Finite Group Databasebeta

← C2×#11720943 #13150081

Subgroups — C2×#11720943 #13150081

Order 1728.

1098 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4×D9C211yesmaximal, characteristic
2C2×C4×C3⋊Dic9C211yesmaximal, characteristic, complemented
3C2×C4×C9×Dic3C211yesmaximal, characteristic, complemented
4C2×(C2×D9)⋊Dic3C212yesmaximal
5C2×Dic9⋊Dic3C212yesmaximal, complemented
6#11720943C218yesmaximal, direct product factor
7C2×#63855—31nomaximal
8C2×#63434—31nomaximal
9C23×C3×D9C2211yescharacteristic
10C22×C3×C4×C9C2211yescharacteristic
11C22×C3⋊Dic9C2212yes—
12C22×C9×Dic3C2212yes—
13C22×C3×Dic9C2211yescharacteristic
14C2×C3×C4×D9C418yescomplemented
15C2×C3×C4×D9C2214yes—
16C4×C3⋊Dic9C2214yescomplemented
17C4×C9×Dic3C2214yescomplemented
18(C2×D9)⋊Dic3C2218yes—
19Dic9⋊Dic3C2218yescomplemented
20C22×C3×C4×D3—31no—
21C2×C4×C3⋊Dic3—31no—
22C2×C3×C4×Dic3D311yescharacteristic
23C2×Dic3⋊Dic3—32no—
24C2×(C2×D3)⋊Dic3—32no—
25#63855—38no—
26C22×C4×D9D311yescharacteristic
27C2×C42×C9—31no—
28C2×(C2×D9)⋊C4—32no—
29C2×Dic9⋊C4—32no—
30C2×C4×Dic9—31no—
31C2×C4×Dic9—61no—
32#63434—38no—
33C23×C3×C9C2311yescharacteristic
34C22×C3×D9—24no—
35C22×C3×D9C2×C414yes—
36C22×C3×D9C2312yes—
37C2×C3×C4×C9C2×C414yes—
38C2×C3×C4×C9C2312yes—
39C2×C3⋊Dic9—24no—
40C2×C3⋊Dic9C2314yes—
41C2×C9×Dic3—24no—
42C2×C9×Dic3C2314yes—
43C2×C3×Dic9C2×C414yes—
44C2×C3×Dic9C2312yes—
45C3×C4×D9C2×C4116yescomplemented
46C2×#926—91no—
47C2×#872—91no—
48C23×C3×D3—31no—
49C22×C32×C4C2×D311yescharacteristic
50C22×C3⋊Dic3—32no—
51C22×C3×Dic3—31no—
52C22×C3×Dic3C2×D312yes—
53C2×C3×C4×D3—38no—
54C2×C3×C4×D3—34no—
55C23×D9C2×D311yescharacteristic
56C4×C3⋊Dic3—34no—
57C3×C4×Dic3C2×D314yes—
58Dic3⋊Dic3—38no—
59(C2×D3)⋊Dic3—38no—
60C22×C4×C9—21no—
61C22×C4×C9—32no—
62C22×C4×C9C2×D311yescharacteristic
63C22×Dic9—32no—
64C22×Dic9—62no—
65C22×Dic9C2×D311yescharacteristic
66C2×C4×D9Dic318yescomplemented
67C2×C4×D9C2×D314yes—
68C42×C9—34no—
69(C2×D9)⋊C4—38no—
70Dic9⋊C4—38no—
71C4×Dic9—34no—
72C4×Dic9—64no—
73C22×C3×C9C22×C412yes—
74C22×C3×C9#4114yes—
75C22×C3×C9C2411yescharacteristic
76C2×C3×D9—28no—
77C2×C3×D9—24no—
78C2×C3×D9C22×C414yes—
79C3×C4×C9C22×C414yes—
80C3⋊Dic9—24no—
81C9×Dic3—24no—
82C3×Dic9C22×C414yes—
83C23×C3×C4—91no—
84C22×C4×D3—31no—
85C2×C3×C42—31no—
86C2×#217—92no—
87C2×(C2×D3)⋊C4—92no—
88#926—98no—
89C2×C4⋊Dic3—92no—
90C2×Dic3⋊C4—92no—
91C2×C4×Dic3—91no—
92C2×C4×Dic3—91no—
93C2×C4×Dic3—181no—
94C2×C4×Dic3D911yescharacteristic, complemented
95#872—98no—
96C23×C32C22×D311yescharacteristic
97C22×C3×D3—34no—
98C22×C3×D3—32no—
99C22×C3×D3—64no—
100C2×C32×C4C4×D314yes—
101C2×C32×C4C22×D312yes—
