Finite Group Databasebeta

← #14722040

Subgroups — #14722040

Order 2816.

900 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077636C211yesmaximal, characteristic, complemented
2#13077630C211yesmaximal, characteristic, complemented
3#13067254C211yesmaximal, characteristic, complemented
4#13067247C212yesmaximal, complemented
5#13067236C212yesmaximal, complemented
6#13067223C212yesmaximal, complemented
7#13067214C211yesmaximal, characteristic, complemented
8#13067214C211yesmaximal, characteristic, complemented
9#13067211C211yesmaximal, characteristic, complemented
10#13067204C212yesmaximal, complemented
11C11×#3510C211yesmaximal, characteristic
12C11×#559—21no—
13C11×#559—21no—
14C11×#556—21no—
15C11×#556—21no—
16C11×#551—22no—
17C11×#551—22no—
18C11×#542C412yes—
19C11×#542C412yes—
20C11×#536C411yescharacteristic
21C11×#535C411yescharacteristic
22C11×#533C2211yescharacteristic
23C11×#529C2212yes—
24C11×#529C2212yes—
25C2×C11×#124C2211yescharacteristic
26C11×#519C411yescharacteristic
27C11×#518C411yescharacteristic
28C4×C11×#41C2211yescharacteristic
29#10622637—21no—
30Q8×C11⋊C8—21no—
31#10622625—21no—
32#10622625—22no—
33#10622624—22no—
34D4×C11⋊C8—21no—
35#10622539C2211yescharacteristic
36#10622539C2211yescharacteristic
37#10622539C2212yescomplemented
38#10622539C2212yescomplemented
39C4×#4318C2211yescharacteristic
40C4×#4318C2211yescharacteristic
41C4×#4318C2212yescomplemented
42C2×#66867C2212yescomplemented
43#10622181C2211yescharacteristic, complemented
44#10622181C2212yescomplemented
45#10622181C2211yescharacteristic, complemented
46#10622181C2211yescharacteristic, complemented
47#10622181C2211yescharacteristic, complemented
48#10622181C2212yescomplemented
49#10622178C2212yes—
50#10622178C2212yes—
51#10622178C2212yes—
52#10622178C2212yes—
53C2×C11×#41C2×C411yescharacteristic
54C22×Q8×C11C2×C411yescharacteristic
55C22×D4×C11C2×C411yescharacteristic
56C11×C4⋊Q8—21no—
57C11×C4⋊Q8C2×C411yescharacteristic
58C11×C4⋊Q8C2×C411yescharacteristic
59C11×#127—21no—
60C11×#126—22no—
61C11×#126—22no—
62C11×#126—22no—
63C11×#126—22no—
64C11×#125C2311yescharacteristic
65C11×#125C2311yescharacteristic
66C11×#124—21no—
67C11×#124—21no—
68C11×#124—22no—
69C11×#124—22no—
70C11×#124—21no—
71C11×#124—21no—
72C11×#124C2×C412yes—
73C11×#124C2312yes—
74C11×#123—22no—
75C11×#123—22no—
76C11×#123—22no—
77C11×#123—22no—
78C11×#123—22no—
79C11×C22⋊Q8—21no—
80C11×C22⋊Q8—21no—
81C11×C22⋊Q8—22no—
82C11×C22⋊Q8—22no—
83C11×C22⋊Q8C2×C412yes—
84C11×C22⋊Q8C2×C412yes—
85C11×#121C2×C412yes—
86C11×#121C2×C412yes—
87C11×#120—22no—
88C4×Q8×C11—21no—
89C4×Q8×C11—21no—
90C4×Q8×C11—21no—
91C4×Q8×C11—21no—
92C4×Q8×C11C2×C412yes—
93C4×Q8×C11C2×C412yes—
94C4×Q8×C11D411yescharacteristic
95C4×Q8×C11D411yescharacteristic
