Finite Group Databasebeta

← C3×#10590687 #13157691

Subgroups — C3×#10590687 #13157691

Order 1728.

690 conjugacy classes of subgroups.

The subgroup lattice has 308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C8×C3⋊D3C211yesmaximal, characteristic
2C3×#63900C212yesmaximal
3C32×#818C212yesmaximal, complemented
4C3×#63576C212yesmaximal, complemented
5C3×D3×#107—32nomaximal
6#10590687C311yesmaximal, characteristic, direct product factor
7C2×C3×C4×C3⋊D3C2211yescharacteristic
8C2×C3×#624—22no—
9C2×C33×C8C2211yescharacteristic
10C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic
11C3×C8×C3⋊D3C414yescomplemented
12C32×C4⋊Dic3C2214yes—
13C3×#3724—22no—
14C2×C8×C3⋊D3C2×C311yescharacteristic
15C2×C3×D3×C8—32no—
16C2×C3×D3×C8—61no—
17C3×D3×C4⋊C4—34no—
18#63900C2×C312yes—
19C32×#107—32no—
20C3×#818—22no—
21C3×#818D312yescomplemented
22C3×#818C2×C312yescomplemented
23C3×#807—34no—
24#63576C2×C312yescomplemented
25C22×C3×C3⋊D3D411yescharacteristic
26C2×C33×C4C2311yescharacteristic
27C2×C3×C3⋊Dic3D411yescharacteristic
28C3×C4×C3⋊D3C2×C412yes—
29C3×C4×C3⋊D3Q812yes—
30C2×C32×Dic3—24no—
31C3×#624—44no—
32C33×C8C2×C412yescomplemented
33C3×C3⋊(C3⋊C8)C2×C412yescomplemented
34C2×C3×#107—91no—
35D3×#107—32no—
36C2×C4×C3⋊D3C22×C311yescharacteristic
37C2×C3×C4×D3—32no—
38C2×C3×C4×D3—61no—
39C2×C3×C4×D3—64no—
40C2×#624—22no—
41C2×C32×C8—21no—
42C2×C32×C8—22no—
43C2×C32×C8—41no—
44C2×C32×C8C2×D312yes—
45C2×C32×C8C22×C311yescharacteristic
46C32×C4⋊C4—34no—
47C2×C3⋊(C3⋊C8)C22×C311yescharacteristic
48C8×C3⋊D3C3×C414yescomplemented
49C3×C4⋊Dic3—24no—
50C3×C4⋊Dic3C2×D314yes—
51C3×C4⋊Dic3C22×C314yes—
52C3×Dic3⋊C4—64no—
53C2×C3×C3⋊C8—32no—
54C2×C3×C3⋊C8—61no—
55C3×D3×C8—38no—
56C3×D3×C8—64no—
57#3724—22no—
58C22×C33C2×D411yescharacteristic
59C2×C3×C3⋊D3C4⋊C412yes—
60C2×C3×C3⋊D3D812yes—
61C2×C3×C3⋊D3Q1612yes—
62C33×C4C22×C411yescharacteristic
63C33×C4C2×Q811yescharacteristic
64C3×C3⋊Dic3C4⋊C412yes—
65C32×Dic3—44no—
66C22×C3×C8—91no—
67C2×C3×C4⋊C4—92no—
68C2×D3×C8—32no—
69C2×D3×C8—61no—
70D3×C4⋊C4—34no—
71C3×#107—32no—
72C3×#107—32no—
73C3×#107—62no—
74C3×#107—92no—
75#818C3×D312yescomplemented
76#807—34no—
77C22×C3⋊D3C3×D411yescharacteristic
78C22×C3×D3—32no—
79C22×C3×D3—61no—
80C2×C32×C4—21no—
81C2×C32×C4—22no—
82C2×C32×C4—41no—
83C2×C32×C4—64no—
84C2×C32×C4C22×D312yes—
85C2×C32×C4C23×C311yescharacteristic
86C2×C3⋊Dic3C3×D411yescharacteristic
87C4×C3⋊D3C2×C3×C412yes—
88C4×C3⋊D3C3×Q812yes—
89C2×C3×Dic3—24no—
90C2×C3×Dic3—24no—
91C2×C3×Dic3—32no—
92C2×C3×Dic3—44no—
93C2×C3×Dic3—61no—
94C3×C4×D3—34no—
95C3×C4×D3—34no—
96C3×C4×D3—62no—
97C3×C4×D3—62no—
98C3×C4×D3—128no—
99#624—44no—
100C32×C8—22no—
101C32×C8—24no—
102C32×C8—42no—
