Finite Group Databasebeta

← #14660220

Subgroups — #14660220

Order 2816.

918 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622752C211yesmaximal, characteristic
2#13077136C211yesmaximal, characteristic
3C2×#10622723C211yesmaximal, characteristic
4#13077034C211yesmaximal, characteristic, complemented
5C2×#10622197C211yesmaximal, characteristic, complemented
6#13068333C211yesmaximal, characteristic, complemented
7C2×C11×#341C211yesmaximal, characteristic, complemented
8C22×#4339C2211yescharacteristic
9C22×C11×M16C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C23×C8×C11C2211yescharacteristic
12C2×#66979C2211yescharacteristic
13C2×#66979C2211yescharacteristic
14C22×#4318C2211yescharacteristic
15#10622752—22no—
16#10622752C414yescomplemented
17C2×#66889—22no—
18#10622746—22no—
19#10622744C412yescomplemented
20#10622735—22no—
21#10622733C412yescomplemented
22M16×Dic11—22no—
23#10622726—22no—
24#10622723—22no—
25#10622723C414yescomplemented
26C2×(C2×D11)⋊C8—22no—
27#10622714—22no—
28C11×#341—22no—
29#10622197—22no—
30#10622189—22no—
31C23×C4×C11C2311yescharacteristic
32C22×C22⋊D11—21no—
33C2×#4339—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×#4339C2×C412yes—
44C2×#4339C2×C412yes—
45C22×D44C2×C411yescharacteristic
46C22×C4×D11—21no—
47C22×Dic22C2×C411yescharacteristic
48C2×C11×M16—21no—
49C2×C11×M16—21no—
50C2×C11×M16—21no—
51C2×C11×M16—21no—
52C2×C11×M16—21no—
53C2×C11×M16—21no—
54C2×C11×M16—21no—
55C2×C11×M16—21no—
56C2×C11×M16C2×C412yes—
57C2×C11×M16C2×C412yes—
58C2×C11×M16D412yes—
59C2×C11×M16D412yes—
60C22×C8×C11—21no—
61C22×C8×C11—21no—
62C22×C8×C11—21no—
63C22×C8×C11—21no—
64C22×C8×C11—21no—
65C22×C8×C11—21no—
66C22×C8×C11—21no—
67C22×C8×C11—21no—
68C22×C8×C11C2×C412yes—
69C2×C22⋊Dic11—21no—
70C2×C22⋊Dic11—21no—
71#66979—21no—
72#66979—21no—
73#66979—21no—
74#66979—21no—
75#66979—21no—
76#66979C2×C412yes—
77#66979C2×C412yes—
78#66979D412yes—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11D412yes—
81C2×C4×Dic11—21no—
82C2×C4×Dic11—21no—
83C2×#4318—21no—
84C2×#4318—21no—
85C2×#4318—21no—
86C2×#4318—21no—
87C2×#4318C2×C412yes—
88C2×#4318D412yes—
89C22×C11⋊C8D412yes—
90#66889—28no—
91#66885—24no—
92(C2×D11)⋊C8—28no—
93#66880—24no—
94#66879—24no—
95C8×Dic11—24no—
96#10956—111nomaximal, Sylow
97C24×C11#4111yescharacteristic
98C23×D11—21no—
99C22×C4×C11C22×C411yescharacteristic
100C22×C4×C11C22×C411yescharacteristic
101C22×C4×C11C22×C411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11#4111yescharacteristic
109C22×C4×C11#4111yescharacteristic
110C22×C4×C11#4111yescharacteristic
111C22×C4×C11#4111yescharacteristic
112C22×C4×C11#4111yescharacteristic
113C2×C22⋊D11—22no—
114C2×C22⋊D11—22no—
115C2×C22⋊D11—41no—
116C2×C22⋊D11—41no—
117C2×C22⋊D11—41no—
118C2×C22⋊D11—41no—
