Finite Group Databasebeta

← #14721511

Subgroups — #14721511

Order 2816.

1018 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082468C211yesmaximal, characteristic
2#13077640C211yesmaximal, characteristic, complemented
3#13067179C211yesmaximal, characteristic, complemented
4#13067175C211yesmaximal, characteristic, complemented
5#13067170C214yesmaximal, complemented
6#13067114C211yesmaximal, characteristic, complemented
7#13067110C211yesmaximal, characteristic, complemented
8#13067105C214yesmaximal, complemented
9C11×#2357C211yesmaximal, characteristic, complemented
10C2×C4×D4×C11C2211yescharacteristic
11#10623336—21no—
12#10623322C2214yes—
13#10623094C412yescomplemented
14#10623090—22no—
15#10623089—22no—
16#10623084C412yescomplemented
17#10623082C412yescomplemented
18#10623073C412yescomplemented
19#10623035—21no—
20#10623025—22no—
21#10623008C2211yescharacteristic
22#10623001C2211yescharacteristic
23C11×#390—21no—
24C11×#388—22no—
25C11×#382C2211yescharacteristic
26C11×#381C2212yes—
27C4×C11×C4⋊C4—21no—
28C4×C11×C4⋊C4C2211yescharacteristic
29C4×C11×C22⋊C4C2212yes—
30C2×C22⋊(C11⋊C8)C2214yes—
31D4×C11⋊C8—22no—
32D4×C11⋊C8—22no—
33#10622538C2211yescharacteristic
34#10622538C2211yescharacteristic
35#10622090C2212yes—
36#10622090C2214yes—
37#10622090C2212yes—
38#10622089C2212yes—
39#10622089C2214yes—
40#10622089C2212yes—
41C22×D4×C11D411yescharacteristic
42C23×C4×C11C2312yes—
43C2×#4339—21no—
44C2×#4339C2×C414yes—
45C4×D4×C11C2×C412yes—
46C4×D4×C11C2×C412yes—
47C4×D4×C11D412yes—
48C4×D4×C11D412yes—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4D411yescharacteristic
52C2×C11×C22⋊C4—22no—
53C2×C11×C22⋊C4—22no—
54C2×C11×C22⋊C4D412yes—
55C2×C42×C11—21no—
56C2×C42×C11—22no—
57C2×C42×C11C2311yescharacteristic
58#67006—24no—
59#66993—22no—
60#66991—22no—
61#66991—22no—
62#66989—22no—
63#66983—21no—
64#66983C2×C414yes—
65#66983C2312yes—
66#66982—24no—
67C4×C22⋊D11—24no—
68C4×C22⋊D11—24no—
69#66979—21no—
70#66979C2×C414yes—
71#66977—21no—
72#66977C2×C414yes—
73#66977C2312yes—
74C22×C11⋊C8—24no—
75#66946—22no—
76#66945—22no—
77C4⋊C4×D11—22no—
78#66940—22no—
79#66938—24no—
80#66937—24no—
81#66936—24no—
82#66932—24no—
83#66928—21no—
84#66927C2×C411yescharacteristic
85C4×D44—21no—
86C4×D44C2×C412yes—
87#66923—21no—
88#66922C2×C411yescharacteristic
89#66922C2×C411yescharacteristic
90#66922C2×C411yescharacteristic
91C4×Dic22—21no—
92C4×Dic22C2×C412yes—
93C11×#95—22no—
94C11×#95—21no—
95C11×#95C2311yescharacteristic
96C11×#95C2312yes—
97C11×#95C2311yescharacteristic
98C22⋊(C11⋊C8)—24no—
99C22⋊(C11⋊C8)C2312yes—
100C22⋊(C11⋊C8)C2312yes—
101C4⋊(C11⋊C8)—21no—
102C4⋊(C11⋊C8)—21no—
103C4×C11⋊C8—21no—
104C4×C11⋊C8—21no—
105#17617—111nomaximal, Sylow
106C24×C11C2×D412yes—
107C2×D4×C11—22no—
108C2×D4×C11—22no—
109C2×D4×C11C22⋊C412yes—
110C2×D4×C11C22⋊C412yes—
