Finite Group Databasebeta

← C3⋊#68003 #11920139

Subgroups — C3⋊#68003 #11920139

Order 1152.

176 conjugacy classes of subgroups; only the 27 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 27 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×#399⋊C3C211yesmaximal, characteristic
2#68003—33nomaximal
3#67651—31nomaximal
4C2×C3⋊SL(2,ℤ/4)—41nomaximal
5C3×#95⋊C3C411yescharacteristic, complemented
6C3×#399D311yescharacteristic
7#399⋊C3D313yes—
8#4526—31no—
9#4525—31no—
10C22×C3×A4—41no—
11C3⋊SL(2,ℤ/4)—42no—
12#1352—91noSylow
13C2×SL(2,ℤ/4)—123no—
14C2×C3×C4⋊C4—31no—
15C2×C3×C22⋊C4—31no—
16C2×#217—61no—
17C3×#95Dic311yescharacteristic, complemented
18#830—61no—
19#95⋊C3Dic313yescomplemented
20C2×C3×A4—41no—
21C2×C3×A4—41no—
22C2×C3×A4—41no—
23C2×C3⋊Dic3—161no—
24#399C3⋊D311yescharacteristic
25#342—91no—
26#323—91no—
27C24×C3S411yescharacteristic
28C22×A4—43no—
29C22×C3×C4—31no—
30C22×C3×C4—31no—
31C22×Dic3—121no—
32SL(2,ℤ/4)—126no—
33C3×C4⋊C4—121no—
34C3×C22⋊C4—121no—
35#217—62no—
36#217—121no—
37C2×C3⋊C8—121no—
38C22×C32—161no—
39C3×A4—41no—
40C3⋊Dic3—162no—
41C2×C4⋊C4—31no—
42C2×C22⋊C4—31no—
43C2×C22⋊C4—181no—
44C22⋊C8—181no—
45#95C3⋊Dic311yescharacteristic, complemented
46C23×C3—61no—
47C23×C3—61no—
48C23×C3#22611yescharacteristic
49C23×C3GL(2,𝔽3)11yescharacteristic
50C23×C3SL(2,ℤ/4)11yescharacteristic
51C2×A4—43no—
52C2×A4—43no—
53C2×A4—43no—
54C2×C3×C4—61no—
55C2×C3×C4—61no—
56C2×C3×C4—121no—
57C2×C3×C4—121no—
58C2×Dic3—122no—
59C2×Dic3—241no—
60C2×Dic3—241no—
61C2×Dic3—483no—
62C3⋊C8—241no—
63C2×C32—161no—
64C2×C32—161no—
65C2×C32—161no—
66C24C3⋊S411yescharacteristic
67C22×C4—31no—
68C22×C4—31no—
69C22×C4—361no—
70C2×C8—361no—
71C4⋊C4—121no—
72C22⋊C4—121no—
73C22⋊C4—182no—
74C22⋊C4—361no—
75C22×C3—31no—
76C22×C3—31no—
77C22×C3—41no—
78C22×C3—61no—
79C22×C3—61no—
80C22×C3—121no—
81C22×C3—163no—
82C22×C3#85911yescharacteristic
83A4—43no—
84C3×C4—121no—
85C3×C4—121no—
86Dic3—242no—
87Dic3—486no—
88C32—161noSylow
89C23—61no—
90C23—61no—
91C23C3⋊#22611yescharacteristic
92C23C3⋊GL(2,𝔽3)11yescharacteristic
93C23C3⋊SL(2,ℤ/4)11yescharacteristic
94C2×C4—61no—
95C2×C4—61no—
96C2×C4—121no—
97C2×C4—121no—
98C2×C4—362no—
99C2×C4—721no—
100C2×C4—721no—
101C8—721no—
102C2×C3—31no—
103C2×C3—31no—
104C2×C3—41no—
105C2×C3—41no—
106C2×C3—163no—
107C2×C3—163no—
108C2×C3—163no—
109C2×C3#462611yescharacteristic
110C22—31no—
111C22—31no—
112C22—41no—
113C22—61no—
114C22—61no—
115C22—121no—
116C22C3⋊#85911yescharacteristic
117C4—121no—
118C4—121no—
119C4—722no—
120C3—163no—
121C3#6800311yescharacteristic, complemented
122C2—31no—
123C2—31no—
124C2—41no—
125C2—41no—
126C2C3⋊#462611yescharacteristic
subgroupG/H
center, hypercenterC2C3⋊#4626
commutator, hypocenterC3×#95⋊C3C4
FrattiniC24C3⋊S4
FittingC3×#399D3
socleC23×C3SL(2,ℤ/4)
prime radical, cosocleC3×#399⋊C3C2
LCSG ▷ C3×#95⋊C3
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
5. C3×#95⋊C3C4semidirect
17. C3×#95Dic3semidirect
19. #95⋊C3Dic3semidirect
45. #95C3⋊Dic3semidirect
121. C3#68003semidirect

Maximal subgroups

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

subgroupindex
C3×#399⋊C32
#680033
#676513
C2×C3⋊SL(2,ℤ/4)4