Finite Group Databasebeta

← C2×C9⋊#1113 #14519331

Subgroups — C2×C9⋊#1113 #14519331

Order 1944.

1098 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 1098 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
1C2×C3×C3⋊(C3⋊D9)C212yesmaximal, complemented
2C2×C3×C9×C3⋊D3C211yesmaximal, characteristic, complemented
3C9⋊#1113C214yesmaximal, direct product factor
4C2×C3⋊#1113—31nomaximal
5C2×#66431—33nomaximal
6C2×D3×C3⋊D9—32nomaximal
7C2×C33×C9C2211yescharacteristic, complemented
8C3×C3⋊(C3⋊D9)C2214yescomplemented
9C3×C9×C3⋊D3C2212yescomplemented
10C2×C3×C3⋊(C3⋊D3)—32no—
11C2×C32×C3⋊D3D311yescharacteristic
12C3⋊#1113—34no—
13C2×C3⋊(C3⋊D9)D312yescomplemented
14C2×C9×C3⋊D3D313yescomplemented
15C2×C3×C3⋊D9—32no—
16C2×C3×C3⋊D9—36no—
17C2×C3×C3⋊D9—66no—
18C2×C3×C3⋊D9—62no—
19C2×C3×D3×C9—32no—
20C2×C3×D3×C9—61no—
21#66431—312no—
22D3×C3⋊D9—38no—
23C33×C9C2311yescharacteristic, complemented, Sylow
24C2×#1113—93no—
25C2×#1113—91no—
26C2×D3×C3⋊D3—92no—
27C22×C3⋊D9—91no—
28C2×D3×D9—96no—
29C2×C34C2×D311yescharacteristic
30C3×C3⋊(C3⋊D3)—34no—
31C32×C3⋊D3C2×D312yes—
32C2×C32×C9—22no—
33C2×C32×C9—21no—
34C2×C32×C9—26no—
35C2×C32×C9—43no—
36C2×C32×C9—41no—
37C2×C32×C9C2×D312yescomplemented
38C2×C32×C9C2×D313yescomplemented
39C3⋊(C3⋊D9)C2×D314yescomplemented
40C9×C3⋊D3C2×D316yescomplemented
41C3×C3⋊D9—34no—
42C3×C3⋊D9—312no—
43C3×C3⋊D9—612no—
44C3×C3⋊D9—64no—
45C3×D3×C9—34no—
46C3×D3×C9—62no—
47C2×C3⋊(C3⋊D3)—32no—
48C2×C3×C3⋊D3—96no—
49C2×C3×C3⋊D3—92no—
50C2×C3×C3⋊D3—92no—
51C2×C3×C3⋊D3—182no—
52C2×C3×C3⋊D3—186no—
53C2×C3×C3⋊D3D913yescomplemented
54C2×C3×C3⋊D3C3⋊D311yescharacteristic
55C2×C32×D3—32no—
56C2×C32×D3—61no—
57#1113—912no—
58#1113—94no—
59D3×C3⋊D3—98no—
60C22×C3×C9—91no—
61C2×C3⋊D9—32no—
62C2×C3⋊D9—36no—
63C2×C3⋊D9—66no—
64C2×C3⋊D9—62no—
65C2×C3⋊D9—94no—
66C2×D3×C9—36no—
67C2×D3×C9—63no—
68C2×C3×D9—96no—
69C2×C3×D9—186no—
70D3×D9—924no—
71C34C22×D311yescharacteristic
72C32×C9—22no—
73C32×C9—21no—
74C32×C9—26no—
75C32×C9—43no—
76C32×C9—41no—
77C32×C9C22×D312yescomplemented
78C32×C9C22×D313yescomplemented
79C22×C3⋊D3—271no—
80C2×D32—272no—
81C2×D32—276no—
82C2×D32—271no—
83C22×D9—273no—
84C2×C33—26no—
85C2×C33—22no—
86C2×C33—21no—
87C2×C33—41no—
88C2×C33—43no—
89C2×C33C2×D913yescomplemented
90C2×C33D3212yes—
91C2×C33C2×C3⋊D311yescharacteristic
92C3⋊(C3⋊D3)—34no—
