Finite Group Databasebeta

← #14720261

Subgroups — #14720261

Order 2816.

1138 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077733C211yesmaximal, characteristic, complemented
2#13077583C211yesmaximal, characteristic, complemented
3#13067063C212yesmaximal, complemented
4#13067055C212yesmaximal, complemented
5#13067050C212yesmaximal, complemented
6#13067045C212yesmaximal, complemented
7#13067011C211yesmaximal, characteristic, complemented
8#13067003C211yesmaximal, characteristic, complemented
9#13066998C211yesmaximal, characteristic, complemented
10C2×Q8⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
11C4×C11×2−1+4C211yesmaximal, characteristic
12C2×C11×2−1+4C411yescharacteristic
13C11×#520—22no—
14C11×#520—21no—
15C11×#520C412yes—
16C11×#520C411yescharacteristic
17C11×#520C411yescharacteristic
18C11×#519—21no—
19C11×#519C412yes—
20C11×#519C411yescharacteristic
21C4×C11×#41—22no—
22C4×C11×#41—21no—
23C4×C11×#41C2212yes—
24C4×C11×#41C2211yescharacteristic
25C4×C11×#41C2211yescharacteristic
26C2×C4×Q8×C11—21no—
27C2×C4×Q8×C11C2211yescharacteristic
28C2×C4×Q8×C11C2212yes—
29#10622637—21no—
30#10622637—21no—
31#10622625—21no—
32#10622625—21no—
33#10622624—22no—
34#10622624—22no—
35#10622539C2212yes—
36#10622538C2211yescharacteristic
37#10622538C2211yescharacteristic
38#10622538C2212yes—
39#10622537C2212yes—
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C4×#4318C2212yes—
42C2×C4×C11⋊C8C2211yescharacteristic
43Q8⋊(C11⋊C8)C2212yes—
44Q8⋊(C11⋊C8)C2212yes—
45Q8⋊(C11⋊C8)C2211yescharacteristic
46Q8⋊(C11⋊C8)C2212yes—
47Q8⋊(C11⋊C8)C2212yes—
48Q8⋊(C11⋊C8)C2212yes—
49Q8⋊(C11⋊C8)C2211yescharacteristic
50D4⋊(C11⋊C8)C2211yescharacteristic
51D4⋊(C11⋊C8)C2212yes—
52D4⋊(C11⋊C8)C2211yescharacteristic
53C11×2−1+4—24no—
54C11×2−1+4—24no—
55C2×C11×#41—21no—
56C2×C11×#41—22no—
57C2×C11×#41C2×C412yes—
58C2×C11×#41C2×C411yescharacteristic
59C2×C11×#41C2×C411yescharacteristic
60C22×Q8×C11—21no—
61C22×Q8×C11C2×C412yes—
62C22×Q8×C11C2×C411yescharacteristic
63C4×Q8×C11—21no—
64C4×Q8×C11—22no—
65C4×Q8×C11—21no—
66C4×Q8×C11—22no—
67C4×Q8×C11—21no—
68C4×Q8×C11—21no—
69C4×Q8×C11—22no—
70C4×Q8×C11—21no—
71C4×Q8×C11—22no—
72C4×Q8×C11C2×C412yes—
73C4×Q8×C11C2×C412yes—
74C4×Q8×C11C2×C412yes—
75C4×Q8×C11C2×C412yes—
76C4×Q8×C11C2×C411yescharacteristic
77C4×Q8×C11D411yescharacteristic
78C4×Q8×C11D411yescharacteristic
79C4×Q8×C11C2312yes—
80C4×Q8×C11C2311yescharacteristic
81C4×D4×C11—22no—
82C4×D4×C11—21no—
83C4×D4×C11—21no—
84C4×D4×C11—22no—
