Finite Group Databasebeta

← C3⋊D3×#483 #11869365

Subgroups — C3⋊D3×#483 #11869365

Order 1152.

1380 conjugacy classes of subgroups.

The subgroup lattice has 429 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊D3×C22⋊Q8C211yesmaximal, characteristic
2C2×C4⋊C4×C3⋊D3C211yesmaximal, characteristic
3C32×#483C211yesmaximal, characteristic, complemented
4#10592742C211yesmaximal, characteristic, complemented
5#10592670C211yesmaximal, characteristic, complemented
6#10592561C212yesmaximal, complemented
7C3⋊D3×#106C212yesmaximal, complemented
8#10592504C212yesmaximal, complemented
9C3⋊D3×#103C212yesmaximal, complemented
10C3⋊D3×C22⋊C8C211yesmaximal, characteristic
11#10592420C211yesmaximal, characteristic, complemented
12D3×#483—34nomaximal
13C2×Q8×C3⋊D3C2211yescharacteristic
14C22×C4×C3⋊D3—21no—
15C22×C4×C3⋊D3C2211yescharacteristic
16C32×C22⋊Q8C2211yescharacteristic
17C2×C32×C4⋊C4C2211yescharacteristic
18#64155C2211yescharacteristic
19C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
20#64133C2211yescharacteristic
21C2×#3750—21no—
22C2×C8×C3⋊D3C2212yes—
23#64106C2211yescharacteristic
24#64105—21no—
25C4⋊C4×C3⋊D3—21no—
26C4⋊C4×C3⋊D3—21no—
27C4⋊C4×C3⋊D3—21no—
28C4⋊C4×C3⋊D3C2211yescharacteristic
29C4⋊C4×C3⋊D3C2212yes—
30C4⋊C4×C3⋊D3C2212yes—
31C22⋊C4×C3⋊D3—21no—
32#64087—21no—
33C32×#106C2212yescomplemented
34C32×#103C2212yescomplemented
35C32×C22⋊C8C2211yescharacteristic
36#63662C2212yescomplemented
37#63657C2211yescharacteristic
38#63647C2212yes—
39#63644C2212yescomplemented
40#63643C2212yescomplemented
41#63637C2212yescomplemented
42#63635C2212yescomplemented
43#63635C2212yescomplemented
44D3×C22⋊Q8—34no—
45C2×D3×C4⋊C4—34no—
46C3×#483D314yescomplemented
47#5043—34no—
48#4971—34no—
49#4862—38no—
50D3×#106—38no—
51#4805—38no—
52D3×#103—38no—
53D3×C22⋊C8—34no—
54#4721—34no—
55C23×C3⋊D3D411yescharacteristic
56C2×C32×Q8C2311yescharacteristic
57C22×C32×C4—21no—
58C22×C32×C4C2311yescharacteristic
59C22×C3⋊Dic3—21no—
60C22×C3⋊Dic3D411yescharacteristic
61Q8×C3⋊D3—24no—
62C2×C4×C3⋊D3—24no—
63C2×C4×C3⋊D3—21no—
64C2×C4×C3⋊D3—21no—
65C2×C4×C3⋊D3—22no—
66C2×C4×C3⋊D3—22no—
67C2×C4×C3⋊D3—44no—
68C2×C4×C3⋊D3D411yescharacteristic
69C2×C4×C3⋊D3D411yescharacteristic
70C2×C4×C3⋊D3C2311yescharacteristic
71C2×C4×C3⋊D3C2311yescharacteristic
72C2×#634—21no—
73C2×#634C2311yescharacteristic
74C2×C32×C8C2312yes—
75C32×C4⋊C4—21no—
76C32×C4⋊C4—21no—
77C32×C4⋊C4C2312yes—
78C32×C4⋊C4C2311yescharacteristic
79C32×C22⋊C4—21no—
80#3757—21no—
81#3752—21no—
82#3752—21no—
83C4⋊(C3⋊Dic3)—21no—
