Finite Group Databasebeta

← D3×#5055 #11873553

Subgroups — D3×#5055 #11873553

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×#124C211yesmaximal, characteristic
2D3×#869C211yesmaximal, characteristic, complemented
3#10592754C211yesmaximal, characteristic, complemented
4C3×#5055C211yesmaximal, characteristic, complemented
5#10591624C212yesmaximal, complemented
6D3×#835C212yesmaximal, complemented
7#10591488C212yesmaximal, complemented
8D3×#832C212yesmaximal
9D3×#803C211yesmaximal, characteristic, complemented
10#10590280C211yesmaximal, characteristic, complemented
11#10590276C211yesmaximal, characteristic, complemented
12C2×#5055—31nomaximal
13D3×#489—31nomaximal
14C2×C3×D3×Q8C2211yescharacteristic
15C2×C3×D3×D4C2211yescharacteristic
16C2×D3×Dic6—21no—
17C32×#124C2211yescharacteristic
18#64078C2211yescharacteristic, complemented
19C3×#947C2211yescharacteristic
20C3×#936C2211yescharacteristic
21C3×#885—21no—
22C3×#885—21no—
23C3×D3×C22⋊C4—21no—
24C3×D3×C22⋊C4—21no—
25C3×#875C2211yescharacteristic
26C3×C42×D3C2211yescharacteristic
27C3×#869C2211yescharacteristic, complemented
28#63918—21no—
29#63918C2212yescomplemented
30D3×C4⋊Dic3—21no—
31D3×C4⋊Dic3C2212yes—
32#63866—21no—
33C2×D3×C3⋊C8C2212yes—
34#63662C2212yescomplemented
35#63659C2212yes—
36#63630C2211yescharacteristic, complemented
37C3×#835C2212yescomplemented
38C3×#832C2212yes—
39C3×#803C2211yescharacteristic, complemented
40#63566C2212yescomplemented
41#63565C2212yescomplemented
42#63563C2212yes—
43#63562C2212yes—
44#63554C2212yescomplemented
45C2×C3×#124—31no—
46D3×C4⋊Q8—31no—
47D3×#124D311yescharacteristic
48C2×#869—31no—
49C3×#489—31no—
50C2×#835—32no—
51C2×#832—32no—
52#5089—31no—
53#5055—31no—
54#5055—31no—
55#5055—31no—
56#5055—32no—
57#5055—32no—
58#5055—31no—
59#5055—61no—
60#5055D311yescharacteristic, direct product factor
61C2×#803—31no—
62D3×#103—32no—
63#4794—32no—
64D3×#102—32no—
65#4765—32no—
66#4714—31no—
67D3×#97—31no—
68C23×C3×D3—21no—
69C2×C32×Q8C2311yescharacteristic
70C2×C32×D4C2311yescharacteristic
71C2×#634—21no—
72C2×C3×#67—21no—
73C3×D3×Q8—24no—
74C3×D3×D4—24no—
75C2×C3×D12C2311yescharacteristic
76C2×C3×C4×D3—21no—
77C2×C3×C4×D3D411yescharacteristic
78C2×C3×C4×D3D411yescharacteristic
79C2×C3×C4×D3C2311yescharacteristic
80C2×C3×Dic6—21no—
81C2×C3×Dic6—21no—
82C2×C3×Dic6C2311yescharacteristic
83C2×#627—22no—
84C2×D3×Dic3—22no—
85D3×Dic6—44no—
86C32×C22⋊C4—21no—
87C32×C22⋊C4—21no—
88C32×C42C2311yescharacteristic
89C4⋊(C3⋊Dic3)—21no—
90C4⋊(C3⋊Dic3)C2312yes—
91C2×C3⋊(C3⋊C8)C2312yes—
92C3×#217—21no—
93C3×#217—21no—
