Finite Group Databasebeta

← #14822261

Subgroups — #14822261

Order 2816.

736 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072993C211yesmaximal, characteristic
2#13071645C211yesmaximal, characteristic
3#13069939C211yesmaximal, characteristic, complemented
4#13069815C211yesmaximal, characteristic
5#13069754C211yesmaximal, characteristic, complemented
6#13069627C211yesmaximal, characteristic
7#13069307C211yesmaximal, characteristic, complemented
8#13069250C211yesmaximal, characteristic, complemented
9#13069228C211yesmaximal, characteristic
10#13069204C211yesmaximal, characteristic, complemented
11#13068958C211yesmaximal, characteristic, complemented
12#13068927C211yesmaximal, characteristic
13#13068710C211yesmaximal, characteristic
14#13068445C211yesmaximal, characteristic, complemented
15C11×#1987C211yesmaximal, characteristic, complemented
16C2×C11×C4⋊Q8C2211yescharacteristic
17C22×Dic44C2211yescharacteristic
18C2×#66950C2211yescharacteristic
19C2×#66950C2211yescharacteristic
20C2×#66945C2211yescharacteristic
21C2×#66940C2211yescharacteristic
22C2×C11×C4⋊C8C2211yescharacteristic
23C4×C11×C4⋊C4C2211yescharacteristic
24#10622844—21no—
25#10622843—21no—
26C2×(C2×D11)⋊C8C2211yescharacteristic
27C2×(C2×D11)⋊C8C2211yescharacteristic
28C2×#66880C2211yescharacteristic
29C2×#66880C2211yescharacteristic
30C2×#66879C2211yescharacteristic
31#10622603—21no—
32#10622600C2211yescharacteristic
33#10622599—21no—
34#10622598C2211yescharacteristic
35C4⋊C4×Dic11C2211yescharacteristic
36#10622587C2211yescharacteristic
37C2×#66874C2211yescharacteristic
38C2×#66874C2211yescharacteristic
39C2×#66874C2211yescharacteristic
40C2×#66874C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42#10622553—21no—
43C4×(C2×D11)⋊C4C2211yescharacteristic
44C4×C4⋊Dic11—21no—
45#10622542C2211yescharacteristic
46#10622542C2211yescharacteristic
47#10622283—21no—
48#10622266—21no—
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×Q8×C11—21no—
60C22×C4×D11C2311yescharacteristic
61C22×Dic22C2311yescharacteristic
62C22×Dic22C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C11×C4⋊Q8—22no—
66C11×C4⋊Q8—41no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C42×C11—21no—
73C2×C42×C11C2311yescharacteristic
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4D411yescharacteristic
79C2×(C2×D11)⋊C4D411yescharacteristic
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×Dic11⋊C4—21no—
86C2×C4×Dic11—21no—
87C2×C4×Dic11—21no—
88C2×C4×Dic11—21no—
89C2×C4×Dic11C2311yescharacteristic
90C22×C11⋊C8C2311yescharacteristic
91C22×C11⋊C8C2311yescharacteristic
92C2×Dic44—22no—
93C2×Dic44—41no—
94C2×Dic44—41no—
95#66950—22no—
96#66950—22no—
97#66950—22no—
98#66950—41no—
99#66945—22no—
100#66945—41no—
101#66940—22no—
102#66940—41no—
103C11×C4⋊C8—41no—
104C11×#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95D411yescharacteristic
115C11⋊#95D411yescharacteristic
116(C2×D11)⋊C8—41no—
117(C2×D11)⋊C8—41no—
118#66880—22no—
119#66880—41no—
120#66879—41no—
121#66874—22no—
122#66874—22no—
123#66874—22no—
124#66874—41no—
125#66872—22no—
126#26750—111nomaximal, Sylow
