Finite Group Databasebeta

← D11×#1988 #14758273

Subgroups — D11×#1988 #14758273

Order 2816.

1510 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×C4⋊Q8C211yesmaximal, characteristic
2C2×D11×C4⋊C8C211yesmaximal, characteristic
3C4×C4⋊C4×D11C211yesmaximal, characteristic
4#13069569C211yesmaximal, characteristic, complemented
5#13069568C211yesmaximal, characteristic, complemented
6#13069567C211yesmaximal, characteristic, complemented
7#13069566C214yesmaximal, complemented
8D11×#340C214yesmaximal
9C11×#1988C211yesmaximal, characteristic, complemented
10C22×Q8×D11—21no—
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×#66997—21no—
13C22×C8×D11C2212yes—
14D11×C4⋊Q8—24no—
15D11×C4⋊Q8C418yescomplemented
16C2×C4⋊C4×D11—21no—
17C2×C4⋊C4×D11C2212yes—
18C2×C4⋊C4×D11C2212yes—
19C2×#66941—21no—
20C2×#66941C2212yes—
21C2×C42×D11—21no—
22C2×C42×D11C2211yescharacteristic
23C2×#66922C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C4×C11×C4⋊C4C2211yescharacteristic
26C2×Dic11⋊C8C2212yes—
27C4⋊C4×Dic11C2212yes—
28C4×C4⋊Dic11C2211yescharacteristic
29C4×Dic11⋊C4—21no—
30C2×C4⋊(C11⋊C8)C2211yescharacteristic
31D11×C4⋊C8—24no—
32D11×#95—21no—
33#10622262—21no—
34C11×#340C2214yes—
35#10622189C2214yes—
36#10622167C2214yes—
37#10622167C2214yes—
38C22×Q8×C11—21no—
39C2×Q8×D11—28no—
40C2×Q8×D11—44no—
41C2×Q8×D11—44no—
42C22×C4×D11—22no—
43C22×C4×D11—22no—
44C22×C4×D11D411yescharacteristic
45C22×C4×D11D411yescharacteristic
46C22×C4×D11C2311yescharacteristic
47C22×Dic22—21no—
48C22×Dic22—22no—
49C22×C8×C11C2312yes—
50C11×C4⋊Q8—22no—
51C11×C4⋊Q8C2×C414yescomplemented
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4C2312yes—
54C2×C11×C4⋊C4C2312yes—
55C2×C42×C11—21no—
56C2×C42×C11C2311yescharacteristic
57#66997—28no—
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11C2312yes—
60C2×C4⋊Dic11C2312yes—
61C2×Dic11⋊C4—22no—
62C2×Dic11⋊C4—22no—
63C2×Dic11⋊C4—22no—
64C2×C4×Dic11—21no—
65C2×C4×Dic11—22no—
66C2×C4×Dic11D411yescharacteristic
67C2×C4×Dic11D411yescharacteristic
68C2×C4×Dic11C2311yescharacteristic
69C22×C11⋊C8C2312yes—
70C2×C8×D11—24no—
71C2×C8×D11—28no—
72C4⋊C4×D11—28no—
73C4⋊C4×D11—24no—
74C4⋊C4×D11—24no—
75C4⋊C4×D11C2×C418yes—
76C4⋊C4×D11Q818yescomplemented
77#66941—28no—
78#66941—24no—
79#66941C2×C418yescomplemented
80C42×D11—44no—
81C42×D11C2×C414yes—
82C42×D11D414yes—
83#66922—22no—
84#66922C2×C414yescomplemented
85C11×C4⋊C8—22no—
86C11×#95—21no—
87C11⋊#95—21no—
88C11⋊#95—22no—
89Dic11⋊C8—24no—
90C4⋊(C11⋊C8)—22no—
91C2×#1988—111nomaximal, Sylow
92C23×D11C2×D411yescharacteristic
93C2×Q8×C11—24no—
94C2×Q8×C11—42no—
95C2×Q8×C11—42no—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2411yescharacteristic
101C22×Dic11—22no—
