Finite Group Databasebeta

← D3×#4555 #11783187

Subgroups — D3×#4555 #11783187

Order 1152.

1031 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×M16C211yesmaximal, characteristic
2D3×#926C211yesmaximal, characteristic
3C2×C4×D3×Dic3C211yesmaximal, characteristic
4#10589421C211yesmaximal, characteristic, complemented
5C3×#4555C211yesmaximal, characteristic, complemented
6#10589162C211yesmaximal, characteristic, complemented
7#10589160C211yesmaximal, characteristic, complemented
8C2×#4555—31nomaximal
9D3×#339—31nomaximal
10C22×C3×C4×D3C2211yescharacteristic
11C22×D3×Dic3—21no—
12C2×C32×M16C2211yescharacteristic
13#64135C2211yescharacteristic
14C2×C4×C3⋊Dic3C2211yescharacteristic
15C3×#926C2211yescharacteristic
16C2×C3×C4×Dic3C2211yescharacteristic
17C2×C3×#208C2211yescharacteristic
18C3×D3×M16—22no—
19C3×D3×M16C414yescomplemented
20C2×C3×ΓL(1,𝔽25)—21no—
21C2×C3×D3×C8—21no—
22D3×#217—21no—
23#63955—21no—
24C2×Dic32—21no—
25D3×C4⋊Dic3C412yescomplemented
26C4×D3×Dic3—22no—
27C4×D3×Dic3—21no—
28C4×D3×Dic3C414yescomplemented
29#63855—21no—
30#63841C412yescomplemented
31C22×C3×M16—31no—
32C2×#926—31no—
33C22×C4×Dic3—31no—
34C2×D3×M16D311yescharacteristic
35D3×#117—31no—
36C2×C42×D3—31no—
37C3×#339—31no—
38#4555—31no—
39#4555—31no—
40#4555—31no—
41#4555—31no—
42#4555—61no—
43#4555D311yescharacteristic, direct product factor
44#4532—31no—
45#4523—31no—
46C23×C3×D3D411yescharacteristic
47C22×C32×C4C2311yescharacteristic
48C22×C3⋊Dic3—21no—
49C22×C3×Dic3—21no—
50C22×C3×Dic3D411yescharacteristic
51C2×C3×C4×D3C2×C412yes—
52C2×C3×C4×D3C2×C411yescharacteristic
53C2×C3×C4×D3C2×C412yes—
54C2×C3×C4×D3C2×C411yescharacteristic
55C2×C3×C4×D3D411yescharacteristic
56C2×C3×C4×D3D411yescharacteristic
57C2×C3×C4×D3D412yes—
58C2×C3×C4×D3Q812yes—
59C2×D3×Dic3—28no—
60C2×D3×Dic3—24no—
61C2×D3×Dic3—22no—
62C32×M16—21no—
63C32×M16C2×C412yescomplemented
64C2×C32×C8—21no—
65#3757—21no—
66C4⋊(C3⋊Dic3)C2×C412yescomplemented
67C4×C3⋊Dic3—21no—
68C4×C3⋊Dic3—21no—
69C4×C3⋊Dic3C2×C412yescomplemented
70C3×#217—21no—
71C3×C4⋊Dic3C2×C412yescomplemented
72C3×C4×Dic3—21no—
73C3×C4×Dic3—21no—
74C3×C4×Dic3C2×C412yescomplemented
75C3×#208—21no—
76C3×#208C2×C412yescomplemented
77C2×C3×C3⋊C8—21no—
78C3×ΓL(1,𝔽25)—24no—
79C3×D3×C8—24no—
80Dic3⋊Dic3—22no—
81(C2×D3)⋊Dic3—22no—
82Dic32—22no—
83Dic32—24no—
84C2×#339—91noSylow
85C23×C3×C4—31no—
86C23×Dic3—61no—
87C22×C4×D3—61no—
88C22×C4×D3C2×D311yescharacteristic
89C2×C3×M16—21no—
90C2×C3×M16—31no—
91C2×C3×M16—34no—
92C2×C3×M16—61no—
93C2×C3×M16—62no—
94C2×C3×M16C2×D311yescharacteristic
95C2×C3×M16C2×D311yescharacteristic
96C22×C3×C8—61no—
97C3×#117—31no—
98C2×C3×C42—31no—
