Finite Group Databasebeta

← D11×#2399 #14920049

Subgroups — D11×#2399 #14920049

Order 2816.

2814 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Q8×D11C212yesmaximal
2#13071910C214yesmaximal, complemented
3#13071909C211yesmaximal, characteristic, complemented
4#13071908C214yesmaximal, complemented
5#13071907C212yesmaximal, complemented
6#13071906C214yesmaximal, complemented
7D11×#398C214yesmaximal
8D11×#395C214yesmaximal
9C4×C4⋊C4×D11C214yesmaximal
10D11×#376C211yesmaximal, characteristic
11C11×#2399C211yesmaximal, characteristic, complemented
12C22×Q8×D11C2212yes—
13C2×C4×Q8×C11C2212yes—
14C2×Q8×Dic11C2212yes—
15C4×Q8×D11—216no—
16C2×C4⋊C4×D11C2218yes—
17C2×C4⋊C4×D11C2214yes—
18C2×C4⋊C4×D11C2212yes—
19C2×#66940C2214yes—
20C2×#66940C2212yes—
21C2×C42×D11C2214yes—
22C2×C42×D11C2211yescharacteristic
23C2×C42×D11C2212yes—
24C2×C4×Dic22C2212yes—
25C2×C4×Dic22C2214yes—
26C11×#398C2214yes—
27C11×#395C2214yes—
28C4×C11×C4⋊C4C2214yes—
29C11×#376C2211yescharacteristic
30#10622842C2214yes—
31#10622597C2218yes—
32#10622596C2214yes—
33#10622593C2214yes—
34#10622592C2214yes—
35#10622592C2218yes—
36C4⋊C4×Dic11C2218yes—
37C4×C4⋊Dic11C2214yes—
38#10622545C2211yescharacteristic
39#10622545C2212yes—
40C4×Dic11⋊C4C2218yes—
41D11×#95C2214yes—
42D11×#95C2214yes—
43D11×#95C2214yes—
44#10622274C2214yes—
45#10622270C2218yes—
46#10622269C2218yes—
47#10622269C2214yes—
48#10622262C2214yes—
49#10622262C2214yes—
50#10622261C2214yes—
51C22×Q8×C11C2312yes—
52C2×Q8×D11—28no—
53C2×Q8×D11—216no—
54C22×C4×D11C2314yes—
55C22×C4×D11C2312yes—
56C22×C4×D11C2314yes—
57C22×C4×D11C2314yes—
58C22×C4×D11C2311yescharacteristic
59C22×Dic22C2314yes—
60C22×Dic22C2312yes—
61C4×Q8×C11—28no—
62C2×C11×C4⋊C4C2314yes—
63C2×C11×C4⋊C4C2312yes—
64C2×C11×C4⋊C4C2318yes—
65C2×C42×C11C2314yes—
66C2×C42×C11C2311yescharacteristic
67C2×C42×C11C2312yes—
68Q8×Dic11—28no—
69C2×C4⋊Dic11C2314yes—
70C2×C4⋊Dic11C2312yes—
71C2×C4⋊Dic11C2318yes—
72C2×Dic11⋊C4C2314yes—
73C2×Dic11⋊C4C2314yes—
74C2×Dic11⋊C4C2314yes—
75C2×Dic11⋊C4C2318yes—
76C2×Dic11⋊C4C2318yes—
77C2×C4×Dic11C2314yes—
78C2×C4×Dic11C2314yes—
79C2×C4×Dic11C2314yes—
80C2×C4×Dic11C2311yescharacteristic
81C2×C4×Dic11C2312yes—
82C2×C4×Dic11C2314yes—
83C2×C4×Dic11C2312yes—
84C4⋊C4×D11—28no—
85C4⋊C4×D11—216no—
86C4⋊C4×D11—232no—
87#66940—28no—
88#66940—216no—
89C42×D11—216no—
90C42×D11D418yes—
91C42×D11Q8116yescomplemented
