Finite Group Databasebeta

← C4×D11×2−1+4 #15660378

Subgroups — C4×D11×2−1+4 #15660378

Order 2816.

11210 conjugacy classes of subgroups.

The subgroup lattice has 444 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
7D11×#520C2110yesmaximal, complemented
8D11×#519C215yesmaximal, complemented
9C4×#41×D11C2110yesmaximal, complemented
10C2×C4×Q8×D11C215yesmaximal, complemented
11C4×C11×2−1+4C211yesmaximal, characteristic, complemented
12C2×C11×2−1+4C2211yescharacteristic
13D11×2−1+4C4132yesdirect product factor
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#10623105C22120yescomplemented
27C4×#4343C22110yescomplemented
28C4×#4343C22110yescomplemented
29#10623103C22120yescomplemented
30#10623103C22120yescomplemented
31C4×Q8×D11C22110yes—
32C4×Q8×D11C22120yes—
33C4×Q8×D11C22110yes—
34C4×Q8×D11C22120yescomplemented
35C4×Q8×D11C22120yescomplemented
36#10623077C22160yescomplemented
37C4×D4×D11C22110yes—
38C4×D4×D11C22130yes—
39C4×#4341C22130yescomplemented
40C4×#4341C22130yescomplemented
41#10623054C22130yescomplemented
42#10623053C22130yescomplemented
43D11×#117C22130yes—
44#10623047C22130yescomplemented
45#10623035C22130yescomplemented
46C2×C4⋊C4×D11C22115yes—
47C2×#66940C22115yescomplemented
48C4×#4339C22130yescomplemented
49C2×C42×D11C22115yes—
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×D11C23110yes—
60C2×Q8×D11C23120yes—
61C2×#4341C23130yes—
62C2×D4×D11C23110yes—
63C2×#4339C23130yes—
64C22×C4×D11C2315yes—
65C22×C4×D11C23115yes—
66C22×C4×D11C23115yes—
67C22×Dic22C23115yes—
68C4×Q8×C11C23110yes—
69C4×Q8×C11C23120yes—
70C4×Q8×C11C23110yes—
71C4×D4×C11C23110yes—
72C4×D4×C11C23130yes—
73C11×#117C23130yes—
74C2×C11×C4⋊C4C23115yes—
75C2×C42×C11C23115yes—
76Q8×Dic11C23110yes—
77Q8×Dic11C23120yes—
78Q8×Dic11C23110yes—
79D4×Dic11C23110yes—
80D4×Dic11C23130yes—
81C4×C22⋊D11C23120yes—
82C4×C22⋊D11C23160yes—
83#66979C23130yes—
84C2×C4⋊Dic11C23115yes—
85C2×Dic11⋊C4C23130yes—
86C2×C4×Dic11C23115yes—
87C2×C4×Dic11C23115yes—
88C2×C4×Dic11C23115yes—
89#66946C23130yes—
90#66946C23110yes—
91#66945C23130yes—
92#66945C23130yes—
93C4⋊C4×D11C23130yes—
94C4⋊C4×D11C23160yes—
95C4⋊C4×D11C23110yes—
96#66940C23130yes—
97#66940C23160yes—
98#66940C23130yes—
99(C22⋊D11)⋊C4C23120yes—
100(C22⋊D11)⋊C4C23160yes—
101C22⋊C4×D11C23120yes—
102#66930C23160yes—
103C4×D44C23110yes—
104C4×D44C23130yes—
105#66925C23160yes—
106C42×D11C23110yes—
107C42×D11C23130yes—
108C42×D11C23130yes—
109C42×D11C23130yes—
110C4×Dic22C23130yes—
111C4×Dic22C23160yes—
112C4×Dic22C23130yes—
113C2×C4×2−1+4—111nomaximal, Sylow
114C23×D11C2415yes—
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×Dic11C24115yes—
126#4343C22×C4180yescomplemented
127Q8×D11C22×C4180yes—
