Finite Group Databasebeta

← D3×#5060 #11874395

Subgroups — D3×#5060 #11874395

Order 1152.

1190 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×#124C211yesmaximal, characteristic
2C2×D3×#216C212yesmaximal, complemented
3C2×D3×#214C212yesmaximal
4D3×#869C211yesmaximal, characteristic, complemented
5#10592759C211yesmaximal, characteristic, complemented
6C3×#5060C211yesmaximal, characteristic, complemented
7#10591627C212yesmaximal, complemented
8#10591491C212yesmaximal, complemented
9#10590376C211yesmaximal, characteristic, complemented
10#10590372C211yesmaximal, characteristic, complemented
11D3×#803C211yesmaximal, characteristic, complemented
12C2×#5060—31nomaximal
13D3×#497—31nomaximal
14C2×C3×D3×Q8C2211yescharacteristic
15C2×C3×D3×D4C2211yescharacteristic
16C2×D3×Dic6C2212yes—
17C32×#124C2211yescharacteristic
18C2×#3756C2212yescomplemented
19C2×#3754C2212yes—
20#64078C2211yescharacteristic, complemented
21C3×#947C2211yescharacteristic
22C2×C3×#216C2212yescomplemented
23C3×#936C2211yescharacteristic
24C2×C3×#214C2212yes—
25C3×#885—22no—
26C3×D3×C22⋊C4—22no—
27C3×#875C2211yescharacteristic
28C3×C42×D3C2211yescharacteristic
29C3×#869C2211yescharacteristic, complemented
30D3×#216—28no—
31D3×#214—28no—
32#63918—22no—
33D3×C4⋊Dic3—22no—
34#63866C2212yescomplemented
35C2×#3719C2212yescomplemented
36C2×#3718C2212yescomplemented
37C2×#3716C2212yes—
38C2×#3715C2212yes—
39C2×D3×C3⋊C8C2212yes—
40#63630C2211yescharacteristic, complemented
41C3×#803C2211yescharacteristic, complemented
42#63554C2212yescomplemented
43C2×C3×#124—31no—
44C22×#216—32no—
45C22×#214—32no—
46C2×D3×Q16—32no—
47C2×D3×SD16—32no—
48D3×C4⋊Q8—31no—
49D3×#124D311yescharacteristic
50C2×#869—31no—
51C3×#497—31no—
52#5190—32no—
53#5167—32no—
54#5086—31no—
55#5060—31no—
56#5060—31no—
57#5060—32no—
58#5060—32no—
59#5060—31no—
60#5060—31no—
61#5060—61no—
62#5060D311yescharacteristic, direct product factor
63C2×#803—31no—
64#4715—31no—
65D3×#97—31no—
66C23×C3×D3—21no—
67C2×C32×Q8C2311yescharacteristic
68C2×C32×D4C2311yescharacteristic
69C2×#634C2312yes—
70C2×C3×#67—21no—
71C3×D3×Q8—24no—
72C3×D3×D4—24no—
73C2×C3×D12C2311yescharacteristic
74C2×C3×C4×D3—21no—
75C2×C3×C4×D3D412yes—
76C2×C3×C4×D3C2311yescharacteristic
77C2×C3×Dic6—21no—
78C2×C3×Dic6C2312yes—
79C2×C3×Dic6C2311yescharacteristic
80C2×#627—22no—
81C2×D3×Dic3—22no—
82D3×Dic6—24no—
83D3×Dic6—24no—
84C32×C22⋊C4—22no—
85C32×C42C2311yescharacteristic
86#3756—24no—
87#3754—24no—
88C4⋊(C3⋊Dic3)—22no—
