Finite Group Databasebeta

← #14754755

Subgroups — #14754755

Order 2816.

1598 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623052C211yesmaximal, characteristic
2C2×#10622744C211yesmaximal, characteristic
3C22×#66873C211yesmaximal, characteristic
4#13071240C211yesmaximal, characteristic, complemented
5#13068874C214yesmaximal, complemented
6#13068860C214yesmaximal, complemented
7#13068332C211yesmaximal, characteristic, complemented
8#13068314C211yesmaximal, characteristic, complemented
9C2×C11×#428C211yesmaximal, characteristic, complemented
10C23×D44C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C2×C11×#117C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C2×#66979C2211yescharacteristic
15C2×#66979C2211yescharacteristic
16C23×C11⋊C8C2211yescharacteristic
17#10623052—24no—
18#10623052—24no—
19C2×#66946C2212yes—
20C2×#66946C2212yes—
21C2×C22⋊C4×D11—22no—
22C2×C4×D44—21no—
23C2×C4×D44—21no—
24C11×#428—24no—
25C2×C11×#107C2212yescomplemented
26C2×C11×#106C2212yescomplemented
27#10622823—22no—
28#10622744C418yescomplemented
29C2×#66885C2214yes—
30#10622590—21no—
31#10622589—21no—
32#10622586C2214yescomplemented
33C2×#66873—24no—
34C2×#66873C2214yes—
35#10622188C2214yescomplemented
36#10622167C2212yescomplemented
37#10622167C2212yescomplemented
38C24×D11—21no—
39C23×C4×C11—21no—
40C23×C4×C11C2311yescharacteristic
41C22×D44—21no—
42C22×D44—22no—
43C22×D44—22no—
44C22×D44—22no—
45C22×D44C2×C414yes—
46C22×D44D414yes—
47C22×D44Q814yes—
48C22×D44C2312yes—
49C22×C4×D11—22no—
50C22×C4×D11—22no—
51C2×C11×M16—22no—
52C2×C11×M16—22no—
53C2×C11×M16C2×C414yescomplemented
54C22×C8×C11C2312yes—
55C11×#117—22no—
56C11×#117D414yes—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4C2312yes—
61C2×C11×C4⋊C4C2311yescharacteristic
62C2×C11×C4⋊C4C2311yescharacteristic
63C2×C11×C22⋊C4—21no—
64C2×C42×C11—21no—
65C2×C22⋊Dic11—21no—
66C2×C22⋊Dic11D412yes—
67C2×(C2×D11)⋊C4—22no—
68C2×(C2×D11)⋊C4—22no—
69#66979—22no—
70#66979—22no—
71#66979—22no—
72#66979C2×C414yescomplemented
73C2×C4⋊Dic11D411yescharacteristic
74C2×C4⋊Dic11D411yescharacteristic
75C2×C4⋊Dic11C2312yes—
76C2×Dic11⋊C4—24no—
77C2×C4×Dic11—21no—
78C2×C4×Dic11C2312yes—
79C22×C11⋊C8—22no—
80C22×C11⋊C8—22no—
81C22×C11⋊C8—22no—
82C22×C11⋊C8C2312yes—
83#66946—24no—
84#66946—24no—
85#66946—24no—
86#66946—24no—
87C22⋊C4×D11—216no—
88C4×D44—28no—
89C4×D44—28no—
90C11×#107—24no—
91C11×#106—24no—
92C11⋊#95—24no—
93#66885C2×C4116yescomplemented
94#66873—28no—
95#20876—111nomaximal, Sylow
96C24×C11C2×D411yescharacteristic
97C23×D11—22no—
98C23×D11—24no—
99C23×D11—24no—
100C23×D11—24no—
101C23×D11—82no—
102C23×D11—82no—
103C22×C4×C11—21no—
104C22×C4×C11—21no—
105C22×C4×C11—22no—
106C22×C4×C11—42no—
107C22×C4×C11—82no—
108C22×C4×C11C22×C412yes—
109C22×C4×C11C2×D412yes—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D412yes—
112C22×C4×C11C2×Q812yes—
113C22×C4×C11#4112yes—
