Finite Group Databasebeta

← D3×#2960 #11659546

Subgroups — D3×#2960 #11659546

Order 768.

1982 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#533C211yesmaximal, characteristic
2C3×#2960C211yesmaximal, characteristic, complemented
3#83328C211yesmaximal, characteristic, complemented
4#79958C214yesmaximal, complemented
5D3×#446C214yesmaximal, complemented
6#79917C214yesmaximal, complemented
7D3×C8×Q8C214yesmaximal, complemented
8D3×#424C212yesmaximal
9#79076C212yesmaximal, complemented
10D3×#423C211yesmaximal, characteristic
11#79044C211yesmaximal, characteristic, complemented
12D3×#405C212yesmaximal
13#78542C212yesmaximal, complemented
14C2×C4×D3×C8C211yesmaximal, characteristic
15#78445C211yesmaximal, characteristic, complemented
16C2×#2960—31nomaximal, Sylow
17C3×#533C2211yescharacteristic
18C2×D3×M16C2212yes—
19C22×D3×C8C2211yescharacteristic
20C22×D3×C8C2211yescharacteristic
21#5728C412yes—
22D3×C4⋊Q8C412yes—
23#5688C412yes—
24D3×#125C412yes—
25D3×C22⋊Q8C414yes—
26#5622C414yes—
27#5578C2214yes—
28C4×D3×Q8C2214yes—
29D3×#117C2212yes—
30#5517C2212yes—
31C2×C42×D3C2211yescharacteristic
32#5470C2211yescharacteristic
33C3×#446C2214yescomplemented
34C3×C8×Q8C2214yescomplemented
35C3×#424C2212yes—
36C3×#423C2211yescharacteristic
37C3×#405C2212yes—
38C2×C3×C4×C8C2211yescharacteristic
39#5122C2212yes—
40#5119C2212yes—
41#5118C2212yes—
42#5102C2212yes—
43#5101C2212yes—
44C2×C8×Dic3C2211yescharacteristic
45C2×C8×Dic3C2211yescharacteristic
46#5024C2214yescomplemented
47Q8×C3⋊C8C2214yescomplemented
48#4999C2212yes—
49#4997C2212yes—
50#4924C2211yescharacteristic
51C2×C4×C3⋊C8C2211yescharacteristic
52#4839C2218yes—
53#4837C2214yes—
54D3×C4⋊C8C2214yes—
55D3×C4⋊C8C2218yes—
56#4831C2214yescomplemented
57#4830C2214yescomplemented
58#4830C2218yescomplemented
59#4828C2218yescomplemented
60#4708C2214yes—
61D3×#97C2214yes—
62#4701C2218yescomplemented
63#4689C2214yes—
64C4×D3×C8C2212yes—
65C4×D3×C8C2214yes—
66C4×D3×C8C2212yes—
67C4×D3×C8C2212yes—
68C4×D3×C8C2212yes—
69#4679C2214yescomplemented
70C8×Dic6C2214yescomplemented
71C8×Dic6C2218yescomplemented
72C2×#533—31no—
73#2960—34no—
74#2960—34no—
75#2960—32no—
76#2960—31no—
77#2960—32no—
78#2960—31no—
79#2960—31no—
80#2960D311yescharacteristic, direct product factor
81C2×#446—34no—
82C2×C8×Q8—34no—
83C2×#424—32no—
84C2×#423—31no—
85C2×#405—32no—
86C22×C4×C8—31no—
87C2×D3×Q8C2×C414yes—
88C22×C4×D3C2×C412yes—
89C22×C4×D3C2311yescharacteristic
90C2×C3×M16C2312yes—
91C22×C3×C8C2311yescharacteristic
92C22×C3×C8C2311yescharacteristic
93C3×C4⋊Q8C2×C412yes—
94C3×#125C2×C412yes—
95C3×C22⋊Q8C2×C414yes—
96C3×C4×Q8C2314yes—
97C3×#117C2312yes—
98C2×C3×C42C2311yescharacteristic
99#946C2×C414yes—
100Q8×Dic3C2×C414yes—
101#944C2×C414yes—
102#926C2312yes—
103#924C2×C414yes—
104C2×C4×Dic3C2×C412yes—
105C2×C4×Dic3C2311yescharacteristic
106C2×#208C2312yes—
107C22×C3⋊C8C2311yescharacteristic
108C22×C3⋊C8C2311yescharacteristic
109D3×M16—28no—
110C2×ΓL(1,𝔽25)C2314yes—
111C2×D3×C8—24no—
112C2×D3×C8Q818yescomplemented
113C2×D3×C8C2312yes—
114C2×D3×C8C2312yes—
115C2×D3×C8C2314yes—
116C2×D3×C8C2311yescharacteristic
117C2×D3×C8C2311yescharacteristic
