Finite Group Databasebeta

← D3×#5089 #11873555

Subgroups — D3×#5089 #11873555

Order 1152.

922 conjugacy classes of subgroups.

The subgroup lattice has 607 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×C4⋊Q8C211yesmaximal, characteristic, complemented
2D3×#875C211yesmaximal, characteristic
3#10592788C211yesmaximal, characteristic, complemented
4C3×#5089C211yesmaximal, characteristic, complemented
5D3×#810C212yesmaximal, complemented
6D3×#809C212yesmaximal
7#10590535C212yesmaximal, complemented
8#10590531C212yesmaximal, complemented
9D3×#803C211yesmaximal, characteristic, complemented
10#10590294C211yesmaximal, characteristic, complemented
11#10590280C211yesmaximal, characteristic, complemented
12C2×#5089—31nomaximal
13D3×#489—31nomaximal
14C2×C3×D3×Q8—21no—
15C2×D3×D12C2211yescharacteristic
16C2×D3×Dic6C2211yescharacteristic
17C32×C4⋊Q8C2211yescharacteristic, complemented
18#64084C2211yescharacteristic
19C3×#944—21no—
20C3×D3×C4⋊C4—21no—
21C3×D3×C4⋊C4C2212yes—
22C3×#888—21no—
23C3×#888C2212yescomplemented
24C3×#875C2211yescharacteristic
25C3×C42×D3C2211yescharacteristic
26C3×#869C2211yescharacteristic, complemented
27D3×(C2×D3)⋊C4—21no—
28D3×(C2×D3)⋊C4—21no—
29#63864C2211yescharacteristic
30#63860C2211yescharacteristic
31#63852—21no—
32#63852—21no—
33C2×D3×C3⋊C8C2212yes—
34#63637C2212yescomplemented
35#63636C2212yes—
36#63630C2211yescharacteristic, complemented
37C3×#810C2212yescomplemented
38C3×#809C2212yes—
39C3×#803C2211yescharacteristic, complemented
40#63567C2212yescomplemented
41#63565C2212yescomplemented
42#63564C2212yes—
43#63562C2212yes—
44#63554C2212yescomplemented
45C2×C3×C4⋊Q8—31no—
46D3×C4⋊Q8D311yescharacteristic, complemented
47D3×#124—31no—
48C2×#875—31no—
49C3×#489—31no—
50#5089—31no—
51#5089—31no—
52#5089—31no—
53#5089—32no—
54#5089—32no—
55#5089—31no—
56#5089—61no—
57#5089D311yescharacteristic, direct product factor
58#5055—31no—
59C2×#810—32no—
60C2×#809—32no—
61C2×#803—31no—
62D3×#103—32no—
63#4794—32no—
64D3×#102—32no—
65#4765—32no—
66#4714—31no—
67D3×#97—31no—
68C22×D32—21no—
69C2×C32×Q8—21no—
70C2×C4⋊(C3⋊D3)C2311yescharacteristic
71C2×#634C2311yescharacteristic
72C3×D3×Q8—44no—
73C2×C3×D12C2311yescharacteristic
74C2×C3×C4×D3—22no—
75C2×C3×C4×D3D411yescharacteristic
76C2×C3×C4×D3D411yescharacteristic
77C2×C3×C4×D3C2311yescharacteristic
78C2×C3×Dic6—21no—
79C2×C3×Dic6—22no—
80C2×C3×Dic6C2311yescharacteristic
81C2×#627—21no—
82C2×#626—21no—
83C2×D3×Dic3—21no—
84D3×D12—24no—
85D3×Dic6—24no—
86C32×C4⋊C4—21no—
87C32×C4⋊C4C2312yes—
88C32×C42C2311yescharacteristic
89#3752—21no—
90#3752—21no—
91C2×C3⋊(C3⋊C8)C2312yes—
92C3×(C2×D3)⋊C4—21no—
93C3×(C2×D3)⋊C4—21no—
94C3×C4⋊Dic3—21no—
95C3×C4⋊Dic3C2312yes—
96C3×Dic3⋊C4—22no—
97C3×Dic3⋊C4—22no—
