Finite Group Databasebeta

← #14660213

Subgroups — #14660213

Order 2816.

900 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×#10622618C211yesmaximal, characteristic
2C2×#10622618C211yesmaximal, characteristic
3C2×#10622745C211yesmaximal, characteristic
4#13077035C211yesmaximal, characteristic, complemented
5#13068355C211yesmaximal, characteristic, complemented
6#13068342C211yesmaximal, characteristic, complemented
7C2×C11×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
8C22×#4339C2211yescharacteristic
9C22×C11×M16C2211yescharacteristic
10C2×C11×#117C2211yescharacteristic
11C2×C11×#117C2211yescharacteristic
12C22×#4318C2211yescharacteristic
13C22×#4318C2211yescharacteristic
14C22×#4318C2211yescharacteristic
15C2×#66888C412yescomplemented
16#10622745—22no—
17#10622745—22no—
18C2×#66887C412yescomplemented
19#10622618—22no—
20#10622618—22no—
21#10622618—22no—
22#10622618C414yescomplemented
23#10622610—22no—
24#10622610—22no—
25C2×#66869—22no—
26C2×#66869C414yescomplemented
27C4×#4318—22no—
28C11×H(3,ℤ/4)—22no—
29#10622196—22no—
30#10622168—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×M16C2×C412yes—
54C22×C8×C11—21no—
55C11×#117—21no—
56C11×#117—21no—
57C11×#117—21no—
58C11×#117—21no—
59C11×#117—21no—
60C11×#117—21no—
61C11×#117C2×C412yes—
62C11×#117D412yes—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C22⋊C4—21no—
66C2×C11×C22⋊C4—21no—
67C2×C42×C11C2×C412yes—
68C2×C42×C11D412yes—
69C2×#4318—21no—
70C2×#4318—21no—
71C2×#4318—21no—
72C2×#4318—21no—
73C2×#4318—21no—
74C2×#4318—21no—
75C2×#4318—21no—
76C2×#4318—21no—
77C2×#4318—21no—
78C2×#4318—21no—
79C2×#4318—21no—
80C2×#4318C2×C412yes—
81C2×#4318C2×C412yes—
82C2×#4318C2×C412yes—
83C2×#4318D412yes—
84C2×#4318D412yes—
85C2×#4318D412yes—
86C2×#4318D412yes—
87C22×C11⋊C8—21no—
88C22×C11⋊C8—21no—
89C22×C11⋊C8—21no—
90#66888—24no—
91#66887—24no—
92#66869—28no—
93#66869—28no—
94#66867—24no—
95C4×C11⋊C8—24no—
96#10955—111nomaximal, Sylow
97C24×C11#4111yescharacteristic
98C23×D11—21no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11C22×C411yescharacteristic
102C22×C4×C11C22×C411yescharacteristic
103C22×C4×C11C22×C411yescharacteristic
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11#4111yescharacteristic
111C22×C4×C11#4111yescharacteristic
112C22×C4×C11#4111yescharacteristic
113C22×C4×C11#4111yescharacteristic
114C22×C4×C11#4111yescharacteristic
115C2×C22⋊D11—22no—
116C2×C22⋊D11—22no—
117C2×C22⋊D11—41no—
118C2×C22⋊D11—41no—
119C2×C22⋊D11—41no—
120C2×C22⋊D11—41no—
121C22×Dic11—21no—
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—41no—
159C11×M16—41no—
160C2×C8×C11—22no—
161C2×C8×C11—41no—
162C2×C8×C11—41no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—41no—
166C11×C4⋊C4—41no—
167C11×C22⋊C4—22no—
168C11×C22⋊C4—22no—
169C11×C22⋊C4—41no—
170C11×C22⋊C4—41no—
171C42×C11—22no—
172C42×C11—22no—
173C42×C11—22no—
174C42×C11C22⋊C414yes—
175#4318—22no—
176#4318—22no—
177#4318—22no—
178#4318—22no—
179#4318—22no—
180#4318—22no—
181#4318—22no—
182#4318—22no—
183#4318—41no—
184#4318—41no—
185#4318C22⋊C414yes—
186#4318C22⋊C414yes—
187C2×C11⋊C8—22no—
188C2×C11⋊C8—22no—
189C2×C11⋊C8—22no—
190C2×C11⋊C8—22no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8—22no—
193C2×C11⋊C8—22no—
194C2×C11⋊C8—41no—
195C2×C11⋊C8—41no—
196C2×#421—111no—
197C2×#421—111no—
198C2×#413—111no—
199#2873—111no—
200#1742—111no—
201#1738—111no—
202C2×H(3,ℤ/4)D1111yescharacteristic, complemented
