Finite Group Databasebeta

← #14763599

Subgroups — #14763599

Order 2816.

1098 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623176C211yesmaximal, characteristic
2#13071233C211yesmaximal, characteristic, complemented
3#13071216C211yesmaximal, characteristic, complemented
4#13069602C211yesmaximal, characteristic, complemented
5#13069452C211yesmaximal, characteristic
6#13069451C211yesmaximal, characteristic
7#13069073C214yesmaximal, complemented
8#13068603C214yesmaximal, complemented
9C11×#1996C211yesmaximal, characteristic, complemented
10C2×C11×C22⋊Q8C2211yescharacteristic
11C2×#66999C412yescomplemented
12C2×#66983C2211yescharacteristic
13C22×Dic11⋊C4C2211yescharacteristic
14#10623176—22no—
15#10623176—22no—
16#10623176—22no—
17#10623176—22no—
18C2×#66951C412yescomplemented
19C2×#66947C412yescomplemented
20C2×#66943C412yescomplemented
21C2×#66939C2212yes—
22C2×(C22⋊D11)⋊C4C2212yes—
23C2×#66930C2212yes—
24C11×#380C2211yescharacteristic
25C4×C11×C22⋊C4C2211yescharacteristic
26#10622825C2211yescharacteristic
27C4×C22⋊Dic11C2211yescharacteristic
28#10622585—22no—
29C2×#66870C2214yes—
30C2×#66870C2214yes—
31#10622556C2212yes—
32#10622555C2212yes—
33#10622555C2212yes—
34#10622546—22no—
35#10622265—22no—
36#10622260—22no—
37C11×#342C2214yes—
38#10622164C2214yes—
39C22×Q8×C11C2×C411yescharacteristic
40C23×C4×C11C2311yescharacteristic
41C22×C22⋊D11C2312yes—
42C23×Dic11C2311yescharacteristic
43C23×Dic11C2311yescharacteristic
44C22×D44C2×C411yescharacteristic
45C22×C4×D11C2×C412yes—
46C11×C22⋊Q8—21no—
47C11×C22⋊Q8—21no—
48C11×C22⋊Q8—21no—
49C11×C22⋊Q8—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4C2×C412yes—
52C2×C11×C4⋊C4C2×C411yescharacteristic
53C2×C11×C22⋊C4C2312yes—
54C2×C11×C22⋊C4C2312yes—
55C2×C11×C22⋊C4C2312yes—
56C2×C42×C11—21no—
57C2×C22⋊Dic11C2312yes—
58C2×C22⋊Dic11C2312yes—
59#66999—24no—
60#66999—24no—
61#66983—21no—
62#66983—21no—
63#66983—21no—
64#66983—21no—
65C2×(C2×D11)⋊C4C2×C412yes—
66C2×(C2×D11)⋊C4C2×C412yes—
67C2×(C2×D11)⋊C4C2×C412yes—
68C2×(C2×D11)⋊C4C2×C412yes—
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11C2×C412yes—
71C2×C4⋊Dic11C2×C412yes—
72C2×C4⋊Dic11C2×C411yescharacteristic
73C2×Dic11⋊C4—22no—
74C2×Dic11⋊C4—22no—
75C2×Dic11⋊C4—22no—
76C2×Dic11⋊C4C2×C412yes—
77C2×Dic11⋊C4C2×C412yes—
78C2×Dic11⋊C4C2×C412yes—
79C2×Dic11⋊C4D412yes—
80C2×Dic11⋊C4D412yes—
81C2×Dic11⋊C4D412yes—
82C2×Dic11⋊C4D412yes—
83C2×C4×Dic11—22no—
84C2×C4×Dic11—21no—
85C2×C4×Dic11C2×C412yes—
86#66951—24no—
87#66951—24no—
88#66947—24no—
89#66947—24no—
90#66943—24no—
91#66943—24no—
92#66939—24no—
93#66939—24no—
94(C22⋊D11)⋊C4—24no—
95(C22⋊D11)⋊C4—24no—
96#66930—44no—
97C11×#95—21no—
98C11×#95—21no—
99C11⋊#95—21no—
100C11⋊#95—21no—
101C11⋊#95—22no—
102C11⋊#95—22no—
103C11⋊#95—24no—
104#66870—44no—
105#66870—44no—
106#21877—111nomaximal, Sylow
107C24×C11C2411yescharacteristic
108C23×D11C22×C412yes—
