Finite Group Databasebeta

← #14763147

Subgroups — #14763147

Order 2816.

1442 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622613C211yesmaximal, characteristic, complemented
2#13071225C211yesmaximal, characteristic, complemented
3#13069549C212yesmaximal, complemented
4#13069544C212yesmaximal, complemented
5#13069441C211yesmaximal, characteristic, complemented
6#13069433C211yesmaximal, characteristic, complemented
7#13069428C211yesmaximal, characteristic, complemented
8#13069423C211yesmaximal, characteristic, complemented
9#13068556C212yesmaximal, complemented
10#13068547C212yesmaximal, complemented
11C2×C11×#535C211yesmaximal, characteristic
12C22×C11×#41C2211yescharacteristic
13C23×D4×C11C2211yescharacteristic
14C11×#535—24no—
15C11×#535C418yescomplemented
16C2×C11×#127C2211yescharacteristic
17C2×C11×#127C2211yescharacteristic
18C2×C11×#124C2211yescharacteristic
19C2×C11×#124C2211yescharacteristic
20C2×C11×#121—22no—
21C2×C11×#120—22no—
22C2×C11×#117C2211yescharacteristic
23C2×#66899C2212yescomplemented
24C2×#66899C2212yescomplemented
25C2×#66896C2212yes—
26C2×#66896C2212yes—
27C2×#66896C2212yes—
28C2×#66896C2212yes—
29C2×#66896C2212yescomplemented
30C2×#66896C2212yescomplemented
31#10622825C2212yes—
32C2×C22⋊(C11⋊C8)C2212yes—
33#10622613—24no—
34#10622594—22no—
35#10622564—22no—
36#10622549C2211yescharacteristic, complemented
37#10622548C2211yescharacteristic, complemented
38C4×C4⋊Dic11C2212yescomplemented
39C2×C4⋊(C11⋊C8)C2212yescomplemented
40C2×#66867C2211yescharacteristic, complemented
41C2×C4×C11⋊C8C2211yescharacteristic, complemented
42C25×C11—21no—
43C2×C11×#41—22no—
44C2×C11×#41—42no—
45C2×C11×#41—42no—
46C2×C11×#41C2×C414yes—
47C22×Q8×C11C2311yescharacteristic
48C22×D4×C11—21no—
49C22×D4×C11—21no—
50C22×D4×C11—22no—
51C22×D4×C11—22no—
52C22×D4×C11—22no—
53C22×D4×C11—42no—
54C22×D4×C11—42no—
55C22×D4×C11C2×C414yes—
56C22×D4×C11C2311yescharacteristic
57C22×D4×C11C2311yescharacteristic
58C22×D4×C11C2311yescharacteristic
59C23×C4×C11—21no—
60C23×C4×C11C2311yescharacteristic
61C11×#127—22no—
62C11×#127—22no—
63C11×#127C2×C414yes—
64C11×#127C2×C414yes—
65C11×#124—22no—
66C11×#124—22no—
67C11×#124C2×C414yes—
68C11×#124C2×C414yes—
69C11×#121—216no—
70C11×#120—216no—
71C11×#117C2×C414yes—
72C11×#117D414yes—
73C2×C11×C4⋊C4D412yes—
74C2×C11×C22⋊C4—22no—
75C2×C11×C22⋊C4—22no—
76C2×C11×C22⋊C4D412yes—
77C2×C42×C11C2311yescharacteristic
78C2×C42×C11C2311yescharacteristic
79C2×C22⋊Dic11—22no—
80C2×C4⋊Dic11—22no—
81C2×C4⋊Dic11C2312yes—
82C2×C4⋊Dic11C2312yes—
83C2×C4×Dic11—22no—
84C22×C11⋊C8C2312yes—
85C22×C11⋊C8C2312yes—
86#66899—42no—
87#66899—42no—
88#66896—42no—
89#66896—42no—
90#66896—42no—
91#66896—42no—
92#66896—42no—
93#66896—42no—
94C11⋊#95—22no—
95C11⋊#95—22no—
96C11⋊#95—22no—
97C22⋊(C11⋊C8)—24no—
98C4⋊(C11⋊C8)—24no—
99#66867—22no—
100C4×C11⋊C8—22no—
101#21813—111nomaximal, Sylow
102C24×C11—21no—
103C24×C11—21no—
104C24×C11—21no—
105C24×C11—24no—
106C24×C11—42no—
107C24×C11—42no—
108C24×C11—82no—
109C24×C11—82no—
110C24×C11C2×D411yescharacteristic
111C11×#41—48no—
112C11×#41—48no—
113C2×Q8×C11—21no—
114C2×Q8×C11—22no—
115C2×Q8×C11—22no—
116C2×Q8×C11C22×C412yes—
117C2×D4×C11—24no—