96C4×D4×C11—22no—
97C4×D4×C11—22no—
98C4×D4×C11—21no—
99C4×D4×C11—21no—
100C4×D4×C11C2×C412yes—
101C4×D4×C11C2×C412yes—
102C4×D4×C11D411yescharacteristic
103C4×D4×C11D412yes—
104C4×D4×C11D412yes—
105C4×D4×C11D411yescharacteristic
106C11×#117—22no—
107C11×#117—22no—
108C11×#117—22no—
109C11×#117C2×C411yescharacteristic
110C11×#117C2×C411yescharacteristic
111C11×#117C2×C411yescharacteristic
112C11×#117C2×C412yes—
113C2×C11×C22⋊C4—21no—
114C2×C11×C22⋊C4—21no—
115C2×C11×C22⋊C4—22no—
116C2×C42×C11C2312yes—
117C2×C42×C11C2311yescharacteristic
118C2×#4318—21no—
119C2×#4318—21no—
120C2×#4318—22no—
121C22×C11⋊C8—22no—
122C22⋊(C11⋊C8)—21no—
123C22⋊(C11⋊C8)—21no—
124C22⋊(C11⋊C8)—22no—
125C22⋊(C11⋊C8)—22no—
126C4⋊(C11⋊C8)—21no—
127C4⋊(C11⋊C8)—21no—
128C4⋊(C11⋊C8)—22no—
129C4⋊(C11⋊C8)—22no—
130#66867—22no—
131#66867C2311yescharacteristic
132#66867C2312yes—
133#66867C2311yescharacteristic
134#66867C2311yescharacteristic
135#66867C2311yescharacteristic
136#66867C2312yes—
137C4×C11⋊C8—21no—
138C4×C11⋊C8—21no—
139C4×C11⋊C8—22no—
140#17691—111nomaximal, Sylow
141C24×C11—21no—
142C11×#41—42no—
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11—21no—
146C2×Q8×C11—42no—
147C2×Q8×C11C22⋊C411yescharacteristic
148C2×Q8×C11C22×C412yes—
149C2×D4×C11—22no—
150C2×D4×C11—22no—
151C2×D4×C11—21no—
152C2×D4×C11—42no—
153C2×D4×C11C22⋊C411yescharacteristic
154C2×D4×C11C22⋊C412yes—
155C2×D4×C11C22×C412yes—
156C22×C4×C11—21no—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11C22×C411yescharacteristic
160C22×C4×C11C22×C412yes—
161C22×C4×C11C2×D412yes—
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D412yes—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4C22⋊C411yescharacteristic
176C11×C4⋊C4C22⋊C411yescharacteristic
177C11×C4⋊C4C22⋊C412yes—
178C11×C4⋊C4C22⋊C412yes—
179C11×C4⋊C4C22×C411yescharacteristic
180C11×C4⋊C4C22×C411yescharacteristic
181C11×C4⋊C4C22×C411yescharacteristic
182C11×C4⋊C4C22×C411yescharacteristic
183C11×C22⋊C4—21no—
184C11×C22⋊C4—21no—
185C11×C22⋊C4—22no—
186C11×C22⋊C4—22no—
187C11×C22⋊C4—22no—
188C11×C22⋊C4—22no—
189C11×C22⋊C4—22no—
190C11×C22⋊C4—22no—
191C11×C22⋊C4—22no—
192C11×C22⋊C4—22no—
193C11×C22⋊C4—22no—
194C11×C22⋊C4—22no—
195C11×C22⋊C4C22⋊C412yes—
196C11×C22⋊C4C22⋊C412yes—
197C11×C22⋊C4C22⋊C412yes—
198C42×C11—22no—
199C42×C11—22no—
200C42×C11—21no—
201C42×C11—21no—
202C42×C11C22×C412yes—
203C42×C11C22×C411yescharacteristic
204C42×C11C2×D412yes—
205C42×C11C2×D411yescharacteristic
206C42×C11C2×D411yescharacteristic
207C42×C11C2×D412yes—
208C42×C11C2411yescharacteristic
209#4318—42no—
210#4318—42no—
211#4318—44no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—22no—
217C2×C11⋊C8—22no—
218C2×C11⋊C8—44no—
219#3510D1111yescharacteristic
