Finite Group Databasebeta

← #14758262

Subgroups — #14758262

Order 2816.

1106 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082019C211yesmaximal, characteristic
2#13077033C211yesmaximal, characteristic
3#13071096C211yesmaximal, characteristic
4#13069561C211yesmaximal, characteristic, complemented
5#13069560C211yesmaximal, characteristic, complemented
6#13069559C211yesmaximal, characteristic, complemented
7#13069558C212yesmaximal, complemented
8#13069558C212yesmaximal, complemented
9#13068324C212yesmaximal
10D11×#339C212yesmaximal
11C11×#1986C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C2×M16×D11C2212yes—
14#10623260C412yescomplemented
15#10623260C412yescomplemented
16#10623220C412yescomplemented
17#10623220C412yescomplemented
18#10623165—21no—
19#10623165—21no—
20#10623154—21no—
21#10623154—21no—
22#10623109—22no—
23#10623109—22no—
24D11×#117C2212yes—
25#10623048C2212yes—
26C2×#66925C2211yescharacteristic
27C2×#66925C2211yescharacteristic
28C2×C42×D11C2211yescharacteristic
29#10623001C2211yescharacteristic
30C4×C11×M16C2211yescharacteristic
31C4×C11×C4⋊C4C2211yescharacteristic
32M16×Dic11C2212yes—
33#10622602—21no—
34#10622585—21no—
35C4×C4⋊Dic11C2211yescharacteristic
36C4×Dic11⋊C4C2211yescharacteristic
37C4×Dic11⋊C4C2211yescharacteristic
38C4×#4318C2211yescharacteristic
39#10622321—22no—
40#10622302—22no—
41#10622281—21no—
42#10622260—21no—
43C11×#339C2212yes—
44C11×#339C2212yes—
45#10622193C2212yes—
46#10622193C2212yes—
47#10622170C2212yes—
48#10622170C2212yes—
49#10622161C2212yes—
50#10622161C2212yes—
51C22×C4×D11—21no—
52C22×C4×D11C2311yescharacteristic
53C2×C11×M16C2312yes—
54C11×C4⋊Q8C2×C411yescharacteristic, complemented
55C11×C4⋊Q8C2×C411yescharacteristic, complemented
56C11×#125C2×C412yescomplemented
57C11×C22⋊Q8—21no—
58C11×C22⋊Q8—21no—
59C4×Q8×C11—21no—
60C4×Q8×C11—21no—
61C11×#117C2312yes—
62C2×C11×C4⋊C4—21no—
63C2×C42×C11C2311yescharacteristic
64C2×C42×C11C2311yescharacteristic
65C2×C42×C11C2311yescharacteristic
66#66999—22no—
67#66999—22no—
68#66997—22no—
69#66997—22no—
70C2×(C2×D11)⋊C4—21no—
71C2×(C2×D11)⋊C4D411yescharacteristic
72C2×(C2×D11)⋊C4D411yescharacteristic
73#66979C2312yes—
74C2×C4⋊Dic11—21no—
75#66977—21no—
76#66977—21no—
77C2×Dic11⋊C4—21no—
78C2×Dic11⋊C4—21no—
79C2×Dic11⋊C4—21no—
80C2×Dic11⋊C4D411yescharacteristic
81C2×Dic11⋊C4D411yescharacteristic
82C2×C4×Dic11—21no—
83C2×C4×Dic11C2311yescharacteristic
84C2×C4×Dic11C2311yescharacteristic
85C2×C4×Dic11C2311yescharacteristic
86C2×#4318C2312yes—
87M16×D11—24no—
88M16×D11Q818yescomplemented
89C2×#4313—22no—
90C2×C8×D11—22no—
91#66950—22no—
92#66950—22no—
93#66949—22no—
94#66949—22no—
95#66949—22no—
96#66949—22no—
97#66945C2×C412yes—
98#66945C2×C412yes—
99C4⋊C4×D11C2×C412yes—
100C4⋊C4×D11C2×C412yes—
