Finite Group Databasebeta

← #14644121

Subgroups — #14644121

Order 2816.

914 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
1D11×#407C211yesmaximal, characteristic
2D11×#407C211yesmaximal, characteristic
3#13070998C211yesmaximal, characteristic
4#13066523C211yesmaximal, characteristic, complemented
5#13066522C211yesmaximal, characteristic, complemented
6#13066521C211yesmaximal, characteristic, complemented
7C11×#1305C211yesmaximal, characteristic, complemented
8C23×C4×D11C2211yescharacteristic
9C2×M16×D11—21no—
10C2×M16×D11C412yescomplemented
11C2×#66945—21no—
12C11×#407C2211yescharacteristic
13C11×#407C2211yescharacteristic
14C11×#380C2211yescharacteristic
15#10622825C2211yescharacteristic
16#10622820C2211yescharacteristic
17#10622820C2211yescharacteristic
18#10622739—21no—
19#10622739C412yescomplemented
20#10622600—21no—
21#10622568C412yes—
22C22⋊C4×Dic11C412yes—
23#10622339—21no—
24#10622339—21no—
25#10622339—21no—
26#10622339C412yescomplemented
27D11×C22⋊C8—21no—
28D11×C22⋊C8—21no—
29D11×C22⋊C8—21no—
30D11×C22⋊C8C412yescomplemented
31#10622279—21no—
32#10622277—21no—
33C24×D11C2×C411yescharacteristic
34C23×C4×C11C2311yescharacteristic
35C23×Dic11C2×C411yescharacteristic
36C22×C4×D11—44no—
37C22×C4×D11C2×C411yescharacteristic
38C22×C4×D11C2×C411yescharacteristic
39C22×C4×D11C2×C411yescharacteristic
40C22×C4×D11C2×C411yescharacteristic
41C22×C4×D11D411yescharacteristic
42C22×C4×D11D411yescharacteristic
43C22×C4×D11D411yescharacteristic
44C22×C4×D11D411yescharacteristic
45C22×C4×D11D411yescharacteristic
46C22×C4×D11D411yescharacteristic
47C22×C4×D11Q811yescharacteristic
48C22×C4×D11Q811yescharacteristic
49C2×C11×M16—21no—
50C2×C11×M16C2×C412yes—
51C2×C11×C4⋊C4—21no—
52C2×C11×C22⋊C4C2×C412yes—
53C2×C22⋊Dic11C2×C412yes—
54C2×(C2×D11)⋊C4—22no—
55C2×(C2×D11)⋊C4—22no—
56C2×C4⋊Dic11—21no—
57C2×C4×Dic11—22no—
58C2×#4318—21no—
59C2×#4318C2×C412yes—
60M16×D11—44no—
61M16×D11—44no—
62C2×#4313—22no—
63C2×#4313—22no—
64C2×C8×D11—22no—
65C2×C8×D11—22no—
66#66945—44no—
67C11×C22⋊C8—21no—
68C11×C22⋊C8—21no—
69C11×C22⋊C8—21no—
70C11×C22⋊C8C2×C412yes—
71C11×#95—21no—
72C11⋊#95—21no—
73C11⋊#95—22no—
74C22⋊(C11⋊C8)—21no—
75C22⋊(C11⋊C8)—21no—
76C22⋊(C11⋊C8)—21no—
77C22⋊(C11⋊C8)C2×C412yes—
78(C2×D11)⋊C8—22no—
79(C2×D11)⋊C8—22no—
80(C2×D11)⋊C8—22no—
81(C2×D11)⋊C8—22no—
82#8108—111nomaximal, Sylow
83C24×C11C22×C411yescharacteristic
84C23×D11—42no—
85C23×D11—42no—
86C23×D11—41no—
87C23×D11—41no—
88C23×D11C4211yescharacteristic
89C23×D11C4211yescharacteristic
90C23×D11C22⋊C411yescharacteristic
91C23×D11C22⋊C411yescharacteristic
92C23×D11C4⋊C411yescharacteristic
93C23×D11C4⋊C411yescharacteristic
94C22×C4×C11—22no—
95C22×C4×C11—42no—
96C22×C4×C11C22×C411yescharacteristic
97C22×C4×C11C22×C411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×Q811yescharacteristic
102C22×Dic11—22no—
103C22×Dic11—42no—
104C22×Dic11C4211yescharacteristic
105C22×Dic11C4211yescharacteristic
106C22×Dic11C22⋊C411yescharacteristic
107C22×Dic11C22⋊C411yescharacteristic
108C22×Dic11C4⋊C411yescharacteristic
109C22×Dic11C4⋊C411yescharacteristic
110C2×C4×D11—24no—
111C2×C4×D11—24no—
112C2×C4×D11—24no—
113C2×C4×D11—42no—
