Finite Group Databasebeta

← D3×#4721 #11869384

Subgroups — D3×#4721 #11869384

Order 1152.

972 conjugacy classes of subgroups.

The subgroup lattice has 611 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×C4⋊Dic3C211yesmaximal, characteristic
2D3×#924C211yesmaximal, characteristic
3#10592420C211yesmaximal, characteristic, complemented
4C3×D3×C22⋊C8C211yesmaximal, characteristic
5C3×#4721C211yesmaximal, characteristic, complemented
6#10591126C211yesmaximal, characteristic, complemented
7#10591124C211yesmaximal, characteristic, complemented
8#10590675C212yesmaximal, complemented
9#10590674C212yesmaximal, complemented
10D3×#817C212yesmaximal, complemented
11D3×#816C212yesmaximal, complemented
12D3×#483—31nomaximal
13C2×#4721—31nomaximal
14C22×C3×C4×D3C2211yescharacteristic
15C22×D3×Dic3—21no—
16C2×D3×Dic6C2211yescharacteristic
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18#64133C2211yescharacteristic
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C3×#924C2211yescharacteristic
21C2×C3×D3×C8C2212yes—
22D3×#217—21no—
23C2×Dic3⋊Dic3—21no—
24#63964—21no—
25D3×C4⋊Dic3—21no—
26D3×C4⋊Dic3—21no—
27D3×C4⋊Dic3C2211yescharacteristic
28D3×C4⋊Dic3C2212yes—
29D3×C4⋊Dic3C2212yes—
30D3×Dic3⋊C4—21no—
31#63857C2211yescharacteristic
32#63856C2211yescharacteristic
33#63851—21no—
34C32×C22⋊C8C2211yescharacteristic
35#63644C2212yescomplemented
36#63643C2212yescomplemented
37C3×#830C2211yescharacteristic
38C3×(C2×D3)⋊C8C2212yes—
39C3×#817C2212yescomplemented
40C3×#816C2212yescomplemented
41#63573C2212yescomplemented
42#63573C2212yescomplemented
43#63567C2212yescomplemented
44#63566C2212yescomplemented
45C22×C4⋊Dic3—31no—
46C2×#924—31no—
47D3×C22⋊Q8—31no—
48C2×D3×C4⋊C4—31no—
49C3×#483—31no—
50C2×C3×C22⋊C8—31no—
51C2×#817—32no—
52C2×#816—32no—
53#5043—31no—
54#4971—31no—
55#4862—32no—
56D3×#106—32no—
57#4805—32no—
58D3×#103—32no—
59D3×C22⋊C8D311yescharacteristic
60#4721—31no—
61#4721—31no—
62#4721—31no—
63#4721—31no—
64#4721—32no—
65#4721—32no—
66#4721—61no—
67#4721D311yescharacteristic, direct product factor
68C23×C3×D3D411yescharacteristic
69C22×C32×C4C2311yescharacteristic
70C22×C3⋊Dic3—21no—
71C2×#634C2311yescharacteristic
72C22×C3×Dic3—21no—
73C22×C3×Dic3D411yescharacteristic
74C2×C3×C4×D3—24no—
75C2×C3×C4×D3D411yescharacteristic
76C2×C3×C4×D3D411yescharacteristic
77C2×C3×C4×D3C2311yescharacteristic
78C2×C3×C4×D3C2311yescharacteristic
79C2×C3×Dic6C2311yescharacteristic
80C2×#627—21no—
81C2×D3×Dic3—21no—
82C2×D3×Dic3—22no—
83C2×D3×Dic3—22no—
84C2×D3×Dic3—21no—
