Finite Group Databasebeta

← #14789914

Subgroups — #14789914

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×#10623219C211yesmaximal, characteristic
2C2×#10622442C211yesmaximal, characteristic, complemented
3C2×#10622676C211yesmaximal, characteristic, complemented
4C4×#66950C211yesmaximal, characteristic
5#13069948C211yesmaximal, characteristic, complemented
6#13069943C211yesmaximal, characteristic, complemented
7#13069756C211yesmaximal, characteristic, complemented
8#13069756C211yesmaximal, characteristic, complemented
9#13069573C211yesmaximal, characteristic, complemented
10#13068927C211yesmaximal, characteristic
11#13068927C211yesmaximal, characteristic
12#13068818C211yesmaximal, characteristic
13#13068816C211yesmaximal, characteristic
14#13068593C211yesmaximal, characteristic
15C11×#1989C211yesmaximal, characteristic, complemented
16C2×C11×#125C2211yescharacteristic
17#10623219—24no—
18#10623219—24no—
19C2×#66950C2211yescharacteristic
20C2×#66949—21no—
21C2×#66949—21no—
22C2×#66945C2211yescharacteristic
23C2×#66945C2211yescharacteristic
24C2×#66941C2211yescharacteristic
25C2×#66941C2211yescharacteristic
26C2×#66940—21no—
27C2×#66940—21no—
28C2×C42×D11C2211yescharacteristic
29C2×#66923C2211yescharacteristic
30C2×C4×Dic22C2211yescharacteristic
31C2×C11×C4⋊C8C2211yescharacteristic
32C4×C11×C4⋊C4C2211yescharacteristic
33C2×(C2×D11)⋊C8C2211yescharacteristic
34C2×(C2×D11)⋊C8C2211yescharacteristic
35C2×#66882C2211yescharacteristic
36C2×#66881C2211yescharacteristic
37C2×#66880C2211yescharacteristic
38C2×#66880C2211yescharacteristic
39#10622676—24no—
40#10622600C2211yescharacteristic
41#10622598C2211yescharacteristic
42#10622587C2211yescharacteristic
43C2×#66874C2211yescharacteristic
44C2×#66874C2211yescharacteristic
45C2×#66872C2211yescharacteristic
46C2×#66871C2211yescharacteristic
47C4×(C2×D11)⋊C4—21no—
48C4×C4⋊Dic11—21no—
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50#10622442—24no—
51#10622281—21no—
52#10622266—21no—
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62#10622167C2211yescharacteristic
63C22×C4×D11D411yescharacteristic
64C22×C4×D11D411yescharacteristic
65C22×C4×D11C2311yescharacteristic
66C22×Dic22—21no—
67C22×Dic22—21no—
68C22×Dic22C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C11×#125—22no—
72C11×#125D414yes—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C42×C11—21no—
80C2×C42×C11C2311yescharacteristic
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11D411yescharacteristic
99C2×C4×Dic11D411yescharacteristic
100C2×C4×Dic11C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103#66950—22no—
104#66950Q814yescomplemented
105#66949—28no—
106#66949—28no—
107#66945—22no—
108#66945—22no—
109#66945—22no—
110#66945—22no—
111#66941—22no—
112#66941—22no—
113#66941—22no—
114#66941—22no—
115#66940—28no—
116#66940—28no—
117C42×D11—22no—
118C42×D11—22no—
119#66923—22no—
120#66923D414yes—
121C4×Dic22—22no—
122C4×Dic22—22no—
123C11×C4⋊C8—22no—
124C11×#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128C11⋊#95—21no—
129(C2×D11)⋊C8—22no—
130(C2×D11)⋊C8—22no—
131#66882—22no—
132#66881—22no—
133#66880—22no—