114C22×C4×C11#4112yes—
115C22×C4×C11C2411yescharacteristic
116C22×Dic11—22no—
117C22×Dic11C2×D412yes—
118C22×Dic11C2×D412yes—
119C2×D44—24no—
120C2×D44—28no—
121C2×D44—24no—
122C2×D44—24no—
123C2×D44—28no—
124C2×D44—28no—
125C2×D44—22no—
126C2×D44—22no—
127C2×D44—22no—
128C2×D44C4⋊C4116yescomplemented
129C2×D44C22×C414yes—
130C2×D44C2×D414yes—
131C2×D44C2×Q814yes—
132C2×C4×D11—28no—
133C2×C4×D11—28no—
134C2×C4×D11—84no—
135C2×C4×D11—84no—
136C11×M16—28no—
137C2×C8×C11—22no—
138C2×C8×C11—22no—
139C2×C8×C11C22×C414yes—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—42no—
145C11×C4⋊C4C2×D412yes—
146C11×C4⋊C4C2×D412yes—
147C11×C22⋊C4—24no—
148C42×C11—24no—
149C22⋊Dic11—24no—
150C22⋊Dic11—24no—
151(C2×D11)⋊C4—28no—
152(C2×D11)⋊C4—28no—
153C4⋊Dic11—22no—
154C4⋊Dic11—22no—
155C4⋊Dic11—22no—
156C4⋊Dic11C22×C414yes—
157Dic11⋊C4—84no—
158C4×Dic11—24no—
159C4×Dic11—22no—
160C4×Dic11—22no—
161C2×C11⋊C8—22no—
162C2×C11⋊C8—22no—
163C2×C11⋊C8—22no—
164C2×C11⋊C8—44no—
165C2×#518—111no—
166C2×#428D1111yescharacteristic, complemented
167C2×#418—111no—
168C22×#102—111no—
169#2317—111no—
170#1864—114no—
171#1862—114no—
172#1735—111no—
173#1729—111no—
174C23×C11—22no—
175C23×C11—22no—
176C23×C11C4×D412yes—
177C23×C11#12012yes—
178C23×C11C22⋊Q812yes—
179C23×C11C22×D411yescharacteristic
180C22×D11—24no—
181C22×D11—24no—
182C22×D11—24no—
183C22×D11—216no—
184C22×D11—44no—
185C22×D11—44no—
186C22×D11—88no—
187C22×D11—88no—
188C22×D11—84no—
189C22×D11—84no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—44no—
196C2×C4×C11—84no—
197C2×C4×C11C2×C4⋊C414yes—
198C2×C4×C11C4×D412yes—
199C2×C4×C11C4×D414yes—
200C2×C4×C11#12012yes—
201C2×C4×C11C22⋊Q812yes—
202C2×C4×C11C22⋊Q814yes—
203C2×C4×C11#12314yes—
204C2×C4×C11C23×C411yescharacteristic
205C2×C4×C11C22×D411yescharacteristic
206C2×C4×C11C22×D411yescharacteristic
207C2×C4×C11C22×Q811yescharacteristic
208C2×C4×C11C2×#4111yescharacteristic
209C2×C4×C11C2×#4111yescharacteristic
210C2×Dic11—24no—
211C2×Dic11—22no—
212C2×Dic11—22no—
213C2×Dic11—24no—
214C2×Dic11—24no—
215C2×Dic11—42no—
216C2×Dic11—42no—
217D44—24no—
218D44—24no—
219D44—24no—
220D44—216no—
221D44C2×C4⋊C418yes—
222C4×D11—88no—
223C4×D11—88no—
224C8×C11—24no—
225C11⋊C8—42no—
226C23×D4—111no—
227C22×M16C2×D1111yescharacteristic
228C23×C8—111no—
229#518—224no—
230#518—224no—
231C2×C4×D4—112no—
232C2×C4×D4—112no—
233C2×C4×D4—221no—
234C2×C4×D4—221no—
235C2×#117—111no—
236C2×#117—111no—
237C2×#117C2×D1111yescharacteristic
238C22×C4⋊C4C2×D1111yescharacteristic
239C22×C22⋊C4—222no—
240#428—24no—
241C2×#107C2×D1112yescomplemented
242C2×#106C2×D1112yescomplemented
243#418—118no—
244C2×#102—114no—
245C2×#102—114no—
246C2×#102—224no—
247#389—114no—
248#385—222no—
249#384—221no—
250#382—221no—
251#340—112no—
252#340—112no—
253#336—114no—
254C22×C11—24no—
255C22×C11—24no—
256C22×C11—22no—
257C22×C11—22no—
258C22×C11#38514yes—
