Finite Group Databasebeta

← #14721503

Subgroups — #14721503

Order 2816.

918 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082483C211yesmaximal, characteristic
2#13077696C211yesmaximal, characteristic, complemented
3#13071579C211yesmaximal, characteristic, complemented
4#13067192C214yesmaximal, complemented
5#13067180C211yesmaximal, characteristic, complemented
6#13067177C211yesmaximal, characteristic
7#13067110C211yesmaximal, characteristic
8#13067101C214yesmaximal, complemented
9C11×#1503C211yesmaximal, characteristic, complemented
10C11×#533C2211yescharacteristic
11#10623263C412yescomplemented
12#10623261C412yescomplemented
13#10623225—22no—
14#10623176—22no—
15#10623155C2214yes—
16#10623116C412yescomplemented
17#10623115—22no—
18#10623101C412yescomplemented
19#10623057—21no—
20#10623054—21no—
21#10623008C2211yescharacteristic
22C2×C4×Dic22C2211yescharacteristic
23C11×#431C2211yescharacteristic
24C4×C11×C4⋊C4C2211yescharacteristic
25#10622591—22no—
26#10622549C2211yescharacteristic
27C4×C4⋊Dic11—21no—
28#10622542—21no—
29#10622538C2211yescharacteristic
30#10622443—22no—
31#10622331C2214yes—
32C8×Dic22—22no—
33#10622264C2212yes—
34#10622261C2212yes—
35C11×#328C2212yes—
36C11×#328C2212yes—
37#10622176C2214yes—
38#10622108C2214yes—
39#10622089C2212yes—
40#10622089C2212yes—
41C2×#4339—21no—
42C22×Dic22D411yescharacteristic
43C11×C4⋊Q8C2×C411yescharacteristic
44C11×C4⋊Q8C2×C411yescharacteristic
45C11×#125—21no—
46C11×C22⋊Q8—21no—
47C11×C22⋊Q8C2312yes—
48C4×Q8×C11—21no—
49C4×Q8×C11C2×C412yes—
50C11×#117—21no—
51C2×C11×C4⋊C4—21no—
52C2×C42×C11—21no—
53C2×C42×C11C2311yescharacteristic
54#67000C2×C414yes—
55#66999—24no—
56Q8×Dic11C2×C414yes—
57#66983—21no—
58#66983C2312yes—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11D411yescharacteristic
61C2×Dic11⋊C4D412yes—
62C2×C4×Dic11—22no—
63C2×C4×Dic11C2312yes—
64#66951—24no—
65#66951—24no—
66#66950—22no—
67#66950—22no—
68#66947—24no—
69#66946C2×C414yes—
70#66945—22no—
71#66945—24no—
72C4⋊C4×D11—22no—
73#66943—24no—
74#66943C2×C414yes—
75#66939—24no—
76(C22⋊D11)⋊C4—24no—
77#66928—22no—
78#66928—21no—
79#66927C2×C411yescharacteristic
80C4×D44—21no—
81C4×D44—22no—
82C4×D44C2×C412yes—
83#66922—22no—
84#66922C2×C411yescharacteristic
85C4×Dic22—22no—
86C4×Dic22C2×C412yes—
87C4×Dic22C2×C412yes—
88C4×Dic22D412yes—
89C4×Dic22D412yes—
90C11×C4⋊C8—21no—
91C11×C22⋊C8C2312yes—
92C4×C8×C11—21no—
93C11×#95C2311yescharacteristic
94C11×#95C2311yescharacteristic
95C11⋊#95—21no—
96C11⋊#95—22no—
97C11⋊#95—22no—
98C11⋊#95—22no—
99C11⋊#95C2312yes—
100C22⋊(C11⋊C8)C2312yes—
101Dic11⋊C8—24no—
102C8×Dic11—24no—
103C4⋊(C11⋊C8)—21no—
104C4×C11⋊C8—21no—
105#17616—111nomaximal, Sylow
106C2×Q8×C11—21no—
107C2×Q8×C11C22×C412yes—
108C22×C4×C11—21no—
109C22×C4×C11—21no—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2411yescharacteristic
113C2×C22⋊D11—22no—
114C22×Dic11—22no—
115C22×Dic11C2×D412yes—
116C22×Dic11C2×D412yes—
117#4339—42no—
118#4339—42no—
119C2×D44—21no—
120C2×D44—21no—
121C2×D44C22×C412yes—
122C2×C4×D11—24no—
123C2×C4×D11—22no—
124C2×Dic22—21no—
125C2×Dic22—22no—
126C2×Dic22—22no—
127C2×Dic22C22⋊C412yes—
128C2×Dic22C22⋊C412yes—
129C2×C8×C11—22no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—42no—
136C11×C4⋊C4C22×C412yes—
137C11×C22⋊C4—22no—
138C42×C11—22no—
139C42×C11—42no—
140C42×C11C22×C411yescharacteristic
141C42×C11C22×C411yescharacteristic
142C42×C11C2×D411yescharacteristic