93C3×C3⋊D3—94no—
94C3×C3⋊D3—912no—
95C3×C3⋊D3—94no—
96C3×C3⋊D3—184no—
97C3×C3⋊D3—1812no—
98C3×C3⋊D3C2×D916yescomplemented
99C3×C3⋊D3C2×C3⋊D312yes—
100C32×D3—34no—
101C32×D3—62no—
102C2×C3×C9—22no—
103C2×C3×C9—26no—
104C2×C3×C9—26no—
105C2×C3×C9—23no—
106C2×C3×C9—43no—
107C2×C3×C9—46no—
108C2×C3×C9—46no—
109C2×C3×C9—41no—
110C2×C3×C9—43no—
111C2×C3×C9—92no—
112C2×C3×C9D3216yescomplemented
113C2×C3×C9D3211yescharacteristic, complemented
114C3⋊D9—34no—
115C3⋊D9—312no—
116C3⋊D9—612no—
117C3⋊D9—64no—
118D3×C9—312no—
119D3×C9—66no—
120C3×D9—912no—
121C3×D9—1812no—
122C22×C32—91no—
123C2×C3⋊D3—92no—
124C2×C3⋊D3—96no—
125C2×C3⋊D3—92no—
126C2×C3⋊D3—182no—
127C2×C3⋊D3—186no—
128C2×C3⋊D3—274no—
129C2×C3⋊D3C3⋊D911yescharacteristic, complemented
130C2×C3×D3—36no—
131C2×C3×D3—32no—
132C2×C3×D3—61no—
133C2×C3×D3—63no—
134C2×C3×D3—276no—
135C2×C3×D3—272no—
136C2×C3×D3—272no—
137C2×C3×D3—546no—
138C2×C3×D3—542no—
139D32—278no—
140D32—2724no—
141D32—274no—
142C22×C9—93no—
143C2×D9—96no—
144C2×D9—186no—
145C2×D9—2712no—
146C33—26no—
147C33—22no—
148C33—21no—
149C33—41no—
150C33—43no—
151C33C22×D913yescomplemented
152C33C2×D3212yes—
153C33C22×C3⋊D311yescharacteristic
154C3×C9—22no—
155C3×C9—26no—
156C3×C9—26no—
157C3×C9—23no—
158C3×C9—43no—
159C3×C9—46no—
160C3×C9—46no—
161C3×C9—41no—
162C3×C9—43no—
163C3×C9C2×D3216yescomplemented
164C3×C9C2×D3211yescharacteristic, complemented
165C22×D3—812no—
166C22×D3—811no—
167C22×D3—813no—
168C2×C32—26no—
169C2×C32—22no—
170C2×C32—26no—
171C2×C32—22no—
172C2×C32—23no—
173C2×C32—21no—
174C2×C32—43no—
175C2×C32—41no—
176C2×C32—46no—
177C2×C32—46no—
178C2×C32—43no—
179C2×C32—41no—
180C2×C32—92no—
181C2×C32D3×D916yescomplemented
182C2×C32C2×C3⋊D911yescharacteristic, complemented
183C2×C32D3×C3⋊D312yes—
184C2×C32#111311yescharacteristic
185C3⋊D3—94no—
186C3⋊D3—912no—
187C3⋊D3—94no—
188C3⋊D3—184no—
189C3⋊D3—1812no—
190C3⋊D3C2×C3⋊D912yescomplemented
191C3×D3—312no—
192C3×D3—34no—
193C3×D3—62no—
194C3×D3—66no—
195C3×D3—2712no—
196C3×D3—274no—
197C3×D3—274no—
198C3×D3—5412no—
199C3×D3—544no—
200C2×C9—26no—
201C2×C9—43no—
202C2×C9—96no—
203C2×C9#111313yescomplemented
204D9—912no—
205D9—1812no—
206C22×C3—93no—
207C22×C3—91no—
208C22×C3—812no—
209C2×D3—32no—
210C2×D3—61no—
211C2×D3—272no—
212C2×D3—276no—
213C2×D3—272no—
214C2×D3—546no—
215C2×D3—542no—
216C2×D3—818no—
