Finite Group Databasebeta

← #14754806

Subgroups — #14754806

Order 2816.

1458 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66871C211yesmaximal, characteristic, complemented
2C2×#10622845C211yesmaximal, characteristic
3C2×#10622846C211yesmaximal, characteristic
4#13071236C211yesmaximal, characteristic, complemented
5#13068870C214yesmaximal, complemented
6#13068863C214yesmaximal, complemented
7#13068335C211yesmaximal, characteristic, complemented
8#13068313C211yesmaximal, characteristic, complemented
9C2×C11×#520C211yesmaximal, characteristic
10C22×C11×#41C2211yescharacteristic
11C11×#520—24no—
12C11×#520—24no—
13C2×C4×Q8×C11C2212yes—
14C2×C4×D4×C11—22no—
15C2×C4×D4×C11C2212yes—
16C2×C11×#117—21no—
17C2×C11×#117C2211yescharacteristic
18C22×C11×C4⋊C4—21no—
19C22×C11×C4⋊C4C2211yescharacteristic
20C2×#66979C2211yescharacteristic
21C22×C4⋊Dic11C2211yescharacteristic
22C22×#4318C2211yescharacteristic
23C23×C11⋊C8C2211yescharacteristic
24#10622846C418yescomplemented
25#10622845—24no—
26C2×#66899C2212yes—
27C2×#66899C2212yes—
28C2×#66896C2212yes—
29C2×#66896C2212yes—
30#10622590—21no—
31#10622589—21no—
32C2×#66871—24no—
33C2×#66871C2214yes—
34#10622559—22no—
35#10622541C2214yes—
36#10622167C2214yes—
37#10622162C2214yes—
38C2×C11×#41—22no—
39C2×C11×#41—22no—
40C2×C11×#41—22no—
41C2×C11×#41C2×C414yes—
42C2×C11×#41D414yes—
43C2×C11×#41Q814yes—
44C22×Q8×C11C2311yescharacteristic
45C22×D4×C11—21no—
46C22×D4×C11C2311yescharacteristic
47C23×C4×C11—21no—
48C23×C4×C11—21no—
49C23×C4×C11—22no—
50C23×C4×C11C2311yescharacteristic
51C23×Dic11—21no—
52C4×Q8×C11—24no—
53C4×Q8×C11—24no—
54C4×D4×C11—216no—
55C4×D4×C11—24no—
56C4×D4×C11—24no—
57C11×#117—28no—
58C11×#117—22no—
59C11×#117—22no—
60C2×C11×C4⋊C4—28no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4D411yescharacteristic
65C2×C11×C4⋊C4D411yescharacteristic
66C2×C11×C4⋊C4D414yes—
67C2×C11×C4⋊C4C2312yes—
68C2×C11×C22⋊C4—22no—
69C2×C11×C22⋊C4D412yes—
70C2×C42×C11—22no—
71C2×C42×C11C2312yes—
72C2×C22⋊Dic11—21no—
73#66979—22no—
74#66979C2×C414yescomplemented
75C2×C4⋊Dic11—22no—
76C2×C4⋊Dic11—22no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11C2312yes—
79C2×C4⋊Dic11C2312yes—
80C2×Dic11⋊C4—24no—
81C2×C4×Dic11—21no—
82C2×#4318—22no—
83C2×#4318—22no—
84C2×#4318—22no—
85C22×C11⋊C8—22no—
86C22×C11⋊C8—22no—
87C22×C11⋊C8C2×C414yescomplemented
88C22×C11⋊C8C2312yes—
89C22×C11⋊C8C2312yes—
90#66899—24no—
91#66899C2×C418yescomplemented
92#66896—24no—
93#66896C2×C418yescomplemented
94C11⋊#95—24no—
95#66871—28no—
96#20881—111nomaximal, Sylow
97C24×C11—21no—
98C24×C11C2×D411yescharacteristic
99C11×#41—28no—
100C11×#41—28no—
101C11×#41—28no—
102C11×#41C4⋊C4116yescomplemented
103C2×Q8×C11—21no—
104C2×Q8×C11—21no—
105C2×Q8×C11—21no—
106C2×Q8×C11C22×C412yes—
107C2×Q8×C11C2×D412yes—
108C2×Q8×C11C2×Q812yes—
109C2×D4×C11—24no—
110C2×D4×C11—24no—
111C2×D4×C11—24no—
112C2×D4×C11—21no—
113C2×D4×C11—21no—
114C2×D4×C11—21no—