94C3×(C2×D3)⋊C4—21no—
95C3×(C2×D3)⋊C4—21no—
96C3×(C2×D3)⋊C4—21no—
97C3×(C2×D3)⋊C4—21no—
98C3×C4⋊Dic3—21no—
99C3×C4⋊Dic3C2312yes—
100C3×C4×Dic3D411yescharacteristic
101C3×C4×Dic3D411yescharacteristic
102C3×C4×Dic3C2311yescharacteristic
103C2×C3×C3⋊C8C2312yes—
104Dic3⋊Dic3—22no—
105Dic3⋊Dic3—22no—
106D3×C3⋊C8—24no—
107C2×#489—91noSylow
108C22×C3×Q8—31no—
109C22×C3×D4—31no—
110C2×D3×Q8—61no—
111C2×D3×Q8C2×D311yescharacteristic
112C2×D3×D4C2×D311yescharacteristic
113C22×Dic6—61no—
114C3×C4⋊Q8—31no—
115C3×#124—21no—
116C3×#124—31no—
117C3×#124—31no—
118C3×#124—31no—
119C3×#124—61no—
120C3×#124—61no—
121C3×#124C2×D311yescharacteristic
122C3×#124C2×D311yescharacteristic
123C2×C3×C22⋊C4—61no—
124C2×C3×C22⋊C4—61no—
125C2×C3×C42—31no—
126#947C2×D311yescharacteristic
127#944—61no—
128#936C2×D311yescharacteristic
129C2×C4⋊Dic3—32no—
130C2×C4⋊Dic3—61no—
131C22×C3⋊C8—32no—
132C2×D3×C8—32no—
133D3×C4⋊C4—32no—
134D3×C4⋊C4—61no—
135#888—32no—
136#888—61no—
137#885—21no—
138#885—21no—
139D3×C22⋊C4—21no—
140D3×C22⋊C4—21no—
141#875C2×D311yescharacteristic
142C42×D3C2×D311yescharacteristic
143#869—31no—
144#869—31no—
145#869—32no—
146#869—61no—
147#869—61no—
148#869—61no—
149#869C2×D311yescharacteristic, complemented
150C3×#103—32no—
151C3×#102—32no—
152C3×#97—31no—
153#835—32no—
154#835—32no—
155#835—32no—
156#835—32no—
157#835—62no—
158#835C2×D312yescomplemented
159#832—32no—
160#832—32no—
161#832—32no—
162#832—32no—
163#832—62no—
164#832C2×D312yes—
165#821—32no—
166#816—32no—
167#815—32no—
168#810—32no—
169#809—32no—
170#803—31no—
171#803—31no—
172#803—32no—
173#803—61no—
174#803C2×D311yescharacteristic, complemented
175C23×C32—21no—
176C22×C3×D3—21no—
177C22×C3×D3—42no—
178C22×C3×D3—42no—
179C22×C3×D3—42no—
180C22×C3×D3C2×D411yescharacteristic
181C32×Q8—22no—
182C32×D4—22no—
183C2×C32×C4—21no—
184C2×C32×C4C2×D411yescharacteristic
185C2×C32×C4C2×D411yescharacteristic
186C2×C32×C4C2411yescharacteristic
187C2×C3⋊Dic3—22no—
188#634—42no—
189C3×#67—42no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3C2×D411yescharacteristic
193C2×C3×Dic3C2×D411yescharacteristic
194C2×C3×Dic3C2×D411yescharacteristic
195C3×D12—22no—
196C3×C4×D3—22no—
197C3×C4×D3—22no—
198C3×C4×D3—42no—
199C3×C4×D3#4114yes—
200C3×Dic6—22no—
201C3×Dic6—42no—
202C3×Dic6—42no—
203#627—44no—
204D3×Dic3—44no—
205C3⋊(C3⋊C8)—22no—
206C3×C3⋊C8—22no—
207C2×C4⋊Q8—91no—
208C2×#124—31no—
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—
218C24×C3—61no—
219C23×D3—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8—31no—
222C2×C3×Q8—61no—
223C2×C3×Q8—64no—
