Finite Group Databasebeta

← #13049721

Subgroups — #13049721

Order 1296.

1140 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 1140 conjugacy classes of subgroups — too many to draw. Only its 119 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×C32×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×C3⋊#1113C211yesmaximal, characteristic, complemented
3C3×#6312C212yesmaximal, complemented
4#10620157C212yesmaximal, complemented
5#10620155C211yesmaximal, characteristic, complemented
6#89049—34nomaximal
7D3×#638—32nomaximal
8C22×C34C2211yescharacteristic, complemented
9C2×C3×C3⋊(C3⋊D3)C2212yescomplemented
10C2×C32×C3⋊D3—22no—
11C2×C32×C3⋊D3C2211yescharacteristic
12C2×C32×C3⋊D3C2211yescharacteristic, complemented
13C3⋊#1113—22no—
14C3×C3⋊(C3⋊Dic3)C2212yescomplemented
15C22×C3×C3⋊D3D314yescomplemented
16C22×C32×D3—32no—
17C22×C32×D3—61no—
18C2×#1113—34no—
19C2×D3×C3⋊D3—32no—
20#6312D312yescomplemented
21C3×#638—32no—
22C3×#638—38no—
23C3×#638—68no—
24#6295—38no—
25#6294—34no—
26#6291—32no—
27#6290—32no—
28D3×C3⋊Dic3—32no—
29C2×C34—21no—
30C2×C34C2311yescharacteristic
31C3×C3⋊(C3⋊D3)—22no—
32C32×C3⋊D3—21no—
33C32×C3⋊D3D412yescomplemented
34C2×#638—91no—
35#3811—91no—
36D3×#67—98no—
37C22×C33—21no—
38C22×C33—28no—
39C22×C33—44no—
40C22×C33C2×D312yescomplemented
41C22×C33C2×D314yescomplemented
42C2×C3⋊(C3⋊D3)C2×D312yescomplemented
43C2×C3×C3⋊D3—28no—
44C2×C3×C3⋊D3—32no—
45C2×C3×C3⋊D3—38no—
46C2×C3×C3⋊D3—68no—
47C2×C3×C3⋊D3C2×D314yes—
48C2×C3×C3⋊D3C2×D314yescomplemented
49C2×C32×D3—32no—
50C2×C32×D3—32no—
51C2×C32×D3—64no—
52C2×C32×D3—61no—
53C2×C32×D3—61no—
54C2×C32×D3—64no—
55#1113—68no—
56D3×C3⋊D3—64no—
57C3⋊(C3⋊Dic3)C2×D312yescomplemented
58C3×C3⋊Dic3—32no—
59C3×C3⋊Dic3—38no—
60C3×C3⋊Dic3—68no—
61C34C2×D411yescharacteristic, complemented, Sylow
62C23×C32—91no—
63C22×C3⋊D3—91no—
64C22×C3⋊D3C3⋊D311yescharacteristic, complemented
65C22×C3×D3—38no—
66C22×C3×D3—64no—
67C2×D32—98no—
68C2×D32—91no—
69#638—32no—
70#638—38no—
71#638—68no—
72#638—92no—
73C2×C3⋊Dic3—91no—
74C3×#67—98no—
75C3×#67—92no—
76C3×#67—188no—
77#626—98no—
78#626—92no—
79#625—98no—
80#624—91no—
81D3×Dic3—98no—
82C2×C33—22no—
83C2×C33—22no—
84C2×C33—24no—
85C2×C33—28no—
86C2×C33—21no—
87C2×C33—44no—
88C2×C33—48no—
89C2×C33—48no—
90C2×C33C22×D312yes—
91C2×C33C22×D314yes—
92C3⋊(C3⋊D3)—22no—
93C3×C3⋊D3—24no—
94C3×C3⋊D3—62no—
95C3×C3⋊D3—68no—
96C3×C3⋊D3—128no—
97C3×C3⋊D3#6718yescomplemented
98C32×D3—34no—
99C32×D3—62no—
100C32×D3—62no—
101C32×D3—62no—
102C2×#67—274no—
103D3×D4—272no—
104C22×C32—28no—
105C22×C32—28no—
106C22×C32—24no—
107C22×C32—44no—
108C22×C32—412no—
109C22×C32—44no—
110C22×C32—91no—
111C22×C32—91no—
112C22×C32—182no—
113C22×C32D3218yescomplemented
114C22×C32D3211yescharacteristic, complemented
115C22×C32C2×C3⋊D311yescharacteristic, complemented
116C2×C3⋊D3—22no—
117C2×C3⋊D3—32no—
118C2×C3⋊D3—38no—
119C2×C3⋊D3—68no—
120C2×C3⋊D3—182no—
121C2×C3⋊D3C2×C3⋊D311yescharacteristic
122C2×C3⋊D3C2×C3⋊D311yescharacteristic, complemented
123C2×C3×D3—38no—
124C2×C3×D3—38no—
125C2×C3×D3—64no—
126C2×C3×D3—64no—
127C2×C3×D3—616no—
128C2×C3×D3—616no—
129C2×C3×D3—98no—
130C2×C3×D3—92no—
131C2×C3×D3—188no—
132D32—1816no—
133D32—182no—
134C3⋊Dic3—32no—
135C3⋊Dic3—38no—
136C3⋊Dic3—68no—
137C3×Dic3—98no—
138C3×Dic3—92no—
139C3×Dic3—188no—
140C33—28no—
141C33—21no—
142C33—44no—
143C33D3×D412yescomplemented
144C33C2×#6714yescomplemented
145C23×C3—94no—
146C22×D3—32no—