102C2×C3⋊Dic3—34no—
103C2×C3⋊Dic3—64no—
104C2×C3×Dic3—24no—
105C2×C3×Dic3—34no—
106C2×C3×Dic3—32no—
107C2×C3×Dic3C22×D314yes—
108C3×C4×D3—316no—
109C23×C9—21no—
110C23×C9C22×D311yescharacteristic
111C22×D9—24no—
112C22×D9C2×Dic314yes—
113C22×D9C22×D312yes—
114C2×C4×C9—24no—
115C2×C4×C9—22no—
116C2×C4×C9—34no—
117C2×C4×C9—64no—
118C2×C4×C9C2×Dic314yes—
119C2×C4×C9C22×D312yes—
120C2×Dic9—34no—
121C2×Dic9—64no—
122C2×Dic9—68no—
123C2×Dic9—64no—
124C2×Dic9C2×Dic314yes—
125C2×Dic9C22×D312yes—
126C4×D9C2×Dic3116yescomplemented
127C2×#117—271noSylow
128C2×C3×C9#11714yescomplemented
129C2×C3×C9C23×C411yescharacteristic
130C2×C3×C9C2×#4112yes—
131C3×D9—24no—
132C24×C3—91no—
133C23×D3—31no—
134C22×C3×C4—21no—
135C22×C3×C4—32no—
136C22×C3×C4—91no—
137C22×C3×C4—98no—
138C22×C3×C4—94no—
139C22×C3×C4C2×D911yescharacteristic
140C22×C3×C4D3211yescharacteristic
141C22×Dic3—31no—
142C22×Dic3—92no—
143C22×Dic3—92no—
144C22×Dic3—182no—
145C22×Dic3C2×D912yes—
146C2×C4×D3—38no—
147C2×C4×D3—34no—
148C3×C42—34no—
149#217—98no—
150(C2×D3)⋊C4—98no—
151C4⋊Dic3—98no—
152Dic3⋊C4—98no—
153C4×Dic3—94no—
154C4×Dic3—94no—
155C4×Dic3—184no—
156C4×Dic3C2×D914yescomplemented
157C22×C32C2×C4×D312yes—
158C22×C32#23514yes—
159C22×C32C23×D311yescharacteristic
160C2×C3×D3—34no—
161C2×C3×D3—68no—
162C2×C3×D3—64no—
163C32×C4C2×C4×D314yes—
164C3⋊Dic3—64no—
165C3×Dic3—24no—
166C3×Dic3—34no—
167C22×C9—21no—
168C22×C9—24no—
169C22×C9—22no—
170C22×C9#23514yes—
171C22×C9C22×Dic312yes—
172C22×C9C23×D311yescharacteristic
173C2×D9—28no—
174C2×D9—24no—
175C2×D9C22×Dic314yes—
176C4×C9—24no—
177C4×C9—64no—
178C4×C9C22×Dic314yes—
179Dic9—68no—
180Dic9—64no—
181Dic9C22×Dic314yes—
182C23×C4—91no—
183#117—278no—
184C2×C4⋊C4—272no—
185C2×C22⋊C4—272no—
186C2×C42—31no—
187C2×C42—271no—
188C3×C9C2×#11711yescharacteristic, complemented, Sylow
189C23×C3—21no—
190C23×C3—94no—
191C23×C3—92no—
192C23×C3—184no—
193C23×C3C22×D911yescharacteristic
194C23×C3C2×D3211yescharacteristic
195C22×D3—32no—
196C22×D3—34no—
197C22×D3—64no—
198C2×C3×C4—24no—
199C2×C3×C4—22no—
200C2×C3×C4—34no—
201C2×C3×C4—64no—
202C2×C3×C4—94no—
203C2×C3×C4—92no—
204C2×C3×C4—916no—
205C2×C3×C4C4×D914yes—
206C2×C3×C4C22×D912yes—
207C2×C3×C4D3×Dic314yes—
208C2×C3×C4C2×D3212yes—
209C2×Dic3—24no—
210C2×Dic3—32no—
211C2×Dic3—34no—
212C2×Dic3—94no—
213C2×Dic3—94no—
214C2×Dic3—184no—
215C2×Dic3—188no—
216C2×Dic3—184no—
217C2×Dic3—184no—
218C2×Dic3C22×D914yes—
219C4×D3—316no—
220C2×C32#87214yes—
221C2×C32C22×C4×D311yescharacteristic
222C2×C32C2×#23512yes—
223C3×D3—64no—
224C2×C9—22no—
225C2×C9—21no—
226C2×C9—24no—
227C2×C9#92614yescomplemented
228C2×C9C2×#23512yes—