118C2×D3×C8C2311yescharacteristic
119C2×D3×C8C2311yescharacteristic
120#897C2×C414yes—
121#896C2×C418yes—
122#892C2×C414yes—
123D3×C4⋊C4C2×C414yes—
124D3×C4⋊C4C2×C418yes—
125D3×C4⋊C4C2×C414yes—
126#890C2×C414yes—
127#889C2×C418yes—
128#888C2×C414yes—
129#888C2×C414yes—
130#887C2×C418yes—
131#887C2×C414yes—
132D3×C22⋊C4C2×C414yes—
133#878C2×C418yes—
134#877C2×C414yes—
135#872C2314yes—
136C42×D3C2×C411yescharacteristic
137C42×D3C2×C411yescharacteristic
138C42×D3C2×C411yescharacteristic
139C42×D3C2×C411yescharacteristic
140C42×D3C2312yes—
141C42×D3C2312yes—
142C42×D3C2314yes—
143#870C2×C412yes—
144#869C2×C412yes—
145C4×Dic6C2314yes—
146C4×Dic6C2318yes—
147C3×C4⋊C8C2314yes—
148C3×C4⋊C8C2318yes—
149C3×#97C2314yes—
150C3×C4×C8C2312yes—
151C3×C4×C8C2314yes—
152C3×C4×C8C2312yes—
153#815C2314yes—
154#815C2314yes—
155Dic3⋊C8C2318yes—
156Dic3⋊C8C2318yes—
157Dic3⋊C8C2318yes—
158C8×Dic3C2314yes—
159C8×Dic3C2312yes—
160C8×Dic3C2314yes—
161C8×Dic3C2312yes—
162C8×Dic3C2312yes—
163C8×Dic3C2312yes—
164C4⋊(C3⋊C8)C2314yes—
165C4⋊(C3⋊C8)C2318yes—
166#803C2314yes—
167C4×C3⋊C8C2312yes—
168C4×C3⋊C8C2312yes—
169C4×C3⋊C8C2314yes—
170C22×M16—32no—
171C23×C8—31no—
172C23×C8—31no—
173#533—32no—
174#533—32no—
175#533—34no—
176#533—34no—
177#533—32no—
178#533—31no—
179#533C2×D311yescharacteristic
180C2×C4⋊Q8—32no—
181C2×#125—32no—
182C2×C22⋊Q8—34no—
183C2×C4×Q8—34no—
184C2×#117—32no—
185C22×C42—31no—
186#446—34no—
187#446—38no—
188#446—34no—
189#446—38no—
190#446—34no—
191#446C2×D314yescomplemented
192C8×Q8—34no—
193C8×Q8—38no—
194C8×Q8—34no—
195C8×Q8—38no—
196C8×Q8—34no—
197C8×Q8C2×D314yescomplemented
198#424—32no—
199#424—32no—
200#424—32no—
201#424—38no—
202#424C2×D312yes—
203#423—32no—
204#423—31no—
205#423—34no—
206#423C2×D311yescharacteristic
207C2×C4⋊C8—34no—
208C2×C4⋊C8—38no—
209#405—32no—
210#405—32no—
211#405—32no—
212#405—34no—
213#405—34no—
214#405C2×D312yes—
215C2×#97—34no—
216C2×C4×C8—31no—
217C2×C4×C8—31no—
218C2×C4×C8—31no—
219C2×C4×C8—32no—
220C2×C4×C8—32no—
221C2×C4×C8—32no—
222C2×C4×C8—32no—
223C2×C4×C8—34no—
224C2×C4×C8C2×D311yescharacteristic
225C23×D3C22×C411yescharacteristic
226C2×C3×Q8C22×C414yes—
227C22×C3×C4C22×C412yes—
228C22×C3×C4C2411yescharacteristic
229C22×Dic3C22×C412yes—
230C22×Dic3C22×C411yescharacteristic
231D3×Q8—216no—
232C2×C4×D3—28no—
233C2×C4×D3C22×C412yes—
234C2×C4×D3C22×C412yes—
235C2×C4×D3C22×C412yes—
236C2×C4×D3C22×C418yes—
237C2×C4×D3C22×C411yescharacteristic
238C2×C4×D3C22×C411yescharacteristic
239C2×C4×D3C22×C412yes—
240C2×C4×D3C2×Q814yes—
241C2×C4×D3#4114yes—
242C2×C4×D3C2411yescharacteristic
243C2×C4×D3C2411yescharacteristic
244C2×Dic6C22×C414yes—
245C2×Dic6C22×C418yes—
246C3×M16—24no—
247C2×C3×C8—22no—
248C2×C3×C8C2×Q814yescomplemented
249C2×C3×C8C2412yes—
250C2×C3×C8C2414yes—
251C2×C3×C8C2411yescharacteristic
252C2×C3×C8C2411yescharacteristic
253C3×C4⋊C4C22×C414yes—
254C3×C4⋊C4C22×C418yes—
255C3×C4⋊C4C22×C414yes—
256C3×C22⋊C4C22×C414yes—
257C3×C42C22×C411yescharacteristic
258C3×C42C22×C411yescharacteristic
259C3×C42C2412yes—
260C3×C42C2414yes—
261#217C22×C414yes—
262(C2×D3)⋊C4C22×C418yes—
263C4⋊Dic3C22×C414yes—
