Finite Group Databasebeta

← C3⋊D3×#365 #11797086

Subgroups — C3⋊D3×#365 #11797086

Order 1152.

456 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 127 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⋊D3×M32C211yesmaximal, characteristic
2C3⋊D3×#108C211yesmaximal, characteristic
3C3⋊D3×#106C211yesmaximal, characteristic
4C32×#365C211yesmaximal, characteristic, complemented
5#10589379C211yesmaximal, characteristic, complemented
6#10589360C211yesmaximal, characteristic, complemented
7#10589353C211yesmaximal, characteristic, complemented
8D3×#365—34nomaximal
9M16×C3⋊D3—21no—
10C2×C8×C3⋊D3C2211yescharacteristic
11C4⋊C4×C3⋊D3—21no—
12C32×M32C2211yescharacteristic
13C32×#108C2211yescharacteristic
14C32×#106C2211yescharacteristic
15#63649—21no—
16#63646C2211yescharacteristic
17#63644C2211yescharacteristic
18#63639C2211yescharacteristic
19#63635—21no—
20#63625C412yescomplemented
21C16×C3⋊D3C412yescomplemented
22D3×M32—34no—
23D3×#108—34no—
24D3×#106—34no—
25C3×#365D314yescomplemented
26#4513—34no—
27#4494—34no—
28#4487—34no—
29C2×C4×C3⋊D3—41no—
30C2×C4×C3⋊D3D411yescharacteristic
31C32×M16—21no—
32C2×C32×C8C2311yescharacteristic
33C32×C4⋊C4—21no—
34C4⋊(C3⋊Dic3)—21no—
35#3750—41no—
36#3748—21no—
37C2×C3⋊(C3⋊C8)D411yescharacteristic
38#3743—41no—
39C8×C3⋊D3—41no—
40C8×C3⋊D3C2×C411yescharacteristic
41C8×C3⋊D3C2×C411yescharacteristic
42C8×C3⋊D3Q811yescharacteristic
43C8×C3⋊D3Q811yescharacteristic
44C32×C16C2×C412yescomplemented
45C3⋊(C3⋊C16)C2×C412yescomplemented
46C2×#365—91noSylow
47D3×M16—64no—
48C2×D3×C8—34no—
49D3×C4⋊C4—64no—
50C3×M32C2×D314yes—
51C3×#108C2×D314yes—
52C3×#106C2×D314yes—
53#822—64no—
54#819—34no—
55#817—34no—
56#812—34no—
57#808—64no—
58#798—38no—
59D3×C16—38no—
60C22×C3⋊D3SD1611yescharacteristic
61C2×C32×C4—41no—
62C2×C32×C4C2×D411yescharacteristic
63C2×C3⋊Dic3—41no—
64C2×C3⋊Dic3SD1611yescharacteristic
65C4×C3⋊D3—82no—
66C4×C3⋊D3C4⋊C411yescharacteristic
67C4×C3⋊D3C4⋊C411yescharacteristic
68C4×C3⋊D3SD1611yescharacteristic
69C4×C3⋊D3SD1611yescharacteristic
70C32×C8—41no—
71C32×C8C22×C411yescharacteristic
72C32×C8C2×Q811yescharacteristic
73C3⋊(C3⋊C8)—41no—
74C3⋊(C3⋊C8)C4⋊C411yescharacteristic
75C3⋊(C3⋊C8)C4⋊C411yescharacteristic
76C2×M32—91no—
77C2×#108—91no—
78C2×#106—91no—
79#365—91no—
80#365—91no—
81#365—91no—
82#365C3⋊D311yescharacteristic, direct product factor
83C2×C4×D3—34no—
84C2×C4×D3—124no—
85C3×M16—24no—
86C2×C3×C8C22×D314yes—
87C3×C4⋊C4—24no—
88C4⋊Dic3—64no—
89Dic3⋊C4—124no—
90#208—64no—
91C2×C3⋊C8—34no—
92ΓL(1,𝔽25)—124no—
93D3×C8—34no—
94D3×C8—34no—
95D3×C8—34no—
96D3×C8—34no—
97D3×C8—124no—
98C3×C16C4×D318yescomplemented
99C3⋊C16—38no—
100C22×C32C2×SD1611yescharacteristic
101C2×C3⋊D3—22no—
102C2×C3⋊D3#10611yescharacteristic
103C2×C3⋊D3#10611yescharacteristic
104C32×C4—81no—
105C32×C4C2×C4⋊C411yescharacteristic
