Finite Group Databasebeta

← C2×D3×#816 #11857757

Subgroups — C2×D3×#816 #11857757

Order 1152.

1713 conjugacy classes of subgroups.

The subgroup lattice has 543 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×Dic6C211yesmaximal, characteristic
2C22×C3×D3×C8C211yesmaximal, characteristic
3C2×D3×C4⋊Dic3C211yesmaximal, characteristic
4C2×#63643C211yesmaximal, characteristic, complemented
5C2×C3×#816C211yesmaximal, characteristic, complemented
6C2×#63567C211yesmaximal, characteristic, complemented
7C2×#63566C211yesmaximal, characteristic, complemented
8D3×#816C218yesmaximal, direct product factor
9C22×#816—31nomaximal
10C2×D3×#103—31nomaximal
11C22×#634C2211yescharacteristic
12C22×C3×C4×D3C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C22×#627—21no—
15C22×D3×Dic3—21no—
16C22×D3×Dic3—21no—
17C2×D3×Dic6—22no—
18C2×D3×Dic6—24no—
19C2×D3×Dic6C418yescomplemented
20C2×D3×Dic6C2214yes—
21C22×C32×C8C2211yescharacteristic
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C2×C3×D3×C8—24no—
26C2×C3×D3×C8C2214yes—
27C2×Dic3⋊Dic3—21no—
28D3×C4⋊Dic3—22no—
29D3×C4⋊Dic3C2214yes—
30#63643C2214yescomplemented
31C3×#816C2214yescomplemented
32#63567C2214yescomplemented
33#63566C2214yescomplemented
34C22×D3×Q8—31no—
35C23×Dic6—31no—
36C23×C3×C8—31no—
37C22×C4⋊Dic3—31no—
38C22×D3×C8D311yescharacteristic
39C2×D3×C4⋊C4—31no—
40C2×C3×#103—31no—
41C2×#835—31no—
42C2×#816—31no—
43C2×#816—31no—
44C2×#816—31no—
45C2×#816—31no—
46C2×#816—38no—
47C2×#816—61no—
48C2×#816D311yescharacteristic, direct product factor
49C2×#810—31no—
50D3×#103—38no—
51C23×C3×D3D411yescharacteristic
52C22×C32×C4C2311yescharacteristic
53C22×C3⋊Dic3—21no—
54C22×C3⋊Dic3—21no—
55C2×#634—21no—
56C2×#634—22no—
57C2×#634C2×C414yescomplemented
58C2×#634C2312yes—
59C22×C3×Dic3—21no—
60C22×C3×Dic3—21no—
61C22×C3×Dic3D411yescharacteristic
62C2×C3×C4×D3C2×C414yes—
63C2×C3×C4×D3D412yes—
64C2×C3×C4×D3D414yes—
65C2×C3×C4×D3C2312yes—
66C2×C3×Dic6—21no—
67C2×C3×Dic6—22no—
68C2×C3×Dic6C2×C414yescomplemented
69C2×C3×Dic6C2312yes—
70C2×#627—28no—
71C2×#627—24no—
72C2×D3×Dic3—28no—
73C2×D3×Dic3—24no—
74C2×D3×Dic3—24no—
75C2×D3×Dic3—44no—
76D3×Dic6—216no—
77D3×Dic6—28no—
78D3×Dic6C2×C4116yescomplemented
79C2×C32×C8—22no—
80C2×C32×C8C2312yes—
81C4⋊(C3⋊Dic3)—21no—
82C4⋊(C3⋊Dic3)C2312yes—
83C3×C4⋊Dic3—21no—
84C3×C4⋊Dic3C2312yes—
85C2×C3×C3⋊C8—22no—
86C2×C3×C3⋊C8C2312yes—
87C3×D3×C8—28no—
88Dic3⋊Dic3—24no—
89C22×#103—91noSylow
90C22×C3×Q8—31no—
91C23×C3×C4—31no—
92C23×Dic3—61no—
93C23×Dic3—61no—
94C2×D3×Q8—38no—
95C2×D3×Q8—34no—
96C2×D3×Q8—62no—
97C2×D3×Q8—64no—
98C22×C4×D3—61no—
