Finite Group Databasebeta

← C2×#10619874 #13048694

Subgroups — C2×#10619874 #13048694

Order 1296.

780 conjugacy classes of subgroups; only the 144 normal subgroups are shown.

normal subgroups only

This group has 780 conjugacy classes of subgroups — too many to draw. Only its 144 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
1C22×C3⋊(C3⋊D9)C211yesmaximal, characteristic, complemented
2C22×C3×C3⋊D9C211yesmaximal, characteristic, complemented
3C2×C3×C9×Dic3C211yesmaximal, characteristic, complemented
4#10619874C214yesmaximal, direct product factor
5C2×#6292—31nomaximal
6C2×C4⋊(C3⋊D9)—31nomaximal
7C2×#6192—33nomaximal
8C22×C32×C9C2211yescharacteristic
9C2×C3⋊(C3⋊D9)—22no—
10C2×C3⋊(C3⋊D9)C2212yescomplemented
11C2×C3×C3⋊D9—22no—
12C2×C3×C3⋊D9C2212yescomplemented
13C3×C9×Dic3C2212yescomplemented
14C22×C3⋊(C3⋊D3)—31no—
15C22×C3×C3⋊D3—31no—
16C2×C32×Dic3D311yescharacteristic
17#6292—34no—
18C22×C3⋊D9—31no—
19C22×C3⋊D9—33no—
20C22×C3⋊D9—63no—
21C22×C3⋊D9—61no—
22C22×C3⋊D9D311yescharacteristic, complemented
23C22×C3×D9—33no—
24C2×C3×C4×C9—31no—
25C4⋊(C3⋊D9)—34no—
26C2×C9×Dic3D313yescomplemented
27#6192—312no—
28C2×C32×C9D412yescomplemented
29C2×C32×C9C2311yescharacteristic
30C3⋊(C3⋊D9)—22no—
31C3×C3⋊D9—22no—
32C2×C4⋊(C3⋊D3)—91no—
33C2×#626—93no—
34C2×#626—91no—
35C2×D36—93no—
36C22×C33C2×D311yescharacteristic
37C2×C3⋊(C3⋊D3)—32no—
38C2×C3⋊(C3⋊D3)—62no—
39C2×C3×C3⋊D3—32no—
40C2×C3×C3⋊D3—62no—
41C32×Dic3C2×D312yes—
42C22×C3×C9—21no—
43C22×C3×C9—23no—
44C22×C3×C9C2×D313yes—
45C22×C3×C9C2×D311yescharacteristic
46C2×C3⋊D9—22no—
47C2×C3⋊D9—32no—
48C2×C3⋊D9—36no—
49C2×C3⋊D9—66no—
50C2×C3⋊D9—62no—
51C2×C3⋊D9—64no—
52C2×C3⋊D9—612no—
53C2×C3⋊D9—66no—
54C2×C3⋊D9—62no—
55C2×C3⋊D9C2×D312yescomplemented
56C2×C3×D9—36no—
57C2×C3×D9—66no—
58C3×C4×C9—32no—
59C9×Dic3C2×D316yescomplemented
60C32×C9C2×D411yescharacteristic, complemented, Sylow
61C22×C3⋊D3—31no—
62C22×C3⋊D3—91no—
63C22×C3⋊D3—93no—
64C22×C3⋊D3—91no—
65C22×C3⋊D3—181no—
66C22×C3⋊D3—183no—
67C22×C3×D3—93no—
68C22×C3×D3—91no—
69C2×C32×C4—31no—
70C4⋊(C3⋊D3)—94no—
71C2×C3×Dic3D913yescomplemented
72C2×C3×Dic3C3⋊D311yescharacteristic
73#626—912no—
74#626—94no—
75C22×D9—33no—
76C22×D9—93no—
77C22×D9—183no—
78C2×C4×C9—33no—
79D36—912no—
80C2×C33D1212yes—
81C2×C33C22×D311yescharacteristic
82C3⋊(C3⋊D3)—62no—
83C3×C3⋊D3—62no—
84C2×C3×C9—22no—
85C2×C3×C9—21no—
86C2×C3×C9—26no—
87C2×C3×C9—23no—
88C2×C3×C9D1216yescomplemented
89C2×C3×C9#6712yescomplemented
90C2×C3×C9C22×D313yes—
91C2×C3×C9C22×D311yescharacteristic
92C3⋊D9—22no—
93C3⋊D9—64no—
94C3⋊D9—612no—
95C3⋊D9—66no—
96C3⋊D9—62no—
97C3×D9—66no—
98C2×#67—271no—
99C2×D12—271no—
100C2×D12—273no—
101C22×C32—23no—
102C22×C32—21no—
103C22×C32C2×D913yes—
104C22×C32D3211yescharacteristic
105C22×C32C2×C3⋊D311yescharacteristic
106C2×C3⋊D3—32no—
107C2×C3⋊D3—62no—
108C2×C3⋊D3—92no—
109C2×C3⋊D3—96no—
110C2×C3⋊D3—92no—
111C2×C3⋊D3—182no—
112C2×C3⋊D3—186no—
113C2×C3⋊D3—184no—
114C2×C3⋊D3—1812no—
115C2×C3⋊D3—186no—
116C2×C3⋊D3—182no—
117C2×C3⋊D3—182no—
118C2×C3×D3—96no—
119C2×C3×D3—92no—
120C2×C3×D3—186no—
121C2×C3×D3—182no—
122C32×C4—32no—
123C3×Dic3C2×D916yescomplemented
124C3×Dic3C2×C3⋊D312yes—
125C22×C9—23no—
126C22×C9D3213yes—
127C2×D9—36no—
128C2×D9—66no—
129C2×D9—96no—
130C2×D9—186no—
131C2×D9—1812no—
132C2×D9—186no—
133C4×C9—36no—
134C33C2×D1211yescharacteristic
135C3×C9—21no—
136C3×C9—23no—
137C3×C9C2×D1213yescomplemented
