—22no—
155#66979—41no—
156C2×C4⋊Dic11—21no—
157C2×Dic11⋊C4—21no—
158C2×Dic11⋊C4D411yescharacteristic
159C2×C4×Dic11—21no—
160C2×C4×Dic11C2311yescharacteristic
161C2×C4×Dic11C2311yescharacteristic
162C2×C4×Dic11C2311yescharacteristic
163C2×#4318C2311yescharacteristic
164C2×#4318C2311yescharacteristic
165M16×D11—22no—
166M16×D11—41no—
167C2×#4313—21no—
168C2×C8×D11—21no—
169#66950C2×C411yescharacteristic
170#66950C2×C411yescharacteristic
171#66949—21no—
172#66949—21no—
173#66948—21no—
174#66948C2×C411yescharacteristic
175#66948C2×C411yescharacteristic
176#66947—21no—
177#66947—21no—
178#66946—21no—
179#66946C2×C411yescharacteristic, complemented
180#66946C2×C411yescharacteristic, complemented
181C4⋊C4×D11—21no—
182#66941—21no—
183#66940C2×C411yescharacteristic, complemented
184#66940C2×C411yescharacteristic, complemented
185#66939—21no—
186#66938—21no—
187#66938—21no—
188#66937—21no—
189#66937—21no—
190#66937—21no—
191#66937—21no—
192#66936—21no—
193#66936—21no—
194#66935—21no—
195#66935—21no—
196#66935—21no—
197(C22⋊D11)⋊C4—21no—
198(C22⋊D11)⋊C4—21no—
199(C22⋊D11)⋊C4—21no—
200(C22⋊D11)⋊C4—21no—
201C22⋊C4×D11—21no—
202C22⋊C4×D11—21no—
203#66931—21no—
204#66931—21no—
205C4×D44—21no—
206C4×D44—21no—
207#66925—21no—
208C42×D11—21no—
209C42×D11—22no—
210C42×D11—41no—
211C11×#104—22no—
212C11×#104—41no—
213C11×#95—21no—
214#66901—22no—
215#66901—41no—
216C11⋊#95—21no—
217C11⋊#95—21no—
218C11⋊#95—21no—
219C11⋊#95—21no—
220C22⋊(C11⋊C8)—21no—
221C22⋊(C11⋊C8)—21no—
222#66889—22no—
223#66889—22no—
224#66889—22no—
225#66889D414yescomplemented
226(C2×D11)⋊C8—21no—
227(C2×D11)⋊C8—21no—
228#66879—21no—
229Dic11⋊C8—21no—
230Dic11⋊C8—21no—
231C8×Dic11—21no—
232#66869—22no—
233#66869—22no—
234#66869—41no—
235#66869—41no—
236#22434—111nomaximal, Sylow
237C24×C11C2×D411yescharacteristic
238C23×D11—21no—
239C23×D11—21no—
240C23×D11C2×D411yescharacteristic
241C11×#41—21no—
242C11×#41—21no—
243C11×#41—21no—
244C11×#41—21no—
245C2×Q8×C11C22×C411yescharacteristic
246C2×D4×C11—21no—
247C2×D4×C11—21no—
248C2×D4×C11—21no—
249C2×D4×C11C22×C411yescharacteristic
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×C11C22×C411yescharacteristic
258C22×C4×C11C22×C411yescharacteristic
259C22×C4×C11C2×D411yescharacteristic
260C22×C4×C11C2×D411yescharacteristic
261C22×C4×C11C2×D411yescharacteristic
262C22×C4×C11C2411yescharacteristic
263C2×C22⋊D11—21no—
264C2×C22⋊D11—21no—
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—42no—
272C2×C22⋊D11—42no—
273C2×C22⋊D11—42no—
274C2×C22⋊D11C22⋊C411yescharacteristic
275C2×C22⋊D11C22⋊C411yescharacteristic
276C2×C22⋊D11C22⋊C411yescharacteristic
277C2×C22⋊D11C22⋊C411yescharacteristic
278C22×Dic11—21no—
279C22×Dic11—21no—
280C22×Dic11—21no—
281C22×Dic11—21no—
282C22×Dic11C2×D411yescharacteristic
