Finite Group Databasebeta

← D11×#2371 #14913440

Subgroups — D11×#2371 #14913440

Order 2816.

2422 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#125C211yesmaximal, characteristic
2#13071722C211yesmaximal, characteristic, complemented
3#13071721C212yesmaximal, complemented
4#13071720C214yesmaximal, complemented
5#13071719C214yesmaximal, complemented
6#13071718C214yesmaximal, complemented
7D11×#387C214yesmaximal
8D11×#387C214yesmaximal
9C4×C4⋊C4×D11C214yesmaximal
10D11×#376C212yesmaximal
11C11×#2371C211yesmaximal, characteristic, complemented
12C2×C11×#125C2211yescharacteristic
13D11×#125C4116yescomplemented
14C2×C4⋊C4×D11C2214yes—
15C2×C4⋊C4×D11C2214yes—
16C2×C4⋊C4×D11C2212yes—
17C2×#66943C2212yes—
18C2×#66942C2214yes—
19C2×C42×D11C2214yes—
20C2×C42×D11C2214yes—
21C2×C42×D11C2211yescharacteristic
22C2×#66923C2211yescharacteristic
23C11×#387C2214yes—
24C11×#387C2214yes—
25C4×C11×C4⋊C4C2214yes—
26C11×#376C2212yes—
27#10622594C2214yes—
28#10622594C2214yes—
29#10622591C2214yes—
30#10622591C2214yes—
31C4⋊C4×Dic11C2214yes—
32C4⋊C4×Dic11C2214yes—
33C4×C4⋊Dic11C2214yes—
34#10622546C2214yes—
35#10622546C2214yes—
36#10622545C2214yes—
37#10622545C2212yes—
38C4×Dic11⋊C4C2214yes—
39C4×Dic11⋊C4C2214yes—
40D11×#95C2212yes—
41D11×#95C2214yes—
42D11×#95C2212yes—
43D11×#95C2214yes—
44D11×#95C2214yes—
45#10622268C2214yes—
46#10622268C2214yes—
47#10622267C2214yes—
48#10622267C2214yes—
49#10622266C2214yes—
50#10622266C2214yes—
51#10622265C2214yes—
52#10622265C2214yes—
53#10622262C2214yes—
54#10622262C2214yes—
55#10622261C2212yes—
56#10622261C2212yes—
57#10622261C2214yes—
58C22×C4×D11C2314yes—
59C22×C4×D11C2312yes—
60C22×C4×D11C2314yes—
61C22×C4×D11C2311yescharacteristic
62C22×C4×D11C2314yes—
63C11×#125C2×C418yescomplemented
64C2×C11×C4⋊C4C2314yes—
65C2×C11×C4⋊C4C2314yes—
66C2×C11×C4⋊C4C2312yes—
67C2×C42×C11C2314yes—
68C2×C42×C11C2314yes—
69C2×C42×C11C2311yescharacteristic
70C2×C4⋊Dic11C2314yes—
71C2×C4⋊Dic11C2312yes—
72C2×C4⋊Dic11C2314yes—
73C2×Dic11⋊C4C2314yes—
74C2×Dic11⋊C4C2314yes—
75C2×Dic11⋊C4C2314yes—
76C2×Dic11⋊C4C2314yes—
77C2×Dic11⋊C4C2314yes—
78C2×C4×Dic11C2314yes—
79C2×C4×Dic11C2314yes—
80C2×C4×Dic11C2314yes—
81C2×C4×Dic11C2314yes—
82C2×C4×Dic11C2314yes—
83C2×C4×Dic11C2314yes—
84C2×C4×Dic11C2311yescharacteristic
85C2×C4×Dic11C2312yes—
86C4⋊C4×D11—216no—
87C4⋊C4×D11C2×C4132yes—
88C4⋊C4×D11C2×C4116yes—
89#66943C2×C4116yescomplemented
90#66942C2×C4132yescomplemented
91C42×D11—216no—
