Finite Group Databasebeta

← D3×#5090 #11865635

Subgroups — D3×#5090 #11865635

Order 1152.

1014 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
2C2×D3×#216C212yesmaximal
3C4×D3×Dic6C211yesmaximal, characteristic
4#10592789C211yesmaximal, characteristic, complemented
5C3×#5090C211yesmaximal, characteristic, complemented
6#10591575C212yesmaximal, complemented
7#10591574C212yesmaximal, complemented
8D3×#835C212yesmaximal
9#10590388C211yesmaximal, characteristic, complemented
10#10590384C211yesmaximal, characteristic, complemented
11D3×C4⋊(C3⋊C8)C211yesmaximal, characteristic
12C2×#5090—31nomaximal
13D3×#462—31nomaximal
14C2×C3×D3×Q8C2212yes—
15C2×D3×Dic6C2211yescharacteristic
16C32×C4⋊Q8C2211yescharacteristic
17C2×#3756C2212yes—
18C4×#634C2211yescharacteristic
19C3×#944C2212yes—
20C2×C3×#216C2212yes—
21C3×D3×C4⋊C4—21no—
22C3×D3×C4⋊C4—21no—
23C3×#888—21no—
24C3×#888—21no—
25C3×C42×D3C2211yescharacteristic
26C3×#869C2211yescharacteristic
27C3×C4×Dic6C2211yescharacteristic
28D3×#216—28no—
29C4×#627—21no—
30D3×C4⋊Dic3C2211yescharacteristic
31D3×Dic3⋊C4—21no—
32C4×D3×Dic3—21no—
33#63844C2211yescharacteristic
34Dic3×Dic6C2211yescharacteristic
35#63837—21no—
36C2×#3719C2212yes—
37C2×#3718C2212yes—
38C2×D3×C3⋊C8C2212yes—
39#63662C2212yes—
40C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
41C3×#835C2212yes—
42C3×C4⋊(C3⋊C8)C2211yescharacteristic
43Dic3⋊(C3⋊C8)C2212yes—
44#63566C2212yes—
45#63565C2212yes—
46C2×C3×C4⋊Q8—31no—
47C22×#216—32no—
48C2×D3×Q16—32no—
49D3×C4⋊Q8D311yescharacteristic
50C4×D3×Q8—31no—
51C2×C4×Dic6—31no—
52C3×#462—31no—
53C2×#835—32no—
54#5182—32no—
55#5090—31no—
56#5090—31no—
57#5090—32no—
58#5090—31no—
59#5090—32no—
60#5090—31no—
61#5090—61no—
62#5090D311yescharacteristic, direct product factor
63#5031—31no—
64C2×C4⋊(C3⋊C8)—31no—
65#4849—31no—
66D3×C4⋊C8—31no—
67D3×#103—32no—
68#4795—32no—
69C2×C32×Q8C2312yes—
70C2×#634C2311yescharacteristic
71C3×D3×Q8—24no—
72C3×D3×Q8—24no—
73C2×C3×C4×D3—22no—
74C2×C3×C4×D3D411yescharacteristic
75C2×C3×C4×D3D411yescharacteristic
76C2×C3×C4×D3C2311yescharacteristic
77C2×C3×Dic6—22no—
78C2×C3×Dic6C2312yes—
79C2×C3×Dic6C2311yescharacteristic
80C2×#627—21no—
81C2×D3×Dic3—21no—
82C2×D3×Dic3—21no—
83D3×Dic6—22no—
84D3×Dic6D414yes—
85C32×C4⋊C4—21no—
86C32×C4⋊C4—21no—
87C32×C42C2311yescharacteristic
88#3756—24no—
89C4⋊(C3⋊Dic3)C2311yescharacteristic
90#3750—21no—
91C4×C3⋊Dic3—21no—
92C2×C3⋊(C3⋊C8)C2312yes—
93C3×#216—24no—
94C3×C4⋊Dic3—21no—
95C3×C4⋊Dic3—21no—
96C3×C4⋊Dic3C2311yescharacteristic
97C3×Dic3⋊C4—21no—
98C3×Dic3⋊C4—22no—
99C3×Dic3⋊C4—22no—
100C3×C4×Dic3—21no—
101C3×C4×Dic3D411yescharacteristic
102C3×C4×Dic3D411yescharacteristic
