Finite Group Databasebeta

← #14721584

Subgroups — #14721584

Order 2816.

1002 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077645C211yesmaximal, characteristic, complemented
2#13071589C211yesmaximal, characteristic, complemented
3#13067172C212yesmaximal, complemented
4#13067154C212yesmaximal, complemented
5#13067149C211yesmaximal, characteristic, complemented
6#13067145C211yesmaximal, characteristic, complemented
7#13067141C212yesmaximal, complemented
8#13067136C211yesmaximal, characteristic, complemented
9#13067132C211yesmaximal, characteristic, complemented
10#13067107C212yesmaximal, complemented
11C11×#3505C211yesmaximal, characteristic
12C11×#553—22no—
13C11×#553C412yescomplemented
14C11×#552C412yescomplemented
15C11×#551—22no—
16C11×#548C412yescomplemented
17C11×#546C412yescomplemented
18C11×#539—21no—
19C11×#538—21no—
20C11×#534—21no—
21C11×#529C2212yes—
22C11×#525C2212yes—
23C2×C11×C22⋊Q8C2211yescharacteristic
24C2×C11×#121C2211yescharacteristic
25C11×#518—21no—
26C2×C4×D4×C11C2211yescharacteristic
27#10622834—21no—
28#10622824C2211yescharacteristic
29#10622824C2211yescharacteristic, complemented
30C4×C22⋊Dic11C2211yescharacteristic
31C4×C22⋊Dic11C2211yescharacteristic, complemented
32#10622820C2211yescharacteristic
33#10622820C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2212yescomplemented
35#10622624—22no—
36#10622624—22no—
37C4⋊C4×Dic11—21no—
38#10622564—21no—
39#10622564—21no—
40#10622549C2211yescharacteristic, complemented
41C4×C4⋊Dic11C2211yescharacteristic, complemented
42#10622539C2212yescomplemented
43#10622176C2212yescomplemented
44#10622176C2212yescomplemented
45#10622176C2212yescomplemented
46#10622176C2212yescomplemented
47#10622175C2212yes—
48#10622175C2212yes—
49#10622175C2212yes—
50#10622175C2212yes—
51C2×C11×#41C2×C412yes—
52C22×Q8×C11C2×C411yescharacteristic
53C22×D4×C11—21no—
54C22×D4×C11C2×C411yescharacteristic
55C22×D4×C11D411yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C11×#126—22no—
59C11×#126—22no—
60C11×#126—22no—
61C11×#125—22no—
62C11×#125C2×C412yes—
63C11×#124—22no—
64C11×#124C2×C412yes—
65C11×#123—22no—
66C11×#123—22no—
67C11×#123—22no—
68C11×#123—22no—
69C11×#123—22no—
70C11×C22⋊Q8—21no—
71C11×C22⋊Q8—21no—
72C11×C22⋊Q8—22no—
73C11×C22⋊Q8C2×C412yes—
74C11×C22⋊Q8C2×C412yes—
75C11×C22⋊Q8C2312yes—
76C11×#121—22no—
77C11×#121—22no—
78C11×#121—21no—
79C11×#121—21no—
80C11×#121—22no—
81C11×#121C2×C412yes—
82C11×#121C2×C412yes—
83C11×#121C2312yes—
84C11×#120—22no—
85C11×#120—22no—
86C4×Q8×C11C2×C412yes—
87C4×D4×C11—22no—
88C4×D4×C11—22no—
89C4×D4×C11—22no—
90C4×D4×C11—22no—
91C4×D4×C11—22no—
92C4×D4×C11C2×C412yes—
93C4×D4×C11C2×C412yes—
94C4×D4×C11C2×C412yes—
95C4×D4×C11D412yes—
96C4×D4×C11D412yes—
97C11×#117—22no—
98C11×#117—22no—
99C11×#117C2×C412yes—
100C2×C11×C4⋊C4—21no—
101C2×C11×C4⋊C4C2×C411yescharacteristic
102C2×C11×C4⋊C4C2×C411yescharacteristic
103C2×C11×C4⋊C4D411yescharacteristic
104C2×C11×C22⋊C4—21no—
105C2×C11×C22⋊C4—21no—
