Finite Group Databasebeta

← #13079019

Subgroups — #13079019

Order 1408.

392 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 133 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
1C2×C11×#125C211yesmaximal, characteristic, complemented
2#10623008C211yesmaximal, characteristic
3#10622682C212yesmaximal, complemented
4#10622681C214yesmaximal, complemented
5#10622680C212yesmaximal, complemented
6#10622579C214yesmaximal, complemented
7C4×#4318C211yesmaximal, characteristic, complemented
8C2×#4339C2212yes—
9C11×#125—22no—
10C11×#125C2212yes—
11C11×#125C2212yes—
12C2×C11×C4⋊C4—22no—
13C2×C11×C4⋊C4C2212yes—
14C2×C42×C11C2211yescharacteristic
15#66983—22no—
16C2×#4318C2212yes—
17#66928C2212yes—
18#66927C2211yescharacteristic
19C4×D44—22no—
20#66922C2211yescharacteristic
21#66874C2218yes—
22#66873C2218yes—
23#66867C2212yes—
24C4×C11⋊C8C2212yes—
25C22×C4×C11—22no—
26C22×C4×C11D412yes—
27C22×C4×C11C2311yescharacteristic
28C2×C22⋊D11—22no—
29#4339—28no—
30C2×D44—22no—
31C2×D44C2312yes—
32C2×C4×D11—22no—
33C2×Dic22C2312yes—
34C11×C4⋊C4—24no—
35C11×C4⋊C4—24no—
36C11×C4⋊C4—22no—
37C11×C4⋊C4C2314yes—
38C42×C11D412yes—
39C42×C11C2311yescharacteristic
40C42×C11C2311yescharacteristic
41(C2×D11)⋊C4—24no—
42C4⋊Dic11—22no—
43#4318—24no—
44C2×C11⋊C8C2314yes—
45#3142—111nomaximal, Sylow
46C23×C11C2×D411yescharacteristic
47C22×D11—22no—
48C2×C4×C11—24no—
49C2×C4×C11—42no—
50C2×C4×C11—44no—
51C2×C4×C11C2×D412yes—
52C2×C4×C11C2×D412yes—
53C2×C4×C11C2×D411yescharacteristic
54C2×C4×C11#4114yes—
55C2×C4×C11C2411yescharacteristic
56C22⋊D11—44no—
57C2×Dic11—22no—
58D44—24no—
59D44—44no—
60C4×D11—44no—
61Dic22—24no—
62C11⋊C8—24no—
63#532—111no—
64C2×#125D1111yescharacteristic, complemented
65#491—112no—
66#490—112no—
67#488—114no—
68#417—114no—
69C4×M16—111no—
70C22×C11—22no—
71C22×C11#12412yes—
72C22×C11C22×D411yescharacteristic
73C2×D11—42no—
74C2×D11—44no—
75C4×C11—22no—
76C4×C11—22no—
77C4×C11—44no—
78C4×C11#12412yes—
79C4×C11C2×#4112yes—
80Dic11—42no—
81C2×#41—112no—
82C2×M16—112no—
83C4⋊Q8—111no—
84#127—111no—
85#125—22no—
86#125C2×D1112yes—
87#125C2×D1112yes—
88#124—112no—
89#121—222no—
90C4×D4—222no—
91C2×C4⋊C4—22no—
92C2×C4⋊C4C2×D1112yes—
93C2×C42C2×D1111yescharacteristic
94#103—118no—
95#102—118no—
96#97—112no—
97C4×C8—112no—
98C2×C11—22no—
99C2×C11C2×#12411yescharacteristic
100C2×C11#57512yes—
101D11—82no—
102#41—228no—
103C2×Q8—112no—
104C2×D4—112no—
105C2×D4—222no—
106C2×D4—222no—
107C22×C4—22no—
108C22×C4—222no—
109C22×C4C22⋊D1112yes—
110C22×C4C22×D1111yescharacteristic
111M16—224no—
112C2×C8—114no—
113C4⋊C4—24no—
114C4⋊C4—24no—
115C4⋊C4—22no—
116C4⋊C4—222no—
117C4⋊C4C22×D1114yes—
118C22⋊C4—224no—
119C42C22⋊D1112yes—
120C42C22×D1111yescharacteristic
121C42C22×D1111yescharacteristic
122C11#314211yescharacteristic, complemented, Sylow
123C23—222no—
124C23C2×C22⋊D1111yescharacteristic
125Q8—224no—
126D4—224no—
127D4—444no—
128D4—444no—
129C2×C4—24no—
130C2×C4—42no—
131C2×C4—44no—
132C2×C4—222no—
133C2×C4—444no—
134C2×C4#434314yes—
135C2×C4C2×C22⋊D1112yes—
136C2×C4C2×C22⋊D1112yes—
137C2×C4C2×C22⋊D1111yescharacteristic
138C2×C4C23×D1111yescharacteristic
139C8—224no—
140C22—22no—
141C22—442no—
142C22—444no—
143C22#6700012yes—
144C22C22×C22⋊D1111yescharacteristic
145C4—22no—
146C4—22no—
147C4—44no—
148C4—442no—
149C4#6700012yes—
150C4C2×#434312yes—
151C2—22no—
152C2—882no—
153C2C2×#6700011yescharacteristic
154C2#1062335312yes—
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC2×C11×#125C2
socleC22×C11C22×D4
prime radical#10623008C2
hypercenterC2×#125D11
hypocenterC11#3142
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
1. C2×C11×#125C2semidirect
3. #10622682C2semidirect
4. #10622681C2semidirect
5. #10622680C2semidirect
6. #10622579C2semidirect
7. C4×#4318C2semidirect
64. C2×#125D11semidirect
122. C11#3142semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1252
#106230082
#106226822
#106226812
#106226802
#106225792
C4×#43182
#314211