147C22×D3—61no—
148C22×D3—272no—
149C22×D3—274no—
150C3×D4—272no—
151#67—92no—
152#67—98no—
153#67—188no—
154#67—272no—
155#67—278no—
156C2×Dic3—274no—
157D12—272no—
158C4×D3—272no—
159C2×C32—21no—
160C2×C32—21no—
161C2×C32—28no—
162C2×C32—28no—
163C2×C32—28no—
164C2×C32—28no—
165C2×C32—24no—
166C2×C32—44no—
167C2×C32—412no—
168C2×C32—48no—
169C2×C32—48no—
170C2×C32—48no—
171C2×C32—48no—
172C2×C32—424no—
173C2×C32—44no—
174C2×C32—92no—
175C2×C32—181no—
176C2×C32C2×D3218yes—
177C2×C32C2×D3211yescharacteristic
178C2×C32C22×C3⋊D311yescharacteristic
179C3⋊D3—21no—
180C3⋊D3—62no—
181C3⋊D3—68no—
182C3⋊D3—128no—
183C3⋊D3#63812yescomplemented
184C3×D3—316no—
185C3×D3—68no—
186C3×D3—68no—
187C3×D3—68no—
188C3×D3—188no—
189C3×D3—182no—
190C3×D3—368no—
191C2×D4—811noSylow
192C22×C3—21no—
193C22×C3—28no—
194C22×C3—44no—
195C22×C3—94no—
196C22×C3—94no—
197C22×C3—188no—
198C22×C3—272no—
199C22×C3D3×C3⋊D312yescomplemented
200C22×C3#111314yescomplemented
201C2×D3—32no—
202C2×D3—32no—
203C2×D3—61no—
204C2×D3—61no—
205C2×D3—64no—
206C2×D3—64no—
207C2×D3—92no—
208C2×D3—98no—
209C2×D3—188no—
210C2×D3—544no—
211C2×D3—548no—
212C3×C4—272no—
213Dic3—92no—
214Dic3—98no—
215Dic3—188no—
216C32—28no—
217C32—28no—
218C32—24no—
219C32—44no—
220C32—412no—
221C32—44no—
222C32D3×#6718yescomplemented
223C32#381111yescharacteristic, complemented
224C32C2×#63811yescharacteristic, complemented
225C23—91no—
226C23—811no—
227D4—272no—
228D4—812no—
229C2×C4—811no—
230C2×C3—22no—
231C2×C3—22no—
232C2×C3—24no—
233C2×C3—28no—
234C2×C3—21no—
235C2×C3—48no—
236C2×C3—48no—
237C2×C3—44no—
238C2×C3—98no—
239C2×C3—184no—
240C2×C3—542no—
241C2×C3C2×D3×C3⋊D312yes—
242C2×C3C2×#111314yes—
243D3—34no—
244D3—62no—
245D3—62no—
246D3—62no—
247D3—182no—
248D3—188no—
249D3—368no—
250C22—91no—
251C22—91no—
252C22—182no—
253C22—272no—
254C22—1622no—
255C22C3⋊#111311yescharacteristic, complemented
256C4—272no—
257C3—21no—
258C3—28no—
259C3—44no—
260C3D3×#63812yescomplemented
261C3#8904914yescomplemented
262C2—21no—
263C2—92no—
264C2—181no—
265C2—542no—
266C2C2×C3⋊#111311yescharacteristic
subgroupG/H
center, FrattiniC2C2×C3⋊#1113
commutator, socle, cosocleC2×C34C23
FittingC22×C34C22
hypercenterC22C3⋊#1113
hypocenterC34C2×D4
LCSG ▷ C2×C34 ▷ C34
UCSC1 ◁ C2 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C22×C32×C3⋊D3C2semidirect
2. C2×C3⋊#1113C2semidirect
3. C3×#6312C2semidirect
4. #10620157C2semidirect
5. #10620155C2semidirect
8. C22×C34C22semidirect
9. C2×C3×C3⋊(C3⋊D3)C22semidirect
12. C2×C32×C3⋊D3C22semidirect
14. C3×C3⋊(C3⋊Dic3)C22semidirect
15. C22×C3×C3⋊D3D3semidirect
20. #6312D3semidirect
33. C32×C3⋊D3D4semidirect
40. C22×C33C2×D3semidirect
41. C22×C33C2×D3semidirect
42. C2×C3⋊(C3⋊D3)C2×D3semidirect
48. C2×C3×C3⋊D3C2×D3semidirect
57. C3⋊(C3⋊Dic3)C2×D3semidirect
61. C34C2×D4semidirect
64. C22×C3⋊D3C3⋊D3semidirect
97. C3×C3⋊D3#67semidirect
113. C22×C32D32semidirect
114. C22×C32D32semidirect
115. C22×C32C2×C3⋊D3semidirect
122. C2×C3⋊D3C2×C3⋊D3semidirect
143. C33D3×D4semidirect
144. C33C2×#67semidirect
183. C3⋊D3#638semidirect
199. C22×C3D3×C3⋊D3semidirect
200. C22×C3#1113semidirect
222. C32D3×#67semidirect
223. C32#3811semidirect
224. C32C2×#638semidirect
255. C22C3⋊#1113semidirect
260. C3D3×#638semidirect
261. C3#89049semidirect

Maximal subgroups

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

subgroupindex
C22×C32×C3⋊D32
C2×C3⋊#11132
C3×#63122
#106201572
#106201552
#890493
D3×#6383