Finite Group Databasebeta

← C3⋊D3×#487 #11873384

Subgroups — C3⋊D3×#487 #11873384

Order 1152.

1272 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊D3×C4⋊Q8C211yesmaximal, characteristic
2C3⋊D3×C4⋊Q8C211yesmaximal, characteristic
3C32×#487C211yesmaximal, characteristic, complemented
4#10592792C211yesmaximal, characteristic, complemented
5#10592778C211yesmaximal, characteristic, complemented
6C3⋊D3×#103C214yesmaximal
7#10592491C214yesmaximal, complemented
8C4×C8×C3⋊D3C211yesmaximal, characteristic
9#10592380C211yesmaximal, characteristic, complemented
10D3×#487—34nomaximal
11C2×Q8×C3⋊D3—21no—
12C2×Q8×C3⋊D3C2212yes—
13C32×C4⋊Q8C2211yescharacteristic
14C32×C4⋊Q8C2211yescharacteristic
15#64153—21no—
16#64153C2212yes—
17C2×C8×C3⋊D3C2212yes—
18C4⋊C4×C3⋊D3—21no—
19C4⋊C4×C3⋊D3—21no—
20C4⋊C4×C3⋊D3—21no—
21C4⋊C4×C3⋊D3C2212yes—
22#64097—21no—
23#64097—21no—
24#64097—21no—
25#64097C2212yes—
26C42×C3⋊D3C2211yescharacteristic
27#64078C2211yescharacteristic
28#64078C2211yescharacteristic
29C32×#103C2214yes—
30C32×C4×C8C2211yescharacteristic
31#63662C2214yes—
32#63643C2214yes—
33C8×C3⋊Dic3C2212yes—
34#63637C2214yes—
35C4×C3⋊(C3⋊C8)C2211yescharacteristic
36D3×C4⋊Q8—34no—
37D3×C4⋊Q8—34no—
38C3×#487D314yescomplemented
39#5093—34no—
40#5079—34no—
41D3×#103—316no—
42#4792—316no—
43C4×D3×C8—34no—
44#4681—34no—
45C2×C32×Q8—21no—
46C2×C32×Q8C2312yes—
47Q8×C3⋊D3—28no—
48Q8×C3⋊D3—44no—
49C2×C4×C3⋊D3—22no—
50C2×C4×C3⋊D3—22no—
51C2×C4×C3⋊D3D411yescharacteristic
52C2×C4×C3⋊D3D411yescharacteristic
53C2×C4×C3⋊D3C2311yescharacteristic
54C2×#634—21no—
55C2×#634—22no—
56C2×#634—22no—
57C2×#634C2312yes—
58C2×C32×C8C2312yes—
59C32×C4⋊C4—21no—
60C32×C4⋊C4—21no—
61C32×C4⋊C4—21no—
62C32×C4⋊C4C2312yes—
63C32×C42C2311yescharacteristic
64C4⋊(C3⋊Dic3)—21no—
65C4⋊(C3⋊Dic3)—21no—
66C4⋊(C3⋊Dic3)—21no—
67C4⋊(C3⋊Dic3)C2312yes—
68#3750—22no—
69#3750—22no—
70#3750—22no—
71#3750—22no—
72C4×C3⋊Dic3D411yescharacteristic
73C4×C3⋊Dic3D411yescharacteristic
74C4×C3⋊Dic3C2311yescharacteristic
75C2×C3⋊(C3⋊C8)C2312yes—
76C8×C3⋊D3—24no—
77C2×#487—91noSylow
78C2×D3×Q8—38no—
79C2×D3×Q8—64no—
80C3×C4⋊Q8C2×D314yes—
81C3×C4⋊Q8C2×D314yes—
82#944—38no—
83#944—64no—
84C2×D3×C8—38no—
85D3×C4⋊C4—38no—
86D3×C4⋊C4—64no—
87D3×C4⋊C4—64no—
88D3×C4⋊C4—64no—
89#888—38no—
90#888—64no—
91#888—64no—
92#888—64no—
93C42×D3—34no—
94#869—34no—
95#869—34no—
96C3×#103C2×D3116yes—
97C3×C4×C8C2×D314yes—
98#835—316no—
99#816—316no—
100C8×Dic3—38no—
101#810—316no—
102C4×C3⋊C8—34no—
