Finite Group Databasebeta

← #13048739

Subgroups — #13048739

Order 1296.

334 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 62 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×C4⋊(C3⋊D9)C211yesmaximal, characteristic, complemented
2C3×C4×C3⋊D9C211yesmaximal, characteristic, complemented
3C9×#634C211yesmaximal, characteristic, complemented
4#10619897C212yesmaximal, complemented
5#10619896C212yesmaximal, complemented
6#89041—31nomaximal
7#88635—31nomaximal
8#88634—31nomaximal
9C2×C3×C3⋊D9C2211yescharacteristic
10C2×C3×C3⋊D9C2212yes—
11C32×C4×C9C2211yescharacteristic
12C9×C3⋊Dic3C2212yes—
13C3×C3⋊Dic9C2211yescharacteristic
14C3×C4⋊(C3⋊D3)—31no—
15C3×C4×C3⋊D3—31no—
16C3×#634D311yescharacteristic
17#6295—32no—
18#6294—32no—
19C4⋊(C3⋊D9)D311yescharacteristic, complemented
20C4×C3⋊D9D311yescharacteristic, complemented
21C3×D36—31no—
22C3×D36—61no—
23C3×C4×D9—31no—
24C3×C4×D9—61no—
25C9×Dic6—31no—
26C9×Dic6—31no—
27C9×Dic6—61no—
28#6192—32no—
29#6192—32no—
30(C3⋊D9)⋊C4—32no—
31Dic3×D9—32no—
32C2×C32×C9C2311yescharacteristic
33C3×C3⋊D9—21no—
34C3×C3⋊D9—22no—
35#3799—91no—
36#3796—91no—
37#3795—91no—
38#3701—91no—
39C2×C3×C3⋊D3—32no—
40C2×C3×C3⋊D3—31no—
41C33×C4C2×D311yescharacteristic
42C3×C3⋊Dic3—31no—
43C3×C3⋊Dic3C2×D312yes—
44C2×C3⋊D9C2×D312yes—
45C2×C3⋊D9C2×D311yescharacteristic
46C2×C3×D9—32no—
47C2×C3×D9—31no—
48C2×C3×D9—61no—
49C2×C3×D9—62no—
50C3×C4×C9—21no—
51C3×C4×C9—21no—
52C3×C4×C9—21no—
53C3×C4×C9—41no—
54C3×C4×C9C2×D311yescharacteristic
55C3×C4×C9C2×D311yescharacteristic
56C3⋊Dic9C2×D311yescharacteristic
57C9×Dic3—32no—
58C9×Dic3—32no—
59C9×Dic3—62no—
60C3×Dic9—31no—
61C3×Dic9—61no—
62C32×C9#4111yescharacteristic, complemented, Sylow
63C4⋊(C3⋊D3)—31no—
64C4×C3⋊D3—31no—
65#634D911yescharacteristic, complemented
66C3×D12—91no—
67C3×D12—91no—
68C3×D12—181no—
69C3×C4×D3—91no—
70C3×C4×D3—91no—
71C3×C4×D3—181no—
72C3×Dic6—31no—
73C3×Dic6—31no—
74C3×Dic6—61no—
75#626—92no—
76#626—92no—
77#625—92no—
78#624—92no—
79D3×Dic3—92no—
80D3×Dic3—92no—
81Q8×C9—91no—
82D36—31no—
83D36—61no—
84D36—92no—
85C4×D9—31no—
86C4×D9—61no—
87C4×D9—92no—
88C2×C33C22×D311yescharacteristic
89C3×C3⋊D3—61no—
90C3×C3⋊D3—62no—
91C2×C3×C9—21no—
92C2×C3×C9—21no—
93C2×C3×C9—21no—
94C2×C3×C9—41no—
95C2×C3×C9C22×D311yescharacteristic
96C2×C3×C9C22×D311yescharacteristic
97C3⋊D9—21no—
98C3⋊D9—22no—
99C3×D9—62no—
100C3×D9—62no—
101C3×D9—61no—
102C3×D9—122no—
103#239—271no—
104#237—271no—
105#235—271no—
106C2×C3⋊D3—32no—
107C2×C3⋊D3—31no—
108C2×C3×D3—92no—
109C2×C3×D3—91no—
110C2×C3×D3—92no—
111C2×C3×D3—91no—
112C2×C3×D3—181no—
113C2×C3×D3—182no—
114C32×C4—21no—
115C32×C4—21no—
116C32×C4—21no—
117C32×C4—41no—
118C32×C4C2×D911yescharacteristic
119C32×C4D3211yescharacteristic
120C32×C4D3211yescharacteristic
121C3⋊Dic3—31no—
122C3⋊Dic3C2×D912yes—
123C3×Dic3—32no—
124C3×Dic3—32no—
125C3×Dic3—62no—
126C3×Dic3—91no—
127C3×Dic3—91no—
128C3×Dic3—181no—
129C2×D9—31no—
130C2×D9—32no—
131C2×D9—61no—
132C2×D9—62no—
133C4×C9—21no—
134C4×C9—21no—
135C4×C9—41no—
136C4×C9—92no—
137C4×C9D3211yescharacteristic
138Dic9—31no—