114C2×C4×D11—42no—
115C2×C4×D11—42no—
116C2×C4×D11—42no—
117C2×C4×D11—42no—
118C2×C4×D11—42no—
119C2×C4×D11—42no—
120C2×C4×D11—42no—
121C2×C4×D11—42no—
122C2×C4×D11C22⋊C411yescharacteristic
123C2×C4×D11C22⋊C411yescharacteristic
124C2×C4×D11C22⋊C411yescharacteristic
125C2×C4×D11C22⋊C411yescharacteristic
126C2×C4×D11C22⋊C411yescharacteristic
127C2×C4×D11C22⋊C411yescharacteristic
128C2×C4×D11C22⋊C411yescharacteristic
129C2×C4×D11C22⋊C411yescharacteristic
130C2×C4×D11C4⋊C411yescharacteristic
131C2×C4×D11C4⋊C411yescharacteristic
132C2×C4×D11C4⋊C411yescharacteristic
133C2×C4×D11C4⋊C411yescharacteristic
134C2×C4×D11C4⋊C411yescharacteristic
135C2×C4×D11C4⋊C411yescharacteristic
136C2×C4×D11C4⋊C411yescharacteristic
137C2×C4×D11C4⋊C411yescharacteristic
138C11×M16—42no—
139C11×M16—42no—
140C2×C8×C11—22no—
141C2×C8×C11—22no—
142C11×C4⋊C4—42no—
143C11×C22⋊C4—42no—
144C22⋊Dic11—42no—
145(C2×D11)⋊C4—44no—
146(C2×D11)⋊C4—44no—
147C4⋊Dic11—42no—
148C4×Dic11—44no—
149#4318—42no—
150#4318—42no—
151C2×C11⋊C8—22no—
152C2×C11⋊C8—22no—
153#4313—44no—
154#4313—44no—
155C8×D11—44no—
156C8×D11—44no—
157C2×#407—111no—
158C2×#407—111no—
159#2280—111no—
160#1305—111no—
161#1305—111no—
162#1305—111no—
163#1305D1111yescharacteristic, complemented
164C23×C11—21no—
165C23×C11—21no—
166C23×C11—41no—
167C23×C11—41no—
168C23×C11C2×C4211yescharacteristic
169C23×C11C2×C22⋊C411yescharacteristic
170C23×C11C2×C4⋊C411yescharacteristic
171C22×D11—21no—
172C22×D11—21no—
173C22×D11—21no—
174C22×D11—21no—
175C22×D11—22no—
176C22×D11—22no—
177C22×D11—22no—
178C22×D11—22no—
179C22×D11—22no—
180C22×D11—22no—
181C22×D11—41no—
182C22×D11—41no—
183C22×D11—41no—
184C22×D11—41no—
185C22×D11—41no—
186C22×D11—41no—
187C22×D11—41no—
188C22×D11—41no—
189C22×D11—41no—
190C22×D11—41no—
191C22×D11—48no—
192C22×D11—48no—
193C22×D11#9511yescharacteristic
194C22×D11#9511yescharacteristic
195C22×D11#9511yescharacteristic
196C22×D11#9511yescharacteristic
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—41no—
201C2×C4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11—42no—
206C2×C4×C11C2×C22⋊C411yescharacteristic
207C2×C4×C11C2×C22⋊C411yescharacteristic
208C2×C4×C11C2×C4⋊C411yescharacteristic
209C2×C4×C11C2×C4⋊C411yescharacteristic
210C2×Dic11—22no—
211C2×Dic11—22no—
212C2×Dic11—22no—
213C2×Dic11—41no—
214C2×Dic11—41no—
215C2×Dic11—41no—
216C2×Dic11—42no—
217C2×Dic11—42no—
218C2×Dic11—42no—
219C2×Dic11#9511yescharacteristic
220C2×Dic11#9511yescharacteristic
221C2×Dic11#9511yescharacteristic
222C2×Dic11#9511yescharacteristic
223C4×D11—22no—
224C4×D11—22no—
225C4×D11—22no—
226C4×D11—22no—
227C4×D11—22no—
228C4×D11—22no—
229C4×D11—22no—
230C4×D11—22no—
231C4×D11—22no—
232C4×D11—41no—
233C4×D11—41no—
234C4×D11—41no—
235C4×D11—41no—
236C4×D11—41no—
237C4×D11—41no—
238C4×D11#9914yes—
239C8×C11—42no—
240C8×C11—42no—
241C11⋊C8—42no—
242C11⋊C8—42no—
243C24×C4—111no—
244C22×M16—112no—
245C22×M16—221no—
246C2×#117—221no—
247#407—111no—
248#407—112no—
249#407—111no—
250#407—112no—
251#407—221no—
252#407—221no—
253#407—221no—
254#407—221no—
255#407C2×D1111yescharacteristic
256#407C2×D1111yescharacteristic
257C2×C22⋊C8—112no—
258C2×C22⋊C8—221no—
