Finite Group Databasebeta

← #14641303

Subgroups — #14641303

Order 2816.

166 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 166 conjugacy classes of subgroups — too many to draw. Only its 37 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#13070061C211yesmaximal, characteristic
2#13066554C211yesmaximal, characteristic
3C11×#1391C211yesmaximal, characteristic
4C11×#410—21no—
5C11×#408C2211yescharacteristic
6#10622845—21no—
7C2×#66881C411yescharacteristic, complemented
8#10622192—21no—
9#10622191—21no—
10#10622190C411yescharacteristic, complemented
11C2×C11×#41D411yescharacteristic
12C2×C11×M16D411yescharacteristic
13C22×C8×C11C2×C411yescharacteristic
14C11×#117—41no—
15C2×C4⋊Dic11—21no—
16C2×#4318—21no—
17C11×#99—22no—
18C11×#99—41no—
19C11×C22⋊C8—41no—
20#66899—41no—
21#66896—41no—
22#66881—41no—
23#66876—41no—
24#7410—111nomaximal, Sylow
25C11×#41—41no—
26C11×#41—41no—
27C2×Q8×C11SD1611yescharacteristic
28C2×D4×C11—21no—
29C2×D4×C11D811yescharacteristic
30C22×C4×C11—21no—
31C22×C4×C11C22⋊C411yescharacteristic
32C22×Dic11—41no—
33C11×M16—41no—
34C2×C8×C11—21no—
35C2×C8×C11—21no—
36C2×C8×C11—41no—
37C11×C4⋊C4—81no—
38C11×C22⋊C4—42no—
39C42×C11—81no—
40C4⋊Dic11—41no—
41C4⋊Dic11—41no—
42#4318—41no—
43#4318—41no—
44C2×C11⋊C8—41no—
45C11⋊C16—81no—
46#2079—111no—
47#1391D1111yescharacteristic
48#1321—111no—
49C23×C11—21no—
50C23×C11#10411yescharacteristic
51Q8×C11—41no—
52D4×C11—41no—
53D4×C11—81no—
54C2×C4×C11—21no—
55C2×C4×C11—21no—
56C2×C4×C11—21no—
57C2×C4×C11—41no—
58C2×C4×C11—41no—
59C2×C4×C11—82no—
60C2×C4×C11#9911yescharacteristic
61C2×C4×C11#10211yescharacteristic
62C2×Dic11—81no—
63C2×Dic11—161no—
64C8×C11—41no—
65C8×C11—41no—
66C11⋊C8—81no—
67C2×#106—111no—
68#417—221no—
69#410—21no—
70#408C2×D1111yescharacteristic
71#349—221no—
72#343—221no—
73#341—111no—
74C22×C11—21no—
75C22×C11—41no—
76C22×C11—41no—
77C22×C11—81no—
78C22×C11#32711yescharacteristic
79C4×C11—21no—
80C4×C11—41no—
81C4×C11—162no—
82C4×C11#35211yescharacteristic
83C4×C11#35411yescharacteristic
84Dic11—161no—
85C2×#41C22⋊D1111yescharacteristic
86C2×M16—221no—
87C2×M16D4411yescharacteristic
88C22×C8C4×D1111yescharacteristic
89#117—41no—
90C2×C4⋊C4—221no—
91M32—441no—
92#106—441no—
93#103—441no—
94#102—441no—
95#99—22no—
96#99—41no—
97C22⋊C8—41no—
98C2×C11—21no—
99C2×C11—41no—
100C2×C11—81no—
101C2×C11#134411yescharacteristic
102#41—41no—
103#41—41no—
104C2×Q8#432511yescharacteristic
105C2×D4—21no—
106C2×D4#432311yescharacteristic
107C22×C4—21no—
108C22×C4—441no—
109C22×C4(C2×D11)⋊C411yescharacteristic
110M16—41no—
111M16—441no—
112M16—441no—
113C2×C8—21no—
114C2×C8—21no—
115C2×C8—41no—
116C2×C8—441no—
117C4⋊C4—81no—
118C4⋊C4—441no—
119C4⋊C4—441no—
120C22⋊C4—42no—
121C42—81no—
122C16—881no—
123C11#741011yescharacteristic, complemented, Sylow
124C23—21no—
125C23#6686911yescharacteristic
126Q8—41no—
127D4—41no—
128D4—81no—
129C2×C4—21no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—41no—
133C2×C4—41no—
134C2×C4—82no—
135C2×C4—881no—
136C2×C4—1761no—
137C2×C4#6687011yescharacteristic
138C2×C4#6687311yescharacteristic
139C8—41no—
140C8—41no—
141C8—881no—
142C22—21no—
143C22—41no—
144C22—41no—
145C22—81no—
146C22#1062208911yescharacteristic
147C4—21no—
148C4—41no—
149C4—162no—
150C4—1761no—
151C4#1062211011yescharacteristic
152C4#1062211111yescharacteristic
153C2—21no—
154C2—41no—
155C2—81no—
156C2#1306661511yescharacteristic
subgroupG/H
centerC2#13066615
commutatorC22×C8×C11C2×C4
Frattini#408C2×D11
FittingC11×#1391C2
socleC2×C11#1344
prime radicalC2×C11×#41D4
cosocleC11×#408C22
hypercenter#1391D11
hypocenterC11#7410
LCSG ▷ C22×C8×C11 ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ #408 ◁ #1391

Complements

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

NH ≅ G/Ntype
7. C2×#66881C4semidirect
10. #10622190C4semidirect
123. C11#7410semidirect

Maximal subgroups

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

subgroupindex
#130700612
#130665542
C11×#13912
#741011