Finite Group Databasebeta

← #14728016

Subgroups — #14728016

Order 2816.

1230 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079599C212yesmaximal, complemented
2#13074303C211yesmaximal, characteristic, complemented
3#13067585C212yesmaximal, complemented
4#13067568C212yesmaximal, complemented
5#13067551C212yesmaximal, complemented
6#13067534C212yesmaximal, complemented
7#13067124C212yesmaximal, complemented
8#13066950C211yesmaximal, characteristic, complemented
9C11×#3449C211yesmaximal, characteristic, complemented
10C22×C11×#41—21no—
11C11×#537—21no—
12C11×#537C2212yes—
13C11×#536—22no—
14C11×#535—22no—
15C11×#534—21no—
16C11×#534C2212yes—
17C11×#532—21no—
18C11×#532C2212yes—
19C11×#525—24no—
20C2×C11×#117C2211yescharacteristic
21C2×#66928C2211yescharacteristic, complemented
22#10622826—21no—
23#10622702—22no—
24#10622687—22no—
25#10622653C2214yescomplemented
26#10622649C2214yescomplemented
27#10622629—24no—
28#10622604C2211yescharacteristic, complemented
29#10622603—21no—
30#10622592C2211yescharacteristic, complemented
31#10622573C2211yescharacteristic
32#10622570—21no—
33#10622560C2211yescharacteristic
34#10622553—21no—
35#10622545C2211yescharacteristic, complemented
36#10622539C2212yescomplemented
37#10622175C2214yescomplemented
38#10622175C2214yescomplemented
39#10622166C2212yescomplemented
40#10622163C2212yes—
41C2×C11×#41—22no—
42C2×C11×#41—22no—
43C2×C11×#41—22no—
44C2×C11×#41—22no—
45C2×C11×#41—44no—
46C2×C11×#41—44no—
47C22×Q8×C11—21no—
48C22×D4×C11—21no—
49C22×D4×C11—22no—
50C23×C4×C11—22no—
51C23×C4×C11D411yescharacteristic
52C22×C22⋊D11—21no—
53C22×D44C2311yescharacteristic
54C22×Dic22C2311yescharacteristic
55C11×C4⋊Q8—21no—
56C11×C4⋊Q8D412yescomplemented
57C11×#127—21no—
58C11×#127D412yescomplemented
59C11×#124—22no—
60C11×#124—22no—
61C11×#123—24no—
62C11×#123—24no—
63C11×C22⋊Q8—24no—
64C11×C22⋊Q8—24no—
65C11×#121—24no—
66C11×#121—24no—
67C11×#121—22no—
68C11×#121—22no—
69C11×#121—22no—
70C11×#121C2314yes—
71C11×#120—24no—
72C11×#120—24no—
73C4×D4×C11—22no—
74C4×D4×C11—22no—
75C4×D4×C11—22no—
76C4×D4×C11D414yescomplemented
77C11×#117—22no—
78C11×#117—22no—
79C2×C11×C4⋊C4D411yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C22⋊C4D411yescharacteristic
82C2×C11×C22⋊C4C2311yescharacteristic
83C2×C42×C11D411yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C2×C22⋊Dic11—21no—
86C2×#4324—24no—
87C2×#4323—24no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×C4×Dic11—21no—
95#66928—22no—
96#66928—22no—
97C11⋊#95—21no—
98C11⋊#95—21no—
99C11⋊#95—21no—
100C11⋊#95C2311yescharacteristic
101C11⋊#95C2311yescharacteristic
102C22⋊(C11⋊C8)C2314yes—
103#66874—24no—
104#66873—24no—
105C4⋊(C11⋊C8)—22no—
106#66867—22no—
107#18332—111nomaximal, Sylow
108C24×C11—22no—
109C24×C11C2×D411yescharacteristic
110C23×D11—21no—
111C11×#41—48no—
112C11×#41—48no—
113C11×#41—44no—
114C11×#41—44no—
115C11×#41—44no—
116C11×#41—44no—
117C2×Q8×C11—22no—
118C2×Q8×C11—22no—
119C2×Q8×C11—44no—
120C2×D4×C11—24no—
121C2×D4×C11—22no—
122C2×D4×C11—24no—
