Finite Group Databasebeta

← #14721502

Subgroups — #14721502

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#13082481C211yesmaximal, characteristic
2#13077697C211yesmaximal, characteristic, complemented
3#13067191C214yesmaximal, complemented
4#13067179C211yesmaximal, characteristic, complemented
5#13067175C211yesmaximal, characteristic
6#13067114C211yesmaximal, characteristic, complemented
7#13067110C211yesmaximal, characteristic
8#13067100C214yesmaximal, complemented
9C11×#2356C211yesmaximal, characteristic, complemented
10C2×C4×Q8×C11C2211yescharacteristic
11#10623347—21no—
12#10623116C412yescomplemented
13#10623115C412yescomplemented
14#10623112—22no—
15#10623110C412yescomplemented
16#10623099—22no—
17#10623098C412yescomplemented
18#10623046—22no—
19#10623035—21no—
20#10623010C2214yes—
21#10623008C2211yescharacteristic
22#10623001C2211yescharacteristic
23C11×#391—21no—
24C11×#387—22no—
25C11×#383C2212yes—
26C11×#382C2211yescharacteristic
27C4×C11×C4⋊C4—21no—
28C4×C11×C4⋊C4C2211yescharacteristic
29C11×#376C2212yes—
30Q8×C11⋊C8—22no—
31Q8×C11⋊C8—22no—
32#10622538C2214yes—
33#10622538C2211yescharacteristic
34#10622538C2211yescharacteristic
35#10622090C2212yes—
36#10622090C2214yes—
37#10622090C2212yes—
38#10622089C2212yes—
39#10622089C2214yes—
40#10622089C2212yes—
41C22×Q8×C11D411yescharacteristic
42C2×#4339—21no—
43C4×Q8×C11C2×C412yes—
44C4×Q8×C11C2×C412yes—
45C4×Q8×C11D412yes—
46C4×Q8×C11D412yes—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4D411yescharacteristic
50C2×C11×C4⋊C4D412yes—
51C2×C42×C11—22no—
52C2×C42×C11—21no—
53C2×C42×C11C2311yescharacteristic
54C2×C42×C11C2312yes—
55#67000—22no—
56#66999—22no—
57#66999—22no—
58#66997—22no—
59#66983—21no—
60#66983C2312yes—
61#66982—24no—
62C4×C22⋊D11—24no—
63#66979—21no—
64#66977—21no—
65#66977C2312yes—
66#66951—24no—
67#66949—24no—
68#66947—24no—
69#66946—22no—
70#66945—22no—
71C4⋊C4×D11—22no—
72#66942—24no—
73#66940—22no—
74#66929—24no—
75#66928—21no—
76#66928C2×C414yes—
77#66927C2×C411yescharacteristic
78C4×D44—21no—
79C4×D44C2×C412yes—
80C4×D44C2×C414yes—
81#66925—24no—
82#66923—21no—
83#66923C2×C414yes—
84#66922C2×C411yescharacteristic
85#66922C2×C411yescharacteristic
86#66922C2×C411yescharacteristic
87C4×Dic22—21no—
88C4×Dic22C2×C412yes—
89C4×Dic22C2×C414yes—
90C11×#95—22no—
91C11×#95—22no—
92C11×#95—21no—
93C11×#95—22no—
94C11×#95C2311yescharacteristic
95C11×#95C2312yes—
96C11×#95C2311yescharacteristic
97C22⋊(C11⋊C8)C2312yes—
98C22⋊(C11⋊C8)C2312yes—
99C4⋊(C11⋊C8)—21no—
100C4⋊(C11⋊C8)—21no—
101C4⋊(C11⋊C8)—24no—
102C4×C11⋊C8—21no—
103C4×C11⋊C8—21no—
104C4×C11⋊C8—24no—
105#17616—111nomaximal, Sylow
106C2×Q8×C11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11C22⋊C412yes—
109C2×Q8×C11C22⋊C412yes—
110C22×C4×C11—21no—
111C22×C4×C11—22no—
112C22×C4×C11—21no—
113C22×C4×C11C2×D412yes—
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D412yes—
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2411yescharacteristic
118C2×C22⋊D11—22no—
119#4339—42no—
120#4339—42no—
121C2×D44—21no—
122C2×D44—21no—
123C2×D44C22×C412yes—
124C2×C4×D11—22no—
125C2×C4×D11—24no—
126C2×Dic22—21no—
127C2×Dic22—21no—
128C2×Dic22C22×C412yes—
129C11×C4⋊C4—42no—
130C11×C4⋊C4—42no—
131C11×C4⋊C4C22⋊C412yes—
132C11×C4⋊C4C22⋊C414yes—
133C11×C4⋊C4C22⋊C412yes—
134C11×C4⋊C4C22⋊C414yes—
135C42×C11—44no—
136C42×C11—42no—