220#2971—111no—
221#2970—111no—
222#1537—111no—
223#1535—112no—
224#1532—112no—
225#1529—112no—
226#1527—111no—
227#1527—111no—
228#1526—111no—
229#1524—112no—
230C23×C11—22no—
231C23×C11—42no—
232C23×C11—81no—
233C23×C11—81no—
234C23×C11C2×C22⋊C411yescharacteristic
235C23×C11C2×C22⋊C412yes—
236Q8×C11—22no—
237Q8×C11—42no—
238Q8×C11—42no—
239Q8×C11—81no—
240Q8×C11—81no—
241D4×C11—22no—
242D4×C11—42no—
243D4×C11—42no—
244D4×C11—42no—
245D4×C11—82no—
246D4×C11—82no—
247C2×C4×C11—22no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—22no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—42no—
258C2×C4×C11—42no—
259C2×C4×C11—82no—
260C2×C4×C11—82no—
261C2×C4×C11C2×C22⋊C412yes—
262C2×C4×C11C2×C22⋊C412yes—
263C2×C4×C11C2×C22⋊C411yescharacteristic
264C2×C4×C11C2×C22⋊C411yescharacteristic
265C2×C4×C11C2×C22⋊C412yes—
266C2×C4×C11C2×C22⋊C411yescharacteristic
267C2×C4×C11C23×C411yescharacteristic
268C2×C4×C11C22×D411yescharacteristic
269C2×C4×C11C22×D411yescharacteristic
270C11⋊C8—22no—
271C11⋊C8—22no—
272C11⋊C8—42no—
273C11⋊C8—41no—
274C11⋊C8—41no—
275C11⋊C8—42no—
276#559—21no—
277#559—21no—
278#556—21no—
279#556—21no—
280#551—22no—
281#551—22no—
282#542Dic1112yes—
283#542Dic1112yes—
284#536Dic1111yescharacteristic
285#535Dic1111yescharacteristic
286#533C2×D1111yescharacteristic
287#529C2×D1112yes—
288#529C2×D1112yes—
289C2×#124C2×D1111yescharacteristic
290#519Dic1111yescharacteristic
291#518Dic1111yescharacteristic
292C4×#41C2×D1111yescharacteristic
293#446—221no—
294C8×Q8—221no—
295#436—222no—
296#436—221no—
297#435—222no—
298C8×D4—221no—
299#432—111no—
300#432—111no—
301#432—112no—
302#432—112no—
303C4×M16—111no—
304C4×M16—111no—
305C4×M16—112no—
306C2×#97—112no—
307#330—112no—
308#330—112no—
309#330—111no—
310#330—111no—
311#330—111no—
312#330—111no—
313#329—112no—
314#329—112no—
315#329—112no—
316#329—112no—
317C22×C11—21no—
318C22×C11—22no—
319C22×C11—22no—
320C22×C11—22no—
321C22×C11—21no—
322C22×C11—21no—
323C22×C11—42no—
324C22×C11—42no—
325C22×C11—42no—
326C22×C11—162no—
327C22×C11C22×C22⋊C411yescharacteristic
328C4×C11—21no—
329C4×C11—22no—
330C4×C11—21no—
331C4×C11—21no—
332C4×C11—22no—
333C4×C11—22no—
334C4×C11—21no—
335C4×C11—21no—
336C4×C11—42no—
337C4×C11—41no—
338C4×C11—41no—
339C4×C11—41no—
340C4×C11—41no—
341C4×C11#41312yes—
342C2×#41C2×Dic1111yescharacteristic
343C22×Q8C2×Dic1111yescharacteristic
344C22×D4C2×Dic1111yescharacteristic
345C2×M16—221no—
346C2×M16—221no—
347C2×M16—222no—
348C22×C8—222no—
349C4⋊Q8—21no—
350C4⋊Q8C2×Dic1111yescharacteristic
351C4⋊Q8C2×Dic1111yescharacteristic
352#127—21no—
353#126—22no—
354#126—22no—
355#126—22no—
356#126—22no—
357#125C22×D1111yescharacteristic
358#125C22×D1111yescharacteristic
359#124—21no—
360#124—21no—
