Finite Group Databasebeta

← D11×#2645 #14920890

Subgroups — D11×#2645 #14920890

Order 2816.

1830 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13074584C213yesmaximal, complemented
2#13074583C212yesmaximal, complemented
3#13074582C213yesmaximal, complemented
4#13074581C211yesmaximal, characteristic, complemented
5#13074580C216yesmaximal, complemented
6D11×#401C212yesmaximal
7D11×#400C216yesmaximal
8D11×#391C213yesmaximal
9D11×#389C213yesmaximal
10D11×#376C211yesmaximal, characteristic
11C11×#2645C211yesmaximal, characteristic, complemented
12C22×Q8×D11C2211yescharacteristic
13C2×C4⋊C4×D11C2213yes—
14C2×C4⋊C4×D11C2216yes—
15C2×C42×D11C2213yes—
16C11×#401C2212yes—
17C11×#400C2216yes—
18C11×#391C2213yes—
19C11×#389C2213yes—
20C11×#376C2211yescharacteristic
21#10622843C2213yes—
22#10622599C2216yes—
23#10622598C2213yes—
24#10622595C2216yes—
25#10622587C2213yes—
26#10622586C2213yes—
27#10622585C2216yes—
28#10622545C2213yes—
29#10622542C2213yes—
30#10622541C2213yes—
31D11×#95C2211yescharacteristic
32D11×#95C2216yes—
33D11×#95C2216yes—
34D11×#95C2213yes—
35D11×#95C2216yes—
36C11⋊#401C2216yes—
37C11⋊#401C2216yes—
38C11⋊#401C2212yes—
39#10622273C2216yes—
40#10622273C2216yes—
41#10622272C2216yes—
42#10622271C2216yes—
43#10622271C2216yes—
44#10622261C2213yes—
45#10622261C2211yescharacteristic
46#10622260C2216yes—
47#10622259C2216yes—
48#10622259C2216yes—
49C22×Q8×C11C2311yescharacteristic
50C2×Q8×D11—212no—
51C22×C4×D11C2313yes—
52C22×C4×D11C2313yes—
53C22×C4×D11C2316yes—
54C22×C4×D11C2312yes—
55C22×C4×D11C2311yescharacteristic
56C22×Dic22C2312yes—
57C22×Dic22C2311yescharacteristic
58C2×C11×C4⋊C4C2313yes—
59C2×C11×C4⋊C4C2316yes—
60C2×C42×C11C2313yes—
61C2×C4⋊Dic11C2313yes—
62C2×C4⋊Dic11C2316yes—
63C2×Dic11⋊C4C2316yes—
64C2×Dic11⋊C4C2316yes—
65C2×Dic11⋊C4C2316yes—
66C2×C4×Dic11C2313yes—
67C2×C4×Dic11C2313yes—
68C2×C4×Dic11C2313yes—
69C4⋊C4×D11—212no—
70C4⋊C4×D11—412no—
71C42×D11—212no—
72C11×#95C2316yes—
73C11×#95C2316yes—
74C11×#95C2316yes—
75C11×#95C2313yes—
76C11×#95C2311yescharacteristic
77C11⋊#95C2316yes—
78C11⋊#95C2316yes—
79C11⋊#95C2316yes—
80C11⋊#95C2316yes—
81C11⋊#95C2316yes—
82C11⋊#95C2316yes—
83C11⋊#95C2316yes—
84C11⋊#95C2313yes—
85C11⋊#95C2313yes—
86C11⋊#95C2313yes—
87C11⋊#95C2313yes—
88C11⋊#95C2316yes—
89C11⋊#95C2316yes—
90C2×#2645—111nomaximal, Sylow
91C23×D11C2411yescharacteristic
92C2×Q8×C11—26no—
93C22×C4×C11C2413yes—
94C22×C4×C11C2412yes—
95C22×C4×C11C2413yes—
96C22×C4×C11C2416yes—
97C22×C4×C11C2411yescharacteristic
98C22×Dic11C2413yes—
99C22×Dic11C2412yes—
100C22×Dic11C2413yes—
101C22×Dic11C2416yes—
102C22×Dic11C2411yescharacteristic
103Q8×D11—416no—
104C2×C4×D11—26no—
105C2×C4×D11—26no—
