Finite Group Databasebeta

← #14783664

Subgroups — #14783664

Order 2816.

988 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622737C211yesmaximal, characteristic, complemented
2#13077179C211yesmaximal, characteristic, complemented
3C2×#10622618C211yesmaximal, characteristic
4C2×#10622752C211yesmaximal, characteristic
5#13077060C211yesmaximal, characteristic
6#13070172C218yesmaximal, complemented
7C2×#10622169C211yesmaximal, characteristic, complemented
8C11×#2905C211yesmaximal, characteristic, complemented
9C22×#4339C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C2×C11×#117C2211yescharacteristic
13C2×#66979C2211yescharacteristic
14C22×#4318C2211yescharacteristic
15C22×#4318C2211yescharacteristic
16C11×#424—22no—
17C11×#424C2214yescomplemented
18C11×#423—22no—
19#10622752—22no—
20#10622752C2214yes—
21C2×#66889—22no—
22#10622742—22no—
23#10622739—22no—
24#10622737—22no—
25#10622737C2214yescomplemented
26C2×#66886—22no—
27#10622732—22no—
28#10622731—22no—
29#10622723C2214yes—
30#10622715C2214yescomplemented
31#10622618—22no—
32#10622618C2214yes—
33C2×#66869—22no—
34#10622169C2214yescomplemented
35C23×C4×C11C2311yescharacteristic
36C22×C22⋊D11—21no—
37C2×#4339—21no—
38C2×#4339—21no—
39C2×#4339—21no—
40C2×#4339—21no—
41C2×#4339—21no—
42C2×#4339—21no—
43C2×#4339—21no—
44C2×#4339—21no—
45C2×#4339—21no—
46C2×#4339—21no—
47C2×#4339Q812yes—
48C2×#4339C2312yes—
49C22×D44Q811yescharacteristic
50C22×C4×D11—21no—
51C22×Dic22Q811yescharacteristic
52C2×C11×M16—21no—
53C2×C11×M16—21no—
54C2×C11×M16—21no—
55C2×C11×M16—21no—
56C2×C11×M16—21no—
57C2×C11×M16—21no—
58C2×C11×M16—21no—
59C2×C11×M16—21no—
60C2×C11×M16—21no—
61C2×C11×M16—21no—
62C2×C11×M16—21no—
63C2×C11×M16C2312yes—
64C22×C8×C11—21no—
65C22×C8×C11C2312yes—
66C11×#117—21no—
67C11×#117—21no—
68C11×#117D412yes—
69C11×#117C2312yes—
70C2×C11×C4⋊C4—21no—
71C2×C11×C22⋊C4—21no—
72C2×C42×C11D412yes—
73C2×C22⋊Dic11—21no—
74#66979—21no—
75#66979—21no—
76#66979D412yes—
77#66979C2312yes—
78C2×C4⋊Dic11—21no—
79C2×C4×Dic11D412yes—
80C2×#4318—21no—
81C2×#4318—21no—
82C2×#4318—21no—
83C2×#4318—21no—
84C2×#4318—21no—
85C2×#4318—21no—
86C2×#4318—21no—
87C2×#4318—21no—
88C2×#4318—21no—
89C2×#4318D412yes—
90C2×#4318C2312yes—
91C2×#4318C2312yes—
92C22×C11⋊C8—21no—
93C22×C11⋊C8D412yes—
94C11×C4⋊C8—28no—
95#66889—28no—
96#66886—28no—
97(C2×D11)⋊C8—28no—
98Dic11⋊C8—28no—
99#66869—28no—
100#23740—111nomaximal, Sylow
101C24×C11#4111yescharacteristic
102C23×D11—21no—
103C22×C4×C11—22no—
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×C11C2×Q811yescharacteristic
111C22×C4×C11C2×Q811yescharacteristic
112C22×C4×C11#4111yescharacteristic
113C22×C4×C11#4111yescharacteristic
114C22×C4×C11#4111yescharacteristic
115C22×C4×C11#4111yescharacteristic
