Finite Group Databasebeta

← D11×#2842 #14960182

Subgroups — D11×#2842 #14960182

Order 2816.

3294 conjugacy classes of subgroups; only the 579 normal subgroups are shown.

normal subgroups only

This group has 3294 conjugacy classes of subgroups — too many to draw. Only its 579 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076881C214yesmaximal, complemented
2#13076880C213yesmaximal, complemented
3#13076879C218yesmaximal, complemented
4D11×#399C214yesmaximal, complemented
5D11×#396C218yesmaximal, complemented
6D11×#379C213yesmaximal
7C11×#2842C211yesmaximal, characteristic, complemented
8C25×D11C2211yescharacteristic
9C2×C4⋊C4×D11C22112yescomplemented
10C2×C22⋊C4×D11C22112yes—
11C2×C22⋊C4×D11C2216yes—
12C11×#399C2214yescomplemented
13C11×#396C2218yescomplemented
14C11×#379C2213yes—
15#10622860C2213yes—
16#10622607C22124yescomplemented
17#10622605C22112yescomplemented
18#10622568C22112yes—
19#10622568C2216yes—
20#10622562C22112yescomplemented
21#10622561C22124yescomplemented
22#10622290C2214yescomplemented
23#10622289C2218yescomplemented
24D11×#95C2214yescomplemented
25C25×C11C2311yescharacteristic
26C24×D11—412no—
27C24×D11Q818yes—
28C24×D11C2312yes—
29C24×D11C2311yescharacteristic
30C24×D11C2312yes—
31C24×D11C2311yescharacteristic
32C22×C4×D11C23112yes—
33C2×C11×C4⋊C4C23112yescomplemented
34C2×C11×C22⋊C4C23112yes—
35C2×C11×C22⋊C4C2316yes—
36C2×C22⋊Dic11C23112yes—
37C2×C22⋊Dic11C2316yes—
38C2×(C2×D11)⋊C4C23124yes—
39C2×(C2×D11)⋊C4C23112yes—
40C2×C4⋊Dic11C23112yescomplemented
41C2×Dic11⋊C4C23124yescomplemented
42C4⋊C4×D11—424no—
43C22⋊C4×D11—424no—
44C22⋊C4×D11—412no—
45C11×#95C2314yescomplemented
46C11⋊#95C23112yescomplemented
47C2×#2842—111nomaximal, Sylow
48C24×C11—46no—
49C24×C11C2×Q814yes—
50C24×C11C2412yes—
51C24×C11C2411yescharacteristic
52C23×D11—224no—
53C23×D11—212no—
54C23×D11—448no—
55C23×D11—412no—
56C23×D11—46no—
57C23×D11—464no—
58C23×D11C2×Q818yes—
59C23×D11C2×Q814yes—
60C23×D11C2×Q818yes—
61C23×D11C2×Q814yes—
62C23×D11C2412yes—
63C23×D11C2411yescharacteristic
64C23×D11C2411yescharacteristic
65C22×C4×C11C24112yes—
66C22×Dic11C24112yes—
67C2×C4×D11—248no—
68C2×C4×D11—224no—
69C11×C4⋊C4—412no—
70C11×C22⋊C4—412no—
71C11×C22⋊C4—46no—
72C22⋊Dic11—46no—
73C22⋊Dic11—412no—
74(C2×D11)⋊C4—424no—
75(C2×D11)⋊C4—412no—
76C4⋊Dic11—412no—
77Dic11⋊C4—424no—
78#2842—114no—
79#2842—118no—
80#2842—113no—
81#2842D1111yescharacteristic, direct product factor
82C2×#399—114no—
83C2×#396—118no—
84C2×#379—113no—
85C23×C11—26no—
86C23×C11—212no—
87C23×C11—412no—
88C23×C11—416no—
89C23×C11C22×Q814yes—
90C23×C11C22×Q812yes—
91C23×C11C2511yescharacteristic
92C22×D11—212no—
93C22×D11—26no—
94C22×D11—248no—
95C22×D11—224no—
96C22×D11—424no—
97C22×D11—412no—
98C22×D11—432no—
99C22×D11—416no—
100C22×D11—4128no—
101C22×D11—432no—
102C22×D11—416no—
103C22×D11C22×Q814yes—
104C22×D11C22×Q812yes—
105C22×D11C22×Q812yes—
106C22×D11H(5,𝔽2)112yes—
107C2×C4×C11—224no—
108C2×C4×C11—212no—
109C2×Dic11—212no—
110C2×Dic11—224no—
111C4×D11—448no—
112C26—111no—
113C22×C4⋊C4—1112no—
114C22×C22⋊C4—1112no—
115C22×C22⋊C4—116no—
116#399—1112no—
117#399—1112no—
118#399—114no—
119#399C2×D1114yescomplemented
120#396—1124no—
121#396—1124no—
122#396—118no—
123#396C2×D1118yescomplemented
124#379—113no—
125#379—1112no—
126#379—116no—
127#379C2×D1113yes—
128C2×#95—114no—
129C22×C11—26no—
130C22×C11—212no—
131C22×C11—416no—
132C22×C11—44no—
133C22×C11—48no—
134C22×C11C23×Q811yescharacteristic
135C22×C11C2×H(5,𝔽2)16yes—
136C2×D11—212no—
137C2×D11—26no—
138C2×D11—432no—
139C2×D11—416no—
140C2×D11—48no—
141C2×D11—44no—
142C2×D11—432no—
143C2×D11—416no—
144C2×D11#543112yes—
145C2×D11#560116yes—
146C4×C11—412no—
147Dic11—412no—
148C25—112no—
149C25—111no—
150C25—118no—
151C25—111no—
152C25—112no—
153C25—4412no—
154C25C22×D1111yescharacteristic
155C23×C4—1112no—
156C2×C4⋊C4—1124no—
157C2×C4⋊C4—1112no—
158C2×C4⋊C4—4424no—
159C2×C4⋊C4C22×D11112yescomplemented
160C2×C22⋊C4—1112no—
161C2×C22⋊C4—116no—
162C2×C22⋊C4—1124no—
163C2×C22⋊C4—1112no—
164C2×C22⋊C4—4424no—
165C2×C22⋊C4—4412no—
166C2×C22⋊C4C22×D11112yes—
167C2×C22⋊C4C22×D1116yes—
168#95—1112no—
169#95C22×D1114yescomplemented
170C2×C11—42no—
171C2×C11—44no—
172C2×C11C2×#54313yes—
173C2×C11C2×#56014yes—
174D11—44no—
175D11—42no—
176D11#284218yesdirect product factor
177C24—46no—
178C24—111no—
179C24—118no—
180C24—114no—
181C24—112no—
182C24—111no—
183C24—114no—
184C24—118no—
185C24—2224no—
186C24—2212no—
187C24—4412no—
188C24—446no—
189C24—4448no—
190C24—4464no—
191C24Q8×D1114yes—
192C24C23×D1112yes—
193C24C23×D1111yescharacteristic
194C22×C4—1112no—
195C22×C4—2248no—
196C22×C4—2224no—
197C22×C4C23×D11112yes—
198C4⋊C4—412no—
199C4⋊C4—4424no—
200C4⋊C4—4412no—
201C22⋊C4—412no—
202C22⋊C4—46no—
203C22⋊C4—4424no—
204C22⋊C4—4412no—
205C22⋊C4—4412no—
206C22⋊C4—446no—
207C11C2×#284211yescharacteristic, complemented, Sylow
208C23—212no—
209C23—26no—
210C23—412no—
211C23—416no—
212C23—112no—
213C23—1112no—
214C23—114no—
215C23—112no—
216C23—2248no—
217C23—2224no—
218C23—2212no—
219C23—226no—
220C23—4424no—
221C23—4412no—
222C23—4432no—
223C23—4416no—
224C23—44128no—
225C23—4432no—
226C23—4416no—
227C23C2×Q8×D1114yes—
228C23C2×Q8×D1112yes—
229C23C24×D1111yescharacteristic
230C2×C4—224no—
231C2×C4—212no—
232C2×C4—2212no—
233C2×C4—2224no—
234C2×C4—4448no—
235C22—212no—
236C22—26no—
237C22—416no—
238C22—48no—
239C22—44no—
240C22—1116no—
241C22—1112no—
242C22—2212no—
243C22—226no—
244C22—4432no—
245C22—4416no—
246C22—4432no—
247C22—4416no—
248C22—448no—
249C22—444no—
250C22C22×Q8×D1111yescharacteristic
251C22D11×H(5,𝔽2)16yes—
252C4—412no—
253C4—4412no—
254C2—44no—
255C2—42no—
256C2—118no—
257C2—444no—
258C2—442no—
259C2D11×#54313yes—
260C2D11×#56014yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2842C2
prime radicalC25×D11C22
hypercenter#2842D11
hypocenterC11C2×#2842
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2842

