Finite Group Databasebeta

← #14789988

Subgroups — #14789988

Order 2816.

1012 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623031C211yesmaximal, characteristic
2C2×#10622412C211yesmaximal, characteristic, complemented
3C2×#10622407C211yesmaximal, characteristic, complemented
4#13071300C211yesmaximal, characteristic
5#13069953C211yesmaximal, characteristic, complemented
6#13069943C211yesmaximal, characteristic, complemented
7#13069765C211yesmaximal, characteristic, complemented
8#13069755C211yesmaximal, characteristic, complemented
9#13069570C211yesmaximal, characteristic, complemented
10#13069566C211yesmaximal, characteristic, complemented
11#13068929C211yesmaximal, characteristic
12#13068817C211yesmaximal, characteristic
13#13068804C211yesmaximal, characteristic
14#13068598C211yesmaximal, characteristic
15C11×#1872C211yesmaximal, characteristic
16C2×C11×C22⋊Q8C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C2×#66979C2211yescharacteristic
20C2×#66979C2211yescharacteristic
21C2×#66977—21no—
22C2×#66977—21no—
23#10623031—24no—
24#10623031—24no—
25C2×#66943—21no—
26C2×#66943C2211yescharacteristic
27C2×#66943C2211yescharacteristic
28C2×#66941—21no—
29C2×#66941C2211yescharacteristic
30C2×#66941C2211yescharacteristic
31C2×C11×#103C2211yescharacteristic
32C2×C11×#103C2211yescharacteristic
33C2×C11×C22⋊C8C2211yescharacteristic
34#10622843C2211yescharacteristic
35C2×#66899C2211yescharacteristic
36C2×#66899C2211yescharacteristic
37#10622825C2211yescharacteristic
38C2×C22⋊(C11⋊C8)C2211yescharacteristic
39C2×#66882C2211yescharacteristic
40C2×#66881C2211yescharacteristic
41C2×Dic11⋊C8C2211yescharacteristic
42C2×Dic11⋊C8C2211yescharacteristic
43#10622598—21no—
44#10622598C2211yescharacteristic
45#10622594—21no—
46C4⋊C4×Dic11C2211yescharacteristic
47C2×#66871C2211yescharacteristic
48C2×#66871C2211yescharacteristic
49#10622564—21no—
50#10622564—21no—
51#10622412—24no—
52#10622407—24no—
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62#10622167C2211yescharacteristic
63C22×Q8×C11C2311yescharacteristic
64C23×C4×C11—21no—
65C23×C4×C11C2311yescharacteristic
66C22×Dic22—21no—
67C22×Dic22—21no—
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C11×C22⋊Q8—22no—
71C11×C22⋊Q8Q814yescomplemented
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—22no—
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C22⋊C4—21no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11—21no—
82C2×C22⋊Dic11D411yescharacteristic
83C2×C22⋊Dic11D411yescharacteristic
84Q8×Dic11—22no—
85Q8×Dic11—22no—
86#66979—22no—
87#66979—22no—
88#66979—22no—
89#66979—22no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11D411yescharacteristic
95C2×C4⋊Dic11D411yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2311yescharacteristic
100#66977—28no—
101#66977—28no—
102C2×Dic11⋊C4—21no—
103C2×Dic11⋊C4—21no—
104C2×Dic11⋊C4—21no—
105C2×Dic11⋊C4—21no—
106C2×C4×Dic11—21no—
107C2×C4×Dic11—21no—
108C2×C4×Dic11—21no—
109C2×C4×Dic11C2311yescharacteristic
110C2×C4×Dic11C2311yescharacteristic
111C22×C11⋊C8C2311yescharacteristic
112C22×C11⋊C8C2311yescharacteristic
113#66943—28no—
114#66943—22no—
115#66943—22no—
116#66943—22no—
117#66943D414yes—
118#66941—28no—
119#66941—22no—
120#66941—22no—
121#66941—22no—
122#66941D414yes—
123C11×#103—22no—
124C11×#103—22no—
125C11×C22⋊C8—22no—
126#66899—22no—
127#66899—22no—