116C22×C4×C11#4111yescharacteristic
117C22×C4×C11C2411yescharacteristic
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—22no—
126#4339—22no—
127#4339—22no—
128#4339—22no—
129#4339—22no—
130#4339—22no—
131#4339—22no—
132#4339—22no—
133#4339—22no—
134#4339—41no—
135#4339—41no—
136#4339—41no—
137#4339—41no—
138#4339—41no—
139#4339—41no—
140#4339—41no—
141#4339—41no—
142C2×D44—21no—
143C2×D44—21no—
144C2×D44—21no—
145C2×D44—21no—
146C2×D44—21no—
147C2×D44C2×Q812yes—
148C2×C4×D11—22no—
149C2×C4×D11—22no—
150C2×C4×D11—41no—
151C2×C4×D11—41no—
152C2×C4×D11—41no—
153C2×C4×D11—41no—
154C2×Dic22—21no—
155C2×Dic22—21no—
156C2×Dic22—21no—
157C2×Dic22—21no—
158C2×Dic22—21no—
159C2×Dic22C2×Q812yes—
160C11×M16—22no—
161C11×M16—22no—
162C11×M16—41no—
163C11×M16—41no—
164C11×M16—41no—
165C11×M16—41no—
166C11×M16—41no—
167C11×M16—41no—
168C2×C8×C11—22no—
169C2×C8×C11—22no—
170C2×C8×C11—22no—
171C2×C8×C11—22no—
172C2×C8×C11—41no—
173C2×C8×C11—41no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—22no—
176C11×C22⋊C4—22no—
177C11×C22⋊C4—22no—
178C42×C11—22no—
179C42×C11C2×D414yes—
180C22⋊Dic11—22no—
181C22⋊Dic11—22no—
182C4⋊Dic11—22no—
183C4⋊Dic11—22no—
184C4×Dic11—22no—
185C4×Dic11C2×D414yes—
186#4318—22no—
187#4318—22no—
188#4318—22no—
189#4318—22no—
190#4318—22no—
191#4318—22no—
192#4318—41no—
193#4318—41no—
194C2×C11⋊C8—22no—
195C2×C11⋊C8—22no—
196C2×C11⋊C8—22no—
197C2×C11⋊C8—41no—
198C2×C11⋊C8—41no—
199C2×C11⋊C8C2×D414yes—
200C2×#430—111no—
201#2905—111no—
202#2905D1111yescharacteristic, complemented
203C2×#421—111no—
204C2×#421—111no—
205#2879—111no—
206#2098—118no—
207C2×H(3,ℤ/4)—111no—
208C23×C11—81no—
209C23×C11C22⋊Q811yescharacteristic
210C23×C11C22⋊Q811yescharacteristic
211C23×C11#12311yescharacteristic
212C23×C11#12311yescharacteristic
213C23×C11#12311yescharacteristic
214C23×C11#12311yescharacteristic
215C23×C11C2×#4111yescharacteristic
216C22×D11—22no—
217C22×D11—41no—
218C22×D11—41no—
219C22×D11—82no—
220C2×C4×C11—24no—
221C2×C4×C11—82no—
222C2×C4×C11C22⋊Q811yescharacteristic
223C2×C4×C11C22⋊Q811yescharacteristic
224C2×C4×C11C22⋊Q811yescharacteristic
225C2×C4×C11C22⋊Q811yescharacteristic
226C2×C4×C11C22⋊Q811yescharacteristic
227C2×C4×C11C22⋊Q811yescharacteristic
228C2×C4×C11C22⋊Q811yescharacteristic
229C2×C4×C11C22⋊Q811yescharacteristic
230C2×C4×C11C22⋊Q811yescharacteristic
231C2×C4×C11C22⋊Q811yescharacteristic
232C2×C4×C11#12311yescharacteristic
233C2×C4×C11#12311yescharacteristic
234C2×C4×C11#12311yescharacteristic
235C2×C4×C11#12311yescharacteristic
236C2×C4×C11#12311yescharacteristic
237C2×C4×C11#12311yescharacteristic
238C2×C4×C11#12311yescharacteristic
239C2×C4×C11#12311yescharacteristic
240C2×C4×C11#12711yescharacteristic
241C2×C4×C11#12711yescharacteristic
