Finite Group Databasebeta

← #14721968

Subgroups — #14721968

Order 2816.

876 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077630C211yesmaximal, characteristic, complemented
2#13077267C211yesmaximal, characteristic, complemented
3#13067254C212yesmaximal, complemented
4#13067247C212yesmaximal, complemented
5#13067236C212yesmaximal, complemented
6#13067231C211yesmaximal, characteristic, complemented
7#13067231C212yesmaximal, complemented
8#13067223C211yesmaximal, characteristic, complemented
9#13067211C211yesmaximal, characteristic, complemented
10#13067204C211yesmaximal, characteristic, complemented
11C11×#3518C211yesmaximal, characteristic
12Q82×C11C411yescharacteristic
13C11×#556—21no—
14C11×#556—22no—
15C11×#556C412yes—
16C11×#556C411yescharacteristic
17C11×#555C412yes—
18C11×#555C411yescharacteristic
19D4×Q8×C11C411yescharacteristic
20C11×#548—21no—
21C11×#542—21no—
22C11×#542—22no—
23C11×#533C2211yescharacteristic
24C11×#533C2212yes—
25C11×#529C2211yescharacteristic
26C11×#529C2212yes—
27C11×#519—21no—
28C4×C11×#41C2211yescharacteristic
29#10622847—21no—
30#10622637—21no—
31#10622624—22no—
32D4×C11⋊C8—21no—
33#10622613—22no—
34#10622612—21no—
35#10622539C2212yes—
36#10622539C2212yes—
37#10622539C2211yescharacteristic
38#10622539C2212yes—
39C4×#4318C2211yescharacteristic
40C4×#4318C2211yescharacteristic
41C2×#66867C2211yescharacteristic
42C2×#66867C2212yes—
43#10622181C2211yescharacteristic
44#10622181C2211yescharacteristic
45#10622181C2212yes—
46#10622181C2212yes—
47#10622181C2212yes—
48#10622181C2212yes—
49#10622181C2212yes—
50#10622178C2211yescharacteristic
51#10622178C2211yescharacteristic
52#10622178C2212yes—
53C2×C11×#41D411yescharacteristic
54C22×Q8×C11—21no—
55C11×C4⋊Q8—22no—
56C11×C4⋊Q8—21no—
57C11×C4⋊Q8C2×C411yescharacteristic
58C11×C4⋊Q8C2×C412yes—
59C11×C4⋊Q8C2×C411yescharacteristic
60C11×C4⋊Q8C2×C412yes—
61C11×#126—22no—
62C11×#126—22no—
63C11×#126—22no—
64C11×#126—21no—
65C11×#126—22no—
66C11×#125C2311yescharacteristic
67C11×#125C2312yes—
68C11×#124—21no—
69C11×#124—22no—
70C11×#124—22no—
71C11×#124—22no—
72C11×#124—22no—
73C11×#124C2311yescharacteristic
74C11×#123—22no—
75C11×#123—21no—
76C11×C22⋊Q8—22no—
77C11×C22⋊Q8—21no—
78C11×C22⋊Q8—21no—
79C11×C22⋊Q8—22no—
80C11×C22⋊Q8—22no—
81C11×C22⋊Q8—21no—
82C11×C22⋊Q8C2×C411yescharacteristic
83C11×C22⋊Q8C2×C412yes—
84C11×#121—21no—
85C11×#121—22no—
86C11×#121C2×C411yescharacteristic
87C11×#121C2×C412yes—
88C4×Q8×C11—21no—
89C4×Q8×C11—22no—
90C4×Q8×C11—21no—
91C4×Q8×C11—21no—
92C4×Q8×C11—22no—
93C4×Q8×C11—21no—
94C4×Q8×C11—22no—
95C4×Q8×C11C2×C411yescharacteristic
96C4×Q8×C11C2×C412yes—
97C4×Q8×C11C2×C411yescharacteristic
98C4×Q8×C11D411yescharacteristic