103C3×C4×Dic3C2311yescharacteristic
104C2×C3×C3⋊C8C2312yes—
105#3724—21no—
106Dic3⋊Dic3—21no—
107Dic3⋊Dic3—21no—
108Dic32—21no—
109Dic32—21no—
110#3719—24no—
111#3718—24no—
112D3×C3⋊C8—24no—
113C2×#462—91noSylow
114C22×C3×Q8—32no—
115C2×D3×Q8—31no—
116C2×D3×Q8C2×D312yes—
117C22×Dic6—31no—
118C2×C3×Q16—32no—
119C3×C4⋊Q8—21no—
120C3×C4⋊Q8—32no—
121C3×C4⋊Q8—31no—
122C3×C4⋊Q8—61no—
123C3×C4⋊Q8—61no—
124C3×C4⋊Q8C2×D311yescharacteristic
125C3×C4⋊Q8C2×D311yescharacteristic
126C3×C4×Q8—31no—
127C2×C3×C4⋊C4—61no—
128C2×C3×C4⋊C4—61no—
129C2×C3×C42—31no—
130Q8×Dic3—31no—
131#944C2×D312yes—
132C2×#216—32no—
133C2×#216—32no—
134C2×#216—32no—
135C2×#216—32no—
136C2×#216—32no—
137C2×#216—62no—
138C2×#216—68no—
139C2×#216C2×D312yes—
140C2×C4⋊Dic3—31no—
141C2×Dic3⋊C4—61no—
142C2×C4×Dic3—61no—
143C22×C3⋊C8—32no—
144D3×Q16—68no—
145C2×Dic12—32no—
146C2×D3×C8—32no—
147D3×C4⋊C4—21no—
148D3×C4⋊C4—21no—
149D3×C4⋊C4—31no—
150D3×C4⋊C4—61no—
151#888—21no—
152#888—21no—
153#887—31no—
154#887—61no—
155C42×D3—61no—
156C42×D3C2×D311yescharacteristic
157#869C2×D311yescharacteristic
158C4×Dic6—31no—
159C4×Dic6—31no—
160C4×Dic6—31no—
161C4×Dic6—31no—
162C4×Dic6—61no—
163C4×Dic6—61no—
164C4×Dic6—61no—
165C4×Dic6—61no—
166C4×Dic6C2×D311yescharacteristic
167C3×C4⋊C8—31no—
168C3×#103—32no—
169#835—32no—
170#835—32no—
171#835—32no—
172#835—32no—
173#835—62no—
174#835C2×D312yes—
175#816—32no—
176Dic3⋊C8—32no—
177#810—32no—
178C4⋊(C3⋊C8)—31no—
179C4⋊(C3⋊C8)—31no—
180C4⋊(C3⋊C8)—32no—
181C4⋊(C3⋊C8)—61no—
182C4⋊(C3⋊C8)C2×D311yescharacteristic
183C22×C3×D3C2×D411yescharacteristic
184C32×Q8—22no—
185C32×Q8—22no—
186C2×C32×C4—22no—
187C2×C32×C4C2×D411yescharacteristic
188C2×C32×C4C2×D411yescharacteristic
189C2×C32×C4C2411yescharacteristic
190C2×C3⋊Dic3—21no—
191C2×C3⋊Dic3—21no—
192#634—21no—
193#634C2×D412yes—
194C2×C3×Dic3—21no—
195C2×C3×Dic3—21no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3C2×D411yescharacteristic
198C2×C3×Dic3C2×D411yescharacteristic
199C2×C3×Dic3C2×D411yescharacteristic
200C3×C4×D3—22no—
201C3×C4×D3—44no—
202C3×C4×D3Q1614yescomplemented
203C3×C4×D3C2×D412yes—
204C3×C4×D3#4112yes—
205C3×Dic6—21no—
206C3×Dic6—22no—
207C3×Dic6—22no—
208C3×Dic6—44no—
209C3×Dic6C2×D412yes—
210#627—24no—
211D3×Dic3—24no—
212D3×Dic3—42no—
213C3⋊(C3⋊C8)—22no—
214C3×C3⋊C8—22no—
215C22×Q16—92no—
216C2×C4⋊Q8—31no—
217C2×C4×Q8—91no—
218#462—31no—
219#462—92no—
220#462—91no—
221#462—91no—
222#462—92no—
223#462—91no—
224C2×C4⋊C8—91no—
225C2×#103—92no—
226C2×C3×Q8—22no—
227C2×C3×Q8—31no—
228C2×C3×Q8—32no—
229C2×C3×Q8—62no—
230C2×C3×Q8—64no—
231C2×C3×Q8—64no—
232C2×C3×Q8C22×D312yes—
233C2×C3×Q8C22×D312yes—
234C22×C3×C4—31no—
235C22×C3×C4—31no—
236C22×C3×C4—31no—