242C2×C4×C11#12711yescharacteristic
243C2×C4×C11#12711yescharacteristic
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C22×Q811yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C22⋊D11—42no—
251C22⋊D11—42no—
252C22⋊D11—42no—
253C22⋊D11—42no—
254C2×Dic11—22no—
255C2×Dic11—24no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—82no—
259D44—22no—
260D44—22no—
261D44—41no—
262D44—41no—
263C4×D11—42no—
264C4×D11—42no—
265C4×D11—42no—
266C4×D11—42no—
267Dic22—22no—
268Dic22—22no—
269Dic22—41no—
270Dic22—41no—
271C8×C11—42no—
272C8×C11—42no—
273C11⋊C8—24no—
274C11⋊C8—42no—
275C22×#41—111no—
276C22×M16—111no—
277C22×M16—111no—
278C22×M16C2×D1111yescharacteristic
279C22×M16C2×D1111yescharacteristic
280C2×#117—111no—
281C2×#117C2×D1111yescharacteristic
282#430—114no—
283#430—222no—
284C2×#108—222no—
285#424—22no—
286#424—114no—
287#424—222no—
288#424C2×D1114yescomplemented
289#423—22no—
290#423—222no—
291#421—114no—
292#421—114no—
293#421—222no—
294#421—222no—
295C2×#104—222no—
296C2×#104—222no—
297#408—114no—
298#408—222no—
299#407—222no—
300H(3,ℤ/4)—114no—
301C22×C11—41no—
302C22×C11—41no—
303C22×C11—41no—
304C22×C11—41no—
305C22×C11—41no—
306C22×C11—41no—
307C22×C11—41no—
308C22×C11#39911yescharacteristic
309C22×C11#39911yescharacteristic
310C22×C11#39911yescharacteristic
311C22×C11#39911yescharacteristic
312C22×C11C2×C22⋊Q811yescharacteristic
313C22×C11C2×#12311yescharacteristic
314C22×C11C2×#12311yescharacteristic
315C2×D11—44no—
316C2×D11—42no—
317C2×D11—82no—
318C2×D11—82no—
319C4×C11—44no—
320C4×C11#39911yescharacteristic
321C4×C11#39911yescharacteristic
322C4×C11#39911yescharacteristic
323C4×C11#39911yescharacteristic
324C4×C11C2×C22⋊Q811yescharacteristic
325C4×C11C2×C22⋊Q811yescharacteristic
326C4×C11C2×#12311yescharacteristic
327C4×C11C2×#12711yescharacteristic
328Dic11—44no—
329Dic11—42no—
330C2×#41—112no—
331C2×#41—112no—
332C2×#41—221no—
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—
342C22×Q8—111no—
343C22×D4—111no—
344C22×D4—221no—
345C23×C4—221no—
346C23×C4C22×D1111yescharacteristic
347C2×M16—21no—
348C2×M16—21no—
349C2×M16—21no—
350C2×M16—21no—
351C2×M16—21no—
352C2×M16—21no—
353C2×M16—21no—
354C2×M16—21no—
355C2×M16—21no—
356C2×M16—21no—
357C2×M16—21no—
358C2×M16—112no—
359C2×M16—112no—
360C2×M16—112no—
361C2×M16—221no—
362C2×M16—221no—
363C2×M16—221no—
364C2×M16—221no—
365C2×M16—221no—
366C2×M16—221no—
367C2×M16—221no—
368C2×M16—221no—
369C2×M16—221no—
370C2×M16C22×D1112yes—
371C22×C8—21no—
372C22×C8—112no—
373C22×C8—221no—
374C22×C8C22×D1112yes—
375#117—21no—
376#117—21no—
377#117—112no—
378#117—112no—
379#117—221no—
380#117—221no—
381#117C22⋊D1112yes—
382#117C22×D1112yes—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—221no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—221no—
