Finite Group Databasebeta

← C2×D3×#835 #11857755

Subgroups — C2×D3×#835 #11857755

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×C3×D3×Q8C211yesmaximal, characteristic
2C2×D3×C4⋊Dic3C211yesmaximal, characteristic
3C22×D3×C3⋊C8C211yesmaximal, characteristic
4C2×#63662C211yesmaximal, characteristic, complemented
5C2×C3×#835C211yesmaximal, characteristic, complemented
6D3×#835C218yesmaximal, direct product factor
7C2×#63566C211yesmaximal, characteristic, complemented
8C2×#63565C211yesmaximal, characteristic, complemented
9C22×#835—31nomaximal
10C2×D3×#103—31nomaximal
11C22×C32×Q8C2211yescharacteristic
12C2×C3×D3×Q8—24no—
13C2×C3×D3×Q8—22no—
14C2×C3×D3×Q8C418yescomplemented
15C2×C3×D3×Q8C2214yes—
16C22×C3×C4×D3—21no—
17C22×C3×C4×D3C2211yescharacteristic
18C22×C3×Dic6—21no—
19C22×C3×Dic6C2211yescharacteristic
20C22×D3×Dic3—21no—
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C22×C3⋊(C3⋊C8)C2211yescharacteristic
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C2×Dic3⋊Dic3—21no—
26D3×C4⋊Dic3—22no—
27D3×C4⋊Dic3C2214yes—
28C2×D3×C3⋊C8—24no—
29C2×D3×C3⋊C8C2214yes—
30#63662C2214yescomplemented
31C3×#835C2214yescomplemented
32#63566C2214yescomplemented
33#63565C2214yescomplemented
34C23×C3×Q8—31no—
35C22×D3×Q8D311yescharacteristic
36C22×C4⋊Dic3—31no—
37C23×C3⋊C8—31no—
38C22×D3×C8—31no—
39C2×D3×C4⋊C4—31no—
40C2×C3×#103—31no—
41C2×#835—31no—
42C2×#835—31no—
43C2×#835—31no—
44C2×#835—31no—
45C2×#835—38no—
46C2×#835—61no—
47C2×#835D311yescharacteristic, direct product factor
48C2×#816—31no—
49C2×#810—31no—
50D3×#103—38no—
51C23×C3×D3D411yescharacteristic
52C2×C32×Q8—22no—
53C2×C32×Q8—21no—
54C2×C32×Q8C2×C414yescomplemented
55C2×C32×Q8C2312yes—
56C22×C32×C4—21no—
57C22×C32×C4C2311yescharacteristic
58C22×C3⋊Dic3—21no—
59C22×C3×Dic3—21no—
60C22×C3×Dic3—21no—
61C22×C3×Dic3D411yescharacteristic
62C3×D3×Q8—216no—
63C3×D3×Q8—28no—
64C3×D3×Q8C2×C4116yescomplemented
65C2×C3×C4×D3—28no—
66C2×C3×C4×D3—24no—
67C2×C3×C4×D3C2×C414yes—
68C2×C3×C4×D3D412yes—
69C2×C3×C4×D3D414yes—
70C2×C3×C4×D3C2312yes—
71C2×C3×Dic6—21no—
72C2×C3×Dic6—22no—
73C2×C3×Dic6—28no—
74C2×C3×Dic6—24no—
75C2×C3×Dic6C2×C414yescomplemented
76C2×C3×Dic6C2312yes—
77C2×D3×Dic3—24no—
78C2×D3×Dic3—44no—
79C4⋊(C3⋊Dic3)—21no—
80C4⋊(C3⋊Dic3)C2312yes—
81C2×C3⋊(C3⋊C8)—22no—
82C2×C3⋊(C3⋊C8)C2312yes—
83C3×C4⋊Dic3—21no—
84C3×C4⋊Dic3C2312yes—
85C2×C3×C3⋊C8—22no—
86C2×C3×C3⋊C8C2312yes—
87Dic3⋊Dic3—24no—
88D3×C3⋊C8—28no—
89C22×#103—91noSylow
90C22×C3×Q8—21no—
91C22×C3×Q8—38no—
92C22×C3×Q8—34no—
93C22×C3×Q8—31no—