103C22×C3⋊D3C2×D411yescharacteristic
104C32×Q8—24no—
105C32×Q8—42no—
106C2×C32×C4—22no—
107C2×C32×C4—22no—
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2411yescharacteristic
111C2×C3⋊Dic3—22no—
112C2×C3⋊Dic3—22no—
113C2×C3⋊Dic3C2×D411yescharacteristic
114C2×C3⋊Dic3C2×D411yescharacteristic
115C2×C3⋊Dic3C2×D411yescharacteristic
116C4×C3⋊D3—44no—
117C4×C3⋊D3—44no—
118C4×C3⋊D3SD1614yes—
119C4×C3⋊D3Q1614yes—
120C4×C3⋊D3#4114yes—
121#634—24no—
122#634—42no—
123#634—44no—
124#634—44no—
125C32×C8—22no—
126C3⋊(C3⋊C8)—22no—
127C2×C4⋊Q8—91no—
128C2×C4⋊Q8—91no—
129#487—91no—
130#487—91no—
131#487—94no—
132#487—91no—
133#487C3⋊D311yescharacteristic, direct product factor
134C2×#103—94no—
135C2×C4×C8—91no—
136C2×C3×Q8—24no—
137C2×C3×Q8C22×D318yes—
138D3×Q8—632no—
139D3×Q8—1216no—
140C2×C4×D3—34no—
141C2×C4×D3—34no—
142C2×C4×D3—34no—
143C2×C4×D3—68no—
144C2×C4×D3—68no—
145C2×Dic6—38no—
146C2×Dic6—68no—
147C2×Dic6—68no—
148C2×Dic6—64no—
149C2×C3×C8C22×D318yes—
150C3×C4⋊C4—24no—
151C3×C4⋊C4—24no—
152C3×C4⋊C4—24no—
153C3×C4⋊C4C22×D318yes—
154C3×C42C22×D314yes—
155C4⋊Dic3—38no—
156C4⋊Dic3—64no—
157C4⋊Dic3—64no—
158C4⋊Dic3—64no—
159Dic3⋊C4—68no—
160Dic3⋊C4—68no—
161Dic3⋊C4—68no—
162Dic3⋊C4—68no—
163C4×Dic3—34no—
164C4×Dic3—34no—
165C4×Dic3—34no—
166C2×C3⋊C8—38no—
167D3×C8—616no—
168C22×C32C22×D411yescharacteristic
169C2×C3⋊D3#12412yes—
170C2×C3⋊D3C2×SD1612yes—
171C2×C3⋊D3C2×Q1612yes—
172C32×C4—42no—
173C32×C4—42no—
174C32×C4C2×SD1612yes—
175C32×C4C2×Q1612yes—
176C32×C4C2×#4112yes—
177C3⋊Dic3—42no—
178C3⋊Dic3—42no—
179C3⋊Dic3#12412yes—
180C3⋊Dic3C2×SD1612yes—
181C3⋊Dic3C2×Q1612yes—
182C22×Q8—92no—
183C22×Q8—181no—
184C22×C8—92no—
185C4⋊Q8—92no—
186C4⋊Q8—92no—
187C4⋊Q8—91no—
188C4⋊Q8—91no—
189C4⋊Q8—181no—
190C4⋊Q8—181no—
191C4⋊Q8—181no—
192C4⋊Q8—181no—
193C4⋊Q8C2×C3⋊D311yescharacteristic
194C4⋊Q8C2×C3⋊D311yescharacteristic
195C2×C4⋊C4—92no—
196C2×C4⋊C4—181no—
197C2×C4⋊C4—181no—
198C2×C4⋊C4—181no—
199C2×C42—91no—
200#103—94no—
201#103—94no—
202#103—94no—
203#103C2×C3⋊D314yes—
204C4×C8—92no—
205C4×C8—91no—
206C4×C8C2×C3⋊D311yescharacteristic
207C22×D3—34no—
208C3×Q8—216no—
209C3×Q8—48no—
210C2×C3×C4—28no—
211C2×C3×C4—28no—
212C2×C3×C4D3×D414yes—
213C2×C3×C4D3×D414yes—
214C2×C3×C4C23×D314yes—
215C2×Dic3—34no—
216C2×Dic3—34no—
217C2×Dic3—34no—
218C2×Dic3—68no—
219C2×Dic3—68no—
220C4×D3—316no—
221C4×D3—316no—
222C4×D3—316no—
223C4×D3—1216no—
224C4×D3—1216no—
225Dic6—616no—
226Dic6—1216no—
227Dic6—1216no—
228Dic6—128no—
229C3×C8—28no—
