Finite Group Databasebeta

← #14759110

Subgroups — #14759110

Order 2816.

1122 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082005C211yesmaximal, characteristic
2#13077253C211yesmaximal, characteristic, complemented
3#13070955C211yesmaximal, characteristic, complemented
4#13069597C211yesmaximal, characteristic, complemented
5#13069592C211yesmaximal, characteristic, complemented
6#13069445C211yesmaximal, characteristic, complemented
7#13069061C212yesmaximal, complemented
8#13069056C212yesmaximal, complemented
9#13068428C212yesmaximal, complemented
10#104×Dic11C212yesmaximal, complemented
11C11×#1963C211yesmaximal, characteristic, complemented
12C11×#532C2211yescharacteristic
13#10623359C2212yes—
14#41×Dic11C2212yes—
15#10623262C412yescomplemented
16#10623250C412yescomplemented
17#10623213C414yescomplemented
18#10623148—22no—
19#10623133—22no—
20#10623069—24no—
21C2×#66925C2211yescharacteristic
22C2×#66925C2211yescharacteristic
23C2×C42×D11C2211yescharacteristic
24#10623001C2211yescharacteristic
25C11×#423C2211yescharacteristic
26C2×C11×#104C2212yes—
27C2×C11×#104C2212yes—
28C11×#376C2211yescharacteristic
29C2×#66901C2212yes—
30C2×#66901C2212yes—
31#10622739C2212yes—
32M16×Dic11C2212yes—
33#10622545C2211yescharacteristic
34C42×Dic11C2211yescharacteristic
35C42×Dic11C2211yescharacteristic
36#10622537C2211yescharacteristic
37#10622453—24no—
38#10622279—22no—
39#10622262—22no—
40#10622193C2212yes—
41#10622193C2212yes—
42#10622161C2212yes—
43#10622161C2212yes—
44C2×C11×#41C2312yes—
45C22×C4×D11—21no—
46C22×C4×D11C2311yescharacteristic
47C2×C11×M16C2312yes—
48C11×C4⋊Q8C2×C411yescharacteristic, complemented
49C11×#127C2×C411yescharacteristic, complemented
50C11×#124C2×C412yescomplemented
51C11×#121—22no—
52C4×D4×C11—22no—
53C2×C42×C11C2311yescharacteristic
54C2×C42×C11C2311yescharacteristic
55C2×C42×C11C2311yescharacteristic
56#66999C2×C414yes—
57Q8×Dic11C2×C414yescomplemented
58#66992—24no—
59#66991C2×C414yes—
60#66990—22no—
61#66988—22no—
62#66988—24no—
63D4×Dic11—24no—
64D4×Dic11C2×C414yescomplemented
65C4×C22⋊D11—24no—
66C2×(C2×D11)⋊C4—21no—
67C2×(C2×D11)⋊C4D412yes—
68#66979—22no—
69#66979C2312yes—
70#66977—22no—
71C2×Dic11⋊C4—21no—
72C2×Dic11⋊C4D412yes—
73C2×C4×Dic11—21no—
74C2×C4×Dic11—22no—
75C2×C4×Dic11—22no—
76C2×C4×Dic11—22no—
77C2×C4×Dic11C2311yescharacteristic
78C2×C4×Dic11C2311yescharacteristic
79C2×C4×Dic11C2311yescharacteristic
80C2×#4318C2312yes—
81#66951—24no—
82#66942—24no—
83#66939—24no—
84#66938—24no—
85#66932—24no—
86#66931—24no—
87#66925—22no—
88#66925—22no—
89#66925C2×C412yes—
90#66925C2×C412yes—
91#66925D414yes—
92C42×D11—22no—
93C42×D11—22no—
94#66923C2×C412yescomplemented
95#66922C2×C412yescomplemented
96C4×Dic22—22no—
97C11×C4⋊C8—22no—
98C11×#104—24no—
99C11×#104—24no—
100C11×#95—22no—
101#66901—24no—
102#66901—24no—
103C11⋊#95—22no—
104(C2×D11)⋊C8—24no—
105#66879—22no—
106C8×Dic11—22no—
107C4⋊(C11⋊C8)—22no—
108#21419—111nomaximal, Sylow
