Finite Group Databasebeta

← #14649507

Subgroups — #14649507

Order 2816.

1348 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076899C211yesmaximal, characteristic
2C2×D11×#95C211yesmaximal, characteristic, complemented
3#13068525C211yesmaximal, characteristic, complemented
4C2×#10622108C211yesmaximal, characteristic, complemented
5C2×#10622089C211yesmaximal, characteristic, complemented
6#13066494C211yesmaximal, characteristic, complemented
7C11×#1294C211yesmaximal, characteristic, complemented
8C23×C4×D11—21no—
9C23×C4×D11C2211yescharacteristic
10C2×#66983C2211yescharacteristic
11C2×#66948C412yescomplemented
12C2×#66935—21no—
13C2×C11×C22⋊C8C2211yescharacteristic
14C11×#380C2211yescharacteristic
15C2×C11×#95C2211yescharacteristic
16C2×C11⋊#95—21no—
17C2×C11⋊#95C2211yescharacteristic
18C2×C22⋊(C11⋊C8)C2211yescharacteristic
19C2×(C2×D11)⋊C8—22no—
20#10622600C412yescomplemented
21#10622571—21no—
22#10622278—22no—
23D11×#95—22no—
24D11×#95—22no—
25#10622108—22no—
26#10622089—22no—
27C24×D11D411yescharacteristic
28C23×C4×C11—21no—
29C23×C4×C11C2311yescharacteristic
30C22×C22⋊D11—21no—
31C23×Dic11—21no—
32C23×Dic11D411yescharacteristic
33C22×D44—22no—
34C22×D44C2×C411yescharacteristic, complemented
35C22×C4×D11—24no—
36C22×C4×D11—28no—
37C22×C4×D11—21no—
38C22×C4×D11—21no—
39C22×C4×D11—21no—
40C22×C4×D11—21no—
41C22×C4×D11—44no—
42C22×C4×D11—44no—
43C22×C4×D11—42no—
44C22×C4×D11—42no—
45C22×C4×D11C2×C412yes—
46C22×C4×D11D412yes—
47C22×C8×C11—21no—
48C2×C11×C4⋊C4C2×C412yescomplemented
49C2×C11×C22⋊C4—21no—
50#66983—21no—
51#66983—21no—
52#66983—21no—
53#66983—21no—
54C2×(C2×D11)⋊C4—22no—
55C2×(C2×D11)⋊C4—21no—
56C2×(C2×D11)⋊C4—22no—
57C2×C4⋊Dic11C2×C411yescharacteristic, complemented
58C22×C11⋊C8—21no—
59#66948—44no—
60#66935—42no—
61#66935—42no—
62C11×C22⋊C8—21no—
63C11×C22⋊C8—21no—
64C11×#95—21no—
65C11×#95—21no—
66C11×#95D412yescomplemented
67C11⋊#95—24no—
68C11⋊#95—21no—
69C11⋊#95—22no—
70C11⋊#95D412yescomplemented
71C22⋊(C11⋊C8)—21no—
72C22⋊(C11⋊C8)—21no—
73(C2×D11)⋊C8—44no—
74#9147—111nomaximal, Sylow
75C24×C11C2×D411yescharacteristic
76C23×D11—21no—
77C23×D11—21no—
78C23×D11—21no—
79C23×D11—21no—
80C23×D11—24no—
81C23×D11—24no—
82C23×D11—21no—
83C23×D11C22⋊C412yes—
84C23×D11D812yes—
85C23×D11SD1612yes—
86C22×C4×C11—24no—
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11—42no—
90C22×C4×C11—42no—
91C22×C4×C11—41no—
92C22×C4×C11—41no—
93C22×C4×C11C22×C411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11#4111yescharacteristic
98C22×C4×C11#4111yescharacteristic
99C2×C22⋊D11—41no—
100C2×C22⋊D11—41no—
101C2×C22⋊D11—41no—
102C2×C22⋊D11—41no—
103C2×C22⋊D11—41no—
104C2×C22⋊D11—41no—
105C22×Dic11—24no—
106C22×Dic11—21no—
107C22×Dic11—21no—
108C22×Dic11—22no—
109C22×Dic11—21no—
110C22×Dic11—42no—
111C22×Dic11—42no—
112C22×Dic11—41no—
113C22×Dic11—41no—
114C22×Dic11C22⋊C412yes—
115C2×D44—21no—
116C2×D44—21no—
117C2×D44—42no—
118C2×D44—44no—
119C2×D44—44no—
120C2×D44—44no—
121C2×C4×D11—216no—
122C2×C4×D11—24no—
123C2×C4×D11—24no—