229C2×C9C23×Dic311yescharacteristic
230D9—24no—
231C24—91no—
232C22×C4—32no—
233C22×C4—91no—
234C22×C4—98no—
235C22×C4—94no—
236C22×C4—272no—
237C22×C4D3×D911yescharacteristic
238C4⋊C4—278no—
239C22⋊C4—278no—
240C42—34no—
241C42—274no—
242C22×C3—24no—
243C22×C3—21no—
244C22×C3—22no—
245C22×C3—94no—
246C22×C3—188no—
247C22×C3—184no—
248C22×C3C2×C4×D912yes—
249C22×C3#369714yes—
250C22×C3C23×D911yescharacteristic
251C22×C3#379814yes—
252C22×C3C2×D3×Dic312yes—
253C22×C3C22×D3211yescharacteristic
254C2×D3—34no—
255C2×D3—64no—
256C2×D3—68no—
257C3×C4—24no—
258C3×C4—64no—
259C3×C4—94no—
260C3×C4C2×C4×D914yes—
261C3×C4C2×D3×Dic314yes—
262Dic3—24no—
263Dic3—34no—
264Dic3—188no—
265Dic3—184no—
266Dic3—184no—
267C32C2×#87211yescharacteristic
268C9—21no—
269C9C2×#92611yescharacteristic, complemented
270C23—92no—
271C23—94no—
272C23—184no—
273C23C2×D3×D911yescharacteristic
274C2×C4—34no—
275C2×C4—64no—
276C2×C4—92no—
277C2×C4—94no—
278C2×C4—916no—
279C2×C4—274no—
280C2×C4—544no—
281C2×C4Dic3×D914yes—
282C2×C4C2×D3×D912yes—
283C2×C3—21no—
284C2×C3—22no—
285C2×C3—24no—
286C2×C3—184no—
287C2×C3#6343414yescomplemented
288C2×C3C22×C4×D911yescharacteristic
289C2×C3C2×#369712yes—
290C2×C3#6385514yes—
291C2×C3C2×#379812yes—
292C2×C3C22×D3×Dic311yescharacteristic
293D3—64no—
294C22—94no—
295C22—184no—
296C22—188no—
297C22#8864014yes—
298C22C2×Dic3×D912yes—
299C22C22×D3×D911yescharacteristic
300C4—64no—
301C4—94no—
302C4—544no—
303C4C2×Dic3×D914yes—
304C3—21no—
305C3C2×#6343411yescharacteristic, complemented
306C3C2×#6385511yescharacteristic
307C2—184no—
308C2#1172094314yesdirect product factor
309C2C2×#8864012yes—
310C2C22×Dic3×D911yescharacteristic
subgroupG/H
center, hypercenterC22×C4D3×D9
commutatorC2×C3×C9C23×C4
FrattiniC22×C3C22×D32
FittingC22×C3×C4×C9C22
socleC23×C32C22×D3
prime radicalC23×C3×D9C22
cosocleC22×C3×C9C24
hypocenterC3×C9C2×#117
LCSG ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×C3⋊Dic9C2semidirect
3. C2×C4×C9×Dic3C2semidirect
5. C2×Dic9⋊Dic3C2semidirect
6. #11720943C2direct (N × H)
14. C2×C3×C4×D9C4semidirect
16. C4×C3⋊Dic9C22semidirect
17. C4×C9×Dic3C22semidirect
19. Dic9⋊Dic3C22semidirect
45. C3×C4×D9C2×C4semidirect
66. C2×C4×D9Dic3semidirect
94. C2×C4×Dic3D9semidirect
126. C4×D9C2×Dic3semidirect
128. C2×C3×C9#117semidirect
156. C4×Dic3C2×D9semidirect
188. C3×C9C2×#117semidirect
227. C2×C9#926semidirect
269. C9C2×#926semidirect
287. C2×C3#63434semidirect
305. C3C2×#63434semidirect
308. C2#11720943direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C4×D92
C2×C4×C3⋊Dic92
C2×C4×C9×Dic32
C2×(C2×D9)⋊Dic32
C2×Dic9⋊Dic32
#117209432
C2×#638553
C2×#634343