115C2×D4×C11C22×C412yes—
116C2×D4×C11C2×D412yes—
117C2×D4×C11C2×Q812yes—
118C22×C4×C11—21no—
119C22×C4×C11—24no—
120C22×C4×C11—24no—
121C22×C4×C11—24no—
122C22×C4×C11—22no—
123C22×C4×C11—28no—
124C22×C4×C11—24no—
125C22×C4×C11—84no—
126C22×C4×C11—82no—
127C22×C4×C11C22×C412yes—
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2×D412yes—
130C22×C4×C11C2×D412yes—
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D412yes—
133C22×C4×C11C2×Q812yes—
134C22×C4×C11#4112yes—
135C22×C4×C11#4112yes—
136C22×C4×C11C2411yescharacteristic
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—42no—
140C22×Dic11—82no—
141C11×C4⋊C4—28no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—24no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4C2×D414yes—
147C11×C22⋊C4—28no—
148C11×C22⋊C4—24no—
149C42×C11—28no—
150C42×C11—22no—
151C42×C11—22no—
152C22⋊Dic11—24no—
153C4⋊Dic11—22no—
154C4⋊Dic11—22no—
155C4⋊Dic11—22no—
156C4⋊Dic11—42no—
157C4⋊Dic11C22×C414yes—
158Dic11⋊C4—84no—
159C4×Dic11—24no—
160#4318—44no—
161C2×C11⋊C8—28no—
162C2×C11⋊C8—22no—
163C2×C11⋊C8—22no—
164C2×C11⋊C8—22no—
165C2×C11⋊C8—22no—
166C2×C11⋊C8—22no—
167C2×C11⋊C8C22×C414yes—
168C2×#520D1111yescharacteristic
169C22×#107—111no—
170C2×#417—111no—
171C2×#416—111no—
172#2317—111no—
173#1863—114no—
174#1862—114no—
175#1736—111no—
176#1729—111no—
177C23×C11—22no—
178C23×C11—22no—
179C23×C11—22no—
180C23×C11—22no—
181C23×C11—22no—
182C23×C11—42no—
183C23×C11—42no—
184C23×C11C4×D412yes—
185C23×C11#12012yes—
186C23×C11C22⋊Q812yes—
187C23×C11C22×D411yescharacteristic
188Q8×C11—22no—
189Q8×C11—22no—
190Q8×C11—22no—
191Q8×C11C2×C4⋊C414yes—
192D4×C11—216no—
193D4×C11—22no—
194D4×C11—22no—
195D4×C11—22no—
196D4×C11C2×C4⋊C414yes—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—216no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—24no—
204C2×C4×C11—24no—
205C2×C4×C11—24no—
206C2×C4×C11—44no—
207C2×C4×C11—84no—
208C2×C4×C11—88no—
209C2×C4×C11C2×C4⋊C414yes—
210C2×C4×C11C4×D414yes—
211C2×C4×C11C4×D412yes—
212C2×C4×C11#12012yes—
213C2×C4×C11C22⋊Q814yes—
214C2×C4×C11C22⋊Q812yes—
215C2×C4×C11#12314yes—
216C2×C4×C11C23×C411yescharacteristic
217C2×C4×C11C22×D411yescharacteristic
218C2×C4×C11C22×D411yescharacteristic
219C2×C4×C11C22×Q811yescharacteristic
220C2×C4×C11C2×#4111yescharacteristic
221C2×C4×C11C2×#4111yescharacteristic
222C2×Dic11—24no—
223C2×Dic11—42no—
224C2×Dic11—42no—
225C2×Dic11—42no—
226C2×Dic11—44no—
227C2×Dic11—84no—
228C11⋊C8—24no—
229C11⋊C8—42no—
230C22×#41C2×D1111yescharacteristic
231C22×M16—111no—
232C23×C8—111no—
233#520—24no—
234#520—24no—
235C2×C4×Q8C2×D1112yes—
236C2×C4×D4—22no—
237C2×C4×D4C2×D1112yes—
238C2×#117—21no—
239C2×#117—111no—
240C2×#117C2×D1111yescharacteristic
241C22×C4⋊C4—21no—
242C22×C4⋊C4—111no—
243C22×C4⋊C4C2×D1111yescharacteristic
244C2×#107—114no—
245C2×#107—224no—
246#417—224no—
247#416—118no—
248C2×#103—112no—
249C2×#103—112no—
250C2×#102—112no—
251C2×#102—112no—
252#389—114no—