387C2×C42—112no—
388C2×C42C22⋊D1112yes—
389#108—228no—
390C4⋊C8—28no—
391C4⋊C8—228no—
392#104—228no—
393#104—228no—
394C22⋊C8—228no—
395C2×C11—21no—
396C2×C11—21no—
397C2×C11—21no—
398C2×C11—21no—
399C2×C11—21no—
400C2×C11—21no—
401C2×C11—21no—
402C2×C11C2×#39911yescharacteristic
403D11—82no—
404C24—221no—
405C24#433911yescharacteristic
406#41—222no—
407#41—222no—
408#41—222no—
409#41—222no—
410#41—222no—
411#41—222no—
412#41—222no—
413#41—222no—
414#41—441no—
415#41—441no—
416#41—441no—
417#41—441no—
418#41—441no—
419#41—441no—
420#41—441no—
421#41—441no—
422C2×Q8—112no—
423C2×Q8—221no—
424C2×Q8—221no—
425C2×Q8—221no—
426C2×Q8—221no—
427C2×Q8—221no—
428C2×D4—112no—
429C2×D4—222no—
430C2×D4—222no—
431C2×D4—221no—
432C2×D4—221no—
433C2×D4—221no—
434C2×D4—221no—
435C2×D4—221no—
436C2×D4—441no—
437C2×D4—441no—
438C2×D4—441no—
439C2×D4—441no—
440C22×C4—22no—
441C22×C4—221no—
442C22×C4—222no—
443C22×C4—222no—
444C22×C4—222no—
445C22×C4—441no—
446C22×C4—441no—
447C22×C4—441no—
448C22×C4—441no—
449C22×C4#433911yescharacteristic
450C22×C4#433911yescharacteristic
451C22×C4#433911yescharacteristic
452C22×C4D4×D1111yescharacteristic
453C22×C4D4×D1111yescharacteristic
454C22×C4D4×D1111yescharacteristic
455C22×C4D4×D1111yescharacteristic
456C22×C4Q8×D1111yescharacteristic
457C22×C4Q8×D1111yescharacteristic
458C22×C4#434311yescharacteristic
459C22×C4#434311yescharacteristic
460C22×C4C2×C22⋊D1111yescharacteristic
461C22×C4C2×C22⋊D1111yescharacteristic
462C22×C4C23×D1111yescharacteristic
463M16—22no—
464M16—22no—
465M16—41no—
466M16—41no—
467M16—41no—
468M16—41no—
469M16—41no—
470M16—41no—
471M16—222no—
472M16—222no—
473M16—222no—
474M16—222no—
475M16—222no—
476M16—222no—
477M16—441no—
478M16—441no—
479C2×C8—22no—
480C2×C8—22no—
481C2×C8—22no—
482C2×C8—22no—
483C2×C8—41no—
484C2×C8—41no—
485C2×C8—114no—
486C2×C8—222no—
487C2×C8—222no—
488C2×C8—222no—
489C2×C8—441no—
490C2×C8—441no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—222no—
494C4⋊C4—222no—
495C22⋊C4—22no—
496C22⋊C4—22no—
497C22⋊C4—222no—
498C22⋊C4—222no—
499C42—22no—
500C42—114no—
501C42—222no—
502C42C2×C22⋊D1114yes—
503C11#2374011yescharacteristic, complemented, Sylow
504C23—81no—
505C23—222no—
506C23—441no—
507C23—441no—
508C23—882no—
509C23#6694711yescharacteristic
510C23#6694711yescharacteristic
511C23#6694911yescharacteristic
512C23#6694911yescharacteristic
513C23#6698211yescharacteristic
514C23#6698211yescharacteristic
515C23C2×#433911yescharacteristic
516Q8—222no—
517Q8—222no—
518Q8—441no—
519Q8—441no—
520D4—222no—
521D4—222no—
522D4—442no—
523D4—442no—
524D4—442no—
525D4—442no—
526D4—441no—
527D4—441no—
528C2×C4—24no—
529C2×C4—82no—
530C2×C4—224no—
531C2×C4—222no—
532C2×C4—441no—
533C2×C4—441no—