Complements

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

NH ≅ G/Ntype
1. #13076881C2semidirect
2. #13076880C2semidirect
3. #13076879C2semidirect
4. D11×#399C2semidirect
5. D11×#396C2semidirect
7. C11×#2842C2semidirect
9. C2×C4⋊C4×D11C22semidirect
12. C11×#399C22semidirect
13. C11×#396C22semidirect
16. #10622607C22semidirect
17. #10622605C22semidirect
20. #10622562C22semidirect
21. #10622561C22semidirect
22. #10622290C22semidirect
23. #10622289C22semidirect
24. D11×#95C22semidirect
33. C2×C11×C4⋊C4C23semidirect
40. C2×C4⋊Dic11C23semidirect
41. C2×Dic11⋊C4C23semidirect
45. C11×#95C23semidirect
46. C11⋊#95C23semidirect
81. #2842D11direct (N × H)
119. #399C2×D11semidirect
123. #396C2×D11semidirect
159. C2×C4⋊C4C22×D11semidirect
169. #95C22×D11semidirect
176. D11#2842direct (N × H)
207. C11C2×#2842semidirect

Maximal subgroups

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

subgroupindex
#130768812
#130768802
#130768792
D11×#3992
D11×#3962
D11×#3792
C11×#28422
C2×#284211