Finite Group Databasebeta

← C2×#64222 #10596495

Subgroups — C2×#64222 #10596495

Order 576.

446 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 113 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×#3797C212yesmaximal
2C2×C4×#157C211yesmaximal, characteristic
3C2×#3773C214yesmaximal
4#64222C218yesmaximal, direct product factor
5C22×#157C2212yes—
6C2×C4×C3⋊D3C2211yescharacteristic
7C2×C3×Dic6—22no—
8C2×#627—22no—
9C2×#624C2214yes—
10#3797—24no—
11#3797C2218yes—
12C4×#157C2214yes—
13#3773C22116yes—
14C2×D3×Q8—62no—
15C22×C3⋊D3C2311yescharacteristic
16C2×#157Q818yescomplemented
17C2×#157C2314yes—
18C2×C32×C4D411yescharacteristic
19C2×C3⋊Dic3D411yescharacteristic
20C4×C3⋊D3D412yes—
21C4×C3⋊D3C2312yes—
22C2×C3×Dic3—24no—
23C3×Dic6—28no—
24#627—28no—
25#624—24no—
26#624C2318yes—
27C2×C4⋊Q8—91nomaximal, Sylow
28C2×C3×Q8—62no—
29D3×Q8—68no—
30D3×Q8—68no—
31C2×C4×D3—64no—
32C2×C4×D3—62no—
33C2×Dic6—22no—
34C2×Dic6—64no—
35C22×C32C2×D411yescharacteristic
36C2×C3⋊D3C2×D411yescharacteristic
37C2×C3⋊D3C2×Q814yes—
38C2×C3⋊D3C2411yescharacteristic
39#157C2×Q818yescomplemented
40C32×C4C2×D412yes—
41C3⋊Dic3C2×D412yes—
42C3×Dic3—28no—
43C22×Q8—92no—
44C4⋊Q8—98no—
45C2×C4⋊C4—94no—
46C2×C42—91no—
47C22×D3—62no—
48C3×Q8—68no—
49C2×C3×C4—22no—
50C2×C3×C4—64no—
51C2×Dic3—24no—
52C2×Dic3—62no—
53C4×D3—68no—
54C4×D3—64no—
55C4×D3—64no—
56C4×D3—68no—
57Dic6—28no—
58Dic6—616no—
59C2×C32C4⋊Q812yescomplemented
60C2×C32C22×D411yescharacteristic
61C3⋊D3C4⋊Q812yescomplemented
62C3⋊D3C22×Q812yes—
63C2×Q8—62no—
64C2×Q8—98no—
65C2×Q8—182no—
66C2×Q8—184no—
67C22×C4—94no—
68C22×C4—92no—
69C22×C4—91no—
70C4⋊C4—916no—
71C42—94no—
72C22×C3—22no—
73C2×D3—62no—
74C2×D3—62no—
75C2×D3—68no—
76C3×C4—24no—
77C3×C4—68no—
78Dic3—28no—
79Dic3—64no—
80C32C2×C4⋊Q811yescharacteristic, complemented, Sylow
81C23—91no—
82Q8—68no—
83Q8—188no—
84C2×C4—64no—
85C2×C4—98no—
86C2×C4—94no—
87C2×C4—98no—
88C2×C4—91no—
89C2×C4—92no—
90C2×C4—92no—
91C2×C4—184no—
92C2×C4GO+(4,𝔽2)11yescharacteristic
93C2×C3—22no—
94C2×C3—24no—
95D3—64no—
96D3—64no—
97C22—91no—
98C22—91no—
99C22—94no—
100C22C2×GO+(4,𝔽2)11yescharacteristic
101C4—68no—
102C4—98no—
103C4—92no—
104C4C2×GO+(4,𝔽2)12yes—
105C3—22no—
106C2—92no—
107C2—92no—
108C2#6422212yesdirect product factor
109C2C22×GO+(4,𝔽2)11yescharacteristic
subgroupG/H
centerC22C2×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊D3C24
FrattiniC2C22×GO+(4,𝔽2)
FittingC2×C32×C4D4
socleC22×C32C2×D4
prime radicalC22×C3⋊D3C23
hypercenterC2×C4GO+(4,𝔽2)
hypocenterC32C2×C4⋊Q8
LCSG ▷ C2×C3⋊D3 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
4. #64222C2direct (N × H)
16. C2×#157Q8semidirect
39. #157C2×Q8semidirect
59. C2×C32C4⋊Q8semidirect
61. C3⋊D3C4⋊Q8semidirect
80. C32C2×C4⋊Q8semidirect
108. C2#64222direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#37972
C2×C4×#1572
C2×#37732
#642222
C2×C4⋊Q89