102C22×Dic11—22no—
103C22×Dic11C2×D411yescharacteristic
104C22×Dic11C2×D411yescharacteristic
105C22×Dic11C2×D411yescharacteristic
106Q8×D11—432no—
107C2×C4×D11—28no—
108C2×C4×D11—28no—
109C2×C4×D11—24no—
110C2×C4×D11—44no—
111C2×C4×D11—44no—
112C2×C4×D11—44no—
113C2×C4×D11—44no—
114C2×C4×D11C22⋊C414yes—
115C2×C4×D11C22⋊C414yes—
116C2×C4×D11D814yes—
117C2×C4×D11SD1614yes—
118C2×C4×D11C22×C412yes—
119C2×C4×D11C2×D412yes—
120C2×C4×D11C2×Q814yes—
121C2×C4×D11#4114yes—
122C2×Dic22—28no—
123C2×Dic22—24no—
124C2×Dic22—44no—
125C2×Dic22—44no—
126C2×Dic22—42no—
127C2×Dic22—42no—
128C2×C8×C11—22no—
129C2×C8×C11—24no—
130C11×C4⋊C4—24no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4C22×C414yes—
134C11×C4⋊C4C2×Q814yescomplemented
135C42×C11—42no—
136C42×C11C22×C412yes—
137C42×C11C2×D412yes—
138C4⋊Dic11—24no—
139C4⋊Dic11—22no—
140C4⋊Dic11—22no—
141C4⋊Dic11C22×C414yes—
142C4⋊Dic11C2×Q814yescomplemented
143Dic11⋊C4—28no—
144Dic11⋊C4—28no—
145Dic11⋊C4—28no—
146C4×Dic11—44no—
147C4×Dic11—42no—
148C4×Dic11C22⋊C414yes—
149C4×Dic11C22⋊C414yes—
150C4×Dic11C22×C412yes—
151C4×Dic11C2×D412yes—
152C2×C11⋊C8—22no—
153C2×C11⋊C8—24no—
154C8×D11—48no—
155C22×C4⋊Q8—111no—
156C22×C4⋊C8—111no—
157C2×C4×C4⋊C4—111no—
158#1988—111no—
159#1988—111no—
160#1988—114no—
161#1988—111no—
162#1988D1111yescharacteristic, direct product factor
163C2×#340—114no—
164C23×C11C22×D411yescharacteristic
165C22×D11C2×C22⋊C412yes—
166C22×D11C22⋊Q814yes—
167C22×D11C2×D812yes—
168C22×D11C2×SD1612yes—
169C22×D11#13714yes—
170Q8×C11—48no—
171C2×C4×C11—22no—
172C2×C4×C11—24no—
173C2×C4×C11—24no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11C2×C22⋊C412yes—
179C2×C4×C11C2×C22⋊C412yes—
180C2×C4×C11C2×D812yes—
181C2×C4×C11C2×SD1612yes—
182C2×C4×C11C23×C411yescharacteristic
183C2×C4×C11C22×D411yescharacteristic
184C2×C4×C11C22×Q812yes—
185C2×C4×C11C2×#4112yes—
186C2×Dic11—22no—
187C2×Dic11—24no—
188C2×Dic11—24no—
189C2×Dic11—42no—
190C2×Dic11—42no—
191C2×Dic11—42no—
192C2×Dic11—42no—
193C2×Dic11C2×C22⋊C412yes—
194C2×Dic11C2×C22⋊C412yes—
195C2×Dic11C2×C22⋊C412yes—
196C2×Dic11C22⋊Q814yes—
197C2×Dic11C2×D812yes—
198C2×Dic11C2×SD1612yes—
199C4×D11—28no—
200C4×D11—416no—
201C4×D11—416no—
202C4×D11#102116yes—
203C4×D11C4×Q818yes—
204C4×D11#12414yes—
205C4×D11C4⋊Q814yes—
206Dic22—48no—
207Dic22—416no—
208C8×C11—42no—
209C11⋊C8—42no—
210C23×Q8—221no—
211C23×C8—112no—
212C2×C4⋊Q8—118no—
213C2×C4⋊Q8—112no—
214C2×C4⋊Q8—111no—
215C2×C4⋊Q8—221no—
216C2×C4⋊Q8—224no—
217C2×C4⋊Q8—221no—
218C2×C4⋊Q8C2×D1111yescharacteristic
219C22×C4⋊C4—112no—
220C22×C4⋊C4—112no—
221C22×C4⋊C4—221no—
222C22×C42—111no—
223C22×C42—221no—
224C2×C4⋊C8—112no—
225C2×C4⋊C8—111no—
226C2×C4⋊C8—224no—
227C2×C4⋊C8C2×D1111yescharacteristic