94C22×C3×Q8—61no—
95C22×C3×Q8—64no—
96C22×C3×Q8—62no—
97C22×C3×Q8C2×D311yescharacteristic
98C22×C3×Q8C2×D311yescharacteristic
99C23×C3×C4—31no—
100C23×C3×C4—61no—
101C23×Dic3—61no—
102C2×D3×Q8—24no—
103C2×D3×Q8—22no—
104C2×D3×Q8Dic318yescomplemented
105C2×D3×Q8C2×D314yes—
106C22×C4×D3—21no—
107C22×C4×D3—61no—
108C22×C4×D3C2×D311yescharacteristic
109C22×Dic6—21no—
110C22×Dic6C2×D311yescharacteristic
111C22×C3×C8—31no—
112C2×C3×C4⋊C4—31no—
113C2×C4⋊Dic3—31no—
114C2×C4⋊Dic3—31no—
115C2×C4⋊Dic3—34no—
116C2×C4⋊Dic3—61no—
117C2×C4⋊Dic3—62no—
118C2×C4⋊Dic3—61no—
119C2×C4⋊Dic3C2×D311yescharacteristic
120C2×Dic3⋊C4—61no—
121C22×C3⋊C8—31no—
122C22×C3⋊C8—31no—
123C22×C3⋊C8—34no—
124C22×C3⋊C8—61no—
125C22×C3⋊C8—64no—
126C22×C3⋊C8C2×D311yescharacteristic
127C2×D3×C8—34no—
128C2×D3×C8—64no—
129D3×C4⋊C4—34no—
130D3×C4⋊C4—62no—
131C3×#103—34no—
132#835—34no—
133#835—34no—
134#835—34no—
135#835—34no—
136#835—64no—
137#835C2×D314yesdirect product factor
138#816—34no—
139#810—34no—
140C23×C32C2×D411yescharacteristic
141C22×C3×D3C22⋊C414yes—
142C22×C3×D3SD1614yes—
143C22×C3×D3Q1614yes—
144C22×C3×D3C2×D412yes—
145C32×Q8—24no—
146C32×Q8—22no—
147C32×Q8C22×C414yescomplemented
148C2×C32×C4—24no—
149C2×C32×C4—22no—
150C2×C32×C4C22×C412yes—
151C2×C32×C4C2×D411yescharacteristic
152C2×C32×C4C2×D412yes—
153C2×C32×C4C2411yescharacteristic
154C2×C3⋊Dic3—22no—
155C2×C3⋊Dic3—42no—
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×D3—216no—
163C3×C4×D3C22⋊C418yes—
164C3×C4×D3C22×C414yes—
165C3×C4×D3C2×D414yes—
166C3×Dic6—24no—
167C3×Dic6—22no—
168C3×Dic6—216no—
169C3×Dic6C22×C414yescomplemented
170D3×Dic3—48no—
171C3⋊(C3⋊C8)—22no—
172C3×C3⋊C8—22no—
173C23×Q8—31no—
174C23×C8—91no—
175C22×C4⋊C4—91no—
176C2×#103—31no—
177C2×#103—98no—
178C2×#103—91no—
179C2×#103—91no—
180C2×#103—91no—
181C24×C3—31no—
182C23×D3#6711yescharacteristic
183C2×C3×Q8—22no—
184C2×C3×Q8—21no—
185C2×C3×Q8—22no—
186C2×C3×Q8—21no—
187C2×C3×Q8—24no—
188C2×C3×Q8—22no—
189C2×C3×Q8—316no—
190C2×C3×Q8—34no—
191C2×C3×Q8—32no—
192C2×C3×Q8—42no—
193C2×C3×Q8—41no—
194C2×C3×Q8—68no—
195C2×C3×Q8—64no—
196C2×C3×Q8—616no—
197C2×C3×Q8—68no—
198C2×C3×Q8—62no—
199C2×C3×Q8—61no—
200C2×C3×Q8C4×D314yescomplemented
201C2×C3×Q8C2×Dic314yescomplemented
202C2×C3×Q8C22×D312yes—
203C2×C3×Q8C22×D312yes—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4—31no—
208C22×C3×C4—34no—
209C22×C3×C4—34no—
210C22×C3×C4—32no—
211C22×C3×C4—32no—
212C22×C3×C4—41no—
213C22×C3×C4—68no—
214C22×C3×C4—64no—
215C22×C3×C4—61no—
216C22×C3×C4—61no—
217C22×C3×C4C22×D311yescharacteristic