118C2×D4×C11—24no—
119C2×D4×C11—28no—
120C2×D4×C11—28no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—22no—
125C2×D4×C11—22no—
126C2×D4×C11—22no—
127C2×D4×C11—22no—
128C2×D4×C11—22no—
129C2×D4×C11—22no—
130C2×D4×C11—48no—
131C2×D4×C11—42no—
132C2×D4×C11—42no—
133C2×D4×C11—48no—
134C2×D4×C11—42no—
135C2×D4×C11—42no—
136C2×D4×C11—82no—
137C2×D4×C11—82no—
138C2×D4×C11—82no—
139C2×D4×C11—82no—
140C2×D4×C11C22×C412yes—
141C2×D4×C11C22×C412yes—
142C2×D4×C11C22×C412yes—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—21no—
146C22×C4×C11—24no—
147C22×C4×C11—42no—
148C22×C4×C11—42no—
149C22×C4×C11C22×C412yes—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D412yes—
152C22×C4×C11C2×D412yes—
153C22×C4×C11C2×D412yes—
154C22×C4×C11C2411yescharacteristic
155C22×Dic11—22no—
156C22×Dic11—22no—
157C11×C4⋊C4C22⋊C418yes—
158C11×C22⋊C4—28no—
159C11×C22⋊C4—28no—
160C11×C22⋊C4C22⋊C418yes—
161C42×C11C22×C412yes—
162C42×C11C22×C412yes—
163C42×C11C2×D412yes—
164C42×C11C2×D412yes—
165C22⋊Dic11—82no—
166C4⋊Dic11—22no—
167C4⋊Dic11—22no—
168C4⋊Dic11—22no—
169C4⋊Dic11—22no—
170C4⋊Dic11—82no—
171C4×Dic11—82no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8—22no—
174C2×C11⋊C8—22no—
175C2×C11⋊C8—22no—
176C2×C11⋊C8—22no—
177C2×C11⋊C8—22no—
178C2×#535D1111yescharacteristic
179C2×#433—111no—
180#2314—111no—
181#1983—112no—
182#1982—112no—
183#1961—111no—
184#1959—111no—
185#1958—111no—
186#1957—111no—
187#1788—112no—
188#1786—112no—
189C23×C11—21no—
190C23×C11—21no—
191C23×C11—22no—
192C23×C11—22no—
193C23×C11—22no—
194C23×C11—22no—
195C23×C11—22no—
196C23×C11—48no—
197C23×C11—41no—
198C23×C11—41no—
199C23×C11—41no—
200C23×C11—41no—
201C23×C11—41no—
202C23×C11—41no—
203C23×C11—42no—
204C23×C11—42no—
205C23×C11—42no—
206C23×C11—42no—
207C23×C11—42no—
208C23×C11—42no—
209C23×C11—88no—
210C23×C11—84no—
211C23×C11—84no—
212C23×C11—88no—
213C23×C11C2×C22⋊C412yes—
214C23×C11C22×D411yescharacteristic
215Q8×C11—24no—
216Q8×C11—42no—
217D4×C11—24no—
218D4×C11—24no—
219D4×C11—24no—
220D4×C11—48no—
221D4×C11—48no—
222D4×C11—42no—
223D4×C11—42no—
224D4×C11—42no—
225D4×C11—88no—
226D4×C11—88no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—22no—
236C2×C4×C11—48no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11C2×C22⋊C414yes—
240C2×C4×C11C2×C22⋊C414yes—
241C2×C4×C11C2×C22⋊C412yes—
242C2×C4×C11C23×C411yescharacteristic
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11H(5,𝔽2)12yes—
245C2×C4×C11H(5,𝔽2)12yes—
246C2×Dic11—42no—
247C2×Dic11—42no—
248C2×Dic11—42no—
249C2×Dic11—42no—
250C2×Dic11—42no—
251C2×Dic11—42no—
252C11⋊C8—42no—
253C11⋊C8—42no—
254C22×#41C2×D1111yescharacteristic
255C23×D4C2×D1111yescharacteristic
256#535—24no—
257#535Dic1118yescomplemented
258C2×#127C2×D1111yescharacteristic
259C2×#127C2×D1111yescharacteristic
260C2×#124C2×D1111yescharacteristic
261C2×#124C2×D1111yescharacteristic
262C2×#121—22no—
263C2×#120—22no—
264C2×#117C2×D1111yescharacteristic
265#433—224no—
266C2×C4⋊C8—112no—
267C2×#103—112no—
268C2×#103—112no—
269C2×#102—112no—
270C2×#102—112no—
271C2×#102—112no—
272C2×#102—112no—
273C2×#102—112no—
274C2×#102—112no—
275C2×C22⋊C8—112no—
276C2×#97—111no—
277C2×C4×C8—111no—