101#66943C2×C412yescomplemented
102#66943C2×C412yescomplemented
103#66942—22no—
104#66942—22no—
105#66942—22no—
106#66942—22no—
107#66941—22no—
108#66941—22no—
109#66941C2×C412yescomplemented
110#66941C2×C412yescomplemented
111C22⋊C4×D11—22no—
112#66931—22no—
113#66931—22no—
114#66930—22no—
115#66925—22no—
116#66925—24no—
117#66925C2×C412yes—
118#66925C2×C412yes—
119#66925D412yes—
120#66925D412yes—
121C42×D11—22no—
122C42×D11—24no—
123#66923C2×C412yescomplemented
124#66922C2×C411yescharacteristic, complemented
125#66922C2×C411yescharacteristic, complemented
126C4×Dic22—21no—
127C4×Dic22—21no—
128C4×Dic22—22no—
129C4×Dic22—22no—
130C11×#97—21no—
131C4×C8×C11—21no—
132C11×#95—21no—
133C11⋊#95—21no—
134C11⋊#95—21no—
135C11⋊#95—21no—
136#66879—22no—
137C8×Dic11—22no—
138#66867—21no—
139C4×C11⋊C8—21no—
140#21307—111nomaximal, Sylow
141C23×D11C2×D411yescharacteristic
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2411yescharacteristic
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11C2×D411yescharacteristic
152C22×Dic11C2×D411yescharacteristic
153C22×Dic11C2×D411yescharacteristic
154C2×C4×D11—22no—
155C2×C4×D11—22no—
156C2×C4×D11—42no—
157C2×C4×D11—42no—
158C2×C4×D11—42no—
159C2×C4×D11C22×C412yes—
160C2×C4×D11C2×D412yes—
161C2×C4×D11C2×Q814yes—
162C2×C4×D11#4114yes—
163C2×Dic22—22no—
164C2×Dic22—22no—
165C2×Dic22—21no—
166C2×Dic22—21no—
167C11×M16—22no—
168C11×M16C2×Q814yes—
169C2×C8×C11—22no—
170C11×C4⋊C4—22no—
171C11×C4⋊C4—22no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—42no—
175C11×C4⋊C4C22×C412yes—
176C11×C4⋊C4C22×C412yes—
177C11×C22⋊C4—22no—
178C42×C11—22no—
179C42×C11—22no—
180C42×C11—22no—
181C42×C11C22×C411yescharacteristic
182C42×C11C22×C411yescharacteristic
183C42×C11C2×D411yescharacteristic
184C42×C11C2×D411yescharacteristic
185C22⋊Dic11—22no—
186(C2×D11)⋊C4—22no—
187(C2×D11)⋊C4—22no—
188(C2×D11)⋊C4—42no—
189(C2×D11)⋊C4C22⋊C412yes—
190(C2×D11)⋊C4C22⋊C412yes—
191(C2×D11)⋊C4C22⋊C412yes—
192(C2×D11)⋊C4C22⋊C412yes—
193C4⋊Dic11—22no—
194C4⋊Dic11—22no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—42no—
198C4⋊Dic11C22×C412yes—
199C4⋊Dic11C22×C412yes—
200Dic11⋊C4—22no—
201Dic11⋊C4—22no—
202Dic11⋊C4—22no—
203Dic11⋊C4—22no—
204Dic11⋊C4—22no—
205Dic11⋊C4—22no—
206Dic11⋊C4—22no—
207Dic11⋊C4—22no—
208Dic11⋊C4—42no—
209Dic11⋊C4—42no—
210Dic11⋊C4—42no—
211Dic11⋊C4C22⋊C412yes—
212Dic11⋊C4C22⋊C412yes—
213Dic11⋊C4C22⋊C412yes—
214Dic11⋊C4C22⋊C412yes—
215C4×Dic11—22no—
216C4×Dic11—22no—
217C4×Dic11—22no—
218C4×Dic11—22no—
219C4×Dic11—22no—
220C4×Dic11—42no—
221C4×Dic11C22×C412yes—
222C4×Dic11C2×D412yes—
223#4318—22no—
224#4318C2×Q814yes—
225C2×C11⋊C8—22no—
226#4313—28no—
227C8×D11—28no—
228#3458—111no—
229#2873—111no—
230#2296—111no—
231#1986—111no—
232#1986—111no—
233#1986—112no—
