Finite Group Databasebeta

← #13047091

Subgroups — #13047091

Order 1296.

268 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 47 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×#4181C211yesmaximal, characteristic, complemented
2C4×#4169C211yesmaximal, characteristic, complemented
3C4×(C3⋊D3)⋊C9C211yesmaximal, characteristic, complemented
4#10619538C211yesmaximal, characteristic, complemented
5#10619537C211yesmaximal, characteristic, complemented
6#10619536C211yesmaximal, characteristic, complemented
7#10619535C211yesmaximal, characteristic, complemented
8#89042—31nomaximal
9#88640—31nomaximal
10C2×#4181C2211yescharacteristic
11C2×#4169C2211yescharacteristic
12C2×(C3⋊D3)⋊C9C2211yescharacteristic
13C4×C32⋊C9C2211yescharacteristic
14#66328C2211yescharacteristic
15#66316C2211yescharacteristic
16(C3⋊Dic3)⋊C9C2211yescharacteristic
17C3×C4×C3⋊D3—31no—
18C3×C4×C3⋊D3—31no—
19C3×C4×C3⋊D3D311yescharacteristic
20#6296—31no—
21#6295—31no—
22#6295—31no—
23#6295—31no—
24C4×C3⋊D9D311yescharacteristic, complemented
25C4×D3×C9—31no—
26C3×C4×D9—31no—
27C3×C4×D9—61no—
28#6195—31no—
29#6194—31no—
30#6192—31no—
31#6189—31no—
32C2×C32⋊C9C2311yescharacteristic
33#4181—21no—
34#4169—21no—
35(C3⋊D3)⋊C9—21no—
36#3798—91no—
37#3798—91no—
38#3798—91no—
39#3697—91no—
40C2×C3×C3⋊D3—31no—
41C2×C3×C3⋊D3—31no—
42C2×C3×C3⋊D3C2×D311yescharacteristic
43C33×C4C2×D311yescharacteristic
44C3×C3⋊Dic3—31no—
45C3×C3⋊Dic3—31no—
46C3×C3⋊Dic3C2×D311yescharacteristic
47C2×C3⋊D9C2×D311yescharacteristic
48C2×D3×C9—31no—
49C2×C3×D9—31no—
50C2×C3×D9—61no—
51C3×C4×C9—21no—
52C3×C4×C9C2×D311yescharacteristic
53C3⋊Dic9C2×D311yescharacteristic
54C9×Dic3—31no—
55C3×Dic9—31no—
56C3×Dic9—61no—
57C32⋊C9#4111yescharacteristic, complemented, Sylow
58C4×C3⋊D3—31no—
59C4×C3⋊D3—31no—
60C4×C3⋊D3D911yescharacteristic, complemented
61C3×C4×D3—31no—
62C3×C4×D3—91no—
63C3×C4×D3—91no—
64C3×C4×D3—91no—
65C3×C4×D3—91no—
66C3×C4×D3—91no—
67C3×C4×D3—181no—
68C3×C4×D3—181no—
69#627—91no—
70#627—91no—
71#627—91no—
72#626—91no—
73#626—91no—
74#626—91no—
75#626—91no—
76#626—91no—
77#626—91no—
78#625—91no—
79#625—91no—
80#625—91no—
81C2×C4×C9—91no—
82#611—91no—
83#611—91no—
84D36—91no—
85C4×D9—31no—
86C4×D9—61no—
87C4×D9—91no—
88Dic18—91no—
89C2×C33C22×D311yescharacteristic
90C3×C3⋊D3—21no—
91C3×C3⋊D3—61no—
92C3×C3⋊D3—61no—
93C2×C3×C9—21no—
94C2×C3×C9C22×D311yescharacteristic
95C3⋊D9—21no—
96D3×C9—61no—
97C3×D9—62no—
98C3×D9—61no—
99#235—271no—
100#235—271no—
101#235—271no—
102C2×C3⋊D3—31no—
103C2×C3⋊D3—31no—
104C2×C3⋊D3C2×D911yescharacteristic
105C2×C3×D3—31no—
106C2×C3×D3—91no—
107C2×C3×D3—91no—
108C2×C3×D3—91no—
109C2×C3×D3—91no—
110C2×C3×D3—91no—
111C2×C3×D3—181no—
112C2×C3×D3—181no—
113C32×C4—21no—
114C32×C4—31no—
115C32×C4—61no—
116C32×C4C2×D911yescharacteristic
117C32×C4D3211yescharacteristic
118C3⋊Dic3—31no—
119C3⋊Dic3—31no—
120C3⋊Dic3C2×D911yescharacteristic
121C3×Dic3—31no—
122C3×Dic3—91no—
123C3×Dic3—91no—
124C3×Dic3—91no—
125C3×Dic3—91no—
126C3×Dic3—91no—
127C3×Dic3—181no—
128C3×Dic3—181no—
129C22×C9—91no—