128Q8×D11C22×C41160yescomplemented
129#4341C22×C41240yescomplemented
130D4×D11C22×C4180yes—
131#4339C22×C41240yescomplemented
132C2×D44C24110yes—
133C2×C4×D11—220no—
134C2×C4×D11—430no—
135C2×C4×D11C22×C41120yes—
136C2×C4×D11C2415yes—
137C2×C4×D11C2415yes—
138C2×C4×D11C2415yes—
139C2×C4×D11C24110yes—
140C2×C4×D11C24130yes—
141C2×C4×D11C24110yes—
142C2×C4×D11C24130yes—
143C2×C4×D11C2411yescharacteristic
144C2×Dic22C22×C41120yescomplemented
145C2×Dic22C24130yes—
146C11×C4⋊C4C24130yes—
147C11×C4⋊C4C24110yes—
148C11×C22⋊C4C24120yes—
149C42×C11C24110yes—
150C42×C11C24130yes—
151C22⋊Dic11C24120yes—
152(C2×D11)⋊C4C24120yes—
153(C2×D11)⋊C4C24120yes—
154C4⋊Dic11C24130yes—
155C4⋊Dic11C24110yes—
156Dic11⋊C4C24120yes—
157Dic11⋊C4C24160yes—
158C4×Dic11C24110yes—
159C4×Dic11C24130yes—
160C4×Dic11C24130yes—
161C4×Dic11C24110yes—
162C4×Dic11C24110yes—
163C4×Dic11C24130yes—
164C22×2−1+4—111no—
165C4×2−1+4—111no—
166C4×2−1+4—1110no—
167C4×2−1+4—115no—
168C4×2−1+4—1110no—
169C4×2−1+4—115no—
170C4×2−1+4D1111yescharacteristic, direct product factor
171C2×#520—1110no—
172C2×#519—115no—
173C2×C4×#41—1110no—
174C22×C4×Q8—115no—
175C23×C11C2515yes—
176C22×D11—210no—
177C22×D11—210no—
178C22×D11C23×C4120yes—
179C22×D11C2515yes—
180C22×D11C2511yescharacteristic
181Q8×C11C23×C4140yes—
182D4×C11C23×C4140yes—
183C2×C4×C11—210no—
184C2×C4×C11—415no—
185C2×C4×C11C23×C4160yes—
186C2×C4×C11C2515yes—
187C2×C4×C11C25110yes—
188C2×C4×C11C25110yes—
189C2×C4×C11C2511yescharacteristic
190C22⋊D11C23×C4180yes—
191C2×Dic11—210no—
192C2×Dic11—415no—
193C2×Dic11C23×C4160yes—
194C2×Dic11C2515yes—
195C2×Dic11C25110yes—
196C2×Dic11C25110yes—
197C2×Dic11C2511yescharacteristic
198D44C23×C4140yes—
199C4×D11—210no—
200C4×D11—220no—
201C4×D11—210no—
202C4×D11—210no—
203C4×D11—430no—
204C4×D11C23×C4140yes—
205C4×D11C23×C41120yes—
206C4×D112−1+414yesdirect product factor
207Dic22C23×C41120yes—
208C2×2−1+4—1132no—
209C2×2−1+4—1110no—
210C2×2−1+4—115no—
211C2×2−1+4C2×D1111yescharacteristic
212C22×#41—1110no—
213C23×Q8—115no—
214#520—1110no—
215#520—1120no—
216#520—1160no—
217#520—1130no—
218#520—1130no—
219#520C2×D11110yescomplemented
220#519—115no—
221#519—1120no—
222#519—1120no—
223#519—1130no—
224#519C2×D1115yescomplemented
225C4×#41—1110no—
226C4×#41—1110no—
227C4×#41—1110no—
228C4×#41—1130no—
229C4×#41—1130no—
230C4×#41—1130no—
231C4×#41—1130no—
232C4×#41C2×D11110yescomplemented
233C2×C4×Q8—115no—
234C2×C4×Q8—1110no—
235C2×C4×Q8—1120no—
236C2×C4×Q8—1120no—
237C2×C4×Q8—1120no—
238C2×C4×Q8—1110no—
239C2×C4×Q8—1115no—
240C2×C4×Q8—1115no—
241C2×C4×Q8C2×D1115yescomplemented
242C2×C4×D4—1110no—
243C2×C4×D4—1130no—
244C2×#117—1130no—
245C22×C4⋊C4—1115no—
246C22×C42—1115no—
