Finite Group Databasebeta

← D11×#2330 #14912598

Subgroups — D11×#2330 #14912598

Order 2816.

2398 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#125C211yesmaximal, characteristic
2#13071358C211yesmaximal, characteristic, complemented
3#13071357C211yesmaximal, characteristic, complemented
4#13071356C212yesmaximal, complemented
5#13071355C211yesmaximal, characteristic, complemented
6#13071354C214yesmaximal, complemented
7#13071353C212yesmaximal, complemented
8#13071352C214yesmaximal, complemented
9D11×#389C212yesmaximal
10D11×#389C214yesmaximal
11D11×#387C214yesmaximal
12D11×#384C211yesmaximal, characteristic
13C4×C4⋊C4×D11C212yesmaximal
14D11×#376C211yesmaximal, characteristic
15C11×#2330C211yesmaximal, characteristic, complemented
16C2×C11×#125C2211yescharacteristic
17D11×#125C4116yescomplemented
18C2×C4⋊C4×D11C2212yes—
19C2×C4⋊C4×D11C2214yes—
20C2×C4⋊C4×D11C2214yes—
21C2×C4⋊C4×D11C2212yes—
22C2×C4⋊C4×D11C2214yes—
23C2×#66943C2212yes—
24C2×#66942C2214yes—
25C2×C42×D11C2211yescharacteristic
26C2×C42×D11C2214yes—
27C2×C42×D11C2211yescharacteristic
28C2×C42×D11C2211yescharacteristic
29C2×#66923C2211yescharacteristic
30C11×#389C2214yes—
31C11×#389C2212yes—
32C11×#387C2214yes—
33C11×#384C2211yescharacteristic
34C4×C11×C4⋊C4C2212yes—
35C11×#376C2211yescharacteristic
36#10622598C2214yes—
37#10622598C2212yes—
38#10622594C2214yes—
39#10622591C2214yes—
40#10622589C2214yes—
41#10622589C2212yes—
42C4⋊C4×Dic11C2212yes—
43C4⋊C4×Dic11C2212yes—
44#10622586C2212yes—
45#10622586C2214yes—
46#10622585C2214yes—
47#10622585C2214yes—
48#10622585C2214yes—
49#10622548C2211yescharacteristic
50C4×C4⋊Dic11C2212yes—
51#10622546C2214yes—
52#10622545C2211yescharacteristic
53#10622545C2211yescharacteristic
54#10622545C2211yescharacteristic
55C4×Dic11⋊C4C2214yes—
56#10622541C2214yes—
57#10622541C2212yes—
58D11×#95C2212yes—
59D11×#95C2212yes—
60D11×#95C2214yes—
61D11×#95C2214yes—
62#10622268C2214yes—
63#10622267C2214yes—
64#10622266C2214yes—
65#10622265C2214yes—
66#10622262C2214yes—
67#10622261C2212yes—
68#10622261C2212yes—
69#10622260C2214yes—
70#10622260C2214yes—
71#10622260C2214yes—
72C22×C4×D11C2311yescharacteristic
73C22×C4×D11C2314yes—
74C22×C4×D11C2311yescharacteristic
75C22×C4×D11C2314yes—
76C22×C4×D11C2312yes—
77C22×C4×D11C2312yes—
78C22×C4×D11C2311yescharacteristic
79C11×#125C2×C418yescomplemented
80C2×C11×C4⋊C4C2312yes—
81C2×C11×C4⋊C4C2314yes—
82C2×C11×C4⋊C4C2314yes—
83C2×C11×C4⋊C4C2314yes—
84C2×C11×C4⋊C4C2312yes—
85C2×C42×C11C2311yescharacteristic
86C2×C42×C11C2314yes—
87C2×C42×C11C2311yescharacteristic
88C2×C42×C11C2311yescharacteristic
89C2×C4⋊Dic11C2312yes—
90C2×C4⋊Dic11C2314yes—
91C2×C4⋊Dic11C2314yes—