128C11⋊#95—21no—
129C11⋊#95—21no—
130C11⋊#95—21no—
131C11⋊#95—21no—
132C11⋊#95—21no—
133C22⋊(C11⋊C8)—22no—
134#66882—22no—
135#66881—22no—
136Dic11⋊C8—22no—
137Dic11⋊C8—22no—
138#66871—22no—
139#66871—22no—
140#24311—111nomaximal, Sylow
141C24×C11C2×D411yescharacteristic
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11C2×Q812yes—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—24no—
157C22×C4×C11—81no—
158C22×C4×C11—81no—
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×Q812yes—
161C22×C4×C11#4112yes—
162C22×C4×C11C2411yescharacteristic
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11—21no—
167C22×Dic11C2×D411yescharacteristic
168C22×Dic11C2×D411yescharacteristic
169C22×Dic11C2×D411yescharacteristic
170C22×Dic11C2×D411yescharacteristic
171C2×Dic22—24no—
172C2×Dic22—24no—
173C2×Dic22—81no—
174C2×Dic22—81no—
175C2×Dic22—81no—
176C2×Dic22—81no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C11×C4⋊C4—24no—
184C11×C4⋊C4—24no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4C2×D412yes—
189C11×C4⋊C4C2×D412yes—
190C11×C4⋊C4C2×Q812yes—
191C11×C22⋊C4—24no—
192C22⋊Dic11—24no—
193C22⋊Dic11—22no—
194C22⋊Dic11—22no—
195C22⋊Dic11—81no—
196C4⋊Dic11—24no—
197C4⋊Dic11—22no—
198C4⋊Dic11—22no—
199C4⋊Dic11—24no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—42no—
207C4⋊Dic11—81no—
208C4⋊Dic11C2×D412yes—
209C4⋊Dic11C2×D412yes—
210Dic11⋊C4—24no—
211Dic11⋊C4—24no—
212Dic11⋊C4—24no—
213Dic11⋊C4—24no—
214C4×Dic11—24no—
215C4×Dic11—21no—
216C4×Dic11—21no—
217C4×Dic11—42no—
218C4×Dic11—81no—
219C4×Dic11C2×D412yes—
220C4×Dic11C2×D412yes—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—21no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8—21no—
227C2×#544—111no—
228C2×#479—111no—
229C2×#477—111no—
230#2323—111no—
231#2059—111no—
232#2057—111no—
233#2026—111no—
234#2024—111no—
235#1989—111no—
236#1988—111no—
237#1873—111no—
238#1872D1111yescharacteristic
239#1854—111no—
240#1852—111no—
241#1798—111no—
242C23×C11—21no—
243C23×C11—21no—
244C23×C11—21no—
245C23×C11—21no—
246C23×C11—21no—
247C23×C11—21no—
248C23×C11C22⋊Q812yes—
249C23×C11C22×D411yescharacteristic
250Q8×C11—22no—
251Q8×C11—22no—
252Q8×C11—41no—
253Q8×C11—41no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
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—84no—
273C2×C4×C11C22⋊Q812yes—
274C2×C4×C11C22×D411yescharacteristic
275C2×C4×C11C22×D411yescharacteristic
276C2×C4×C11C22×Q811yescharacteristic
277C2×C4×C11C2×#4111yescharacteristic
278C2×C4×C112−1+411yescharacteristic
279C2×C4×C112−1+411yescharacteristic
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—22no—
286C2×Dic11—21no—
287C2×Dic11—22no—
288C2×Dic11—21no—
289C2×Dic11—21no—
290C2×Dic11—21no—
291C2×Dic11—21no—
292C2×Dic11—41no—
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#12012yes—
303C2×Dic11#12012yes—
304Dic22—84no—
305Dic22—84no—
306C8×C11—41no—
307C8×C11—41no—
308C11⋊C8—41no—
309C11⋊C8—41no—
310#544—224no—
311#544—224no—
312C2×C4⋊Q8—111no—
313C2×C4⋊Q8—111no—
314C2×C4⋊Q8—221no—
315C2×#125—111no—
316C2×#125—111no—
317C2×#125—221no—
318C2×C22⋊Q8—221no—
319C2×C22⋊Q8—221no—
320C2×C22⋊Q8C2×D1111yescharacteristic
321C2×C4×Q8—111no—
322C2×#117—111no—
323C2×#117—111no—
324C22×C4⋊C4C2×D1111yescharacteristic
325#479—224no—
326#477—224no—
327C2×#107—111no—
328C2×#107—111no—
329C2×#107—111no—
330C2×#106—111no—
331C2×C4⋊C8—111no—