123C2×D4×C11—22no—
124C2×D4×C11—22no—
125C2×D4×C11—22no—
126C2×D4×C11—22no—
127C2×D4×C11—44no—
128C2×D4×C11—44no—
129C2×D4×C11—44no—
130C2×D4×C11C2×D414yes—
131C22×C4×C11—22no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—22no—
135C22×C4×C11—24no—
136C22×C4×C11—22no—
137C22×C4×C11—24no—
138C22×C4×C11—48no—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2411yescharacteristic
145C2×C22⋊D11—42no—
146C2×C22⋊D11—42no—
147C2×C22⋊D11—81no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C2×D44—22no—
152C2×D44—81no—
153C2×Dic22—22no—
154C2×Dic22—81no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4C2×D414yes—
161C11×C22⋊C4—24no—
162C11×C22⋊C4—24no—
163C11×C22⋊C4—22no—
164C11×C22⋊C4—24no—
165C11×C22⋊C4—22no—
166C11×C22⋊C4—24no—
167C42×C11—21no—
168C42×C11—21no—
169C42×C11C2×D412yes—
170C42×C11C2×D412yes—
171C22⋊Dic11—81no—
172#4324—84no—
173#4323—84no—
174(C2×D11)⋊C4—42no—
175(C2×D11)⋊C4—41no—
176(C2×D11)⋊C4—41no—
177(C2×D11)⋊C4—42no—
178(C2×D11)⋊C4—42no—
179(C2×D11)⋊C4—81no—
180Dic11⋊C4—81no—
181C4×Dic11—42no—
182C2×C11⋊C8—24no—
183#3449D1111yescharacteristic, complemented
184#3213—112no—
185#2610—111no—
186#1604—112no—
187#1601—112no—
188#1598—112no—
189#1595—112no—
190#1505—112no—
191#1464—111no—
192C23×C11—21no—
193C23×C11—21no—
194C23×C11—24no—
195C23×C11—41no—
196C23×C11—41no—
197C23×C11—44no—
198C23×C11—82no—
199C23×C11—82no—
200C23×C11AGL(1,ℤ/8)12yes—
201C23×C11C22×D411yescharacteristic
202C22×D11—41no—
203C22×D11—41no—
204C22×D11—41no—
205C22×D11—41no—
206C22×D11—41no—
207C22×D11—41no—
208C22×D11—41no—
209Q8×C11—44no—
210Q8×C11—44no—
211D4×C11—44no—
212D4×C11—44no—
213D4×C11—44no—
214D4×C11—48no—
215D4×C11—44no—
216D4×C11—44no—
217D4×C11—82no—
218D4×C11—82no—
219D4×C11—82no—
220C2×C4×C11—24no—
221C2×C4×C11—24no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—24no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—48no—
232C2×C4×C11—48no—
233C2×C4×C11—44no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11#12011yescharacteristic
237C2×C4×C11#12011yescharacteristic
238C2×C4×C11#12012yes—
239C2×C4×C11AGL(1,ℤ/8)12yes—
240C2×C4×C11C22×D412yes—
241C22⋊D11—84no—
242C2×Dic11—22no—
243C2×Dic11—41no—
244C2×Dic11—41no—
245C2×Dic11—41no—
246C2×Dic11—41no—
247C2×Dic11—41no—
248C2×Dic11—41no—
249C2×Dic11—41no—
250C2×Dic11—41no—
251D44—44no—
252Dic22—44no—
253C11⋊C8—44no—
254C22×#41—21no—
255#537—21no—
256#537C2×D1112yes—
257#536—22no—
258#535—22no—
259#534—21no—
260#534C2×D1112yes—
261#532—21no—
262#532C2×D1112yes—
263C2×#124—111no—
264#525—24no—
265C2×#117C2×D1111yescharacteristic
266#496—222no—
267#489—222no—
268#463—224no—
269#448—114no—
270#447—114no—
271#432—112no—
272#395—111no—
273#394—111no—
274#393—111no—
275#392—111no—
276#390—221no—
277#388—221no—
278#388—221no—
279#386—221no—
280#376—111no—
281#327—114no—
282#327—114no—
283#324—112no—
284#323—112no—
285C22×C11—21no—
286C22×C11—21no—
287C22×C11—22no—
288C22×C11—42no—
289C22×C11—41no—
290C22×C11—41no—
291C22×C11—44no—
292C22×C11—44no—
293C22×C11—44no—
294C22×C11—81no—
