Finite Group Databasebeta

← C3×#1630 #72345

Subgroups — C3×#1630 #72345

Order 384.

218 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 68 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×#559C211yesmaximal, characteristic
2C3×#492C211yesmaximal, characteristic
3C3×#477C212yesmaximal, complemented
4C3×#331C211yesmaximal, characteristic
5C3×Q8⋊C8C212yesmaximal, complemented
6#1630C311yesmaximal, characteristic, direct product factor, Sylow
7C2×C3×SD16—22no—
8C3×C4⋊Q8C2211yescharacteristic
9C3×#127C2211yescharacteristic
10C3×#124—22no—
11C3×#123—22no—
12C3×C4×Q8C2212yes—
13C3×C4×D4—22no—
14C3×#107—22no—
15C3×C4⋊C8C2212yes—
16C3×#103—22no—
17C3×C4×C8C2211yescharacteristic
18#559C2×C311yescharacteristic
19#492C2×C311yescharacteristic
20#477C2×C312yescomplemented
21#331C2×C311yescharacteristic
22Q8⋊C8C2×C312yescomplemented
23C2×C3×Q8—21no—
24C2×C3×Q8D412yes—
25C2×C3×D4—22no—
26C2×C3×D4D412yes—
27C22×C3×C4—22no—
28C3×SD16—44no—
29C2×C3×C8—21no—
30C2×C3×C8—22no—
31C3×C4⋊C4—22no—
32C3×C4⋊C4—22no—
33C3×C4⋊C4D412yes—
34C3×C22⋊C4—24no—
35C3×C22⋊C4—22no—
36C3×C42—22no—
37C3×C42C2311yescharacteristic
38C2×SD16—22no—
39C4⋊Q8C22×C311yescharacteristic
40#127C22×C311yescharacteristic
41#124—22no—
42#123—22no—
43C4×Q8C22×C312yes—
44C4×D4—22no—
45#107—22no—
46C4⋊C8C22×C312yes—
47#103—22no—
48C4×C8C22×C311yescharacteristic
49C23×C3—22no—
50C3×Q8—22no—
51C3×Q8—22no—
52C3×Q8—42no—
53C3×D4—42no—
54C3×D4—42no—
55C3×D4—42no—
56C2×C3×C4—22no—
57C2×C3×C4—22no—
58C2×C3×C4—41no—
59C2×C3×C4—82no—
60C2×C3×C4C2×D411yescharacteristic
61C2×C3×C4C2×D412yes—
62C3×C8—22no—
63C3×C8—42no—
64C2×Q8—21no—
65C2×Q8C3×D412yes—
66C2×D4—22no—
67C2×D4C3×D412yes—
68C22×C4—22no—
69SD16—44no—
70C2×C8—21no—
71C2×C8—22no—
72C4⋊C4—22no—
73C4⋊C4—22no—
74C4⋊C4C3×D412yes—
75C22⋊C4—24no—
76C22⋊C4—22no—
77C42—22no—
78C42C23×C311yescharacteristic
79C22×C3—44no—
80C22×C3—42no—
81C22×C3#12011yescharacteristic
82C3×C4—21no—
83C3×C4—42no—
84C3×C4—42no—
85C3×C4—81no—
86C3×C4#13512yes—
87C3×C4#13712yes—
88C23—22no—
89Q8—22no—
90Q8—22no—
91Q8—42no—
92D4—42no—
93D4—42no—
94D4—42no—
95C2×C4—22no—
96C2×C4—22no—
97C2×C4—41no—
98C2×C4—82no—
99C2×C4C2×C3×D411yescharacteristic
100C2×C4C2×C3×D412yes—
101C8—22no—
102C8—42no—
103C2×C3—82no—
104C2×C3#45212yes—
105C2×C3#45311yescharacteristic
106C22—44no—
107C22—42no—
108C22C3×#12011yescharacteristic
109C4—21no—
110C4—42no—
111C4—42no—
112C4—81no—
113C4C3×#13512yes—
114C4C3×#13712yes—
115C3#163011yescharacteristic, direct product factor, Sylow
116C2—82no—
117C2C3×#45212yes—
118C2C3×#45311yescharacteristic
subgroupG/H
center, socleC22×C3#120
commutator, Frattini, cosocleC42C23×C3
prime radicalC3×#127C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ G

Complements

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

NH ≅ G/Ntype
3. C3×#477C2semidirect
5. C3×Q8⋊C8C2semidirect
6. #1630C3direct (N × H)
20. #477C2×C3semidirect
22. Q8⋊C8C2×C3semidirect
115. C3#1630direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#5592
C3×#4922
C3×#4772
C3×#3312
C3×Q8⋊C82
#16303