137C42×C11C22×C411yescharacteristic
138C42×C11C22×C414yes—
139C42×C11C22×C411yescharacteristic
140C42×C11C2×D411yescharacteristic
141C42×C11C2×D411yescharacteristic
142C42×C11C2×D414yes—
143C22⋊Dic11—22no—
144(C2×D11)⋊C4—24no—
145(C2×D11)⋊C4—22no—
146(C2×D11)⋊C4—24no—
147(C2×D11)⋊C4—24no—
148(C2×D11)⋊C4—22no—
149C4⋊Dic11—21no—
150C4⋊Dic11—21no—
151C4⋊Dic11—21no—
152C4⋊Dic11—21no—
153C4⋊Dic11C22×C412yes—
154C4⋊Dic11C22×C412yes—
155Dic11⋊C4—22no—
156Dic11⋊C4—24no—
157Dic11⋊C4—24no—
158Dic11⋊C4—24no—
159Dic11⋊C4—22no—
160C4×Dic11—22no—
161C4×Dic11—24no—
162C2×C11⋊C8—22no—
163C2×C11⋊C8—22no—
164#3507—111no—
165#2982—111no—
166#2356D1111yescharacteristic, complemented
167#1521—114no—
168#1518—111no—
169#1517—111no—
170#1503—111no—
171#1502—111no—
172#1500—114no—
173C23×C11C22×D411yescharacteristic
174C22×D11—22no—
175Q8×C11—24no—
176Q8×C11—24no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—42no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—42no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—42no—
189C2×C4×C11—41no—
190C2×C4×C11—42no—
191C2×C4×C11C2×C22⋊C414yes—
192C2×C4×C11C2×C22⋊C411yescharacteristic
193C2×C4×C11C2×C22⋊C414yes—
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—
203C2×Dic11—22no—
204C2×Dic11—22no—
205C2×Dic11—22no—
206D44—42no—
207D44—42no—
208D44—81no—
209C4×D11—44no—
210C4×D11—84no—
211Dic22—42no—
212Dic22—42no—
213Dic22—81no—
214C11⋊C8—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#533—111no—
225#532—111no—
226#529—114no—
227#520—221no—
228C2×C4×Q8C2×D1111yescharacteristic
229C8×Q8—222no—
230C8×Q8—222no—
231#431—114no—
232#431—111no—
233#431—111no—
234#391—21no—
235#387—22no—
236#383C2×D1112yes—
237#382C2×D1111yescharacteristic
238C4×C4⋊C4—21no—
239C4×C4⋊C4C2×D1111yescharacteristic
240#376C2×D1112yes—
241#328—112no—
242#328—114no—
243#328—112no—
244#327—112no—
245#327—114no—
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—24no—
258C4×C11—21no—
259C4×C11—24no—
260C4×C11—21no—
261C4×C11—42no—
262C4×C11—81no—
263C4×C11—82no—
264C4×C11#41612yes—
265C4×C11#41612yes—
266Dic11—42no—
267Dic11—42no—
268Dic11—42no—
269C2×#41—221no—
270C22×Q8C22⋊D1111yescharacteristic
271C4⋊Q8—111no—
272C4⋊Q8—111no—
273C4⋊Q8—111no—
274C4⋊Q8—222no—
275#127—111no—
276#126—224no—
277#126—224no—
278#125—114no—
279#125—224no—
280#125—221no—
281#124—114no—
282#124—222no—
283#124—221no—
284#123—224no—
285#123—224no—
286C22⋊Q8—112no—
287C22⋊Q8—222no—
288C22⋊Q8—222no—
289C22⋊Q8—221no—
290C22⋊Q8—224no—
291#121—112no—
292#121—221no—
293C4×Q8—114no—
294C4×Q8—112no—
295C4×Q8—222no—
296C4×Q8—221no—
297C4×Q8C4×D1112yes—
298C4×Q8C4×D1112yes—
299C4×Q8D4412yes—
300C4×Q8D4412yes—
301C4×D4—114no—
302C4×D4—112no—
303C4×D4—224no—
304C4×D4—222no—
305C4×D4—221no—
306#117—221no—
307#117—222no—
308#117—224no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—222no—
312C2×C4⋊C4C22⋊D1111yescharacteristic
313C2×C4⋊C4C22⋊D1112yes—
314C2×C42—22no—
315C2×C42—21no—
316C2×C42C22×D1112yes—
317C2×C42C22×D1111yescharacteristic
318C4⋊C8—224no—
319C4⋊C8—221no—
320C4⋊C8—221no—
321C22⋊C8—112no—
322C22⋊C8—112no—
323C4×C8—224no—
324C4×C8—221no—
325C4×C8—221no—
326#95—22no—
327#95—22no—
328#95—21no—
329#95—22no—
330#95C22×D1111yescharacteristic
331#95C22×D1112yes—
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—22no—
342C2×Q8—22no—
343C2×Q8—112no—