124C2×C4×D11—22no—
125C2×C4×D11—22no—
126C2×C4×D11—22no—
127C2×C4×D11—22no—
128C2×C4×D11—42no—
129C2×C4×D11—42no—
130C2×C4×D11—44no—
131C2×C4×D11—44no—
132C2×C4×D11—44no—
133C2×C4×D11—44no—
134C2×C4×D11—48no—
135C2×C4×D11—416no—
136C2×C4×D11—416no—
137C2×C4×D11—48no—
138C2×C8×C11—42no—
139C2×C8×C11—41no—
140C11×C4⋊C4—42no—
141C11×C22⋊C4—41no—
142C11×C22⋊C4—41no—
143(C2×D11)⋊C4—44no—
144(C2×D11)⋊C4—44no—
145(C2×D11)⋊C4—41no—
146(C2×D11)⋊C4—41no—
147C4⋊Dic11—21no—
148C4⋊Dic11—21no—
149C2×C11⋊C8—42no—
150C2×C11⋊C8—41no—
151#2847—111no—
152C22×#95—111no—
153#1779—111no—
154C2×#327—111no—
155C2×#327—111no—
156#1294—111no—
157#1294D1111yescharacteristic, complemented
158C23×C11—22no—
159C23×C11—22no—
160C23×C11C2×C22⋊C411yescharacteristic
161C23×C11#12011yescharacteristic
162C23×C11#12311yescharacteristic
163C23×C11C2×D811yescharacteristic
164C23×C11C2×SD1611yescharacteristic
165C23×C11AGL(1,ℤ/8)11yescharacteristic
166C23×C11#13711yescharacteristic
167C22×D11—24no—
168C22×D11—24no—
169C22×D11—24no—
170C22×D11—28no—
171C22×D11—24no—
172C22×D11—28no—
173C22×D11—22no—
174C22×D11—22no—
175C22×D11—22no—
176C22×D11—22no—
177C22×D11—22no—
178C22×D11—22no—
179C22×D11—22no—
180C22×D11—22no—
181C22×D11—28no—
182C22×D11—28no—
183C22×D11—41no—
184C22×D11—42no—
185C22×D11—41no—
186C22×D11—41no—
187C22×D11—42no—
188C22×D11#9914yes—
189C22×D11#10214yes—
190C22×D11#10414yes—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—24no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—42no—
199C2×C4×C11—44no—
200C2×C4×C11—44no—
201C2×C4×C11—42no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11C4×D411yescharacteristic
206C2×C4×C11C4×D411yescharacteristic
207C2×C4×C11#12111yescharacteristic
208C2×C4×C11#12111yescharacteristic
209C22⋊D11—81no—
210C22⋊D11—81no—
211C22⋊D11—81no—
212C22⋊D11—81no—
213C2×Dic11—24no—
214C2×Dic11—22no—
215C2×Dic11—22no—
216C2×Dic11—22no—
217C2×Dic11—42no—
218C2×Dic11—44no—
219C2×Dic11—44no—
220C2×Dic11—42no—
221C2×Dic11—42no—
222C2×Dic11—42no—
223C2×Dic11—41no—
224C2×Dic11—41no—
225C2×Dic11—41no—
226D44—81no—
227D44—81no—
228D44—88no—
229C4×D11—44no—
230C4×D11—44no—
231C4×D11—44no—
232C4×D11—44no—
233C4×D11—432no—
234C8×C11—81no—
235C11⋊C8—81no—
236C24×C4—111no—
237C24×C4—221no—
238C2×#121—111no—
239C2×#121—112no—
240C2×#120—221no—
241C2×C22⋊C8—111no—
242C2×C22⋊C8—222no—
243C2×C22⋊C8C2×D1111yescharacteristic
244#386—222no—
245#386—221no—
246#380—112no—
247#380C2×D1111yescharacteristic
248C2×#95—111no—
249C2×#95—222no—
250C2×#95—221no—
251C2×#95—222no—
252C2×#95C2×D1111yescharacteristic
253#327—222no—
254#327—222no—
255C22×C11—21no—
256C22×C11—21no—
257C22×C11—21no—
258C22×C11—21no—
259C22×C11—22no—
260C22×C11—22no—
261C22×C11—22no—
262C22×C11—22no—
263C22×C11#38611yescharacteristic
264C22×C11C2×#9912yes—
265C22×C11C2×#10211yescharacteristic
266C22×C11#41711yescharacteristic
267C22×C11C2×#10412yes—
268C22×C11#44711yescharacteristic
269C22×C11#44811yescharacteristic
270C22×C11#48011yescharacteristic
271C22×C11#48111yescharacteristic
272C2×D11—28no—
