Finite Group Databasebeta

← #10622650

Subgroups — #10622650

Order 704.

162 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 43 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×#4339C211yesmaximal, characteristic, complemented
2C11×#121C211yesmaximal, characteristic, complemented
3C2×#4324C211yesmaximal, characteristic, complemented
4C2×#4323C211yesmaximal, characteristic, complemented
5C22⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
6#66874C211yesmaximal, characteristic, complemented
7#66873C211yesmaximal, characteristic, complemented
8C2×D4×C11—21no—
9C2×D4×C11C2211yescharacteristic
10C22×C4×C11C2211yescharacteristic
11C2×C22⋊D11—21no—
12#4339—22no—
13#4339—22no—
14C2×D44C2211yescharacteristic
15C2×C4×D11—21no—
16C2×Dic22C2211yescharacteristic
17C11×C4⋊C4C2211yescharacteristic
18C11×C22⋊C4—21no—
19#4324—22no—
20#4323—22no—
21C2×C11⋊C8C2211yescharacteristic
22C2×C11⋊C8C2211yescharacteristic
23C23×C11—21no—
24C23×C11D411yescharacteristic
25C22×D11—21no—
26D4×C11—21no—
27D4×C11—21no—
28D4×C11—42no—
29C2×C4×C11—21no—
30C2×C4×C11—21no—
31C2×C4×C11—21no—
32C2×C4×C11D411yescharacteristic
33C2×C4×C11C2311yescharacteristic
34C22⋊D11—24no—
35C2×Dic11—21no—
36D44—21no—
37D44D412yescomplemented
38C4×D11—24no—
39Dic22—21no—
40Dic22D412yescomplemented
41C11⋊C8—21no—
42C11⋊C8—21no—
43#449—111nomaximal, Sylow
44C22×C11—21no—
45C22×C11—21no—
46C22×C11—21no—
47C22×C11—41no—
48C22×C11—41no—
49C22×C11—41no—
50C22×C11C2×D411yescharacteristic
51C2×D11—22no—
52C2×D11—41no—
53C2×D11—41no—
54C4×C11—21no—
55C4×C11—41no—
56C4×C11C2×D411yescharacteristic
57C4×C11C2×D411yescharacteristic
58Dic11—22no—
59C2×#41—111no—
60C2×SD16—111no—
61C2×D8—111no—
62#121D1111yescharacteristic, complemented
63#103—111no—
64#102—111no—
65C22⋊C8—111no—
66C2×C11—41no—
67C2×C11—81no—
68C2×C11#12011yescharacteristic
69C2×C11#13511yescharacteristic
70C2×C11AGL(1,ℤ/8)11yescharacteristic
71D11—42no—
72#41—222no—
73#41—222no—
74C2×Q8—111no—
75C2×D4—21no—
76C2×D4—111no—
77C2×D4—221no—
78C2×D4C2×D1111yescharacteristic
79C22×C4—221no—
80C22×C4C2×D1111yescharacteristic
81SD16—222no—
82D8—222no—
83C2×C8—111no—
84C2×C8—111no—
85C4⋊C4C2×D1111yescharacteristic
86C22⋊C4—21no—
87C11#44911yescharacteristic, complemented, Sylow
88C23—21no—
89C23—221no—
90C23C22⋊D1111yescharacteristic
91Q8—112no—
92Q8—221no—
93D4—21no—
94D4—21no—
95D4—42no—
96D4—112no—
97D4—224no—
98D4—221no—
99C2×C4—21no—
100C2×C4—21no—
101C2×C4—21no—
102C2×C4—224no—
103C2×C4—221no—
104C2×C4C22⋊D1111yescharacteristic
105C2×C4C22×D1111yescharacteristic
106C8—221no—
107C8—221no—
108C22—21no—
109C22—21no—
110C22—21no—
111C22—41no—
112C22—41no—
113C22—41no—
114C22—222no—
115C22—441no—
116C22—441no—
117C22C2×C22⋊D1111yescharacteristic
118C4—21no—
119C4—41no—
120C4—222no—
121C4D4×D1111yescharacteristic
122C4D4×D1111yescharacteristic
123C2—41no—
124C2—81no—
125C2—442no—
126C2#6698511yescharacteristic
127C2#6699011yescharacteristic
128C2#6700311yescharacteristic
subgroupG/H
centerC22C2×C22⋊D11
commutator, cosocleC2×C4×C11C23
FrattiniC2×C4C22×D11
FittingC11×#121C2
socleC22×C11C2×D4
hypercenter#121D11
hypocenterC11#449
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×#4339C2semidirect
2. C11×#121C2semidirect
3. C2×#4324C2semidirect
4. C2×#4323C2semidirect
5. C22⋊(C11⋊C8)C2semidirect
6. #66874C2semidirect
7. #66873C2semidirect
37. D44D4semidirect
40. Dic22D4semidirect
62. #121D11semidirect
87. C11#449semidirect

Maximal subgroups

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

subgroupindex
C2×#43392
C11×#1212
C2×#43242
C2×#43232
C22⋊(C11⋊C8)2
#668742
#668732
#44911