218C22×C3×C4C22×D311yescharacteristic
219C22×Dic3—21no—
220C22×Dic3—21no—
221C22×Dic3—64no—
222C22×Dic3—61no—
223C22×Dic3—61no—
224C22×Dic3—121no—
225C22×Dic3—124no—
226C22×Dic3#6711yescharacteristic
227D3×Q8—216no—
228D3×Q8—28no—
229D3×Q8C2×Dic3116yescomplemented
230C2×C4×D3—28no—
231C2×C4×D3—24no—
232C2×C4×D3—64no—
233C2×C4×D3—124no—
234C2×C4×D3C2×Dic314yes—
235C2×C4×D3#6712yes—
236C2×C4×D3#6714yes—
237C2×C4×D3C22×D312yes—
238C2×Dic6—21no—
239C2×Dic6—22no—
240C2×Dic6—28no—
241C2×Dic6—24no—
242C2×Dic6C2×Dic314yescomplemented
243C2×Dic6C22×D312yes—
244C2×C3×C8—32no—
245C2×C3×C8—62no—
246C3×C4⋊C4—32no—
247C3×C4⋊C4—61no—
248C4⋊Dic3—21no—
249C4⋊Dic3—32no—
250C4⋊Dic3—32no—
251C4⋊Dic3—62no—
252C4⋊Dic3—64no—
253C4⋊Dic3—61no—
254C4⋊Dic3—61no—
255C4⋊Dic3—121no—
256C4⋊Dic3C22×D312yes—
257Dic3⋊C4—64no—
258C2×C3⋊C8—22no—
259C2×C3⋊C8—32no—
260C2×C3⋊C8—32no—
261C2×C3⋊C8—62no—
262C2×C3⋊C8—68no—
263C2×C3⋊C8—62no—
264C2×C3⋊C8—62no—
265C2×C3⋊C8—122no—
266C2×C3⋊C8C22×D312yes—
267D3×C8—68no—
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×C4—24no—
277C32×C4C2×C22⋊C412yes—
278C32×C4C23×C411yescharacteristic
279C32×C4C22×D411yescharacteristic
280C3⋊Dic3—42no—
281C3×Dic3—24no—
282C3×Dic3—42no—
283C3×Dic3C2×C22⋊C414yes—
284C22×Q8—38no—
285C22×Q8—34no—
286C22×Q8—31no—
287C22×Q8—61no—
288C22×Q8—62no—
289C22×Q8—64no—
290C22×Q8D3211yescharacteristic
291C23×C4—31no—
292C23×C4—61no—
293C23×C4—181no—
294C22×C8—31no—
295C22×C8—94no—
296C22×C8—91no—
297C22×C8—184no—
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×C3D3×D411yescharacteristic
313C23×C3C2×#6711yescharacteristic
314C22×D3#21514yes—
315C22×D3#21614yes—
316C22×D3#21714yes—
317C22×D3C2×#6712yes—
318C3×Q8—24no—
319C3×Q8—24no—
320C3×Q8—22no—
321C3×Q8—22no—
322C3×Q8—24no—
323C3×Q8—34no—
324C3×Q8—42no—
325C3×Q8—44no—
326C3×Q8—616no—
327C3×Q8—64no—
328C3×Q8—62no—
329C3×Q8C2×C4×D314yescomplemented
330C3×Q8C22×Dic314yescomplemented
331C2×C3×C4—24no—
332C2×C3×C4—24no—
333C2×C3×C4—22no—
334C2×C3×C4—22no—
335C2×C3×C4—21no—
336C2×C3×C4—22no—
337C2×C3×C4—22no—
338C2×C3×C4—21no—
339C2×C3×C4—34no—
340C2×C3×C4—32no—
341C2×C3×C4—38no—
342C2×C3×C4—34no—
343C2×C3×C4—34no—
344C2×C3×C4—42no—
345C2×C3×C4—44no—
346C2×C3×C4—616no—
347C2×C3×C4—64no—
348C2×C3×C4—62no—
349C2×C3×C4—62no—
350C2×C3×C4—122no—
351C2×C3×C4C2×C4×D312yes—
352C2×C3×C4D3×D411yescharacteristic
353C2×C3×C4D3×D412yes—
354C2×C3×C4C22×Dic312yes—
355C2×C3×C4C2×#6711yescharacteristic
356C2×C3×C4C2×#6712yes—
357C2×C3×C4C23×D311yescharacteristic
358C2×C3×C4C23×D311yescharacteristic
