Finite Group Databasebeta

← #14720832

Subgroups — #14720832

Order 2816.

934 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077748C211yesmaximal, characteristic, complemented
2#13077260C211yesmaximal, characteristic, complemented
3#13067081C212yesmaximal, complemented
4#13067071C211yesmaximal, characteristic, complemented
5#13067055C211yesmaximal, characteristic, complemented
6#13067045C212yesmaximal, complemented
7#13067037C211yesmaximal, characteristic, complemented
8#13067024C212yesmaximal, complemented
9#13067011C212yesmaximal, complemented
10#13066998C211yesmaximal, characteristic, complemented
11C11×#3482C211yesmaximal, characteristic
12C11×#557C411yescharacteristic
13C11×#556—21no—
14C11×#556C411yescharacteristic
15C11×#552—22no—
16C11×#552C412yes—
17D4×Q8×C11C411yescharacteristic
18C11×#548C412yes—
19C11×#547—21no—
20C11×#547C411yescharacteristic
21C11×#533—21no—
22C11×#533C2211yescharacteristic
23C11×#529—22no—
24C11×#529C2212yes—
25C4×C11×#41—21no—
26C4×C11×#41C2211yescharacteristic
27C4×C11×#41C2211yescharacteristic
28C2×C4×Q8×C11C2212yes—
29#10622847—21no—
30Q8×C11⋊C8—21no—
31#10622625—21no—
32#10622625—22no—
33#10622613—22no—
34#10622612—21no—
35#10622538C2212yes—
36#10622538C2211yescharacteristic
37#10622538C2212yes—
38#10622538C2212yes—
39#10622537C2212yes—
40#10622537C2211yescharacteristic
41C4×#4318C2211yescharacteristic
42C2×C4×C11⋊C8C2211yescharacteristic
43Q8⋊(C11⋊C8)C2211yescharacteristic
44Q8⋊(C11⋊C8)C2212yes—
45Q8⋊(C11⋊C8)C2212yes—
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
53C2×C11×#41—21no—
54C2×C11×#41C2×C411yescharacteristic
55C2×C11×#41D411yescharacteristic
56C22×Q8×C11C2×C412yes—
57C11×C4⋊Q8—21no—
58C11×C4⋊Q8—21no—
59C11×C4⋊Q8C2×C411yescharacteristic
60C11×C4⋊Q8C2×C411yescharacteristic
61C11×#126—22no—
62C11×#126—22no—
63C11×#126—22no—
64C11×#125—22no—
65C11×#125—22no—
66C11×#125—21no—
67C11×#125C2×C412yes—
68C11×#124—22no—
69C11×#124C2×C412yes—
70C11×#123—22no—
71C11×#123—22no—
72C11×#123—22no—
73C11×C22⋊Q8—21no—
74C11×C22⋊Q8—21no—
75C11×C22⋊Q8—21no—
76C11×C22⋊Q8—22no—
77C11×C22⋊Q8—22no—
78C11×C22⋊Q8C2×C412yes—
79C11×C22⋊Q8C2×C412yes—
80C11×#121—22no—
81C11×#121C2×C412yes—
82C4×Q8×C11—21no—
83C4×Q8×C11—22no—
84C4×Q8×C11—22no—
85C4×Q8×C11—21no—
86C4×Q8×C11C2×C412yes—
87C4×Q8×C11C2×C412yes—
88C4×Q8×C11C2×C411yescharacteristic
89C4×Q8×C11C2×C411yescharacteristic
90C4×Q8×C11D411yescharacteristic
91C4×Q8×C11C2311yescharacteristic
92C4×Q8×C11C2312yes—
93C4×D4×C11—21no—
94C4×D4×C11—22no—
95C4×D4×C11—21no—
96C4×D4×C11—21no—
97C4×D4×C11—22no—
98C4×D4×C11C2×C411yescharacteristic
99C4×D4×C11C2×C411yescharacteristic
100C4×D4×C11C2×C412yes—
101C4×D4×C11D411yescharacteristic
102C4×D4×C11D412yes—
103C4×D4×C11C2311yescharacteristic
104C11×#117—21no—
