Finite Group Databasebeta

← #14647229

Subgroups — #14647229

Order 2816.

404 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 115 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#13066930C212yesmaximal
2#13066449C212yesmaximal, complemented
3#13066445C212yesmaximal, complemented
4C11×#2298C211yesmaximal, characteristic
5C2×C11×#117C2211yescharacteristic
6C11×#388—22no—
7C11×#387—22no—
8C4×C11×C4⋊C4C412yes—
9C4×C11×C22⋊C4C412yes—
10C11×#376C2211yescharacteristic
11C43×C11C2211yescharacteristic
12#10622538C2214yes—
13#10622166—22no—
14#10622163—22no—
15C23×C4×C11C2×C411yescharacteristic
16C11×#117—22no—
17C11×#117—22no—
18C2×C11×C4⋊C4—22no—
19C2×C11×C4⋊C4D412yes—
20C2×C11×C22⋊C4—22no—
21C2×C11×C22⋊C4D412yes—
22C2×C42×C11—22no—
23C2×C42×C11C2×C412yes—
24C2×C42×C11C2×C412yes—
25C2×C42×C11C2×C411yescharacteristic
26C2×C42×C11C2311yescharacteristic
27C11×#95—22no—
28C11×#95—22no—
29C11×#95—22no—
30C22⋊(C11⋊C8)—24no—
31C4⋊(C11⋊C8)—24no—
32C4×C11⋊C8—24no—
33#8733—111nomaximal, Sylow
34C24×C11C22⋊C411yescharacteristic
35C22×C4×C11—22no—
36C22×C4×C11—21no—
37C22×C4×C11—21no—
38C22×C4×C11—24no—
39C22×C4×C11—22no—
40C22×C4×C11C22⋊C411yescharacteristic
41C22×C4×C11C22⋊C412yes—
42C22×C4×C11C22×C411yescharacteristic
43C22×C4×C11C2×D412yes—
44C11×C4⋊C4—24no—
45C11×C4⋊C4—44no—
46C11×C22⋊C4—24no—
47C11×C22⋊C4—44no—
48C42×C11—21no—
49C42×C11—21no—
50C42×C11—24no—
51C42×C11—24no—
52C42×C11—44no—
53C42×C11#4112yes—
54C42×C11#4112yes—
55C2×C11⋊C8—44no—
56#2298D1111yescharacteristic
57#1458—112no—
58#1276—112no—
59#1274—112no—
60C23×C11—21no—
61C23×C11—22no—
62C23×C11—42no—
63C23×C11C2×C22⋊C411yescharacteristic
64C2×C4×C11—24no—
65C2×C4×C11—22no—
66C2×C4×C11—21no—
67C2×C4×C11—22no—
68C2×C4×C11—42no—
69C2×C4×C11—42no—
70C2×C4×C11—42no—
71C2×C4×C11—42no—
72C2×C4×C11—42no—
73C2×C4×C11—42no—
74C2×C4×C11—42no—
75C2×C4×C11—42no—
76C2×C4×C11—42no—
77C2×C4×C11#11711yescharacteristic
78C2×C4×C11#11711yescharacteristic
79C2×C4×C11#12314yes—
80C2×C4×C11#13114yes—
81C11⋊C8—84no—
82C2×#117C2×D1111yescharacteristic
83#431—114no—
84#388—22no—
85#387—22no—
86C4×C4⋊C4Dic1112yes—
87C4×C22⋊C4Dic1112yes—
88#376C2×D1111yescharacteristic
89C43C2×D1111yescharacteristic
90#324—222no—
91#323—222no—
92C22×C11—22no—
93C22×C11—41no—
94C22×C11—42no—
95C22×C11—82no—
96C22×C11#38111yescharacteristic
97C22×C11#40812yes—
98C4×C11—24no—
99C4×C11—44no—
100C4×C11—41no—
101C4×C11—42no—
102C4×C11—82no—
103C4×C11#43312yes—
104C4×C11#43312yes—
105C23×C4C2×Dic1111yescharacteristic
106#117—22no—
107#117—22no—
108C2×C4⋊C4—22no—
109C2×C4⋊C4C22⋊D1112yes—
110C2×C22⋊C4—22no—
111C2×C22⋊C4C22⋊D1112yes—
112C2×C42—22no—
113C2×C42C2×Dic1112yes—
114C2×C42C2×Dic1112yes—
115C2×C42C2×Dic1111yescharacteristic
116C2×C42C22×D1111yescharacteristic
117C4⋊C8—224no—
118C22⋊C8—224no—
119C4×C8—224no—
120#95—22no—
121#95—22no—
122#95—22no—
123C2×C11—22no—
124C2×C11—81no—
125C2×C11#181811yescharacteristic
126C2×C11#182712yes—
127C24C22⋊Dic1111yescharacteristic
128C22×C4—22no—
129C22×C4—21no—
130C22×C4—21no—
131C22×C4—24no—
132C22×C4—22no—
133C22×C4C22⋊Dic1111yescharacteristic
134C22×C4C22⋊Dic1112yes—
135C22×C4C22×Dic1111yescharacteristic
136C22×C4C2×C22⋊D1112yes—
137C2×C8—444no—
138C4⋊C4—24no—
139C4⋊C4—44no—
140C22⋊C4—24no—
141C22⋊C4—44no—
142C42—21no—
143C42—21no—
144C42—24no—
145C42—24no—
146C42—44no—
147C42#433912yes—
148C42#433912yes—
149C11#873311yescharacteristic, complemented, Sylow
150C23—21no—
151C23—22no—
152C23—42no—
153C23C2×C22⋊Dic1111yescharacteristic
154C2×C4—24no—
155C2×C4—22no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—42no—
159C2×C4—42no—
160C2×C4—42no—
161C2×C4—42no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—42no—
165C2×C4—42no—
166C2×C4—42no—
167C2×C4#6697911yescharacteristic
168C2×C4#6697911yescharacteristic
169C2×C4#6698214yes—
170C2×C4#6700114yes—
171C8—884no—
172C22—22no—
173C22—41no—
174C22—42no—
175C22—82no—
176C22#1062282411yescharacteristic
177C22#1062284712yes—
178C4—24no—
179C4—44no—
180C4—41no—
181C4—42no—
182C4—82no—
183C4#1062261312yes—
184C4#1062261312yes—
185C2—22no—
186C2—81no—
187C2#1306868711yescharacteristic
188C2#1306872012yes—
subgroupG/H
centerC2×C4#66979
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2298C2
socleC22×C11#381
prime radicalC24×C11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#2298D11
hypocenterC11#8733
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #376 ◁ #2298

Complements

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

NH ≅ G/Ntype
2. #13066449C2semidirect
3. #13066445C2semidirect
149. C11#8733semidirect

Maximal subgroups

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

subgroupindex
#130669302
#130664492
#130664452
C11×#22982
#873311