98C3×C4×Dic3D411yescharacteristic
99C3×C4×Dic3D411yescharacteristic
100C3×C4×Dic3C2311yescharacteristic
101C2×C3×C3⋊C8C2312yes—
102#3722—21no—
103#3722—21no—
104(C2×D3)⋊Dic3—21no—
105(C2×D3)⋊Dic3—21no—
106D3×C3⋊C8—24no—
107C2×#489—91noSylow
108C22×C3×Q8—61no—
109C2×D3×Q8—21no—
110C2×D3×Q8—31no—
111C2×D3×D4—31no—
112C22×D12—31no—
113C22×Dic6—31no—
114C3×C4⋊Q8—21no—
115C3×C4⋊Q8—32no—
116C3×C4⋊Q8—31no—
117C3×C4⋊Q8—61no—
118C3×C4⋊Q8—61no—
119C3×C4⋊Q8C2×D311yescharacteristic, complemented
120C3×C4⋊Q8C2×D311yescharacteristic, complemented
121C3×#124—31no—
122C2×C3×C4⋊C4—32no—
123C2×C3×C4⋊C4—61no—
124C2×C3×C42—31no—
125#947—31no—
126#944—21no—
127#936—31no—
128C2×(C2×D3)⋊C4—61no—
129C2×(C2×D3)⋊C4—61no—
130C22×C3⋊C8—32no—
131C2×D3×C8—32no—
132D3×C4⋊C4—21no—
133D3×C4⋊C4C2×D312yes—
134#888—21no—
135#888C2×D312yescomplemented
136#885—61no—
137#885—61no—
138D3×C22⋊C4—61no—
139D3×C22⋊C4—61no—
140#875—31no—
141#875—31no—
142#875—31no—
143#875—31no—
144#875—61no—
145#875—61no—
146#875—61no—
147#875C2×D311yescharacteristic
148C42×D3C2×D311yescharacteristic
149#869C2×D311yescharacteristic, complemented
150C3×#103—32no—
151C3×#102—32no—
152C3×#97—31no—
153#835—32no—
154#832—32no—
155#821—32no—
156#816—32no—
157#815—32no—
158#810—32no—
159#810—32no—
160#810—32no—
161#810—32no—
162#810—62no—
163#810C2×D312yescomplemented
164#809—32no—
165#809—32no—
166#809—32no—
167#809—32no—
168#809—62no—
169#809C2×D312yes—
170#803—31no—
171#803—31no—
172#803—32no—
173#803—61no—
174#803C2×D311yescharacteristic, complemented
175C22×C3⋊D3—21no—
176C22×C3×D3—21no—
177C22×C3×D3C2×D411yescharacteristic
178C2×D32—42no—
179C2×D32—42no—
180C2×D32—42no—
181C32×Q8—42no—
182C2×C32×C4—22no—
183C2×C32×C4C2×D411yescharacteristic
184C2×C32×C4C2×D411yescharacteristic
185C2×C32×C4C2411yescharacteristic
186C2×C3⋊Dic3—21no—
187C4⋊(C3⋊D3)—22no—
188#634—22no—
189C2×C3×Dic3—21no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3C2×D411yescharacteristic
192C2×C3×Dic3C2×D411yescharacteristic
193C2×C3×Dic3C2×D411yescharacteristic
194C3×D12—22no—
195C3×C4×D3—22no—
196C3×C4×D3—22no—
197C3×C4×D3—44no—
198C3×C4×D3#4114yes—
199C3×Dic6—22no—
200C3×Dic6—44no—
201C3×Dic6—42no—
202#627—42no—
203#626—42no—
204D3×Dic3—42no—
205C3⋊(C3⋊C8)—22no—
206C3×C3⋊C8—22no—
207C2×C4⋊Q8—31no—
208C2×#124—91no—
209#489—31no—
210#489—91no—
211#489—92no—
212#489—92no—
213#489—91no—
214#489—91no—
215C2×#103—92no—
216C2×#102—92no—
217C2×#97—91no—
218C23×D3—61no—
219C23×D3—61no—
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8—31no—
223C2×C3×Q8—41no—
224C2×C3×Q8—62no—
225C2×C3×Q8—61no—
226C2×C3×Q8—124no—
227C2×C3×D4—31no—
228C22×C3×C4—31no—
229C22×C3×C4—31no—
230C22×C3×C4—31no—
231C22×C3×C4—62no—
232C2×#67—61no—
233C22×Dic3—61no—