119C22×Dic11—21no—
120C22×Dic11—22no—
121C22×Dic11—41no—
122#4339—22no—
123#4339—22no—
124#4339—22no—
125#4339—22no—
126#4339—22no—
127#4339—22no—
128#4339—22no—
129#4339—22no—
130#4339—41no—
131#4339—41no—
132#4339—41no—
133#4339—41no—
134#4339—41no—
135#4339—41no—
136#4339—41no—
137#4339—41no—
138C2×D44—21no—
139C2×D44—21no—
140C2×D44—21no—
141C2×D44—21no—
142C2×D44—21no—
143C2×D44C4212yes—
144C2×C4×D11—22no—
145C2×C4×D11—22no—
146C2×C4×D11—41no—
147C2×C4×D11—41no—
148C2×C4×D11—41no—
149C2×C4×D11—41no—
150C2×Dic22—21no—
151C2×Dic22—21no—
152C2×Dic22—21no—
153C2×Dic22—21no—
154C2×Dic22—21no—
155C2×Dic22C4212yes—
156C11×M16—22no—
157C11×M16—22no—
158C11×M16—22no—
159C11×M16—22no—
160C11×M16—22no—
161C11×M16—41no—
162C11×M16—41no—
163C11×M16C22⋊C414yes—
164C2×C8×C11—22no—
165C2×C8×C11—22no—
166C2×C8×C11—22no—
167C2×C8×C11—22no—
168C2×C8×C11—22no—
169C2×C8×C11—22no—
170C2×C8×C11—22no—
171C2×C8×C11—41no—
172C2×C8×C11—41no—
173C2×C8×C11—41no—
174C2×C8×C11—41no—
175C2×C8×C11—41no—
176C2×C8×C11—41no—
177C22⋊Dic11—22no—
178C22⋊Dic11—22no—
179C22⋊Dic11—22no—
180C22⋊Dic11—41no—
181C4⋊Dic11—22no—
182C4⋊Dic11—22no—
183C4⋊Dic11—41no—
184C4⋊Dic11C22⋊C414yes—
185C4×Dic11—22no—
186C4×Dic11—22no—
187C4×Dic11—22no—
188C4×Dic11—41no—
189#4318—22no—
190#4318—22no—
191#4318—22no—
192#4318—22no—
193C2×C11⋊C8—22no—
194C2×C11⋊C8—22no—
195C2×C11⋊C8C22⋊C414yes—
196C2×#421—111no—
197#2896—111no—
198C2×#408—111no—
199#2873—111no—
200C2×#344—111no—
201C2×#341D1111yescharacteristic, complemented
202#1735—111no—
203C23×C11—42no—
204C23×C11#11711yescharacteristic
205C23×C11C4×D411yescharacteristic
206C23×C11C4×D411yescharacteristic
207C23×C11#12111yescharacteristic
208C23×C11#12311yescharacteristic
209C23×C11#12411yescharacteristic
210C23×C11#12611yescharacteristic
211C22×D11—22no—
212C22×D11—44no—
213C22×D11—41no—
214C22×D11—41no—
215C2×C4×C11C2×C4211yescharacteristic
216C2×C4×C11C2×C22⋊C411yescharacteristic
217C2×C4×C11C2×C22⋊C411yescharacteristic
218C2×C4×C11C2×C22⋊C411yescharacteristic
219C2×C4×C11#11711yescharacteristic
220C2×C4×C11#11711yescharacteristic
221C2×C4×C11C4×D411yescharacteristic
222C2×C4×C11C4×D411yescharacteristic
223C2×C4×C11C4×D411yescharacteristic
224C2×C4×C11C4×D411yescharacteristic
225C2×C4×C11C4×D411yescharacteristic
226C2×C4×C11C4×D411yescharacteristic
227C2×C4×C11C4×D411yescharacteristic
228C2×C4×C11C4×D411yescharacteristic
229C2×C4×C11C4×D411yescharacteristic
230C2×C4×C11C4×D411yescharacteristic
231C2×C4×C11#12011yescharacteristic
232C2×C4×C11#12111yescharacteristic
233C2×C4×C11#12111yescharacteristic
234C2×C4×C11#12111yescharacteristic
235C2×C4×C11#12111yescharacteristic
236C2×C4×C11#12111yescharacteristic
237C2×C4×C11#12311yescharacteristic
238C2×C4×C11#12311yescharacteristic
