Finite Group Databasebeta

← #14763768

Subgroups — #14763768

Order 2816.

1014 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623262C211yesmaximal, characteristic
2C2×#10622452C211yesmaximal, characteristic
3#13071221C211yesmaximal, characteristic
4#13069573C211yesmaximal, characteristic, complemented
5#13069571C211yesmaximal, characteristic, complemented
6#13069540C211yesmaximal, characteristic, complemented
7#13069046C211yesmaximal, characteristic
8#13069046C211yesmaximal, characteristic
9#13069036C211yesmaximal, characteristic
10#13069036C211yesmaximal, characteristic
11#13068629C211yesmaximal, characteristic, complemented
12#13068629C211yesmaximal, characteristic, complemented
13#13068619C211yesmaximal, characteristic, complemented
14#13068619C211yesmaximal, characteristic, complemented
15C11×#1981C211yesmaximal, characteristic, complemented
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×#66999C2211yescharacteristic
18C2×#66999C2211yescharacteristic
19C2×Q8×Dic11C2211yescharacteristic
20C2×Q8×Dic11C2211yescharacteristic
21C22×#4313C2211yescharacteristic
22C22×C8×D11C2211yescharacteristic
23#10623262—24no—
24#10623262C418yescomplemented
25C2×#66951—21no—
26C2×#66951—21no—
27C2×#66942—21no—
28C2×#66942—21no—
29C2×#66925C2211yescharacteristic
30C2×#66923C2211yescharacteristic
31C2×C11×C4⋊C8C2211yescharacteristic
32C2×C11×#103C2211yescharacteristic
33C2×C11×#103C2211yescharacteristic
34C2×C11×#103C2211yescharacteristic
35C2×C11×#103C2211yescharacteristic
36C4×C11×C4⋊C4C2211yescharacteristic
37C2×#66899C2211yescharacteristic
38C2×#66899C2211yescharacteristic
39C2×#66899C2211yescharacteristic
40C2×#66899C2211yescharacteristic
41C2×Dic11⋊C8C2211yescharacteristic
42C2×Dic11⋊C8C2211yescharacteristic
43#10622600C2211yescharacteristic
44#10622600C2211yescharacteristic
45#10622590C2211yescharacteristic
46#10622589C2211yescharacteristic
47#10622553—21no—
48C4×C4⋊Dic11C2211yescharacteristic
49#10622546—21no—
50C2×C4⋊(C11⋊C8)C2211yescharacteristic
51#10622452—24no—
52#10622282—21no—
53#10622265—21no—
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×Q8×C11C2311yescharacteristic
64C22×C4×D11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C11×C4⋊Q8—22no—
68C11×C4⋊Q8C2×C414yes—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C42×C11—21no—
74C2×C42×C11C2311yescharacteristic
75#66999—22no—
76#66999—22no—
77#66999C2×C414yes—
78#66999C2×C414yes—
79Q8×Dic11—22no—
80Q8×Dic11—22no—
81Q8×Dic11C2×C414yes—
82Q8×Dic11C2×C414yes—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4D411yescharacteristic
88C2×(C2×D11)⋊C4D411yescharacteristic
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4D411yescharacteristic
102C2×Dic11⋊C4D411yescharacteristic
103C2×C4×Dic11—21no—
104C2×C4×Dic11—21no—
105C2×C4×Dic11—21no—
106C2×C4×Dic11C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109C2×#4313—22no—
110C2×#4313—41no—
111C2×#4313—41no—
112C2×C8×D11—22no—
113C2×C8×D11—41no—
114C2×C8×D11—41no—
115#66951—28no—
116#66951—28no—
117#66942—28no—
118#66942—28no—
119#66925C2×C414yes—
120#66925D414yes—
121#66923—22no—
122#66923C2×C414yes—
123C11×C4⋊C8—22no—
124C11×#103—41no—
125C11×#103—41no—
126C11×#103—41no—
127C11×#103—41no—
128C11×#95—21no—
129#66899—41no—
130#66899—41no—
131#66899—41no—
