Finite Group Databasebeta

← #14721516

Subgroups — #14721516

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#13071589C211yesmaximal, characteristic, complemented
3#13067181C211yesmaximal, characteristic, complemented
4#13067177C211yesmaximal, characteristic, complemented
5#13067173C214yesmaximal, complemented
6#13067116C211yesmaximal, characteristic, complemented
7#13067112C211yesmaximal, characteristic, complemented
8#13067108C214yesmaximal, complemented
9C11×#2972C211yesmaximal, 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
23C8×D4×C11—22no—
24C8×D4×C11—22no—
25C11×#431C2211yescharacteristic
26C11×#431C2211yescharacteristic
27C2×C11×C22⋊C8C2214yes—
28#10622834—21no—
29#10622824C2212yes—
30C4×C22⋊Dic11C2212yes—
31C4⋊C4×Dic11—21no—
32#10622564—22no—
33#10622549C2211yescharacteristic
34C4×C4⋊Dic11C2211yescharacteristic
35#10622108C2212yes—
36#10622108C2214yes—
37#10622108C2212yes—
38#10622105C2212yes—
39#10622105C2214yes—
40#10622105C2212yes—
41C22×D4×C11D411yescharacteristic
42C23×C4×C11C2312yes—
43C2×#4339—21no—
44C2×#4339C2×C414yes—
45C22×C8×C11—24no—
46C4×D4×C11C2×C412yes—
47C4×D4×C11C2×C412yes—
48C4×D4×C11D412yes—
49C4×D4×C11D412yes—
50C2×C11×C4⋊C4D411yescharacteristic
51C2×C11×C22⋊C4D412yes—
52C2×C42×C11C2311yescharacteristic
53#67006—24no—
54C2×C22⋊Dic11—22no—
55C2×C22⋊Dic11—22no—
56#66993—22no—
57#66991—22no—
58#66991—22no—
59#66989—22no—
60#66983—21no—
61#66983C2×C414yes—
62#66983C2312yes—
63#66982—24no—
64C4×C22⋊D11—24no—
65C4×C22⋊D11—24no—
66#66979—21no—
67#66979C2×C414yes—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11—21no—
70#66977—21no—
71#66977C2×C414yes—
72#66977C2312yes—
73C2×C4×Dic11—21no—
74C2×C4×Dic11—22no—
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×C4⋊C8—21no—
94C11×C4⋊C8—21no—
95C11×C22⋊C8—24no—
96C11×C22⋊C8C2312yes—
97C11×C22⋊C8C2312yes—
98C4×C8×C11—21no—
99C4×C8×C11—21no—
100C11⋊#95—21no—
101C11⋊#95—22no—
102C11⋊#95C2311yescharacteristic
103C11⋊#95C2311yescharacteristic
104C11⋊#95C2312yes—
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—82no—
112C22×C4×C11C22×C414yes—
113C22×C4×C11C2×D412yes—
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D414yes—
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2411yescharacteristic
118C2×C22⋊D11—24no—
119C2×C22⋊D11—24no—
120C2×C22⋊D11—22no—
121C22×Dic11—21no—
122C22×Dic11—22no—
123C22×Dic11—21no—
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—
135C2×C8×C11—22no—
136C2×C8×C11—22no—
137C2×C8×C11—84no—
138C11×C4⋊C4C22⋊C412yes—
139C11×C4⋊C4C22⋊C412yes—
140C11×C22⋊C4C22⋊C414yes—
141C11×C22⋊C4C22⋊C414yes—
142C42×C11C22×C411yescharacteristic
143C42×C11C22×C411yescharacteristic
144C42×C11C2×D411yescharacteristic
145C42×C11C2×D411yescharacteristic
146C22⋊Dic11—24no—
147C22⋊Dic11—24no—
148C22⋊Dic11—22no—
149C22⋊Dic11—44no—
150C22⋊Dic11—82no—
151(C2×D11)⋊C4—22no—
152(C2×D11)⋊C4—24no—
153(C2×D11)⋊C4—22no—
154C4⋊Dic11—21no—
155C4⋊Dic11—21no—