259C2×C22⋊C8—221no—
260C2×C22⋊C8—221no—
261#381—221no—
262#380—111no—
263#380—221no—
264#380C2×D1111yescharacteristic
265#379—112no—
266C4×C22⋊C4—112no—
267C4×C22⋊C4—221no—
268C22×C11—21no—
269C22×C11—21no—
270C22×C11—21no—
271C22×C11—21no—
272C22×C11—21no—
273C22×C11—21no—
274C22×C11—21no—
275C22×C11—21no—
276C22×C11—42no—
277C22×C11—42no—
278C22×C11C2×#9511yescharacteristic
279C22×C11#41311yescharacteristic
280C22×C11#41311yescharacteristic
281C2×D11—21no—
282C2×D11—21no—
283C2×D11—21no—
284C2×D11—21no—
285C2×D11—21no—
286C2×D11—21no—
287C2×D11—21no—
288C2×D11—21no—
289C2×D11—21no—
290C2×D11—21no—
291C2×D11—44no—
292C2×D11—42no—
293C2×D11—42no—
294C2×D11—42no—
295C2×D11—42no—
296C2×D11—44no—
297C2×D11—44no—
298C2×D11—44no—
299C2×D11#34212yes—
300C2×D11#34412yes—
301C4×C11—21no—
302C4×C11—21no—
303C4×C11—21no—
304C4×C11—82no—
305C4×C11C2×#9912yes—
306Dic11—21no—
307Dic11—21no—
308Dic11—21no—
309Dic11—82no—
310Dic11#34212yes—
311C25—111no—
312C23×C4—111no—
313C23×C4—111no—
314C23×C4—111no—
315C23×C4—111no—
316C23×C4—111no—
317C23×C4—111no—
318C23×C4—111no—
319C23×C4—111no—
320C23×C4—111no—
321C23×C4—111no—
322C23×C4—111no—
323C23×C4—111no—
324C23×C4—111no—
325C23×C4—444no—
326C23×C4C22×D1111yescharacteristic
327C2×M16—21no—
328C2×M16—112no—
329C2×M16—222no—
330C2×M16—222no—
331C2×M16—221no—
332C2×M16—444no—
333C2×M16—444no—
334C2×M16C4×D1112yes—
335C22×C8—222no—
336C22×C8—222no—
337#117—444no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—221no—
340C2×C22⋊C4—112no—
341C2×C22⋊C4—222no—
342C2×C22⋊C4—222no—
343C2×C22⋊C4C4×D1112yes—
344C2×C42—222no—
345C22⋊C8—21no—
346C22⋊C8—21no—
347C22⋊C8—21no—
348C22⋊C8—112no—
349C22⋊C8—222no—
350C22⋊C8—222no—
351C22⋊C8—222no—
352C22⋊C8—222no—
353C22⋊C8—221no—
354C22⋊C8—221no—
355C22⋊C8—221no—
356C22⋊C8C4×D1112yes—
357#95—21no—
358#95—222no—
359#95—221no—
360C2×C11—21no—
361C2×C11—21no—
362C2×C11—41no—
363C2×C11—41no—
364C2×C11C2×#34211yescharacteristic
365C2×C11#174211yescharacteristic
366C2×C11C2×#34411yescharacteristic
367D11—22no—
368D11—22no—
369D11—41no—
370D11—41no—
371C24—111no—
372C24—111no—
373C24—111no—
374C24—111no—
375C24—111no—
376C24—111no—
377C24—441no—
378C24—441no—
379C24—442no—
380C24—442no—
381C24C2×C4×D1111yescharacteristic
382C22×C4—22no—
383C22×C4—42no—
384C22×C4—111no—
385C22×C4—111no—
386C22×C4—111no—
387C22×C4—111no—
388C22×C4—111no—
389C22×C4—111no—
390C22×C4—111no—
391C22×C4—111no—
392C22×C4—111no—
393C22×C4—111no—
394C22×C4—111no—
395C22×C4—111no—
396C22×C4—111no—
397C22×C4—111no—
398C22×C4—111no—
399C22×C4—111no—
400C22×C4—111no—
401C22×C4—111no—
402C22×C4—111no—
403C22×C4—111no—
404C22×C4—111no—
405C22×C4—111no—
406C22×C4—224no—
407C22×C4—224no—
408C22×C4—224no—
409C22×C4—222no—
410C22×C4—442no—
411C22×C4—442no—
412C22×C4—442no—
413C22×C4—442no—
414C22×C4—442no—
415C22×C4—442no—
416C22×C4—442no—
417C22×C4—442no—
418C22×C4—442no—
419C22×C4—442no—
420C22×C4C2×C4×D1111yescharacteristic
421C22×C4C2×C4×D1111yescharacteristic
422C22×C4D4×D1111yescharacteristic
423C22×C4D4×D1111yescharacteristic
424C22×C4D4×D1111yescharacteristic
425C22×C4Q8×D1111yescharacteristic
426M16—42no—
427M16—42no—
428M16—444no—
429M16—444no—