132#66899—41no—
133C11⋊#95—21no—
134C11⋊#95—21no—
135C11⋊#95—21no—
136C11⋊#95—21no—
137C11⋊#95—21no—
138Dic11⋊C8—22no—
139Dic11⋊C8—22no—
140C4⋊(C11⋊C8)—22no—
141#21898—111nomaximal, Sylow
142C23×D11C2×D411yescharacteristic
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11—21no—
152C2×Q8×C11—21no—
153C2×Q8×C11C22×C412yes—
154C2×Q8×C11C22×C412yes—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2411yescharacteristic
162C22×Dic11—21no—
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11C2×D411yescharacteristic
167C22×Dic11C2×D411yescharacteristic
168C22×Dic11C2×D411yescharacteristic
169C2×C4×D11—21no—
170C2×C4×D11—21no—
171C2×C4×D11—21no—
172C2×C4×D11—21no—
173C2×C4×D11C22×C412yes—
174C2×C4×D11C2×D412yes—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C11×C4⋊C4—24no—
182C11×C4⋊C4—24no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C42×C11—81no—
188C42×C11C22×C412yes—
189C42×C11C2×D412yes—
190(C2×D11)⋊C4—24no—
191(C2×D11)⋊C4—24no—
192(C2×D11)⋊C4—81no—
193(C2×D11)⋊C4—81no—
194(C2×D11)⋊C4C22⋊C414yes—
195(C2×D11)⋊C4C22⋊C414yes—
196C4⋊Dic11—24no—
197C4⋊Dic11—24no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11C22×C412yes—
205C4⋊Dic11C22×C412yes—
206Dic11⋊C4—24no—
207Dic11⋊C4—24no—
208Dic11⋊C4—24no—
209Dic11⋊C4—24no—
210Dic11⋊C4—81no—
211Dic11⋊C4—81no—
212Dic11⋊C4C22⋊C414yes—
213Dic11⋊C4C22⋊C414yes—
214C4×Dic11—24no—
215C4×Dic11—24no—
216C4×Dic11—81no—
217C4×Dic11C22×C412yes—
218C4×Dic11C2×D412yes—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—21no—
225#4313—44no—
226C8×D11—44no—
227C2×#541—111no—
228C2×#424—111no—
229#2314—111no—
230#1989—111no—
231#1989—111no—
232#1981—111no—
233#1981D1111yescharacteristic, complemented
234#1894—111no—
235#1894—111no—
236#1892—111no—
237#1892—111no—
238#1805—111no—
239#1805—111no—
240#1803—111no—
241#1803—111no—
242C23×C11C22×D411yescharacteristic
243C22×D11—21no—
244C22×D11—21no—
245C22×D11—21no—
246C22×D11—21no—
247C22×D11—21no—
248C22×D11—21no—
249C22×D11C2×C22⋊C412yes—
250Q8×C11—22no—
251Q8×C11—22no—
252Q8×C11—22no—
253Q8×C11—22no—
254Q8×C11—41no—
255Q8×C11—41no—
256Q8×C11—41no—
257Q8×C11—41no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
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×C11C2×C22⋊C412yes—
275C2×C4×C11C2×C22⋊C412yes—
276C2×C4×C11C23×C411yescharacteristic
277C2×C4×C11C22×D411yescharacteristic
278C2×C4×C11H(5,𝔽2)11yescharacteristic
279C2×C4×C11H(5,𝔽2)11yescharacteristic
280C2×C4×C112−1+411yescharacteristic
281C2×C4×C112−1+411yescharacteristic
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—21no—
287C2×Dic11—21no—
288C2×Dic11—22no—
289C2×Dic11—22no—
290C2×Dic11—41no—
291C2×Dic11—41no—
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×Dic11C2×C22⋊C412yes—
301C2×Dic11C2×C22⋊C412yes—
302C2×Dic11C2×C22⋊C412yes—
303C4×D11—22no—
304C4×D11—22no—
305C4×D11—22no—
306C4×D11—22no—
307C8×C11—41no—
308C8×C11—41no—
309C11⋊C8—41no—
310C11⋊C8—41no—
311C22×M16—111no—
312C23×C8—111no—
313#541—118no—
314#541—224no—
315C2×C4⋊Q8C2×D1111yescharacteristic
316C2×#126—221no—
317C2×#126—221no—
318C2×#125—111no—
319C2×#125—221no—
320C2×#125—221no—
321C2×C22⋊Q8—111no—
322C2×C22⋊Q8—111no—
323C2×C4×Q8—111no—
324C2×C4×Q8—111no—
325C2×#117—111no—
326#424—224no—
327C2×C4⋊C8—111no—
328C2×C4⋊C8—111no—
329C2×C4⋊C8—111no—
