Finite Group Databasebeta

← #14789913

Subgroups — #14789913

Order 2816.

1066 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623048C211yesmaximal, characteristic
2C2×#10622409C211yesmaximal, characteristic, complemented
3C2×#10622412C211yesmaximal, characteristic, complemented
4C22⋊Q8×Dic11C211yesmaximal, characteristic
5#13069948C211yesmaximal, characteristic, complemented
6#13069943C211yesmaximal, characteristic, complemented
7#13069755C211yesmaximal, characteristic, complemented
8#13069755C211yesmaximal, characteristic, complemented
9#13069572C211yesmaximal, characteristic, complemented
10#13069570C211yesmaximal, characteristic, complemented
11#13068929C211yesmaximal, characteristic
12#13068817C211yesmaximal, characteristic
13#13068815C211yesmaximal, characteristic
14#13068594C211yesmaximal, characteristic
15C11×#1873C211yesmaximal, characteristic
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C2×#66979C2211yescharacteristic
20C22×C4×Dic11C2211yescharacteristic
21#10623048—24no—
22#10623048—24no—
23C2×#66943C2211yescharacteristic
24C2×#66943C2211yescharacteristic
25C2×#66941C2211yescharacteristic
26C2×#66941C2211yescharacteristic
27C2×#66931—21no—
28C2×#66931—21no—
29C2×C4×Dic22—21no—
30C2×C4×Dic22—21no—
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#10622598C2211yescharacteristic
44#10622594—21no—
45C4⋊C4×Dic11—21no—
46C4⋊C4×Dic11C2211yescharacteristic
47C2×#66872C2211yescharacteristic
48C2×#66871C2211yescharacteristic
49#10622563—21no—
50C22⋊C4×Dic11—21no—
51#10622412—24no—
52#10622409—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×C11C2311yescharacteristic
65C23×Dic11D411yescharacteristic
66C23×Dic11D411yescharacteristic
67C22×Dic22—21no—
68C22×Dic22—21no—
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C11×C22⋊Q8—22no—
72C11×C22⋊Q8Q814yescomplemented
73C11×#117—22no—
74C11×#117—22no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—21no—
81C2×C42×C11—21no—
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11—21no—
84Q8×Dic11—22no—
85Q8×Dic11—22no—
86#66979—22no—
87#66979—22no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11—22no—
102C2×C4×Dic11—22no—
103C2×C4×Dic11—21no—
104C2×C4×Dic11—21no—
105C2×C4×Dic11D411yescharacteristic
106C2×C4×Dic11D411yescharacteristic
107C2×C4×Dic11C2311yescharacteristic
108C2×C4×Dic11C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110C22×C11⋊C8C2311yescharacteristic
111#66943—22no—
112#66943—22no—
113#66943D414yes—
114#66943D414yes—
115#66941—22no—
116#66941—22no—
117#66941—22no—
118#66941—22no—
119#66931—28no—
120#66931—28no—
121C4×Dic22—28no—
122C4×Dic22—28no—
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#66872—22no—
139#66871—22no—
140#24306—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×C11C2×D411yescharacteristic
157C22×C4×C11C2×Q812yes—
158C22×C4×C11#4112yes—
159C22×C4×C11C2411yescharacteristic
160C22×Dic11—22no—
161C22×Dic11—22no—
162C22×Dic11—22no—
163C22×Dic11—22no—
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11—21no—
167C22×Dic11—21no—
168C22×Dic11—41no—
169C22×Dic11—41no—
170C22×Dic11C2×D411yescharacteristic
171C22×Dic11C2×D411yescharacteristic
172C22×Dic11C2×D411yescharacteristic
