Finite Group Databasebeta

← #10593377

Subgroups — #10593377

Order 576.

166 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 166 conjugacy classes of subgroups — too many to draw. Only its 37 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
1#63919C211yesmaximal, characteristic
2#63873C211yesmaximal, characteristic
3C4×#622C211yesmaximal, characteristic
4#63740C214yesmaximal
5C2×C3×Dic6—21no—
6C2×#627C2212yes—
7C2×#622C2212yes—
8C4×C3⋊Dic3C2211yescharacteristic
9C3×C4⋊Dic3—21no—
10#3724—21no—
11#3724—21no—
12#3724C2212yes—
13#944—61no—
14#888—61no—
15C2×C32×C4D411yescharacteristic
16C2×C3⋊Dic3D411yescharacteristic
17C2×C3⋊Dic3C2311yescharacteristic
18C2×C3×Dic3—22no—
19C2×C3×Dic3—22no—
20C3×Dic6—42no—
21#627—24no—
22#622—22no—
23#487—91nomaximal, Sylow
24C2×C3×Q8—61no—
25C2×Dic6—21no—
26C2×Dic6—62no—
27C3×C4⋊C4—61no—
28C4⋊Dic3—21no—
29Dic3⋊C4—62no—
30Dic3⋊C4—62no—
31Dic3⋊C4—62no—
32C4×Dic3—61no—
33C4×Dic3—61no—
34C22×C32C2×D411yescharacteristic
35C32×C4SD1612yes—
36C3⋊Dic3Q1612yes—
37C3⋊Dic3#4112yes—
38C3×Dic3—42no—
39C3×Dic3—42no—
40C4⋊Q8—91no—
41C4⋊Q8—91no—
42#103—94no—
43C4×C8—91no—
44C3×Q8—122no—
45C2×C3×C4—21no—
46C2×C3×C4—21no—
47C2×C3×C4—62no—
48C2×C3×C4—62no—
49C2×Dic3—22no—
50C2×Dic3—22no—
51C2×Dic3—61no—
52C2×Dic3—61no—
53C2×Dic3—61no—
54C2×Dic3—61no—
55Dic6—42no—
56Dic6—124no—
57C2×C32#12411yescharacteristic
58C2×C32C2×SD1611yescharacteristic
59C2×C32C2×Q1611yescharacteristic
60C2×Q8—61no—
61C2×Q8—92no—
62C2×C8—92no—
63C4⋊C4—61no—
64C4⋊C4—92no—
65C4⋊C4—181no—
66C4⋊C4—181no—
67C42—91no—
68C22×C3—21no—
69C22×C3—21no—
70C3×C4—22no—
71C3×C4—22no—
72C3×C4—122no—
73C3×C4—122no—
74Dic3—42no—
75Dic3—42no—
76Dic3—62no—
77Dic3—62no—
78Dic3—62no—
79Dic3—62no—
80C32#48711yescharacteristic, complemented, Sylow
81Q8—122no—
82Q8—184no—
83C2×C4—62no—
84C2×C4—62no—
85C2×C4—91no—
86C2×C4—91no—
87C2×C4GO+(4,𝔽2)11yescharacteristic
88C8—182no—
89C2×C3—21no—
90C2×C3—21no—
91C2×C3—21no—
92C2×C3—21no—
93C2×C3—21no—
94C2×C3—21no—
95C22C2×GO+(4,𝔽2)11yescharacteristic
96C4—92no—
97C4—92no—
98C4—122no—
99C4—122no—
100C4#377512yes—
101C3—21no—
102C3—21no—
103C2#6422111yescharacteristic
104C2#6422811yescharacteristic
105C2C2×#377511yescharacteristic
subgroupG/H
center, FrattiniC22C2×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C23
FittingC2×C32×C4D4
socle, prime radicalC22×C32C2×D4
hypercenterC2×C4GO+(4,𝔽2)
hypocenterC32#487
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
80. C32#487semidirect

Maximal subgroups

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

subgroupindex
#639192
#638732
C4×#6222
#637402
#4879