Finite Group Databasebeta

← #67626

Subgroups — #67626

Order 384.

200 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 61 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×#380C211yesmaximal, characteristic
2#5207C211yesmaximal, characteristic
3#5207C211yesmaximal, characteristic
4#1305—31nomaximal, Sylow
5C23×C3×C4C2211yescharacteristic
6C2×C3×C4⋊C4—21no—
7C2×C3×C22⋊C4C412yes—
8C2×#208—21no—
9C2×#208C412yescomplemented
10C3×#95—21no—
11#830—21no—
12#830—21no—
13#830—21no—
14#830C412yescomplemented
15#407—31no—
16#407—31no—
17#380D311yescharacteristic
18C24×C3C2×C411yescharacteristic
19C22×C3×C4—22no—
20C22×C3×C4—42no—
21C22×C3×C4C2×C411yescharacteristic
22C22×C3×C4C2×C411yescharacteristic
23C22×C3×C4D411yescharacteristic
24C22×C3×C4D411yescharacteristic
25C22×C3×C4D411yescharacteristic
26C22×C3×C4Q811yescharacteristic
27C3×C4⋊C4—42no—
28C3×C22⋊C4—42no—
29#208—42no—
30#208—42no—
31C2×C3⋊C8—22no—
32C2×C3⋊C8—22no—
33C23×C4C2×D311yescharacteristic
34C2×M16—32no—
35C2×M16—61no—
36C2×C4⋊C4—21no—
37C2×C22⋊C4Dic312yes—
38C22⋊C8—32no—
39C22⋊C8—61no—
40C22⋊C8—61no—
41C22⋊C8—61no—
42#95—21no—
43C23×C3—21no—
44C23×C3—21no—
45C23×C3—41no—
46C23×C3—41no—
47C23×C3C4211yescharacteristic
48C23×C3C22⋊C411yescharacteristic
49C23×C3C4⋊C411yescharacteristic
50C2×C3×C4—22no—
51C2×C3×C4—22no—
52C2×C3×C4—22no—
53C2×C3×C4—41no—
54C2×C3×C4—41no—
55C2×C3×C4—41no—
56C2×C3×C4—42no—
57C2×C3×C4—42no—
58C2×C3×C4—42no—
59C2×C3×C4C22⋊C411yescharacteristic
60C2×C3×C4C22⋊C411yescharacteristic
61C2×C3×C4C4⋊C411yescharacteristic
62C2×C3×C4C4⋊C411yescharacteristic
63C3⋊C8—42no—
64C3⋊C8—42no—
65C24C2×Dic311yescharacteristic
66C22×C4—22no—
67C22×C4—42no—
68C22×C4Dic611yescharacteristic
69C22×C4C4×D311yescharacteristic
70C22×C4C4×D311yescharacteristic
71C22×C4D1211yescharacteristic
72C22×C4#6711yescharacteristic
73C22×C4#6711yescharacteristic
74M16—122no—
75M16—122no—
76C2×C8—62no—
77C2×C8—62no—
78C4⋊C4—42no—
79C22⋊C4—42no—
80C22×C3—21no—
81C22×C3—21no—
82C22×C3—21no—
83C22×C3—21no—
84C22×C3—21no—
85C22×C3—21no—
86C22×C3—21no—
87C22×C3—21no—
88C22×C3—42no—
89C22×C3—42no—
90C22×C3#9511yescharacteristic
91C22×C3#10011yescharacteristic
92C22×C3#10111yescharacteristic
93C3×C4—21no—
94C3×C4—21no—
95C3×C4—21no—
96C3×C4—82no—
97C3×C4#9912yes—
98C23—21no—
99C23—21no—
100C23—41no—
101C23—41no—
102C23C4×Dic311yescharacteristic
103C23C4⋊Dic311yescharacteristic
104C23#21711yescharacteristic
105C2×C4—22no—
106C2×C4—22no—
107C2×C4—22no—
108C2×C4—41no—
109C2×C4—41no—
110C2×C4—41no—
111C2×C4—42no—
112C2×C4—42no—
113C2×C4—42no—
114C2×C4Dic3⋊C411yescharacteristic
115C2×C4Dic3⋊C411yescharacteristic
116C2×C4(C2×D3)⋊C411yescharacteristic
117C2×C4(C2×D3)⋊C411yescharacteristic
118C8—122no—
119C8—122no—
120C2×C3—21no—
121C2×C3—21no—
122C2×C3—41no—
123C2×C3—41no—
124C2×C3#34211yescharacteristic
125C2×C3#34311yescharacteristic
126C2×C3#34411yescharacteristic
127C22—21no—
128C22—21no—
129C22—21no—
130C22—21no—
131C22—21no—
132C22—21no—
133C22—21no—
134C22—21no—
135C22—42no—
136C22—42no—
137C22C3⋊#9511yescharacteristic
138C22#83311yescharacteristic
139C22#83611yescharacteristic
140C4—21no—
141C4—21no—
142C4—21no—
143C4—82no—
144C4#80612yes—
145C3#130511yescharacteristic, complemented, Sylow
146C2—21no—
147C2—21no—
148C2—41no—
149C2—41no—
150C2#452711yescharacteristic
151C2#453011yescharacteristic
152C2#453311yescharacteristic
subgroupG/H
centerC22C3⋊#95
commutatorC23×C3C42
FrattiniC23×C4C2×D3
FittingC3×#380C2
socleC22×C3#95
prime radicalC24×C3C2×C4
cosocleC23×C3×C4C22
hypercenter#380D3
hypocenterC3#1305
LCSG ▷ C23×C3 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
9. C2×#208C4semidirect
14. #830C4semidirect
145. C3#1305semidirect

Maximal subgroups

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

subgroupindex
C3×#3802
#52072
#13053