247C22×C11—25no—
248C22×C11—25no—
249C22×C11C24×C4110yes—
250C22×C11C2611yescharacteristic
251C2×D11—25no—
252C2×D11—25no—
253C2×D11—240no—
254C2×D11C24×C4110yes—
255C2×D11C24×C412yes—
256C2×D11C2×2−1+412yes—
257C2×D11#58512yes—
258C4×C11—25no—
259C4×C11—210no—
260C4×C11C24×C4120yes—
261C4×C11C2×2−1+412yescomplemented
262Dic11—25no—
263Dic11—210no—
264Dic11C24×C4120yes—
265Dic11C2×2−1+412yescomplemented
2662−1+4—11160no—
2672−1+4—1180no—
2682−1+4C4×D11116yesdirect product factor
269C2×#41—11160no—
270C2×#41—1110no—
271C2×#41—1130no—
272C2×#41—1130no—
273C2×#41C22×D11110yes—
274C22×Q8—1180no—
275C22×Q8—1110no—
276C22×Q8—1120no—
277C22×Q8—1115no—
278C22×Q8C22×D1115yes—
279C22×D4—1110no—
280C23×C4—1115no—
281C23×C4—115no—
282C23×C4—1115no—
283C4×Q8—1110no—
284C4×Q8—1120no—
285C4×Q8—1110no—
286C4×Q8—1130no—
287C4×Q8—1160no—
288C4×Q8—1130no—
289C4×Q8—1130no—
290C4×Q8—1160no—
291C4×Q8—1130no—
292C4×Q8C22×D11110yes—
293C4×Q8C22×D11120yes—
294C4×Q8C22×D11110yes—
295C4×D4—1110no—
296C4×D4—1130no—
297C4×D4—1120no—
298C4×D4—1160no—
299C4×D4—1110no—
300C4×D4—1130no—
301C4×D4—1120no—
302C4×D4—1160no—
303C4×D4—1110no—
304C4×D4—1130no—
305C4×D4C22×D11110yes—
306C4×D4C22×D11130yes—
307#117—1130no—
308#117—1130no—
309#117—1130no—
310#117—1160no—
311#117—1160no—
312#117C22×D11130yes—
313C2×C4⋊C4—1130no—
314C2×C4⋊C4—1115no—
315C2×C4⋊C4—1130no—
316C2×C4⋊C4—1160no—
317C2×C4⋊C4—1110no—
318C2×C4⋊C4C22×D11115yes—
319C2×C22⋊C4—1120no—
320C2×C42—1115no—
321C2×C42—1115no—
322C2×C42—1115no—
323C2×C42—1130no—
324C2×C42—1110no—
325C2×C42—1130no—
326C2×C42—1130no—
327C2×C42C22×D11115yes—
328C2×C11—210no—
329C2×C11C25×C411yescharacteristic
330C2×C11C22×2−1+411yescharacteristic
331C2×C11C2×#58511yescharacteristic
332D11—210no—
333D11C4×2−1+414yesdirect product factor
334C24—115no—
335#41—1180no—
336#41—11240no—
337#41—11240no—
338#41C2×C4×D11180yescomplemented
339C2×Q8—1180no—
340C2×Q8—11160no—
341C2×Q8—11120no—
342C2×Q8—1130no—
343C2×Q8C2×C4×D11140yescomplemented
344C2×Q8C23×D11110yes—
345C2×D4—1120no—
346C2×D4—1180no—
347C2×D4—1110no—
348C2×D4C23×D11110yes—
349C22×C4—1115no—
350C22×C4—11120no—
351C22×C4—1110no—
352C22×C4—1130no—
353C22×C4—111no—
354C22×C4—115no—
355C22×C4—1115no—
356C22×C4—115no—
357C22×C4—115no—
358C22×C4—1110no—
359C22×C4—115no—
360C22×C4—1130no—
361C22×C4—2220no—
362C22×C4—4430no—
363C22×C4C23×D1115yes—
364C22×C4C23×D11115yes—
365C22×C4C23×D11115yes—
366C4⋊C4—1160no—
367C4⋊C4—1130no—
368C4⋊C4—1120no—
369C4⋊C4—1110no—
370C4⋊C4C23×D11130yes—
371C4⋊C4C23×D11110yes—
372C22⋊C4—1120no—
373C22⋊C4—1120no—
374C22⋊C4—1120no—
375C22⋊C4C23×D11120yes—
376C42—1110no—
377C42—1110no—
378C42—1130no—
379C42—1130no—
380C42—1130no—
381C42—1110no—
382C42C23×D11130yes—
