Finite Group Databasebeta

← #14641399

Subgroups — #14641399

Order 2816.

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

normal subgroups only

This group has 194 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#13069966C211yesmaximal, characteristic
2#13066560C211yesmaximal, characteristic
3C11×#1295C211yesmaximal, characteristic
4#10623031C411yescharacteristic
5C2×C11×#97—21no—
6C11×#382C2211yescharacteristic
7#10622577—21no—
8#10622168C411yescharacteristic
9#10622166—21no—
10#10622161—21no—
11C22×C8×C11—41no—
12C2×C11×C4⋊C4C2×C411yescharacteristic
13C2×C11×C4⋊C4D411yescharacteristic
14C2×C42×C11D411yescharacteristic
15#66979—21no—
16#66977—41no—
17C2×#4318—21no—
18#66943—41no—
19#66941—41no—
20C11×#97—22no—
21C11×#97—41no—
22C11×#95—41no—
23C22⋊(C11⋊C8)—41no—
24#66872—41no—
25#66871—41no—
26#7442—111nomaximal, Sylow
27C22×C4×C11—21no—
28C22×C4×C11—21no—
29C22×C4×C11—21no—
30C22×C4×C11C22⋊C411yescharacteristic
31C2×Dic22—41no—
32C2×C8×C11—42no—
33C2×C8×C11—42no—
34C2×C8×C11—42no—
35C11×C4⋊C4—41no—
36C11×C4⋊C4—41no—
37C42×C11—21no—
38C42×C11SD1611yescharacteristic
39C42×C11Q1611yescharacteristic
40C22⋊Dic11—41no—
41C4⋊Dic11—21no—
42C4⋊Dic11—21no—
43C4⋊Dic11—41no—
44Dic11⋊C4—42no—
45C4×Dic11—41no—
46#4318—22no—
47#4318—41no—
48C2×C11⋊C8—41no—
49C2×C11⋊C8—81no—
50#2061—111no—
51#1324—111no—
52#1295D1111yescharacteristic
53C23×C11#9911yescharacteristic
54C2×C4×C11—21no—
55C2×C4×C11—21no—
56C2×C4×C11—21no—
57C2×C4×C11—21no—
58C2×C4×C11—41no—
59C2×C4×C11—41no—
60C2×C4×C11—41no—
61C2×C4×C11—41no—
62C2×C4×C11—81no—
63C2×C4×C11—81no—
64C2×C4×C11#10311yescharacteristic
65C2×C4×C11#10411yescharacteristic
66C2×Dic11—41no—
67C2×Dic11—41no—
68Dic22—161no—
69C8×C11—44no—
70C11⋊C8—42no—
71C11⋊C8—161no—
72#544—111no—
73#428—221no—
74C2×#97—21no—
75#382C2×D1111yescharacteristic
76#343—111no—
77#339—221no—
78#324—221no—
79C22×C11—21no—
80C22×C11—21no—
81C22×C11#32811yescharacteristic
82C22×C11AΣL(1,𝔽16)11yescharacteristic
83C22×C11#35611yescharacteristic
84C4×C11—21no—
85C4×C11—21no—
86C4×C11—41no—
87C4×C11—41no—
88C4×C11—81no—
89C4×C11—81no—
90Dic11—81no—
91Dic11—81no—
92C2×M16—221no—
93C22×C8—41no—
94C4⋊Q8—441no—
95#125—441no—
96C22⋊Q8—441no—
97#117—221no—
98C2×C4⋊C4C4×D1111yescharacteristic
99C2×C4⋊C4D4411yescharacteristic
100C2×C42C22⋊D1111yescharacteristic
101#107—441no—
102#106—441no—
103C22⋊C8—441no—
104#97—22no—
105#97—41no—
106#95—41no—
107C2×C11—21no—
108C2×C11—21no—
109C2×C11#135411yescharacteristic
110C2×C11#140311yescharacteristic
111C2×C11#140411yescharacteristic
112C2×Q8—441no—
113C22×C4—21no—
114C22×C4—21no—
115C22×C4—21no—
116C22×C4(C2×D11)⋊C411yescharacteristic
117M16—222no—
118M16—441no—
119C2×C8—42no—
120C2×C8—42no—
121C2×C8—42no—
122C2×C8—441no—
123C2×C8—881no—
124C4⋊C4—41no—
125C4⋊C4—41no—
126C4⋊C4—221no—
127C4⋊C4—221no—
128C4⋊C4—441no—
129C4⋊C4—442no—
130C22⋊C4—441no—
131C42—21no—
132C42—441no—
133C42#432411yescharacteristic
134C42#432611yescharacteristic
135C11#744211yescharacteristic, complemented, Sylow
136C23#6687011yescharacteristic
137Q8—1761no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—41no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—81no—
147C2×C4—81no—
148C2×C4—441no—
149C2×C4—441no—
150C2×C4#6686911yescharacteristic
151C2×C4#6687411yescharacteristic
152C8—44no—
153C8—442no—
154C8—1761no—
155C22—21no—
156C22—21no—
157C22#1062209011yescharacteristic
158C22#1062211311yescharacteristic
159C22#1062211611yescharacteristic
160C4—21no—
161C4—21no—
162C4—41no—
163C4—41no—
164C4—81no—
165C4—81no—
166C4—881no—
167C4—881no—
168C2—21no—
169C2—21no—
170C2#1306664511yescharacteristic
171C2#1306676511yescharacteristic
172C2#1306676811yescharacteristic
subgroupG/H
centerC22#10622113
commutatorC2×C11×C4⋊C4C2×C4
Frattini#382C2×D11
FittingC11×#1295C2
socleC22×C11AΣL(1,𝔽16)
prime radicalC23×C11#99
cosocleC11×#382C22
hypercenter#1295D11
hypocenterC11#7442
LCSG ▷ C2×C11×C4⋊C4 ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #382 ◁ #1295

Complements

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

NH ≅ G/Ntype
135. C11#7442semidirect

Maximal subgroups

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

subgroupindex
#130699662
#130665602
C11×#12952
#744211