99C22×C4×D3—61no—
100C22×C4×D3C2×D311yescharacteristic
101C22×Dic6—31no—
102C22×Dic6—31no—
103C22×Dic6—38no—
104C22×Dic6—34no—
105C22×Dic6—61no—
106C22×Dic6—62no—
107C22×Dic6—64no—
108C22×Dic6—61no—
109C22×Dic6—61no—
110C22×Dic6C2×D311yescharacteristic
111C22×C3×C8—21no—
112C22×C3×C8—31no—
113C22×C3×C8—34no—
114C22×C3×C8—64no—
115C22×C3×C8C2×D311yescharacteristic
116C22×C3×C8C2×D311yescharacteristic
117C2×C3×C4⋊C4—31no—
118C2×C4⋊Dic3—31no—
119C2×C4⋊Dic3—31no—
120C2×C4⋊Dic3—34no—
121C2×C4⋊Dic3—61no—
122C2×C4⋊Dic3—62no—
123C2×C4⋊Dic3—61no—
124C2×C4⋊Dic3C2×D311yescharacteristic
125C2×Dic3⋊C4—61no—
126C22×C3⋊C8C2×D311yescharacteristic
127C2×D3×C8—24no—
128C2×D3×C8C2×D314yes—
129D3×C4⋊C4—34no—
130D3×C4⋊C4—62no—
131C3×#103—34no—
132#835—34no—
133#816—34no—
134#816—34no—
135#816—34no—
136#816—34no—
137#816—64no—
138#816C2×D314yesdirect product factor
139#810—34no—
140C23×C32C2×D411yescharacteristic
141C22×C3×D3C22⋊C414yes—
142C22×C3×D3SD1614yes—
143C22×C3×D3Q1614yes—
144C22×C3×D3C2×D412yes—
145C2×C32×C4C22×C412yes—
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4C2×D412yes—
148C2×C32×C4C2411yescharacteristic
149C2×C3⋊Dic3—24no—
150C2×C3⋊Dic3—22no—
151C2×C3⋊Dic3—22no—
152C2×C3⋊Dic3—42no—
153#634—24no—
154#634—22no—
155#634C22×C414yescomplemented
156C2×C3×Dic3—24no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3—22no—
159C2×C3×Dic3—42no—
160C2×C3×Dic3C22⋊C414yes—
161C2×C3×Dic3C2×D412yes—
162C3×C4×D3C22⋊C418yes—
163C3×C4×D3C22×C414yes—
164C3×C4×D3C2×D414yes—
165C3×Dic6—24no—
166C3×Dic6—22no—
167C3×Dic6C22×C414yescomplemented
168#627—216no—
169D3×Dic3—216no—
170D3×Dic3—48no—
171C32×C8—22no—
172C3×C3⋊C8—22no—
173C23×Q8—91no—
174C23×C8—31no—
175C22×C4⋊C4—91no—
176C2×#103—31no—
177C2×#103—98no—
178C2×#103—91no—
179C2×#103—91no—
180C2×#103—91no—
181C24×C3—31no—
182C23×D3D1211yescharacteristic
183C2×C3×Q8—34no—
184C2×C3×Q8—32no—
185C2×C3×Q8—61no—
186C2×C3×Q8—62no—
187C22×C3×C4—21no—
188C22×C3×C4—31no—
189C22×C3×C4—34no—
190C22×C3×C4—32no—
191C22×C3×C4—34no—
192C22×C3×C4—32no—
193C22×C3×C4—61no—
194C22×C3×C4—61no—
195C22×C3×C4C22×D311yescharacteristic
196C22×C3×C4C22×D311yescharacteristic
197C22×Dic3—21no—
198C22×Dic3—21no—
199C22×Dic3—68no—
200C22×Dic3—64no—
201C22×Dic3—64no—
202C22×Dic3—61no—
203C22×Dic3—61no—
204C22×Dic3—61no—
205C22×Dic3—61no—
206C22×Dic3—121no—
207C22×Dic3—121no—
208C22×Dic3—124no—
209C22×Dic3D1211yescharacteristic
210D3×Q8—316no—
211D3×Q8—616no—
212D3×Q8—68no—
213C2×C4×D3—68no—
214C2×C4×D3—64no—
215C2×C4×D3—64no—
216C2×C4×D3—124no—
217C2×C4×D3C4×D314yes—
218C2×C4×D3D1212yes—
219C2×C4×D3#6714yes—