332C2×C4⋊C8—111no—
333C2×#103—111no—
334C2×#103—111no—
335C2×#103C2×D1111yescharacteristic
336C2×#103C2×D1111yescharacteristic
337C2×C22⋊C8—111no—
338C2×C22⋊C8C2×D1111yescharacteristic
339#391—111no—
340#389—111no—
341#389—221no—
342#388—221no—
343#388—221no—
344#387—221no—
345#380—111no—
346C4×C4⋊C4—111no—
347#340—111no—
348#340—111no—
349#340—111no—
350#340—111no—
351#340—111no—
352#340—111no—
353#340C2×D1111yescharacteristic
354#340C2×D1111yescharacteristic
355#336—111no—
356#336—111no—
357C22×C11—22no—
358C22×C11—22no—
359C22×C11—22no—
360C22×C11—41no—
361C22×C11—41no—
362C22×C11—41no—
363C22×C11—41no—
364C22×C11C2×#12011yescharacteristic
365C22×C11C2×C22⋊Q811yescharacteristic
366C22×C11#53611yescharacteristic
367C22×C11#57611yescharacteristic
368C22×C11#57711yescharacteristic
369C22×C11#57811yescharacteristic
370C22×C11#57811yescharacteristic
371C4×C11—22no—
372C4×C11—42no—
373C4×C11—42no—
374C4×C11—42no—
375C4×C11—42no—
376C4×C11#54811yescharacteristic
377C4×C11#54811yescharacteristic
378C4×C11D4×Q811yescharacteristic
379C4×C11D4×Q811yescharacteristic
380Dic11—22no—
381Dic11—22no—
382Dic11—41no—
383Dic11—42no—
384Dic11—41no—
385Dic11—42no—
386Dic11—81no—
387Dic11—81no—
388C22×Q8—221no—
389C22×Q8—221no—
390C22×Q8C22×D1111yescharacteristic
391C23×C4—21no—
392C23×C4C22×D1111yescharacteristic
393C22×C8—111no—
394C22×C8—111no—
395C22×C8C22×D1111yescharacteristic
396C22×C8C22×D1111yescharacteristic
397C4⋊Q8—114no—
398C4⋊Q8—222no—
399C4⋊Q8—222no—
400C4⋊Q8—228no—
401C4⋊Q8—222no—
402#125—114no—
403#125—222no—
404#125—222no—
405#125—228no—
406#125—222no—
407C22⋊Q8—22no—
408C22⋊Q8—228no—
409C22⋊Q8—228no—
410C22⋊Q8Dic2214yescomplemented
411C4×Q8—222no—
412C4×Q8—222no—
413#117—222no—
414#117—222no—
415#117—222no—
416#117—222no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—111no—
422C2×C4⋊C4—111no—
423C2×C4⋊C4—111no—
424C2×C4⋊C4—111no—
425C2×C4⋊C4—111no—
426C2×C4⋊C4—111no—
427C2×C4⋊C4—221no—
428C2×C4⋊C4—221no—
429C2×C4⋊C4—221no—
430C2×C4⋊C4—221no—
431C2×C4⋊C4—221no—
432C2×C4⋊C4—221no—
433C2×C4⋊C4—221no—
434C2×C4⋊C4—221no—
435C2×C4⋊C4C22×D1111yescharacteristic
436C2×C4⋊C4C22×D1111yescharacteristic
437C2×C4⋊C4C22×D1111yescharacteristic
438C2×C22⋊C4—21no—
439C2×C22⋊C4—111no—
440C2×C22⋊C4—111no—
441C2×C22⋊C4—221no—
442C2×C22⋊C4—221no—
443C2×C42—111no—
444C2×C42—111no—
445C2×C42—221no—
446C2×C42—221no—
447C2×C42—221no—
448#107—222no—
449#107—222no—
450#107—222no—
451#106—222no—
452C4⋊C8—222no—
453C4⋊C8—222no—
454#103—22no—
455#103—22no—
456#103—222no—
457#103—222no—
458C22⋊C8—22no—
459C22⋊C8—222no—
460#95—221no—
461#95—221no—
462#95—221no—
463#95—221no—
464#95—221no—
465C2×C11—42no—
466C2×C11#240911yescharacteristic
467C2×C11#301111yescharacteristic
468C2×C11#301211yescharacteristic
469C2×C11#308211yescharacteristic
470C2×C11#308311yescharacteristic
471C2×C11#324211yescharacteristic
472C2×C11#324311yescharacteristic
473C24D4×D1111yescharacteristic
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—224no—
480C2×Q8—224no—
481C2×Q8—881no—
482C2×Q8—881no—
483C2×Q8—881no—
484C2×Q8—881no—
485C2×Q8C2×Dic2212yes—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—24no—
495C22×C4—81no—
496C22×C4—81no—
497C22×C4—111no—
498C22×C4—111no—
499C22×C4—111no—
500C22×C4—111no—
501C22×C4—221no—
502C22×C4—221no—
503C22×C4—221no—
504C22×C4—221no—
505C22×C4C2×Dic2212yes—
506C22×C4D4×D1111yescharacteristic