203C23×C11—81no—
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—41no—
213C22×D11—41no—
214C22×D11—82no—
215C2×C4×C11—24no—
216C2×C4×C11—42no—
217C2×C4×C11—82no—
218C2×C4×C11—82no—
219C2×C4×C11C2×C4211yescharacteristic
220C2×C4×C11C2×C22⋊C411yescharacteristic
221C2×C4×C11C2×C22⋊C411yescharacteristic
222C2×C4×C11C2×C22⋊C411yescharacteristic
223C2×C4×C11#11711yescharacteristic
224C2×C4×C11#11711yescharacteristic
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×C11C4×D411yescharacteristic
232C2×C4×C11C4×D411yescharacteristic
233C2×C4×C11C4×D411yescharacteristic
234C2×C4×C11C4×D411yescharacteristic
235C2×C4×C11#12011yescharacteristic
236C2×C4×C11#12111yescharacteristic
237C2×C4×C11#12111yescharacteristic
238C2×C4×C11#12111yescharacteristic
239C2×C4×C11#12111yescharacteristic
240C2×C4×C11#12111yescharacteristic
241C2×C4×C11#12311yescharacteristic
242C2×C4×C11#12311yescharacteristic
243C2×C4×C11#12411yescharacteristic
244C2×C4×C11#12411yescharacteristic
245C2×C4×C11#12611yescharacteristic
246C2×C4×C11#12711yescharacteristic
247C22⋊D11—42no—
248C22⋊D11—42no—
249C22⋊D11—42no—
250C22⋊D11—42no—
251C2×Dic11—22no—
252C2×Dic11—41no—
253C2×Dic11—41no—
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—42no—
267C11⋊C8—24no—
268C11⋊C8—24no—
269C11⋊C8—42no—
270C22×#41—111no—
271C22×M16—111no—
272C22×M16—111no—
273C22×M16—111no—
274C22×M16C2×D1111yescharacteristic
275C2×#117C2×D1111yescharacteristic
276C2×#117C2×D1111yescharacteristic
277#421—114no—
278#421—222no—
279#421—222no—
280#421—222no—
281C2×#104—114no—
282C2×#104—222no—
283#413—222no—
284#413—222no—
285C2×#101—112no—
286C2×#100—112no—
287#405—222no—
288#405—222no—
289C4×M16—222no—
290#343—222no—
291#341—222no—
292H(3,ℤ/4)—22no—
293C22×C11—41no—
294C22×C11—41no—
295C22×C11—41no—
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—42no—
308C2×D11—82no—
309C2×D11—82no—
310C2×D11—82no—
311C4×C11—44no—
312C4×C11—82no—
313C4×C11C4×C22⋊C411yescharacteristic
314C4×C11C4×C22⋊C411yescharacteristic
315C4×C11#38611yescharacteristic
316C4×C11#38611yescharacteristic
317C4×C11#38811yescharacteristic
318C4×C11#38811yescharacteristic
319C4×C11#39011yescharacteristic
320C4×C11#39011yescharacteristic
321Dic11—42no—
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—112no—
345C2×M16—112no—
346C2×M16—112no—
347C2×M16—112no—
348C2×M16—112no—
349C2×M16—112no—
350C2×M16—112no—
351C2×M16—221no—
352C2×M16—221no—
353C2×M16—221no—
354C2×M16—221no—
355C2×M16—221no—
356C2×M16—221no—
357C2×M16—221no—
358C2×M16—221no—
359C2×M16—221no—
360C2×M16—221no—
361C2×M16—221no—
362C2×M16C4×D1112yes—
363C22×C8—21no—
364C22×C8—221no—
365C22×C8—221no—
366C22×C8—221no—
367#117—21no—
368#117—21no—
369#117—21no—
370#117—21no—
371#117—21no—
372#117—21no—
373#117C4×D1112yes—
374#117C22⋊D1112yes—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C42C4×D1112yes—
380C2×C42D4412yes—
381#104—228no—
382#104—228no—
383#101—224no—
384#100—224no—
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—21no—
394C2×C11#143711yescharacteristic
395D11—82no—
396C24—221no—
397C24#434111yescharacteristic
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—22no—
433C22×C4—22no—
434C22×C4—221no—
435C22×C4—222no—
436C22×C4—222no—
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#434311yescharacteristic
453C22×C4#434311yescharacteristic
454C22×C4C2×C22⋊D1111yescharacteristic
455M16—22no—
456M16—22no—
457M16—41no—
458M16—41no—
459M16—114no—
