Finite Group Databasebeta

← D11×#2402 #14920076

Subgroups — D11×#2402 #14920076

Order 2816.

2078 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071924C212yesmaximal, complemented
2#13071923C214yesmaximal, complemented
3#13071922C214yesmaximal, complemented
4#13071921C211yesmaximal, characteristic, complemented
5#13071920C214yesmaximal, complemented
6D11×#400C214yesmaximal
7D11×#398C214yesmaximal
8C4×C4⋊C4×D11C214yesmaximal
9C4×C4⋊C4×D11C212yesmaximal
10D11×#376C211yesmaximal, characteristic
11C11×#2402C211yesmaximal, characteristic, complemented
12C2×C4⋊C4×D11C2214yes—
13C2×C4⋊C4×D11C2214yes—
14C2×C4⋊C4×D11C2214yes—
15C2×C42×D11C2212yes—
16C2×C42×D11C2214yes—
17C2×C42×D11C2211yescharacteristic
18C11×#400C2214yes—
19C11×#398C2214yes—
20C4×C11×C4⋊C4C2214yes—
21C4×C11×C4⋊C4C2212yes—
22C11×#376C2211yescharacteristic
23#10622599C2214yes—
24#10622597C2214yes—
25#10622597C2214yes—
26#10622596C2214yes—
27#10622595C2214yes—
28#10622593C2214yes—
29C4⋊C4×Dic11C2214yes—
30C4⋊C4×Dic11C2214yes—
31C4⋊C4×Dic11C2214yes—
32C4×C4⋊Dic11C2212yes—
33C4×C4⋊Dic11C2214yes—
34#10622545C2212yes—
35#10622545C2211yescharacteristic
36C4×Dic11⋊C4C2214yes—
37C4×Dic11⋊C4C2214yes—
38C4×Dic11⋊C4C2214yes—
39D11×#95C2214yes—
40D11×#95C2212yes—
41D11×#95C2214yes—
42D11×#95C2214yes—
43D11×#95C2212yes—
44#10622274C2214yes—
45#10622273C2214yes—
46#10622273C2214yes—
47#10622272C2214yes—
48#10622271C2214yes—
49#10622271C2214yes—
50#10622270C2214yes—
51#10622270C2214yes—
52#10622262C2212yes—
53#10622262C2214yes—
54#10622262C2212yes—
55#10622262C2214yes—
56#10622261C2214yes—
57C22×C4×D11C2314yes—
58C22×C4×D11C2314yes—
59C22×C4×D11C2312yes—
60C22×C4×D11C2314yes—
61C22×C4×D11C2311yescharacteristic
62C2×C11×C4⋊C4C2314yes—
63C2×C11×C4⋊C4C2314yes—
64C2×C11×C4⋊C4C2314yes—
65C2×C42×C11C2312yes—
66C2×C42×C11C2314yes—
67C2×C42×C11C2311yescharacteristic
68C2×C4⋊Dic11C2314yes—
69C2×C4⋊Dic11C2314yes—
70C2×C4⋊Dic11C2314yes—
71C2×Dic11⋊C4C2314yes—
72C2×Dic11⋊C4C2314yes—
73C2×Dic11⋊C4C2314yes—
74C2×Dic11⋊C4C2314yes—
75C2×Dic11⋊C4C2314yes—
76C2×Dic11⋊C4C2314yes—
77C2×C4×Dic11C2314yes—
78C2×C4×Dic11C2314yes—
79C2×C4×Dic11C2314yes—
80C2×C4×Dic11C2314yes—
81C2×C4×Dic11C2312yes—
82C2×C4×Dic11C2312yes—
83C2×C4×Dic11C2311yescharacteristic
84C4⋊C4×D11—216no—
85C4⋊C4×D11—216no—
86C4⋊C4×D11—216no—
87C42×D11—216no—
88C42×D11—28no—
89C42×D11Q818yes—
90C11×#95C2314yes—
91C11×#95C2314yes—
92C11×#95C2314yes—
93C11×#95C2312yes—
94C11×#95C2312yes—
95C11⋊#95C2314yes—
96C11⋊#95C2314yes—
97C11⋊#95C2314yes—
98C11⋊#95C2312yes—
99C11⋊#95C2314yes—
100C11⋊#95C2314yes—
101C11⋊#95C2312yes—
102C11⋊#95C2314yes—
103C11⋊#95C2314yes—
104C11⋊#95C2314yes—
105C11⋊#95C2314yes—
106C11⋊#95C2314yes—
107C11⋊#95C2314yes—
108C2×#2402—111nomaximal, Sylow
109C23×D11C2411yescharacteristic
110C22×C4×C11C2414yes—
111C22×C4×C11C2414yes—
112C22×C4×C11C2412yes—
113C22×C4×C11C2414yes—
114C22×C4×C11C2411yescharacteristic
115C22×Dic11C2414yes—
116C22×Dic11C2414yes—
117C22×Dic11C2412yes—
118C22×Dic11C2414yes—
119C22×Dic11C2411yescharacteristic
120C2×C4×D11—28no—
121C2×C4×D11—28no—
122C2×C4×D11—28no—
123C2×C4×D11—28no—
124C2×C4×D11—28no—
