Finite Group Databasebeta

← D11×#2866 #14959815

Subgroups — D11×#2866 #14959815

Order 2816.

2186 conjugacy classes of subgroups; only the 591 normal subgroups are shown.

normal subgroups only

This group has 2186 conjugacy classes of subgroups — too many to draw. Only its 591 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#13077009C217yesmaximal, complemented
2#13077008C211yesmaximal, characteristic, complemented
3#13077007C217yesmaximal, complemented
4D11×#388C217yesmaximal
5D11×#387C217yesmaximal, complemented
6C43×D11C211yesmaximal, characteristic, complemented
7C11×#2866C211yesmaximal, characteristic, complemented
8C2×C4⋊C4×D11C2217yes—
9C2×C22⋊C4×D11C2217yes—
10C2×C42×D11C2217yes—
11C11×#388C2217yes—
12C11×#387C2217yescomplemented
13C43×C11C2211yescharacteristic, complemented
14#10622603C2217yes—
15#10622594C2217yescomplemented
16#10622591C2217yescomplemented
17#10622564C2217yes—
18#10622558C2217yes—
19#10622557C2217yes—
20#10622553C2217yes—
21#10622546C2217yescomplemented
22C42×Dic11C2217yescomplemented
23#10622283C2217yes—
24#10622282C2217yes—
25D11×#95C2217yes—
26D11×#95C2217yes—
27#10622268C2217yescomplemented
28#10622267C2217yescomplemented
29#10622266C2217yescomplemented
30#10622265C2217yescomplemented
31C24×D11C2311yescharacteristic
32C22×C4×D11C2317yes—
33C22×C4×D11C2317yes—
34C2×C11×C4⋊C4C2317yes—
35C2×C11×C22⋊C4C2317yes—
36C2×C42×C11C2317yes—
37C2×C22⋊Dic11C2317yes—
38C2×(C2×D11)⋊C4C2317yes—
39C2×(C2×D11)⋊C4C2317yes—
40C2×C4⋊Dic11C2317yes—
41C2×Dic11⋊C4C2317yes—
42C2×Dic11⋊C4C2317yes—
43C2×C4×Dic11C2317yes—
44C2×C4×Dic11C2317yes—
45C2×C4×Dic11C2317yes—
46C4⋊C4×D11—228no—
47C22⋊C4×D11—228no—
48C42×D11—228no—
49C11×#95C2317yes—
50C11×#95C2317yes—
51C11⋊#95C2317yes—
52C11⋊#95C2317yes—
53C11⋊#95C2317yes—
54C11⋊#95C2317yes—
55C11⋊#95C2317yes—
56C11⋊#95C2317yes—
57C2×#2866—111nomaximal, Sylow
58C24×C11C2411yescharacteristic
59C23×D11—214no—
60C23×D11C2411yescharacteristic
61C23×D11C2411yescharacteristic
62C22×C4×C11C2417yes—
63C22×C4×C11C2417yes—
64C22×Dic11C2417yes—
65C22×Dic11C2417yes—
66C2×C4×D11—214no—
67C2×C4×D11—214no—
68C2×C4×D11—214no—
69C2×C4×D11—214no—
70C2×C4×D11—214no—
71C2×C4×D11#41128yes—
72C11×C4⋊C4—214no—
73C11×C22⋊C4—214no—
74C42×C11—214no—
75C22⋊Dic11—214no—
76(C2×D11)⋊C4—214no—
77(C2×D11)⋊C4—214no—
78C4⋊Dic11—214no—
79Dic11⋊C4—214no—
80Dic11⋊C4—214no—
81C4×Dic11—214no—
82C4×Dic11—214no—
83C4×Dic11—214no—
84#2866—117no—
85#2866—117no—
86#2866—111no—
87#2866D1111yescharacteristic, direct product factor
88C2×#388—117no—
89C2×#387—117no—
90C2×C43—111no—
91C23×C11—27no—
92C23×C11C2511yescharacteristic
93C22×D11—27no—
94C22×D11—428no—
95C22×D11C2×#41114yes—
96C2×C4×C11—27no—
97C2×C4×C11—27no—
98C2×C4×C11—27no—
99C2×C4×C11—27no—
100C2×C4×C11—27no—
101C2×C4×C11C2×#41114yes—
102C2×Dic11—27no—
103C2×Dic11—27no—
104C2×Dic11—27no—
105C2×Dic11—27no—
106C2×Dic11—27no—
107C2×Dic11C2×#41114yes—
108C4×D11—256no—
109C4×D11—428no—
110C22×C4⋊C4—117no—
111C22×C22⋊C4—117no—
112C22×C42—117no—
113#388—117no—
114#388—117no—
115#388—117no—
116#388—117no—
