Finite Group Databasebeta

← #14660232

Subgroups — #14660232

Order 2816.

990 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622618C211yesmaximal, characteristic
2C2×#10622752C211yesmaximal, characteristic
3#13077034C211yesmaximal, characteristic, complemented
4#13071106C211yesmaximal, characteristic
5#13068348C211yesmaximal, characteristic, complemented
6C2×#10622161C211yesmaximal, characteristic, complemented
7C2×C11×#339C211yesmaximal, characteristic, complemented
8C22×#4339C2211yescharacteristic
9C22×C11×M16C2211yescharacteristic
10C2×C11×#117C2211yescharacteristic
11C22×C42×C11C2211yescharacteristic
12C2×#66979C2211yescharacteristic
13C2×#66979C2211yescharacteristic
14C22×#4318C2211yescharacteristic
15#10622826—22no—
16#10622752—22no—
17#10622752C414yescomplemented
18C2×#66889—22no—
19#10622735—22no—
20M16×Dic11—22no—
21#10622714—22no—
22#10622618—22no—
23#10622618C414yescomplemented
24#10622552C412yescomplemented
25C4×(C2×D11)⋊C4—22no—
26#10622542C412yescomplemented
27C2×#66869—22no—
28C11×#339—22no—
29#10622165—22no—
30#10622161—22no—
31C23×C4×C11—21no—
32C23×C4×C11C2311yescharacteristic
33C22×C22⋊D11—21no—
34C2×#4339—21no—
35C2×#4339—21no—
36C2×#4339—21no—
37C2×#4339—21no—
38C2×#4339—21no—
39C2×#4339—21no—
40C2×#4339—21no—
41C2×#4339—21no—
42C2×#4339—21no—
43C2×#4339—21no—
44C2×#4339C2×C412yes—
45C2×#4339C2×C412yes—
46C22×D44C2×C411yescharacteristic
47C22×C4×D11—21no—
48C22×Dic22C2×C411yescharacteristic
49C2×C11×M16—21no—
50C2×C11×M16—21no—
51C2×C11×M16—21no—
52C2×C11×M16C2×C412yes—
53C2×C11×M16D412yes—
54C2×C11×M16D412yes—
55C22×C8×C11—21no—
56C11×#117—21no—
57C11×#117—21no—
58C11×#117—21no—
59C11×#117C2×C412yes—
60C2×C11×C4⋊C4—21no—
61C2×C11×C22⋊C4—21no—
62C2×C42×C11—21no—
63C2×C42×C11—21no—
64C2×C42×C11—21no—
65C2×C42×C11—21no—
66C2×C42×C11—21no—
67C2×C42×C11—21no—
68C2×C42×C11C2×C412yes—
69C2×C22⋊Dic11—21no—
70C2×C22⋊Dic11D412yes—
71C2×(C2×D11)⋊C4—24no—
72#66979—21no—
73#66979—21no—
74#66979—21no—
75#66979—21no—
76#66979—21no—
77#66979—21no—
78#66979—21no—
79#66979C2×C412yes—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11C2×C412yes—
82C2×C4×Dic11—21no—
83C2×C4×Dic11D412yes—
84C2×#4318—21no—
85C2×#4318—21no—
86C2×#4318—21no—
87C2×#4318C2×C412yes—
88C2×#4318D412yes—
89C2×#4318D412yes—
90C22×C11⋊C8—21no—
91C11⋊#95—24no—
92#66889—28no—
93#66879—24no—
94C8×Dic11—24no—
95#66869—28no—
96#10959—111nomaximal, Sylow
97C24×C11C2×D411yescharacteristic
98C23×D11—21no—
99C22×C4×C11—22no—
100C22×C4×C11—44no—
101C22×C4×C11—41no—
102C22×C4×C11—41no—
103C22×C4×C11—41no—
104C22×C4×C11C22×C411yescharacteristic
105C22×C4×C11C22×C411yescharacteristic
106C22×C4×C11C22×C411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11#4111yescharacteristic
113C22×C4×C11#4111yescharacteristic
114C22×C4×C11#4111yescharacteristic
115C22×C4×C11#4111yescharacteristic
116C22×C4×C11#4111yescharacteristic
117C22×C4×C11#4111yescharacteristic