228C4×C4⋊C4—112no—
229C4×C4⋊C4—111no—
230C4×C4⋊C4—221no—
231C4×C4⋊C4—221no—
232C4×C4⋊C4C2×D1111yescharacteristic
233C2×#95—221no—
234#340—114no—
235#340—114no—
236#340—114no—
237#340C2×D1114yes—
238C22×C11C22×C22⋊C411yescharacteristic
239C22×C11C2×C22⋊Q812yes—
240C22×C11C22×D811yescharacteristic
241C22×C11C22×SD1611yescharacteristic
242C22×C11C2×#13712yes—
243C2×D11#39114yes—
244C2×D11C2×#10214yes—
245C2×D11#41914yes—
246C2×D11#47418yes—
247C2×D11#47518yes—
248C4×C11—22no—
249C4×C11—44no—
250C4×C11—44no—
251C4×C11C2×#10214yes—
252C4×C11C2×C4×Q812yes—
253C4×C11C2×#12411yescharacteristic
254C4×C11C2×C4⋊Q811yescharacteristic
255Dic11—22no—
256Dic11—44no—
257Dic11—44no—
258Dic11#39114yes—
259Dic11C2×#10214yes—
260C22×Q8—21no—
261C22×Q8—222no—
262C22×Q8—228no—
263C22×Q8—221no—
264C22×Q8—444no—
265C22×Q8—444no—
266C23×C4—111no—
267C23×C4—111no—
268C23×C4—111no—
269C23×C4—222no—
270C23×C4—222no—
271C22×C8—112no—
272C22×C8—228no—
273C22×C8—224no—
274C22×C8C22×D1112yes—
275C4⋊Q8—22no—
276C4⋊Q8—118no—
277C4⋊Q8—114no—
278C4⋊Q8—228no—
279C4⋊Q8—224no—
280C4⋊Q8—228no—
281C4⋊Q8—222no—
282C4⋊Q8C4×D1114yescomplemented
283C2×C4⋊C4—21no—
284C2×C4⋊C4—112no—
285C2×C4⋊C4—112no—
286C2×C4⋊C4—118no—
287C2×C4⋊C4—118no—
288C2×C4⋊C4—224no—
289C2×C4⋊C4—224no—
290C2×C4⋊C4—228no—
291C2×C4⋊C4—222no—
292C2×C4⋊C4—222no—
293C2×C4⋊C4—222no—
294C2×C4⋊C4—221no—
295C2×C4⋊C4C22×D1112yes—
296C2×C4⋊C4C22×D1112yes—
297C2×C42—21no—
298C2×C42—111no—
299C2×C42—111no—
300C2×C42—111no—
301C2×C42—114no—
302C2×C42—114no—
303C2×C42—222no—
304C2×C42—221no—
305C2×C42—444no—
306C2×C42C22×D1111yescharacteristic
307C4⋊C8—22no—
308C4⋊C8—224no—
309C4⋊C8—222no—
310#95—21no—
311#95—222no—
312#95—221no—
313C2×C11C2×#39111yescharacteristic
314C2×C11C22×#10211yescharacteristic
315C2×C11C2×#41911yescharacteristic
316C2×C11C2×#47412yes—
317C2×C11C2×#47512yes—
318D11#198818yesdirect product factor
319C24—111no—
320C2×Q8—24no—
321C2×Q8—42no—
322C2×Q8—42no—
323C2×Q8—228no—
324C2×Q8—224no—
325C2×Q8—444no—
326C2×Q8—444no—
327C2×Q8—4432no—
328C2×Q8—442no—
329C2×Q8—442no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—111no—
333C22×C4—111no—
334C22×C4—114no—
335C22×C4—114no—
336C22×C4—114no—
337C22×C4—112no—
338C22×C4—112no—
339C22×C4—114no—
340C22×C4—114no—
341C22×C4—111no—
342C22×C4—114no—
343C22×C4—224no—
344C22×C4—228no—
345C22×C4—228no—
346C22×C4—222no—
347C22×C4—222no—
348C22×C4—444no—
349C22×C4—444no—
350C22×C4—444no—
351C22×C4—444no—
352C22×C4D4×D1111yescharacteristic
353C22×C4D4×D1111yescharacteristic
354C22×C4C23×D1111yescharacteristic
355C2×C8—22no—
356C2×C8—24no—
357C2×C8—222no—
358C2×C8—224no—
359C2×C8—448no—
360C4⋊C4—24no—
361C4⋊C4—22no—
362C4⋊C4—22no—
363C4⋊C4—114no—
