Finite Group Databasebeta

← C3⋊D3×#461 #11865463

Subgroups — C3⋊D3×#461 #11865463

Order 1152.

1632 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×C3⋊D3C212yesmaximal
2C3⋊D3×C4⋊Q8C211yesmaximal, characteristic, complemented
3C4×D4×C3⋊D3C211yesmaximal, characteristic
4C32×#461C211yesmaximal, characteristic, complemented
5#10592861C212yesmaximal, complemented
6#10592782C211yesmaximal, characteristic, complemented
7#10592718C211yesmaximal, characteristic, complemented
8#10592540C211yesmaximal, characteristic, complemented
9C3⋊D3×C4⋊C8C211yesmaximal, characteristic, complemented
10#10592517C212yesmaximal, complemented
11C3⋊D3×#103C212yesmaximal, complemented
12D3×#461—34nomaximal
13C2×Q8×C3⋊D3C2212yes—
14C2×D4×C3⋊D3C2211yescharacteristic
15C22×C4×C3⋊D3—21no—
16C2×C32×SD16C2212yes—
17C32×C4⋊Q8C2211yescharacteristic, complemented
18C32×C4×D4C2211yescharacteristic
19#64153C2212yescomplemented
20C2×#3755C2212yes—
21D4×C3⋊Dic3C2211yescharacteristic
22C2×#3754C2212yes—
23C4×#638—21no—
24SD16×C3⋊D3—28no—
25C2×#3744C2212yes—
26C2×C8×C3⋊D3C2212yes—
27#64102C2211yescharacteristic
28C4⋊C4×C3⋊D3—21no—
29C4⋊C4×C3⋊D3—21no—
30C4⋊C4×C3⋊D3C2211yescharacteristic
31#64097—21no—
32#64097—21no—
33#64090—21no—
34C22⋊C4×C3⋊D3—21no—
35C4×C4⋊(C3⋊D3)C2211yescharacteristic
36C42×C3⋊D3C2211yescharacteristic
37#64078C2211yescharacteristic, complemented
38C32×C4⋊C8C2211yescharacteristic, complemented
39C32×#103C2212yescomplemented
40#63662C2212yescomplemented
41#63643C2212yescomplemented
42#63641C2212yescomplemented
43#63637C2212yescomplemented
44C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
45C2×D3×SD16—38no—
46D3×C4⋊Q8—34no—
47C4×D3×D4—34no—
48C3×#461D314yescomplemented
49#5162—38no—
50#5083—34no—
51#5019—34no—
52#4841—34no—
53D3×C4⋊C8—34no—
54#4818—38no—
55D3×#103—38no—
56C23×C3⋊D3—21no—
57C2×C32×Q8C2312yes—
58C2×C32×D4C2311yescharacteristic
59C22×C32×C4—21no—
60C2×#638—21no—
61C22×C3⋊Dic3—21no—
62Q8×C3⋊D3—24no—
63Q8×C3⋊D3—24no—
64D4×C3⋊D3—22no—
65D4×C3⋊D3D414yes—
66C2×C4⋊(C3⋊D3)C2311yescharacteristic
67C2×C4×C3⋊D3—21no—
68C2×C4×C3⋊D3—22no—
69C2×C4×C3⋊D3—21no—
70C2×C4×C3⋊D3—21no—
71C2×C4×C3⋊D3—44no—
72C2×C4×C3⋊D3D411yescharacteristic
73C2×C4×C3⋊D3D411yescharacteristic
74C2×C4×C3⋊D3C2311yescharacteristic
75C2×#634—22no—
76C2×#634C2312yes—
77C32×SD16—24no—
78C2×C32×C8C2312yes—
79C32×C4⋊C4—21no—
80C32×C4⋊C4—21no—
81C32×C4⋊C4C2311yescharacteristic
82C32×C22⋊C4—21no—
83C32×C42C2311yescharacteristic
84#3757—21no—
85#3755—24no—
86#3754—24no—
87#3752—21no—
88#3752—21no—
89C4⋊(C3⋊Dic3)—21no—
90C4⋊(C3⋊Dic3)—21no—
91C4⋊(C3⋊Dic3)C2311yescharacteristic
92#3750—21no—
93#3750—22no—
94#3750—22no—
95C4×C3⋊Dic3D411yescharacteristic
96C4×C3⋊Dic3D411yescharacteristic
97C4×C3⋊Dic3C2311yescharacteristic