85C4×D4×C11—21no—
86C4×D4×C11—22no—
87C4×D4×C11—22no—
88C4×D4×C11—22no—
89C4×D4×C11—22no—
90C4×D4×C11C2×C412yes—
91C4×D4×C11C2×C411yescharacteristic
92C4×D4×C11D412yes—
93C4×D4×C11D411yescharacteristic
94C4×D4×C11D412yes—
95C4×D4×C11D411yescharacteristic
96C4×D4×C11C2311yescharacteristic
97C11×#117—22no—
98C11×#117—21no—
99C11×#117—22no—
100C11×#117—22no—
101C11×#117—22no—
102C11×#117—21no—
103C11×#117—22no—
104C11×#117C2×C412yes—
105C11×#117C2×C411yescharacteristic
106C11×#117C2×C412yes—
107C11×#117C2×C411yescharacteristic
108C2×C11×C4⋊C4—21no—
109C2×C11×C4⋊C4—22no—
110C2×C11×C4⋊C4—22no—
111C2×C11×C4⋊C4—21no—
112C2×C11×C4⋊C4C2×C412yes—
113C2×C11×C4⋊C4C2×C411yescharacteristic
114C2×C42×C11—21no—
115C2×C42×C11—22no—
116C2×C42×C11—21no—
117C2×C42×C11—22no—
118C2×C42×C11C2311yescharacteristic
119C2×C42×C11C2312yes—
120C2×#4318—22no—
121C2×#4318—22no—
122C22×C11⋊C8—21no—
123C22×C11⋊C8—21no—
124C22⋊(C11⋊C8)—21no—
125C22⋊(C11⋊C8)—21no—
126C22⋊(C11⋊C8)—22no—
127C22⋊(C11⋊C8)—22no—
128C4⋊(C11⋊C8)—21no—
129C4⋊(C11⋊C8)—22no—
130C4⋊(C11⋊C8)—22no—
131C4⋊(C11⋊C8)—21no—
132C4⋊(C11⋊C8)C2312yes—
133C4⋊(C11⋊C8)C2311yescharacteristic
134C4⋊(C11⋊C8)C2311yescharacteristic
135#66867—22no—
136#66867—22no—
137C4×C11⋊C8—21no—
138C4×C11⋊C8—21no—
139C4×C11⋊C8C2311yescharacteristic
140C4×C11⋊C8C2311yescharacteristic
141C4×C11⋊C8C2312yes—
142#17454—111nomaximal, Sylow
143C11×#41—216no—
144C11×#41—28no—
145C11×#41—24no—
146C11×#41—24no—
147C11×#41—22no—
148C11×#41—22no—
149C11×#41—22no—
150C11×#41M1614yescomplemented
151C2×Q8×C11—28no—
152C2×Q8×C11—24no—
153C2×Q8×C11—24no—
154C2×Q8×C11—22no—
155C2×Q8×C11—21no—
156C2×Q8×C11—22no—
157C2×Q8×C11C22⋊C411yescharacteristic
158C2×Q8×C11M1614yescomplemented
159C2×Q8×C11C22×C411yescharacteristic
160C2×Q8×C11C22×C412yes—
161C2×D4×C11—22no—
162C2×D4×C11—21no—
163C2×D4×C11C22⋊C412yes—
164C2×D4×C11C22⋊C411yescharacteristic
165C2×D4×C11C22×C411yescharacteristic
166C22×C4×C11—22no—
167C22×C4×C11—21no—
168C22×C4×C11—22no—
169C22×C4×C11—21no—
170C22×C4×C11—22no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—22no—
175C22×C4×C11C22×C412yes—
176C22×C4×C11C22×C411yescharacteristic
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2×D412yes—
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D412yes—
181C11×C4⋊C4—22no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4—22no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—22no—
188C11×C4⋊C4—22no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4C22⋊C412yes—