239C2×C4×C11#12411yescharacteristic
240C2×C4×C11#12411yescharacteristic
241C2×C4×C11#12611yescharacteristic
242C2×C4×C11#12711yescharacteristic
243C22⋊D11—42no—
244C22⋊D11—42no—
245C22⋊D11—42no—
246C22⋊D11—42no—
247C2×Dic11—22no—
248C2×Dic11—24no—
249C2×Dic11—41no—
250C2×Dic11—41no—
251C2×Dic11—42no—
252C2×Dic11—82no—
253C2×Dic11—82no—
254D44—22no—
255D44—22no—
256D44—41no—
257D44—41no—
258C4×D11—42no—
259C4×D11—42no—
260C4×D11—42no—
261C4×D11—42no—
262Dic22—22no—
263Dic22—22no—
264Dic22—41no—
265Dic22—41no—
266C8×C11—24no—
267C8×C11—42no—
268C8×C11—42no—
269C11⋊C8—24no—
270C22×#41—111no—
271C22×M16—111no—
272C22×M16C2×D1111yescharacteristic
273C22×M16C2×D1111yescharacteristic
274C23×C8C2×D1111yescharacteristic
275C2×#117—111no—
276C2×#117—111no—
277#421—114no—
278#421—222no—
279C2×#104—222no—
280#419—112no—
281#418—112no—
282#417—222no—
283#416—222no—
284#408—114no—
285#408—222no—
286C2×C22⋊C8—222no—
287#405—222no—
288#405—222no—
289C4×M16—222no—
290#344—222no—
291#341—22no—
292#340—222no—
293C22×C11—22no—
294C22×C11—22no—
295C22×C11—22no—
296C22×C11—41no—
297C22×C11—41no—
298C22×C11—41no—
299C22×C11—41no—
300C22×C11C4×C22⋊C411yescharacteristic
301C22×C11#38611yescharacteristic
302C22×C11#38811yescharacteristic
303C22×C11#38811yescharacteristic
304C22×C11#38811yescharacteristic
305C22×C11#38811yescharacteristic
306C22×C11#39011yescharacteristic
307C2×D11—44no—
308C2×D11—42no—
309C2×D11—82no—
310C2×D11—82no—
311C4×C11C4×C22⋊C411yescharacteristic
312C4×C11C4×C22⋊C411yescharacteristic
313C4×C11#38611yescharacteristic
314C4×C11#38611yescharacteristic
315C4×C11#38811yescharacteristic
316C4×C11#38811yescharacteristic
317C4×C11#39011yescharacteristic
318C4×C11#39011yescharacteristic
319Dic11—44no—
320Dic11—42no—
321Dic11—82no—
322C2×#41—112no—
323C2×#41—112no—
324C2×#41—221no—
325C2×#41—221no—
326C2×#41—221no—
327C2×#41—221no—
328C2×#41—221no—
329C2×#41—221no—
330C2×#41—221no—
331C2×#41—221no—
332C2×#41—221no—
333C2×#41—221no—
334C22×Q8—111no—
335C22×D4—111no—
336C22×D4—221no—
337C23×C4—221no—
338C23×C4C22×D1111yescharacteristic
339C2×M16—21no—
340C2×M16—21no—
341C2×M16—21no—
342C2×M16—21no—
343C2×M16—21no—
344C2×M16—21no—
345C2×M16—21no—
346C2×M16—21no—
347C2×M16—112no—
348C2×M16—112no—
349C2×M16—221no—
350C2×M16—221no—
351C2×M16—221no—
352C2×M16—221no—
353C2×M16C4×D1112yes—
354C2×M16C4×D1112yes—
355C2×M16D4412yes—
356C2×M16C22⋊D1112yes—
357C22×C8—21no—
358C22×C8—21no—
359C22×C8—21no—
360C22×C8—21no—
361C22×C8—21no—
362C22×C8—21no—
363C22×C8—21no—
364C22×C8—21no—
365C22×C8—112no—
366C22×C8C4×D1112yes—
367#117—112no—
368#117—112no—
369#117—112no—
370#117—221no—
371#117—221no—
372#117—221no—
373#117—221no—
374#117—221no—
375C2×C4⋊C4—112no—
376C2×C4⋊C4—221no—
377C2×C22⋊C4—221no—
378C2×C22⋊C4—221no—