85C2×D3×Dic3—44no—
86D3×Dic6—24no—
87C2×C32×C8C2312yes—
88#3757—21no—
89C4⋊(C3⋊Dic3)—21no—
90C4⋊(C3⋊Dic3)C2312yes—
91C4⋊(C3⋊Dic3)C2311yescharacteristic
92#3750—21no—
93C3×#217—21no—
94C3×C4⋊Dic3—21no—
95C3×C4⋊Dic3C2311yescharacteristic
96C3×C4⋊Dic3C2312yes—
97C3×Dic3⋊C4—21no—
98C2×C3×C3⋊C8C2312yes—
99C3×D3×C8—24no—
100#3724—21no—
101Dic3⋊Dic3—21no—
102Dic3⋊Dic3—21no—
103Dic3⋊Dic3—22no—
104Dic3⋊Dic3—22no—
105(C2×D3)⋊Dic3—21no—
106(C2×D3)⋊Dic3—21no—
107C2×#483—91noSylow
108C23×C3×C4—31no—
109C23×Dic3—61no—
110C2×D3×Q8—31no—
111C22×C4×D3—61no—
112C22×C4×D3C2×D311yescharacteristic
113C22×Dic6—31no—
114C22×C3×C8—32no—
115C3×C22⋊Q8—31no—
116C2×C3×C4⋊C4—31no—
117C2×#217—61no—
118#946—31no—
119C2×C4⋊Dic3—31no—
120C2×C4⋊Dic3—31no—
121C2×C4⋊Dic3—32no—
122C2×C4⋊Dic3—31no—
123C2×C4⋊Dic3—32no—
124C2×C4⋊Dic3—61no—
125C2×C4⋊Dic3—61no—
126C2×C4⋊Dic3—61no—
127C2×C4⋊Dic3—61no—
128C2×C4⋊Dic3C2×D311yescharacteristic
129#924—31no—
130#924—31no—
131#924—31no—
132#924—31no—
133#924—61no—
134#924—61no—
135#924—61no—
136#924C2×D311yescharacteristic
137C2×Dic3⋊C4—61no—
138C2×Dic3⋊C4—61no—
139C2×D3×C8C2×D312yes—
140#897—31no—
141#896—61no—
142D3×C4⋊C4—32no—
143D3×C4⋊C4—32no—
144D3×C4⋊C4—31no—
145D3×C4⋊C4—61no—
146D3×C4⋊C4—61no—
147D3×C4⋊C4—61no—
148D3×C22⋊C4—61no—
149#878—61no—
150C3×#106—32no—
151C3×#103—32no—
152C3×C22⋊C8—21no—
153C3×C22⋊C8—31no—
154C3×C22⋊C8—32no—
155C3×C22⋊C8C2×D311yescharacteristic
156C3×C22⋊C8C2×D311yescharacteristic
157#835—32no—
158#830C2×D311yescharacteristic
159(C2×D3)⋊C8C2×D312yes—
160#817—32no—
161#817—32no—
162#817—32no—
163#817—32no—
164#817—62no—
165#817C2×D312yescomplemented
166#816—32no—
167#816—32no—
168#816—32no—
169#816—32no—
170#816—62no—
171#816C2×D312yescomplemented
172#810—32no—
173#808—32no—
174#808—32no—
175C23×C32C2×D411yescharacteristic
176C22×C3×D3—22no—
177C22×C3×D3—22no—
178C22×C3×D3SD1614yes—
179C22×C3×D3C2×D411yescharacteristic
180C22×C3×D3C2×D411yescharacteristic
181C2×C32×C4—22no—
182C2×C32×C4C2×D411yescharacteristic
183C2×C32×C4C2411yescharacteristic
184C2×C3⋊Dic3—21no—
185C2×C3⋊Dic3—21no—
186C2×C3⋊Dic3—22no—
187C2×C3⋊Dic3—42no—
188#634—22no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3—21no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3—22no—
193C2×C3×Dic3—42no—
194C2×C3×Dic3C2×D411yescharacteristic
195C2×C3×Dic3C2×D411yescharacteristic
196C3×C4×D3—22no—
197C3×C4×D3—22no—
198C3×C4×D3—22no—
199C3×C4×D3#4114yes—
200C3×Dic6—22no—
201#627—42no—
202D3×Dic3—42no—
203D3×Dic3—44no—
204D3×Dic3—44no—
205D3×Dic3—42no—
