Finite Group Databasebeta

← #15660400

Subgroups — #15660400

Order 2816.

11222 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623457C211yesmaximal, characteristic
22−1+4×Dic11C211yesmaximal, characteristic, complemented
3C4×#67040C215yesmaximal, complemented
4#13081825C215yesmaximal, complemented
5C4×#67042C2110yesmaximal, complemented
6#13081822C2110yesmaximal, complemented
7#13081818C215yesmaximal, complemented
8#13081815C2110yesmaximal, complemented
9C2×#10623105C215yesmaximal, complemented
10D11×#520C2110yesmaximal, complemented
11C4×C11×2−1+4C211yesmaximal, characteristic, complemented
12C2×C11×2−1+4C2211yescharacteristic
13#10623457C4132yescomplemented
14C2×#67042C22110yes—
15C2×#41×D11C22110yes—
16C2×#67040C2215yes—
17C22×#4343C2215yes—
18C11×#520C22110yescomplemented
19C11×#519C2215yescomplemented
20C4×C11×#41C22110yescomplemented
21C2×C4×Q8×C11C2215yescomplemented
22#10623358C22110yescomplemented
23#41×Dic11C22110yescomplemented
24#10623343C2215yescomplemented
25C2×Q8×Dic11C2215yescomplemented
26#10623105C22120yescomplemented
27#10623105C22110yescomplemented
28#10623105C22120yescomplemented
29#10623105C22120yescomplemented
30#10623105C22110yescomplemented
31C4×#4343C22120yescomplemented
32C4×#4343C22120yescomplemented
33#10623103C22110yescomplemented
34#10623103C22110yescomplemented
35C4×Q8×D11C22120yescomplemented
36#10623077C22130yescomplemented
37#10623077C22110yescomplemented
38#10623076C22130yescomplemented
39#10623076C22130yescomplemented
40C4×D4×D11C22160yescomplemented
41#10623054C22130yescomplemented
42#10623053C22130yescomplemented
43#10623052C22130yescomplemented
44D11×#117C22130yescomplemented
45#10623035C22130yescomplemented
46C2×#66946C22115yescomplemented
47C2×C4⋊C4×D11C22115yescomplemented
48C4×#4339C22130yescomplemented
49C2×C4×D44C22115yescomplemented
50C2×#66925C22115yescomplemented
51C11×2−1+4C2×C4116yescomplemented
52C2×C11×#41C23110yes—
53C22×Q8×C11C2315yes—
54#67042C2×C41160yescomplemented
55#41×D11C2×C41160yescomplemented
56#67040C2×C4180yescomplemented
57C2×#4343C2×C4180yescomplemented
58C2×#4343C23120yes—
59C2×#4343C23110yes—
60C2×Q8×D11C23110yes—
61C2×#4341C23110yes—
62C2×D4×D11C23130yes—
63C2×#4339C23130yes—
64C22×D44C23115yes—
65C22×C4×D11C23130yes—
66C22×C4×D11C23115yes—
67C4×Q8×C11C23120yes—
68C4×Q8×C11C23110yes—
69C4×Q8×C11C23110yes—
70C4×D4×C11C23130yes—
71C4×D4×C11C23110yes—
72C11×#117C23130yes—
73C2×C11×C4⋊C4C23115yes—
74C2×C42×C11C23115yes—
75Q8×Dic11C23110yes—
76Q8×Dic11C23120yes—
77Q8×Dic11C23110yes—
78D4×Dic11C23130yes—
79D4×Dic11C23110yes—
80C4×C22⋊D11C23120yes—
81C4×C22⋊D11C23160yes—
82C2×(C2×D11)⋊C4C23115yes—
83C2×(C2×D11)⋊C4C23115yes—
84#66979C23130yes—
85C2×C4⋊Dic11C23115yes—
86C2×Dic11⋊C4C2315yes—
87C2×Dic11⋊C4C23115yes—
88C2×C4×Dic11C23115yes—
89#66946C23130yes—
90#66946C23160yes—
91#66946C23130yes—
92#66945C23130yes—
93#66945C23130yes—
94C4⋊C4×D11C23130yes—
95C4⋊C4×D11C23160yes—
96C4⋊C4×D11C23110yes—
97#66940C23130yes—
