Finite Group Databasebeta

← #14757464

Subgroups — #14757464

Order 2816.

1686 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#124C211yesmaximal, characteristic
2C2×#10622415C212yesmaximal, complemented
3C2×#10622383C212yesmaximal
4C2×#10622320C211yesmaximal, characteristic, complemented
5#13071021C211yesmaximal, characteristic, complemented
6#13069433C211yesmaximal, characteristic, complemented
7#13069432C211yesmaximal, characteristic, complemented
8#13069430C211yesmaximal, characteristic, complemented
9#13069426C212yesmaximal, complemented
10#13069424C212yesmaximal, complemented
11C11×#1959C211yesmaximal, characteristic, complemented
12C22×Q8×D11C2211yescharacteristic
13C22×D4×D11C2211yescharacteristic
14C2×C11×#124C2211yescharacteristic
15C2×#67000C2211yescharacteristic
16C2×#66989C2211yescharacteristic
17C22×#4313C2212yes—
18D11×#124—24no—
19D11×#124C418yescomplemented
20C2×#66945C2212yes—
21C2×#66938—22no—
22C2×C22⋊C4×D11—22no—
23C2×#66928C2211yescharacteristic
24C2×C42×D11C2211yescharacteristic
25C2×C11×#103C2212yescomplemented
26C2×C11×#102C2212yes—
27C2×C11×#97C2211yescharacteristic, complemented
28C11×#384C2211yescharacteristic, complemented
29C2×#66899C2212yescomplemented
30C2×#66896C2212yes—
31C2×#66885C2212yes—
32C2×#66880C2212yescomplemented
33C2×C8×Dic11C2212yescomplemented
34#10622600—22no—
35#10622590C2212yescomplemented
36C4⋊C4×Dic11—22no—
37C2×#66874C2212yescomplemented
38C2×#66873C2212yes—
39#10622548C2211yescharacteristic, complemented
40C2×#66867C2211yescharacteristic, complemented
41#10622415—28no—
42#10622383—28no—
43#10622320—24no—
44C24×D11—21no—
45C22×Q8×C11C2311yescharacteristic
46C22×D4×C11C2311yescharacteristic
47C22×C22⋊D11—21no—
48C2×Q8×D11—22no—
49C2×Q8×D11—24no—
50C2×Q8×D11—24no—
51C2×Q8×D11C2×C414yes—
52C2×D4×D11—24no—
53C2×D4×D11—22no—
54C2×D4×D11—24no—
55C2×D4×D11C2×C414yes—
56C22×D44C2311yescharacteristic
57C22×C4×D11—21no—
58C22×C4×D11D412yes—
59C22×C4×D11C2311yescharacteristic
60C22×Dic22—21no—
61C22×Dic22C2311yescharacteristic
62C22×C8×C11C2312yes—
63C11×#124—22no—
64C11×#124C2×C414yes—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4C2312yes—
67C2×C11×C22⋊C4—22no—
68C2×C42×C11C2311yescharacteristic
69C2×C22⋊Dic11—22no—
70#67000—22no—
71#67000C2×C414yes—
72#66989—22no—
73#66989C2×C414yes—
74C2×(C2×D11)⋊C4—22no—
75C2×(C2×D11)⋊C4—22no—
76C2×(C2×D11)⋊C4—22no—
77C2×C4⋊Dic11—22no—
78C2×C4⋊Dic11C2312yes—
79C2×C4×Dic11—22no—
80C2×C4×Dic11D412yes—
81C2×C4×Dic11C2311yescharacteristic
82C22×C11⋊C8C2312yes—
83C2×#4313—24no—
84C2×#4313—24no—
85C2×#4313D418yes—
86#66945—24no—
87#66945—24no—
88#66938—216no—
89C22⋊C4×D11—216no—
90#66928—22no—
91#66928C2×C414yes—
92C42×D11C2×C414yes—
93C42×D11D414yes—
94C11×#103—24no—
95C11×#102—24no—
96C11×#97—22no—
97#66899—24no—
98#66896—24no—
99C11⋊#95—24no—
100#66885—24no—
101#66880—24no—
102C8×Dic11—24no—
103#66874—24no—
104#66873—24no—
105#66867—22no—
106#21204—111nomaximal, Sylow
107C24×C11—21no—
108C23×D11—21no—
109C23×D11—24no—
110C23×D11—44no—
111C23×D11—44no—
112C23×D11—42no—
113C23×D11—42no—
114C23×D11C2×D411yescharacteristic
115C2×Q8×C11—21no—
116C2×Q8×C11—22no—
117C2×Q8×C11—22no—