92C2×C4⋊Dic11C2312yes—
93C2×C4⋊Dic11C2314yes—
94C2×Dic11⋊C4C2314yes—
95C2×Dic11⋊C4C2314yes—
96C2×Dic11⋊C4C2314yes—
97C2×Dic11⋊C4C2314yes—
98C2×Dic11⋊C4C2314yes—
99C2×Dic11⋊C4C2314yes—
100C2×Dic11⋊C4C2314yes—
101C2×Dic11⋊C4C2314yes—
102C2×C4×Dic11C2311yescharacteristic
103C2×C4×Dic11C2311yescharacteristic
104C2×C4×Dic11C2311yescharacteristic
105C2×C4×Dic11C2314yes—
106C2×C4×Dic11C2314yes—
107C2×C4×Dic11C2314yes—
108C2×C4×Dic11C2312yes—
109C2×C4×Dic11C2311yescharacteristic
110C2×C4×Dic11C2312yes—
111C2×C4×Dic11C2311yescharacteristic
112C4⋊C4×D11—28no—
113C4⋊C4×D11—48no—
114C4⋊C4×D11—48no—
115C4⋊C4×D11C2×C4132yes—
116C4⋊C4×D11C2×C4116yes—
117#66943C2×C4116yescomplemented
118#66942C2×C4132yescomplemented
119C42×D11—24no—
120C42×D11—48no—
121C42×D11C2×C418yes—
122C42×D11Q818yes—
123#66923C2×C418yescomplemented
124C11×#95C2312yes—
125C11×#95C2314yes—
126C11×#95C2314yes—
127C11×#95C2312yes—
128C11⋊#95C2312yes—
129C11⋊#95C2314yes—
130C11⋊#95C2314yes—
131C11⋊#95C2312yes—
132C11⋊#95C2312yes—
133C11⋊#95C2312yes—
134C11⋊#95C2312yes—
135C11⋊#95C2312yes—
136C11⋊#95C2314yes—
137C11⋊#95C2314yes—
138C11⋊#95C2314yes—
139C11⋊#95C2314yes—
140C2×#2330—111nomaximal, Sylow
141C23×D11C2411yescharacteristic
142C22×C4×C11C2411yescharacteristic
143C22×C4×C11C2411yescharacteristic
144C22×C4×C11C2414yes—
145C22×C4×C11C2414yes—
146C22×C4×C11C2412yes—
147C22×C4×C11C2412yes—
148C22×C4×C11C2411yescharacteristic
149C22×Dic11C2411yescharacteristic
150C22×Dic11C2411yescharacteristic
151C22×Dic11C2414yes—
152C22×Dic11C2414yes—
153C22×Dic11C2412yes—
154C22×Dic11C2412yes—
155C22×Dic11C2411yescharacteristic
156C2×C4×D11—22no—
157C2×C4×D11—22no—
158C2×C4×D11—28no—
159C2×C4×D11—24no—
160C2×C4×D11—28no—
161C2×C4×D11—24no—
162C2×C4×D11—28no—
163C2×C4×D11—24no—
164C2×C4×D11—28no—
165C2×C4×D11—28no—
166C2×C4×D11—24no—
167C2×C4×D11—24no—
168C2×C4×D11—24no—
169C2×C4×D11C22×C418yes—
170C2×C4×D11C22×C4116yes—
171C2×C4×D11C22×C414yes—
172C2×C4×D11C2×Q818yes—
173C2×C4×D11C2×Q814yes—
174C2×C4×D11#4114yes—
175C11×C4⋊C4—24no—
176C11×C4⋊C4—44no—
177C11×C4⋊C4—44no—
178C11×C4⋊C4C22×C4116yes—
179C11×C4⋊C4C22×C418yes—
180C42×C11—22no—
181C42×C11—44no—
182C42×C11C22×C414yes—
183C42×C11C2×Q814yes—
184C4⋊Dic11—24no—
185C4⋊Dic11—44no—
186C4⋊Dic11—44no—
187C4⋊Dic11C22×C418yes—
188C4⋊Dic11C22×C4116yes—
189Dic11⋊C4—28no—
190Dic11⋊C4—44no—
191Dic11⋊C4—44no—
192Dic11⋊C4—44no—
193Dic11⋊C4—44no—
194Dic11⋊C4C22×C4116yes—
195Dic11⋊C4C22×C4116yes—
196Dic11⋊C4C22×C4116yes—
197C4×Dic11—22no—
198C4×Dic11—22no—
199C4×Dic11—22no—
200C4×Dic11—44no—
201C4×Dic11—44no—
202C4×Dic11—44no—
203C4×Dic11C22×C418yes—
204C4×Dic11C22×C414yes—
205C4×Dic11C2×Q818yes—
