Finite Group Databasebeta

← #14640375

Subgroups — #14640375

Order 2816.

352 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 107 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#13068596C212yesmaximal
2C11×#1817C211yesmaximal, characteristic
3C22×C42×C11C2211yescharacteristic
4C2×C11×C22⋊C8C412yes—
5C2×C22⋊(C11⋊C8)—22no—
6C2×C4⋊(C11⋊C8)—22no—
7C11×#336—22no—
8#10622162C414yes—
9C23×C4×C11C2×C411yescharacteristic
10C23×C4×C11D411yescharacteristic
11C23×C4×C11Q811yescharacteristic
12C22×C8×C11—22no—
13C2×C42×C11—42no—
14C2×C42×C11C2×C412yes—
15C2×C42×C11D412yes—
16C22×C11⋊C8—24no—
17C11×C22⋊C8—42no—
18C22⋊(C11⋊C8)—42no—
19C22⋊(C11⋊C8)—42no—
20C4⋊(C11⋊C8)—44no—
21#7044—111nomaximal, Sylow
22C24×C11C4⋊C411yescharacteristic
23C22×C4×C11—22no—
24C22×C4×C11—24no—
25C22×C4×C11—41no—
26C22×C4×C11—41no—
27C22×C4×C11—42no—
28C22×C4×C11—41no—
29C22×C4×C11C4211yescharacteristic
30C22×C4×C11C22⋊C411yescharacteristic
31C22×C4×C11C22⋊C412yes—
32C22×C4×C11C4⋊C412yes—
33C22×C4×C11D811yescharacteristic
34C22×C4×C11SD1612yes—
35C22×C4×C11Q1611yescharacteristic
36C2×C8×C11—44no—
37C2×C8×C11—42no—
38C42×C11—24no—
39C42×C11—42no—
40C2×C11⋊C8—44no—
41C2×C11⋊C8—44no—
42C2×C11⋊C8—44no—
43#1817D1111yescharacteristic
44#1797—112no—
45C23×C11—21no—
46C23×C11—22no—
47C23×C11—21no—
48C23×C11—22no—
49C23×C11#9511yescharacteristic
50C23×C11#10611yescharacteristic
51C23×C11#10711yescharacteristic
52C2×C4×C11—22no—
53C2×C4×C11—22no—
54C2×C4×C11—22no—
55C2×C4×C11—22no—
56C2×C4×C11—22no—
57C2×C4×C11—21no—
58C2×C4×C11—22no—
59C2×C4×C11—41no—
60C2×C4×C11—42no—
61C2×C4×C11—41no—
62C2×C4×C11—44no—
63C2×C4×C11—44no—
64C2×C4×C11#9912yes—
65C2×C4×C11#10212yes—
66C2×C4×C11#10312yes—
67C2×C4×C11#10814yes—
68C8×C11—82no—
69C11⋊C8—84no—
70C22×C42C2×D1111yescharacteristic
71C2×C4⋊C8—222no—
72C2×C22⋊C8—222no—
73C2×C22⋊C8Dic1112yes—
74#336—22no—
75#336—114no—
76C22×C11—21no—
77C22×C11—21no—
78C22×C11—22no—
79C22×C11—22no—
80C22×C11—42no—
81C22×C11—41no—
82C22×C11—41no—
83C22×C11H(3,ℤ/4)11yescharacteristic
84C22×C11#34011yescharacteristic
85C22×C11#34112yes—
86C22×C11#34211yescharacteristic
87C22×C11#34412yes—
88C4×C11—22no—
89C4×C11—22no—
90C4×C11—24no—
91C4×C11—22no—
92C4×C11—41no—
93C23×C4Dic2211yescharacteristic
94C23×C4D4411yescharacteristic
95C23×C4C2×Dic1111yescharacteristic
96C22×C8—22no—
97C22×C8—224no—
98C2×C42—42no—
99C2×C42C4×D1112yes—
100C2×C42C22⋊D1112yes—
101C4⋊C8—444no—
102C22⋊C8—42no—
103C22⋊C8—442no—
104C22⋊C8—442no—
105C2×C11—41no—
106C2×C11—41no—
107C2×C11#128712yes—
108C2×C11#128911yescharacteristic
109C2×C11#129811yescharacteristic
110C2×C11#130112yes—
111C2×C11#130611yescharacteristic
112C24C4⋊Dic1111yescharacteristic
113C22×C4—24no—
114C22×C4—22no—
115C22×C4—41no—
116C22×C4—41no—
117C22×C4—41no—
118C22×C4—42no—
119C22×C4#431412yes—
120C22×C4D8811yescharacteristic
121C22×C4Dic4411yescharacteristic
122C22×C4C4×Dic1111yescharacteristic
123C22×C4Dic11⋊C412yes—
124C22×C4(C2×D11)⋊C412yes—
125C22×C4C22⋊Dic1111yescharacteristic
126C2×C8—44no—
127C2×C8—42no—
128C2×C8—444no—
129C2×C8—444no—
130C2×C8—444no—
131C42—24no—
132C42—42no—
133C11#704411yescharacteristic, complemented, Sylow
134C23—21no—
135C23—22no—
136C23—21no—
137C23—22no—
138C23#6688111yescharacteristic
139C23#6688211yescharacteristic
140C23C11⋊#9511yescharacteristic
141C2×C4—22no—
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—22no—
146C2×C4—21no—
147C2×C4—22no—
148C2×C4—42no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—44no—
152C2×C4—44no—
153C2×C4#6688012yes—
154C2×C4#6688512yes—
155C2×C4#6688614yes—
156C2×C4#6689812yes—
157C8—82no—
158C8—884no—
159C22—22no—
160C22—22no—
161C22—21no—
162C22—21no—
163C22—41no—
164C22—41no—
165C22—42no—
166C22#1062216411yescharacteristic
167C22#1062217112yes—
168C22#1062218911yescharacteristic
169C22#1062219511yescharacteristic
170C22#1062219612yes—
171C4—24no—
172C4—22no—
173C4—22no—
174C4—22no—
175C4—41no—
176C2—41no—
177C2—41no—
178C2#1306647912yes—
179C2#1306648411yescharacteristic
180C2#1306650311yescharacteristic
181C2#1306651212yes—
182C2#1306652411yescharacteristic
subgroupG/H
centerC23C11⋊#95
commutatorC22×C4×C11C42
FrattiniC22×C42C2×D11
FittingC11×#1817C2
socleC23×C11#95
prime radicalC24×C11C4⋊C4
cosocleC22×C42×C11C22
hypercenter#1817D11
hypocenterC11#7044
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1817

Complements

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

NH ≅ G/Ntype
133. C11#7044semidirect

Maximal subgroups

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

subgroupindex
#130685962
C11×#18172
#704411