Finite Group Databasebeta

← C3⋊D3×#474 #11868225

Subgroups — C3⋊D3×#474 #11868225

Order 1152.

1440 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊D3×C4⋊Q8C211yesmaximal, characteristic, complemented
2C4×D4×C3⋊D3C211yesmaximal, characteristic
3C32×#474C211yesmaximal, characteristic, complemented
4#10592786C211yesmaximal, characteristic, complemented
5#10592706C211yesmaximal, characteristic, complemented
6#10592589C212yesmaximal, complemented
7C3⋊D3×#107C212yesmaximal, complemented
8#10592545C211yesmaximal, characteristic, complemented
9C3⋊D3×C4⋊C8C211yesmaximal, characteristic, complemented
10C3⋊D3×#102C212yesmaximal
11#10592458C212yesmaximal, complemented
12D3×#474—34nomaximal
13C2×Q8×C3⋊D3—21no—
14C2×D4×C3⋊D3C2211yescharacteristic
15C22×C4×C3⋊D3—21no—
16C32×C4⋊Q8C2211yescharacteristic, complemented
17C32×C4×D4C2211yescharacteristic
18#64153—21no—
19D4×C3⋊Dic3C2211yescharacteristic
20C4×#638—21no—
21C2×C8×C3⋊D3C2212yes—
22#64102C2211yescharacteristic
23C4⋊C4×C3⋊D3—21no—
24C4⋊C4×C3⋊D3C2211yescharacteristic
25C4⋊C4×C3⋊D3C2212yes—
26#64097—21no—
27#64097C2212yescomplemented
28#64090—21no—
29C22⋊C4×C3⋊D3—21no—
30C4×C4⋊(C3⋊D3)C2211yescharacteristic
31C42×C3⋊D3C2211yescharacteristic
32#64078C2211yescharacteristic, complemented
33C32×#107C2212yescomplemented
34C32×C4⋊C8C2211yescharacteristic, complemented
35C32×#102C2212yes—
36#63659C2212yes—
37#63648C2212yes—
38#63645C2212yescomplemented
39#63641C2212yescomplemented
40#63636C2212yes—
41#63634C2212yescomplemented
42#63634C2212yescomplemented
43C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
44D3×C4⋊Q8—34no—
45C4×D3×D4—34no—
46C3×#474D314yescomplemented
47#5087—34no—
48#5007—34no—
49#4890—38no—
50D3×#107—38no—
51#4846—34no—
52D3×C4⋊C8—34no—
53D3×#102—38no—
54#4759—38no—
55C23×C3⋊D3—21no—
56C2×C32×Q8—21no—
57C2×C32×D4C2311yescharacteristic
58C22×C32×C4—21no—
59C2×#638—21no—
60C22×C3⋊Dic3—21no—
61Q8×C3⋊D3—44no—
62D4×C3⋊D3—22no—
63D4×C3⋊D3Q814yescomplemented
64C2×C4⋊(C3⋊D3)C2311yescharacteristic
65C2×C4×C3⋊D3—21no—
66C2×C4×C3⋊D3—22no—
67C2×C4×C3⋊D3—21no—
68C2×C4×C3⋊D3—21no—
69C2×C4×C3⋊D3—44no—
70C2×C4×C3⋊D3D411yescharacteristic
71C2×C4×C3⋊D3D411yescharacteristic
72C2×C4×C3⋊D3C2311yescharacteristic
73C2×#634—21no—
74C2×#634—22no—
75C2×C32×C8C2312yes—
76C32×C4⋊C4—21no—
77C32×C4⋊C4C2312yes—
78C32×C4⋊C4C2311yescharacteristic
79C32×C22⋊C4—21no—
80C32×C42C2311yescharacteristic
81#3757—21no—
82#3752—21no—
83#3752—21no—
84C4⋊(C3⋊Dic3)—21no—
85C4⋊(C3⋊Dic3)C2312yes—
86C4⋊(C3⋊Dic3)C2311yescharacteristic
87#3750—21no—
88#3750—22no—
89#3750—22no—
90C4×C3⋊Dic3D411yescharacteristic
91C4×C3⋊Dic3D411yescharacteristic
92C4×C3⋊Dic3C2311yescharacteristic
