Finite Group Databasebeta

← C3⋊D3×#819 #13159909

Subgroups — C3⋊D3×#819 #13159909

Order 1728.

756 conjugacy classes of subgroups; only the 176 normal subgroups are shown.

normal subgroups only

This group has 756 conjugacy classes of subgroups — too many to draw. Only its 176 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
1C2×C3×C8×C3⋊D3C211yesmaximal, characteristic
2C3⋊D3×#208C212yesmaximal
3#11722189C211yesmaximal, characteristic, complemented
4C32×#819C211yesmaximal, characteristic, complemented
5#11722060C212yesmaximal, complemented
6C3⋊D3×#108—31nomaximal
7D3×#819—34nomaximal
8C2×C3×C4×C3⋊D3C2211yescharacteristic
9C2×C33×C8C2211yescharacteristic
10#88855C2212yes—
11C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic
12C3×C8×C3⋊D3C412yes—
13C3×C8×C3⋊D3C412yes—
14C32×#208C2212yes—
15#88787—22no—
16C3⋊D3×C3⋊C8—22no—
17M16×C3⋊D3—32no—
18C2×C8×C3⋊D3D311yescharacteristic
19C2×C3×D3×C8—34no—
20D3×#208—38no—
21C32×#108—31no—
22#63649—32no—
23#63646—31no—
24#63646—34no—
25#63646—64no—
26C3×#819D314yescomplemented
27#63577—38no—
28C22×C3×C3⋊D3Q811yescharacteristic
29C2×C33×C4C2311yescharacteristic
30C2×C3×C3⋊Dic3Q811yescharacteristic
31C3×C4×C3⋊D3C2×C411yescharacteristic
32C3×C4×C3⋊D3C2×C411yescharacteristic
33C3×C4×C3⋊D3D411yescharacteristic
34C3×C4×C3⋊D3D411yescharacteristic
35C33×C8C2×C412yes—
36C3⋊(C3⋊(C3⋊C8))—22no—
37C3×C3⋊(C3⋊C8)C2×C412yes—
38C32×C3⋊C8—22no—
39C2×#819—91no—
40D3×#108—94no—
41C2×C4×C3⋊D3C2×D311yescharacteristic
42C2×C3×C4×D3—34no—
43C32×M16—32no—
44C2×C32×C8—24no—
45C2×C32×C8C2×D314yes—
46C2×C32×C8C2×D311yescharacteristic
47#3748—32no—
48#3748—38no—
49#3748—68no—
50C2×C3⋊(C3⋊C8)C2×D311yescharacteristic
51#3743—62no—
52C8×C3⋊D3—62no—
53C8×C3⋊D3Dic312yes—
54C8×C3⋊D3Dic312yes—
55C3×#208C2×D318yes—
56C2×C3×C3⋊C8—34no—
57C3×D3×C8—38no—
58C3×D3×C8—38no—
59#3711—68no—
60D3×C3⋊C8—68no—
61C22×C33C2×Q811yescharacteristic
62C2×C3×C3⋊D3—22no—
63C2×C3×C3⋊D3C4⋊C411yescharacteristic
64C2×C3×C3⋊D3C4⋊C411yescharacteristic
65C33×C4C22×C411yescharacteristic
66C33×C4C2×D411yescharacteristic
67C3×C3⋊Dic3C4⋊C411yescharacteristic
68C3×C3⋊Dic3C4⋊C411yescharacteristic
69C22×C3×C8—91no—
70C2×#208—92no—
71D3×M16—98no—
72C2×D3×C8—34no—
73C3×#108—34no—
74#822—98no—
75#819—94no—
76#819—91no—
77#819—92no—
78#819—184no—
79#819C3⋊D311yescharacteristic, direct product factor
80C22×C3⋊D3Dic611yescharacteristic
81C22×C3×D3—34no—
82C2×C32×C4—24no—
83C2×C32×C4C22×D314yes—
84C2×C32×C4C22×D311yescharacteristic
85C2×C3⋊Dic3Dic611yescharacteristic
86C4×C3⋊D3D1211yescharacteristic
87C4×C3⋊D3D1211yescharacteristic
88C4×C3⋊D3C2×Dic311yescharacteristic
89C4×C3⋊D3C2×Dic311yescharacteristic
90C2×C3×Dic3—34no—
91C3×C4×D3—34no—
92C3×C4×D3—34no—
93C3×C4×D3—34no—
94C3×C4×D3—34no—
95C32×C8—28no—
96C32×C8—62no—
97C32×C8C4×D318yes—
98C32×C8C2×Dic312yes—
99C3⋊(C3⋊C8)—62no—
100C3⋊(C3⋊C8)—68no—
101C3⋊(C3⋊C8)—128no—
102C3⋊(C3⋊C8)C2×Dic312yes—
103C3×C3⋊C8—28no—
104C3×C3⋊C8—38no—
105C2×#108—271noSylow
106C2×C33—21no—
107C2×C33C2×C4⋊C411yescharacteristic
108C3×C3⋊D3—21no—
109C3×C3⋊D3#10812yescomplemented
110C22×C3×C4—91no—
111C2×C4×D3—34no—
112C3×M16—38no—
113C2×C3×C8—24no—
114C2×C3×C8—91no—
115C2×C3×C8—92no—
116C2×C3×C8—92no—
117C2×C3×C8D3214yes—
118C2×C3×C8C2×C3⋊D311yescharacteristic
119#208—98no—
120#208—92no—
121#208—188no—
122#208—182no—
123#208C2×C3⋊D312yes—
124C2×C3⋊C8—34no—
125C2×C3⋊C8—182no—
126ΓL(1,𝔽25)—188no—
127D3×C8—38no—
