Finite Group Databasebeta

← #13076604

Subgroups — #13076604

Order 1408.

368 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 141 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×#391C211yesmaximal, characteristic
2#10622843C212yesmaximal
3#10622599C212yesmaximal
4#10622541C212yesmaximal
5#10622274C214yesmaximal
6#10622268C214yesmaximal
7C22×Q8×C11C2211yescharacteristic
8C2×C11×C4⋊C4C2211yescharacteristic
9C2×C42×C11C2211yescharacteristic
10C2×C4⋊Dic11C2212yes—
11C2×C4⋊Dic11C2212yes—
12C2×C4⋊Dic11C2212yes—
13C2×C4⋊Dic11C2212yes—
14C2×Dic11⋊C4C2214yes—
15C2×C4×Dic11C2212yes—
16C11×#95C2214yes—
17C11⋊#95C2212yes—
18C11⋊#95C2214yes—
19C11⋊#95C2214yes—
20C11⋊#95C2214yes—
21C2×Q8×C11—41no—
22C2×Q8×C11—41no—
23C2×Q8×C11Q814yes—
24C22×C4×C11C2312yes—
25C22×C4×C11C2311yescharacteristic
26C22×C4×C11C2312yes—
27C22×C4×C11C2312yes—
28C22×Dic11C2314yes—
29C22×Dic11C2314yes—
30C11×C4⋊C4—41no—
31C42×C11—41no—
32C4⋊Dic11—24no—
33C4⋊Dic11—42no—
34C4⋊Dic11—42no—
35C4⋊Dic11—42no—
36Dic11⋊C4—28no—
37C4×Dic11—42no—
38#2809—111nomaximal, Sylow
39C23×C11C2411yescharacteristic
40Q8×C11—44no—
41C2×C4×C11—22no—
42C2×C4×C11—22no—
43C2×C4×C11—22no—
44C2×C4×C11—21no—
45C2×C4×C11—21no—
46C2×C4×C11—22no—
47C2×C4×C11—22no—
48C2×C4×C11—24no—
49C2×C4×C11C2×Q812yes—
50C2×C4×C11C2×Q814yes—
51C2×C4×C11#4114yes—
52C2×Dic11—24no—
53C2×Dic11—24no—
54C2×Dic11—24no—
55C2×Dic11—24no—
56C2×Dic11—24no—
57C2×Dic11—24no—
58#400—112no—
59#398—114no—
60#391—112no—
61#391D1111yescharacteristic
62#389—112no—
63#387—114no—
64C22×C11C22×Q811yescharacteristic
65C22×C11C2×#4112yes—
66C22×C11H(5,𝔽2)11yescharacteristic
67C22×C11H(5,𝔽2)11yescharacteristic
68C22×C112−1+412yes—
69C4×C11—24no—
70C4×C11—24no—
71C4×C11—22no—
72C4×C11—42no—
73Dic11—44no—
74Dic11—44no—
75C22×Q8C2×D1111yescharacteristic
76C2×C4⋊C4—114no—
77C2×C4⋊C4—112no—
78C2×C4⋊C4—112no—
79C2×C4⋊C4—112no—
80C2×C4⋊C4—112no—
81C2×C4⋊C4C2×D1111yescharacteristic
82C2×C42—112no—
83C2×C42C2×D1111yescharacteristic
84#95—112no—
85#95—114no—
86#95—114no—
87#95—114no—
88#95C2×D1114yes—
89C2×C11#53912yes—
90C2×C11#54311yescharacteristic
91C2×C11#55511yescharacteristic
92C2×C11#55712yes—
93C2×C11#56311yescharacteristic
94C2×Q8—41no—
95C2×Q8—41no—
96C2×Q8Dic2214yes—
97C22×C4—114no—
98C22×C4—114no—
99C22×C4C22×D1112yes—
100C22×C4C22×D1111yescharacteristic
101C22×C4C22×D1112yes—
102C22×C4C22×D1112yes—
103C4⋊C4—41no—
104C4⋊C4—228no—
105C4⋊C4—224no—
106C4⋊C4—442no—
107C4⋊C4—442no—
108C4⋊C4—442no—
109C42—41no—
110C42—442no—
111C11#280911yescharacteristic, complemented, Sylow
112C23C23×D1111yescharacteristic
113Q8—44no—
114C2×C4—22no—
115C2×C4—21no—
116C2×C4—22no—
117C2×C4—21no—
118C2×C4—22no—
119C2×C4—22no—
120C2×C4—22no—
121C2×C4—24no—
122C2×C4—224no—
123C2×C4—224no—
124C2×C4—224no—
125C2×C4—224no—
126C2×C4—224no—
127C2×C4—224no—
128C2×C4C2×Dic2212yes—
129C2×C4C2×Dic2214yes—
130C2×C4#434314yes—
131C22C22×Dic2211yescharacteristic
132C22#6703711yescharacteristic
133C22#6703711yescharacteristic
134C22C2×#434312yes—
135C22#6704312yes—
136C4—22no—
137C4—24no—
138C4—24no—
139C4—42no—
140C4—444no—
141C4—444no—
142C2#1062301411yescharacteristic
143C2#1062310112yes—
144C2#1062317612yes—
145C2#1062320311yescharacteristic
146C2#1062326511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, prime radical, cosocleC23×C11C24
FittingC11×#391C2
hypercenter#391D11
hypocenterC11#2809
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
111. C11#2809semidirect

Maximal subgroups

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

subgroupindex
C11×#3912
#106228432
#106225992
#106225412
#106222742
#106222682
#280911