118C2×C22⋊D11—22no—
119C2×C22⋊D11—22no—
120C2×C22⋊D11—41no—
121C2×C22⋊D11—41no—
122C2×C22⋊D11—41no—
123C2×C22⋊D11—41no—
124C22×Dic11—21no—
125C22×Dic11—41no—
126C22×Dic11C22⋊C414yes—
127#4339—22no—
128#4339—22no—
129#4339—22no—
130#4339—22no—
131#4339—22no—
132#4339—22no—
133#4339—22no—
134#4339—22no—
135#4339—41no—
136#4339—41no—
137#4339—41no—
138#4339—41no—
139#4339—41no—
140#4339—41no—
141#4339—41no—
142#4339—41no—
143C2×D44—21no—
144C2×D44—21no—
145C2×D44—21no—
146C2×D44—21no—
147C2×D44—21no—
148C2×D44C4212yes—
149C2×C4×D11—22no—
150C2×C4×D11—22no—
151C2×C4×D11—41no—
152C2×C4×D11—41no—
153C2×C4×D11—41no—
154C2×C4×D11—41no—
155C2×Dic22—21no—
156C2×Dic22—21no—
157C2×Dic22—21no—
158C2×Dic22—21no—
159C2×Dic22—21no—
160C2×Dic22C4212yes—
161C11×M16—22no—
162C11×M16—22no—
163C11×M16—22no—
164C11×M16C22⋊C414yescomplemented
165C2×C8×C11—22no—
166C2×C8×C11—22no—
167C2×C8×C11—22no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—41no—
170C11×C22⋊C4—22no—
171C11×C22⋊C4—41no—
172C42×C11—22no—
173C42×C11—22no—
174C42×C11—22no—
175C42×C11—41no—
176C42×C11—41no—
177C42×C11—41no—
178C22⋊Dic11—22no—
179C22⋊Dic11—22no—
180C22⋊Dic11—22no—
181C22⋊Dic11—41no—
182(C2×D11)⋊C4—48no—
183C4⋊Dic11—22no—
184C4⋊Dic11—22no—
185C4⋊Dic11—22no—
186C4⋊Dic11—41no—
187C4×Dic11—22no—
188C4×Dic11—22no—
189C4×Dic11—22no—
190C4×Dic11—41no—
191#4318—22no—
192#4318—22no—
193#4318—22no—
194#4318C22⋊C414yescomplemented
195C2×C11⋊C8—22no—
196C2×C11⋊C8—22no—
197C2×C11⋊C8—22no—
198C2×#421—111no—
199C2×#421—111no—
200#2873—111no—
201#2297—111no—
202#1740—111no—
203C2×#339—111no—
204C2×#339D1111yescharacteristic, complemented
205C23×C11—42no—
206C23×C11C2×C22⋊C411yescharacteristic
207C23×C11C4×D411yescharacteristic
208C23×C11C4×D411yescharacteristic
209C23×C11#12111yescharacteristic
210C23×C11#12111yescharacteristic
211C23×C11#12411yescharacteristic
212C23×C11#12711yescharacteristic
213C22×D11—22no—
214C22×D11—44no—
215C22×D11—41no—
216C22×D11—41no—
217C2×C4×C11—24no—
218C2×C4×C11—42no—
219C2×C4×C11—44no—
220C2×C4×C11—44no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—82no—
224C2×C4×C11C2×C4211yescharacteristic
225C2×C4×C11C2×C22⋊C411yescharacteristic
226C2×C4×C11C2×C22⋊C411yescharacteristic
227C2×C4×C11#11711yescharacteristic
228C2×C4×C11#11711yescharacteristic
229C2×C4×C11#11711yescharacteristic
230C2×C4×C11C4×D411yescharacteristic
231C2×C4×C11C4×D411yescharacteristic
232C2×C4×C11C4×D411yescharacteristic
233C2×C4×C11C4×D411yescharacteristic
234C2×C4×C11C4×D411yescharacteristic
235C2×C4×C11C4×D411yescharacteristic
236C2×C4×C11C4×D411yescharacteristic
237C2×C4×C11C4×D411yescharacteristic
238C2×C4×C11C4×D411yescharacteristic
239C2×C4×C11C4×D411yescharacteristic
240C2×C4×C11#12011yescharacteristic
241C2×C4×C11#12111yescharacteristic
242C2×C4×C11#12111yescharacteristic
243C2×C4×C11#12111yescharacteristic
244C2×C4×C11#12111yescharacteristic
