Finite Group Databasebeta

← #14721957

Subgroups — #14721957

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#13077636C211yesmaximal, characteristic, complemented
2#13077267C211yesmaximal, characteristic, complemented
3#13067247C212yesmaximal, complemented
4#13067243C212yesmaximal, complemented
5#13067231C211yesmaximal, characteristic, complemented
6#13067223C211yesmaximal, characteristic, complemented
7#13067223C212yesmaximal, complemented
8#13067218C212yesmaximal, complemented
9#13067211C211yesmaximal, characteristic, complemented
10#13067204C211yesmaximal, characteristic, complemented
11C11×#3515C211yesmaximal, characteristic
12C11×#557C411yescharacteristic
13C11×#554C411yescharacteristic
14C11×#554C411yescharacteristic
15C11×#553C412yes—
16C11×#552—22no—
17C11×#552—21no—
18C11×#552C412yes—
19C11×#547—21no—
20C11×#547C411yescharacteristic
21C11×#541—21no—
22C11×#539—22no—
23C11×#533C2211yescharacteristic
24C11×#529C2211yescharacteristic
25C11×#529C2212yes—
26C2×C11×#125C2212yes—
27C11×#520—21no—
28C4×C11×#41C2211yescharacteristic
29#10622847—21no—
30Q8×C11⋊C8—21no—
31#10622625—21no—
32#10622625—22no—
33#10622613—22no—
34#10622612—21no—
35#10622539C2212yes—
36#10622539C2212yes—
37#10622539C2211yescharacteristic
38#10622539C2212yes—
39C4×#4318C2211yescharacteristic
40C4×#4318C2211yescharacteristic
41C4×#4318C2212yes—
42C2×#66867C2211yescharacteristic
43#10622181C2211yescharacteristic
44#10622181C2211yescharacteristic
45#10622181C2212yes—
46#10622181C2212yes—
47#10622181C2212yes—
48#10622181C2212yes—
49#10622181C2212yes—
50#10622178C2211yescharacteristic
51#10622178C2211yescharacteristic
52#10622178C2212yes—
53C2×C11×#41—21no—
54C2×C11×#41D411yescharacteristic
55C11×C4⋊Q8—21no—
56C11×C4⋊Q8C2×C411yescharacteristic
57C11×C4⋊Q8C2×C411yescharacteristic
58C11×#126—22no—
59C11×#126—22no—
60C11×#126—22no—
61C11×#126—21no—
62C11×#125—22no—
63C11×#125—22no—
64C11×#125—21no—
65C11×#125—22no—
66C11×#125—22no—
67C11×#125C2×C412yes—
68C11×#125C2×C412yes—
69C11×#125C2311yescharacteristic
70C11×#125C2312yes—
71C11×#124C2311yescharacteristic
72C11×#123—22no—
73C11×#123—21no—
74C11×#123—22no—
75C11×#123—22no—
76C11×#123—22no—
77C11×C22⋊Q8—21no—
78C11×C22⋊Q8—21no—
79C11×C22⋊Q8—21no—
80C11×C22⋊Q8—22no—
81C11×C22⋊Q8—21no—
82C11×C22⋊Q8—22no—
83C11×C22⋊Q8C2×C411yescharacteristic
84C11×C22⋊Q8C2×C412yes—
85C11×#121—22no—
86C11×#121C2×C412yes—
87C11×#121C2×C411yescharacteristic
88C4×Q8×C11—21no—
89C4×Q8×C11—21no—
90C4×Q8×C11—21no—
91C4×Q8×C11C2×C412yes—
92C4×Q8×C11C2×C411yescharacteristic
93C4×Q8×C11C2×C411yescharacteristic
94C4×Q8×C11D411yescharacteristic
95C4×D4×C11—21no—
96C4×D4×C11—22no—
97C4×D4×C11—21no—
98C4×D4×C11—22no—
99C4×D4×C11C2×C411yescharacteristic
100C4×D4×C11C2×C412yes—
101C4×D4×C11C2×C411yescharacteristic
102C4×D4×C11C2×C412yes—
103C4×D4×C11D411yescharacteristic
104C4×D4×C11D412yes—
105C11×#117—22no—
106C11×#117—21no—
107C11×#117—22no—
108C11×#117C2×C412yes—
109C11×#117D411yescharacteristic
110C11×#117D412yes—
111C2×C11×C4⋊C4—22no—
112C2×C11×C4⋊C4—22no—
113C2×C11×C4⋊C4—21no—
114C2×C11×C4⋊C4C2×C412yes—
115C2×C11×C4⋊C4C2×C412yes—
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)—22no—
127C4⋊(C11⋊C8)—22no—
128C4⋊(C11⋊C8)—21no—
129C4⋊(C11⋊C8)—22no—
130#66867—21no—
131#66867C2311yescharacteristic
132#66867C2311yescharacteristic
133#66867C2311yescharacteristic
134#66867C2312yes—
135#66867C2311yescharacteristic
136#66867C2312yes—
137C4×C11⋊C8—21no—
138C4×C11⋊C8—21no—
139C4×C11⋊C8—22no—
140#17682—111nomaximal, Sylow
141C11×#41—42no—
142C11×#41—44no—
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11C22⋊C411yescharacteristic
146C2×Q8×C11C22×C411yescharacteristic
147C2×D4×C11—22no—
148C2×D4×C11—21no—
149C2×D4×C11C22⋊C411yescharacteristic