264C4⋊Dic3C22×C418yes—
265C4⋊Dic3C22×C414yes—
266Dic3⋊C4C22×C418yes—
267Dic3⋊C4C22×C418yes—
268Dic3⋊C4C22×C418yes—
269Dic3⋊C4C22×C418yes—
270C4×Dic3C22×C411yescharacteristic
271C4×Dic3C22×C411yescharacteristic
272C4×Dic3C22×C412yes—
273C4×Dic3C22×C412yes—
274C4×Dic3C22×C412yes—
275C4×Dic3C22×C412yes—
276C4×Dic3C22×C418yes—
277C4×Dic3C2412yes—
278C4×Dic3C2414yes—
279#208—24no—
280C2×C3⋊C8—22no—
281C2×C3⋊C8C2×Q814yescomplemented
282C2×C3⋊C8C2412yes—
283C2×C3⋊C8C2414yes—
284C2×C3⋊C8C2411yescharacteristic
285C2×C3⋊C8C2411yescharacteristic
286ΓL(1,𝔽25)—28no—
287D3×C8—24no—
288D3×C8—24no—
289D3×C8—28no—
290D3×C8C2×Q814yes—
291D3×C8C2×Q814yes—
292D3×C8C2×Q814yescomplemented
293D3×C8C2×Q814yescomplemented
294C22×Q8—34no—
295C23×C4—31no—
296C23×C4—32no—
297C2×M16—32no—
298C2×M16—34no—
299C2×M16—68no—
300C2×M16C22×D312yes—
301C22×C8—31no—
302C22×C8—38no—
303C22×C8—31no—
304C22×C8—31no—
305C22×C8—31no—
306C22×C8—31no—
307C22×C8—31no—
308C22×C8—32no—
309C22×C8—32no—
310C22×C8—34no—
311C22×C8—64no—
312C22×C8C22×D311yescharacteristic
313C22×C8C22×D311yescharacteristic
314C4⋊Q8—34no—
315C4⋊Q8—34no—
316C4⋊Q8—34no—
317C4⋊Q8—32no—
318C4⋊Q8C4×D312yes—
319#125—38no—
320#125—34no—
321#125—32no—
322#125C4×D312yes—
323C22⋊Q8—34no—
324C22⋊Q8—34no—
325C22⋊Q8—38no—
326C22⋊Q8—34no—
327C22⋊Q8—38no—
328C22⋊Q8C4×D314yes—
329C4×Q8—34no—
330C4×Q8—34no—
331C4×Q8—38no—
332C4×Q8—38no—
333C4×Q8—34no—
334C4×Q8C22×D314yes—
335#117—32no—
336#117—34no—
337#117—34no—
338#117—34no—
339#117C22×D312yes—
340C2×C4⋊C4—34no—
341C2×C4⋊C4—38no—
342C2×C4⋊C4—34no—
343C2×C22⋊C4—34no—
344C2×C42—32no—
345C2×C42—31no—
346C2×C42—31no—
347C2×C42—31no—
348C2×C42—31no—
349C2×C42—31no—
350C2×C42—34no—
351C2×C42—32no—
352C2×C42—32no—
353C2×C42C22×D311yescharacteristic
354C4⋊C8—38no—
355C4⋊C8—38no—
356C4⋊C8—38no—
357C4⋊C8—34no—
358C4⋊C8—38no—
359C4⋊C8C22×D314yes—
360C4⋊C8C22×D318yes—
361#97—34no—
362#97—34no—
363#97—34no—
364#97C22×D314yes—
365C4×C8—32no—
366C4×C8—32no—
367C4×C8—32no—
368C4×C8—34no—
369C4×C8—32no—
370C4×C8—34no—
371C4×C8—32no—
372C4×C8—32no—
373C4×C8—34no—
374C4×C8C22×D312yes—
375C4×C8C22×D312yes—
376C4×C8C22×D314yes—
377C23×C3C23×C411yescharacteristic
378C22×D3—24no—
379C22×D3C4×Q814yes—
380C22×D3C23×C411yescharacteristic
381C22×D3C23×C411yescharacteristic
382C3×Q8—28no—
383C2×C3×C4—24no—
384C2×C3×C4C23×C412yes—
385C2×C3×C4C23×C418yes—
386C2×C3×C4C23×C411yescharacteristic
387C2×C3×C4C23×C412yes—
388C2×C3×C4C22×Q812yes—
389C2×C3×C4C2×#4112yes—
390C2×C3×C4C2511yescharacteristic
391C2×Dic3—24no—
392C2×Dic3C4×Q814yes—
393C2×Dic3C23×C412yes—
394C2×Dic3C23×C418yes—
395C2×Dic3C23×C411yescharacteristic
396C2×Dic3C23×C411yescharacteristic
397C2×Dic3C23×C412yes—
398C4×D3—24no—
399C4×D3—216no—
400C4×D3—24no—
401C4×D3—24no—
402C4×D3C4×Q814yes—
403C4×D3C4×Q814yes—
404C4×D3#13118yes—
405C4×D3C22×Q812yes—
406C4×D3C22×Q812yes—
407C4×D3C2×#4112yes—
408C4×D3C2×#4112yes—
409Dic6—28no—
410Dic6—216no—
411C3×C8—22no—
412C3×C8—24no—
413C3×C8C22×Q812yes—
414C3×C8C22×Q812yes—
415C3⋊C8—22no—
416C3⋊C8—24no—
417C3⋊C8C22×Q812yes—
418C3⋊C8C22×Q812yes—
419C24—31no—
420C2×Q8—38no—
421C2×Q8—34no—
422C2×Q8—616no—
