Finite Group Databasebeta

← C3×#1270 #67830

Subgroups — C3×#1270 #67830

Order 384.

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

normal subgroups only

This group has 202 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×#390C211yesmaximal, characteristic
2C3×#336C212yesmaximal, complemented
3#1270C311yesmaximal, characteristic, direct product factor, Sylow
4C22×C3×D4C411yescharacteristic
5C22×C3×C8—22no—
6C2×C3×C4⋊C4C411yescharacteristic
7C2×C3×C22⋊C4—22no—
8C2×C3×C42C2211yescharacteristic
9#390C2×C311yescharacteristic
10#336C2×C312yescomplemented
11C24×C3—21no—
12C2×C3×D4—21no—
13C2×C3×D4—41no—
14C2×C3×D4—41no—
15C2×C3×D4C812yescomplemented
16C22×C3×C4—21no—
17C22×C3×C4C2×C411yescharacteristic
18C22×C3×C4D412yes—
19C2×C3×C8—24no—
20C2×C3×C8—42no—
21C2×C3×C8—42no—
22C3×C4⋊C4—41no—
23C3×C22⋊C4—42no—
24C3×C22⋊C4—42no—
25C3×C42—41no—
26C22×D4C3×C411yescharacteristic
27C22×C8—22no—
28C2×C4⋊C4C3×C411yescharacteristic
29C2×C22⋊C4—22no—
30C2×C42C22×C311yescharacteristic
31C23×C3—22no—
32C23×C3—41no—
33C23×C3—41no—
34C23×C3—42no—
35C23×C3—42no—
36C23×C3C22⋊C411yescharacteristic
37C3×D4—42no—
38C3×D4—42no—
39C2×C3×C4—22no—
40C2×C3×C4—21no—
41C2×C3×C4—21no—
42C2×C3×C4—22no—
43C2×C3×C4—41no—
44C2×C3×C4—42no—
45C2×C3×C4C2×C811yescharacteristic
46C2×C3×C4M1611yescharacteristic
47C2×C3×C4D812yes—
48C2×C3×C4SD1612yes—
49C3×C8—44no—
50C24—21no—
51C2×D4—21no—
52C2×D4—41no—
53C2×D4—41no—
54C2×D4C3×C812yescomplemented
55C22×C4—21no—
56C22×C4C2×C3×C411yescharacteristic
57C22×C4C3×D412yes—
58C2×C8—24no—
59C2×C8—42no—
60C2×C8—42no—
61C4⋊C4—41no—
62C22⋊C4—42no—
63C22⋊C4—42no—
64C42—41no—
65C22×C3—42no—
66C22×C3—44no—
67C22×C3—82no—
68C22×C3—81no—
69C22×C3—81no—
70C22×C3C22⋊C811yescharacteristic
71C22×C3#9911yescharacteristic
72C22×C3#10011yescharacteristic
73C22×C3#10212yes—
74C22×C3#10412yes—
75C3×C4—21no—
76C3×C4—21no—
77C3×C4—22no—
78C3×C4—22no—
79C3×C4—81no—
80C23—22no—
81C23—41no—
82C23—41no—
83C23—42no—
84C23—42no—
85C23C3×C22⋊C411yescharacteristic
86D4—42no—
87D4—42no—
88C2×C4—22no—
89C2×C4—21no—
90C2×C4—21no—
91C2×C4—22no—
92C2×C4—41no—
93C2×C4—42no—
94C2×C4C2×C3×C811yescharacteristic
95C2×C4C3×M1611yescharacteristic
96C2×C4C3×D812yes—
97C2×C4C3×SD1612yes—
98C8—44no—
99C2×C3—82no—
100C2×C3#32311yescharacteristic
101C2×C3D4⋊C812yes—
102C2×C3#32712yes—
103C2×C3#32911yescharacteristic
104C2×C3#33111yescharacteristic
105C22—42no—
106C22—44no—
107C22—82no—
108C22—81no—
109C22—81no—
110C22C3×C22⋊C811yescharacteristic
111C22C3×#9911yescharacteristic
112C22C3×#10011yescharacteristic
113C22C3×#10212yes—
114C22C3×#10412yes—
115C4—21no—
116C4—21no—
117C4—22no—
118C4—22no—
119C4—81no—
120C3#127011yescharacteristic, direct product factor, Sylow
121C2—82no—
122C2C3×#32311yescharacteristic
123C2C3×D4⋊C812yes—
124C2C3×#32712yes—
125C2C3×#32911yescharacteristic
126C2C3×#33111yescharacteristic
subgroupG/H
center, socleC23×C3C22⋊C4
commutatorC2×C4C2×C3×C8
Frattini, cosocleC2×C42C22×C3
prime radicalC22×C3×D4C4
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C3 ◁ C2×C3×C42 ◁ G

Complements

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

NH ≅ G/Ntype
2. C3×#336C2semidirect
3. #1270C3direct (N × H)
10. #336C2×C3semidirect
15. C2×C3×D4C8semidirect
54. C2×D4C3×C8semidirect
120. C3#1270direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#3902
C3×#3362
#12703