150C2×D4×C11C22⋊C412yes—
151C2×D4×C11C22×C411yescharacteristic
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—21no—
155C22×C4×C11—22no—
156C22×C4×C11C22×C412yes—
157C22×C4×C11C22×C411yescharacteristic
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—22no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—22no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4C22⋊C411yescharacteristic
179C11×C4⋊C4C22⋊C411yescharacteristic
180C11×C4⋊C4C22⋊C412yes—
181C11×C4⋊C4C22⋊C412yes—
182C11×C4⋊C4C22×C411yescharacteristic
183C11×C4⋊C4C22×C411yescharacteristic
184C11×C4⋊C4C22×C412yes—
185C11×C4⋊C4C22×C412yes—
186C11×C22⋊C4—22no—
187C11×C22⋊C4—22no—
188C11×C22⋊C4—21no—
189C11×C22⋊C4—21no—
190C11×C22⋊C4—22no—
191C11×C22⋊C4—22no—
192C11×C22⋊C4—21no—
193C11×C22⋊C4—21no—
194C11×C22⋊C4—21no—
195C11×C22⋊C4C22⋊C412yes—
196C11×C22⋊C4C22⋊C412yes—
197C11×C22⋊C4C22⋊C412yes—
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—44no—
210#4318—42no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—22no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—22no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—42no—
218#3515D1111yescharacteristic
219#2971—111no—
220#2923—111no—
221#1535—112no—
222#1534—112no—
223#1531—111no—
224#1529—111no—
225#1529—112no—
226#1528—112no—
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—42no—
235Q8×C11—81no—
236D4×C11—22no—
237D4×C11—42no—
238D4×C11—41no—
239D4×C11—44no—
240D4×C11—81no—
241C2×C4×C11—22no—
242C2×C4×C11—21no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—42no—
248C2×C4×C11—41no—
249C2×C4×C11—42no—
250C2×C4×C11—41no—
251C2×C4×C11—42no—
252C2×C4×C11—44no—
253C2×C4×C11—42no—
254C2×C4×C11—82no—
255C2×C4×C11—82no—
256C2×C4×C11C2×C22⋊C411yescharacteristic
257C2×C4×C11C2×C22⋊C412yes—
258C2×C4×C11C2×C22⋊C411yescharacteristic
259C2×C4×C11C2×C22⋊C412yes—
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—41no—
270C11⋊C8—42no—
271#557Dic1111yescharacteristic
272#554Dic1111yescharacteristic
273#554Dic1111yescharacteristic
274#553Dic1112yes—
275#552—22no—
276#552—21no—
277#552Dic1112yes—
278#547—21no—
279#547Dic1111yescharacteristic
280#541—21no—
281#539—22no—
282#533C2×D1111yescharacteristic
283#529C2×D1111yescharacteristic
284#529C2×D1112yes—
285C2×#125C2×D1112yes—
286#520—21no—
287C4×#41C2×D1111yescharacteristic
288C8×Q8—221no—
289#436—221no—
290#436—222no—
291#433—222no—
292#432—112no—
293#432—112no—
294#432—111no—
295#432—112no—
296#424—221no—
297#408—221no—
298C4×M16—111no—
299C4×M16—111no—
300C4×M16—112no—
301C2×#97—111no—
302#330—111no—
303#330—111no—
304#330—112no—
305#330—112no—
306#330—112no—
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—41no—
332C4×C11—42no—
333C4×C11—41no—
334C4×C11—42no—
335C4×C11#42112yes—
336C2×#41—21no—
337C2×#41C22⋊D1111yescharacteristic
338C2×M16—221no—
339C2×M16—222no—
340C2×M16—221no—
341C22×C8—221no—
342C4⋊Q8—21no—
343C4⋊Q8C2×Dic1111yescharacteristic
344C4⋊Q8C2×Dic1111yescharacteristic
345#126—22no—
346#126—22no—
347#126—22no—
348#126—21no—
349#125—22no—
350#125—22no—
351#125—21no—
352#125—22no—
353#125—22no—
354#125C2×Dic1112yes—
355#125C2×Dic1112yes—
356#125C22×D1111yescharacteristic
357#125C22×D1112yes—
358#124C22×D1111yescharacteristic
359#123—22no—
360#123—21no—
361#123—22no—
362#123—22no—
363#123—22no—
364C22⋊Q8—21no—
365C22⋊Q8—21no—
366C22⋊Q8—21no—
367C22⋊Q8—22no—
368C22⋊Q8—21no—
369C22⋊Q8—22no—
370C22⋊Q8C2×Dic1111yescharacteristic
371C22⋊Q8C2×Dic1112yes—
372#121—22no—
373#121C2×Dic1112yes—
374#121C2×Dic1111yescharacteristic
375C4×Q8—21no—
376C4×Q8—21no—
377C4×Q8—21no—
378C4×Q8C2×Dic1112yes—
379C4×Q8C2×Dic1111yescharacteristic
380C4×Q8C2×Dic1111yescharacteristic
381C4×Q8C22⋊D1111yescharacteristic
382C4×D4—21no—
383C4×D4—22no—
384C4×D4—21no—
385C4×D4—22no—
