Finite Group Databasebeta

← #13069923

Subgroups — #13069923

Order 1408.

264 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 63 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#10623279C211yesmaximal, characteristic
2#10622732C211yesmaximal, characteristic, complemented
3#10622619C212yesmaximal, complemented
4#10622615C212yesmaximal, complemented
5C11×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
6C2×#4339C2212yes—
7C2×C11×M16C2211yescharacteristic
8C11×#117C2212yes—
9#66979C2211yescharacteristic
10C22×C11⋊C8C2211yescharacteristic
11#66962—22no—
12#66961—22no—
13#66957—22no—
14Dic11⋊C8—22no—
15#66874—22no—
16#66873—22no—
17#66870—24no—
18C22×C4×C11C2311yescharacteristic
19C2×C22⋊D11—22no—
20#4339—22no—
21#4339—22no—
22#4339—22no—
23#4339—22no—
24C2×D44D412yes—
25C2×C4×D11—22no—
26C2×Dic22D412yes—
27C11×M16—22no—
28C2×C8×C11D412yes—
29C11×C4⋊C4—22no—
30C11×C22⋊C4—22no—
31C42×C11—22no—
32C22⋊Dic11D412yes—
33C4⋊Dic11—21no—
34C4×Dic11—21no—
35C2×C11⋊C8—22no—
36C2×C11⋊C8—21no—
37Dic44—22no—
38D88—22no—
39#4314—24no—
40#2053—111nomaximal, Sylow
41C23×C11C2×D411yescharacteristic
42C22×D11—22no—
43C2×C4×C11—42no—
44C2×C4×C11C2×D411yescharacteristic
45C2×C4×C11C2×D412yes—
46C2×C4×C11#4112yes—
47C2×C4×C11#4111yescharacteristic
48C22⋊D11—42no—
49C22⋊D11—42no—
50C2×Dic11—22no—
51C2×Dic11—22no—
52D44—22no—
53D44—22no—
54C4×D11—42no—
55C4×D11—42no—
56Dic22—22no—
57Dic22—22no—
58C8×C11—22no—
59C11⋊C8—41no—
60#575—111no—
61#424—111no—
62#416—112no—
63#410—112no—
64H(3,ℤ/4)D1111yescharacteristic, complemented
65C22×C11—41no—
66C22×C11#12112yes—
67C22×C11#12111yescharacteristic
68C2×D11—42no—
69C2×D11—82no—
70C4×C11—82no—
71C4×C11#12011yescharacteristic
72C4×C11#12312yes—
73C4×C11#12411yescharacteristic
74Dic11—42no—
75Dic11—42no—
76C2×#41—112no—
77#137—222no—
78AGL(1,ℤ/8)—222no—
79#135—222no—
80C2×M16C2×D1111yescharacteristic
81C22×C8—111no—
82#117—111no—
83#117C2×D1112yes—
84C4⋊C8—222no—
85#103—222no—
86#102—222no—
87#99—224no—
88C2×C11—21no—
89C2×C11—22no—
90C2×C11#39411yescharacteristic
91D11—82no—
92#41—222no—
93#41—222no—
94#41—222no—
95#41—222no—
96C2×Q8—112no—
97C2×D4—112no—
98C2×D4—222no—
99C22×C4—222no—
100C22×C4C22×D1111yescharacteristic
101Q16—222no—
102SD16—224no—
103D8—222no—
104M16—22no—
105C2×C8—221no—
106C2×C8—222no—
107C2×C8D4412yes—
108C4⋊C4—22no—
109C4⋊C4—221no—
110C22⋊C4—22no—
111C22⋊C4—112no—
112C42—22no—
113C42—221no—
114C11#205311yescharacteristic, complemented, Sylow
115C23—222no—
116C23D4×D1111yescharacteristic
117Q8—222no—
118Q8—222no—
119D4—222no—
120D4—222no—
121D4—442no—
122D4—442no—
123C2×C4—42no—
124C2×C4—222no—
125C2×C4—222no—
126C2×C4—442no—
127C2×C4—442no—
128C2×C4C2×D4411yescharacteristic
129C2×C4#433912yes—
130C2×C4D4×D1112yes—
131C2×C4#434311yescharacteristic
132C8—22no—
133C8—441no—
134C22—41no—
135C22—442no—
136C22—882no—
137C22#6693712yes—
138C22#6694811yescharacteristic
139C4—82no—
140C4—442no—
141C4—442no—
142C4#6692811yescharacteristic
143C4#6693511yescharacteristic
144C4#6694712yes—
145C2—22no—
146C2—21no—
147C2—882no—
148C2#1062228511yescharacteristic
subgroupG/H
centerC4#66928
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC11×H(3,ℤ/4)C2
socleC2×C11#394
prime radical#10623279C2
hypercenterH(3,ℤ/4)D11
hypocenterC11#2053
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C22×C4 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
2. #10622732C2semidirect
3. #10622619C2semidirect
4. #10622615C2semidirect
5. C11×H(3,ℤ/4)C2semidirect
64. H(3,ℤ/4)D11semidirect
114. C11#2053semidirect

Maximal subgroups

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

subgroupindex
#106232792
#106227322
#106226192
#106226152
C11×H(3,ℤ/4)2
#205311