106C2×C11×C22⋊C4—22no—
107C2×C11×C22⋊C4D411yescharacteristic
108C2×C11×C22⋊C4D411yescharacteristic
109C2×C42×C11C2311yescharacteristic
110C2×C22⋊Dic11—21no—
111C2×C22⋊Dic11—21no—
112C2×C22⋊Dic11—21no—
113C2×C22⋊Dic11—21no—
114C2×C4⋊Dic11—21no—
115C2×C4⋊Dic11—21no—
116C2×C4×Dic11—21no—
117C2×C4×Dic11—21no—
118C2×C4×Dic11—21no—
119C2×#4318—21no—
120C2×#4318—21no—
121C22×C11⋊C8—22no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95C2311yescharacteristic
126C11⋊#95C2311yescharacteristic
127C11⋊#95C2311yescharacteristic
128C11⋊#95C2311yescharacteristic
129C22⋊(C11⋊C8)—22no—
130C22⋊(C11⋊C8)—21no—
131C22⋊(C11⋊C8)—21no—
132C22⋊(C11⋊C8)C2312yes—
133C22⋊(C11⋊C8)C2312yes—
134C4⋊(C11⋊C8)—22no—
135#66867—22no—
136#17625—111nomaximal, Sylow
137C24×C11—21no—
138C24×C11C2×D411yescharacteristic
139C24×C11C2×D411yescharacteristic
140C11×#41—82no—
141C2×Q8×C11—21no—
142C2×Q8×C11—81no—
143C2×Q8×C11C22×C412yes—
144C2×D4×C11—22no—
145C2×D4×C11—22no—
146C2×D4×C11—22no—
147C2×D4×C11—22no—
148C2×D4×C11—21no—
149C2×D4×C11—41no—
150C2×D4×C11—41no—
151C2×D4×C11—42no—
152C2×D4×C11—42no—
153C2×D4×C11—81no—
154C2×D4×C11C22⋊C412yes—
155C2×D4×C11C22⋊C412yes—
156C2×D4×C11C22×C412yes—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—22no—
161C22×C4×C11—22no—
162C22×C4×C11—81no—
163C22×C4×C11—81no—
164C22×C4×C11C22×C411yescharacteristic
165C22×C4×C11C22×C411yescharacteristic
166C22×C4×C11C22×C412yes—
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2×D412yes—
172C22×C4×C11C2×D411yescharacteristic
173C22×C4×C11C2×D411yescharacteristic
174C22×C4×C11C2411yescharacteristic
175C22×Dic11—21no—
176C22×Dic11—21no—
177C22×Dic11—21no—
178C22×Dic11—21no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4—22no—
185C11×C4⋊C4—22no—
186C11×C4⋊C4—22no—
187C11×C4⋊C4C22⋊C412yes—
188C11×C4⋊C4C22⋊C412yes—
189C11×C4⋊C4C22×C412yes—
190C11×C4⋊C4C22×C412yes—
191C11×C22⋊C4—22no—
192C11×C22⋊C4—22no—
193C11×C22⋊C4—22no—
194C11×C22⋊C4—22no—
195C11×C22⋊C4—22no—
196C11×C22⋊C4—22no—
197C11×C22⋊C4—22no—
198C11×C22⋊C4—22no—
199C11×C22⋊C4—22no—
200C11×C22⋊C4—22no—
201C11×C22⋊C4C22⋊C412yes—
202C11×C22⋊C4C22⋊C412yes—
203C11×C22⋊C4C22⋊C412yes—
204C11×C22⋊C4C22⋊C412yes—
205C42×C11—22no—
206C42×C11—22no—
207C42×C11C22×C412yes—
208C42×C11C2×D412yes—
209C22⋊Dic11—42no—
210C22⋊Dic11—42no—
211C22⋊Dic11—81no—
212C22⋊Dic11—81no—
213C4⋊Dic11—42no—
214C4⋊Dic11—42no—
215C4×Dic11—42no—
216C4×Dic11—81no—
217C4×Dic11—81no—
218#4318—81no—
219#4318—81no—
220C2×C11⋊C8—22no—
221C2×C11⋊C8—22no—
222C2×C11⋊C8—82no—
223#3505D1111yescharacteristic
224#2973—111no—
225#2357—111no—
226#1516—112no—
227#1512—112no—
228#1511—111no—
229#1510—111no—
230#1509—112no—
231#1508—111no—
232#1507—111no—
233#1501—112no—
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—22no—
239C23×C11—41no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11—41no—
243C23×C11—42no—
244C23×C11—81no—
245C23×C11—81no—
246C23×C11C2×C22⋊C411yescharacteristic
247C23×C11C2×C22⋊C412yes—
