Finite Group Databasebeta

← C3×#81938 #11874972

Subgroups — C3×#81938 #11874972

Order 1152.

761 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5728C212yesmaximal
2C32×#500C211yesmaximal, characteristic, complemented
3C3×#5080C212yesmaximal, complemented
4C3×#4880C214yesmaximal
5C3×#4878C214yesmaximal, complemented
6C3×C4×D3×C8C211yesmaximal, characteristic
7C3×#4682C211yesmaximal, characteristic, complemented
8C3×#3160—31nomaximal
9#81938C311yesmaximal, characteristic, direct product factor
10C32×C4⋊Q8C2212yes—
11C3×#946—22no—
12C3×Q8×Dic3—22no—
13C2×C3×D3×C8C2212yes—
14C3×#897—22no—
15C3×#892C2214yes—
16C3×#890C2214yes—
17C3×#887—22no—
18C3×C42×D3C2211yescharacteristic
19C3×#869C2212yes—
20C32×#107C2214yes—
21C32×C4×C8C2211yescharacteristic
22C3×#818C2214yes—
23C3×C8×Dic3C2212yes—
24C3×#808C2218yes—
25C3×C4×C3⋊C8C2211yescharacteristic
26C3×#533—32no—
27#5728C2×C312yes—
28C3×#500—21no—
29C3×#500—31no—
30C3×#500D311yescharacteristic, complemented
31C3×#500C2×C311yescharacteristic, complemented
32C3×#499—34no—
33C3×#498—32no—
34C3×#427—34no—
35C2×C3×C4×C8—31no—
36#5080C2×C312yescomplemented
37#4880C2×C314yes—
38#4878C2×C314yescomplemented
39C4×D3×C8C2×C311yescharacteristic
40#4682C2×C311yescharacteristic, complemented
41C2×C32×Q8—22no—
42C2×C3×C4×D3D411yescharacteristic
43C2×C3×C4×D3D411yescharacteristic
44C2×C3×C4×D3C2311yescharacteristic
45C2×C3×Dic6—22no—
46C2×C32×C8C2312yes—
47C32×C4⋊C4—22no—
48C32×C4⋊C4C2314yes—
49C32×C42C2311yescharacteristic
50C3×(C2×D3)⋊C4—24no—
51C3×C4⋊Dic3—22no—
52C3×C4⋊Dic3—24no—
53C3×C4⋊Dic3C2314yes—
54C3×Dic3⋊C4—24no—
55C3×C4×Dic3—24no—
56C3×C4×Dic3D411yescharacteristic
57C3×C4×Dic3D411yescharacteristic
58C3×C4×Dic3C2311yescharacteristic
59C2×C3×C3⋊C8C2312yes—
60C3×D3×C8Q818yescomplemented
61#3160—31noSylow
62C22×C3×C8—32no—
63C3×C4⋊Q8—22no—
64C3×C4⋊Q8—32no—
65C3×C4⋊Q8C2×D312yes—
66C3×C4⋊Q8C22×C312yes—
67C3×#125—34no—
68C3×C22⋊Q8—62no—
69C3×C22⋊Q8—62no—
70C3×C4×Q8—62no—
71C3×C4×Q8—62no—
72C3×#117—34no—
73C2×C3×C42—31no—
74#946—22no—
75Q8×Dic3—22no—
76C2×D3×C8C22×C312yes—
77#897—22no—
78#892C22×C314yes—
79#890C22×C314yes—
80#887—22no—
81C42×D3C22×C311yescharacteristic
82#869C22×C312yes—
83C3×#107—24no—
84C3×#107—34no—
85C3×#107C2×D314yes—
86C3×#107C22×C314yes—
87C3×#106—38no—
88C3×C4×C8—21no—
89C3×C4×C8—32no—
90C3×C4×C8—31no—
91C3×C4×C8C2×D311yescharacteristic
92C3×C4×C8C22×C311yescharacteristic
93#818C22×C314yes—
94C8×Dic3C22×C312yes—
95#808C22×C318yes—
96C4×C3⋊C8C22×C311yescharacteristic
97C22×C3×D3C2×D411yescharacteristic
98C32×Q8—44no—
99C2×C32×C4—24no—
100C2×C32×C4C2×D411yescharacteristic
101C2×C32×C4C2×D411yescharacteristic
102C2×C32×C4C2411yescharacteristic
103C2×C3×Dic3—24no—
104C2×C3×Dic3C2×D411yescharacteristic
105C2×C3×Dic3C2×D411yescharacteristic
106C2×C3×Dic3C2×D411yescharacteristic
