Finite Group Databasebeta

← #14641366

Subgroups — #14641366

Order 2816.

206 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 41 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#13069777C211yesmaximal, characteristic
2#13066442C211yesmaximal, characteristic
3C11×#1394C211yesmaximal, characteristic
4#10623031C411yescharacteristic
5C2×C11×#101—21no—
6C11×#391C2211yescharacteristic
7#10622838—21no—
8#10622168C411yescharacteristic
9#10622162—21no—
10#10622161—21no—
11C22×Q8×C11D411yescharacteristic
12C2×C11×M16—41no—
13C2×C11×C4⋊C4C2×C411yescharacteristic
14C2×C42×C11D411yescharacteristic
15#66979—21no—
16#66977—41no—
17C2×#4318—21no—
18C22×C11⋊C8—41no—
19#66943—41no—
20#66941—41no—
21C11×#101—22no—
22C11×#101—41no—
23C11×#95—41no—
24#66899—41no—
25#66899—41no—
26#7431—111nomaximal, Sylow
27C2×Q8×C11—21no—
28C2×Q8×C11—41no—
29C2×Q8×C11—41no—
30C2×Q8×C11SD1611yescharacteristic
31C2×Q8×C11Q1611yescharacteristic
32C22×C4×C11—21no—
33C22×C4×C11—21no—
34C22×C4×C11—21no—
35C22×C4×C11C22⋊C411yescharacteristic
36C2×Dic22—41no—
37C11×M16—42no—
38C11×M16—81no—
39C2×C8×C11—81no—
40C11×C4⋊C4—41no—
41C42×C11—41no—
42C22⋊Dic11—41no—
43C4⋊Dic11—21no—
44C4⋊Dic11—21no—
45C4⋊Dic11—41no—
46Dic11⋊C4—42no—
47C4×Dic11—41no—
48#4318—41no—
49#4318—41no—
50C2×C11⋊C8—41no—
51C2×C11⋊C8—42no—
52C2×C11⋊C8—81no—
53C2×C11⋊C8—81no—
54#2028—111no—
55#1394D1111yescharacteristic
56#1272—111no—
57C23×C11#9911yescharacteristic
58Q8×C11—41no—
59Q8×C11—41no—
60Q8×C11—81no—
61C2×C4×C11—21no—
62C2×C4×C11—21no—
63C2×C4×C11—21no—
64C2×C4×C11—21no—
65C2×C4×C11—21no—
66C2×C4×C11—21no—
67C2×C4×C11—41no—
68C2×C4×C11—41no—
69C2×C4×C11—41no—
70C2×C4×C11—41no—
71C2×C4×C11—41no—
72C2×C4×C11—81no—
73C2×C4×C11#10311yescharacteristic
74C2×C4×C11#10411yescharacteristic
75C2×Dic11—41no—
76C2×Dic11—41no—
77Dic22—161no—
78C8×C11—82no—
79C11⋊C8—81no—
80C11⋊C8—82no—
81#544—111no—
82#419—221no—
83C2×#101—21no—
84#391C2×D1111yescharacteristic
85#343—111no—
86#339—221no—
87#336—221no—
88C22×C11—21no—
89C22×C11—21no—
90C22×C11#32811yescharacteristic
91C22×C11AΣL(1,𝔽16)11yescharacteristic
92C22×C11#35411yescharacteristic
93C4×C11—21no—
94C4×C11—21no—
95C4×C11—41no—
96C4×C11—41no—
97C4×C11—41no—
98C4×C11—41no—
99C4×C11—81no—
100Dic11—81no—
101Dic11—81no—
102C22×Q8C22⋊D1111yescharacteristic
103C2×M16—41no—
104C2×M16—221no—
105C22×C8—441no—
106C4⋊Q8—441no—
107#125—441no—
108C22⋊Q8—441no—
109#117—221no—
110C2×C4⋊C4C4×D1111yescharacteristic
111C2×C42D4411yescharacteristic
112#103—441no—
113#103—441no—
114#101—22no—
115#101—41no—
116#95—41no—
117C2×C11—21no—
118C2×C11—21no—
119C2×C11#135111yescharacteristic
120C2×C11#140311yescharacteristic
121C2×C11#140511yescharacteristic
122C2×Q8—21no—
123C2×Q8—41no—
124C2×Q8—41no—
125C2×Q8—441no—
126C2×Q8#432411yescharacteristic
127C2×Q8#432611yescharacteristic
128C22×C4—21no—
129C22×C4—21no—
130C22×C4—21no—
131C22×C4(C2×D11)⋊C411yescharacteristic
132M16—42no—
133M16—81no—
134M16—441no—
135M16—441no—
136C2×C8—81no—
137C2×C8—441no—
138C2×C8—442no—
139C2×C8—881no—
140C2×C8—881no—
141C4⋊C4—41no—
142C4⋊C4—221no—
143C4⋊C4—221no—
144C4⋊C4—441no—
145C4⋊C4—442no—
146C22⋊C4—441no—
147C42—41no—
148C42—441no—
149C11#743111yescharacteristic, complemented, Sylow
150C23#6687011yescharacteristic
151Q8—41no—
152Q8—41no—
153Q8—81no—
154Q8—1761no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—81no—
167C2×C4—441no—
168C2×C4—441no—
169C2×C4#6686911yescharacteristic
170C2×C4#6687411yescharacteristic
171C8—82no—
172C8—881no—
173C8—882no—
174C22—21no—
175C22—21no—
176C22#1062209011yescharacteristic
177C22#1062210911yescharacteristic
178C22#1062211111yescharacteristic
179C4—21no—
180C4—21no—
181C4—41no—
182C4—41no—
183C4—41no—
184C4—41no—
185C4—81no—
186C4—881no—
187C4—881no—
188C2—21no—
189C2—21no—
190C2#1306663611yescharacteristic
191C2#1306676311yescharacteristic
192C2#1306676911yescharacteristic
subgroupG/H
centerC22#10622109
commutatorC2×C11×C4⋊C4C2×C4
Frattini#391C2×D11
FittingC11×#1394C2
socleC22×C11AΣL(1,𝔽16)
prime radicalC23×C11#99
cosocleC11×#391C22
hypercenter#1394D11
hypocenterC11#7431
LCSG ▷ C2×C11×C4⋊C4 ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #391 ◁ #1394

Complements

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

NH ≅ G/Ntype
149. C11#7431semidirect

Maximal subgroups

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

subgroupindex
#130697772
#130664422
C11×#13942
#743111