156C4⋊Dic11—21no—
157C4⋊Dic11—21no—
158C4⋊Dic11—42no—
159C4⋊Dic11—42no—
160C4⋊Dic11C22×C412yes—
161C4⋊Dic11C22×C412yes—
162Dic11⋊C4—22no—
163Dic11⋊C4—24no—
164Dic11⋊C4—22no—
165C4×Dic11—22no—
166C4×Dic11—24no—
167C4×Dic11—42no—
168C4×Dic11—82no—
169#3506—111no—
170#2972D1111yescharacteristic, complemented
171#2357—111no—
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—42no—
188C2×C4×C11—41no—
189C2×C4×C11—44no—
190C2×C4×C11—44no—
191C2×C4×C11—41no—
192C2×C4×C11C2×C22⋊C414yes—
193C2×C4×C11C2×C22⋊C411yescharacteristic
194C2×C4×C11C2×C22⋊C411yescharacteristic
195C2×C4×C11C2×C22⋊C411yescharacteristic
196C2×C4×C11C2×C22⋊C411yescharacteristic
197C2×C4×C11#13512yes—
198C2×C4×C11#13512yes—
199C2×C4×C11C23×C411yescharacteristic
200C2×C4×C11C22×D411yescharacteristic
201C22⋊D11—42no—
202C22⋊D11—42no—
203C22⋊D11—84no—
204C22⋊D11—84no—
205C2×Dic11—22no—
206C2×Dic11—22no—
207C2×Dic11—22no—
208C2×Dic11—22no—
209C2×Dic11—41no—
210C2×Dic11—41no—
211C2×Dic11—42no—
212C2×Dic11—41no—
213C2×Dic11—42no—
214C2×Dic11—41no—
215C2×Dic11—41no—
216C2×Dic11—42no—
217D44—42no—
218D44—42no—
219D44—81no—
220C4×D11—44no—
221C4×D11—84no—
222Dic22—42no—
223Dic22—42no—
224Dic22—81no—
225C8×C11—42no—
226C8×C11—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—22no—
241C8×D4—22no—
242#431C2×D1111yescharacteristic
243#431C2×D1111yescharacteristic
244C2×C22⋊C8C2×D1114yes—
245#390—221no—
246#388—222no—
247#382—111no—
248#381—112no—
249C4×C4⋊C4—111no—
250C4×C4⋊C4—221no—
251C4×C22⋊C4—112no—
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#41612yes—
277C4×C11#41612yes—
278Dic11—42no—
279Dic11—42no—
280Dic11—42no—
281Dic11—42no—
282Dic11—81no—
283Dic11—82no—
284C2×#41—114no—
285C2×#41—221no—
286C22×D4D4411yescharacteristic
287C23×C4C22×D1112yes—
288C22×C8—24no—
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×D4C22⋊D1112yes—
322C4×D4C22⋊D1112yes—
323#117—114no—
324#117—221no—
325#117—222no—
326C2×C4⋊C4—222no—
327C2×C4⋊C4—221no—
328C2×C4⋊C4—221no—
329C2×C4⋊C4D4411yescharacteristic
330C2×C22⋊C4—222no—
331C2×C22⋊C4—222no—
332C2×C22⋊C4D4412yes—
333C2×C42—221no—
334C2×C42—222no—
335C2×C42C22×D1111yescharacteristic
336C4⋊C8—21no—
337C4⋊C8—21no—
338C22⋊C8—24no—
339C22⋊C8C22×D1112yes—
340C22⋊C8C22×D1112yes—
341C4×C8—21no—
342C4×C8—21no—
343#95—111no—
344#95—112no—
345#95—111no—
346#95—222no—
347#95—221no—
348C2×C11—21no—
349C2×C11—21no—
350C2×C11—44no—
351C2×C11#288311yescharacteristic
352C2×C11C2×#41611yescharacteristic
353C2×C11#290111yescharacteristic
354D11—82no—
355C24C2×D4412yes—
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—82no—
373C22×C4—221no—
374C22×C4—222no—
375C22×C4—224no—
376C22×C4—222no—
377C22×C4—221no—
378C22×C4C2×C4×D1114yes—
379C22×C4C2×D4412yes—
380C22×C4C2×D4411yescharacteristic
381C22×C4C2×D4411yescharacteristic
382C22×C4C2×C22⋊D1114yes—
383C22×C4C23×D1111yescharacteristic
384C2×C8—22no—
385C2×C8—22no—
386C2×C8—84no—
387C4⋊C4—112no—
388C4⋊C4—112no—
389C4⋊C4—221no—