206C4×Dic11C2×Q814yes—
207C22×#125—111no—
208#2330—114no—
209#2330—112no—
210#2330—114no—
211#2330—111no—
212#2330—112no—
213#2330—111no—
214#2330—111no—
215#2330D1111yescharacteristic, direct product factor
216C2×#389—112no—
217C2×#389—114no—
218C2×#387—114no—
219C2×#384—111no—
220C2×C4×C4⋊C4—112no—
221C2×#376—111no—
222C23×C11C2511yescharacteristic
223C22×D11C23×C412yes—
224C22×D11C22×Q812yes—
225C22×D11C2×#4112yes—
226C22×D11H(5,𝔽2)14yes—
227C22×D112−1+414yes—
228C2×C4×C11—22no—
229C2×C4×C11—24no—
230C2×C4×C11—22no—
231C2×C4×C11—24no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—24no—
237C2×C4×C11—24no—
238C2×C4×C11—22no—
239C2×C4×C11—24no—
240C2×C4×C11—22no—
241C2×C4×C11C23×C414yes—
242C2×C4×C11C23×C418yes—
243C2×C4×C11C23×C412yes—
244C2×C4×C11C22×Q814yes—
245C2×C4×C11C22×Q812yes—
246C2×C4×C11C2×#4112yes—
247C2×Dic11—22no—
248C2×Dic11—24no—
249C2×Dic11—22no—
250C2×Dic11—24no—
251C2×Dic11—22no—
252C2×Dic11—22no—
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11—24no—
256C2×Dic11—24no—
257C2×Dic11—22no—
258C2×Dic11—24no—
259C2×Dic11—22no—
260C2×Dic11C23×C414yes—
261C2×Dic11C23×C418yes—
262C2×Dic11C23×C412yes—
263C2×Dic11C22×Q814yes—
264C2×Dic11C22×Q812yes—
265C2×Dic11C2×#4112yes—
266C4×D11—232no—
267C4×D11—216no—
268C4×D11—216no—
269C4×D11—44no—
270C4×D11—416no—
271C4×D11—44no—
272C4×D11C4×Q8116yes—
273C2×#125—1116no—
274C2×#125—114no—
275C2×#125—112no—
276C2×#125—111no—
277C2×#125C2×D1111yescharacteristic
278C22×C4⋊C4—112no—
279C22×C4⋊C4—114no—
280C22×C4⋊C4—112no—
281C22×C4⋊C4—114no—
282C22×C4⋊C4—114no—
283C22×C42—111no—
284C22×C42—111no—
285C22×C42—111no—
286C22×C42—114no—
287#389—114no—
288#389—114no—
289#389—114no—
290#389—114no—
291#389—112no—
292#389—114no—
293#389—112no—
294#389—114no—
295#389—112no—
296#389—114no—
297#389—114no—
298#389—114no—
299#389C2×D1114yes—
300#389C2×D1112yes—
301#387—114no—
302#387—114no—
303#387—114no—
304#387—114no—
305#387—114no—
306#387—114no—
307#387—114no—
308#387C2×D1114yes—
309#384—114no—
310#384—112no—
311#384—111no—
312#384C2×D1111yescharacteristic
313C4×C4⋊C4—112no—
314C4×C4⋊C4—112no—
315C4×C4⋊C4—114no—
316C4×C4⋊C4—112no—
317C4×C4⋊C4—114no—
318C4×C4⋊C4C2×D1112yes—
319#376—111no—
320#376—111no—
321#376—111no—
322#376—112no—
323#376—112no—
324#376C2×D1111yescharacteristic
325C2×#95—112no—
326C2×#95—112no—
327C2×#95—114no—
328C2×#95—114no—
329C22×C11C24×C411yescharacteristic
330C22×C11C23×Q811yescharacteristic
331C22×C11C22×#4111yescharacteristic
332C22×C11C2×H(5,𝔽2)12yes—
333C22×C11C2×2−1+412yes—
334C2×D11C2×C4×Q814yes—
335C2×D11#52018yes—
336C2×D11#54014yes—
337C2×D11#54114yes—
338C2×D11#54418yes—
339C4×C11—28no—
340C4×C11—24no—