224C2×C3×Q8—61no—
225C2×C3×Q8C22×D311yescharacteristic
226C2×C3×Q8C22×D311yescharacteristic
227C2×C3×D4—21no—
228C2×C3×D4—31no—
229C2×C3×D4—64no—
230C2×C3×D4—61no—
231C2×C3×D4C22×D311yescharacteristic
232C2×C3×D4C22×D311yescharacteristic
233C22×C3×C4—31no—
234C22×C3×C4—31no—
235C22×C3×C4—31no—
236C22×C3×C4—61no—
237C2×#67—21no—
238C22×Dic3—62no—
239D3×Q8—24no—
240D3×Q8—124no—
241D3×D4—24no—
242C2×D12C22×D311yescharacteristic
243C2×C4×D3—21no—
244C2×C4×D3—62no—
245C2×C4×D3#6711yescharacteristic
246C2×C4×D3#6711yescharacteristic
247C2×C4×D3C22×D311yescharacteristic
248C2×Dic6—21no—
249C2×Dic6—21no—
250C2×Dic6—62no—
251C2×Dic6—61no—
252C2×Dic6—61no—
253C2×Dic6—62no—
254C2×Dic6—121no—
255C2×Dic6—124no—
256C2×Dic6C22×D311yescharacteristic
257C2×C3×C8—32no—
258C3×C4⋊C4—32no—
259C3×C4⋊C4—61no—
260C3×C22⋊C4—21no—
261C3×C22⋊C4—21no—
262C3×C22⋊C4—21no—
263C3×C22⋊C4—21no—
264C3×C22⋊C4—41no—
265C3×C22⋊C4—41no—
266C3×C22⋊C4—61no—
267C3×C22⋊C4—61no—
268C3×C22⋊C4—61no—
269C3×C22⋊C4—61no—
270C3×C22⋊C4—61no—
271C3×C22⋊C4—61no—
272C3×C42—21no—
273C3×C42—31no—
274C3×C42—31no—
275C3×C42—31no—
276C3×C42C22×D311yescharacteristic
277C3×C42C22×D311yescharacteristic
278#217—21no—
279#217—21no—
280(C2×D3)⋊C4—21no—
281(C2×D3)⋊C4—21no—
282(C2×D3)⋊C4—21no—
283(C2×D3)⋊C4—21no—
284C4⋊Dic3—21no—
285C4⋊Dic3—32no—
286C4⋊Dic3—32no—
287C4⋊Dic3—62no—
288C4⋊Dic3—62no—
289C4⋊Dic3—62no—
290C4⋊Dic3—61no—
291C4⋊Dic3—61no—
292C4⋊Dic3—121no—
293C4⋊Dic3C22×D312yes—
294Dic3⋊C4—62no—
295Dic3⋊C4—62no—
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×C32—41no—
306C22×C32—41no—
307C22×C32—41no—
308C22×C32C22×D411yescharacteristic
309C2×C3×D3—41no—
310C2×C3×D3—41no—
311C2×C3×D3—41no—
312C2×C3×D3—84no—
313C2×C3×D3#12412yes—
314C2×C3×D3AGL(1,ℤ/8)12yes—
315C2×C3×D3#13712yes—
316C32×C4—21no—
317C32×C4—21no—
318C32×C4—41no—
319C32×C4C2×#4112yes—
320C3⋊Dic3—42no—
321C3×Dic3—21no—
322C3×Dic3—21no—
323C3×Dic3—41no—
324C3×Dic3—42no—
325C3×Dic3#12412yes—
326C22×Q8—31no—
327C22×Q8—181no—
328C22×D4—31no—
329C22×C8—92no—
330C4⋊Q8—31no—
331C4⋊Q8—92no—
332C4⋊Q8—91no—
333C4⋊Q8—181no—
334C4⋊Q8—181no—
335#124—31no—
336#124—31no—
337#124—31no—
338#124—61no—
339#124—61no—
340#124D3211yescharacteristic
341C2×C4⋊C4—92no—
342C2×C4⋊C4—181no—
343C2×C22⋊C4—61no—
344C2×C22⋊C4—61no—
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—21no—
358C23×C3—21no—
359C23×C3—31no—
360C23×C3—41no—
361C23×C3—61no—
362C23×C3—122no—
363C23×C3—122no—
364C23×C3—122no—
365C22×D3—21no—
366C22×D3—42no—
367C22×D3—42no—
368C22×D3—42no—
369C22×D3C2×#6711yescharacteristic
370C3×Q8—22no—
371C3×Q8—22no—