248C23×C11C2×C22⋊C411yescharacteristic
249C23×C11C22×D411yescharacteristic
250Q8×C11—42no—
251Q8×C11—81no—
252D4×C11—42no—
253D4×C11—42no—
254D4×C11—42no—
255D4×C11—44no—
256D4×C11—42no—
257D4×C11—42no—
258D4×C11—81no—
259D4×C11—82no—
260D4×C11—82no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—22no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—42no—
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—42no—
276C2×C4×C11—42no—
277C2×C4×C11—82no—
278C2×C4×C11—82no—
279C2×C4×C11—81no—
280C2×C4×C11—81no—
281C2×C4×C11C2×C22⋊C412yes—
282C2×C4×C11C2×C22⋊C412yes—
283C2×C4×C11C2×C22⋊C412yes—
284C2×C4×C11C2×C22⋊C411yescharacteristic
285C2×C4×C11C2×C22⋊C411yescharacteristic
286C2×C4×C11C23×C411yescharacteristic
287C2×C4×C11C22×D411yescharacteristic
288C2×Dic11—22no—
289C2×Dic11—41no—
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—
300C11⋊C8—42no—
301C11⋊C8—42no—
302#553—22no—
303#553Dic1112yescomplemented
304#552Dic1112yescomplemented
305#551—22no—
306#548Dic1112yescomplemented
307#546Dic1112yescomplemented
308#539—21no—
309#538—21no—
310#534—21no—
311#529C2×D1112yes—
312#525C2×D1112yes—
313C2×C22⋊Q8C2×D1111yescharacteristic
314C2×#121C2×D1111yescharacteristic
315#518—21no—
316C2×C4×D4C2×D1111yescharacteristic
317#435—222no—
318#435—222no—
319#432—112no—
320#407—111no—
321#407—111no—
322C2×C22⋊C8—112no—
323#390—221no—
324#388—221no—
325#388—221no—
326#382—111no—
327#381—111no—
328#381—111no—
329C4×C4⋊C4—111no—
330C4×C4⋊C4—221no—
331C4×C22⋊C4—111no—
332C4×C22⋊C4—111no—
333#328—112no—
334#328—112no—
335#328—112no—
336#328—112no—
337#327—112no—
338#327—112no—
339#327—112no—
340#327—112no—
341C22×C11—21no—
342C22×C11—21no—
343C22×C11—21no—
344C22×C11—22no—
345C22×C11—21no—
346C22×C11—21no—
347C22×C11—21no—
348C22×C11—22no—
349C22×C11—21no—
350C22×C11—22no—
351C22×C11—21no—
352C22×C11—42no—
353C22×C11—42no—
354C22×C11—42no—
355C22×C11—81no—
356C22×C11—81no—
357C22×C11—81no—
358C22×C11—81no—
359C22×C11—162no—
360C22×C11C22×C22⋊C411yescharacteristic
361C22×C11#57511yescharacteristic
362C22×C11#57511yescharacteristic
363C4×C11—21no—
364C4×C11—21no—
365C4×C11—22no—
366C4×C11—21no—
367C4×C11—21no—
368C4×C11—22no—
369C4×C11—22no—
370C4×C11—42no—
371C4×C11—42no—
372C4×C11—42no—
373Dic11—42no—
374Dic11—81no—
375Dic11—81no—
376Dic11—81no—
377C2×#41C2×Dic1112yes—
378C22×Q8C2×Dic1111yescharacteristic
379C22×D4—21no—
380C22×D4C2×Dic1111yescharacteristic
381C22×D4C22⋊D1111yescharacteristic
382C23×C4C22×D1111yescharacteristic
383C23×C4C22×D1111yescharacteristic
384C2×M16—221no—
385C2×M16—221no—
386C22×C8—222no—
387#126—22no—
388#126—22no—
389#126—22no—
390#125—22no—
391#125C2×Dic1112yes—
392#124—22no—
393#124C2×Dic1112yes—
394#123—22no—
395#123—22no—
396#123—22no—
397#123—22no—
398#123—22no—
399C22⋊Q8—21no—
400C22⋊Q8—21no—
401C22⋊Q8—22no—
402C22⋊Q8C2×Dic1112yes—
403C22⋊Q8C2×Dic1112yes—
404C22⋊Q8C22×D1112yes—
405#121—22no—
406#121—22no—
407#121—21no—
408#121—21no—
409#121—22no—
410#121C2×Dic1112yes—