507C22×C4#434112yes—
508C22×C4C23×D1111yescharacteristic
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—221no—
516C2×C8—221no—
517C2×C8—221no—
518C2×C8—221no—
519C2×C8—221no—
520C2×C8—221no—
521C4⋊C4—24no—
522C4⋊C4—24no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—112no—
527C4⋊C4—112no—
528C4⋊C4—222no—
529C4⋊C4—222no—
530C4⋊C4—224no—
531C4⋊C4—224no—
532C4⋊C4—224no—
533C4⋊C4—224no—
534C4⋊C4—224no—
535C4⋊C4—224no—
536C4⋊C4—221no—
537C4⋊C4—221no—
538C4⋊C4—221no—
539C4⋊C4—221no—
540C4⋊C4—221no—
541C4⋊C4—221no—
542C4⋊C4—442no—
543C4⋊C4—881no—
544C4⋊C4C2×Dic2212yes—
545C4⋊C4D4×D1112yes—
546C4⋊C4D4×D1112yes—
547C22⋊C4—24no—
548C22⋊C4—222no—
549C22⋊C4—222no—
550C22⋊C4—224no—
551C22⋊C4—881no—
552C42—112no—
553C42—112no—
554C42—224no—
555C42—221no—
556C42—221no—
557C42—442no—
558C42—881no—
559C11#2431111yescharacteristic, complemented, Sylow
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23#6693112yes—
567C23C2×D4×D1111yescharacteristic
568Q8—22no—
569Q8—22no—
570Q8—41no—
571Q8—41no—
572Q8—884no—
573Q8—884no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—84no—
593C2×C4—112no—
594C2×C4—112no—
595C2×C4—221no—
596C2×C4—221no—
597C2×C4—221no—
598C2×C4—221no—
599C2×C4—221no—
600C2×C4—221no—
601C2×C4—221no—
602C2×C4—221no—
603C2×C4—222no—
604C2×C4—222no—
605C2×C4—221no—
606C2×C4—221no—
607C2×C4—441no—
608C2×C4—441no—
609C2×C4—441no—
610C2×C4—441no—
611C2×C4—441no—
612C2×C4—441no—
613C2×C4—441no—
614C2×C4—441no—
615C2×C4—441no—
616C2×C4—441no—
617C2×C4#6693112yes—
618C2×C4C22×Dic2211yescharacteristic
619C2×C4C2×D4×D1111yescharacteristic
620C2×C4C2×D4×D1111yescharacteristic
621C2×C4C2×#434111yescharacteristic
622C2×C4#6704311yescharacteristic
623C2×C4#6704311yescharacteristic
624C8—41no—
625C8—41no—
626C8—441no—
627C8—441no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22C2×#6693111yescharacteristic
636C22D11×#12011yescharacteristic
637C22#1062317911yescharacteristic
638C22#1062329311yescharacteristic
639C22#1062329711yescharacteristic
640C22#1062330511yescharacteristic
641C22#1062331011yescharacteristic
642C4—22no—
643C4—42no—
644C4—42no—
645C4—42no—
646C4—42no—
647C4—222no—
648C4—222no—
649C4—441no—
650C4—442no—
651C4—441no—
652C4—442no—
653C4—881no—
654C4—881no—
655C4D4×Dic2211yescharacteristic
656C4D4×Dic2211yescharacteristic
657C4#1062312911yescharacteristic
658C4#1062312911yescharacteristic
659C2—42no—
660C2#1307197811yescharacteristic
661C2#1307790611yescharacteristic
662C2#1307792111yescharacteristic
663C2#1307845411yescharacteristic
664C2#1307847111yescharacteristic
665C2#1307988011yescharacteristic
666C2#1307990311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1872C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#1872D11
hypocenterC11#24311
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
2. C2×#10622412C2semidirect
3. C2×#10622407C2semidirect
5. #13069953C2semidirect
6. #13069943C2semidirect
7. #13069765C2semidirect
8. #13069755C2semidirect
9. #13069570C2semidirect
10. #13069566C2semidirect
71. C11×C22⋊Q8Q8semidirect
410. C22⋊Q8Dic22semidirect
559. C11#24311semidirect

Maximal subgroups

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

subgroupindex
C2×#106230312
C2×#106224122
C2×#106224072
#130713002
#130699532
#130699432
#130697652
#130697552
#130695702
#130695662
#130689292
#130688172
#130688042
#130685982
C11×#18722
#2431111