Finite Group Databasebeta

← #14644117

Subgroups — #14644117

Order 2816.

986 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#407C211yesmaximal, characteristic
2D11×#407C211yesmaximal, characteristic
3D11×#380C211yesmaximal, 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×C4⋊C4×D11—21no—
12C2×C22⋊C4×D11C412yes—
13C11×#407C2211yescharacteristic
14C11×#407C2211yescharacteristic
15C11×#380C2211yescharacteristic
16#10622825C2211yescharacteristic
17#10622820C2211yescharacteristic
18#10622820C2211yescharacteristic
19#10622739—21no—
20#10622739C412yescomplemented
21#10622600—21no—
22#10622555C412yes—
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#10622280—21no—
32D11×#95—21no—
33C24×D11C2×C411yescharacteristic
34C23×C4×C11C2311yescharacteristic
35C23×Dic11C2×C411yescharacteristic
36C22×C4×D11—22no—
37C22×C4×D11—44no—
38C22×C4×D11C2×C411yescharacteristic
39C22×C4×D11C2×C411yescharacteristic
40C22×C4×D11C2×C411yescharacteristic
41C22×C4×D11C2×C411yescharacteristic
42C22×C4×D11D411yescharacteristic
43C22×C4×D11D411yescharacteristic
44C22×C4×D11D411yescharacteristic
45C22×C4×D11D411yescharacteristic
46C22×C4×D11D411yescharacteristic
47C22×C4×D11D411yescharacteristic
48C22×C4×D11Q811yescharacteristic
49C22×C4×D11Q811yescharacteristic
50C2×C11×M16—21no—
51C2×C11×M16C2×C412yescomplemented
52C2×C11×C4⋊C4—21no—
53C2×C11×C22⋊C4C2×C412yes—
54C2×C22⋊Dic11C2×C412yes—
55C2×(C2×D11)⋊C4—22no—
56C2×C4⋊Dic11—21no—
57C2×Dic11⋊C4—22no—
58C2×#4318—21no—
59C2×#4318C2×C412yescomplemented
60M16×D11—44no—
61M16×D11—44no—
62C2×#4313—22no—
63C2×#4313—22no—
64C2×C8×D11—22no—
65C2×C8×D11—22no—
66C4⋊C4×D11—44no—
67C22⋊C4×D11—44no—
68C11×C22⋊C8—21no—
69C11×C22⋊C8—21no—
70C11×C22⋊C8—21no—
71C11×C22⋊C8C2×C412yescomplemented
72C11×#95—21no—
73C11⋊#95—21no—
74C11⋊#95—22no—
75C22⋊(C11⋊C8)—21no—
76C22⋊(C11⋊C8)—21no—
77C22⋊(C11⋊C8)—21no—
78C22⋊(C11⋊C8)C2×C412yescomplemented
79(C2×D11)⋊C8—22no—
80(C2×D11)⋊C8—22no—
81(C2×D11)⋊C8—22no—
82(C2×D11)⋊C8—22no—
83#8107—111nomaximal, Sylow
84C24×C11C22×C411yescharacteristic
85C23×D11—22no—
86C23×D11—22no—
87C23×D11—42no—
88C23×D11—42no—
89C23×D11C4211yescharacteristic
90C23×D11C4211yescharacteristic
91C23×D11C22⋊C411yescharacteristic
92C23×D11C22⋊C411yescharacteristic
93C23×D11C4⋊C411yescharacteristic
94C23×D11C4⋊C411yescharacteristic
95C22×C4×C11—22no—
96C22×C4×C11—42no—
97C22×C4×C11C22×C411yescharacteristic
98C22×C4×C11C22×C411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×Q811yescharacteristic
103C22×Dic11—22no—
104C22×Dic11—42no—
105C22×Dic11C4211yescharacteristic
106C22×Dic11C4211yescharacteristic
107C22×Dic11C22⋊C411yescharacteristic
108C22×Dic11C22⋊C411yescharacteristic
109C22×Dic11C4⋊C411yescharacteristic
110C22×Dic11C4⋊C411yescharacteristic
111C2×C4×D11—24no—
112C2×C4×D11—24no—
113C2×C4×D11—24no—
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—44no—
121C2×C4×D11—44no—
122C2×C4×D11—44no—
123C2×C4×D11—42no—
