Finite Group Databasebeta

← #14813836

Subgroups — #14813836

Order 2816.

944 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D8×Dic11C211yesmaximal, characteristic
2#13072399C211yesmaximal, characteristic, complemented
3D4×Dic11⋊C4C211yesmaximal, characteristic, complemented
4#13070152C211yesmaximal, characteristic, complemented
5#13070109C211yesmaximal, characteristic, complemented
6#13070022C211yesmaximal, characteristic, complemented
7#13069852C211yesmaximal, characteristic, complemented
8#13069289C211yesmaximal, characteristic, complemented
9#13069170C211yesmaximal, characteristic, complemented
10#13068966C211yesmaximal, characteristic
11#13068952C211yesmaximal, characteristic, complemented
12#13068952C211yesmaximal, characteristic, complemented
13#13068863C211yesmaximal, characteristic, complemented
14#13068861C211yesmaximal, characteristic, complemented
15C2×C11×#463C211yesmaximal, characteristic
16C22×C11×SD16C2211yescharacteristic
17C22×C11×D8C2211yescharacteristic
18C2×C11×#124C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C2×D4×Dic11C2211yescharacteristic
21C2×D4×Dic11C2211yescharacteristic
22C2×D4×Dic11C2211yescharacteristic
23C22×Dic11⋊C4—21no—
24C11×#463—24no—
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C2×C11×#102C2211yescharacteristic
28#10622843C2211yescharacteristic
29#10622843C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32#10622834C2211yescharacteristic
33C2×#66896C2211yescharacteristic
34C2×#66896C2211yescharacteristic
35C2×#66896C2211yescharacteristic
36C2×#66896C2211yescharacteristic
37#10622823—21no—
38D8×Dic11—24no—
39C2×#66882C2211yescharacteristic
40C2×C8×Dic11C2211yescharacteristic
41#10622589C2211yescharacteristic
42#10622586C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44#10622565—21no—
45#10622565—21no—
46#10622559—21no—
47#10622559—21no—
48#10622556—21no—
49#10622555—21no—
50C4×Dic11⋊C4C2211yescharacteristic
51#10622541C2211yescharacteristic
52#10622541C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C22×D4×C11C2311yescharacteristic
64C23×C4×C11—21no—
65C23×Dic11—21no—
66C23×Dic11—21no—
67C23×Dic11—21no—
68C2×C11×SD16—22no—
69C2×C11×SD16—22no—
70C2×C11×SD16—22no—
71C2×C11×D8—22no—
72C2×C11×D8—22no—
73C2×C11×D8D414yes—
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C11×#124—22no—
77C11×#124—41no—
78C4×D4×C11—22no—
79C4×D4×C11—41no—
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—21no—
84C2×C42×C11C2311yescharacteristic
85C2×C22⋊Dic11—21no—
86C2×C22⋊Dic11—21no—
87C2×C22⋊Dic11—21no—
88C2×C22⋊Dic11—21no—
89C2×C22⋊Dic11—21no—
90D4×Dic11—22no—
91D4×Dic11—22no—
92D4×Dic11—22no—
93D4×Dic11—22no—
94D4×Dic11—41no—
95D4×Dic11—41no—
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2311yescharacteristic
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4—21no—
102C2×Dic11⋊C4—21no—
103C2×Dic11⋊C4—21no—
104C2×Dic11⋊C4—21no—
105C2×Dic11⋊C4—44no—
106C2×Dic11⋊C4D411yescharacteristic
107C2×Dic11⋊C4D411yescharacteristic
108C2×C4×Dic11C2311yescharacteristic
109C2×C4×Dic11C2311yescharacteristic
110C22×C11⋊C8C2311yescharacteristic
111C22×C11⋊C8C2311yescharacteristic
112C11×C4⋊C8—22no—
113C11×#103—22no—
114C11×#102—22no—
115#66899—22no—
116#66899—41no—
117#66896—22no—
118#66896—22no—
119#66896—22no—
120#66896—22no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128C11⋊#95D411yescharacteristic
129C11⋊#95D411yescharacteristic
130#66882—22no—
131C8×Dic11—22no—
132#66871—41no—
133#26164—111nomaximal, Sylow
134C24×C11—21no—