206C32×C8—22no—
207C3×C3⋊C8—22no—
208C2×C22⋊Q8—91no—
209C22×C4⋊C4—91no—
210#483—31no—
211#483—92no—
212#483—92no—
213#483—91no—
214#483—91no—
215#483—91no—
216C2×#106—92no—
217C2×#103—92no—
218C2×C22⋊C8—31no—
219C24×C3—31no—
220C23×D3D1211yescharacteristic
221C2×C3×Q8—31no—
222C22×C3×C4—21no—
223C22×C3×C4—31no—
224C22×C3×C4—31no—
225C22×C3×C4—31no—
226C22×C3×C4—31no—
227C22×C3×C4—31no—
228C22×C3×C4—64no—
229C22×C3×C4—61no—
230C22×C3×C4C22×D311yescharacteristic
231C22×C3×C4C22×D311yescharacteristic
232C22×Dic3—21no—
233C22×Dic3—61no—
234C22×Dic3—61no—
235C22×Dic3—62no—
236C22×Dic3—62no—
237C22×Dic3—61no—
238C22×Dic3—61no—
239C22×Dic3—121no—
240C22×Dic3—124no—
241C22×Dic3D1211yescharacteristic
242D3×Q8—64no—
243C2×C4×D3—24no—
244C2×C4×D3—61no—
245C2×C4×D3—61no—
246C2×C4×D3—62no—
247C2×C4×D3—62no—
248C2×C4×D3—124no—
249C2×C4×D3D1211yescharacteristic
250C2×C4×D3D1211yescharacteristic
251C2×C4×D3C22×D311yescharacteristic
252C2×C4×D3C22×D311yescharacteristic
253C2×Dic6—31no—
254C2×Dic6—31no—
255C2×Dic6—61no—
256C2×Dic6—64no—
257C2×Dic6—61no—
258C2×Dic6—61no—
259C2×Dic6C22×D311yescharacteristic
260C2×C3×C8—22no—
261C2×C3×C8—32no—
262C2×C3×C8—64no—
263C2×C3×C8C22×D312yes—
264C2×C3×C8C22×D312yes—
265C3×C4⋊C4—31no—
266C3×C4⋊C4—32no—
267C3×C4⋊C4—61no—
268C3×C4⋊C4—61no—
269C3×C22⋊C4—61no—
270#217—21no—
271#217—61no—
272#217—61no—
273#217—61no—
274#217—61no—
275#217—121no—
276(C2×D3)⋊C4—61no—
277(C2×D3)⋊C4—61no—
278C4⋊Dic3—21no—
279C4⋊Dic3—31no—
280C4⋊Dic3—32no—
281C4⋊Dic3—32no—
282C4⋊Dic3—31no—
283C4⋊Dic3—62no—
284C4⋊Dic3—61no—
285C4⋊Dic3—61no—
286C4⋊Dic3—62no—
287C4⋊Dic3—62no—
288C4⋊Dic3—61no—
289C4⋊Dic3—61no—
290C4⋊Dic3—61no—
291C4⋊Dic3—121no—
292C4⋊Dic3C22×D312yes—
293C4⋊Dic3C22×D311yescharacteristic
294Dic3⋊C4—21no—
295Dic3⋊C4—61no—
296Dic3⋊C4—61no—
297Dic3⋊C4—61no—
298Dic3⋊C4—61no—
299Dic3⋊C4—61no—
300Dic3⋊C4—61no—
301Dic3⋊C4—62no—
302Dic3⋊C4—62no—
303Dic3⋊C4—121no—
304C2×C3⋊C8C22×D312yes—
305D3×C8—24no—
306C22×C32—21no—
307C22×C32—21no—
308C22×C32C2×SD1612yes—
309C22×C32C22×D411yescharacteristic
310C2×C3×D3—21no—
311C2×C3×D3—21no—
312C2×C3×D3—28no—
313C2×C3×D3#12312yes—
314C2×C3×D3C2×SD1612yes—
315C2×C3×D3C2×SD1612yes—
316C2×C3×D3#13712yes—
317C32×C4—21no—
318C32×C4C2×#4112yes—
319C3⋊Dic3—41no—
320C3⋊Dic3—42no—
321C3⋊Dic3—41no—
322C3×Dic3—21no—
323C3×Dic3—41no—
324C3×Dic3—42no—
325C3×Dic3—41no—
326C3×Dic3#12312yes—
327C22×Q8—91no—
328C23×C4—31no—
329C23×C4—181no—
330C22×C8—32no—
331C22⋊Q8—31no—
332C22⋊Q8—91no—
333C22⋊Q8—91no—
334C22⋊Q8—91no—
335C22⋊Q8—181no—