386C4×D4C2×Dic1111yescharacteristic
387C4×D4C2×Dic1112yes—
388C4×D4C2×Dic1111yescharacteristic
389C4×D4C2×Dic1112yes—
390C4×D4C22⋊D1111yescharacteristic
391C4×D4C22⋊D1112yes—
392#117—22no—
393#117—21no—
394#117—22no—
395#117C2×Dic1112yes—
396#117C22⋊D1111yescharacteristic
397#117C22⋊D1112yes—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4C2×Dic1112yes—
402C2×C4⋊C4C2×Dic1112yes—
403C2×C42C22×D1112yes—
404C2×C42C22×D1111yescharacteristic
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—111no—
417#97—112no—
418#97—112no—
419#97—221no—
420C4×C8—221no—
421C4×C8—221no—
422C4×C8—222no—
423C2×C11—41no—
424C2×C11—42no—
425C2×C11—81no—
426C2×C11#288911yescharacteristic
427C2×C11C2×#42111yescharacteristic
428C2×C11#290111yescharacteristic
429#41—42no—
430#41—44no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8C22⋊Dic1111yescharacteristic
434C2×Q8C22×Dic1111yescharacteristic
435C2×D4—22no—
436C2×D4—21no—
437C2×D4C22⋊Dic1111yescharacteristic
438C2×D4C22⋊Dic1112yes—
439C2×D4C22×Dic1111yescharacteristic
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4C22×Dic1112yes—
445C22×C4C22×Dic1111yescharacteristic
446C22×C4C2×C22⋊D1111yescharacteristic
447C22×C4C2×C22⋊D1112yes—
448C22×C4C2×C22⋊D1112yes—
449C22×C4C2×C22⋊D1111yescharacteristic
450M16—444no—
451M16—442no—
452M16—442no—
453C2×C8—221no—
454C2×C8—222no—
455C2×C8—221no—
456C2×C8—222no—
457C2×C8—221no—
458C2×C8—221no—
459C2×C8—442no—
460C4⋊C4—22no—
461C4⋊C4—21no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4—22no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—21no—
468C4⋊C4—22no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—22no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4C22⋊Dic1111yescharacteristic
477C4⋊C4C22⋊Dic1111yescharacteristic
478C4⋊C4C22⋊Dic1112yes—
479C4⋊C4C22⋊Dic1112yes—
480C4⋊C4C22×Dic1111yescharacteristic
481C4⋊C4C22×Dic1111yescharacteristic
482C4⋊C4C22×Dic1112yes—
483C4⋊C4C22×Dic1112yes—
484C22⋊C4—22no—
485C22⋊C4—22no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—22no—
489C22⋊C4—22no—
490C22⋊C4—21no—
491C22⋊C4—21no—
492C22⋊C4—21no—
493C22⋊C4C22⋊Dic1112yes—
494C22⋊C4C22⋊Dic1112yes—
495C22⋊C4C22⋊Dic1112yes—
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#1768211yescharacteristic, complemented, Sylow
507C23—21no—
508C23C2×C22⋊Dic1111yescharacteristic
509C23C2×C22⋊Dic1112yes—
510Q8—22no—
511Q8—41no—
512Q8—42no—
513Q8—81no—
514D4—22no—
515D4—42no—
516D4—41no—
517D4—44no—
518D4—81no—
519C2×C4—22no—
520C2×C4—21no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—42no—
526C2×C4—41no—
527C2×C4—42no—
528C2×C4—41no—
529C2×C4—42no—
530C2×C4—44no—
531C2×C4—42no—
532C2×C4—82no—
533C2×C4—82no—
534C2×C4C2×C22⋊Dic1111yescharacteristic
535C2×C4C2×C22⋊Dic1112yes—
536C2×C4C2×C22⋊Dic1111yescharacteristic
537C2×C4C2×C22⋊Dic1112yes—
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—441no—
548C8—442no—
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—41no—
569C4—42no—
570C4—41no—
571C4—42no—
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×#3515C2
socleC22×C11C22×C22⋊C4
cosocleC42×C11C24
hypercenter#3515D11
hypocenterC11#17682
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3515

Complements

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

NH ≅ G/Ntype
1. #13077636C2semidirect
2. #13077267C2semidirect
3. #13067247C2semidirect
4. #13067243C2semidirect
5. #13067231C2semidirect
6. #13067223C2semidirect
7. #13067223C2semidirect
8. #13067218C2semidirect
9. #13067211C2semidirect
10. #13067204C2semidirect
506. C11#17682semidirect

Maximal subgroups

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

subgroupindex
#130776362
#130772672
#130672472
#130672432
#130672312
#130672232
#130672182
#130672112
#130672042
C11×#35152
#1768211