237C22×C3×C4—62no—
238C22×Dic3—61no—
239C22×Dic3—61no—
240D3×Q8—24no—
241D3×Q8—24no—
242D3×Q8—34no—
243D3×Q8—62no—
244C2×C4×D3—22no—
245C2×C4×D3—61no—
246C2×C4×D3—61no—
247C2×C4×D3#6711yescharacteristic
248C2×C4×D3#6711yescharacteristic
249C2×C4×D3C22×D311yescharacteristic
250C2×Dic6—22no—
251C2×Dic6—31no—
252C2×Dic6—31no—
253C2×Dic6—34no—
254C2×Dic6—61no—
255C2×Dic6—62no—
256C2×Dic6—61no—
257C2×Dic6—61no—
258C2×Dic6C22×D312yes—
259C2×Dic6C22×D311yescharacteristic
260C3×Q16—64no—
261C2×C3×C8—32no—
262C3×C4⋊C4—21no—
263C3×C4⋊C4—21no—
264C3×C4⋊C4—21no—
265C3×C4⋊C4—21no—
266C3×C4⋊C4—31no—
267C3×C4⋊C4—41no—
268C3×C4⋊C4—41no—
269C3×C4⋊C4—62no—
270C3×C4⋊C4—62no—
271C3×C4⋊C4—61no—
272C3×C4⋊C4—61no—
273C3×C4⋊C4—61no—
274C3×C42—21no—
275C3×C42—31no—
276C3×C42—31no—
277C3×C42—31no—
278C3×C42—61no—
279C3×C42C22×D311yescharacteristic
280C3×C42C22×D311yescharacteristic
281#216—24no—
282#216—64no—
283#216—64no—
284#216—64no—
285#216—64no—
286#216—64no—
287#216—124no—
288C4⋊Dic3—21no—
289C4⋊Dic3—21no—
290C4⋊Dic3—31no—
291C4⋊Dic3—31no—
292C4⋊Dic3—61no—
293C4⋊Dic3—61no—
294C4⋊Dic3—61no—
295C4⋊Dic3C22×D311yescharacteristic
296Dic3⋊C4—21no—
297Dic3⋊C4—22no—
298Dic3⋊C4—22no—
299Dic3⋊C4—61no—
300Dic3⋊C4—61no—
301Dic3⋊C4—61no—
302Dic3⋊C4—61no—
303Dic3⋊C4—61no—
304Dic3⋊C4—61no—
305Dic3⋊C4—121no—
306C4×Dic3—21no—
307C4×Dic3—61no—
308C4×Dic3—61no—
309C4×Dic3—61no—
310C4×Dic3—61no—
311C4×Dic3—61no—
312C4×Dic3—61no—
313C4×Dic3—121no—
314C4×Dic3#6711yescharacteristic
315C4×Dic3#6711yescharacteristic
316C4×Dic3C22×D311yescharacteristic
317C2×C3⋊C8—32no—
318C2×C3⋊C8—32no—
319C2×C3⋊C8—62no—
320C2×C3⋊C8—64no—
321C2×C3⋊C8C22×D312yes—
322Dic12—64no—
323D3×C8—64no—
324C22×C32C22×D411yescharacteristic
325C2×C3×D3#12112yes—
326C2×C3×D3C2×Q1612yes—
327C2×C3×D3#13712yes—
328C32×C4—21no—
329C32×C4—42no—
330C32×C4C2×Q1612yescomplemented
331C32×C4C22×D411yescharacteristic
332C32×C4C2×#4111yescharacteristic
333C3⋊Dic3—22no—
334C3⋊Dic3—41no—
335C3×Dic3—22no—
336C3×Dic3—21no—
337C3×Dic3—42no—
338C3×Dic3—41no—
339C3×Dic3#12112yes—
340C3×Dic3C2×Q1612yescomplemented
341C22×Q8—32no—
342C22×Q8—91no—
343C2×Q16—32no—
344C2×Q16—92no—
345C2×Q16—92no—
346C2×Q16—92no—
347C2×Q16—188no—
348C22×C8—92no—
349C4⋊Q8—32no—
350C4⋊Q8—31no—
351C4⋊Q8—61no—
352C4⋊Q8—61no—
353C4⋊Q8D3211yescharacteristic
354C4×Q8—31no—
355C4×Q8—91no—
356C4×Q8—91no—
357C4×Q8—91no—
358C4×Q8—181no—
359C4×Q8—181no—
360C2×C4⋊C4—61no—
361C2×C4⋊C4—61no—
362C2×C4⋊C4—91no—
363C2×C4⋊C4—181no—
364C2×C42—31no—
365C2×C42—181no—
366C4⋊C8—31no—
367C4⋊C8—92no—
368C4⋊C8—91no—
369#103—32no—
370#103—92no—
371#103—92no—
372#103—92no—
373C23×C3—31no—
374C22×D3C2×#6711yescharacteristic
375C3×Q8—22no—
