Finite Group Databasebeta

← #14759107

Subgroups — #14759107

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#13082006C211yesmaximal, characteristic
2#13077254C211yesmaximal, characteristic, complemented
3#13069597C211yesmaximal, characteristic, complemented
4#13069593C211yesmaximal, characteristic, complemented
5#13069448C211yesmaximal, characteristic, complemented
6#13069444C211yesmaximal, characteristic, complemented
7#13069064C212yesmaximal, complemented
8#13069059C212yesmaximal, complemented
9#13068427C212yesmaximal, complemented
10C4×#66869C212yesmaximal, complemented
11C4×C11×#117C211yesmaximal, characteristic, complemented
12C2×C11×#117C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C22×C42×C11C2211yescharacteristic
15#10623322C2212yes—
16#10623066C412yescomplemented
17#10623065C414yescomplemented
18#10623059—24no—
19#10623049C412yescomplemented
20#10623046—22no—
21#10623025—22no—
22#10623008C2211yescharacteristic
23C4×#4339C2212yes—
24#10623001C2211yescharacteristic
25C4×C11×C4⋊C4—22no—
26C4×C11×C22⋊C4—22no—
27C11×#376C2211yescharacteristic
28C11×#376C2211yescharacteristic
29C43×C11C2211yescharacteristic
30C43×C11C2211yescharacteristic
31#10622820C2212yes—
32#10622613—24no—
33C2×#66869C2212yes—
34C2×#66869C2212yes—
35C2×#66869C2212yes—
36C2×#66869C2212yes—
37#10622537C2211yescharacteristic
38#10622537C2211yescharacteristic
39C4×#4318C2212yes—
40#10622161C2212yes—
41#10622161C2212yes—
42#10622161C2212yes—
43#10622161C2212yes—
44C23×C4×C11—21no—
45C23×C4×C11C2311yescharacteristic
46C2×#4339C2312yes—
47C11×#117—22no—
48C11×#117—22no—
49C11×#117C2×C412yes—
50C11×#117C2×C412yes—
51C11×#117D414yes—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4D412yes—
54C2×C11×C22⋊C4—21no—
55C2×C11×C22⋊C4D412yes—
56C2×C42×C11—21no—
57C2×C42×C11—22no—
58C2×C42×C11—22no—
59C2×C42×C11—22no—
60C2×C42×C11—22no—
61C2×C42×C11C2311yescharacteristic
62C2×C42×C11C2311yescharacteristic
63C2×C42×C11C2311yescharacteristic
64C2×C42×C11C2311yescharacteristic
65C2×C42×C11C2311yescharacteristic
66C2×C42×C11C2311yescharacteristic
67#67006—22no—
68#66983—22no—
69#66983C2×C414yes—
70#66982—22no—
71C4×C22⋊D11—24no—
72C4×C22⋊D11—24no—
73#66979C2312yes—
74#66977—22no—
75#66977C2×C414yes—
76C2×#4318C2312yes—
77C2×#4318C2312yes—
78#66951—24no—
79#66949—24no—
80#66947—24no—
81#66942—24no—
82#66938—24no—
83#66937—24no—
84#66936—24no—
85#66932—24no—
86#66928C2×C412yescomplemented
87#66927C2×C411yescharacteristic, complemented
88C4×D44—22no—
89C4×D44C2×C414yescomplemented
90#66925—22no—
91C42×D11—22no—
92#66923C2×C412yescomplemented
93#66922C2×C411yescharacteristic, complemented
94#66922C2×C412yescomplemented
95C4×Dic22—22no—
96C4×Dic22C2×C414yescomplemented
97C11×#95—22no—
98C11×#95—22no—
99C22⋊(C11⋊C8)—24no—
100#66869—24no—
101#66869—24no—
102#66869—24no—
103#66869—24no—
104C4⋊(C11⋊C8)—22no—
105C4⋊(C11⋊C8)—22no—
106#66867—22no—
107C4×C11⋊C8—22no—
108#21419—111nomaximal, Sylow