84C4⋊(C3⋊Dic3)—21no—
85C4⋊(C3⋊Dic3)C2312yes—
86C4⋊(C3⋊Dic3)C2311yescharacteristic
87#3750—21no—
88#3750—21no—
89#3750—21no—
90#3750—22no—
91#3750—22no—
92C2×C3⋊(C3⋊C8)C2312yes—
93C8×C3⋊D3—24no—
94C2×#483—91noSylow
95C2×D3×Q8—34no—
96C22×C4×D3—34no—
97C22×C4×D3—64no—
98C3×C22⋊Q8C2×D314yes—
99C2×C3×C4⋊C4C2×D314yes—
100#946—34no—
101C2×C4⋊Dic3—34no—
102#924—34no—
103C2×Dic3⋊C4—64no—
104C2×D3×C8—38no—
105#897—34no—
106#896—64no—
107D3×C4⋊C4—38no—
108D3×C4⋊C4—38no—
109D3×C4⋊C4—34no—
110D3×C4⋊C4—64no—
111D3×C4⋊C4—64no—
112D3×C4⋊C4—64no—
113D3×C22⋊C4—64no—
114#878—64no—
115C3×#106C2×D318yescomplemented
116C3×#103C2×D318yescomplemented
117C3×C22⋊C8C2×D314yes—
118#835—38no—
119#830—34no—
120(C2×D3)⋊C8—38no—
121#817—38no—
122#816—38no—
123#810—38no—
124#808—38no—
125#808—38no—
126C23×C32C2×D411yescharacteristic
127C22×C3⋊D3—22no—
128C22×C3⋊D3—22no—
129C22×C3⋊D3SD1614yes—
130C22×C3⋊D3C2×D411yescharacteristic
131C22×C3⋊D3C2×D411yescharacteristic
132C32×Q8—22no—
133C2×C32×C4—22no—
134C2×C32×C4—22no—
135C2×C32×C4—21no—
136C2×C32×C4—21no—
137C2×C32×C4—42no—
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2411yescharacteristic
140C2×C3⋊Dic3—22no—
141C2×C3⋊Dic3—21no—
142C2×C3⋊Dic3—22no—
143C2×C3⋊Dic3—21no—
144C2×C3⋊Dic3—42no—
145C2×C3⋊Dic3C2×D411yescharacteristic
146C2×C3⋊Dic3C2×D411yescharacteristic
147C4×C3⋊D3—22no—
148C4×C3⋊D3—22no—
149C4×C3⋊D3—22no—
150C4×C3⋊D3—42no—
151C4×C3⋊D3—44no—
152C4×C3⋊D3—44no—
153C4×C3⋊D3—42no—
154C4×C3⋊D3#4114yes—
155#634—22no—
156#634—42no—
157C32×C8—22no—
158C3⋊(C3⋊C8)—22no—
159C2×C22⋊Q8—91no—
160C22×C4⋊C4—91no—
161#483—91no—
162#483—91no—
163#483—92no—
164#483—92no—
165#483—91no—
166#483C3⋊D311yescharacteristic, direct product factor
167C2×#106—92no—
168C2×#103—92no—
169C2×C22⋊C8—91no—
170C23×D3—34no—
171C2×C3×Q8C22×D314yes—
172C22×C3×C4—24no—
173C22×C3×C4C22×D314yes—
174C22×Dic3—34no—
175C22×Dic3—64no—
176D3×Q8—616no—
177C2×C4×D3—34no—
178C2×C4×D3—34no—
179C2×C4×D3—34no—
180C2×C4×D3—34no—
181C2×C4×D3—616no—
182C2×C4×D3—64no—
183C2×C4×D3—64no—
184C2×C4×D3—68no—
185C2×C4×D3—68no—
186C2×C4×D3—1216no—
187C2×Dic6—34no—
188C2×Dic6—64no—
189C2×C3×C8C22×D318yes—
190C3×C4⋊C4—24no—
191C3×C4⋊C4—24no—
192C3×C4⋊C4C22×D314yes—
193C3×C4⋊C4C22×D318yes—
194C3×C22⋊C4—24no—
195#217—64no—
196(C2×D3)⋊C4—64no—
197(C2×D3)⋊C4—64no—
198C4⋊Dic3—34no—
199C4⋊Dic3—38no—
200C4⋊Dic3—64no—
201C4⋊Dic3—64no—
202Dic3⋊C4—64no—
203Dic3⋊C4—64no—
204Dic3⋊C4—68no—
205Dic3⋊C4—68no—
206Dic3⋊C4—64no—
207C2×C3⋊C8—38no—
208D3×C8—616no—
209C22×C32—21no—
210C22×C32—21no—
