Finite Group Databasebeta

← C3⋊D3×#480 #11869321

Subgroups — C3⋊D3×#480 #11869321

Order 1152.

1536 conjugacy classes of subgroups.

The subgroup lattice has 471 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊D3×#121C211yesmaximal, characteristic
2C2×C4⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
3C32×#480C211yesmaximal, characteristic, complemented
4#10592732C211yesmaximal, characteristic, complemented
5#10592666C211yesmaximal, characteristic, complemented
6#10592581C212yesmaximal, complemented
7C3⋊D3×#107C212yesmaximal, complemented
8#10592473C212yesmaximal, complemented
9C3⋊D3×#102C212yesmaximal, complemented
10#10592435C211yesmaximal, characteristic, complemented
11C3⋊D3×C22⋊C8C211yesmaximal, characteristic, complemented
12D3×#480—34nomaximal
13C2×D4×C3⋊D3—21no—
14C2×D4×C3⋊D3C2211yescharacteristic
15C22×C4×C3⋊D3—21no—
16C22×C4×C3⋊D3C2211yescharacteristic
17C32×#121C2211yescharacteristic
18C2×C32×C4⋊C4C2211yescharacteristic, complemented
19#64148—21no—
20#64147C2211yescharacteristic
21#64139C2211yescharacteristic
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
23C2×#3750—21no—
24C2×C8×C3⋊D3C2212yes—
25#64104C2211yescharacteristic
26C4⋊C4×C3⋊D3—21no—
27C4⋊C4×C3⋊D3—21no—
28C4⋊C4×C3⋊D3C2211yescharacteristic
29C4⋊C4×C3⋊D3C2212yes—
30C4⋊C4×C3⋊D3C2212yescomplemented
31#64093—21no—
32C22⋊C4×C3⋊D3—21no—
33C32×#107C2212yescomplemented
34C32×#102C2212yescomplemented
35C32×C22⋊C8C2211yescharacteristic, complemented
36#63659C2212yescomplemented
37#63657C2211yescharacteristic, complemented
38#63648C2212yescomplemented
39#63647C2212yescomplemented
40#63645C2212yescomplemented
41#63636C2212yescomplemented
42#63634C2212yescomplemented
43#63634C2212yescomplemented
44D3×#121—34no—
45C2×D3×C4⋊C4—34no—
46C3×#480D314yescomplemented
47#5033—34no—
48#4967—34no—
49#4882—38no—
50D3×#107—38no—
51#4774—38no—
52D3×#102—38no—
53#4736—34no—
54D3×C22⋊C8—34no—
55C23×C3⋊D3—21no—
56C23×C3⋊D3D411yescharacteristic
57C2×C32×D4—21no—
58C2×C32×D4C2311yescharacteristic
59C22×C32×C4—21no—
60C22×C32×C4C2311yescharacteristic
61C2×#638—21no—
62C2×#638—21no—
63C2×#638—21no—
64C22×C3⋊Dic3—21no—
65C22×C3⋊Dic3D411yescharacteristic
66D4×C3⋊D3—24no—
67D4×C3⋊D3—44no—
68C2×C4⋊(C3⋊D3)—21no—
69C2×C4⋊(C3⋊D3)C2311yescharacteristic
70C2×C4×C3⋊D3—24no—
71C2×C4×C3⋊D3—21no—
72C2×C4×C3⋊D3—22no—
73C2×C4×C3⋊D3—22no—
74C2×C4×C3⋊D3—44no—
75C2×C4×C3⋊D3D411yescharacteristic
76C2×C4×C3⋊D3D411yescharacteristic
77C2×C4×C3⋊D3C2311yescharacteristic
78C2×C4×C3⋊D3C2311yescharacteristic
79C2×C32×C8C2312yes—
80C32×C4⋊C4—21no—
81C32×C4⋊C4C2312yes—
82C32×C4⋊C4C2311yescharacteristic
83C32×C22⋊C4—21no—
84#3757—21no—
85#3752—21no—
86#3752—21no—
87C4⋊(C3⋊Dic3)—21no—
88C4⋊(C3⋊Dic3)C2312yes—
89C4⋊(C3⋊Dic3)C2311yescharacteristic
90#3750—21no—
91#3750—22no—
92#3750—22no—