191C11×C4⋊C4C22⋊C411yescharacteristic
192C11×C4⋊C4C22⋊C412yes—
193C11×C4⋊C4C22⋊C411yescharacteristic
194C11×C4⋊C4C22×C411yescharacteristic
195C11×C4⋊C4C22×C412yes—
196C11×C4⋊C4C22×C411yescharacteristic
197C11×C22⋊C4—22no—
198C11×C22⋊C4—21no—
199C11×C22⋊C4—21no—
200C11×C22⋊C4—22no—
201C11×C22⋊C4—21no—
202C11×C22⋊C4C22⋊C412yes—
203C11×C22⋊C4C22⋊C412yes—
204C11×C22⋊C4C22⋊C412yes—
205C42×C11—21no—
206C42×C11—22no—
207C42×C11—22no—
208C42×C11—22no—
209C42×C11—22no—
210C42×C11—22no—
211C42×C11—21no—
212C42×C11—22no—
213C42×C11—21no—
214C42×C11C22×C411yescharacteristic
215C42×C11C22×C412yes—
216C42×C11C2×D411yescharacteristic
217C42×C11C2×D411yescharacteristic
218C42×C11C2×D412yes—
219C42×C11C2×D412yes—
220C42×C11C2411yescharacteristic
221#4318—44no—
222#4318—82no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—21no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8—21no—
227C2×C11⋊C8—22no—
228C2×C11⋊C8—22no—
229C2×C11⋊C8—42no—
230C2×C11⋊C8—81no—
231C4×2−1+4D1111yescharacteristic
232#2989—111no—
233#2965—111no—
234#1491—112no—
235#1489—112no—
236#1488—112no—
237#1487—112no—
238#1479—111no—
239#1477—111no—
240#1476—111no—
241C2×Q8⋊C8—111no—
242C23×C11—21no—
243C23×C11C2×C22⋊C412yes—
244C23×C11C2×C22⋊C411yescharacteristic
245Q8×C11—28no—
246Q8×C11—21no—
247Q8×C11—22no—
248Q8×C11—22no—
249Q8×C11—24no—
250Q8×C11C2×M1612yes—
251Q8×C11C2×M1614yes—
252D4×C11—28no—
253D4×C11—24no—
254D4×C11—24no—
255D4×C11—21no—
256D4×C11—22no—
257D4×C11C2×M1612yes—
258C2×C4×C11—28no—
259C2×C4×C11—28no—
260C2×C4×C11—22no—
261C2×C4×C11—21no—
262C2×C4×C11—24no—
263C2×C4×C11—22no—
264C2×C4×C11—22no—
265C2×C4×C11—21no—
266C2×C4×C11—22no—
267C2×C4×C11—21no—
268C2×C4×C11—22no—
269C2×C4×C11—24no—
270C2×C4×C11—21no—
271C2×C4×C11—22no—
272C2×C4×C11—21no—
273C2×C4×C11—41no—
274C2×C4×C11—42no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11—81no—
278C2×C4×C11—82no—
279C2×C4×C11—81no—
280C2×C4×C11—82no—
281C2×C4×C11C2×C22⋊C411yescharacteristic
282C2×C4×C11C2×C22⋊C412yes—
283C2×C4×C11C2×C22⋊C411yescharacteristic
284C2×C4×C11C2×C22⋊C412yes—
285C2×C4×C11C2×C22⋊C412yes—
286C2×C4×C11C2×C22⋊C411yescharacteristic
287C2×C4×C11C2×M1612yes—
288C2×C4×C11C2×M1612yes—
289C2×C4×C11C23×C411yescharacteristic
290C2×C4×C11C22×D411yescharacteristic
291C2×C4×C11C22×D411yescharacteristic
292C11⋊C8—22no—
293C11⋊C8—41no—
294C11⋊C8—42no—
295C11⋊C8—42no—
296C11⋊C8—41no—
297C11⋊C8—41no—
298C2×2−1+4Dic1111yescharacteristic
299#520—22no—
300#520—21no—
301#520Dic1112yes—
302#520Dic1111yescharacteristic
