Finite Group Databasebeta

← #14664970

Subgroups — #14664970

Order 2816.

274 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 79 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#13070428C212yesmaximal
2#13066651C214yesmaximal, complemented
3C11×#3139C211yesmaximal, characteristic
4C11×#533C411yescharacteristic
5C2×C11×C4⋊Q8C411yescharacteristic
6C11×#491C412yes—
7C11×#491C2212yes—
8C11×#487—22no—
9C11×#419—22no—
10C4×C11×M16C2211yescharacteristic
11#10622191—22no—
12#10622104C2214yes—
13#10622101—22no—
14C22×Q8×C11—21no—
15C2×C11×M16D412yes—
16C11×C4⋊Q8—21no—
17C11×C4⋊Q8—21no—
18C11×C4⋊Q8—41no—
19C11×C4⋊Q8C2×C412yes—
20C11×#125C2×C412yes—
21C11×C22⋊Q8—41no—
22C4×Q8×C11—41no—
23C11×#117—21no—
24C2×C11×C4⋊C4—41no—
25C2×C42×C11C2×C411yescharacteristic
26C11×#103—24no—
27C11×#103—24no—
28C11×#97C2×C411yescharacteristic
29C11×#97C2311yescharacteristic
30C4×C8×C11D412yes—
31#66876—24no—
32#11916—111nomaximal, Sylow
33C2×Q8×C11—22no—
34C2×Q8×C11—41no—
35C2×Q8×C11—44no—
36C2×Q8×C11—41no—
37C22×C4×C11—21no—
38C22×C4×C11—41no—
39C22×C4×C11C22⋊C411yescharacteristic
40C11×M16—42no—
41C2×C8×C11C22⋊C412yes—
42C2×C8×C11C2×D412yes—
43C11×C4⋊C4—22no—
44C11×C4⋊C4—42no—
45C11×C4⋊C4—41no—
46C11×C4⋊C4—42no—
47C11×C4⋊C4—42no—
48C11×C22⋊C4—41no—
49C42×C11—21no—
50C42×C11—41no—
51C42×C11C22⋊C411yescharacteristic
52C42×C11C22×C411yescharacteristic
53C11⋊C16—44no—
54#3139D1111yescharacteristic
55#2165—112no—
56#1356—114no—
57C23×C11#10011yescharacteristic
58Q8×C11—44no—
59Q8×C11—82no—
60Q8×C11—82no—
61C2×C4×C11—21no—
62C2×C4×C11—22no—
63C2×C4×C11—21no—
64C2×C4×C11—42no—
65C2×C4×C11—42no—
66C2×C4×C11—42no—
67C2×C4×C11—82no—
68C2×C4×C11#10011yescharacteristic
69C2×C4×C11C2×C22⋊C411yescharacteristic
70C8×C11—22no—
71C8×C11—22no—
72#533Dic1111yescharacteristic
73C2×C4⋊Q8Dic1111yescharacteristic
74#491Dic1112yes—
75#491C2×D1112yes—
76#487—22no—
77#419—22no—
78C4×M16C2×D1111yescharacteristic
79#364—222no—
80#349—222no—
81#347—114no—
82C22×C11—21no—
83C22×C11—41no—
84C22×C11C2×#10011yescharacteristic
85C4×C11—22no—
86C4×C11—21no—
87C4×C11—41no—
88C4×C11—82no—
89C4×C11—82no—
90C4×C11#42112yes—
91C22×Q8—21no—
92C2×M16C22⋊D1112yes—
93C4⋊Q8—21no—
94C4⋊Q8—21no—
95C4⋊Q8—41no—
96C4⋊Q8C2×Dic1112yes—
97#125C2×Dic1112yes—
98C22⋊Q8—41no—
99C4×Q8—41no—
100#117—21no—
101C2×C4⋊C4—41no—
102C2×C42C2×Dic1111yescharacteristic
103M32—224no—
104#103—24no—
105#103—24no—
106#97C2×Dic1111yescharacteristic
107#97C22×D1111yescharacteristic
108C4×C8C22⋊D1112yes—
109C2×C11—21no—
110C2×C11—41no—
111C2×C11#153311yescharacteristic
112C2×Q8—22no—
113C2×Q8—41no—
114C2×Q8—44no—
115C2×Q8—41no—
116C22×C4—21no—
117C22×C4—41no—
118C22×C4C22⋊Dic1111yescharacteristic
119M16—42no—
120C2×C8C22⋊Dic1112yes—
121C2×C8C2×C22⋊D1112yes—
122C4⋊C4—22no—
123C4⋊C4—42no—
124C4⋊C4—42no—
125C4⋊C4—42no—
126C4⋊C4—41no—
127C22⋊C4—41no—
128C42—21no—
129C42—41no—
130C42C22⋊Dic1111yescharacteristic
131C42C22×Dic1111yescharacteristic
132C16—444no—
133C11#1191611yescharacteristic, complemented, Sylow
134C23#6689711yescharacteristic
135Q8—44no—
136Q8—82no—
137Q8—82no—
138C2×C4—21no—
139C2×C4—22no—
140C2×C4—21no—
141C2×C4—42no—
142C2×C4—42no—
143C2×C4—42no—
144C2×C4—82no—
145C2×C4#6689711yescharacteristic
146C2×C4C2×C22⋊Dic1111yescharacteristic
147C8—22no—
148C8—22no—
149C22—21no—
150C22—41no—
151C22C2×#6689711yescharacteristic
152C4—22no—
153C4—21no—
154C4—41no—
155C4—82no—
156C4—82no—
157C4#1062284912yes—
158C2—21no—
159C2—41no—
160C2#1306724011yescharacteristic
subgroupG/H
centerC2#13067240
commutatorC42×C11C22×C4
Frattini#97C22×D11
FittingC11×#3139C2
socleC2×C11#1533
prime radicalC23×C11#100
cosocleC11×#97C23
hypercenter#3139D11
hypocenterC11#11916
LCSG ▷ C42×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×M16 ◁ #3139

Complements

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

NH ≅ G/Ntype
2. #13066651C2semidirect
133. C11#11916semidirect

Maximal subgroups

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

subgroupindex
#130704282
#130666512
C11×#31392
#1191611