89C2×C3⋊(C3⋊C8)C2312yes—
90C3×#217—22no—
91C3×#216—24no—
92C3×#214—24no—
93C3×(C2×D3)⋊C4—22no—
94C3×(C2×D3)⋊C4—22no—
95C3×C4⋊Dic3—22no—
96C3×C4×Dic3D412yes—
97C3×C4×Dic3C2311yescharacteristic
98C2×C3×C3⋊C8C2312yes—
99Dic3⋊Dic3—24no—
100#3719—24no—
101#3718—24no—
102#3716—24no—
103#3715—24no—
104D3×C3⋊C8D418yes—
105C2×#497—91noSylow
106C22×C3×Q8—31no—
107C22×C3×D4—31no—
108C2×D3×Q8—32no—
109C2×D3×Q8C2×D311yescharacteristic
110C2×D3×D4C2×D311yescharacteristic
111C22×Dic6—32no—
112C2×C3×Q16—32no—
113C2×C3×SD16—32no—
114C3×C4⋊Q8—31no—
115C3×#124—21no—
116C3×#124—31no—
117C3×#124—31no—
118C3×#124—31no—
119C3×#124—62no—
120C3×#124C2×D311yescharacteristic
121C3×#124C2×D311yescharacteristic
122C2×C3×C22⋊C4—62no—
123C2×C3×C42—31no—
124#947C2×D311yescharacteristic
125#944—32no—
126C2×#216—32no—
127C2×#216—32no—
128C2×#216—32no—
129C2×#216—32no—
130C2×#216—32no—
131C2×#216—62no—
132C2×#216—68no—
133C2×#216C2×D312yescomplemented
134C2×#215—32no—
135#936C2×D311yescharacteristic
136C2×#214—32no—
137C2×#214—32no—
138C2×#214—32no—
139C2×#214—32no—
140C2×#214—62no—
141C2×#214—68no—
142C2×#214C2×D312yes—
143C2×C4⋊Dic3—62no—
144C22×C3⋊C8—32no—
145D3×Q16—68no—
146D3×SD16—68no—
147C2×Dic12—32no—
148C2×#204—32no—
149C2×D3×C8—32no—
150D3×C4⋊C4—62no—
151#888—62no—
152#885—22no—
153D3×C22⋊C4—22no—
154#875C2×D311yescharacteristic
155C42×D3C2×D311yescharacteristic
156#869—32no—
157#869—31no—
158#869—31no—
159#869—61no—
160#869—62no—
161#869C2×D311yescharacteristic, complemented
162C3×#97—31no—
163#815—32no—
164#803—31no—
165#803—31no—
166#803—32no—
167#803—61no—
168#803C2×D311yescharacteristic, complemented
169C23×C32—21no—
170C22×C3×D3—21no—
171C22×C3×D3—42no—
172C22×C3×D3—44no—
173C22×C3×D3C2×D411yescharacteristic
174C32×Q8—22no—
175C32×D4—22no—
176C2×C32×C4—21no—
177C2×C32×C4C2×D412yes—
178C2×C32×C4C2411yescharacteristic
179C2×C3⋊Dic3—22no—
180#634—22no—
181#634—22no—
182C3×#67—42no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—21no—
185C2×C3×Dic3C2×D412yes—
186C2×C3×Dic3C2×D411yescharacteristic
187C3×D12—22no—
188C3×C4×D3—24no—
189C3×C4×D3—42no—
190C3×C4×D3C2×D414yes—
191C3×Dic6—22no—
192C3×Dic6—22no—
193C3×Dic6—22no—
194C3×Dic6—42no—
195#627—44no—
196D3×Dic3—44no—
197C3⋊(C3⋊C8)C2×D414yes—
198C3×C3⋊C8C2×D414yes—
199C22×Q16—92no—
200C22×SD16—92no—
201C2×C4⋊Q8—91no—
202C2×#124—31no—
203#497—31no—
204#497—91no—
205#497—91no—
206#497—92no—
207#497—92no—
208#497—91no—
209C2×#97—91no—
210C24×C3—61no—
211C23×D3—21no—
212C2×C3×Q8—21no—