109C2×Q8×C11—21no—
110C2×Q8×C11—21no—
111C2×Q8×C11—81no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—81no—
115C22×C4×C11C22×C412yes—
116C22×C4×C11C22×C412yes—
117C22×C4×C11C22×C411yescharacteristic
118C22×C4×C11C22×C411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C2×C22⋊D11—22no—
124C2×C22⋊D11—22no—
125C2×C22⋊D11—24no—
126C2×C22⋊D11—24no—
127C22×Dic11—22no—
128C22×Dic11—22no—
129C22×Dic11—22no—
130C22×Dic11—22no—
131C22×Dic11—81no—
132C22×Dic11C22×C412yes—
133C22×Dic11C22×C412yes—
134C22×Dic11C22×C412yes—
135C22×Dic11C2×D412yes—
136C22×Dic11C2×D412yes—
137C22×Dic11C2×D412yes—
138C22×Dic11C2×D412yes—
139C2×D44—21no—
140C2×D44—21no—
141C2×D44—81no—
142C2×C4×D11—24no—
143C2×C4×D11—82no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—81no—
149C11×C22⋊C4—22no—
150C11×C22⋊C4—22no—
151C11×C22⋊C4—22no—
152C11×C22⋊C4—24no—
153C11×C22⋊C4—22no—
154C42×C11—81no—
155C22⋊Dic11—22no—
156C22⋊Dic11—24no—
157C22⋊Dic11—22no—
158(C2×D11)⋊C4—24no—
159(C2×D11)⋊C4—24no—
160(C2×D11)⋊C4—24no—
161(C2×D11)⋊C4—22no—
162(C2×D11)⋊C4—22no—
163C4⋊Dic11—24no—
164C4⋊Dic11—24no—
165C4⋊Dic11—21no—
166C4⋊Dic11—21no—
167C4⋊Dic11—81no—
168Dic11⋊C4—24no—
169Dic11⋊C4—44no—
170Dic11⋊C4—82no—
171Dic11⋊C4—82no—
172Dic11⋊C4C22⋊C414yes—
173Dic11⋊C4C22⋊C414yes—
174Dic11⋊C4C22⋊C414yes—
175Dic11⋊C4C22⋊C414yes—
176C4×Dic11—24no—
177C4×Dic11—44no—
178C4×Dic11—81no—
179C2×#539—111no—
180#2316—111no—
181#2313—111no—
182#1996—111no—
183#1996D1111yescharacteristic, complemented
184#1964—111no—
185#1964—111no—
186#1899—114no—
187#1799—114no—
188C23×C11—41no—
189C23×C11—41no—
190C23×C11C23×C411yescharacteristic
191C23×C11C22×D411yescharacteristic
192C23×C11C22×D411yescharacteristic
193C23×C11H(5,𝔽2)12yes—
194C23×C112−1+412yes—
195C22×D11—22no—
196C22×D11—24no—
197C22×D11—42no—
198C22×D11—42no—
199Q8×C11—81no—
200Q8×C11—81no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11C2×C22⋊C411yescharacteristic
218C2×C4×C11C2×C22⋊C411yescharacteristic
219C2×C4×C11C2×C22⋊C411yescharacteristic
220C2×C4×C11C2×C22⋊C411yescharacteristic
221C22⋊D11—42no—
222C22⋊D11—42no—
223C22⋊D11—44no—
224C2×Dic11—24no—
225C2×Dic11—22no—
226C2×Dic11—22no—
227C2×Dic11—24no—
228C2×Dic11—22no—
229C2×Dic11—24no—
230C2×Dic11—42no—
231C2×Dic11—42no—
232C2×Dic11—42no—
233C2×Dic11—42no—
234C2×Dic11—42no—
235C2×Dic11—42no—
236C2×Dic11—42no—
237C2×Dic11—42no—
238C2×Dic11—42no—
239C2×Dic11C2×C22⋊C414yes—
240C2×Dic11C2×C22⋊C414yes—
241D44—81no—
242D44—81no—
243C4×D11—84no—
244#539—222no—
245#539—222no—
246#539—222no—
247#539—222no—
248C2×#126—112no—
249C2×#125—112no—
250C2×#123—112no—
251C2×#123—112no—
252C2×C22⋊Q8—112no—
253C2×C22⋊Q8C2×D1111yescharacteristic
254C2×#121—111no—
255C2×C4×D4—112no—
256C2×#117—112no—
257C22×C4⋊C4—111no—
258C2×#99—114no—
259C2×#99—114no—
260#389—222no—
261#389—222no—
262#387—222no—
263#387—222no—
264#381—112no—
265#380—111no—
266#380—112no—
267#380—112no—