130C2×D9—31no—
131C2×D9—61no—
132C2×D9—91no—
133C4×C9—31no—
134C4×C9—61no—
135C4×C9—91no—
136Dic9—31no—
137Dic9—61no—
138Dic9—91no—
139C33#23511yescharacteristic
140C3×C9—21no—
141C3×C9#23511yescharacteristic, complemented
142C2×C3×C4—91no—
143C2×C3×C4—271no—
144C2×C3×C4—271no—
145#67—271no—
146#67—271no—
147#67—271no—
148#67—271no—
149#67—271no—
150#67—271no—
151D12—271no—
152D12—271no—
153D12—271no—
154C4×D3—31no—
155C4×D3—91no—
156C4×D3—91no—
157C4×D3—91no—
158C4×D3—91no—
159C4×D3—91no—
160C4×D3—181no—
161C4×D3—181no—
162Dic6—271no—
163Dic6—271no—
164Dic6—271no—
165C2×C32—21no—
166C2×C32—31no—
167C2×C32—61no—
168C2×C32C22×D911yescharacteristic
169C2×C32C2×D3211yescharacteristic
170C3⋊D3—21no—
171C3⋊D3—61no—
172C3⋊D3—61no—
173C3×D3—61no—
174C3×D3—181no—
175C3×D3—182no—
176C3×D3—181no—
177C3×D3—182no—
178C3×D3—181no—
179C3×D3—181no—
180C3×D3—181no—
181C2×C9—31no—
182C2×C9—61no—
183C2×C9—181no—
184D9—61no—
185D9—62no—
186D9—181no—
187#41—811noSylow
188C22×C3—91no—
189C22×C3—271no—
190C22×C3—271no—
191C2×D3—31no—
192C2×D3—91no—
193C2×D3—91no—
194C2×D3—91no—
195C2×D3—91no—
196C2×D3—91no—
197C2×D3—181no—
198C2×D3—181no—
199C3×C4—21no—
200C3×C4—31no—
201C3×C4—61no—
202C3×C4—91no—
203C3×C4—271no—
204C3×C4—271no—
205C3×C4D3×D911yescharacteristic
206C3×C4((C3⋊D3)⋊C3)⋊C211yescharacteristic
207Dic3—31no—
208Dic3—91no—
209Dic3—91no—
210Dic3—91no—
211Dic3—91no—
212Dic3—91no—
213Dic3—181no—
214Dic3—181no—
215C32—21no—
216C32—31no—
217C32—61no—
218C32#369711yescharacteristic, complemented
219C32#379811yescharacteristic
220C9—31no—
221C9—61no—
222Q8—811no—
223D4—811no—
224D4—811no—
225D4—811no—
226C2×C4—91no—
227C2×C4—271no—
228C2×C4—271no—
229C2×C3—21no—
230C2×C3—31no—
231C2×C3—61no—
232C2×C3—181no—
233C2×C3—541no—
234C2×C3—541no—
235C2×C3C2×D3×D911yescharacteristic
236C2×C3C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
237D3—61no—
238D3—181no—
239D3—182no—
240D3—181no—
241D3—182no—
242D3—181no—
243D3—181no—
244D3—181no—
245C22—91no—
246C22—271no—
247C22—271no—
248C4—91no—
249C4—271no—
250C4—271no—
251C4((C3⋊D3)⋊C9)⋊C211yescharacteristic
252C3—21no—
253C3—31no—
254C3—61no—
255C3#8864011yescharacteristic
256C3#8865011yescharacteristic
257C2—181no—
258C2—541no—
259C2—541no—
260C2C2×((C3⋊D3)⋊C9)⋊C211yescharacteristic
subgroupG/H
center, hypercenterC4((C3⋊D3)⋊C9)⋊C2
commutator, cosocleC2×C32⋊C9C23
Frattini, socleC2×C32C2×D32
FittingC4×C32⋊C9C22
hypocenterC32⋊C9#41
LCSG ▷ C2×C32⋊C9 ▷ C32⋊C9
UCSC1 ◁ C4

Complements

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

NH ≅ G/Ntype
1. C4×#4181C2semidirect
2. C4×#4169C2semidirect
3. C4×(C3⋊D3)⋊C9C2semidirect
4. #10619538C2semidirect
5. #10619537C2semidirect
6. #10619536C2semidirect
7. #10619535C2semidirect
24. C4×C3⋊D9D3semidirect
57. C32⋊C9#41semidirect
60. C4×C3⋊D3D9semidirect
141. C3×C9#235semidirect
218. C32#3697semidirect

Maximal subgroups

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

subgroupindex
C4×#41812
C4×#41692
C4×(C3⋊D3)⋊C92
#106195382
#106195372
#106195362
#106195352
#890423
#886403