344C2×Q8—221no—
345C2×Q8—221no—
346C2×Q8(C2×D11)⋊C412yes—
347C2×Q8(C2×D11)⋊C412yes—
348C2×D4—112no—
349C2×D4—222no—
350C2×D4—221no—
351C2×D4—221no—
352C22×C4—21no—
353C22×C4—22no—
354C22×C4—21no—
355C22×C4—222no—
356C22×C4—224no—
357C22×C4C2×C22⋊D1112yes—
358C22×C4C2×C22⋊D1112yes—
359C22×C4C2×C22⋊D1111yescharacteristic
360C22×C4C2×C22⋊D1111yescharacteristic
361C22×C4C23×D1111yescharacteristic
362C2×C8—222no—
363C2×C8—222no—
364C4⋊C4—42no—
365C4⋊C4—42no—
366C4⋊C4—112no—
367C4⋊C4—112no—
368C4⋊C4—221no—
369C4⋊C4—224no—
370C4⋊C4—221no—
371C4⋊C4—224no—
372C4⋊C4—221no—
373C4⋊C4—222no—
374C4⋊C4—224no—
375C4⋊C4—221no—
376C4⋊C4—222no—
377C4⋊C4(C2×D11)⋊C412yes—
378C4⋊C4(C2×D11)⋊C412yes—
379C4⋊C4(C2×D11)⋊C414yes—
380C4⋊C4(C2×D11)⋊C414yes—
381C22⋊C4—222no—
382C22⋊C4—224no—
383C22⋊C4—224no—
384C22⋊C4—222no—
385C22⋊C4—224no—
386C22⋊C4—222no—
387C42—44no—
388C42—42no—
389C42—224no—
390C42—222no—
391C42C2×C4×D1111yescharacteristic
392C42C2×C4×D1114yes—
393C42C2×C4×D1111yescharacteristic
394C42C2×D4414yes—
395C42C2×D4411yescharacteristic
396C42C2×D4411yescharacteristic
397C11#1761611yescharacteristic, complemented, Sylow
398C23—222no—
399C23C22×C22⋊D1111yescharacteristic
400Q8—24no—
401Q8—24no—
402Q8—442no—
403Q8—442no—
404Q8—881no—
405D4—442no—
406D4—442no—
407D4—442no—
408D4—442no—
409D4—881no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—42no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—42no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—42no—
422C2×C4—41no—
423C2×C4—42no—
424C2×C4—222no—
425C2×C4—222no—
426C2×C4—222no—
427C2×C4—444no—
428C2×C4—884no—
429C2×C4C2×(C2×D11)⋊C414yes—
430C2×C4C2×(C2×D11)⋊C414yes—
431C2×C4C2×(C2×D11)⋊C411yescharacteristic
432C2×C4C2×(C2×D11)⋊C411yescharacteristic
433C2×C4C2×(C2×D11)⋊C411yescharacteristic
434C2×C4C2×(C2×D11)⋊C411yescharacteristic
435C2×C4#6700312yes—
436C2×C4#6700312yes—
437C2×C4C22×C4×D1111yescharacteristic
438C2×C4C22×D4411yescharacteristic
439C8—442no—
440C8—442no—
441C22—21no—
442C22—21no—
443C22—442no—
444C22—442no—
445C22—442no—
446C22C22×(C2×D11)⋊C411yescharacteristic
447C22C2×#6700311yescharacteristic
448C22C2×#6700311yescharacteristic
449C4—21no—
450C4—21no—
451C4—24no—
452C4—24no—
453C4—21no—
454C4—21no—
455C4—42no—
456C4—81no—
457C4—82no—
458C4—442no—
459C4—442no—
460C4—442no—
461C4#1062261512yes—
462C4#1062261512yes—
463C2—21no—
464C2—21no—
465C2—882no—
466C2#1307707911yescharacteristic
467C2C2×#1062261511yescharacteristic
468C2#1307716411yescharacteristic
subgroupG/H
centerC22C22×(C2×D11)⋊C4
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2356C2
socleC22×C11C22×C22⋊C4
prime radical#10623008C22
cosocleC22×C4×C11C24
hypercenter#2356D11
hypocenterC11#17616
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×Q8 ◁ #2356

Complements

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

NH ≅ G/Ntype
2. #13077697C2semidirect
3. #13067191C2semidirect
4. #13067179C2semidirect
6. #13067114C2semidirect
8. #13067100C2semidirect
9. C11×#2356C2semidirect
12. #10623116C4semidirect
13. #10623115C4semidirect
15. #10623110C4semidirect
17. #10623098C4semidirect
166. #2356D11semidirect
397. C11#17616semidirect

Maximal subgroups

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

subgroupindex
#130824812
#130776972
#130671912
#130671792
#130671752
#130671142
#130671102
#130671002
C11×#23562
#1761611