99C4×D4×C11—21no—
100C4×D4×C11—22no—
101C4×D4×C11C2×C411yescharacteristic
102C4×D4×C11C2×C412yes—
103C4×D4×C11C2×C411yescharacteristic
104C4×D4×C11C2×C412yes—
105C4×D4×C11D411yescharacteristic
106C4×D4×C11D412yes—
107C11×#117—22no—
108C11×#117—21no—
109C11×#117—21no—
110C11×#117—22no—
111C11×#117C2×C412yes—
112C11×#117C2×C412yes—
113C11×#117C2×C412yes—
114C11×#117D411yescharacteristic
115C11×#117D412yes—
116C2×C42×C11C2311yescharacteristic
117C2×C42×C11C2312yes—
118C2×#4318—21no—
119C2×#4318—21no—
120C22×C11⋊C8—21no—
121C22×C11⋊C8—22no—
122C22⋊(C11⋊C8)—22no—
123C22⋊(C11⋊C8)—22no—
124C22⋊(C11⋊C8)—22no—
125C22⋊(C11⋊C8)—21no—
126C4⋊(C11⋊C8)—22no—
127C4⋊(C11⋊C8)—22no—
128C4⋊(C11⋊C8)—21no—
129C4⋊(C11⋊C8)—22no—
130#66867—21no—
131#66867—22no—
132#66867C2311yescharacteristic
133#66867C2311yescharacteristic
134#66867C2311yescharacteristic
135#66867C2312yes—
136#66867C2312yes—
137#66867C2311yescharacteristic
138C4×C11⋊C8—21no—
139C4×C11⋊C8—21no—
140#17683—111nomaximal, Sylow
141C11×#41—42no—
142C2×Q8×C11—22no—
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11—22no—
146C2×Q8×C11—44no—
147C2×Q8×C11C22⋊C411yescharacteristic
148C2×Q8×C11C22×C411yescharacteristic
149C2×D4×C11—21no—
150C2×D4×C11—22no—
151C2×D4×C11C22⋊C411yescharacteristic
152C2×D4×C11C22⋊C412yes—
153C2×D4×C11C22×C411yescharacteristic
154C22×C4×C11—22no—
155C22×C4×C11—21no—
156C22×C4×C11C22×C411yescharacteristic
157C22×C4×C11C22×C412yes—
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D412yes—
160C22×C4×C11C2×D412yes—
161C22×C4×C11C2×D411yescharacteristic
162C11×C4⋊C4—22no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—22no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—22no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4C22⋊C412yes—
175C11×C4⋊C4C22⋊C411yescharacteristic
176C11×C4⋊C4C22⋊C412yes—
177C11×C4⋊C4C22⋊C411yescharacteristic
178C11×C4⋊C4C22×C412yes—
179C11×C4⋊C4C22×C411yescharacteristic
180C11×C4⋊C4C22×C412yes—
181C11×C4⋊C4C22×C411yescharacteristic
182C11×C22⋊C4—22no—
183C11×C22⋊C4—22no—
184C11×C22⋊C4—22no—
185C11×C22⋊C4—21no—
186C11×C22⋊C4—22no—
187C11×C22⋊C4—21no—
188C11×C22⋊C4—22no—
189C11×C22⋊C4—21no—
190C11×C22⋊C4—22no—
191C11×C22⋊C4—21no—
192C11×C22⋊C4—21no—
193C11×C22⋊C4C22⋊C412yes—
194C11×C22⋊C4C22⋊C412yes—
195C11×C22⋊C4C22⋊C412yes—
196C42×C11—22no—
197C42×C11—22no—
198C42×C11—22no—
199C42×C11—22no—
200C42×C11—21no—
201C42×C11C22×C412yes—
202C42×C11C22×C411yescharacteristic
203C42×C11C2×D411yescharacteristic
204C42×C11C2×D411yescharacteristic
205C42×C11C2×D412yes—
206C42×C11C2×D412yes—
207C42×C11C2411yescharacteristic
208#4318—42no—
209#4318—42no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—22no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—22no—
