Finite Group Databasebeta

← C3⋊#10620070 #14519270

Subgroups — C3⋊#10620070 #14519270

Order 1944.

650 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 650 conjugacy classes of subgroups — too many to draw. Only its 95 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×#66436C211yesmaximal, characteristic, complemented
2C22×C3⋊(C3⋊D9)C311yesmaximal, characteristic, complemented
3C3⋊((C3⋊D3)⋊A4)—31nomaximal
4A4×C3⋊D9—31nomaximal
5#10620070—39nomaximal
6C3⋊(D9⋊A4)—32nomaximal
7C3⋊#4207—41nomaximal
8C22×C32×C9C2×C311yescharacteristic, complemented
9C2×C3⋊(C3⋊D9)—31no—
10C2×C3⋊(C3⋊D9)—31no—
11C3×C22⋊H(3,𝔽3)D311yescharacteristic
12C3×#1094—21no—
13#66436—29no—
14#66436D319yescomplemented
15C3×C9⋊A4—22no—
16C3×C9⋊A4D312yescomplemented
17C3×C9×A4—21no—
18C3×C9×A4D311yescharacteristic, complemented
19C3×#737—41noSylow
20C22×C3⋊(C3⋊D3)—31no—
21A4×C3⋊D3—91no—
22C22×C3⋊D9—32no—
23C22×C3⋊D9—31no—
24C22×C3⋊D9—39no—
25(C3⋊D3)⋊A4—93no—
26A4×D9—93no—
27D9⋊A4—96no—
28C2×C32×C9—31no—
29C3⋊(C3⋊D9)—31no—
30C3⋊(C3⋊D9)A411yescharacteristic, complemented
31#4207—129no—
32C3⋊AGL(1,ℤ/9)—122no—
33C3⋊((C3⋊D3)⋊C3)—121no—
34C3×C3⋊D9—121no—
35C22×C33C3×D311yescharacteristic
36C2×C3⋊(C3⋊D3)—91no—
37C2×C3⋊(C3⋊D3)—91no—
38C32×A4—21no—
39C32×A4C3⋊D311yescharacteristic
40C22×C3×C9C3×D311yescharacteristic
41C22×C3×C9C3×D312yes—
42C22×C3×C9C3×D319yescomplemented
43C2×C3⋊D9—91no—
44C2×C3⋊D9—92no—
45C2×C3⋊D9—99no—
46C2×C3⋊D9—92no—
47C2×C3⋊D9—91no—
48C2×C3⋊D9—99no—
49C22⋊H(3,𝔽3)—23no—
50C22⋊H(3,𝔽3)C3⋊D313yes—
51#1094—29no—
52C3×C22⋊C9—22no—
53C3×C22⋊C9—21no—
54C9⋊A4—218no—
55C9⋊A4—26no—
56C9⋊A4C3⋊D316yescomplemented
57C9×A4—29no—
58C9×A4—23no—
59C9×A4C3⋊D313yescomplemented
60#737—49no—
61#737—89no—
62C3×3−1+2—42no—
63C3×3−1+2—81no—
64C3×3−1+2—82no—
65C3×H(3,𝔽3)—41no—
66C32×C9—41no—
67C32×C9—81no—
68C32×C9C2×A411yescharacteristic, complemented
69C22×C3⋊D3—91no—
70C22×C3⋊D3—93no—
71C22×C3⋊D3—273no—
72D3×A4—273no—
73D3×A4—271no—
74C22×D9—96no—
75C22×D9—93no—
76C2×C33—31no—
77C3⋊(C3⋊D3)—31no—
78C3⋊(C3⋊D3)—91no—
79C3×C3⋊D3—361no—
80C2×C3×C9—31no—
81C2×C3×C9—32no—
82C2×C3×C9—39no—
83C3⋊D9—31no—
84C3⋊D9—32no—
85C3⋊D9—39no—
86C3⋊D9—91no—
87C3⋊D9—92no—
88C3⋊D9—99no—
89AGL(1,ℤ/9)—366no—
90(C3⋊D3)⋊C3—363no—
91C3×D9—363no—
92C22×C32—33no—
93C22×C32C3×C3⋊D313yes—
94C22×C32C3×C3⋊D311yescharacteristic
95C2×C3⋊D3—271no—
96C2×C3⋊D3—273no—
97C2×C3⋊D3—279no—
98C2×C3⋊D3—279no—
99C2×C3⋊D3—273no—
100C2×C3⋊D3—271no—
101C3×A4—21no—
