Finite Group Databasebeta

← #14822251

Subgroups — #14822251

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#13072986C211yesmaximal, characteristic
2#13071643C211yesmaximal, characteristic
3#13069940C211yesmaximal, characteristic, complemented
4#13069812C211yesmaximal, characteristic
5#13069756C211yesmaximal, characteristic, complemented
6#13069626C211yesmaximal, characteristic
7#13069562C211yesmaximal, characteristic, complemented
8#13069304C211yesmaximal, characteristic, complemented
9#13069248C211yesmaximal, characteristic, complemented
10#13069226C211yesmaximal, characteristic
11#13069199C211yesmaximal, characteristic, complemented
12#13068958C211yesmaximal, characteristic, complemented
13#13068928C211yesmaximal, characteristic
14#13068445C211yesmaximal, characteristic, complemented
15C11×#1825C211yesmaximal, characteristic
16C2×C11×#117C2211yescharacteristic
17C2×#66977C2211yescharacteristic
18C2×#66977C2211yescharacteristic
19C22×Dic44C2211yescharacteristic
20C2×#66941C2211yescharacteristic
21C2×#66940C2211yescharacteristic
22C2×C11×C22⋊C8C2211yescharacteristic
23C11×#380C2211yescharacteristic
24C4×C22⋊Dic11C2211yescharacteristic
25C2×C22⋊(C11⋊C8)C2211yescharacteristic
26C2×#66880C2211yescharacteristic
27C2×#66880C2211yescharacteristic
28C2×#66879C2211yescharacteristic
29C2×Dic11⋊C8C2211yescharacteristic
30C4⋊C4×Dic11C2211yescharacteristic
31C4⋊C4×Dic11C2211yescharacteristic
32#10622587C2211yescharacteristic
33#10622587C2211yescharacteristic
34#10622587C2211yescharacteristic
35#10622586C2211yescharacteristic
36C2×#66874C2211yescharacteristic
37C2×#66874C2211yescharacteristic
38C2×#66874C2211yescharacteristic
39C2×#66874C2211yescharacteristic
40C2×#66872C2211yescharacteristic
41#10622560—21no—
42#10622558—21no—
43#10622557—21no—
44#10622557—21no—
45#10622546—21no—
46C4×Dic11⋊C4—21no—
47#10622271—21no—
48#10622259—21no—
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C22×Dic22—21no—
61C22×Dic22C2311yescharacteristic
62C22×Dic22C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C11×#117—22no—
66C11×#117—41no—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C22⋊C4—21no—
72C2×C11×C22⋊C4—21no—
73C2×C42×C11—21no—
74C2×C22⋊Dic11—21no—
75C2×C22⋊Dic11—21no—
76C2×C22⋊Dic11D411yescharacteristic
77C2×C22⋊Dic11D411yescharacteristic
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4⋊Dic11C2311yescharacteristic
80#66977—22no—
81#66977—22no—
82#66977—22no—
83#66977—41no—
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×C4×Dic11—21no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11C2311yescharacteristic
93C2×C4×Dic11C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C2×Dic44—22no—
97C2×Dic44—41no—
98C2×Dic44—41no—
99#66941—22no—
100#66941—41no—
101#66940—22no—
102#66940—41no—
103C11×C22⋊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
116C22⋊(C11⋊C8)—41no—
117#66880—22no—
118#66880—22no—
119#66879—41no—
120Dic11⋊C8—41no—
121#66874—22no—
122#66874—22no—
123#66874—41no—
124#66874—41no—
125#66872—22no—
126#26750—111nomaximal, Sylow
127C24×C11C2×D411yescharacteristic
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2411yescharacteristic
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11C2×D411yescharacteristic
145C22×Dic11C2×D411yescharacteristic
146C22×Dic11C2×D411yescharacteristic
147C22×Dic11C2×D411yescharacteristic
148C2×Dic22—21no—
149C2×Dic22—21no—
150C2×Dic22—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—42no—
160C2×Dic22—42no—
161C2×Dic22—81no—
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—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4#4112yes—