430M16—442no—
431M16—442no—
432C2×C8—22no—
433C2×C8—22no—
434C2×C8—222no—
435C2×C8—222no—
436C2×C8—444no—
437C2×C8—444no—
438C4⋊C4—42no—
439C4⋊C4—442no—
440C22⋊C4—42no—
441C22⋊C4—444no—
442C22⋊C4—444no—
443C22⋊C4—442no—
444C42—444no—
445C11#810811yescharacteristic, complemented, Sylow
446C23—21no—
447C23—21no—
448C23—41no—
449C23—41no—
450C23—111no—
451C23—111no—
452C23—111no—
453C23—111no—
454C23—222no—
455C23—222no—
456C23—222no—
457C23—222no—
458C23—222no—
459C23—222no—
460C23—221no—
461C23—221no—
462C23—221no—
463C23—221no—
464C23—441no—
465C23—441no—
466C23—441no—
467C23—441no—
468C23—441no—
469C23—441no—
470C23—441no—
471C23—441no—
472C23—441no—
473C23—441no—
474C23—448no—
475C23—448no—
476C23C42×D1111yescharacteristic
477C23C22⋊C4×D1111yescharacteristic
478C23C4⋊C4×D1111yescharacteristic
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—111no—
489C2×C4—114no—
490C2×C4—111no—
491C2×C4—111no—
492C2×C4—111no—
493C2×C4—222no—
494C2×C4—222no—
495C2×C4—222no—
496C2×C4—222no—
497C2×C4—222no—
498C2×C4—222no—
499C2×C4—222no—
500C2×C4—222no—
501C2×C4—222no—
502C2×C4—222no—
503C2×C4—222no—
504C2×C4—222no—
505C2×C4—441no—
506C2×C4—441no—
507C2×C4—441no—
508C2×C4—441no—
509C2×C4—441no—
510C2×C4—441no—
511C2×C4—441no—
512C2×C4—441no—
513C2×C4—441no—
514C2×C4—442no—
515C2×C4—442no—
516C2×C4—442no—
517C2×C4C22⋊C4×D1111yescharacteristic
518C2×C4C22⋊C4×D1111yescharacteristic
519C2×C4C4⋊C4×D1111yescharacteristic
520C2×C4C4⋊C4×D1111yescharacteristic
521C8—42no—
522C8—42no—
523C8—442no—
524C8—442no—
525C22—21no—
526C22—21no—
527C22—21no—
528C22—21no—
529C22—21no—
530C22—21no—
531C22—21no—
532C22—21no—
533C22—42no—
534C22—42no—
535C22—112no—
536C22—112no—
537C22—221no—
538C22—221no—
539C22—221no—
540C22—221no—
541C22—221no—
542C22—221no—
543C22—221no—
544C22—221no—
545C22—221no—
546C22—221no—
547C22—442no—
548C22—442no—
549C22—442no—
550C22—442no—
551C22—444no—
552C22—444no—
553C22—444no—
554C22—444no—
555C22D11×#9511yescharacteristic
556C22#1062235811yescharacteristic
557C22#1062236411yescharacteristic
558C4—21no—
559C4—21no—
560C4—21no—
561C4—82no—
562C4—112no—
563C4—221no—
564C4—221no—
565C4—221no—
566C4—882no—
567C4D11×#9912yes—
568C2—21no—
569C2—21no—
570C2—41no—
571C2—41no—
572C2—222no—
573C2—222no—
574C2—441no—
575C2—441no—
576C2D11×#34211yescharacteristic
577C2#1306835311yescharacteristic
578C2D11×#34411yescharacteristic
subgroupG/H
centerC22D11×#95
commutatorC23×C11C2×C42
FrattiniC23×C4C22×D11
FittingC11×#1305C2
socleC22×C11C2×#95
prime radicalC24×D11C2×C4
cosocleC23×C4×C11C23
hypercenter#1305D11
hypocenterC11#8108
LCSG ▷ C23×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1305

Complements

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

NH ≅ G/Ntype
4. #13066523C2semidirect
5. #13066522C2semidirect
6. #13066521C2semidirect
7. C11×#1305C2semidirect
10. C2×M16×D11C4semidirect
19. #10622739C4semidirect
26. #10622339C4semidirect
30. D11×C22⋊C8C4semidirect
163. #1305D11semidirect
445. C11#8108semidirect

Maximal subgroups

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

subgroupindex
D11×#4072
#130709982
#130665232
#130665222
#130665212
C11×#13052
#810811