273C2×D11—28no—
274C2×D11—28no—
275C2×D11—28no—
276C2×D11—24no—
277C2×D11—24no—
278C2×D11—24no—
279C2×D11—24no—
280C2×D11—24no—
281C2×D11—24no—
282C2×D11—81no—
283C2×D11—81no—
284C2×D11—81no—
285C2×D11—82no—
286C2×D11—82no—
287C2×D11#32718yescomplemented
288C4×C11—21no—
289C4×C11—21no—
290C4×C11—21no—
291C4×C11—21no—
292C4×C11—44no—
293C4×C11—82no—
294Dic11—44no—
295Dic11—42no—
296Dic11—81no—
297C25—111no—
298C22×D4—111no—
299C22×D4—222no—
300C22×D4—221no—
301C23×C4—21no—
302C23×C4—111no—
303C23×C4—112no—
304C23×C4—112no—
305C23×C4—224no—
306C23×C4—228no—
307C23×C4—221no—
308C23×C4—221no—
309C23×C4—221no—
310C23×C4—221no—
311C23×C4—221no—
312C23×C4—444no—
313C23×C4—442no—
314C23×C4—444no—
315C23×C4—442no—
316C23×C4C22×D1111yescharacteristic
317C22×C8—21no—
318C22×C8—221no—
319#121—221no—
320#121—221no—
321#121—221no—
322#121—221no—
323#121—444no—
324#120—442no—
325#120—442no—
326C2×C4⋊C4—111no—
327C2×C4⋊C4C4×D1112yescomplemented
328C2×C22⋊C4—21no—
329C2×C22⋊C4—222no—
330C2×C22⋊C4—222no—
331C2×C22⋊C4—221no—
332C22⋊C8—21no—
333C22⋊C8—21no—
334C22⋊C8—221no—
335C22⋊C8—221no—
336C22⋊C8—444no—
337#95—21no—
338#95—21no—
339#95—112no—
340#95—222no—
341#95—224no—
342#95—221no—
343#95D4412yescomplemented
344C2×C11—21no—
345C2×C11—21no—
346C2×C11—21no—
347C2×C11—21no—
348C2×C11C2×#32712yes—
349C2×C11#150412yes—
350C2×C11#187411yescharacteristic
351C2×C11#189611yescharacteristic
352C2×C11#189811yescharacteristic
353D11—28no—
354D11—161no—
355C24—112no—
356C24—112no—
357C24—112no—
358C24—224no—
359C24—224no—
360C24—221no—
361C24—221no—
362C24—221no—
363C24—221no—
364C24—221no—
365C24D4×D1111yescharacteristic
366C2×D4—221no—
367C2×D4—221no—
368C2×D4—442no—
369C2×D4—444no—
370C2×D4—444no—
371C2×D4—444no—
372C2×D4—441no—
373C2×D4—441no—
374C2×D4—441no—
375C2×D4—441no—
376C2×D4—441no—
377C2×D4—441no—
378C22×C4—24no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—42no—
382C22×C4—42no—
383C22×C4—41no—
384C22×C4—41no—
385C22×C4—112no—
386C22×C4—224no—
387C22×C4—224no—
388C22×C4—2216no—
389C22×C4—224no—
390C22×C4—222no—
391C22×C4—221no—
392C22×C4—221no—
393C22×C4—222no—
394C22×C4—222no—
395C22×C4—222no—
396C22×C4—222no—
397C22×C4—221no—
398C22×C4—442no—
399C22×C4—442no—
400C22×C4—444no—
401C22×C4—444no—
402C22×C4—444no—
403C22×C4—444no—
404C22×C4—4416no—
405C22×C4—448no—
406C22×C4—4416no—
407C22×C4—448no—
408C22×C4—442no—
409C22×C4—442no—
410C22×C4—441no—
411C22×C4—441no—
412C22×C4C2×C4×D1111yescharacteristic
413C22×C4C2×D4411yescharacteristic
414C22×C4#433911yescharacteristic
415C22×C4D4×D1111yescharacteristic
416C22×C4D4×D1111yescharacteristic
417C22×C4#434311yescharacteristic
418C2×C8—42no—
419C2×C8—41no—
420C2×C8—442no—
421C2×C8—441no—
422C4⋊C4—42no—
423C4⋊C4—221no—
424C4⋊C4—221no—
425C22⋊C4—41no—
426C22⋊C4—41no—
427C22⋊C4—444no—
428C22⋊C4—444no—
429C22⋊C4—441no—
430C22⋊C4—441no—
431C11#914711yescharacteristic, complemented, Sylow
432C23—22no—
433C23—22no—
434C23—114no—
435C23—114no—
436C23—114no—
437C23—228no—
438C23—228no—
439C23—224no—
440C23—224no—
