Finite Group Databasebeta

← #15660393

Subgroups — #15660393

Order 2816.

10930 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×2−1+4C211yesmaximal, characteristic
22−1+4×Dic11C211yesmaximal, characteristic, complemented
3C4×#67040C215yesmaximal, complemented
4#13081827C2110yesmaximal, complemented
5C4×#67043C2110yesmaximal, complemented
6#13081825C215yesmaximal, complemented
7#13081816C2110yesmaximal, complemented
8#13081815C2110yesmaximal, complemented
9C2×#10623103C215yesmaximal, complemented
10D11×#519C215yesmaximal, complemented
11C4×C11×2−1+4C211yesmaximal, characteristic, complemented
12C2×C11×2−1+4C2211yescharacteristic
13D11×2−1+4C4132yescomplemented
14C2×#67043C22110yes—
15C2×#41×D11C22110yes—
16C2×#67040C2215yes—
17C22×Q8×D11C2215yes—
18C11×#520C22110yescomplemented
19C11×#519C2215yescomplemented
20C4×C11×#41C22110yescomplemented
21C2×C4×Q8×C11C2215yescomplemented
22#10623358C22110yescomplemented
23#41×Dic11C22110yescomplemented
24#10623343C2215yescomplemented
25C2×Q8×Dic11C2215yescomplemented
26#10623105C22110yescomplemented
27#10623105C22110yescomplemented
28C4×#4343C22120yescomplemented
29#10623103C22110yes—
30#10623103C22120yes—
31#10623103C22110yes—
32#10623103C22120yescomplemented
33#10623103C22120yescomplemented
34C4×Q8×D11C22120yescomplemented
35C4×Q8×D11C22120yescomplemented
36#10623077C22130yescomplemented
37#10623077C22130yescomplemented
38#10623076C22110yes—
39#10623076C22130yes—
40C4×#4341C22160yescomplemented
41#10623054C22130yescomplemented
42#10623053C22130yescomplemented
43D11×#117C22130yes—
44#10623047C22130yescomplemented
45#10623035C22130yescomplemented
46C2×#66945C22115yes—
47C2×#66940C22115yescomplemented
48C4×#4339C22130yescomplemented
49C2×#66925C22115yes—
50C2×C4×Dic22C22115yescomplemented
51C11×2−1+4C2×C4116yescomplemented
52C2×C11×#41C23110yes—
53C22×Q8×C11C2315yes—
54#67043C2×C41160yescomplemented
55#41×D11C2×C41160yescomplemented
56#67040C2×C4180yescomplemented
57C2×#4343C23110yes—
58C2×Q8×D11C2×C4180yescomplemented
59C2×Q8×D11C23120yes—
60C2×Q8×D11C23110yes—
61C2×#4341C23130yes—
62C2×D4×D11C23110yes—
63C2×#4339C23130yes—
64C22×C4×D11C23115yes—
65C22×Dic22C23115yes—
66C4×Q8×C11C23110yes—
67C4×Q8×C11C23120yes—
68C4×Q8×C11C23110yes—
69C4×D4×C11C23130yes—
70C4×D4×C11C23110yes—
71C11×#117C23130yes—
72C2×C11×C4⋊C4C23115yes—
73C2×C42×C11C23115yes—
74Q8×Dic11C23110yes—
75Q8×Dic11C23120yes—
76Q8×Dic11C23110yes—
77D4×Dic11C23130yes—
78D4×Dic11C23110yes—
79C4×C22⋊D11C23120yes—
80C4×C22⋊D11C23160yes—
81C2×(C2×D11)⋊C4C2315yes—
82C2×(C2×D11)⋊C4C23115yes—
83#66979C23130yes—
84C2×C4⋊Dic11C23115yes—
85C2×Dic11⋊C4C23115yes—
86C2×Dic11⋊C4C23115yes—
87C2×C4×Dic11C23130yes—
88C2×C4×Dic11C23115yes—
89#66946C23130yes—
90#66946C23110yes—
91#66945C23130yes—
92#66945C23160yes—
93#66945C23110yes—
94C4⋊C4×D11C23130yes—
95C4⋊C4×D11C23130yes—
96#66940C23130yes—
97#66940C23160yes—
98#66940C23130yes—
99(C22⋊D11)⋊C4C23120yes—
100(C22⋊D11)⋊C4C23160yes—
101C22⋊C4×D11C23120yes—
102#66930C23160yes—
103C4×D44C23110yes—
104C4×D44C23130yes—
105#66925C23110yes—
106#66925C23130yes—
107#66925C23130yes—
108#66925C23130yes—
109C42×D11C23160yes—
110C4×Dic22C23130yes—
111C4×Dic22C23160yes—
112C4×Dic22C23130yes—
113#62653—111nomaximal, Sylow
114C23×D11C2415yes—
115C11×#41C22×C4180yes—
116C2×Q8×C11C22×C4140yes—