105C11×#117—21no—
106C11×#117—22no—
107C11×#117—21no—
108C11×#117—22no—
109C11×#117C2×C411yescharacteristic
110C11×#117D411yescharacteristic
111C11×#117D412yes—
112C2×C11×C4⋊C4—22no—
113C2×C11×C4⋊C4C2×C412yes—
114C2×C42×C11—22no—
115C2×C42×C11—21no—
116C2×C42×C11C2311yescharacteristic
117C2×C42×C11C2312yes—
118C2×#4318—21no—
119C2×#4318—22no—
120C2×#4318—21no—
121C22×C11⋊C8—21no—
122C22⋊(C11⋊C8)—22no—
123C22⋊(C11⋊C8)—22no—
124C22⋊(C11⋊C8)—22no—
125C22⋊(C11⋊C8)—21no—
126C4⋊(C11⋊C8)—21no—
127C4⋊(C11⋊C8)—22no—
128C4⋊(C11⋊C8)—22no—
129C4⋊(C11⋊C8)—22no—
130C4⋊(C11⋊C8)C2311yescharacteristic
131C4⋊(C11⋊C8)C2312yes—
132C4⋊(C11⋊C8)C2311yescharacteristic
133#66867—21no—
134C4×C11⋊C8—21no—
135C4×C11⋊C8—21no—
136C4×C11⋊C8—22no—
137C4×C11⋊C8C2311yescharacteristic
138C4×C11⋊C8C2311yescharacteristic
139C4×C11⋊C8C2312yes—
140#17525—111nomaximal, Sylow
141C11×#41—22no—
142C11×#41—41no—
143C11×#41—42no—
144C11×#41—44no—
145C2×Q8×C11—22no—
146C2×Q8×C11—21no—
147C2×Q8×C11—24no—
148C2×Q8×C11—42no—
149C2×Q8×C11C22⋊C411yescharacteristic
150C2×Q8×C11C22×C412yes—
151C2×Q8×C11C22×C411yescharacteristic
152C2×D4×C11—21no—
153C2×D4×C11—22no—
154C2×D4×C11C22⋊C411yescharacteristic
155C2×D4×C11C22⋊C412yes—
156C2×D4×C11C22×C411yescharacteristic
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11C22×C412yes—
163C22×C4×C11C22×C411yescharacteristic
164C22×C4×C11C2×D412yes—
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D412yes—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—22no—
170C11×C4⋊C4—22no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4C22⋊C411yescharacteristic
182C11×C4⋊C4C22⋊C412yes—
183C11×C4⋊C4C22⋊C411yescharacteristic
184C11×C4⋊C4C22⋊C412yes—
185C11×C4⋊C4C22×C411yescharacteristic
186C11×C4⋊C4C22×C412yes—
187C11×C4⋊C4C22×C411yescharacteristic
188C11×C22⋊C4—22no—
189C11×C22⋊C4—22no—
190C11×C22⋊C4—21no—
191C11×C22⋊C4—22no—
192C11×C22⋊C4—21no—
193C11×C22⋊C4—22no—
194C11×C22⋊C4—22no—
195C11×C22⋊C4—21no—
196C11×C22⋊C4C22⋊C412yes—
197C11×C22⋊C4C22⋊C412yes—
198C11×C22⋊C4C22⋊C412yes—
199C42×C11—21no—
200C42×C11—22no—
201C42×C11—21no—
202C42×C11—22no—
203C42×C11—21no—
204C42×C11—22no—
205C42×C11C22×C411yescharacteristic
206C42×C11C22×C412yes—
207C42×C11C2×D411yescharacteristic
208C42×C11C2×D411yescharacteristic
209C42×C11C2×D412yes—
210C42×C11C2×D412yes—
211C42×C11C2411yescharacteristic
212#4318—42no—
213#4318—82no—
214#4318—81no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—22no—
220C2×C11⋊C8—22no—
221C2×C11⋊C8—42no—
222#3482D1111yescharacteristic
223#2991—111no—
224#2922—111no—
225#1495—112no—
226#1493—111no—
227#1489—111no—
228#1487—112no—
229#1485—111no—
230#1482—112no—
231#1479—112no—
232#1476—111no—
233C23×C11—21no—
234C23×C11C2×C22⋊C411yescharacteristic
