Finite Group Databasebeta

← #13048737

Subgroups — #13048737

Order 1296.

314 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 66 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⋊D9C211yesmaximal, characteristic
2C9×#634C211yesmaximal, characteristic, complemented
3C3×#6226C211yesmaximal, characteristic, complemented
4#10619896C212yesmaximal
5#10619895C212yesmaximal, complemented
6#89040—31nomaximal
7(C3⋊D9)⋊Q8—31nomaximal
8D9×Dic6—31nomaximal
9C2×C3×C3⋊D9C2211yescharacteristic
10C32×C4×C9C2211yescharacteristic
11C9×C3⋊Dic3C2212yes—
12C3×C3⋊Dic9C2212yes—
13C3×C3⋊Dic9C2211yescharacteristic
14C3×C4×C3⋊D3—31no—
15C3×#634—31no—
16C3×#634D311yescharacteristic
17#6296—32no—
18#6294—32no—
19C4×C3⋊D9D311yescharacteristic
20#6226D311yescharacteristic, complemented
21C3×C4×D9—31no—
22C3×C4×D9—61no—
23C9×Dic6—31no—
24C9×Dic6—31no—
25C9×Dic6—61no—
26C3×Dic18—31no—
27C3×Dic18—61no—
28(C3⋊D9)⋊C4—32no—
29Dic3×D9—32no—
30#6189—32no—
31#6189—32no—
32C2×C32×C9C2311yescharacteristic
33C3×C3⋊D9Q812yescomplemented
34#3797—91no—
35D3×Dic6—91no—
36D3×Dic6—91no—
37Q8×D9—91no—
38C2×C3×C3⋊D3—31no—
39C33×C4C2×D311yescharacteristic
40C3×C3⋊Dic3—32no—
41C3×C3⋊Dic3—31no—
42C3×C3⋊Dic3C2×D312yes—
43C2×C3⋊D9C2×D311yescharacteristic
44C2×C3×D9—31no—
45C2×C3×D9—61no—
46C3×C4×C9—21no—
47C3×C4×C9—21no—
48C3×C4×C9—21no—
49C3×C4×C9—41no—
50C3×C4×C9C2×D311yescharacteristic
51C3×C4×C9C2×D311yescharacteristic
52C3⋊Dic9C2×D311yescharacteristic
53C3⋊Dic9C2×D312yes—
54C9×Dic3—32no—
55C9×Dic3—32no—
56C9×Dic3—62no—
57C3×Dic9—31no—
58C3×Dic9—32no—
59C3×Dic9—62no—
60C3×Dic9—61no—
61C32×C9C2×Q811yescharacteristic, complemented, Sylow
62C4×C3⋊D3—31no—
63#634—31no—
64#634D911yescharacteristic, complemented
65C3×C4×D3—91no—
66C3×C4×D3—91no—
67C3×C4×D3—181no—
68C3×Dic6—31no—
69C3×Dic6—31no—
70C3×Dic6—61no—
71C3×Dic6—91no—
72C3×Dic6—91no—
73C3×Dic6—181no—
74#627—92no—
75#627—92no—
76#627—92no—
77#624—92no—
78D3×Dic3—92no—
79D3×Dic3—92no—
80Q8×C9—91no—
81C4×D9—31no—
82C4×D9—61no—
83C4×D9—92no—
84Dic18—31no—
85Dic18—61no—
86Dic18—92no—
87C2×C33C22×D311yescharacteristic
88C3×C3⋊D3—32no—
89C2×C3×C9—21no—
90C2×C3×C9—21no—
91C2×C3×C9—21no—
92C2×C3×C9—41no—
93C2×C3×C9C22×D311yescharacteristic
94C2×C3×C9C22×D311yescharacteristic
95C3⋊D9Dic612yescomplemented
96C3×D9—32no—
97C3×D9—62no—
98D3×Q8—271no—
99D3×Q8—271no—
100C2×Dic6—271no—
101C2×C3⋊D3—31no—
102C2×C3×D3—91no—
103C2×C3×D3—91no—
104C2×C3×D3—181no—
105C32×C4—21no—
106C32×C4—21no—
107C32×C4—21no—
108C32×C4—41no—
109C32×C4C2×D911yescharacteristic
110C32×C4D3211yescharacteristic
111C32×C4D3211yescharacteristic
112C3⋊Dic3—32no—
113C3⋊Dic3—31no—
114C3⋊Dic3C2×D912yes—
115C3×Dic3—32no—
116C3×Dic3—32no—
117C3×Dic3—62no—
118C3×Dic3—92no—
119C3×Dic3—91no—
120C3×Dic3—92no—
121C3×Dic3—91no—
122C3×Dic3—182no—
123C3×Dic3—181no—
124C2×D9—31no—
125C2×D9—61no—
126C4×C9—21no—
127C4×C9—21no—
128C4×C9—41no—
129C4×C9—92no—
130C4×C9D3211yescharacteristic