245C2×C4×C11#12311yescharacteristic
246C2×C4×C11#12311yescharacteristic
247C2×C4×C11#12311yescharacteristic
248C2×C4×C11#12411yescharacteristic
249C2×C4×C11#12411yescharacteristic
250C2×C4×C11#12611yescharacteristic
251C2×C4×C11#12611yescharacteristic
252C22⋊D11—42no—
253C22⋊D11—42no—
254C22⋊D11—42no—
255C22⋊D11—42no—
256C2×Dic11—22no—
257C2×Dic11—24no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—44no—
261C2×Dic11—42no—
262C2×Dic11—82no—
263D44—22no—
264D44—22no—
265D44—41no—
266D44—41no—
267C4×D11—42no—
268C4×D11—42no—
269C4×D11—42no—
270C4×D11—42no—
271Dic22—22no—
272Dic22—22no—
273Dic22—41no—
274Dic22—41no—
275C8×C11—24no—
276C11⋊C8—24no—
277C22×#41—111no—
278C22×M16—111no—
279C22×M16C2×D1111yescharacteristic
280C2×#117—111no—
281C2×#117—111no—
282C2×#117C2×D1111yescharacteristic
283C22×C42C2×D1111yescharacteristic
284#421—114no—
285#421—114no—
286#421—222no—
287#421—222no—
288C2×#104—222no—
289C2×#104—222no—
290#405—222no—
291#405—222no—
292C4×M16—222no—
293#391—112no—
294#390—112no—
295#386—222no—
296C4×C22⋊C4—222no—
297#342—222no—
298#339—22no—
299#339—222no—
300C22×C11—22no—
301C22×C11—22no—
302C22×C11—22no—
303C22×C11—41no—
304C22×C11—41no—
305C22×C11—41no—
306C22×C11—41no—
307C22×C11C4×C22⋊C411yescharacteristic
308C22×C11#38611yescharacteristic
309C22×C11#38811yescharacteristic
310C22×C11#38811yescharacteristic
311C22×C11#39011yescharacteristic
312C22×C11#39011yescharacteristic
313C22×C11#39011yescharacteristic
314C2×D11—44no—
315C2×D11—42no—
316C2×D11—82no—
317C2×D11—82no—
318C4×C11—44no—
319C4×C11—82no—
320C4×C11C4×C22⋊C411yescharacteristic
321C4×C11C4×C22⋊C411yescharacteristic
322C4×C11#38611yescharacteristic
323C4×C11#38611yescharacteristic
324C4×C11#38811yescharacteristic
325C4×C11#38811yescharacteristic
326C4×C11#38811yescharacteristic
327C4×C11#38811yescharacteristic
328Dic11—44no—
329Dic11—42no—
330Dic11—82no—
331C2×#41—112no—
332C2×#41—112no—
333C2×#41—221no—
334C2×#41—221no—
335C2×#41—221no—
336C2×#41—221no—
337C2×#41—221no—
338C2×#41—221no—
339C2×#41—221no—
340C2×#41—221no—
341C2×#41—221no—
342C2×#41—221no—
343C22×Q8—111no—
344C22×D4—111no—
345C22×D4—221no—
346C23×C4—21no—
347C23×C4—221no—
348C23×C4C22×D1111yescharacteristic
349C2×M16—21no—
350C2×M16—21no—
351C2×M16—21no—
352C2×M16—112no—
353C2×M16—112no—
354C2×M16—112no—
355C2×M16—221no—
356C2×M16—221no—
357C2×M16—221no—
358C2×M16C4×D1112yes—
359C2×M16D4412yes—
360C2×M16C22⋊D1112yes—
361C22×C8—21no—
362C22×C8—221no—
363#117—21no—
364#117—21no—
365#117—21no—
366#117—112no—
367#117—221no—
368#117—221no—
369#117—221no—
370#117—221no—
371#117—221no—
372#117—221no—
373#117—221no—
374#117C4×D1112yes—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—112no—
377C2×C4⋊C4—221no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—112no—
380C2×C22⋊C4—221no—
381C2×C22⋊C4—224no—
382C2×C42—21no—
383C2×C42—21no—
384C2×C42—21no—
385C2×C42—21no—