213C2×C3×Q8—32no—
214C2×C3×Q8—31no—
215C2×C3×Q8—61no—
216C2×C3×Q8—64no—
217C2×C3×Q8C22×D311yescharacteristic
218C2×C3×Q8C22×D311yescharacteristic
219C2×C3×D4—21no—
220C2×C3×D4—31no—
221C2×C3×D4—64no—
222C2×C3×D4—61no—
223C2×C3×D4C22×D311yescharacteristic
224C2×C3×D4C22×D311yescharacteristic
225C22×C3×C4—31no—
226C22×C3×C4—32no—
227C22×C3×C4—61no—
228C2×#67—21no—
229C22×Dic3—62no—
230D3×Q8—24no—
231D3×Q8—64no—
232D3×Q8—64no—
233D3×D4—24no—
234C2×D12C22×D311yescharacteristic
235C2×C4×D3—21no—
236C2×C4×D3—62no—
237C2×C4×D3#6712yes—
238C2×C4×D3C22×D311yescharacteristic
239C2×Dic6—21no—
240C2×Dic6—32no—
241C2×Dic6—32no—
242C2×Dic6—62no—
243C2×Dic6—64no—
244C2×Dic6—64no—
245C2×Dic6—62no—
246C2×Dic6—62no—
247C2×Dic6C22×D312yes—
248C2×Dic6C22×D311yescharacteristic
249C3×Q16—64no—
250C3×SD16—64no—
251C2×C3×C8—32no—
252C3×C4⋊C4—62no—
253C3×C22⋊C4—22no—
254C3×C22⋊C4—22no—
255C3×C22⋊C4—42no—
256C3×C22⋊C4—62no—
257C3×C22⋊C4—62no—
258C3×C22⋊C4—62no—
259C3×C42—21no—
260C3×C42—32no—
261C3×C42—31no—
262C3×C42C22×D311yescharacteristic
263C3×C42C22×D311yescharacteristic
264#217—22no—
265#216—24no—
266#216—64no—
267#216—64no—
268#216—64no—
269#216—64no—
270#216—64no—
271#216—124no—
272#215—64no—
273#214—24no—
274#214—64no—
275#214—64no—
276#214—64no—
277#214—64no—
278#214—124no—
279(C2×D3)⋊C4—22no—
280(C2×D3)⋊C4—22no—
281C4⋊Dic3—22no—
282C4⋊Dic3—64no—
283C4⋊Dic3—62no—
284C4⋊Dic3—62no—
285C4⋊Dic3—122no—
286Dic3⋊C4—64no—
287C4×Dic3#6712yes—
288C4×Dic3C22×D311yescharacteristic
289C2×C3⋊C8—32no—
290C2×C3⋊C8—32no—
291C2×C3⋊C8—38no—
292C2×C3⋊C8—62no—
293C2×C3⋊C8C22×D312yes—
294Dic12—64no—
295#204—64no—
296D3×C8—38no—
297C22×C32—41no—
298C22×C32—42no—
299C22×C32C22×D411yescharacteristic
300C2×C3×D3—41no—
301C2×C3×D3—42no—
302C2×C3×D3—84no—
303C2×C3×D3#12712yes—
304C2×C3×D3#13714yes—
305C32×C4—22no—
306C32×C4—41no—
307C32×C4C22×D412yes—
308C3⋊Dic3—42no—
309C3×Dic3—22no—
310C3×Dic3—42no—
311C3×Dic3—41no—
312C3×Dic3#12712yes—
313C22×Q8—31no—
314C22×Q8—92no—
315C22×D4—31no—
316C2×Q16—32no—
317C2×Q16—92no—
318C2×Q16—92no—
319C2×Q16—92no—
320C2×Q16—188no—
321C2×SD16—32no—
322C2×SD16—92no—
323C2×SD16—92no—
324C2×SD16—92no—
325C2×SD16—188no—
326C22×C8—92no—
327C4⋊Q8—31no—
328C4⋊Q8—92no—
329C4⋊Q8—91no—
330C4⋊Q8—182no—
331#124—31no—
332#124—31no—
333#124—31no—
334#124—62no—
335#124D3211yescharacteristic
336C2×C4⋊C4—182no—
337C2×C22⋊C4—62no—
338C2×C42—31no—
339#97—31no—
340#97—92no—
341#97—91no—
342C23×C3—21no—
343C23×C3—21no—
344C23×C3—31no—
345C23×C3—41no—