361#124—22no—
362#124—22no—
363#124—21no—
364#124—21no—
365#124C2×Dic1112yes—
366#124C22×D1112yes—
367#123—22no—
368#123—22no—
369#123—22no—
370#123—22no—
371#123—22no—
372C22⋊Q8—21no—
373C22⋊Q8—21no—
374C22⋊Q8—22no—
375C22⋊Q8—22no—
376C22⋊Q8C2×Dic1112yes—
377C22⋊Q8C2×Dic1112yes—
378#121C2×Dic1112yes—
379#121C2×Dic1112yes—
380#120—22no—
381C4×Q8—21no—
382C4×Q8—21no—
383C4×Q8—21no—
384C4×Q8—21no—
385C4×Q8C2×Dic1112yes—
386C4×Q8C2×Dic1112yes—
387C4×Q8C22⋊D1111yescharacteristic
388C4×Q8C22⋊D1111yescharacteristic
389C4×D4—22no—
390C4×D4—22no—
391C4×D4—21no—
392C4×D4—21no—
393C4×D4C2×Dic1112yes—
394C4×D4C2×Dic1112yes—
395C4×D4C22⋊D1112yes—
396C4×D4C22⋊D1112yes—
397C4×D4C22⋊D1111yescharacteristic
398C4×D4C22⋊D1111yescharacteristic
399#117—22no—
400#117—22no—
401#117—22no—
402#117C2×Dic1111yescharacteristic
403#117C2×Dic1111yescharacteristic
404#117C2×Dic1111yescharacteristic
405#117C2×Dic1112yes—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—22no—
409C2×C42C22×D1111yescharacteristic
410C2×C42C22×D1112yes—
411C4⋊C8—221no—
412C4⋊C8—222no—
413C4⋊C8—222no—
414C4⋊C8—221no—
415C22⋊C8—222no—
416C22⋊C8—221no—
417C22⋊C8—221no—
418C22⋊C8—222no—
419#97—111no—
420#97—112no—
421#97—111no—
422#97—111no—
423#97—111no—
424#97—112no—
425#97—222no—
426C4×C8—221no—
427C4×C8—222no—
428C4×C8—221no—
429C2×C11—42no—
430C2×C11—41no—
431C2×C11—82no—
432C2×C11C2×#41311yescharacteristic
433C2×C11#290111yescharacteristic
434C2×C11#290111yescharacteristic
435C24—21no—
436#41—42no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—42no—
441C2×Q8C22⋊Dic1111yescharacteristic
442C2×Q8C22×Dic1112yes—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—21no—
446C2×D4—42no—
447C2×D4C22⋊Dic1111yescharacteristic
448C2×D4C22⋊Dic1112yes—
449C2×D4C22×Dic1112yes—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4C22×Dic1111yescharacteristic
454C22×C4C22×Dic1112yes—
455C22×C4C2×C22⋊D1111yescharacteristic
456C22×C4C2×C22⋊D1111yescharacteristic
457C22×C4C2×C22⋊D1112yes—
458C22×C4C2×C22⋊D1112yes—
459M16—442no—
460M16—444no—
461M16—442no—
462C2×C8—221no—
463C2×C8—221no—
464C2×C8—221no—
465C2×C8—222no—
466C2×C8—221no—
467C2×C8—222no—
468C2×C8—444no—
469C4⋊C4—22no—
470C4⋊C4—22no—
471C4⋊C4—22no—
472C4⋊C4—22no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4C22⋊Dic1111yescharacteristic
480C4⋊C4C22⋊Dic1111yescharacteristic
481C4⋊C4C22⋊Dic1112yes—
482C4⋊C4C22⋊Dic1112yes—
483C4⋊C4C22×Dic1111yescharacteristic
484C4⋊C4C22×Dic1111yescharacteristic
485C4⋊C4C22×Dic1111yescharacteristic
486C4⋊C4C22×Dic1111yescharacteristic
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—22no—
490C22⋊C4—22no—
491C22⋊C4—22no—
492C22⋊C4—22no—
493C22⋊C4—22no—
494C22⋊C4—22no—
495C22⋊C4—22no—
496C22⋊C4—22no—
497C22⋊C4—22no—
