Finite Group Databasebeta

← C3×#3556⋊C3 #11919848

Subgroups — C3×#3556⋊C3 #11919848

Order 1152.

382 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 38 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×#564⋊C3C211yesmaximal, characteristic, complemented
2C3×#3556C311yesmaximal, characteristic, complemented
3#3556⋊C3C313yesmaximal, direct product factor
4C3×#126⋊C3—44nomaximal
5C2×C3×C42⋊C3—41nomaximal
6C3×#564—31no—
7C3×#564C2×C311yescharacteristic, complemented
8C3×#557—34no—
9C3×#541—34no—
10C3×#533—31no—
11#564⋊C3C2×C313yescomplemented
12C3×C42⋊C3—41no—
13C3×C42⋊C3—44no—
14#3556C3211yescharacteristic, complemented, Sylow
15C3×C4⋊Q8—32no—
16C3×C4⋊Q8—34no—
17C3×#126—34no—
18C3×#126A414yes—
19C3×#125—38no—
20C3×#125—34no—
21C3×#125—34no—
22C3×#125—31no—
23C3×#125—31no—
24C3×#125—34no—
25C3×C22⋊Q8—34no—
26C3×C4×Q8—34no—
27C3×C4×Q8—34no—
28C3×C4×Q8—34no—
29C3×#117—32no—
30C2×C3×C42A411yescharacteristic
31#126⋊C3—412no—
32C2×C42⋊C3—43no—
33C2×C3×A4—161no—
34#564—31no—
35#564C2×C3211yescharacteristic, complemented
36#557—34no—
37#541—34no—
38#533—31no—
39C2×C3×Q8—34no—
40C22×C3×C4—31no—
41C3×C4⋊C4—34no—
42C3×C4⋊C4—32no—
43C3×C4⋊C4—32no—
44C3×C4⋊C4—34no—
45C3×C4⋊C4—34no—
46C3×C4⋊C4—34no—
47C3×C4⋊C4—38no—
48C3×C4⋊C4—34no—
49C3×C22⋊C4—34no—
50C3×C42—31no—
51C3×C42—34no—
52C3×C42—34no—
53C3×C42C2×A411yescharacteristic
54C3×C42C2×A414yes—
55C42⋊C3—43no—
56C42⋊C3—412no—
57C3×A4—161no—
58C4⋊Q8—32no—
59C4⋊Q8—34no—
60#126—34no—
61#126C3×A414yes—
62#125—34no—
63#125—38no—
64#125—34no—
65#125—31no—
66#125—31no—
67#125—34no—
68C22⋊Q8—34no—
69C4×Q8—34no—
70C4×Q8—34no—
71C4×Q8—34no—
72#117—32no—
73C2×C42C3×A411yescharacteristic
74C23×C3C22⋊A411yescharacteristic
75C2×A4—163no—
76C3×Q8—68no—
77C2×C3×C4—31no—
78C2×C3×C4—34no—
79C2×C3×C4—34no—
80C2×C3×C4—31no—
81C2×C3×C4—62no—
82C2×C32—641no—
83C2×Q8—34no—
84C22×C4—31no—
85C4⋊C4—34no—
86C4⋊C4—32no—
87C4⋊C4—32no—
88C4⋊C4—34no—
89C4⋊C4—34no—
90C4⋊C4—34no—
91C4⋊C4—38no—
92C4⋊C4—34no—
93C22⋊C4—34no—
94C42—31no—
95C42—34no—
96C42—34no—
97C42C2×C3×A411yescharacteristic
98C42C2×C3×A414yes—
99C22×C3—61no—
100C22×C3C2×C22⋊A411yescharacteristic
101A4—163no—
102C3×C4—32no—
103C3×C4—61no—
104C3×C4—64no—
105C3×C4—64no—
106C32—641noSylow
107C23C3×C22⋊A411yescharacteristic
108Q8—68no—
109C2×C4—31no—
110C2×C4—34no—
111C2×C4—34no—
112C2×C4—31no—
113C2×C4—62no—
114C2×C3—31no—
115C2×C3—41no—
116C2×C3—643no—
117C22—61no—
118C22C2×C3×C22⋊A411yescharacteristic
119C4—32no—
120C4—61no—
121C4—64no—
122C4—64no—
123C3—643no—
124C3#3556⋊C311yescharacteristic, direct product factor
125C2—31no—
126C2—41no—
subgroupG/H
center, hypercenterC3#3556⋊C3
commutator, cosocle, hypocenter#564C2×C32
FrattiniC22C2×C3×C22⋊A4
FittingC3×#3556C3
socleC22×C3C2×C22⋊A4
LCSG ▷ #564
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×#564⋊C3C2semidirect
2. C3×#3556C3semidirect
3. #3556⋊C3C3direct (N × H)
7. C3×#564C2×C3semidirect
11. #564⋊C3C2×C3semidirect
14. #3556C32semidirect
35. #564C2×C32semidirect
124. C3#3556⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#564⋊C32
C3×#35563
#3556⋊C33
C3×#126⋊C34
C2×C3×C42⋊C34