135C24×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—21no—
146C2×D4×C11—21no—
147C2×D4×C11—21no—
148C2×D4×C11—21no—
149C2×D4×C11—21no—
150C2×D4×C11C2×D412yes—
151C2×D4×C11C2×D412yes—
152C2×D4×C11#4112yes—
153C2×D4×C11#4112yes—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—42no—
157C22×C4×C11—42no—
158C22×C4×C11—81no—
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2411yescharacteristic
162C22×Dic11—24no—
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11—21no—
167C22×Dic11—42no—
168C22×Dic11—42no—
169C22×Dic11—42no—
170C22×Dic11—42no—
171C22×Dic11—42no—
172C22×Dic11—42no—
173C22×Dic11—81no—
174C22×Dic11—81no—
175C22×Dic11C2×D411yescharacteristic
176C22×Dic11C2×D411yescharacteristic
177C22×Dic11C2×D411yescharacteristic
178C22×Dic11C2×D411yescharacteristic
179C11×SD16—44no—
180C11×D8—28no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11—21no—
186C2×C8×C11C2×D412yes—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C22⋊C4—42no—
190C11×C22⋊C4—42no—
191C11×C22⋊C4—42no—
192C42×C11—21no—
193C42×C11—21no—
194C22⋊Dic11—24no—
195C22⋊Dic11—42no—
196C22⋊Dic11—42no—
197C22⋊Dic11—42no—
198C22⋊Dic11—81no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11#4112yes—
207Dic11⋊C4—22no—
208Dic11⋊C4—22no—
209Dic11⋊C4—42no—
210Dic11⋊C4—42no—
211Dic11⋊C4—42no—
212Dic11⋊C4—81no—
213Dic11⋊C4—81no—
214C4×Dic11—21no—
215C4×Dic11—21no—
216C4×Dic11—21no—
217C4×Dic11—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—21no—
224C2×#463D1111yescharacteristic
225C2×C4×D8—111no—
226#2447—111no—
227D4×C4⋊C4—111no—
228#2095—111no—
229#2087—111no—
230#2071—111no—
231#2042—111no—
232#1933—111no—
233#1916—111no—
234#1879—111no—
235#1877—111no—
236#1877—111no—
237#1862—111no—
238#1862—111no—
239C23×C11—22no—
240C23×C11—22no—
241C23×C11—22no—
242C23×C11—22no—
243C23×C11—41no—
244C23×C11—41no—
245C23×C11—41no—
246C23×C11—41no—
247C23×C11—41no—
248C23×C11—41no—
249C23×C11—41no—
250C23×C11—41no—
251C23×C11—41no—
252C23×C11—41no—
253C23×C11C22×D411yescharacteristic
254Q8×C11—41no—
255Q8×C11—41no—
256Q8×C11—41no—
257Q8×C11—41no—
258D4×C11—22no—
259D4×C11—22no—
260D4×C11—22no—
261D4×C11—22no—
262D4×C11—22no—
263D4×C11—41no—
264D4×C11—41no—
265D4×C11#12314yes—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11—41no—
278C2×C4×C11—84no—
279C2×C4×C11C22×D411yescharacteristic
280C2×C4×C11C2×#4111yescharacteristic
281C2×C4×C11C2×#4111yescharacteristic
282C2×C4×C11C2×#4111yescharacteristic
283C2×C4×C11H(5,𝔽2)11yescharacteristic
284C2×C4×C112−1+411yescharacteristic
285C2×Dic11—21no—
286C2×Dic11—21no—
287C2×Dic11—21no—
288C2×Dic11—21no—
289C2×Dic11—21no—
290C2×Dic11—22no—
291C2×Dic11—21no—
292C2×Dic11—21no—
293C2×Dic11—21no—
294C2×Dic11—21no—
295C2×Dic11—21no—
296C2×Dic11—48no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C2×Dic11—41no—
303C2×Dic11—41no—
304C2×Dic11—41no—
305C2×Dic11—41no—
306C2×Dic11—41no—
307C2×Dic11—41no—
308C2×Dic11—84no—
309C2×Dic11—84no—
310C2×Dic11#13512yes—
311C2×Dic11AGL(1,ℤ/8)12yes—
312C8×C11—22no—
313C8×C11—41no—
314C11⋊C8—41no—
315C11⋊C8—41no—
316C22×SD16C2×D1111yescharacteristic
317C22×D8C2×D1111yescharacteristic
318C2×#124C2×D1111yescharacteristic
319C2×C4×D4—111no—
320C2×C4×D4—111no—
321C2×C4×D4—111no—
322C2×C4×D4C2×D1111yescharacteristic
323C22×C4⋊C4—221no—
324#463—24no—
325C4×D8—224no—
326C2×#107—111no—
327C2×#107—111no—
328C2×C4⋊C8C2×D1111yescharacteristic
329C2×#103—111no—
330C2×#103—111no—
331C2×#103C2×D1111yescharacteristic
332C2×#102—111no—
333C2×#102—111no—
334C2×#102—111no—
335C2×#102—111no—