93C2×C3⋊(C3⋊C8)C2312yes—
94C8×C3⋊D3—24no—
95C2×#480—91noSylow
96C2×D3×D4—34no—
97C2×D3×D4—64no—
98C22×C4×D3—34no—
99C22×C4×D3—64no—
100C3×#121C2×D314yes—
101C2×C3×C4⋊C4C2×D314yescomplemented
102#939—64no—
103#938—34no—
104#930—34no—
105C2×C4⋊Dic3—34no—
106C2×Dic3⋊C4—64no—
107C2×D3×C8—38no—
108#895—34no—
109D3×C4⋊C4—34no—
110D3×C4⋊C4—38no—
111D3×C4⋊C4—38no—
112D3×C4⋊C4—64no—
113D3×C4⋊C4—64no—
114#884—64no—
115D3×C22⋊C4—64no—
116C3×#107C2×D318yescomplemented
117C3×#102C2×D318yescomplemented
118C3×C22⋊C8C2×D314yescomplemented
119#832—38no—
120#830—34no—
121#821—38no—
122(C2×D3)⋊C8—38no—
123#818—38no—
124#809—38no—
125#807—38no—
126#807—38no—
127C23×C32—21no—
128C23×C32C2×D411yescharacteristic
129C22×C3⋊D3—22no—
130C22×C3⋊D3—22no—
131C22×C3⋊D3—21no—
132C22×C3⋊D3—42no—
133C22×C3⋊D3—42no—
134C22×C3⋊D3—42no—
135C22×C3⋊D3D814yes—
136C22×C3⋊D3C2×D411yescharacteristic
137C22×C3⋊D3C2×D411yescharacteristic
138C32×D4—22no—
139C32×D4—42no—
140C2×C32×C4—22no—
141C2×C32×C4—22no—
142C2×C32×C4—21no—
143C2×C32×C4—42no—
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4C2411yescharacteristic
146#638—42no—
147#638—42no—
148#638—42no—
149C2×C3⋊Dic3—22no—
150C2×C3⋊Dic3—22no—
151C2×C3⋊Dic3—21no—
152C2×C3⋊Dic3—42no—
153C2×C3⋊Dic3C2×D411yescharacteristic
154C2×C3⋊Dic3C2×D411yescharacteristic
155C4⋊(C3⋊D3)—22no—
156C4⋊(C3⋊D3)—42no—
157C4×C3⋊D3—22no—
158C4×C3⋊D3—22no—
159C4×C3⋊D3—22no—
160C4×C3⋊D3—44no—
161C4×C3⋊D3—44no—
162C4×C3⋊D3—42no—
163C4×C3⋊D3#4114yes—
164C32×C8—22no—
165C3⋊(C3⋊C8)—22no—
166C2×#121—91no—
167C22×C4⋊C4—91no—
168#480—91no—
169#480—91no—
170#480—92no—
171#480—92no—
172#480—91no—
173#480C3⋊D311yescharacteristic, direct product factor
174C2×#107—92no—
175C2×#102—92no—
176C2×C22⋊C8—91no—
177C23×D3—34no—
178C23×D3—64no—
179C2×C3×D4—24no—
180C2×C3×D4C22×D314yes—
181C22×C3×C4—24no—
182C22×C3×C4C22×D314yes—
183C2×#67—64no—
184C2×#67—64no—
185C2×#67—64no—
186C22×Dic3—34no—
187C22×Dic3—64no—
188D3×D4—616no—
189D3×D4—1216no—
190C2×D12—34no—
191C2×D12—64no—
192C2×C4×D3—34no—
193C2×C4×D3—34no—
194C2×C4×D3—34no—
195C2×C4×D3—34no—
196C2×C4×D3—616no—
197C2×C4×D3—64no—
198C2×C4×D3—68no—
199C2×C4×D3—68no—
200C2×C4×D3—1216no—
201C2×C3×C8C22×D318yes—
202C3×C4⋊C4—24no—
203C3×C4⋊C4C22×D314yes—
204C3×C4⋊C4C22×D318yes—
205C3×C22⋊C4—24no—
206#217—64no—
207(C2×D3)⋊C4—64no—
208(C2×D3)⋊C4—64no—
209C4⋊Dic3—34no—
210C4⋊Dic3—38no—
211C4⋊Dic3—64no—
212Dic3⋊C4—64no—
213Dic3⋊C4—68no—
214Dic3⋊C4—68no—
215C2×C3⋊C8—38no—
216D3×C8—616no—
217C22×C32—21no—
218C22×C32—21no—
219C22×C32—41no—
220C22×C32—41no—
221C22×C32—41no—
222C22×C32C2×D812yes—
223C22×C32C22×D411yescharacteristic
224C2×C3⋊D3—21no—
225C2×C3⋊D3—21no—
226C2×C3⋊D3—28no—
227C2×C3⋊D3—41no—
228C2×C3⋊D3—41no—
229C2×C3⋊D3—41no—
230C2×C3⋊D3—84no—
231C2×C3⋊D3#12312yes—
232C2×C3⋊D3C2×D812yes—