341C4×C11—24no—
342C4×C11—41no—
343C4×C11—44no—
344C4×C11—41no—
345C4×C11C2×C4×Q814yes—
346Dic11—28no—
347Dic11—24no—
348Dic11—24no—
349Dic11—41no—
350Dic11—44no—
351Dic11—41no—
352Dic11C2×C4×Q814yes—
353C23×C4—111no—
354C23×C4—112no—
355C23×C4—114no—
356C23×C4—112no—
357C23×C4—111no—
358C23×C4—114no—
359C23×C4—111no—
360#125—1132no—
361#125—1116no—
362#125—118no—
363#125C4×D1118yescomplemented
364C2×C4⋊C4—114no—
365C2×C4⋊C4—112no—
366C2×C4⋊C4—114no—
367C2×C4⋊C4—114no—
368C2×C4⋊C4—114no—
369C2×C4⋊C4—1116no—
370C2×C4⋊C4—1132no—
371C2×C4⋊C4—114no—
372C2×C4⋊C4—112no—
373C2×C4⋊C4—114no—
374C2×C4⋊C4—114no—
375C2×C4⋊C4—114no—
376C2×C4⋊C4—114no—
377C2×C4⋊C4—114no—
378C2×C4⋊C4—114no—
379C2×C4⋊C4—228no—
380C2×C4⋊C4—448no—
381C2×C4⋊C4—448no—
382C2×C4⋊C4C22×D1112yes—
383C2×C4⋊C4C22×D1114yes—
384C2×C4⋊C4C22×D1114yes—
385C2×C4⋊C4C22×D1112yes—
386C2×C4⋊C4C22×D1114yes—
387C2×C42—112no—
388C2×C42—111no—
389C2×C42—112no—
390C2×C42—111no—
391C2×C42—118no—
392C2×C42—118no—
393C2×C42—111no—
394C2×C42—111no—
395C2×C42—111no—
396C2×C42—114no—
397C2×C42—114no—
398C2×C42—114no—
399C2×C42—224no—
400C2×C42—448no—
401C2×C42C22×D1111yescharacteristic
402C2×C42C22×D1114yes—
403C2×C42C22×D1111yescharacteristic
404C2×C42C22×D1111yescharacteristic
405#95—112no—
406#95—112no—
407#95—112no—
408#95—112no—
409#95—112no—
410#95—112no—
411#95—114no—
412#95—114no—
413#95—114no—
414#95—114no—
415#95—114no—
416#95—114no—
417#95C22×D1112yes—
418#95C22×D1112yes—
419#95C22×D1114yes—
420#95C22×D1114yes—
421C2×C11C22×C4×Q811yescharacteristic
422C2×C11C2×#52012yes—
423C2×C11C2×#54011yescharacteristic
424C2×C11C2×#54111yescharacteristic
425C2×C11C2×#54412yes—
426D11#233018yesdirect product factor
427C24—111no—
428C22×C4—111no—
429C22×C4—114no—
430C22×C4—114no—
431C22×C4—114no—
432C22×C4—112no—
433C22×C4—112no—
434C22×C4—114no—
435C22×C4—118no—
436C22×C4—1116no—
437C22×C4—118no—
438C22×C4—111no—
439C22×C4—111no—
440C22×C4—114no—
441C22×C4—224no—
442C22×C4—228no—
443C22×C4—224no—
444C22×C4—224no—
445C22×C4—228no—
446C22×C4—224no—
447C22×C4—222no—
448C22×C4—222no—
449C22×C4—228no—
450C22×C4—228no—
451C22×C4—224no—
452C22×C4—228no—
453C22×C4—224no—
454C22×C4C23×D1111yescharacteristic
455C22×C4C23×D1111yescharacteristic
456C22×C4C23×D1114yes—
457C22×C4C23×D1114yes—
458C22×C4C23×D1112yes—
459C22×C4C23×D1112yes—
460C22×C4C23×D1111yescharacteristic
461C4⋊C4—24no—
462C4⋊C4—44no—
463C4⋊C4—44no—
464C4⋊C4—1116no—
465C4⋊C4—1116no—
466C4⋊C4—1116no—
467C4⋊C4—1116no—
468C4⋊C4—118no—
469C4⋊C4—228no—
470C4⋊C4—224no—
471C4⋊C4—444no—
472C4⋊C4—444no—
473C4⋊C4—444no—
474C4⋊C4—444no—
475C4⋊C4—444no—
476C4⋊C4—444no—
477C4⋊C4C2×C4×D11116yes—
