Finite Group Databasebeta

← C2×#440 #2940

Subgroups — C2×#440 #2940

Order 128.

272 conjugacy classes of subgroups; only the 148 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 148 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
1C22×SD16C211yesmaximal, characteristic
2C2×C4×Q8C211yesmaximal, characteristic, complemented
3C2×C4×D4C211yesmaximal, characteristic
4#440C218yesmaximal, direct product factor
5C2×#107C211yesmaximal, characteristic, complemented
6C2×#103C211yesmaximal, characteristic, complemented
7C2×#102C211yesmaximal, characteristic
8C2×#97C211yesmaximal, characteristic, complemented
9C22×Q8C2211yescharacteristic
10C22×D4C2211yescharacteristic
11C23×C4—21no—
12C2×SD16C418yescomplemented
13C2×SD16C2214yes—
14C22×C8C2211yescharacteristic
15C22×C8C2211yescharacteristic
16C4×Q8—22no—
17C4×Q8C2214yescomplemented
18C4×D4—22no—
19C4×D4C2214yes—
20C2×C4⋊C4—21no—
21C2×C4⋊C4C2211yescharacteristic
22C2×C4⋊C4C2211yescharacteristic
23C2×C22⋊C4—21no—
24C2×C42—21no—
25C2×C42C2211yescharacteristic
26#107C2214yescomplemented
27#103C2214yescomplemented
28#102C2214yes—
29#97C2214yescomplemented
30C24—21no—
31C2×Q8—21no—
32C2×Q8—22no—
33C2×Q8C2×C414yescomplemented
34C2×Q8C2312yes—
35C2×D4—21no—
36C2×D4—22no—
37C2×D4C2×C414yes—
38C2×D4C2312yes—
39C22×C4—21no—
40C22×C4—21no—
41C22×C4—21no—
42C22×C4—24no—
43C22×C4—44no—
44C22×C4D411yescharacteristic
45C22×C4D411yescharacteristic
46C22×C4C2311yescharacteristic
47SD16C2×C4116yescomplemented
48C2×C8—22no—
49C2×C8C2×C414yescomplemented
50C2×C8C2312yes—
51C2×C8C2312yes—
52C4⋊C4—24no—
53C4⋊C4—21no—
54C4⋊C4—21no—
55C4⋊C4C2312yes—
56C4⋊C4C2312yes—
57C22⋊C4—24no—
58C42—24no—
59C42D412yes—
60C42C2312yes—
61C23—24no—
62C23—22no—
63C23—42no—
64C23—42no—
65C23C2×D411yescharacteristic
66Q8—24no—
67Q8—22no—
68Q8C22×C414yescomplemented
69D4—24no—
70D4—22no—
71D4C22×C414yes—
72C2×C4—24no—
73C2×C4—22no—
74C2×C4—22no—
75C2×C4—22no—
76C2×C4—22no—
77C2×C4—22no—
78C2×C4—48no—
79C2×C4—42no—
80C2×C4—42no—
81C2×C4C22×C412yes—
82C2×C4C2×D412yes—
83C2×C4C2×D412yes—
84C2×C4C2×D411yescharacteristic
85C2×C4#4112yes—
86C2×C4C2411yescharacteristic
87C8—22no—
88C8C22×C414yescomplemented
89C22—24no—
90C22—42no—
91C22—42no—
92C22—48no—
93C22C4×D412yes—
94C22AGL(1,ℤ/8)12yes—
95C22#13712yes—
96C22C22×D411yescharacteristic
97C4—24no—
98C4—22no—
99C4—22no—
100C4—42no—
101C4—42no—
102C4C4×D412yes—
103C4C23×C411yescharacteristic
104C4C2×#4111yescharacteristic
105C2—44no—
106C2#44014yesdirect product factor
107C2C2×C4×D411yescharacteristic
108C2C2×AGL(1,ℤ/8)11yescharacteristic
109C2C2×#13711yescharacteristic
subgroupG/H
center, socleC23C2×D4
commutatorC4C23×C4
Frattini, cosocleC2×C4C24
prime radicalC22×D4C22
LCSG ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C42 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×C4×Q8C2semidirect
4. #440C2direct (N × H)
5. C2×#107C2semidirect
6. C2×#103C2semidirect
8. C2×#97C2semidirect
12. C2×SD16C4semidirect
17. C4×Q8C22semidirect
26. #107C22semidirect
27. #103C22semidirect
29. #97C22semidirect
33. C2×Q8C2×C4semidirect
47. SD16C2×C4semidirect
49. C2×C8C2×C4semidirect
68. Q8C22×C4semidirect
88. C8C22×C4semidirect
106. C2#440direct (N × H)

Maximal subgroups

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

subgroupindex
C22×SD162
C2×C4×Q82
C2×C4×D42
#4402
C2×#1072
C2×#1032
C2×#1022
C2×#972