173C22×Dic11C2×D411yescharacteristic
174C2×Dic22—24no—
175C2×Dic22—24no—
176C2×Dic22—42no—
177C2×Dic22—42no—
178C2×Dic22—42no—
179C2×Dic22—42no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11—21no—
186C11×C4⋊C4—24no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4C2×D412yes—
191C11×C4⋊C4C2×D412yes—
192C11×C4⋊C4C2×Q812yes—
193C11×C22⋊C4—24no—
194C11×C22⋊C4—24no—
195C42×C11—24no—
196C22⋊Dic11—24no—
197C22⋊Dic11—42no—
198C4⋊Dic11—24no—
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—42no—
208C4⋊Dic11C2×D412yes—
209C4⋊Dic11C2×D412yes—
210Dic11⋊C4—24no—
211Dic11⋊C4—24no—
212Dic11⋊C4—24no—
213Dic11⋊C4—24no—
214C4×Dic11—24no—
215C4×Dic11—22no—
216C4×Dic11—22no—
217C4×Dic11—21no—
218C4×Dic11—21no—
219C4×Dic11—42no—
220C4×Dic11—42no—
221C4×Dic11C2×D412yes—
222C4×Dic11C2×D412yes—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—21no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8—21no—
227C2×C11⋊C8—21no—
228C2×C11⋊C8—21no—
229C2×#533—111no—
230C2×#479—111no—
231C2×#479—111no—
232C4×C22⋊Q8—111no—
233#2058—111no—
234#2057—111no—
235#2024—111no—
236#2024—111no—
237#1989—111no—
238#1989—111no—
239#1873—111no—
240#1873D1111yescharacteristic
241#1854—111no—
242#1854—111no—
243#1797—111no—
244C23×C11—21no—
245C23×C11—21no—
246C23×C11—21no—
247C23×C11—21no—
248C23×C11—21no—
249C23×C11—21no—
250C23×C11C22⋊Q812yes—
251C23×C11C22×D411yescharacteristic
252Q8×C11—22no—
253Q8×C11—22no—
254Q8×C11—41no—
255Q8×C11—41no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
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—22no—
265C2×C4×C11—22no—
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×C11C22⋊Q812yes—
275C2×C4×C11C22×D411yescharacteristic
276C2×C4×C11C22×D411yescharacteristic
277C2×C4×C11C22×Q811yescharacteristic
278C2×C4×C11C2×#4111yescharacteristic
279C2×C4×C112−1+411yescharacteristic
280C2×C4×C112−1+411yescharacteristic
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—21no—
287C2×Dic11—21no—
288C2×Dic11—21no—
289C2×Dic11—22no—
290C2×Dic11—22no—
291C2×Dic11—44no—
292C2×Dic11—44no—
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#12012yes—
304C2×Dic11#12012yes—
305C2×Dic11#13512yes—
306C2×Dic11#13712yes—
307Dic22—48no—
308Dic22—48no—
309C8×C11—41no—
310C8×C11—41no—
311C11⋊C8—41no—
312C11⋊C8—41no—
313#533—224no—
314#533—224no—
315C2×C4⋊Q8—111no—
316C2×C4⋊Q8—111no—
317C2×#125—111no—
318C2×#125—111no—
319C2×C22⋊Q8—221no—
320C2×C22⋊Q8—221no—
321C2×C22⋊Q8C2×D1111yescharacteristic
322C2×C4×Q8—111no—
323C2×C4×Q8—221no—
324C2×C4×Q8—221no—
325C2×#117—111no—
326C2×#117C2×D1111yescharacteristic
327C22×C42—111no—
328#479—224no—
329#479—224no—
330C2×#107—111no—
331C2×#107—111no—
332C2×#106—111no—
333C2×#106—111no—
334C2×C4⋊C8—111no—
335C2×C4⋊C8—111no—
336C2×#103—111no—
337C2×#103—111no—
338C2×#103C2×D1111yescharacteristic
339C2×#103C2×D1111yescharacteristic
340C2×C22⋊C8—111no—
341C2×C22⋊C8C2×D1111yescharacteristic
342#391—111no—
343#389—111no—
344#387—221no—
345#385—221no—
346#380—111no—
347C4×C4⋊C4—111no—
348C4×C4⋊C4—221no—
349C4×C22⋊C4—221no—
350#340—111no—
351#340—111no—
352#340—111no—
353#340—111no—
354#340—111no—
355#340—111no—
356#340C2×D1111yescharacteristic
357#340C2×D1111yescharacteristic
358#336—111no—