93C2×C3⋊(C3⋊C8)C2312yes—
94C8×C3⋊D3—24no—
95C2×#474—91noSylow
96C2×D3×Q8—64no—
97C2×D3×D4—34no—
98C22×C4×D3—64no—
99C3×C4⋊Q8C2×D314yescomplemented
100C3×C4×D4C2×D314yes—
101#944—64no—
102D4×Dic3—34no—
103C4×#67—64no—
104C2×D3×C8—38no—
105#893—34no—
106D3×C4⋊C4—34no—
107D3×C4⋊C4—38no—
108D3×C4⋊C4—64no—
109#888—38no—
110#888—64no—
111#67⋊C4—64no—
112D3×C22⋊C4—64no—
113C4×D12—34no—
114C42×D3—34no—
115#869—34no—
116C3×#107C2×D318yescomplemented
117C3×C4⋊C8C2×D314yescomplemented
118C3×#102C2×D318yes—
119#832—38no—
120#821—38no—
121#818—38no—
122Dic3⋊C8—38no—
123#809—38no—
124#807—38no—
125#807—38no—
126C4⋊(C3⋊C8)—34no—
127C23×C32—21no—
128C22×C3⋊D3—21no—
129C22×C3⋊D3—24no—
130C22×C3⋊D3—42no—
131C22×C3⋊D3—42no—
132C22×C3⋊D3C2×D411yescharacteristic
133C32×Q8—42no—
134C32×D4—21no—
135C32×D4C2×Q812yescomplemented
136C2×C32×C4—22no—
137C2×C32×C4—21no—
138C2×C32×C4—42no—
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2411yescharacteristic
142#638—24no—
143C2×C3⋊Dic3—22no—
144C2×C3⋊Dic3—21no—
145C2×C3⋊Dic3—42no—
146C2×C3⋊Dic3C2×D411yescharacteristic
147C2×C3⋊Dic3C2×D411yescharacteristic
148C2×C3⋊Dic3C2×D411yescharacteristic
149C4⋊(C3⋊D3)—21no—
150C4⋊(C3⋊D3)C2×Q812yescomplemented
151C4×C3⋊D3—22no—
152C4×C3⋊D3—42no—
153C4×C3⋊D3—44no—
154C4×C3⋊D3—42no—
155C4×C3⋊D3—42no—
156C4×C3⋊D3D814yes—
157C4×C3⋊D3C2×Q812yes—
158C4×C3⋊D3#4112yes—
159#634—42no—
160#634—44no—
161C32×C8—22no—
162C3⋊(C3⋊C8)—22no—
163C2×C4⋊Q8—91no—
164C2×C4×D4—91no—
165#474—91no—
166#474—91no—
167#474—92no—
168#474—91no—
169#474—92no—
170#474C3⋊D311yescharacteristic, direct product factor
171C2×#107—92no—
172C2×C4⋊C8—91no—
173C2×#102—92no—
174C23×D3—64no—
175C2×C3×Q8—24no—
176C2×C3×D4C22×D314yes—
177C22×C3×C4—24no—
178C2×#67—64no—
179C22×Dic3—64no—
180D3×Q8—1216no—
181D3×D4—316no—
182D3×D4—68no—
183C2×D12—34no—
184C2×C4×D3—34no—
185C2×C4×D3—34no—
186C2×C4×D3—34no—
187C2×C4×D3—64no—
188C2×C4×D3—64no—
189C2×C4×D3—68no—
190C2×C4×D3—64no—
191C2×C4×D3—1216no—
192C2×Dic6—68no—
193C2×Dic6—64no—
194C2×C3×C8C22×D318yes—
195C3×C4⋊C4—24no—
196C3×C4⋊C4C22×D314yes—
197C3×C4⋊C4C22×D318yes—
198C3×C22⋊C4—24no—
199C3×C42C22×D314yes—
200#217—64no—
201(C2×D3)⋊C4—64no—
202(C2×D3)⋊C4—64no—
203C4⋊Dic3—34no—
204C4⋊Dic3—38no—
205C4⋊Dic3—64no—
206Dic3⋊C4—64no—
207Dic3⋊C4—68no—
208Dic3⋊C4—68no—
209C4×Dic3—34no—
210C4×Dic3—34no—
211C4×Dic3—34no—
212C2×C3⋊C8—38no—
213D3×C8—616no—
214C22×C32—22no—
215C22×C32—41no—
216C22×C32—41no—
217C22×C32C22×D411yescharacteristic
218C2×C3⋊D3—22no—
219C2×C3⋊D3—41no—
220C2×C3⋊D3—41no—
221C2×C3⋊D3—48no—
222C2×C3⋊D3C22⋊Q812yes—
223C2×C3⋊D3C2×D812yes—
224C2×C3⋊D3#13712yes—
225C32×C4—21no—
226C32×C4—42no—