283C22×Dic11C2×D411yescharacteristic
284C22×Dic11C2×D411yescharacteristic
285#4343—22no—
286#4343—41no—
287Q8×D11—22no—
288Q8×D11—41no—
289#4341—22no—
290#4341—41no—
291#4341—42no—
292#4341—42no—
293D4×D11—22no—
294D4×D11—41no—
295D4×D11—42no—
296D4×D11—42no—
297D4×D11—44no—
298#4339—22no—
299#4339—22no—
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—42no—
309#4339—42no—
310#4339—42no—
311#4339—42no—
312#4339—42no—
313#4339—42no—
314#4339C2×D412yes—
315#4339#4112yes—
316C2×D44—21no—
317C2×D44—21no—
318C2×D44—21no—
319C2×D44—22no—
320C2×D44—21no—
321C2×D44—41no—
322C2×D44C22×C411yescharacteristic
323C2×D44C22×C411yescharacteristic
324C2×C4×D11—21no—
325C2×C4×D11—21no—
326C2×C4×D11—21no—
327C2×C4×D11—21no—
328C2×C4×D11—21no—
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—42no—
337C2×C4×D11—42no—
338C2×C4×D11—42no—
339C2×C4×D11—42no—
340C2×C4×D11—42no—
341C2×C4×D11—42no—
342C2×C4×D11—42no—
343C2×C4×D11C22×C411yescharacteristic
344C2×C4×D11C22×C411yescharacteristic
345C2×C4×D11C2×D411yescharacteristic
346C2×C4×D11C2×D411yescharacteristic
347C2×Dic22—22no—
348C2×Dic22—21no—
349C2×Dic22—21no—
350C2×Dic22—41no—
351C2×Dic22C22×C411yescharacteristic
352C2×Dic22C22×C411yescharacteristic
353C11×M16—21no—
354C11×M16—21no—
355C11×M16—21no—
356C11×M16—42no—
357C11×M16C2×D412yescomplemented
358C2×C8×C11—21no—
359C2×C8×C11—21no—
360C2×C8×C11—42no—
361C11×C4⋊C4—21no—
362C11×C4⋊C4—21no—
363C11×C4⋊C4C22×C411yescharacteristic
364C11×C4⋊C4C22×C411yescharacteristic
365C11×C22⋊C4—21no—
366C11×C22⋊C4—21no—
367C11×C22⋊C4—21no—
368C11×C22⋊C4—21no—
369C11×C22⋊C4—21no—
370C11×C22⋊C4—42no—
371C42×C11—21no—
372C42×C11—21no—
373C42×C11—21no—
374C42×C11—21no—
375C42×C11—21no—
376C22⋊Dic11—21no—
377C22⋊Dic11—21no—
378C22⋊Dic11—42no—
379C22⋊Dic11C22⋊C411yescharacteristic
380C22⋊Dic11C22⋊C411yescharacteristic
381C22⋊Dic11C22⋊C411yescharacteristic
382C22⋊Dic11C22⋊C411yescharacteristic
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)⋊C4—21no—
389(C2×D11)⋊C4—21no—
390(C2×D11)⋊C4—21no—
391(C2×D11)⋊C4—42no—
392(C2×D11)⋊C4C22⋊C411yescharacteristic
393(C2×D11)⋊C4C22⋊C411yescharacteristic
394(C2×D11)⋊C4C22⋊C411yescharacteristic
395(C2×D11)⋊C4C22⋊C411yescharacteristic
396C4⋊Dic11—21no—
397C4⋊Dic11—21no—
398C4⋊Dic11—42no—
399Dic11⋊C4—21no—
400Dic11⋊C4—21no—
401Dic11⋊C4—21no—
402Dic11⋊C4—21no—
403Dic11⋊C4—42no—
404Dic11⋊C4C22⋊C411yescharacteristic
405Dic11⋊C4C22⋊C411yescharacteristic
406Dic11⋊C4C22⋊C411yescharacteristic
407Dic11⋊C4C22⋊C411yescharacteristic
408C4×Dic11—21no—
409C4×Dic11—21no—
410C4×Dic11—21no—
411C4×Dic11—21no—
412C4×Dic11—21no—
413C4×Dic11—42no—
414C4×Dic11C22×C411yescharacteristic
415C4×Dic11C22×C411yescharacteristic
416C4×Dic11C2×D411yescharacteristic
417C4×Dic11C2×D411yescharacteristic