372C3×Q8—42no—
373C3×Q8—62no—
374C3×Q8—122no—
375C3×Q8—122no—
376C3×D4—22no—
377C3×D4—22no—
378C3×D4—42no—
379C3×D4—62no—
380C3×D4—122no—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—21no—
384C2×C3×C4—21no—
385C2×C3×C4—21no—
386C2×C3×C4—31no—
387C2×C3×C4—34no—
388C2×C3×C4—31no—
389C2×C3×C4—31no—
390C2×C3×C4—41no—
391C2×C3×C4—62no—
392C2×C3×C4—62no—
393C2×C3×C4—61no—
394C2×C3×C4—62no—
395C2×C3×C4—122no—
396C2×C3×C4D3×D411yescharacteristic
397C2×C3×C4D3×D411yescharacteristic
398C2×C3×C4C2×#6711yescharacteristic
399C2×C3×C4C2×#6711yescharacteristic
400C2×C3×C4C23×D311yescharacteristic
401C2×C3×C4C23×D311yescharacteristic
402#67—42no—
403C2×Dic3—22no—
404C2×Dic3—21no—
405C2×Dic3—62no—
406C2×Dic3—62no—
407C2×Dic3—122no—
408C2×Dic3—124no—
409C2×Dic3C2×#6711yescharacteristic
410C2×Dic3C2×#6711yescharacteristic
411C2×Dic3C2×#6711yescharacteristic
412D12—22no—
413C4×D3—22no—
414C4×D3—22no—
415C4×D3—42no—
416C4×D3—124no—
417C4×D3#23714yes—
418Dic6—22no—
419Dic6—42no—
420Dic6—42no—
421Dic6—124no—
422Dic6—124no—
423Dic6—122no—
424Dic6—122no—
425Dic6—242no—
426C3×C8—62no—
427C3⋊C8—22no—
428C3⋊C8—62no—
429C3⋊C8—62no—
430C3⋊C8—122no—
431C2×C32—81no—
432C2×C32C2×#12411yescharacteristic
433C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
434C2×C32C2×#13711yescharacteristic
435C3×D3—81no—
436C3×D3#48914yescomplemented
437C24—61no—
438C2×Q8—31no—
439C2×Q8—61no—
440C2×Q8—64no—
441C2×Q8—61no—
442C2×Q8—182no—
443C2×Q8—181no—
444C2×Q8—364no—
445C2×Q8C2×D3211yescharacteristic
446C2×D4—31no—
447C2×D4—64no—
448C2×D4—61no—
449C2×D4C2×D3211yescharacteristic
450C22×C4—31no—
451C22×C4—31no—
452C22×C4—31no—
453C22×C4—61no—
454C22×C4—182no—
455C2×C8—32no—
456C2×C8—92no—
457C2×C8—184no—
458C4⋊C4—32no—
459C4⋊C4—61no—
460C4⋊C4—92no—
461C4⋊C4—182no—
462C4⋊C4—182no—
463C4⋊C4—181no—
464C22⋊C4—21no—
465C22⋊C4—21no—
466C22⋊C4—61no—
467C22⋊C4—61no—
468C22⋊C4—61no—
469C22⋊C4—61no—
470C22⋊C4—61no—
471C22⋊C4—61no—
472C42—31no—
473C42—31no—
474C42—31no—
475C42C2×D3211yescharacteristic
476C22×C3—21no—
477C22×C3—32no—
478C22×C3—32no—
479C22×C3—32no—
480C22×C3—41no—
481C22×C3—41no—
482C22×C3—41no—
483C22×C3—41no—
484C22×C3—41no—
485C22×C3—41no—
486C22×C3—81no—
487C22×C3—81no—
488C22×C3—81no—
489C22×C3—121no—
490C22×C3—121no—
491C22×C3—121no—
492C22×C3—244no—
493C22×C3C2×D3×D411yescharacteristic
494C22×C3C22×#6711yescharacteristic
495C2×D3—41no—
496C2×D3—41no—
497C2×D3—41no—
498C2×D3—84no—
499C2×D3#93612yes—
500C2×D3#94912yes—
501C2×D3#95112yes—
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—41no—
511C3×C4—41no—