124C2×C4×D11—42no—
125C2×C4×D11—42no—
126C2×C4×D11C22⋊C411yescharacteristic
127C2×C4×D11C22⋊C411yescharacteristic
128C2×C4×D11C22⋊C411yescharacteristic
129C2×C4×D11C22⋊C411yescharacteristic
130C2×C4×D11C22⋊C411yescharacteristic
131C2×C4×D11C22⋊C411yescharacteristic
132C2×C4×D11C22⋊C411yescharacteristic
133C2×C4×D11C22⋊C411yescharacteristic
134C2×C4×D11C4⋊C411yescharacteristic
135C2×C4×D11C4⋊C411yescharacteristic
136C2×C4×D11C4⋊C411yescharacteristic
137C2×C4×D11C4⋊C411yescharacteristic
138C2×C4×D11C4⋊C411yescharacteristic
139C2×C4×D11C4⋊C411yescharacteristic
140C2×C4×D11C4⋊C411yescharacteristic
141C2×C4×D11C4⋊C411yescharacteristic
142C11×M16—42no—
143C11×M16—42no—
144C2×C8×C11—22no—
145C2×C8×C11—22no—
146C11×C4⋊C4—42no—
147C11×C22⋊C4—42no—
148C22⋊Dic11—42no—
149(C2×D11)⋊C4—44no—
150C4⋊Dic11—42no—
151Dic11⋊C4—44no—
152#4318—42no—
153#4318—42no—
154C2×C11⋊C8—22no—
155C2×C11⋊C8—22no—
156#4313—44no—
157#4313—44no—
158C8×D11—44no—
159C8×D11—44no—
160C2×#407—111no—
161C2×#407—111no—
162C2×#380—111no—
163#1305—111no—
164#1305—111no—
165#1305—111no—
166#1305D1111yescharacteristic, complemented
167C23×C11—21no—
168C23×C11—21no—
169C23×C11—41no—
170C23×C11—41no—
171C23×C11C2×C4211yescharacteristic
172C23×C11C2×C22⋊C411yescharacteristic
173C23×C11C2×C4⋊C411yescharacteristic
174C22×D11—21no—
175C22×D11—21no—
176C22×D11—22no—
177C22×D11—22no—
178C22×D11—22no—
179C22×D11—22no—
180C22×D11—22no—
181C22×D11—22no—
182C22×D11—22no—
183C22×D11—22no—
184C22×D11—22no—
185C22×D11—22no—
186C22×D11—41no—
187C22×D11—41no—
188C22×D11—41no—
189C22×D11—41no—
190C22×D11—41no—
191C22×D11—41no—
192C22×D11—48no—
193C22×D11—48no—
194C22×D11#9511yescharacteristic
195C22×D11#9511yescharacteristic
196C22×D11#9511yescharacteristic
197C22×D11#9511yescharacteristic
198C22×D11#10012yes—
199C22×D11#10112yes—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11C2×C22⋊C411yescharacteristic
210C2×C4×C11C2×C22⋊C411yescharacteristic
211C2×C4×C11C2×C4⋊C411yescharacteristic
212C2×C4×C11C2×C4⋊C411yescharacteristic
213C2×Dic11—22no—
214C2×Dic11—22no—
215C2×Dic11—22no—
216C2×Dic11—41no—
217C2×Dic11—41no—
218C2×Dic11—41no—
219C2×Dic11—42no—
220C2×Dic11—42no—
221C2×Dic11—42no—
222C2×Dic11#9511yescharacteristic
223C2×Dic11#9511yescharacteristic
224C2×Dic11#9511yescharacteristic
225C2×Dic11#9511yescharacteristic
226C4×D11—22no—
227C4×D11—22no—
228C4×D11—22no—
229C4×D11—22no—
230C4×D11—22no—
231C4×D11—22no—
232C4×D11—22no—
233C4×D11—22no—
234C4×D11—22no—
235C4×D11—41no—
236C4×D11—41no—
237C4×D11—41no—
238C4×D11—41no—
239C4×D11—41no—
240C4×D11—41no—
241C4×D11—88no—
242C4×D11#9914yes—
243C8×C11—42no—
244C8×C11—42no—
245C11⋊C8—42no—
246C11⋊C8—42no—
247C24×C4—111no—
248C22×M16—112no—
249C22×M16—221no—
250C22×C4⋊C4—221no—
251C22×C22⋊C4—112no—
252#407—111no—
253#407—112no—
254#407—111no—
255#407—112no—
256#407—221no—
257#407—221no—
258#407—221no—
259#407—221no—
260#407C2×D1111yescharacteristic
