Finite Group Databasebeta

← C3×#1393 #67953

Subgroups — C3×#1393 #67953

Order 384.

232 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 64 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
1C2×C3×#99C212yesmaximal
2C3×#390C211yesmaximal, characteristic
3#1393C311yesmaximal, characteristic, direct product factor, Sylow
4C22×C3×D4C2211yescharacteristic
5C2×C3×C4⋊C4C411yescharacteristic, complemented
6C2×C3×C22⋊C4—22no—
7C2×C3×C22⋊C4—22no—
8C2×C3×C42C411yescharacteristic, complemented
9C3×#99—22no—
10C3×#99C414yescomplemented
11C2×#99C2×C312yes—
12#390C2×C311yescharacteristic
13C24×C3D412yes—
14C2×C3×D4—41no—
15C2×C3×D4—41no—
16C2×C3×D4C2×C412yes—
17C2×C3×D4D411yescharacteristic
18C2×C3×D4Q811yescharacteristic
19C22×C3×C4—21no—
20C22×C3×C4—21no—
21C22×C3×C4—42no—
22C22×C3×C4C2×C411yescharacteristic
23C3×C4⋊C4—41no—
24C3×C22⋊C4—24no—
25C3×C22⋊C4—44no—
26C3×C22⋊C4—42no—
27C3×C42—41no—
28C22×D4C22×C311yescharacteristic
29C2×C4⋊C4C3×C411yescharacteristic, complemented
30C2×C22⋊C4—22no—
31C2×C22⋊C4—22no—
32C2×C42C3×C411yescharacteristic, complemented
33#99—22no—
34#99C3×C414yescomplemented
35C23×C3—22no—
36C23×C3—22no—
37C23×C3—42no—
38C23×C3—42no—
39C23×C3C22⋊C412yes—
40C23×C3C22⋊C411yescharacteristic
41C23×C3C4⋊C412yes—
42C3×D4—42no—
43C3×D4—41no—
44C3×D4—41no—
45C2×C3×C4—21no—
46C2×C3×C4—21no—
47C2×C3×C4—22no—
48C2×C3×C4—41no—
49C2×C3×C4—41no—
50C2×C3×C4—44no—
51C2×C3×C4—42no—
52C2×C3×C4—41no—
53C2×C3×C4—82no—
54C2×C3×C4—82no—
55C2×C3×C4C4211yescharacteristic
56C2×C3×C4C4⋊C411yescharacteristic
57C24C3×D412yes—
58C2×D4—41no—
59C2×D4—41no—
60C2×D4C2×C3×C412yes—
61C2×D4C3×D411yescharacteristic
62C2×D4C3×Q811yescharacteristic
63C22×C4—21no—
64C22×C4—21no—
65C22×C4—42no—
66C22×C4C2×C3×C411yescharacteristic
67C4⋊C4—41no—
68C22⋊C4—24no—
69C22⋊C4—44no—
70C22⋊C4—42no—
71C42—41no—
72C22×C3—21no—
73C22×C3—21no—
74C22×C3—22no—
75C22×C3—22no—
76C22×C3—42no—
77C22×C3—42no—
78C22×C3—42no—
79C22×C3—42no—
80C22×C3—82no—
81C22×C3#9511yescharacteristic
82C22×C3#9911yescharacteristic
83C22×C3#9911yescharacteristic
84C3×C4—21no—
85C3×C4—21no—
86C3×C4—42no—
87C3×C4—84no—
88C3×C4—81no—
89C23—22no—
90C23—22no—
91C23—42no—
92C23—42no—
93C23C3×C22⋊C411yescharacteristic
94C23C3×C22⋊C412yes—
95C23C3×C4⋊C412yes—
96D4—42no—
97D4—41no—
98D4—41no—
99C2×C4—21no—
100C2×C4—21no—
101C2×C4—22no—
102C2×C4—41no—
103C2×C4—41no—
104C2×C4—44no—
105C2×C4—42no—
106C2×C4—41no—
107C2×C4—82no—
108C2×C4—82no—
109C2×C4C3×C4211yescharacteristic
110C2×C4C3×C4⋊C411yescharacteristic
111C2×C3—21no—
112C2×C3—21no—
113C2×C3—42no—
114C2×C3—42no—
115C2×C3#34211yescharacteristic
116C2×C3#35311yescharacteristic
117C2×C3#35411yescharacteristic
118C22—21no—
119C22—21no—
120C22—22no—
121C22—22no—
122C22—42no—
123C22—42no—
124C22—42no—
125C22—42no—
126C22—82no—
127C22C3×#9511yescharacteristic
128C22C3×#9911yescharacteristic
129C22C3×#9911yescharacteristic
130C4—21no—
131C4—21no—
132C4—42no—
133C4—84no—
134C4—81no—
135C3#139311yescharacteristic, direct product factor, Sylow
136C2—21no—
137C2—21no—
138C2—42no—
139C2—42no—
140C2C3×#34211yescharacteristic
141C2C3×#35311yescharacteristic
142C2C3×#35411yescharacteristic
subgroupG/H
center, socleC22×C3#99
commutatorC2×C4C3×C42
Frattini, cosocleC22×D4C22×C3
prime radicalC22×C3×D4C22
LCSG ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C23×C3 ◁ C22×C3×D4 ◁ G

Complements

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

NH ≅ G/Ntype
3. #1393C3direct (N × H)
5. C2×C3×C4⋊C4C4semidirect
8. C2×C3×C42C4semidirect
10. C3×#99C4semidirect
29. C2×C4⋊C4C3×C4semidirect
32. C2×C42C3×C4semidirect
34. #99C3×C4semidirect
135. C3#1393direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#992
C3×#3902
#13933