111C22×C4×C11—21no—
112C22×C4×C11—22no—
113C22×C4×C11—21no—
114C22×C4×C11—82no—
115C22×C4×C11C22×C414yes—
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D412yes—
118C22×C4×C11C2×D414yes—
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2411yescharacteristic
121C2×C22⋊D11—24no—
122C2×C22⋊D11—24no—
123C2×C22⋊D11—22no—
124#4339—42no—
125#4339—42no—
126#4339—84no—
127C2×D44—21no—
128C2×D44—21no—
129C2×D44C22×C412yes—
130C2×C4×D11—22no—
131C2×C4×D11—24no—
132C2×Dic22—21no—
133C2×Dic22—21no—
134C2×Dic22C22×C412yes—
135C11×C4⋊C4—42no—
136C11×C4⋊C4—42no—
137C11×C4⋊C4C22⋊C412yes—
138C11×C4⋊C4C22⋊C412yes—
139C11×C22⋊C4—44no—
140C11×C22⋊C4—82no—
141C11×C22⋊C4C22⋊C414yes—
142C11×C22⋊C4C22⋊C414yes—
143C42×C11—42no—
144C42×C11—82no—
145C42×C11C22×C411yescharacteristic
146C42×C11C22×C411yescharacteristic
147C42×C11C2×D411yescharacteristic
148C42×C11C2×D411yescharacteristic
149C22⋊Dic11—24no—
150C22⋊Dic11—24no—
151C22⋊Dic11—22no—
152(C2×D11)⋊C4—22no—
153(C2×D11)⋊C4—24no—
154(C2×D11)⋊C4—22no—
155C4⋊Dic11—21no—
156C4⋊Dic11—21no—
157C4⋊Dic11—21no—
158C4⋊Dic11—21no—
159C4⋊Dic11C22×C412yes—
160C4⋊Dic11C22×C412yes—
161Dic11⋊C4—22no—
162Dic11⋊C4—24no—
163Dic11⋊C4—22no—
164C4×Dic11—22no—
165C4×Dic11—24no—
166C2×C11⋊C8—22no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8—84no—
169#3506—111no—
170#2972—111no—
171#2357D1111yescharacteristic, complemented
172#1518—111no—
173#1517—111no—
174#1516—114no—
175#1503—111no—
176#1502—111no—
177#1501—114no—
178C23×C11—22no—
179C23×C11—22no—
180C23×C11—42no—
181C23×C11—42no—
182C23×C11C2×C22⋊C414yes—
183C23×C11C22×D411yescharacteristic
184C22×D11—22no—
185D4×C11—24no—
186D4×C11—24no—
187C2×C4×C11—22no—
188C2×C4×C11—44no—
189C2×C4×C11—42no—
190C2×C4×C11—41no—
191C2×C4×C11—44no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—42no—
201C2×C4×C11C2×C22⋊C414yes—
202C2×C4×C11C2×C22⋊C411yescharacteristic
203C2×C4×C11C2×C22⋊C411yescharacteristic
204C2×C4×C11C2×C22⋊C411yescharacteristic
205C2×C4×C11C2×C22⋊C411yescharacteristic
206C2×C4×C11#13512yes—
207C2×C4×C11#13512yes—
208C2×C4×C11C23×C411yescharacteristic
209C2×C4×C11C22×D411yescharacteristic
210C22⋊D11—42no—
211C22⋊D11—42no—
212C22⋊D11—84no—
213C22⋊D11—84no—
214C2×Dic11—22no—
215C2×Dic11—22no—
216C2×Dic11—22no—
217D44—42no—
218D44—42no—
219D44—81no—
220C4×D11—44no—
221C4×D11—84no—
222Dic22—42no—
223Dic22—42no—
224Dic22—81no—
225C11⋊C8—42no—
226C11⋊C8—42no—
227#559—222no—
228#556—112no—
229#555—112no—
230#553—222no—
231#550—112no—
232#547—112no—
233#538—222no—
234#535—221no—
235#533—111no—
236#532—111no—
237#525—114no—
238#520—221no—
239C2×C4×D4C2×D1111yescharacteristic
240C8×D4—222no—
241C8×D4—222no—
242#431—111no—
243#431—111no—
244C2×C22⋊C8—114no—
245#390—21no—
246#388—22no—
247#382C2×D1111yescharacteristic
248#381C2×D1112yes—
249C4×C4⋊C4—21no—