98C2×C3⋊(C3⋊C8)C2312yes—
99#3744—24no—
100C8×C3⋊D3—24no—
101C2×#461—91noSylow
102C2×D3×Q8—38no—
103C2×D3×D4—34no—
104C22×C4×D3—64no—
105C2×C3×SD16C2×D318yes—
106C3×C4⋊Q8C2×D314yescomplemented
107C3×C4×D4C2×D314yes—
108#944—38no—
109C2×#215—38no—
110D4×Dic3—34no—
111C2×#214—38no—
112C4×#67—64no—
113D3×SD16—632no—
114C2×#204—38no—
115C2×D3×C8—38no—
116#893—34no—
117D3×C4⋊C4—34no—
118D3×C4⋊C4—64no—
119D3×C4⋊C4—64no—
120#888—64no—
121#888—64no—
122#67⋊C4—64no—
123D3×C22⋊C4—64no—
124C4×D12—34no—
125C42×D3—34no—
126#869—34no—
127C3×C4⋊C8C2×D314yescomplemented
128C3×#103C2×D318yescomplemented
129#835—38no—
130#816—38no—
131Dic3⋊C8—38no—
132#810—38no—
133C4⋊(C3⋊C8)—34no—
134C23×C32—21no—
135C22×C3⋊D3—21no—
136C22×C3⋊D3—24no—
137C22×C3⋊D3—42no—
138C22×C3⋊D3—42no—
139C22×C3⋊D3C2×D411yescharacteristic
140C32×Q8—22no—
141C32×Q8—22no—
142C32×D4—21no—
143C32×D4C2×D412yes—
144C2×C32×C4—22no—
145C2×C32×C4—21no—
146C2×C32×C4—42no—
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4C2411yescharacteristic
150#638—24no—
151C2×C3⋊Dic3—22no—
152C2×C3⋊Dic3—21no—
153C2×C3⋊Dic3—42no—
154C2×C3⋊Dic3C2×D411yescharacteristic
155C2×C3⋊Dic3C2×D411yescharacteristic
156C2×C3⋊Dic3C2×D411yescharacteristic
157C4⋊(C3⋊D3)—21no—
158C4⋊(C3⋊D3)C2×D412yes—
159C4×C3⋊D3—22no—
160C4×C3⋊D3—44no—
161C4×C3⋊D3—42no—
162C4×C3⋊D3—42no—
163C4×C3⋊D3—42no—
164C4×C3⋊D3SD1614yescomplemented
165C4×C3⋊D3C2×D412yes—
166C4×C3⋊D3#4112yes—
167#634—22no—
168#634—22no—
169#634—44no—
170C32×C8—22no—
171C3⋊(C3⋊C8)—22no—
172C22×SD16—92no—
173C2×C4⋊Q8—91no—
174C2×C4×D4—91no—
175#461—92no—
176#461—91no—
177#461—91no—
178#461—91no—
179#461—92no—
180#461C3⋊D311yescharacteristic, direct product factor
181C2×C4⋊C8—91no—
182C2×#103—92no—
183C23×D3—64no—
184C2×C3×Q8C22×D318yes—
185C2×C3×D4C22×D314yes—
186C22×C3×C4—24no—
187C2×#67—64no—
188C22×Dic3—64no—
189D3×Q8—616no—
190D3×Q8—616no—
191D3×D4—316no—
192D3×D4—68no—
193C2×D12—34no—
194C2×C4×D3—34no—
195C2×C4×D3—34no—
196C2×C4×D3—34no—
197C2×C4×D3—64no—
198C2×C4×D3—64no—
199C2×C4×D3—68no—
200C2×C4×D3—64no—
201C2×C4×D3—1216no—
202C2×Dic6—38no—
203C2×Dic6—68no—
204C3×SD16—216no—
205C2×C3×C8C22×D318yes—
206C3×C4⋊C4—24no—
207C3×C4⋊C4—24no—
208C3×C4⋊C4C22×D314yes—
209C3×C22⋊C4—24no—
210C3×C42C22×D314yes—
211#217—64no—
212#215—616no—
213#214—616no—
214(C2×D3)⋊C4—64no—
215(C2×D3)⋊C4—64no—
216C4⋊Dic3—34no—
217C4⋊Dic3—64no—
218C4⋊Dic3—64no—
219Dic3⋊C4—64no—
220Dic3⋊C4—68no—
221Dic3⋊C4—68no—
222C4×Dic3—34no—
223C4×Dic3—34no—
224C4×Dic3—34no—
225C2×C3⋊C8—38no—
226#204—616no—
227D3×C8—616no—
228C22×C32—22no—
229C22×C32—41no—
230C22×C32—41no—
231C22×C32C22×D411yescharacteristic
232C2×C3⋊D3—22no—
233C2×C3⋊D3—41no—
234C2×C3⋊D3—41no—
235C2×C3⋊D3—48no—
236C2×C3⋊D3#12112yes—
237C2×C3⋊D3C2×SD1612yes—
238C2×C3⋊D3#13712yes—
239C32×C4—21no—