127C23×D11C2×D411yescharacteristic
128C2×Q8×C11—42no—
129C2×Q8×C11—42no—
130C2×Q8×C11—81no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2411yescharacteristic
138C22×Dic11—21no—
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11C2×D411yescharacteristic
143C22×Dic11C2×D411yescharacteristic
144C22×Dic11C2×D411yescharacteristic
145C2×C4×D11—21no—
146C2×C4×D11—21no—
147C2×C4×D11—21no—
148C2×C4×D11—21no—
149C2×C4×D11—21no—
150C2×C4×D11—21no—
151C2×Dic22—21no—
152C2×Dic22—21no—
153C2×Dic22—21no—
154C2×Dic22—21no—
155C2×Dic22—21no—
156C2×Dic22—21no—
157C2×Dic22—21no—
158C2×Dic22—21no—
159C2×Dic22—21no—
160C2×Dic22—21no—
161C2×Dic22—21no—
162C2×Dic22#4112yes—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—42no—
175C11×C4⋊C4#4112yes—
176C11×C4⋊C4#4112yes—
177C11×C4⋊C4#4112yes—
178C42×C11—21no—
179C42×C11—21no—
180C42×C11—42no—
181(C2×D11)⋊C4—24no—
182(C2×D11)⋊C4—22no—
183(C2×D11)⋊C4—41no—
184(C2×D11)⋊C4—42no—
185(C2×D11)⋊C4—42no—
186(C2×D11)⋊C4—81no—
187C4⋊Dic11—24no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—42no—
193C4⋊Dic11—42no—
194Dic11⋊C4—42no—
195C4×Dic11—21no—
196C4×Dic11—21no—
197C4×Dic11—42no—
198C4×Dic11—42no—
199C4×Dic11—81no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206Dic44—44no—
207#2492—111no—
208#2362—111no—
209#2056—111no—
210#2035—111no—
211#2024—111no—
212#2001—111no—
213#1987D1111yescharacteristic, complemented
214#1935—111no—
215#1927—111no—
216#1924—111no—
217#1920—111no—
218#1878—111no—
219#1873—111no—
220#1825—111no—
221#1763—111no—
222C23×C11C22×D411yescharacteristic
223C22×D11—21no—
224C22×D11—21no—
225C22×D11—21no—
226C22×D11—21no—
227C22×D11—21no—
228C22×D11—21no—
229C22×D11—21no—
230Q8×C11—84no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11#13712yes—
249C2×C4×C11C2×#4111yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C2×C4×C11C2×#4111yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C2×C4×C11H(5,𝔽2)11yescharacteristic
254C2×C4×C11H(5,𝔽2)11yescharacteristic
255C2×Dic11—21no—
256C2×Dic11—22no—
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C4×D11—41no—
277C4×D11—41no—
278C4×D11—41no—
279C4×D11—41no—
280Dic22—22no—
281Dic22—22no—
282Dic22—41no—
283Dic22—41no—
284Dic22—41no—
285Dic22—41no—
286Dic22—41no—
287Dic22—41no—
288C8×C11—41no—
289C8×C11—41no—
290C11⋊C8—41no—
291C11⋊C8—41no—
292C22×Q16—111no—
293C2×C4⋊Q8C2×D1111yescharacteristic
294C2×C22⋊Q8—111no—
295C2×C22⋊Q8—111no—
296C2×C4×Q8—111no—
297C2×#117—111no—
298C2×#106—111no—
299C2×C4⋊C8C2×D1111yescharacteristic
300C2×#103—111no—
301C2×#103—111no—
302C2×#103—111no—
303C2×#103—111no—
304C2×#103—111no—
305C2×#103—111no—
306C2×C22⋊C8—111no—
307C2×C22⋊C8—111no—
308C2×#97—111no—
309#400—221no—
310#393—221no—
311#391—111no—
312#391—111no—
313#391—111no—
314#391—221no—
315#389—111no—
316#388—221no—
317#388—221no—
318#388—221no—
319#387—221no—
320#380—111no—
321C4×C4⋊C4—111no—
322C4×C4⋊C4—221no—
323C4×C4⋊C4C2×D1111yescharacteristic
324C4×C22⋊C4—111no—
325#340—111no—
326#340—111no—
327#340—111no—
328#340—111no—
329#340C2×D1111yescharacteristic
330#340C2×D1111yescharacteristic
331#340C2×D1111yescharacteristic
