Finite Group Databasebeta

← C3⋊#85556 #11923126

Subgroups — C3⋊#85556 #11923126

Order 1152.

260 conjugacy classes of subgroups; only the 23 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 23 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×#5465C211yesmaximal, characteristic
2#85556—33nomaximal
3#71949—31nomaximal
4C2×C3⋊#226—41nomaximal
5C3⋊#859—42nomaximal
6C3×H(3,𝔽4)D311yescharacteristic
7#5465D313yes—
8#5060—31no—
9#5055—32no—
10#4540—31no—
11#4540—32no—
12C22×C3×A4—81no—
13C2×C3×SL(2,𝔽3)—41no—
14C2×C3×SL(2,𝔽3)—42no—
15C3⋊#226—42no—
16#1659—91noSylow
17C2×#226—123no—
18C3×#124—32no—
19C3×#124—31no—
20C3×#120—61no—
21C2×#216—61no—
22C2×#214—61no—
23#869—31no—
24#859—126no—
25#835—62no—
26#832—62no—
27#803—32no—
28#803—31no—
29C2×C3×A4—82no—
30C2×C3×A4—81no—
31C2×C3⋊Dic3—161no—
32C3×SL(2,𝔽3)—41no—
33C3×SL(2,𝔽3)—42no—
34H(3,𝔽4)C3⋊D311yescharacteristic
35#497—91no—
36#489—92no—
37#329—91no—
38#329—92no—
39C24×C3—21no—
40C22×A4—83no—
41C2×C3×Q8S412yes—
42C2×C3×Q8S411yescharacteristic
43C2×C3×D4—32no—
44C2×C3×D4—31no—
45C2×Dic6—61no—
46C2×SL(2,𝔽3)—46no—
47C2×SL(2,𝔽3)—43no—
48#226—126no—
49C3×C22⋊C4—61no—
50C3×C22⋊C4—62no—
51C3×C42—31no—
52#216—122no—
53#214—122no—
54C4⋊Dic3—62no—
55C2×C3⋊C8—61no—
56C2×C3⋊C8—62no—
57C22×C32—161no—
58C3×A4—81no—
59C3⋊Dic3—162no—
60C2×Q16—181no—
61C2×SD16—181no—
62C4⋊Q8—91no—
63#124—32no—
64#124—31no—
65#120—61no—
66#103—182no—
67#102—182no—
68#97—92no—
69#97—91no—
70C23×C3—61no—
71C23×C3—82no—
72C23×C3—81no—
73C2×A4—86no—
74C2×A4—83no—
75C3×Q8—41no—
76C3×Q8—42no—
77C3×D4—121no—
78C3×D4—122no—
79C2×C3×C4—32no—
80C2×C3×C4—31no—
81C2×Dic3—121no—
82C2×Dic3—483no—
83Dic6—121no—
84Dic6—121no—
85SL(2,𝔽3)—43no—
86SL(2,𝔽3)—46no—
87C3⋊C8—62no—
88C3⋊C8—122no—
89C2×C32—162no—
90C2×C32—161no—
91C24—21no—
92C2×Q8—181no—
93C2×Q8C3⋊S412yes—
94C2×Q8C3⋊S411yescharacteristic
95C2×D4—32no—
96C2×D4—31no—
97Q16—362no—
98SD16—362no—
99C2×C8—181no—
100C2×C8—182no—
101C4⋊C4—182no—
102C22⋊C4—61no—
103C22⋊C4—62no—
104C42—31no—
105C22×C3—81no—
106C22×C3—122no—
107C22×C3—121no—
108C22×C3—163no—
109C22×C3—241no—
110C22×C3#102011yescharacteristic
111A4—83no—
112C3×C4—62no—
113C3×C4—61no—
114Dic3—241no—
115Dic3—486no—
116C32—161noSylow
117C23—61no—
118C23—82no—
119C23—81no—
120Q8—41no—
121Q8—42no—
122Q8—361no—
123Q8—361no—
124D4—121no—
125D4—122no—
126C2×C4—32no—
127C2×C4—31no—
128C2×C4—361no—
129C8—182no—
130C8—362no—
131C2×C3—166no—
132C2×C3—163no—
133C2×C3—241no—
134C2×C3#593312yes—
135C2×C3#593511yescharacteristic
136C22—81no—
137C22—122no—
138C22—121no—
139C22—241no—
140C22C3⋊#102011yescharacteristic
141C4—62no—
142C4—61no—
143C4—721no—
144C3—163no—
145C3#8555611yescharacteristic, complemented
146C2—241no—
147C2C3⋊#593312yes—
148C2C3⋊#593511yescharacteristic
subgroupG/H
center, Frattini, hypercenterC22C3⋊#1020
commutator, prime radical, cosocle, hypocenterC3×#5465C2
FittingC3×H(3,𝔽4)D3
socleC22×C3#1020
LCSG ▷ C3×#5465
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
145. C3#85556semidirect

Maximal subgroups

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

subgroupindex
C3×#54652
#855563
#719493
C2×C3⋊#2264
C3⋊#8594