234#1986—112no—
235#1986—111no—
236#1986D1111yescharacteristic, complemented
237#1733—112no—
238C2×#339—112no—
239C23×C11C22×D411yescharacteristic
240C22×D11—41no—
241C22×D11—41no—
242C22×D11C2×C22⋊C412yes—
243C22×D11#12412yes—
244C22×D11C4⋊Q812yes—
245Q8×C11—81no—
246Q8×C11—81no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11C2×C22⋊C411yescharacteristic
258C2×C4×C11C2×C22⋊C411yescharacteristic
259C2×C4×C11C2×C22⋊C411yescharacteristic
260C2×C4×C11C2×C22⋊C411yescharacteristic
261C2×C4×C11C23×C411yescharacteristic
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11C22×Q812yes—
264C2×C4×C11C2×#4112yes—
265C2×Dic11—22no—
266C2×Dic11—22no—
267C2×Dic11—22no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11C2×C22⋊C412yes—
276C2×Dic11C2×C22⋊C412yes—
277C2×Dic11C2×C22⋊C412yes—
278C2×Dic11#12412yes—
279C2×Dic11C4⋊Q812yes—
280C4×D11—48no—
281C4×D11—82no—
282C4×D11—82no—
283C4×D11C4×Q818yes—
284C4×D11C22⋊Q814yes—
285C4×D11C22⋊Q814yes—
286Dic22—82no—
287Dic22—82no—
288Dic22—81no—
289Dic22—81no—
290C8×C11—24no—
291C11⋊C8—24no—
292C22×M16—112no—
293#544—112no—
294#544—112no—
295#544—112no—
296#544—112no—
297#544—221no—
298#544—221no—
299#543—221no—
300#543—221no—
301#533—112no—
302#533—111no—
303#533—222no—
304#533—222no—
305#533C2×D1111yescharacteristic
306C2×#117—111no—
307C2×#117—111no—
308C2×#117—112no—
309C22×C42—111no—
310#405—222no—
311#405—222no—
312C4×M16—112no—
313C4×M16—111no—
314C4×M16C2×D1111yescharacteristic
315#389—221no—
316#389—221no—
317#385—221no—
318#385—221no—
319C4×C4⋊C4—111no—
320C4×C4⋊C4—111no—
321C4×C4⋊C4—111no—
322C4×C4⋊C4C2×D1111yescharacteristic
323#339—112no—
324#339—112no—
325#339—112no—
326#339—112no—
327#339—112no—
328#339—112no—
329#339C2×D1112yes—
330#339C2×D1112yes—
331C22×C11—21no—
332C22×C11—21no—
333C22×C11C22×C22⋊C411yescharacteristic
334C22×C11C2×#12411yescharacteristic
335C22×C11C2×C4⋊Q811yescharacteristic
336C2×D11—22no—
337C2×D11—22no—
338C2×D11—42no—
339C2×D11—42no—
340C2×D11#39114yes—
341C4×C11—21no—
342C4×C11—21no—
343C4×C11—21no—
344C4×C11—21no—
345C4×C11—42no—
346C4×C11—42no—
347C4×C11—42no—
348C4×C11—81no—
349C4×C11C2×C4×Q812yes—
350C4×C11C2×C22⋊Q812yes—
351Dic11—22no—
352Dic11—22no—
353Dic11—42no—
354Dic11—42no—
355Dic11—42no—
356Dic11—81no—
357Dic11#39114yes—
358C23×C4—111no—
359C23×C4—221no—
360C2×M16—112no—
361C2×M16—118no—
362C2×M16—222no—
363C2×M16—224no—
364C2×M16C22×D1112yes—
365C22×C8—222no—
366C4⋊Q8—112no—
367C4⋊Q8—112no—
368C4⋊Q8—111no—
369C4⋊Q8—111no—
370C4⋊Q8—222no—
371C4⋊Q8—222no—
372C4⋊Q8—222no—
373C4⋊Q8—222no—
374C4⋊Q8C4×D1111yescharacteristic, complemented
375C4⋊Q8C4×D1111yescharacteristic, complemented
376#125—112no—
377#125—112no—
378#125—112no—
379#125—222no—
380#125—222no—
381#125—222no—
382#125—222no—