138C3×C9C2×#6711yescharacteristic, complemented
139C23×C3—271no—
140C22×D3—93no—
141C22×D3—91no—
142C22×D3—273no—
143C22×D3—271no—
144C22×D3—271no—
145C22×D3—543no—
146C22×D3—541no—
147C2×C3×C4—33no—
148C2×C3×C4—31no—
149#67—274no—
150C2×Dic3C3⋊D911yescharacteristic, complemented
151D12—274no—
152D12—2712no—
153C2×C32—26no—
154C2×C32—23no—
155C2×C32—22no—
156C2×C32—21no—
157C2×C32D3616yescomplemented
158C2×C32C22×D913yes—
159C2×C32#62612yes—
160C2×C32C4⋊(C3⋊D3)12yes—
161C2×C32C2×D3211yescharacteristic
162C2×C32C22×C3⋊D311yescharacteristic
163C3⋊D3—62no—
164C3⋊D3—184no—
165C3⋊D3—1812no—
166C3⋊D3—186no—
167C3⋊D3—182no—
168C3⋊D3—182no—
169C3×D3—186no—
170C3×D3—182no—
171C2×C9—26no—
172C2×C9—23no—
173C2×C9#62616yescomplemented
174C2×C9C2×D3213yes—
175D9—66no—
176D9—1812no—
177D9—186no—
178C2×D4—811noSylow
179C22×C3—23no—
180C22×C3—21no—
181C22×C3—272no—
182C22×C3—542no—
183C22×C3D3×D913yes—
184C22×C3C2×C3⋊D911yescharacteristic
185C22×C3D3×C3⋊D311yescharacteristic
186C2×D3—96no—
187C2×D3—92no—
188C2×D3—186no—
189C2×D3—182no—
190C2×D3—276no—
191C2×D3—272no—
192C2×D3—272no—
193C2×D3—546no—
194C2×D3—542no—
195C2×D3—5412no—
196C2×D3—544no—
197C2×D3—546no—
198C2×D3—542no—
199C2×D3—542no—
200C3×C4—36no—
201C3×C4—32no—
202Dic3C2×C3⋊D912yescomplemented
203C32—23no—
204C32—21no—
205C32C2×D3613yescomplemented
206C32C2×#62611yescharacteristic
207C32C2×C4⋊(C3⋊D3)11yescharacteristic
208C9—23no—
209C9C2×#62613yescomplemented
210C23—271no—
211C23—811no—
212D4—814no—
213C2×C4—31no—
214C2×C3—23no—
215C2×C3—21no—
216C2×C3—26no—
217C2×C3—22no—
218C2×C3—542no—
219C2×C3#619216yescomplemented
220C2×C3C4⋊(C3⋊D9)12yescomplemented
221C2×C3C2×D3×D913yes—
222C2×C3C22×C3⋊D911yescharacteristic
223C2×C3#629212yes—
224C2×C3C2×D3×C3⋊D311yescharacteristic
225D3—186no—
226D3—182no—
227D3—5412no—
228D3—544no—
229D3—546no—
230D3—542no—
231D3—542no—
232C22—272no—
233C22—542no—
234C22—812no—
235C22—1622no—
236C22D3×C3⋊D911yescharacteristic
237C4—32no—
238C3—23no—
239C3—21no—
240C3C2×#619213yescomplemented
241C3C2×C4⋊(C3⋊D9)11yescharacteristic, complemented
242C3C2×#629211yescharacteristic
243C2—542no—
244C2—1622no—
245C2#1061987412yesdirect product factor
246C2C2×D3×C3⋊D911yescharacteristic
subgroupG/H
center, hypercenterC22D3×C3⋊D9
commutator, cosocleC2×C32×C9C23
FrattiniC2×C3C2×D3×C3⋊D3
FittingC22×C32×C9C22
socleC22×C33C2×D3
hypocenterC32×C9C2×D4
LCSG ▷ C2×C32×C9 ▷ C32×C9
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C22×C3⋊(C3⋊D9)C2semidirect
2. C22×C3×C3⋊D9C2semidirect
3. C2×C3×C9×Dic3C2semidirect
4. #10619874C2direct (N × H)
10. C2×C3⋊(C3⋊D9)C22semidirect
12. C2×C3×C3⋊D9C22semidirect
13. C3×C9×Dic3C22semidirect
22. C22×C3⋊D9D3semidirect
26. C2×C9×Dic3D3semidirect
28. C2×C32×C9D4semidirect
55. C2×C3⋊D9C2×D3semidirect
59. C9×Dic3C2×D3semidirect
60. C32×C9C2×D4semidirect
71. C2×C3×Dic3D9semidirect
88. C2×C3×C9D12semidirect
89. C2×C3×C9#67semidirect
123. C3×Dic3C2×D9semidirect
137. C3×C9C2×D12semidirect
138. C3×C9C2×#67semidirect
150. C2×Dic3C3⋊D9semidirect
157. C2×C32D36semidirect
173. C2×C9#626semidirect
202. Dic3C2×C3⋊D9semidirect
205. C32C2×D36semidirect
209. C9C2×#626semidirect
219. C2×C3#6192semidirect
220. C2×C3C4⋊(C3⋊D9)semidirect
240. C3C2×#6192semidirect
241. C3C2×C4⋊(C3⋊D9)semidirect
245. C2#10619874direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3⋊(C3⋊D9)2
C22×C3×C3⋊D92
C2×C3×C9×Dic32
#106198742
C2×#62923
C2×C4⋊(C3⋊D9)3
C2×#61923