423C2×Q8C2×C4×D314yes—
424C22×C4—31no—
425C22×C4—31no—
426C22×C4—32no—
427C22×C4—31no—
428C22×C4—34no—
429C22×C4—34no—
430C22×C4—31no—
431C22×C4—31no—
432C22×C4—32no—
433C22×C4—32no—
434C22×C4—32no—
435C22×C4—32no—
436C22×C4—38no—
437C22×C4—68no—
438C22×C4C2×C4×D312yes—
439C22×C4C23×D311yescharacteristic
440M16—24no—
441M16—68no—
442M16—64no—
443C2×C8—22no—
444C2×C8—34no—
445C2×C8—31no—
446C2×C8—31no—
447C2×C8—34no—
448C2×C8—34no—
449C2×C8—34no—
450C2×C8—34no—
451C2×C8—32no—
452C2×C8—34no—
453C2×C8—64no—
454C2×C8—64no—
455C2×C8—68no—
456C2×C8—62no—
457C2×C8D3×Q814yescomplemented
458C2×C8C23×D312yes—
459C2×C8C23×D314yes—
460C2×C8C23×D311yescharacteristic
461C2×C8C23×D311yescharacteristic
462C4⋊C4—38no—
463C4⋊C4—34no—
464C4⋊C4—38no—
465C4⋊C4—38no—
466C4⋊C4—38no—
467C4⋊C4—38no—
468C4⋊C4—34no—
469C4⋊C4C2×C4×D314yes—
470C4⋊C4C2×C4×D318yes—
471C4⋊C4C2×C4×D314yes—
472C22⋊C4—34no—
473C22⋊C4—38no—
474C22⋊C4C2×C4×D314yes—
475C42—32no—
476C42—32no—
477C42—32no—
478C42—31no—
479C42—32no—
480C42—31no—
481C42—38no—
482C42—32no—
483C42—34no—
484C42C2×C4×D311yescharacteristic
485C42C2×C4×D311yescharacteristic
486C42C23×D312yes—
487C42C23×D314yes—
488C22×C3—22no—
489C22×C3C2×C4×Q812yes—
490C22×C3C24×C411yescharacteristic
491C2×D3—22no—
492C2×D3—28no—
493C2×D3C2×C4×Q812yes—
494C2×D3C2×C4×Q812yes—
495C2×D3C2×#13114yes—
496C3×C4—28no—
497C3×C4—22no—
498C3×C4C2×C4×Q812yes—
499C3×C4C2×#13114yes—
500C3×C4C23×Q811yescharacteristic
501C3×C4C22×#4111yescharacteristic
502Dic3—28no—
503Dic3—22no—
504Dic3C2×C4×Q812yes—
505Dic3C2×C4×Q812yes—
506Dic3C2×#13114yes—
507C23—31no—
508C23—31no—
509C23—34no—
510C23—64no—
511C23C22×C4×D311yescharacteristic
512Q8—28no—
513Q8—616no—
514Q8—68no—
515C2×C4—24no—
516C2×C4—31no—
517C2×C4—31no—
518C2×C4—32no—
519C2×C4—34no—
520C2×C4—32no—
521C2×C4—32no—
522C2×C4—32no—
523C2×C4—32no—
524C2×C4—38no—
525C2×C4—34no—
526C2×C4—34no—
527C2×C4—32no—
528C2×C4—38no—
529C2×C4—64no—
530C2×C4—64no—
531C2×C4—616no—
532C2×C4—64no—
533C2×C4—64no—
534C2×C4C22×C4×D312yes—
535C2×C4C22×C4×D318yes—
536C2×C4C22×C4×D312yes—
537C2×C4C22×C4×D311yescharacteristic
538C2×C4C2×D3×Q812yes—
539C2×C4D3×#4112yes—
540C2×C4C24×D311yescharacteristic
541C8—22no—
542C8—24no—
543C8—32no—
544C8—32no—
545C8—62no—
546C8—64no—
547C8C2×D3×Q812yes—
548C8C2×D3×Q812yes—
549C2×C3—22no—
550C2×C3C22×C4×Q811yescharacteristic
551C2×C3C22×#13112yes—
552D3—22no—
553D3#296014yesdirect product factor
554C22—22no—
555C22—32no—
556C22—34no—
557C22—32no—
558C22—68no—
559C22—62no—
560C22C4×D3×Q812yes—
561C22C23×C4×D311yescharacteristic
562C4—22no—
563C4—28no—
564C4—32no—
565C4—32no—
566C4—34no—
567C4—62no—
568C4—68no—
569C4C4×D3×Q812yes—
570C4D3×#13114yes—
571C4C22×D3×Q811yescharacteristic
572C4C2×D3×#4111yescharacteristic
573C3C2×#296011yescharacteristic, complemented, Sylow
574C2—22no—
575C2—34no—
576C2—62no—
577C2C2×C4×D3×Q811yescharacteristic
578C2C2×D3×#13112yes—
subgroupG/H
centerC2×C8C23×D3
commutator, socleC22×C3C24×C4
FrattiniC2×C4C24×D3
FittingC3×#2960C2
prime radicalC23×D3C22×C4
cosocleC2×C3×C4C25
hypercenter#2960D3
hypocenterC3C2×#2960
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C8 ◁ #2960