303#520Dic1111yescharacteristic
304#519—21no—
305#519Dic1112yes—
306#519Dic1111yescharacteristic
307C4×#41—22no—
308C4×#41—21no—
309C4×#41C2×D1111yescharacteristic
310C4×#41C2×D1112yes—
311C4×#41C2×D1111yescharacteristic
312C2×C4×Q8—21no—
313C2×C4×Q8C2×D1111yescharacteristic
314C2×C4×Q8C2×D1112yes—
315#446—221no—
316#446—221no—
317#436—221no—
318#436—221no—
319#435—222no—
320#435—222no—
321#432—112no—
322#431—111no—
323#431—112no—
324#431—111no—
325#423—112no—
326C2×C4⋊C8—111no—
327C4×M16—112no—
328C2×C4×C8—111no—
329Q8⋊C8—112no—
330Q8⋊C8—112no—
331Q8⋊C8—111no—
332Q8⋊C8—111no—
333Q8⋊C8—112no—
334Q8⋊C8—112no—
335Q8⋊C8—112no—
336D4⋊C8—111no—
337D4⋊C8—111no—
338D4⋊C8—112no—
339C22×C11—21no—
340C22×C11—21no—
341C22×C11—22no—
342C22×C11—22no—
343C22×C11—22no—
344C22×C11—22no—
345C22×C11—41no—
346C22×C11—41no—
347C22×C11#40712yes—
348C22×C11C22×C22⋊C411yescharacteristic
349C4×C11—24no—
350C4×C11—22no—
351C4×C11—22no—
352C4×C11—21no—
353C4×C11—22no—
354C4×C11—21no—
355C4×C11—21no—
356C4×C11—22no—
357C4×C11—41no—
358C4×C11—42no—
359C4×C11—41no—
360C4×C11#40712yes—
361C4×C11C22×M1611yescharacteristic
362C4×C11C22×M1611yescharacteristic
363C4×C11#57711yescharacteristic
364C4×C11#57811yescharacteristic
3652−1+4—24no—
3662−1+4—24no—
367C2×#41—21no—
368C2×#41—22no—
369C2×#41C2×Dic1112yes—
370C2×#41C2×Dic1111yescharacteristic
371C2×#41C2×Dic1111yescharacteristic
372C22×Q8—21no—
373C22×Q8C2×Dic1112yes—
374C22×Q8C2×Dic1111yescharacteristic
375C2×M16—222no—
376C2×M16—222no—
377C22×C8—221no—
378C22×C8—221no—
379C4×Q8—21no—
380C4×Q8—22no—
381C4×Q8—21no—
382C4×Q8—22no—
383C4×Q8—21no—
384C4×Q8—21no—
385C4×Q8—22no—
386C4×Q8—21no—
387C4×Q8—22no—
388C4×Q8C2×Dic1112yes—
389C4×Q8C2×Dic1112yes—
390C4×Q8C2×Dic1112yes—
391C4×Q8C2×Dic1111yescharacteristic
392C4×Q8C2×Dic1112yes—
393C4×Q8C22⋊D1111yescharacteristic
394C4×Q8C22⋊D1111yescharacteristic
395C4×Q8C22×D1112yes—
396C4×Q8C22×D1111yescharacteristic
397C4×D4—22no—
398C4×D4—21no—
399C4×D4—21no—
400C4×D4—22no—
401C4×D4—21no—
402C4×D4—22no—
403C4×D4—22no—
404C4×D4—22no—
405C4×D4—22no—
406C4×D4C2×Dic1111yescharacteristic
407C4×D4C2×Dic1112yes—
408C4×D4C22⋊D1112yes—
409C4×D4C22⋊D1111yescharacteristic
410C4×D4C22⋊D1112yes—
411C4×D4C22⋊D1111yescharacteristic
412C4×D4C22×D1111yescharacteristic
413#117—22no—
414#117—21no—
415#117—22no—
416#117—22no—
417#117—22no—
418#117—21no—
419#117—22no—
420#117C2×Dic1112yes—
421#117C2×Dic1111yescharacteristic
422#117C2×Dic1112yes—
423#117C2×Dic1111yescharacteristic
