Finite Group Databasebeta

← C3×#83752 #11858505

Subgroups — C3×#83752 #11858505

Order 1152.

1133 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×C32×M16C211yesmaximal, characteristic
2C2×C3×#926C212yesmaximal
3C3×#5121C218yesmaximal, complemented
4C3×#5106C214yesmaximal, complemented
5C3×#2911—31nomaximal
6#83752C311yesmaximal, characteristic, direct product factor
7C23×C32×C4C2211yescharacteristic
8C2×C32×M16C418yescomplemented
9C2×C32×M16C2214yes—
10C22×C32×C8C2212yes—
11C2×C3×#217—22no—
12C3×#926—22no—
13C3×#926—22no—
14C3×#926C2214yes—
15C3×#926C2214yes—
16C2×C3×C4⋊Dic3C2214yes—
17C2×C3×C4×Dic3—22no—
18C3×#818C2218yescomplemented
19C3×#817C2218yescomplemented
20C22×C3×M16—21no—
21C22×C3×M16D311yescharacteristic
22C22×C3×M16C2×C311yescharacteristic
23C2×C3×#117—32no—
24C2×#926C2×C312yes—
25C3×#428—38no—
26C3×#427—34no—
27#5121C2×C318yescomplemented
28#5106C2×C314yescomplemented
29C24×C32D411yescharacteristic
30C22×C32×C4C2×C414yes—
31C22×C32×C4D412yes—
32C22×C32×C4D411yescharacteristic
33C22×C32×C4Q814yes—
34C22×C32×C4C2312yes—
35C22×C32×C4C2311yescharacteristic
36C22×C3×Dic3—24no—
37C32×M16C2×C4116yescomplemented
38C2×C32×C8C2×C418yescomplemented
39C2×C32×C8C2314yes—
40C3×#217—24no—
41C3×#217—24no—
42C3×C4⋊Dic3—24no—
43C3×C4⋊Dic3C2318yes—
44C3×C4×Dic3—24no—
45C3×C4×Dic3—24no—
46#2911—31noSylow
47C23×C3×C4—21no—
48C23×C3×C4C2×D311yescharacteristic
49C23×C3×C4C22×C311yescharacteristic
50C2×C3×M16—28no—
51C2×C3×M16—24no—
52C2×C3×M16Dic318yescomplemented
53C2×C3×M16C3×C418yescomplemented
54C2×C3×M16C2×D314yes—
55C2×C3×M16C22×C314yes—
56C22×C3×C8—22no—
57C22×C3×C8C2×D312yes—
58C22×C3×C8C22×C312yes—
59C3×#117—34no—
60C3×#117—34no—
61C3×#117—62no—
62C3×#117—62no—
63C2×C3×C4⋊C4—34no—
64C2×C3×C22⋊C4—62no—
65C2×C3×C42—62no—
66C2×#217—22no—
67#926—22no—
68#926—22no—
69#926C22×C314yes—
70#926C22×C314yes—
71C2×C4⋊Dic3C22×C314yes—
72C2×C4×Dic3—22no—
73C3×#107—38no—
74C3×#106—38no—
75#818C22×C318yescomplemented
76#817C22×C318yescomplemented
77C23×C32—42no—
78C23×C32C4⋊C414yes—
79C23×C32C2×D411yescharacteristic
80C23×C32C2×D412yes—
81C2×C32×C4C4⋊C418yes—
82C2×C32×C4C4⋊C414yes—
83C2×C32×C4C22×C412yes—
84C2×C32×C4C22×C414yes—
85C2×C32×C4C2×D412yes—
86C2×C32×C4C2×D411yescharacteristic
87C2×C32×C4C2×Q814yes—
88C2×C32×C4C2×Q812yes—
89C2×C32×C4C2411yescharacteristic
90C2×C3×Dic3—28no—
91C2×C3×Dic3—48no—
92C32×C8C22×C418yes—
93C22×M16C3×D311yescharacteristic
94C2×#117—32no—
95#428—38no—
96#427—34no—
97C24×C3—21no—
98C24×C3D1211yescharacteristic
99C24×C3C3×D411yescharacteristic
100C22×C3×C4—24no—
101C22×C3×C4—22no—
102C22×C3×C4—21no—
103C22×C3×C4—24no—
104C22×C3×C4—21no—
105C22×C3×C4—22no—
106C22×C3×C4—64no—
107C22×C3×C4Dic614yes—
108C22×C3×C4D1211yescharacteristic
109C22×C3×C4D1212yes—
110C22×C3×C4C2×Dic314yes—
111C22×C3×C4C2×C3×C414yes—
112C22×C3×C4C3×D412yes—
113C22×C3×C4C3×D411yescharacteristic
114C22×C3×C4C3×Q814yes—