418C4×Dic11C2×D412yescomplemented
419#4318—21no—
420#4318—21no—
421#4318—21no—
422#4318—21no—
423C2×C11⋊C8—21no—
424C2×C11⋊C8—21no—
425#4313—42no—
426C8×D11—42no—
427D4×#41—111no—
428D4×M16—111no—
429C2×#421—111no—
430C22×#104—111no—
431#2290—111no—
432#1980—111no—
433#1963—111no—
434#1897—111no—
435#1896—111no—
436#1871—111no—
437#1871D1111yescharacteristic, complemented
438#1806—111no—
439#1789—111no—
440#1789—111no—
441#1759—111no—
442C23×C11—21no—
443C23×C11—21no—
444C23×C11—21no—
445C23×C11—41no—
446C23×C11—41no—
447C23×C11C2×C22⋊C411yescharacteristic
448C23×C11C2×C22⋊C411yescharacteristic
449C23×C11C22×D411yescharacteristic
450C22×D11—21no—
451C22×D11—21no—
452C22×D11—21no—
453C22×D11—22no—
454C22×D11—21no—
455C22×D11—41no—
456C22×D11—42no—
457C22×D11—42no—
458C22×D11—42no—
459C22×D11—42no—
460C22×D11—81no—
461C22×D11—81no—
462C22×D11C2×C22⋊C411yescharacteristic
463C22×D11C2×C22⋊C411yescharacteristic
464Q8×C11—21no—
465Q8×C11—21no—
466D4×C11—21no—
467D4×C11—21no—
468D4×C11—42no—
469D4×C11—41no—
470D4×C11—41no—
471D4×C11—81no—
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—22no—
483C2×C4×C11—21no—
484C2×C4×C11—21no—
485C2×C4×C11—21no—
486C2×C4×C11—41no—
487C2×C4×C11—41no—
488C2×C4×C11—41no—
489C2×C4×C11—41no—
490C2×C4×C11—41no—
491C2×C4×C11—41no—
492C2×C4×C11—41no—
493C2×C4×C11C2×C22⋊C411yescharacteristic
494C2×C4×C11C2×C22⋊C411yescharacteristic
495C2×C4×C11C23×C411yescharacteristic
496C2×C4×C11C22×D411yescharacteristic
497C2×C4×C11C22×D411yescharacteristic
498C2×C4×C11C2×#4111yescharacteristic
499C2×C4×C11H(5,𝔽2)11yescharacteristic
500C2×C4×C11H(5,𝔽2)11yescharacteristic
501C22⋊D11—22no—
502C22⋊D11—22no—
503C22⋊D11—22no—
504C22⋊D11—22no—
505C22⋊D11—41no—
506C22⋊D11—41no—
507C22⋊D11—42no—
508C22⋊D11—42no—
509C22⋊D11—42no—
510C22⋊D11—42no—
511C22⋊D11—42no—
512C22⋊D11—41no—
513C22⋊D11—41no—
514C22⋊D11—81no—
515C2×Dic11—21no—
516C2×Dic11—21no—
517C2×Dic11—21no—
518C2×Dic11—21no—
519C2×Dic11—22no—
520C2×Dic11—41no—
521C2×Dic11—41no—
522C2×Dic11—42no—
523C2×Dic11—42no—
524C2×Dic11—41no—
525C2×Dic11—41no—
526C2×Dic11—41no—
527C2×Dic11—41no—
528C2×Dic11—41no—
529C2×Dic11C2×C22⋊C411yescharacteristic
530C2×Dic11C2×C22⋊C411yescharacteristic
531C2×Dic11C2×C22⋊C411yescharacteristic
532C2×Dic11C2×C22⋊C411yescharacteristic
533C2×Dic11C2×C22⋊C411yescharacteristic
534C2×Dic11C2×C22⋊C411yescharacteristic
535D44—21no—
536D44—21no—
537D44—21no—
538D44—42no—
539D44—42no—
540D44—42no—
541D44—81no—
542D44C4×D412yes—
543C4×D11—21no—
544C4×D11—21no—
545C4×D11—21no—
546C4×D11—21no—
547C4×D11—21no—
548C4×D11—21no—
549C4×D11—22no—
550C4×D11—21no—
551C4×D11—21no—
552C4×D11—22no—
553C4×D11—42no—
554C4×D11—42no—
555C4×D11—42no—
556C4×D11—42no—
557C4×D11—42no—
558C4×D11—48no—
559C4×D11—41no—
