Finite Group Databasebeta

← #14660247

Subgroups — #14660247

Order 2816.

926 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622745C211yesmaximal, characteristic
2C2×#10622619C211yesmaximal, characteristic
3C2×#10622742C211yesmaximal, characteristic
4C2×#10622735C211yesmaximal, characteristic, complemented
5C2×#10622194C211yesmaximal, characteristic, complemented
6#13068313C211yesmaximal, characteristic, complemented
7C2×C11×#344C211yesmaximal, characteristic, complemented
8C22×#4339C2211yescharacteristic
9C22×C11×M16C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C2×C11×#117C2211yescharacteristic
12C2×#66979C2211yescharacteristic
13C22×#4318C2211yescharacteristic
14C23×C11⋊C8C2211yescharacteristic
15C2×#66888C412yescomplemented
16#10622745—22no—
17#10622745—22no—
18C2×#66887C412yescomplemented
19#10622742—22no—
20#10622742—21no—
21#10622742—21no—
22#10622735—22no—
23#10622735—22no—
24C2×(C2×D11)⋊C8C414yescomplemented
25C2×#66879—21no—
26C2×C8×Dic11—21no—
27#10622619—22no—
28#10622619—22no—
29C2×#66870C414yes—
30C11×#344—22no—
31#10622194—22no—
32#10622162—22no—
33C23×C4×C11C2311yescharacteristic
34C22×C22⋊D11C2×C412yes—
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×#4339—21no—
45C2×#4339—21no—
46C2×#4339—21no—
47C22×D44C2×C411yescharacteristic
48C22×C4×D11C2×C412yes—
49C22×Dic22C2×C411yescharacteristic
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×M16—21no—
57C2×C11×M16—21no—
58C2×C11×M16—21no—
59C2×C11×M16C2×C412yes—
60C2×C11×M16D412yes—
61C2×C11×M16D412yes—
62C22×C8×C11—21no—
63C22×C8×C11C2×C412yes—
64C11×#117—21no—
65C11×#117—21no—
66C11×#117—21no—
67C11×#117—21no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C22⋊C4C2×C412yes—
70C2×C42×C11—21no—
71C2×C22⋊Dic11C2×C412yes—
72#66979—21no—
73#66979—21no—
74#66979D412yes—
75#66979D412yes—
76C2×C4⋊Dic11—21no—
77C2×C4×Dic11—21no—
78C2×#4318—21no—
79C2×#4318—21no—
80C2×#4318—21no—
81C2×#4318—21no—
82C2×#4318—21no—
83C2×#4318C2×C412yes—
84C22×C11⋊C8—21no—
85C22×C11⋊C8—21no—
86C22×C11⋊C8—21no—
87C22×C11⋊C8—21no—
88C22×C11⋊C8—21no—
89C22×C11⋊C8C2×C412yes—
90C22×C11⋊C8D412yes—
91C22×C11⋊C8D411yescharacteristic
92C22×C11⋊C8D411yescharacteristic
93#66888—24no—
94#66887—24no—
95(C2×D11)⋊C8—24no—
96(C2×D11)⋊C8—24no—
97#66879—24no—
98C8×Dic11—24no—
99#66870—28no—
100#10961—111nomaximal, Sylow
101C24×C11C22×C411yescharacteristic
102C23×D11C4212yes—
103C22×C4×C11—22no—
104C22×C4×C11C22×C411yescharacteristic
105C22×C4×C11C22×C411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
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—22no—
121C2×C22⋊D11—22no—
122C2×C22⋊D11—22no—
123C2×C22⋊D11—22no—
124C22×Dic11—22no—
125C22×Dic11C4212yes—
126#4339—41no—
127#4339—41no—
128#4339—41no—
129#4339—41no—
130#4339—41no—
131#4339—41no—
132#4339—41no—
133#4339—41no—
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×D44—21no—
148C2×C4×D11—22no—
149C2×C4×D11—22no—
150C2×C4×D11—22no—
151C2×C4×D11—22no—
152C2×C4×D11—22no—
153C2×C4×D11—22no—
154C2×Dic22—21no—
155C2×Dic22—21no—
156C2×Dic22—21no—
157C2×Dic22—21no—
158C2×Dic22—21no—
159C2×Dic22—21no—
160C11×M16—22no—
161C11×M16—22no—
162C11×M16—22no—
163C11×M16—41no—
164C11×M16—41no—
165C11×M16—41no—
166C11×M16—41no—
167C11×M16C22⋊C414yes—
168C2×C8×C11—22no—
169C2×C8×C11—22no—
170C2×C8×C11—22no—
171C2×C8×C11—22no—
172C2×C8×C11—22no—