376C3×Q8—22no—
377C3×Q8—22no—
378C3×Q8—22no—
379C3×Q8—32no—
380C3×Q8—42no—
381C3×Q8—42no—
382C3×Q8—61no—
383C3×Q8—62no—
384C3×Q8—62no—
385C3×Q8—124no—
386C2×C3×C4—22no—
387C2×C3×C4—22no—
388C2×C3×C4—21no—
389C2×C3×C4—21no—
390C2×C3×C4—21no—
391C2×C3×C4—31no—
392C2×C3×C4—31no—
393C2×C3×C4—34no—
394C2×C3×C4—32no—
395C2×C3×C4—32no—
396C2×C3×C4—31no—
397C2×C3×C4—42no—
398C2×C3×C4—62no—
399C2×C3×C4—61no—
400C2×C3×C4—62no—
401C2×C3×C4—61no—
402C2×C3×C4—124no—
403C2×C3×C4D3×D411yescharacteristic
404C2×C3×C4D3×D411yescharacteristic
405C2×C3×C4C2×#6711yescharacteristic
406C2×C3×C4C2×#6711yescharacteristic
407C2×C3×C4C23×D311yescharacteristic
408C2×C3×C4C23×D311yescharacteristic
409C2×Dic3—21no—
410C2×Dic3—21no—
411C2×Dic3—22no—
412C2×Dic3—64no—
413C2×Dic3—61no—
414C2×Dic3—61no—
415C2×Dic3—61no—
416C2×Dic3—61no—
417C2×Dic3—121no—
418C2×Dic3—121no—
419C2×Dic3—122no—
420C2×Dic3C2×#6711yescharacteristic
421C2×Dic3C2×#6711yescharacteristic
422C2×Dic3C2×#6711yescharacteristic
423C4×D3—22no—
424C4×D3—44no—
425C4×D3—64no—
426C4×D3—122no—
427C4×D3#21614yescomplemented
428C4×D3D3×D412yes—
429C4×D3#23712yes—
430Dic6—21no—
431Dic6—22no—
432Dic6—22no—
433Dic6—32no—
434Dic6—32no—
435Dic6—44no—
436Dic6—62no—
437Dic6—64no—
438Dic6—61no—
439Dic6—61no—
440Dic6—64no—
441Dic6—121no—
442Dic6D3×D412yes—
443C3×C8—62no—
444C3⋊C8—22no—
445C3⋊C8—62no—
446C3⋊C8—62no—
447C3⋊C8—122no—
448C2×C32C2×#12111yescharacteristic
449C2×C32C22×Q1611yescharacteristic
450C2×C32C2×#13711yescharacteristic
451C3×D3#46214yescomplemented
452C2×Q8—31no—
453C2×Q8—32no—
454C2×Q8—62no—
455C2×Q8—64no—
456C2×Q8—64no—
457C2×Q8—94no—
458C2×Q8—91no—
459C2×Q8—181no—
460C2×Q8—182no—
461C2×Q8C2×D3212yes—
462C22×C4—31no—
463C22×C4—31no—
464C22×C4—31no—
465C22×C4—62no—
466C22×C4—181no—
467C22×C4—181no—
468Q16—64no—
469Q16—184no—
470Q16—184no—
471Q16—184no—
472C2×C8—32no—
473C2×C8—92no—
474C2×C8—184no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—31no—
478C4⋊C4—62no—
479C4⋊C4—62no—
480C4⋊C4—61no—
481C4⋊C4—61no—
482C4⋊C4—61no—
483C4⋊C4—91no—
484C4⋊C4—181no—
485C4⋊C4—181no—
486C4⋊C4—181no—
487C4⋊C4—181no—
488C42—31no—
489C42—31no—
490C42—31no—
491C42—61no—
492C42—181no—
493C42—181no—
494C42—181no—
495C42C2×D3211yescharacteristic
496C22×C3—21no—
497C22×C3—32no—
498C22×C3—32no—
499C22×C3—32no—
500C22×C3C2×D3×D411yescharacteristic
501C22×C3C22×#6711yescharacteristic
502C2×D3#93812yes—
503C2×D3#94212yes—
504C2×D3C2×#21612yes—
505C3×C4—21no—
506C3×C4—21no—
507C3×C4—21no—
508C3×C4—21no—
509C3×C4—22no—
510C3×C4—32no—
511C3×C4—32no—
512C3×C4—41no—
513C3×C4—42no—
514C3×C4—42no—
515C3×C4—61no—
516C3×C4—62no—
517C3×C4—82no—
518C3×C4—121no—
519C3×C4—122no—
