Finite Group Databasebeta

← #14821897

Subgroups — #14821897

Order 2816.

764 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072993C211yesmaximal, characteristic
2#13071626C211yesmaximal, characteristic
3#13069938C211yesmaximal, characteristic, complemented
4#13069818C211yesmaximal, characteristic
5#13069625C211yesmaximal, characteristic
6#13069565C211yesmaximal, characteristic, complemented
7#13069290C211yesmaximal, characteristic, complemented
8#13069258C211yesmaximal, characteristic, complemented
9#13069223C211yesmaximal, characteristic
10#13069207C211yesmaximal, characteristic, complemented
11#13068955C211yesmaximal, characteristic, complemented
12#13068922C211yesmaximal, characteristic
13#13068705C211yesmaximal, characteristic
14#103×Dic11C211yesmaximal, characteristic, complemented
15C11×#2024C211yesmaximal, characteristic, complemented
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×#66999C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C22×#4326C2211yescharacteristic
20C2×#66950C2211yescharacteristic
21C2×C4⋊C4×D11C2211yescharacteristic
22C2×C11×#103C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C11×#391C2211yescharacteristic
25#10622844—21no—
26#10622843—21no—
27C2×#66899C2211yescharacteristic
28C2×(C2×D11)⋊C8C2211yescharacteristic
29C2×(C2×D11)⋊C8C2211yescharacteristic
30C2×#66882C2211yescharacteristic
31C2×#66880C2211yescharacteristic
32C2×#66880C2211yescharacteristic
33C2×C8×Dic11C2211yescharacteristic
34#10622603—21no—
35#10622600C2211yescharacteristic
36#10622599—21no—
37C4⋊C4×Dic11C2211yescharacteristic
38#10622587C2211yescharacteristic
39#10622586C2211yescharacteristic
40C2×#66874C2211yescharacteristic
41C4×(C2×D11)⋊C4C2211yescharacteristic
42C4×C4⋊Dic11C2211yescharacteristic
43#10622542C2211yescharacteristic
44C2×C4⋊(C11⋊C8)C2211yescharacteristic
45#10622281—21no—
46#10622279—21no—
47#10622265—21no—
48#10622260—21no—
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51C11×#336C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C22×Q8×C11—21no—
60C22×Q8×C11C2311yescharacteristic
61C22×C4×D11—21no—
62C22×C4×D11C2311yescharacteristic
63C22×Dic22C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C11×C4⋊Q8—22no—
67C11×C4⋊Q8—41no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C42×C11C2311yescharacteristic
73#66999—22no—
74#66999—22no—
75Q8×Dic11—22no—
76Q8×Dic11—41no—
77C2×#4326—22no—
78C2×#4326—41no—
79C2×#4326—41no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4D411yescharacteristic
84C2×(C2×D11)⋊C4D411yescharacteristic
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×C4×Dic11—21no—
94C2×C4×Dic11—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99#66950—22no—
100#66950—41no—
101C4⋊C4×D11—22no—
102C4⋊C4×D11—41no—
103C11×#103—22no—
104C11×#103—41no—
105C11×#95—21no—
106C11×#95—21no—
107#66899—22no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95D411yescharacteristic
117C11⋊#95D411yescharacteristic
118(C2×D11)⋊C8—41no—
119(C2×D11)⋊C8—41no—
120#66882—22no—
121#66880—22no—
122#66880—22no—
123C8×Dic11—41no—
124#66874—41no—
125C4⋊(C11⋊C8)—41no—
126#26726—111nomaximal, Sylow
127C23×D11C2×D411yescharacteristic