217C2×D3—814no—
218C2×D3—8112no—
219C32—22no—
220C32—26no—
221C32—21no—
222C32—26no—
223C32—22no—
224C32—23no—
225C32—43no—
226C32—41no—
227C32—46no—
228C32—46no—
229C32—41no—
230C32—43no—
231C32C2×D3×D916yescomplemented
232C32C22×C3⋊D911yescharacteristic, complemented
233C32C2×D3×C3⋊D312yes—
234C32C2×#111311yescharacteristic
235C9—26no—
236C9—43no—
237C9C2×#111313yescomplemented
238C23—2431noSylow
239C2×C3—21no—
240C2×C3—26no—
241C2×C3—22no—
242C2×C3—43no—
243C2×C3—41no—
244C2×C3—92no—
245C2×C3—96no—
246C2×C3—814no—
247C2×C3D3×C3⋊D912yescomplemented
248C2×C3#6643113yescomplemented
249C2×C3C3⋊#111311yescharacteristic
250D3—34no—
251D3—62no—
252D3—274no—
253D3—274no—
254D3—2712no—
255D3—5412no—
256D3—544no—
257C22—91no—
258C22—812no—
259C22—2434no—
260C3—21no—
261C3—26no—
262C3—22no—
263C3—41no—
264C3—43no—
265C3C2×D3×C3⋊D912yescomplemented
266C3C2×#6643113yescomplemented
267C3C2×C3⋊#111311yescharacteristic
268C2—92no—
269C2—814no—
270C2C9⋊#111311yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2C9⋊#1113
commutator, cosocle, hypocenterC33×C9C23
FrattiniC3C2×C3⋊#1113
FittingC2×C33×C9C22
socleC2×C34C2×D3
LCSG ▷ C33×C9
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×C3×C3⋊(C3⋊D9)C2semidirect
2. C2×C3×C9×C3⋊D3C2semidirect
3. C9⋊#1113C2direct (N × H)
7. C2×C33×C9C22semidirect
8. C3×C3⋊(C3⋊D9)C22semidirect
9. C3×C9×C3⋊D3C22semidirect
13. C2×C3⋊(C3⋊D9)D3semidirect
14. C2×C9×C3⋊D3D3semidirect
23. C33×C9C23semidirect
37. C2×C32×C9C2×D3semidirect
38. C2×C32×C9C2×D3semidirect
39. C3⋊(C3⋊D9)C2×D3semidirect
40. C9×C3⋊D3C2×D3semidirect
53. C2×C3×C3⋊D3D9semidirect
77. C32×C9C22×D3semidirect
78. C32×C9C22×D3semidirect
89. C2×C33C2×D9semidirect
98. C3×C3⋊D3C2×D9semidirect
112. C2×C3×C9D32semidirect
113. C2×C3×C9D32semidirect
129. C2×C3⋊D3C3⋊D9semidirect
151. C33C22×D9semidirect
163. C3×C9C2×D32semidirect
164. C3×C9C2×D32semidirect
181. C2×C32D3×D9semidirect
182. C2×C32C2×C3⋊D9semidirect
190. C3⋊D3C2×C3⋊D9semidirect
203. C2×C9#1113semidirect
231. C32C2×D3×D9semidirect
232. C32C22×C3⋊D9semidirect
237. C9C2×#1113semidirect
247. C2×C3D3×C3⋊D9semidirect
248. C2×C3#66431semidirect
265. C3C2×D3×C3⋊D9semidirect
266. C3C2×#66431semidirect
270. C2C9⋊#1113direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C3⋊(C3⋊D9)2
C2×C3×C9×C3⋊D32
C9⋊#11132
C2×C3⋊#11133
C2×#664313
C2×D3×C3⋊D93