261#407C2×D1111yescharacteristic
262C2×C22⋊C8—112no—
263C2×C22⋊C8—221no—
264C2×C22⋊C8—221no—
265C2×C22⋊C8—221no—
266#380—111no—
267#380—112no—
268#380—221no—
269#380—221no—
270#380C2×D1111yescharacteristic
271C2×#95—221no—
272C22×C11—21no—
273C22×C11—21no—
274C22×C11—21no—
275C22×C11—21no—
276C22×C11—21no—
277C22×C11—21no—
278C22×C11—21no—
279C22×C11—21no—
280C22×C11—42no—
281C22×C11—42no—
282C22×C11C2×#9511yescharacteristic
283C22×C11C2×#10011yescharacteristic
284C22×C11C2×#10111yescharacteristic
285C2×D11—24no—
286C2×D11—24no—
287C2×D11—21no—
288C2×D11—21no—
289C2×D11—21no—
290C2×D11—21no—
291C2×D11—21no—
292C2×D11—21no—
293C2×D11—21no—
294C2×D11—21no—
295C2×D11—42no—
296C2×D11—42no—
297C2×D11—44no—
298C2×D11—44no—
299C2×D11—44no—
300C2×D11—44no—
301C2×D11#34212yes—
302C2×D11#34312yes—
303C2×D11#34312yes—
304C2×D11#34412yes—
305C4×C11—21no—
306C4×C11—21no—
307C4×C11—21no—
308C4×C11—82no—
309C4×C11C2×#9912yes—
310Dic11—21no—
311Dic11—21no—
312Dic11—21no—
313Dic11—82no—
314Dic11#34212yes—
315C25—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—111no—
326C23×C4—111no—
327C23×C4—111no—
328C23×C4—111no—
329C23×C4—222no—
330C23×C4—444no—
331C23×C4C22×D1111yescharacteristic
332C2×M16—21no—
333C2×M16—112no—
334C2×M16—222no—
335C2×M16—222no—
336C2×M16—221no—
337C2×M16—444no—
338C2×M16—444no—
339C2×M16C4×D1112yescomplemented
340C22×C8—222no—
341C22×C8—222no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—222no—
344C2×C4⋊C4—221no—
345C2×C4⋊C4—444no—
346C2×C22⋊C4—112no—
347C2×C22⋊C4—222no—
348C2×C22⋊C4—444no—
349C2×C22⋊C4C4×D1112yes—
350C22⋊C8—21no—
351C22⋊C8—21no—
352C22⋊C8—21no—
353C22⋊C8—112no—
354C22⋊C8—222no—
355C22⋊C8—222no—
356C22⋊C8—222no—
357C22⋊C8—222no—
358C22⋊C8—221no—
359C22⋊C8—221no—
360C22⋊C8—221no—
361C22⋊C8C4×D1112yescomplemented
362#95—21no—
363#95—222no—
364#95—221no—
365C2×C11—21no—
366C2×C11—21no—
367C2×C11—41no—
368C2×C11—41no—
369C2×C11C2×#34211yescharacteristic
370C2×C11C2×#34311yescharacteristic
371C2×C11C2×#34411yescharacteristic
372D11—22no—
373D11—22no—
374D11—22no—
375D11—22no—
376C24—111no—
377C24—111no—
378C24—111no—
379C24—111no—
380C24—111no—
381C24—111no—
382C24—222no—
383C24—222no—
384C24—442no—
385C24—442no—
386C24C2×C4×D1111yescharacteristic
387C22×C4—22no—
388C22×C4—42no—
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—111no—
407C22×C4—111no—
408C22×C4—111no—
409C22×C4—111no—
410C22×C4—111no—
411C22×C4—224no—
412C22×C4—224no—
413C22×C4—224no—
414C22×C4—222no—
415C22×C4—442no—
416C22×C4—442no—
417C22×C4—442no—
418C22×C4—442no—
419C22×C4—442no—
420C22×C4—442no—
421C22×C4—442no—
422C22×C4—442no—
423C22×C4—442no—
424C22×C4—444no—
425C22×C4—444no—
426C22×C4—444no—
427C22×C4—442no—
428C22×C4C2×C4×D1111yescharacteristic
429C22×C4C2×C4×D1111yescharacteristic
430C22×C4D4×D1111yescharacteristic
431C22×C4D4×D1111yescharacteristic
432C22×C4D4×D1111yescharacteristic
433C22×C4Q8×D1111yescharacteristic
434M16—42no—
435M16—42no—