259C22×C11C2×C4×D411yescharacteristic
260C22×C11C2×#12011yescharacteristic
261C22×C11C2×C22⋊Q811yescharacteristic
262C22×C11#57612yes—
263C22×C11#57712yes—
264C2×D11—28no—
265C2×D11—48no—
266C2×D11—48no—
267C2×D11—44no—
268C2×D11—44no—
269C2×D11—816no—
270C4×C11—42no—
271C4×C11—42no—
272C4×C11—82no—
273C4×C11#38514yes—
274C4×C11C22×C4⋊C411yescharacteristic
275C4×C11C2×C4×D411yescharacteristic
276C4×C11C2×C22⋊Q811yescharacteristic
277C4×C11C2×#12311yescharacteristic
278Dic11—44no—
279Dic11—42no—
280Dic11—42no—
281C25—221no—
282C22×D4—114no—
283C22×D4—114no—
284C22×D4—114no—
285C22×D4—112no—
286C22×D4—222no—
287C22×D4—221no—
288C22×D4—222no—
289C22×D4—222no—
290C23×C4—21no—
291C23×C4—222no—
292C23×C4—222no—
293C23×C4C22×D1111yescharacteristic
294C2×M16—22no—
295C2×M16—22no—
296C2×M16C4×D1114yescomplemented
297C22×C8—112no—
298C22×C8—222no—
299C22×C8—222no—
300C22×C8—222no—
301C22×C8C22×D1112yes—
302C4×D4—228no—
303C4×D4—228no—
304C4×D4—224no—
305C4×D4—224no—
306C4×D4—224no—
307C4×D4—224no—
308#117—22no—
309#117—114no—
310#117—222no—
311#117—222no—
312#117—222no—
313#117C22⋊D1114yes—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—112no—
318C2×C4⋊C4—111no—
319C2×C4⋊C4—111no—
320C2×C4⋊C4—224no—
321C2×C4⋊C4C22×D1112yes—
322C2×C4⋊C4C22×D1111yescharacteristic
323C2×C4⋊C4C22×D1111yescharacteristic
324C2×C22⋊C4—21no—
325C2×C22⋊C4—112no—
326C2×C22⋊C4—2216no—
327C2×C22⋊C4—222no—
328C2×C22⋊C4—222no—
329C2×C22⋊C4—221no—
330C2×C42—21no—
331C2×C42—112no—
332C2×C42—221no—
333#107—24no—
334#106—24no—
335#102—1116no—
336#102—228no—
337#95—224no—
338C2×C11—24no—
339C2×C11C2×#38511yescharacteristic
340C2×C11#294612yes—
341C2×C11#300811yescharacteristic
342C2×C11#300911yescharacteristic
343C2×C11#308112yes—
344D11—48no—
345C24—222no—
346C24—224no—
347C24—224no—
348C24—224no—
349C24—882no—
350C24—882no—
351C24D4×D1111yescharacteristic
352C2×D4—1116no—
353C2×D4—114no—
354C2×D4—114no—
355C2×D4—114no—
356C2×D4—224no—
357C2×D4—228no—
358C2×D4—224no—
359C2×D4—228no—
360C2×D4—224no—
361C2×D4—228no—
362C2×D4—222no—
363C2×D4—222no—
364C2×D4—222no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—22no—
368C22×C4—42no—
369C22×C4—82no—
370C22×C4—112no—
371C22×C4—112no—
372C22×C4—228no—
373C22×C4—228no—
374C22×C4—222no—
375C22×C4—884no—
376C22×C4—884no—
377C22×C4C2×C4×D1112yes—
378C22×C4#433912yes—
379C22×C4D4×D1112yes—
380C22×C4D4×D1111yescharacteristic
381C22×C4Q8×D1112yes—
382C22×C4#434312yes—
383C22×C4C2×C22⋊D1112yes—
384C22×C4C23×D1111yescharacteristic
385M16—28no—
386C2×C8—22no—
387C2×C8—22no—
388C2×C8—222no—
389C2×C8—222no—
390C2×C8—222no—
391C2×C8—444no—
392C2×C8C2×C4×D1114yes—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—22no—
396C4⋊C4—22no—
397C4⋊C4—42no—
398C4⋊C4—114no—
399C4⋊C4—222no—
400C4⋊C4—222no—
401C4⋊C4—222no—
402C4⋊C4—884no—
403C4⋊C4C2×C22⋊D1112yes—
404C4⋊C4C2×C22⋊D1112yes—
405C22⋊C4—24no—