359C2×Dic3—24no—
360C2×Dic3—22no—
361C2×Dic3—22no—
362C2×Dic3—42no—
363C2×Dic3—62no—
364C2×Dic3—62no—
365C2×Dic3—122no—
366C2×Dic3—128no—
367C2×Dic3—122no—
368C2×Dic3—122no—
369C2×Dic3—242no—
370C2×Dic3#21714yes—
371C2×Dic3C2×#6712yes—
372C4×D3—216no—
373C4×D3—128no—
374C4×D3#21718yes—
375C4×D3C22×Dic314yes—
376C4×D3C2×#6714yes—
377Dic6—24no—
378Dic6—22no—
379Dic6—216no—
380Dic6C22×Dic314yescomplemented
381C3×C8—62no—
382C3⋊C8—22no—
383C3⋊C8—62no—
384C3⋊C8—62no—
385C3⋊C8—122no—
386C2×C32C2×#10314yescomplemented
387C2×C32C22×C22⋊C411yescharacteristic
388C2×C32C22×SD1611yescharacteristic
389C2×C32C22×Q1611yescharacteristic
390C3×D3C2×#10318yescomplemented
391C24—31no—
392C2×Q8—21no—
393C2×Q8—22no—
394C2×Q8—316no—
395C2×Q8—32no—
396C2×Q8—34no—
397C2×Q8—64no—
398C2×Q8—68no—
399C2×Q8—68no—
400C2×Q8—616no—
401C2×Q8—61no—
402C2×Q8—62no—
403C2×Q8D3×Dic314yescomplemented
404C2×Q8C2×D3212yes—
405C22×C4—21no—
406C22×C4—31no—
407C22×C4—32no—
408C22×C4—34no—
409C22×C4—32no—
410C22×C4—34no—
411C22×C4—64no—
412C22×C4—68no—
413C22×C4—61no—
414C22×C4—61no—
415C22×C4—184no—
416C22×C4—181no—
417C22×C4—364no—
418C22×C4C2×D3211yescharacteristic
419C2×C8—32no—
420C2×C8—62no—
421C2×C8—92no—
422C2×C8—188no—
423C2×C8—182no—
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×C3D3×SD1612yes—
439C22×C3D3×Q1612yes—
440C22×C3C2×#21512yes—
441C22×C3C2×#21612yes—
442C22×C3C2×#21712yes—
443C22×C3C2×D3×D411yescharacteristic
444C22×C3C22×#6711yescharacteristic
445C2×D3#835116yesdirect product factor
446C2×D3C2×#21514yes—
447C2×D3C2×#21614yes—
448C2×D3C2×#21714yes—
449C3×C4—24no—
450C3×C4—24no—
451C3×C4—21no—
452C3×C4—21no—
453C3×C4—22no—
454C3×C4—34no—
455C3×C4—44no—
456C3×C4—64no—
457C3×C4—122no—
458C3×C4D3×C22⋊C412yes—
459C3×C4C2×#21712yes—
460C3×C4C22×C4×D311yescharacteristic
461C3×C4C2×D3×D411yescharacteristic
462C3×C4C23×Dic311yescharacteristic
463C3×C4C22×#6711yescharacteristic
464Dic3—24no—
465Dic3—42no—
466Dic3—122no—
467Dic3—122no—
468Dic3—242no—
469Dic3C2×#21714yes—
470C32C22×#10311yescharacteristic, complemented, Sylow
471C23—32no—
472C23—34no—
473C23—34no—
474C23—34no—
475C23D3×#6711yescharacteristic
476Q8—22no—
477Q8—24no—
478Q8—34no—
479Q8—616no—
480Q8—62no—
481Q8—64no—
482Q8C2×D3×Dic314yescomplemented
483C2×C4—22no—
484C2×C4—24no—
485C2×C4—32no—
486C2×C4—34no—
487C2×C4—34no—
488C2×C4—34no—
489C2×C4—38no—
490C2×C4—616no—
491C2×C4—62no—
492C2×C4—64no—
493C2×C4—62no—
494C2×C4—122no—
495C2×C4—182no—
496C2×C4—368no—
497C2×C4—362no—
498C2×C4C2×D3×Dic312yes—