250C4×C4⋊C4C2×D1111yescharacteristic
251C4×C22⋊C4C2×D1112yes—
252#328—112no—
253#328—114no—
254#328—112no—
255#327—112no—
256#327—114no—
257#327—112no—
258C22×C11—21no—
259C22×C11—21no—
260C22×C11—24no—
261C22×C11—24no—
262C22×C11—24no—
263C22×C11—82no—
264C22×C11—82no—
265C22×C11C22×C22⋊C411yescharacteristic
266C22×C11C2×#13511yescharacteristic
267C22×C11C2×#13511yescharacteristic
268C2×D11—42no—
269C2×D11—42no—
270C2×D11—42no—
271C4×C11—21no—
272C4×C11—21no—
273C4×C11—24no—
274C4×C11—21no—
275C4×C11—21no—
276C4×C11—42no—
277C4×C11—81no—
278C4×C11—82no—
279C4×C11#41612yes—
280C4×C11#41612yes—
281Dic11—42no—
282Dic11—42no—
283Dic11—42no—
284C2×#41—114no—
285C2×#41—221no—
286C22×D4C22⋊D1111yescharacteristic
287C23×C4C22×D1112yes—
288C22×C8—224no—
289C4⋊Q8—111no—
290C4⋊Q8—111no—
291C4⋊Q8—111no—
292#127—111no—
293#127—222no—
294#126—224no—
295#125—221no—
296#124—222no—
297#124—224no—
298#124—221no—
299#123—224no—
300#123—224no—
301C22⋊Q8—114no—
302C22⋊Q8—112no—
303C22⋊Q8—221no—
304#121—114no—
305#121—112no—
306#121—222no—
307#121—222no—
308#121—221no—
309#121—224no—
310#120—224no—
311C4×Q8—112no—
312C4×Q8—222no—
313C4×Q8—221no—
314C4×D4—112no—
315C4×D4—224no—
316C4×D4—224no—
317C4×D4—222no—
318C4×D4—221no—
319C4×D4C4×D1112yes—
320C4×D4C4×D1112yes—
321C4×D4D4412yes—
322C4×D4D4412yes—
323#117—114no—
324#117—221no—
325#117—222no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—222no—
329C2×C4⋊C4C22⋊D1111yescharacteristic
330C2×C22⋊C4—22no—
331C2×C22⋊C4—22no—
332C2×C22⋊C4C22⋊D1112yes—
333C2×C42—21no—
334C2×C42—22no—
335C2×C42C22×D1111yescharacteristic
336C4⋊C8—221no—
337C4⋊C8—221no—
338C22⋊C8—112no—
339C22⋊C8—112no—
340C22⋊C8—224no—
341C4×C8—221no—
342C4×C8—221no—
343#95—22no—
344#95—21no—
345#95C22×D1111yescharacteristic
346#95C22×D1112yes—
347#95C22×D1111yescharacteristic
348C2×C11—21no—
349C2×C11—21no—
350C2×C11—44no—
351C2×C11#288311yescharacteristic
352C2×C11C2×#41611yescharacteristic
353C2×C11#290111yescharacteristic
354D11—82no—
355C24C2×C22⋊D1112yes—
356#41—442no—
357#41—442no—
358#41—884no—
359C2×Q8—112no—
360C2×Q8—221no—
361C2×Q8—221no—
362C2×D4—22no—
363C2×D4—22no—
364C2×D4—112no—
365C2×D4—222no—
366C2×D4—224no—
367C2×D4—224no—
368C2×D4—221no—
369C2×D4—221no—
370C2×D4(C2×D11)⋊C412yes—
371C2×D4(C2×D11)⋊C412yes—
372C22×C4—21no—
373C22×C4—22no—
374C22×C4—21no—
375C22×C4—82no—
376C22×C4—222no—
377C22×C4—224no—
378C22×C4C2×C4×D1114yes—
379C22×C4C2×D4414yes—
380C22×C4C2×C22⋊D1112yes—
381C22×C4C2×C22⋊D1111yescharacteristic
382C22×C4C2×C22⋊D1111yescharacteristic
383C22×C4C23×D1111yescharacteristic
384C2×C8—222no—
385C2×C8—222no—
386C2×C8—884no—
387C4⋊C4—42no—
388C4⋊C4—42no—
389C4⋊C4—112no—
390C4⋊C4—112no—
391C4⋊C4—221no—
392C4⋊C4—224no—
393C4⋊C4—221no—
394C4⋊C4—221no—
395C4⋊C4—222no—
396C4⋊C4—221no—
397C4⋊C4—222no—
398C4⋊C4(C2×D11)⋊C412yes—