103C32×C8C4×D314yescomplemented
104C32×C8C2×C3×C412yescomplemented
105C3⋊(C3⋊C8)C2×C3×C412yescomplemented
106C3×C3⋊C8—34no—
107C3×C3⋊C8—62no—
108C2×#107—91noSylow
109C2×C33C2×C4⋊C411yescharacteristic
110C2×C33C2×D811yescharacteristic
111C2×C33C2×Q1611yescharacteristic
112C3×C3⋊D3#10714yescomplemented
113C22×C3×C4—91no—
114C22×C3×C4—182no—
115C2×C4×D3—32no—
116C2×C4×D3—61no—
117C2×C4×D3—64no—
118C2×C3×C8—22no—
119C2×C3×C8—21no—
120C2×C3×C8—41no—
121C2×C3×C8—91no—
122C2×C3×C8—94no—
123C2×C3×C8D3211yescharacteristic
124C2×C3×C8C2×C3×D312yes—
125C3×C4⋊C4—34no—
126C3×C4⋊C4—34no—
127C3×C4⋊C4—64no—
128C3×C4⋊C4—182no—
129C4⋊Dic3C2×C3×D314yes—
130Dic3⋊C4—64no—
131C2×C3⋊C8—32no—
132C2×C3⋊C8—61no—
133D3×C8—38no—
134D3×C8—64no—
135C22×C32—21no—
136C22×C32—22no—
137C22×C32—41no—
138C22×C32D3×D412yes—
139C22×C32C2×C3×D411yescharacteristic
140C2×C3⋊D3C3×C4⋊C412yes—
141C2×C3⋊D3C3×D812yes—
142C2×C3⋊D3C3×Q1612yes—
143C2×C3×D3—34no—
144C2×C3×D3—34no—
145C2×C3×D3—34no—
146C2×C3×D3—62no—
147C2×C3×D3—62no—
148C2×C3×D3—62no—
149C32×C4—21no—
150C32×C4—21no—
151C32×C4—22no—
152C32×C4—22no—
153C32×C4—41no—
154C32×C4—41no—
155C32×C4—124no—
156C32×C4C2×C4×D312yes—
157C32×C4D3×Q812yes—
158C32×C4C22×C3×C411yescharacteristic
159C32×C4C2×C3×Q811yescharacteristic
160C3⋊Dic3C3×C4⋊C412yes—
161C3×Dic3—34no—
162C3×Dic3—44no—
163C3×Dic3—44no—
164C3×Dic3—62no—
165C3×Dic3—84no—
166C22×C8—91no—
167C2×C4⋊C4—92no—
168#107—32no—
169#107—92no—
170C33C2×#10711yescharacteristic, complemented, Sylow
171C23×C3—91no—
172C22×D3—32no—
173C22×D3—61no—
174C2×C3×C4—22no—
175C2×C3×C4—21no—
176C2×C3×C4—41no—
177C2×C3×C4—64no—
178C2×C3×C4—64no—
179C2×C3×C4—91no—
180C2×C3×C4—92no—
181C2×C3×C4—92no—
182C2×C3×C4—124no—
183C2×C3×C4—364no—
184C2×C3×C4C2×D3211yescharacteristic
185C2×C3×C4C22×C3×D312yes—
186C2×Dic3—24no—
187C2×Dic3—32no—
188C2×Dic3—61no—
189C4×D3—34no—
190C4×D3—34no—
191C4×D3—62no—
192C4×D3—62no—
193C4×D3—128no—
194C3×C8—24no—
195C3×C8—22no—
196C3×C8—42no—
197C3×C8—92no—
198C3×C8#62412yescomplemented
199C3×C8C3×C4×D314yescomplemented
200C3⋊C8—34no—
201C3⋊C8—62no—
202C2×C32—22no—
203C2×C32—22no—
204C2×C32—22no—
205C2×C32—21no—
206C2×C32—21no—
207C2×C32—21no—
208C2×C32—41no—
209C2×C32—41no—
210C2×C32—41no—
211C2×C32D3×C4⋊C412yes—
212C2×C32D3×D812yes—
213C2×C32D3×Q1612yes—
214C2×C32C2×C3×C4⋊C411yescharacteristic
215C2×C32C2×C3×D811yescharacteristic
216C2×C32C2×C3×Q1611yescharacteristic
217C3⋊D3C3×#10714yescomplemented
218C3×D3—38no—
219C3×D3—64no—
220C22×C4—91no—
221C22×C4—182no—
222C2×C8—91no—
223C2×C8—94no—
224C2×C8C3×D3211yescharacteristic
225C4⋊C4—34no—
226C4⋊C4—182no—
227C22×C3—21no—
228C22×C3—22no—
229C22×C3—41no—
230C22×C3—92no—
231C22×C3—92no—