383C42C23×D11110yes—
384C11C2×C4×2−1+411yescharacteristic, complemented, Sylow
385C23—111no—
386C23—1120no—
387C23—115no—
388C23—2210no—
389C23—2210no—
390C23C24×D1115yes—
391Q8—11120no—
392Q8C22×C4×D11140yes—
393D4—1180no—
394D4—1140no—
395D4C22×C4×D11140yes—
396C2×C4—210no—
397C2×C4—415no—
398C2×C4—1160no—
399C2×C4—111no—
400C2×C4—1110no—
401C2×C4—1140no—
402C2×C4—11120no—
403C2×C4—114no—
404C2×C4—115no—
405C2×C4—1110no—
406C2×C4—2210no—
407C2×C4—2210no—
408C2×C4—2220no—
409C2×C4—2210no—
410C2×C4—2210no—
411C2×C4—4430no—
412C2×C4—4415no—
413C2×C4C22×C4×D11160yes—
414C2×C4C24×D1115yes—
415C2×C4C24×D11110yes—
416C2×C4C24×D11110yes—
417C2×C4C24×D1111yescharacteristic
418C22—25no—
419C22—25no—
420C22—112no—
421C22—112no—
422C22—112no—
423C22—1110no—
424C22—2240no—
425C22—225no—
426C22—225no—
427C22C23×C4×D11110yes—
428C22C25×D1111yescharacteristic
429C4—25no—
430C4—210no—
431C4—1120no—
432C4—112no—
433C4—225no—
434C4—2210no—
435C4C23×C4×D11120yes—
436C4D11×2−1+412yesdirect product factor
437C2—210no—
438C2—114no—
439C2—2210no—
440C2C24×C4×D1111yescharacteristic
441C2C2×D11×2−1+411yescharacteristic
442C2D11×#58511yescharacteristic
subgroupG/H
centerC2×C4C24×D11
commutatorC2×C11C25×C4
FrattiniC22C25×D11
FittingC4×C11×2−1+4C2
socle, cosocleC22×C11C26
prime radicalC2×D11×2−1+4C2
hypercenterC4×2−1+4D11
hypocenterC11C2×C4×2−1+4
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ 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. D11×#520C2semidirect
8. D11×#519C2semidirect
9. C4×#41×D11C2semidirect
10. C2×C4×Q8×D11C2semidirect
11. C4×C11×2−1+4C2semidirect
13. D11×2−1+4C4direct (N × H)
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. C4×#4343C22semidirect
28. C4×#4343C22semidirect
29. #10623103C22semidirect
30. #10623103C22semidirect
34. C4×Q8×D11C22semidirect
35. C4×Q8×D11C22semidirect
36. #10623077C22semidirect
39. C4×#4341C22semidirect
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
115. C11×#41C22×C4semidirect
116. C2×Q8×C11C22×C4semidirect
126. #4343C22×C4semidirect
128. Q8×D11C22×C4semidirect
129. #4341C22×C4semidirect
131. #4339C22×C4semidirect
144. C2×Dic22C22×C4semidirect
170. C4×2−1+4D11direct (N × H)
206. C4×D112−1+4direct (N × H)
219. #520C2×D11semidirect
224. #519C2×D11semidirect
232. C4×#41C2×D11semidirect
241. C2×C4×Q8C2×D11semidirect
261. C4×C11C2×2−1+4semidirect
265. Dic11C2×2−1+4semidirect
268. 2−1+4C4×D11direct (N × H)
333. D11C4×2−1+4direct (N × H)
338. #41C2×C4×D11semidirect
343. C2×Q8C2×C4×D11semidirect
384. C11C2×C4×2−1+4semidirect
436. C4D11×2−1+4direct (N × H)

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
D11×#5202
D11×#5192
C4×#41×D112
C2×C4×Q8×D112
C4×C11×2−1+42
C2×C4×2−1+411