92C42×D11—216no—
93C42×D11C2×C418yes—
94#66923C2×C418yescomplemented
95C11×#95C2312yes—
96C11×#95C2312yes—
97C11×#95C2314yes—
98C11×#95C2314yes—
99C11×#95C2314yes—
100C11⋊#95C2314yes—
101C11⋊#95C2314yes—
102C11⋊#95C2314yes—
103C11⋊#95C2314yes—
104C11⋊#95C2314yes—
105C11⋊#95C2312yes—
106C11⋊#95C2312yes—
107C11⋊#95C2314yes—
108C11⋊#95C2314yes—
109C11⋊#95C2314yes—
110C11⋊#95C2314yes—
111C11⋊#95C2314yes—
112C11⋊#95C2314yes—
113C2×#2371—111nomaximal, Sylow
114C23×D11C2411yescharacteristic
115C22×C4×C11C2414yes—
116C22×C4×C11C2411yescharacteristic
117C22×C4×C11C2412yes—
118C22×C4×C11C2414yes—
119C22×C4×C11C2414yes—
120C22×Dic11C2414yes—
121C22×Dic11C2411yescharacteristic
122C22×Dic11C2412yes—
123C22×Dic11C2414yes—
124C22×Dic11C2414yes—
125C2×C4×D11—28no—
126C2×C4×D11—28no—
127C2×C4×D11—28no—
128C2×C4×D11—28no—
129C2×C4×D11—28no—
130C2×C4×D11—28no—
131C2×C4×D11—24no—
132C2×C4×D11—28no—
133C2×C4×D11—28no—
134C2×C4×D11C22×C418yes—
135C2×C4×D11C22×C414yes—
136C2×C4×D11C22×C4116yes—
137C2×C4×D11#41116yes—
138C11×C4⋊C4—28no—
139C11×C4⋊C4C22×C4116yes—
140C11×C4⋊C4C22×C418yes—
141C42×C11—28no—
142C42×C11—28no—
143C42×C11C22×C414yes—
144C4⋊Dic11—28no—
145C4⋊Dic11C22×C418yes—
146C4⋊Dic11C22×C4116yes—
147Dic11⋊C4—28no—
148Dic11⋊C4—28no—
149Dic11⋊C4C22×C4116yes—
150Dic11⋊C4C22×C4116yes—
151Dic11⋊C4C22×C4116yes—
152C4×Dic11—28no—
153C4×Dic11—28no—
154C4×Dic11—28no—
155C4×Dic11—28no—
156C4×Dic11—28no—
157C4×Dic11—28no—
158C4×Dic11C22×C418yes—
159C4×Dic11C22×C414yes—
160C22×#125—111no—
161#2371—114no—
162#2371—114no—
163#2371—114no—
164#2371—112no—
165#2371—111no—
166#2371D1111yescharacteristic, direct product factor
167C2×#387—114no—
168C2×#387—114no—
169C2×C4×C4⋊C4—114no—
170C2×#376—112no—
171C23×C11C2511yescharacteristic
172C22×D11C23×C412yes—
173C22×D11C2×#4118yes—
174C22×D112−1+414yes—
175C2×C4×C11—24no—
176C2×C4×C11—24no—
177C2×C4×C11—24no—
178C2×C4×C11—24no—
179C2×C4×C11—22no—
180C2×C4×C11—24no—
181C2×C4×C11—24no—
182C2×C4×C11—24no—
183C2×C4×C11—24no—
184C2×C4×C11C23×C414yes—
185C2×C4×C11C23×C412yes—
186C2×C4×C11C23×C418yes—
187C2×C4×C11C2×#4118yes—
188C2×Dic11—24no—
189C2×Dic11—24no—
190C2×Dic11—24no—
191C2×Dic11—24no—
192C2×Dic11—22no—
193C2×Dic11—24no—
194C2×Dic11—24no—
195C2×Dic11—24no—
196C2×Dic11—24no—
197C2×Dic11C23×C412yes—
198C2×Dic11C23×C414yes—
199C2×Dic11C23×C418yes—
200C2×Dic11C2×#4118yes—
201C4×D11—216no—
202C4×D11—232no—
203C4×D11—28no—
204C4×D11—232no—
205C4×D11—416no—
206C2×#125—1116no—