230C3⋊C8—68no—
231C2×C32C2×#12411yescharacteristic
232C2×C32C22×SD1611yescharacteristic
233C2×C32C22×Q1611yescharacteristic
234C3⋊D3#48714yesdirect product factor
235C2×Q8—21no—
236C2×Q8—92no—
237C2×Q8—182no—
238C2×Q8—182no—
239C2×Q8—188no—
240C2×Q8—181no—
241C2×Q8—364no—
242C2×Q8C22×C3⋊D312yes—
243C22×C4—91no—
244C22×C4—91no—
245C22×C4—91no—
246C22×C4—182no—
247C22×C4—182no—
248C2×C8—92no—
249C2×C8—184no—
250C2×C8C22×C3⋊D312yes—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—92no—
255C4⋊C4—182no—
256C4⋊C4—182no—
257C4⋊C4—182no—
258C4⋊C4—182no—
259C4⋊C4—181no—
260C4⋊C4—181no—
261C4⋊C4—181no—
262C4⋊C4C22×C3⋊D312yes—
263C42—91no—
264C42—91no—
265C42—91no—
266C42C22×C3⋊D311yescharacteristic
267C22×C3C2×D3×D414yes—
268C2×D3—38no—
269C2×D3—38no—
270C2×D3—38no—
271C3×C4—48no—
272C3×C4—48no—
273C3×C4D3×SD1618yes—
274C3×C4D3×Q1618yes—
275C3×C4D3×#4118yes—
276Dic3—38no—
277Dic3—38no—
278Dic3—38no—
279Dic3—128no—
280Dic3—128no—
281C32C2×#48711yescharacteristic, complemented, Sylow
282C23—91no—
283Q8—24no—
284Q8—42no—
285Q8—184no—
286Q8—364no—
287Q8—364no—
288Q8—362no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—91no—
292C2×C4—91no—
293C2×C4—91no—
294C2×C4—94no—
295C2×C4—94no—
296C2×C4—94no—
297C2×C4—182no—
298C2×C4—182no—
299C2×C4—364no—
300C2×C4—364no—
301C2×C4D4×C3⋊D311yescharacteristic
302C2×C4D4×C3⋊D311yescharacteristic
303C2×C4C23×C3⋊D311yescharacteristic
304C8—22no—
305C8—182no—
306C2×C3D3×#12414yes—
307C2×C3C2×D3×SD1614yes—
308C2×C3C2×D3×Q1614yes—
309D3—316no—
310C22—92no—
311C22—92no—
312C22—92no—
313C22C2×D4×C3⋊D311yescharacteristic
314C4—42no—
315C4—42no—
316C4—92no—
317C4—92no—
318C4—92no—
319C4—362no—
320C4—362no—
321C4SD16×C3⋊D312yes—
322C4Q16×C3⋊D312yes—
323C4#41×C3⋊D312yes—
324C3D3×#48714yescomplemented
325C2—94no—
326C2C3⋊D3×#12411yescharacteristic
327C2C2×SD16×C3⋊D311yescharacteristic
328C2C2×Q16×C3⋊D311yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#487C2
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenter#487C3⋊D3
hypocenterC32C2×#487
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
3. C32×#487C2semidirect
4. #10592792C2semidirect
5. #10592778C2semidirect
7. #10592491C2semidirect
9. #10592380C2semidirect
38. C3×#487D3semidirect
133. #487C3⋊D3direct (N × H)
234. C3⋊D3#487direct (N × H)
281. C32C2×#487semidirect
324. C3D3×#487semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×C4⋊Q82
C32×#4872
#105927922
#105927782
C3⋊D3×#1032
#105924912
C4×C8×C3⋊D32
#105923802
D3×#4873