107C3×C4×D3—22no—
108C3×C4×D3—22no—
109C3×C4×D3C2×Q814yes—
110C3×Dic6—44no—
111C32×C8C2×Q814yes—
112C3×C3⋊C8C2×Q814yes—
113#533—32no—
114#500—31no—
115#500C3×D311yescharacteristic, complemented
116#499—34no—
117#498—32no—
118#427—34no—
119C2×C4×C8—31no—
120C2×C3×Q8—22no—
121C2×C3×Q8—22no—
122C2×C3×Q8—42no—
123C2×C3×Q8—62no—
124C22×C3×C4—31no—
125C22×C3×C4—31no—
126C22×C3×C4—31no—
127C2×C4×D3C3×D411yescharacteristic
128C2×C4×D3C3×D411yescharacteristic
129C2×C4×D3C23×C311yescharacteristic
130C2×Dic6—22no—
131C2×C3×C8—22no—
132C2×C3×C8—32no—
133C2×C3×C8—38no—
134C2×C3×C8C22×D312yes—
135C2×C3×C8C23×C312yes—
136C3×C4⋊C4—22no—
137C3×C4⋊C4—22no—
138C3×C4⋊C4—24no—
139C3×C4⋊C4—34no—
140C3×C4⋊C4—42no—
141C3×C4⋊C4—64no—
142C3×C4⋊C4—64no—
143C3×C4⋊C4—62no—
144C3×C4⋊C4C22×D314yes—
145C3×C4⋊C4C23×C314yes—
146C3×C22⋊C4—64no—
147C3×C42—21no—
148C3×C42—31no—
149C3×C42—31no—
150C3×C42—31no—
151C3×C42—64no—
152C3×C42C22×D311yescharacteristic
153C3×C42C23×C311yescharacteristic
154(C2×D3)⋊C4—24no—
155C4⋊Dic3—22no—
156C4⋊Dic3—24no—
157C4⋊Dic3C23×C314yes—
158Dic3⋊C4—24no—
159C4×Dic3—24no—
160C4×Dic3C3×D411yescharacteristic
161C4×Dic3C3×D411yescharacteristic
162C4×Dic3C23×C311yescharacteristic
163C2×C3⋊C8C23×C312yes—
164D3×C8C3×Q818yescomplemented
165C22×C32C22×D411yescharacteristic
166C2×C3×D3—21no—
167C2×C3×D3—21no—
168C2×C3×D3C4⋊Q812yes—
169C32×C4—44no—
170C32×C4#13512yes—
171C32×C4#13512yes—
172C32×C4C22×Q812yes—
173C3×Dic3—21no—
174C3×Dic3—21no—
175C3×Dic3—44no—
176C3×Dic3C4⋊Q812yes—
177C22×C8—32no—
178C4⋊Q8—32no—
179C4⋊Q8C2×C3×D312yes—
180#125—34no—
181C22⋊Q8—62no—
182C22⋊Q8—62no—
183C4×Q8—62no—
184C4×Q8—62no—
185#117—34no—
186C2×C42—31no—
187#107—34no—
188#107C2×C3×D314yes—
189#106—38no—
190C4×C8—32no—
191C4×C8—31no—
192C4×C8C2×C3×D311yescharacteristic
193C23×C3—31no—
194C22×D3C2×C3×D411yescharacteristic
195C3×Q8—44no—
196C3×Q8—44no—
197C3×Q8—84no—
198C3×Q8—124no—
199C2×C3×C4—24no—
200C2×C3×C4—24no—
201C2×C3×C4—21no—
202C2×C3×C4—21no—
203C2×C3×C4—21no—
204C2×C3×C4—31no—
205C2×C3×C4—34no—
206C2×C3×C4—31no—
207C2×C3×C4—31no—
208C2×C3×C4—44no—
209C2×C3×C4—62no—
210C2×C3×C4—62no—
211C2×C3×C4—64no—
212C2×C3×C4D3×D411yescharacteristic
213C2×C3×C4D3×D411yescharacteristic
214C2×C3×C4C2×C3×D411yescharacteristic
215C2×C3×C4C2×C3×D411yescharacteristic
216C2×C3×C4C23×D311yescharacteristic
217C2×C3×C4C24×C311yescharacteristic
218C2×Dic3—24no—
219C2×Dic3C2×C3×D411yescharacteristic
220C2×Dic3C2×C3×D411yescharacteristic
221C2×Dic3C2×C3×D411yescharacteristic
222C4×D3—22no—
223C4×D3—22no—
224C4×D3C2×C3×Q814yes—
225Dic6—44no—
226C3×C8—24no—
227C3×C8—34no—
228C3×C8D3×Q814yes—
229C3×C8C2×C3×Q814yes—
230C3⋊C8C2×C3×Q814yes—
231C2×C32C2×C4⋊Q811yescharacteristic
232C2×C32C2×#13511yescharacteristic
233C2×C32C2×#13511yescharacteristic
234C3×D3—22no—
235C2×Q8—22no—
