Finite Group Databasebeta

← C2×#482 #3087

Subgroups — C2×#482 #3087

Order 128.

234 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 100 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×#121C211yesmaximal, characteristic
2C2×#117C211yesmaximal, characteristic, complemented
3#482C218yesmaximal, direct product factor
4C2×#107C211yesmaximal, characteristic, complemented
5C2×#106C211yesmaximal, characteristic, complemented
6C2×#102C211yesmaximal, characteristic, complemented
7C2×#102C211yesmaximal, characteristic, complemented
8C2×C22⋊C8C211yesmaximal, characteristic, complemented
9C22×D4—21no—
10C22×D4C2211yescharacteristic
11C23×C4C2211yescharacteristic
12C22×C8C2211yescharacteristic
13C22×C8C2211yescharacteristic
14#121—22no—
15#121C2214yes—
16#117—22no—
17#117C2214yescomplemented
18C2×C4⋊C4C2211yescharacteristic
19C2×C4⋊C4C2211yescharacteristic
20C2×C4⋊C4C2211yescharacteristic
21C2×C22⋊C4—21no—
22C2×C22⋊C4—21no—
23C2×C42—21no—
24#107C2214yescomplemented
25#106C2214yescomplemented
26#102C2214yescomplemented
27#102C2214yescomplemented
28C22⋊C8C2214yescomplemented
29C24—21no—
30C24D411yescharacteristic
31C2×D4—24no—
32C2×D4—21no—
33C2×D4—22no—
34C2×D4—22no—
35C2×D4—44no—
36C2×D4C2312yes—
37C22×C4—22no—
38C22×C4—22no—
39C22×C4—21no—
40C22×C4—21no—
41C22×C4—21no—
42C22×C4D412yes—
43C22×C4D411yescharacteristic
44C22×C4C2312yes—
45C22×C4C2311yescharacteristic
46C2×C8—22no—
47C2×C8—22no—
48C2×C8C2312yes—
49C2×C8C2312yes—
50C4⋊C4—21no—
51C4⋊C4—21no—
52C4⋊C4—21no—
53C4⋊C4C2312yes—
54C4⋊C4C2312yes—
55C4⋊C4C2312yes—
56C22⋊C4—24no—
57C22⋊C4—24no—
58C42—24no—
59C23—22no—
60C23—22no—
61C23—22no—
62C23—22no—
63C23—42no—
64C23—42no—
65C23—42no—
66C23C2×D412yes—
67C23C2×D411yescharacteristic
68D4—22no—
69D4—22no—
70D4—48no—
71D4—42no—
72C2×C4—22no—
73C2×C4—24no—
74C2×C4—22no—
75C2×C4—22no—
76C2×C4—22no—
77C2×C4—22no—
78C2×C4—22no—
79C2×C4—42no—
80C2×C4—42no—
81C2×C4—42no—
82C2×C4C2×D412yes—
83C2×C4C2×D411yescharacteristic
84C2×C4#4112yes—
85C2×C4#4112yes—
86C2×C4C2411yescharacteristic
87C8—22no—
88C8—22no—
89C22—22no—
90C22—22no—
91C22—22no—
92C22—44no—
93C22—42no—
94C22—42no—
95C22—42no—
96C22—84no—
97C22#12312yes—
98C22#13512yes—
99C22AGL(1,ℤ/8)12yes—
100C22C22×D411yescharacteristic
101C4—22no—
102C4—42no—
103C4—42no—
104C4—42no—
105C4#12312yes—
106C4C2×#4111yescharacteristic
107C4C2×#4111yescharacteristic
108C2—42no—
109C2—82no—
110C2#48214yesdirect product factor
111C2C2×#12311yescharacteristic
112C2C2×#13511yescharacteristic
113C2C2×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
center, socleC23C2×D4
commutator, Frattini, cosocleC2×C4C24
prime radicalC2×#121C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C4 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#117C2semidirect
3. #482C2direct (N × H)
4. C2×#107C2semidirect
5. C2×#106C2semidirect
6. C2×#102C2semidirect
7. C2×#102C2semidirect
8. C2×C22⋊C8C2semidirect
17. #117C22semidirect
24. #107C22semidirect
25. #106C22semidirect
26. #102C22semidirect
27. #102C22semidirect
28. C22⋊C8C22semidirect
110. C2#482direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#1212
C2×#1172
#4822
C2×#1072
C2×#1062
C2×#1022
C2×C22⋊C82