117#388—117no—
118#388—117no—
119#388—117no—
120#388C2×D1117yes—
121#387—117no—
122#387—117no—
123#387—117no—
124#387—117no—
125#387—117no—
126#387—117no—
127#387—117no—
128#387C2×D1117yescomplemented
129C2×#95—117no—
130C2×#95—117no—
131C43—117no—
132C43C2×D1111yescharacteristic, complemented
133C22×C11—47no—
134C22×C11C22×#4117yes—
135C2×D11—47no—
136C2×D11—88no—
137C2×D11#529128yes—
138C4×C11—214no—
139C4×C11—47no—
140Dic11—214no—
141Dic11—47no—
142C25—111no—
143C23×C4—117no—
144C23×C4—117no—
145C2×C4⋊C4—117no—
146C2×C4⋊C4—117no—
147C2×C4⋊C4—117no—
148C2×C4⋊C4—2228no—
149C2×C4⋊C4C22×D1117yes—
150C2×C22⋊C4—117no—
151C2×C22⋊C4—117no—
152C2×C22⋊C4—117no—
153C2×C22⋊C4—2228no—
154C2×C22⋊C4C22×D1117yes—
155C2×C42—117no—
156C2×C42—117no—
157C2×C42—117no—
158C2×C42—2228no—
159C2×C42C22×D1117yes—
160#95—117no—
161#95—117no—
162#95—117no—
163#95—117no—
164#95—117no—
165#95—117no—
166#95C22×D1117yes—
167#95C22×D1117yes—
168C2×C11—81no—
169C2×C11C2×#52917yes—
170D11—81no—
171D11#286618yesdirect product factor
172C24—111no—
173C24—111no—
174C24—2214no—
175C24C23×D1111yescharacteristic
176C22×C4—117no—
177C22×C4—1128no—
178C22×C4—117no—
179C22×C4—2214no—
180C22×C4—2214no—
181C22×C4—2214no—
182C22×C4—2214no—
183C22×C4—2214no—
184C22×C4C23×D1117yes—
185C22×C4C23×D1117yes—
186C4⋊C4—214no—
187C4⋊C4—2214no—
188C4⋊C4—2214no—
189C4⋊C4—2214no—
190C22⋊C4—214no—
191C22⋊C4—2214no—
192C22⋊C4—2214no—
193C22⋊C4—2214no—
194C42—214no—
195C42—2214no—
196C42—2214no—
197C42—2214no—
198C11C2×#286611yescharacteristic, complemented, Sylow
199C23—27no—
200C23—1114no—
201C23—227no—
202C23—4428no—
203C23C24×D1111yescharacteristic
204C2×C4—27no—
205C2×C4—27no—
206C2×C4—27no—
207C2×C4—27no—
208C2×C4—27no—
209C2×C4—1114no—
210C2×C4—2256no—
211C2×C4—227no—
212C2×C4—227no—
213C2×C4—227no—
214C2×C4—227no—
215C2×C4—227no—
216C2×C4—4428no—
217C2×C4#41×D11114yes—
218C22—47no—
219C22—1128no—
220C22—447no—
221C22—888no—
222C22C2×#41×D1117yes—
223C4—214no—
224C4—47no—
225C4—2214no—
226C4—447no—
227C2—81no—
228C2—118no—
229C2—881no—
230C2D11×#52917yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2866C2
prime radicalC24×D11C23
hypercenter#2866D11
hypocenterC11C2×#2866
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2866

Complements

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

NH ≅ G/Ntype
1. #13077009C2semidirect
2. #13077008C2semidirect
3. #13077007C2semidirect
5. D11×#387C2semidirect
6. C43×D11C2semidirect
7. C11×#2866C2semidirect
12. C11×#387C22semidirect
13. C43×C11C22semidirect
15. #10622594C22semidirect
16. #10622591C22semidirect
21. #10622546C22semidirect
22. C42×Dic11C22semidirect
27. #10622268C22semidirect
28. #10622267C22semidirect
29. #10622266C22semidirect
30. #10622265C22semidirect
87. #2866D11direct (N × H)
128. #387C2×D11semidirect
132. C43C2×D11semidirect
171. D11#2866direct (N × H)
198. C11C2×#2866semidirect

Maximal subgroups

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

subgroupindex
#130770092
#130770082
#130770072
D11×#3882
D11×#3872
C43×D112
C11×#28662
C2×#286611