220C2×C4×D3C22×D312yes—
221C2×Dic6—21no—
222C2×Dic6—22no—
223C2×Dic6—34no—
224C2×Dic6—34no—
225C2×Dic6—32no—
226C2×Dic6—32no—
227C2×Dic6—316no—
228C2×Dic6—62no—
229C2×Dic6—64no—
230C2×Dic6—616no—
231C2×Dic6—68no—
232C2×Dic6—68no—
233C2×Dic6—64no—
234C2×Dic6—61no—
235C2×Dic6—61no—
236C2×Dic6—62no—
237C2×Dic6—62no—
238C2×Dic6—68no—
239C2×Dic6—64no—
240C2×Dic6—121no—
241C2×Dic6—122no—
242C2×Dic6C4×D314yescomplemented
243C2×Dic6C22×D312yes—
244C2×C3×C8—22no—
245C2×C3×C8—22no—
246C2×C3×C8—22no—
247C2×C3×C8—32no—
248C2×C3×C8—42no—
249C2×C3×C8—68no—
250C2×C3×C8—62no—
251C2×C3×C8C22×D312yes—
252C2×C3×C8C22×D312yes—
253C3×C4⋊C4—32no—
254C3×C4⋊C4—61no—
255C4⋊Dic3—21no—
256C4⋊Dic3—32no—
257C4⋊Dic3—32no—
258C4⋊Dic3—62no—
259C4⋊Dic3—64no—
260C4⋊Dic3—61no—
261C4⋊Dic3—61no—
262C4⋊Dic3—121no—
263C4⋊Dic3C22×D312yes—
264Dic3⋊C4—64no—
265C2×C3⋊C8—22no—
266C2×C3⋊C8C22×D312yes—
267D3×C8—28no—
268C22×C32C2×C22⋊C412yes—
269C22×C32C2×SD1612yes—
270C22×C32C2×Q1612yes—
271C22×C32C22×D411yescharacteristic
272C2×C3×D3#103116yescomplemented
273C2×C3×D3C2×C22⋊C414yes—
274C2×C3×D3C2×SD1614yes—
275C2×C3×D3C2×Q1614yes—
276C32×C4C2×C22⋊C412yes—
277C32×C4C23×C411yescharacteristic
278C32×C4C22×D411yescharacteristic
279C3⋊Dic3—24no—
280C3⋊Dic3—42no—
281C3×Dic3—24no—
282C3×Dic3—42no—
283C3×Dic3C2×C22⋊C414yes—
284C22×Q8—31no—
285C22×Q8—94no—
286C22×Q8—98no—
287C22×Q8—91no—
288C22×Q8—181no—
289C22×Q8—182no—
290C22×Q8—184no—
291C23×C4—31no—
292C23×C4—181no—
293C23×C4—181no—
294C22×C8—31no—
295C22×C8—34no—
296C22×C8—64no—
297C22×C8D3211yescharacteristic
298C2×C4⋊C4—31no—
299C2×C4⋊C4—94no—
300C2×C4⋊C4—91no—
301C2×C4⋊C4—182no—
302C2×C4⋊C4—181no—
303#103—34no—
304#103—94no—
305#103—94no—
306#103—94no—
307C23×C3—21no—
308C23×C3—34no—
309C23×C3—34no—
310C23×C3—34no—
311C23×C3—32no—
312C23×C3C2×D1211yescharacteristic
313C23×C3D3×D411yescharacteristic
314C22×D3#20414yes—
315C22×D3Dic1214yes—
316C22×D3(C2×D3)⋊C414yes—
317C22×D3C2×D1212yes—
318C3×Q8—34no—
319C3×Q8—64no—
320C3×Q8—62no—
321C2×C3×C4—21no—
322C2×C3×C4—22no—
323C2×C3×C4—21no—
324C2×C3×C4—22no—
325C2×C3×C4—34no—
326C2×C3×C4—32no—
327C2×C3×C4—38no—
328C2×C3×C4—34no—
329C2×C3×C4—34no—
330C2×C3×C4—64no—
331C2×C3×C4—62no—
332C2×C3×C4—62no—
333C2×C3×C4—122no—
334C2×C3×C4C2×C4×D312yes—
335C2×C3×C4C2×C4×D312yes—
336C2×C3×C4C2×D1211yescharacteristic
337C2×C3×C4D3×D411yescharacteristic
338C2×C3×C4D3×D412yes—
339C2×C3×C4C2×#6712yes—
340C2×C3×C4C23×D311yescharacteristic
341C2×C3×C4C23×D311yescharacteristic
342C2×Dic3—24no—
343C2×Dic3—22no—
344C2×Dic3—22no—
345C2×Dic3—42no—
346C2×Dic3—616no—
347C2×Dic3—64no—