173C2×C8×C11—22no—
174C11×C4⋊C4—41no—
175C11×C4⋊C4—41no—
176C11×C22⋊C4—22no—
177C11×C22⋊C4—22no—
178C42×C11—41no—
179C42×C11—41no—
180C22⋊Dic11—22no—
181C22⋊Dic11C22⋊C414yes—
182C4⋊Dic11—22no—
183C4⋊Dic11—22no—
184C4×Dic11—22no—
185C4×Dic11—22no—
186#4318—22no—
187#4318—22no—
188#4318—41no—
189#4318—41no—
190C2×C11⋊C8—22no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8—22no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—22no—
196C2×C11⋊C8—22no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—41no—
200C2×C11⋊C8—41no—
201C2×C11⋊C8C22⋊C412yes—
202C2×C11⋊C8C22⋊C412yes—
203C2×#413—111no—
204C2×#410—111no—
205C2×#408—111no—
206C2×#405—111no—
207C2×#344—111no—
208C2×#344D1111yescharacteristic, complemented
209#1729—111no—
210C23×C11—42no—
211C23×C11C2×C4211yescharacteristic
212C23×C11C2×C22⋊C411yescharacteristic
213C23×C11#11711yescharacteristic
214C23×C11C4×D411yescharacteristic
215C23×C11C4×D411yescharacteristic
216C23×C11C4×D411yescharacteristic
217C23×C11C4×D411yescharacteristic
218C22×D11—22no—
219C22×D11—22no—
220C22×D11—22no—
221C22×D11—44no—
222C2×C4×C11—44no—
223C2×C4×C11—42no—
224C2×C4×C11C2×C22⋊C411yescharacteristic
225C2×C4×C11C2×C22⋊C411yescharacteristic
226C2×C4×C11#11711yescharacteristic
227C2×C4×C11#11711yescharacteristic
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×C11C4×D411yescharacteristic
236C2×C4×C11#12011yescharacteristic
237C2×C4×C11#12111yescharacteristic
238C2×C4×C11#12111yescharacteristic
239C2×C4×C11#12111yescharacteristic
240C2×C4×C11#12111yescharacteristic
241C2×C4×C11#12111yescharacteristic
242C2×C4×C11#12111yescharacteristic
243C2×C4×C11#12311yescharacteristic
244C2×C4×C11#12311yescharacteristic
245C2×C4×C11#12311yescharacteristic
246C2×C4×C11#12411yescharacteristic
247C2×C4×C11#12411yescharacteristic
248C2×C4×C11#12411yescharacteristic
249C2×C4×C11#12611yescharacteristic
250C2×C4×C11#12611yescharacteristic
251C2×C4×C11#12711yescharacteristic
252C22⋊D11—42no—
253C22⋊D11—42no—
254C22⋊D11—42no—
255C22⋊D11—42no—
256C2×Dic11—22no—
257C2×Dic11—22no—
258C2×Dic11—22no—
259C2×Dic11—24no—
260C2×Dic11—44no—
261D44—41no—
262D44—41no—
263D44—41no—
264D44—41no—
265C4×D11—42no—
266C4×D11—42no—
267C4×D11—42no—
268C4×D11—42no—
269Dic22—41no—
270Dic22—41no—
271Dic22—41no—
272Dic22—41no—
273C8×C11—24no—
274C8×C11—42no—
275C11⋊C8—22no—
276C11⋊C8—22no—
277C11⋊C8—42no—
278C22×#41—111no—
279C22×M16—111no—
280C22×M16C2×D1111yescharacteristic
281C22×M16C2×D1111yescharacteristic
282C23×C8—111no—
283C2×#117—111no—
284C2×#117C2×D1111yescharacteristic
285#413—222no—
286#413—222no—
287C2×#101—112no—
288C2×#100—112no—
289#410—222no—
290#410—222no—
291C2×#99—114no—
292#408—222no—
293#408—221no—
294#408—221no—
295C2×C22⋊C8—114no—
296#405—222no—
297#405—222no—
298C2×#97—221no—
299C2×C4×C8—221no—
300#344—22no—
301#344—222no—
302#336—222no—
303C22×C11—22no—
304C22×C11—22no—
305C22×C11—22no—
306C22×C11—41no—
307C22×C11—41no—
308C22×C11—41no—
309C22×C11—41no—
310C22×C11C4×C22⋊C411yescharacteristic
311C22×C11C4×C22⋊C411yescharacteristic
312C22×C11C4×C22⋊C411yescharacteristic
313C22×C11#38611yescharacteristic
314C22×C11#38811yescharacteristic
315C22×C11#38811yescharacteristic
316C22×C11#39011yescharacteristic
317C2×D11—42no—
318C2×D11—44no—
319C2×D11—82no—
320C2×D11—82no—
321C4×C11—82no—
322C4×C11#38611yescharacteristic
