Finite Group Databasebeta

← C2×#3798 #64300

Subgroups — C2×#3798 #64300

Order 288.

355 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 355 conjugacy classes of subgroups — too many to draw. Only its 116 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×C4×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×C3×C4×D3C212yesmaximal, complemented
3C2×#627C211yesmaximal, characteristic, complemented
4C2×#626C212yesmaximal, complemented
5C2×#625C211yesmaximal, characteristic, complemented
6#3798C218yesmaximal, direct product factor
7C2×#235—32nomaximal
8C22×C3⋊D3C2211yescharacteristic
9C22×C3×D3C2212yes—
10C2×C32×C4C2211yescharacteristic
11C2×C3⋊Dic3C2211yescharacteristic
12C4×C3⋊D3C2214yescomplemented
13C2×C3×Dic3C2212yes—
14C3×C4×D3C2218yescomplemented
15#627C2214yescomplemented
16#626C2218yescomplemented
17#625C2214yescomplemented
18C22×C3×C4—32no—
19C2×#67—32no—
20C2×#67—32no—
21#235—316no—
22C2×D12—32no—
23C2×C4×D3—32no—
24C2×C4×D3—61no—
25C2×C4×D3D312yescomplemented
26C2×Dic6—32no—
27C22×C32C2311yescharacteristic
28C2×C3⋊D3—22no—
29C2×C3⋊D3C2312yes—
30C2×C3×D3—24no—
31C2×C3×D3C2314yes—
32C32×C4C2312yes—
33C3⋊Dic3C2312yes—
34C3×Dic3C2314yes—
35C2×#41—91noSylow
36C23×C3—32no—
37C22×D3—32no—
38C22×D3—61no—
39C22×D3C2×D312yes—
40C2×C3×C4—21no—
41C2×C3×C4—32no—
42C2×C3×C4—38no—
43C2×C3×C4C2×D312yes—
44#67—38no—
45#67—38no—
46C2×Dic3—32no—
47C2×Dic3—61no—
48C2×Dic3C2×D312yes—
49D12—38no—
50C4×D3—38no—
51C4×D3—64no—
52C4×D3C2×D318yescomplemented
53Dic6—38no—
54C2×C32#4112yescomplemented
55C2×C32C2411yescharacteristic
56C3⋊D3—22no—
57C3×D3—24no—
58#41—98no—
59C2×Q8—91no—
60C2×D4—92no—
61C2×D4—91no—
62C22×C4—32no—
63C22×C4—91no—
64C22×C3—21no—
65C22×C3—34no—
66C22×C3—64no—
67C22×C3C22×D312yes—
68C2×D3—24no—
69C2×D3—34no—
70C2×D3—62no—
71C2×D3—64no—
72C2×D3—64no—
73C2×D3C22×D314yes—
74C3×C4—22no—
75C3×C4—34no—
76C3×C4C22×D314yes—
77Dic3—34no—
78Dic3—62no—
79Dic3C22×D314yes—
80C32C2×#4111yescharacteristic, complemented, Sylow
81C23—32no—
82C23—91no—
83Q8—94no—
84D4—98no—
85D4—94no—
86C2×C4—32no—
87C2×C4—38no—
88C2×C4—91no—
89C2×C4—94no—
90C2×C4D3211yescharacteristic
91C2×C3—21no—
92C2×C3—22no—
93C2×C3—64no—
94C2×C3#23514yescomplemented
95C2×C3C23×D312yes—
96D3—24no—
97D3—64no—
98D3—64no—
99C22—34no—
100C22—64no—
101C22—92no—
102C22—182no—
103C22C2×D3211yescharacteristic
104C4—34no—
105C4—92no—
106C4C2×D3212yes—
107C3—21no—
108C3C2×#23512yescomplemented
109C2—64no—
110C2—182no—
111C2#379812yesdirect product factor
112C2C22×D3211yescharacteristic
subgroupG/H
center, hypercenterC2×C4D32
commutator, cosocleC2×C32C24
FrattiniC2C22×D32
FittingC2×C32×C4C22
socleC22×C32C23
hypocenterC32C2×#41
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C2×C4×C3⋊D3C2semidirect
2. C2×C3×C4×D3C2semidirect
3. C2×#627C2semidirect
4. C2×#626C2semidirect
5. C2×#625C2semidirect
6. #3798C2direct (N × H)
12. C4×C3⋊D3C22semidirect
14. C3×C4×D3C22semidirect
15. #627C22semidirect
16. #626C22semidirect
17. #625C22semidirect
25. C2×C4×D3D3semidirect
52. C4×D3C2×D3semidirect
54. C2×C32#41semidirect
80. C32C2×#41semidirect
94. C2×C3#235semidirect
108. C3C2×#235semidirect
111. C2#3798direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×C3⋊D32
C2×C3×C4×D32
C2×#6272
C2×#6262
C2×#6252
#37982
C2×#2353