253#385—222no—
254#384—221no—
255#382—221no—
256#340—114no—
257#336—114no—
258C22×C11—24no—
259C22×C11—24no—
260C22×C11—22no—
261C22×C11—22no—
262C22×C11—24no—
263C22×C11—44no—
264C22×C11—44no—
265C22×C11—42no—
266C22×C11—42no—
267C22×C11#38514yes—
268C22×C11C2×C4×D411yescharacteristic
269C22×C11C2×#12011yescharacteristic
270C22×C11C2×C22⋊Q811yescharacteristic
271C22×C11#57612yes—
272C22×C11#57812yes—
273C4×C11—24no—
274C4×C11—42no—
275C4×C11—44no—
276C4×C11—42no—
277C4×C11#38514yes—
278C4×C11C22×C4⋊C411yescharacteristic
279C4×C11C2×C4×D411yescharacteristic
280C4×C11C2×C22⋊Q811yescharacteristic
281C4×C11C2×#12311yescharacteristic
282Dic11—44no—
283Dic11—82no—
284C2×#41—22no—
285C2×#41—22no—
286C2×#41—22no—
287C2×#41Dic2214yes—
288C2×#41C4×D1114yes—
289C2×#41C22⋊D1114yes—
290C22×Q8C22×D1111yescharacteristic
291C22×D4—21no—
292C22×D4C22×D1111yescharacteristic
293C23×C4—21no—
294C23×C4—21no—
295C23×C4—22no—
296C23×C4—221no—
297C23×C4C22×D1111yescharacteristic
298C2×M16—222no—
299C2×M16—222no—
300C2×M16—222no—
301C22×C8—114no—
302C22×C8—112no—
303C22×C8—112no—
304C22×C8—222no—
305C22×C8—222no—
306C4×Q8—24no—
307C4×Q8—24no—
308C4×D4—216no—
309C4×D4—24no—
310C4×D4—24no—
311#117—28no—
312#117—22no—
313#117—22no—
314#117—114no—
315#117—222no—
316C2×C4⋊C4—28no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—112no—
321C2×C4⋊C4—112no—
322C2×C4⋊C4—222no—
323C2×C4⋊C4—222no—
324C2×C4⋊C4—221no—
325C2×C4⋊C4—224no—
326C2×C4⋊C4C22⋊D1111yescharacteristic
327C2×C4⋊C4C22⋊D1111yescharacteristic
328C2×C4⋊C4C22⋊D1114yes—
329C2×C4⋊C4C22×D1112yes—
330C2×C22⋊C4—22no—
331C2×C22⋊C4—221no—
332C2×C22⋊C4C22⋊D1112yes—
333C2×C42—22no—
334C2×C42—221no—
335C2×C42C22×D1112yes—
336#107—228no—
337#103—118no—
338#103—224no—
339#102—118no—
340#102—224no—
341#95—224no—
342C2×C11—24no—
343C2×C11—44no—
344C2×C11C2×#38511yescharacteristic
345C2×C11#295112yes—
346C2×C11#300811yescharacteristic
347C2×C11#301111yescharacteristic
348C2×C11#308312yes—
349C24—21no—
350C24C2×C22⋊D1111yescharacteristic
351#41—28no—
352#41—28no—
353#41—28no—
354#41Dic11⋊C4116yescomplemented
355C2×Q8—21no—
356C2×Q8—21no—
357C2×Q8—21no—
358C2×Q8C2×Dic2212yes—
359C2×Q8C2×C4×D1112yes—
360C2×Q8C2×C22⋊D1112yes—
361C2×D4—24no—
362C2×D4—24no—
363C2×D4—24no—
364C2×D4—21no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4C2×Dic2212yes—
368C2×D4C2×C4×D1112yes—
369C2×D4C2×C22⋊D1112yes—
370C22×C4—21no—
371C22×C4—24no—
372C22×C4—24no—
373C22×C4—24no—
374C22×C4—22no—
375C22×C4—28no—
376C22×C4—24no—
377C22×C4—84no—
378C22×C4—82no—
379C22×C4—222no—
380C22×C4—222no—
381C22×C4—442no—
382C22×C4—882no—
383C22×C4C2×Dic2212yes—
384C22×C4C2×C4×D1112yes—
385C22×C4#433912yes—
386C22×C4#433912yes—
387C22×C4C2×C22⋊D1112yes—
388C22×C4C2×C22⋊D1112yes—
389C22×C4C2×C22⋊D1112yes—
390C22×C4C2×C22⋊D1111yescharacteristic
391C22×C4C2×C22⋊D1112yes—
392C22×C4C23×D1111yescharacteristic
393M16—444no—
394C2×C8—114no—
395C2×C8—228no—
396C2×C8—222no—
397C2×C8—222no—
