Finite Group Databasebeta

← #14813602

Subgroups — #14813602

Order 2816.

904 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622422C211yesmaximal, characteristic, complemented
2C2×#10622577C211yesmaximal, characteristic, complemented
3#13072046C211yesmaximal, characteristic
4C4⋊C4×C22⋊D11C211yesmaximal, characteristic
5#13070157C211yesmaximal, characteristic, complemented
6#13070091C211yesmaximal, characteristic, complemented
7#13070055C211yesmaximal, characteristic, complemented
8#13069817C211yesmaximal, characteristic, complemented
9#13069253C211yesmaximal, characteristic, complemented
10#13069185C211yesmaximal, characteristic, complemented
11#13069050C211yesmaximal, characteristic, complemented
12#13068911C211yesmaximal, characteristic
13#13068817C211yesmaximal, characteristic, complemented
14#13068810C211yesmaximal, characteristic, complemented
15C11×#1872C211yesmaximal, characteristic, complemented
16C2×C11×C22⋊Q8C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C2×#66999C2211yescharacteristic
19C2×C4×C22⋊D11—21no—
20C2×C4×C22⋊D11C2211yescharacteristic
21C2×#66979C2211yescharacteristic
22C22×#4318C2211yescharacteristic
23C2×C4⋊C4×D11C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27#10622843C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30#10622825C2211yescharacteristic
31#10622823—21no—
32C2×(C2×D11)⋊C8C2211yescharacteristic
33C2×(C2×D11)⋊C8C2211yescharacteristic
34C2×#66882C2211yescharacteristic
35C2×#66881C2211yescharacteristic
36#10622603—21no—
37#10622602—21no—
38#10622600C2211yescharacteristic
39#10622600C2211yescharacteristic
40#10622589C2211yescharacteristic
41C4⋊C4×Dic11C2211yescharacteristic
42#10622586C2211yescharacteristic
43#10622585—21no—
44#10622585—21no—
45#10622577—24no—
46C2×#66872C2211yescharacteristic
47C2×#66872C2211yescharacteristic
48C2×#66871C2211yescharacteristic
49C2×#66871C2211yescharacteristic
50#10622572—21no—
51#10622565—21no—
52#10622422—24no—
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C23×C4×C11—21no—
63C23×C4×C11C2311yescharacteristic
64C22×C22⋊D11D411yescharacteristic
65C22×C4×D11—21no—
66C22×C4×D11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C11×C22⋊Q8—22no—
70C11×C22⋊Q8—22no—
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—41no—
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C22⋊C4—21no—
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11D411yescharacteristic
82#66999—22no—
83#66999—41no—
84C4×C22⋊D11—22no—
85C4×C22⋊D11—22no—
86C4×C22⋊D11—44no—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4D411yescharacteristic
91#66979—22no—
92#66979—41no—
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4—21no—
102C2×Dic11⋊C4D411yescharacteristic
103C2×C4×Dic11—21no—
104C2×C4×Dic11—21no—
105C2×C4×Dic11C2311yescharacteristic
106C2×#4318—22no—
107C2×#4318—22no—
108C2×#4318—22no—
109C22×C11⋊C8C2311yescharacteristic
110C22×C11⋊C8C2311yescharacteristic
111C4⋊C4×D11—22no—
112C4⋊C4×D11—41no—
113C11×#103—22no—
114C11×#103—41no—
115C11×C22⋊C8—22no—
116#66899—22no—
117#66899—22no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125(C2×D11)⋊C8—22no—
126(C2×D11)⋊C8—22no—
127#66882—22no—
128#66881—41no—
129#66872—22no—
130#66872—22no—
131#66871—22no—
132#66871D414yescomplemented
133#26148—111nomaximal, Sylow
134C24×C11C2×D411yescharacteristic
135C23×D11C2×D411yescharacteristic
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—42no—