134#66880—22no—
135#66874—22no—
136#66874—22no—
137#66872—22no—
138#66871—22no—
139C4⋊(C11⋊C8)—22no—
140#24306—111nomaximal, Sylow
141C23×D11C2×D411yescharacteristic
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2411yescharacteristic
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11C2×D411yescharacteristic
154C22×Dic11C2×D411yescharacteristic
155C22×Dic11C2×D411yescharacteristic
156C2×C4×D11—22no—
157C2×C4×D11—22no—
158C2×C4×D11—22no—
159C2×C4×D11—22no—
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×C4×D11—21no—
163C2×C4×D11—21no—
164C2×C4×D11—41no—
165C2×C4×D11—41no—
166C2×C4×D11C2×Q812yes—
167C2×C4×D11#4112yes—
168C2×Dic22—24no—
169C2×Dic22—24no—
170C2×Dic22—21no—
171C2×Dic22—21no—
172C2×Dic22—21no—
173C2×Dic22—21no—
174C2×Dic22—21no—
175C2×Dic22—42no—
176C2×Dic22—42no—
177C2×Dic22—42no—
178C2×Dic22—42no—
179C2×Dic22C2×Q812yes—
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—24no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4C2×D412yes—
194C11×C4⋊C4C2×D412yes—
195C11×C4⋊C4C2×Q812yes—
196C42×C11—42no—
197C42×C11C2×D412yes—
198C42×C11C2×D412yes—
199(C2×D11)⋊C4—24no—
200(C2×D11)⋊C4—24no—
201(C2×D11)⋊C4—24no—
202(C2×D11)⋊C4—42no—
203C4⋊Dic11—24no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11—42no—
209C4⋊Dic11C2×D412yes—
210C4⋊Dic11C2×D412yes—
211Dic11⋊C4—24no—
212Dic11⋊C4—24no—
213Dic11⋊C4—24no—
214Dic11⋊C4—24no—
215Dic11⋊C4—42no—
216C4×Dic11—24no—
217C4×Dic11—24no—
218C4×Dic11—22no—
219C4×Dic11—22no—
220C4×Dic11—21no—
221C4×Dic11—21no—
222C4×Dic11—42no—
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#1989D1111yescharacteristic, complemented
239#1873—111no—
240#1873—111no—
241#1854—111no—
242#1854—111no—
243#1797—111no—
244C23×C11C22×D411yescharacteristic
245C22×D11—21no—
246C22×D11—21no—
247C22×D11—21no—
248C22×D11—21no—
249C22×D11—21no—
250C22×D11—21no—
251C22×D11C22⋊Q812yes—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11#12012yes—
269C2×C4×C11#12012yes—
270C2×C4×C11C22×D411yescharacteristic
271C2×C4×C11C22×D411yescharacteristic
272C2×C4×C11C22×Q811yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C2×C4×C112−1+411yescharacteristic
275C2×C4×C112−1+411yescharacteristic
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—22no—
283C2×Dic11—22no—
284C2×Dic11—22no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11C22⋊Q812yes—
295C2×Dic11#13512yes—
296C2×Dic11#13712yes—
297C4×D11—22no—
298C4×D11—22no—
299C4×D11—22no—
300C4×D11—22no—
301C4×D11—44no—
302C4×D11—44no—
303Dic22—22no—
304Dic22—22no—
305Dic22—48no—
306Dic22—48no—
307Dic22—41no—
308Dic22—41no—
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×#125C2×D1111yescharacteristic
319C2×C22⋊Q8—111no—
320C2×C22⋊Q8—221no—
321C2×C22⋊Q8—221no—
322C2×C4×Q8—111no—
323C2×C4×Q8—221no—
324C2×C4×Q8—221no—
325C2×#117—111no—
326C2×#117—111no—
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⋊C8C2×D1111yescharacteristic
336C2×#103—111no—
337C2×#103—111no—
338C2×#103—111no—
339C2×#103—111no—
340C2×C22⋊C8—111no—
341C2×C22⋊C8—111no—
342#391—111no—
343#389—111no—
344#387—221no—
345#385—221no—
346#380—111no—
347C4×C4⋊C4—221no—
