Finite Group Databasebeta

← #14653168

Subgroups — #14653168

Order 2816.

478 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 111 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#13079044C211yesmaximal, characteristic
2#13067175C214yesmaximal, complemented
3#13066908C211yesmaximal, characteristic, complemented
4C11×#1835C211yesmaximal, characteristic, complemented
5C2×#66957—22no—
6#10623008C2212yes—
7C2×C4×C8×C11C2211yescharacteristic
8C11×#382C2212yes—
9#10622538C2212yes—
10#10622312C411yescharacteristic, complemented
11#10622309—22no—
12#10622308C411yescharacteristic, complemented
13#10622306C412yescomplemented
14C11×#340—22no—
15#10622092—22no—
16#10622089—28no—
17C2×#4339—22no—
18C22×C8×C11D412yes—
19C2×C11×C4⋊C4—22no—
20C2×C42×C11C2311yescharacteristic
21#66983—24no—
22C2×Dic44—22no—
23#66957—48no—
24C2×D88—22no—
25C2×#4314—24no—
26#66928—22no—
27#66927C2×C412yes—
28C4×D44—24no—
29#66922C2×C412yes—
30C4×C8×C11C2×C411yescharacteristic
31C4×C8×C11C2×C411yescharacteristic
32C4×C8×C11D412yes—
33C11×#95—24no—
34C22⋊(C11⋊C8)D414yes—
35C4⋊(C11⋊C8)—22no—
36C4×C11⋊C8—22no—
37#9760—111nomaximal, Sylow
38C22×C4×C11—42no—
39C22×C4×C11C2×D412yes—
40C22×C4×C11C2×D411yescharacteristic
41C2×C22⋊D11—42no—
42#4339—48no—
43C2×D44—22no—
44C2×D44—24no—
45C2×C4×D11—42no—
46C2×Dic22—22no—
47C2×C8×C11—24no—
48C2×C8×C11C22⋊C412yes—
49C2×C8×C11C22⋊C412yes—
50C11×C4⋊C4—44no—
51C42×C11C22×C411yescharacteristic
52C42×C11C2×D411yescharacteristic
53C42×C11#4112yes—
54(C2×D11)⋊C4—44no—
55C4⋊Dic11—24no—
56C2×C11⋊C8—24no—
57Dic44—44no—
58D88—44no—
59#4314—48no—
60#3147—111no—
61#1835D1111yescharacteristic, complemented
62#1517—114no—
63#1452—111no—
64C23×C11#12711yescharacteristic
65C22×D11—42no—
66C2×C4×C11—42no—
67C2×C4×C11—84no—
68C2×C4×C11—82no—
69C2×C4×C11C2×C22⋊C411yescharacteristic
70C2×C4×C11C4×D412yes—
71C2×C4×C11#12112yes—
72C2×C4×C11#12411yescharacteristic
73C2×C4×C11AGL(1,ℤ/8)14yes—
74C22⋊D11—84no—
75C2×Dic11—42no—
76D44—44no—
77D44—84no—
78C4×D11—84no—
79Dic22—44no—
80C8×C11—22no—
81C8×C11—22no—
82C11⋊C8—44no—
83C2×#135—222no—
84#532—112no—
85#495—222no—
86#494—111no—
87#493—111no—
88#492—112no—
89#431—112no—
90C2×C4×C8C2×D1111yescharacteristic
91#382C2×D1112yes—
92#340—22no—
93#327—228no—
94#322—222no—
95C22×C11—22no—
96C22×C11#39011yescharacteristic
97C22×C11#49612yes—
98C2×D11—82no—
99C2×D11—84no—
100C4×C11—22no—
101C4×C11—22no—
102C4×C11—162no—
103C4×C11#41812yes—
104C4×C11#49012yes—
105Dic11—82no—
106C2×#41—222no—
107#135—448no—
108C2×Q16—222no—
109C2×SD16—224no—
110C2×D8—222no—
111C22×C8C22⋊D1112yes—
112C4⋊Q8—112no—
113#127—112no—
114#124—222no—
115#121—224no—
116C4×D4—224no—
117C2×C4⋊C4—22no—
118C2×C42C22×D1111yescharacteristic
119C4⋊C8—222no—
120C22⋊C8—114no—
121C4×C8—222no—
122C4×C8C4×D1111yescharacteristic
123C4×C8C4×D1111yescharacteristic
124C4×C8D4412yes—
125#95—24no—
126C2×C11—22no—
127C2×C11#196111yescharacteristic
128C2×C11#197612yes—
129D11—162no—
130#41—448no—
131C2×Q8—222no—
132C2×D4—224no—
133C2×D4—222no—
134C2×D4—442no—
135C22×C4—42no—
136C22×C4—442no—
137C22×C4D4×D1112yes—
138C22×C4C2×C22⋊D1111yescharacteristic
139Q16—444no—
140SD16—448no—
141D8—444no—
142C2×C8—24no—
143C2×C8—224no—
144C2×C8(C2×D11)⋊C412yes—
145C2×C8(C2×D11)⋊C412yes—
146C4⋊C4—44no—
147C4⋊C4—224no—
148C22⋊C4—444no—
149C42C2×C4×D1111yescharacteristic
150C42C2×D4411yescharacteristic
151C42#434312yes—
152C11#976011yescharacteristic, complemented, Sylow
153C23—442no—
154C23#6699311yescharacteristic
155Q8—444no—
156D4—444no—
157D4—884no—
158D4—884no—
159C2×C4—42no—
160C2×C4—84no—
161C2×C4—82no—
162C2×C4—442no—
163C2×C4—884no—
164C2×C4#6694612yes—
165C2×C4#6694812yes—
166C2×C4C2×(C2×D11)⋊C411yescharacteristic
167C2×C4#6700011yescharacteristic
168C2×C4#6700214yes—
169C8—22no—
170C8—22no—
171C8—444no—
172C22—22no—
173C22—882no—
174C22—884no—
175C22#1062260111yescharacteristic
176C22#1062267112yes—
177C4—22no—
178C4—22no—
179C4—162no—
180C4—882no—
181C4#1062261412yes—
182C4#1062268012yes—
183C2—22no—
184C2—1762no—
185C2#1306943911yescharacteristic
186C2#1306951212yes—
subgroupG/H
centerC22#10622601
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1835C2
socleC22×C11#390
prime radical#13079044C2
cosocleC2×C42×C11C23
hypercenter#1835D11
hypocenterC11#9760
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1835

Complements

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

NH ≅ G/Ntype
2. #13067175C2semidirect
3. #13066908C2semidirect
4. C11×#1835C2semidirect
10. #10622312C4semidirect
12. #10622308C4semidirect
13. #10622306C4semidirect
61. #1835D11semidirect
152. C11#9760semidirect

Maximal subgroups

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

subgroupindex
#130790442
#130671752
#130669082
C11×#18352
#976011