Finite Group Databasebeta

← #10593378

Subgroups — #10593378

Order 576.

152 conjugacy classes of subgroups; only the 31 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 31 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#63870C211yesmaximal, characteristic
3#63777C211yesmaximal, characteristic
4#63740C212yesmaximal
5#63740C212yesmaximal
6C2×#627C2212yes—
7C2×#622C2212yes—
8C4×C3⋊Dic3C2211yescharacteristic
9C3×C4⋊Dic3—21no—
10C3×Dic3⋊C4—21no—
11#3724—21no—
12#3724C2211yescharacteristic
13#3724C2211yescharacteristic
14Dic3⋊Dic3—21no—
15#889—61no—
16#888—61no—
17C2×C32×C4D411yescharacteristic
18C2×C3⋊Dic3D411yescharacteristic
19C2×C3⋊Dic3C2311yescharacteristic
20C2×C3×Dic3—21no—
21C2×C3×Dic3—21no—
22C2×C3×Dic3—22no—
23#627—24no—
24#622—22no—
25#491—91nomaximal, Sylow
26C2×Dic6—62no—
27C3×C4⋊C4—61no—
28C3×C4⋊C4—61no—
29C4⋊Dic3—21no—
30C4⋊Dic3—61no—
31Dic3⋊C4—21no—
32Dic3⋊C4—61no—
33Dic3⋊C4—61no—
34Dic3⋊C4—62no—
35Dic3⋊C4—61no—
36C4×Dic3—61no—
37C4×Dic3—61no—
38C22×C32C2×D411yescharacteristic
39C32×C4—21no—
40C3⋊Dic3—21no—
41C3⋊Dic3#4112yes—
42C3×Dic3—42no—
43C3×Dic3—41no—
44C3×Dic3—41no—
45C4⋊Q8—91no—
46#125—91no—
47#103—92no—
48#103—92no—
49#97—91no—
50C2×C3×C4—21no—
51C2×C3×C4—21no—
52C2×C3×C4—61no—
53C2×C3×C4—61no—
54C2×C3×C4—62no—
55C2×Dic3—21no—
56C2×Dic3—21no—
57C2×Dic3—22no—
58C2×Dic3—61no—
59C2×Dic3—61no—
60C2×Dic3—61no—
61C2×Dic3—61no—
62Dic6—124no—
63C2×C32#12411yescharacteristic
64C2×C32#13711yescharacteristic
65C2×C32#13711yescharacteristic
66C2×Q8—92no—
67C2×C8—92no—
68C4⋊C4—61no—
69C4⋊C4—61no—
70C4⋊C4—91no—
71C4⋊C4—91no—
72C4⋊C4—181no—
73C4⋊C4—181no—
74C42—91no—
75C22×C3—21no—
76C22×C3—21no—
77C3×C4—22no—
78C3×C4—41no—
79C3×C4—122no—
80C3×C4—121no—
81C3×C4—121no—
82Dic3—42no—
83Dic3—41no—
84Dic3—41no—
85Dic3—62no—
86Dic3—62no—
87Dic3—62no—
88Dic3—121no—
89C32#49111yescharacteristic, complemented, Sylow
90Q8—184no—
91C2×C4—61no—
92C2×C4—61no—
93C2×C4—62no—
94C2×C4—91no—
95C2×C4—91no—
96C2×C4GO+(4,𝔽2)11yescharacteristic
97C8—182no—
98C2×C3—21no—
99C2×C3—21no—
100C2×C3—21no—
101C2×C3—21no—
102C2×C3—21no—
103C2×C3—21no—
104C22C2×GO+(4,𝔽2)11yescharacteristic
105C4—21no—
106C4—92no—
107C4—122no—
108C4—121no—
109C4—121no—
110C4—181no—
111C3—21no—
112C3—21no—
113C2#6422111yescharacteristic
114C2#6422611yescharacteristic
115C2#6423911yescharacteristic
subgroupG/H
center, FrattiniC22C2×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C23
FittingC2×C32×C4D4
socle, prime radicalC22×C32C2×D4
hypercenterC2×C4GO+(4,𝔽2)
hypocenterC32#491
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
89. C32#491semidirect

Maximal subgroups

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

subgroupindex
#639192
#638702
#637772
#637402
#4919