560C4×D11—41no—
561C4×D11—81no—
562Dic22—21no—
563Dic22—21no—
564Dic22—21no—
565Dic22—42no—
566Dic22—42no—
567Dic22C4×D412yes—
568C8×C11—22no—
569C8×C11—41no—
570C11⋊C8—41no—
571C11⋊C8—41no—
572C22×#41—111no—
573C22×#41—111no—
574C22×M16—111no—
575C22×M16C2×D1111yescharacteristic, complemented
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—221no—
592#525—221no—
593#525C2×D1111yescharacteristic
594C4×#41—111no—
595C2×C4×D4—111no—
596C2×C4×D4—221no—
597C2×#117—111no—
598C22×C42—111no—
599#436—221no—
600#435—221no—
601#435—221no—
602C8×D4—221no—
603#423—111no—
604#421—224no—
605C2×#104—111no—
606C2×#104—111no—
607C2×#104—111no—
608C2×#104—111no—
609C2×#104—111no—
610C2×#104—111no—
611C2×#104—111no—
612C2×#104—111no—
613C2×#104—111no—
614C2×#104—111no—
615C2×#104—224no—
616C2×#104C2×D1111yescharacteristic, complemented
617C2×#104C2×D1111yescharacteristic, complemented
618#407—111no—
619#407—111no—
620C4×M16—111no—
621#388—221no—
622#387—221no—
623#386—221no—
624#385—221no—
625C4×C4⋊C4—111no—
626C4×C22⋊C4—111no—
627C4×C22⋊C4C2×D1111yescharacteristic, complemented
628#376—111no—
629#339—111no—
630#339—111no—
631#339C2×D1111yescharacteristic, complemented
632#339C2×D1111yescharacteristic, complemented
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—41no—
642C22×C11—41no—
643C22×C11—41no—
644C22×C11—81no—
645C22×C11—81no—
646C22×C11C22×C22⋊C411yescharacteristic
647C22×C11D4211yescharacteristic
648C22×C11#54611yescharacteristic
649C2×D11—21no—
650C2×D11—21no—
651C2×D11—21no—
652C2×D11—22no—
653C2×D11—21no—
654C2×D11—21no—
655C2×D11—42no—
656C2×D11—42no—
657C2×D11—41no—
658C2×D11—41no—
659C2×D11—41no—
660C2×D11—41no—
661C2×D11—41no—
662C2×D11—84no—
663C2×D11—84no—
664C2×D11#42112yescomplemented
665C4×C11—21no—
666C4×C11—21no—
667C4×C11—42no—
668C4×C11—41no—
669C4×C11—41no—
670C4×C11—41no—
671C4×C11—81no—
672C4×C11C2×C4×D411yescharacteristic
673C4×C11#51811yescharacteristic
674C4×C11D4211yescharacteristic
675C4×C11#54611yescharacteristic
676Dic11—22no—
677Dic11—21no—
678Dic11—21no—
679Dic11—21no—
680Dic11—21no—
681Dic11—21no—
682Dic11—21no—
683Dic11—42no—
684Dic11—41no—
685Dic11—81no—
686C2×#41—111no—
687C2×#41—111no—
688C2×#41—111no—
689C2×#41—111no—
690C2×#41—111no—
691C2×#41—111no—
692C2×#41—221no—
693C2×#41—222no—
694C2×#41—222no—
695C2×#41—221no—
696C2×#41—221no—
697C2×#41—221no—
698C2×#41—222no—
699C2×#41—222no—
700C2×#41—441no—
701C2×#41—441no—
702C2×#41—441no—
703C2×#41—441no—
704C2×#41C22×D1111yescharacteristic
705C22×Q8—111no—
706C22×Q8—111no—
707C22×D4—111no—
708C22×D4—111no—
709C22×D4—111no—
710C22×D4—221no—
711C22×D4—221no—
712C22×D4—221no—
713C23×C4—111no—
714C23×C4—221no—
715C23×C4—221no—
716C23×C4—221no—
717C23×C4C22×D1111yescharacteristic
718C2×M16—21no—
719C2×M16—22no—
