Finite Group Databasebeta

← C11×#1620 #13064458

Subgroups — C11×#1620 #13064458

Order 1408.

240 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 68 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
1C11×#559C211yesmaximal, characteristic, complemented
2C11×#493C211yesmaximal, characteristic
3C11×#460C212yesmaximal, complemented
4C11×#331C211yesmaximal, characteristic, complemented
5C11×Q8⋊C8C212yesmaximal, complemented
6C2×C11×SD16—22no—
7C2×C11×D8—22no—
8C11×#127C2211yescharacteristic
9C11×#127C2211yescharacteristic
10C11×#124—22no—
11C11×#123—22no—
12C4×Q8×C11C2212yes—
13C4×D4×C11—22no—
14C11×C4⋊C8C2212yes—
15C11×#102—22no—
16C4×C8×C11C2211yescharacteristic
17C2×Q8×C11D412yes—
18C2×D4×C11—22no—
19C2×D4×C11—22no—
20C2×D4×C11—21no—
21C2×D4×C11D412yes—
22C22×C4×C11—22no—
23C11×SD16—44no—
24C11×D8—44no—
25C2×C8×C11—21no—
26C2×C8×C11—22no—
27C11×C4⋊C4—22no—
28C11×C4⋊C4D412yes—
29C11×C22⋊C4—24no—
30C11×C22⋊C4—22no—
31C42×C11—22no—
32C42×C11C2311yescharacteristic
33#1620C1111yesmaximal, characteristic, direct product factor, Sylow
34C23×C11—22no—
35C23×C11—41no—
36Q8×C11—22no—
37Q8×C11—22no—
38D4×C11—42no—
39D4×C11—42no—
40D4×C11—42no—
41D4×C11—42no—
42D4×C11—42no—
43D4×C11—42no—
44C2×C4×C11—22no—
45C2×C4×C11—22no—
46C2×C4×C11—82no—
47C2×C4×C11C2×D411yescharacteristic
48C2×C4×C11C2×D412yes—
49C8×C11—22no—
50C8×C11—42no—
51#559C2×C1111yescharacteristic, complemented
52#493C2×C1111yescharacteristic
53#460C2×C1112yescomplemented
54#331C2×C1111yescharacteristic, complemented
55Q8⋊C8C2×C1112yescomplemented
56C22×C11—44no—
57C22×C11—42no—
58C22×C11—82no—
59C22×C11—81no—
60C22×C11#12011yescharacteristic
61C4×C11—21no—
62C4×C11—42no—
63C4×C11—42no—
64C4×C11#13512yes—
65C4×C11AGL(1,ℤ/8)12yes—
66C2×SD16—22no—
67C2×D8—22no—
68#127C22×C1111yescharacteristic
69#127C22×C1111yescharacteristic
70#124—22no—
71#123—22no—
72C4×Q8C22×C1112yes—
73C4×D4—22no—
74C4⋊C8C22×C1112yes—
75#102—22no—
76C4×C8C22×C1111yescharacteristic
77C2×C11—82no—
78C2×C11—161no—
79C2×C11#44912yes—
80C2×C11#45311yescharacteristic
81C2×Q8D4×C1112yes—
82C2×D4—22no—
83C2×D4—22no—
84C2×D4—21no—
85C2×D4D4×C1112yes—
86C22×C4—22no—
87SD16—44no—
88D8—44no—
89C2×C8—21no—
90C2×C8—22no—
91C4⋊C4—22no—
92C4⋊C4D4×C1112yes—
93C22⋊C4—24no—
94C22⋊C4—22no—
95C42—22no—
96C42C23×C1111yescharacteristic
97C11#162011yescharacteristic, direct product factor, Sylow
98C23—22no—
99C23—41no—
100Q8—22no—
101Q8—22no—
102D4—42no—
103D4—42no—
104D4—42no—
105D4—42no—
106D4—42no—
107D4—42no—
108C2×C4—22no—
109C2×C4—22no—
110C2×C4—82no—
111C2×C4C2×D4×C1111yescharacteristic
112C2×C4C2×D4×C1112yes—
113C8—22no—
114C8—42no—
115C22—44no—
116C22—42no—
117C22—82no—
118C22—81no—
119C22C11×#12011yescharacteristic
120C4—21no—
121C4—42no—
122C4—42no—
123C4C11×#13512yes—
124C4C11×AGL(1,ℤ/8)12yes—
125C2—82no—
126C2—161no—
127C2C11×#44912yes—
128C2C11×#45311yescharacteristic
subgroupG/H
center, socleC22×C11#120
commutator, Frattini, cosocleC42C23×C11
prime radicalC11×#493C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#559C2semidirect
3. C11×#460C2semidirect
4. C11×#331C2semidirect
5. C11×Q8⋊C8C2semidirect
33. #1620C11direct (N × H)
51. #559C2×C11semidirect
53. #460C2×C11semidirect
54. #331C2×C11semidirect
55. Q8⋊C8C2×C11semidirect
97. C11#1620direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#5592
C11×#4932
C11×#4602
C11×#3312
C11×Q8⋊C82
#162011