235C23×C11C2×C22⋊C412yes—
236Q8×C11—21no—
237Q8×C11—22no—
238Q8×C11—22no—
239Q8×C11—22no—
240Q8×C11—44no—
241Q8×C11—42no—
242Q8×C11#13112yes—
243D4×C11—21no—
244D4×C11—21no—
245D4×C11—22no—
246D4×C11—42no—
247D4×C11—42no—
248D4×C11—44no—
249C2×C4×C11—21no—
250C2×C4×C11—22no—
251C2×C4×C11—21no—
252C2×C4×C11—22no—
253C2×C4×C11—21no—
254C2×C4×C11—22no—
255C2×C4×C11—21no—
256C2×C4×C11—22no—
257C2×C4×C11—21no—
258C2×C4×C11—22no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—42no—
264C2×C4×C11—42no—
265C2×C4×C11—44no—
266C2×C4×C11—44no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—42no—
270C2×C4×C11C2×C22⋊C412yes—
271C2×C4×C11C2×C22⋊C411yescharacteristic
272C2×C4×C11C2×C22⋊C411yescharacteristic
273C2×C4×C11C2×C22⋊C412yes—
274C2×C4×C11C2×C22⋊C412yes—
275C2×C4×C11C2×C22⋊C411yescharacteristic
276C2×C4×C11C23×C411yescharacteristic
277C2×C4×C11C22×D411yescharacteristic
278C2×C4×C11C22×D411yescharacteristic
279C11⋊C8—41no—
280C11⋊C8—41no—
281C11⋊C8—42no—
282C11⋊C8—41no—
283C11⋊C8—42no—
284C11⋊C8—41no—
285#557Dic1111yescharacteristic
286#556—21no—
287#556Dic1111yescharacteristic
288#552—22no—
289#552Dic1112yes—
290D4×Q8Dic1111yescharacteristic
291#548Dic1112yes—
292#547—21no—
293#547Dic1111yescharacteristic
294#533—21no—
295#533C2×D1111yescharacteristic
296#529—22no—
297#529C2×D1112yes—
298C4×#41—21no—
299C4×#41C2×D1111yescharacteristic
300C4×#41C2×D1111yescharacteristic
301C2×C4×Q8C2×D1112yes—
302C8×Q8—221no—
303#436—221no—
304#436—222no—
305#433—222no—
306#431—112no—
307#431—112no—
308#431—111no—
309#431—112no—
310#424—221no—
311#423—112no—
312#423—111no—
313#408—221no—
314C4×M16—111no—
315C2×C4×C8—111no—
316Q8⋊C8—111no—
317Q8⋊C8—111no—
318Q8⋊C8—112no—
319Q8⋊C8—112no—
320Q8⋊C8—112no—
321Q8⋊C8—112no—
322Q8⋊C8—112no—
323D4⋊C8—111no—
324D4⋊C8—111no—
325D4⋊C8—112no—
326C22×C11—22no—
327C22×C11—21no—
328C22×C11—21no—
329C22×C11—22no—
330C22×C11—21no—
331C22×C11—22no—
332C22×C11—41no—
333C22×C11—41no—
334C22×C11—41no—
335C22×C11C22×C22⋊C411yescharacteristic
336C4×C11—21no—
337C4×C11—22no—
338C4×C11—22no—
339C4×C11—22no—
340C4×C11—21no—
341C4×C11—21no—
342C4×C11—22no—
343C4×C11—42no—
344C4×C11—41no—
345C4×C11—41no—
346C4×C11—42no—
347C4×C11#42112yes—
348C4×C11C2×#13111yescharacteristic
349C4×C11#56811yescharacteristic
350C4×C11#57711yescharacteristic
351C4×C11#57811yescharacteristic
352C2×#41—21no—
353C2×#41C2×Dic1111yescharacteristic
354C2×#41C22⋊D1111yescharacteristic
355C22×Q8C2×Dic1112yes—
356C2×M16—221no—
357C2×M16—222no—
358C2×M16—221no—
359C22×C8—221no—
360C4⋊Q8—21no—
361C4⋊Q8—21no—
362C4⋊Q8C2×Dic1111yescharacteristic
363C4⋊Q8C2×Dic1111yescharacteristic
364#126—22no—
365#126—22no—
366#126—22no—
367#125—22no—
368#125—22no—
369#125—21no—
370#125C2×Dic1112yes—
371#124—22no—
372#124C2×Dic1112yes—