512C3×C4—61no—
513C3×C4—61no—
514C3×C4—81no—
515C3×C4—121no—
516C3×C4—122no—
517C3×C4C2×#23712yes—
518C3×C4D3×#4112yes—
519Dic3—21no—
520Dic3—21no—
521Dic3—42no—
522Dic3—41no—
523Dic3—122no—
524Dic3—122no—
525Dic3—242no—
526Dic3#93612yes—
527C32C2×#48911yescharacteristic, complemented, Sylow
528C23—21no—
529C23—31no—
530C23—61no—
531C23—122no—
532C23—122no—
533C23—122no—
534Q8—22no—
535Q8—62no—
536Q8—122no—
537Q8—122no—
538Q8—362no—
539Q8—364no—
540D4—22no—
541D4—62no—
542D4—122no—
543C2×C4—21no—
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—122no—
553C2×C4—182no—
554C2×C4—364no—
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—81no—
565C2×C3—81no—
566C2×C3—161no—
567C2×C3—241no—
568C2×C3D3×#12411yescharacteristic
569C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
570C2×C3D3×#13711yescharacteristic
571C2×C3C2×#93611yescharacteristic
572C2×C3C2×#94911yescharacteristic
573C2×C3C2×#95111yescharacteristic
574D3—81no—
575D3#505514yesdirect product factor
576C22—32no—
577C22—32no—
578C22—32no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—121no—
583C22—121no—
584C22—121no—
585C22—244no—
586C22C2×D3×#6711yescharacteristic
587C4—21no—
588C4—21no—
589C4—32no—
590C4—41no—
591C4—61no—
592C4—61no—
593C4—121no—
594C4—122no—
595C4—362no—
596C4D3×#23712yes—
597C3—21no—
598C3D3×#48911yescharacteristic, complemented
599C3C2×#505511yescharacteristic, complemented
600C2—34no—
601C2—81no—
602C2—241no—
603C2D3×#93611yescharacteristic
604C2D3×#94911yescharacteristic
605C2D3×#95111yescharacteristic
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×#489
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. D3×#869C2semidirect
3. #10592754C2semidirect
4. C3×#5055C2semidirect
5. #10591624C2semidirect
6. D3×#835C2semidirect
7. #10591488C2semidirect
9. D3×#803C2semidirect
10. #10590280C2semidirect
11. #10590276C2semidirect
18. #64078C22semidirect
27. C3×#869C22semidirect
29. #63918C22semidirect
34. #63662C22semidirect
36. #63630C22semidirect
37. C3×#835C22semidirect
39. C3×#803C22semidirect
40. #63566C22semidirect
41. #63565C22semidirect
44. #63554C22semidirect
60. #5055D3direct (N × H)
149. #869C2×D3semidirect
158. #835C2×D3semidirect
174. #803C2×D3semidirect
436. C3×D3#489semidirect
527. C32C2×#489semidirect
575. D3#5055direct (N × H)
598. C3D3×#489semidirect
599. C3C2×#5055semidirect

Maximal subgroups

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

subgroupindex
C3×D3×#1242
D3×#8692
#105927542
C3×#50552
#105916242
D3×#8352
#105914882
D3×#8322
D3×#8032
#105902802
#105902762
C2×#50553
D3×#4893