118C2×Q8×C11C22×C412yes—
119C2×D4×C11—22no—
120C2×D4×C11—21no—
121C2×D4×C11—22no—
122C2×D4×C11C22×C412yes—
123C22×C4×C11—21no—
124C22×C4×C11—22no—
125C22×C4×C11C2×D412yes—
126C22×C4×C11C2411yescharacteristic
127C2×C22⋊D11—24no—
128C2×C22⋊D11—42no—
129C2×C22⋊D11—42no—
130C22×Dic11—21no—
131C22×Dic11—22no—
132C22×Dic11C2×D412yes—
133C22×Dic11C2×D411yescharacteristic
134Q8×D11—216no—
135Q8×D11—48no—
136D4×D11—216no—
137D4×D11—48no—
138C2×D44—21no—
139C2×D44—22no—
140C2×D44—22no—
141C2×D44C22×C412yes—
142C2×C4×D11—24no—
143C2×C4×D11—42no—
144C2×C4×D11—42no—
145C2×C4×D11—42no—
146C2×C4×D11—42no—
147C2×C4×D11C22⋊C418yes—
148C2×C4×D11C22×C412yes—
149C2×C4×D11C2×D412yes—
150C2×C4×D11C2×D414yes—
151C2×C4×D11#4114yes—
152C2×Dic22—24no—
153C2×Dic22—22no—
154C2×Dic22—21no—
155C2×Dic22—22no—
156C2×Dic22—42no—
157C2×Dic22—42no—
158C2×Dic22C22×C412yes—
159C2×C8×C11—22no—
160C2×C8×C11—22no—
161C2×C8×C11C2×D414yes—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—44no—
165C11×C22⋊C4—28no—
166C42×C11C22×C412yes—
167C42×C11C2×D412yes—
168C22⋊Dic11—28no—
169(C2×D11)⋊C4—28no—
170(C2×D11)⋊C4—28no—
171(C2×D11)⋊C4—44no—
172C4⋊Dic11—22no—
173C4⋊Dic11—22no—
174C4⋊Dic11—44no—
175C4×Dic11—44no—
176C4×Dic11C22⋊C418yes—
177C4×Dic11C22×C412yes—
178C4×Dic11C2×D412yes—
179C2×C11⋊C8—22no—
180C2×C11⋊C8—22no—
181C2×C11⋊C8C2×D414yes—
182#4313—216no—
183C22×#124—111no—
184C2×#419—112no—
185C2×#418—112no—
186C2×C4×M16—111no—
187#2285—111no—
188#1959—111no—
189#1959—111no—
190#1959—111no—
191#1959D1111yescharacteristic, complemented
192#1958—112no—
193#1958—112no—
194C23×C11—22no—
195C23×C11—41no—
196C23×C11—41no—
197C23×C11—42no—
198C23×C11—42no—
199C23×C11C22×D411yescharacteristic
200C22×D11—22no—
201C22×D11—22no—
202C22×D11—22no—
203C22×D11—416no—
204C22×D11—41no—
205C22×D11—41no—
206C22×D11—42no—
207C22×D11—42no—
208C22×D11—48no—
209C22×D11—88no—
210C22×D11—84no—
211C22×D11—84no—
212C22×D11C2×C22⋊C412yes—
213C22×D11#12412yes—
214C22×D11#12712yes—
215Q8×C11—24no—
216Q8×C11—42no—
217D4×C11—24no—
218D4×C11—42no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—41no—
223C2×C4×C11—41no—
224C2×C4×C11—42no—
225C2×C4×C11—44no—
226C2×C4×C11C2×C22⋊C414yes—
227C2×C4×C11C23×C411yescharacteristic
228C2×C4×C11C22×D412yes—
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C2×#4112yes—
231C22⋊D11—48no—
232C2×Dic11—22no—
233C2×Dic11—22no—
234C2×Dic11—22no—
235C2×Dic11—41no—
236C2×Dic11—41no—
237C2×Dic11—42no—
238C2×Dic11—44no—
239C2×Dic11C2×C22⋊C414yes—
240C2×Dic11C2×C22⋊C412yes—
241C2×Dic11#12412yes—
242C2×Dic11#12712yes—
243D44—24no—
244D44—42no—
245C4×D11—48no—
246C4×D11—48no—
247C4×D11C4×D418yes—
248C4×D11#12118yes—
249Dic22—24no—
250Dic22—42no—
251Dic22—48no—
252C8×C11—24no—
253C11⋊C8—24no—
254C23×Q8—111no—
255C23×D4—111no—
256C22×M16—112no—
257C2×#124—111no—
258C2×#124—111no—
259C2×#124—118no—
260C2×#124—111no—
261C2×#124—222no—
262C2×#124—224no—
263C2×#124C2×D1111yescharacteristic
264C2×#117—112no—
265C22×C22⋊C4—222no—
266C22×C42—111no—
267#419—228no—
268#418—228no—
269C2×#103—112no—
270C2×#103—112no—
271C2×#103—112no—
272C2×#103C2×D1112yescomplemented
273C2×#102—112no—
274C2×#102—112no—