207C2×#125—114no—
208C2×#125—112no—
209C2×#125—111no—
210C2×#125C2×D1111yescharacteristic
211C22×C4⋊C4—114no—
212C22×C4⋊C4—112no—
213C22×C4⋊C4—114no—
214C22×C42—111no—
215C22×C42—114no—
216C22×C42—114no—
217#387—114no—
218#387—114no—
219#387—114no—
220#387—114no—
221#387—114no—
222#387—114no—
223#387—114no—
224#387—114no—
225#387—114no—
226#387—114no—
227#387—114no—
228#387—114no—
229#387—114no—
230#387—114no—
231#387C2×D1114yes—
232#387C2×D1114yes—
233C4×C4⋊C4—114no—
234C4×C4⋊C4—114no—
235C4×C4⋊C4—114no—
236C4×C4⋊C4—114no—
237C4×C4⋊C4—114no—
238C4×C4⋊C4—114no—
239C4×C4⋊C4—114no—
240C4×C4⋊C4C2×D1114yes—
241#376—114no—
242#376—112no—
243#376—112no—
244#376—114no—
245#376—112no—
246#376C2×D1112yes—
247C2×#95—112no—
248C2×#95—114no—
249C2×#95—112no—
250C2×#95—114no—
251C2×#95—114no—
252C22×C11C24×C411yescharacteristic
253C22×C11C22×#4114yes—
254C22×C11C2×2−1+412yes—
255C2×D11C4×#4118yes—
256C2×D11#51914yes—
257C2×D11#552116yes—
258C4×C11—24no—
259C4×C11—28no—
260C4×C11—22no—
261C4×C11—28no—
262C4×C11—44no—
263Dic11—24no—
264Dic11—28no—
265Dic11—22no—
266Dic11—28no—
267Dic11—44no—
268C23×C4—114no—
269C23×C4—111no—
270C23×C4—112no—
271C23×C4—114no—
272C23×C4—114no—
273#125—1132no—
274#125—1116no—
275#125—118no—
276#125C4×D1118yescomplemented
277C2×C4⋊C4—114no—
278C2×C4⋊C4—114no—
279C2×C4⋊C4—114no—
280C2×C4⋊C4—114no—
281C2×C4⋊C4—112no—
282C2×C4⋊C4—1132no—
283C2×C4⋊C4—1116no—
284C2×C4⋊C4—114no—
285C2×C4⋊C4—114no—
286C2×C4⋊C4—114no—
287C2×C4⋊C4—2216no—
288C2×C4⋊C4C22×D1114yes—
289C2×C4⋊C4C22×D1114yes—
290C2×C4⋊C4C22×D1112yes—
291C2×C42—112no—
292C2×C42—111no—
293C2×C42—118no—
294C2×C42—114no—
295C2×C42—114no—
296C2×C42—114no—
297C2×C42—114no—
298C2×C42—114no—
299C2×C42—114no—
300C2×C42—2216no—
301C2×C42—2216no—
302C2×C42C22×D1114yes—
303C2×C42C22×D1114yes—
304C2×C42C22×D1111yescharacteristic
305#95—112no—
306#95—114no—
307#95—114no—
308#95—114no—
309#95—114no—
310#95—114no—
311#95—112no—
312#95—114no—
313#95—114no—
314#95—114no—
315#95—114no—
316#95—114no—
317#95—114no—
318#95C22×D1112yes—
319#95C22×D1112yes—
320#95C22×D1114yes—
321#95C22×D1114yes—
322#95C22×D1114yes—
323C2×C11C2×C4×#4112yes—
324C2×C11C2×#51911yescharacteristic
325C2×C11C2×#55214yes—
326D11#237118yesdirect product factor
327C24—111no—
328C22×C4—111no—
329C22×C4—114no—
330C22×C4—112no—
331C22×C4—114no—
332C22×C4—114no—
333C22×C4—118no—
334C22×C4—1116no—
335C22×C4—1116no—
336C22×C4—114no—
337C22×C4—228no—
338C22×C4—228no—
