Finite Group Databasebeta

← #14646768

Subgroups — #14646768

Order 2816.

320 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 93 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#13077546C211yesmaximal, characteristic
2#13067377C212yesmaximal
3#13067253C212yesmaximal
4#13066527C211yesmaximal, characteristic
5C11×#1307C211yesmaximal, characteristic
6#10623001C2211yescharacteristic
7C11×#432C2212yes—
8C11×#423C2211yescharacteristic
9#10622735C412yes—
10#10622732C412yes—
11#10622539C2212yes—
12C2×C4×C11⋊C8C2211yescharacteristic
13#10622444—22no—
14#10622443—22no—
15#10622118—22no—
16#10622117—22no—
17#10622103—24no—
18C2×C11×M16C2×C412yes—
19C2×C42×C11C2311yescharacteristic
20#66979C2×C412yes—
21#66977—22no—
22C22×C11⋊C8C2×C411yescharacteristic
23C22×C11⋊C8C2×C411yescharacteristic
24#66923D412yes—
25#66922Q812yes—
26C4×Dic22—22no—
27C11×C4⋊C8—22no—
28C11×C4⋊C8—22no—
29C11×C22⋊C8—22no—
30C11×#97—22no—
31C22⋊(C11⋊C8)—22no—
32#66879—22no—
33Dic11⋊C8—24no—
34C8×Dic11—22no—
35C4⋊(C11⋊C8)—22no—
36#66867—22no—
37C4×C11⋊C8D412yes—
38C4×C11⋊C8D412yes—
39#8631—111nomaximal, Sylow
40C22×C4×C11C22×C411yescharacteristic
41C22×C4×C11#4112yes—
42C2×Dic22—22no—
43C11×M16—42no—
44C2×C8×C11—22no—
45C2×C8×C11—42no—
46C42×C11C2×D412yes—
47C42×C11C2×D411yescharacteristic
48C42×C11C2×Q811yescharacteristic
49C22⋊Dic11—22no—
50C4⋊Dic11—22no—
51C4⋊Dic11C4⋊C414yes—
52Dic11⋊C4—24no—
53C4×Dic11—22no—
54C2×C11⋊C8—22no—
55C2×C11⋊C8—41no—
56C2×C11⋊C8—42no—
57C2×C11⋊C8C22⋊C412yes—
58C2×C11⋊C8C22⋊C411yescharacteristic
59C2×C11⋊C8C22⋊C411yescharacteristic
60#2960—111no—
61#1568—112no—
62#1537—112no—
63#1307—111no—
64#1307D1111yescharacteristic
65C23×C11#11711yescharacteristic
66C2×C4×C11—21no—
67C2×C4×C11—21no—
68C2×C4×C11—42no—
69C2×C4×C11C2×C22⋊C411yescharacteristic
70C2×C4×C11C2×C4⋊C411yescharacteristic
71C2×C4×C11#12112yes—
72C2×C4×C11C22⋊Q812yes—
73C2×Dic11—24no—
74Dic22—44no—
75C8×C11—42no—
76C8×C11—82no—
77C11⋊C8—21no—
78C11⋊C8—22no—
79C11⋊C8—82no—
80C11⋊C8#10112yes—
81#533—111no—
82#446—222no—
83C8×Q8—222no—
84#432—112no—
85#432C2×D1112yes—
86#424—112no—
87#423C2×D1111yescharacteristic
88#405—112no—
89C2×C4×C8—111no—
90#335—222no—
91#334—222no—
92#330—224no—
93C22×C11—21no—
94C22×C11—22no—
95C22×C11#38011yescharacteristic
96C4×C11—21no—
97C4×C11—22no—
98C4×C11—22no—
99C4×C11C2×#10111yescharacteristic
100C4×C11#41311yescharacteristic
101Dic11—44no—
102C2×M16C4×D1112yes—
103C22×C8—111no—
104C22×C8—111no—
105C4⋊Q8—112no—
106#125—112no—
107C22⋊Q8—222no—
108C4×Q8—222no—
109#117—112no—
110C2×C42C22×D1111yescharacteristic
111C4⋊C8—22no—
112C4⋊C8—22no—
113C4⋊C8—224no—
114C4⋊C8—222no—
115C22⋊C8—22no—
116C22⋊C8—222no—
117#97—22no—
118#97—222no—
119#97—222no—
120C4×C8—112no—
121C4×C8—112no—
122C4×C8—222no—
123C2×C11—41no—
124C2×C11#180111yescharacteristic
125C2×C11#181412yes—
126C2×Q8—222no—
127C22×C4C2×C4×D1111yescharacteristic
128C22×C4#433912yes—
129M16—42no—
130C2×C8—22no—
131C2×C8—42no—
132C2×C8—111no—
133C2×C8—111no—
134C2×C8—112no—
135C2×C8—222no—
136C2×C8—441no—
137C2×C8—442no—
138C4⋊C4—114no—
139C4⋊C4—224no—
140C4⋊C4—222no—
141C22⋊C4—222no—
142C42—222no—
143C42D4×D1112yes—
144C42D4×D1111yescharacteristic
145C42Q8×D1111yescharacteristic
146C11#863111yescharacteristic, complemented, Sylow
147C23#6692511yescharacteristic
148Q8—444no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—42no—
152C2×C4—224no—
153C2×C4C22⋊C4×D1111yescharacteristic
154C2×C4#6693712yes—
155C2×C4C4⋊C4×D1111yescharacteristic
156C2×C4#6694912yes—
157C8—42no—
158C8—82no—
159C8—112no—
160C8—222no—
161C8—221no—
162C8—882no—
163C22—21no—
164C22—22no—
165C22#1062228011yescharacteristic
166C4—21no—
167C4—22no—
168C4—22no—
169C4—444no—
170C4#1062235811yescharacteristic
171C4D11×#10111yescharacteristic
172C2—41no—
173C2#1306861111yescharacteristic
174C2#1306866912yes—
subgroupG/H
centerC22#10622280
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1307C2
socleC22×C11#380
prime radicalC23×C11#117
cosocleC2×C42×C11C23
hypercenter#1307D11
hypocenterC11#8631
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1307

Complements

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

NH ≅ G/Ntype
146. C11#8631semidirect

Maximal subgroups

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

subgroupindex
#130775462
#130673772
#130672532
#130665272
C11×#13072
#863111