386C2×C42—21no—
387C2×C42—21no—
388C2×C42—112no—
389C2×C42—221no—
390C2×C42C4×D1112yes—
391#104—228no—
392#104—228no—
393#97—224no—
394C4×C8—224no—
395#95—224no—
396C2×C11—21no—
397C2×C11—21no—
398C2×C11—21no—
399C2×C11—21no—
400C2×C11—21no—
401C2×C11—21no—
402C2×C11#143711yescharacteristic
403C2×C11#188412yes—
404D11—82no—
405C24—221no—
406C24D4×D1111yescharacteristic
407#41—222no—
408#41—222no—
409#41—222no—
410#41—222no—
411#41—222no—
412#41—222no—
413#41—222no—
414#41—222no—
415#41—441no—
416#41—441no—
417#41—441no—
418#41—441no—
419#41—441no—
420#41—441no—
421#41—441no—
422#41—441no—
423C2×Q8—112no—
424C2×Q8—221no—
425C2×Q8—221no—
426C2×Q8—221no—
427C2×Q8—221no—
428C2×Q8—221no—
429C2×D4—112no—
430C2×D4—222no—
431C2×D4—222no—
432C2×D4—221no—
433C2×D4—221no—
434C2×D4—221no—
435C2×D4—221no—
436C2×D4—221no—
437C2×D4—441no—
438C2×D4—441no—
439C2×D4—441no—
440C2×D4—441no—
441C22×C4—22no—
442C22×C4—44no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—114no—
447C22×C4—221no—
448C22×C4—222no—
449C22×C4—222no—
450C22×C4—441no—
451C22×C4—441no—
452C22×C4—441no—
453C22×C4—441no—
454C22×C4—441no—
455C22×C4C2×C4×D1111yescharacteristic
456C22×C4C2×C4×D1111yescharacteristic
457C22×C4C2×C4×D1111yescharacteristic
458C22×C4C2×D4411yescharacteristic
459C22×C4#433911yescharacteristic
460C22×C4#433911yescharacteristic
461C22×C4D4×D1111yescharacteristic
462C22×C4D4×D1111yescharacteristic
463C22×C4D4×D1111yescharacteristic
464C22×C4#434111yescharacteristic
465C22×C4#434111yescharacteristic
466C22×C4#434311yescharacteristic
467C22×C4#434311yescharacteristic
468C22×C4C2×C22⋊D1111yescharacteristic
469M16—22no—
470M16—22no—
471M16—22no—
472M16—114no—
473M16—222no—
474M16—222no—
475M16—222no—
476M16(C2×D11)⋊C414yescomplemented
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—222no—
481C2×C8—222no—
482C2×C8—222no—
483C4⋊C4—22no—
484C4⋊C4—41no—
485C4⋊C4—222no—
486C4⋊C4—222no—
487C4⋊C4—222no—
488C4⋊C4—441no—
489C22⋊C4—22no—
490C22⋊C4—41no—
491C22⋊C4—222no—
492C22⋊C4—222no—
493C22⋊C4—222no—
494C22⋊C4—448no—
495C22⋊C4—441no—
496C42—22no—
497C42—22no—
498C42—22no—
499C42—41no—
500C42—41no—
501C42—41no—
502C42—222no—
503C42—222no—
504C42—222no—
505C42—441no—
506C11#1095911yescharacteristic, complemented, Sylow
507C23—42no—
508C23—222no—
509C23—444no—
510C23—441no—
511C23—441no—
512C23C22⋊C4×D1111yescharacteristic
513C23(C22⋊D11)⋊C411yescharacteristic
514C23#6693711yescharacteristic
515C23#6693811yescharacteristic
516C23#6694611yescharacteristic
517C23#6694811yescharacteristic
518C23#6699311yescharacteristic
519Q8—222no—
520Q8—222no—
521Q8—441no—
522Q8—441no—
523D4—222no—
524D4—222no—
525D4—442no—
526D4—442no—
527D4—442no—
528D4—442no—
529D4—441no—
530D4—441no—
531C2×C4—24no—
532C2×C4—42no—
533C2×C4—44no—
534C2×C4—44no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—82no—
538C2×C4—224no—
539C2×C4—222no—
540C2×C4—441no—
541C2×C4—441no—