339C22×C4—228no—
340C22×C4—228no—
341C22×C4—224no—
342C22×C4—228no—
343C22×C4—228no—
344C22×C4—228no—
345C22×C4—228no—
346C22×C4C23×D1114yes—
347C22×C4C23×D1111yescharacteristic
348C22×C4C23×D1112yes—
349C22×C4C23×D1114yes—
350C22×C4C23×D1114yes—
351C4⋊C4—28no—
352C4⋊C4—1116no—
353C4⋊C4—1116no—
354C4⋊C4—1116no—
355C4⋊C4—1116no—
356C4⋊C4—118no—
357C4⋊C4—228no—
358C4⋊C4—228no—
359C4⋊C4—228no—
360C4⋊C4C2×C4×D11116yes—
361C4⋊C4C2×C4×D1118yes—
362C42—28no—
363C42—28no—
364C42—118no—
365C42—114no—
366C42—228no—
367C42—228no—
368C42—228no—
369C42—228no—
370C42—228no—
371C42—228no—
372C42C2×C4×D1114yes—
373C11C2×#237111yescharacteristic, complemented, Sylow
374C23—112no—
375C23—118no—
376C23—114no—
377C23C24×D1111yescharacteristic
378C2×C4—24no—
379C2×C4—24no—
380C2×C4—24no—
381C2×C4—24no—
382C2×C4—24no—
383C2×C4—22no—
384C2×C4—24no—
385C2×C4—24no—
386C2×C4—24no—
387C2×C4—114no—
388C2×C4—112no—
389C2×C4—118no—
390C2×C4—118no—
391C2×C4—2232no—
392C2×C4—2216no—
393C2×C4—2232no—
394C2×C4—228no—
395C2×C4—224no—
396C2×C4—224no—
397C2×C4—224no—
398C2×C4—224no—
399C2×C4—224no—
400C2×C4—222no—
401C2×C4—224no—
402C2×C4—224no—
403C2×C4—224no—
404C2×C4—4416no—
405C2×C4C22×C4×D1114yes—
406C2×C4C22×C4×D1112yes—
407C2×C4C22×C4×D1118yes—
408C2×C4#41×D1118yes—
409C22—1116no—
410C22—118no—
411C22—114no—
412C22C23×C4×D1111yescharacteristic
413C22C2×#41×D1114yes—
414C22D11×2−1+412yes—
415C4—28no—
416C4—24no—
417C4—28no—
418C4—22no—
419C4—44no—
420C4—228no—
421C4—224no—
422C4—228no—
423C4—222no—
424C4—444no—
425C2—118no—
426C2C4×#41×D1112yes—
427C2D11×#51911yescharacteristic
428C2D11×#55214yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2371C2
socle, cosocleC23×C11C25
prime radicalC23×D11C24
hypercenter#2371D11
hypocenterC11C2×#2371
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2371

Complements

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

NH ≅ G/Ntype
2. #13071722C2semidirect
3. #13071721C2semidirect
4. #13071720C2semidirect
5. #13071719C2semidirect
6. #13071718C2semidirect
11. C11×#2371C2semidirect
13. D11×#125C4semidirect
63. C11×#125C2×C4semidirect
89. #66943C2×C4semidirect
90. #66942C2×C4semidirect
94. #66923C2×C4semidirect
166. #2371D11direct (N × H)
276. #125C4×D11semidirect
326. D11#2371direct (N × H)
373. C11C2×#2371semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1252
#130717222
#130717212
#130717202
#130717192
#130717182
D11×#3872
C4×C4⋊C4×D112
D11×#3762
C11×#23712
C2×#237111