143C42×C11C2×D411yescharacteristic
144(C2×D11)⋊C4—24no—
145(C2×D11)⋊C4—24no—
146(C2×D11)⋊C4—24no—
147(C2×D11)⋊C4—22no—
148(C2×D11)⋊C4—22no—
149C4⋊Dic11—24no—
150C4⋊Dic11—24no—
151C4⋊Dic11—21no—
152C4⋊Dic11—42no—
153C4⋊Dic11C22⋊C412yes—
154C4⋊Dic11C22⋊C412yes—
155C4⋊Dic11C22×C412yes—
156Dic11⋊C4—24no—
157Dic11⋊C4C22⋊C414yes—
158Dic11⋊C4C22⋊C414yes—
159C4×Dic11—24no—
160C4×Dic11—44no—
161C4×Dic11C22×C414yes—
162C4×Dic11C2×D414yes—
163C2×C11⋊C8—22no—
164#3507—111no—
165#2982—111no—
166#2356—111no—
167#1521—114no—
168#1518—111no—
169#1517—111no—
170#1503D1111yescharacteristic, complemented
171#1502—111no—
172#1500—114no—
173C23×C11C22×D411yescharacteristic
174C22×D11—22no—
175Q8×C11—42no—
176Q8×C11—81no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11C2×C22⋊C411yescharacteristic
188C2×C4×C11C2×C22⋊C411yescharacteristic
189C2×C4×C11C2×C22⋊C411yescharacteristic
190C2×C4×C11C2×C22⋊C411yescharacteristic
191C2×C4×C11#13512yes—
192C2×C4×C11#13512yes—
193C2×C4×C11C23×C411yescharacteristic
194C2×C4×C11C22×D411yescharacteristic
195C22⋊D11—42no—
196C22⋊D11—42no—
197C2×Dic11—22no—
198C2×Dic11—22no—
199C2×Dic11—22no—
200C2×Dic11—42no—
201C2×Dic11—42no—
202C2×Dic11—42no—
203C2×Dic11—42no—
204C2×Dic11C2×C22⋊C414yes—
205C2×Dic11C2×C22⋊C414yes—
206D44—42no—
207D44—42no—
208D44—81no—
209C4×D11—44no—
210C4×D11—84no—
211Dic22—24no—
212Dic22—24no—
213Dic22—42no—
214C8×C11—42no—
215C11⋊C8—42no—
216#559—112no—
217#557—112no—
218#556—112no—
219#556—222no—
220#554—112no—
221#552—222no—
222#539—222no—
223#536—221no—
224#533C2×D1111yescharacteristic
225#532—111no—
226#529—114no—
227#520—221no—
228C2×C4×Q8—111no—
229C8×Q8—222no—
230C8×Q8—222no—
231#431—111no—
232#431—114no—
233#431C2×D1111yescharacteristic
234#391—221no—
235#387—222no—
236#383—112no—
237#382—111no—
238C4×C4⋊C4—221no—
239C4×C4⋊C4C2×D1111yescharacteristic
240#376—112no—
241#328—114no—
242#328C2×D1112yes—
243#328C2×D1112yes—
244#327—114no—
245#327—112no—
246#327—112no—
247C22×C11—21no—
248C22×C11—21no—
249C22×C11C22×C22⋊C411yescharacteristic
250C22×C11C2×#13511yescharacteristic
251C22×C11C2×#13511yescharacteristic
252C2×D11—42no—
253C2×D11—42no—
254C2×D11—42no—
255C4×C11—21no—
256C4×C11—21no—
257C4×C11—21no—
258C4×C11—21no—
259C4×C11—42no—
260C4×C11—42no—
261C4×C11—42no—
262C4×C11—81no—
263C4×C11#41612yes—
264C4×C11#41612yes—
265Dic11—24no—
266Dic11—24no—
267Dic11—42no—
268Dic11—82no—
269C2×#41—221no—
270C22×Q8—111no—
271C4⋊Q8—111no—
272C4⋊Q8—222no—
273C4⋊Q8C4×D1111yescharacteristic
274C4⋊Q8C4×D1111yescharacteristic
275#127—111no—
276#126—224no—
277#126—224no—
278#125—21no—
279#125—114no—
280#125—224no—
281#124—114no—
282#124—222no—
283#124—221no—
284#123—224no—
285#123—224no—
286C22⋊Q8—21no—
287C22⋊Q8—222no—
288C22⋊Q8—222no—
289C22⋊Q8—224no—
290C22⋊Q8C22×D1112yes—
291#121—112no—
292#121—221no—
293C4×Q8—21no—
294C4×Q8—112no—
295C4×Q8—112no—
296C4×Q8—112no—
297C4×Q8—112no—
298C4×Q8—114no—
299C4×Q8—222no—
300C4×Q8C4×D1112yes—
301C4×D4—114no—
302C4×D4—112no—
303C4×D4—222no—
304C4×D4—224no—
305C4×D4—221no—
306#117—21no—
307#117—224no—
308#117—222no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—111no—
311C2×C4⋊C4—112no—
312C2×C4⋊C4—222no—
313C2×C4⋊C4—221no—
314C2×C42—21no—
315C2×C42—112no—
316C2×C42—222no—
317C2×C42C22×D1111yescharacteristic
318C4⋊C8—21no—
319C4⋊C8—224no—
320C4⋊C8—221no—
321C22⋊C8—112no—
322C22⋊C8C22×D1112yes—
323C4×C8—21no—
324C4×C8—224no—
325C4×C8—221no—
326#95—112no—