373#123—22no—
374#123—22no—
375#123—22no—
376C22⋊Q8—21no—
377C22⋊Q8—21no—
378C22⋊Q8—21no—
379C22⋊Q8—22no—
380C22⋊Q8—22no—
381C22⋊Q8C2×Dic1112yes—
382C22⋊Q8C2×Dic1112yes—
383#121—22no—
384#121C2×Dic1112yes—
385C4×Q8—21no—
386C4×Q8—22no—
387C4×Q8—22no—
388C4×Q8—21no—
389C4×Q8C2×Dic1112yes—
390C4×Q8C2×Dic1112yes—
391C4×Q8C2×Dic1111yescharacteristic
392C4×Q8C2×Dic1111yescharacteristic
393C4×Q8C22⋊D1111yescharacteristic
394C4×Q8C22×D1111yescharacteristic
395C4×Q8C22×D1112yes—
396C4×D4—21no—
397C4×D4—22no—
398C4×D4—21no—
399C4×D4—21no—
400C4×D4—22no—
401C4×D4C2×Dic1111yescharacteristic
402C4×D4C2×Dic1111yescharacteristic
403C4×D4C2×Dic1112yes—
404C4×D4C22⋊D1111yescharacteristic
405C4×D4C22⋊D1112yes—
406C4×D4C22×D1111yescharacteristic
407#117—21no—
408#117—21no—
409#117—22no—
410#117—21no—
411#117—22no—
412#117C2×Dic1111yescharacteristic
413#117C22⋊D1112yes—
414#117C22⋊D1111yescharacteristic
415C2×C4⋊C4—22no—
416C2×C4⋊C4C2×Dic1112yes—
417C2×C42—22no—
418C2×C42—21no—
419C2×C42C22×D1112yes—
420C2×C42C22×D1111yescharacteristic
421C4⋊C8—111no—
422C4⋊C8—112no—
423C4⋊C8—111no—
424C4⋊C8—221no—
425C4⋊C8—222no—
426C4⋊C8—222no—
427C4⋊C8—222no—
428C22⋊C8—222no—
429C22⋊C8—222no—
430C22⋊C8—222no—
431C22⋊C8—221no—
432#97—221no—
433C4×C8—111no—
434C4×C8—111no—
435C4×C8—112no—
436C4×C8—221no—
437C4×C8—221no—
438C4×C8—222no—
439C2×C11—42no—
440C2×C11—41no—
441C2×C11—81no—
442C2×C11#288011yescharacteristic
443C2×C11#289811yescharacteristic
444C2×C11C2×#42111yescharacteristic
445#41—22no—
446#41—41no—
447#41—42no—
448#41—44no—
449C2×Q8—22no—
450C2×Q8—21no—
451C2×Q8—24no—
452C2×Q8—42no—
453C2×Q8C22⋊Dic1111yescharacteristic
454C2×Q8C22×Dic1112yes—
455C2×Q8C22×Dic1111yescharacteristic
456C2×D4—21no—
457C2×D4—22no—
458C2×D4C22⋊Dic1111yescharacteristic
459C2×D4C22⋊Dic1112yes—
460C2×D4C22×Dic1111yescharacteristic
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4C22×Dic1112yes—
467C22×C4C22×Dic1111yescharacteristic
468C22×C4C2×C22⋊D1111yescharacteristic
469C22×C4C2×C22⋊D1112yes—
470C22×C4C2×C22⋊D1111yescharacteristic
471C22×C4C2×C22⋊D1112yes—
472M16—442no—
473M16—882no—
474M16—881no—
475C2×C8—221no—
476C2×C8—221no—
477C2×C8—222no—
478C2×C8—221no—
479C2×C8—221no—
480C2×C8—222no—
481C2×C8—442no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—21no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—22no—
491C4⋊C4—21no—
492C4⋊C4—22no—
493C4⋊C4—21no—
494C4⋊C4—22no—
495C4⋊C4C22⋊Dic1111yescharacteristic
496C4⋊C4C22⋊Dic1112yes—
497C4⋊C4C22⋊Dic1111yescharacteristic
498C4⋊C4C22⋊Dic1112yes—
499C4⋊C4C22×Dic1111yescharacteristic
500C4⋊C4C22×Dic1112yes—
501C4⋊C4C22×Dic1111yescharacteristic
502C22⋊C4—22no—
503C22⋊C4—22no—
504C22⋊C4—21no—
505C22⋊C4—22no—
506C22⋊C4—21no—
507C22⋊C4—22no—
508C22⋊C4—22no—
