Finite Group Databasebeta

← C3×#83339 #11874969

Subgroups — C3×#83339 #11874969

Order 1152.

823 conjugacy classes of subgroups.

The subgroup lattice has 323 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#533C211yesmaximal, characteristic
2C3×#5470C211yesmaximal, characteristic
3C3×#5080C212yesmaximal, complemented
4C3×#5078C212yesmaximal, complemented
5C3×#5065C214yesmaximal, complemented
6C3×#4998C214yesmaximal
7C2×C3×C4×C3⋊C8C211yesmaximal, characteristic
8C3×#3160—31nomaximal
9#83339C311yesmaximal, characteristic, direct product factor
10C32×C4⋊Q8C2212yes—
11C32×#125C2212yes—
12C32×C22⋊Q8—22no—
13C32×C4×Q8—22no—
14C32×#117C2212yes—
15C2×C32×C42C2211yescharacteristic
16C3×#926C2212yes—
17C3×#924—22no—
18C22×C3×C3⋊C8C2212yes—
19C3×#870C2212yes—
20C3×#869C2212yes—
21C3×C4×Dic6—22no—
22C3×#808C2218yes—
23C3×#807C2218yes—
24C3×C4×C3⋊C8C2212yes—
25C3×C4×C3⋊C8C2211yescharacteristic
26C3×C4×C3⋊C8C2211yescharacteristic
27C3×#533—21no—
28C3×#533—31no—
29C3×#533D311yescharacteristic
30C3×#533C2×C311yescharacteristic
31#5470C2×C311yescharacteristic
32C3×#500—32no—
33C3×#499—34no—
34C3×#498—32no—
35C3×#427—34no—
36C2×C3×C4×C8—31no—
37#5080C2×C312yescomplemented
38#5078C2×C312yescomplemented
39#5065C2×C314yescomplemented
40#4998C2×C314yes—
41C2×C4×C3⋊C8C2×C311yescharacteristic
42C2×C32×Q8—22no—
43C22×C32×C4D412yes—
44C22×C32×C4C2311yescharacteristic
45C2×C3×Dic6—22no—
46C32×C4⋊C4—24no—
47C32×C4⋊C4—22no—
48C32×C4⋊C4C2314yes—
49C32×C22⋊C4—22no—
50C32×C42—22no—
51C32×C42D412yes—
52C32×C42C2311yescharacteristic
53C32×C42C2311yescharacteristic
54C3×#217—22no—
55C3×C4⋊Dic3—22no—
56C3×C4⋊Dic3C2314yes—
57C3×Dic3⋊C4—24no—
58C3×C4×Dic3—22no—
59C2×C3×C3⋊C8Q818yescomplemented
60C2×C3×C3⋊C8C2312yes—
61C2×C3×C3⋊C8C2312yes—
62#3160—31noSylow
63C22×C3×C8—32no—
64C3×C4⋊Q8—22no—
65C3×C4⋊Q8—32no—
66C3×C4⋊Q8C2×D312yes—
67C3×C4⋊Q8C22×C312yes—
68C3×#125—22no—
69C3×#125—32no—
70C3×#125C2×D312yes—
71C3×#125C22×C312yes—
72C3×C22⋊Q8—24no—
73C3×C22⋊Q8—22no—
74C3×C22⋊Q8—22no—
75C3×C22⋊Q8—62no—
76C3×C4×Q8—24no—
77C3×C4×Q8—22no—
78C3×C4×Q8—22no—
79C3×C4×Q8—62no—
80C3×#117—22no—
81C3×#117—32no—
82C3×#117C2×D312yes—
83C3×#117C22×C312yes—
84C2×C3×C42—21no—
85C2×C3×C42C2×D311yescharacteristic
86C2×C3×C42C22×C311yescharacteristic
87#926C22×C312yes—
88#924—22no—
89C22×C3⋊C8C22×C312yes—
90#870C22×C312yes—
91#869C22×C312yes—
92C4×Dic6—22no—
93C3×#107—38no—
94C3×#106—38no—
95C3×C4×C8—31no—
96C3×C4×C8—32no—
97C3×C4×C8—31no—
98#808C22×C318yes—
99#807C22×C318yes—
100C4×C3⋊C8C22×C312yes—
101C4×C3⋊C8C22×C311yescharacteristic
102C4×C3⋊C8C22×C311yescharacteristic
103C23×C32C2×D411yescharacteristic
104C32×Q8—44no—
105C2×C32×C4—24no—
106C2×C32×C4—24no—