278#388—222no—
279#387—222no—
280#384—111no—
281#382—111no—
282#380—112no—
283C4×C4⋊C4—112no—
284C22×C11—22no—
285C22×C11—24no—
286C22×C11—41no—
287C22×C11—41no—
288C22×C11—42no—
289C22×C11—42no—
290C22×C11—42no—
291C22×C11—42no—
292C22×C11—44no—
293C22×C11—44no—
294C22×C11—44no—
295C22×C11—816no—
296C22×C11—81no—
297C22×C11—81no—
298C22×C11—81no—
299C22×C11—81no—
300C22×C11—81no—
301C22×C11—81no—
302C22×C11—82no—
303C22×C11—82no—
304C22×C11—82no—
305C22×C11C22×C22⋊C411yescharacteristic
306C22×C11#53511yescharacteristic
307C22×C11#53511yescharacteristic
308C22×C11#57612yes—
309C22×C11#57712yes—
310C4×C11—22no—
311C4×C11—24no—
312C4×C11—24no—
313C4×C11—42no—
314C4×C11#51812yes—
315C4×C11#53512yes—
316Dic11—82no—
317Dic11—82no—
318C25—21no—
319C2×#41—22no—
320C2×#41—42no—
321C2×#41—42no—
322C2×#41C2×Dic1114yes—
323C22×Q8C22×D1111yescharacteristic
324C22×D4—21no—
325C22×D4—21no—
326C22×D4—22no—
327C22×D4—22no—
328C22×D4—22no—
329C22×D4—42no—
330C22×D4—42no—
331C22×D4C2×Dic1114yes—
332C22×D4C22×D1111yescharacteristic
333C22×D4C22×D1111yescharacteristic
334C22×D4C22×D1111yescharacteristic
335C23×C4—21no—
336C23×C4C22×D1111yescharacteristic
337C22×C8—112no—
338C22×C8—112no—
339#127—22no—
340#127—22no—
341#127C2×Dic1114yes—
342#127C2×Dic1114yes—
343#124—22no—
344#124—22no—
345#124C2×Dic1114yes—
346#124C2×Dic1114yes—
347#121—216no—
348#120—216no—
349#117C2×Dic1114yes—
350#117C22⋊D1114yes—
351C2×C4⋊C4—112no—
352C2×C4⋊C4—112no—
353C2×C4⋊C4—222no—
354C2×C4⋊C4C22⋊D1112yes—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—222no—
358C2×C22⋊C4C22⋊D1112yes—
359C2×C42—222no—
360C2×C42C22×D1111yescharacteristic
361C2×C42C22×D1111yescharacteristic
362C4⋊C8—224no—
363#103—442no—
364#103—442no—
365#102—442no—
366#102—442no—
367#102—442no—
368#102—442no—
369#102—442no—
370#102—442no—
371C22⋊C8—224no—
372#97—222no—
373C4×C8—222no—
374#95—222no—
375#95—222no—
376#95—222no—
377C2×C11—42no—
378C2×C11—82no—
379C2×C11—82no—
380C2×C11—82no—
381C2×C11#230911yescharacteristic
382C2×C11#289712yes—
383C2×C11#322011yescharacteristic
384C2×C11#322211yescharacteristic
385C2×C11#322412yes—
386C24—21no—
387C24—21no—
388C24—21no—
389C24—24no—
390C24—42no—
391C24—42no—
392C24—82no—
393C24—82no—
394C24C2×C22⋊D1111yescharacteristic
395#41—48no—
396#41—48no—
397C2×Q8—21no—
398C2×Q8—22no—
399C2×Q8—22no—
400C2×Q8C22×Dic1112yes—
401C2×D4—24no—
402C2×D4—24no—
403C2×D4—28no—
404C2×D4—28no—
405C2×D4—22no—
406C2×D4—22no—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—21no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4—48no—
415C2×D4—42no—
416C2×D4—42no—
417C2×D4—48no—
418C2×D4—42no—
419C2×D4—42no—
420C2×D4—82no—
421C2×D4—82no—
422C2×D4—82no—
423C2×D4—82no—
424C2×D4C22×Dic1112yes—
425C2×D4C22×Dic1112yes—
426C2×D4C22×Dic1112yes—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—21no—
430C22×C4—24no—
431C22×C4—42no—
432C22×C4—42no—
433C22×C4—222no—
434C22×C4—222no—
435C22×C4C22×Dic1112yes—
436C22×C4C2×C22⋊D1111yescharacteristic
437C22×C4C2×C22⋊D1112yes—
438C22×C4C2×C22⋊D1112yes—
439C22×C4C2×C22⋊D1112yes—
440C22×C4C23×D1111yescharacteristic
441C2×C8—222no—
442C2×C8—222no—
443C2×C8—222no—
444C2×C8—222no—
445C2×C8—222no—
