Finite Group Databasebeta

← C2×#1412 #13593

Subgroups — C2×#1412 #13593

Order 256.

195 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 195 conjugacy classes of subgroups — too many to draw. Only its 47 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×#490C211yesmaximal, characteristic
2C2×#353C212yesmaximal
3#1412C214yesmaximal, direct product factor
4C2×#127C2211yescharacteristic
5C2×#125C411yescharacteristic, complemented
6#490—22no—
7#490C412yescomplemented
8#490C2212yes—
9C2×#102—22no—
10C2×#99—22no—
11C2×#97C411yescharacteristic, complemented
12#353—22no—
13#353C2214yes—
14C22×D4—41no—
15C22×D4D412yes—
16C22×C8—21no—
17#127—41no—
18#127C2×C411yescharacteristic
19#127D412yes—
20#127C2311yescharacteristic
21#125—21no—
22#125—41no—
23#125C2×C412yescomplemented
24C2×C4⋊C4—21no—
25C2×C4⋊C4—41no—
26C2×C22⋊C4—42no—
27C2×C42C2×C411yescharacteristic
28#102—24no—
29#102—24no—
30#99—24no—
31#99—42no—
32#97—21no—
33#97C2×C412yescomplemented
34C24—22no—
35C2×D4—22no—
36C2×D4—42no—
37C2×D4—42no—
38C2×D4—41no—
39C2×D4—42no—
40C2×D4—41no—
41C2×D4—84no—
42C2×D4C22⋊C412yes—
43C2×D4C2×D412yes—
44C22×C4—21no—
45C22×C4—41no—
46C22×C4—82no—
47C22×C4C22⋊C411yescharacteristic
48C2×C8—22no—
49C2×C8—41no—
50C2×C8—41no—
51C4⋊C4—22no—
52C4⋊C4—42no—
53C4⋊C4—42no—
54C4⋊C4—41no—
55C22⋊C4—44no—
56C22⋊C4—82no—
57C42—21no—
58C42C22⋊C411yescharacteristic
59C42C22×C411yescharacteristic
60C23—22no—
61C23—22no—
62C23—42no—
63C23—42no—
64C23—84no—
65C23#9911yescharacteristic
66D4—42no—
67D4—42no—
68D4—82no—
69D4—82no—
70D4—84no—
71D4—82no—
72C2×C4—21no—
73C2×C4—21no—
74C2×C4—21no—
75C2×C4—21no—
76C2×C4—42no—
77C2×C4—42no—
78C2×C4—82no—
79C2×C4—84no—
80C2×C4—164no—
81C2×C4#9911yescharacteristic
82C2×C4C2×C22⋊C411yescharacteristic
83C8—42no—
84C22—22no—
85C22—42no—
86C22—42no—
87C22—82no—
88C22—82no—
89C22—84no—
90C22—162no—
91C22#35411yescharacteristic
92C22#35411yescharacteristic
93C22C2×#9911yescharacteristic
94C4—21no—
95C4—21no—
96C4—41no—
97C4—41no—
98C4—82no—
99C4—164no—
100C2—21no—
101C2—21no—
102C2—82no—
103C2—82no—
104C2#141212yesdirect product factor
105C2C2×#35411yescharacteristic
subgroupG/H
center, socleC22#354
commutatorC42C22×C4
Frattini, cosocle#127C23
prime radicalC2×#127C22
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×#127 ◁ G
LECSG ▷ #127 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #1412C2direct (N × H)
5. C2×#125C4semidirect
7. #490C4semidirect
11. C2×#97C4semidirect
23. #125C2×C4semidirect
33. #97C2×C4semidirect
104. C2#1412direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#4902
C2×#3532
#14122