98#66940C23110yes—
99(C22⋊D11)⋊C4C23120yes—
100(C22⋊D11)⋊C4C23160yes—
101C22⋊C4×D11C23160yes—
102#66930C23120yes—
103C4×D44C23130yes—
104C4×D44C23160yes—
105C4×D44C23130yes—
106#66925C23110yes—
107#66925C23130yes—
108#66925C23130yes—
109#66925C23130yes—
110C42×D11C23160yes—
111C4×Dic22C23110yes—
112C4×Dic22C23130yes—
113#62654—111nomaximal, Sylow
114C23×D11C24115yes—
115C11×#41C22×C4180yescomplemented
116C2×Q8×C11C22×C4140yescomplemented
117C2×Q8×C11C24110yes—
118C2×D4×C11C24110yes—
119C22×C4×C11C2415yes—
120C22×C4×C11C24115yes—
121C22×C4×C11C24115yes—
122C2×C22⋊D11C24120yes—
123C22×Dic11C2415yes—
124C22×Dic11C24115yes—
125C22×Dic11C2415yes—
126#4343C22×C4180yescomplemented
127#4343C22×C41160yescomplemented
128Q8×D11C22×C4180yescomplemented
129#4341C22×C4180yescomplemented
130D4×D11C22×C41240yescomplemented
131#4339C22×C41240yescomplemented
132C2×D44C22×C41120yescomplemented
133C2×D44C24130yes—
134C2×C4×D11—830no—
135C2×C4×D11C22×C41120yescomplemented
136C2×C4×D11C24120yes—
137C2×C4×D11C24160yes—
138C2×C4×D11C24130yes—
139C2×C4×D11C24110yes—
140C2×Dic22C24110yes—
141C11×C4⋊C4C24130yes—
142C11×C4⋊C4C24110yes—
143C11×C22⋊C4C24120yes—
144C42×C11C24130yes—
145C42×C11C24110yes—
146C22⋊Dic11C24120yes—
147(C2×D11)⋊C4C24110yes—
148(C2×D11)⋊C4C24110yes—
149(C2×D11)⋊C4C24130yes—
150(C2×D11)⋊C4C24130yes—
151C4⋊Dic11C24130yes—
152C4⋊Dic11C24110yes—
153Dic11⋊C4C2415yes—
154Dic11⋊C4C24130yes—
155Dic11⋊C4C2411yescharacteristic
156Dic11⋊C4C2415yes—
157Dic11⋊C4C2415yes—
158Dic11⋊C4C24110yes—
159C4×Dic11C24120yes—
160C4×Dic11C24120yes—
161C4×Dic11C24130yes—
162C4×Dic11C24110yes—
163C2×#585—111no—
164C4×2−1+4—111no—
165C4×2−1+4—115no—
166C4×2−1+4—115no—
167C4×2−1+4D1111yescharacteristic, complemented
168C4×H(5,𝔽2)—1110no—
169C4×H(5,𝔽2)—1110no—
170#3428—115no—
171#3428—1110no—
172C2×#520—1110no—
173C2×#520—115no—
174C23×C11C2515yes—
175C22×D11—415no—
176C22×D11—415no—
177C22×D11C23×C4160yes—
178C22×D11C25110yes—
179Q8×C11C23×C4140yes—
180D4×C11C23×C4140yes—
181C2×C4×C11—415no—
182C2×C4×C11—45no—
183C2×C4×C11C23×C4160yes—
184C2×C4×C11C2515yes—
185C2×C4×C11C25110yes—
186C2×C4×C11C2511yescharacteristic
187C2×C4×C11C25110yes—
188C22⋊D11C23×C4180yes—
189C2×Dic11—415no—
190C2×Dic11—45no—
191C2×Dic11C23×C4120yes—
192C2×Dic11C2511yescharacteristic
193C2×Dic11C2515yes—
194C2×Dic11C25110yes—
195C2×Dic11C2515yes—
196C2×Dic11C2511yescharacteristic
197D44C23×C41120yes—
198C4×D11—460no—
199C4×D11—420no—
200C4×D11C23×C4140yes—
201C4×D11C23×C41120yes—
202Dic22C23×C4140yes—
203#585—1132no—
204C2×2−1+4—115no—
205C2×2−1+4C2×D1111yescharacteristic
206C2×H(5,𝔽2)—1110no—
207C22×#41—1110no—
208C22×#41—115no—
209#520—1110no—
210#520—1120no—
211#520—1110no—
212#520—1120no—
213#520—1120no—
214#520—1110no—
215#520—1130no—
216#520—1110no—
217#520—1130no—
218#520—1130no—
219#520C2×D11110yescomplemented
220#519—115no—
221#519—1110no—
222#519—1110no—
223#519C2×D1115yescomplemented
224#518—1130no—
225#518—1130no—
226#518—1130no—
227C4×#41—1110no—