346C23×C3—61no—
347C23×C3—122no—
348C23×C3—124no—
349C22×D3—21no—
350C22×D3—42no—
351C22×D3—44no—
352C22×D3C2×#6711yescharacteristic
353C3×Q8—22no—
354C3×Q8—22no—
355C3×Q8—42no—
356C3×Q8—62no—
357C3×Q8—62no—
358C3×Q8—62no—
359C3×Q8—122no—
360C3×D4—22no—
361C3×D4—22no—
362C3×D4—42no—
363C3×D4—62no—
364C3×D4—122no—
365C2×C3×C4—21no—
366C2×C3×C4—21no—
367C2×C3×C4—21no—
368C2×C3×C4—22no—
369C2×C3×C4—31no—
370C2×C3×C4—34no—
371C2×C3×C4—32no—
372C2×C3×C4—41no—
373C2×C3×C4—64no—
374C2×C3×C4—61no—
375C2×C3×C4—62no—
376C2×C3×C4—122no—
377C2×C3×C4D3×D412yes—
378C2×C3×C4C2×#6712yes—
379C2×C3×C4C23×D311yescharacteristic
380C2×C3×C4C23×D311yescharacteristic
381#67—42no—
382C2×Dic3—22no—
383C2×Dic3—21no—
384C2×Dic3—62no—
385C2×Dic3—62no—
386C2×Dic3—122no—
387C2×Dic3—124no—
388C2×Dic3C2×#6712yes—
389C2×Dic3C2×#6711yescharacteristic
390D12—22no—
391C4×D3—24no—
392C4×D3—42no—
393C4×D3—124no—
394C4×D3D3×D414yes—
395Dic6—22no—
396Dic6—22no—
397Dic6—22no—
398Dic6—42no—
399Dic6—62no—
400Dic6—62no—
401Dic6—62no—
402Dic6—62no—
403Dic6—122no—
404Dic6—122no—
405Dic6—124no—
406Dic6—124no—
407C3×C8—34no—
408C3⋊C8—34no—
409C3⋊C8—34no—
410C3⋊C8—64no—
411C3⋊C8D3×D414yes—
412C2×C32—81no—
413C2×C32C2×#12711yescharacteristic
414C2×C32C2×#13712yes—
415C3×D3—81no—
416C3×D3#49714yescomplemented
417C24—61no—
418C2×Q8—31no—
419C2×Q8—32no—
420C2×Q8—61no—
421C2×Q8—64no—
422C2×Q8—92no—
423C2×Q8—182no—
424C2×Q8—184no—
425C2×Q8—184no—
426C2×Q8C2×D3211yescharacteristic
427C2×D4—31no—
428C2×D4—64no—
429C2×D4—61no—
430C2×D4C2×D3211yescharacteristic
431C22×C4—31no—
432C22×C4—32no—
433C22×C4—61no—
434C22×C4—182no—
435Q16—64no—
436Q16—184no—
437Q16—184no—
438Q16—184no—
439SD16—64no—
440SD16—184no—
441SD16—184no—
442SD16—184no—
443C2×C8—32no—
444C2×C8—98no—
445C2×C8—92no—
446C4⋊C4—62no—
447C4⋊C4—184no—
448C4⋊C4—182no—
449C22⋊C4—22no—
450C22⋊C4—62no—
451C22⋊C4—62no—
452C22⋊C4—62no—
453C42—31no—
454C42—32no—
455C42C2×D3211yescharacteristic
456C22×C3—21no—
457C22×C3—32no—
458C22×C3—34no—
459C22×C3—41no—
460C22×C3—42no—
461C22×C3—41no—
462C22×C3—42no—
463C22×C3—81no—
464C22×C3—82no—
465C22×C3—121no—
466C22×C3—122no—
467C22×C3—244no—
468C22×C3C2×D3×D411yescharacteristic
469C22×C3C22×#6711yescharacteristic
470C2×D3—41no—
471C2×D3—42no—
472C2×D3—84no—
473C2×D3#94012yes—
474C2×D3#95114yes—
475C3×C4—22no—
476C3×C4—22no—
477C3×C4—22no—
478C3×C4—32no—
479C3×C4—42no—
480C3×C4—41no—
481C3×C4—41no—
482C3×C4—62no—
483C3×C4—81no—
484C3×C4—121no—
485C3×C4—122no—
486C3×C4C2×D3×D412yes—