411#121C2×Dic1112yes—
412#121C22×D1112yes—
413#120—22no—
414#120—22no—
415C4×Q8C2×Dic1112yes—
416C4×D4—22no—
417C4×D4—22no—
418C4×D4—22no—
419C4×D4—22no—
420C4×D4—22no—
421C4×D4C2×Dic1112yes—
422C4×D4C2×Dic1112yes—
423C4×D4C2×Dic1112yes—
424C4×D4C22⋊D1112yes—
425C4×D4C22⋊D1112yes—
426#117—22no—
427#117—22no—
428#117C2×Dic1112yes—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—221no—
431C2×C4⋊C4—221no—
432C2×C4⋊C4C2×Dic1111yescharacteristic
433C2×C4⋊C4C2×Dic1111yescharacteristic
434C2×C4⋊C4C22⋊D1111yescharacteristic
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—22no—
438C2×C22⋊C4—221no—
439C2×C22⋊C4—221no—
440C2×C22⋊C4—221no—
441C2×C22⋊C4—221no—
442C2×C22⋊C4C22⋊D1111yescharacteristic
443C2×C22⋊C4C22⋊D1111yescharacteristic
444C2×C42—221no—
445C2×C42—221no—
446C2×C42—221no—
447C2×C42C22×D1111yescharacteristic
448C4⋊C8—222no—
449C22⋊C8—112no—
450C22⋊C8—112no—
451C22⋊C8—222no—
452C22⋊C8—221no—
453C22⋊C8—221no—
454#97—222no—
455#95—111no—
456#95—111no—
457#95—111no—
458#95—111no—
459#95—221no—
460#95—221no—
461#95—221no—
462C2×C11—21no—
463C2×C11—21no—
464C2×C11—41no—
465C2×C11—42no—
466C2×C11—41no—
467C2×C11—82no—
468C2×C11#288311yescharacteristic
469C2×C11#289611yescharacteristic
470C2×C11#290111yescharacteristic
471C24—21no—
472C24C2×C22⋊D1111yescharacteristic
473C24C2×C22⋊D1111yescharacteristic
474#41—82no—
475C2×Q8—21no—
476C2×Q8—81no—
477C2×Q8C22×Dic1112yes—
478C2×D4—22no—
479C2×D4—22no—
480C2×D4—22no—
481C2×D4—22no—
482C2×D4—21no—
483C2×D4—41no—
484C2×D4—41no—
485C2×D4—42no—
486C2×D4—42no—
487C2×D4—81no—
488C2×D4C22⋊Dic1112yes—
489C2×D4C22⋊Dic1112yes—
490C2×D4C22×Dic1112yes—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—81no—
497C22×C4—81no—
498C22×C4—221no—
499C22×C4—221no—
500C22×C4—221no—
501C22×C4—221no—
502C22×C4C22×Dic1111yescharacteristic
503C22×C4C22×Dic1111yescharacteristic
504C22×C4C22×Dic1112yes—
505C22×C4C2×C22⋊D1111yescharacteristic
506C22×C4C2×C22⋊D1111yescharacteristic
507C22×C4C2×C22⋊D1111yescharacteristic
508C22×C4C2×C22⋊D1111yescharacteristic
509C22×C4C2×C22⋊D1111yescharacteristic
510C22×C4C2×C22⋊D1111yescharacteristic
511C22×C4C2×C22⋊D1112yes—
512C22×C4C23×D1111yescharacteristic
513M16—881no—
514M16—881no—
515C2×C8—222no—
516C2×C8—222no—
517C2×C8—882no—
518C4⋊C4—22no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—22no—
522C4⋊C4—22no—
523C4⋊C4—22no—
524C4⋊C4—22no—
525C4⋊C4—22no—
526C4⋊C4—442no—
527C4⋊C4—442no—
528C4⋊C4C22⋊Dic1112yes—
529C4⋊C4C22⋊Dic1112yes—
530C4⋊C4C22×Dic1112yes—
531C4⋊C4C22×Dic1112yes—
532C22⋊C4—22no—
533C22⋊C4—22no—
534C22⋊C4—22no—
535C22⋊C4—22no—
536C22⋊C4—22no—
537C22⋊C4—22no—
538C22⋊C4—22no—
539C22⋊C4—22no—
540C22⋊C4—22no—
541C22⋊C4—22no—
542C22⋊C4—442no—
543C22⋊C4—442no—
544C22⋊C4—881no—
545C22⋊C4—881no—
546C22⋊C4C22⋊Dic1112yes—
547C22⋊C4C22⋊Dic1112yes—
548C22⋊C4C22⋊Dic1112yes—
549C22⋊C4C22⋊Dic1112yes—
550C42—22no—
551C42—22no—
552C42—442no—
553C42—881no—
554C42—881no—
555C42C22×Dic1112yes—
556C42C2×C22⋊D1112yes—