139Dic9—61no—
140C33#23911yescharacteristic
141C3×C9—21no—
142C3×C9—21no—
143C3×C9—21no—
144C3×C9—41no—
145C3×C9#23511yescharacteristic, complemented
146C3×C9#23711yescharacteristic, complemented
147C3×Q8—91no—
148C3×D4—271no—
149C2×C3×C4—271no—
150#67—272no—
151#67—272no—
152C2×Dic3—272no—
153D12—91no—
154D12—91no—
155D12—181no—
156D12—272no—
157C4×D3—91no—
158C4×D3—91no—
159C4×D3—181no—
160C4×D3—272no—
161C4×D3—272no—
162Dic6—31no—
163Dic6—31no—
164Dic6—61no—
165C2×C32—21no—
166C2×C32—21no—
167C2×C32—21no—
168C2×C32—41no—
169C2×C32C22×D911yescharacteristic
170C2×C32C2×D3211yescharacteristic
171C2×C32C2×D3211yescharacteristic
172C3⋊D3—61no—
173C3⋊D3—62no—
174C3×D3—182no—
175C3×D3—182no—
176C3×D3—181no—
177C3×D3—181no—
178C3×D3—182no—
179C3×D3—362no—
180C2×C9—21no—
181C2×C9—21no—
182C2×C9—41no—
183C2×C9C2×D3211yescharacteristic
184D9—62no—
185D9—61no—
186D9—62no—
187D9—122no—
188#41—811noSylow
189C22×C3—272no—
190C22×C3—271no—
191C2×D3—91no—
192C2×D3—92no—
193C2×D3—91no—
194C2×D3—92no—
195C2×D3—181no—
196C2×D3—182no—
197C3×C4—21no—
198C3×C4—21no—
199C3×C4—21no—
200C3×C4—41no—
201C3×C4—92no—
202C3×C4—271no—
203C3×C4D3×D911yescharacteristic
204C3×C4D3×D911yescharacteristic
205C3×C4#111311yescharacteristic
206Dic3—32no—
207Dic3—32no—
208Dic3—62no—
209Dic3—91no—
210Dic3—91no—
211Dic3—181no—
212C32—21no—
213C32—21no—
214C32—21no—
215C32—41no—
216C32#370111yescharacteristic, complemented
217C32#379611yescharacteristic
218C32#379911yescharacteristic
219C9—21no—
220C9—21no—
221C9—41no—
222C9#379511yescharacteristic, complemented
223Q8—91no—
224D4—271no—
225D4—812no—
226C2×C4—271no—
227C2×C4—812no—
228C2×C3—21no—
229C2×C3—21no—
230C2×C3—21no—
231C2×C3—41no—
232C2×C3—541no—
233C2×C3—542no—
234C2×C3C2×D3×D911yescharacteristic
235C2×C3C2×D3×D911yescharacteristic
236C2×C3C2×#111311yescharacteristic
237D3—182no—
238D3—182no—
239D3—181no—
240D3—181no—
241D3—182no—
242D3—362no—
243C22—271no—
244C22—272no—
245C4—92no—
246C4—271no—
247C4#6643111yescharacteristic
248C3—21no—
249C3—21no—
250C3—21no—
251C3—41no—
252C3#8863411yescharacteristic, complemented
253C3#8863511yescharacteristic, complemented
254C3#8904111yescharacteristic
255C2—541no—
256C2—542no—
257C2C2×#6643111yescharacteristic
subgroupG/H
centerC2C2×#66431
commutator, cosocleC2×C32×C9C23
FrattiniC2×C3C2×#1113
FittingC32×C4×C9C22
socleC2×C33C22×D3
hypercenterC4#66431
hypocenterC32×C9#41
LCSG ▷ C2×C32×C9 ▷ C32×C9
UCSC1 ◁ C2 ◁ C4

Complements

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

NH ≅ G/Ntype
1. C3×C4⋊(C3⋊D9)C2semidirect
2. C3×C4×C3⋊D9C2semidirect
3. C9×#634C2semidirect
4. #10619897C2semidirect
5. #10619896C2semidirect
19. C4⋊(C3⋊D9)D3semidirect
20. C4×C3⋊D9D3semidirect
62. C32×C9#41semidirect
65. #634D9semidirect
145. C3×C9#235semidirect
146. C3×C9#237semidirect
216. C32#3701semidirect
222. C9#3795semidirect
252. C3#88634semidirect
253. C3#88635semidirect

Maximal subgroups

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

subgroupindex
C3×C4⋊(C3⋊D9)2
C3×C4×C3⋊D92
C9×#6342
#106198972
#106198962
#890413
#886353
#886343