240C32×C4—42no—
241C32×C4—41no—
242C32×C4C2×SD1612yescomplemented
243C32×C4C22×D411yescharacteristic
244C32×C4C2×#4111yescharacteristic
245C3⋊Dic3—21no—
246C3⋊Dic3—42no—
247C3⋊Dic3—41no—
248C3⋊Dic3#12112yes—
249C3⋊Dic3C2×SD1612yescomplemented
250C22×Q8—92no—
251C22×D4—91no—
252C23×C4—181no—
253C2×SD16—92no—
254C2×SD16—92no—
255C2×SD16—92no—
256C2×SD16—188no—
257C2×SD16C2×C3⋊D312yes—
258C22×C8—92no—
259C4⋊Q8—92no—
260C4⋊Q8—91no—
261C4⋊Q8—181no—
262C4⋊Q8—181no—
263C4⋊Q8C2×C3⋊D311yescharacteristic, complemented
264C4×D4—91no—
265C4×D4—91no—
266C4×D4—91no—
267C4×D4—181no—
268C4×D4—181no—
269C4×D4C2×C3⋊D311yescharacteristic
270C2×C4⋊C4—91no—
271C2×C4⋊C4—181no—
272C2×C4⋊C4—181no—
273C2×C22⋊C4—181no—
274C2×C42—91no—
275C4⋊C8—92no—
276C4⋊C8—91no—
277C4⋊C8C2×C3⋊D311yescharacteristic, complemented
278#103—92no—
279#103—92no—
280#103—92no—
281#103C2×C3⋊D312yescomplemented
282C23×C3—24no—
283C22×D3—34no—
284C22×D3—616no—
285C22×D3—64no—
286C22×D3—128no—
287C22×D3—128no—
288C3×Q8—28no—
289C3×Q8—28no—
290C3×D4—24no—
291C3×D4D3×D418yes—
292C2×C3×C4—28no—
293C2×C3×C4—24no—
294C2×C3×C4—48no—
295C2×C3×C4D3×D414yes—
296C2×C3×C4D3×D414yes—
297C2×C3×C4C23×D314yes—
298#67—616no—
299C2×Dic3—34no—
300C2×Dic3—34no—
301C2×Dic3—34no—
302C2×Dic3—68no—
303C2×Dic3—64no—
304C2×Dic3—128no—
305D12—38no—
306D12—64no—
307C4×D3—316no—
308C4×D3—38no—
309C4×D3—38no—
310C4×D3—68no—
311C4×D3—128no—
312C4×D3—128no—
313C4×D3—1216no—
314C4×D3—128no—
315Dic6—68no—
316Dic6—68no—
317Dic6—1216no—
318C3×C8—28no—
319C3⋊C8—68no—
320C2×C32—42no—
321C2×C32C2×#12111yescharacteristic
322C2×C32C22×SD1611yescharacteristic
323C2×C32C2×#13711yescharacteristic
324C3⋊D3—42no—
325C3⋊D3#46114yesdirect product factor
326C24—181no—
327C2×Q8—92no—
328C2×Q8—182no—
329C2×Q8—184no—
330C2×Q8—184no—
331C2×Q8C22×C3⋊D312yes—
332C2×D4—94no—
333C2×D4—91no—
334C2×D4—182no—
335C2×D4—181no—
336C2×D4C22×C3⋊D311yescharacteristic
337C22×C4—21no—
338C22×C4—91no—
339C22×C4—91no—
340C22×C4—91no—
341C22×C4—181no—
342C22×C4—181no—
343C22×C4—182no—
344C22×C4—181no—
345C22×C4—181no—
346C22×C4—364no—
347SD16—24no—
348SD16—184no—
349SD16—184no—
350SD16—184no—
351C2×C8—92no—
352C2×C8—184no—
353C2×C8C22×C3⋊D312yes—
354C4⋊C4—21no—
355C4⋊C4—21no—
356C4⋊C4—91no—
357C4⋊C4—181no—
358C4⋊C4—182no—
359C4⋊C4—182no—
360C4⋊C4—181no—
361C4⋊C4—181no—
362C4⋊C4C22×C3⋊D311yescharacteristic
363C22⋊C4—21no—
364C22⋊C4—181no—
365C22⋊C4—181no—
366C22⋊C4—181no—
367C42—91no—
368C42—91no—
369C42—91no—
370C42C22×C3⋊D311yescharacteristic
371C22×C3—28no—
372C22×C3—44no—
373C22×C3—44no—
374C22×C3C2×D3×D414yes—
375C2×D3—38no—
376C2×D3—38no—
377C2×D3—38no—
378C2×D3—68no—
379C2×D3—1232no—
380C2×D3—124no—
381C2×D3—124no—
382C3×C4—24no—
383C3×C4—44no—
384C3×C4—48no—
385C3×C4D3×SD1618yescomplemented
