Finite Group Databasebeta

← #14770235

Subgroups — #14770235

Order 2816.

1246 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623094C211yesmaximal, characteristic
2C2×#10622301C211yesmaximal, characteristic, complemented
3C4⋊C4×D44C211yesmaximal, characteristic, complemented
4#13069577C211yesmaximal, characteristic, complemented
5#13069564C211yesmaximal, characteristic, complemented
6#13069051C212yesmaximal, complemented
7#13068930C212yesmaximal, complemented
8#13068710C212yesmaximal, complemented
9#13068616C211yesmaximal, characteristic, complemented
10#13068334C212yesmaximal, complemented
11C4×C11×#102C211yesmaximal, characteristic, complemented
12C2×C4×D4×C11C2211yescharacteristic
13C2×#66991C2212yes—
14C2×#66983—21no—
15C2×#66979—21no—
16C22×#4313C2212yes—
17#10623094—24no—
18#10623094C418yescomplemented
19C2×#66945C2212yes—
20C2×C4⋊C4×D11C2212yes—
21C2×#66938—22no—
22C2×C4×D44—21no—
23C2×C4×D44C2211yescharacteristic
24C2×#66922C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27C2×C4×C8×C11C2211yescharacteristic
28C4×C11×C4⋊C4C2211yescharacteristic
29C2×#66896C2212yes—
30C2×(C2×D11)⋊C8C2212yes—
31#10622600C2212yes—
32#10622548C2211yescharacteristic
33#10622541—21no—
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35#10622301—24no—
36#10622281—22no—
37C11×#340C2211yescharacteristic
38C11×#340C2211yescharacteristic
39#10622189C2212yes—
40#10622189C2212yes—
41#10622167C2212yes—
42#10622167C2212yes—
43#10622167C2212yes—
44C22×D4×C11C2311yescharacteristic
45C23×C4×C11—21no—
46C22×C22⋊D11—22no—
47C22×D44D411yescharacteristic
48C22×C4×D11—22no—
49C22×C4×D11C2312yes—
50C22×Dic22—21no—
51C22×C8×C11C2311yescharacteristic
52C22×C8×C11C2311yescharacteristic
53C4×D4×C11—22no—
54C4×D4×C11C2×C414yescomplemented
55C2×C11×C4⋊C4C2311yescharacteristic
56C2×C11×C4⋊C4C2311yescharacteristic
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C11×C22⋊C4—21no—
59C2×C42×C11—21no—
60C2×C42×C11C2311yescharacteristic
61C2×C22⋊Dic11—22no—
62#66991—24no—
63#66991C2×C418yescomplemented
64#66983—28no—
65C2×(C2×D11)⋊C4—22no—
66C2×(C2×D11)⋊C4—22no—
67C2×(C2×D11)⋊C4D412yes—
68#66979—28no—
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11—21no—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11D411yescharacteristic
73C2×C4⋊Dic11C2312yes—
74C2×C4⋊Dic11C2312yes—
75C2×Dic11⋊C4—22no—
76C2×C4×Dic11—22no—
77C22×C11⋊C8C2312yes—
78C2×#4313—24no—
79C2×#4313—24no—
80C2×#4313—42no—
81#66945—24no—
82#66945C2×C418yescomplemented
83C4⋊C4×D11—24no—
84C4⋊C4×D11—42no—
85#66938—216no—
86C4×D44—44no—
87C4×D44C2×C414yes—
88C4×D44D414yes—
89#66922—22no—
90#66922C2×C414yescomplemented
91C11×#102—22no—
92C11×#102—22no—
93C4×C8×C11—22no—
94C11×#95—21no—
95#66896—42no—
96C11⋊#95—22no—
97(C2×D11)⋊C8—24no—
98C4⋊(C11⋊C8)—22no—
99#22503—111nomaximal, Sylow
100C24×C11—21no—
101C23×D11C2×D412yes—
102C2×D4×C11—21no—
103C2×D4×C11—21no—
104C2×D4×C11—21no—
105C2×D4×C11—21no—
106C2×D4×C11—21no—
107C2×D4×C11C22×C412yes—
108C22×C4×C11—21no—
109C22×C4×C11—21no—
110C22×C4×C11—24no—
111C22×C4×C11—21no—
112C22×C4×C11—42no—
113C22×C4×C11—42no—
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2411yescharacteristic
