Finite Group Databasebeta

← #67636

Subgroups — #67636

Order 384.

158 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 41 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
1C3×#385C211yesmaximal, characteristic
2#4525C211yesmaximal, characteristic
3#4525C211yesmaximal, characteristic
4#1326—31nomaximal, Sylow
5C23×C3×C4C411yescharacteristic
6C2×C3×C4⋊C4—21no—
7C2×C3×C22⋊C4C411yescharacteristic
8C2×C3×C22⋊C4C2211yescharacteristic
9C3×#95—21no—
10#830—21no—
11#830—21no—
12#385D311yescharacteristic
13#323—31no—
14#323—31no—
15C24×C3C2×C411yescharacteristic
16C22×C3×C4—21no—
17C22×C3×C4—21no—
18C22×C3×C4—42no—
19C22×C3×C4—41no—
20C22×C3×C4D411yescharacteristic
21C22×C3×C4D411yescharacteristic
22C3×C4⋊C4—42no—
23C3×C22⋊C4—21no—
24C3×C22⋊C4—41no—
25C3×C22⋊C4C812yescomplemented
26C2×C3⋊C8—41no—
27C2×C3⋊C8—41no—
28C23×C4Dic311yescharacteristic
29C2×C4⋊C4—21no—
30C2×C22⋊C4Dic311yescharacteristic
31C2×C22⋊C4C2×D311yescharacteristic
32C22⋊C8—61no—
33C22⋊C8—61no—
34#95—21no—
35C23×C3—21no—
36C23×C3—21no—
37C23×C3—41no—
38C23×C3—41no—
39C23×C3C22⋊C411yescharacteristic
40C23×C3C2×C811yescharacteristic
41C23×C3M1611yescharacteristic
42C2×C3×C4—22no—
43C2×C3×C4—22no—
44C2×C3×C4—21no—
45C2×C3×C4—21no—
46C2×C3×C4—41no—
47C2×C3×C4—41no—
48C2×C3×C4—41no—
49C2×C3×C4—42no—
50C2×C3×C4—41no—
51C2×C3×C4—41no—
52C2×C3×C4—41no—
53C2×C3×C4—42no—
54C3⋊C8—81no—
55C3⋊C8—81no—
56C24C2×Dic311yescharacteristic
57C22×C4—21no—
58C22×C4—21no—
59C22×C4—42no—
60C22×C4—41no—
61C22×C4#6711yescharacteristic
62C22×C4#6711yescharacteristic
63C2×C8—121no—
64C2×C8—121no—
65C4⋊C4—42no—
66C22⋊C4—21no—
67C22⋊C4—41no—
68C22⋊C4C3⋊C812yescomplemented
69C22×C3—21no—
70C22×C3—21no—
71C22×C3—21no—
72C22×C3—21no—
73C22×C3—41no—
74C22×C3—41no—
75C22×C3—42no—
76C22×C3—41no—
77C22×C3—41no—
78C22×C3C22⋊C811yescharacteristic
79C22×C3#9911yescharacteristic
80C22×C3#10111yescharacteristic
81C3×C4—42no—
82C3×C4—41no—
83C3×C4—42no—
84C3×C4—41no—
85C23—21no—
86C23—21no—
87C23—41no—
88C23—41no—
89C23C2×C3⋊C811yescharacteristic
90C23#20811yescharacteristic
91C23#21711yescharacteristic
92C2×C4—22no—
93C2×C4—22no—
94C2×C4—21no—
95C2×C4—21no—
96C2×C4—41no—
97C2×C4—41no—
98C2×C4—41no—
99C2×C4—42no—
100C2×C4—41no—
101C2×C4—41no—
102C2×C4—41no—
103C2×C4—42no—
104C8—241no—
105C8—241no—
106C2×C3—21no—
107C2×C3—21no—
108C2×C3—41no—
109C2×C3—41no—
110C2×C3#32411yescharacteristic
111C2×C3AΣL(1,𝔽16)11yescharacteristic
112C2×C3#35211yescharacteristic
113C22—21no—
114C22—21no—
115C22—21no—
116C22—21no—
117C22—41no—
118C22—41no—
119C22—42no—
120C22—41no—
121C22—41no—
122C22#83011yescharacteristic
123C22#83411yescharacteristic
124C22#83611yescharacteristic
125C4—42no—
126C4—41no—
127C4—42no—
128C4—41no—
129C3#132611yescharacteristic, complemented, Sylow
130C2—21no—
131C2—21no—
132C2—41no—
133C2—41no—
134C2#452811yescharacteristic
135C2#453611yescharacteristic
136C2#453911yescharacteristic
subgroupG/H
centerC22#834
commutatorC23×C3C2×C8
FrattiniC2×C22⋊C4C2×D3
FittingC3×#385C2
socleC22×C3#99
prime radicalC24×C3C2×C4
cosocleC2×C3×C22⋊C4C22
hypercenter#385D3
hypocenterC3#1326
LCSG ▷ C23×C3 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #385

Complements

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

NH ≅ G/Ntype
25. C3×C22⋊C4C8semidirect
68. C22⋊C4C3⋊C8semidirect
129. C3#1326semidirect

Maximal subgroups

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

subgroupindex
C3×#3852
#45252
#13263