Finite Group Databasebeta

← #10593392

Subgroups — #10593392

Order 576.

152 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 35 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#63873C211yesmaximal, characteristic
2#63870C211yesmaximal, characteristic
3#63777C211yesmaximal, characteristic
4#63743C212yesmaximal
5#63742C212yesmaximal
6C2×C3×Dic6—21no—
7C2×#622C2212yes—
8C4×C3⋊Dic3C2211yescharacteristic
9C3×Dic3⋊C4—21no—
10#3724—21no—
11#3724C2211yescharacteristic
12#3724C2211yescharacteristic
13#3724C2212yes—
14Dic3⋊Dic3—21no—
15#944—61no—
16#889—61no—
17C2×C32×C4D411yescharacteristic
18C2×C3⋊Dic3D411yescharacteristic
19C2×C3⋊Dic3C2311yescharacteristic
20C2×C3×Dic3—21no—
21C2×C3×Dic3—21no—
22C2×C3×Dic3—22no—
23C3×Dic6—42no—
24#622Q814yescomplemented
25#501—91nomaximal, Sylow
26C2×C3×Q8—61no—
27C2×Dic6—21no—
28C3×C4⋊C4—61no—
29C4⋊Dic3—61no—
30Dic3⋊C4—21no—
31Dic3⋊C4—61no—
32Dic3⋊C4—61no—
33Dic3⋊C4—62no—
34Dic3⋊C4—61no—
35Dic3⋊C4—62no—
36C4×Dic3—61no—
37C4×Dic3—61no—
38C22×C32C2×D411yescharacteristic
39C32×C4—21no—
40C3⋊Dic3—21no—
41C3⋊Dic3C2×Q812yes—
42C3×Dic3—42no—
43C3×Dic3—41no—
44C3×Dic3—41no—
45C4⋊Q8—91no—
46#125—91no—
47#107—92no—
48#106—92no—
49#97—91no—
50C3×Q8—122no—
51C2×C3×C4—21no—
52C2×C3×C4—21no—
53C2×C3×C4—61no—
54C2×C3×C4—62no—
55C2×C3×C4—61no—
56C2×Dic3—21no—
57C2×Dic3—21no—
58C2×Dic3—22no—
59C2×Dic3—61no—
60C2×Dic3—61no—
61C2×Dic3—61no—
62C2×Dic3—61no—
63Dic6—42no—
64C2×C32C4⋊Q811yescharacteristic
65C2×C32AGL(1,ℤ/8)11yescharacteristic
66C2×C32#13711yescharacteristic
67C2×Q8—61no—
68C2×C8—92no—
69C4⋊C4—61no—
70C4⋊C4—91no—
71C4⋊C4—92no—
72C4⋊C4—91no—
73C4⋊C4—181no—
74C4⋊C4—181no—
75C42—91no—
76C22×C3—21no—
77C22×C3—21no—
78C3×C4—22no—
79C3×C4—41no—
80C3×C4—122no—
81C3×C4—121no—
82C3×C4—121no—
83Dic3—42no—
84Dic3—41no—
85Dic3—41no—
86Dic3—62no—
87Dic3—62no—
88Dic3—62no—
89Dic3—121no—
90C32#50111yescharacteristic, complemented, Sylow
91Q8—122no—
92C2×C4—61no—
93C2×C4—61no—
94C2×C4—62no—
95C2×C4—91no—
96C2×C4—91no—
97C2×C4GO+(4,𝔽2)11yescharacteristic
98C8—94no—
99C2×C3—21no—
100C2×C3—21no—
101C2×C3—21no—
102C2×C3—21no—
103C2×C3—21no—
104C2×C3—21no—
105C22C2×GO+(4,𝔽2)11yescharacteristic
106C4—21no—
107C4—92no—
108C4—121no—
109C4—122no—
110C4—121no—
111C4—181no—
112C3—21no—
113C3—21no—
114C2#6422211yescharacteristic
115C2#6422611yescharacteristic
116C2#6423611yescharacteristic
subgroupG/H
center, FrattiniC22C2×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C23
FittingC2×C32×C4D4
socle, prime radicalC22×C32C2×D4
hypercenterC2×C4GO+(4,𝔽2)
hypocenterC32#501
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
24. #622Q8semidirect
90. C32#501semidirect

Maximal subgroups

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

subgroupindex
#638732
#638702
#637772
#637432
#637422
#5019