106C32×C4C2×SD1611yescharacteristic
107C3⋊Dic3—81no—
108C3⋊Dic3#10611yescharacteristic
109C3⋊Dic3#10611yescharacteristic
110C2×M16—181no—
111C22×C8—91no—
112C2×C4⋊C4—181no—
113M32—91no—
114M32—92no—
115M32C2×C3⋊D311yescharacteristic
116C2×C16—92no—
117#108—91no—
118#108—181no—
119#108C2×C3⋊D311yescharacteristic
120#106—91no—
121#106—181no—
122#106C2×C3⋊D311yescharacteristic
123C22×D3—34no—
124C2×C3×C4—44no—
125C2×C3×C4D3×D414yes—
126C2×Dic3—34no—
127C2×Dic3—124no—
128C4×D3—34no—
129C4×D3—34no—
130C4×D3—34no—
131C4×D3—34no—
132C4×D3—248no—
133C3×C8—44no—
134C3×C8C2×C4×D314yes—
135C3×C8D3×Q814yes—
136C3⋊C8—34no—
137C3⋊C8—34no—
138C3⋊C8—124no—
139C2×C32—21no—
140C2×C32C2×#10611yescharacteristic
141C3⋊D3—21no—
142C3⋊D3#36512yesdirect product factor
143C22×C4—91no—
144C22×C4—361no—
145M16—21no—
146M16—181no—
147M16—361no—
148C2×C8—91no—
149C2×C8—91no—
150C2×C8—91no—
151C2×C8—91no—
152C2×C8—91no—
153C2×C8—361no—
154C2×C8C22×C3⋊D311yescharacteristic
155C4⋊C4—21no—
156C4⋊C4—181no—
157C4⋊C4—361no—
158C16—92no—
159C16C4×C3⋊D312yescomplemented
160C22×C3D3×SD1614yes—
161C2×D3—34no—
162C2×D3—34no—
163C2×D3—68no—
164C3×C4—84no—
165C3×C4D3×C4⋊C414yes—
166C3×C4D3×SD1614yes—
167Dic3—34no—
168Dic3—34no—
169Dic3—244no—
170C32C2×#36511yescharacteristic, complemented, Sylow
171C23—91no—
172C2×C4—41no—
173C2×C4—91no—
174C2×C4—91no—
175C2×C4—91no—
176C2×C4—91no—
177C2×C4—91no—
178C2×C4—361no—
179C2×C4—722no—
180C2×C4D4×C3⋊D311yescharacteristic
181C8—41no—
182C8—91no—
183C8—91no—
184C8—361no—
185C8C2×C4×C3⋊D311yescharacteristic
186C8Q8×C3⋊D311yescharacteristic
187C2×C3—24no—
188C2×C3D3×#10614yes—
189D3—38no—
190D3—64no—
191C22—91no—
192C22—91no—
193C22—182no—
194C22SD16×C3⋊D311yescharacteristic
195C4—81no—
196C4—91no—
197C4—91no—
198C4—721no—
199C4C4⋊C4×C3⋊D311yescharacteristic
200C4SD16×C3⋊D311yescharacteristic
201C3D3×#36514yescomplemented
202C2—21no—
203C2—92no—
204C2—181no—
205C2C3⋊D3×#10611yescharacteristic
subgroupG/H
centerC2C3⋊D3×#106
commutatorC32×C8C22×C4
FrattiniC2×C8C22×C3⋊D3
FittingC32×#365C2
socleC2×C32C2×#106
prime radicalC22×C3⋊D3SD16
cosocleC2×C32×C8C23
hypercenter#365C3⋊D3
hypocenterC32C2×#365
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #365

Complements

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

NH ≅ G/Ntype
4. C32×#365C2semidirect
5. #10589379C2semidirect
6. #10589360C2semidirect
7. #10589353C2semidirect
20. #63625C4semidirect
21. C16×C3⋊D3C4semidirect
25. C3×#365D3semidirect
44. C32×C16C2×C4semidirect
45. C3⋊(C3⋊C16)C2×C4semidirect
82. #365C3⋊D3direct (N × H)
98. C3×C16C4×D3semidirect
142. C3⋊D3#365direct (N × H)
159. C16C4×C3⋊D3semidirect
170. C32C2×#365semidirect
201. C3D3×#365semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×M322
C3⋊D3×#1082
C3⋊D3×#1062
C32×#3652
#105893792
#105893602
#105893532
D3×#3653