117C2×C22⋊D11—28no—
118C2×C22⋊D11—82no—
119C2×C22⋊D11—82no—
120C22×Dic11—22no—
121C22×Dic11—22no—
122C22×Dic11C2×D412yes—
123C2×D44—22no—
124C2×D44—22no—
125C2×D44C22⋊C414yes—
126C2×C4×D11—22no—
127C2×C4×D11—22no—
128C2×C4×D11—22no—
129C2×C4×D11—22no—
130C2×C4×D11—44no—
131C2×C4×D11—44no—
132C2×C4×D11—82no—
133C2×C4×D11C22×C414yes—
134C2×C4×D11C2×D414yes—
135C2×Dic22—24no—
136C2×Dic22—81no—
137C2×Dic22—81no—
138C2×C8×C11—21no—
139C2×C8×C11—21no—
140C2×C8×C11—21no—
141C2×C8×C11—21no—
142C2×C8×C11—21no—
143C2×C8×C11#4112yes—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4C22×C412yes—
149C11×C4⋊C4#4112yes—
150C11×C22⋊C4—24no—
151C42×C11—42no—
152C42×C11C22×C412yes—
153C42×C11C2×D412yes—
154C22⋊Dic11—28no—
155(C2×D11)⋊C4—28no—
156(C2×D11)⋊C4—44no—
157(C2×D11)⋊C4C22⋊C418yes—
158C4⋊Dic11—24no—
159C4⋊Dic11—22no—
160C4⋊Dic11—22no—
161C4⋊Dic11—22no—
162C4⋊Dic11—42no—
163C4⋊Dic11—81no—
164C4⋊Dic11C22⋊C414yes—
165C4⋊Dic11C22×C414yes—
166Dic11⋊C4—44no—
167C4×Dic11—28no—
168C2×C11⋊C8—22no—
169C2×C11⋊C8—22no—
170C2×C11⋊C8—22no—
171#4313—48no—
172C2×#555—111no—
173C2×#436—111no—
174D4×C4⋊C4—111no—
175#1990—111no—
176#1987—111no—
177#1895—112no—
178#1874—112no—
179#1825—112no—
180#1802—111no—
181C4×#102D1111yescharacteristic, complemented
182#1736—112no—
183C23×C11—22no—
184C23×C11—41no—
185C23×C11—41no—
186C23×C11—41no—
187C23×C11—41no—
188C23×C11—41no—
189C23×C11—41no—
190C23×C11C22×D411yescharacteristic
191C22×D11—22no—
192C22×D11—22no—
193C22×D11—22no—
194C22×D11—22no—
195C22×D11—22no—
196C22×D11—22no—
197C22×D11C2×C22⋊C414yes—
198D4×C11—22no—
199D4×C11—22no—
200D4×C11—41no—
201D4×C11—41no—
202C2×C4×C11—21no—
203C2×C4×C11—21no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—48no—
211C2×C4×C11—41no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11C2×C22⋊C412yes—
215C2×C4×C11C2×C22⋊C412yes—
216C2×C4×C11AGL(1,ℤ/8)12yes—
217C2×C4×C11#13712yes—
218C2×C4×C11C23×C411yescharacteristic
219C2×C4×C11C22×D411yescharacteristic
220C2×C4×C11C2×#4111yescharacteristic
221C2×C4×C11C2×#4111yescharacteristic
222C2×C4×C11H(5,𝔽2)11yescharacteristic
223C2×C4×C112−1+411yescharacteristic
224C22⋊D11—88no—
225C2×Dic11—22no—
226C2×Dic11—22no—
227C2×Dic11—24no—
228C2×Dic11—42no—
229C2×Dic11—42no—
230C2×Dic11—42no—
231C2×Dic11—42no—
232C2×Dic11—42no—
233C2×Dic11C2×C22⋊C414yes—
234D44—28no—
235C4×D11—24no—
236C4×D11—24no—
237C4×D11—24no—
238C4×D11—24no—
239C4×D11—88no—
240Dic22—84no—
241C8×C11—22no—
242C8×C11—41no—
243C11⋊C8—42no—
244C22×M16—112no—
245#555—118no—
246#555—224no—
247C2×C4⋊Q8—111no—
248C2×#124—222no—
249C2×#121—112no—
250C2×#121—221no—
251C2×C4×D4—111no—
252C2×C4×D4—221no—
253C2×C4×D4C2×D1111yescharacteristic
254C2×#117—112no—
255C2×#117—221no—
256C22×C4⋊C4—112no—
257#436—224no—
258C2×C4⋊C8—111no—
259C2×#102—112no—
260C2×#102C2×D1111yescharacteristic
261C2×#102C2×D1111yescharacteristic
262C2×C22⋊C8—112no—
263C2×C4×C8C2×D1111yescharacteristic
264#389—221no—
265#385—222no—
266#384—111no—
267#380—112no—
268C4×C4⋊C4C2×D1111yescharacteristic
269#340—112no—
270#340—112no—
271#340—112no—
272#340—112no—
273#340—112no—
274#340C2×D1111yescharacteristic
275#340C2×D1111yescharacteristic