177C11×C22⋊C4—42no—
178C11×C22⋊C4—81no—
179C42×C11—42no—
180C22⋊Dic11—24no—
181C22⋊Dic11—22no—
182C22⋊Dic11—41no—
183C22⋊Dic11—42no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11#4112yes—
187C4⋊Dic11#4112yes—
188Dic11⋊C4—24no—
189Dic11⋊C4—42no—
190Dic11⋊C4—42no—
191Dic11⋊C4—42no—
192Dic11⋊C4—42no—
193C4×Dic11—21no—
194C4×Dic11—21no—
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#1987—111no—
214#1935—111no—
215#1927—111no—
216#1924—111no—
217#1920—111no—
218#1878—111no—
219#1873—111no—
220#1825D1111yescharacteristic
221#1763—111no—
222C23×C11—21no—
223C23×C11—21no—
224C23×C11—21no—
225C23×C11—21no—
226C23×C11—21no—
227C23×C11—21no—
228C23×C11—21no—
229C23×C11C22×D411yescharacteristic
230C2×C4×C11—21no—
231C2×C4×C11—22no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
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—41no—
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—21no—
257C2×Dic11—22no—
258C2×Dic11—22no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—22no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11#13712yes—
279Dic22—22no—
280Dic22—22no—
281Dic22—41no—
282Dic22—41no—
283Dic22—41no—
284Dic22—41no—
285Dic22—41no—
286Dic22—41no—
287Dic22—84no—
288C8×C11—41no—
289C8×C11—41no—
290C11⋊C8—41no—
291C11⋊C8—41no—
292C22×Q16—111no—
293C2×C4⋊Q8—111no—
294C2×C22⋊Q8—111no—
295C2×C22⋊Q8—111no—
296C2×C4×Q8—111no—
297C2×#117C2×D1111yescharacteristic
298C2×#106—111no—
299C2×C4⋊C8—111no—
300C2×#103—111no—
301C2×#103—111no—
302C2×#103—111no—
303C2×#103—111no—
304C2×#103—111no—
305C2×#103—111no—
306C2×C22⋊C8—111no—
307C2×C22⋊C8C2×D1111yescharacteristic
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#380C2×D1111yescharacteristic
321C4×C4⋊C4—111no—
322C4×C4⋊C4—111no—
323C4×C4⋊C4—221no—
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—41no—
336C22×C11—41no—
337C22×C11—41no—
338C22×C11—41no—
339C22×C11—41no—
340C22×C11—41no—
341C22×C11—41no—
342C22×C11#52511yescharacteristic
343C22×C11#54611yescharacteristic
344C22×C11#54611yescharacteristic
345C22×C11C2×#13711yescharacteristic
346C22×C11#57511yescharacteristic
347C22×C11#57711yescharacteristic
348C22×C11#57811yescharacteristic
349C4×C11—42no—
350C4×C11—41no—
351C4×C11—81no—
352C4×C11—81no—
353C4×C11—81no—
354C4×C11#52911yescharacteristic
355C4×C11#53811yescharacteristic
356C4×C11#55511yescharacteristic
357C4×C11#55911yescharacteristic
358Dic11—22no—
359Dic11—41no—
360Dic11—42no—
361Dic11—42no—
362Dic11—41no—
363Dic11—42no—
364Dic11—41no—
365Dic11—81no—
366C22×Q8—111no—
367C22×Q8—111no—
368C22×Q8—221no—
369C23×C4C22×D1111yescharacteristic
370C2×Q16—222no—
371C2×Q16—441no—
372C2×Q16—441no—
373C22×C8—111no—
374C22×C8—111no—
375C22×C8C22×D1111yescharacteristic
376C22×C8C22×D1111yescharacteristic
377C4⋊Q8—222no—
378C4⋊Q8—441no—
379C22⋊Q8—222no—
380C22⋊Q8—222no—
381C22⋊Q8—222no—
382C22⋊Q8—441no—
383C4×Q8—222no—
384C4×Q8—441no—
385#117—22no—
386#117—41no—
387C2×C4⋊C4—111no—
388C2×C4⋊C4—111no—
389C2×C4⋊C4—221no—
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—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—111no—
401C2×C22⋊C4—111no—
402C2×C22⋊C4—221no—
403C2×C22⋊C4—221no—
404C2×C42—21no—
405C2×C42—111no—
406C2×C42—111no—
407C2×C42—221no—
408C2×C42—221no—
409C2×C42—221no—
410#106—222no—
411C4⋊C8—441no—
412#103—222no—
413#103—222no—
414#103—222no—
415#103—222no—
416#103—441no—
417#103—441no—
418C22⋊C8—41no—
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—81no—
434C2×C11#245911yescharacteristic
435C2×C11#311611yescharacteristic
