Finite Group Databasebeta

← C2×#10619879 #13048701

Subgroups — C2×#10619879 #13048701

Order 1296.

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

normal subgroups only

This group has 660 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⋊D9C211yesmaximal, characteristic, complemented
2C22×C3×D3×C9C211yesmaximal, characteristic, complemented
3C2×C3⋊(C3⋊Dic9)C211yesmaximal, characteristic, complemented
4#10619879C214yesmaximal, direct product factor
5C2×#6290—31nomaximal
6C2×#6233—31nomaximal
7C2×#6194—33nomaximal
8C22×C32×C9C2211yescharacteristic
9C2×C3×C3⋊D9—22no—
10C2×C3×C3⋊D9C2212yescomplemented
11C2×C3×D3×C9—22no—
12C2×C3×D3×C9C2212yescomplemented
13C3⋊(C3⋊Dic9)C2212yescomplemented
14C22×C3×C3⋊D3—31no—
15C22×C32×D3D311yescharacteristic
16C2×C3⋊(C3⋊Dic3)—31no—
17#6290—34no—
18C23×C3×C9—31no—
19C22×C3⋊D9D311yescharacteristic, complemented
20C22×D3×C9D313yescomplemented
21C22×C3×D9—33no—
22#6233—34no—
23C2×C3⋊Dic9—31no—
24C2×C3⋊Dic9—33no—
25C2×C3⋊Dic9—63no—
26C2×C3⋊Dic9—61no—
27#6194—312no—
28C2×C32×C9D412yescomplemented
29C2×C32×C9C2311yescharacteristic
30C3×C3⋊D9—22no—
31C3×D3×C9—22no—
32C2×#638—91no—
33C2×#625—93no—
34C2×#625—91no—
35C2×#611—93no—
36C22×C33C2×D311yescharacteristic
37C2×C3×C3⋊D3—32no—
38C2×C3×C3⋊D3—62no—
39C2×C32×D3—22no—
40C2×C32×D3C2×D312yes—
41C3⋊(C3⋊Dic3)—32no—
42C22×C3×C9—21no—
43C22×C3×C9—23no—
44C22×C3×C9—32no—
45C22×C3×C9—62no—
46C22×C3×C9C2×D313yes—
47C22×C3×C9C2×D311yescharacteristic
48C2×C3⋊D9—22no—
49C2×C3⋊D9C2×D312yescomplemented
50C2×D3×C9—26no—
51C2×D3×C9C2×D316yescomplemented
52C2×C3×D9—36no—
53C2×C3×D9—66no—
54C3⋊Dic9—32no—
55C3⋊Dic9—36no—
56C3⋊Dic9—66no—
57C3⋊Dic9—62no—
58C32×C9C2×D411yescharacteristic, complemented, Sylow
59C23×C32—31no—
60C22×C3⋊D3—31no—
61C22×C3×D3—93no—
62C22×C3×D3—91no—
63C22×C3×D3D913yescomplemented
64C22×C3×D3C3⋊D311yescharacteristic
65#638—94no—
66C2×C3⋊Dic3—91no—
67C2×C3⋊Dic3—93no—
68C2×C3⋊Dic3—91no—
69C2×C3⋊Dic3—181no—
70C2×C3⋊Dic3—183no—
71#625—912no—
72#625—94no—
73C23×C9—33no—
74C22×D9—33no—
75#611—912no—
76C2×Dic9—93no—
77C2×Dic9—183no—
78C2×C33#6712yes—
79C2×C33C22×D311yescharacteristic
80C3×C3⋊D3—62no—
81C32×D3—22no—
82C2×C3×C9—22no—
83C2×C3×C9—21no—
84C2×C3×C9—26no—
85C2×C3×C9—23no—
86C2×C3×C9—62no—
87C2×C3×C9#6716yescomplemented
88C2×C3×C9#6712yescomplemented
89C2×C3×C9C22×D313yes—
90C2×C3×C9C22×D311yescharacteristic
91C3⋊D9—22no—
92D3×C9—26no—
93C3×D9—66no—
94C2×#67—271no—
95C2×#67—273no—
96C2×#67—271no—
97C22×C32—23no—
98C22×C32—21no—
99C22×C32—32no—
100C22×C32—62no—
101C22×C32C2×D913yes—
102C22×C32D3211yescharacteristic
103C22×C32C2×C3⋊D311yescharacteristic
104C2×C3⋊D3—32no—
105C2×C3⋊D3—62no—
106C2×C3×D3—26no—
107C2×C3×D3—22no—
108C2×C3×D3—96no—
109C2×C3×D3—92no—
110C2×C3×D3—186no—
111C2×C3×D3—182no—
112C2×C3×D3C2×D916yescomplemented
113C2×C3×D3C2×C3⋊D312yes—
114C3⋊Dic3—92no—
115C3⋊Dic3—96no—
116C3⋊Dic3—92no—
117C3⋊Dic3—182no—
118C3⋊Dic3—186no—
119C22×C9—23no—
120C22×C9—36no—
121C22×C9—66no—
122C22×C9D3213yes—
123C2×D9—36no—
124C2×D9—66no—
125Dic9—96no—
126Dic9—186no—
127C33C2×#6711yescharacteristic
128C3×C9—21no—