232C22×C3—92no—
233C22×C3#380211yescharacteristic
234C22×C3C3×D3×D412yes—
235C2×D3—34no—
236C2×D3—34no—
237C2×D3—34no—
238C2×D3—62no—
239C2×D3—62no—
240C2×D3—62no—
241C3×C4—21no—
242C3×C4—22no—
243C3×C4—21no—
244C3×C4—22no—
245C3×C4—41no—
246C3×C4—41no—
247C3×C4—92no—
248C3×C4—124no—
249C3×C4—124no—
250C3×C4—244no—
251C3×C4#379711yescharacteristic
252C3×C4C2×#62411yescharacteristic
253C3×C4C2×C3×C4×D312yes—
254C3×C4C3×D3×Q812yes—
255Dic3—34no—
256Dic3—44no—
257Dic3—62no—
258C32—21no—
259C32—22no—
260C32—41no—
261C32D3×#10712yescomplemented
262C32C2×C3×#10711yescharacteristic, complemented
263C23—91no—
264C2×C4—64no—
265C2×C4—91no—
266C2×C4—92no—
267C2×C4—92no—
268C2×C4—364no—
269C2×C4C2×C3×D3211yescharacteristic
270C8—92no—
271C8C3×#62412yescomplemented
272C2×C3—22no—
273C2×C3—21no—
274C2×C3—21no—
275C2×C3—22no—
276C2×C3—21no—
277C2×C3—22no—
278C2×C3—41no—
279C2×C3—41no—
280C2×C3—41no—
281C2×C3—94no—
282C2×C3#6379711yescharacteristic
283C2×C3#6380211yescharacteristic
284C2×C3#6390011yescharacteristic
285C2×C3C3×D3×C4⋊C412yes—
286C2×C3C3×D3×D812yes—
287C2×C3C3×D3×Q1612yes—
288D3—38no—
289D3—64no—
290C22—92no—
291C22—92no—
292C22—92no—
293C22C3×#380211yescharacteristic
294C4—92no—
295C4—124no—
296C4C3×#379711yescharacteristic
297C4C2×C3×#62411yescharacteristic
298C3—21no—
299C3—22no—
300C3—41no—
301C3#1059068711yescharacteristic, direct product factor
302C3C3×D3×#10712yescomplemented
303C2—94no—
304C2C3×#6379711yescharacteristic
305C2C3×#6380211yescharacteristic
306C2C3×#6390011yescharacteristic
subgroupG/H
centerC22×C3#3802
commutatorC32×C4C22×C3×C4
FrattiniC2×C4C2×C3×D32
FittingC2×C33×C8C22
socleC22×C33C2×D4
prime radicalC22×C3×C3⋊D3D4
cosocleC2×C32×C4C23×C3
hypercenterC2×C3×C8D32
hypocenterC32C2×C3×#107
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C2×C3×C8

Complements

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

NH ≅ G/Ntype
3. C32×#818C2semidirect
4. C3×#63576C2semidirect
6. #10590687C3direct (N × H)
11. C3×C8×C3⋊D3C4semidirect
21. C3×#818D3semidirect
22. C3×#818C2×C3semidirect
24. #63576C2×C3semidirect
32. C33×C8C2×C4semidirect
33. C3×C3⋊(C3⋊C8)C2×C4semidirect
48. C8×C3⋊D3C3×C4semidirect
75. #818C3×D3semidirect
103. C32×C8C4×D3semidirect
104. C32×C8C2×C3×C4semidirect
105. C3⋊(C3⋊C8)C2×C3×C4semidirect
112. C3×C3⋊D3#107semidirect
170. C33C2×#107semidirect
198. C3×C8#624semidirect
199. C3×C8C3×C4×D3semidirect
217. C3⋊D3C3×#107semidirect
261. C32D3×#107semidirect
262. C32C2×C3×#107semidirect
271. C8C3×#624semidirect
301. C3#10590687direct (N × H)
302. C3C3×D3×#107semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C8×C3⋊D32
C3×#639002
C32×#8182
C3×#635762
C3×D3×#1073
#105906873