233C2×C3⋊D3C2×D812yes—
234C2×C3⋊D3#13712yes—
235C32×C4—21no—
236C32×C4—42no—
237C32×C4—41no—
238C32×C4C2×#4112yes—
239C3⋊Dic3—21no—
240C3⋊Dic3—42no—
241C3⋊Dic3—41no—
242C3⋊Dic3#12312yes—
243C22×D4—91no—
244C22×D4—181no—
245C23×C4—91no—
246C23×C4—181no—
247C22×C8—92no—
248#121—91no—
249#121—91no—
250#121—91no—
251#121—181no—
252#121—181no—
253#121C2×C3⋊D311yescharacteristic
254C2×C4⋊C4—91no—
255C2×C4⋊C4—92no—
256C2×C4⋊C4—92no—
257C2×C4⋊C4—91no—
258C2×C4⋊C4—181no—
259C2×C4⋊C4—181no—
260C2×C4⋊C4—181no—
261C2×C4⋊C4C2×C3⋊D311yescharacteristic, complemented
262C2×C22⋊C4—181no—
263#107—92no—
264#107—92no—
265#107—92no—
266#107C2×C3⋊D312yescomplemented
267#102—92no—
268#102—92no—
269#102—92no—
270#102C2×C3⋊D312yescomplemented
271C22⋊C8—91no—
272C22⋊C8—92no—
273C22⋊C8C2×C3⋊D311yescharacteristic, complemented
274C23×C3—24no—
275C23×C3D3×D414yes—
276C22×D3—34no—
277C22×D3—316no—
278C22×D3—34no—
279C22×D3—68no—
280C22×D3—68no—
281C22×D3—64no—
282C22×D3—128no—
283C22×D3—128no—
284C22×D3—128no—
285C3×D4—28no—
286C3×D4—48no—
287C2×C3×C4—28no—
288C2×C3×C4—28no—
289C2×C3×C4—24no—
290C2×C3×C4—48no—
291C2×C3×C4D3×D414yes—
292C2×C3×C4C23×D314yes—
293#67—128no—
294#67—128no—
295#67—128no—
296C2×Dic3—34no—
297C2×Dic3—34no—
298C2×Dic3—68no—
299C2×Dic3—68no—
300C2×Dic3—64no—
301C2×Dic3—128no—
302D12—68no—
303D12—128no—
304C4×D3—316no—
305C4×D3—68no—
306C4×D3—68no—
307C4×D3—68no—
308C4×D3—1216no—
309C4×D3—1216no—
310C4×D3—128no—
311C3×C8—28no—
312C3⋊C8—68no—
313C2×C32—22no—
314C2×C32—81no—
315C2×C32C2×#12311yescharacteristic
316C2×C32C22×D811yescharacteristic
317C2×C32C2×#13711yescharacteristic
318C3⋊D3—22no—
319C3⋊D3—81no—
320C3⋊D3#48014yesdirect product factor
321C24—91no—
322C24—181no—
323C2×D4—21no—
324C2×D4—91no—
325C2×D4—181no—
326C2×D4—184no—
327C2×D4—181no—
328C2×D4—181no—
329C2×D4—181no—
330C2×D4—364no—
331C2×D4C22×C3⋊D311yescharacteristic
332C22×C4—21no—
333C22×C4—91no—
334C22×C4—91no—
335C22×C4—91no—
336C22×C4—91no—
337C22×C4—91no—
338C22×C4—184no—
339C22×C4—181no—
340C22×C4—182no—
341C22×C4—182no—
342C22×C4—181no—
343C22×C4—364no—
344C22×C4C22×C3⋊D311yescharacteristic
345C2×C8—92no—
346C2×C8—184no—
347C2×C8C22×C3⋊D312yes—
348C4⋊C4—21no—
349C4⋊C4—92no—
350C4⋊C4—91no—
351C4⋊C4—182no—
352C4⋊C4—182no—
353C4⋊C4—181no—
354C4⋊C4—181no—
355C4⋊C4C22×C3⋊D312yes—
356C4⋊C4C22×C3⋊D311yescharacteristic
357C22⋊C4—21no—
358C22⋊C4—181no—
359C22⋊C4—181no—
360C22⋊C4—181no—
361C22×C3—24no—
362C22×C3—24no—
363C22×C3—44no—
364C22×C3—44no—
365C22×C3—44no—
366C22×C3D3×D818yes—
367C22×C3C2×D3×D414yes—
368C2×D3—38no—
369C2×D3—38no—
370C2×D3—38no—
371C2×D3—38no—
372C2×D3—632no—
373C2×D3—64no—
374C2×D3—64no—
375C2×D3—124no—
376C2×D3—124no—
377C2×D3—124no—
378C2×D3—2416no—
379C3×C4—24no—
380C3×C4—48no—
381C3×C4—44no—
382C3×C4D3×#4118yes—
383Dic3—38no—
384Dic3—64no—
