Finite Group Databasebeta

← #14647186

Subgroups — #14647186

Order 2816.

526 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 131 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#13068378C212yesmaximal
2#13066497C214yesmaximal, complemented
3C11×#2285C211yesmaximal, characteristic
4C2×C11×#117C412yes—
5C22×C42×C11C2211yescharacteristic
6C11×#384C412yes—
7C11×#382C2212yes—
8C11×#380—22no—
9C4×C11×C4⋊C4—22no—
10C2×C22⋊(C11⋊C8)—22no—
11C2×#66867C2214yes—
12#10622162—22no—
13C23×C4×C11C2×C411yescharacteristic
14C23×C4×C11D412yes—
15C11×#117—44no—
16C2×C11×C4⋊C4—22no—
17C2×C11×C4⋊C4—22no—
18C2×C11×C4⋊C4C2×C414yes—
19C2×C11×C22⋊C4—22no—
20C2×C42×C11—24no—
21C2×C42×C11—22no—
22C2×C42×C11C2×C411yescharacteristic
23C2×C42×C11D412yes—
24C2×C42×C11C2311yescharacteristic
25C22×C11⋊C8—24no—
26C11×#95—24no—
27C22⋊(C11⋊C8)—28no—
28#66867—28no—
29#8722—111nomaximal, Sylow
30C24×C11C22⋊C411yescharacteristic
31C22×C4×C11—22no—
32C22×C4×C11—22no—
33C22×C4×C11—22no—
34C22×C4×C11—24no—
35C22×C4×C11—24no—
36C22×C4×C11—24no—
37C22×C4×C11—42no—
38C22×C4×C11C22⋊C411yescharacteristic
39C22×C4×C11C22⋊C412yes—
40C22×C4×C11C22×C411yescharacteristic
41C22×C4×C11C2×D412yes—
42C11×C4⋊C4—44no—
43C11×C4⋊C4—44no—
44C11×C4⋊C4—44no—
45C11×C22⋊C4—44no—
46C42×C11—22no—
47C42×C11—24no—
48C42×C11—44no—
49C42×C11#4114yes—
50C2×C11⋊C8—28no—
51C2×C11⋊C8—44no—
52C2×C11⋊C8—44no—
53#2285D1111yescharacteristic
54#1749—112no—
55#1295—114no—
56C23×C11—21no—
57C23×C11—21no—
58C23×C11—22no—
59C23×C11—22no—
60C23×C11#10012yes—
61C23×C11C2×C22⋊C411yescharacteristic
62C2×C4×C11—28no—
63C2×C4×C11—21no—
64C2×C4×C11—22no—
65C2×C4×C11—21no—
66C2×C4×C11—21no—
67C2×C4×C11—21no—
68C2×C4×C11—22no—
69C2×C4×C11—22no—
70C2×C4×C11—22no—
71C2×C4×C11—48no—
72C2×C4×C11—44no—
73C2×C4×C11—44no—
74C2×C4×C11—44no—
75C2×C4×C11#10112yes—
76C2×C4×C11#10414yes—
77C2×C4×C11#11712yes—
78C2×C4×C11#12314yes—
79C11⋊C8—48no—
80C2×#117Dic1112yes—
81C22×C42C2×D1111yescharacteristic
82C2×C22⋊C8—222no—
83C2×#97—114no—
84#384Dic1112yes—
85#382C2×D1112yes—
86#380—22no—
87C4×C4⋊C4—22no—
88#336—222no—
89C22×C11—22no—
90C22×C11—24no—
91C22×C11—41no—
92C22×C11—42no—
93C22×C11—41no—
94C22×C11#38111yescharacteristic
95C22×C11C2×#10011yescharacteristic
96C22×C11C2×#10111yescharacteristic
97C22×C11C2×#10412yes—
98C22×C11#42112yes—
99C4×C11—22no—
100C4×C11—22no—
101C4×C11—24no—
102C4×C11—24no—
103C4×C11—84no—
104C23×C4C2×Dic1111yescharacteristic
105C23×C4C22⋊D1112yes—
106C22×C8—224no—
107#117—44no—
108C2×C4⋊C4—22no—
109C2×C4⋊C4—22no—
110C2×C4⋊C4C2×Dic1114yes—
111C2×C22⋊C4—22no—
112C2×C42—24no—
113C2×C42—22no—
114C2×C42C2×Dic1111yescharacteristic
115C2×C42C22⋊D1112yes—
116C2×C42C22×D1111yescharacteristic
117C22⋊C8—228no—
118#97—228no—
119#95—24no—
120C2×C11—42no—
121C2×C11#152611yescharacteristic
122C2×C11#153012yes—
123C2×C11#153711yescharacteristic
124C2×C11#182111yescharacteristic
125C2×C11#182612yes—
126C24C22⋊Dic1111yescharacteristic
127C22×C4—22no—
128C22×C4—22no—
129C22×C4—22no—
130C22×C4—24no—
131C22×C4—24no—
132C22×C4—24no—
133C22×C4—42no—
134C22×C4C22⋊Dic1111yescharacteristic
135C22×C4C22⋊Dic1112yes—
136C22×C4C22×Dic1111yescharacteristic
137C22×C4C2×C22⋊D1112yes—
138C2×C8—228no—
139C2×C8—444no—
140C2×C8—444no—
141C4⋊C4—44no—
142C4⋊C4—44no—
143C4⋊C4—44no—
144C22⋊C4—44no—
145C42—22no—
146C42—24no—
147C42—44no—
148C42#433914yes—
149C11#872211yescharacteristic, complemented, Sylow
150C23—21no—
151C23—21no—
152C23—22no—
153C23—22no—
154C23#6689712yes—
155C23C2×C22⋊Dic1111yescharacteristic
156C2×C4—28no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—48no—
166C2×C4—44no—
167C2×C4—44no—
168C2×C4—44no—
169C2×C4#6690012yes—
170C2×C4#6690114yes—
171C2×C4#6697912yes—
172C2×C4#6698214yes—
173C8—448no—
174C22—22no—
175C22—24no—
176C22—42no—
177C22—41no—
178C22—41no—
179C22#1062282411yescharacteristic
180C22C2×#6689711yescharacteristic
181C22C2×#6690011yescharacteristic
182C22C2×#6690112yes—
183C22#1062284912yes—
184C4—22no—
185C4—22no—
186C4—24no—
187C4—24no—
188C4—84no—
189C2—42no—
190C2#1306721111yescharacteristic
191C2#1306722712yes—
192C2#1306725411yescharacteristic
193C2#1306869611yescharacteristic
194C2#1306871512yes—
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2285C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#2285D11
hypocenterC11#8722
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2285

Complements

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

NH ≅ G/Ntype
2. #13066497C2semidirect
149. C11#8722semidirect

Maximal subgroups

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

subgroupindex
#130683782
#130664972
C11×#22852
#872211