151C22×C4×C11—42no—
152C22×C4×C11—81no—
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11#4112yes—
155C22×C4×C11#4112yes—
156C22×C4×C11C2411yescharacteristic
157C2×C22⋊D11—22no—
158C2×C22⋊D11—22no—
159C2×C22⋊D11—22no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—21no—
164C22×Dic11C2×D411yescharacteristic
165C22×Dic11C2×D411yescharacteristic
166C22×Dic11C2×D411yescharacteristic
167C2×C4×D11—21no—
168C2×C4×D11—21no—
169C2×C4×D11—21no—
170C2×C4×D11—21no—
171C2×C4×D11—21no—
172C2×C4×D11—21no—
173C2×C4×D11—42no—
174C2×C4×D11—42no—
175C2×C4×D11—81no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—42no—
188C11×C4⋊C4—42no—
189C11×C4⋊C4C2×D412yes—
190C11×C22⋊C4—42no—
191C22⋊Dic11—22no—
192C22⋊Dic11—42no—
193C22⋊Dic11—42no—
194(C2×D11)⋊C4—22no—
195(C2×D11)⋊C4—42no—
196(C2×D11)⋊C4—42no—
197(C2×D11)⋊C4—42no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11C2×D412yes—
206Dic11⋊C4—22no—
207Dic11⋊C4—42no—
208Dic11⋊C4—42no—
209Dic11⋊C4—42no—
210Dic11⋊C4—42no—
211Dic11⋊C4—81no—
212C4×Dic11—21no—
213C4×Dic11—21no—
214C4×Dic11—42no—
215C4×Dic11—42no—
216#4318—28no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8C2×D412yes—
222C2×C11⋊C8#4112yes—
223C2×#484—111no—
224C2×#428—111no—
225#2415—111no—
226D4×C4⋊C4—111no—
227#2096—111no—
228#2083—111no—
229#2077—111no—
230#2036—111no—
231#1927—111no—
232#1918—111no—
233#1894—111no—
234#1872D1111yescharacteristic, complemented
235#1870—111no—
236#1854—111no—
237#1853—111no—
238C23×C11—21no—
239C23×C11—21no—
240C23×C11—21no—
241C23×C11—21no—
242C23×C11—21no—
243C23×C11—21no—
244C23×C11#12312yes—
245C23×C11C22×D411yescharacteristic
246C22×D11—21no—
247C22×D11—21no—
248C22×D11—21no—
249C22×D11—21no—
250C22×D11—21no—
251C22×D11—21no—
252C22×D11#13712yes—
253Q8×C11—41no—
254Q8×C11—41no—
255Q8×C11—41no—
256Q8×C11—41no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—22no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—84no—
276C2×C4×C11#12312yes—
277C2×C4×C11C22×D411yescharacteristic
278C2×C4×C11C2×#4111yescharacteristic
279C2×C4×C11C2×#4111yescharacteristic
280C2×C4×C11C2×#4111yescharacteristic
281C2×C4×C11H(5,𝔽2)11yescharacteristic
282C2×C4×C112−1+411yescharacteristic
283C22⋊D11—28no—
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—21no—
287C2×Dic11—21no—
288C2×Dic11—22no—
289C2×Dic11—21no—
290C2×Dic11—21no—
291C2×Dic11—21no—
292C2×Dic11—21no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C2×Dic11—41no—
303C2×Dic11—41no—
304C2×Dic11AGL(1,ℤ/8)12yes—
305C4×D11—41no—
306C4×D11—41no—
307C4×D11—41no—
308C4×D11—41no—
309C4×D11—84no—
310C8×C11—41no—
311C8×C11—41no—
312C11⋊C8—22no—
313C11⋊C8—22no—
314C22×M16—111no—
315C2×C22⋊Q8—111no—
316C2×C22⋊Q8C2×D1111yescharacteristic
317C2×C4×D4—111no—
318C2×C4×D4—221no—
319C2×#117—111no—
320C22×C4⋊C4—111no—
321C22×C4⋊C4C2×D1111yescharacteristic
322#484—224no—
323#428—224no—
324C2×#107—111no—
325C2×#107—111no—
326C2×#107—111no—
327C2×#106—111no—
328C2×#106—111no—
329C2×#106—111no—
330C2×#103—111no—
331C2×#103—111no—
332C2×#103C2×D1111yescharacteristic
333C2×#103C2×D1111yescharacteristic
334C2×C22⋊C8—111no—
335C2×C22⋊C8—111no—
336C2×C22⋊C8C2×D1111yescharacteristic
337#397—221no—
338#394—221no—
339#391—111no—
340#389—111no—
341#389—221no—
342#389—221no—
343#388—221no—
344#385—221no—
345#385—221no—
346#384—111no—
347#380—111no—
348#380—111no—
349#380—111no—
350C4×C4⋊C4—111no—
351#340—111no—
352#340—111no—
353#340—111no—
354#340—111no—
