Finite Group Databasebeta

← C3⋊#85665 #11923433

Subgroups — C3⋊#85665 #11923433

Order 1152.

594 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 594 conjugacy classes of subgroups — too many to draw. Only its 44 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×#5948C211yesmaximal, characteristic
2C22×#948C311yesmaximal, characteristic, complemented
3#85665—31nomaximal
4C3×C22⋊SL(2,𝔽3)C411yescharacteristic
5C3⋊(#131⋊C3)—44nomaximal
6A4×C3⋊C8—41nomaximal
7C22×C3×#41C2×C311yescharacteristic
8#5948—21no—
9#5948D311yescharacteristic
10C2×#948—34no—
11C2×#948—34no—
12C22×#208—31no—
13C23×C3⋊C8—31no—
14C3×#41⋊C3—44no—
15C3×C4×A4—41no—
16C22×#131—31noSylow
17C2×C3×#41—34no—
18C2×C3×#41—34no—
19C22×C3×Q8C3×C411yescharacteristic
20C22×C3×D4—31no—
21C23×C3×C4—31no—
22C22⋊SL(2,𝔽3)—21no—
23C22⋊SL(2,𝔽3)Dic311yescharacteristic
24#948—312no—
25#948—34no—
26#948—34no—
27#948A414yescomplemented
28C2×#208—312no—
29C22×C3⋊C8—36no—
30C22×C3⋊C8—36no—
31C22×C3⋊C8—31no—
32C22×C3⋊C8A411yescharacteristic
33#131⋊C3—124no—
34C8×A4—121no—
35C2×C3×A4—41no—
36C3×SL(2,𝔽3)—44no—
37C3×C3⋊C8—161no—
38C22×#41C3×D311yescharacteristic
39C2×#131—94no—
40C2×#131—94no—
41C22×M16—91no—
42C23×C8—91no—
43C24×C3—31no—
44C3×#41—34no—
45C3×#41—312no—
46C3×#41—34no—
47C3×#41C2×A414yes—
48C2×C3×Q8—34no—
49C2×C3×D4—312no—
50C22×C3×C4—36no—
51C22×C3×C4—36no—
52C22×C3×C4—31no—
53C22×C3×C4C2×A411yescharacteristic
54#41⋊C3—44no—
55#41⋊C3—84no—
56C4×A4—41no—
57C4×A4—81no—
58#208—312no—
59#208—34no—
60C2×C3⋊C8—36no—
61C2×C3⋊C8—312no—
62C2×C3⋊C8—31no—
63C2×C3⋊C8—34no—
64C2×C3⋊C8—31no—
65C3×A4—41no—
66C32×C4—161no—
67C2×#41—34no—
68C2×#41—34no—
69C22×Q8C3×Dic311yescharacteristic
70C22×D4—31no—
71C23×C4—31no—
72#131—34no—
73#131—94no—
74#131—912no—
75#131—94no—
76C2×M16—912no—
77C22×C8—31no—
78C22×C8—96no—
79C22×C8—96no—
80C22×C8—91no—
81C23×C3—36no—
82C23×C3—63no—
83C23×C3—61no—
84C23×C3C4×A411yescharacteristic
85C2×A4—41no—
86C2×A4—81no—
87C3×Q8—34no—
88C3×Q8C4×A414yes—
89C3×D4—34no—
90C3×D4—312no—
91C2×C3×C4—36no—
92C2×C3×C4—312no—
93C2×C3×C4—31no—
94C2×C3×C4—34no—
95C2×C3×C4—31no—
96SL(2,𝔽3)—44no—
97SL(2,𝔽3)—84no—
98C3×C8—481no—
99C3⋊C8—31no—
100C3⋊C8—34no—
101C3⋊C8C22⋊A411yescharacteristic
102C2×C32—161no—
103C24—31no—
104#41—34no—
105#41—312no—
106#41—34no—
107#41D3×A414yes—
108C2×Q8—34no—
109C2×D4—312no—
110C22×C4—36no—
111C22×C4—36no—
112C22×C4—31no—
113C22×C4D3×A411yescharacteristic
114M16—912no—
115M16—94no—
116C2×C8—91no—
117C2×C8—94no—
118C2×C8—96no—
119C2×C8—912no—
120C2×C8—91no—
121C22×C3—31no—
122C22×C3—31no—
123C22×C3—34no—
124C22×C3—66no—
125C22×C3—66no—
126C22×C3#131⋊C311yescharacteristic, complemented
127A4—41no—
128A4—81no—
129C3×C4—31no—
130C3×C4—34no—
131C3×C4—161no—
132C3×C4—321no—
133C3×C4C2×C22⋊A411yescharacteristic
134C32—161noSylow
135C23—36no—
136C23—63no—
137C23—61no—
138C23Dic3×A411yescharacteristic
139Q8—34no—
140Q8Dic3×A414yes—
141D4—34no—
142D4—312no—
143C2×C4—36no—
144C2×C4—312no—
145C2×C4—31no—
146C2×C4—34no—
147C2×C4—31no—
148C8—31no—
149C8—91no—
150C8—94no—
151C2×C3—31no—
152C2×C3—31no—
153C2×C3—64no—
154C2×C3—161no—
155C2×C3—321no—
156C2×C3C4×C22⋊A411yescharacteristic
157C22—31no—
158C22—31no—
159C22—34no—
160C22—66no—
161C22—66no—
162C22C3⋊(#131⋊C3)11yescharacteristic, complemented
163C4—31no—
164C4—34no—
165C4D3×C22⋊A411yescharacteristic
166C3—161no—
167C3—321no—
168C3#8566511yescharacteristic, complemented
169C2—31no—
170C2—31no—
171C2—64no—
172C2Dic3×C22⋊A411yescharacteristic
subgroupG/H
center, Frattini, hypercenterC4D3×C22⋊A4
commutator, hypocenterC22×C3×Q8C3×C4
Fitting, cosocleC22×C3×#41C2×C3
socleC23×C3C4×A4
prime radicalC3×#5948C2
LCSG ▷ C22×C3×Q8
UCSC1 ◁ C4

Complements

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

NH ≅ G/Ntype
2. C22×#948C3semidirect
27. #948A4semidirect
126. C22×C3#131⋊C3semidirect
162. C22C3⋊(#131⋊C3)semidirect
168. C3#85665semidirect

Maximal subgroups

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

subgroupindex
C3×#59482
C22×#9483
#856653
C3⋊(#131⋊C3)4
A4×C3⋊C84