348C4×C4⋊C4C2×D1111yescharacteristic
349C4×C22⋊C4—221no—
350#340—111no—
351#340—111no—
352#340—111no—
353#340—111no—
354#340C2×D1111yescharacteristic
355#340C2×D1111yescharacteristic
356#340C2×D1111yescharacteristic
357#340C2×D1111yescharacteristic
358#336—111no—
359#336—111no—
360C22×C11C2×#12011yescharacteristic
361C22×C11C2×C22⋊Q811yescharacteristic
362C22×C11#53611yescharacteristic
363C22×C11C2×#13511yescharacteristic
364C22×C11C2×#13711yescharacteristic
365C22×C11#57511yescharacteristic
366C22×C11#57511yescharacteristic
367C2×D11—22no—
368C2×D11—22no—
369C2×D11—22no—
370C2×D11—41no—
371C2×D11—41no—
372C2×D11—41no—
373C2×D11—41no—
374C4×C11—22no—
375C4×C11—22no—
376C4×C11—42no—
377C4×C11—42no—
378C4×C11—42no—
379C4×C11—81no—
380C4×C11#54811yescharacteristic
381C4×C11#54811yescharacteristic
382C4×C11D4×Q811yescharacteristic
383C4×C11D4×Q811yescharacteristic
384Dic11—22no—
385Dic11—22no—
386Dic11—22no—
387Dic11—42no—
388Dic11—42no—
389Dic11—42no—
390Dic11—81no—
391C22×Q8—111no—
392C22×Q8—221no—
393C22×Q8—221no—
394C23×C4—111no—
395C23×C4—111no—
396C23×C4—111no—
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—22no—
406#125—114no—
407#125—222no—
408#125D4414yes—
409C22⋊Q8—114no—
410C22⋊Q8—222no—
411C22⋊Q8—228no—
412C22⋊Q8—228no—
413C4×Q8—228no—
414C4×Q8—228no—
415C4×Q8—222no—
416C4×Q8—222no—
417#117—222no—
418#117—222no—
419#117—222no—
420#117—222no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
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⋊C4C22×D1111yescharacteristic
434C2×C4⋊C4C22×D1111yescharacteristic
435C2×C4⋊C4C22×D1111yescharacteristic
436C2×C4⋊C4C22×D1111yescharacteristic
437C2×C22⋊C4—221no—
438C2×C22⋊C4—221no—
439C2×C22⋊C4—221no—
440C2×C22⋊C4—221no—
441C2×C42—21no—
442C2×C42—111no—
443C2×C42—111no—
444C2×C42—111no—
445C2×C42—221no—
446C2×C42—221no—
447C2×C42—222no—
448C2×C42—222no—
449C2×C42—221no—
450C2×C42C22×D1111yescharacteristic
451#107—222no—
452#107—222no—
453#106—222no—
454#106—222no—
455C4⋊C8—22no—
456C4⋊C8—222no—
457#103—222no—
458#103—222no—
459#103—222no—
460#103—222no—
461C22⋊C8—222no—
462C22⋊C8—222no—
463#95—21no—
464#95—221no—
465#95—221no—
466#95—221no—
467#95—221no—
468C2×C11#240911yescharacteristic
469C2×C11#300211yescharacteristic
470C2×C11#300711yescharacteristic
471C2×C11#307611yescharacteristic
472C2×C11#307811yescharacteristic
473C2×C11#323111yescharacteristic
474C2×C11#324011yescharacteristic
475D11—42no—
476C24—111no—
477C2×Q8—112no—
478C2×Q8—224no—
479C2×Q8—224no—
480C2×Q8—221no—
481C2×Q8—221no—
482C2×Q8—221no—
483C2×Q8—221no—
484C2×Q8—221no—
485C2×Q8—442no—
486C2×Q8—442no—
487C2×Q8—442no—
488C2×Q8—442no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—111no—
494C22×C4—111no—
495C22×C4—111no—
496C22×C4—112no—
497C22×C4—112no—
498C22×C4—222no—
499C22×C4—222no—
500C22×C4—221no—
501C22×C4—221no—
502C22×C4—221no—
503C22×C4—221no—
504C22×C4—221no—
505C22×C4—221no—
506C22×C4—221no—
507C22×C4—222no—
508C22×C4—222no—
509C22×C4—221no—
510C22×C4—441no—
511C22×C4—441no—
512C22×C4D4×D1111yescharacteristic
513C22×C4D4×D1111yescharacteristic
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—24no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—112no—