460M16—114no—
461M16—222no—
462M16—222no—
463M16—222no—
464M16—222no—
465M16—222no—
466M16—222no—
467M16—222no—
468M16—222no—
469M16—441no—
470M16—441no—
471C2×C8—22no—
472C2×C8—41no—
473C2×C8—41no—
474C2×C8—222no—
475C2×C8—222no—
476C2×C8—222no—
477C2×C8—222no—
478C2×C8—222no—
479C2×C8—222no—
480C2×C8—222no—
481C2×C8—441no—
482C2×C8—441no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—41no—
486C4⋊C4—41no—
487C22⋊C4—22no—
488C22⋊C4—22no—
489C22⋊C4—41no—
490C22⋊C4—41no—
491C42—22no—
492C42—22no—
493C42—22no—
494C42(C2×D11)⋊C414yes—
495C11#1095511yescharacteristic, complemented, Sylow
496C23—81no—
497C23—222no—
498C23—441no—
499C23—441no—
500C23—882no—
501C23(C22⋊D11)⋊C411yescharacteristic
502C23(C22⋊D11)⋊C411yescharacteristic
503C23#6693811yescharacteristic
504C23#6693911yescharacteristic
505C23#6694511yescharacteristic
506C23#6695111yescharacteristic
507C23#6699211yescharacteristic
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—24no—
521C2×C4—42no—
522C2×C4—82no—
523C2×C4—82no—
524C2×C4—222no—
525C2×C4—441no—
526C2×C4—441no—
527C2×C4—442no—
528C2×C4—442no—
529C2×C4—442no—
530C2×C4—442no—
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#6693511yescharacteristic
540C2×C4#6693711yescharacteristic
541C2×C4#6693711yescharacteristic
542C2×C4#6693811yescharacteristic
543C2×C4#6694511yescharacteristic
544C2×C4#6694611yescharacteristic
545C2×C4#6694611yescharacteristic
546C2×C4#6694611yescharacteristic
547C2×C4#6694611yescharacteristic
548C2×C4#6694711yescharacteristic
549C2×C4#6694711yescharacteristic
550C2×C4#6694811yescharacteristic
551C2×C4#6694811yescharacteristic
552C2×C4#6695111yescharacteristic
553C2×C4C2×(C2×D11)⋊C411yescharacteristic
554C2×C4C4×C22⋊D1111yescharacteristic
555C2×C4C4×C22⋊D1111yescharacteristic
556C2×C4#6699211yescharacteristic
557C2×C4#6699311yescharacteristic
558C2×C4#6700011yescharacteristic
559C8—42no—
560C8—224no—
561C8—224no—
562C8—442no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—442no—
571C22—882no—
572C22—882no—
573C22—882no—
574C22#1062227911yescharacteristic
575C22#1062228211yescharacteristic
576C22#1062228311yescharacteristic
577C22#1062228311yescharacteristic
578C22#1062257011yescharacteristic
579C22#1062257111yescharacteristic
580C22#1062260311yescharacteristic
581C4—44no—
582C4—82no—
583C4—442no—
584C4#1062227811yescharacteristic
585C4#1062227811yescharacteristic
586C4#1062227911yescharacteristic
587C4#1062228211yescharacteristic
588C4C4×(C2×D11)⋊C411yescharacteristic
589C4#1062257011yescharacteristic
590C4#1062260111yescharacteristic
591C4#1062260311yescharacteristic
592C2—21no—
593C2—21no—
594C2—21no—
595C2—21no—
596C2—21no—
597C2—21no—
598C2—21no—
599C2—882no—
600C2#1306685211yescharacteristic
subgroupG/H
centerC4#10622278
commutatorC2×C4×C11C2×C42
FrattiniC23×C4C22×D11
FittingC2×C11×H(3,ℤ/4)C2
socleC2×C11#1437
prime radicalC22×#4339C22
cosocleC23×C4×C11C23
hypercenterC2×H(3,ℤ/4)D11
hypocenterC11#10955
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
4. #13077035C2semidirect
5. #13068355C2semidirect
6. #13068342C2semidirect
7. C2×C11×H(3,ℤ/4)C2semidirect
15. C2×#66888C4semidirect
18. C2×#66887C4semidirect
22. #10622618C4semidirect
26. C2×#66869C4semidirect
202. C2×H(3,ℤ/4)D11semidirect
495. C11#10955semidirect

Maximal subgroups

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

subgroupindex
C2×#106226182
C2×#106227452
#130770352
#130683552
#130683422
C2×C11×H(3,ℤ/4)2
#1095511