268#380C2×D1111yescharacteristic
269C4×C22⋊C4—111no—
270C4×C22⋊C4C2×D1111yescharacteristic
271#342—114no—
272#342C2×D1114yes—
273C22×C11—21no—
274C22×C11—21no—
275C22×C11—21no—
276C22×C11—21no—
277C22×C11—21no—
278C22×C11—21no—
279C22×C11—42no—
280C22×C11—42no—
281C22×C11C22×C22⋊C411yescharacteristic
282C22×C11#52012yes—
283C22×C11#53511yescharacteristic
284C22×C11#53611yescharacteristic
285C22×C11#53712yes—
286C2×D11—42no—
287C2×D11—42no—
288C2×D11—42no—
289C2×D11—84no—
290C4×C11—21no—
291C4×C11—21no—
292C4×C11—21no—
293C4×C11—21no—
294C4×C11—42no—
295C4×C11—42no—
296C4×C11—82no—
297C4×C11—82no—
298Dic11—24no—
299Dic11—24no—
300Dic11—42no—
301Dic11—82no—
302Dic11—82no—
303C22×Q8C4×D1111yescharacteristic
304C22×D4—112no—
305C22×D4—111no—
306C23×C4—111no—
307C23×C4—111no—
308C23×C4—112no—
309C23×C4C22×D1111yescharacteristic
310#126—224no—
311#126—224no—
312#125—224no—
313#125—224no—
314#123—224no—
315#123—224no—
316#123—224no—
317#123—224no—
318C22⋊Q8—21no—
319C22⋊Q8—21no—
320C22⋊Q8—21no—
321C22⋊Q8—21no—
322C22⋊Q8—224no—
323C22⋊Q8—224no—
324#121—221no—
325#121—221no—
326#121—221no—
327#121—221no—
328C4×D4—224no—
329C4×D4—224no—
330#117—444no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—112no—
333C2×C4⋊C4—112no—
334C2×C4⋊C4—112no—
335C2×C4⋊C4—112no—
336C2×C4⋊C4—112no—
337C2×C4⋊C4—112no—
338C2×C4⋊C4—112no—
339C2×C4⋊C4—111no—
340C2×C4⋊C4—112no—
341C2×C4⋊C4—112no—
342C2×C4⋊C4—222no—
343C2×C4⋊C4—222no—
344C2×C4⋊C4—222no—
345C2×C4⋊C4—221no—
346C2×C4⋊C4C4×D1112yes—
347C2×C4⋊C4C4×D1111yescharacteristic
348C2×C22⋊C4—112no—
349C2×C22⋊C4—112no—
350C2×C22⋊C4—112no—
351C2×C22⋊C4—112no—
352C2×C22⋊C4—112no—
353C2×C22⋊C4—112no—
354C2×C22⋊C4C22×D1112yes—
355C2×C22⋊C4C22×D1112yes—
356C2×C22⋊C4C22×D1112yes—
357C2×C42—21no—
358C2×C42—112no—
359C2×C42—222no—
360C2×C42—221no—
361#99—444no—
362#99—444no—
363#95—21no—
364#95—21no—
365#95—222no—
366#95—222no—
367#95—224no—
368#95—221no—
369#95—221no—
370C2×C11—21no—
371C2×C11—22no—
372C2×C11—22no—
373C2×C11—21no—
374C2×C11#231111yescharacteristic
375C2×C11#288311yescharacteristic
376C2×C11#288411yescharacteristic
377D11—82no—
378C24—112no—
379C24C23×D1111yescharacteristic
380C2×Q8—21no—
381C2×Q8—21no—
382C2×Q8—81no—
383C2×D4—222no—
384C2×D4—222no—
385C2×D4—224no—
386C2×D4—224no—
387C2×D4—221no—
388C2×D4—221no—
389C2×D4—881no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—81no—
393C22×C4—112no—
394C22×C4—112no—
395C22×C4—112no—
396C22×C4—112no—
397C22×C4—112no—
398C22×C4—112no—
399C22×C4—112no—
400C22×C4—224no—
401C22×C4—222no—
402C22×C4—222no—
403C22×C4—222no—
404C22×C4—222no—
405C22×C4—882no—
406C22×C4—881no—
407C22×C4C2×C4×D1112yes—
408C22×C4C2×C4×D1112yes—
409C22×C4C2×C4×D1111yescharacteristic
410C22×C4C2×C4×D1111yescharacteristic
411C22×C4D4×D1111yescharacteristic
412C22×C4D4×D1111yescharacteristic
413C22×C4D4×D1111yescharacteristic
414C22×C4D4×D1111yescharacteristic
