Finite Group Databasebeta

← C3×#73166 #11919402

Subgroups — C3×#73166 #11919402

Order 1152.

300 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 54 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×#376⋊C3C213yesmaximal
2C3×#2276C311yesmaximal, characteristic, complemented
3#73166C313yesmaximal, direct product factor
4C3×Q8×A4—41nomaximal
5C3×#95⋊C3C2211yescharacteristic
6C2×C3×C4×Q8—31no—
7C3×C4×C4⋊C4—33no—
8C3×#376C2×C313yes—
9#376⋊C3C2×C319yes—
10C3×C4×A4—43no—
11#2276C3211yescharacteristic, complemented, Sylow
12C22×C3×Q8A411yescharacteristic
13Q8×A4—43no—
14C3×C4×Q8—36no—
15C3×C4×Q8—32no—
16C2×C3×C4⋊C4—33no—
17C2×C3×C42—33no—
18C2×C3×C42—32no—
19C3×#95—33no—
20C3×#95C22×C311yescharacteristic
21#95⋊C3C22×C313yes—
22C2×C3×A4—41no—
23C32×Q8—161no—
24C2×C4×Q8—31no—
25C4×C4⋊C4—33no—
26#376C2×C3213yes—
27C2×C3×Q8—33no—
28C2×C3×Q8—31no—
29C22×C3×C4—31no—
30C22×C3×C4—33no—
31C22×C3×C4C2×A413yes—
32C4×A4—49no—
33C3×C4⋊C4—36no—
34C3×C4⋊C4—36no—
35C3×C42—36no—
36C3×C42—36no—
37C3×C42—122no—
38C3×A4—41no—
39C32×C4—163no—
40C22×Q8C3×A411yescharacteristic
41C4×Q8—36no—
42C4×Q8—32no—
43C2×C4⋊C4—33no—
44C2×C42—33no—
45C2×C42—32no—
46#95—33no—
47#95C22×C3211yescharacteristic
48C23×C3C22×A411yescharacteristic
49C2×A4—43no—
50C3×Q8—32no—
51C3×Q8—33no—
52C3×Q8—163no—
53C3×Q8C42⋊C311yescharacteristic
54C2×C3×C4—33no—
55C2×C3×C4—33no—
56C2×C3×C4—32no—
57C2×C3×C4—36no—
58C2×C3×C4—62no—
59C2×C3×C4—63no—
60C2×C3×C4—63no—
61C2×C32—161no—
62C2×Q8—33no—
63C2×Q8—31no—
64C22×C4—31no—
65C22×C4—33no—
66C22×C4C2×C3×A413yes—
67C4⋊C4—36no—
68C4⋊C4—36no—
69C42—36no—
70C42—36no—
71C42—122no—
72C22×C3—31no—
73C22×C3—31no—
74C22×C3#99411yescharacteristic
75A4—43no—
76C3×C4—33no—
77C3×C4—66no—
78C3×C4—62no—
79C3×C4—169no—
80C3×C4C2×C42⋊C313yes—
81C32—161noSylow
82C23C22×C3×A411yescharacteristic
83Q8—32no—
84Q8—33no—
85Q8C3×C42⋊C311yescharacteristic
86C2×C4—33no—
87C2×C4—33no—
88C2×C4—32no—
89C2×C4—36no—
90C2×C4—62no—
91C2×C4—63no—
92C2×C4—63no—
93C2×C3—31no—
94C2×C3—31no—
95C2×C3—163no—
96C2×C3C22×C42⋊C311yescharacteristic
97C22—31no—
98C22—31no—
99C22C3×#99411yescharacteristic
100C4—33no—
101C4—66no—
102C4—62no—
103C4C2×C3×C42⋊C313yes—
104C3—163no—
105C3#7316611yescharacteristic, direct product factor
106C2—31no—
107C2—31no—
108C2C22×C3×C42⋊C311yescharacteristic
subgroupG/H
centerC2×C3C22×C42⋊C3
commutator, cosocle, hypocenter#95C22×C32
FrattiniC23C22×C3×A4
FittingC3×#2276C3
socleC23×C3C22×A4
prime radicalC3×#95⋊C3C22
hypercenterC3×Q8C42⋊C3
LCSG ▷ #95
UCSC1 ◁ C2×C3 ◁ C3×Q8

Complements

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

NH ≅ G/Ntype
2. C3×#2276C3semidirect
3. #73166C3direct (N × H)
11. #2276C32semidirect
105. C3#73166direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#376⋊C32
C3×#22763
#731663
C3×Q8×A44