131Dic9—32no—
132Dic9—31no—
133Dic9—62no—
134Dic9—61no—
135C33D3×Q811yescharacteristic
136C3×C9—21no—
137C3×C9—21no—
138C3×C9—21no—
139C3×C9—41no—
140C3×C9C2×Dic611yescharacteristic, complemented
141C3×C9D3×Q811yescharacteristic, complemented
142C3×Q8—91no—
143C3×Q8—271no—
144C2×C3×C4—271no—
145C2×Dic3—272no—
146C4×D3—91no—
147C4×D3—91no—
148C4×D3—181no—
149C4×D3—272no—
150C4×D3—272no—
151Dic6—31no—
152Dic6—31no—
153Dic6—61no—
154Dic6—91no—
155Dic6—91no—
156Dic6—181no—
157Dic6—272no—
158Dic6—272no—
159Dic6—272no—
160C2×C32—21no—
161C2×C32—21no—
162C2×C32—21no—
163C2×C32—41no—
164C2×C32C22×D911yescharacteristic
165C2×C32C2×D3211yescharacteristic
166C2×C32C2×D3211yescharacteristic
167C3⋊D3—32no—
168C3×D3—92no—
169C3×D3—92no—
170C3×D3—182no—
171C2×C9—21no—
172C2×C9—21no—
173C2×C9—41no—
174C2×C9C2×D3211yescharacteristic
175D9—32no—
176D9—62no—
177C2×Q8—811noSylow
178C22×C3—271no—
179C2×D3—91no—
180C2×D3—91no—
181C2×D3—181no—
182C3×C4—21no—
183C3×C4—21no—
184C3×C4—21no—
185C3×C4—41no—
186C3×C4—92no—
187C3×C4—271no—
188C3×C4—272no—
189C3×C4D3×D911yescharacteristic
190C3×C4D3×D911yescharacteristic
191C3×C4#111311yescharacteristic
192Dic3—32no—
193Dic3—32no—
194Dic3—62no—
195Dic3—92no—
196Dic3—91no—
197Dic3—92no—
198Dic3—91no—
199Dic3—182no—
200Dic3—181no—
201C32—21no—
202C32—21no—
203C32—21no—
204C32—41no—
205C32Q8×D911yescharacteristic, complemented
206C32D3×Dic611yescharacteristic
207C32#379711yescharacteristic
208C9—21no—
209C9—21no—
210C9—41no—
211C9D3×Dic611yescharacteristic, complemented
212Q8—91no—
213Q8—271no—
214Q8—812no—
215C2×C4—271no—
216C2×C4—812no—
217C2×C3—21no—
218C2×C3—21no—
219C2×C3—21no—
220C2×C3—41no—
221C2×C3—272no—
222C2×C3C2×D3×D911yescharacteristic
223C2×C3C2×D3×D911yescharacteristic
224C2×C3C2×#111311yescharacteristic
225D3—92no—
226D3—92no—
227D3—182no—
228C22—271no—
229C4—92no—
230C4—271no—
231C4—272no—
232C4#6643111yescharacteristic
233C3—21no—
234C3—21no—
235C3—21no—
236C3—41no—
237C3D9×Dic611yescharacteristic, complemented
238C3(C3⋊D9)⋊Q811yescharacteristic, complemented
239C3#8904011yescharacteristic
240C2—272no—
241C2C2×#6643111yescharacteristic
subgroupG/H
centerC2C2×#66431
commutator, cosocleC2×C32×C9C23
FrattiniC2×C3C2×#1113
FittingC32×C4×C9C22
socleC2×C33C22×D3
prime radicalC2×C3×C3⋊D9C22
hypercenterC4#66431
hypocenterC32×C9C2×Q8
LCSG ▷ C2×C32×C9 ▷ C32×C9
UCSC1 ◁ C2 ◁ C4

Complements

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

NH ≅ G/Ntype
2. C9×#634C2semidirect
3. C3×#6226C2semidirect
5. #10619895C2semidirect
20. #6226D3semidirect
33. C3×C3⋊D9Q8semidirect
61. C32×C9C2×Q8semidirect
64. #634D9semidirect
95. C3⋊D9Dic6semidirect
140. C3×C9C2×Dic6semidirect
141. C3×C9D3×Q8semidirect
205. C32Q8×D9semidirect
211. C9D3×Dic6semidirect
237. C3D9×Dic6semidirect
238. C3(C3⋊D9)⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C3×C4×C3⋊D92
C9×#6342
C3×#62262
#106198962
#106198952
#890403
(C3⋊D9)⋊Q83
D9×Dic63