Finite Group Databasebeta

← #14640468

Subgroups — #14640468

Order 2816.

172 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 45 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#13070104C211yesmaximal, characteristic
2#13066486C211yesmaximal, characteristic
3C11×#1322C211yesmaximal, characteristic
4C2×C11×C4⋊C8C2211yescharacteristic
5C2×#66882C411yescharacteristic
6#10622541—21no—
7#10622539—21no—
8C11×C22⋊C16—21no—
9#10622189—21no—
10#10622189C411yescharacteristic
11C22×C8×C11C2×C411yescharacteristic
12C22×C8×C11D411yescharacteristic
13C2×C42×C11D411yescharacteristic
14C2×C4⋊Dic11—21no—
15C2×C4⋊Dic11—21no—
16C2×Dic11⋊C4—41no—
17C2×C11×C16—41no—
18C11×C4⋊C8—41no—
19C11⋊#95—41no—
20C22⋊(C11⋊C8)—41no—
21#66882—41no—
22C4⋊(C11⋊C8)—41no—
23#66867—22no—
24#7083—111nomaximal, Sylow
25C22×C4×C11C22⋊C411yescharacteristic
26C22×C4×C11D811yescharacteristic
27C22×C4×C11SD1611yescharacteristic
28C22×Dic11—41no—
29C22×Dic11—41no—
30C2×C8×C11—21no—
31C2×C8×C11—21no—
32C2×C8×C11—41no—
33C2×C8×C11—41no—
34C42×C11—21no—
35C42×C11—21no—
36C4⋊Dic11—22no—
37C4⋊Dic11—41no—
38C4⋊Dic11—41no—
39C4⋊Dic11—41no—
40Dic11⋊C4—82no—
41C2×C11⋊C8—42no—
42C11×C16—81no—
43#2086—111no—
44#1322D1111yescharacteristic
45#1290—111no—
46C23×C11#10211yescharacteristic
47C2×C4×C11—21no—
48C2×C4×C11—21no—
49C2×C4×C11—21no—
50C2×C4×C11—21no—
51C2×C4×C11—21no—
52C2×C4×C11—21no—
53C2×C4×C11—41no—
54C2×C4×C11#9911yescharacteristic
55C2×C4×C11#10411yescharacteristic
56C2×Dic11—42no—
57C2×Dic11—81no—
58C2×Dic11—81no—
59C2×Dic11—81no—
60C2×Dic11—81no—
61C2×Dic11—81no—
62C8×C11—41no—
63C8×C11—41no—
64C11⋊C8—82no—
65#432—221no—
66C2×#107—111no—
67C2×C4⋊C8C2×D1111yescharacteristic
68#389—221no—
69C22⋊C16—21no—
70#340—111no—
71#340—221no—
72C22×C11—21no—
73C22×C11—21no—
74C22×C11#32711yescharacteristic
75C22×C11#35911yescharacteristic
76C22×C11#36111yescharacteristic
77C4×C11—21no—
78C4×C11—41no—
79C4×C11—41no—
80C4×C11#35211yescharacteristic
81C4×C11#35611yescharacteristic
82Dic11—82no—
83Dic11—161no—
84C22×C8C4×D1111yescharacteristic
85C22×C8C22⋊D1111yescharacteristic
86C2×C4⋊C4—221no—
87C2×C4⋊C4—221no—
88C2×C4⋊C4—441no—
89C2×C42D4411yescharacteristic
90C2×C16—41no—
91#107—441no—
92C4⋊C8—41no—
93C4⋊C8—441no—
94C22⋊C8—441no—
95#97—222no—
96#95—441no—
97C2×C11—21no—
98C2×C11—21no—
99C2×C11#134011yescharacteristic
100C2×C11#134611yescharacteristic
101C2×C11#134911yescharacteristic
102C22×C4—441no—
103C22×C4—441no—
104C22×C4#431411yescharacteristic
105C22×C4D8811yescharacteristic
106C22×C4(C2×D11)⋊C411yescharacteristic
107C2×C8—21no—
108C2×C8—21no—
109C2×C8—41no—
110C2×C8—41no—
111C2×C8—442no—
112C4⋊C4—222no—
113C4⋊C4—441no—
114C4⋊C4—441no—
115C4⋊C4—441no—
116C4⋊C4—882no—
117C42—21no—
118C42—21no—
119C16—81no—
120C11#708311yescharacteristic, complemented, Sylow
121C23#6688511yescharacteristic
122C2×C4—21no—
123C2×C4—21no—
124C2×C4—21no—
125C2×C4—21no—
126C2×C4—21no—
127C2×C4—21no—
128C2×C4—41no—
129C2×C4—442no—
130C2×C4—881no—
131C2×C4—881no—
132C2×C4—881no—
133C2×C4—881no—
134C2×C4—881no—
135C2×C4#6687011yescharacteristic
136C2×C4#6688911yescharacteristic
137C8—41no—
138C8—41no—
139C8—882no—
140C22—21no—
141C22—21no—
142C22#1062210811yescharacteristic
143C22#1062214811yescharacteristic
144C22#1062215411yescharacteristic
145C4—21no—
146C4—41no—
147C4—41no—
148C4—882no—
149C4—1761no—
150C4#1062211011yescharacteristic
151C4#1062211611yescharacteristic
152C2—21no—
153C2—21no—
154C2#1306660511yescharacteristic
155C2#1306662311yescharacteristic
156C2#1306663211yescharacteristic
subgroupG/H
centerC22#10622108
commutatorC22×C8×C11C2×C4
FrattiniC2×C4⋊C8C2×D11
FittingC11×#1322C2
socleC22×C11#327
prime radicalC23×C11#102
cosocleC2×C11×C4⋊C8C22
hypercenter#1322D11
hypocenterC11#7083
LCSG ▷ C22×C8×C11 ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C8 ◁ #1322

Complements

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

NH ≅ G/Ntype
120. C11#7083semidirect

Maximal subgroups

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

subgroupindex
#130701042
#130664862
C11×#13222
#708311