109C23×D11C2×D411yescharacteristic
110C11×#41—22no—
111C11×#41—22no—
112C11×#41—22no—
113C11×#41—22no—
114C2×Q8×C11C22×C412yes—
115C2×D4×C11—22no—
116C2×D4×C11—22no—
117C2×D4×C11C22×C412yes—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—22no—
121C22×C4×C11C2×D412yes—
122C22×C4×C11C2411yescharacteristic
123C2×C22⋊D11—24no—
124C22×Dic11—24no—
125C22×Dic11—21no—
126C22×Dic11—21no—
127C22×Dic11C2×D411yescharacteristic
128C22×Dic11C2×D412yes—
129C2×C4×D11—24no—
130C2×C4×D11—21no—
131C2×C4×D11—21no—
132C2×C4×D11—21no—
133C2×C4×D11—21no—
134C2×C4×D11—44no—
135C2×C4×D11C22×C412yes—
136C2×C4×D11C2×D412yes—
137C2×Dic22—22no—
138C11×M16—22no—
139C11×M16—22no—
140C2×C8×C11—22no—
141C11×C4⋊C4—22no—
142C11×C22⋊C4—24no—
143C42×C11—21no—
144C42×C11—21no—
145C42×C11C22×C411yescharacteristic
146C42×C11C22×C411yescharacteristic
147C42×C11C2×D412yes—
148C42×C11#4112yes—
149C42×C11#4112yes—
150C22⋊Dic11—24no—
151C22⋊Dic11—24no—
152C22⋊Dic11—22no—
153(C2×D11)⋊C4—24no—
154(C2×D11)⋊C4—24no—
155(C2×D11)⋊C4C22⋊C414yes—
156(C2×D11)⋊C4C22⋊C414yes—
157C4⋊Dic11—24no—
158C4⋊Dic11—22no—
159C4⋊Dic11C22×C414yes—
160Dic11⋊C4—24no—
161Dic11⋊C4—24no—
162Dic11⋊C4—24no—
163Dic11⋊C4C22⋊C414yes—
164Dic11⋊C4C22⋊C414yes—
165C4×Dic11—24no—
166C4×Dic11—24no—
167C4×Dic11—22no—
168C4×Dic11—21no—
169C4×Dic11—21no—
170C4×Dic11—44no—
171C4×Dic11—44no—
172C4×Dic11C22×C412yes—
173C4×Dic11C2×D412yes—
174C4×Dic11#4112yes—
175C4×Dic11#4112yes—
176#4318—22no—
177#4318—22no—
178C2×C11⋊C8—22no—
179#3455—111no—
180#2921—111no—
181C4×#117—111no—
182#1995—111no—
183#1994—111no—
184#1963D1111yescharacteristic, complemented
185#1962—111no—
186#1897—112no—
187#1896—112no—
188#1759—112no—
189C4×#104—112no—
190C23×C11—22no—
191C23×C11C22×D411yescharacteristic
192C22×D11—21no—
193C22×D11—21no—
194C22×D11—42no—
195C22×D11C2×C22⋊C412yes—
196Q8×C11—22no—
197Q8×C11—22no—
198D4×C11—22no—
199D4×C11—22no—
200D4×C11—42no—
201D4×C11—42no—
202D4×C11—82no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11C2×C22⋊C412yes—
212C2×C4×C11C2×C22⋊C412yes—
213C2×C4×C11C23×C411yescharacteristic
214C2×C4×C11C22×D411yescharacteristic
215C2×C4×C11C2×#4111yescharacteristic
216C2×C4×C11C2×#4111yescharacteristic
217C2×C4×C11C2×#4111yescharacteristic
218C2×C4×C11C2×#4111yescharacteristic
219C22⋊D11—84no—
220C2×Dic11—24no—
221C2×Dic11—21no—
222C2×Dic11—22no—
223C2×Dic11—21no—
224C2×Dic11—24no—
225C2×Dic11—22no—
226C2×Dic11—42no—
227C2×Dic11—42no—
228C2×Dic11—84no—
229C2×Dic11C2×C22⋊C414yes—
230C2×Dic11C2×C22⋊C412yes—
231C4×D11—22no—
232C4×D11—22no—
233C4×D11—22no—
234C4×D11—22no—
235C4×D11—48no—
236Dic22—82no—
237C8×C11—42no—
238C11⋊C8—42no—
239#542—114no—
240#541—112no—
241#540—112no—
242#539—222no—
243#538—222no—
244#533—111no—
245#532C2×D1111yescharacteristic
246#529—224no—
247#525—112no—
248C4×#41—112no—
249C2×#117—111no—
250C2×#117—111no—
251C22×C42—111no—
252#433—224no—
253#423—111no—
254#423C2×D1111yescharacteristic
255C2×#104—112no—
256C2×#104—112no—
