Finite Group Databasebeta

← C3⋊#85559 #11923128

Subgroups — C3⋊#85559 #11923128

Order 1152.

286 conjugacy classes of subgroups; only the 17 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 17 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×#5464C211yesmaximal, characteristic, complemented
2#85559—33nomaximal
3#71950—31nomaximal
4C3⋊#1020—42nomaximal
5C3⋊#857—41nomaximal
6C3×H(3,𝔽4)D311yescharacteristic, complemented
7#5464D313yescomplemented
8#5061—31no—
9#5032—32no—
10#4541—31no—
11#4536—32no—
12C3×C22⋊A4—42no—
13C3×C42⋊C3—41no—
14C3×C42⋊C3—81no—
15#2199—91noSylow
16#1020—126no—
17#1004—31no—
18C3×#124—31no—
19C3×#124—61no—
20C3×#120—32no—
21#953—62no—
22#942—61no—
23#857—123no—
24#834—32no—
25#833—31no—
26#806—62no—
27#805—61no—
28C3⋊S4—161no—
29C3⋊S4—164no—
30H(3,𝔽4)C3⋊D311yescharacteristic, complemented
31B(4,𝔽2)—92no—
32#455—91no—
33#354—91no—
34AΣL(1,𝔽16)—92no—
35C24×C3S412yescomplemented
36C22⋊A4—46no—
37C2×C3×Q8—31no—
38C2×C3×D4—31no—
39C2×C3×D4—61no—
40C2×#67—62no—
41C2×#67—122no—
42#237—121no—
43D3×D4—121no—
44#235—61no—
45C3×C22⋊C4—32no—
46C3×C22⋊C4—62no—
47C3×C42—21no—
48C3×C42S411yescharacteristic, complemented
49#217—62no—
50#217—122no—
51#216—121no—
52#215—121no—
53#208—61no—
54C42⋊C3—43no—
55C42⋊C3—83no—
56C3×A4—164no—
57C3×A4—161no—
58C3×A4—322no—
59H(5,𝔽2)—91no—
60#137—181no—
61#124—31no—
62#124—61no—
63#120—32no—
64#120—182no—
65#104—181no—
66#100—91no—
67#99—92no—
68#99—182no—
69C23×C3—32no—
70C23×C3—122no—
71C22×D3—62no—
72S4—483no—
73S4—4812no—
74C3×Q8—121no—
75C3×D4—121no—
76C3×D4—241no—
77C2×C3×C4—31no—
78C2×C3×C4—61no—
79#67—122no—
80#67—121no—
81#67—244no—
82C2×Dic3—62no—
83C2×Dic3—122no—
84D12—61no—
85C4×D3—121no—
86Dic6—61no—
87C3⋊C8—121no—
88C3⋊D3—641no—
89C24C3⋊S412yescomplemented
90#41—181no—
91#41—361no—
92C2×Q8—31no—
93C2×D4—31no—
94C2×D4—61no—
95C2×D4—182no—
96C2×D4—361no—
97C2×D4—362no—
98Q16—361no—
99SD16—361no—
100M16—181no—
101C22⋊C4—32no—
102C22⋊C4—62no—
103C22⋊C4—182no—
104C22⋊C4—362no—
105C42—21no—
106C42C3⋊S411yescharacteristic, complemented
107C22×C3—44no—
108C22×C3—62no—
109C22×C3—82no—
110C22×C3—122no—
111C22×C3#102011yescharacteristic
112C2×D3—121no—
113C2×D3—242no—
114A4—1612no—
115A4—163no—
116A4—326no—
117C3×C4—61no—
118C3×C4—121no—
119Dic3—121no—
120Dic3—242no—
121C32—641noSylow
122C23—32no—
123C23—122no—
124C23—182no—
125Q8—121no—
126Q8—181no—
127D4—121no—
128D4—181no—
129D4—241no—
130D4—362no—
131D4—361no—
132D4—724no—
133C2×C4—31no—
134C2×C4—61no—
135C2×C4—182no—
136C2×C4—361no—
137C2×C4—362no—
138C8—361no—
139C2×C3—31no—
140C2×C3—122no—
141D3—241no—
142D3—1923no—
143C22—44no—
144C22—62no—
145C22—82no—
146C22—122no—
147C22—361no—
148C22—722no—
149C22C3⋊#102011yescharacteristic
150C4—61no—
151C4—121no—
152C4—361no—
153C4—722no—
154C3—643no—
155C3#8555911yescharacteristic, complemented
156C2—31no—
157C2—122no—
158C2—721no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenterC3×#5464C2
FrattiniC22C3⋊#1020
FittingC3×H(3,𝔽4)D3
socleC22×C3#1020
LCSG ▷ C3×#5464
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×#5464C2semidirect
6. C3×H(3,𝔽4)D3semidirect
7. #5464D3semidirect
30. H(3,𝔽4)C3⋊D3semidirect
35. C24×C3S4semidirect
48. C3×C42S4semidirect
89. C24C3⋊S4semidirect
106. C42C3⋊S4semidirect
155. C3#85559semidirect

Maximal subgroups

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

subgroupindex
C3×#54642
#855593
#719503
C3⋊#10204
C3⋊#8574