275C2×#102—112no—
276C2×#102C2×D1112yes—
277C4×M16—224no—
278C2×#97—111no—
279C2×#97C2×D1111yescharacteristic, complemented
280C2×C4×C8—112no—
281#384—111no—
282#384C2×D1111yescharacteristic, complemented
283#382—112no—
284#380—222no—
285C4×C4⋊C4—222no—
286C22×C11—44no—
287C22×C11—42no—
288C22×C11—82no—
289C22×C11—81no—
290C22×C11—81no—
291C22×C11C22×C22⋊C411yescharacteristic
292C22×C11C2×#12411yescharacteristic
293C22×C11C2×#12711yescharacteristic
294C22×C11#57512yes—
295C22×C11#57512yes—
296C2×D11—24no—
297C2×D11—24no—
298C2×D11—22no—
299C2×D11—22no—
300C2×D11—44no—
301C2×D11—42no—
302C2×D11—816no—
303C2×D11—82no—
304C2×D11—81no—
305C2×D11—81no—
306C2×D11#39014yes—
307C4×C11—24no—
308C4×C11—42no—
309C4×C11—82no—
310C4×C11C2×C4×D412yes—
311C4×C11C2×#12112yes—
312Dic11—24no—
313Dic11—42no—
314Dic11—82no—
315Dic11#39014yes—
316C25—221no—
317C22×Q8—114no—
318C22×Q8—111no—
319C22×Q8—221no—
320C22×Q8—222no—
321C22×Q8—224no—
322C22×Q8—224no—
323C22×Q8C22×D1111yescharacteristic
324C22×D4—114no—
325C22×D4—111no—
326C22×D4—224no—
327C22×D4—224no—
328C22×D4—222no—
329C22×D4—221no—
330C22×D4C22×D1111yescharacteristic
331C23×C4—111no—
332C23×C4—112no—
333C23×C4—221no—
334C2×M16—118no—
335C2×M16—224no—
336C2×M16—224no—
337C22×C8—112no—
338C22×C8C22×D1112yes—
339#124—22no—
340#124—114no—
341#124—114no—
342#124—114no—
343#124—2216no—
344#124—222no—
345#124—222no—
346#124—222no—
347#124C4×D1114yes—
348#117—224no—
349#117—224no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—112no—
352C2×C4⋊C4—222no—
353C2×C4⋊C4C22×D1112yes—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—2216no—
356C2×C22⋊C4—222no—
357C2×C22⋊C4—222no—
358C2×C22⋊C4—222no—
359C2×C22⋊C4—222no—
360C2×C42—112no—
361C2×C42—111no—
362C2×C42—114no—
363C2×C42—114no—
364C2×C42—222no—
365C2×C42C22×D1111yescharacteristic
366#103—24no—
367#103—224no—
368#103—224no—
369#103—224no—
370#102—24no—
371#102—224no—
372#102—224no—
373#102—224no—
374#97—22no—
375#97—222no—
376C4×C8—224no—
377#95—224no—
378C2×C11—82no—
379C2×C11C2×#39011yescharacteristic
380C2×C11#289612yes—
381C2×C11#314012yes—
382C2×C11#315311yescharacteristic
383C2×C11#315311yescharacteristic
384D11—24no—
385D11—82no—
386C24—21no—
387C24—111no—
388C24—224no—
389C24—221no—
390C24—442no—
391C24—442no—
392C24—444no—
393C24—444no—
394C2×Q8—21no—
395C2×Q8—22no—
396C2×Q8—22no—
397C2×Q8—112no—
398C2×Q8—224no—
399C2×Q8—2216no—
400C2×Q8—221no—
401C2×Q8—222no—
402C2×Q8—222no—
403C2×Q8—442no—
404C2×Q8—442no—
405C2×Q8—448no—
406C2×Q8C2×C4×D1112yes—
407C2×D4—22no—
408C2×D4—21no—
409C2×D4—22no—
410C2×D4—112no—
411C2×D4—2216no—
412C2×D4—224no—
413C2×D4—222no—
414C2×D4—221no—
415C2×D4—222no—
416C2×D4—448no—
417C2×D4—442no—
418C2×D4—442no—
419C2×D4C2×C4×D1112yes—
420C22×C4—21no—
421C22×C4—22no—
422C22×C4—111no—
423C22×C4—112no—
424C22×C4—112no—
425C22×C4—114no—
426C22×C4—114no—
427C22×C4—112no—
428C22×C4—118no—
429C22×C4—224no—
430C22×C4—221no—
431C22×C4—222no—
432C22×C4—442no—
433C22×C4—442no—
434C22×C4—442no—
435C22×C4—442no—
436C22×C4D4×D1112yes—
437C22×C4C23×D1111yescharacteristic
438M16—2216no—
439C2×C8—22no—
440C2×C8—22no—
441C2×C8—114no—
442C2×C8—222no—