330C2×C4⋊C8C2×D1111yescharacteristic
331C2×#103—111no—
332C2×#103—111no—
333C2×#103—111no—
334C2×#103—111no—
335C2×#103C2×D1111yescharacteristic
336C2×#103C2×D1111yescharacteristic
337C2×#103C2×D1111yescharacteristic
338C2×#103C2×D1111yescharacteristic
339#388—221no—
340#388—221no—
341#387—221no—
342#387—221no—
343#384—111no—
344#382—111no—
345#380—111no—
346#380—111no—
347C4×C4⋊C4—111no—
348C4×C4⋊C4C2×D1111yescharacteristic
349#340—111no—
350#340—111no—
351#340—111no—
352#340—111no—
353#340—111no—
354#340—111no—
355#340—111no—
356#340—111no—
357C22×C11C22×C22⋊C411yescharacteristic
358C22×C11#53711yescharacteristic
359C22×C11#53711yescharacteristic
360C22×C11#57711yescharacteristic
361C22×C11#57711yescharacteristic
362C22×C11#57811yescharacteristic
363C22×C11#57811yescharacteristic
364C2×D11—22no—
365C2×D11—22no—
366C2×D11—22no—
367C2×D11—41no—
368C2×D11—41no—
369C2×D11—41no—
370C2×D11—41no—
371C4×C11—22no—
372C4×C11—22no—
373C4×C11—42no—
374C4×C11—42no—
375C4×C11—81no—
376C4×C11—81no—
377C4×C11#52011yescharacteristic
378C4×C11#52011yescharacteristic
379C4×C11#53511yescharacteristic
380C4×C11#53611yescharacteristic
381Dic11—22no—
382Dic11—22no—
383Dic11—22no—
384Dic11—42no—
385Dic11—42no—
386Dic11—81no—
387Dic11—81no—
388C22×Q8C22×D1111yescharacteristic
389C22×Q8C22×D1111yescharacteristic
390C23×C4—111no—
391C2×M16—222no—
392C2×M16—441no—
393C2×M16—441no—
394C22×C8—111no—
395C22×C8—111no—
396C22×C8—222no—
397C22×C8—441no—
398C22×C8—441no—
399C22×C8C22×D1111yescharacteristic
400C22×C8C22×D1111yescharacteristic
401C4⋊Q8—22no—
402C4⋊Q8C4×D1114yes—
403#126—228no—
404#126—228no—
405#125—114no—
406#125—228no—
407#125—228no—
408#125—222no—
409C22⋊Q8—114no—
410C22⋊Q8—114no—
411C22⋊Q8—222no—
412C22⋊Q8—222no—
413C4×Q8—114no—
414C4×Q8—114no—
415C4×Q8—222no—
416C4×Q8—222no—
417#117—114no—
418#117—114no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
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×C22⋊C4—111no—
438C2×C22⋊C4—111no—
439C2×C22⋊C4—221no—
440C2×C22⋊C4—221no—
441C2×C22⋊C4—221no—
442C2×C22⋊C4—221no—
443C2×C42—21no—
444C2×C42—111no—
445C2×C42—221no—
446C2×C42—221no—
447C2×C42—221no—
448C2×C42C22×D1111yescharacteristic
449C4⋊C8—22no—
450C4⋊C8—222no—
451C4⋊C8—222no—
452C4⋊C8—222no—
453#103—41no—
454#103—41no—
455#103—41no—
456#103—41no—
457#103—441no—
458#103—441no—
459#103—441no—
460#103—441no—
461#95—21no—
462#95—221no—
463#95—221no—
464#95—221no—
465#95—221no—
466#95—221no—
467C2×C11#231111yescharacteristic
468C2×C11#289811yescharacteristic
469C2×C11#289811yescharacteristic
470C2×C11#325811yescharacteristic
471C2×C11#325811yescharacteristic
472C2×C11#326011yescharacteristic
473C2×C11#326111yescharacteristic
474D11—42no—
475C24—111no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8C2×C4×D1112yes—
487C2×Q8C2×C4×D1112yes—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—111no—
493C22×C4—111no—
494C22×C4—111no—
495C22×C4—112no—
496C22×C4—112no—
497C22×C4—221no—
498C22×C4—221no—
499C22×C4—221no—
500C22×C4—221no—
501C22×C4—221no—
502C22×C4—221no—
503C22×C4—221no—
504C22×C4—221no—
505C22×C4D4×D1111yescharacteristic
506C22×C4D4×D1111yescharacteristic
507C22×C4C23×D1111yescharacteristic
508M16—444no—
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—
521C2×C8—444no—
522C4⋊C4—24no—