216C2×C11⋊C8—42no—
217C2×C11⋊C8—44no—
218#3518D1111yescharacteristic
219#2970—111no—
220#2923—111no—
221#1537—112no—
222#1535—112no—
223#1532—112no—
224#1531—112no—
225#1531—111no—
226#1529—111no—
227#1526—111no—
228#1524—111no—
229C23×C11—21no—
230C23×C11C2×C22⋊C411yescharacteristic
231C23×C11C2×C22⋊C412yes—
232Q8×C11—22no—
233Q8×C11—41no—
234Q8×C11—44no—
235Q8×C11—42no—
236Q8×C11—82no—
237Q8×C11—81no—
238D4×C11—22no—
239D4×C11—42no—
240D4×C11—41no—
241D4×C11—82no—
242D4×C11—81no—
243C2×C4×C11—22no—
244C2×C4×C11—21no—
245C2×C4×C11—22no—
246C2×C4×C11—21no—
247C2×C4×C11—22no—
248C2×C4×C11—21no—
249C2×C4×C11—42no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—42no—
253C2×C4×C11—42no—
254C2×C4×C11—44no—
255C2×C4×C11—42no—
256C2×C4×C11C2×C22⋊C411yescharacteristic
257C2×C4×C11C2×C22⋊C412yes—
258C2×C4×C11C2×C22⋊C412yes—
259C2×C4×C11C2×C22⋊C411yescharacteristic
260C2×C4×C11C2×C22⋊C412yes—
261C2×C4×C11C2×C22⋊C411yescharacteristic
262C2×C4×C11C23×C411yescharacteristic
263C2×C4×C11C22×D411yescharacteristic
264C2×C4×C11C22×D411yescharacteristic
265C11⋊C8—22no—
266C11⋊C8—41no—
267C11⋊C8—41no—
268C11⋊C8—42no—
269C11⋊C8—42no—
270C11⋊C8—41no—
271Q82Dic1111yescharacteristic
272#556—21no—
273#556—22no—
274#556Dic1111yescharacteristic
275#556Dic1112yes—
276#555Dic1111yescharacteristic
277#555Dic1112yes—
278D4×Q8Dic1111yescharacteristic
279#548—21no—
280#542—21no—
281#542—22no—
282#533C2×D1112yes—
283#533C2×D1111yescharacteristic
284#529C2×D1111yescharacteristic
285#529C2×D1112yes—
286#519—21no—
287C4×#41C2×D1111yescharacteristic
288#446—221no—
289#435—222no—
290C8×D4—221no—
291#433—222no—
292#432—112no—
293#432—112no—
294#432—112no—
295#432—111no—
296#424—221no—
297#408—221no—
298C4×M16—111no—
299C4×M16—111no—
300C2×#97—111no—
301C2×#97—112no—
302#330—111no—
303#330—112no—
304#330—112no—
305#330—112no—
306#330—111no—
307#330—112no—
308#330—112no—
309#329—111no—
310#329—111no—
311#329—112no—
312C22×C11—21no—
313C22×C11—22no—
314C22×C11—21no—
315C22×C11—22no—
316C22×C11—22no—
317C22×C11—21no—
318C22×C11—41no—
319C22×C11—41no—
320C22×C11—41no—
321C22×C11C22×C22⋊C411yescharacteristic
322C4×C11—21no—
323C4×C11—21no—
324C4×C11—22no—
325C4×C11—21no—
326C4×C11—22no—
327C4×C11—21no—
328C4×C11—22no—
329C4×C11—21no—
330C4×C11—41no—
331C4×C11—42no—
332C4×C11—41no—
333C4×C11—42no—
334C4×C11—41no—
335C4×C11#42112yes—
336C2×#41C22⋊D1111yescharacteristic
337C22×Q8—21no—
338C2×M16—221no—
339C2×M16—221no—
340C22×C8—221no—
341C22×C8—222no—
342C4⋊Q8—22no—
343C4⋊Q8—21no—
344C4⋊Q8C2×Dic1112yes—
345C4⋊Q8C2×Dic1111yescharacteristic
346C4⋊Q8C2×Dic1112yes—
347C4⋊Q8C2×Dic1111yescharacteristic
348#126—22no—