557C11#1762511yescharacteristic, complemented, Sylow
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—22no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23—41no—
567C23—42no—
568C23—81no—
569C23—81no—
570C23C2×C22⋊Dic1111yescharacteristic
571C23C2×C22⋊Dic1112yes—
572C23C2×C22⋊Dic1111yescharacteristic
573C23C22×C22⋊D1111yescharacteristic
574Q8—42no—
575Q8—81no—
576D4—42no—
577D4—42no—
578D4—42no—
579D4—44no—
580D4—42no—
581D4—42no—
582D4—81no—
583D4—82no—
584D4—82no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—42no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—82no—
602C2×C4—82no—
603C2×C4—81no—
604C2×C4—81no—
605C2×C4—222no—
606C2×C4—441no—
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×C4C2×C22⋊Dic1112yes—
618C2×C4C2×C22⋊Dic1112yes—
619C2×C4C2×C22⋊Dic1112yes—
620C2×C4C2×C22⋊Dic1111yescharacteristic
621C2×C4C2×C22⋊Dic1111yescharacteristic
622C2×C4C23×Dic1111yescharacteristic
623C2×C4C22×C22⋊D1111yescharacteristic
624C8—442no—
625C8—442no—
626C22—21no—
627C22—21no—
628C22—21no—
629C22—22no—
630C22—21no—
631C22—21no—
632C22—21no—
633C22—22no—
634C22—21no—
635C22—22no—
636C22—21no—
637C22—42no—
638C22—42no—
639C22—42no—
640C22—81no—
641C22—81no—
642C22—81no—
643C22—81no—
644C22—162no—
645C22#1062335311yescharacteristic
646C22#1062335311yescharacteristic
647C22C22×C22⋊Dic1111yescharacteristic
648C4—21no—
649C4—21no—
650C4—22no—
651C4—21no—
652C4—21no—
653C4—22no—
654C4—22no—
655C4—42no—
656C4—42no—
657C4—42no—
658C4—442no—
659C4—881no—
660C4—881no—
661C4—881no—
662C2—21no—
663C2—21no—
664C2—41no—
665C2—41no—
666C2—42no—
667C2—82no—
668C2#1307707711yescharacteristic
669C2#1307713511yescharacteristic
670C2#1307716311yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#3505C2
socleC22×C11C22×C22⋊C4
cosocleC22×C4×C11C24
hypercenter#3505D11
hypocenterC11#17625
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #3505

Complements

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

NH ≅ G/Ntype
1. #13077645C2semidirect
2. #13071589C2semidirect
3. #13067172C2semidirect
4. #13067154C2semidirect
5. #13067149C2semidirect
6. #13067145C2semidirect
7. #13067141C2semidirect
8. #13067136C2semidirect
9. #13067132C2semidirect
10. #13067107C2semidirect
13. C11×#553C4semidirect
14. C11×#552C4semidirect
16. C11×#548C4semidirect
17. C11×#546C4semidirect
29. #10622824C22semidirect
31. C4×C22⋊Dic11C22semidirect
34. C2×C22⋊(C11⋊C8)C22semidirect
40. #10622549C22semidirect
41. C4×C4⋊Dic11C22semidirect
42. #10622539C22semidirect
43. #10622176C22semidirect
44. #10622176C22semidirect
45. #10622176C22semidirect
46. #10622176C22semidirect
303. #553Dic11semidirect
304. #552Dic11semidirect
306. #548Dic11semidirect
307. #546Dic11semidirect
557. C11#17625semidirect

Maximal subgroups

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

subgroupindex
#130776452
#130715892
#130671722
#130671542
#130671492
#130671452
#130671412
#130671362
#130671322
#130671072
C11×#35052
#1762511