399C4⋊C4(C2×D11)⋊C412yes—
400C22⋊C4—44no—
401C22⋊C4—82no—
402C22⋊C4—224no—
403C22⋊C4—224no—
404C22⋊C4—222no—
405C22⋊C4—224no—
406C22⋊C4—222no—
407C22⋊C4—222no—
408C22⋊C4(C2×D11)⋊C414yes—
409C22⋊C4(C2×D11)⋊C414yes—
410C42—42no—
411C42—82no—
412C42—224no—
413C42—222no—
414C42C2×C4×D1111yescharacteristic
415C42C2×C4×D1111yescharacteristic
416C42C2×D4411yescharacteristic
417C42C2×D4411yescharacteristic
418C11#1761711yescharacteristic, complemented, Sylow
419C23—22no—
420C23—22no—
421C23—42no—
422C23—42no—
423C23—222no—
424C23C2×(C2×D11)⋊C414yes—
425C23C22×C22⋊D1111yescharacteristic
426Q8—442no—
427Q8—442no—
428Q8—881no—
429D4—24no—
430D4—24no—
431D4—442no—
432D4—442no—
433D4—442no—
434D4—442no—
435D4—881no—
436D4—884no—
437D4—884no—
438C2×C4—22no—
439C2×C4—42no—
440C2×C4—41no—
441C2×C4—44no—
442C2×C4—41no—
443C2×C4—44no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—42no—
452C2×C4—222no—
453C2×C4—222no—
454C2×C4—222no—
455C2×C4—444no—
456C2×C4—884no—
457C2×C4C2×(C2×D11)⋊C414yes—
458C2×C4C2×(C2×D11)⋊C411yescharacteristic
459C2×C4C2×(C2×D11)⋊C411yescharacteristic
460C2×C4C2×(C2×D11)⋊C411yescharacteristic
461C2×C4C2×(C2×D11)⋊C411yescharacteristic
462C2×C4#6700312yes—
463C2×C4#6700312yes—
464C2×C4C22×C4×D1111yescharacteristic
465C2×C4C22×D4411yescharacteristic
466C8—442no—
467C8—442no—
468C22—21no—
469C22—21no—
470C22—24no—
471C22—24no—
472C22—24no—
473C22—82no—
474C22—82no—
475C22—442no—
476C22—442no—
477C22—442no—
478C22C22×(C2×D11)⋊C411yescharacteristic
479C22C2×#6700311yescharacteristic
480C22C2×#6700311yescharacteristic
481C4—21no—
482C4—21no—
483C4—24no—
484C4—21no—
485C4—21no—
486C4—42no—
487C4—81no—
488C4—82no—
489C4—442no—
490C4—442no—
491C4—442no—
492C4#1062261512yes—
493C4#1062261512yes—
494C2—21no—
495C2—21no—
496C2—44no—
497C2—882no—
498C2#1307707611yescharacteristic
499C2C2×#1062261511yescharacteristic
500C2#1307716411yescharacteristic
subgroupG/H
centerC22C22×(C2×D11)⋊C4
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2357C2
socleC22×C11C22×C22⋊C4
prime radical#13082468C2
cosocleC22×C4×C11C24
hypercenter#2357D11
hypocenterC11#17617
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2357

Complements

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

NH ≅ G/Ntype
2. #13077640C2semidirect
3. #13067179C2semidirect
4. #13067175C2semidirect
5. #13067170C2semidirect
6. #13067114C2semidirect
7. #13067110C2semidirect
8. #13067105C2semidirect
9. C11×#2357C2semidirect
13. #10623094C4semidirect
16. #10623084C4semidirect
17. #10623082C4semidirect
18. #10623073C4semidirect
171. #2357D11semidirect
418. C11#17617semidirect

Maximal subgroups

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

subgroupindex
#130824682
#130776402
#130671792
#130671752
#130671702
#130671142
#130671102
#130671052
C11×#23572
#1761711