720C2×M16—41no—
721C2×M16—111no—
722C2×M16—111no—
723C2×M16—221no—
724C2×M16—222no—
725C2×M16—441no—
726C2×M16C22×D1111yescharacteristic
727C2×M16C22×D1111yescharacteristic
728C22×C8—21no—
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—21no—
739#123—221no—
740#123—221no—
741#123—221no—
742#123—221no—
743#123—221no—
744C22⋊Q8—111no—
745C22⋊Q8—111no—
746C22⋊Q8—221no—
747C22⋊Q8—221no—
748C22⋊Q8—221no—
749C22⋊Q8—221no—
750C22⋊Q8C4×D1111yescharacteristic, complemented
751C22⋊Q8C4×D1111yescharacteristic, complemented
752#121—111no—
753#121—111no—
754#121—221no—
755#121—221no—
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#121C4×D1111yescharacteristic, complemented
765#121C4×D1111yescharacteristic, complemented
766#120—21no—
767#120—221no—
768#120—221no—
769#120—221no—
770#120—221no—
771#120—221no—
772C4×Q8—111no—
773C4×Q8—111no—
774C4×D4—21no—
775C4×D4—21no—
776C4×D4—111no—
777C4×D4—111no—
778C4×D4—111no—
779C4×D4—111no—
780C4×D4—111no—
781C4×D4—111no—
782C4×D4—111no—
783C4×D4—111no—
784C4×D4—111no—
785C4×D4—111no—
786C4×D4—221no—
787C4×D4—221no—
788C4×D4—221no—
789C4×D4—221no—
790C4×D4—221no—
791C4×D4—221no—
792C4×D4—221no—
793C4×D4—221no—
794C4×D4—221no—
795C4×D4—221no—
796#117—221no—
797#117—222no—
798#117—441no—
799#117C22×D1111yescharacteristic
800C2×C4⋊C4—111no—
801C2×C4⋊C4—221no—
802C2×C4⋊C4—221no—
803C2×C4⋊C4—221no—
804C2×C22⋊C4—21no—
805C2×C22⋊C4—111no—
806C2×C22⋊C4—111no—
807C2×C22⋊C4—221no—
808C2×C22⋊C4—221no—
809C2×C22⋊C4—221no—
810C2×C22⋊C4—221no—
811C2×C42—111no—
812C2×C42—111no—
813C2×C42—111no—
814C2×C42—221no—
815C2×C42—222no—
816C2×C42—221no—
817C2×C42—441no—
818C2×C42C22×D1111yescharacteristic
819C2×C42C22×D1111yescharacteristic
820C4⋊C8—221no—
821C4⋊C8—221no—
822#104—22no—
823#104—41no—
824#104—114no—
825#104—222no—
826#104—222no—
827#104—222no—
828#104—222no—
829#104—222no—
830#104—222no—
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—221no—
842#95—221no—
843#95—221no—
844#95—221no—
845C2×C11—21no—
846C2×C11—21no—
847C2×C11—41no—
848C2×C11—41no—
849C2×C11—81no—
850C2×C11D4×C22⋊C411yescharacteristic
851C2×C11C2×#42111yescharacteristic
852C2×C11#290111yescharacteristic
853D11—22no—
854D11—41no—
855D11—42no—
856D11—81no—
857C24—111no—
858C24—221no—
859C24—221no—
860C24D4×D1111yescharacteristic
861#41—21no—
862#41—21no—
863#41—21no—
864#41—21no—
865#41—112no—
866#41—112no—
867#41—222no—
868#41—222no—
869#41—221no—
870#41—221no—
871#41—222no—
872#41—222no—
873#41—221no—
874#41—221no—
875#41—221no—
876#41—221no—
877#41—442no—
878#41—442no—
879#41—441no—
880#41—441no—
881#41—442no—
882#41—442no—
883#41—442no—
884#41—442no—
885#41—441no—
886#41—442no—
887#41—442no—
888#41—441no—
889C2×Q8—111no—
890C2×Q8—111no—
891C2×Q8—221no—
892C2×Q8—222no—