125C2×C4×D11—28no—
126C2×C4×D11—28no—
127C2×C4×D11—28no—
128C2×C4×D11—28no—
129C2×C4×D11C2×Q818yes—
130C2×C4×D11C2×Q814yes—
131C2×C4×D11#41116yes—
132C2×C4×D11#4118yes—
133C11×C4⋊C4—28no—
134C11×C4⋊C4—28no—
135C11×C4⋊C4—28no—
136C42×C11—28no—
137C42×C11—24no—
138C42×C11C2×Q814yes—
139C4⋊Dic11—28no—
140C4⋊Dic11—28no—
141C4⋊Dic11—28no—
142Dic11⋊C4—28no—
143Dic11⋊C4—28no—
144Dic11⋊C4—28no—
145Dic11⋊C4—28no—
146Dic11⋊C4—28no—
147Dic11⋊C4—28no—
148C4×Dic11—28no—
149C4×Dic11—28no—
150C4×Dic11—28no—
151C4×Dic11—28no—
152C4×Dic11—24no—
153C4×Dic11C2×Q818yes—
154C4×Dic11C2×Q814yes—
155#2402—114no—
156#2402—114no—
157#2402—114no—
158#2402—112no—
159#2402—111no—
160#2402D1111yescharacteristic, direct product factor
161C2×#400—114no—
162C2×#398—114no—
163C2×C4×C4⋊C4—114no—
164C2×C4×C4⋊C4—112no—
165C2×#376—111no—
166C23×C11C2511yescharacteristic
167C22×D11C22×Q812yes—
168C22×D11C2×#4114yes—
169C22×D11C2×#4118yes—
170C2×C4×C11—24no—
171C2×C4×C11—24no—
172C2×C4×C11—24no—
173C2×C4×C11—24no—
174C2×C4×C11—24no—
175C2×C4×C11—24no—
176C2×C4×C11—24no—
177C2×C4×C11—24no—
178C2×C4×C11—24no—
179C2×C4×C11C22×Q814yes—
180C2×C4×C11C22×Q812yes—
181C2×C4×C11C2×#4118yes—
182C2×C4×C11C2×#4114yes—
183C2×Dic11—24no—
184C2×Dic11—24no—
185C2×Dic11—24no—
186C2×Dic11—24no—
187C2×Dic11—24no—
188C2×Dic11—24no—
189C2×Dic11—24no—
190C2×Dic11—24no—
191C2×Dic11—24no—
192C2×Dic11C22×Q814yes—
193C2×Dic11C22×Q812yes—
194C2×Dic11C2×#4118yes—
195C2×Dic11C2×#4114yes—
196C4×D11—232no—
197C4×D11—216no—
198C4×D11—416no—
199C4×D11—416no—
200C4×D11#125116yes—
201C22×C4⋊C4—114no—
202C22×C4⋊C4—114no—
203C22×C4⋊C4—114no—
204C22×C42—111no—
205C22×C42—112no—
206C22×C42—114no—
207#400—114no—
208#400—114no—
209#400—114no—
210#400—114no—
211#400—114no—
212#400—114no—
213#400—114no—
214#400C2×D1114yes—
215#398—114no—
216#398—114no—
217#398—114no—
218#398—114no—
219#398—114no—
220#398—114no—
221#398—114no—
222#398C2×D1114yes—
223C4×C4⋊C4—114no—
224C4×C4⋊C4—114no—
225C4×C4⋊C4—114no—
226C4×C4⋊C4—114no—
227C4×C4⋊C4—114no—
228C4×C4⋊C4—114no—
229C4×C4⋊C4—112no—
230C4×C4⋊C4—114no—
231C4×C4⋊C4—112no—
232C4×C4⋊C4—114no—
233C4×C4⋊C4—112no—
234C4×C4⋊C4—114no—
235C4×C4⋊C4C2×D1112yes—
236C4×C4⋊C4C2×D1114yes—
237#376—112no—
238#376—111no—
239#376—114no—
240#376C2×D1111yescharacteristic
241C2×#95—112no—
242C2×#95—114no—
243C2×#95—114no—
244C2×#95—112no—
245C2×#95—114no—
246C22×C11C23×Q811yescharacteristic
247C22×C11C22×#4112yes—
248C22×C11C22×#4114yes—
249C2×D11C2×#12514yes—
250C2×D11#529116yes—
251C2×D11#53318yes—
252C4×C11—28no—
253C4×C11—24no—
254C4×C11—44no—
255C4×C11—44no—
256C4×C11C2×#12514yes—
257Dic11—28no—
258Dic11—24no—
259Dic11—44no—
260Dic11—44no—
261Dic11C2×#12514yes—
262C23×C4—111no—
263C23×C4—114no—
264C23×C4—112no—
265C23×C4—114no—
266C23×C4—114no—
267C2×C4⋊C4—114no—
268C2×C4⋊C4—114no—
269C2×C4⋊C4—114no—
270C2×C4⋊C4—114no—
271C2×C4⋊C4—114no—
272C2×C4⋊C4—114no—
273C2×C4⋊C4—114no—
274C2×C4⋊C4—114no—
275C2×C4⋊C4—114no—
276C2×C4⋊C4—2216no—
277C2×C4⋊C4—2216no—
278C2×C4⋊C4—2216no—
279C2×C4⋊C4C22×D1114yes—
280C2×C4⋊C4C22×D1114yes—
281C2×C4⋊C4C22×D1114yes—
282C2×C42—112no—
283C2×C42—111no—
284C2×C42—118no—