295C22×C11—88no—
296C22×C11C2×#12011yescharacteristic
297C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
298C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
299C2×D11—81no—
300C2×D11—81no—
301C2×D11—81no—
302C2×D11—81no—
303C2×D11—81no—
304C2×D11—81no—
305C2×D11—81no—
306C4×C11—21no—
307C4×C11—22no—
308C4×C11—21no—
309C4×C11—22no—
310C4×C11—22no—
311C4×C11—44no—
312C4×C11—41no—
313C4×C11—41no—
314Dic11—42no—
315Dic11—81no—
316Dic11—81no—
317C2×#41—22no—
318C2×#41—22no—
319C2×#41—22no—
320C2×#41—22no—
321C2×#41—44no—
322C2×#41—44no—
323C22×Q8—21no—
324C22×Q8—111no—
325C22×D4—21no—
326C22×D4—22no—
327C22×D4—111no—
328C22×D4—221no—
329C23×C4—22no—
330C23×C4C22⋊D1111yescharacteristic
331C2×SD16—224no—
332C2×D8—224no—
333C4⋊Q8—21no—
334C4⋊Q8C22⋊D1112yescomplemented
335#127—21no—
336#127C22⋊D1112yescomplemented
337#124—22no—
338#124—22no—
339#124—222no—
340#124—222no—
341#123—24no—
342#123—24no—
343C22⋊Q8—24no—
344C22⋊Q8—24no—
345#121—24no—
346#121—24no—
347#121—22no—
348#121—22no—
349#121—22no—
350#121C22×D1114yes—
351#120—24no—
352#120—24no—
353C4×D4—22no—
354C4×D4—22no—
355C4×D4—22no—
356C4×D4C22⋊D1114yescomplemented
357#117—22no—
358#117—22no—
359C2×C4⋊C4—221no—
360C2×C4⋊C4C22⋊D1111yescharacteristic
361C2×C4⋊C4C22×D1111yescharacteristic
362C2×C22⋊C4—221no—
363C2×C22⋊C4—221no—
364C2×C22⋊C4—221no—
365C2×C22⋊C4—221no—
366C2×C22⋊C4—221no—
367C2×C22⋊C4—221no—
368C2×C22⋊C4C22⋊D1111yescharacteristic
369C2×C22⋊C4C22×D1111yescharacteristic
370C2×C42—221no—
371C2×C42C22⋊D1111yescharacteristic
372C2×C42C22×D1111yescharacteristic
373C4⋊C8—222no—
374#103—224no—
375#102—224no—
376C22⋊C8—114no—
377#97—222no—
378#95—111no—
379#95—111no—
380#95—221no—
381#95—221no—
382#95—221no—
383C2×C11—21no—
384C2×C11—21no—
385C2×C11—42no—
386C2×C11—84no—
387C2×C11#300311yescharacteristic
388C2×C11#301811yescharacteristic
389C2×C11#302711yescharacteristic
390D11—161no—
391C24—22no—
392C24—221no—
393C24C2×C22⋊D1111yescharacteristic
394#41—48no—
395#41—48no—
396#41—44no—
397#41—44no—
398#41—44no—
399#41—44no—
400C2×Q8—22no—
401C2×Q8—22no—
402C2×Q8—44no—
403C2×Q8—222no—
404C2×Q8—881no—
405C2×D4—24no—
406C2×D4—22no—
407C2×D4—24no—
408C2×D4—22no—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—44no—
413C2×D4—44no—
414C2×D4—44no—
415C2×D4—222no—
416C2×D4—442no—
417C2×D4—442no—
418C2×D4—881no—
419C2×D4—881no—
420C2×D4C2×C22⋊D1114yes—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—24no—
426C22×C4—22no—
427C22×C4—24no—
428C22×C4—48no—
429C22×C4—221no—
430C22×C4—221no—
431C22×C4—221no—
432C22×C4C2×C22⋊D1111yescharacteristic
433C22×C4C2×C22⋊D1111yescharacteristic
434C22×C4C2×C22⋊D1111yescharacteristic
435C22×C4C2×C22⋊D1111yescharacteristic
436C22×C4C2×C22⋊D1111yescharacteristic
437C22×C4C23×D1111yescharacteristic
438SD16—884no—
439D8—884no—
440C2×C8—224no—
441C4⋊C4—22no—
442C4⋊C4—22no—
443C4⋊C4—22no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—881no—
447C4⋊C4C2×C22⋊D1114yes—
448C22⋊C4—24no—
449C22⋊C4—24no—
450C22⋊C4—22no—
451C22⋊C4—24no—
452C22⋊C4—22no—