893C2×Q8—221no—
894C2×Q8—222no—
895C2×Q8—441no—
896C2×Q8—441no—
897C2×Q8C2×C4×D1111yescharacteristic
898C2×D4—21no—
899C2×D4—21no—
900C2×D4—21no—
901C2×D4—111no—
902C2×D4—111no—
903C2×D4—111no—
904C2×D4—111no—
905C2×D4—111no—
906C2×D4—111no—
907C2×D4—222no—
908C2×D4—221no—
909C2×D4—221no—
910C2×D4—221no—
911C2×D4—221no—
912C2×D4—221no—
913C2×D4—221no—
914C2×D4—222no—
915C2×D4—221no—
916C2×D4—221no—
917C2×D4—221no—
918C2×D4—221no—
919C2×D4—221no—
920C2×D4—221no—
921C2×D4—441no—
922C2×D4—441no—
923C2×D4—442no—
924C2×D4—442no—
925C2×D4—444no—
926C2×D4—442no—
927C2×D4—442no—
928C2×D4—442no—
929C2×D4C2×C4×D1111yescharacteristic
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—111no—
938C22×C4—111no—
939C22×C4—111no—
940C22×C4—111no—
941C22×C4—111no—
942C22×C4—111no—
943C22×C4—111no—
944C22×C4—221no—
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—221no—
957C22×C4—221no—
958C22×C4—221no—
959C22×C4—221no—
960C22×C4—442no—
961C22×C4—442no—
962C22×C4—442no—
963C22×C4—442no—
964C22×C4—442no—
965C22×C4—442no—
966C22×C4—442no—
967C22×C4C2×C4×D1111yescharacteristic
968C22×C4C2×C4×D1111yescharacteristic
969C22×C4D4×D1111yescharacteristic
970C22×C4D4×D1111yescharacteristic
971C22×C4D4×D1111yescharacteristic
972C22×C4C23×D1111yescharacteristic
973M16—21no—
974M16—21no—
975M16—21no—
976M16—42no—
977M16—221no—
978M16—221no—
979M16—221no—
980M16—221no—
981M16—442no—
982M16D4×D1112yescomplemented
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—42no—
986C2×C8—221no—
987C2×C8—221no—
988C2×C8—442no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—111no—
992C4⋊C4—111no—
993C4⋊C4—111no—
994C4⋊C4—111no—
995C4⋊C4—221no—
996C4⋊C4—221no—
997C4⋊C4—221no—
998C4⋊C4—221no—
999C4⋊C4—221no—
1000C4⋊C4—221no—
1001C4⋊C4—442no—
1002C4⋊C4—442no—
1003C4⋊C4C2×C4×D1111yescharacteristic
1004C4⋊C4C2×C4×D1111yescharacteristic
1005C22⋊C4—21no—
1006C22⋊C4—21no—
1007C22⋊C4—21no—
1008C22⋊C4—21no—
1009C22⋊C4—21no—
1010C22⋊C4—42no—
1011C22⋊C4—111no—
1012C22⋊C4—111no—
1013C22⋊C4—111no—
1014C22⋊C4—111no—
1015C22⋊C4—111no—
1016C22⋊C4—111no—
1017C22⋊C4—111no—
1018C22⋊C4—111no—
1019C22⋊C4—221no—
1020C22⋊C4—221no—
1021C22⋊C4—221no—
1022C22⋊C4—221no—
1023C22⋊C4—221no—
1024C22⋊C4—221no—
1025C22⋊C4—221no—
1026C22⋊C4—221no—
1027C22⋊C4—221no—
1028C22⋊C4—221no—
1029C22⋊C4—442no—
1030C22⋊C4—442no—
1031C42—21no—
1032C42—21no—
1033C42—21no—
1034C42—21no—
1035C42—21no—
1036C42—111no—
1037C42—111no—
1038C42—111no—
1039C42—111no—
1040C42—112no—
1041C42—221no—
1042C42—221no—
1043C42—221no—
1044C42—221no—
1045C42—221no—
1046C42—442no—
1047C11#2243411yescharacteristic, complemented, Sylow
1048C23—21no—
1049C23—21no—
1050C23—21no—
1051C23—41no—
1052C23—41no—
1053C23—111no—
1054C23—111no—
1055C23—222no—
1056C23—221no—
1057C23—221no—
1058C23—221no—