406C22⋊C4—228no—
407C22⋊C4—228no—
408C22⋊C4—224no—
409C22⋊C4—224no—
410C42—24no—
411C42—224no—
412C42—222no—
413C42—222no—
414C11#2087611yescharacteristic, complemented, Sylow
415C23—22no—
416C23—22no—
417C23—224no—
418C23—224no—
419C23—224no—
420C23—2216no—
421C23—444no—
422C23—444no—
423C23—884no—
424C23—884no—
425C23—888no—
426C23—888no—
427C23#6694612yes—
428C23#6694912yes—
429C23#6699012yes—
430C23C2×D4×D1111yescharacteristic
431D4—118no—
432D4—224no—
433D4—224no—
434D4—224no—
435D4—2216no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—44no—
441C2×C4—42no—
442C2×C4—84no—
443C2×C4—224no—
444C2×C4—224no—
445C2×C4—224no—
446C2×C4—222no—
447C2×C4—222no—
448C2×C4—442no—
449C2×C4—442no—
450C2×C4—888no—
451C2×C4—888no—
452C2×C4C4⋊C4×D1114yes—
453C2×C4#6694612yes—
454C2×C4#6694714yes—
455C2×C4#6694912yes—
456C2×C4C4×C22⋊D1114yes—
457C2×C4#6699012yes—
458C2×C4#6699914yes—
459C2×C4C22×C4×D1111yescharacteristic
460C2×C4C2×#433911yescharacteristic
461C2×C4C2×D4×D1111yescharacteristic
462C2×C4C2×Q8×D1111yescharacteristic
463C2×C4C2×#434311yescharacteristic
464C2×C4C22×C22⋊D1111yescharacteristic
465C8—24no—
466C8—442no—
467C22—22no—
468C22—22no—
469C22—24no—
470C22—24no—
471C22—228no—
472C22—444no—
473C22—444no—
474C22—448no—
475C22—448no—
476C22—8816no—
477C22#1062260214yes—
478C22C2×#6694611yescharacteristic
479C22C2×#6694911yescharacteristic
480C22#1062330512yes—
481C22#1062330912yes—
482C22C2×#6699011yescharacteristic
483C4—42no—
484C4—42no—
485C4—82no—
486C4—442no—
487C4—442no—
488C4—444no—
489C4#1062260214yes—
490C4C2×C4⋊C4×D1111yescharacteristic
491C4C2×#6694711yescharacteristic
492C4C2×C4×C22⋊D1111yescharacteristic
493C4C2×#6699911yescharacteristic
494C2—24no—
495C2—448no—
496C2C2×#1062260211yescharacteristic
497C2#1307744612yes—
498C2#1307788311yescharacteristic
499C2#1307789211yescharacteristic
500C2#1307844512yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#428C2
socleC23×C11C22×D4
prime radicalC23×D44C22
cosocleC22×C4×C11C24
hypercenterC2×#428D11
hypocenterC11#20876
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
4. #13071240C2semidirect
5. #13068874C2semidirect
6. #13068860C2semidirect
7. #13068332C2semidirect
8. #13068314C2semidirect
9. C2×C11×#428C2semidirect
25. C2×C11×#107C22semidirect
26. C2×C11×#106C22semidirect
28. #10622744C4semidirect
32. #10622586C22semidirect
35. #10622188C22semidirect
36. #10622167C22semidirect
37. #10622167C22semidirect
53. C2×C11×M16C2×C4semidirect
72. #66979C2×C4semidirect
93. #66885C2×C4semidirect
128. C2×D44C4⋊C4semidirect
166. C2×#428D11semidirect
241. C2×#107C2×D11semidirect
242. C2×#106C2×D11semidirect
296. C2×M16C4×D11semidirect
414. C11#20876semidirect

Maximal subgroups

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

subgroupindex
C2×#106230522
C2×#106227442
C22×#668732
#130712402
#130688742
#130688602
#130683322
#130683142
C2×C11×#4282
#2087611