128C2×Q8×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11—42no—
134C2×Q8×C11—42no—
135C2×Q8×C11—81no—
136C2×Q8×C11#4112yes—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2411yescharacteristic
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11C2×D411yescharacteristic
149C22×Dic11C2×D411yescharacteristic
150C22×Dic11C2×D411yescharacteristic
151C2×C4×D11—21no—
152C2×C4×D11—21no—
153C2×C4×D11—21no—
154C2×C4×D11—21no—
155C2×C4×D11—21no—
156C2×C4×D11—21no—
157C2×C4×D11—42no—
158C2×C4×D11—42no—
159C2×C4×D11—81no—
160C2×Dic22—21no—
161C2×Dic22—21no—
162C2×Dic22—21no—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—42no—
178C11×C4⋊C4#4112yes—
179C42×C11—21no—
180C42×C11—21no—
181#4326—44no—
182(C2×D11)⋊C4—24no—
183(C2×D11)⋊C4—41no—
184(C2×D11)⋊C4—42no—
185(C2×D11)⋊C4—81no—
186(C2×D11)⋊C4Q1614yescomplemented
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—42no—
192C4⋊Dic11—42no—
193C4⋊Dic11#4112yes—
194C4⋊Dic11#4112yes—
195Dic11⋊C4—24no—
196Dic11⋊C4—42no—
197Dic11⋊C4—81no—
198C4×Dic11—21no—
199C4×Dic11—21no—
200C4×Dic11—42no—
201C4×Dic11—81no—
202C4×Dic11—81no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209#2492—111no—
210#2360—111no—
211#2056—111no—
212#2036—111no—
213#2024D1111yescharacteristic, complemented
214#2001—111no—
215#1987—111no—
216#1933—111no—
217#1928—111no—
218#1923—111no—
219#1921—111no—
220#1878—111no—
221#1872—111no—
222#1824—111no—
223C4×#103—111no—
224C23×C11C22×D411yescharacteristic
225C22×D11—21no—
226C22×D11—21no—
227C22×D11—21no—
228C22×D11—21no—
229C22×D11—21no—
230C22×D11—21no—
231C22×D11C2×Q1612yes—
232Q8×C11—22no—
233Q8×C11—22no—
234Q8×C11—41no—
235Q8×C11—41no—
236Q8×C11—84no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11C2×Q1612yes—
255C2×C4×C11C2×#4111yescharacteristic
256C2×C4×C11C2×#4111yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
258C2×C4×C11C2×#4111yescharacteristic
259C2×C4×C11H(5,𝔽2)11yescharacteristic
260C2×C4×C11H(5,𝔽2)11yescharacteristic
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—22no—
265C2×Dic11—21no—
266C2×Dic11—22no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11C2×Q1612yes—
282C4×D11—41no—
283C4×D11—41no—
284C4×D11—41no—
285C4×D11—41no—
286C4×D11—84no—
287Dic22—41no—
288Dic22—41no—
289Dic22—41no—
290Dic22—41no—
291C8×C11—41no—
292C8×C11—41no—
293C11⋊C8—41no—
294C11⋊C8—41no—
295C22×Q16—111no—
296C2×C4⋊Q8C2×D1111yescharacteristic
297C2×C22⋊Q8—111no—
298C2×C22⋊Q8—111no—
299C2×C4×Q8—111no—
300C22×C4⋊C4—111no—
301C2×#107—111no—
302C2×C4⋊C8—111no—
303C2×#103—111no—
304C2×#103—111no—
305C2×#103—111no—
306C2×#103—111no—
307C2×#103C2×D1111yescharacteristic
308C2×#103C2×D1111yescharacteristic
309C2×C22⋊C8—111no—
310C2×C22⋊C8—111no—
311C2×C4×C8—111no—
312#400—221no—
313#393—221no—
314#391—111no—
315#391—111no—
316#391—221no—
317#391C2×D1111yescharacteristic
318#389—111no—
319#389—221no—
320#388—221no—
321#387—221no—
322#385—221no—
323#380—111no—
324C4×C4⋊C4—111no—
325C4×C4⋊C4—111no—
326C4×C22⋊C4—111no—
327C4×C22⋊C4—221no—
328#340—111no—
329#340—111no—
330#340—111no—
331#340—111no—
332#340—111no—
333#340—111no—
334#340C2×D1111yescharacteristic
335#340C2×D1111yescharacteristic