323C4×C11#38611yescharacteristic
324C4×C11#38811yescharacteristic
325C4×C11#38811yescharacteristic
326C4×C11#38811yescharacteristic
327C4×C11#38811yescharacteristic
328C4×C11#39011yescharacteristic
329C4×C11#39011yescharacteristic
330Dic11—44no—
331Dic11—42no—
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—
342C2×#41—221no—
343C2×#41—221no—
344C22×Q8—111no—
345C22×D4—112no—
346C22×D4—111no—
347C23×C4—112no—
348C23×C4C22×D1111yescharacteristic
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—221no—
360C2×M16—221no—
361C2×M16—221no—
362C2×M16—221no—
363C2×M16—221no—
364C2×M16C4×D1112yes—
365C2×M16D4412yes—
366C2×M16C22⋊D1112yes—
367C22×C8—21no—
368C22×C8—112no—
369C22×C8—112no—
370C22×C8—111no—
371C22×C8—111no—
372C22×C8—221no—
373C22×C8—221no—
374C22×C8—221no—
375C22×C8—221no—
376C22×C8—221no—
377C22×C8C4×D1112yes—
378#117—21no—
379#117—21no—
380#117—21no—
381#117—21no—
382#117—112no—
383#117—112no—
384#117—221no—
385#117—221no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—221no—
388C2×C22⋊C4—112no—
389C2×C22⋊C4C4×D1112yes—
390C2×C42—21no—
391C2×C42—221no—
392#101—224no—
393#100—224no—
394#99—228no—
395C22⋊C8—224no—
396C22⋊C8—224no—
397#97—224no—
398C4×C8—224no—
399C2×C11—21no—
400C2×C11—21no—
401C2×C11—21no—
402C2×C11—21no—
403C2×C11—21no—
404C2×C11—21no—
405C2×C11#143711yescharacteristic
406C2×C11#175712yes—
407D11—82no—
408C24—112no—
409C24C2×C4×D1111yescharacteristic
410#41—441no—
411#41—441no—
412#41—441no—
413#41—441no—
414#41—441no—
415#41—441no—
416#41—441no—
417#41—441no—
418#41—441no—
419#41—441no—
420#41—441no—
421#41—441no—
422#41—441no—
423#41—441no—
424#41—441no—
425#41—441no—
426C2×Q8—221no—
427C2×Q8—221no—
428C2×Q8—221no—
429C2×Q8—221no—
430C2×Q8—221no—
431C2×Q8—221no—
432C2×D4—222no—
433C2×D4—222no—
434C2×D4—222no—
435C2×D4—222no—
436C2×D4—222no—
437C2×D4—222no—
438C2×D4—221no—
439C2×D4—221no—
440C2×D4—221no—
441C2×D4—221no—
442C2×D4—221no—
443C2×D4—221no—
444C22×C4—22no—
445C22×C4—112no—
446C22×C4—222no—
447C22×C4—222no—
448C22×C4—222no—
449C22×C4—222no—
450C22×C4—222no—
451C22×C4—222no—
452C22×C4—222no—
453C22×C4C2×C4×D1111yescharacteristic
454C22×C4C2×C4×D1111yescharacteristic
455C22×C4C2×D4411yescharacteristic
456C22×C4#433911yescharacteristic
457C22×C4#433911yescharacteristic
458C22×C4D4×D1111yescharacteristic
459C22×C4D4×D1111yescharacteristic
460C22×C4D4×D1111yescharacteristic
461C22×C4D4×D1111yescharacteristic
462C22×C4#434111yescharacteristic
463C22×C4#434111yescharacteristic
464C22×C4#434311yescharacteristic
465C22×C4#434311yescharacteristic
466C22×C4C2×C22⋊D1111yescharacteristic
467M16—22no—
468M16—22no—
469M16—22no—
470M16—41no—
471M16—41no—
472M16—41no—
473M16—41no—
474M16—222no—
475M16—222no—
476M16—441no—
477M16—441no—
478M16(C2×D11)⋊C414yes—
479C2×C8—22no—
480C2×C8—22no—
481C2×C8—22no—
482C2×C8—22no—
483C2×C8—22no—
484C2×C8—22no—
485C2×C8—112no—
486C2×C8—112no—
487C2×C8—222no—
488C2×C8—221no—
489C2×C8—221no—
490C2×C8—222no—
491C2×C8—222no—
492C2×C8—221no—
493C2×C8—221no—
494C2×C8—222no—
495C2×C8—222no—
496C2×C8—441no—
497C2×C8—441no—
498C4⋊C4—41no—
499C4⋊C4—41no—
500C4⋊C4—222no—
501C4⋊C4—222no—
502C22⋊C4—22no—
503C22⋊C4—22no—
504C22⋊C4—114no—
505C22⋊C4—222no—
506C42—41no—
507C42—41no—
508C42—222no—
509C42—222no—
510C11#1096111yescharacteristic, complemented, Sylow
511C23—42no—