92C4×Dic22—28no—
93C4×Dic22—216no—
94C11×#95C2314yes—
95C11×#95C2314yes—
96C11×#95C2314yes—
97C11⋊#95C2318yes—
98C11⋊#95C2314yes—
99C11⋊#95C2314yes—
100C11⋊#95C2314yes—
101C11⋊#95C2318yes—
102C11⋊#95C2318yes—
103C2×#2399—111nomaximal, Sylow
104C23×D11C2411yescharacteristic
105C2×Q8×C11—24no—
106C2×Q8×C11—28no—
107C22×C4×C11C2414yes—
108C22×C4×C11C2412yes—
109C22×C4×C11C2414yes—
110C22×C4×C11C2414yes—
111C22×C4×C11C2411yescharacteristic
112C22×Dic11C2414yes—
113C22×Dic11C2412yes—
114C22×Dic11C2414yes—
115C22×Dic11C2414yes—
116C22×Dic11C2411yescharacteristic
117Q8×D11—264no—
118C2×C4×D11—28no—
119C2×C4×D11—28no—
120C2×C4×D11—216no—
121C2×C4×D11—28no—
122C2×C4×D11—28no—
123C2×C4×D11—216no—
124C2×C4×D11C2×D418yes—
125C2×C4×D11C2×D414yes—
126C2×C4×D11C2×Q8116yes—
127C2×C4×D11C2×Q818yes—
128C2×C4×D11#41116yes—
129C2×Dic22—28no—
130C2×Dic22—28no—
131C2×Dic22—28no—
132C2×Dic22—24no—
133C2×Dic22—28no—
134C11×C4⋊C4—28no—
135C11×C4⋊C4—24no—
136C11×C4⋊C4—216no—
137C42×C11—28no—
138C42×C11C2×D414yes—
139C42×C11C2×Q818yescomplemented
140C4⋊Dic11—28no—
141C4⋊Dic11—216no—
142C4⋊Dic11—24no—
143Dic11⋊C4—28no—
144Dic11⋊C4—28no—
145Dic11⋊C4—216no—
146Dic11⋊C4—28no—
147Dic11⋊C4—216no—
148C4×Dic11—28no—
149C4×Dic11—28no—
150C4×Dic11—28no—
151C4×Dic11C2×D414yes—
152C4×Dic11C2×D418yes—
153C4×Dic11C2×Q8116yescomplemented
154C4×Dic11C2×Q818yescomplemented
155C22×C4×Q8—112no—
156#2399—114no—
157#2399—114no—
158#2399—114no—
159#2399—111no—
160#2399—112no—
161#2399D1111yescharacteristic, direct product factor
162C2×#398—114no—
163C2×#395—114no—
164C2×C4×C4⋊C4—114no—
165C2×#376—111no—
166C23×C11C2511yescharacteristic
167C22×D11C22×D412yes—
168C22×D11C22×Q814yes—
169C22×D11C2×#4118yes—
170Q8×C11—216no—
171C2×C4×C11—24no—
172C2×C4×C11—28no—
173C2×C4×C11—24no—
174C2×C4×C11—24no—
175C2×C4×C11—24no—
176C2×C4×C11—28no—
177C2×C4×C11C22×D414yes—
178C2×C4×C11C22×D412yes—
179C2×C4×C11C22×Q818yes—
180C2×C4×C11C22×Q814yes—
181C2×C4×C11C2×#4118yes—
182C2×Dic11—24no—
183C2×Dic11—28no—
184C2×Dic11—24no—
185C2×Dic11—24no—
186C2×Dic11—24no—
187C2×Dic11—28no—
188C2×Dic11C22×D414yes—
189C2×Dic11C22×D412yes—
190C2×Dic11C22×Q818yes—
191C2×Dic11C22×Q814yes—
192C2×Dic11C2×#4118yes—
193C4×D11—216no—
194C4×D11—232no—
195C4×D11—232no—
196C4×D11—416no—
197C4×D11C4⋊Q8116yes—
198Dic22—232no—
199Dic22—216no—
200C23×Q8—112no—
201C2×C4×Q8—112no—
202C2×C4×Q8—112no—
203C2×C4×Q8—114no—