228C4×#41—1120no—
229C4×#41—1120no—
230C4×#41—1130no—
231C4×#41—1130no—
232C4×#41C2×D11110yescomplemented
233C2×C4×Q8—115no—
234C2×C4×Q8—1120no—
235C2×C4×Q8C2×D1115yescomplemented
236C2×C4×D4—1160no—
237C2×C4×D4—1115no—
238C2×C4×D4—1115no—
239C2×#117—1130no—
240C2×#117—1115no—
241C22×C4⋊C4—1115no—
242C22×C11—25no—
243C22×C11—25no—
244C22×C11C24×C4110yes—
245C22×C11C2611yescharacteristic
246C2×D11—210no—
247C2×D11—210no—
248C2×D11—460no—
249C2×D11C24×C4120yes—
250C4×C11—210no—
251C4×C11—21no—
252C4×C11—25no—
253C4×C11C24×C4120yes—
254Dic11—210no—
255Dic11—25no—
256Dic11—21no—
257Dic11C24×C4110yes—
258Dic11C24×C412yes—
2592−1+4—1180no—
2602−1+4C4×D11116yescomplemented
261H(5,𝔽2)—11160no—
262C2×#41—11160no—
263C2×#41—1180no—
264C2×#41—1120no—
265C2×#41—1110no—
266C2×#41—1110no—
267C2×#41—1130no—
268C2×#41C22×D11110yes—
269C22×Q8—1110no—
270C22×Q8C22×D1115yes—
271C22×D4—1130no—
272C22×D4—1115no—
273C23×C4—1115no—
274C23×C4—1130no—
275C4×Q8—1110no—
276C4×Q8—1120no—
277C4×Q8—1110no—
278C4×Q8—1130no—
279C4×Q8—1110no—
280C4×Q8—1130no—
281C4×Q8—1110no—
282C4×Q8C22×D11120yes—
283C4×Q8C22×D11110yes—
284C4×Q8C22×D11110yes—
285C4×D4—1130no—
286C4×D4—1110no—
287C4×D4—1160no—
288C4×D4—1120no—
289C4×D4—1160no—
290C4×D4—1130no—
291C4×D4—1130no—
292C4×D4—1160no—
293C4×D4—1120no—
294C4×D4—1160no—
295C4×D4—1130no—
296C4×D4—1130no—
297C4×D4C22×D11130yes—
298C4×D4C22×D11110yes—
299#117—1130no—
300#117—1130no—
301#117—1130no—
302#117—1120no—
303#117—1130no—
304#117—1110no—
305#117—1130no—
306#117—1130no—
307#117C22×D11130yes—
308C2×C4⋊C4—1115no—
309C2×C4⋊C4—1115no—
310C2×C4⋊C4—115no—
311C2×C4⋊C4—1130no—
312C2×C4⋊C4—1160no—
313C2×C4⋊C4—1110no—
314C2×C4⋊C4C22×D11115yes—
315C2×C22⋊C4—1115no—
316C2×C22⋊C4—1115no—
317C2×C22⋊C4—1160no—
318C2×C42—1115no—
319C2×C42—1160no—
320C2×C42C22×D11115yes—
321C2×C11—210no—
322C2×C11C25×C411yescharacteristic
323C2×C11H(7,𝔽2)11yescharacteristic
324C2×C112−1+611yescharacteristic
325D11—220no—
326C24—1115no—
327#41—1180no—
328#41—11160no—
329#41—1180no—
330#41—11240no—
331#41C2×C4×D11180yescomplemented
332C2×Q8—1180no—
333C2×Q8—1110no—
334C2×Q8C2×C4×D11140yescomplemented
335C2×Q8C23×D11110yes—
336C2×D4—1120no—
337C2×D4—11240no—
338C2×D4—11120no—
339C2×D4—1130no—
340C2×D4C23×D11110yes—
341C22×C4—115no—
342C22×C4—11120no—
343C22×C4—1130no—
344C22×C4—1110no—
345C22×C4—115no—
346C22×C4—1115no—
347C22×C4—1120no—
348C22×C4—1160no—
349C22×C4—8830no—
350C22×C4C23×D1115yes—
351C22×C4C23×D11115yes—
352C22×C4C23×D11115yes—
353C4⋊C4—1110no—
354C4⋊C4—115no—
355C4⋊C4—111no—
356C4⋊C4—1130no—
357C4⋊C4—1130no—
358C4⋊C4—115no—
359C4⋊C4—115no—
360C4⋊C4—1110no—
361C4⋊C4C23×D11130yes—
362C4⋊C4C23×D11110yes—
363C22⋊C4—1120no—
364C22⋊C4—1110no—
365C22⋊C4—1130no—
366C22⋊C4—1130no—
367C22⋊C4—1110no—
368C22⋊C4C23×D11120yes—
369C42—1120no—
370C42—1120no—
371C42—1110no—
372C42—1130no—
373C42C23×D11130yes—
374C42C23×D11110yes—
375C11#6265411yescharacteristic, complemented, Sylow
376C23—1110no—