349#126—22no—
350#126—22no—
351#126—21no—
352#126—22no—
353#125C22×D1111yescharacteristic
354#125C22×D1112yes—
355#124—21no—
356#124—22no—
357#124—22no—
358#124—22no—
359#124—22no—
360#124C22×D1111yescharacteristic
361#123—22no—
362#123—21no—
363C22⋊Q8—22no—
364C22⋊Q8—21no—
365C22⋊Q8—21no—
366C22⋊Q8—22no—
367C22⋊Q8—22no—
368C22⋊Q8—21no—
369C22⋊Q8C2×Dic1111yescharacteristic
370C22⋊Q8C2×Dic1112yes—
371#121—21no—
372#121—22no—
373#121C2×Dic1111yescharacteristic
374#121C2×Dic1112yes—
375C4×Q8—21no—
376C4×Q8—22no—
377C4×Q8—21no—
378C4×Q8—21no—
379C4×Q8—22no—
380C4×Q8—21no—
381C4×Q8—22no—
382C4×Q8C2×Dic1111yescharacteristic
383C4×Q8C2×Dic1112yes—
384C4×Q8C2×Dic1111yescharacteristic
385C4×Q8C22⋊D1111yescharacteristic
386C4×D4—21no—
387C4×D4—22no—
388C4×D4C2×Dic1111yescharacteristic
389C4×D4C2×Dic1112yes—
390C4×D4C2×Dic1111yescharacteristic
391C4×D4C2×Dic1112yes—
392C4×D4C22⋊D1111yescharacteristic
393C4×D4C22⋊D1112yes—
394#117—22no—
395#117—21no—
396#117—21no—
397#117—22no—
398#117C2×Dic1112yes—
399#117C2×Dic1112yes—
400#117C2×Dic1112yes—
401#117C22⋊D1111yescharacteristic
402#117C22⋊D1112yes—
403C2×C42C22×D1111yescharacteristic
404C2×C42C22×D1112yes—
405C4⋊C8—222no—
406C4⋊C8—222no—
407C4⋊C8—221no—
408C4⋊C8—222no—
409C22⋊C8—222no—
410C22⋊C8—222no—
411C22⋊C8—222no—
412C22⋊C8—221no—
413#97—111no—
414#97—111no—
415#97—111no—
416#97—112no—
417#97—111no—
418#97—112no—
419#97—221no—
420#97—222no—
421C4×C8—221no—
422C4×C8—221no—
423C2×C11—41no—
424C2×C11—42no—
425C2×C11—81no—
426C2×C11#288911yescharacteristic
427C2×C11C2×#42111yescharacteristic
428C2×C11#290111yescharacteristic
429#41—42no—
430C2×Q8—22no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—22no—
434C2×Q8—44no—
435C2×Q8C22⋊Dic1111yescharacteristic
436C2×Q8C22×Dic1111yescharacteristic
437C2×D4—21no—
438C2×D4—22no—
439C2×D4C22⋊Dic1111yescharacteristic
440C2×D4C22⋊Dic1112yes—
441C2×D4C22×Dic1111yescharacteristic
442C22×C4—22no—
443C22×C4—21no—
444C22×C4C22×Dic1111yescharacteristic
445C22×C4C22×Dic1112yes—
446C22×C4C2×C22⋊D1111yescharacteristic
447C22×C4C2×C22⋊D1112yes—
448C22×C4C2×C22⋊D1112yes—
449C22×C4C2×C22⋊D1111yescharacteristic
450M16—442no—
451M16—442no—
452C2×C8—221no—
453C2×C8—222no—
454C2×C8—221no—
455C2×C8—221no—
456C2×C8—221no—
457C2×C8—222no—
458C2×C8—444no—
459C2×C8—442no—
460C4⋊C4—22no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—22no—
464C4⋊C4—21no—
465C4⋊C4—22no—
466C4⋊C4—21no—
467C4⋊C4—22no—
468C4⋊C4—21no—
469C4⋊C4—22no—
470C4⋊C4—21no—
471C4⋊C4—22no—
472C4⋊C4C22⋊Dic1112yes—
473C4⋊C4C22⋊Dic1111yescharacteristic
474C4⋊C4C22⋊Dic1112yes—
475C4⋊C4C22⋊Dic1111yescharacteristic
476C4⋊C4C22×Dic1111yescharacteristic
477C4⋊C4C22×Dic1112yes—