102C3×A4—23no—
103C3×A4—33no—
104C3×A4—63no—
105C3×A4C3⋊(C3⋊D3)11yescharacteristic
106C22×C9C3×C3⋊D313yes—
107C22×C9C3×C3⋊D316yes—
108C2×D9—273no—
109C2×D9—276no—
110C2×D9—276no—
111C2×D9—273no—
112C22⋊C9—26no—
113C22⋊C9—23no—
114C33—41no—
115C33—81no—
116C33D3×A411yescharacteristic
1173−1+2—46no—
1183−1+2—89no—
1193−1+2—86no—
1203−1+2—818no—
121H(3,𝔽3)—43no—
122H(3,𝔽3)—83no—
123C3×C9—43no—
124C3×C9—81no—
125C3×C9—82no—
126C3×C9—83no—
127C3×C9—89no—
128C3×C9D3×A411yescharacteristic
129C3×C9D3×A412yes—
130C3×C9D3×A419yescomplemented
131C22×D3—273no—
132C22×D3—271no—
133C22×D3—813no—
134C2×A4—811no—
135C2×C32—39no—
136C2×C32—33no—
137C2×C32—31no—
138C3⋊D3—91no—
139C3⋊D3—93no—
140C3⋊D3—273no—
141C3⋊D3—279no—
142C3⋊D3—273no—
143C3⋊D3—271no—
144C3×D3—1081no—
145C3×D3—1083no—
146C2×C9—33no—
147C2×C9—36no—
148D9—93no—
149D9—96no—
150D9—273no—
151D9—276no—
152C22×C3—33no—
153C22×C3#420713yescomplemented
154C22×C3C3×C3⋊(C3⋊D3)11yescharacteristic
155C2×D3—811no—
156C2×D3—813no—
157C2×D3—819no—
158C2×D3—819no—
159C2×D3—811no—
160C2×D3—813no—
161A4—31no—
162A4—61no—
163A4—63no—
164C32—33no—
165C32—41no—
166C32—83no—
167C32—81no—
168C32—123no—
169C32—243no—
170C32A4×C3⋊D313yes—
171C32A4×C3⋊D311yescharacteristic
172C9—83no—
173C9—86no—
174C9A4×C3⋊D313yes—
175C9A4×C3⋊D316yes—
176C23—811noSylow
177C2×C3—39no—
178C2×C3—31no—
179C2×C3—33no—
180C2×C3—3241no—
181D3—271no—
182D3—273no—
183D3—813no—
184D3—819no—
185D3—811no—
186D3—813no—
187C22—2431no—
188C22—2431no—
189C22C3⋊#420711yescharacteristic, complemented
190C3—33no—
191C3—121no—
192C3—241no—
193C3—243no—
194C3#1062007013yescomplemented
195C3A4×C3⋊(C3⋊D3)11yescharacteristic
196C2—31no—
197C2—811no—
198C2—2431no—
subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC22×C32×C9C2×C3
FrattiniC3A4×C3⋊(C3⋊D3)
socleC22×C32C3×C3⋊D3
LCSG ▷ C22×C32×C9
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×#66436C2semidirect
2. C22×C3⋊(C3⋊D9)C3semidirect
8. C22×C32×C9C2×C3semidirect
14. #66436D3semidirect
16. C3×C9⋊A4D3semidirect
18. C3×C9×A4D3semidirect
30. C3⋊(C3⋊D9)A4semidirect
42. C22×C3×C9C3×D3semidirect
56. C9⋊A4C3⋊D3semidirect
59. C9×A4C3⋊D3semidirect
68. C32×C9C2×A4semidirect
130. C3×C9D3×A4semidirect
153. C22×C3#4207semidirect
189. C22C3⋊#4207semidirect
194. C3#10620070semidirect

Maximal subgroups

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

subgroupindex
C3×#664362
C22×C3⋊(C3⋊D9)3
C3⋊((C3⋊D3)⋊A4)3
A4×C3⋊D93
#106200703
C3⋊(D9⋊A4)3
C3⋊#42074