336C2×#102C2×D1111yescharacteristic
337C2×C4×C8—111no—
338#397—221no—
339#397—221no—
340#391—111no—
341#391—111no—
342#390—111no—
343#389—111no—
344#389—111no—
345#389—111no—
346#385—221no—
347#385—221no—
348#385—221no—
349#384—111no—
350#381—221no—
351#380—221no—
352C4×C4⋊C4—111no—
353#340—111no—
354#340—111no—
355#340—111no—
356#340—111no—
357#336—111no—
358#336—111no—
359#336—111no—
360#336—111no—
361C22×C11—24no—
362C22×C11—42no—
363C22×C11—42no—
364C22×C11—42no—
365C22×C11—42no—
366C22×C11—42no—
367C22×C11—42no—
368C22×C11—42no—
369C22×C11—42no—
370C22×C11—42no—
371C22×C11—81no—
372C22×C11—81no—
373C22×C11—81no—
374C22×C11—81no—
375C22×C11#52511yescharacteristic
376C22×C11D4211yescharacteristic
377C22×C11#54811yescharacteristic
378C22×C11C2×#13511yescharacteristic
379C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
380C22×C11#57611yescharacteristic
381C22×C11#57811yescharacteristic
382C4×C11—41no—
383C4×C11—41no—
384C4×C11—81no—
385C4×C11—81no—
386C4×C11C2×#12311yescharacteristic
387C4×C11#53911yescharacteristic
388C4×C11#54711yescharacteristic
389C4×C11#55311yescharacteristic
390Dic11—22no—
391Dic11—22no—
392Dic11—42no—
393Dic11—41no—
394Dic11—41no—
395Dic11—81no—
396Dic11—81no—
397Dic11—81no—
398C22×Q8C22×D1111yescharacteristic
399C22×D4C22×D1111yescharacteristic
400C22×D4C22×D1111yescharacteristic
401C23×C4—21no—
402C23×C4—221no—
403C23×C4—221no—
404C23×C4—221no—
405C2×SD16—22no—
406C2×SD16—22no—
407C2×SD16—22no—
408C2×D8—22no—
409C2×D8—22no—
410C2×D8C22⋊D1114yes—
411C22×C8—111no—
412C22×C8—111no—
413C22×C8C22×D1111yescharacteristic
414C22×C8C22×D1111yescharacteristic
415#124—22no—
416#124—41no—
417C4×D4—22no—
418C4×D4—41no—
419C4×D4—222no—
420C4×D4—222no—
421C4×D4—222no—
422C4×D4—222no—
423C4×D4—441no—
424C4×D4—441no—
425C2×C4⋊C4—111no—
426C2×C4⋊C4—111no—
427C2×C4⋊C4—111no—
428C2×C4⋊C4—111no—
429C2×C4⋊C4—111no—
430C2×C4⋊C4—111no—
431C2×C4⋊C4—221no—
432C2×C4⋊C4—221no—
433C2×C4⋊C4—221no—
434C2×C4⋊C4—221no—
435C2×C4⋊C4—221no—
436C2×C4⋊C4—444no—
437C2×C4⋊C4C22×D1111yescharacteristic
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—221no—
442C2×C22⋊C4—221no—
443C2×C22⋊C4—221no—
444C2×C22⋊C4—221no—
445C2×C22⋊C4—221no—
446C2×C42—111no—
447C2×C42—111no—
448C2×C42C22×D1111yescharacteristic
449#107—222no—
450#107—441no—
451C4⋊C8—22no—
452#103—22no—
453#103—222no—
454#103—441no—
455#102—22no—
456#102—222no—
457#102—222no—
458#102—222no—
459#102—222no—
460C4×C8—222no—
461#95—111no—
462#95—111no—
463#95—221no—
464#95—221no—
465#95—221no—
466#95—221no—
467#95—221no—
468#95—221no—
469#95—221no—
470C2×C11—44no—
471C2×C11—82no—
472C2×C11#244311yescharacteristic
473C2×C11#310511yescharacteristic
474C2×C11#312411yescharacteristic
475C2×C11#326411yescharacteristic
476C2×C11#328311yescharacteristic
477C2×C11#336111yescharacteristic
478C2×C11#336711yescharacteristic
479C24—21no—
480C24—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4#434112yes—
496C2×D4#434112yes—
497C2×D4C2×C22⋊D1112yes—
498C2×D4C2×C22⋊D1112yes—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—81no—
504C22×C4—111no—
505C22×C4—111no—
506C22×C4—111no—
507C22×C4—111no—
508C22×C4—224no—
509C22×C4—221no—
510C22×C4—221no—
511C22×C4—221no—
512C22×C4—221no—
513C22×C4—442no—
514C22×C4—442no—
515C22×C4—442no—
516C22×C4—442no—
517C22×C4—442no—
518C22×C4—442no—
519C22×C4—881no—
520C22×C4—881no—
521C22×C4D4×D1111yescharacteristic
522C22×C4D4×D1111yescharacteristic
523C22×C4C23×D1111yescharacteristic
524SD16—44no—
525D8—28no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—221no—