542C2×C4—442no—
543C2×C4—442no—
544C2×C4—442no—
545C2×C4—442no—
546C2×C4—444no—
547C2×C4—442no—
548C2×C4—882no—
549C2×C4C42×D1111yescharacteristic
550C2×C4#6692511yescharacteristic
551C2×C4C4×D4411yescharacteristic
552C2×C4C4×D4411yescharacteristic
553C2×C4C22⋊C4×D1111yescharacteristic
554C2×C4(C22⋊D11)⋊C411yescharacteristic
555C2×C4(C22⋊D11)⋊C411yescharacteristic
556C2×C4(C22⋊D11)⋊C411yescharacteristic
557C2×C4#6693511yescharacteristic
558C2×C4#6693711yescharacteristic
559C2×C4#6693811yescharacteristic
560C2×C4#6693911yescharacteristic
561C2×C4#6694511yescharacteristic
562C2×C4#6694511yescharacteristic
563C2×C4#6694611yescharacteristic
564C2×C4#6694611yescharacteristic
565C2×C4#6694611yescharacteristic
566C2×C4#6694711yescharacteristic
567C2×C4#6694711yescharacteristic
568C2×C4#6694811yescharacteristic
569C2×C4#6695111yescharacteristic
570C2×C4#6695111yescharacteristic
571C2×C4C2×(C2×D11)⋊C411yescharacteristic
572C2×C4C4×C22⋊D1111yescharacteristic
573C2×C4C4×C22⋊D1111yescharacteristic
574C2×C4#6699211yescharacteristic
575C2×C4#6699211yescharacteristic
576C2×C4#6700011yescharacteristic
577C8—24no—
578C8—224no—
579C22—22no—
580C22—22no—
581C22—22no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—444no—
587C22—442no—
588C22—882no—
589C22—882no—
590C22#1062227811yescharacteristic
591C22#1062227911yescharacteristic
592C22#1062228211yescharacteristic
593C22#1062228311yescharacteristic
594C22#1062257011yescharacteristic
595C22#1062257011yescharacteristic
596C22#1062260111yescharacteristic
597C4—44no—
598C4—82no—
599C4—442no—
600C4—444no—
601C4—882no—
602C4#1062227811yescharacteristic
603C4#1062227911yescharacteristic
604C4#1062228211yescharacteristic
605C4#1062228311yescharacteristic
606C4C4×(C2×D11)⋊C411yescharacteristic
607C4#1062257111yescharacteristic
608C4#1062260311yescharacteristic
609C4#1062260311yescharacteristic
610C2—21no—
611C2—21no—
612C2—21no—
613C2—21no—
614C2—21no—
615C2—21no—
616C2—882no—
617C2#1306685211yescharacteristic
618C2#1306899812yes—
subgroupG/H
centerC2×C4#66935
commutatorC2×C4×C11C2×C42
FrattiniC23×C4C22×D11
FittingC2×C11×#339C2
socleC22×C11#386
prime radicalC22×#4339C22
cosocleC23×C4×C11C23
hypercenterC2×#339D11
hypocenterC11#10959
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#339

Complements

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

NH ≅ G/Ntype
3. #13077034C2semidirect
5. #13068348C2semidirect
6. C2×#10622161C2semidirect
7. C2×C11×#339C2semidirect
17. #10622752C4semidirect
23. #10622618C4semidirect
24. #10622552C4semidirect
26. #10622542C4semidirect
164. C11×M16C22⋊C4semidirect
194. #4318C22⋊C4semidirect
204. C2×#339D11semidirect
476. M16(C2×D11)⋊C4semidirect
506. C11#10959semidirect

Maximal subgroups

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

subgroupindex
C2×#106226182
C2×#106227522
#130770342
#130711062
#130683482
C2×#106221612
C2×C11×#3392
#1095911