499C2×C4D3×#6712yes—
500C2×C4D3×#6711yescharacteristic
501C2×C4C22×D3211yescharacteristic
502C8—62no—
503C8—182no—
504C2×C3—24no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—38no—
509C2×C3D3×#10314yescomplemented
510C2×C3C2×#83514yescomplemented
511C2×C3C2×D3×C22⋊C411yescharacteristic
512C2×C3C2×D3×SD1611yescharacteristic
513C2×C3C2×D3×Q1611yescharacteristic
514C2×C3C22×#21511yescharacteristic
515C2×C3C22×#21611yescharacteristic
516C2×C3C22×#21711yescharacteristic
517D3C2×#83518yesdirect product factor
518C22—316no—
519C22—34no—
520C22—34no—
521C22—34no—
522C22D3×#21512yes—
523C22D3×#21612yes—
524C22D3×#21712yes—
525C22C2×D3×#6711yescharacteristic
526C4—24no—
527C4—34no—
528C4—64no—
529C4—122no—
530C4—362no—
531C4D3×#21712yes—
532C4C22×D3×Dic311yescharacteristic
533C4C2×D3×#6711yescharacteristic
534C3—21no—
535C3C2×D3×#10311yescharacteristic, complemented
536C3C22×#83511yescharacteristic, complemented
537C2—38no—
538C2D3×#83514yesdirect product factor
539C2C2×D3×#21511yescharacteristic
540C2C2×D3×#21611yescharacteristic
541C2C2×D3×#21711yescharacteristic
subgroupG/H
centerC23D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC23×C32C2×D4
prime radicalC23×C3×D3D4
cosocleC2×C32×C4C24
hypercenterC22×Q8D32
hypocenterC32C22×#103
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
4. C2×#63662C2semidirect
5. C2×C3×#835C2semidirect
6. D3×#835C2direct (N × H)
7. C2×#63566C2semidirect
8. C2×#63565C2semidirect
14. C2×C3×D3×Q8C4semidirect
30. #63662C22semidirect
31. C3×#835C22semidirect
32. #63566C22semidirect
33. #63565C22semidirect
47. C2×#835D3direct (N × H)
54. C2×C32×Q8C2×C4semidirect
64. C3×D3×Q8C2×C4semidirect
75. C2×C3×Dic6C2×C4semidirect
104. C2×D3×Q8Dic3semidirect
137. #835C2×D3direct (N × H)
147. C32×Q8C22×C4semidirect
169. C3×Dic6C22×C4semidirect
200. C2×C3×Q8C4×D3semidirect
201. C2×C3×Q8C2×Dic3semidirect
229. D3×Q8C2×Dic3semidirect
242. C2×Dic6C2×Dic3semidirect
272. C2×C3×D3#103semidirect
329. C3×Q8C2×C4×D3semidirect
330. C3×Q8C22×Dic3semidirect
380. Dic6C22×Dic3semidirect
386. C2×C32C2×#103semidirect
390. C3×D3C2×#103semidirect
403. C2×Q8D3×Dic3semidirect
445. C2×D3#835direct (N × H)
470. C32C22×#103semidirect
482. Q8C2×D3×Dic3semidirect
509. C2×C3D3×#103semidirect
510. C2×C3C2×#835semidirect
517. D3C2×#835direct (N × H)
535. C3C2×D3×#103semidirect
536. C3C22×#835semidirect
538. C2D3×#835direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×D3×Q82
C2×D3×C4⋊Dic32
C22×D3×C3⋊C82
C2×#636622
C2×C3×#8352
D3×#8352
C2×#635662
C2×#635652
C22×#8353
C2×D3×#1033