512C23—222no—
513C23—222no—
514C23—222no—
515C23—444no—
516C23C42×D1111yescharacteristic
517C23C4×D4411yescharacteristic
518C23C22⋊C4×D1111yescharacteristic
519C23(C22⋊D11)⋊C411yescharacteristic
520C23#6694511yescharacteristic
521C23#6694611yescharacteristic
522C23C4×C22⋊D1111yescharacteristic
523Q8—441no—
524Q8—441no—
525Q8—441no—
526Q8—441no—
527D4—442no—
528D4—442no—
529D4—442no—
530D4—442no—
531D4—441no—
532D4—441no—
533D4—441no—
534D4—441no—
535C2×C4—44no—
536C2×C4—42no—
537C2×C4—224no—
538C2×C4—222no—
539C2×C4—222no—
540C2×C4—222no—
541C2×C4—444no—
542C2×C4—442no—
543C2×C4—442no—
544C2×C4—442no—
545C2×C4—442no—
546C2×C4#6692511yescharacteristic
547C2×C4C4×D4411yescharacteristic
548C2×C4C22⋊C4×D1111yescharacteristic
549C2×C4(C22⋊D11)⋊C411yescharacteristic
550C2×C4(C22⋊D11)⋊C411yescharacteristic
551C2×C4(C22⋊D11)⋊C411yescharacteristic
552C2×C4#6693511yescharacteristic
553C2×C4#6693711yescharacteristic
554C2×C4#6693711yescharacteristic
555C2×C4#6693811yescharacteristic
556C2×C4#6693811yescharacteristic
557C2×C4#6693911yescharacteristic
558C2×C4#6694511yescharacteristic
559C2×C4#6694611yescharacteristic
560C2×C4#6694611yescharacteristic
561C2×C4#6694611yescharacteristic
562C2×C4#6694711yescharacteristic
563C2×C4#6694711yescharacteristic
564C2×C4#6694811yescharacteristic
565C2×C4#6694811yescharacteristic
566C2×C4#6695111yescharacteristic
567C2×C4#6695111yescharacteristic
568C2×C4C2×(C2×D11)⋊C411yescharacteristic
569C2×C4C4×C22⋊D1111yescharacteristic
570C2×C4#6699211yescharacteristic
571C2×C4#6699211yescharacteristic
572C2×C4#6699311yescharacteristic
573C2×C4#6700011yescharacteristic
574C8—24no—
575C8—42no—
576C8—222no—
577C8—222no—
578C8—442no—
579C22—22no—
580C22—22no—
581C22—22no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—442no—
587C22—444no—
588C22—882no—
589C22—882no—
590C22#1062227811yescharacteristic
591C22#1062227911yescharacteristic
592C22#1062227911yescharacteristic
593C22#1062228311yescharacteristic
594C22C4×(C2×D11)⋊C411yescharacteristic
595C22#1062257011yescharacteristic
596C22#1062260311yescharacteristic
597C4—82no—
598C4—444no—
599C4—442no—
600C4#1062227811yescharacteristic
601C4#1062228211yescharacteristic
602C4#1062228211yescharacteristic
603C4#1062228311yescharacteristic
604C4#1062257011yescharacteristic
605C4#1062257111yescharacteristic
606C4#1062260111yescharacteristic
607C4#1062260311yescharacteristic
608C2—21no—
609C2—21no—
610C2—21no—
611C2—21no—
612C2—21no—
613C2—21no—
614C2—882no—
615C2#1306685211yescharacteristic
616C2#1306841512yes—
subgroupG/H
centerC2×C4C22⋊C4×D11
commutatorC23×C11C2×C42
FrattiniC23×C4C22×D11
FittingC2×C11×#344C2
socleC22×C11C4×C22⋊C4
prime radicalC22×#4339C22
cosocleC23×C4×C11C23
hypercenterC2×#344D11
hypocenterC11#10961
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#344

Complements

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

NH ≅ G/Ntype
4. C2×#10622735C2semidirect
5. C2×#10622194C2semidirect
6. #13068313C2semidirect
7. C2×C11×#344C2semidirect
15. C2×#66888C4semidirect
18. C2×#66887C4semidirect
24. C2×(C2×D11)⋊C8C4semidirect
208. C2×#344D11semidirect
510. C11#10961semidirect

Maximal subgroups

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

subgroupindex
C2×#106227452
C2×#106226192
C2×#106227422
C2×#106227352
C2×#106221942
#130683132
C2×C11×#3442
#1096111