276C22×C11—42no—
277C22×C11—42no—
278C22×C11—42no—
279C22×C11—81no—
280C22×C11—81no—
281C22×C11—81no—
282C22×C11—81no—
283C22×C11C22×C22⋊C411yescharacteristic
284C22×C11#54611yescharacteristic
285C22×C11#54711yescharacteristic
286C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
287C22×C11C2×#13711yescharacteristic
288C22×C11#57611yescharacteristic
289C22×C11#57711yescharacteristic
290C2×D11—24no—
291C2×D11—24no—
292C2×D11—24no—
293C2×D11—42no—
294C2×D11—42no—
295C2×D11—42no—
296C2×D11—42no—
297C4×C11—22no—
298C4×C11—42no—
299C4×C11—42no—
300C4×C11—81no—
301C4×C11#41714yes—
302C4×C11C4×#4111yescharacteristic
303C4×C11#52011yescharacteristic
304C4×C11#54611yescharacteristic
305C4×C11#54711yescharacteristic
306Dic11—24no—
307Dic11—44no—
308Dic11—82no—
309C22×Q8—221no—
310C22×D4—111no—
311C22×D4—222no—
312C22×D4C22×D1111yescharacteristic
313C23×C4—21no—
314C23×C4—112no—
315C23×C4—222no—
316C2×M16—224no—
317C2×M16—224no—
318C2×M16—442no—
319C22×C8—112no—
320C22×C8C22×D1111yescharacteristic
321C22×C8C22×D1111yescharacteristic
322C4⋊Q8—114no—
323C4⋊Q8—222no—
324#124—2216no—
325#121—118no—
326#121—228no—
327#121—224no—
328C4×D4—22no—
329C4×D4—114no—
330C4×D4—114no—
331C4×D4—444no—
332C4×D4C4×D1114yescomplemented
333#117—118no—
334#117—224no—
335#117—228no—
336C2×C4⋊C4—111no—
337C2×C4⋊C4—112no—
338C2×C4⋊C4—112no—
339C2×C4⋊C4—221no—
340C2×C4⋊C4—224no—
341C2×C4⋊C4—222no—
342C2×C4⋊C4—221no—
343C2×C4⋊C4—221no—
344C2×C4⋊C4—442no—
345C2×C4⋊C4C22×D1111yescharacteristic
346C2×C4⋊C4C22×D1111yescharacteristic
347C2×C4⋊C4C22×D1111yescharacteristic
348C2×C22⋊C4—21no—
349C2×C22⋊C4—112no—
350C2×C22⋊C4—222no—
351C2×C22⋊C4—222no—
352C2×C22⋊C4—222no—
353C2×C42—21no—
354C2×C42—222no—
355C2×C42C22×D1111yescharacteristic
356C4⋊C8—222no—
357#102—22no—
358#102—22no—
359#102—442no—
360C22⋊C8—224no—
361C4×C8—22no—
362#95—21no—
363#95—222no—
364C2×C11—82no—
365C2×C11#233911yescharacteristic
366C2×C11C2×#41711yescharacteristic
367C2×C11#289711yescharacteristic
368C2×C11#332511yescharacteristic
369C2×C11#332911yescharacteristic
370C2×C11#335411yescharacteristic
371C2×C11#335711yescharacteristic
372D11—44no—
373C24—21no—
374C24—112no—
375C2×Q8—224no—
376C2×Q8—881no—
377C2×Q8—881no—
378C2×D4—21no—
379C2×D4—21no—
380C2×D4—21no—
381C2×D4—21no—
382C2×D4—21no—
383C2×D4—114no—
384C2×D4—228no—
385C2×D4—222no—
386C2×D4—222no—
387C2×D4—882no—
388C2×D4—882no—
389C2×D4C2×C4×D1112yes—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—24no—
393C22×C4—21no—
394C22×C4—42no—
395C22×C4—42no—
396C22×C4—112no—
397C22×C4—114no—
398C22×C4—114no—
399C22×C4—222no—
400C22×C4—222no—
401C22×C4—222no—
402C22×C4—222no—
403C22×C4—222no—
404C22×C4—222no—
405C22×C4—444no—
406C22×C4—444no—
407C22×C4—882no—
408C22×C4D4×D1111yescharacteristic
409C22×C4D4×D1111yescharacteristic
410C22×C4C23×D1111yescharacteristic
411M16—448no—
412C2×C8—21no—
413C2×C8—21no—
414C2×C8—21no—
415C2×C8—21no—
416C2×C8—21no—
417C2×C8—222no—
418C2×C8—222no—
419C2×C8—222no—
420C2×C8#433912yes—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—114no—
426C4⋊C4—114no—
427C4⋊C4—224no—
428C4⋊C4—222no—
429C4⋊C4—222no—
430C4⋊C4—222no—
