Finite Group Databasebeta

← #13047163

Subgroups — #13047163

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
1#10619675C211yesmaximal, characteristic, complemented
2#638⋊C9C211yesmaximal, characteristic, complemented
3C2×#66316C211yesmaximal, characteristic, complemented
4#10619538C211yesmaximal, characteristic, complemented
5#10619535C211yesmaximal, characteristic, complemented
6#4181⋊C4C211yesmaximal, characteristic, complemented
7((C3⋊D3)⋊C9)⋊C4C211yesmaximal, characteristic, complemented
8#89046—31nomaximal
9#88663—31nomaximal
10C22×C32⋊C9C2211yescharacteristic
11C2×#4181C2211yescharacteristic
12C2×(C3⋊D3)⋊C9C2211yescharacteristic
13#66328C2211yescharacteristic
14#66316C2211yescharacteristic
15#66316C2211yescharacteristic
16(C3⋊Dic3)⋊C9C2211yescharacteristic
17C3×#638—31no—
18C3×#638D311yescharacteristic
19C2×C3×C3⋊Dic3—31no—
20#6296—31no—
21#6295—31no—
22#6294—31no—
23#6294—31no—
24C2×C3⋊Dic9D311yescharacteristic, complemented
25C9×#67—31no—
26C3×#611—31no—
27C3×#611—61no—
28#6194—31no—
29D3×Dic9—31no—
30Dic3×D9—31no—
31#6189—31no—
32C2×C32⋊C9—21no—
33C2×C32⋊C9C2311yescharacteristic
34#4181—21no—
35(C3⋊D3)⋊C9—21no—
36#3805—91no—
37#3804—91no—
38#3804—91no—
39#3699—91no—
40C22×C33C2×D311yescharacteristic
41C2×C3×C3⋊D3—31no—
42C2×C3×C3⋊D3C2×D311yescharacteristic
43C3×C3⋊Dic3—31no—
44C3×C3⋊Dic3—31no—
45C3×C3⋊Dic3—31no—
46C3×C3⋊Dic3C2×D311yescharacteristic
47C22×C3×C9—21no—
48C22×C3×C9C2×D311yescharacteristic
49C2×D3×C9—31no—
50C2×C3×D9—31no—
51C2×C3×D9—61no—
52C3⋊Dic9C2×D311yescharacteristic
53C3⋊Dic9C2×D311yescharacteristic
54C9×Dic3—31no—
55C3×Dic9—31no—
56C3×Dic9—61no—
57C32⋊C9#4111yescharacteristic, complemented, Sylow
58#638—31no—
59#638D911yescharacteristic, complemented
60C2×C3⋊Dic3—31no—
61C3×#67—31no—
62C3×#67—91no—
63C3×#67—91no—
64C3×#67—91no—
65C3×#67—181no—
66C2×C3×Dic3—91no—
67C2×C3×Dic3—91no—
68C2×C3×Dic3—181no—
69#627—91no—
70#627—91no—
71#627—91no—
72#626—91no—
73#626—91no—
74#625—91no—
75#624—91no—
76#624—91no—
77D3×Dic3—91no—
78D3×Dic3—91no—
79D3×Dic3—91no—
80D3×Dic3—91no—
81D4×C9—91no—
82#611—31no—
83#611—61no—
84#611—91no—
85C2×Dic9—91no—
86C2×Dic9—91no—
87C4×D9—91no—
88Dic18—91no—
89C2×C33—21no—
90C2×C33C22×D311yescharacteristic
91C3×C3⋊D3—21no—
92C3×C3⋊D3—61no—
93C2×C3×C9—21no—
94C2×C3×C9—21no—
95C2×C3×C9—41no—
96C2×C3×C9C22×D311yescharacteristic
97D3×C9—61no—
98C3×D9—61no—
99C3×D9—121no—
100#237—271no—
101#237—271no—
102#235—271no—
103C22×C32—21no—
104C22×C32—31no—
105C22×C32—61no—
106C22×C32C2×D911yescharacteristic
107C22×C32D3211yescharacteristic
108C2×C3⋊D3—31no—
109C2×C3⋊D3C2×D911yescharacteristic
110C2×C3×D3—31no—
111C2×C3×D3—91no—
112C2×C3×D3—91no—
113C2×C3×D3—91no—
114C2×C3×D3—181no—
115C3⋊Dic3—31no—
116C3⋊Dic3—31no—
117C3⋊Dic3—31no—
118C3⋊Dic3C2×D911yescharacteristic
119C3×Dic3—31no—
120C3×Dic3—91no—
121C3×Dic3—91no—
122C3×Dic3—91no—
123C3×Dic3—91no—
124C3×Dic3—91no—
125C3×Dic3—91no—
126C3×Dic3—91no—
127C3×Dic3—181no—
128C3×Dic3—181no—
129C3×Dic3—181no—
130C22×C9—31no—
131C22×C9—61no—
132C22×C9—91no—
133C2×D9—31no—
134C2×D9—61no—
