Finite Group Databasebeta

← C2×#63780 #10593807

Subgroups — C2×#63780 #10593807

Order 576.

302 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 302 conjugacy classes of subgroups — too many to draw. Only its 52 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×#634C211yesmaximal, characteristic
2C2×#3792C212yesmaximal
3#63780C214yesmaximal, direct product factor
4C22×C32×C4C411yescharacteristic
5C22×C3⋊Dic3C411yescharacteristic
6C22×C3⋊Dic3C2211yescharacteristic
7C2×#634—22no—
8C2×#634—22no—
9C2×#634C412yes—
10C2×#634C2212yes—
11#3792—22no—
12#3792C2214yes—
13C2×#622—22no—
14C22×Dic6—62no—
15C23×C32C2×C411yescharacteristic
16C2×C32×C4—21no—
17C2×C32×C4—21no—
18C2×C32×C4C2×C412yes—
19C2×C3⋊Dic3—21no—
20C2×C3⋊Dic3—21no—
21C2×C3⋊Dic3C2×C412yes—
22C2×C3⋊Dic3C2×C411yescharacteristic
23C2×C3⋊Dic3D412yes—
24C2×C3⋊Dic3D412yes—
25C2×C3⋊Dic3C2311yescharacteristic
26#634—24no—
27#634—24no—
28#622—24no—
29C2×#101—91nomaximal, Sylow
30C22×C3×C4—22no—
31C22×Dic3—62no—
32C22×Dic3—62no—
33C2×Dic6—64no—
34C2×Dic6—64no—
35C2×Dic6—68no—
36C2×Dic6—68no—
37C22×C32—22no—
38C22×C32C22⋊C411yescharacteristic
39C22×C32C22⋊C411yescharacteristic
40C22×C32C22×C411yescharacteristic
41C32×C4—22no—
42C3⋊Dic3—22no—
43C3⋊Dic3C22⋊C412yes—
44C3⋊Dic3C2×D412yes—
45C22×Q8—91no—
46C2×M16—92no—
47#101—94no—
48C23×C3—22no—
49C2×C3×C4—24no—
50C2×C3×C4—24no—
51C2×C3×C4—24no—
52C2×Dic3—62no—
53C2×Dic3—64no—
54C2×Dic3—64no—
55C2×Dic3—64no—
56C2×Dic3—62no—
57C2×Dic3—64no—
58C2×Dic3—64no—
59Dic6—616no—
60Dic6—616no—
61C2×C32—21no—
62C2×C32—21no—
63C2×C32#10112yescomplemented
64C2×C32C2×C22⋊C411yescharacteristic
65C2×Q8—92no—
66C2×Q8—92no—
67C2×Q8—182no—
68C2×Q8—182no—
69C22×C4—91no—
70C22×C4—91no—
71C22×C4#15711yescharacteristic
72M16—94no—
73M16—182no—
74C2×C8—182no—
75C22×C3—28no—
76C22×C3—22no—
77C22×C3—22no—
78C22×C3—22no—
79C3×C4—28no—
80Dic3—64no—
81Dic3—64no—
82Dic3—68no—
83C32C2×#10111yescharacteristic, complemented, Sylow
84C23C2×#15711yescharacteristic
85Q8—184no—
86Q8—184no—
87C2×C4—21no—
88C2×C4—21no—
89C2×C4—91no—
90C2×C4—91no—
91C2×C4—92no—
92C2×C4—92no—
93C2×C4—92no—
94C2×C4—181no—
95C2×C4—181no—
96C2×C4C2×#15712yes—
97C8—184no—
98C2×C3—24no—
99C2×C3—24no—
100C2×C3—24no—
101C2×C3—22no—
102C22—22no—
103C22C22⋊#15711yescharacteristic
104C22C22⋊#15711yescharacteristic
105C22C22×#15711yescharacteristic
106C4—22no—
107C4—92no—
108C4—92no—
109C4—182no—
110C3—22no—
111C2—21no—
112C2—21no—
113C2#6378012yesdirect product factor
114C2C2×C22⋊#15711yescharacteristic
subgroupG/H
centerC22C22⋊#157
commutatorC22×C32C22×C4
FrattiniC22C22×#157
FittingC22×C32×C4C4
socleC22×C32C22⋊C4
prime radicalC23×C32C2×C4
cosocleC2×C3⋊Dic3C23
hypercenterC22×C4#157
hypocenterC32C2×#101
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
3. #63780C2direct (N × H)
63. C2×C32#101semidirect
83. C32C2×#101semidirect
113. C2#63780direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#6342
C2×#37922
#637802
C2×#1019