99C2×#217—61no—
100#926—31no—
101#926—31no—
102#926—32no—
103#926—61no—
104#926—61no—
105#926—61no—
106#926C2×D311yescharacteristic
107C2×C4⋊Dic3—32no—
108C2×C4×Dic3—31no—
109C2×C4×Dic3—31no—
110C2×C4×Dic3—34no—
111C2×C4×Dic3—61no—
112C2×C4×Dic3—62no—
113C2×C4×Dic3—61no—
114C2×C4×Dic3—61no—
115C2×C4×Dic3—61no—
116C2×C4×Dic3C2×D311yescharacteristic
117C2×#208C2×D311yescharacteristic
118D3×M16—22no—
119D3×M16Dic314yescomplemented
120C2×ΓL(1,𝔽25)—21no—
121C2×D3×C8—21no—
122#892—32no—
123D3×C4⋊C4—32no—
124D3×C22⋊C4—61no—
125#877—61no—
126#872—61no—
127C42×D3—34no—
128C42×D3—62no—
129C42×D3—61no—
130C23×C32C2×D411yescharacteristic
131C22×C3×D3—24no—
132C22×C3×D3C22⋊C411yescharacteristic
133C22×C3×D3C22⋊C412yes—
134C22×C3×D3C22⋊C411yescharacteristic
135C22×C3×D3C4⋊C412yes—
136C2×C32×C4C22×C411yescharacteristic
137C2×C32×C4C22×C411yescharacteristic
138C2×C32×C4C22×C411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2×Q811yescharacteristic
142C2×C3⋊Dic3—24no—
143C2×C3⋊Dic3—22no—
144C2×C3⋊Dic3—22no—
145C2×C3×Dic3—24no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—22no—
148C2×C3×Dic3C22⋊C412yes—
149C2×C3×Dic3C22⋊C411yescharacteristic
150C2×C3×Dic3C22⋊C411yescharacteristic
151C2×C3×Dic3C4⋊C412yes—
152C3×C4×D3C4212yes—
153C3×C4×D3C4212yes—
154C3×C4×D3C22⋊C412yes—
155C3×C4×D3C22⋊C412yes—
156C3×C4×D3C4⋊C412yes—
157C3×C4×D3C4⋊C412yes—
158C3×C4×D3C4⋊C412yes—
159C3×C4×D3C4⋊C412yes—
160D3×Dic3—216no—
161D3×Dic3—44no—
162C32×C8—22no—
163C3×C3⋊C8—22no—
164C22×M16—31no—
165C2×#117—91no—
166C22×C42—91no—
167#339—31no—
168#339—91no—
169#339—91no—
170#339—91no—
171C24×C3—31no—
172C23×D3D1211yescharacteristic
173C22×C3×C4—21no—
174C22×C3×C4—31no—
175C22×C3×C4—32no—
176C22×C3×C4—31no—
177C22×C3×C4—31no—
178C22×C3×C4—32no—
179C22×C3×C4—31no—
180C22×C3×C4—32no—
181C22×C3×C4—31no—
182C22×C3×C4—32no—
183C22×C3×C4—61no—
184C22×C3×C4C22×D311yescharacteristic
185C22×C3×C4C22×D311yescharacteristic
186C22×Dic3—21no—
187C22×Dic3—64no—
188C22×Dic3—68no—
189C22×Dic3—62no—
190C22×Dic3—61no—
191C22×Dic3—61no—
192C22×Dic3—121no—
193C22×Dic3D1211yescharacteristic
194C2×C4×D3—68no—
195C2×C4×D3—64no—
196C2×C4×D3—62no—
197C2×C4×D3Dic612yes—
198C2×C4×D3C4×D312yes—
199C2×C4×D3C4×D311yescharacteristic
200C2×C4×D3C4×D311yescharacteristic
201C2×C4×D3C2×Dic312yes—
202C2×C4×D3#6711yescharacteristic
203C2×C4×D3#6712yes—
204C2×C4×D3#6711yescharacteristic
205C3×M16—21no—
206C3×M16—21no—
207C3×M16—22no—
208C3×M16—32no—
209C3×M16—41no—
210C3×M16—64no—
211C3×M16—61no—
212C3×M16C4×D312yescomplemented
213C3×M16C2×Dic312yescomplemented
214C2×C3×C8—21no—
215C2×C3×C8—21no—
216C2×C3×C8—41no—
217C2×C3×C8—64no—
218C2×C3×C8—61no—