135C4×C9—91no—
136Dic9—31no—
137Dic9—61no—
138Dic9—91no—
139Dic9—91no—
140C33#23711yescharacteristic
141C3×C9—21no—
142C3×C9#23511yescharacteristic, complemented
143C3×D4—91no—
144C3×D4—271no—
145C2×C3×C4—271no—
146#67—31no—
147#67—91no—
148#67—91no—
149#67—91no—
150#67—181no—
151#67—271no—
152#67—271no—
153C2×Dic3—91no—
154C2×Dic3—91no—
155C2×Dic3—181no—
156C2×Dic3—271no—
157C2×Dic3—271no—
158D12—271no—
159C4×D3—271no—
160C4×D3—271no—
161C4×D3—271no—
162C4×D3—271no—
163Dic6—271no—
164Dic6—271no—
165Dic6—271no—
166C2×C32—21no—
167C2×C32—21no—
168C2×C32—21no—
169C2×C32—31no—
170C2×C32—41no—
171C2×C32—61no—
172C2×C32—61no—
173C2×C32—62no—
174C2×C32C22×D911yescharacteristic
175C2×C32C2×D3211yescharacteristic
176C3⋊D3—21no—
177C3⋊D3—61no—
178C3×D3—61no—
179C3×D3—181no—
180C3×D3—181no—
181C3×D3—181no—
182C3×D3—361no—
183C2×C9—31no—
184C2×C9—61no—
185C2×C9—61no—
186C2×C9—121no—
187C2×C9—181no—
188D9—61no—
189D9—121no—
190#41—811noSylow
191C22×C3—21no—
192C22×C3—31no—
193C22×C3—61no—
194C22×C3—91no—
195C22×C3—271no—
196C22×C3D3×D911yescharacteristic
197C22×C3((C3⋊D3)⋊C3)⋊C211yescharacteristic
198C2×D3—31no—
199C2×D3—91no—
200C2×D3—91no—
201C2×D3—91no—
202C2×D3—181no—
203C3×C4—91no—
204C3×C4—271no—
205C3×C4—271no—
206C3×C4—271no—
207Dic3—31no—
208Dic3—91no—
209Dic3—91no—
210Dic3—91no—
211Dic3—91no—
212Dic3—91no—
213Dic3—91no—
214Dic3—91no—
215Dic3—181no—
216Dic3—181no—
217Dic3—181no—
218C32—21no—
219C32—31no—
220C32—61no—
221C32#369911yescharacteristic, complemented
222C32#380411yescharacteristic
223C9—31no—
224C9—61no—
225Q8—811no—
226D4—91no—
227D4—271no—
228D4—811no—
229C2×C4—271no—
230C2×C4—811no—
231C2×C4—811no—
232C2×C3—22no—
233C2×C3—21no—
234C2×C3—21no—
235C2×C3—21no—
236C2×C3—31no—
237C2×C3—61no—
238C2×C3—61no—
239C2×C3—121no—
240C2×C3—181no—
241C2×C3—541no—
242C2×C3C2×D3×D911yescharacteristic
243C2×C3C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
244D3—61no—
245D3—181no—
246D3—181no—
247D3—181no—
248D3—361no—
249C22—91no—
250C22—271no—
251C22((C3⋊D3)⋊C9)⋊C211yescharacteristic
252C4—91no—
253C4—271no—
254C4—271no—
255C4—271no—
256C3—21no—
257C3—31no—
258C3—61no—
259C3#8866211yescharacteristic
260C3#8867111yescharacteristic
261C2—21no—
262C2—181no—
263C2—541no—
264C2C2×((C3⋊D3)⋊C9)⋊C211yescharacteristic
subgroupG/H
centerC2C2×((C3⋊D3)⋊C9)⋊C2
commutator, cosocleC2×C32⋊C9C23
Frattini, socleC2×C32C2×D32
FittingC22×C32⋊C9C22
hypercenterC22((C3⋊D3)⋊C9)⋊C2
hypocenterC32⋊C9#41
LCSG ▷ C2×C32⋊C9 ▷ C32⋊C9
UCSC1 ◁ C2 ◁ C22

Complements

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

NH ≅ G/Ntype
1. #10619675C2semidirect
2. #638⋊C9C2semidirect
3. C2×#66316C2semidirect
4. #10619538C2semidirect
5. #10619535C2semidirect
6. #4181⋊C4C2semidirect
7. ((C3⋊D3)⋊C9)⋊C4C2semidirect
24. C2×C3⋊Dic9D3semidirect
57. C32⋊C9#41semidirect
59. #638D9semidirect
142. C3×C9#235semidirect
221. C32#3699semidirect

Maximal subgroups

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

subgroupindex
#106196752
#638⋊C92
C2×#663162
#106195382
#106195352
#4181⋊C42
((C3⋊D3)⋊C9)⋊C42
#890463
#886633