109C24×C11C2×D411yescharacteristic
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11—24no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—44no—
120C22×C4×C11C22×C412yes—
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D412yes—
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2×D412yes—
125C22×C4×C11C2411yescharacteristic
126C2×C22⋊D11—24no—
127C2×C22⋊D11—22no—
128#4339—22no—
129#4339—22no—
130#4339—22no—
131#4339—22no—
132C2×D44—22no—
133C2×D44C22×C412yes—
134C2×C4×D11—24no—
135C2×C4×D11—22no—
136C2×Dic22—22no—
137C2×Dic22C22×C412yes—
138C11×C4⋊C4—24no—
139C11×C4⋊C4C22⋊C414yes—
140C11×C4⋊C4C22⋊C414yes—
141C11×C22⋊C4—24no—
142C11×C22⋊C4C22⋊C414yes—
143C11×C22⋊C4C22⋊C414yes—
144C42×C11—24no—
145C42×C11—21no—
146C42×C11—21no—
147C42×C11—21no—
148C42×C11—21no—
149C42×C11—44no—
150C42×C11—44no—
151C42×C11C22×C412yes—
152C42×C11C22×C411yescharacteristic
153C42×C11C22×C411yescharacteristic
154C42×C11C2×D412yes—
155C42×C11C2×D412yes—
156C42×C11#4112yes—
157C42×C11#4112yes—
158C42×C11#4112yes—
159C42×C11#4112yes—
160C22⋊Dic11—24no—
161C22⋊Dic11—22no—
162(C2×D11)⋊C4—24no—
163(C2×D11)⋊C4—24no—
164(C2×D11)⋊C4—24no—
165C4⋊Dic11—22no—
166C4⋊Dic11—22no—
167C4⋊Dic11C22×C414yes—
168Dic11⋊C4—24no—
169Dic11⋊C4—24no—
170Dic11⋊C4—24no—
171C4×Dic11—24no—
172C4×Dic11—22no—
173#4318—22no—
174#4318—22no—
175#4318—22no—
176#4318—22no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—22no—
179#3455—111no—
180#2921—111no—
181C4×#117D1111yescharacteristic, complemented
182#1995—111no—
183#1994—111no—
184#1963—111no—
185#1962—111no—
186#1897—112no—
187#1896—112no—
188#1759—112no—
189C4×#104—112no—
190C23×C11—21no—
191C23×C11—21no—
192C23×C11—42no—
193C23×C11C2×C22⋊C412yes—
194C23×C11C22×D411yescharacteristic
195C22×D11—22no—
196C2×C4×C11—24no—
197C2×C4×C11—21no—
198C2×C4×C11—22no—
199C2×C4×C11—21no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—48no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11C2×C22⋊C414yes—
214C2×C4×C11C2×C22⋊C412yes—
215C2×C4×C11C2×C22⋊C412yes—
216C2×C4×C11C2×C22⋊C412yes—
217C2×C4×C11C23×C411yescharacteristic
218C2×C4×C11C22×D411yescharacteristic
219C2×C4×C11C2×#4111yescharacteristic
220C2×C4×C11C2×#4111yescharacteristic
221C2×C4×C11C2×#4111yescharacteristic
222C2×C4×C11C2×#4111yescharacteristic
223C22⋊D11—42no—
224C22⋊D11—42no—
225C22⋊D11—84no—
226C2×Dic11—22no—
227C2×Dic11—24no—
228D44—22no—
229D44—22no—
230D44—82no—
231C4×D11—42no—
232C4×D11—42no—
233C4×D11—84no—
234Dic22—22no—
235Dic22—22no—
236Dic22—82no—
237C11⋊C8—42no—
238C11⋊C8—42no—
239#542—114no—
240#541—112no—
241#540—112no—
242#539—222no—
243#538—222no—
244#533—111no—
245#532—111no—
246#529—224no—
247#525—112no—
248C4×#41—112no—
249C2×#117C2×D1111yescharacteristic
250C2×#117C2×D1111yescharacteristic
251C22×C42C2×D1111yescharacteristic
252#433—224no—
253#423—111no—
254#423—111no—
255C2×#104—112no—
256C2×#104—112no—
257C2×#104—112no—
258C2×#104—112no—
259#407—112no—
260C4×M16—112no—
261C4×C4⋊C4—22no—