285C2×C42—114no—
286C2×C42—114no—
287C2×C42—114no—
288C2×C42—112no—
289C2×C42—114no—
290C2×C42—2216no—
291C2×C42—228no—
292C2×C42C22×D1112yes—
293C2×C42C22×D1114yes—
294C2×C42C22×D1111yescharacteristic
295#95—114no—
296#95—114no—
297#95—114no—
298#95—114no—
299#95—112no—
300#95—114no—
301#95—114no—
302#95—114no—
303#95—114no—
304#95—114no—
305#95—114no—
306#95—114no—
307#95—112no—
308#95C22×D1114yes—
309#95C22×D1112yes—
310#95C22×D1114yes—
311#95C22×D1114yes—
312#95C22×D1112yes—
313C2×C11C22×#12511yescharacteristic
314C2×C11C2×#52914yes—
315C2×C11C2×#53312yes—
316D11#240218yesdirect product factor
317C24—111no—
318C22×C4—111no—
319C22×C4—114no—
320C22×C4—118no—
321C22×C4—112no—
322C22×C4—114no—
323C22×C4—118no—
324C22×C4—1116no—
325C22×C4—114no—
326C22×C4—114no—
327C22×C4—228no—
328C22×C4—228no—
329C22×C4—228no—
330C22×C4—228no—
331C22×C4—228no—
332C22×C4—228no—
333C22×C4—228no—
334C22×C4—228no—
335C22×C4—228no—
336C22×C4C23×D1114yes—
337C22×C4C23×D1114yes—
338C22×C4C23×D1112yes—
339C22×C4C23×D1114yes—
340C22×C4C23×D1111yescharacteristic
341C4⋊C4—28no—
342C4⋊C4—28no—
343C4⋊C4—28no—
344C4⋊C4—228no—
345C4⋊C4—228no—
346C4⋊C4—228no—
347C4⋊C4—228no—
348C4⋊C4—228no—
349C4⋊C4—228no—
350C4⋊C4—228no—
351C4⋊C4—228no—
352C4⋊C4—228no—
353C42—28no—
354C42—24no—
355C42—118no—
356C42—114no—
357C42—228no—
358C42—228no—
359C42—228no—
360C42—228no—
361C42—224no—
362C42Q8×D1114yes—
363C11C2×#240211yescharacteristic, complemented, Sylow
364C23—112no—
365C23—114no—
366C23—118no—
367C23C24×D1111yescharacteristic
368C2×C4—24no—
369C2×C4—24no—
370C2×C4—24no—
371C2×C4—24no—
372C2×C4—24no—
373C2×C4—24no—
374C2×C4—24no—
375C2×C4—24no—
376C2×C4—24no—
377C2×C4—112no—
378C2×C4—114no—
379C2×C4—1116no—
380C2×C4—114no—
381C2×C4—118no—
382C2×C4—2232no—
383C2×C4—2216no—
384C2×C4—224no—
385C2×C4—224no—
386C2×C4—224no—
387C2×C4—224no—
388C2×C4—224no—
389C2×C4—224no—
390C2×C4—224no—
391C2×C4—224no—
392C2×C4—224no—
393C2×C4—4416no—
394C2×C4—4416no—
395C2×C4C2×Q8×D1114yes—
396C2×C4C2×Q8×D1112yes—
397C2×C4#41×D1118yes—
398C2×C4#41×D1114yes—
399C22—114no—
400C22—1116no—
401C22—118no—
402C22C22×Q8×D1111yescharacteristic
403C22C2×#41×D1112yes—
404C22C2×#41×D1114yes—
405C4—28no—
406C4—24no—
407C4—44no—
408C4—44no—
409C4—114no—
410C4—228no—
411C4—224no—
412C4—444no—
413C4—444no—
414C4D11×#12514yes—
415C2—118no—
416C2C2×D11×#12511yescharacteristic
417C2D11×#52914yes—
418C2D11×#53312yes—
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC11×#2402C2
prime radicalC23×D11C24
hypercenter#2402D11
hypocenterC11C2×#2402
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #2402

Complements

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

NH ≅ G/Ntype
1. #13071924C2semidirect
2. #13071923C2semidirect
3. #13071922C2semidirect
4. #13071921C2semidirect
5. #13071920C2semidirect
11. C11×#2402C2semidirect
160. #2402D11direct (N × H)
316. D11#2402direct (N × H)
363. C11C2×#2402semidirect

Maximal subgroups

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

subgroupindex
#130719242
#130719232
#130719222
#130719212
#130719202
D11×#4002
D11×#3982
C4×C4⋊C4×D112
D11×#3762
C11×#24022
C2×#240211