Finite Group Databasebeta

← #13048738

Subgroups — #13048738

Order 1296.

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

normal subgroups only

This group has 332 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
1C4×C9×C3⋊D3C211yesmaximal, characteristic, complemented
2C3×C4⋊(C3⋊D9)C211yesmaximal, characteristic, complemented
3C3×#6226C211yesmaximal, characteristic, complemented
4#10619899C212yesmaximal, complemented
5#10619896C212yesmaximal, complemented
6#89041—31nomaximal
7#88642—31nomaximal
8#88641—31nomaximal
9C2×C9×C3⋊D3C2211yescharacteristic
10C2×C3×C3⋊D9C2212yes—
11C32×C4×C9C2211yescharacteristic
12C9×C3⋊Dic3C2211yescharacteristic
13C3×C3⋊Dic9C2212yes—
14C3×C4⋊(C3⋊D3)—31no—
15C3×C4×C3⋊D3D311yescharacteristic
16C3×#634—31no—
17#6295—32no—
18#6294—32no—
19C4⋊(C3⋊D9)D311yescharacteristic, complemented
20#6226D311yescharacteristic, complemented
21C4×D3×C9—31no—
22C4×D3×C9—31no—
23C4×D3×C9—61no—
24C3×D36—31no—
25C3×D36—61no—
26C3×Dic18—31no—
27C3×Dic18—61no—
28#6195—32no—
29#6194—32no—
30(C3⋊D9)⋊C4—32no—
31Dic3×D9—32no—
32C2×C32×C9C2311yescharacteristic
33C9×C3⋊D3—21no—
34C3×C3⋊D9—22no—
35#3799—91no—
36#3796—91no—
37#3795—91no—
38#3697—91no—
39C2×C3×C3⋊D3—32no—
40C2×C3×C3⋊D3C2×D311yescharacteristic
41C33×C4C2×D311yescharacteristic
42C3×C3⋊Dic3—32no—
43C3×C3⋊Dic3C2×D311yescharacteristic
44C2×C3⋊D9C2×D312yes—
45C2×D3×C9—31no—
46C2×D3×C9—31no—
47C2×D3×C9—61no—
48C2×C3×D9—32no—
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×D312yes—
57C9×Dic3—31no—
58C9×Dic3—31no—
59C9×Dic3—61no—
60C3×Dic9—32no—
61C3×Dic9—62no—
62C32×C9#4111yescharacteristic, complemented, Sylow
63C4⋊(C3⋊D3)—31no—
64C4×C3⋊D3D911yescharacteristic, complemented
65#634—31no—
66C3×D12—91no—
67C3×D12—91no—
68C3×D12—181no—
69C3×C4×D3—31no—
70C3×C4×D3—31no—
71C3×C4×D3—61no—
72C3×Dic6—91no—
73C3×Dic6—91no—
74C3×Dic6—181no—
75#626—92no—
76#626—92no—
77#625—92no—
78#624—92no—
79D3×Dic3—92no—
80D3×Dic3—92no—
81C2×C4×C9—91no—
82#611—92no—
83D36—31no—
84D36—61no—
85C4×D9—92no—
86Dic18—31no—
87Dic18—61no—
88C2×C33C22×D311yescharacteristic
89C3×C3⋊D3—21no—
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—22no—
98D3×C9—62no—
99D3×C9—61no—
100D3×C9—61no—
101C3×D9—62no—
102C3×D9—122no—
103#239—271no—
104#237—271no—
105#235—271no—
106C2×C3⋊D3—32no—
107C2×C3⋊D3C2×D911yescharacteristic
108C2×C3×D3—31no—
109C2×C3×D3—31no—
110C2×C3×D3—61no—
111C2×C3×D3—92no—
112C2×C3×D3—92no—
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—32no—
122C3⋊Dic3C2×D911yescharacteristic
123C3×Dic3—31no—
124C3×Dic3—31no—
125C3×Dic3—61no—
126C3×Dic3—92no—
127C3×Dic3—92no—
128C3×Dic3—182no—
129C22×C9—91no—
130C2×D9—32no—
131C2×D9—62no—
132C4×C9—21no—
133C4×C9—21no—
134C4×C9—41no—
135C4×C9—91no—
136C4×C9D3211yescharacteristic
137Dic9—32no—
138Dic9—62no—