115C22×C3×C4C22×D312yes—
116C22×C3×C4C22×D311yescharacteristic
117C22×C3×C4C23×C312yes—
118C22×C3×C4C23×C311yescharacteristic
119C22×Dic3—24no—
120C3×M16—216no—
121C3×M16C2×Dic3116yescomplemented
122C3×M16C2×C3×C4116yescomplemented
123C2×C3×C8—28no—
124C2×C3×C8—24no—
125C2×C3×C8C2×Dic318yescomplemented
126C2×C3×C8C2×C3×C418yescomplemented
127C2×C3×C8C22×D314yes—
128C2×C3×C8C23×C314yes—
129C3×C4⋊C4—38no—
130C3×C4⋊C4—64no—
131C3×C22⋊C4—64no—
132C3×C22⋊C4—64no—
133C3×C42—64no—
134C3×C42—64no—
135#217—24no—
136#217—24no—
137C4⋊Dic3—24no—
138C4⋊Dic3C23×C318yes—
139C4×Dic3—24no—
140C4×Dic3—24no—
141C22×C32—22no—
142C22×C32—24no—
143C22×C32—44no—
144C22×C32C2×C4⋊C412yes—
145C22×C32C2×C4⋊C414yes—
146C22×C32C22×D411yescharacteristic
147C32×C4C2×C4⋊C414yes—
148C32×C4C2×C4⋊C412yes—
149C32×C4C23×C411yescharacteristic
150C32×C4C22×Q811yescharacteristic
151C3×Dic3—48no—
152C23×C4C2×C3×D311yescharacteristic
153C2×M16C3×Dic318yescomplemented
154C2×M16C2×C3×D314yes—
155C22×C8C2×C3×D312yes—
156#117—34no—
157#117—34no—
158#117—62no—
159#117—62no—
160C2×C4⋊C4—34no—
161C2×C22⋊C4—62no—
162C2×C42—62no—
163#107—38no—
164#106—38no—
165C23×C3—24no—
166C23×C3—21no—
167C23×C3—22no—
168C23×C3—42no—
169C23×C3—42no—
170C23×C3—44no—
171C23×C3C4⋊Dic314yes—
172C23×C3C3×C4⋊C414yes—
173C23×C3C2×D1211yescharacteristic
174C23×C3C2×D1212yes—
175C23×C3C2×C3×D411yescharacteristic
176C23×C3C2×C3×D412yes—
177C2×C3×C4—21no—
178C2×C3×C4—24no—
179C2×C3×C4—28no—
180C2×C3×C4—22no—
181C2×C3×C4—24no—
182C2×C3×C4—21no—
183C2×C3×C4—22no—
184C2×C3×C4—22no—
185C2×C3×C4—24no—
186C2×C3×C4—68no—
187C2×C3×C4—128no—
188C2×C3×C4C4⋊Dic314yes—
189C2×C3×C4C4⋊Dic318yes—
190C2×C3×C4C3×C4⋊C418yes—
191C2×C3×C4C3×C4⋊C414yes—
192C2×C3×C4C2×Dic614yes—
193C2×C3×C4C2×Dic612yes—
194C2×C3×C4C2×D1212yes—
195C2×C3×C4C2×D1211yescharacteristic
196C2×C3×C4C22×Dic312yes—
197C2×C3×C4C22×Dic314yes—
198C2×C3×C4C22×C3×C412yes—
199C2×C3×C4C22×C3×C414yes—
200C2×C3×C4C2×C3×D411yescharacteristic
201C2×C3×C4C2×C3×D412yes—
202C2×C3×C4C2×C3×Q814yes—
203C2×C3×C4C2×C3×Q812yes—
204C2×C3×C4C23×D311yescharacteristic
205C2×C3×C4C24×C311yescharacteristic
206C2×Dic3—28no—
207C2×Dic3—48no—
208C3×C8—28no—
209C3×C8C22×Dic318yes—
210C3×C8C22×C3×C418yes—
211C2×C32—22no—
212C2×C32—24no—
213C2×C32C22×C4⋊C411yescharacteristic
214C2×C32#57512yes—
215C24C3×D1211yescharacteristic
216C22×C4—64no—
217C22×C4C3×Dic614yes—
218C22×C4C3×D1212yes—
219C22×C4C3×D1211yescharacteristic
220C22×C4C2×C3×Dic314yes—
221C22×C4C22×C3×D312yes—
222C22×C4C22×C3×D311yescharacteristic
223M16C2×C3×Dic3116yescomplemented
224C2×C8C2×C3×Dic318yescomplemented
225C2×C8C22×C3×D314yes—
226C4⋊C4—38no—
227C4⋊C4—64no—
228C22⋊C4—64no—
229C22⋊C4—64no—
230C42—64no—
231C42—64no—
232C22×C3—24no—
233C22×C3—24no—
234C22×C3—22no—
235C22×C3—24no—
236C22×C3—22no—
237C22×C3—22no—
238C22×C3—24no—
239C22×C3—21no—
240C22×C3—44no—
241C22×C3—44no—
242C22×C3—44no—
