Finite Group Databasebeta

← #13069869

Subgroups — #13069869

Order 1408.

296 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 71 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
1C22×C11×D8C211yesmaximal, characteristic
2C2×#66897C212yesmaximal, complemented
3#10622828C212yesmaximal, complemented
4#10622715C211yesmaximal, characteristic, complemented
5#10622190C211yesmaximal, characteristic, complemented
6C22×D4×C11C2212yes—
7C2×C11×D8—24no—
8C2×C11×D8—22no—
9C22×C8×C11C2211yescharacteristic
10#66979C2211yescharacteristic
11C2×#4318C2212yes—
12C2×#4318C2211yescharacteristic
13#66897—24no—
14#66896—24no—
15Dic11⋊C8—22no—
16C24×C11—22no—
17C2×D4×C11—22no—
18C2×D4×C11—22no—
19C2×D4×C11—22no—
20C2×D4×C11—22no—
21C2×D4×C11—22no—
22C2×D4×C11D414yes—
23C22×C4×C11C2311yescharacteristic
24C11×D8—28no—
25C2×C8×C11—22no—
26C2×C8×C11D412yes—
27C22⋊Dic11—21no—
28C4⋊Dic11D412yes—
29C4×Dic11—21no—
30#4318—22no—
31#4318—22no—
32#4318—22no—
33C2×C11⋊C8—21no—
34C2×C11⋊C8—22no—
35#2045—111nomaximal, Sylow
36C23×C11—24no—
37C23×C11—42no—
38C23×C11—42no—
39C23×C11—84no—
40C23×C11#4111yescharacteristic
41D4×C11—24no—
42D4×C11—24no—
43D4×C11—42no—
44D4×C11—42no—
45C2×C4×C11C2×D411yescharacteristic
46C2×C4×C11C2×D412yes—
47C2×C4×C11C2×D411yescharacteristic
48C2×C4×C11#4112yes—
49C2×Dic11—22no—
50C8×C11—22no—
51C11⋊C8—41no—
52C11⋊C8—42no—
53C22×D8D1111yescharacteristic
54#424—111no—
55#418—112no—
56C2×#100—112no—
57#341—111no—
58C22×C11—22no—
59C22×C11—44no—
60C22×C11—84no—
61C22×C11—84no—
62C22×C11—84no—
63C22×C11#12111yescharacteristic
64C22×C11#12312yes—
65C4×C11#12011yescharacteristic
66C4×C11#12112yes—
67C4×C11#12411yescharacteristic
68Dic11—42no—
69C22×D4C2×D1112yes—
70C2×D8—24no—
71C2×D8—22no—
72C2×M16—112no—
73C2×M16—111no—
74C22×C8C2×D1111yescharacteristic
75#117—111no—
76C4⋊C8—222no—
77#102—224no—
78#100—224no—
79C2×C11—22no—
80C2×C11—84no—
81C2×C11#39411yescharacteristic
82C2×C11#47212yes—
83C24—22no—
84C2×D4—22no—
85C2×D4—22no—
86C2×D4—22no—
87C2×D4—22no—
88C2×D4—22no—
89C2×D4C22⋊D1114yes—
90C22×C4C22×D1111yescharacteristic
91D8—28no—
92M16—222no—
93M16—222no—
94M16—222no—
95C2×C8—22no—
96C2×C8—222no—
97C2×C8—221no—
98C2×C8C22⋊D1112yes—
99C4⋊C4—112no—
100C22⋊C4—221no—
101C42—221no—
102C11#204511yescharacteristic, complemented, Sylow
103C23—24no—
104C23—42no—
105C23—42no—
106C23—84no—
107C23#434111yescharacteristic
108D4—24no—
109D4—24no—
110D4—42no—
111D4—42no—
112C2×C4—222no—
113C2×C4D4×D1111yescharacteristic
114C2×C4#434112yes—
115C2×C4C2×C22⋊D1111yescharacteristic
116C2×C4C2×C22⋊D1112yes—
117C8—22no—
118C8—442no—
119C8—441no—
120C22—22no—
121C22—44no—
122C22—84no—
123C22—84no—
124C22—84no—
125C22#6698812yes—
126C22#6699111yescharacteristic
127C4—442no—
128C4#6698911yescharacteristic
129C4#6699212yes—
130C4#6700611yescharacteristic
131C2—22no—
132C2—84no—
133C2#1062277312yes—
134C2#1062283511yescharacteristic
subgroupG/H
centerC22#66991
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
Fitting, prime radicalC22×C11×D8C2
socleC22×C11#121
hypercenterC22×D8D11
hypocenterC11#2045
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
2. C2×#66897C2semidirect
3. #10622828C2semidirect
4. #10622715C2semidirect
5. #10622190C2semidirect
102. C11#2045semidirect

Maximal subgroups

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

subgroupindex
C22×C11×D82
C2×#668972
#106228282
#106227152
#106221902
#204511