Finite Group Databasebeta

← #14647302

Subgroups — #14647302

Order 2816.

398 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 99 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#13068696C212yesmaximal
2#13066524C214yesmaximal
3C11×#2313C211yesmaximal, characteristic
4C22×C11×C4⋊C4C2211yescharacteristic
5C11×#387—24no—
6C11×#381C2212yes—
7C11×#380C412yes—
8C4×C11×C22⋊C4C412yes—
9#10622820C2214yes—
10#10622168—24no—
11C23×C4×C11C2×C411yescharacteristic
12C23×C4×C11C2×C411yescharacteristic
13C23×C4×C11C2311yescharacteristic
14C2×C11×C4⋊C4—24no—
15C2×C11×C4⋊C4—22no—
16C2×C11×C4⋊C4D414yes—
17C2×C11×C22⋊C4C2×C414yes—
18C2×C42×C11—22no—
19C2×#4318—24no—
20C11×#95—22no—
21C11×#95—22no—
22C11×#95—24no—
23C22⋊(C11⋊C8)—28no—
24#8755—111nomaximal, Sylow
25C24×C11C22×C411yescharacteristic
26C22×C4×C11—22no—
27C22×C4×C11—22no—
28C22×C4×C11—24no—
29C22×C4×C11—42no—
30C22×C4×C11—81no—
31C22×C4×C11—81no—
32C22×C4×C11C22⋊C412yes—
33C22×C4×C11C22⋊C412yes—
34C22×C4×C11C2×D412yes—
35C22×C4×C11#4114yes—
36C11×C4⋊C4—28no—
37C11×C4⋊C4—82no—
38C11×C22⋊C4—44no—
39C42×C11—82no—
40#4318—48no—
41C2×C11⋊C8—44no—
42#2313D1111yescharacteristic
43#1821—112no—
44#1306—114no—
45C23×C11—22no—
46C23×C11—41no—
47C23×C11—41no—
48C23×C11C2×C22⋊C411yescharacteristic
49C23×C11#11712yes—
50C2×C4×C11—24no—
51C2×C4×C11—22no—
52C2×C4×C11—22no—
53C2×C4×C11—44no—
54C2×C4×C11—42no—
55C2×C4×C11—42no—
56C2×C4×C11—44no—
57C2×C4×C11—44no—
58C2×C4×C11—44no—
59C2×C4×C11—82no—
60C2×C4×C11—82no—
61C2×C4×C11#12314yes—
62C11⋊C8—84no—
63C22×C4⋊C4C2×D1111yescharacteristic
64#407—114no—
65#387—24no—
66#381C2×D1112yes—
67#380Dic1112yes—
68C4×C22⋊C4Dic1112yes—
69#343—224no—
70C22×C11—21no—
71C22×C11—21no—
72C22×C11—22no—
73C22×C11—22no—
74C22×C11—22no—
75C22×C11—44no—
76C22×C11#38111yescharacteristic
77C22×C11#41012yes—
78C4×C11—24no—
79C4×C11—42no—
80C4×C11—42no—
81C4×C11—84no—
82C23×C4C2×Dic1111yescharacteristic
83C23×C4C2×Dic1111yescharacteristic
84C23×C4C22×D1111yescharacteristic
85C2×M16—224no—
86C2×C4⋊C4—24no—
87C2×C4⋊C4—22no—
88C2×C4⋊C4C22⋊D1114yes—
89C2×C22⋊C4C2×Dic1114yes—
90C2×C42—22no—
91C22⋊C8—228no—
92#95—22no—
93#95—22no—
94#95—24no—
95C2×C11—22no—
96C2×C11—42no—
97C2×C11#182011yescharacteristic
98C2×C11#182911yescharacteristic
99C2×C11#183011yescharacteristic
100C24C22×Dic1111yescharacteristic
101C22×C4—22no—
102C22×C4—22no—
103C22×C4—24no—
104C22×C4—42no—
105C22×C4—81no—
106C22×C4—81no—
107C22×C4C22⋊Dic1112yes—
108C22×C4C22⋊Dic1112yes—
109C22×C4#433914yes—
110C22×C4C2×C22⋊D1112yes—
111M16—448no—
112C2×C8—444no—
113C4⋊C4—28no—
114C4⋊C4—82no—
115C22⋊C4—44no—
116C42—82no—
117C11#875511yescharacteristic, complemented, Sylow
118C23—22no—
119C23—41no—
120C23—41no—
121C23#6697912yes—
122C23C2×C22⋊Dic1111yescharacteristic
123C2×C4—24no—
124C2×C4—22no—
125C2×C4—22no—
126C2×C4—44no—
127C2×C4—42no—
128C2×C4—42no—
129C2×C4—44no—
130C2×C4—44no—
131C2×C4—44no—
132C2×C4—82no—
133C2×C4—82no—
134C2×C4#6698214yes—
135C8—884no—
136C22—21no—
137C22—21no—
138C22—22no—
139C22—22no—
140C22—22no—
141C22—44no—
142C22#1062282411yescharacteristic
143C22#1062285312yes—
144C4—24no—
145C4—42no—
146C4—42no—
147C4—84no—
148C2—22no—
149C2—42no—
150C2#1306869311yescharacteristic
151C2#1306872711yescharacteristic
152C2#1306873011yescharacteristic
subgroupG/H
centerC22#10622824
commutator, prime radicalC24×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#2313C2
socleC22×C11#381
cosocleC23×C4×C11C23
hypercenter#2313D11
hypocenterC11#8755
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2313

Complements

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

NH ≅ G/Ntype
117. C11#8755semidirect

Maximal subgroups

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

subgroupindex
#130686962
#130665242
C11×#23132
#875511