520C3×C4D3×Q1612yescomplemented
521C3×C4C2×#21612yescomplemented
522C3×C4C2×D3×D411yescharacteristic
523C3×C4C2×D3×D411yescharacteristic
524C3×C4C2×#23711yescharacteristic
525C3×C4D3×#4111yescharacteristic
526Dic3—21no—
527Dic3—22no—
528Dic3—41no—
529Dic3—42no—
530Dic3—62no—
531Dic3—62no—
532Dic3—122no—
533Dic3—121no—
534Dic3—121no—
535Dic3—241no—
536Dic3#93812yes—
537Dic3C2×#21612yescomplemented
538C32C2×#46211yescharacteristic, complemented, Sylow
539C23—31no—
540Q8—22no—
541Q8—22no—
542Q8—32no—
543Q8—61no—
544Q8—62no—
545Q8—62no—
546Q8—92no—
547Q8—124no—
548Q8—184no—
549Q8—181no—
550C2×C4—22no—
551C2×C4—31no—
552C2×C4—31no—
553C2×C4—32no—
554C2×C4—32no—
555C2×C4—34no—
556C2×C4—31no—
557C2×C4—62no—
558C2×C4—61no—
559C2×C4—61no—
560C2×C4—62no—
561C2×C4—124no—
562C2×C4—184no—
563C2×C4—181no—
564C2×C4—181no—
565C2×C4—362no—
566C2×C4D3×#6711yescharacteristic
567C2×C4D3×#6711yescharacteristic
568C2×C4C22×D3211yescharacteristic
569C8—62no—
570C8—182no—
571C2×C3—21no—
572C2×C3—21no—
573C2×C3—21no—
574C2×C3—34no—
575C2×C3D3×#12111yescharacteristic
576C2×C3C2×D3×Q1611yescharacteristic
577C2×C3D3×#13711yescharacteristic
578C2×C3C2×#93811yescharacteristic
579C2×C3C2×#94211yescharacteristic
580C2×C3C22×#21611yescharacteristic
581D3#509014yesdirect product factor
582C22—32no—
583C22—32no—
584C22—32no—
585C22C2×D3×#6711yescharacteristic
586C4—21no—
587C4—32no—
588C4—32no—
589C4—42no—
590C4—62no—
591C4—61no—
592C4—122no—
593C4—121no—
594C4—182no—
595C4—361no—
596C4D3×#21612yescomplemented
597C4D32×D411yescharacteristic
598C4D3×#23711yescharacteristic
599C3—21no—
600C3D3×#46211yescharacteristic, complemented
601C3C2×#509011yescharacteristic, complemented
602C2—34no—
603C2D3×#93811yescharacteristic
604C2D3×#94211yescharacteristic
605C2C2×D3×#21611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenterC4⋊Q8D32
hypocenterC32C2×#462
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
4. #10592789C2semidirect
5. C3×#5090C2semidirect
6. #10591575C2semidirect
7. #10591574C2semidirect
9. #10590388C2semidirect
10. #10590384C2semidirect
62. #5090D3direct (N × H)
202. C3×C4×D3Q16semidirect
330. C32×C4C2×Q16semidirect
340. C3×Dic3C2×Q16semidirect
427. C4×D3#216semidirect
451. C3×D3#462semidirect
520. C3×C4D3×Q16semidirect
521. C3×C4C2×#216semidirect
537. Dic3C2×#216semidirect
538. C32C2×#462semidirect
581. D3#5090direct (N × H)
596. C4D3×#216semidirect
600. C3D3×#462semidirect
601. C3C2×#5090semidirect

Maximal subgroups

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

subgroupindex
C3×D3×C4⋊Q82
C2×D3×#2162
C4×D3×Dic62
#105927892
C3×#50902
#105915752
#105915742
D3×#8352
#105903882
#105903842
D3×C4⋊(C3⋊C8)2
C2×#50903
D3×#4623