377C23—1160no—
378C23—4415no—
379C23—4415no—
380C23C24×D1115yes—
381Q8—1140no—
382Q8C22×C4×D11140yes—
383D4—1180no—
384D4—11120no—
385D4C22×C4×D11140yes—
386C2×C4—415no—
387C2×C4—45no—
388C2×C4—1120no—
389C2×C4—115no—
390C2×C4—111no—
391C2×C4—1140no—
392C2×C4—11120no—
393C2×C4—115no—
394C2×C4—111no—
395C2×C4—1110no—
396C2×C4—4460no—
397C2×C4—4420no—
398C2×C4—4415no—
399C2×C4—445no—
400C2×C4C22×C4×D11160yes—
401C2×C4C24×D1115yes—
402C2×C4C24×D11110yes—
403C2×C4C24×D1111yescharacteristic
404C2×C4C24×D11110yes—
405C22—25no—
406C22—25no—
407C22—1120no—
408C22—2210no—
409C22—2210no—
410C22—4460no—
411C22C23×C4×D11110yes—
412C22C25×D1111yescharacteristic
413C4—210no—
414C4—21no—
415C4—25no—
416C4—112no—
417C4—1110no—
418C4—2210no—
419C4—225no—
420C4—221no—
421C4C23×C4×D11120yes—
422C2—210no—
423C2—2220no—
424C2C24×C4×D1111yescharacteristic
425C2#1308342711yescharacteristic
426C2#1308342811yescharacteristic
subgroupG/H
center, FrattiniC22C25×D11
commutatorC2×C11C25×C4
FittingC4×C11×2−1+4C2
socle, cosocleC22×C11C26
prime radicalC2×#10623457C2
hypercenterC4×2−1+4D11
hypocenterC11#62654
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. #13081825C2semidirect
5. C4×#67042C2semidirect
6. #13081822C2semidirect
7. #13081818C2semidirect
8. #13081815C2semidirect
9. C2×#10623105C2semidirect
10. D11×#520C2semidirect
11. C4×C11×2−1+4C2semidirect
13. #10623457C4semidirect
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. #10623105C22semidirect
29. #10623105C22semidirect
30. #10623105C22semidirect
31. C4×#4343C22semidirect
32. C4×#4343C22semidirect
33. #10623103C22semidirect
34. #10623103C22semidirect
35. C4×Q8×D11C22semidirect
36. #10623077C22semidirect
37. #10623077C22semidirect
38. #10623076C22semidirect
39. #10623076C22semidirect
40. C4×D4×D11C22semidirect
41. #10623054C22semidirect
42. #10623053C22semidirect
43. #10623052C22semidirect
44. D11×#117C22semidirect
45. #10623035C22semidirect
46. C2×#66946C22semidirect
47. C2×C4⋊C4×D11C22semidirect
48. C4×#4339C22semidirect
49. C2×C4×D44C22semidirect
50. C2×#66925C22semidirect
51. C11×2−1+4C2×C4semidirect
54. #67042C2×C4semidirect
55. #41×D11C2×C4semidirect
56. #67040C2×C4semidirect
57. C2×#4343C2×C4semidirect
115. C11×#41C22×C4semidirect
116. C2×Q8×C11C22×C4semidirect
126. #4343C22×C4semidirect
127. #4343C22×C4semidirect
128. Q8×D11C22×C4semidirect
129. #4341C22×C4semidirect
130. D4×D11C22×C4semidirect
131. #4339C22×C4semidirect
132. C2×D44C22×C4semidirect
135. C2×C4×D11C22×C4semidirect
167. C4×2−1+4D11semidirect
219. #520C2×D11semidirect
223. #519C2×D11semidirect
232. C4×#41C2×D11semidirect
235. C2×C4×Q8C2×D11semidirect
260. 2−1+4C4×D11semidirect
331. #41C2×C4×D11semidirect
334. C2×Q8C2×C4×D11semidirect
375. C11#62654semidirect

Maximal subgroups

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

subgroupindex
C2×#106234572
2−1+4×Dic112
C4×#670402
#130818252
C4×#670422
#130818222
#130818182
#130818152
C2×#106231052
D11×#5202
C4×C11×2−1+42
#6265411