243C22×C3—48no—
244C22×C3C2×C4⋊Dic312yes—
245C22×C3C2×C4⋊Dic314yes—
246C22×C3C2×C3×C4⋊C412yes—
247C22×C3C2×C3×C4⋊C414yes—
248C22×C3C22×D1211yescharacteristic
249C22×C3C22×C3×D411yescharacteristic
250C3×C4—22no—
251C3×C4—24no—
252C3×C4—21no—
253C3×C4—21no—
254C3×C4—128no—
255C3×C4C2×C4⋊Dic314yes—
256C3×C4C2×C4⋊Dic312yes—
257C3×C4C2×C3×C4⋊C412yes—
258C3×C4C2×C3×C4⋊C414yes—
259C3×C4C22×Dic611yescharacteristic
260C3×C4C23×Dic311yescharacteristic
261C3×C4C23×C3×C411yescharacteristic
262C3×C4C22×C3×Q811yescharacteristic
263Dic3—48no—
264C32#291111yescharacteristic, complemented, Sylow
265C23—42no—
266C23C3×C4⋊Dic314yes—
267C23C2×C3×D1211yescharacteristic
268C23C2×C3×D1212yes—
269C2×C4—68no—
270C2×C4—128no—
271C2×C4C3×C4⋊Dic318yes—
272C2×C4C3×C4⋊Dic314yes—
273C2×C4C2×C3×Dic614yes—
274C2×C4C2×C3×Dic612yes—
275C2×C4C2×C3×D1211yescharacteristic
276C2×C4C2×C3×D1212yes—
277C2×C4C22×C3×Dic312yes—
278C2×C4C22×C3×Dic314yes—
279C2×C4C23×C3×D311yescharacteristic
280C8C22×C3×Dic318yes—
281C2×C3—24no—
282C2×C3—22no—
283C2×C3—24no—
284C2×C3—22no—
285C2×C3—24no—
286C2×C3—22no—
287C2×C3—21no—
288C2×C3—44no—
289C2×C3#574812yes—
290C2×C3C22×C4⋊Dic311yescharacteristic
291C2×C3C22×C3×C4⋊C411yescharacteristic
292C2×C3C3×#57512yes—
293C22—24no—
294C22—22no—
295C22—44no—
296C22C2×C3×C4⋊Dic312yes—
297C22C2×C3×C4⋊Dic314yes—
298C22C22×C3×D1211yescharacteristic
299C4—128no—
300C4C2×C3×C4⋊Dic312yes—
301C4C2×C3×C4⋊Dic314yes—
302C4C22×C3×Dic611yescharacteristic
303C4C23×C3×Dic311yescharacteristic
304C3—21no—
305C3#8375211yescharacteristic, direct product factor
306C3C3×#291111yescharacteristic, complemented
307C2—22no—
308C2—24no—
309C2C3×#574812yes—
310C2C22×C3×C4⋊Dic311yescharacteristic
subgroupG/H
centerC2×C3×C4C2×D12
commutatorC3×C4C23×C3×C4
FrattiniC2×C4C23×C3×D3
FittingC22×C32×M16C2
socleC22×C32C22×D4
prime radicalC24×C32D4
cosocleC2×C3×C4C24×C3
hypercenterC22×C3×M16D3
hypocenterC3C3×#2911
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C23×C3×C4 ◁ C22×C3×M16

Complements

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

NH ≅ G/Ntype
3. C3×#5121C2semidirect
4. C3×#5106C2semidirect
6. #83752C3direct (N × H)
8. C2×C32×M16C4semidirect
18. C3×#818C22semidirect
19. C3×#817C22semidirect
27. #5121C2×C3semidirect
28. #5106C2×C3semidirect
37. C32×M16C2×C4semidirect
38. C2×C32×C8C2×C4semidirect
52. C2×C3×M16Dic3semidirect
53. C2×C3×M16C3×C4semidirect
75. #818C22×C3semidirect
76. #817C22×C3semidirect
121. C3×M16C2×Dic3semidirect
122. C3×M16C2×C3×C4semidirect
125. C2×C3×C8C2×Dic3semidirect
126. C2×C3×C8C2×C3×C4semidirect
153. C2×M16C3×Dic3semidirect
223. M16C2×C3×Dic3semidirect
224. C2×C8C2×C3×Dic3semidirect
264. C32#2911semidirect
305. C3#83752direct (N × H)
306. C3C3×#2911semidirect

Maximal subgroups

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

subgroupindex
C22×C32×M162
C2×C3×#9262
C3×#51212
C3×#51062
C3×#29113
#837523