106C2×C4×D11—212no—
107C2×C4×D11—212no—
108C2×C4×D11—26no—
109C2×C4×D11—212no—
110C2×C4×D11—212no—
111C2×C4×D11—26no—
112C2×C4×D11—212no—
113C2×C4×D11#41112yes—
114C2×Dic22—212no—
115C2×Dic22—26no—
116C11×C4⋊C4—26no—
117C11×C4⋊C4—46no—
118C42×C11—26no—
119C4⋊Dic11—26no—
120C4⋊Dic11—46no—
121Dic11⋊C4—212no—
122Dic11⋊C4—46no—
123Dic11⋊C4—46no—
124C4×Dic11—26no—
125C4×Dic11—26no—
126C4×Dic11—26no—
127#2645—112no—
128#2645—116no—
129#2645—113no—
130#2645—113no—
131#2645—111no—
132#2645D1111yescharacteristic, direct product factor
133C2×#401—112no—
134C2×#400—116no—
135C2×#391—113no—
136C2×#389—113no—
137C2×#376—111no—
138C23×C11C2511yescharacteristic
139C22×D11C2×#4116yes—
140C22×D11H(5,𝔽2)12yes—
141C22×D112−1+416yes—
142Q8×C11—44no—
143C2×C4×C11—23no—
144C2×C4×C11—23no—
145C2×C4×C11—26no—
146C2×C4×C11—26no—
147C2×C4×C11—23no—
148C2×C4×C11—26no—
149C2×C4×C11—26no—
150C2×C4×C11—23no—
151C2×C4×C11—26no—
152C2×C4×C11C2×#4116yes—
153C2×Dic11—23no—
154C2×Dic11—23no—
155C2×Dic11—26no—
156C2×Dic11—26no—
157C2×Dic11—26no—
158C2×Dic11—23no—
159C2×Dic11—26no—
160C2×Dic11—23no—
161C2×Dic11—26no—
162C2×Dic11C2×#4116yes—
163C4×D11—48no—
164C4×D11—412no—
165C4×D11—412no—
166C4×D11—424no—
167C4×D11#126116yes—
168Dic22—44no—
169Dic22—48no—
170C23×Q8—111no—
171C22×C4⋊C4—113no—
172C22×C4⋊C4—116no—
173C22×C42—113no—
174#401—116no—
175#401—116no—
176#401—112no—
177#401C2×D1112yes—
178#400—116no—
179#400—116no—
180#400—116no—
181#400—116no—
182#400—116no—
183#400—116no—
184#400—116no—
185#400C2×D1116yes—
186#391—113no—
187#391—113no—
188#391—113no—
189#391—116no—
190#391—116no—
191#391C2×D1113yes—
192#389—116no—
193#389—113no—
194#389—113no—
195#389—113no—
196#389—116no—
197#389C2×D1113yes—
198#376—113no—
199#376—111no—
200#376—113no—
201#376C2×D1111yescharacteristic
202C2×#95—113no—
203C2×#95—116no—
204C2×#95—116no—
205C2×#95—116no—
206C2×#95—111no—
207C22×C11C22×#4113yes—
208C22×C11C2×H(5,𝔽2)11yescharacteristic
209C22×C11C2×2−1+413yes—
210C2×D11C2×#12614yes—
211C2×D11#541112yes—
212C2×D11#542112yes—
213C4×C11—42no—
214C4×C11—43no—
215C4×C11—43no—
216C4×C11—46no—
217C4×C11C2×#12614yes—
218Dic11—42no—
219Dic11—43no—
220Dic11—43no—
221Dic11—46no—
222Dic11C2×#12614yes—
223C22×Q8—112no—
224C22×Q8—111no—
225C22×Q8—2212no—
226C22×Q8C22×D1111yescharacteristic
227C23×C4—111no—
228C23×C4—116no—
229C23×C4—113no—
230C23×C4—112no—
231C23×C4—113no—
232C2×C4⋊C4—116no—
233C2×C4⋊C4—113no—
234C2×C4⋊C4—116no—
235C2×C4⋊C4—116no—
236C2×C4⋊C4—116no—
237C2×C4⋊C4—2212no—
238C2×C4⋊C4—4412no—
239C2×C4⋊C4C22×D1113yes—
240C2×C4⋊C4C22×D1116yes—
241C2×C42—113no—
242C2×C42—113no—
243C2×C42—113no—
244C2×C42—2212no—
245C2×C42C22×D1113yes—
246#95—113no—
247#95—113no—