355#340C2×D1111yescharacteristic
356#340C2×D1111yescharacteristic
357#336—111no—
358#336—111no—
359C22×C11—22no—
360C22×C11—22no—
361C22×C11—22no—
362C22×C11—41no—
363C22×C11—41no—
364C22×C11—41no—
365C22×C11—41no—
366C22×C11C2×#12311yescharacteristic
367C22×C11D4211yescharacteristic
368C22×C11#54711yescharacteristic
369C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
370C22×C11C2×#13711yescharacteristic
371C22×C11#57711yescharacteristic
372C22×C11#57811yescharacteristic
373C2×D11—22no—
374C2×D11—22no—
375C2×D11—22no—
376C2×D11—41no—
377C2×D11—41no—
378C2×D11—41no—
379C2×D11—41no—
380C4×C11—22no—
381C4×C11—42no—
382C4×C11—81no—
383C4×C11—81no—
384C4×C11—81no—
385C4×C11#52511yescharacteristic
386C4×C11#53911yescharacteristic
387C4×C11#54811yescharacteristic
388C4×C11#55311yescharacteristic
389Dic11—22no—
390Dic11—41no—
391Dic11—41no—
392Dic11—42no—
393Dic11—81no—
394Dic11—81no—
395Dic11—81no—
396C22×Q8C22×D1111yescharacteristic
397C22×D4—111no—
398C23×C4—21no—
399C23×C4—111no—
400C23×C4—221no—
401C23×C4C22×D1111yescharacteristic
402C2×M16—222no—
403C2×M16—222no—
404C2×M16—222no—
405C22×C8—111no—
406C22×C8—111no—
407C22×C8C22×D1111yescharacteristic
408C22×C8C22×D1111yescharacteristic
409C22⋊Q8—22no—
410C22⋊Q8—22no—
411C22⋊Q8—222no—
412C22⋊Q8—441no—
413C4×D4—222no—
414C4×D4—222no—
415C4×D4—444no—
416#117—222no—
417#117—441no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—41no—
422C2×C4⋊C4—111no—
423C2×C4⋊C4—111no—
424C2×C4⋊C4—111no—
425C2×C4⋊C4—111no—
426C2×C4⋊C4—111no—
427C2×C4⋊C4—222no—
428C2×C4⋊C4—221no—
429C2×C4⋊C4—221no—
430C2×C4⋊C4—221no—
431C2×C4⋊C4—221no—
432C2×C4⋊C4—221no—
433C2×C4⋊C4—441no—
434C2×C4⋊C4C22×D1111yescharacteristic
435C2×C4⋊C4C22×D1111yescharacteristic
436C2×C4⋊C4C22×D1111yescharacteristic
437C2×C22⋊C4—21no—
438C2×C22⋊C4—111no—
439C2×C22⋊C4—111no—
440C2×C22⋊C4—221no—
441C2×C22⋊C4—221no—
442C2×C22⋊C4—221no—
443C2×C22⋊C4—221no—
444C2×C22⋊C4—221no—
445C2×C42—111no—
446C2×C42—221no—
447C2×C42—221no—
448#107—114no—
449#107—222no—
450#107—222no—
451#106—222no—
452#106—222no—
453#106—441no—
454#103—22no—
455#103—41no—
456#103—222no—
457#103—222no—
458C22⋊C8—22no—
459C22⋊C8—222no—
460C22⋊C8—222no—
461#95—221no—
462#95—221no—
463#95—221no—
464#95—221no—
465#95—221no—
466#95—221no—
467#95—221no—
468C2×C11—42no—
469C2×C11#244311yescharacteristic
470C2×C11#309211yescharacteristic
471C2×C11#309711yescharacteristic
472C2×C11#327011yescharacteristic
473C2×C11#327211yescharacteristic
474C2×C11#334411yescharacteristic
475C2×C11#335311yescharacteristic
476D11—42no—
477C24—111no—
478C24D4×D1111yescharacteristic
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×D4—222no—
486C2×D4—222no—
487C2×D4—222no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—81no—
499C22×C4—111no—
500C22×C4—111no—
501C22×C4—111no—
502C22×C4—221no—
503C22×C4—221no—
504C22×C4—221no—
505C22×C4—221no—
506C22×C4—221no—
507C22×C4—221no—
508C22×C4—221no—
509C22×C4—221no—
510C22×C4—221no—
511C22×C4—221no—
512C22×C4—442no—
513C22×C4—442no—
514C22×C4—881no—
515C22×C4#433912yes—
516C22×C4D4×D1111yescharacteristic
517C22×C4#434112yes—
518C22×C4C23×D1111yescharacteristic
519M16—228no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—112no—
527C2×C8—112no—
528C2×C8—221no—
529C2×C8—221no—
530C2×C8—221no—
531C2×C8—221no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—42no—
538C4⋊C4—42no—
539C4⋊C4—112no—
540C4⋊C4—222no—
541C4⋊C4—221no—