236C2×Q8—62no—
237C22×C4—31no—
238C22×C4—31no—
239C22×C4—31no—
240C2×C8—32no—
241C2×C8—38no—
242C2×C8C22×C3×D312yes—
243C4⋊C4—22no—
244C4⋊C4—34no—
245C4⋊C4—64no—
246C4⋊C4—64no—
247C4⋊C4—62no—
248C4⋊C4C22×C3×D314yes—
249C22⋊C4—64no—
250C42—31no—
251C42—31no—
252C42—31no—
253C42—64no—
254C42C22×C3×D311yescharacteristic
255C22×C3—21no—
256C22×C3—32no—
257C22×C3—61no—
258C22×C3—61no—
259C22×C3C2×D3×D411yescharacteristic
260C22×C3C22×C3×D411yescharacteristic
261C2×D3—21no—
262C2×D3—21no—
263C2×D3C3×C4⋊Q812yes—
264C3×C4—22no—
265C3×C4—22no—
266C3×C4—22no—
267C3×C4—32no—
268C3×C4—44no—
269C3×C4—44no—
270C3×C4—61no—
271C3×C4—61no—
272C3×C4—84no—
273C3×C4—124no—
274C3×C4#91212yes—
275C3×C4#91912yes—
276C3×C4C3×#13512yes—
277C3×C4C3×#13512yes—
278C3×C4C2×D3×Q812yes—
279C3×C4C22×C3×Q812yes—
280Dic3—21no—
281Dic3—21no—
282Dic3—44no—
283Dic3C3×C4⋊Q812yes—
284C32#316011yescharacteristic, complemented, Sylow
285C23—31no—
286Q8—44no—
287Q8—124no—
288C2×C4—24no—
289C2×C4—31no—
290C2×C4—34no—
291C2×C4—31no—
292C2×C4—31no—
293C2×C4—62no—
294C2×C4—62no—
295C2×C4—64no—
296C2×C4C3×D3×D411yescharacteristic
297C2×C4C3×D3×D411yescharacteristic
298C2×C4C23×C3×D311yescharacteristic
299C8—34no—
300C8C3×D3×Q814yes—
301C2×C3—21no—
302C2×C3—21no—
303C2×C3—21no—
304C2×C3—62no—
305C2×C3D3×C4⋊Q811yescharacteristic
306C2×C3C2×#91211yescharacteristic
307C2×C3C2×#91911yescharacteristic
308C2×C3C2×C3×C4⋊Q811yescharacteristic
309C2×C3C2×C3×#13511yescharacteristic
310C2×C3C2×C3×#13511yescharacteristic
311D3—22no—
312C22—32no—
313C22—61no—
314C22—61no—
315C22C2×C3×D3×D411yescharacteristic
316C4—32no—
317C4—44no—
318C4—61no—
319C4—61no—
320C4—124no—
321C4C3×#91212yes—
322C4C3×#91912yes—
323C4C2×C3×D3×Q812yes—
324C3—21no—
325C3#8193811yescharacteristic, direct product factor
326C3C3×#316011yescharacteristic, complemented
327C2—62no—
328C2C3×D3×C4⋊Q811yescharacteristic
329C2C2×C3×#91211yescharacteristic
330C2C2×C3×#91911yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#500C2
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenterC3×#500D3
hypocenterC3C3×#3160
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#500

Complements

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

NH ≅ G/Ntype
2. C32×#500C2semidirect
3. C3×#5080C2semidirect
5. C3×#4878C2semidirect
7. C3×#4682C2semidirect
9. #81938C3direct (N × H)
30. C3×#500D3semidirect
31. C3×#500C2×C3semidirect
36. #5080C2×C3semidirect
38. #4878C2×C3semidirect
40. #4682C2×C3semidirect
60. C3×D3×C8Q8semidirect
115. #500C3×D3semidirect
164. D3×C8C3×Q8semidirect
284. C32#3160semidirect
325. C3#81938direct (N × H)
326. C3C3×#3160semidirect

Maximal subgroups

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

subgroupindex
C3×#57282
C32×#5002
C3×#50802
C3×#48802
C3×#48782
C3×C4×D3×C82
C3×#46822
C3×#31603
#819383