359#336—111no—
360C22×C11—22no—
361C22×C11—22no—
362C22×C11—22no—
363C22×C11—41no—
364C22×C11—41no—
365C22×C11—41no—
366C22×C11—41no—
367C22×C11C2×#12011yescharacteristic
368C22×C11C2×C22⋊Q811yescharacteristic
369C22×C11#53611yescharacteristic
370C22×C11C2×#13511yescharacteristic
371C22×C11C2×#13711yescharacteristic
372C22×C11#57511yescharacteristic
373C22×C11#57511yescharacteristic
374C4×C11—22no—
375C4×C11—42no—
376C4×C11—42no—
377C4×C11—42no—
378C4×C11—42no—
379C4×C11#54811yescharacteristic
380C4×C11#54811yescharacteristic
381C4×C11D4×Q811yescharacteristic
382C4×C11D4×Q811yescharacteristic
383Dic11—22no—
384Dic11—22no—
385Dic11—22no—
386Dic11—22no—
387Dic11—42no—
388Dic11—42no—
389Dic11—81no—
390Dic11—81no—
391C22×Q8—221no—
392C22×Q8—221no—
393C22×Q8C22×D1111yescharacteristic
394C23×C4—111no—
395C23×C4—111no—
396C23×C4C22×D1111yescharacteristic
397C22×C8—111no—
398C22×C8—111no—
399C22×C8C22×D1111yescharacteristic
400C22×C8C22×D1111yescharacteristic
401C4⋊Q8—222no—
402C4⋊Q8—222no—
403C4⋊Q8—222no—
404C4⋊Q8—222no—
405#125—114no—
406#125—114no—
407#125—222no—
408#125—222no—
409C22⋊Q8—22no—
410C22⋊Q8—228no—
411C22⋊Q8—228no—
412C22⋊Q8Dic2214yescomplemented
413C4×Q8—228no—
414C4×Q8—228no—
415C4×Q8—222no—
416C4×Q8—222no—
417#117—22no—
418#117—22no—
419#117—222no—
420#117—222no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—111no—
423C2×C4⋊C4—111no—
424C2×C4⋊C4—111no—
425C2×C4⋊C4—111no—
426C2×C4⋊C4—221no—
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⋊C4C22×D1111yescharacteristic
435C2×C4⋊C4C22×D1111yescharacteristic
436C2×C4⋊C4C22×D1111yescharacteristic
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—221no—
440C2×C22⋊C4—221no—
441C2×C42—21no—
442C2×C42—111no—
443C2×C42—111no—
444C2×C42—111no—
445C2×C42—111no—
446C2×C42—222no—
447C2×C42—222no—
448C2×C42—221no—
449C2×C42—221no—
450C2×C42—221no—
451#107—222no—
452#107—222no—
453#106—222no—
454#106—222no—
455C4⋊C8—222no—
456C4⋊C8—222no—
457#103—22no—
458#103—22no—
459#103—222no—
460#103—222no—
461C22⋊C8—22no—
462C22⋊C8—222no—
463#95—221no—
464#95—221no—
465#95—221no—
466#95—221no—
467#95—221no—
468C2×C11—42no—
469C2×C11#240911yescharacteristic
470C2×C11#300211yescharacteristic
471C2×C11#300711yescharacteristic
472C2×C11#307611yescharacteristic
473C2×C11#307811yescharacteristic
474C2×C11#323111yescharacteristic
475C2×C11#324011yescharacteristic
476C24D4×D1111yescharacteristic
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—224no—
483C2×Q8—224no—
484C2×Q8—442no—
485C2×Q8—442no—
486C2×Q8—442no—
487C2×Q8—442no—
488C2×Q8C2×Dic2212yes—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—111no—
498C22×C4—111no—
499C22×C4—111no—
500C22×C4—111no—
501C22×C4—222no—
502C22×C4—222no—
503C22×C4—222no—
504C22×C4—222no—
505C22×C4—221no—
506C22×C4—221no—
507C22×C4—221no—
508C22×C4—221no—
509C22×C4—441no—
510C22×C4—441no—
511C22×C4C2×Dic2212yes—
512C22×C4D4×D1111yescharacteristic
513C22×C4#434112yes—
514C22×C4C23×D1111yescharacteristic
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—221no—
522C2×C8—221no—
523C2×C8—221no—
524C2×C8—221no—
525C2×C8—221no—
526C2×C8—221no—
527C4⋊C4—24no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—112no—
532C4⋊C4—112no—