398C2×C8—222no—
399C2×C8—222no—
400C2×C8—222no—
401C4⋊C4—28no—
402C4⋊C4—22no—
403C4⋊C4—24no—
404C4⋊C4—22no—
405C4⋊C4—22no—
406C4⋊C4—114no—
407C4⋊C4—222no—
408C4⋊C4—222no—
409C4⋊C4—222no—
410C4⋊C4—442no—
411C4⋊C4—884no—
412C4⋊C4C2×C22⋊D1114yes—
413C22⋊C4—28no—
414C22⋊C4—24no—
415C22⋊C4—224no—
416C42—28no—
417C42—22no—
418C42—22no—
419C42—224no—
420C11#2088111yescharacteristic, complemented, Sylow
421C23—22no—
422C23—22no—
423C23—22no—
424C23—22no—
425C23—22no—
426C23—42no—
427C23—42no—
428C23#6697712yes—
429C23C4×C22⋊D1112yes—
430C23#6700612yes—
431C23C22×C22⋊D1111yescharacteristic
432Q8—22no—
433Q8—22no—
434Q8—22no—
435Q8C2×Dic11⋊C414yes—
436D4—216no—
437D4—22no—
438D4—22no—
439D4—22no—
440D4C2×Dic11⋊C414yes—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—216no—
445C2×C4—24no—
446C2×C4—24no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—24no—
450C2×C4—44no—
451C2×C4—84no—
452C2×C4—88no—
453C2×C4—224no—
454C2×C4—442no—
455C2×C4—442no—
456C2×C4—444no—
457C2×C4—442no—
458C2×C4—884no—
459C2×C4C2×Dic11⋊C414yes—
460C2×C4#6697714yes—
461C2×C4#6697712yes—
462C2×C4C4×C22⋊D1114yes—
463C2×C4C4×C22⋊D1112yes—
464C2×C4#6698214yes—
465C2×C4#6700612yes—
466C2×C4C22×Dic2211yescharacteristic
467C2×C4C22×C4×D1111yescharacteristic
468C2×C4C2×#433911yescharacteristic
469C2×C4C2×#433911yescharacteristic
470C2×C4C22×C22⋊D1111yescharacteristic
471C2×C4C22×C22⋊D1111yescharacteristic
472C8—224no—
473C8—442no—
474C22—22no—
475C22—22no—
476C22—24no—
477C22—24no—
478C22—24no—
479C22—42no—
480C22—42no—
481C22—44no—
482C22—44no—
483C22#1062282314yes—
484C22C2×#6697711yescharacteristic
485C22C2×C4×C22⋊D1111yescharacteristic
486C22#1062336612yes—
487C22#1062336912yes—
488C22C2×#6700611yescharacteristic
489C4—24no—
490C4—42no—
491C4—44no—
492C4—42no—
493C4—444no—
494C4—882no—
495C4#1062282314yes—
496C4C22×Dic11⋊C411yescharacteristic
497C4C2×#6697711yescharacteristic
498C4C2×C4×C22⋊D1111yescharacteristic
499C4C2×#6698211yescharacteristic
500C2—24no—
501C2—44no—
502C2C2×#1062282311yescharacteristic
503C2#1307748912yes—
504C2#1307788411yescharacteristic
505C2#1307791111yescharacteristic
506C2#1307846712yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#520C2
socleC23×C11C22×D4
prime radicalC22×C11×#41C22
cosocleC22×C4×C11C24
hypercenterC2×#520D11
hypocenterC11#20881
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. C22×#66871C2semidirect
4. #13071236C2semidirect
5. #13068870C2semidirect
6. #13068863C2semidirect
7. #13068335C2semidirect
8. #13068313C2semidirect
24. #10622846C4semidirect
74. #66979C2×C4semidirect
87. C22×C11⋊C8C2×C4semidirect
91. #66899C2×C4semidirect
93. #66896C2×C4semidirect
102. C11×#41C4⋊C4semidirect
354. #41Dic11⋊C4semidirect
420. C11#20881semidirect

Maximal subgroups

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

subgroupindex
C22×#668712
C2×#106228452
C2×#106228462
#130712362
#130688702
#130688632
#130683352
#130683132
C2×C11×#5202
#2088111