219C3×C4⋊C4—32no—
220C3×C22⋊C4—61no—
221C3×C42—32no—
222C3×C42—61no—
223C3×C42—61no—
224#217—21no—
225#217—62no—
226#217—61no—
227#217—61no—
228#217—121no—
229(C2×D3)⋊C4—62no—
230C4⋊Dic3—32no—
231C4⋊Dic3—32no—
232C4⋊Dic3—62no—
233C4⋊Dic3—62no—
234C4⋊Dic3C4×D312yescomplemented
235Dic3⋊C4—62no—
236C4×Dic3—21no—
237C4×Dic3—21no—
238C4×Dic3—32no—
239C4×Dic3—32no—
240C4×Dic3—62no—
241C4×Dic3—64no—
242C4×Dic3—62no—
243C4×Dic3—61no—
244C4×Dic3—61no—
245C4×Dic3—61no—
246C4×Dic3—61no—
247C4×Dic3—64no—
248C4×Dic3—62no—
249C4×Dic3—121no—
250C4×Dic3—121no—
251C4×Dic3C4×D312yescomplemented
252#208—21no—
253#208C2×Dic312yescomplemented
254C2×C3⋊C8—21no—
255ΓL(1,𝔽25)—24no—
256D3×C8—24no—
257C22×C32—22no—
258C22×C32C2×C22⋊C411yescharacteristic
259C22×C32C2×C22⋊C411yescharacteristic
260C22×C32C2×C4⋊C411yescharacteristic
261C2×C3×D3—22no—
262C2×C3×D3—24no—
263C2×C3×D3—24no—
264C2×C3×D3#9512yes—
265C2×C3×D3#9512yes—
266C2×C3×D3#10414yes—
267C32×C4C2×C4211yescharacteristic
268C32×C4C2×C22⋊C411yescharacteristic
269C32×C4C2×C4⋊C411yescharacteristic
270C32×C4C2×C4⋊C411yescharacteristic
271C3⋊Dic3—24no—
272C3⋊Dic3—42no—
273C3×Dic3—24no—
274C3×Dic3—42no—
275C3×Dic3#9512yes—
276C3×Dic3#9512yes—
277C23×C4—31no—
278C23×C4—181no—
279C2×M16—31no—
280C2×M16—34no—
281C2×M16—61no—
282C2×M16—62no—
283C2×M16D3211yescharacteristic
284C22×C8—61no—
285#117—31no—
286#117—92no—
287#117—91no—
288#117—181no—
289#117—181no—
290C2×C4⋊C4—92no—
291C2×C22⋊C4—181no—
292C2×C42—31no—
293C2×C42—94no—
294C2×C42—91no—
295C2×C42—181no—
296C2×C42—182no—
297C2×C42—181no—
298C23×C3—21no—
299C23×C3—31no—
300C23×C3—31no—
301C23×C3—32no—
302C23×C3—32no—
303C23×C3—64no—
304C23×C3C2×D1211yescharacteristic
305C23×C3D3×D411yescharacteristic
306C22×D3—24no—
307C22×D3C4⋊Dic312yes—
308C22×D3(C2×D3)⋊C411yescharacteristic
309C22×D3(C2×D3)⋊C412yes—
310C22×D3(C2×D3)⋊C411yescharacteristic
311C2×C3×C4—21no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—32no—
318C2×C3×C4—31no—
319C2×C3×C4—31no—
320C2×C3×C4—32no—
321C2×C3×C4—32no—
322C2×C3×C4—32no—
323C2×C3×C4—32no—
324C2×C3×C4—32no—
325C2×C3×C4—32no—
326C2×C3×C4—32no—
327C2×C3×C4—32no—
328C2×C3×C4—32no—
329C2×C3×C4—64no—
330C2×C3×C4—62no—
331C2×C3×C4—62no—
332C2×C3×C4C2×Dic611yescharacteristic
333C2×C3×C4C2×C4×D311yescharacteristic
334C2×C3×C4C2×C4×D311yescharacteristic
335C2×C3×C4C2×C4×D311yescharacteristic
336C2×C3×C4C2×C4×D311yescharacteristic
337C2×C3×C4C2×C4×D311yescharacteristic
338C2×C3×C4D3×D411yescharacteristic
339C2×C3×C4D3×D411yescharacteristic
340C2×C3×C4D3×Q811yescharacteristic
341C2×C3×C4C22×Dic311yescharacteristic
342C2×C3×C4C2×#6711yescharacteristic
343C2×C3×C4C2×#6711yescharacteristic