383#125C4×D1112yescomplemented
384C22⋊Q8—21no—
385C22⋊Q8—21no—
386C22⋊Q8—222no—
387C22⋊Q8—222no—
388C22⋊Q8—222no—
389C22⋊Q8—222no—
390C22⋊Q8—222no—
391C22⋊Q8—222no—
392C22⋊Q8—222no—
393C22⋊Q8—222no—
394C22⋊Q8—222no—
395C22⋊Q8—222no—
396C22⋊Q8—221no—
397C22⋊Q8—221no—
398C4×Q8—21no—
399C4×Q8—21no—
400C4×Q8—222no—
401C4×Q8—222no—
402C4×Q8—221no—
403C4×Q8—221no—
404#117—112no—
405#117—112no—
406#117—112no—
407#117—112no—
408#117—112no—
409#117—112no—
410#117—112no—
411#117—222no—
412#117—224no—
413#117—222no—
414#117C22×D1112yes—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—111no—
417C2×C4⋊C4—111no—
418C2×C4⋊C4—112no—
419C2×C4⋊C4—112no—
420C2×C4⋊C4—221no—
421C2×C4⋊C4—221no—
422C2×C4⋊C4—221no—
423C2×C4⋊C4—221no—
424C2×C22⋊C4—111no—
425C2×C22⋊C4—111no—
426C2×C22⋊C4—222no—
427C2×C22⋊C4—221no—
428C2×C42—111no—
429C2×C42—111no—
430C2×C42—111no—
431C2×C42—222no—
432C2×C42—224no—
433C2×C42—221no—
434C2×C42C22×D1111yescharacteristic
435C2×C42C22×D1111yescharacteristic
436C2×C42C22×D1111yescharacteristic
437#97—21no—
438#97—222no—
439#97—221no—
440C4×C8—21no—
441C4×C8—222no—
442C4×C8—221no—
443#95—21no—
444#95—221no—
445#95—221no—
446#95—221no—
447C2×C11—21no—
448C2×C11—21no—
449C2×C11C2×#39111yescharacteristic
450C2×C11#290111yescharacteristic
451C2×C11#290111yescharacteristic
452D11—24no—
453C24—111no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—222no—
457C2×Q8—222no—
458C2×Q8—221no—
459C2×Q8—221no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—111no—
463C22×C4—112no—
464C22×C4—112no—
465C22×C4—114no—
466C22×C4—114no—
467C22×C4—111no—
468C22×C4—111no—
469C22×C4—222no—
470C22×C4—222no—
471C22×C4—221no—
472C22×C4—221no—
473C22×C4—442no—
474C22×C4—442no—
475C22×C4—442no—
476C22×C4D4×D1111yescharacteristic
477C22×C4D4×D1111yescharacteristic
478C22×C4C23×D1111yescharacteristic
479M16—22no—
480M16—114no—
481M16—228no—
482M16—222no—
483M16Q8×D1114yes—
484C2×C8—22no—
485C2×C8—228no—
486C2×C8—222no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—42no—
492C4⋊C4—112no—
493C4⋊C4—112no—
494C4⋊C4—112no—
495C4⋊C4—112no—
496C4⋊C4—112no—
497C4⋊C4—112no—
498C4⋊C4—222no—
499C4⋊C4—222no—
500C4⋊C4—222no—
501C4⋊C4—222no—
502C4⋊C4—222no—
503C4⋊C4—222no—
504C4⋊C4—222no—
505C4⋊C4—222no—
506C4⋊C4—222no—
507C4⋊C4—222no—
508C4⋊C4—221no—
509C4⋊C4—221no—
510C4⋊C4—442no—
511C4⋊C4—442no—
512C4⋊C4—442no—
513C4⋊C4—442no—
514C4⋊C4C2×C4×D1112yes—
515C4⋊C4C2×C4×D1112yes—
516C22⋊C4—22no—
517C22⋊C4—112no—
518C22⋊C4—112no—
519C22⋊C4—112no—
520C22⋊C4—112no—
521C22⋊C4—222no—
522C22⋊C4—222no—
523C22⋊C4—222no—
524C22⋊C4—442no—
525C42—22no—
526C42—22no—
527C42—22no—
528C42—112no—
529C42—112no—
530C42—222no—
531C42—222no—
532C42—222no—
533C42—222no—
534C42—222no—
535C42—442no—
536C42C2×C4×D1111yescharacteristic
537C42C2×C4×D1111yescharacteristic