424C2×C4⋊C4—21no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4C2×Dic1112yes—
429C2×C4⋊C4C2×Dic1111yescharacteristic
430C2×C42—21no—
431C2×C42—22no—
432C2×C42—21no—
433C2×C42—22no—
434C2×C42C22×D1111yescharacteristic
435C2×C42C22×D1112yes—
436C4⋊C8—112no—
437C4⋊C8—111no—
438C4⋊C8—111no—
439C4⋊C8—221no—
440C4⋊C8—222no—
441C4⋊C8—222no—
442C4⋊C8—221no—
443C22⋊C8—221no—
444C22⋊C8—221no—
445C22⋊C8—222no—
446C22⋊C8—222no—
447#97—222no—
448#97—222no—
449C4×C8—111no—
450C4×C8—111no—
451C4×C8—112no—
452C4×C8—221no—
453C4×C8—221no—
454C2×C11—22no—
455C2×C11—42no—
456C2×C11—42no—
457C2×C11C2×#40711yescharacteristic
458C2×C11#289811yescharacteristic
459C2×C11#290111yescharacteristic
460#41—216no—
461#41—28no—
462#41—24no—
463#41—24no—
464#41—22no—
465#41—22no—
466#41—22no—
467#41#431814yescomplemented
468C2×Q8—28no—
469C2×Q8—24no—
470C2×Q8—24no—
471C2×Q8—22no—
472C2×Q8—22no—
473C2×Q8—21no—
474C2×Q8#431814yescomplemented
475C2×Q8C22⋊Dic1111yescharacteristic
476C2×Q8C22×Dic1111yescharacteristic
477C2×Q8C22×Dic1112yes—
478C2×D4—22no—
479C2×D4—21no—
480C2×D4C22⋊Dic1112yes—
481C2×D4C22⋊Dic1111yescharacteristic
482C2×D4C22×Dic1111yescharacteristic
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4C22×Dic1112yes—
493C22×C4C22×Dic1111yescharacteristic
494C22×C4C2×C22⋊D1111yescharacteristic
495C22×C4C2×C22⋊D1112yes—
496C22×C4C2×C22⋊D1111yescharacteristic
497C22×C4C2×C22⋊D1112yes—
498M16—444no—
499M16—882no—
500C2×C8—221no—
501C2×C8—221no—
502C2×C8—222no—
503C2×C8—221no—
504C2×C8—221no—
505C2×C8—222no—
506C2×C8—442no—
507C2×C8—881no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—21no—
517C4⋊C4C22⋊Dic1112yes—
518C4⋊C4C22⋊Dic1111yescharacteristic
519C4⋊C4C22⋊Dic1112yes—
520C4⋊C4C22⋊Dic1111yescharacteristic
521C4⋊C4C22×Dic1111yescharacteristic
522C4⋊C4C22×Dic1112yes—
523C4⋊C4C22×Dic1111yescharacteristic
524C22⋊C4—22no—
525C22⋊C4—21no—
526C22⋊C4—21no—
527C22⋊C4—22no—
528C22⋊C4—21no—
529C22⋊C4C22⋊Dic1112yes—
530C22⋊C4C22⋊Dic1112yes—
531C22⋊C4C22⋊Dic1112yes—
532C42—21no—
533C42—22no—
534C42—22no—
535C42—22no—
536C42—22no—
537C42—22no—
538C42—21no—
539C42—22no—
540C42—21no—
541C42C22×Dic1111yescharacteristic
542C42C22×Dic1112yes—
543C42C2×C22⋊D1111yescharacteristic
544C42C2×C22⋊D1112yes—
545C42C2×C22⋊D1111yescharacteristic
546C42C2×C22⋊D1112yes—
547C42C23×D1111yescharacteristic
548C11#1745411yescharacteristic, complemented, Sylow
549C23—21no—
550C23C2×C22⋊Dic1112yes—
551C23C2×C22⋊Dic1111yescharacteristic
552Q8—28no—
553Q8—21no—
554Q8—22no—