535C4⋊C4—112no—
536C4⋊C4—224no—
537C4⋊C4—224no—
538C4⋊C4—224no—
539C4⋊C4—224no—
540C4⋊C4—224no—
541C4⋊C4—221no—
542C4⋊C4—221no—
543C4⋊C4—221no—
544C4⋊C4—221no—
545C4⋊C4—442no—
546C4⋊C4—442no—
547C4⋊C4C2×D4412yes—
548C4⋊C4C2×D4412yes—
549C4⋊C4Q8×D1112yes—
550C22⋊C4—224no—
551C22⋊C4—224no—
552C22⋊C4—224no—
553C22⋊C4—442no—
554C42—42no—
555C42—224no—
556C42—224no—
557C42—222no—
558C42—222no—
559C42—221no—
560C42—221no—
561C42—442no—
562C42C2×D4412yes—
563C42D4×D1112yes—
564C11#2430611yescharacteristic, complemented, Sylow
565C23—112no—
566C23—221no—
567C23—221no—
568C23—221no—
569C23—221no—
570C23—221no—
571C23—221no—
572C23C2×D4×D1111yescharacteristic
573Q8—222no—
574Q8—222no—
575Q8—448no—
576Q8—448no—
577Q8—441no—
578Q8—441no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—112no—
596C2×C4—112no—
597C2×C4—112no—
598C2×C4—221no—
599C2×C4—221no—
600C2×C4—221no—
601C2×C4—221no—
602C2×C4—221no—
603C2×C4—221no—
604C2×C4—222no—
605C2×C4—222no—
606C2×C4—222no—
607C2×C4—222no—
608C2×C4—222no—
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#6693512yes—
623C2×C4#6693512yes—
624C2×C4C22×D4411yescharacteristic
625C2×C4C2×D4×D1111yescharacteristic
626C2×C4C2×Q8×D1111yescharacteristic
627C2×C4#6704011yescharacteristic
628C2×C4#41×D1111yescharacteristic
629C2×C4#6704311yescharacteristic
630C8—41no—
631C8—41no—
632C8—441no—
633C8—441no—
634C22—222no—
635C22—222no—
636C22—222no—
637C22—441no—
638C22—441no—
639C22—441no—
640C22—441no—
641C22C2×#6693511yescharacteristic
642C22D11×C22⋊Q811yescharacteristic
643C22#1062315911yescharacteristic
644C22D11×#13511yescharacteristic
645C22#1062329911yescharacteristic
646C22#1062330411yescharacteristic
647C22D11×#13711yescharacteristic
648C4—22no—
649C4—22no—
650C4—42no—
651C4—42no—
652C4—42no—
653C4—81no—
654C4—222no—
655C4—222no—
656C4—222no—
657C4—442no—
658C4—442no—
659C4—442no—
660C4—881no—
661C4Q8×D4411yescharacteristic
662C4#1062310711yescharacteristic
663C4#1062320811yescharacteristic
664C4#1062325811yescharacteristic
665C2—442no—
666C2#1307197911yescharacteristic
667C2#1307783611yescharacteristic
668C2#1307787711yescharacteristic
669C2#1307840111yescharacteristic
670C2#1307841911yescharacteristic
671C2#1307977411yescharacteristic
672C2#1307985511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1989C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenter#1989D11
hypocenterC11#24306
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1989

Complements

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

NH ≅ G/Ntype
2. C2×#10622442C2semidirect
3. C2×#10622676C2semidirect
5. #13069948C2semidirect
6. #13069943C2semidirect
7. #13069756C2semidirect
8. #13069756C2semidirect
9. #13069573C2semidirect
15. C11×#1989C2semidirect
104. #66950Q8semidirect
238. #1989D11semidirect
564. C11#24306semidirect

Maximal subgroups

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

subgroupindex
C2×#106232192
C2×#106224422
C2×#106226762
C4×#669502
#130699482
#130699432
#130697562
#130695732
#130689272
#130688182
#130688162
#130685932
C11×#19892
#2430611