453C22⋊C4—24no—
454C22⋊C4—442no—
455C22⋊C4—442no—
456C22⋊C4—441no—
457C22⋊C4—441no—
458C22⋊C4—442no—
459C22⋊C4—881no—
460C22⋊C4—881no—
461C42—21no—
462C42—21no—
463C42—442no—
464C42C2×C22⋊D1112yes—
465C42C2×C22⋊D1112yes—
466C11#1833211yescharacteristic, complemented, Sylow
467C23—21no—
468C23—21no—
469C23—24no—
470C23—41no—
471C23—41no—
472C23—44no—
473C23—82no—
474C23—82no—
475C23—441no—
476C23—441no—
477C23—441no—
478C23—441no—
479C23—441no—
480C23—441no—
481C23—441no—
482C23#6698512yes—
483C23C22×C22⋊D1111yescharacteristic
484Q8—44no—
485Q8—44no—
486Q8—444no—
487D4—44no—
488D4—44no—
489D4—44no—
490D4—48no—
491D4—44no—
492D4—44no—
493D4—82no—
494D4—82no—
495D4—82no—
496D4—444no—
497D4—884no—
498C2×C4—24no—
499C2×C4—24no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—24no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—48no—
510C2×C4—48no—
511C2×C4—44no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—222no—
515C2×C4—441no—
516C2×C4—441no—
517C2×C4—441no—
518C2×C4—441no—
519C2×C4—441no—
520C2×C4—441no—
521C2×C4—441no—
522C2×C4—441no—
523C2×C4#6698512yes—
524C2×C4#6700611yescharacteristic
525C2×C4#6700611yescharacteristic
526C2×C4#6700612yes—
527C2×C4C22×C22⋊D1112yes—
528C8—444no—
529C22—21no—
530C22—21no—
531C22—22no—
532C22—42no—
533C22—41no—
534C22—41no—
535C22—44no—
536C22—44no—
537C22—44no—
538C22—81no—
539C22—88no—
540C22—881no—
541C22—881no—
542C22—881no—
543C22—881no—
544C22—881no—
545C22—881no—
546C22—881no—
547C22C2×#6698511yescharacteristic
548C22C2×#6698511yescharacteristic
549C22C2×#6700611yescharacteristic
550C4—22no—
551C4—21no—
552C4—22no—
553C4—21no—
554C4—22no—
555C4—41no—
556C4—44no—
557C4—41no—
558C4—442no—
559C4—881no—
560C4—881no—
561C2—21no—
562C2—21no—
563C2—42no—
564C2—84no—
565C2—1761no—
566C2#1307784311yescharacteristic
567C2#1307796511yescharacteristic
568C2#1307801811yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3449C2
socleC22×C11C2×#120
hypercenter#3449D11
hypocenterC11#18332
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3449

Complements

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

NH ≅ G/Ntype
1. #13079599C2semidirect
2. #13074303C2semidirect
3. #13067585C2semidirect
4. #13067568C2semidirect
5. #13067551C2semidirect
6. #13067534C2semidirect
7. #13067124C2semidirect
8. #13066950C2semidirect
9. C11×#3449C2semidirect
21. C2×#66928C22semidirect
25. #10622653C22semidirect
26. #10622649C22semidirect
28. #10622604C22semidirect
30. #10622592C22semidirect
35. #10622545C22semidirect
36. #10622539C22semidirect
37. #10622175C22semidirect
38. #10622175C22semidirect
39. #10622166C22semidirect
56. C11×C4⋊Q8D4semidirect
58. C11×#127D4semidirect
76. C4×D4×C11D4semidirect
183. #3449D11semidirect
334. C4⋊Q8C22⋊D11semidirect
336. #127C22⋊D11semidirect
356. C4×D4C22⋊D11semidirect
466. C11#18332semidirect

Maximal subgroups

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

subgroupindex
#130795992
#130743032
#130675852
#130675682
#130675512
#130675342
#130671242
#130669502
C11×#34492
#1833211