262C4×C22⋊C4—22no—
263#376C2×D1111yescharacteristic
264#376C2×D1111yescharacteristic
265C43C2×D1111yescharacteristic
266C43C2×D1111yescharacteristic
267#339—112no—
268#339—112no—
269#339—112no—
270#339—112no—
271C22×C11—22no—
272C22×C11—24no—
273C22×C11—22no—
274C22×C11—42no—
275C22×C11—42no—
276C22×C11C22×C22⋊C411yescharacteristic
277C22×C11#52511yescharacteristic
278C22×C11#52511yescharacteristic
279C2×D11—44no—
280C2×D11—42no—
281C4×C11—24no—
282C4×C11—22no—
283C4×C11—24no—
284C4×C11—22no—
285C4×C11—22no—
286C4×C11—42no—
287C4×C11—42no—
288C4×C11—42no—
289C4×C11C4×#4111yescharacteristic
290C4×C11C4×#4111yescharacteristic
291C4×C11#53211yescharacteristic
292C4×C11#53211yescharacteristic
293Dic11—44no—
294Dic11—42no—
295C2×#41—112no—
296C23×C4—21no—
297C23×C4C22×D1111yescharacteristic
298C2×M16—112no—
299C2×M16—112no—
300C4⋊Q8—112no—
301C4⋊Q8—111no—
302#127—111no—
303#126—224no—
304#126—224no—
305#125—112no—
306#125—224no—
307#124—112no—
308#124—224no—
309#123—222no—
310#123—224no—
311#123—224no—
312C22⋊Q8—114no—
313C22⋊Q8—222no—
314C22⋊Q8—224no—
315#121—114no—
316#121—222no—
317#121—224no—
318#120—222no—
319C4×Q8—114no—
320C4×Q8—222no—
321C4×D4—114no—
322C4×D4—224no—
323C4×D4—224no—
324C4×D4—222no—
325#117—22no—
326#117—22no—
327#117—112no—
328#117—222no—
329#117C4×D1112yes—
330#117C4×D1112yes—
331#117D4414yes—
332C2×C4⋊C4—21no—
333C2×C4⋊C4C22⋊D1112yes—
334C2×C22⋊C4—21no—
335C2×C22⋊C4C22⋊D1112yes—
336C2×C42—21no—
337C2×C42—22no—
338C2×C42—22no—
339C2×C42—22no—
340C2×C42—22no—
341C2×C42—222no—
342C2×C42C22×D1111yescharacteristic
343C2×C42C22×D1111yescharacteristic
344C2×C42C22×D1111yescharacteristic
345C2×C42C22×D1111yescharacteristic
346C2×C42C22×D1111yescharacteristic
347C2×C42C22×D1111yescharacteristic
348C4⋊C8—222no—
349C4⋊C8—222no—
350#104—224no—
351#104—224no—
352#104—224no—
353#104—224no—
354C22⋊C8—224no—
355#97—222no—
356C4×C8—222no—
357#95—22no—
358#95—22no—
359C2×C11—21no—
360C2×C11—21no—
361C2×C11—42no—
362C2×C11#229711yescharacteristic
363C2×C11#290112yes—
364D11—82no—
365C24C2×C22⋊D1111yescharacteristic
366#41—222no—
367#41—222no—
368#41—222no—
369#41—222no—
370C2×Q8—112no—
371C2×Q8—222no—
372C2×D4—112no—
373C2×D4—222no—
374C2×D4—224no—
375C2×D4—222no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—24no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—44no—
386C22×C4—222no—
387C22×C4—224no—
388C22×C4C2×C4×D1112yes—
389C22×C4C2×D4412yes—
390C22×C4C2×C22⋊D1111yescharacteristic
391C22×C4C2×C22⋊D1112yes—
392C22×C4C2×C22⋊D1112yes—
393C22×C4C23×D1111yescharacteristic
394M16—222no—
395M16—222no—
396M16—222no—
397M16—222no—
398C2×C8—222no—
399C2×C8—222no—
400C4⋊C4—24no—
401C4⋊C4—114no—
402C4⋊C4—224no—
403C4⋊C4—222no—
404C4⋊C4—224no—
405C4⋊C4—224no—
406C4⋊C4—222no—
407C4⋊C4(C2×D11)⋊C414yes—
408C4⋊C4(C2×D11)⋊C414yes—
409C22⋊C4—24no—
410C22⋊C4—224no—
411C22⋊C4—222no—
412C22⋊C4—224no—
413C22⋊C4—224no—
414C22⋊C4—224no—
415C22⋊C4(C2×D11)⋊C414yes—