348C2×Dic3—64no—
349C2×Dic3—62no—
350C2×Dic3—62no—
351C2×Dic3—62no—
352C2×Dic3—62no—
353C2×Dic3—122no—
354C2×Dic3—124no—
355C2×Dic3—122no—
356C2×Dic3—128no—
357C2×Dic3—122no—
358C2×Dic3—122no—
359C2×Dic3—242no—
360C2×Dic3(C2×D3)⋊C414yes—
361C2×Dic3C2×D1212yes—
362C4×D3—616no—
363C4×D3—128no—
364C4×D3(C2×D3)⋊C418yes—
365C4×D3C2×C4×D314yes—
366C4×D3C2×#6714yes—
367Dic6—24no—
368Dic6—22no—
369Dic6—34no—
370Dic6—34no—
371Dic6—64no—
372Dic6—616no—
373Dic6—64no—
374Dic6—64no—
375Dic6—62no—
376Dic6—62no—
377Dic6—616no—
378Dic6—122no—
379Dic6—124no—
380Dic6C2×C4×D314yescomplemented
381C3×C8—22no—
382C3×C8—22no—
383C3×C8—42no—
384C3×C8—62no—
385C3⋊C8—22no—
386C2×C32C2×#10314yescomplemented
387C2×C32C22×C22⋊C411yescharacteristic
388C2×C32C22×SD1611yescharacteristic
389C2×C32C22×Q1611yescharacteristic
390C3×D3C2×#10318yescomplemented
391C24—31no—
392C2×Q8—32no—
393C2×Q8—34no—
394C2×Q8—61no—
395C2×Q8—62no—
396C2×Q8—916no—
397C2×Q8—92no—
398C2×Q8—94no—
399C2×Q8—184no—
400C2×Q8—188no—
401C2×Q8—188no—
402C2×Q8—1816no—
403C2×Q8—181no—
404C2×Q8—182no—
405C22×C4—31no—
406C22×C4—32no—
407C22×C4—34no—
408C22×C4—32no—
409C22×C4—34no—
410C22×C4—61no—
411C22×C4—61no—
412C22×C4—184no—
413C22×C4—188no—
414C22×C4—184no—
415C22×C4—181no—
416C22×C4—181no—
417C22×C4—364no—
418C22×C4C2×D3211yescharacteristic
419C2×C8—22no—
420C2×C8—32no—
421C2×C8—68no—
422C2×C8—62no—
423C2×C8C2×D3212yes—
424C4⋊C4—32no—
425C4⋊C4—61no—
426C4⋊C4—92no—
427C4⋊C4—184no—
428C4⋊C4—181no—
429C22×C3—21no—
430C22×C3—22no—
431C22×C3—22no—
432C22×C3—22no—
433C22×C3—34no—
434C22×C3—34no—
435C22×C3—34no—
436C22×C3—316no—
437C22×C3D3×C22⋊C412yes—
438C22×C3C2×#20412yes—
439C22×C3C2×Dic1212yes—
440C22×C3D3×SD1612yes—
441C22×C3D3×Q1612yes—
442C22×C3C2×(C2×D3)⋊C412yes—
443C22×C3C22×D1211yescharacteristic
444C22×C3C2×D3×D411yescharacteristic
445C2×D3#816116yesdirect product factor
446C2×D3C2×#20414yes—
447C2×D3C2×Dic1214yes—
448C2×D3C2×(C2×D3)⋊C414yes—
449C3×C4—21no—
450C3×C4—21no—
451C3×C4—22no—
452C3×C4—34no—
453C3×C4—64no—
454C3×C4—122no—
455C3×C4D3×C22⋊C412yes—
456C3×C4C2×(C2×D3)⋊C412yes—
457C3×C4C22×C4×D311yescharacteristic
458C3×C4C22×C4×D311yescharacteristic
459C3×C4C2×D3×D411yescharacteristic
460C3×C4C22×#6711yescharacteristic
461Dic3—24no—
462Dic3—42no—
463Dic3—64no—
464Dic3—64no—
465Dic3—124no—
466Dic3—122no—
467Dic3—122no—
468Dic3—242no—
469Dic3C2×(C2×D3)⋊C414yes—
470C32C22×#10311yescharacteristic, complemented, Sylow
471C23—32no—
472C23—34no—
473C23—34no—
474C23—34no—
475C23D3×D1211yescharacteristic
476Q8—34no—
477Q8—62no—
478Q8—64no—
479Q8—94no—
480Q8—1816no—
481Q8—182no—