542C4⋊C4—221no—
543C4⋊C4—221no—
544C4⋊C4—221no—
545C4⋊C4—221no—
546C4⋊C4—221no—
547C4⋊C4—221no—
548C4⋊C4—442no—
549C4⋊C4—442no—
550C4⋊C4—442no—
551C4⋊C4—442no—
552C4⋊C4—881no—
553C4⋊C4D4×D1112yes—
554C22⋊C4—42no—
555C22⋊C4—222no—
556C22⋊C4—222no—
557C22⋊C4—442no—
558C22⋊C4—442no—
559C22⋊C4—442no—
560C22⋊C4—442no—
561C22⋊C4—442no—
562C42—221no—
563C42—221no—
564C42—442no—
565C42—442no—
566C11#2614811yescharacteristic, complemented, Sylow
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—112no—
574C23—221no—
575C23—221no—
576C23—221no—
577C23—221no—
578C23—221no—
579C23—221no—
580C23#6693612yes—
581C23C2×D4×D1111yescharacteristic
582Q8—41no—
583Q8—41no—
584Q8—41no—
585Q8—41no—
586D4—228no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—84no—
606C2×C4—112no—
607C2×C4—221no—
608C2×C4—221no—
609C2×C4—221no—
610C2×C4—221no—
611C2×C4—221no—
612C2×C4—221no—
613C2×C4—222no—
614C2×C4—221no—
615C2×C4—221no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4—441no—
619C2×C4—441no—
620C2×C4—441no—
621C2×C4—441no—
622C2×C4—441no—
623C2×C4—441no—
624C2×C4—441no—
625C2×C4—441no—
626C2×C4—441no—
627C2×C4—441no—
628C2×C4—441no—
629C2×C4—441no—
630C2×C4—441no—
631C2×C4—884no—
632C2×C4#6693612yes—
633C2×C4C2×#433911yescharacteristic
634C2×C4C2×D4×D1111yescharacteristic
635C2×C4C2×#434111yescharacteristic
636C2×C4#6703711yescharacteristic
637C2×C4#41×D1111yescharacteristic
638C2×C4#6704311yescharacteristic
639C8—41no—
640C8—41no—
641C8—222no—
642C8—222no—
643C22—22no—
644C22—22no—
645C22—22no—
646C22—41no—
647C22—41no—
648C22—41no—
649C22—41no—
650C22—222no—
651C22—222no—
652C22—222no—
653C22—441no—
654C22—441no—
655C22—441no—
656C22—441no—
657C22C2×#6693611yescharacteristic
658C22#1062312111yescharacteristic
659C22#1062318611yescharacteristic
660C22#1062329311yescharacteristic
661C22#1062329711yescharacteristic
662C22D11×AGL(1,ℤ/8)11yescharacteristic
663C22D11×#13711yescharacteristic
664C4—22no—
665C4—42no—
666C4—81no—
667C4—81no—
668C4—81no—
669C4—222no—
670C4—441no—
671C4—442no—
672C4—441no—
673C4—881no—
674C4—881no—
675C4—881no—
676C4#1062307811yescharacteristic
677C4#1062309511yescharacteristic
678C4#1062312911yescharacteristic
679C4#1062313211yescharacteristic
680C2—42no—
681C2—442no—
682C2#1307235311yescharacteristic
683C2#1307853711yescharacteristic
684C2#1307858111yescharacteristic
685C2#1308018911yescharacteristic
686C2#1308021411yescharacteristic
687C2#1308107411yescharacteristic
688C2#1308119311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1872C2
socleC23×C11C22×D4
prime radicalC22×C22⋊D11D4
hypercenter#1872D11
hypocenterC11#26148
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1872

Complements

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

NH ≅ G/Ntype
1. C2×#10622422C2semidirect
2. C2×#10622577C2semidirect
5. #13070157C2semidirect
6. #13070091C2semidirect
7. #13070055C2semidirect
8. #13069817C2semidirect
9. #13069253C2semidirect
10. #13069185C2semidirect
11. #13069050C2semidirect
13. #13068817C2semidirect
14. #13068810C2semidirect
15. C11×#1872C2semidirect
132. #66871D4semidirect
234. #1872D11semidirect
566. C11#26148semidirect

Maximal subgroups

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

subgroupindex
C2×#106224222
C2×#106225772
#130720462
C4⋊C4×C22⋊D112
#130701572
#130700912
#130700552
#130698172
#130692532
#130691852
#130690502
#130689112
#130688172
#130688102
C11×#18722
#2614811