416C22⋊C4(C2×D11)⋊C414yes—
417C42—24no—
418C42—21no—
419C42—21no—
420C42—21no—
421C42—21no—
422C42—44no—
423C42—44no—
424C42—224no—
425C42—222no—
426C42C2×C4×D1112yes—
427C42C2×C4×D1111yescharacteristic
428C42C2×C4×D1111yescharacteristic
429C42C2×D4412yes—
430C42C2×D4412yes—
431C42#433912yes—
432C42#433912yes—
433C42#433912yes—
434C42#433912yes—
435C11#2141911yescharacteristic, complemented, Sylow
436C23—21no—
437C23—21no—
438C23—42no—
439C23—222no—
440C23C2×(C2×D11)⋊C412yes—
441C23C22×C22⋊D1111yescharacteristic
442Q8—222no—
443Q8—222no—
444Q8—882no—
445D4—222no—
446D4—222no—
447D4—442no—
448D4—442no—
449D4—882no—
450D4—884no—
451C2×C4—24no—
452C2×C4—21no—
453C2×C4—22no—
454C2×C4—21no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—48no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—224no—
469C2×C4—222no—
470C2×C4—442no—
471C2×C4—442no—
472C2×C4—884no—
473C2×C4C2×(C2×D11)⋊C414yes—
474C2×C4C2×(C2×D11)⋊C412yes—
475C2×C4C2×(C2×D11)⋊C412yes—
476C2×C4C2×(C2×D11)⋊C412yes—
477C2×C4C22×C4×D1111yescharacteristic
478C2×C4C22×D4411yescharacteristic
479C2×C4C2×#433911yescharacteristic
480C2×C4C2×#433911yescharacteristic
481C2×C4C2×#433911yescharacteristic
482C2×C4C2×#433911yescharacteristic
483C8—442no—
484C8—442no—
485C22—22no—
486C22—22no—
487C22—24no—
488C22—42no—
489C22—42no—
490C22—442no—
491C22—444no—
492C22C22×(C2×D11)⋊C411yescharacteristic
493C22#1062332211yescharacteristic
494C22#1062332211yescharacteristic
495C4—24no—
496C4—22no—
497C4—24no—
498C4—22no—
499C4—22no—
500C4—42no—
501C4—42no—
502C4—42no—
503C4—442no—
504C4—444no—
505C4C4×#433911yescharacteristic
506C4C4×#433911yescharacteristic
507C4#1062300811yescharacteristic
508C4#1062300811yescharacteristic
509C2—21no—
510C2—21no—
511C2—42no—
512C2—882no—
513C2#1307110611yescharacteristic
514C2#1307716412yes—
subgroupG/H
centerC2×C4C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×#117C2
socleC22×C11C22×C22⋊C4
prime radical#13082006C2
cosocleC22×C4×C11C24
hypercenterC4×#117D11
hypocenterC11#21419
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×#117 ◁ C4×#117

Complements

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

NH ≅ G/Ntype
2. #13077254C2semidirect
3. #13069597C2semidirect
4. #13069593C2semidirect
5. #13069448C2semidirect
6. #13069444C2semidirect
7. #13069064C2semidirect
8. #13069059C2semidirect
9. #13068427C2semidirect
10. C4×#66869C2semidirect
11. C4×C11×#117C2semidirect
16. #10623066C4semidirect
17. #10623065C4semidirect
19. #10623049C4semidirect
86. #66928C2×C4semidirect
87. #66927C2×C4semidirect
89. C4×D44C2×C4semidirect
92. #66923C2×C4semidirect
93. #66922C2×C4semidirect
94. #66922C2×C4semidirect
96. C4×Dic22C2×C4semidirect
181. C4×#117D11semidirect
435. C11#21419semidirect

Maximal subgroups

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

subgroupindex
#130820062
#130772542
#130695972
#130695932
#130694482
#130694442
#130690642
#130690592
#130684272
C4×#668692
C4×C11×#1172
#2141911