332#340C2×D1111yescharacteristic
333#336—111no—
334#336—111no—
335C22×C11#52511yescharacteristic
336C22×C11#54611yescharacteristic
337C22×C11#54611yescharacteristic
338C22×C11C2×#13711yescharacteristic
339C22×C11#57511yescharacteristic
340C22×C11#57711yescharacteristic
341C22×C11#57811yescharacteristic
342C2×D11—41no—
343C2×D11—41no—
344C2×D11—41no—
345C2×D11—41no—
346C2×D11—41no—
347C2×D11—41no—
348C2×D11—41no—
349C4×C11—22no—
350C4×C11—42no—
351C4×C11—42no—
352C4×C11—41no—
353C4×C11—42no—
354C4×C11—81no—
355C4×C11#52911yescharacteristic
356C4×C11#53811yescharacteristic
357C4×C11#55511yescharacteristic
358C4×C11#55911yescharacteristic
359Dic11—41no—
360Dic11—42no—
361Dic11—41no—
362Dic11—41no—
363Dic11—81no—
364Dic11—81no—
365Dic11—81no—
366C22×Q8—21no—
367C22×Q8—111no—
368C22×Q8—111no—
369C23×C4—111no—
370C2×Q16—222no—
371C2×Q16—441no—
372C2×Q16—441no—
373C22×C8—111no—
374C22×C8—111no—
375C22×C8C22×D1111yescharacteristic
376C22×C8C22×D1111yescharacteristic
377C4⋊Q8—22no—
378C4⋊Q8—41no—
379C22⋊Q8—222no—
380C22⋊Q8—222no—
381C22⋊Q8—222no—
382C22⋊Q8—441no—
383C4×Q8—222no—
384C4×Q8—441no—
385#117—222no—
386#117—441no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—111no—
389C2×C4⋊C4—111no—
390C2×C4⋊C4—221no—
391C2×C4⋊C4—221no—
392C2×C4⋊C4—221no—
393C2×C4⋊C4—221no—
394C2×C4⋊C4C22×D1111yescharacteristic
395C2×C4⋊C4C22×D1111yescharacteristic
396C2×C4⋊C4C22×D1111yescharacteristic
397C2×C4⋊C4C22×D1111yescharacteristic
398C2×C22⋊C4—111no—
399C2×C22⋊C4—111no—
400C2×C22⋊C4—221no—
401C2×C22⋊C4—221no—
402C2×C22⋊C4—221no—
403C2×C22⋊C4—221no—
404C2×C42—21no—
405C2×C42—111no—
406C2×C42—221no—
407C2×C42—221no—
408C2×C42—221no—
409C2×C42C22×D1111yescharacteristic
410#106—222no—
411C4⋊C8—41no—
412#103—222no—
413#103—222no—
414#103—222no—
415#103—222no—
416#103—441no—
417#103—441no—
418C22⋊C8—441no—
419C22⋊C8—441no—
420#97—441no—
421#95—21no—
422#95—111no—
423#95—111no—
424#95—221no—
425#95—221no—
426#95—221no—
427#95—221no—
428#95—221no—
429#95—221no—
430#95—221no—
431#95—221no—
432#95—221no—
433C2×C11#245911yescharacteristic
434C2×C11#311611yescharacteristic
435C2×C11#312111yescharacteristic
436C2×C11#331111yescharacteristic
437C2×C11#331211yescharacteristic
438C2×C11#331311yescharacteristic
439C2×C11#333111yescharacteristic
440D11—81no—
441C24—111no—
442C2×Q8—42no—
443C2×Q8—42no—
444C2×Q8—81no—
445C2×Q8—112no—
446C2×Q8—221no—
447C2×Q8—221no—
448C2×Q8—221no—
449C2×Q8—221no—
450C2×Q8—221no—
451C2×Q8—221no—
452C2×Q8—221no—
453C2×Q8—221no—
454C2×Q8—221no—
455C2×Q8—221no—
456C2×Q8—221no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—111no—
462C22×C4—111no—
463C22×C4—111no—
464C22×C4—221no—
465C22×C4—221no—
466C22×C4—221no—
467C22×C4—221no—
468C22×C4—221no—
469C22×C4—221no—
470C22×C4—221no—
471C22×C4—221no—
472C22×C4—221no—
473C22×C4—221no—
474C22×C4D4×D1111yescharacteristic
475C22×C4D4×D1111yescharacteristic
476C22×C4C23×D1111yescharacteristic
477Q16—444no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—221no—
485C2×C8—221no—
486C2×C8—221no—
487C2×C8—221no—
488C2×C8—221no—
489C2×C8—221no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—42no—