234D3×Q8—44no—
235D3×Q8—64no—
236D3×D4—64no—
237C2×D12—31no—
238C2×D12—31no—
239C2×D12—61no—
240C2×D12—64no—
241C2×D12—61no—
242C2×D12C22×D311yescharacteristic
243C2×C4×D3—22no—
244C2×C4×D3—61no—
245C2×C4×D3#6711yescharacteristic
246C2×C4×D3#6711yescharacteristic
247C2×C4×D3C22×D311yescharacteristic
248C2×Dic6—21no—
249C2×Dic6—22no—
250C2×Dic6—31no—
251C2×Dic6—31no—
252C2×Dic6—61no—
253C2×Dic6—64no—
254C2×Dic6—61no—
255C2×Dic6—61no—
256C2×Dic6C22×D311yescharacteristic
257C2×C3×C8—32no—
258C3×C4⋊C4—21no—
259C3×C4⋊C4—21no—
260C3×C4⋊C4—22no—
261C3×C4⋊C4—32no—
262C3×C4⋊C4—41no—
263C3×C4⋊C4—62no—
264C3×C4⋊C4—62no—
265C3×C4⋊C4—61no—
266C3×C4⋊C4C22×D312yes—
267C3×C4⋊C4C22×D312yes—
268C3×C22⋊C4—61no—
269C3×C22⋊C4—61no—
270C3×C42—21no—
271C3×C42—31no—
272C3×C42—31no—
273C3×C42—31no—
274C3×C42C22×D311yescharacteristic
275C3×C42C22×D311yescharacteristic
276#217—61no—
277#217—61no—
278(C2×D3)⋊C4—21no—
279(C2×D3)⋊C4—21no—
280(C2×D3)⋊C4—61no—
281(C2×D3)⋊C4—61no—
282(C2×D3)⋊C4—61no—
283(C2×D3)⋊C4—61no—
284(C2×D3)⋊C4—61no—
285(C2×D3)⋊C4—61no—
286(C2×D3)⋊C4—61no—
287(C2×D3)⋊C4—61no—
288(C2×D3)⋊C4—61no—
289(C2×D3)⋊C4—61no—
290(C2×D3)⋊C4—121no—
291(C2×D3)⋊C4—121no—
292C4⋊Dic3—21no—
293C4⋊Dic3C22×D312yes—
294Dic3⋊C4—22no—
295Dic3⋊C4—22no—
296C4×Dic3#6711yescharacteristic
297C4×Dic3#6711yescharacteristic
298C4×Dic3C22×D311yescharacteristic
299C2×C3⋊C8—32no—
300C2×C3⋊C8—32no—
301C2×C3⋊C8—62no—
302C2×C3⋊C8—64no—
303C2×C3⋊C8C22×D312yes—
304D3×C8—64no—
305C22×C32C22×D411yescharacteristic
306C2×C3⋊D3—41no—
307C2×C3⋊D3—41no—
308C2×C3⋊D3—41no—
309C2×C3×D3—41no—
310C2×C3×D3—41no—
311C2×C3×D3—41no—
312C2×C3×D3#12412yes—
313C2×C3×D3AGL(1,ℤ/8)12yes—
314C2×C3×D3#13712yes—
315D32—84no—
316C32×C4—21no—
317C32×C4—21no—
318C32×C4—42no—
319C32×C4C2×#4112yes—
320C3⋊Dic3—41no—
321C3×Dic3—21no—
322C3×Dic3—21no—
323C3×Dic3—41no—
324C3×Dic3—42no—
325C3×Dic3#12412yes—
326C22×Q8—61no—
327C22×Q8—91no—
328C22×D4—91no—
329C22×C8—92no—
330C4⋊Q8—32no—
331C4⋊Q8—31no—
332C4⋊Q8—61no—
333C4⋊Q8—61no—
334C4⋊Q8D3211yescharacteristic, complemented
335#124—31no—
336#124—91no—
337#124—91no—
338#124—91no—
339#124—181no—
340#124—181no—
341C2×C4⋊C4—32no—
342C2×C4⋊C4—61no—
343C2×C22⋊C4—181no—
344C2×C22⋊C4—181no—
345C2×C42—31no—
346#103—32no—
347#103—92no—
348#103—92no—
349#103—92no—
350#102—32no—
351#102—92no—
352#102—92no—
353#102—92no—
354#97—31no—
355#97—92no—
356#97—91no—
357C23×C3—31no—
358C23×C3—61no—
359C22×D3—21no—
360C22×D3—61no—
361C22×D3—61no—
362C22×D3—121no—
363C22×D3—122no—
364C22×D3—122no—
365C22×D3—122no—
366C22×D3—122no—
367C22×D3—122no—
368C22×D3—122no—
369C22×D3C2×#6711yescharacteristic
370C3×Q8—42no—
371C3×Q8—42no—
372C3×Q8—62no—
373C3×Q8—82no—
374C3×Q8—122no—
375C3×Q8—124no—
376C3×D4—62no—