336#336—111no—
337#336C2×D1111yescharacteristic
338C22×C11#52511yescharacteristic
339C22×C11#54611yescharacteristic
340C22×C11#54611yescharacteristic
341C22×C11C22×Q1611yescharacteristic
342C22×C11#57511yescharacteristic
343C22×C11#57711yescharacteristic
344C22×C11#57711yescharacteristic
345C2×D11—22no—
346C2×D11—22no—
347C2×D11—22no—
348C2×D11—41no—
349C2×D11—41no—
350C2×D11—41no—
351C2×D11—41no—
352C4×C11—22no—
353C4×C11—42no—
354C4×C11—41no—
355C4×C11—42no—
356C4×C11—81no—
357C4×C11—81no—
358C4×C11#52911yescharacteristic
359C4×C11#53811yescharacteristic
360C4×C11#55511yescharacteristic
361C4×C11#55911yescharacteristic
362Dic11—22no—
363Dic11—42no—
364Dic11—41no—
365Dic11—42no—
366Dic11—41no—
367Dic11—81no—
368Dic11—81no—
369C22×Q8—21no—
370C22×Q8—111no—
371C22×Q8C22×D1111yescharacteristic
372C23×C4—111no—
373C23×C4—221no—
374C2×Q16—222no—
375C2×Q16—441no—
376C2×Q16—441no—
377C22×C8—111no—
378C22×C8—111no—
379C22×C8C22×D1111yescharacteristic
380C22×C8C22×D1111yescharacteristic
381C4⋊Q8—22no—
382C4⋊Q8—41no—
383C22⋊Q8—222no—
384C22⋊Q8—222no—
385C22⋊Q8—222no—
386C22⋊Q8—441no—
387C4×Q8—222no—
388C4×Q8—441no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—111no—
391C2×C4⋊C4—111no—
392C2×C4⋊C4—111no—
393C2×C4⋊C4—222no—
394C2×C4⋊C4—221no—
395C2×C4⋊C4—221no—
396C2×C4⋊C4—221no—
397C2×C4⋊C4—221no—
398C2×C4⋊C4—221no—
399C2×C4⋊C4—441no—
400C2×C4⋊C4C22×D1111yescharacteristic
401C2×C4⋊C4C22×D1111yescharacteristic
402C2×C4⋊C4C22×D1111yescharacteristic
403C2×C22⋊C4—111no—
404C2×C22⋊C4—111no—
405C2×C22⋊C4—221no—
406C2×C22⋊C4—221no—
407C2×C22⋊C4—221no—
408C2×C42—111no—
409C2×C42—221no—
410C2×C42—221no—
411C2×C42—221no—
412C2×C42C22×D1111yescharacteristic
413#107—222no—
414C4⋊C8—441no—
415#103—22no—
416#103—41no—
417#103—222no—
418#103—222no—
419#103—222no—
420#103—441no—
421C22⋊C8—441no—
422C22⋊C8—441no—
423C4×C8—441no—
424#95—21no—
425#95—21no—
426#95—111no—
427#95—111no—
428#95—221no—
429#95—221no—
430#95—221no—
431#95—221no—
432#95—221no—
433#95—221no—
434#95—221no—
435#95—221no—
436C2×C11#245911yescharacteristic
437C2×C11#310411yescharacteristic
438C2×C11#312511yescharacteristic
439C2×C11#329911yescharacteristic
440C2×C11#329911yescharacteristic
441C2×C11#331111yescharacteristic
442C2×C11#332311yescharacteristic
443D11—42no—
444C24—111no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—42no—
451C2×Q8—42no—
452C2×Q8—81no—
453C2×Q8—221no—
454C2×Q8—221no—
455C2×Q8—221no—
456C2×Q8—221no—
457C2×Q8—221no—
458C2×Q8—221no—
459C2×Q8#434312yes—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—111no—
465C22×C4—111no—
466C22×C4—111no—
467C22×C4—221no—
468C22×C4—221no—
469C22×C4—221no—
470C22×C4—221no—
471C22×C4—221no—
472C22×C4—221no—
473C22×C4—221no—
474C22×C4—221no—
475C22×C4—221no—
476C22×C4—221no—
477C22×C4—442no—
478C22×C4—442no—
479C22×C4—881no—
480C22×C4D4×D1111yescharacteristic
481C22×C4D4×D1111yescharacteristic
482C22×C4C23×D1111yescharacteristic
483Q16—444no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—221no—
491C2×C8—221no—
492C2×C8—221no—
493C2×C8—221no—
494C2×C8—221no—
495C2×C8—221no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—42no—