534C2×C4—442no—
535C2×C4—442no—
536C2×C4—442no—
537C2×C4—442no—
538C2×C4—882no—
539C2×C4#6694711yescharacteristic
540C2×C4#6694711yescharacteristic
541C2×C4#6694711yescharacteristic
542C2×C4#6694711yescharacteristic
543C2×C4#6694711yescharacteristic
544C2×C4#6694711yescharacteristic
545C2×C4#6694911yescharacteristic
546C2×C4#6694911yescharacteristic
547C2×C4#6694911yescharacteristic
548C2×C4#6694911yescharacteristic
549C2×C4#6694911yescharacteristic
550C2×C4#6694911yescharacteristic
551C2×C4#6698211yescharacteristic
552C2×C4#6698211yescharacteristic
553C2×C4#6699311yescharacteristic
554C2×C4#6699311yescharacteristic
555C2×C4#6699311yescharacteristic
556C2×C4#6699311yescharacteristic
557C2×C4#6699911yescharacteristic
558C2×C4#6699911yescharacteristic
559C2×C4#6699911yescharacteristic
560C2×C4#6699911yescharacteristic
561C2×C4C2×#433911yescharacteristic
562C2×C4C2×D4×D1111yescharacteristic
563C2×C4C2×D4×D1111yescharacteristic
564C2×C4C2×Q8×D1111yescharacteristic
565C2×C4C2×#434311yescharacteristic
566C2×C4C22×C22⋊D1111yescharacteristic
567C8—42no—
568C8—42no—
569C8—224no—
570C8—442no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—444no—
579C22—442no—
580C22—882no—
581C22—882no—
582C22#1062260511yescharacteristic
583C22#1062260511yescharacteristic
584C22#1062260511yescharacteristic
585C22#1062260511yescharacteristic
586C22C2×#6694711yescharacteristic
587C22C2×#6694911yescharacteristic
588C22C2×#6698211yescharacteristic
589C4—44no—
590C4—444no—
591C4—442no—
592C4#1062260511yescharacteristic
593C4#1062260511yescharacteristic
594C4#1062260511yescharacteristic
595C4#1062260511yescharacteristic
596C4C2×#6694711yescharacteristic
597C4C2×#6694911yescharacteristic
598C4C2×#6699311yescharacteristic
599C4C2×#6699911yescharacteristic
600C2—21no—
601C2—21no—
602C2—21no—
603C2—21no—
604C2—21no—
605C2—21no—
606C2—21no—
607C2—882no—
608C2C2×#1062260511yescharacteristic
subgroupG/H
centerC4C2×#66993
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2905C2
socleC2×C11C2×#399
prime radicalC22×#4339C22
hypercenter#2905D11
hypocenterC11#23740
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C23×C4 ◁ #2905

Complements

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

NH ≅ G/Ntype
1. C2×#10622737C2semidirect
2. #13077179C2semidirect
6. #13070172C2semidirect
7. C2×#10622169C2semidirect
8. C11×#2905C2semidirect
17. C11×#424C22semidirect
25. #10622737C22semidirect
30. #10622715C22semidirect
34. #10622169C22semidirect
202. #2905D11semidirect
288. #424C2×D11semidirect
503. C11#23740semidirect

Maximal subgroups

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

subgroupindex
C2×#106227372
#130771792
C2×#106226182
C2×#106227522
#130770602
#130701722
C2×#106221692
C11×#29052
#2374011