377C2×C3×C4—22no—
378C2×C3×C4—22no—
379C2×C3×C4—21no—
380C2×C3×C4—21no—
381C2×C3×C4—21no—
382C2×C3×C4—31no—
383C2×C3×C4—34no—
384C2×C3×C4—31no—
385C2×C3×C4—31no—
386C2×C3×C4—42no—
387C2×C3×C4—62no—
388C2×C3×C4—62no—
389C2×C3×C4—62no—
390C2×C3×C4—61no—
391C2×C3×C4—124no—
392C2×C3×C4D3×D411yescharacteristic
393C2×C3×C4D3×D411yescharacteristic
394C2×C3×C4C2×#6711yescharacteristic
395C2×C3×C4C2×#6711yescharacteristic
396C2×C3×C4C23×D311yescharacteristic
397C2×C3×C4C23×D311yescharacteristic
398#67—122no—
399C2×Dic3—21no—
400C2×Dic3—22no—
401C2×Dic3—61no—
402C2×Dic3—61no—
403C2×Dic3—121no—
404C2×Dic3—122no—
405C2×Dic3C2×#6711yescharacteristic
406C2×Dic3C2×#6711yescharacteristic
407C2×Dic3C2×#6711yescharacteristic
408D12—22no—
409D12—62no—
410D12—62no—
411D12—122no—
412D12—122no—
413C4×D3—22no—
414C4×D3—22no—
415C4×D3—44no—
416C4×D3—122no—
417C4×D3#23914yes—
418Dic6—22no—
419Dic6—44no—
420Dic6—42no—
421Dic6—62no—
422Dic6—62no—
423Dic6—122no—
424Dic6—122no—
425Dic6—122no—
426C3×C8—62no—
427C3⋊C8—22no—
428C3⋊C8—62no—
429C3⋊C8—62no—
430C3⋊C8—122no—
431C2×C32C2×#12411yescharacteristic
432C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
433C2×C32C2×#13711yescharacteristic
434C3⋊D3—81no—
435C3×D3—81no—
436C3×D3#48914yescomplemented
437C24—181no—
438C2×Q8—21no—
439C2×Q8—31no—
440C2×Q8—62no—
441C2×Q8—61no—
442C2×Q8—91no—
443C2×Q8—124no—
444C2×Q8—181no—
445C2×Q8—184no—
446C2×D4—31no—
447C2×D4—91no—
448C2×D4—184no—
449C2×D4—181no—
450C22×C4—31no—
451C22×C4—31no—
452C22×C4—31no—
453C22×C4—62no—
454C22×C4—181no—
455C2×C8—32no—
456C2×C8—92no—
457C2×C8—184no—
458C4⋊C4—21no—
459C4⋊C4—32no—
460C4⋊C4—62no—
461C4⋊C4—62no—
462C4⋊C4—61no—
463C4⋊C4C2×D3212yes—
464C22⋊C4—61no—
465C22⋊C4—61no—
466C22⋊C4—181no—
467C22⋊C4—181no—
468C22⋊C4—181no—
469C22⋊C4—181no—
470C22⋊C4—181no—
471C22⋊C4—181no—
472C42—31no—
473C42—31no—
474C42—31no—
475C42C2×D3211yescharacteristic
476C22×C3—21no—
477C22×C3—32no—
478C22×C3—32no—
479C22×C3—32no—
480C22×C3—121no—
481C22×C3—121no—
482C22×C3—121no—
483C22×C3C2×D3×D411yescharacteristic
484C22×C3C22×#6711yescharacteristic
485C2×D3—41no—
486C2×D3—41no—
487C2×D3—41no—
488C2×D3—121no—
489C2×D3—121no—
490C2×D3—121no—
491C2×D3—121no—
492C2×D3—121no—
493C2×D3—121no—
494C2×D3—241no—
495C2×D3—241no—
496C2×D3—241no—
497C2×D3—244no—
498C2×D3—244no—
499C2×D3#93212yes—
500C2×D3#94212yes—
501C2×D3#94712yes—
502C3×C4—21no—
503C3×C4—21no—
504C3×C4—21no—
505C3×C4—21no—
506C3×C4—22no—
507C3×C4—32no—
508C3×C4—41no—
509C3×C4—41no—
510C3×C4—42no—
511C3×C4—42no—
512C3×C4—61no—
513C3×C4—61no—
514C3×C4—82no—
515C3×C4—122no—
516C3×C4—121no—
517C3×C4C2×#23912yes—
518C3×C4D3×#4112yes—
519Dic3—21no—
520Dic3—21no—
521Dic3—41no—
522Dic3—42no—
523Dic3—121no—
524Dic3—121no—
525Dic3—241no—