533C4⋊C4—224no—
534C4⋊C4—224no—
535C4⋊C4—224no—
536C4⋊C4—224no—
537C4⋊C4—224no—
538C4⋊C4—224no—
539C4⋊C4—221no—
540C4⋊C4—221no—
541C4⋊C4—221no—
542C4⋊C4—221no—
543C4⋊C4—221no—
544C4⋊C4—221no—
545C4⋊C4—442no—
546C4⋊C4—442no—
547C4⋊C4C2×Dic2212yes—
548C4⋊C4D4×D1112yes—
549C4⋊C4D4×D1112yes—
550C22⋊C4—24no—
551C22⋊C4—24no—
552C22⋊C4—224no—
553C22⋊C4—442no—
554C42—24no—
555C42—112no—
556C42—112no—
557C42—222no—
558C42—222no—
559C42—224no—
560C42—221no—
561C42—221no—
562C42—442no—
563C42—442no—
564C11#2430611yescharacteristic, complemented, Sylow
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23#6693112yes—
572C23C2×D4×D1111yescharacteristic
573Q8—22no—
574Q8—22no—
575Q8—41no—
576Q8—41no—
577Q8—448no—
578Q8—448no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—112no—
598C2×C4—112no—
599C2×C4—112no—
600C2×C4—112no—
601C2×C4—221no—
602C2×C4—221no—
603C2×C4—221no—
604C2×C4—221no—
605C2×C4—221no—
606C2×C4—221no—
607C2×C4—221no—
608C2×C4—221no—
609C2×C4—222no—
610C2×C4—222no—
611C2×C4—444no—
612C2×C4—444no—
613C2×C4—441no—
614C2×C4—441no—
615C2×C4—441no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4—441no—
619C2×C4—441no—
620C2×C4—441no—
621C2×C4—441no—
622C2×C4—441no—
623C2×C4#6693112yes—
624C2×C4C22×Dic2211yescharacteristic
625C2×C4C2×D4×D1111yescharacteristic
626C2×C4C2×D4×D1111yescharacteristic
627C2×C4C2×#434111yescharacteristic
628C2×C4#6704311yescharacteristic
629C2×C4#6704311yescharacteristic
630C8—41no—
631C8—41no—
632C8—441no—
633C8—441no—
634C22—22no—
635C22—22no—
636C22—22no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22C2×#6693111yescharacteristic
642C22D11×#12011yescharacteristic
643C22#1062317911yescharacteristic
644C22D11×#13511yescharacteristic
645C22#1062329911yescharacteristic
646C22D11×#13711yescharacteristic
647C22#1062330811yescharacteristic
648C4—22no—
649C4—42no—
650C4—42no—
651C4—42no—
652C4—42no—
653C4—222no—
654C4—222no—
655C4—222no—
656C4—222no—
657C4—442no—
658C4—442no—
659C4—881no—
660C4—881no—
661C4D4×Dic2211yescharacteristic
662C4D4×Dic2211yescharacteristic
663C4#1062312911yescharacteristic
664C4#1062312911yescharacteristic
665C2—42no—
666C2#1307197811yescharacteristic
667C2#1307783711yescharacteristic
668C2#1307787311yescharacteristic
669C2#1307840011yescharacteristic
670C2#1307841811yescharacteristic
671C2#1307977311yescharacteristic
672C2#1307986011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1873C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#1873D11
hypocenterC11#24306
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1873

Complements

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

NH ≅ G/Ntype
2. C2×#10622409C2semidirect
3. C2×#10622412C2semidirect
5. #13069948C2semidirect
6. #13069943C2semidirect
7. #13069755C2semidirect
8. #13069755C2semidirect
9. #13069572C2semidirect
10. #13069570C2semidirect
72. C11×C22⋊Q8Q8semidirect
412. C22⋊Q8Dic22semidirect
564. C11#24306semidirect

Maximal subgroups

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

subgroupindex
C2×#106230482
C2×#106224092
C2×#106224122
C22⋊Q8×Dic112
#130699482
#130699432
#130697552
#130695722
#130695702
#130689292
#130688172
#130688152
#130685942
C11×#18732
#2430611