129C3×C9—23no—
130C3×C9C2×#6713yescomplemented
131C3×C9C2×#6711yescharacteristic, complemented
132C23×C3—33no—
133C23×C3—31no—
134C23×C3—271no—
135C22×D3—93no—
136C22×D3—91no—
137C22×D3C3⋊D911yescharacteristic, complemented
138#67—274no—
139#67—2712no—
140#67—274no—
141C2×Dic3—273no—
142C2×Dic3—271no—
143C2×Dic3—271no—
144C2×Dic3—543no—
145C2×Dic3—541no—
146C2×C32—26no—
147C2×C32—23no—
148C2×C32—22no—
149C2×C32—21no—
150C2×C32—62no—
151C2×C32#61116yescomplemented
152C2×C32C22×D913yes—
153C2×C32#62512yes—
154C2×C32#63812yes—
155C2×C32C2×D3211yescharacteristic
156C2×C32C22×C3⋊D311yescharacteristic
157C3⋊D3—62no—
158C3×D3—26no—
159C3×D3—22no—
160C3×D3—186no—
161C3×D3—182no—
162C2×C9—26no—
163C2×C9—23no—
164C2×C9—66no—
165C2×C9#62516yescomplemented
166C2×C9C2×D3213yes—
167D9—66no—
168C2×D4—811noSylow
169C22×C3—23no—
170C22×C3—21no—
171C22×C3—36no—
172C22×C3—32no—
173C22×C3—66no—
174C22×C3—62no—
175C22×C3—272no—
176C22×C3—542no—
177C22×C3D3×D913yes—
178C22×C3C2×C3⋊D911yescharacteristic
179C22×C3D3×C3⋊D311yescharacteristic
180C2×D3—22no—
181C2×D3—96no—
182C2×D3—92no—
183C2×D3—186no—
184C2×D3—182no—
185C2×D3C2×C3⋊D912yescomplemented
186Dic3—276no—
187Dic3—272no—
188Dic3—272no—
189Dic3—546no—
190Dic3—542no—
191C32—23no—
192C32—21no—
193C32C2×#61113yescomplemented
194C32C2×#62511yescharacteristic
195C32C2×#63811yescharacteristic
196C9—23no—
197C9C2×#62513yescomplemented
198C23—31no—
199C23—271no—
200D4—814no—
201C2×C4—811no—
202C2×C3—23no—
203C2×C3—21no—
204C2×C3—26no—
205C2×C3—22no—
206C2×C3—66no—
207C2×C3—62no—
208C2×C3—542no—
209C2×C3#619416yescomplemented
210C2×C3#623312yescomplemented
211C2×C3C2×D3×D913yes—
212C2×C3C22×C3⋊D911yescharacteristic
213C2×C3#629012yes—
214C2×C3C2×D3×C3⋊D311yescharacteristic
215D3—22no—
216D3—186no—
217D3—182no—
218C22—32no—
219C22—62no—
220C22—272no—
221C22—542no—
222C22D3×C3⋊D911yescharacteristic
223C4—812no—
224C3—23no—
225C3—21no—
226C3C2×#619413yescomplemented
227C3C2×#623311yescharacteristic, complemented
228C3C2×#629011yescharacteristic
229C2—62no—
230C2—542no—
231C2#1061987912yesdirect product factor
232C2C2×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⋊D9C2semidirect
2. C22×C3×D3×C9C2semidirect
3. C2×C3⋊(C3⋊Dic9)C2semidirect
4. #10619879C2direct (N × H)
10. C2×C3×C3⋊D9C22semidirect
12. C2×C3×D3×C9C22semidirect
13. C3⋊(C3⋊Dic9)C22semidirect
19. C22×C3⋊D9D3semidirect
20. C22×D3×C9D3semidirect
28. C2×C32×C9D4semidirect
49. C2×C3⋊D9C2×D3semidirect
51. C2×D3×C9C2×D3semidirect
58. C32×C9C2×D4semidirect
63. C22×C3×D3D9semidirect
87. C2×C3×C9#67semidirect
88. C2×C3×C9#67semidirect
112. C2×C3×D3C2×D9semidirect
130. C3×C9C2×#67semidirect
131. C3×C9C2×#67semidirect
137. C22×D3C3⋊D9semidirect
151. C2×C32#611semidirect
165. C2×C9#625semidirect
185. C2×D3C2×C3⋊D9semidirect
193. C32C2×#611semidirect
197. C9C2×#625semidirect
209. C2×C3#6194semidirect
210. C2×C3#6233semidirect
226. C3C2×#6194semidirect
227. C3C2×#6233semidirect
231. C2#10619879direct (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⋊D92
C22×C3×D3×C92
C2×C3⋊(C3⋊Dic9)2
#106198792
C2×#62903
C2×#62333
C2×#61943