478C4⋊C4C22×Dic1111yescharacteristic
479C4⋊C4C22×Dic1112yes—
480C22⋊C4—22no—
481C22⋊C4—22no—
482C22⋊C4—22no—
483C22⋊C4—21no—
484C22⋊C4—22no—
485C22⋊C4—21no—
486C22⋊C4—22no—
487C22⋊C4—21no—
488C22⋊C4—22no—
489C22⋊C4—21no—
490C22⋊C4—21no—
491C22⋊C4C22⋊Dic1112yes—
492C22⋊C4C22⋊Dic1112yes—
493C22⋊C4C22⋊Dic1112yes—
494C42—22no—
495C42—22no—
496C42—22no—
497C42—22no—
498C42—21no—
499C42C22×Dic1112yes—
500C42C22×Dic1111yescharacteristic
501C42C2×C22⋊D1111yescharacteristic
502C42C2×C22⋊D1111yescharacteristic
503C42C2×C22⋊D1112yes—
504C42C2×C22⋊D1112yes—
505C42C23×D1111yescharacteristic
506C11#1768311yescharacteristic, complemented, Sylow
507C23—21no—
508C23C2×C22⋊Dic1111yescharacteristic
509C23C2×C22⋊Dic1112yes—
510Q8—22no—
511Q8—41no—
512Q8—44no—
513Q8—42no—
514Q8—82no—
515Q8—81no—
516D4—22no—
517D4—42no—
518D4—41no—
519D4—82no—
520D4—81no—
521C2×C4—22no—
522C2×C4—21no—
523C2×C4—22no—
524C2×C4—21no—
525C2×C4—22no—
526C2×C4—21no—
527C2×C4—42no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—44no—
533C2×C4—42no—
534C2×C4C2×C22⋊Dic1111yescharacteristic
535C2×C4C2×C22⋊Dic1112yes—
536C2×C4C2×C22⋊Dic1112yes—
537C2×C4C2×C22⋊Dic1111yescharacteristic
538C2×C4C2×C22⋊Dic1112yes—
539C2×C4C2×C22⋊Dic1111yescharacteristic
540C2×C4C23×Dic1111yescharacteristic
541C2×C4C22×C22⋊D1111yescharacteristic
542C2×C4C22×C22⋊D1111yescharacteristic
543C8—222no—
544C8—441no—
545C8—441no—
546C8—442no—
547C8—442no—
548C8—441no—
549C22—21no—
550C22—22no—
551C22—21no—
552C22—22no—
553C22—22no—
554C22—21no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22C22×C22⋊Dic1111yescharacteristic
559C4—21no—
560C4—21no—
561C4—22no—
562C4—21no—
563C4—22no—
564C4—21no—
565C4—22no—
566C4—21no—
567C4—41no—
568C4—42no—
569C4—41no—
570C4—42no—
571C4—41no—
572C4#1062284912yes—
573C2—41no—
574C2—42no—
575C2—81no—
576C2#1307709911yescharacteristic
577C2C2×#1062284911yescharacteristic
578C2#1307716311yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
Fitting, prime radicalC11×#3518C2
socleC22×C11C22×C22⋊C4
cosocleC42×C11C24
hypercenter#3518D11
hypocenterC11#17683
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3518

Complements

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

NH ≅ G/Ntype
1. #13077630C2semidirect
2. #13077267C2semidirect
3. #13067254C2semidirect
4. #13067247C2semidirect
5. #13067236C2semidirect
6. #13067231C2semidirect
7. #13067231C2semidirect
8. #13067223C2semidirect
9. #13067211C2semidirect
10. #13067204C2semidirect
506. C11#17683semidirect

Maximal subgroups

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

subgroupindex
#130776302
#130772672
#130672542
#130672472
#130672362
#130672312
#130672232
#130672112
#130672042
C11×#35182
#1768311