386C3×C4C2×D3×D414yes—
387C3×C4D3×#4114yes—
388Dic3—38no—
389Dic3—38no—
390Dic3—64no—
391Dic3—124no—
392Dic3—128no—
393C32C2×#46111yescharacteristic, complemented, Sylow
394C23—21no—
395C23—91no—
396C23—184no—
397C23—181no—
398C23—362no—
399C23—362no—
400Q8—22no—
401Q8—22no—
402Q8—182no—
403Q8—182no—
404Q8—364no—
405D4—21no—
406D4—92no—
407D4—184no—
408D4—181no—
409D4D4×C3⋊D312yes—
410C2×C4—21no—
411C2×C4—22no—
412C2×C4—42no—
413C2×C4—91no—
414C2×C4—91no—
415C2×C4—92no—
416C2×C4—92no—
417C2×C4—94no—
418C2×C4—91no—
419C2×C4—182no—
420C2×C4—181no—
421C2×C4—182no—
422C2×C4—362no—
423C2×C4—362no—
424C2×C4—364no—
425C2×C4—362no—
426C2×C4—362no—
427C2×C4D4×C3⋊D311yescharacteristic
428C2×C4D4×C3⋊D311yescharacteristic
429C2×C4C23×C3⋊D311yescharacteristic
430C8—22no—
431C8—182no—
432C2×C3—48no—
433C2×C3D3×#12114yes—
434C2×C3C2×D3×SD1614yes—
435C2×C3D3×#13714yes—
436D3—316no—
437D3—128no—
438C22—22no—
439C22—41no—
440C22—41no—
441C22—92no—
442C22—92no—
443C22—92no—
444C22—182no—
445C22—368no—
446C22—361no—
447C22—361no—
448C22C2×D4×C3⋊D311yescharacteristic
449C4—21no—
450C4—41no—
451C4—42no—
452C4—92no—
453C4—92no—
454C4—181no—
455C4—361no—
456C4—362no—
457C4SD16×C3⋊D312yescomplemented
458C4C2×D4×C3⋊D311yescharacteristic
459C4#41×C3⋊D311yescharacteristic
460C3D3×#46114yescomplemented
461C2—42no—
462C2—94no—
463C2—362no—
464C2C3⋊D3×#12111yescharacteristic
465C2C2×SD16×C3⋊D311yescharacteristic
466C2C3⋊D3×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#461C2
socleC22×C32C22×D4
prime radicalC2×D4×C3⋊D3C22
hypercenter#461C3⋊D3
hypocenterC32C2×#461
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
2. C3⋊D3×C4⋊Q8C2semidirect
4. C32×#461C2semidirect
5. #10592861C2semidirect
6. #10592782C2semidirect
7. #10592718C2semidirect
8. #10592540C2semidirect
9. C3⋊D3×C4⋊C8C2semidirect
10. #10592517C2semidirect
11. C3⋊D3×#103C2semidirect
17. C32×C4⋊Q8C22semidirect
19. #64153C22semidirect
37. #64078C22semidirect
38. C32×C4⋊C8C22semidirect
39. C32×#103C22semidirect
40. #63662C22semidirect
41. #63643C22semidirect
42. #63641C22semidirect
43. #63637C22semidirect
44. C4⋊(C3⋊(C3⋊C8))C22semidirect
48. C3×#461D3semidirect
106. C3×C4⋊Q8C2×D3semidirect
127. C3×C4⋊C8C2×D3semidirect
128. C3×#103C2×D3semidirect
164. C4×C3⋊D3SD16semidirect
180. #461C3⋊D3direct (N × H)
242. C32×C4C2×SD16semidirect
249. C3⋊Dic3C2×SD16semidirect
263. C4⋊Q8C2×C3⋊D3semidirect
277. C4⋊C8C2×C3⋊D3semidirect
281. #103C2×C3⋊D3semidirect
325. C3⋊D3#461direct (N × H)
385. C3×C4D3×SD16semidirect
393. C32C2×#461semidirect
457. C4SD16×C3⋊D3semidirect
460. C3D3×#461semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×C3⋊D32
C3⋊D3×C4⋊Q82
C4×D4×C3⋊D32
C32×#4612
#105928612
#105927822
#105927182
#105925402
C3⋊D3×C4⋊C82
#105925172
C3⋊D3×#1032
D3×#4613