498C22⋊C4—22no—
499C22⋊C4C22⋊Dic1112yes—
500C22⋊C4C22⋊Dic1112yes—
501C22⋊C4C22⋊Dic1112yes—
502C42—22no—
503C42—22no—
504C42—21no—
505C42—21no—
506C42C22×Dic1112yes—
507C42C22×Dic1111yescharacteristic
508C42C2×C22⋊D1112yes—
509C42C2×C22⋊D1111yescharacteristic
510C42C2×C22⋊D1111yescharacteristic
511C42C2×C22⋊D1112yes—
512C42C23×D1111yescharacteristic
513C11#1769111yescharacteristic, complemented, Sylow
514C23—22no—
515C23—42no—
516C23—81no—
517C23—81no—
518C23C2×C22⋊Dic1111yescharacteristic
519C23C2×C22⋊Dic1112yes—
520Q8—22no—
521Q8—42no—
522Q8—42no—
523Q8—81no—
524Q8—81no—
525D4—22no—
526D4—42no—
527D4—42no—
528D4—42no—
529D4—82no—
530D4—82no—
531C2×C4—22no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—22no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—82no—
544C2×C4—82no—
545C2×C4C2×C22⋊Dic1112yes—
546C2×C4C2×C22⋊Dic1112yes—
547C2×C4C2×C22⋊Dic1111yescharacteristic
548C2×C4C2×C22⋊Dic1111yescharacteristic
549C2×C4C2×C22⋊Dic1112yes—
550C2×C4C2×C22⋊Dic1111yescharacteristic
551C2×C4C23×Dic1111yescharacteristic
552C2×C4C22×C22⋊D1111yescharacteristic
553C2×C4C22×C22⋊D1111yescharacteristic
554C8—222no—
555C8—222no—
556C8—442no—
557C8—441no—
558C8—442no—
559C8—441no—
560C22—21no—
561C22—22no—
562C22—22no—
563C22—22no—
564C22—21no—
565C22—21no—
566C22—42no—
567C22—42no—
568C22—42no—
569C22—162no—
570C22C22×C22⋊Dic1111yescharacteristic
571C4—21no—
572C4—22no—
573C4—21no—
574C4—21no—
575C4—22no—
576C4—22no—
577C4—21no—
578C4—21no—
579C4—42no—
580C4—41no—
581C4—41no—
582C4—41no—
583C4—41no—
584C4#1062285012yes—
585C2—41no—
586C2—42no—
587C2—82no—
588C2C2×#1062285011yescharacteristic
589C2#1307716311yescharacteristic
590C2#1307716311yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#3510C2
socleC22×C11C22×C22⋊C4
prime radicalC11×#535C4
cosocleC42×C11C24
hypercenter#3510D11
hypocenterC11#17691
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3510

Complements

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

NH ≅ G/Ntype
1. #13077636C2semidirect
2. #13077630C2semidirect
3. #13067254C2semidirect
4. #13067247C2semidirect
5. #13067236C2semidirect
6. #13067223C2semidirect
7. #13067214C2semidirect
8. #13067214C2semidirect
9. #13067211C2semidirect
10. #13067204C2semidirect
37. #10622539C22semidirect
38. #10622539C22semidirect
41. C4×#4318C22semidirect
42. C2×#66867C22semidirect
43. #10622181C22semidirect
44. #10622181C22semidirect
45. #10622181C22semidirect
46. #10622181C22semidirect
47. #10622181C22semidirect
48. #10622181C22semidirect
513. C11#17691semidirect

Maximal subgroups

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

subgroupindex
#130776362
#130776302
#130672542
#130672472
#130672362
#130672232
#130672142
#130672112
#130672042
C11×#35102
#1769111