379C2×C42—221no—
380C2×C42—221no—
381#104—228no—
382#103—224no—
383#102—224no—
384C22⋊C8—228no—
385#97—224no—
386C4×C8—224no—
387C2×C11—21no—
388C2×C11—21no—
389C2×C11—21no—
390C2×C11—21no—
391C2×C11—21no—
392C2×C11—21no—
393C2×C11#143711yescharacteristic
394C2×C11#188112yes—
395D11—82no—
396C24—221no—
397C24#434311yescharacteristic
398#41—222no—
399#41—222no—
400#41—222no—
401#41—222no—
402#41—222no—
403#41—222no—
404#41—222no—
405#41—222no—
406#41—441no—
407#41—441no—
408#41—441no—
409#41—441no—
410#41—441no—
411#41—441no—
412#41—441no—
413#41—441no—
414C2×Q8—112no—
415C2×Q8—221no—
416C2×Q8—221no—
417C2×Q8—221no—
418C2×Q8—221no—
419C2×Q8—221no—
420C2×D4—112no—
421C2×D4—222no—
422C2×D4—222no—
423C2×D4—221no—
424C2×D4—221no—
425C2×D4—221no—
426C2×D4—221no—
427C2×D4—221no—
428C2×D4—441no—
429C2×D4—441no—
430C2×D4—441no—
431C2×D4—441no—
432C22×C4—221no—
433C22×C4—222no—
434C22×C4—222no—
435C22×C4—222no—
436C22×C4—441no—
437C22×C4—441no—
438C22×C4—441no—
439C22×C4—441no—
440C22×C4—441no—
441C22×C4C2×C4×D1111yescharacteristic
442C22×C4C2×C4×D1111yescharacteristic
443C22×C4C2×C4×D1111yescharacteristic
444C22×C4C2×D4411yescharacteristic
445C22×C4#433911yescharacteristic
446C22×C4#433911yescharacteristic
447C22×C4D4×D1111yescharacteristic
448C22×C4D4×D1111yescharacteristic
449C22×C4D4×D1111yescharacteristic
450C22×C4D4×D1111yescharacteristic
451C22×C4#434111yescharacteristic
452C22×C4#434111yescharacteristic
453C22×C4#434311yescharacteristic
454C22×C4C2×C22⋊D1111yescharacteristic
455M16—22no—
456M16—22no—
457M16—22no—
458M16—22no—
459M16—22no—
460M16—41no—
461M16—41no—
462M16—222no—
463M16—222no—
464M16—222no—
465M16—222no—
466M16(C2×D11)⋊C414yes—
467C2×C8—22no—
468C2×C8—22no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—22no—
472C2×C8—22no—
473C2×C8—22no—
474C2×C8—41no—
475C2×C8—41no—
476C2×C8—41no—
477C2×C8—41no—
478C2×C8—41no—
479C2×C8—41no—
480C2×C8—114no—
481C2×C8—222no—
482C2×C8—222no—
483C4⋊C4—114no—
484C4⋊C4—222no—
485C4⋊C4—222no—
486C4⋊C4—441no—
487C22⋊C4—222no—
488C22⋊C4—222no—
489C22⋊C4—222no—
490C22⋊C4—441no—
491C42—222no—
492C42—222no—
493C42—222no—
494C42—441no—
495C11#1095611yescharacteristic, complemented, Sylow
496C23—42no—
497C23—222no—
498C23—444no—
499C23—441no—
500C23—441no—
501C23#6694511yescharacteristic
502C23#6694611yescharacteristic
503C23#6694611yescharacteristic
504C23#6694711yescharacteristic
505C23#6694811yescharacteristic
506C23#6695111yescharacteristic
507C23#6700011yescharacteristic
508Q8—222no—
509Q8—222no—
510Q8—441no—
511Q8—441no—
512D4—222no—
513D4—222no—
514D4—442no—
515D4—442no—
516D4—442no—
517D4—442no—
518D4—441no—
519D4—441no—
520C2×C4—224no—
521C2×C4—222no—
522C2×C4—441no—
523C2×C4—441no—
524C2×C4—442no—
525C2×C4—442no—
526C2×C4—442no—
527C2×C4—442no—