117C2×Q8×C11C24110yes—
118C2×D4×C11C24110yes—
119C22×C4×C11C24115yes—
120C22×C4×C11C2415yes—
121C22×C4×C11C24115yes—
122C2×C22⋊D11C24120yes—
123C22×Dic11C2415yes—
124C22×Dic11C24115yes—
125C22×Dic11C24115yes—
126#4343C22×C4180yes—
127Q8×D11C22×C4180yes—
128Q8×D11C22×C41160yes—
129#4341C22×C41240yes—
130D4×D11C22×C4180yes—
131#4339C22×C41240yes—
132C2×D44C24110yes—
133C2×C4×D11C22×C41120yes—
134C2×C4×D11C24120yes—
135C2×C4×D11C24120yes—
136C2×C4×D11C24130yes—
137C2×C4×D11C24110yes—
138C2×Dic22C22×C41120yes—
139C2×Dic22C24130yes—
140C11×C4⋊C4C24110yes—
141C11×C4⋊C4C24130yes—
142C11×C22⋊C4C24120yes—
143C42×C11C24130yes—
144C42×C11C24110yes—
145C22⋊Dic11C24120yes—
146(C2×D11)⋊C4C2411yescharacteristic
147(C2×D11)⋊C4C2415yes—
148(C2×D11)⋊C4C2415yes—
149(C2×D11)⋊C4C2415yes—
150(C2×D11)⋊C4C24110yes—
151(C2×D11)⋊C4C24130yes—
152C4⋊Dic11C24110yes—
153C4⋊Dic11C24130yes—
154Dic11⋊C4C24110yes—
155Dic11⋊C4C24130yes—
156Dic11⋊C4C24130yes—
157Dic11⋊C4C24110yes—
158C4×Dic11C24120yes—
159C4×Dic11C24160yes—
160C4×Dic11C24130yes—
161C4×Dic11C24110yes—
162C22×2−1+4—111no—
163C4×2−1+4—111no—
164C4×2−1+4—1110no—
165C4×2−1+4—115no—
166C4×2−1+4—1110no—
167C4×2−1+4—115no—
168C4×2−1+4D1111yescharacteristic, complemented
169#3428—1110no—
170#3428—1110no—
171C2×#519—115no—
172C2×#519—115no—
173C23×C11C2515yes—
174C22×D11—45no—
175C22×D11—45no—
176C22×D11C23×C4120yes—
177C22×D11C2511yescharacteristic
178C22×D11C2515yes—
179Q8×C11C23×C4140yes—
180D4×C11C23×C4140yes—
181C2×C4×C11—45no—
182C2×C4×C11—415no—
183C2×C4×C11C23×C4160yes—
184C2×C4×C11C25110yes—
185C2×C4×C11C2515yes—
186C2×C4×C11C2511yescharacteristic
187C2×C4×C11C25110yes—
188C22⋊D11C23×C4180yes—
189C2×Dic11—45no—
190C2×Dic11—415no—
191C2×Dic11C23×C4160yes—
192C2×Dic11C2511yescharacteristic
193C2×Dic11C2515yes—
194C2×Dic11C25110yes—
195C2×Dic11C25110yes—
196D44C23×C4140yes—
197C4×D11—420no—
198C4×D11—420no—
199C4×D11C23×C4140yes—
200C4×D11C23×C41120yes—
201Dic22C23×C41120yes—
202C2×2−1+4—1132no—
203C2×2−1+4—1110no—
204C2×2−1+4—115no—
205C2×2−1+4C2×D1111yescharacteristic
206C22×#41—1110no—
207C23×Q8—115no—
208#520—1110no—
209#520—1110no—
210#520—1110no—
211#520—1130no—
212#520—1130no—
213#520—1130no—
214#520—1130no—
215#520C2×D11110yescomplemented
216#519—115no—
217#519—1110no—
218#519—1120no—
219#519—1110no—
220#519—1120no—
221#519—1120no—
222#519—1130no—
223#519C2×D1115yescomplemented
224#518—1130no—
225#518—1110no—
226C4×#41—1110no—
227C4×#41—1120no—
228C4×#41—1160no—
229C4×#41—1130no—
230C4×#41—1130no—
231C4×#41C2×D11110yescomplemented
232C2×C4×Q8—115no—
233C2×C4×Q8—1120no—
234C2×C4×Q8—1120no—
235C2×C4×Q8—1115no—
236C2×C4×Q8—1115no—
237C2×C4×Q8C2×D1115yescomplemented
238C2×#117—1130no—
239C2×#117—1115no—
240C2×#117—1115no—
241C22×C11—25no—
242C22×C11—25no—
243C22×C11C24×C4110yes—
244C22×C11C2611yescharacteristic
245C2×D11—21no—
246C2×D11—21no—
247C2×D11—25no—
248C2×D11—25no—
249C2×D11—420no—
250C2×D11C24×C412yes—
251C2×D11C24×C4110yes—
252C4×C11—21no—
253C4×C11—210no—
254C4×C11—25no—
255C4×C11C24×C4120yes—
256Dic11—25no—
257Dic11—210no—
258Dic11—21no—
259Dic11C24×C4120yes—
2602−1+4—11160no—
2612−1+4—1180no—
2622−1+4C4×D11116yescomplemented
263C2×#41—11160no—
264C2×#41—1110no—
265C2×#41—1130no—
266C2×#41—1130no—
267C2×#41C22×D11110yes—
268C22×Q8—1180no—
269C22×Q8—1120no—