327#95—222no—
328#95—222no—
329#95—222no—
330#95—221no—
331#95C22×D1111yescharacteristic
332#95C22×D1111yescharacteristic
333C2×C11—21no—
334C2×C11—21no—
335C2×C11#288411yescharacteristic
336C2×C11C2×#41611yescharacteristic
337C2×C11#290111yescharacteristic
338D11—82no—
339#41—442no—
340#41—442no—
341C2×Q8—21no—
342C2×Q8—112no—
343C2×Q8—112no—
344C2×Q8—221no—
345C2×Q8—222no—
346C2×Q8—222no—
347C2×Q8C2×C4×D1112yes—
348C2×D4—112no—
349C2×D4—222no—
350C2×D4—221no—
351C2×D4—221no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—112no—
355C22×C4—112no—
356C22×C4—224no—
357C22×C4—222no—
358C22×C4—222no—
359C22×C4D4×D1111yescharacteristic
360C22×C4D4×D1111yescharacteristic
361C22×C4C23×D1111yescharacteristic
362C2×C8—22no—
363C2×C8—222no—
364C4⋊C4—21no—
365C4⋊C4—21no—
366C4⋊C4—21no—
367C4⋊C4—22no—
368C4⋊C4—22no—
369C4⋊C4—42no—
370C4⋊C4—112no—
371C4⋊C4—112no—
372C4⋊C4—114no—
373C4⋊C4—114no—
374C4⋊C4—112no—
375C4⋊C4—224no—
376C4⋊C4—224no—
377C4⋊C4—224no—
378C4⋊C4—221no—
379C4⋊C4—442no—
380C4⋊C4C2×C4×D1112yes—
381C22⋊C4—22no—
382C22⋊C4—224no—
383C22⋊C4—224no—
384C22⋊C4—224no—
385C22⋊C4—222no—
386C22⋊C4—222no—
387C42—22no—
388C42—42no—
389C42—114no—
390C42—114no—
391C42—224no—
392C42—444no—
393C42C2×C4×D1111yescharacteristic
394C42C2×C4×D1111yescharacteristic
395C42D4×D1111yescharacteristic
396C42D4×D1111yescharacteristic
397C11#1761611yescharacteristic, complemented, Sylow
398C23—222no—
399C23C2×D4×D1111yescharacteristic
400Q8—42no—
401Q8—81no—
402Q8—224no—
403Q8—224no—
404Q8—442no—
405D4—442no—
406D4—442no—
407D4—442no—
408D4—442no—
409D4—881no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—114no—
421C2×C4—114no—
422C2×C4—222no—
423C2×C4—222no—
424C2×C4—222no—
425C2×C4—442no—
426C2×C4—444no—
427C2×C4—442no—
428C2×C4—442no—
429C2×C4—442no—
430C2×C4—884no—
431C2×C4C22⋊C4×D1111yescharacteristic
432C2×C4C22⋊C4×D1111yescharacteristic
433C2×C4C22⋊C4×D1111yescharacteristic
434C2×C4C22⋊C4×D1111yescharacteristic
435C2×C4#6696912yes—
436C2×C4#6697212yes—
437C2×C4C22×C4×D1111yescharacteristic
438C2×C4C2×D4×D1111yescharacteristic
439C8—42no—
440C8—442no—
441C22—21no—
442C22—21no—
443C22—442no—
444C22—442no—
445C22—442no—
446C22C2×C22⋊C4×D1111yescharacteristic
447C22C2×#6696911yescharacteristic
448C22C2×#6697211yescharacteristic
449C4—21no—
450C4—21no—
451C4—21no—
452C4—21no—
453C4—42no—
454C4—42no—
455C4—42no—
456C4—81no—
457C4—224no—
458C4—224no—
459C4—442no—
460C4—882no—
461C4#1062241712yes—
462C4#1062241712yes—
463C2—21no—
464C2—21no—
465C2—882no—
466C2#1307707811yescharacteristic
467C2C2×#1062241711yescharacteristic
468C2#1307716011yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1503C2
socleC22×C11C22×C22⋊C4
prime radical#10623008C22
cosocleC22×C4×C11C24
hypercenter#1503D11
hypocenterC11#17616
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1503

Complements

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

NH ≅ G/Ntype
2. #13077696C2semidirect
3. #13071579C2semidirect
4. #13067192C2semidirect
5. #13067180C2semidirect
8. #13067101C2semidirect
9. C11×#1503C2semidirect
11. #10623263C4semidirect
12. #10623261C4semidirect
16. #10623116C4semidirect
18. #10623101C4semidirect
170. #1503D11semidirect
397. C11#17616semidirect

Maximal subgroups

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

subgroupindex
#130824832
#130776962
#130715792
#130671922
#130671802
#130671772
#130671102
#130671012
C11×#15032
#1761611