555Q8—24no—
556Q8—22no—
557Q8C2×#431812yes—
558Q8C2×#431814yes—
559D4—28no—
560D4—24no—
561D4—24no—
562D4—21no—
563D4—22no—
564D4C2×#431812yes—
565C2×C4—28no—
566C2×C4—28no—
567C2×C4—24no—
568C2×C4—22no—
569C2×C4—21no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—24no—
573C2×C4—21no—
574C2×C4—22no—
575C2×C4—21no—
576C2×C4—22no—
577C2×C4—21no—
578C2×C4—22no—
579C2×C4—21no—
580C2×C4—41no—
581C2×C4—42no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—81no—
585C2×C4—82no—
586C2×C4—81no—
587C2×C4—82no—
588C2×C4C2×#431812yes—
589C2×C4C2×#431812yes—
590C2×C4C2×C22⋊Dic1111yescharacteristic
591C2×C4C2×C22⋊Dic1112yes—
592C2×C4C2×C22⋊Dic1111yescharacteristic
593C2×C4C2×C22⋊Dic1112yes—
594C2×C4C2×C22⋊Dic1112yes—
595C2×C4C2×C22⋊Dic1111yescharacteristic
596C2×C4C23×Dic1111yescharacteristic
597C2×C4C22×C22⋊D1111yescharacteristic
598C2×C4C22×C22⋊D1111yescharacteristic
599C8—222no—
600C8—441no—
601C8—442no—
602C8—442no—
603C8—441no—
604C8—441no—
605C22—21no—
606C22—21no—
607C22—22no—
608C22—22no—
609C22—22no—
610C22—22no—
611C22—41no—
612C22—41no—
613C22#1062282012yes—
614C22C22×C22⋊Dic1111yescharacteristic
615C4—24no—
616C4—22no—
617C4—22no—
618C4—21no—
619C4—22no—
620C4—21no—
621C4—21no—
622C4—22no—
623C4—41no—
624C4—42no—
625C4—41no—
626C4#1062282012yes—
627C4C22×#431811yescharacteristic
628C4C22×#431811yescharacteristic
629C4#1062336811yescharacteristic
630C4#1062336911yescharacteristic
631C2—22no—
632C2—42no—
633C2—42no—
634C2C2×#1062282011yescharacteristic
635C2#1307714911yescharacteristic
636C2#1307716311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC4×C11×2−1+4C2
socleC22×C11C22×C22⋊C4
prime radicalC2×C11×2−1+4C4
cosocleC42×C11C24
hypercenterC4×2−1+4D11
hypocenterC11#17454
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ C4×2−1+4

Complements

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

NH ≅ G/Ntype
1. #13077733C2semidirect
2. #13077583C2semidirect
3. #13067063C2semidirect
4. #13067055C2semidirect
5. #13067050C2semidirect
6. #13067045C2semidirect
7. #13067011C2semidirect
8. #13067003C2semidirect
9. #13066998C2semidirect
10. C2×Q8⋊(C11⋊C8)C2semidirect
150. C11×#41M16semidirect
158. C2×Q8×C11M16semidirect
467. #41#4318semidirect
474. C2×Q8#4318semidirect
548. C11#17454semidirect

Maximal subgroups

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

subgroupindex
#130777332
#130775832
#130670632
#130670552
#130670502
#130670452
#130670112
#130670032
#130669982
C2×Q8⋊(C11⋊C8)2
C4×C11×2−1+42
#1745411