344C2×Dic3—24no—
345C2×Dic3—22no—
346C2×Dic3—22no—
347C2×Dic3—616no—
348C2×Dic3—64no—
349C2×Dic3—64no—
350C2×Dic3—62no—
351C2×Dic3—62no—
352C2×Dic3—62no—
353C2×Dic3—62no—
354C2×Dic3—122no—
355C2×Dic3—124no—
356C2×Dic3—122no—
357C2×Dic3—124no—
358C2×Dic3C4⋊Dic312yes—
359C2×Dic3(C2×D3)⋊C412yes—
360C2×Dic3(C2×D3)⋊C411yescharacteristic
361C2×Dic3(C2×D3)⋊C411yescharacteristic
362C4×D3—616no—
363C4×D3—124no—
364C4×D3C4×Dic312yes—
365C4×D3C4×Dic312yes—
366C4×D3Dic3⋊C412yes—
367C4×D3Dic3⋊C412yes—
368C4×D3Dic3⋊C412yes—
369C4×D3Dic3⋊C412yes—
370C4×D3#21712yes—
371C4×D3#21712yes—
372C3×C8—22no—
373C3×C8—22no—
374C3×C8—42no—
375C3×C8—62no—
376C3⋊C8—22no—
377C2×C32—21no—
378C2×C32—21no—
379C2×C32C2×#9511yescharacteristic
380C2×C32C2×#10412yes—
381C3×D3—22no—
382C3×D3#33914yescomplemented
383C24—31no—
384C22×C4—31no—
385C22×C4—32no—
386C22×C4—32no—
387C22×C4—31no—
388C22×C4—31no—
389C22×C4—32no—
390C22×C4—32no—
391C22×C4—31no—
392C22×C4—31no—
393C22×C4—61no—
394C22×C4—184no—
395C22×C4—188no—
396C22×C4—182no—
397C22×C4—181no—
398C22×C4C2×D3211yescharacteristic
399M16—21no—
400M16—32no—
401M16—64no—
402M16—61no—
403M16D3×Dic312yescomplemented
404C2×C8—21no—
405C2×C8—64no—
406C2×C8—61no—
407C4⋊C4—32no—
408C4⋊C4—92no—
409C4⋊C4—182no—
410C22⋊C4—61no—
411C22⋊C4—182no—
412C22⋊C4—181no—
413C42—32no—
414C42—61no—
415C42—61no—
416C42—92no—
417C42—184no—
418C42—182no—
419C42—181no—
420C42—181no—
421C22×C3—22no—
422C22×C3—22no—
423C22×C3—21no—
424C22×C3—21no—
425C22×C3—21no—
426C22×C3—32no—
427C22×C3—34no—
428C22×C3—32no—
429C22×C3—42no—
430C22×C3—64no—
431C22×C3—64no—
432C22×C3—62no—
433C22×C3D3×C22⋊C411yescharacteristic
434C22×C3D3×C22⋊C411yescharacteristic
435C22×C3D3×C4⋊C411yescharacteristic
436C22×C3C2×C4⋊Dic311yescharacteristic
437C22×C3C2×(C2×D3)⋊C411yescharacteristic
438C22×C3C2×(C2×D3)⋊C411yescharacteristic
439C2×D3—22no—
440C2×D3—24no—
441C2×D3—24no—
442C2×D3#82514yes—
443C2×D3C3⋊#9512yes—
444C2×D3C3⋊#9512yes—
445C3×C4—21no—
446C3×C4—21no—
447C3×C4—21no—
448C3×C4—21no—
449C3×C4—32no—
450C3×C4—32no—
451C3×C4—64no—
452C3×C4—122no—
453C3×C4C42×D311yescharacteristic
454C3×C4D3×C22⋊C411yescharacteristic
455C3×C4D3×C4⋊C411yescharacteristic
456C3×C4D3×C4⋊C411yescharacteristic
457C3×C4C2×C4×Dic311yescharacteristic
458C3×C4C2×Dic3⋊C411yescharacteristic
459C3×C4C2×Dic3⋊C411yescharacteristic
460C3×C4C2×#21711yescharacteristic
461Dic3—24no—
462Dic3—42no—
463Dic3—64no—
464Dic3—64no—
465Dic3—124no—
466Dic3—122no—
467Dic3—122no—
468Dic3—242no—
469Dic3C3⋊#9512yes—
470Dic3C3⋊#9512yes—
471C32C2×#33911yescharacteristic, complemented, Sylow
472C23—31no—
473C23—32no—
474C23—31no—
475C23—32no—
476C23—64no—