478C4⋊C4C2×C4×D1118yes—
479C42—22no—
480C42—44no—
481C42—118no—
482C42—114no—
483C42—118no—
484C42—114no—
485C42—222no—
486C42—222no—
487C42—222no—
488C42—444no—
489C42—444no—
490C42—444no—
491C42C2×C4×D1114yes—
492C42Q8×D1114yes—
493C11C2×#233011yescharacteristic, complemented, Sylow
494C23—112no—
495C23—112no—
496C23—112no—
497C23—114no—
498C23—114no—
499C23C24×D1111yescharacteristic
500C2×C4—22no—
501C2×C4—24no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—24no—
505C2×C4—22no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—22no—
511C2×C4—24no—
512C2×C4—22no—
513C2×C4—112no—
514C2×C4—112no—
515C2×C4—112no—
516C2×C4—1116no—
517C2×C4—114no—
518C2×C4—118no—
519C2×C4—114no—
520C2×C4—2216no—
521C2×C4—2216no—
522C2×C4—2232no—
523C2×C4—222no—
524C2×C4—224no—
525C2×C4—222no—
526C2×C4—222no—
527C2×C4—222no—
528C2×C4—224no—
529C2×C4—221no—
530C2×C4—221no—
531C2×C4—224no—
532C2×C4—224no—
533C2×C4—222no—
534C2×C4—224no—
535C2×C4—222no—
536C2×C4—444no—
537C2×C4—4416no—
538C2×C4—444no—
539C2×C4C22×C4×D1114yes—
540C2×C4C22×C4×D1118yes—
541C2×C4C22×C4×D1112yes—
542C2×C4C2×Q8×D1114yes—
543C2×C4C2×Q8×D1112yes—
544C2×C4#41×D1112yes—
545C22—114no—
546C22—114no—
547C22—118no—
548C22—114no—
549C22—118no—
550C22C23×C4×D1111yescharacteristic
551C22C22×Q8×D1111yescharacteristic
552C22C2×#41×D1111yescharacteristic
553C22D11×H(5,𝔽2)12yes—
554C22D11×2−1+412yes—
555C4—24no—
556C4—28no—
557C4—24no—
558C4—41no—
559C4—44no—
560C4—41no—
561C4—114no—
562C4—224no—
563C4—224no—
564C4—228no—
565C4—441no—
566C4—444no—
567C4—441no—
568C4C4×Q8×D1114yes—
569C2—118no—
570C2C2×C4×Q8×D1111yescharacteristic
571C2D11×#52012yes—
572C2D11×#54011yescharacteristic
573C2D11×#54111yescharacteristic
574C2D11×#54412yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2330C2
socle, cosocleC23×C11C25
prime radicalC23×D11C24
hypercenter#2330D11
hypocenterC11C2×#2330
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2330

Complements

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

NH ≅ G/Ntype
2. #13071358C2semidirect
3. #13071357C2semidirect
4. #13071356C2semidirect
5. #13071355C2semidirect
6. #13071354C2semidirect
7. #13071353C2semidirect
8. #13071352C2semidirect
15. C11×#2330C2semidirect
17. D11×#125C4semidirect
79. C11×#125C2×C4semidirect
117. #66943C2×C4semidirect
118. #66942C2×C4semidirect
123. #66923C2×C4semidirect
215. #2330D11direct (N × H)
363. #125C4×D11semidirect
426. D11#2330direct (N × H)
493. C11C2×#2330semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1252
#130713582
#130713572
#130713562
#130713552
#130713542
#130713532
#130713522
D11×#3892
D11×#3872
D11×#3842
C4×C4⋊C4×D112
D11×#3762
C11×#23302
C2×#233011