Finite Group Databasebeta

← C3×#1634 #72349

Subgroups — C3×#1634 #72349

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×#555C211yesmaximal, characteristic
2C3×#494C211yesmaximal, characteristic, complemented
3C3×#476C212yesmaximal, complemented
4C3×#333C211yesmaximal, characteristic, complemented
5C3×D4⋊C8C212yesmaximal, complemented
6#1634C311yesmaximal, characteristic, direct product factor, Sylow
7C2×C3×Q16—22no—
8C3×C4⋊Q8C2211yescharacteristic
9C3×C4⋊Q8C2211yescharacteristic
10C3×#124—22no—
11C3×#121—22no—
12C3×C4×D4C2212yes—
13C3×#117—22no—
14C3×#106—22no—
15C3×C4⋊C8C2212yes—
16C3×#102—22no—
17C3×C4×C8C2211yescharacteristic
18#555C2×C311yescharacteristic
19#494C2×C311yescharacteristic, complemented
20#476C2×C312yescomplemented
21#333C2×C311yescharacteristic, complemented
22D4⋊C8C2×C312yescomplemented
23C2×C3×Q8—21no—
24C2×C3×Q8D412yes—
25C2×C3×D4—22no—
26C2×C3×D4D412yes—
27C22×C3×C4—22no—
28C3×Q16—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×Q16—22no—
39C4⋊Q8C22×C311yescharacteristic
40C4⋊Q8C22×C311yescharacteristic
41#124—22no—
42#121—22no—
43C4×D4C22×C312yes—
44#117—22no—
45#106—22no—
46C4⋊C8C22×C312yes—
47#102—22no—
48C4×C8C22×C311yescharacteristic
49C23×C3—22no—
50C3×Q8—42no—
51C3×Q8—42no—
52C3×D4—22no—
53C3×D4—22no—
54C3×D4—82no—
55C2×C3×C4—22no—
56C2×C3×C4—22no—
57C2×C3×C4—42no—
58C2×C3×C4—42no—
59C2×C3×C4—41no—
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—
69Q16—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—42no—
80C22×C3—42no—
81C22×C3—42no—
82C22×C3#12011yescharacteristic
83C3×C4—21no—
84C3×C4—42no—
85C3×C4—42no—
86C3×C4—81no—
87C3×C4#13512yes—
88C3×C4#13712yes—
89C23—22no—
90Q8—42no—
91Q8—42no—
92D4—22no—
93D4—22no—
94D4—82no—
95C2×C4—22no—
96C2×C4—22no—
97C2×C4—42no—
98C2×C4—42no—
99C2×C4—41no—
100C2×C4C2×C3×D411yescharacteristic
101C2×C4C2×C3×D412yes—
102C8—22no—
103C8—42no—
104C2×C3—82no—
105C2×C3#45212yes—
106C2×C3#45311yescharacteristic
107C22—42no—
108C22—42no—
109C22—42no—
110C22C3×#12011yescharacteristic
111C4—21no—
112C4—42no—
113C4—42no—
114C4—81no—
115C4C3×#13512yes—
116C4C3×#13712yes—
117C3#163411yescharacteristic, direct product factor, Sylow
118C2—82no—
119C2C3×#45212yes—
120C2C3×#45311yescharacteristic
subgroupG/H
center, socleC22×C3#120
commutator, Frattini, cosocleC42C23×C3
prime radicalC3×#555C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ G

Complements

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

NH ≅ G/Ntype
2. C3×#494C2semidirect
3. C3×#476C2semidirect
4. C3×#333C2semidirect
5. C3×D4⋊C8C2semidirect
6. #1634C3direct (N × H)
19. #494C2×C3semidirect
20. #476C2×C3semidirect
21. #333C2×C3semidirect
22. D4⋊C8C2×C3semidirect
117. C3#1634direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#5552
C3×#4942
C3×#4762
C3×#3332
C3×D4⋊C82
#16343