487C3×C4C2×D3×D412yes—
488Dic3—22no—
489Dic3—42no—
490Dic3—41no—
491Dic3—122no—
492Dic3—122no—
493Dic3—242no—
494Dic3#94012yes—
495C32C2×#49711yescharacteristic, complemented, Sylow
496C23—21no—
497C23—31no—
498C23—61no—
499C23—122no—
500C23—124no—
501Q8—22no—
502Q8—62no—
503Q8—62no—
504Q8—62no—
505Q8—122no—
506Q8—182no—
507Q8—182no—
508Q8—364no—
509D4—22no—
510D4—62no—
511D4—122no—
512C2×C4—21no—
513C2×C4—31no—
514C2×C4—34no—
515C2×C4—32no—
516C2×C4—64no—
517C2×C4—61no—
518C2×C4—62no—
519C2×C4—122no—
520C2×C4—182no—
521C2×C4—364no—
522C2×C4D3×#6712yes—
523C2×C4C22×D3211yescharacteristic
524C8—34no—
525C8—94no—
526C2×C3—22no—
527C2×C3—21no—
528C2×C3—34no—
529C2×C3—81no—
530C2×C3—81no—
531C2×C3—161no—
532C2×C3—241no—
533C2×C3D3×#12711yescharacteristic
534C2×C3D3×#13712yes—
535C2×C3C2×#94011yescharacteristic
536C2×C3C2×#95112yes—
537D3—81no—
538D3#506014yesdirect product factor
539C22—34no—
540C22—32no—
541C22—42no—
542C22—41no—
543C22—122no—
544C22—121no—
545C22—244no—
546C22C2×D3×#6711yescharacteristic
547C4—22no—
548C4—32no—
549C4—41no—
550C4—62no—
551C4—121no—
552C4—122no—
553C4—362no—
554C4D32×D412yes—
555C3—21no—
556C3D3×#49711yescharacteristic, complemented
557C3C2×#506011yescharacteristic, complemented
558C2—34no—
559C2—81no—
560C2—241no—
561C2D3×#94011yescharacteristic
562C2D3×#95112yes—
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#124C22
socleC22×C32C22×D4
prime radicalC2×C3×D3×D4C22
hypercenter#124D32
hypocenterC32C2×#497
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
2. C2×D3×#216C2semidirect
4. D3×#869C2semidirect
5. #10592759C2semidirect
6. C3×#5060C2semidirect
7. #10591627C2semidirect
8. #10591491C2semidirect
9. #10590376C2semidirect
10. #10590372C2semidirect
11. D3×#803C2semidirect
18. C2×#3756C22semidirect
20. #64078C22semidirect
22. C2×C3×#216C22semidirect
29. C3×#869C22semidirect
34. #63866C22semidirect
35. C2×#3719C22semidirect
36. C2×#3718C22semidirect
40. #63630C22semidirect
41. C3×#803C22semidirect
42. #63554C22semidirect
62. #5060D3direct (N × H)
133. C2×#216C2×D3semidirect
161. #869C2×D3semidirect
168. #803C2×D3semidirect
416. C3×D3#497semidirect
495. C32C2×#497semidirect
538. D3#5060direct (N × H)
556. C3D3×#497semidirect
557. C3C2×#5060semidirect

Maximal subgroups

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

subgroupindex
C3×D3×#1242
C2×D3×#2162
C2×D3×#2142
D3×#8692
#105927592
C3×#50602
#105916272
#105914912
#105903762
#105903722
D3×#8032
C2×#50603
D3×#4973