526Dic3#94712yes—
527C32C2×#48911yescharacteristic, complemented, Sylow
528C23—31no—
529C23—61no—
530C23—181no—
531C23—362no—
532C23—362no—
533C23—362no—
534Q8—42no—
535Q8—62no—
536Q8—122no—
537Q8—124no—
538Q8—182no—
539Q8—362no—
540D4—62no—
541D4—182no—
542D4—362no—
543C2×C4—22no—
544C2×C4—31no—
545C2×C4—34no—
546C2×C4—31no—
547C2×C4—31no—
548C2×C4—62no—
549C2×C4—62no—
550C2×C4—61no—
551C2×C4—62no—
552C2×C4—124no—
553C2×C4—181no—
554C2×C4—362no—
555C2×C4D3×#6711yescharacteristic
556C2×C4D3×#6711yescharacteristic
557C2×C4C22×D3211yescharacteristic
558C8—62no—
559C8—182no—
560C2×C3—21no—
561C2×C3—21no—
562C2×C3—21no—
563C2×C3—34no—
564C2×C3—241no—
565C2×C3D3×#12411yescharacteristic
566C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
567C2×C3D3×#13711yescharacteristic
568C2×C3C2×#93211yescharacteristic
569C2×C3C2×#94211yescharacteristic
570C2×C3C2×#94711yescharacteristic
571D3—81no—
572D3—241no—
573D3—241no—
574D3—481no—
575D3#508914yesdirect product factor
576C22—32no—
577C22—32no—
578C22—32no—
579C22—121no—
580C22—121no—
581C22—121no—
582C22—361no—
583C22—361no—
584C22—361no—
585C22—724no—
586C22C2×D3×#6711yescharacteristic
587C4—21no—
588C4—21no—
589C4—32no—
590C4—42no—
591C4—61no—
592C4—61no—
593C4—122no—
594C4—121no—
595C4—361no—
596C4D3×#23912yes—
597C3—21no—
598C3D3×#48911yescharacteristic, complemented
599C3C2×#508911yescharacteristic, complemented
600C2—34no—
601C2—241no—
602C2—721no—
603C2D3×#93211yescharacteristic
604C2D3×#94211yescharacteristic
605C2D3×#94711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC2×D3×D12C22
hypercenterC4⋊Q8D32
hypocenterC32C2×#489
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×D3×C4⋊Q8C2semidirect
3. #10592788C2semidirect
4. C3×#5089C2semidirect
5. D3×#810C2semidirect
7. #10590535C2semidirect
8. #10590531C2semidirect
9. D3×#803C2semidirect
10. #10590294C2semidirect
11. #10590280C2semidirect
17. C32×C4⋊Q8C22semidirect
23. C3×#888C22semidirect
26. C3×#869C22semidirect
34. #63637C22semidirect
36. #63630C22semidirect
37. C3×#810C22semidirect
39. C3×#803C22semidirect
40. #63567C22semidirect
41. #63565C22semidirect
44. #63554C22semidirect
46. D3×C4⋊Q8D3semidirect
57. #5089D3direct (N × H)
119. C3×C4⋊Q8C2×D3semidirect
120. C3×C4⋊Q8C2×D3semidirect
135. #888C2×D3semidirect
149. #869C2×D3semidirect
163. #810C2×D3semidirect
174. #803C2×D3semidirect
334. C4⋊Q8D32semidirect
436. C3×D3#489semidirect
527. C32C2×#489semidirect
575. D3#5089direct (N × H)
598. C3D3×#489semidirect
599. C3C2×#5089semidirect

Maximal subgroups

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

subgroupindex
C3×D3×C4⋊Q82
D3×#8752
#105927882
C3×#50892
D3×#8102
D3×#8092
#105905352
#105905312
D3×#8032
#105902942
#105902802
C2×#50893
D3×#4893