385Dic3—128no—
386Dic3—124no—
387C32C2×#48011yescharacteristic, complemented, Sylow
388C23—21no—
389C23—91no—
390C23—91no—
391C23—94no—
392C23—182no—
393C23—182no—
394C23—181no—
395C23—362no—
396C23—362no—
397C23—362no—
398C23D4×C3⋊D311yescharacteristic
399D4—22no—
400D4—42no—
401D4—182no—
402D4—362no—
403D4—362no—
404D4—362no—
405D4—362no—
406C2×C4—22no—
407C2×C4—21no—
408C2×C4—22no—
409C2×C4—42no—
410C2×C4—91no—
411C2×C4—94no—
412C2×C4—91no—
413C2×C4—182no—
414C2×C4—182no—
415C2×C4—182no—
416C2×C4—182no—
417C2×C4—181no—
418C2×C4—182no—
419C2×C4—364no—
420C2×C4—364no—
421C2×C4—362no—
422C2×C4—362no—
423C2×C4D4×C3⋊D311yescharacteristic
424C2×C4C23×C3⋊D311yescharacteristic
425C8—22no—
426C8—182no—
427C2×C3—28no—
428C2×C3—84no—
429C2×C3D3×#12314yes—
430C2×C3C2×D3×D814yes—
431C2×C3D3×#13714yes—
432D3—316no—
433D3—68no—
434D3—244no—
435C22—21no—
436C22—21no—
437C22—41no—
438C22—41no—
439C22—41no—
440C22—92no—
441C22—92no—
442C22—92no—
443C22—92no—
444C22—188no—
445C22—181no—
446C22—181no—
447C22—361no—
448C22—361no—
449C22—361no—
450C22—724no—
451C22D8×C3⋊D312yes—
452C22C2×D4×C3⋊D311yescharacteristic
453C4—21no—
454C4—42no—
455C4—41no—
456C4—92no—
457C4—181no—
458C4—362no—
459C4—361no—
460C4#41×C3⋊D312yes—
461C3D3×#48014yescomplemented
462C2—22no—
463C2—81no—
464C2—94no—
465C2—182no—
466C2—721no—
467C2C3⋊D3×#12311yescharacteristic
468C2C2×D8×C3⋊D311yescharacteristic
469C2C3⋊D3×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#480C2
socleC22×C32C22×D4
prime radicalC3⋊D3×#121C2
hypercenter#480C3⋊D3
hypocenterC32C2×#480
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×C3⋊D3C2semidirect
3. C32×#480C2semidirect
4. #10592732C2semidirect
5. #10592666C2semidirect
6. #10592581C2semidirect
7. C3⋊D3×#107C2semidirect
8. #10592473C2semidirect
9. C3⋊D3×#102C2semidirect
10. #10592435C2semidirect
11. C3⋊D3×C22⋊C8C2semidirect
18. C2×C32×C4⋊C4C22semidirect
22. C2×C4⋊(C3⋊Dic3)C22semidirect
30. C4⋊C4×C3⋊D3C22semidirect
33. C32×#107C22semidirect
34. C32×#102C22semidirect
35. C32×C22⋊C8C22semidirect
36. #63659C22semidirect
37. #63657C22semidirect
38. #63648C22semidirect
39. #63647C22semidirect
40. #63645C22semidirect
41. #63636C22semidirect
42. #63634C22semidirect
43. #63634C22semidirect
46. C3×#480D3semidirect
101. C2×C3×C4⋊C4C2×D3semidirect
116. C3×#107C2×D3semidirect
117. C3×#102C2×D3semidirect
118. C3×C22⋊C8C2×D3semidirect
173. #480C3⋊D3direct (N × H)
261. C2×C4⋊C4C2×C3⋊D3semidirect
266. #107C2×C3⋊D3semidirect
270. #102C2×C3⋊D3semidirect
273. C22⋊C8C2×C3⋊D3semidirect
320. C3⋊D3#480direct (N × H)
387. C32C2×#480semidirect
461. C3D3×#480semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×#1212
C2×C4⋊C4×C3⋊D32
C32×#4802
#105927322
#105926662
#105925812
C3⋊D3×#1072
#105924732
C3⋊D3×#1022
#105924352
C3⋊D3×C22⋊C82
D3×#4803