441C23—224no—
442C23—228no—
443C23—224no—
444C23—228no—
445C23—222no—
446C23—222no—
447C23—222no—
448C23—222no—
449C23—222no—
450C23—222no—
451C23—222no—
452C23—222no—
453C23—441no—
454C23—442no—
455C23—441no—
456C23—441no—
457C23—442no—
458C23C22⋊C4×D1111yescharacteristic
459C23#6693511yescharacteristic
460C23#6694711yescharacteristic
461C23D8×D1111yescharacteristic
462C23SD16×D1111yescharacteristic
463C23#6696711yescharacteristic
464C23#6697111yescharacteristic
465D4—881no—
466D4—881no—
467D4—888no—
468D4—881no—
469D4—881no—
470D4—881no—
471D4—881no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—24no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—42no—
480C2×C4—44no—
481C2×C4—44no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—224no—
487C2×C4—222no—
488C2×C4—222no—
489C2×C4—222no—
490C2×C4—444no—
491C2×C4—444no—
492C2×C4—444no—
493C2×C4—444no—
494C2×C4—4432no—
495C2×C4—442no—
496C2×C4—444no—
497C2×C4—444no—
498C2×C4—442no—
499C2×C4—442no—
500C2×C4—442no—
501C2×C4—441no—
502C2×C4—441no—
503C2×C4—441no—
504C2×C4C4×D4411yescharacteristic
505C2×C4#6693711yescharacteristic
506C2×C4#6694611yescharacteristic
507C2×C4#6694811yescharacteristic
508C8—81no—
509C8—881no—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—21no—
514C22—22no—
515C22—22no—
516C22—22no—
517C22—22no—
518C22—118no—
519C22—228no—
520C22—228no—
521C22—228no—
522C22—228no—
523C22—224no—
524C22—224no—
525C22—224no—
526C22—224no—
527C22—224no—
528C22—224no—
529C22—881no—
530C22—881no—
531C22—882no—
532C22—882no—
533C22—881no—
534C22#1062227811yescharacteristic
535C22D11×#9912yes—
536C22D11×#10211yescharacteristic
537C22#1062238611yescharacteristic
538C22#1062241611yescharacteristic
539C22#1062241911yescharacteristic
540C22D11×#10412yes—
541C22#1062247611yescharacteristic
542C22#1062249511yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—21no—
547C4—44no—
548C4—82no—
549C4—444no—
550C4—442no—
551C4—881no—
552C2—21no—
553C2—21no—
554C2—21no—
555C2—21no—
556C2—228no—
557C2—1761no—
558C2D11×#32712yes—
559C2#1306711912yes—
560C2#1306893211yescharacteristic
561C2#1306905811yescharacteristic
562C2#1306906811yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1294C2
socleC23×C11C2×C22⋊C4
prime radical#13076899C2
cosocleC23×C4×C11C23
hypercenter#1294D11
hypocenterC11#9147
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
2. C2×D11×#95C2semidirect
3. #13068525C2semidirect
4. C2×#10622108C2semidirect
5. C2×#10622089C2semidirect
6. #13066494C2semidirect
7. C11×#1294C2semidirect
11. C2×#66948C4semidirect
20. #10622600C4semidirect
34. C22×D44C2×C4semidirect
48. C2×C11×C4⋊C4C2×C4semidirect
57. C2×C4⋊Dic11C2×C4semidirect
66. C11×#95D4semidirect
70. C11⋊#95D4semidirect
157. #1294D11semidirect
287. C2×D11#327semidirect
327. C2×C4⋊C4C4×D11semidirect
343. #95D44semidirect
431. C11#9147semidirect

Maximal subgroups

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

subgroupindex
#130768992
C2×D11×#952
#130685252
C2×#106221082
C2×#106220892
#130664942
C11×#12942
#914711