415C4⋊C4—22no—
416C4⋊C4—22no—
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—81no—
420C4⋊C4—114no—
421C4⋊C4—114no—
422C4⋊C4—114no—
423C4⋊C4—114no—
424C4⋊C4—224no—
425C4⋊C4—224no—
426C4⋊C4—224no—
427C4⋊C4—221no—
428C4⋊C4—221no—
429C4⋊C4—444no—
430C4⋊C4—882no—
431C4⋊C4—882no—
432C4⋊C4—881no—
433C22⋊C4—22no—
434C22⋊C4—22no—
435C22⋊C4—22no—
436C22⋊C4—22no—
437C22⋊C4—24no—
438C22⋊C4—224no—
439C22⋊C4—224no—
440C22⋊C4—224no—
441C22⋊C4—222no—
442C22⋊C4—222no—
443C22⋊C4—222no—
444C22⋊C4—222no—
445C22⋊C4—224no—
446C42—81no—
447C42—224no—
448C42—444no—
449C42—881no—
450C11#2187711yescharacteristic, complemented, Sylow
451C23—41no—
452C23—41no—
453C23—222no—
454C23—224no—
455C23—442no—
456C23—442no—
457C23C22×C4×D1111yescharacteristic
458C23C2×D4×D1111yescharacteristic
459C23C2×D4×D1111yescharacteristic
460C23#6704012yes—
461C23#6704212yes—
462Q8—81no—
463Q8—81no—
464D4—442no—
465D4—444no—
466D4—442no—
467D4—881no—
468D4—881no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—114no—
486C2×C4—114no—
487C2×C4—222no—
488C2×C4—224no—
489C2×C4—224no—
490C2×C4—222no—
491C2×C4—222no—
492C2×C4—224no—
493C2×C4—442no—
494C2×C4—442no—
495C2×C4—442no—
496C2×C4—442no—
497C2×C4—442no—
498C2×C4—442no—
499C2×C4—442no—
500C2×C4—442no—
501C2×C4—442no—
502C2×C4—884no—
503C2×C4C22⋊C4×D1111yescharacteristic
504C2×C4C22⋊C4×D1111yescharacteristic
505C2×C4C22⋊C4×D1111yescharacteristic
506C2×C4C22⋊C4×D1111yescharacteristic
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—42no—
514C22—42no—
515C22—442no—
516C22—442no—
517C22—442no—
518C22—884no—
519C22C2×C22⋊C4×D1111yescharacteristic
520C22#1062310512yes—
521C22#1062316012yes—
522C22#1062320511yescharacteristic
523C22#1062325511yescharacteristic
524C4—21no—
525C4—21no—
526C4—21no—
527C4—21no—
528C4—42no—
529C4—42no—
530C4—82no—
531C4—82no—
532C4—224no—
533C4—224no—
534C4—442no—
535C4—882no—
536C4—882no—
537C2—21no—
538C2—22no—
539C2—22no—
540C2—21no—
541C2—882no—
542C2#1307120711yescharacteristic
543C2#1307707411yescharacteristic
544C2#1307707811yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC24C23×D11
FittingC11×#1996C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#66983C22
cosocleC24×C11C24
hypercenter#1996D11
hypocenterC11#21877
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1996

Complements

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

NH ≅ G/Ntype
2. #13071233C2semidirect
3. #13071216C2semidirect
4. #13069602C2semidirect
7. #13069073C2semidirect
8. #13068603C2semidirect
9. C11×#1996C2semidirect
11. C2×#66999C4semidirect
18. C2×#66951C4semidirect
19. C2×#66947C4semidirect
20. C2×#66943C4semidirect
183. #1996D11semidirect
450. C11#21877semidirect

Maximal subgroups

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

subgroupindex
C2×#106231762
#130712332
#130712162
#130696022
#130694522
#130694512
#130690732
#130686032
C11×#19962
#2187711