390C4⋊C4—224no—
391C4⋊C4—221no—
392C4⋊C4—221no—
393C4⋊C4—222no—
394C4⋊C4—221no—
395C4⋊C4—222no—
396C4⋊C4—442no—
397C4⋊C4—442no—
398C4⋊C4(C2×D11)⋊C412yes—
399C4⋊C4(C2×D11)⋊C412yes—
400C22⋊C4—224no—
401C22⋊C4—224no—
402C22⋊C4—222no—
403C22⋊C4—224no—
404C22⋊C4—222no—
405C22⋊C4—222no—
406C22⋊C4—444no—
407C22⋊C4—882no—
408C22⋊C4(C2×D11)⋊C414yes—
409C22⋊C4(C2×D11)⋊C414yes—
410C42—224no—
411C42—222no—
412C42—442no—
413C42—882no—
414C42C2×C4×D1111yescharacteristic
415C42C2×C4×D1111yescharacteristic
416C42C2×C22⋊D1111yescharacteristic
417C42C2×C22⋊D1111yescharacteristic
418C11#1761711yescharacteristic, complemented, Sylow
419C23—22no—
420C23—22no—
421C23—42no—
422C23—42no—
423C23—222no—
424C23C2×(C2×D11)⋊C414yes—
425C23C22×D4411yescharacteristic
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—42no—
439C2×C4—41no—
440C2×C4—44no—
441C2×C4—41no—
442C2×C4—44no—
443C2×C4—222no—
444C2×C4—222no—
445C2×C4—222no—
446C2×C4—222no—
447C2×C4—441no—
448C2×C4—441no—
449C2×C4—444no—
450C2×C4—442no—
451C2×C4—442no—
452C2×C4—441no—
453C2×C4—441no—
454C2×C4—441no—
455C2×C4—442no—
456C2×C4—884no—
457C2×C4#6695712yes—
458C2×C4#6695712yes—
459C2×C4C2×(C2×D11)⋊C414yes—
460C2×C4C2×(C2×D11)⋊C411yescharacteristic
461C2×C4C2×(C2×D11)⋊C411yescharacteristic
462C2×C4C2×(C2×D11)⋊C411yescharacteristic
463C2×C4C2×(C2×D11)⋊C411yescharacteristic
464C2×C4C22×C4×D1111yescharacteristic
465C2×C4C22×C22⋊D1111yescharacteristic
466C8—42no—
467C8—42no—
468C22—21no—
469C22—21no—
470C22—24no—
471C22—24no—
472C22—24no—
473C22—82no—
474C22—82no—
475C22—442no—
476C22—442no—
477C22—442no—
478C22C2×#6695711yescharacteristic
479C22C2×#6695711yescharacteristic
480C22C22×(C2×D11)⋊C411yescharacteristic
481C4—21no—
482C4—21no—
483C4—24no—
484C4—21no—
485C4—21no—
486C4—442no—
487C4—442no—
488C4—442no—
489C4—442no—
490C4—881no—
491C4—882no—
492C4#1062272612yes—
493C4#1062272612yes—
494C2—21no—
495C2—21no—
496C2—44no—
497C2—882no—
498C2#1307707611yescharacteristic
499C2C2×#1062272611yescharacteristic
500C2#1307716111yescharacteristic
subgroupG/H
centerC22C22×(C2×D11)⋊C4
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2972C2
socleC22×C11C22×C22⋊C4
prime radical#13082468C2
cosocleC22×C4×C11C24
hypercenter#2972D11
hypocenterC11#17617
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2972

Complements

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

NH ≅ G/Ntype
2. #13071589C2semidirect
3. #13067181C2semidirect
4. #13067177C2semidirect
5. #13067173C2semidirect
6. #13067116C2semidirect
7. #13067112C2semidirect
8. #13067108C2semidirect
9. C11×#2972C2semidirect
13. #10623094C4semidirect
16. #10623084C4semidirect
17. #10623082C4semidirect
18. #10623073C4semidirect
170. #2972D11semidirect
418. C11#17617semidirect

Maximal subgroups

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

subgroupindex
#130824682
#130715892
#130671812
#130671772
#130671732
#130671162
#130671122
#130671082
C11×#29722
#1761711