211C22×C32C2×SD1612yes—
212C22×C32C22×D411yescharacteristic
213C2×C3⋊D3—21no—
214C2×C3⋊D3—21no—
215C2×C3⋊D3—28no—
216C2×C3⋊D3#12312yes—
217C2×C3⋊D3C2×SD1612yes—
218C2×C3⋊D3C2×SD1612yes—
219C2×C3⋊D3#13712yes—
220C32×C4—21no—
221C32×C4—41no—
222C32×C4—42no—
223C32×C4—41no—
224C32×C4C2×#4112yes—
225C3⋊Dic3—21no—
226C3⋊Dic3—41no—
227C3⋊Dic3—42no—
228C3⋊Dic3—41no—
229C3⋊Dic3#12312yes—
230C22×Q8—91no—
231C23×C4—91no—
232C23×C4—181no—
233C22×C8—92no—
234C22⋊Q8—91no—
235C22⋊Q8—91no—
236C22⋊Q8—91no—
237C22⋊Q8—181no—
238C22⋊Q8—181no—
239C22⋊Q8C2×C3⋊D311yescharacteristic
240C2×C4⋊C4—91no—
241C2×C4⋊C4—92no—
242C2×C4⋊C4—92no—
243C2×C4⋊C4—91no—
244C2×C4⋊C4—181no—
245C2×C4⋊C4—181no—
246C2×C4⋊C4—181no—
247C2×C4⋊C4—181no—
248C2×C4⋊C4C2×C3⋊D311yescharacteristic
249C2×C22⋊C4—181no—
250#106—92no—
251#106—92no—
252#106—92no—
253#106C2×C3⋊D312yescomplemented
254#103—92no—
255#103—92no—
256#103—92no—
257#103C2×C3⋊D312yescomplemented
258C22⋊C8—91no—
259C22⋊C8—92no—
260C22⋊C8C2×C3⋊D311yescharacteristic
261C23×C3D3×D414yes—
262C22×D3—34no—
263C22×D3—316no—
264C22×D3—34no—
265C22×D3—68no—
266C22×D3—68no—
267C3×Q8—28no—
268C2×C3×C4—28no—
269C2×C3×C4—28no—
270C2×C3×C4—24no—
271C2×C3×C4—24no—
272C2×C3×C4—48no—
273C2×C3×C4D3×D414yes—
274C2×C3×C4C23×D314yes—
275C2×Dic3—34no—
276C2×Dic3—34no—
277C2×Dic3—68no—
278C2×Dic3—64no—
279C2×Dic3—68no—
280C2×Dic3—64no—
281C2×Dic3—128no—
282C4×D3—316no—
283C4×D3—68no—
284C4×D3—68no—
285C4×D3—68no—
286C4×D3—128no—
287C4×D3—1216no—
288C4×D3—1216no—
289C4×D3—128no—
290Dic6—68no—
291Dic6—128no—
292C3×C8—28no—
293C3⋊C8—68no—
294C2×C32—22no—
295C2×C32C2×#12311yescharacteristic
296C2×C32C22×SD1611yescharacteristic
297C2×C32C2×#13711yescharacteristic
298C3⋊D3—22no—
299C3⋊D3#48314yesdirect product factor
300C24—91no—
301C2×Q8—91no—
302C2×Q8—181no—
303C2×Q8—184no—
304C2×Q8C22×C3⋊D311yescharacteristic
305C22×C4—21no—
306C22×C4—91no—
307C22×C4—91no—
308C22×C4—91no—
309C22×C4—91no—
310C22×C4—91no—
311C22×C4—184no—
312C22×C4—181no—
313C22×C4—181no—
314C22×C4—182no—
315C22×C4—182no—
316C22×C4—181no—
317C22×C4—364no—
318C22×C4C22×C3⋊D311yescharacteristic
319C2×C8—92no—
320C2×C8—184no—
321C2×C8C22×C3⋊D312yes—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—92no—
325C4⋊C4—91no—
326C4⋊C4—182no—
327C4⋊C4—182no—
328C4⋊C4—181no—
329C4⋊C4—181no—
330C4⋊C4—181no—
331C4⋊C4—181no—
332C4⋊C4—181no—
333C4⋊C4C22×C3⋊D312yes—
334C4⋊C4C22×C3⋊D311yescharacteristic
335C22⋊C4—21no—
336C22⋊C4—181no—
337C22⋊C4—181no—
338C22⋊C4—181no—
339C22×C3—24no—
340C22×C3—24no—
341C22×C3D3×SD1618yes—