528C2×C4—442no—
529C2×C4—882no—
530C2×C4—882no—
531C2×C4C42×D1111yescharacteristic
532C2×C4#6692511yescharacteristic
533C2×C4C4×D4411yescharacteristic
534C2×C4C4×D4411yescharacteristic
535C2×C4C22⋊C4×D1111yescharacteristic
536C2×C4C22⋊C4×D1111yescharacteristic
537C2×C4(C22⋊D11)⋊C411yescharacteristic
538C2×C4(C22⋊D11)⋊C411yescharacteristic
539C2×C4(C22⋊D11)⋊C411yescharacteristic
540C2×C4(C22⋊D11)⋊C411yescharacteristic
541C2×C4#6693511yescharacteristic
542C2×C4#6693711yescharacteristic
543C2×C4#6693711yescharacteristic
544C2×C4#6693811yescharacteristic
545C2×C4#6693811yescharacteristic
546C2×C4#6693911yescharacteristic
547C2×C4#6694511yescharacteristic
548C2×C4#6694611yescharacteristic
549C2×C4#6694611yescharacteristic
550C2×C4#6694711yescharacteristic
551C2×C4#6694811yescharacteristic
552C2×C4#6695111yescharacteristic
553C2×C4C2×(C2×D11)⋊C411yescharacteristic
554C2×C4C4×C22⋊D1111yescharacteristic
555C2×C4C4×C22⋊D1111yescharacteristic
556C2×C4#6699211yescharacteristic
557C2×C4#6699211yescharacteristic
558C2×C4#6699311yescharacteristic
559C8—24no—
560C8—42no—
561C8—42no—
562C8—224no—
563C22—22no—
564C22—22no—
565C22—22no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—444no—
571C22—442no—
572C22—882no—
573C22—882no—
574C22#1062227811yescharacteristic
575C22#1062227911yescharacteristic
576C22#1062228211yescharacteristic
577C22#1062228311yescharacteristic
578C22#1062260111yescharacteristic
579C22#1062260311yescharacteristic
580C22#1062260311yescharacteristic
581C4—442no—
582C4—444no—
583C4—882no—
584C4#1062227811yescharacteristic
585C4#1062227911yescharacteristic
586C4#1062228211yescharacteristic
587C4#1062228311yescharacteristic
588C4C4×(C2×D11)⋊C411yescharacteristic
589C4#1062257011yescharacteristic
590C4#1062257011yescharacteristic
591C4#1062257111yescharacteristic
592C2—21no—
593C2—21no—
594C2—21no—
595C2—21no—
596C2—21no—
597C2—21no—
598C2—882no—
599C2#1306685211yescharacteristic
600C2#1306897912yes—
subgroupG/H
centerC2×C4#66935
commutatorC2×C4×C11C2×C42
FrattiniC23×C4C22×D11
FittingC2×C11×#341C2
socleC22×C11#386
prime radicalC22×#4339C22
cosocleC23×C4×C11C23
hypercenterC2×#341D11
hypocenterC11#10956
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#341

Complements

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

NH ≅ G/Ntype
4. #13077034C2semidirect
5. C2×#10622197C2semidirect
6. #13068333C2semidirect
7. C2×C11×#341C2semidirect
16. #10622752C4semidirect
19. #10622744C4semidirect
21. #10622733C4semidirect
25. #10622723C4semidirect
201. C2×#341D11semidirect
495. C11#10956semidirect

Maximal subgroups

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

subgroupindex
C2×#106227522
#130771362
C2×#106227232
#130770342
C2×#106221972
#130683332
C2×C11×#3412
#1095611