107C2×C32×C4C2×D412yes—
108C2×C32×C4C2×D412yes—
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×Q814yes—
111C2×C32×C4C2411yescharacteristic
112C2×C3×Dic3—24no—
113C3×Dic6—44no—
114C3×C3⋊C8C2×Q814yes—
115C3×C3⋊C8C2×Q814yes—
116#533—31no—
117#533C3×D311yescharacteristic
118#500—32no—
119#499—34no—
120#498—32no—
121#427—34no—
122C2×C4×C8—31no—
123C2×C3×Q8—24no—
124C2×C3×Q8—22no—
125C2×C3×Q8—22no—
126C2×C3×Q8—62no—
127C22×C3×C4—22no—
128C22×C3×C4—21no—
129C22×C3×C4#6712yes—
130C22×C3×C4C3×D412yes—
131C22×C3×C4C22×D311yescharacteristic
132C22×C3×C4C23×C311yescharacteristic
133C2×Dic6—22no—
134C2×C3×C8—38no—
135C2×C3×C8—32no—
136C2×C3×C8—32no—
137C3×C4⋊C4—28no—
138C3×C4⋊C4—24no—
139C3×C4⋊C4—24no—
140C3×C4⋊C4—22no—
141C3×C4⋊C4—24no—
142C3×C4⋊C4—22no—
143C3×C4⋊C4—24no—
144C3×C4⋊C4—34no—
145C3×C4⋊C4—64no—
146C3×C4⋊C4—62no—
147C3×C4⋊C4C22×D314yes—
148C3×C4⋊C4C23×C314yes—
149C3×C22⋊C4—24no—
150C3×C22⋊C4—22no—
151C3×C22⋊C4—22no—
152C3×C22⋊C4—62no—
153C3×C42—24no—
154C3×C42—22no—
155C3×C42—22no—
156C3×C42—22no—
157C3×C42—21no—
158C3×C42—21no—
159C3×C42—62no—
160C3×C42#6712yes—
161C3×C42C3×D412yes—
162C3×C42C22×D311yescharacteristic
163C3×C42C22×D311yescharacteristic
164C3×C42C23×C311yescharacteristic
165C3×C42C23×C311yescharacteristic
166#217—22no—
167C4⋊Dic3—22no—
168C4⋊Dic3C23×C314yes—
169Dic3⋊C4—24no—
170C4×Dic3—22no—
171C2×C3⋊C8C3×Q818yescomplemented
172C2×C3⋊C8C23×C312yes—
173C2×C3⋊C8C23×C312yes—
174C22×C32—22no—
175C22×C32C4⋊Q812yes—
176C22×C32C22×D411yescharacteristic
177C32×C4—22no—
178C32×C4—44no—
179C32×C4C4⋊Q812yes—
180C32×C4#13514yes—
181C32×C4C22×Q812yes—
182C3×Dic3—44no—
183C22×C8—32no—
184C4⋊Q8—32no—
185C4⋊Q8C2×C3×D312yes—
186#125—32no—
187#125C2×C3×D312yes—
188C22⋊Q8—22no—
189C22⋊Q8—62no—
190C4×Q8—22no—
191C4×Q8—62no—
192#117—32no—
193#117C2×C3×D312yes—
194C2×C42C2×C3×D311yescharacteristic
195#107—38no—
196#106—38no—
197C4×C8—31no—
198C4×C8—32no—
199C4×C8—31no—
200C23×C3—21no—
201C23×C3C2×#6711yescharacteristic
202C23×C3C2×C3×D411yescharacteristic
203C3×Q8—48no—
204C3×Q8—44no—
205C3×Q8—44no—
206C3×Q8—124no—
207C2×C3×C4—24no—
208C2×C3×C4—24no—
209C2×C3×C4—28no—
210C2×C3×C4—24no—
211C2×C3×C4—24no—
212C2×C3×C4—21no—
213C2×C3×C4—24no—
214C2×C3×C4—21no—
215C2×C3×C4—22no—
216C2×C3×C4—22no—
217C2×C3×C4—44no—
218C2×C3×C4—64no—
219C2×C3×C4D3×Q814yes—
220C2×C3×C4C2×#6712yes—
221C2×C3×C4C2×#6712yes—
222C2×C3×C4C2×#6711yescharacteristic
223C2×C3×C4C2×C3×D412yes—
224C2×C3×C4C2×C3×D411yescharacteristic
225C2×C3×C4C2×C3×D412yes—
226C2×C3×C4C2×C3×Q814yes—
227C2×C3×C4C23×D311yescharacteristic
228C2×C3×C4C24×C311yescharacteristic
229C2×Dic3—24no—
230Dic6—44no—
231C3×C8—34no—
232C3×C8—34no—
233C3⋊C8C2×C3×Q814yes—