364C4⋊C4—114no—
365C4⋊C4—228no—
366C4⋊C4—228no—
367C4⋊C4—228no—
368C4⋊C4—224no—
369C4⋊C4—222no—
370C4⋊C4—222no—
371C4⋊C4C2×C4×D1114yes—
372C4⋊C4Q8×D1114yescomplemented
373C42—42no—
374C42—114no—
375C42—114no—
376C42—112no—
377C42—112no—
378C42—444no—
379C42—442no—
380C42C2×C4×D1112yes—
381C42D4×D1112yes—
382C11C2×#198811yescharacteristic, complemented, Sylow
383C23—112no—
384C23—112no—
385C23—112no—
386C23—114no—
387C23—114no—
388C23C2×D4×D1111yescharacteristic
389Q8—48no—
390Q8—4416no—
391Q8—448no—
392C2×C4—22no—
393C2×C4—24no—
394C2×C4—24no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—112no—
400C2×C4—112no—
401C2×C4—112no—
402C2×C4—112no—
403C2×C4—114no—
404C2×C4—114no—
405C2×C4—118no—
406C2×C4—1116no—
407C2×C4—114no—
408C2×C4—112no—
409C2×C4—228no—
410C2×C4—222no—
411C2×C4—224no—
412C2×C4—224no—
413C2×C4—4416no—
414C2×C4—4416no—
415C2×C4—442no—
416C2×C4—442no—
417C2×C4—442no—
418C2×C4—442no—
419C2×C4C22⋊C4×D1112yes—
420C2×C4C22⋊C4×D1112yes—
421C2×C4D8×D1112yes—
422C2×C4SD16×D1112yes—
423C2×C4C22×C4×D1111yescharacteristic
424C2×C4C2×D4×D1111yescharacteristic
425C2×C4C2×Q8×D1112yes—
426C2×C4#41×D1112yes—
427C8—42no—
428C8—442no—
429C22—118no—
430C22—118no—
431C22—114no—
432C22—114no—
433C22—114no—
434C22C2×C22⋊C4×D1111yescharacteristic
435C22D11×C22⋊Q812yes—
436C22C2×D8×D1111yescharacteristic
437C22C2×SD16×D1111yescharacteristic
438C22D11×#13712yes—
439C4—22no—
440C4—44no—
441C4—44no—
442C4—114no—
443C4—114no—
444C4—222no—
445C4—444no—
446C4—444no—
447C4D11×#10214yes—
448C4C4×Q8×D1112yes—
449C4D11×#12411yescharacteristic
450C4D11×C4⋊Q811yescharacteristic
451C2—118no—
452C2D11×#39111yescharacteristic
453C2C2×D11×#10211yescharacteristic
454C2D11×#41911yescharacteristic
455C2D11×#47412yes—
456C2D11×#47512yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1988C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1988D11
hypocenterC11C2×#1988
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1988

Complements

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

NH ≅ G/Ntype
4. #13069569C2semidirect
5. #13069568C2semidirect
6. #13069567C2semidirect
7. #13069566C2semidirect
9. C11×#1988C2semidirect
15. D11×C4⋊Q8C4semidirect
51. C11×C4⋊Q8C2×C4semidirect
76. C4⋊C4×D11Q8semidirect
79. #66941C2×C4semidirect
84. #66922C2×C4semidirect
134. C11×C4⋊C4C2×Q8semidirect
142. C4⋊Dic11C2×Q8semidirect
162. #1988D11direct (N × H)
282. C4⋊Q8C4×D11semidirect
318. D11#1988direct (N × H)
372. C4⋊C4Q8×D11semidirect
382. C11C2×#1988semidirect

Maximal subgroups

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

subgroupindex
C2×D11×C4⋊Q82
C2×D11×C4⋊C82
C4×C4⋊C4×D112
#130695692
#130695682
#130695672
#130695662
D11×#3402
C11×#19882
C2×#198811