1059C23—221no—
1060C23—441no—
1061C23—442no—
1062C23—442no—
1063C23—442no—
1064C23—442no—
1065C23—881no—
1066C23—881no—
1067C23C22⋊C4×D1111yescharacteristic
1068C23C22⋊C4×D1111yescharacteristic
1069C23C2×D4×D1111yescharacteristic
1070Q8—21no—
1071Q8—21no—
1072Q8—112no—
1073Q8—221no—
1074Q8—221no—
1075Q8—221no—
1076Q8—442no—
1077Q8—442no—
1078D4—21no—
1079D4—21no—
1080D4—42no—
1081D4—41no—
1082D4—41no—
1083D4—81no—
1084D4—112no—
1085D4—222no—
1086D4—222no—
1087D4—222no—
1088D4—222no—
1089D4—221no—
1090D4—221no—
1091D4—221no—
1092D4—442no—
1093D4—442no—
1094D4—442no—
1095D4—441no—
1096D4—441no—
1097D4—442no—
1098D4—442no—
1099D4—442no—
1100D4—442no—
1101D4—442no—
1102D4—441no—
1103D4—441no—
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—22no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—111no—
1128C2×C4—111no—
1129C2×C4—111no—
1130C2×C4—111no—
1131C2×C4—111no—
1132C2×C4—111no—
1133C2×C4—221no—
1134C2×C4—221no—
1135C2×C4—221no—
1136C2×C4—221no—
1137C2×C4—221no—
1138C2×C4—221no—
1139C2×C4—221no—
1140C2×C4—221no—
1141C2×C4—221no—
1142C2×C4—222no—
1143C2×C4—221no—
1144C2×C4—221no—
1145C2×C4—222no—
1146C2×C4—221no—
1147C2×C4—222no—
1148C2×C4—442no—
1149C2×C4—442no—
1150C2×C4—442no—
1151C2×C4—442no—
1152C2×C4—442no—
1153C2×C4—448no—
1154C2×C4—441no—
1155C2×C4—441no—
1156C2×C4—442no—
1157C2×C4—442no—
1158C2×C4—441no—
1159C2×C4—441no—
1160C2×C4—441no—
1161C2×C4—441no—
1162C2×C4—441no—
1163C2×C4—441no—
1164C2×C4—441no—
1165C2×C4—881no—
1166C2×C4C22⋊C4×D1111yescharacteristic
1167C2×C4C22⋊C4×D1111yescharacteristic
1168C2×C4C22×C4×D1111yescharacteristic
1169C2×C4C2×D4×D1111yescharacteristic
1170C2×C4C2×D4×D1111yescharacteristic
1171C2×C4#6703711yescharacteristic
1172C2×C4#41×D1111yescharacteristic
1173C2×C4#6704211yescharacteristic
1174C8—22no—
1175C8—41no—
1176C8—441no—
1177C8—441no—
1178C22—21no—
1179C22—21no—
1180C22—21no—
1181C22—21no—
1182C22—21no—
1183C22—21no—
1184C22—21no—
1185C22—21no—
1186C22—41no—
1187C22—41no—
1188C22—41no—
1189C22—81no—
1190C22—81no—
1191C22—112no—
1192C22—221no—
1193C22—221no—
1194C22—221no—
1195C22—222no—
1196C22—221no—
1197C22—221no—
1198C22—442no—
1199C22—442no—
1200C22—441no—
1201C22—441no—
1202C22—441no—
1203C22—441no—
1204C22—441no—
1205C22—884no—
1206C22—884no—
1207C22C2×C22⋊C4×D1111yescharacteristic
1208C22#1062314011yescharacteristic
1209C22#1062314111yescharacteristic
1210C4—21no—
1211C4—21no—
1212C4—42no—
1213C4—41no—
1214C4—41no—
1215C4—41no—
1216C4—81no—
1217C4—221no—
1218C4—221no—
1219C4—222no—
1220C4—221no—
1221C4—221no—
1222C4—221no—
1223C4—221no—
1224C4—442no—
1225C4—441no—
1226C4—881no—
1227C4C4×D4×D1111yescharacteristic
1228C4#1062307611yescharacteristic
1229C4#1062312111yescharacteristic
1230C4#1062318511yescharacteristic
1231C2—21no—