523C4⋊C4—24no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—114no—
529C4⋊C4—114no—
530C4⋊C4—112no—
531C4⋊C4—112no—
532C4⋊C4—224no—
533C4⋊C4—224no—
534C4⋊C4—224no—
535C4⋊C4—224no—
536C4⋊C4—224no—
537C4⋊C4—224no—
538C4⋊C4—221no—
539C4⋊C4—221no—
540C4⋊C4—221no—
541C4⋊C4—221no—
542C4⋊C4—221no—
543C4⋊C4—221no—
544C4⋊C4—881no—
545C4⋊C4—881no—
546C22⋊C4—114no—
547C22⋊C4—114no—
548C22⋊C4—224no—
549C22⋊C4—224no—
550C22⋊C4—881no—
551C22⋊C4—881no—
552C42—81no—
553C42—112no—
554C42—112no—
555C42—224no—
556C42—224no—
557C42—881no—
558C42C2×C4×D1112yes—
559C42D4×D1112yes—
560C11#2189811yescharacteristic, complemented, Sylow
561C23—112no—
562C23—221no—
563C23—221no—
564C23—221no—
565C23—221no—
566C23—221no—
567C23—221no—
568C23C2×D4×D1111yescharacteristic
569Q8—22no—
570Q8—22no—
571Q8—22no—
572Q8—22no—
573Q8—41no—
574Q8—41no—
575Q8—41no—
576Q8—41no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—41no—
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—41no—
593C2×C4—112no—
594C2×C4—112no—
595C2×C4—112no—
596C2×C4—221no—
597C2×C4—221no—
598C2×C4—221no—
599C2×C4—221no—
600C2×C4—221no—
601C2×C4—221no—
602C2×C4—222no—
603C2×C4—222no—
604C2×C4—222no—
605C2×C4—222no—
606C2×C4—222no—
607C2×C4—222no—
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—441no—
618C2×C4C22⋊C4×D1112yes—
619C2×C4C22⋊C4×D1112yes—
620C2×C4C22×C4×D1111yescharacteristic
621C2×C4C2×D4×D1111yescharacteristic
622C2×C4#6703711yescharacteristic
623C2×C4#6703711yescharacteristic
624C2×C4#6704311yescharacteristic
625C2×C4#6704311yescharacteristic
626C8—41no—
627C8—41no—
628C8—441no—
629C8—441no—
630C22—222no—
631C22—222no—
632C22—222no—
633C22—441no—
634C22—441no—
635C22—441no—
636C22—441no—
637C22C2×C22⋊C4×D1111yescharacteristic
638C22#1062313911yescharacteristic
639C22#1062313911yescharacteristic
640C22#1062329311yescharacteristic
641C22#1062329711yescharacteristic
642C22#1062330911yescharacteristic
643C22#1062331011yescharacteristic
644C4—22no—
645C4—22no—
646C4—42no—
647C4—42no—
648C4—81no—
649C4—81no—
650C4—222no—
651C4—222no—
652C4—222no—
653C4—442no—
654C4—442no—
655C4—881no—
656C4—881no—
657C4#1062307711yescharacteristic
658C4#1062307711yescharacteristic
659C4#1062320611yescharacteristic
660C4#1062324611yescharacteristic
661C2—442no—
662C2#1307120611yescharacteristic
663C2#1307714411yescharacteristic
664C2#1307714811yescharacteristic
665C2#1308003811yescharacteristic
666C2#1308004011yescharacteristic
667C2#1308005911yescharacteristic
668C2#1308006811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1981C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1981D11
hypocenterC11#21898
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1981

Complements

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

NH ≅ G/Ntype
4. #13069573C2semidirect
5. #13069571C2semidirect
6. #13069540C2semidirect
11. #13068629C2semidirect
12. #13068629C2semidirect
13. #13068619C2semidirect
14. #13068619C2semidirect
15. C11×#1981C2semidirect
24. #10623262C4semidirect
233. #1981D11semidirect
560. C11#21898semidirect

Maximal subgroups

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

subgroupindex
C2×#106232622
C2×#106224522
#130712212
#130695732
#130695712
#130695402
#130690462
#130690362
#130686292
#130686192
C11×#19812
#2189811