227C32×C4—41no—
228C32×C4C2×D812yes—
229C32×C4C22×Q811yescharacteristic
230C32×C4C2×#4111yescharacteristic
231C3⋊Dic3—21no—
232C3⋊Dic3—42no—
233C3⋊Dic3—41no—
234C3⋊Dic3C22⋊Q812yes—
235C3⋊Dic3C2×D812yes—
236C22×Q8—181no—
237C22×D4—91no—
238C23×C4—181no—
239C22×C8—92no—
240C4⋊Q8—92no—
241C4⋊Q8—91no—
242C4⋊Q8—181no—
243C4⋊Q8—181no—
244C4⋊Q8C2×C3⋊D311yescharacteristic, complemented
245C4×D4—91no—
246C4×D4—91no—
247C4×D4—91no—
248C4×D4—181no—
249C4×D4—181no—
250C4×D4C2×C3⋊D311yescharacteristic
251C2×C4⋊C4—91no—
252C2×C4⋊C4—92no—
253C2×C4⋊C4—181no—
254C2×C22⋊C4—181no—
255C2×C42—91no—
256#107—92no—
257#107—92no—
258#107—92no—
259#107C2×C3⋊D312yescomplemented
260C4⋊C8—92no—
261C4⋊C8—91no—
262C4⋊C8C2×C3⋊D311yescharacteristic, complemented
263#102—92no—
264#102—92no—
265#102—92no—
266#102C2×C3⋊D312yes—
267C23×C3—24no—
268C22×D3—34no—
269C22×D3—616no—
270C22×D3—64no—
271C22×D3—128no—
272C22×D3—128no—
273C3×Q8—48no—
274C3×D4—24no—
275C3×D4D3×Q818yescomplemented
276C2×C3×C4—28no—
277C2×C3×C4—24no—
278C2×C3×C4—48no—
279C2×C3×C4D3×D414yes—
280C2×C3×C4D3×D414yes—
281C2×C3×C4C23×D314yes—
282#67—616no—
283C2×Dic3—34no—
284C2×Dic3—34no—
285C2×Dic3—34no—
286C2×Dic3—68no—
287C2×Dic3—64no—
288C2×Dic3—128no—
289D12—38no—
290D12—64no—
291C4×D3—316no—
292C4×D3—38no—
293C4×D3—38no—
294C4×D3—68no—
295C4×D3—128no—
296C4×D3—128no—
297C4×D3—1216no—
298C4×D3—128no—
299Dic6—1216no—
300Dic6—128no—
301C3×C8—28no—
302C3⋊C8—68no—
303C2×C32—42no—
304C2×C32C2×C22⋊Q811yescharacteristic
305C2×C32C22×D811yescharacteristic
306C2×C32C2×#13711yescharacteristic
307C3⋊D3—42no—
308C3⋊D3#47414yesdirect product factor
309C24—181no—
310C2×Q8—21no—
311C2×Q8—182no—
312C2×Q8—181no—
313C2×Q8—364no—
314C2×D4—94no—
315C2×D4—91no—
316C2×D4—182no—
317C2×D4—181no—
318C2×D4C22×C3⋊D311yescharacteristic
319C22×C4—21no—
320C22×C4—91no—
321C22×C4—91no—
322C22×C4—91no—
323C22×C4—181no—
324C22×C4—181no—
325C22×C4—182no—
326C22×C4—181no—
327C22×C4—181no—
328C22×C4—364no—
329C2×C8—92no—
330C2×C8—184no—
331C2×C8C22×C3⋊D312yes—
332C4⋊C4—21no—
333C4⋊C4—92no—
334C4⋊C4—91no—
335C4⋊C4—181no—
336C4⋊C4—182no—
337C4⋊C4—182no—
338C4⋊C4—181no—
339C4⋊C4C22×C3⋊D312yes—
340C4⋊C4C22×C3⋊D311yescharacteristic
341C22⋊C4—21no—
342C22⋊C4—181no—
343C22⋊C4—181no—
344C22⋊C4—181no—
345C42—91no—
346C42—91no—
347C42—91no—
348C42C22×C3⋊D311yescharacteristic
349C22×C3—28no—
350C22×C3—44no—
351C22×C3—44no—
352C22×C3C2×D3×D414yes—
353C2×D3—38no—
354C2×D3—38no—
355C2×D3—38no—
356C2×D3—68no—
357C2×D3—1232no—
358C2×D3—124no—
359C2×D3—124no—
360C3×C4—24no—
361C3×C4—48no—
362C3×C4—44no—
363C3×C4D3×D818yes—
364C3×C4C2×D3×Q814yes—
365C3×C4D3×#4114yes—
366Dic3—38no—
367Dic3—38no—