270C22×Q8—1110no—
271C22×Q8—1115no—
272C22×Q8C22×D1115yes—
273C22×D4—1110no—
274C23×C4—1115no—
275C4×Q8—1110no—
276C4×Q8—1120no—
277C4×Q8—1110no—
278C4×Q8—1130no—
279C4×Q8—1160no—
280C4×Q8—1130no—
281C4×Q8—1130no—
282C4×Q8—1160no—
283C4×Q8—1130no—
284C4×Q8C22×D11110yes—
285C4×Q8C22×D11120yes—
286C4×Q8C22×D11110yes—
287C4×D4—1110no—
288C4×D4—1130no—
289C4×D4—1160no—
290C4×D4—1120no—
291C4×D4—1110no—
292C4×D4—1130no—
293C4×D4—1160no—
294C4×D4—1120no—
295C4×D4—1130no—
296C4×D4—1110no—
297C4×D4C22×D11130yes—
298C4×D4C22×D11110yes—
299#117—1130no—
300#117—1110no—
301#117—1130no—
302#117—1160no—
303#117—1160no—
304#117—1130no—
305#117—1110no—
306#117—1130no—
307#117—1130no—
308#117C22×D11130yes—
309C2×C4⋊C4—1115no—
310C2×C4⋊C4—1115no—
311C2×C4⋊C4—1115no—
312C2×C4⋊C4—1130no—
313C2×C4⋊C4—1130no—
314C2×C4⋊C4C22×D11115yes—
315C2×C22⋊C4—1115no—
316C2×C22⋊C4—115no—
317C2×C22⋊C4—1120no—
318C2×C42—1130no—
319C2×C42—1115no—
320C2×C42—1160no—
321C2×C42C22×D11115yes—
322C2×C11—210no—
323C2×C11C25×C411yescharacteristic
324C2×C112−1+611yescharacteristic
325C2×C112−1+611yescharacteristic
326D11—22no—
327D11—210no—
328C24—115no—
329#41—1180no—
330#41—11240no—
331#41—11240no—
332#41C2×C4×D11180yes—
333C2×Q8—1180no—
334C2×Q8—11160no—
335C2×Q8—11120no—
336C2×Q8—1130no—
337C2×Q8C2×C4×D11140yes—
338C2×Q8C23×D11110yes—
339C2×D4—1120no—
340C2×D4—1180no—
341C2×D4—1110no—
342C2×D4C23×D11110yes—
343C22×C4—1115no—
344C22×C4—11120no—
345C22×C4—1130no—
346C22×C4—1110no—
347C22×C4—115no—
348C22×C4—1115no—
349C22×C4—1120no—
350C22×C4—1120no—
351C22×C4C23×D11115yes—
352C22×C4C23×D1115yes—
353C22×C4C23×D11115yes—
354C4⋊C4—1110no—
355C4⋊C4—1130no—
356C4⋊C4—1130no—
357C4⋊C4—1110no—
358C4⋊C4—1130no—
359C4⋊C4—1110no—
360C4⋊C4C23×D11110yes—
361C4⋊C4C23×D11130yes—
362C22⋊C4—1120no—
363C22⋊C4—1110no—
364C22⋊C4—115no—
365C22⋊C4—111no—
366C22⋊C4—1130no—
367C22⋊C4—115no—
368C22⋊C4—115no—
369C22⋊C4C23×D11120yes—
370C42—1160no—
371C42—1120no—
372C42—1110no—
373C42—1130no—
374C42C23×D11130yes—
375C42C23×D11110yes—
376C11#6265311yescharacteristic, complemented, Sylow
377C23—111no—
378C23—115no—
379C23—1120no—
380C23—445no—
381C23—445no—
382C23C24×D1115yes—
383Q8—11120no—
384Q8C22×C4×D11140yes—
385D4—1180no—
386D4—1140no—
387D4C22×C4×D11140yes—
388C2×C4—45no—
389C2×C4—415no—
390C2×C4—1160no—
391C2×C4—1110no—
392C2×C4—1140no—
393C2×C4—11120no—
394C2×C4—1110no—
395C2×C4—115no—
396C2×C4—111no—
397C2×C4—4420no—
398C2×C4—4420no—
399C2×C4—4415no—
400C2×C4—445no—
401C2×C4C22×C4×D11160yes—
402C2×C4C24×D11110yes—
403C2×C4C24×D1115yes—
404C2×C4C24×D1111yescharacteristic
405C2×C4C24×D11110yes—
406C22—25no—
407C22—25no—
408C22—112no—
409C22—1110no—
410C22—225no—
411C22—221no—
412C22—225no—
413C22—221no—
414C22—4420no—
415C22C23×C4×D11110yes—
416C22C25×D1111yescharacteristic
417C4—21no—
418C4—25no—
419C4—210no—
420C4—1120no—
421C4—2210no—
422C4—225no—
423C4—221no—
424C4C23×C4×D11120yes—
425C2—210no—
426C2—222no—
427C2—2210no—
428C2C24×C4×D1111yescharacteristic
429C2#1308342811yescharacteristic
430C2#1308342911yescharacteristic
subgroupG/H
center, FrattiniC22C25×D11
commutatorC2×C11C25×C4
FittingC4×C11×2−1+4C2
socle, cosocleC22×C11C26
prime radicalC2×D11×2−1+4C2
hypercenterC4×2−1+4D11
hypocenterC11#62653
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×2−1+4