496C4⋊C4—224no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4—221no—
500C4⋊C4—221no—
501C4⋊C4—442no—
502C4⋊C4—442no—
503C4⋊C4—442no—
504C4⋊C4#433912yes—
505C4⋊C4#434312yes—
506C4⋊C4#434312yes—
507C22⋊C4—224no—
508C22⋊C4—222no—
509C22⋊C4—441no—
510C22⋊C4—442no—
511C22⋊C4—442no—
512C22⋊C4—881no—
513C42—21no—
514C42—21no—
515C42—42no—
516C42—221no—
517C42—221no—
518C42—442no—
519C42—442no—
520C42—881no—
521C11#2675011yescharacteristic, complemented, Sylow
522C23—221no—
523C23—221no—
524C23—221no—
525C23—221no—
526C23—221no—
527C23—221no—
528C23—221no—
529C23C2×D4×D1111yescharacteristic
530Q8—84no—
531Q8—222no—
532Q8—222no—
533Q8—441no—
534Q8—441no—
535Q8—441no—
536Q8—441no—
537Q8—441no—
538Q8—441no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—22no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—221no—
557C2×C4—221no—
558C2×C4—221no—
559C2×C4—221no—
560C2×C4—221no—
561C2×C4—222no—
562C2×C4—221no—
563C2×C4—221no—
564C2×C4—221no—
565C2×C4—221no—
566C2×C4—441no—
567C2×C4—441no—
568C2×C4—441no—
569C2×C4—441no—
570C2×C4—441no—
571C2×C4—441no—
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#6696812yes—
582C2×C4C2×#433911yescharacteristic
583C2×C4#6703711yescharacteristic
584C2×C4C2×#434311yescharacteristic
585C2×C4C2×#434311yescharacteristic
586C2×C4#41×D1111yescharacteristic
587C2×C4#6704211yescharacteristic
588C8—41no—
589C8—41no—
590C8—441no—
591C8—441no—
592C22—441no—
593C22—441no—
594C22—441no—
595C22—441no—
596C22—441no—
597C22—441no—
598C22—441no—
599C22#1062302111yescharacteristic
600C22#1062315811yescharacteristic
601C22#1062316111yescharacteristic
602C22C2×#6696811yescharacteristic
603C22#1062329711yescharacteristic
604C22#1062330411yescharacteristic
605C22#1062330611yescharacteristic
606C4—22no—
607C4—41no—
608C4—42no—
609C4—42no—
610C4—42no—
611C4—81no—
612C4—441no—
613C4—441no—
614C4—441no—
615C4—442no—
616C4—881no—
617C4—881no—
618C4—881no—
619C4#1062311111yescharacteristic
620C4#1062311611yescharacteristic
621C4#1062320911yescharacteristic
622C4#1062326511yescharacteristic
623C2—881no—
624C2#1307256011yescharacteristic
625C2#1307878011yescharacteristic
626C2#1307885011yescharacteristic
627C2#1308065311yescharacteristic
628C2#1308066311yescharacteristic
629C2#1308067911yescharacteristic
630C2#1308092911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1987C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenter#1987D11
hypocenterC11#26750
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1987

Complements

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

NH ≅ G/Ntype
3. #13069939C2semidirect
5. #13069754C2semidirect
7. #13069307C2semidirect
8. #13069250C2semidirect
10. #13069204C2semidirect
11. #13068958C2semidirect
14. #13068445C2semidirect
15. C11×#1987C2semidirect
213. #1987D11semidirect
521. C11#26750semidirect

Maximal subgroups

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

subgroupindex
#130729932
#130716452
#130699392
#130698152
#130697542
#130696272
#130693072
#130692502
#130692282
#130692042
#130689582
#130689272
#130687102
#130684452
C11×#19872
#2675011