368Dic3—64no—
369Dic3—128no—
370Dic3—124no—
371C32C2×#47411yescharacteristic, complemented, Sylow
372C23—21no—
373C23—91no—
374C23—184no—
375C23—181no—
376C23—362no—
377C23—362no—
378Q8—42no—
379Q8—364no—
380Q8—362no—
381D4—21no—
382D4—92no—
383D4—184no—
384D4—181no—
385D4Q8×C3⋊D312yescomplemented
386C2×C4—21no—
387C2×C4—22no—
388C2×C4—42no—
389C2×C4—91no—
390C2×C4—91no—
391C2×C4—92no—
392C2×C4—92no—
393C2×C4—94no—
394C2×C4—91no—
395C2×C4—182no—
396C2×C4—181no—
397C2×C4—182no—
398C2×C4—362no—
399C2×C4—362no—
400C2×C4—364no—
401C2×C4—362no—
402C2×C4—362no—
403C2×C4D4×C3⋊D311yescharacteristic
404C2×C4D4×C3⋊D311yescharacteristic
405C2×C4C23×C3⋊D311yescharacteristic
406C8—22no—
407C8—182no—
408C2×C3—48no—
409C2×C3D3×C22⋊Q814yes—
410C2×C3C2×D3×D814yes—
411C2×C3D3×#13714yes—
412D3—316no—
413D3—128no—
414C22—22no—
415C22—41no—
416C22—41no—
417C22—92no—
418C22—92no—
419C22—92no—
420C22—182no—
421C22—368no—
422C22—361no—
423C22—361no—
424C22C2×D4×C3⋊D311yescharacteristic
425C4—21no—
426C4—41no—
427C4—42no—
428C4—92no—
429C4—92no—
430C4—181no—
431C4—361no—
432C4—362no—
433C4D8×C3⋊D312yes—
434C4C2×Q8×C3⋊D311yescharacteristic
435C4#41×C3⋊D311yescharacteristic
436C3D3×#47414yescomplemented
437C2—42no—
438C2—94no—
439C2—362no—
440C2C3⋊D3×C22⋊Q811yescharacteristic
441C2C2×D8×C3⋊D311yescharacteristic
442C2C3⋊D3×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#474C2
socleC22×C32C22×D4
prime radicalC2×D4×C3⋊D3C22
hypercenter#474C3⋊D3
hypocenterC32C2×#474
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. C3⋊D3×C4⋊Q8C2semidirect
3. C32×#474C2semidirect
4. #10592786C2semidirect
5. #10592706C2semidirect
6. #10592589C2semidirect
7. C3⋊D3×#107C2semidirect
8. #10592545C2semidirect
9. C3⋊D3×C4⋊C8C2semidirect
11. #10592458C2semidirect
16. C32×C4⋊Q8C22semidirect
27. #64097C22semidirect
32. #64078C22semidirect
33. C32×#107C22semidirect
34. C32×C4⋊C8C22semidirect
38. #63645C22semidirect
39. #63641C22semidirect
41. #63634C22semidirect
42. #63634C22semidirect
43. C4⋊(C3⋊(C3⋊C8))C22semidirect
46. C3×#474D3semidirect
63. D4×C3⋊D3Q8semidirect
99. C3×C4⋊Q8C2×D3semidirect
116. C3×#107C2×D3semidirect
117. C3×C4⋊C8C2×D3semidirect
135. C32×D4C2×Q8semidirect
150. C4⋊(C3⋊D3)C2×Q8semidirect
170. #474C3⋊D3direct (N × H)
244. C4⋊Q8C2×C3⋊D3semidirect
259. #107C2×C3⋊D3semidirect
262. C4⋊C8C2×C3⋊D3semidirect
275. C3×D4D3×Q8semidirect
308. C3⋊D3#474direct (N × H)
371. C32C2×#474semidirect
385. D4Q8×C3⋊D3semidirect
436. C3D3×#474semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×C4⋊Q82
C4×D4×C3⋊D32
C32×#4742
#105927862
#105927062
#105925892
C3⋊D3×#1072
#105925452
C3⋊D3×C4⋊C82
C3⋊D3×#1022
#105924582
D3×#4743