Complements

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

NH ≅ G/Ntype
2. 2−1+4×Dic11C2semidirect
3. C4×#67040C2semidirect
4. #13081827C2semidirect
5. C4×#67043C2semidirect
6. #13081825C2semidirect
7. #13081816C2semidirect
8. #13081815C2semidirect
9. C2×#10623103C2semidirect
10. D11×#519C2semidirect
11. C4×C11×2−1+4C2semidirect
13. D11×2−1+4C4semidirect
18. C11×#520C22semidirect
19. C11×#519C22semidirect
20. C4×C11×#41C22semidirect
21. C2×C4×Q8×C11C22semidirect
22. #10623358C22semidirect
23. #41×Dic11C22semidirect
24. #10623343C22semidirect
25. C2×Q8×Dic11C22semidirect
26. #10623105C22semidirect
27. #10623105C22semidirect
28. C4×#4343C22semidirect
32. #10623103C22semidirect
33. #10623103C22semidirect
34. C4×Q8×D11C22semidirect
35. C4×Q8×D11C22semidirect
36. #10623077C22semidirect
37. #10623077C22semidirect
40. C4×#4341C22semidirect
41. #10623054C22semidirect
42. #10623053C22semidirect
44. #10623047C22semidirect
45. #10623035C22semidirect
47. C2×#66940C22semidirect
48. C4×#4339C22semidirect
50. C2×C4×Dic22C22semidirect
51. C11×2−1+4C2×C4semidirect
54. #67043C2×C4semidirect
55. #41×D11C2×C4semidirect
56. #67040C2×C4semidirect
58. C2×Q8×D11C2×C4semidirect
168. C4×2−1+4D11semidirect
215. #520C2×D11semidirect
223. #519C2×D11semidirect
231. C4×#41C2×D11semidirect
237. C2×C4×Q8C2×D11semidirect
262. 2−1+4C4×D11semidirect
376. C11#62653semidirect

Maximal subgroups

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

subgroupindex
C2×D11×2−1+42
2−1+4×Dic112
C4×#670402
#130818272
C4×#670432
#130818252
#130818162
#130818152
C2×#106231032
D11×#5192
C4×C11×2−1+42
#6265311