257C2×#104C2×D1112yes—
258C2×#104C2×D1112yes—
259#407—112no—
260C4×M16—112no—
261C4×C4⋊C4—222no—
262C4×C22⋊C4—222no—
263#376—111no—
264#376C2×D1111yescharacteristic
265C43—111no—
266C43—111no—
267#339—112no—
268#339—112no—
269#339—112no—
270#339—112no—
271C22×C11—22no—
272C22×C11—44no—
273C22×C11—42no—
274C22×C11C22×C22⋊C411yescharacteristic
275C22×C11#52511yescharacteristic
276C22×C11#52511yescharacteristic
277C2×D11—24no—
278C2×D11—22no—
279C2×D11—42no—
280C2×D11—42no—
281C4×C11—22no—
282C4×C11—22no—
283C4×C11—42no—
284C4×C11—42no—
285C4×C11—42no—
286C4×C11C4×#4111yescharacteristic
287C4×C11C4×#4111yescharacteristic
288C4×C11#53211yescharacteristic
289C4×C11#53211yescharacteristic
290Dic11—24no—
291Dic11—24no—
292Dic11—22no—
293Dic11—42no—
294Dic11—44no—
295C2×#41C22×D1112yes—
296C23×C4—111no—
297C23×C4—221no—
298C2×M16—112no—
299C2×M16C22×D1112yes—
300C4⋊Q8—112no—
301C4⋊Q8C4×D1111yescharacteristic, complemented
302#127C4×D1111yescharacteristic, complemented
303#126—224no—
304#126—224no—
305#125—112no—
306#125—224no—
307#124—224no—
308#124C4×D1112yescomplemented
309#123—224no—
310#123—224no—
311#123—222no—
312C22⋊Q8—114no—
313C22⋊Q8—224no—
314C22⋊Q8—222no—
315#121—22no—
316#121—114no—
317#121—224no—
318#120—222no—
319C4×Q8—114no—
320C4×Q8—222no—
321C4×D4—22no—
322C4×D4—114no—
323C4×D4—224no—
324C4×D4—224no—
325#117—112no—
326#117—112no—
327#117—114no—
328#117—112no—
329#117—222no—
330#117—222no—
331#117—222no—
332C2×C4⋊C4—112no—
333C2×C4⋊C4—221no—
334C2×C22⋊C4—112no—
335C2×C22⋊C4—221no—
336C2×C42—111no—
337C2×C42—111no—
338C2×C42—111no—
339C2×C42—222no—
340C2×C42—222no—
341C2×C42—221no—
342C2×C42—222no—
343C2×C42—222no—
344C2×C42—222no—
345C2×C42C22×D1111yescharacteristic
346C2×C42C22×D1111yescharacteristic
347C2×C42C22×D1111yescharacteristic
348C4⋊C8—22no—
349C4⋊C8—222no—
350#104—24no—
351#104—24no—
352#104—224no—
353#104—224no—
354C22⋊C8—224no—
355#97—222no—
356C4×C8—222no—
357#95—22no—
358#95—222no—
359C2×C11—21no—
360C2×C11—21no—
361C2×C11—82no—
362C2×C11#229711yescharacteristic
363C2×C11#290112yes—
364D11—42no—
365C24—111no—
366#41—22no—
367#41—22no—
368#41—22no—
369#41—22no—
370C2×Q8—222no—
371C2×Q8C2×C4×D1112yes—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—224no—
375C2×D4C2×C4×D1112yes—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—22no—
379C22×C4—111no—
380C22×C4—112no—
381C22×C4—112no—
382C22×C4—112no—
383C22×C4—224no—
384C22×C4—224no—
385C22×C4—221no—
386C22×C4—221no—
387C22×C4—221no—
388C22×C4—221no—
389C22×C4—221no—
390C22×C4—221no—
391C22×C4—444no—
392C22×C4D4×D1112yes—
393C22×C4C23×D1111yescharacteristic
394M16—22no—
395M16—22no—
396M16—222no—
397M16—222no—
398C2×C8—22no—
399C2×C8—222no—
400C4⋊C4—22no—
401C4⋊C4—114no—
402C4⋊C4—114no—
403C4⋊C4—114no—
404C4⋊C4—224no—
405C4⋊C4—224no—
406C4⋊C4—224no—
407C4⋊C4—224no—
408C4⋊C4—222no—
409C22⋊C4—24no—
410C22⋊C4—114no—
411C22⋊C4—114no—
412C22⋊C4—224no—
413C22⋊C4—224no—
414C22⋊C4—224no—
415C22⋊C4—224no—