Complements

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

NH ≅ G/Ntype
2. C3×#2960C2semidirect
3. #83328C2semidirect
4. #79958C2semidirect
5. D3×#446C2semidirect
6. #79917C2semidirect
7. D3×C8×Q8C2semidirect
9. #79076C2semidirect
11. #79044C2semidirect
13. #78542C2semidirect
15. #78445C2semidirect
33. C3×#446C22semidirect
34. C3×C8×Q8C22semidirect
46. #5024C22semidirect
47. Q8×C3⋊C8C22semidirect
56. #4831C22semidirect
57. #4830C22semidirect
58. #4830C22semidirect
59. #4828C22semidirect
62. #4701C22semidirect
69. #4679C22semidirect
70. C8×Dic6C22semidirect
71. C8×Dic6C22semidirect
80. #2960D3direct (N × H)
112. C2×D3×C8Q8semidirect
191. #446C2×D3semidirect
197. C8×Q8C2×D3semidirect
248. C2×C3×C8C2×Q8semidirect
281. C2×C3⋊C8C2×Q8semidirect
292. D3×C8C2×Q8semidirect
293. D3×C8C2×Q8semidirect
457. C2×C8D3×Q8semidirect
553. D3#2960direct (N × H)
573. C3C2×#2960semidirect

Maximal subgroups

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

subgroupindex
D3×#5332
C3×#29602
#833282
#799582
D3×#4462
#799172
D3×C8×Q82
D3×#4242
#790762
D3×#4232
#790442
D3×#4052
#785422
C2×C4×D3×C82
#784452
C2×#29603