1232C2—21no—
1233C2—41no—
1234C2—41no—
1235C2—81no—
1236C2—222no—
1237C2—441no—
1238C2—442no—
1239C2—881no—
1240C2#1307143411yescharacteristic
1241C2D11×#42111yescharacteristic
1242C2#1307716011yescharacteristic
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
hypocenterC11#22434
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. C2×#10622752C2semidirect
4. C2×D11×#104C2semidirect
5. #13071062C2semidirect
6. #13069533C2semidirect
7. #13069446C2semidirect
8. #13069065C2semidirect
9. #13069058C2semidirect
10. #13068917C2semidirect
11. #13068635C2semidirect
12. #13068561C2semidirect
13. #13068558C2semidirect
14. #13068425C2semidirect
15. C11×#1871C2semidirect
18. C22×C11×M16C22semidirect
22. C2×#66979C22semidirect
23. C2×M16×D11C22semidirect
26. #10623164C4semidirect
27. #10623163C4semidirect
28. #10623162C4semidirect
29. #10623161C4semidirect
30. #10623143C4semidirect
31. #10623140C4semidirect
32. #10623130C4semidirect
33. #10623129C4semidirect
42. C2×C42×D11C22semidirect
43. C2×C11×#104C22semidirect
44. C2×C11×#104C22semidirect
45. C4×C11×C22⋊C4C22semidirect
46. C2×#66901C22semidirect
47. C2×#66901C22semidirect
48. #10622820C22semidirect
52. C2×#66889C22semidirect
53. C2×#66889C22semidirect
56. #10622739C22semidirect
57. #10622731C22semidirect
58. M16×Dic11C22semidirect
63. C4×(C2×D11)⋊C4C22semidirect
64. #10622545C22semidirect
65. C4×Dic11⋊C4C22semidirect
68. C2×#66869C22semidirect
69. C2×#66869C22semidirect
73. C11×#339C22semidirect
74. C11×#339C22semidirect
75. #10622170C22semidirect
76. #10622170C22semidirect
99. C2×#4339C2×C4semidirect
100. C2×#4339C2×C4semidirect
103. C22×D44C2×C4semidirect
108. C22×Dic22C2×C4semidirect
116. C11×C22⋊Q8C2×C4semidirect
117. C11×C22⋊Q8C2×C4semidirect
118. C11×#121C2×C4semidirect
119. C11×#121C2×C4semidirect
129. #67000C2×C4semidirect
130. #66997C2×C4semidirect
132. #66993C2×C4semidirect
140. #66989C2×C4semidirect
179. #66946C2×C4semidirect
180. #66946C2×C4semidirect
183. #66940C2×C4semidirect
184. #66940C2×C4semidirect
225. #66889D4semidirect
357. C11×M16C2×D4semidirect
418. C4×Dic11C2×D4semidirect
437. #1871D11semidirect
575. C22×M16C2×D11semidirect
616. C2×#104C2×D11semidirect
617. C2×#104C2×D11semidirect
627. C4×C22⋊C4C2×D11semidirect
631. #339C2×D11semidirect
632. #339C2×D11semidirect
664. C2×D11#421semidirect
750. C22⋊Q8C4×D11semidirect
751. C22⋊Q8C4×D11semidirect
764. #121C4×D11semidirect
765. #121C4×D11semidirect
982. M16D4×D11semidirect
1047. C11#22434semidirect

Maximal subgroups

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

subgroupindex
#130820992
M16×C22⋊D112
C2×#106227522
C2×D11×#1042
#130710622
#130695332
#130694462
#130690652
#130690582
#130689172
#130686352
#130685612
#130685582
#130684252
C11×#18712
#2243411