482Q8—184no—
483C2×C4—32no—
484C2×C4—34no—
485C2×C4—34no—
486C2×C4—34no—
487C2×C4—38no—
488C2×C4—62no—
489C2×C4—64no—
490C2×C4—62no—
491C2×C4—122no—
492C2×C4—1816no—
493C2×C4—182no—
494C2×C4—184no—
495C2×C4—182no—
496C2×C4—368no—
497C2×C4—362no—
498C2×C4C4×D3212yes—
499C2×C4D3×D1211yescharacteristic
500C2×C4D3×#6712yes—
501C2×C4C22×D3211yescharacteristic
502C8—22no—
503C8—62no—
504C2×C3—21no—
505C2×C3—21no—
506C2×C3—24no—
507C2×C3—21no—
508C2×C3—38no—
509C2×C3D3×#10314yescomplemented
510C2×C3C2×#81614yescomplemented
511C2×C3C2×D3×C22⋊C411yescharacteristic
512C2×C3C22×#20411yescharacteristic
513C2×C3C22×Dic1211yescharacteristic
514C2×C3C2×D3×SD1611yescharacteristic
515C2×C3C2×D3×Q1611yescharacteristic
516C2×C3C22×(C2×D3)⋊C411yescharacteristic
517D3C2×#81618yesdirect product factor
518C22—34no—
519C22—34no—
520C22—316no—
521C22—34no—
522C22D3×#20412yes—
523C22D3×Dic1212yes—
524C22D3×(C2×D3)⋊C412yes—
525C22C2×D3×D1211yescharacteristic
526C4—34no—
527C4—64no—
528C4—122no—
529C4—184no—
530C4—362no—
531C4D3×(C2×D3)⋊C412yes—
532C4C2×C4×D3211yescharacteristic
533C4C2×D3×#6711yescharacteristic
534C3—21no—
535C3C2×D3×#10311yescharacteristic, complemented
536C3C22×#81611yescharacteristic, complemented
537C2—38no—
538C2D3×#81614yesdirect product factor
539C2C2×D3×#20411yescharacteristic
540C2C2×D3×Dic1211yescharacteristic
541C2C2×D3×(C2×D3)⋊C411yescharacteristic
subgroupG/H
centerC23D3×D12
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC23×C3×D3D4
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32C22×#103
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
4. C2×#63643C2semidirect
5. C2×C3×#816C2semidirect
6. C2×#63567C2semidirect
7. C2×#63566C2semidirect
8. D3×#816C2direct (N × H)
19. C2×D3×Dic6C4semidirect
30. #63643C22semidirect
31. C3×#816C22semidirect
32. #63567C22semidirect
33. #63566C22semidirect
48. C2×#816D3direct (N × H)
57. C2×#634C2×C4semidirect
68. C2×C3×Dic6C2×C4semidirect
78. D3×Dic6C2×C4semidirect
138. #816C2×D3direct (N × H)
155. #634C22×C4semidirect
167. C3×Dic6C22×C4semidirect
242. C2×Dic6C4×D3semidirect
272. C2×C3×D3#103semidirect
380. Dic6C2×C4×D3semidirect
386. C2×C32C2×#103semidirect
390. C3×D3C2×#103semidirect
445. C2×D3#816direct (N × H)
470. C32C22×#103semidirect
509. C2×C3D3×#103semidirect
510. C2×C3C2×#816semidirect
517. D3C2×#816direct (N × H)
535. C3C2×D3×#103semidirect
536. C3C22×#816semidirect
538. C2D3×#816direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D3×Dic62
C22×C3×D3×C82
C2×D3×C4⋊Dic32
C2×#636432
C2×C3×#8162
C2×#635672
C2×#635662
D3×#8162
C22×#8163
C2×D3×#1033