248#95—113no—
249#95—113no—
250#95—116no—
251#95—116no—
252#95—116no—
253#95—116no—
254#95—116no—
255#95—116no—
256#95—116no—
257#95—116no—
258#95—116no—
259#95C22×D1113yes—
260#95C22×D1111yescharacteristic
261#95C22×D1116yes—
262#95C22×D1116yes—
263#95C22×D1116yes—
264C2×C11C22×#12611yescharacteristic
265C2×C11C2×#54113yes—
266C2×C11C2×#54213yes—
267D11#264518yesdirect product factor
268C24—111no—
269C2×Q8—26no—
270C2×Q8—2212no—
271C2×Q8—226no—
272C2×Q8—4416no—
273C22×C4—111no—
274C22×C4—1112no—
275C22×C4—113no—
276C22×C4—112no—
277C22×C4—113no—
278C22×C4—116no—
279C22×C4—226no—
280C22×C4—226no—
281C22×C4—2212no—
282C22×C4—2212no—
283C22×C4—226no—
284C22×C4—2212no—
285C22×C4—2212no—
286C22×C4—226no—
287C22×C4—2212no—
288C22×C4C23×D1113yes—
289C22×C4C23×D1112yes—
290C22×C4C23×D1113yes—
291C22×C4C23×D1116yes—
292C22×C4C23×D1111yescharacteristic
293C4⋊C4—26no—
294C4⋊C4—46no—
295C4⋊C4—2212no—
296C4⋊C4—226no—
297C4⋊C4—446no—
298C4⋊C4—446no—
299C4⋊C4—446no—
300C42—26no—
301C42—226no—
302C42—226no—
303C42—226no—
304C11C2×#264511yescharacteristic, complemented, Sylow
305C23—116no—
306C23—112no—
307C23—116no—
308C23C24×D1111yescharacteristic
309Q8—44no—
310Q8—448no—
311Q8—444no—
312C2×C4—23no—
313C2×C4—23no—
314C2×C4—26no—
315C2×C4—26no—
316C2×C4—23no—
317C2×C4—26no—
318C2×C4—26no—
319C2×C4—23no—
320C2×C4—26no—
321C2×C4—116no—
322C2×C4—1116no—
323C2×C4—223no—
324C2×C4—223no—
325C2×C4—226no—
326C2×C4—226no—
327C2×C4—226no—
328C2×C4—223no—
329C2×C4—226no—
330C2×C4—223no—
331C2×C4—226no—
332C2×C4—448no—
333C2×C4—4412no—
334C2×C4—4412no—
335C2×C4—4424no—
336C2×C4#41×D1116yes—
337C22—114no—
338C22—1112no—
339C22—1112no—
340C22C2×#41×D1113yes—
341C22D11×H(5,𝔽2)11yescharacteristic
342C22D11×2−1+413yes—
343C4—42no—
344C4—43no—
345C4—43no—
346C4—46no—
347C4—114no—
348C4—442no—
349C4—443no—
350C4—443no—
351C4—446no—
352C4D11×#12614yes—
353C2—118no—
354C2C2×D11×#12611yescharacteristic
355C2D11×#54113yes—
356C2D11×#54213yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2645C2
prime radicalC23×D11C24
hypercenter#2645D11
hypocenterC11C2×#2645
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2645

Complements

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

NH ≅ G/Ntype
1. #13074584C2semidirect
2. #13074583C2semidirect
3. #13074582C2semidirect
4. #13074581C2semidirect
5. #13074580C2semidirect
11. C11×#2645C2semidirect
132. #2645D11direct (N × H)
267. D11#2645direct (N × H)
304. C11C2×#2645semidirect

Maximal subgroups

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

subgroupindex
#130745842
#130745832
#130745822
#130745812
#130745802
D11×#4012
D11×#4002
D11×#3912
D11×#3892
D11×#3762
C11×#26452
C2×#264511