Finite Group Databasebeta

← #71270

Subgroups — #71270

Order 384.

218 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 53 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#5713C211yesmaximal, characteristic
2C3×#492C211yesmaximal, characteristic
3#5091C212yesmaximal, complemented
4#4544C211yesmaximal, characteristic
5#4456C212yesmaximal, complemented
6#1630—31nomaximal, Sylow
7C2×C3×SD16—22no—
8C3×C4⋊Q8C2211yescharacteristic
9C3×#127C2211yescharacteristic
10#936—22no—
11#935—22no—
12D4×Dic3—22no—
13C4×Dic6C2212yes—
14C3×C4×C8C2211yescharacteristic
15#810—22no—
16#807—22no—
17C4⋊(C3⋊C8)C2212yes—
18#559—31no—
19#492D311yescharacteristic
20#477—32no—
21#331—31no—
22Q8⋊C8—32no—
23C2×C3×Q8—21no—
24C2×C3×D4—22no—
25C2×C3×D4D412yes—
26C22×Dic3—22no—
27C2×Dic6D412yes—
28C3×SD16—44no—
29C2×C3×C8—21no—
30C3×C4⋊C4—22no—
31C3×C42C2311yescharacteristic
32#217—24no—
33#217—22no—
34C4⋊Dic3D412yes—
35Dic3⋊C4—22no—
36C4×Dic3—22no—
37C2×C3⋊C8—22no—
38C2×SD16—22no—
39C4⋊Q8C2×D311yescharacteristic
40#127C2×D311yescharacteristic
41#124—62no—
42#123—62no—
43C4×Q8—32no—
44C4×D4—62no—
45#107—62no—
46C4⋊C8—32no—
47#103—62no—
48C4×C8C2×D311yescharacteristic
49C23×C3—22no—
50C3×Q8—42no—
51C3×D4—42no—
52C3×D4—42no—
53C3×D4—42no—
54C2×C3×C4—41no—
55C2×C3×C4C2×D412yes—
56C2×C3×C4C2×D411yescharacteristic
57C2×Dic3—22no—
58C2×Dic3—22no—
59C2×Dic3—82no—
60Dic6—22no—
61Dic6—22no—
62C3×C8—22no—
63C3⋊C8—42no—
64C2×Q8—21no—
65C2×Q8—32no—
66C2×D4—22no—
67C2×D4#6712yes—
68C22×C4—62no—
69SD16—44no—
70C2×C8—21no—
71C2×C8—62no—
72C4⋊C4—22no—
73C4⋊C4—32no—
74C4⋊C4—62no—
75C22⋊C4—64no—
76C22⋊C4—62no—
77C42—62no—
78C42C22×D311yescharacteristic
79C22×C3—44no—
80C22×C3—42no—
81C22×C3#12011yescharacteristic
82C3×C4—21no—
83C3×C4—81no—
84C3×C4#13512yes—
85C3×C4#13712yes—
86Dic3—42no—
87Dic3—42no—
88C23—22no—
89Q8—42no—
90Q8—62no—
91Q8—62no—
92D4—42no—
93D4—42no—
94D4—42no—
95C2×C4—41no—
96C2×C4—62no—
97C2×C4—62no—
98C2×C4—242no—
99C2×C4D3×D412yes—
100C2×C4C2×#6711yescharacteristic
101C8—22no—
102C8—122no—
103C2×C3—82no—
104C2×C3#45212yes—
105C2×C3#45311yescharacteristic
106C22—44no—
107C22—42no—
108C22#93711yescharacteristic
109C4—21no—
110C4—81no—
111C4—122no—
112C4—122no—
113C4#91512yes—
114C4#91612yes—
115C3#163011yescharacteristic, complemented, Sylow
116C2—82no—
117C2#507711yescharacteristic
118C2#517312yes—
subgroupG/H
centerC22#937
commutator, cosocleC3×C42C23
FrattiniC42C22×D3
FittingC3×#492C2
socleC22×C3#120
prime radicalC3×#127C22
hypercenter#492D3
hypocenterC3#1630
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
3. #5091C2semidirect
5. #4456C2semidirect
115. C3#1630semidirect

Maximal subgroups

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

subgroupindex
#57132
C3×#4922
#50912
#45442
#44562
#16303