538C42D4×D1111yescharacteristic
539C42D4×D1111yescharacteristic
540C11#2130711yescharacteristic, complemented, Sylow
541C23—112no—
542C23—112no—
543C23—112no—
544C23—441no—
545C23—441no—
546C23C2×D4×D1111yescharacteristic
547Q8—81no—
548Q8—81no—
549Q8—881no—
550Q8—881no—
551Q8—882no—
552Q8—882no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—112no—
564C2×C4—112no—
565C2×C4—112no—
566C2×C4—118no—
567C2×C4—114no—
568C2×C4—114no—
569C2×C4—112no—
570C2×C4—112no—
571C2×C4—222no—
572C2×C4—222no—
573C2×C4—222no—
574C2×C4—448no—
575C2×C4—441no—
576C2×C4—441no—
577C2×C4—441no—
578C2×C4—441no—
579C2×C4—441no—
580C2×C4—441no—
581C2×C4—441no—
582C2×C4—882no—
583C2×C4—882no—
584C2×C4C22⋊C4×D1111yescharacteristic
585C2×C4C22⋊C4×D1111yescharacteristic
586C2×C4C22⋊C4×D1111yescharacteristic
587C2×C4C22⋊C4×D1111yescharacteristic
588C2×C4C22×C4×D1111yescharacteristic
589C2×C4C2×D4×D1111yescharacteristic
590C2×C4C2×Q8×D1112yes—
591C2×C4#41×D1112yes—
592C8—24no—
593C8—224no—
594C22—21no—
595C22—21no—
596C22—114no—
597C22—222no—
598C22—222no—
599C22—442no—
600C22—442no—
601C22C2×C22⋊C4×D1111yescharacteristic
602C22D11×#12411yescharacteristic
603C22D11×C4⋊Q811yescharacteristic
604C4—21no—
605C4—21no—
606C4—21no—
607C4—21no—
608C4—42no—
609C4—42no—
610C4—42no—
611C4—81no—
612C4—114no—
613C4—222no—
614C4—222no—
615C4—442no—
616C4—442no—
617C4—442no—
618C4—881no—
619C4C4×Q8×D1112yes—
620C4D11×C22⋊Q812yes—
621C2—21no—
622C2—21no—
623C2—224no—
624C2D11×#39111yescharacteristic
625C2#1307716011yescharacteristic
626C2#1307716211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1986C2
socleC22×C11C22×C22⋊C4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1986D11
hypocenterC11#21307
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1986

Complements

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

NH ≅ G/Ntype
4. #13069561C2semidirect
5. #13069560C2semidirect
6. #13069559C2semidirect
7. #13069558C2semidirect
8. #13069558C2semidirect
11. C11×#1986C2semidirect
14. #10623260C4semidirect
15. #10623260C4semidirect
16. #10623220C4semidirect
17. #10623220C4semidirect
54. C11×C4⋊Q8C2×C4semidirect
55. C11×C4⋊Q8C2×C4semidirect
56. C11×#125C2×C4semidirect
88. M16×D11Q8semidirect
101. #66943C2×C4semidirect
102. #66943C2×C4semidirect
109. #66941C2×C4semidirect
110. #66941C2×C4semidirect
123. #66923C2×C4semidirect
124. #66922C2×C4semidirect
125. #66922C2×C4semidirect
236. #1986D11semidirect
374. C4⋊Q8C4×D11semidirect
375. C4⋊Q8C4×D11semidirect
383. #125C4×D11semidirect
540. C11#21307semidirect

Maximal subgroups

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

subgroupindex
#130820192
#130770332
#130710962
#130695612
#130695602
#130695592
#130695582
#130683242
D11×#3392
C11×#19862
#2130711