436C2×C11#312111yescharacteristic
437C2×C11#331111yescharacteristic
438C2×C11#331211yescharacteristic
439C2×C11#331311yescharacteristic
440C2×C11#333111yescharacteristic
441C24D4×D1111yescharacteristic
442C2×Q8—112no—
443C2×Q8—221no—
444C2×Q8—221no—
445C2×Q8—221no—
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—442no—
455C2×Q8—442no—
456C2×Q8—881no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—111no—
468C22×C4—111no—
469C22×C4—111no—
470C22×C4—111no—
471C22×C4—221no—
472C22×C4—221no—
473C22×C4—221no—
474C22×C4—221no—
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—21no—
496C4⋊C4—21no—
497C4⋊C4—112no—
498C4⋊C4—112no—
499C4⋊C4—224no—
500C4⋊C4—221no—
501C4⋊C4—221no—
502C4⋊C4—442no—
503C4⋊C4—442no—
504C4⋊C4—442no—
505C4⋊C4—442no—
506C4⋊C4#433912yes—
507C22⋊C4—42no—
508C22⋊C4—81no—
509C22⋊C4—222no—
510C22⋊C4—224no—
511C22⋊C4—441no—
512C22⋊C4—442no—
513C42—42no—
514C42—221no—
515C42—221no—
516C42—221no—
517C42—221no—
518C42—442no—
519C42—442no—
520C42—881no—
521C11#2675011yescharacteristic, complemented, Sylow
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23—21no—
529C23C2×D4×D1111yescharacteristic
530Q8—222no—
531Q8—222no—
532Q8—441no—
533Q8—441no—
534Q8—441no—
535Q8—441no—
536Q8—441no—
537Q8—441no—
538Q8—884no—
539C2×C4—21no—
540C2×C4—22no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
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—41no—
557C2×C4—41no—
558C2×C4—112no—
559C2×C4—221no—
560C2×C4—221no—
561C2×C4—221no—
562C2×C4—221no—
563C2×C4—221no—
564C2×C4—221no—
565C2×C4—221no—
566C2×C4—221no—
567C2×C4—221no—
568C2×C4—221no—
569C2×C4—221no—
570C2×C4—222no—
571C2×C4—222no—
572C2×C4—222no—
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×C4C2×#433911yescharacteristic
583C2×C4#6703711yescharacteristic
584C2×C4#41×D1111yescharacteristic
585C2×C4#41×D1111yescharacteristic
586C2×C4#41×D1111yescharacteristic
587C2×C4#6704211yescharacteristic
588C8—41no—
589C8—41no—
590C8—441no—
591C8—441no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22#1062302111yescharacteristic
600C22#1062318511yescharacteristic
601C22#1062318711yescharacteristic
602C22#1062329911yescharacteristic
603C22#1062330211yescharacteristic
604C22#1062330611yescharacteristic
605C22D11×#13711yescharacteristic
606C4—42no—
607C4—41no—
608C4—81no—
609C4—81no—
610C4—81no—
611C4—222no—
612C4—441no—
613C4—442no—
614C4—441no—
615C4—441no—
616C4—442no—
617C4—442no—
618C4—881no—
619C4#1062305911yescharacteristic
620C4#1062306311yescharacteristic
621C4#1062318811yescharacteristic
622C4#1062319511yescharacteristic
623C2—81no—
624C2#1307255011yescharacteristic
625C2#1307877311yescharacteristic
626C2#1307884011yescharacteristic
627C2#1308065011yescharacteristic
628C2#1308067011yescharacteristic
629C2#1308067811yescharacteristic
630C2#1308092811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1825C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#1825D11
hypocenterC11#26750
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1825

Complements

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

NH ≅ G/Ntype
3. #13069940C2semidirect
5. #13069756C2semidirect
7. #13069562C2semidirect
8. #13069304C2semidirect
9. #13069248C2semidirect
11. #13069199C2semidirect
12. #13068958C2semidirect
14. #13068445C2semidirect
521. C11#26750semidirect

Maximal subgroups

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

subgroupindex
#130729862
#130716432
#130699402
#130698122
#130697562
#130696262
#130695622
#130693042
#130692482
#130692262
#130691992
#130689582
#130689282
#130684452
C11×#18252
#2675011