436M16—444no—
437M16—444no—
438M16—442no—
439M16—442no—
440C2×C8—22no—
441C2×C8—22no—
442C2×C8—222no—
443C2×C8—222no—
444C2×C8—444no—
445C2×C8—444no—
446C4⋊C4—42no—
447C4⋊C4—442no—
448C4⋊C4—444no—
449C22⋊C4—42no—
450C22⋊C4—444no—
451C22⋊C4—442no—
452C11#810711yescharacteristic, complemented, Sylow
453C23—21no—
454C23—21no—
455C23—41no—
456C23—41no—
457C23—111no—
458C23—111no—
459C23—111no—
460C23—111no—
461C23—112no—
462C23—112no—
463C23—222no—
464C23—222no—
465C23—222no—
466C23—222no—
467C23—222no—
468C23—222no—
469C23—222no—
470C23—222no—
471C23—222no—
472C23—222no—
473C23—221no—
474C23—221no—
475C23—441no—
476C23—441no—
477C23—441no—
478C23—441no—
479C23—441no—
480C23—441no—
481C23—448no—
482C23—448no—
483C23C42×D1111yescharacteristic
484C23C22⋊C4×D1111yescharacteristic
485C23C4⋊C4×D1111yescharacteristic
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—111no—
496C2×C4—114no—
497C2×C4—111no—
498C2×C4—111no—
499C2×C4—111no—
500C2×C4—222no—
501C2×C4—222no—
502C2×C4—222no—
503C2×C4—222no—
504C2×C4—222no—
505C2×C4—222no—
506C2×C4—222no—
507C2×C4—222no—
508C2×C4—222no—
509C2×C4—222no—
510C2×C4—222no—
511C2×C4—222no—
512C2×C4—441no—
513C2×C4—441no—
514C2×C4—441no—
515C2×C4—441no—
516C2×C4—441no—
517C2×C4—441no—
518C2×C4—441no—
519C2×C4—441no—
520C2×C4—441no—
521C2×C4—442no—
522C2×C4—442no—
523C2×C4—442no—
524C2×C4—888no—
525C2×C4C22⋊C4×D1111yescharacteristic
526C2×C4C22⋊C4×D1111yescharacteristic
527C2×C4C4⋊C4×D1111yescharacteristic
528C2×C4C4⋊C4×D1111yescharacteristic
529C8—42no—
530C8—42no—
531C8—442no—
532C8—442no—
533C22—21no—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—42no—
542C22—42no—
543C22—112no—
544C22—112no—
545C22—112no—
546C22—112no—
547C22—224no—
548C22—224no—
549C22—221no—
550C22—221no—
551C22—221no—
552C22—221no—
553C22—221no—
554C22—221no—
555C22—221no—
556C22—221no—
557C22—442no—
558C22—442no—
559C22—444no—
560C22—444no—
561C22—444no—
562C22—444no—
563C22D11×#9511yescharacteristic
564C22D11×#10011yescharacteristic
565C22D11×#10111yescharacteristic
566C4—21no—
567C4—21no—
568C4—21no—
569C4—82no—
570C4—112no—
571C4—221no—
572C4—221no—
573C4—221no—
574C4—882no—
575C4D11×#9912yes—
576C2—21no—
577C2—21no—
578C2—41no—
579C2—41no—
580C2—222no—
581C2—222no—
582C2—222no—
583C2—222no—
584C2D11×#34211yescharacteristic
585C2D11×#34311yescharacteristic
586C2D11×#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#8107
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
20. #10622739C4semidirect
26. #10622339C4semidirect
30. D11×C22⋊C8C4semidirect
51. C2×C11×M16C2×C4semidirect
59. C2×#4318C2×C4semidirect
71. C11×C22⋊C8C2×C4semidirect
78. C22⋊(C11⋊C8)C2×C4semidirect
166. #1305D11semidirect
339. C2×M16C4×D11semidirect
361. C22⋊C8C4×D11semidirect
452. C11#8107semidirect

Maximal subgroups

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

subgroupindex
D11×#4072
D11×#3802
#130665232
#130665222
#130665212
C11×#13052
#810711