502C4⋊C4—112no—
503C4⋊C4—112no—
504C4⋊C4—224no—
505C4⋊C4—221no—
506C4⋊C4—221no—
507C4⋊C4—221no—
508C4⋊C4—221no—
509C4⋊C4—442no—
510C4⋊C4—442no—
511C4⋊C4—442no—
512C4⋊C4—881no—
513C4⋊C4#434112yes—
514C22⋊C4—114no—
515C22⋊C4—224no—
516C22⋊C4—441no—
517C22⋊C4—442no—
518C22⋊C4—881no—
519C42—21no—
520C42—21no—
521C42—221no—
522C42—221no—
523C42—442no—
524C42—881no—
525C42—881no—
526C11#2672611yescharacteristic, complemented, Sylow
527C23—112no—
528C23—221no—
529C23—221no—
530C23—221no—
531C23—221no—
532C23—221no—
533C23—221no—
534C23C2×D4×D1111yescharacteristic
535Q8—22no—
536Q8—22no—
537Q8—41no—
538Q8—41no—
539Q8—84no—
540Q8—441no—
541Q8—441no—
542Q8—441no—
543Q8—441no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—112no—
562C2×C4—221no—
563C2×C4—221no—
564C2×C4—221no—
565C2×C4—221no—
566C2×C4—221no—
567C2×C4—222no—
568C2×C4—221no—
569C2×C4—221no—
570C2×C4—222no—
571C2×C4—221no—
572C2×C4—441no—
573C2×C4—441no—
574C2×C4—441no—
575C2×C4—441no—
576C2×C4—441no—
577C2×C4—441no—
578C2×C4—441no—
579C2×C4—441no—
580C2×C4—441no—
581C2×C4—441no—
582C2×C4—441no—
583C2×C4—441no—
584C2×C4—441no—
585C2×C4—441no—
586C2×C4—884no—
587C2×C4Q16×D1112yes—
588C2×C4C2×#434111yescharacteristic
589C2×C4#6703711yescharacteristic
590C2×C4C2×#434311yescharacteristic
591C2×C4#41×D1111yescharacteristic
592C2×C4#41×D1111yescharacteristic
593C2×C4#6704211yescharacteristic
594C8—41no—
595C8—41no—
596C8—441no—
597C8—441no—
598C22—222no—
599C22—222no—
600C22—222no—
601C22—441no—
602C22—441no—
603C22—441no—
604C22—441no—
605C22#1062312211yescharacteristic
606C22#1062315811yescharacteristic
607C22#1062320711yescharacteristic
608C22#1062329311yescharacteristic
609C22C2×Q16×D1111yescharacteristic
610C22#1062330411yescharacteristic
611C22#1062330911yescharacteristic
612C4—22no—
613C4—41no—
614C4—42no—
615C4—42no—
616C4—81no—
617C4—81no—
618C4—222no—
619C4—441no—
620C4—442no—
621C4—442no—
622C4—441no—
623C4—881no—
624C4—881no—
625C4#1062315511yescharacteristic
626C4#1062317511yescharacteristic
627C4#1062320111yescharacteristic
628C4#1062321211yescharacteristic
629C2—442no—
630C2#1307255611yescharacteristic
631C2#1307865711yescharacteristic
632C2#1307890011yescharacteristic
633C2#1308048511yescharacteristic
634C2#1308049111yescharacteristic
635C2#1308065111yescharacteristic
636C2#1308083611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2024C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenter#2024D11
hypocenterC11#26726
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2024

Complements

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

NH ≅ G/Ntype
3. #13069938C2semidirect
6. #13069565C2semidirect
7. #13069290C2semidirect
8. #13069258C2semidirect
10. #13069207C2semidirect
11. #13068955C2semidirect
14. #103×Dic11C2semidirect
15. C11×#2024C2semidirect
186. (C2×D11)⋊C4Q16semidirect
213. #2024D11semidirect
526. C11#26726semidirect

Maximal subgroups

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

subgroupindex
#130729932
#130716262
#130699382
#130698182
#130696252
#130695652
#130692902
#130692582
#130692232
#130692072
#130689552
#130689222
#130687052
#103×Dic112
C11×#20242
#2672611