Finite Group Databasebeta

← #10591062

Subgroups — #10591062

Order 576.

230 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 72 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#64135C211yesmaximal, characteristic
2C3×#830C212yesmaximal
3#63572C212yesmaximal, complemented
4#63555C211yesmaximal, characteristic, complemented
5#63553C211yesmaximal, characteristic, complemented
6#4720—32nomaximal
7C22×C32×C4C2211yescharacteristic
8#3757C412yes—
9C4⋊(C3⋊Dic3)C412yes—
10C4×C3⋊Dic3C2211yescharacteristic
11C4×C3⋊Dic3C2211yescharacteristic
12C2×C3×C3⋊C8C2212yes—
13C2×C3×C3⋊C8C2212yes—
14#926—32no—
15#926—61no—
16C3×C22⋊C8—32no—
17#830D312yes—
18#815—32no—
19Dic3⋊C8—32no—
20Dic3⋊C8—32no—
21C8×Dic3—32no—
22C23×C32C2×C411yescharacteristic
23C2×C32×C4—22no—
24C2×C32×C4C2×C411yescharacteristic
25C2×C32×C4C2311yescharacteristic
26C2×C3⋊Dic3C2×C412yes—
27C2×C3⋊Dic3C2×C412yes—
28C3×C3⋊C8—22no—
29C3×C3⋊C8—22no—
30#433—91noSylow
31C22×C3×C4—21no—
32C22×C3×C4C2×D312yes—
33C2×C3×C8—32no—
34C2×C3×C8—32no—
35#217—32no—
36#217—32no—
37#217—62no—
38C4⋊Dic3—32no—
39C4⋊Dic3—32no—
40C4⋊Dic3—62no—
41C4×Dic3—32no—
42C4×Dic3—32no—
43C4×Dic3—61no—
44C4×Dic3—61no—
45C2×C3⋊C8C2×D312yes—
46C2×C3⋊C8C2×D312yes—
47C22×C32—21no—
48C22×C32—22no—
49C22×C32C22×C411yescharacteristic
50C32×C4—21no—
51C32×C4#4112yes—
52C3⋊Dic3—22no—
53C3⋊Dic3—22no—
54#117—91no—
55C4⋊C8—92no—
56C22⋊C8—32no—
57#97—91no—
58C4×C8—91no—
59C23×C3—21no—
60C23×C3C4×D312yes—
61C2×C3×C4—24no—
62C2×C3×C4—22no—
63C2×C3×C4—22no—
64C2×C3×C4—21no—
65C2×C3×C4—21no—
66C2×C3×C4C4×D312yes—
67C2×C3×C4C22×D312yes—
68C2×Dic3—32no—
69C2×Dic3—32no—
70C2×Dic3—32no—
71C2×Dic3—32no—
72C2×Dic3—62no—
73C2×Dic3—62no—
74C3×C8—62no—
75C3×C8—62no—
76C3⋊C8—22no—
77C3⋊C8—22no—
78C2×C32—41no—
79C2×C32#11711yescharacteristic
80C2×C32#13112yes—
81C22×C4D3211yescharacteristic
82C2×C8—32no—
83C2×C8—32no—
84C4⋊C4—92no—
85C22⋊C4—92no—
86C42—91no—
87C42—91no—
88C22×C3—22no—
89C22×C3—22no—
90C22×C3—22no—
91C22×C3—22no—
92C22×C3—21no—
93C22×C3—42no—
94C22×C3C2×C4×D312yes—
95C3×C4—22no—
96C3×C4—22no—
97C3×C4—22no—
98C3×C4#23712yes—
99C3×C4#23712yes—
100Dic3—62no—
101Dic3—62no—
102Dic3—62no—
103Dic3—62no—
104Dic3—122no—
105Dic3—122no—
106C32#43311yescharacteristic, complemented, Sylow
107C23#62411yescharacteristic
108C2×C4—22no—
109C2×C4—92no—
110C2×C4—92no—
111C2×C4#62411yescharacteristic
112C2×C4C2×D3211yescharacteristic
113C8—62no—
114C8—62no—
115C2×C3—22no—
116C2×C3—21no—
117C2×C3—42no—
118C2×C3—42no—
119C2×C3#87712yes—
120C2×C3#90112yes—
121C2×C3#90712yes—
122C22—22no—
123C22—21no—
124C22C2×#62411yescharacteristic
125C4—21no—
126C4—182no—
127C4—182no—
128C4#380512yes—
129C3—21no—
130C3#472012yescomplemented
131C2—41no—
132C2#6381712yes—
133C2#6395711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×D32
commutator, socleC22×C32C22×C4
FittingC22×C32×C4C22
prime radicalC23×C32C2×C4
cosocleC2×C32×C4C23
hypercenterC22×C4D32
hypocenterC32#433
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
3. #63572C2semidirect
4. #63555C2semidirect
5. #63553C2semidirect
106. C32#433semidirect
130. C3#4720semidirect

Maximal subgroups

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

subgroupindex
#641352
C3×#8302
#635722
#635552
#635532
#47203