234C3⋊C8C2×C3×Q814yes—
235C2×C32—22no—
236C2×C32C2×C4⋊Q811yescharacteristic
237C2×C32C2×#13512yes—
238C2×Q8—22no—
239C2×Q8—62no—
240C22×C4C3×#6712yes—
241C22×C4C22×C3×D311yescharacteristic
242C2×C8—32no—
243C2×C8—32no—
244C2×C8—38no—
245C4⋊C4—24no—
246C4⋊C4—22no—
247C4⋊C4—34no—
248C4⋊C4—64no—
249C4⋊C4—62no—
250C4⋊C4C22×C3×D314yes—
251C22⋊C4—22no—
252C22⋊C4—62no—
253C42—22no—
254C42—62no—
255C42C3×#6712yes—
256C42C22×C3×D311yescharacteristic
257C42C22×C3×D311yescharacteristic
258C22×C3—22no—
259C22×C3—22no—
260C22×C3—22no—
261C22×C3—21no—
262C22×C3—42no—
263C22×C3#94412yes—
264C22×C3C3×C4⋊Q812yes—
265C22×C3C22×#6711yescharacteristic
266C22×C3C22×C3×D411yescharacteristic
267C3×C4—22no—
268C3×C4—22no—
269C3×C4—22no—
270C3×C4—24no—
271C3×C4—22no—
272C3×C4—42no—
273C3×C4—48no—
274C3×C4—44no—
275C3×C4—44no—
276C3×C4—124no—
277C3×C4#94412yes—
278C3×C4#95014yes—
279C3×C4C3×C4⋊Q812yes—
280C3×C4C3×#13514yes—
281C3×C4C2×D3×Q812yes—
282C3×C4C22×C3×Q812yes—
283Dic3—44no—
284C32#316011yescharacteristic, complemented, Sylow
285C23C2×C3×#6711yescharacteristic
286Q8—44no—
287Q8—124no—
288C2×C4—24no—
289C2×C4—24no—
290C2×C4—64no—
291C2×C4C3×D3×Q814yes—
292C2×C4C2×C3×#6712yes—
293C2×C4C2×C3×#6711yescharacteristic
294C2×C4C2×C3×#6712yes—
295C2×C4C23×C3×D311yescharacteristic
296C8—34no—
297C8—34no—
298C2×C3—22no—
299C2×C3—22no—
300C2×C3—21no—
301C2×C3—22no—
302C2×C3—42no—
303C2×C3C2×#94411yescharacteristic
304C2×C3C2×#95012yes—
305C2×C3C2×C3×C4⋊Q811yescharacteristic
306C2×C3C2×C3×#13512yes—
307C22—22no—
308C22C3×#94412yes—
309C22C22×C3×#6711yescharacteristic
310C4—22no—
311C4—44no—
312C4—124no—
313C4C3×#94412yes—
314C4C3×#95014yes—
315C4C2×C3×D3×Q812yes—
316C3—21no—
317C3#8333911yescharacteristic, direct product factor
318C3C3×#316011yescharacteristic, complemented
319C2—22no—
320C2C2×C3×#94411yescharacteristic
321C2C2×C3×#95012yes—
subgroupG/H
centerC2×C3×C4C2×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#533C2
socleC22×C32C22×D4
prime radicalC23×C32C2×D4
hypercenterC3×#533D3
hypocenterC3C3×#3160
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×C42 ◁ C3×#533

Complements

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

NH ≅ G/Ntype
3. C3×#5080C2semidirect
4. C3×#5078C2semidirect
5. C3×#5065C2semidirect
9. #83339C3direct (N × H)
37. #5080C2×C3semidirect
38. #5078C2×C3semidirect
39. #5065C2×C3semidirect
59. C2×C3×C3⋊C8Q8semidirect
171. C2×C3⋊C8C3×Q8semidirect
284. C32#3160semidirect
317. C3#83339direct (N × H)
318. C3C3×#3160semidirect

Maximal subgroups

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

subgroupindex
C32×#5332
C3×#54702
C3×#50802
C3×#50782
C3×#50652
C3×#49982
C2×C3×C4×C3⋊C82
C3×#31603
#833393