443C2×C8—222no—
444C2×C8D4×D1114yes—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—44no—
448C4⋊C4—222no—
449C4⋊C4—222no—
450C4⋊C4—444no—
451C22⋊C4—28no—
452C22⋊C4—228no—
453C22⋊C4—228no—
454C22⋊C4—228no—
455C22⋊C4—444no—
456C42—118no—
457C42—112no—
458C42—112no—
459C42—444no—
460C42C2×C4×D1112yes—
461C42D4×D1112yes—
462C11#2120411yescharacteristic, complemented, Sylow
463C23—22no—
464C23—41no—
465C23—42no—
466C23—42no—
467C23—41no—
468C23—112no—
469C23—112no—
470C23—112no—
471C23—222no—
472C23—222no—
473C23—222no—
474C23—448no—
475C23—4416no—
476C23—441no—
477C23—442no—
478C23—442no—
479C23—441no—
480C23—884no—
481C23—884no—
482C23—888no—
483C23C2×D4×D1111yescharacteristic
484Q8—24no—
485Q8—42no—
486Q8—224no—
487Q8—448no—
488Q8—442no—
489D4—24no—
490D4—42no—
491D4—224no—
492D4—448no—
493D4—442no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—42no—
500C2×C4—44no—
501C2×C4—112no—
502C2×C4—112no—
503C2×C4—112no—
504C2×C4—118no—
505C2×C4—118no—
506C2×C4—114no—
507C2×C4—222no—
508C2×C4—222no—
509C2×C4—222no—
510C2×C4—448no—
511C2×C4—448no—
512C2×C4—441no—
513C2×C4—441no—
514C2×C4—442no—
515C2×C4—444no—
516C2×C4C22⋊C4×D1114yes—
517C2×C4C22×C4×D1111yescharacteristic
518C2×C4C2×D4×D1112yes—
519C2×C4C2×D4×D1111yescharacteristic
520C2×C4#41×D1112yes—
521C8—24no—
522C8—224no—
523C22—44no—
524C22—42no—
525C22—81no—
526C22—81no—
527C22—82no—
528C22—114no—
529C22—222no—
530C22—222no—
531C22—224no—
532C22—224no—
533C22—444no—
534C22—442no—
535C22—8816no—
536C22—881no—
537C22—881no—
538C22—882no—
539C22C2×C22⋊C4×D1111yescharacteristic
540C22D11×#12411yescharacteristic
541C22D11×#12711yescharacteristic
542C22#1062330412yes—
543C22#1062330812yes—
544C4—24no—
545C4—42no—
546C4—82no—
547C4—114no—
548C4—224no—
549C4—442no—
550C4—882no—
551C4C4×D4×D1112yes—
552C4D11×#12112yes—
553C2—82no—
554C2—224no—
555C2—882no—
556C2D11×#39011yescharacteristic
557C2#1307713212yes—
558C2#1307900112yes—
559C2#1307907911yescharacteristic
560C2#1307908111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1959C2
socleC23×C11C22×D4
prime radicalC22×D4×D11C22
cosocleC22×C4×C11C24
hypercenter#1959D11
hypocenterC11#21204
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1959

Complements

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

NH ≅ G/Ntype
2. C2×#10622415C2semidirect
4. C2×#10622320C2semidirect
5. #13071021C2semidirect
6. #13069433C2semidirect
7. #13069432C2semidirect
8. #13069430C2semidirect
9. #13069426C2semidirect
10. #13069424C2semidirect
11. C11×#1959C2semidirect
19. D11×#124C4semidirect
25. C2×C11×#103C22semidirect
27. C2×C11×#97C22semidirect
28. C11×#384C22semidirect
29. C2×#66899C22semidirect
32. C2×#66880C22semidirect
33. C2×C8×Dic11C22semidirect
35. #10622590C22semidirect
37. C2×#66874C22semidirect
39. #10622548C22semidirect
40. C2×#66867C22semidirect
191. #1959D11semidirect
272. C2×#103C2×D11semidirect
279. C2×#97C2×D11semidirect
282. #384C2×D11semidirect
462. C11#21204semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1242
C2×#106224152
C2×#106223832
C2×#106223202
#130710212
#130694332
#130694322
#130694302
#130694262
#130694242
C11×#19592
#2120411