446C2×C8—222no—
447C4⋊C4—222no—
448C4⋊C4—222no—
449C4⋊C4—222no—
450C4⋊C4—222no—
451C4⋊C4—882no—
452C4⋊C4C22⋊Dic1118yes—
453C22⋊C4—28no—
454C22⋊C4—28no—
455C22⋊C4—882no—
456C22⋊C4C22⋊Dic1118yes—
457C42—882no—
458C42C22×Dic1112yes—
459C42C22×Dic1112yes—
460C42C2×C22⋊D1112yes—
461C42C2×C22⋊D1112yes—
462C11#2181311yescharacteristic, complemented, Sylow
463C23—21no—
464C23—21no—
465C23—22no—
466C23—22no—
467C23—22no—
468C23—22no—
469C23—22no—
470C23—48no—
471C23—41no—
472C23—41no—
473C23—41no—
474C23—41no—
475C23—41no—
476C23—41no—
477C23—42no—
478C23—42no—
479C23—42no—
480C23—42no—
481C23—42no—
482C23—42no—
483C23—88no—
484C23—84no—
485C23—84no—
486C23—88no—
487C23C2×C22⋊Dic1112yes—
488C23C22×C22⋊D1111yescharacteristic
489Q8—24no—
490Q8—42no—
491D4—24no—
492D4—24no—
493D4—24no—
494D4—48no—
495D4—48no—
496D4—42no—
497D4—42no—
498D4—42no—
499D4—88no—
500D4—88no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—22no—
510C2×C4—48no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—442no—
514C2×C4—442no—
515C2×C4—442no—
516C2×C4—442no—
517C2×C4—442no—
518C2×C4—442no—
519C2×C4C2×C22⋊Dic1114yes—
520C2×C4C2×C22⋊Dic1114yes—
521C2×C4C2×C22⋊Dic1112yes—
522C2×C4#6703712yes—
523C2×C4#6703712yes—
524C2×C4C23×Dic1111yescharacteristic
525C2×C4C22×C22⋊D1111yescharacteristic
526C8—442no—
527C8—442no—
528C22—22no—
529C22—24no—
530C22—41no—
531C22—41no—
532C22—42no—
533C22—42no—
534C22—42no—
535C22—42no—
536C22—44no—
537C22—44no—
538C22—44no—
539C22—816no—
540C22—81no—
541C22—81no—
542C22—81no—
543C22—81no—
544C22—81no—
545C22—81no—
546C22—82no—
547C22—82no—
548C22—82no—
549C22#1062333611yescharacteristic
550C22#1062333611yescharacteristic
551C22#1062336612yes—
552C22#1062336712yes—
553C22C22×C22⋊Dic1111yescharacteristic
554C4—22no—
555C4—24no—
556C4—24no—
557C4—42no—
558C4—882no—
559C4—882no—
560C4#1062332912yes—
561C4#1062333612yes—
562C2—42no—
563C2—82no—
564C2—82no—
565C2—82no—
566C2#1307119811yescharacteristic
567C2#1307714212yes—
568C2#1307966611yescharacteristic
569C2#1307968811yescharacteristic
570C2#1307971012yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#535C2
socleC23×C11C22×D4
cosocleC22×C4×C11C24
hypercenterC2×#535D11
hypocenterC11#21813
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#535

Complements

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

NH ≅ G/Ntype
1. C2×#10622613C2semidirect
2. #13071225C2semidirect
3. #13069549C2semidirect
4. #13069544C2semidirect
5. #13069441C2semidirect
6. #13069433C2semidirect
7. #13069428C2semidirect
8. #13069423C2semidirect
9. #13068556C2semidirect
10. #13068547C2semidirect
15. C11×#535C4semidirect
23. C2×#66899C22semidirect
24. C2×#66899C22semidirect
29. C2×#66896C22semidirect
30. C2×#66896C22semidirect
36. #10622549C22semidirect
37. #10622548C22semidirect
38. C4×C4⋊Dic11C22semidirect
39. C2×C4⋊(C11⋊C8)C22semidirect
40. C2×#66867C22semidirect
41. C2×C4×C11⋊C8C22semidirect
257. #535Dic11semidirect
462. C11#21813semidirect

Maximal subgroups

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

subgroupindex
C2×#106226132
#130712252
#130695492
#130695442
#130694412
#130694332
#130694282
#130694232
#130685562
#130685472
C2×C11×#5352
#2181311