139C33#23511yescharacteristic
140C3×C9—21no—
141C3×C9—21no—
142C3×C9—21no—
143C3×C9—41no—
144C3×C9#23711yescharacteristic, complemented
145C3×C9#23911yescharacteristic, complemented
146C3×Q8—271no—
147C3×D4—271no—
148C2×C3×C4—91no—
149#67—272no—
150#67—272no—
151C2×Dic3—272no—
152D12—91no—
153D12—91no—
154D12—181no—
155D12—272no—
156C4×D3—31no—
157C4×D3—31no—
158C4×D3—61no—
159C4×D3—272no—
160C4×D3—272no—
161Dic6—91no—
162Dic6—91no—
163Dic6—181no—
164C2×C32—21no—
165C2×C32—21no—
166C2×C32—21no—
167C2×C32—41no—
168C2×C32C22×D911yescharacteristic
169C2×C32C2×D3211yescharacteristic
170C2×C32C2×D3211yescharacteristic
171C3⋊D3—21no—
172C3⋊D3—62no—
173C3×D3—62no—
174C3×D3—61no—
175C3×D3—61no—
176C3×D3—182no—
177C3×D3—182no—
178C3×D3—362no—
179C2×C9—21no—
180C2×C9—21no—
181C2×C9—41no—
182C2×C9—181no—
183C2×C9C2×D3211yescharacteristic
184D9—62no—
185D9—122no—
186#41—811noSylow
187C22×C3—91no—
188C22×C3—272no—
189C2×D3—31no—
190C2×D3—31no—
191C2×D3—61no—
192C2×D3—92no—
193C2×D3—92no—
194C2×D3—182no—
195C3×C4—21no—
196C3×C4—21no—
197C3×C4—21no—
198C3×C4—41no—
199C3×C4—91no—
200C3×C4—272no—
201C3×C4D3×D911yescharacteristic
202C3×C4D3×D911yescharacteristic
203C3×C4#111311yescharacteristic
204Dic3—31no—
205Dic3—31no—
206Dic3—61no—
207Dic3—92no—
208Dic3—92no—
209Dic3—182no—
210C32—21no—
211C32—21no—
212C32—21no—
213C32—41no—
214C32#369711yescharacteristic, complemented
215C32#379511yescharacteristic
216C32#379911yescharacteristic
217C9—21no—
218C9—21no—
219C9—41no—
220C9#379611yescharacteristic, complemented
221Q8—271no—
222D4—271no—
223D4—812no—
224C2×C4—91no—
225C2×C4—812no—
226C2×C3—21no—
227C2×C3—21no—
228C2×C3—21no—
229C2×C3—41no—
230C2×C3—181no—
231C2×C3—542no—
232C2×C3C2×D3×D911yescharacteristic
233C2×C3C2×D3×D911yescharacteristic
234C2×C3C2×#111311yescharacteristic
235D3—62no—
236D3—61no—
237D3—61no—
238D3—182no—
239D3—182no—
240D3—362no—
241C22—91no—
242C22—272no—
243C4—91no—
244C4—272no—
245C4#6643111yescharacteristic
246C3—21no—
247C3—21no—
248C3—21no—
249C3—41no—
250C3#8864111yescharacteristic, complemented
251C3#8864211yescharacteristic, complemented
252C3#8904111yescharacteristic
253C2—181no—
254C2—542no—
255C2C2×#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. C4×C9×C3⋊D3C2semidirect
2. C3×C4⋊(C3⋊D9)C2semidirect
3. C3×#6226C2semidirect
4. #10619899C2semidirect
5. #10619896C2semidirect
19. C4⋊(C3⋊D9)D3semidirect
20. #6226D3semidirect
62. C32×C9#41semidirect
64. C4×C3⋊D3D9semidirect
144. C3×C9#237semidirect
145. C3×C9#239semidirect
214. C32#3697semidirect
220. C9#3796semidirect
250. C3#88641semidirect
251. C3#88642semidirect

Maximal subgroups

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

subgroupindex
C4×C9×C3⋊D32
C3×C4⋊(C3⋊D9)2
C3×#62262
#106198992
#106198962
#890413
#886423
#886413