416C22⋊C4—222no—
417C42—21no—
418C42—21no—
419C42—112no—
420C42—112no—
421C42—112no—
422C42—112no—
423C42—224no—
424C42—224no—
425C42—222no—
426C42—221no—
427C42—221no—
428C42—444no—
429C42—444no—
430C42C2×C4×D1111yescharacteristic
431C42C2×C4×D1111yescharacteristic
432C42D4×D1112yes—
433C42#434112yes—
434C42#434112yes—
435C11#2141911yescharacteristic, complemented, Sylow
436C23—22no—
437C23—112no—
438C23—221no—
439C23—221no—
440C23—442no—
441C23C2×D4×D1111yescharacteristic
442Q8—22no—
443Q8—22no—
444Q8—882no—
445D4—22no—
446D4—22no—
447D4—42no—
448D4—42no—
449D4—82no—
450D4—884no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—114no—
460C2×C4—112no—
461C2×C4—224no—
462C2×C4—222no—
463C2×C4—221no—
464C2×C4—221no—
465C2×C4—222no—
466C2×C4—222no—
467C2×C4—222no—
468C2×C4—222no—
469C2×C4—224no—
470C2×C4—222no—
471C2×C4—448no—
472C2×C4—442no—
473C2×C4—442no—
474C2×C4—884no—
475C2×C4C22⋊C4×D1112yes—
476C2×C4C22⋊C4×D1112yes—
477C2×C4C22×C4×D1111yescharacteristic
478C2×C4C2×D4×D1111yescharacteristic
479C2×C4C2×#434111yescharacteristic
480C2×C4C2×#434111yescharacteristic
481C2×C4#41×D1111yescharacteristic
482C2×C4#41×D1111yescharacteristic
483C8—42no—
484C8—442no—
485C22—22no—
486C22—44no—
487C22—42no—
488C22—224no—
489C22—222no—
490C22—442no—
491C22—442no—
492C22C2×C22⋊C4×D1111yescharacteristic
493C22#1062313711yescharacteristic
494C22#1062313711yescharacteristic
495C4—22no—
496C4—22no—
497C4—42no—
498C4—42no—
499C4—42no—
500C4—224no—
501C4—224no—
502C4—222no—
503C4—442no—
504C4—444no—
505C4C4×#434111yescharacteristic
506C4C4×#434111yescharacteristic
507C4#1062319911yescharacteristic
508C4#1062324711yescharacteristic
509C2—21no—
510C2—21no—
511C2—82no—
512C2—442no—
513C2#1307110311yescharacteristic
514C2#1307716212yes—
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1963C2
socleC22×C11C22×C22⋊C4
prime radical#13082005C2
cosocleC22×C4×C11C24
hypercenter#1963D11
hypocenterC11#21419
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1963

Complements

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

NH ≅ G/Ntype
2. #13077253C2semidirect
3. #13070955C2semidirect
4. #13069597C2semidirect
5. #13069592C2semidirect
6. #13069445C2semidirect
7. #13069061C2semidirect
8. #13069056C2semidirect
9. #13068428C2semidirect
10. #104×Dic11C2semidirect
11. C11×#1963C2semidirect
15. #10623262C4semidirect
16. #10623250C4semidirect
17. #10623213C4semidirect
48. C11×C4⋊Q8C2×C4semidirect
49. C11×#127C2×C4semidirect
50. C11×#124C2×C4semidirect
57. Q8×Dic11C2×C4semidirect
64. D4×Dic11C2×C4semidirect
94. #66923C2×C4semidirect
95. #66922C2×C4semidirect
184. #1963D11semidirect
301. C4⋊Q8C4×D11semidirect
302. #127C4×D11semidirect
308. #124C4×D11semidirect
435. C11#21419semidirect

Maximal subgroups

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

subgroupindex
#130820052
#130772532
#130709552
#130695972
#130695922
#130694452
#130690612
#130690562
#130684282
#104×Dic112
C11×#19632
#2141911