204C2×C4×Q8—114no—
205C2×C4×Q8—112no—
206C2×C4×Q8—2216no—
207C2×C4×Q8C2×D1112yes—
208C22×C4⋊C4—114no—
209C22×C4⋊C4—118no—
210C22×C4⋊C4—112no—
211C22×C42—111no—
212C22×C42—112no—
213C22×C42—114no—
214#398—114no—
215#398—114no—
216#398—118no—
217#398—118no—
218#398—114no—
219#398C2×D1114yes—
220#395—114no—
221#395—118no—
222#395—114no—
223#395—118no—
224#395—114no—
225#395C2×D1114yes—
226C4×C4⋊C4—118no—
227C4×C4⋊C4—118no—
228C4×C4⋊C4—114no—
229C4×C4⋊C4—114no—
230C4×C4⋊C4—114no—
231C4×C4⋊C4C2×D1114yes—
232#376—112no—
233#376—111no—
234#376—114no—
235#376C2×D1111yescharacteristic
236C2×#95—114no—
237C2×#95—114no—
238C2×#95—114no—
239C22×C11C23×D411yescharacteristic
240C22×C11C23×Q812yes—
241C22×C11C22×#4114yes—
242C2×D11#52518yes—
243C2×D11C2×C4⋊Q814yes—
244C2×D11#533116yes—
245C4×C11—24no—
246C4×C11—28no—
247C4×C11—28no—
248C4×C11—44no—
249C4×C11C2×C4⋊Q814yes—
250Dic11—24no—
251Dic11—28no—
252Dic11—28no—
253Dic11—44no—
254Dic11C2×C4⋊Q814yes—
255C22×Q8—112no—
256C22×Q8—114no—
257C22×Q8—228no—
258C22×Q8—2216no—
259C22×Q8C22×D1112yes—
260C23×C4—111no—
261C23×C4—112no—
262C23×C4—114no—
263C23×C4—114no—
264C23×C4—114no—
265C4×Q8—28no—
266C4×Q8—2216no—
267C4×Q8—228no—
268C4×Q8—2216no—
269C4×Q8—228no—
270C4×Q8—228no—
271C2×C4⋊C4—114no—
272C2×C4⋊C4—114no—
273C2×C4⋊C4—114no—
274C2×C4⋊C4—114no—
275C2×C4⋊C4—112no—
276C2×C4⋊C4—118no—
277C2×C4⋊C4—118no—
278C2×C4⋊C4—118no—
279C2×C4⋊C4—228no—
280C2×C4⋊C4—2216no—
281C2×C4⋊C4—2232no—
282C2×C4⋊C4C22×D1114yes—
283C2×C4⋊C4C22×D1112yes—
284C2×C4⋊C4C22×D1118yes—
285C2×C42—112no—
286C2×C42—114no—
287C2×C42—111no—
288C2×C42—112no—
289C2×C42—118no—
290C2×C42—1116no—
291C2×C42—114no—
292C2×C42—114no—
293C2×C42—114no—
294C2×C42—2216no—
295C2×C42C22×D1114yes—
296C2×C42C22×D1111yescharacteristic
297C2×C42C22×D1112yes—
298#95—114no—
299#95—118no—
300#95—118no—
301#95—114no—
302#95—118no—
303#95—114no—
304#95C22×D1114yes—
305#95C22×D1114yes—
306#95C22×D1114yes—
307C2×C11C2×#52512yes—
308C2×C11C22×C4⋊Q811yescharacteristic
309C2×C11C2×#53314yes—
310D11#239918yesdirect product factor
311C24—111no—
312C2×Q8—24no—
313C2×Q8—28no—
314C2×Q8—228no—
315C2×Q8—228no—
316C2×Q8—228no—
317C2×Q8—2264no—
318C2×Q8—224no—
319C2×Q8—228no—
320C22×C4—111no—
321C22×C4—114no—
322C22×C4—118no—
323C22×C4—114no—
324C22×C4—112no—
325C22×C4—114no—
326C22×C4—118no—
327C22×C4—1116no—
328C22×C4—1116no—
329C22×C4—114no—
330C22×C4—228no—