431C4⋊C4—444no—
432C4⋊C4—442no—
433C4⋊C4—881no—
434C4⋊C4C2×C4×D1112yes—
435C4⋊C4#433912yes—
436C22⋊C4—24no—
437C22⋊C4—118no—
438C22⋊C4—228no—
439C22⋊C4—228no—
440C22⋊C4—444no—
441C42—42no—
442C42—228no—
443C42C2×C4×D1112yes—
444C42D4×D1112yes—
445C11#2250311yescharacteristic, complemented, Sylow
446C23—22no—
447C23—41no—
448C23—41no—
449C23—41no—
450C23—41no—
451C23—41no—
452C23—41no—
453C23—114no—
454C23—222no—
455C23—222no—
456C23—222no—
457C23—222no—
458C23—222no—
459C23—222no—
460C23C2×D4×D1111yescharacteristic
461Q8—884no—
462D4—22no—
463D4—22no—
464D4—41no—
465D4—41no—
466D4—228no—
467D4—888no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—48no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—114no—
481C2×C4—222no—
482C2×C4—222no—
483C2×C4—224no—
484C2×C4—224no—
485C2×C4—224no—
486C2×C4—224no—
487C2×C4—224no—
488C2×C4—442no—
489C2×C4—442no—
490C2×C4—442no—
491C2×C4—442no—
492C2×C4—442no—
493C2×C4—888no—
494C2×C4C22⋊C4×D1112yes—
495C2×C4C22⋊C4×D1112yes—
496C2×C4#6696412yes—
497C2×C4#6696812yes—
498C2×C4C22×C4×D1111yescharacteristic
499C2×C4C2×#433911yescharacteristic
500C2×C4C2×#433911yescharacteristic
501C2×C4C2×D4×D1111yescharacteristic
502C2×C4#6704211yescharacteristic
503C2×C4#6704311yescharacteristic
504C8—22no—
505C8—41no—
506C8—442no—
507C22—42no—
508C22—42no—
509C22—42no—
510C22—81no—
511C22—81no—
512C22—81no—
513C22—81no—
514C22—224no—
515C22—224no—
516C22—224no—
517C22—442no—
518C22—442no—
519C22—442no—
520C22—442no—
521C22C2×C22⋊C4×D1111yescharacteristic
522C22#1062308111yescharacteristic
523C22#1062308211yescharacteristic
524C22C2×#6696411yescharacteristic
525C22C2×#6696811yescharacteristic
526C22#1062330011yescharacteristic
527C22#1062330111yescharacteristic
528C4—22no—
529C4—42no—
530C4—42no—
531C4—81no—
532C4—224no—
533C4—444no—
534C4—882no—
535C4#1062238414yes—
536C4C4×#433911yescharacteristic
537C4#1062305411yescharacteristic
538C4#1062308111yescharacteristic
539C4#1062308211yescharacteristic
540C2—82no—
541C2—444no—
542C2#1307144711yescharacteristic
543C2C2×#1062238411yescharacteristic
544C2#1307713811yescharacteristic
545C2#1308086011yescharacteristic
546C2#1308091211yescharacteristic
547C2#1308121311yescharacteristic
548C2#1308124411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×#102C2
socleC23×C11C22×D4
prime radicalC2×#10623094C2
cosocleC22×C4×C11C24
hypercenterC4×#102D11
hypocenterC11#22503
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
2. C2×#10622301C2semidirect
3. C4⋊C4×D44C2semidirect
4. #13069577C2semidirect
5. #13069564C2semidirect
6. #13069051C2semidirect
7. #13068930C2semidirect
8. #13068710C2semidirect
9. #13068616C2semidirect
10. #13068334C2semidirect
11. C4×C11×#102C2semidirect
18. #10623094C4semidirect
54. C4×D4×C11C2×C4semidirect
63. #66991C2×C4semidirect
82. #66945C2×C4semidirect
90. #66922C2×C4semidirect
181. C4×#102D11semidirect
332. C4×D4C4×D11semidirect
445. C11#22503semidirect

Maximal subgroups

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

subgroupindex
C2×#106230942
C2×#106223012
C4⋊C4×D442
#130695772
#130695642
#130690512
#130689302
#130687102
#130686162
#130683342
C4×C11×#1022
#2250311