477C23D3×D1211yescharacteristic
478C2×C4—32no—
479C2×C4—32no—
480C2×C4—31no—
481C2×C4—31no—
482C2×C4—32no—
483C2×C4—32no—
484C2×C4—32no—
485C2×C4—32no—
486C2×C4—32no—
487C2×C4—32no—
488C2×C4—32no—
489C2×C4—32no—
490C2×C4—64no—
491C2×C4—62no—
492C2×C4—62no—
493C2×C4—1816no—
494C2×C4—184no—
495C2×C4—182no—
496C2×C4—182no—
497C2×C4—364no—
498C2×C4D3×Dic611yescharacteristic
499C2×C4C4×D3211yescharacteristic
500C2×C4C4×D3211yescharacteristic
501C2×C4C2×D3×Dic311yescharacteristic
502C2×C4D3×#6711yescharacteristic
503C2×C4D3×#6711yescharacteristic
504C8—22no—
505C8—62no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—21no—
509C2×C3—21no—
510C2×C3—22no—
511C2×C3—21no—
512C2×C3—34no—
513C2×C3—41no—
514C2×C3—41no—
515C2×C3—62no—
516C2×C3D3×#9511yescharacteristic
517C2×C3D3×#10412yes—
518C2×C3C2×#82512yes—
519C2×C3C2×C3⋊#9511yescharacteristic
520D3—22no—
521D3#455514yesdirect product factor
522C22—22no—
523C22—34no—
524C22—32no—
525C22—32no—
526C22—64no—
527C22—64no—
528C22—62no—
529C22D3×C4⋊Dic311yescharacteristic
530C22D3×(C2×D3)⋊C411yescharacteristic
531C22D3×(C2×D3)⋊C411yescharacteristic
532C4—32no—
533C4—32no—
534C4—64no—
535C4—122no—
536C4—184no—
537C4—362no—
538C4C4×D3×Dic311yescharacteristic
539C4D3×Dic3⋊C411yescharacteristic
540C4D3×Dic3⋊C411yescharacteristic
541C4D3×#21711yescharacteristic
542C3—21no—
543C3D3×#33911yescharacteristic, complemented
544C3C2×#455511yescharacteristic, complemented
545C2—21no—
546C2—21no—
547C2—34no—
548C2—62no—
549C2D3×#82512yes—
550C2D3×C3⋊#9511yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC32×C4C2×C42
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32C2×C22⋊C4
prime radicalC23×C3×D3D4
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32C2×#339
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
4. #10589421C2semidirect
5. C3×#4555C2semidirect
6. #10589162C2semidirect
7. #10589160C2semidirect
19. C3×D3×M16C4semidirect
25. D3×C4⋊Dic3C4semidirect
28. C4×D3×Dic3C4semidirect
30. #63841C4semidirect
43. #4555D3direct (N × H)
63. C32×M16C2×C4semidirect
66. C4⋊(C3⋊Dic3)C2×C4semidirect
69. C4×C3⋊Dic3C2×C4semidirect
71. C3×C4⋊Dic3C2×C4semidirect
74. C3×C4×Dic3C2×C4semidirect
76. C3×#208C2×C4semidirect
119. D3×M16Dic3semidirect
212. C3×M16C4×D3semidirect
213. C3×M16C2×Dic3semidirect
234. C4⋊Dic3C4×D3semidirect
251. C4×Dic3C4×D3semidirect
253. #208C2×Dic3semidirect
382. C3×D3#339semidirect
403. M16D3×Dic3semidirect
471. C32C2×#339semidirect
521. D3#4555direct (N × H)
543. C3D3×#339semidirect
544. C3C2×#4555semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×M162
D3×#9262
C2×C4×D3×Dic32
#105894212
C3×#45552
#105891622
#105891602
C2×#45553
D3×#3393