331C22×C4—2216no—
332C22×C4—228no—
333C22×C4—228no—
334C22×C4—228no—
335C22×C4—2216no—
336C22×C4C23×D1114yes—
337C22×C4C23×D1112yes—
338C22×C4C23×D1114yes—
339C22×C4C23×D1114yes—
340C22×C4C23×D1111yescharacteristic
341C4⋊C4—28no—
342C4⋊C4—24no—
343C4⋊C4—216no—
344C4⋊C4—228no—
345C4⋊C4—228no—
346C4⋊C4—228no—
347C4⋊C4—2216no—
348C4⋊C4—2216no—
349C4⋊C4—228no—
350C4⋊C4—224no—
351C4⋊C4—2216no—
352C42—28no—
353C42—118no—
354C42—114no—
355C42—1116no—
356C42—118no—
357C42—228no—
358C42—228no—
359C42—228no—
360C42D4×D1114yes—
361C42Q8×D1118yescomplemented
362C11C2×#239911yescharacteristic, complemented, Sylow
363C23—112no—
364C23—114no—
365C23—118no—
366C23C24×D1111yescharacteristic
367Q8—216no—
368Q8—2216no—
369Q8—2232no—
370C2×C4—24no—
371C2×C4—28no—
372C2×C4—24no—
373C2×C4—24no—
374C2×C4—24no—
375C2×C4—28no—
376C2×C4—112no—
377C2×C4—114no—
378C2×C4—1116no—
379C2×C4—114no—
380C2×C4—118no—
381C2×C4—118no—
382C2×C4—2216no—
383C2×C4—2232no—
384C2×C4—2232no—
385C2×C4—224no—
386C2×C4—228no—
387C2×C4—224no—
388C2×C4—224no—
389C2×C4—224no—
390C2×C4—228no—
391C2×C4—4416no—
392C2×C4C2×D4×D1114yes—
393C2×C4C2×D4×D1112yes—
394C2×C4C2×Q8×D1118yes—
395C2×C4C2×Q8×D1114yes—
396C2×C4#41×D1118yes—
397C22—114no—
398C22—1116no—
399C22—118no—
400C22C22×D4×D1111yescharacteristic
401C22C22×Q8×D1112yes—
402C22C2×#41×D1114yes—
403C4—28no—
404C4—24no—
405C4—28no—
406C4—44no—
407C4—114no—
408C4—228no—
409C4—224no—
410C4—228no—
411C4—444no—
412C4D11×C4⋊Q814yes—
413C2—118no—
414C2D11×#52512yes—
415C2C2×D11×C4⋊Q811yescharacteristic
416C2D11×#53314yes—
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC11×#2399C2
prime radicalC23×D11C24
hypercenter#2399D11
hypocenterC11C2×#2399
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #2399

Complements

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

NH ≅ G/Ntype
2. #13071910C2semidirect
3. #13071909C2semidirect
4. #13071908C2semidirect
5. #13071907C2semidirect
6. #13071906C2semidirect
11. C11×#2399C2semidirect
91. C42×D11Q8semidirect
139. C42×C11C2×Q8semidirect
153. C4×Dic11C2×Q8semidirect
154. C4×Dic11C2×Q8semidirect
161. #2399D11direct (N × H)
310. D11#2399direct (N × H)
361. C42Q8×D11semidirect
362. C11C2×#2399semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Q8×D112
#130719102
#130719092
#130719082
#130719072
#130719062
D11×#3982
D11×#3952
C4×C4⋊C4×D112
D11×#3762
C11×#23992
C2×#239911