532C2×C8—221no—
533C2×C8—221no—
534C2×C8—221no—
535C2×C8—221no—
536C2×C8—221no—
537C2×C8C2×C22⋊D1112yes—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—112no—
541C4⋊C4—222no—
542C4⋊C4—222no—
543C4⋊C4—221no—
544C4⋊C4—221no—
545C4⋊C4—221no—
546C4⋊C4—221no—
547C4⋊C4—221no—
548C4⋊C4—221no—
549C4⋊C4—221no—
550C4⋊C4—442no—
551C4⋊C4—442no—
552C4⋊C4—442no—
553C4⋊C4—881no—
554C4⋊C4—881no—
555C22⋊C4—42no—
556C22⋊C4—42no—
557C22⋊C4—42no—
558C22⋊C4—224no—
559C22⋊C4—442no—
560C22⋊C4—442no—
561C22⋊C4—442no—
562C22⋊C4—881no—
563C42—21no—
564C42—21no—
565C42—221no—
566C42—221no—
567C42—221no—
568C42—221no—
569C11#2616411yescharacteristic, complemented, Sylow
570C23—22no—
571C23—22no—
572C23—22no—
573C23—22no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23C2×D4×D1111yescharacteristic
585Q8—41no—
586Q8—41no—
587Q8—41no—
588Q8—41no—
589D4—22no—
590D4—22no—
591D4—22no—
592D4—22no—
593D4—22no—
594D4—41no—
595D4—41no—
596D4#6698814yes—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—84no—
610C2×C4—112no—
611C2×C4—112no—
612C2×C4—221no—
613C2×C4—221no—
614C2×C4—221no—
615C2×C4—221no—
616C2×C4—221no—
617C2×C4—221no—
618C2×C4—221no—
619C2×C4—221no—
620C2×C4—221no—
621C2×C4—221no—
622C2×C4—222no—
623C2×C4—448no—
624C2×C4—441no—
625C2×C4—441no—
626C2×C4—441no—
627C2×C4—441no—
628C2×C4—441no—
629C2×C4—441no—
630C2×C4—441no—
631C2×C4—441no—
632C2×C4—441no—
633C2×C4—441no—
634C2×C4—441no—
635C2×C4—884no—
636C2×C4—884no—
637C2×C4C2×#434111yescharacteristic
638C2×C4C2×#434111yescharacteristic
639C2×C4#6703711yescharacteristic
640C2×C4#41×D1111yescharacteristic
641C2×C4#6704311yescharacteristic
642C2×C4C22×C22⋊D1111yescharacteristic
643C8—22no—
644C8—41no—
645C8—441no—
646C8—441no—
647C22—24no—
648C22—42no—
649C22—42no—
650C22—42no—
651C22—42no—
652C22—42no—
653C22—42no—
654C22—42no—
655C22—42no—
656C22—42no—
657C22—81no—
658C22—81no—
659C22—81no—
660C22—81no—
661C22#1062312911yescharacteristic
662C22#1062313711yescharacteristic
663C22D11×#13511yescharacteristic
664C22#1062330211yescharacteristic
665C22D11×AGL(1,ℤ/8)11yescharacteristic
666C22#1062330511yescharacteristic
667C22D4×C22⋊D1111yescharacteristic
668C4—41no—
669C4—41no—
670C4—81no—
671C4—81no—
672C4—222no—
673C4—222no—
674C4—441no—
675C4—441no—
676C4—442no—
677C4—881no—
678C4—881no—
679C4—881no—
680C4#1062313211yescharacteristic
681C4#1062313311yescharacteristic
682C4C2×#6698811yescharacteristic
683C4#1062335511yescharacteristic
684C2—44no—
685C2—82no—
686C2#1307234711yescharacteristic
687C2#1307866211yescharacteristic
688C2#1307887511yescharacteristic
689C2#1308009011yescharacteristic
690C2#1308033211yescharacteristic
691C2#1308127111yescharacteristic
692C2#1308132911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#463C2
socleC23×C11C22×D4
prime radicalC22×C11×D8C22
hypercenterC2×#463D11
hypocenterC11#26164
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
2. #13072399C2semidirect
3. D4×Dic11⋊C4C2semidirect
4. #13070152C2semidirect
5. #13070109C2semidirect
6. #13070022C2semidirect
7. #13069852C2semidirect
8. #13069289C2semidirect
9. #13069170C2semidirect
11. #13068952C2semidirect
12. #13068952C2semidirect
13. #13068863C2semidirect
14. #13068861C2semidirect
569. C11#26164semidirect

Maximal subgroups

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

subgroupindex
C2×D8×Dic112
#130723992
D4×Dic11⋊C42
#130701522
#130701092
#130700222
#130698522
#130692892
#130691702
#130689662
#130689522
#130688632
#130688612
C2×C11×#4632
#2616411