342C22×C3C2×D3×D414yes—
343C2×D3—38no—
344C2×D3—38no—
345C2×D3—38no—
346C2×D3—38no—
347C2×D3—632no—
348C2×D3—64no—
349C2×D3—64no—
350C3×C4—24no—
351C3×C4—44no—
352C3×C4—48no—
353C3×C4—44no—
354C3×C4D3×#4118yes—
355Dic3—38no—
356Dic3—64no—
357Dic3—124no—
358Dic3—128no—
359Dic3—124no—
360C32C2×#48311yescharacteristic, complemented, Sylow
361C23—91no—
362C23—91no—
363C23—94no—
364C23—182no—
365C23—182no—
366C23D4×C3⋊D311yescharacteristic
367Q8—22no—
368Q8—182no—
369Q8—362no—
370C2×C4—22no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—22no—
374C2×C4—42no—
375C2×C4—91no—
376C2×C4—94no—
377C2×C4—91no—
378C2×C4—182no—
379C2×C4—182no—
380C2×C4—182no—
381C2×C4—182no—
382C2×C4—181no—
383C2×C4—181no—
384C2×C4—182no—
385C2×C4—364no—
386C2×C4—364no—
387C2×C4—362no—
388C2×C4—362no—
389C2×C4—362no—
390C2×C4D4×C3⋊D311yescharacteristic
391C2×C4C23×C3⋊D311yescharacteristic
392C8—22no—
393C8—182no—
394C2×C3—28no—
395C2×C3D3×#12314yes—
396C2×C3C2×D3×SD1614yes—
397C2×C3D3×#13714yes—
398D3—316no—
399D3—68no—
400C22—21no—
401C22—21no—
402C22—92no—
403C22—92no—
404C22—92no—
405C22—92no—
406C22—188no—
407C22—181no—
408C22—181no—
409C22SD16×C3⋊D312yes—
410C22C2×D4×C3⋊D311yescharacteristic
411C4—21no—
412C4—41no—
413C4—42no—
414C4—41no—
415C4—92no—
416C4—181no—
417C4—361no—
418C4—362no—
419C4—361no—
420C4#41×C3⋊D312yes—
421C3D3×#48314yescomplemented
422C2—22no—
423C2—94no—
424C2—182no—
425C2C3⋊D3×#12311yescharacteristic
426C2C2×SD16×C3⋊D311yescharacteristic
427C2C3⋊D3×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#483C2
socleC22×C32C22×D4
prime radicalC23×C3⋊D3D4
hypercenter#483C3⋊D3
hypocenterC32C2×#483
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
3. C32×#483C2semidirect
4. #10592742C2semidirect
5. #10592670C2semidirect
6. #10592561C2semidirect
7. C3⋊D3×#106C2semidirect
8. #10592504C2semidirect
9. C3⋊D3×#103C2semidirect
11. #10592420C2semidirect
33. C32×#106C22semidirect
34. C32×#103C22semidirect
36. #63662C22semidirect
39. #63644C22semidirect
40. #63643C22semidirect
41. #63637C22semidirect
42. #63635C22semidirect
43. #63635C22semidirect
46. C3×#483D3semidirect
115. C3×#106C2×D3semidirect
116. C3×#103C2×D3semidirect
166. #483C3⋊D3direct (N × H)
253. #106C2×C3⋊D3semidirect
257. #103C2×C3⋊D3semidirect
299. C3⋊D3#483direct (N × H)
360. C32C2×#483semidirect
421. C3D3×#483semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×C22⋊Q82
C2×C4⋊C4×C3⋊D32
C32×#4832
#105927422
#105926702
#105925612
C3⋊D3×#1062
#105925042
C3⋊D3×#1032
C3⋊D3×C22⋊C82
#105924202
D3×#4833