128D3×C8—38no—
129D3×C8—188no—
130C22×C32—24no—
131C22×C32C2×Dic611yescharacteristic
132C22×C32D3×Q814yes—
133C2×C3⋊D3—22no—
134C2×C3⋊D3C4⋊Dic311yescharacteristic
135C2×C3⋊D3C4⋊Dic311yescharacteristic
136C2×C3×D3—34no—
137C2×C3×D3—34no—
138C2×C3×D3—68no—
139C32×C4—24no—
140C32×C4—24no—
141C32×C4C2×C4×D314yes—
142C32×C4C2×D1211yescharacteristic
143C32×C4D3×D414yes—
144C32×C4C22×Dic311yescharacteristic
145C3⋊Dic3C4⋊Dic311yescharacteristic
146C3⋊Dic3C4⋊Dic311yescharacteristic
147C3×Dic3—34no—
148C3×Dic3—34no—
149C2×M16—272no—
150C22×C8—91no—
151#108—31no—
152#108—272no—
153#108—271no—
154C33C2×#10811yescharacteristic, complemented, Sylow
155C23×C3—91no—
156C22×D3—34no—
157C2×C3×C4—24no—
158C2×C3×C4—91no—
159C2×C3×C4—91no—
160C2×C3×C4—91no—
161C2×C3×C4—91no—
162C2×C3×C4—91no—
163C2×C3×C4C2×D3214yes—
164C2×C3×C4C22×C3⋊D311yescharacteristic
165C2×Dic3—34no—
166C4×D3—34no—
167C4×D3—34no—
168C4×D3—34no—
169C4×D3—34no—
170C3×C8—28no—
171C3×C8—68no—
172C3×C8—92no—
173C3×C8D3×Dic318yes—
174C3×C8C4×C3⋊D312yes—
175C3⋊C8—22no—
176C3⋊C8—38no—
177C3⋊C8—188no—
178C3⋊C8—182no—
179C3⋊C8—368no—
180C2×C32—21no—
181C2×C32—24no—
182C2×C32—24no—
183C2×C32—44no—
184C2×C32D3×C4⋊C414yes—
185C2×C32C2×C4⋊Dic311yescharacteristic
186C3⋊D3—21no—
187C3⋊D3#81912yesdirect product factor
188C3×D3—38no—
189C3×D3—64no—
190C22×C4—91no—
191M16—32no—
192M16—272no—
193M16—542no—
194C2×C8—91no—
195C2×C8—92no—
196C2×C8—92no—
197C2×C8—542no—
198C2×C8D3×C3⋊D311yescharacteristic
199C22×C3—24no—
200C22×C3—91no—
201C22×C3—91no—
202C22×C3—182no—
203C22×C3D3×Dic614yes—
204C22×C3Q8×C3⋊D311yescharacteristic
205C2×D3—34no—
206C2×D3—34no—
207C2×D3—68no—
208C3×C4—24no—
209C3×C4—24no—
210C3×C4—91no—
211C3×C4—91no—
212C3×C4D3×D1214yes—
213C3×C4C2×D3×Dic314yes—
214C3×C4C2×C4×C3⋊D311yescharacteristic
215C3×C4D4×C3⋊D311yescharacteristic
216Dic3—34no—
217Dic3—34no—
218C32—24no—
219C32D3×#10814yescomplemented
220C32C2×#81911yescharacteristic, complemented
221C23—91no—
222C2×C4—91no—
223C2×C4—91no—
224C2×C4—91no—
225C2×C4—91no—
226C2×C4—91no—
227C2×C4C2×D3×C3⋊D311yescharacteristic
228C8—62no—
229C8—92no—
230C8—542no—
231C8Dic3×C3⋊D312yes—
232C2×C3—21no—
233C2×C3—24no—
234C2×C3—24no—
235C2×C3—44no—
236C2×C3—92no—
237C2×C3—181no—
238C2×C3D3×C4⋊Dic314yes—
239C2×C3C4⋊C4×C3⋊D311yescharacteristic
240D3—38no—
241D3—64no—
242C22—91no—
243C22—91no—
244C22—182no—
245C22C3⋊D3×Dic611yescharacteristic
246C4—91no—
247C4—91no—
248C4C3⋊D3×D1211yescharacteristic
249C4C2×Dic3×C3⋊D311yescharacteristic
250C3—24no—
251C3D3×#81914yescomplemented
252C3C3⋊D3×#10811yescharacteristic, complemented
253C2—21no—
254C2—92no—
255C2—181no—
256C2C3⋊D3×C4⋊Dic311yescharacteristic
subgroupG/H
centerC4C3⋊D3×D12
commutatorC33×C4C22×C4
FrattiniC2×C4C2×D3×C3⋊D3
FittingC2×C33×C8C22
socleC2×C33C2×C4⋊C4
prime radicalC22×C3×C3⋊D3Q8
cosocleC2×C33×C4C23
hypercenterC2×C8D3×C3⋊D3
hypocenterC33C2×#108
LCSG ▷ C33×C4 ▷ C2×C33 ▷ C33
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
3. #11722189C2semidirect
4. C32×#819C2semidirect
5. #11722060C2semidirect
26. C3×#819D3semidirect
79. #819C3⋊D3direct (N × H)
109. C3×C3⋊D3#108semidirect
154. C33C2×#108semidirect
187. C3⋊D3#819direct (N × H)
219. C32D3×#108semidirect
220. C32C2×#819semidirect
251. C3D3×#819semidirect
252. C3C3⋊D3×#108semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C8×C3⋊D32
C3⋊D3×#2082
#117221892
C32×#8192
#117220602
C3⋊D3×#1083
D3×#8193