509C22⋊C4—21no—
510C22⋊C4C22⋊Dic1112yes—
511C22⋊C4C22⋊Dic1112yes—
512C22⋊C4C22⋊Dic1112yes—
513C42—21no—
514C42—22no—
515C42—21no—
516C42—22no—
517C42—21no—
518C42—22no—
519C42C22×Dic1111yescharacteristic
520C42C22×Dic1112yes—
521C42C2×C22⋊D1111yescharacteristic
522C42C2×C22⋊D1112yes—
523C42C2×C22⋊D1111yescharacteristic
524C42C2×C22⋊D1112yes—
525C42C23×D1111yescharacteristic
526C11#1752511yescharacteristic, complemented, Sylow
527C23—21no—
528C23C2×C22⋊Dic1111yescharacteristic
529C23C2×C22⋊Dic1112yes—
530Q8—21no—
531Q8—22no—
532Q8—22no—
533Q8—22no—
534Q8—44no—
535Q8—42no—
536Q8#6700112yes—
537D4—21no—
538D4—21no—
539D4—22no—
540D4—42no—
541D4—42no—
542D4—44no—
543C2×C4—21no—
544C2×C4—22no—
545C2×C4—21no—
546C2×C4—22no—
547C2×C4—21no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—21no—
551C2×C4—22no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—44no—
560C2×C4—44no—
561C2×C4—42no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4C2×C22⋊Dic1112yes—
565C2×C4C2×C22⋊Dic1111yescharacteristic
566C2×C4C2×C22⋊Dic1111yescharacteristic
567C2×C4C2×C22⋊Dic1112yes—
568C2×C4C2×C22⋊Dic1112yes—
569C2×C4C2×C22⋊Dic1111yescharacteristic
570C2×C4C23×Dic1111yescharacteristic
571C2×C4C22×C22⋊D1111yescharacteristic
572C2×C4C22×C22⋊D1111yescharacteristic
573C8—441no—
574C8—441no—
575C8—442no—
576C8—441no—
577C8—442no—
578C8—441no—
579C22—22no—
580C22—21no—
581C22—21no—
582C22—22no—
583C22—21no—
584C22—22no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22C22×C22⋊Dic1111yescharacteristic
589C4—21no—
590C4—22no—
591C4—22no—
592C4—22no—
593C4—21no—
594C4—21no—
595C4—22no—
596C4—42no—
597C4—41no—
598C4—41no—
599C4—42no—
600C4#1062284912yes—
601C4C2×#6700111yescharacteristic
602C4#1062335011yescharacteristic
603C4#1062336811yescharacteristic
604C4#1062336911yescharacteristic
605C2—42no—
606C2—41no—
607C2—81no—
608C2#1307706511yescharacteristic
609C2#1307714911yescharacteristic
610C2C2×#1062284911yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
Fitting, prime radicalC11×#3482C2
socleC22×C11C22×C22⋊C4
cosocleC42×C11C24
hypercenter#3482D11
hypocenterC11#17525
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #3482

Complements

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

NH ≅ G/Ntype
1. #13077748C2semidirect
2. #13077260C2semidirect
3. #13067081C2semidirect
4. #13067071C2semidirect
5. #13067055C2semidirect
6. #13067045C2semidirect
7. #13067037C2semidirect
8. #13067024C2semidirect
9. #13067011C2semidirect
10. #13066998C2semidirect
526. C11#17525semidirect

Maximal subgroups

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

subgroupindex
#130777482
#130772602
#130670812
#130670712
#130670552
#130670452
#130670372
#130670242
#130670112
#130669982
C11×#34822
#1752511