336C22⋊Q8—181no—
337C2×C4⋊C4—31no—
338C2×C4⋊C4—92no—
339C2×C4⋊C4—92no—
340C2×C4⋊C4—91no—
341C2×C4⋊C4—91no—
342C2×C4⋊C4—181no—
343C2×C4⋊C4—181no—
344C2×C4⋊C4—181no—
345C2×C4⋊C4—181no—
346C2×C22⋊C4—181no—
347#106—32no—
348#106—92no—
349#106—92no—
350#106—92no—
351#103—32no—
352#103—92no—
353#103—92no—
354#103—92no—
355C22⋊C8—31no—
356C22⋊C8—32no—
357C22⋊C8D3211yescharacteristic
358C23×C3—21no—
359C23×C3—31no—
360C23×C3—34no—
361C23×C3—31no—
362C23×C3—62no—
363C23×C3—62no—
364C23×C3C2×D1211yescharacteristic
365C23×C3D3×D411yescharacteristic
366C22×D3—22no—
367C22×D3—22no—
368C22×D3#20414yes—
369C22×D3C2×D1211yescharacteristic
370C22×D3C2×D1211yescharacteristic
371C3×Q8—62no—
372C2×C3×C4—22no—
373C2×C3×C4—22no—
374C2×C3×C4—21no—
375C2×C3×C4—21no—
376C2×C3×C4—31no—
377C2×C3×C4—34no—
378C2×C3×C4—31no—
379C2×C3×C4—42no—
380C2×C3×C4—62no—
381C2×C3×C4—62no—
382C2×C3×C4—62no—
383C2×C3×C4—62no—
384C2×C3×C4—62no—
385C2×C3×C4—61no—
386C2×C3×C4—61no—
387C2×C3×C4—122no—
388C2×C3×C4C2×D1211yescharacteristic
389C2×C3×C4D3×D411yescharacteristic
390C2×C3×C4C23×D311yescharacteristic
391C2×C3×C4C23×D311yescharacteristic
392C2×Dic3—22no—
393C2×Dic3—21no—
394C2×Dic3—21no—
395C2×Dic3—22no—
396C2×Dic3—42no—
397C2×Dic3—61no—
398C2×Dic3—62no—
399C2×Dic3—61no—
400C2×Dic3—61no—
401C2×Dic3—61no—
402C2×Dic3—62no—
403C2×Dic3—121no—
404C2×Dic3—121no—
405C2×Dic3—122no—
406C2×Dic3—122no—
407C2×Dic3—122no—
408C2×Dic3—124no—
409C2×Dic3—124no—
410C2×Dic3—122no—
411C2×Dic3—122no—
412C2×Dic3—242no—
413C2×Dic3C2×D1211yescharacteristic
414C2×Dic3C2×D1211yescharacteristic
415C4×D3—22no—
416C4×D3—22no—
417C4×D3—22no—
418C4×D3—122no—
419C4×D3—124no—
420C4×D3—124no—
421C4×D3—122no—
422C4×D3#23714yes—
423Dic6—22no—
424Dic6—62no—
425Dic6—62no—
426Dic6—122no—
427Dic6—122no—
428Dic6—122no—
429C3×C8—22no—
430C3×C8—22no—
431C3×C8—42no—
432C3×C8—62no—
433C3⋊C8—22no—
434C2×C32—22no—
435C2×C32C2×#12311yescharacteristic
436C2×C32C22×SD1611yescharacteristic
437C2×C32C2×#13711yescharacteristic
438C3×D3—22no—
439C3×D3#48314yescomplemented
440C24—31no—
441C2×Q8—31no—
442C2×Q8—91no—
443C2×Q8—181no—
444C2×Q8—184no—
445C22×C4—31no—
446C22×C4—31no—
447C22×C4—31no—
448C22×C4—31no—
449C22×C4—31no—
450C22×C4—64no—
451C22×C4—61no—
452C22×C4—181no—
453C22×C4—181no—
454C22×C4—182no—
455C22×C4—182no—
456C22×C4—181no—
457C22×C4—364no—
458C22×C4C2×D3211yescharacteristic
459C2×C8—32no—
460C2×C8—64no—
461C2×C8C2×D3212yes—
462C4⋊C4—32no—
463C4⋊C4—31no—
464C4⋊C4—61no—
465C4⋊C4—61no—
466C4⋊C4—92no—
467C4⋊C4—91no—
468C4⋊C4—182no—
469C4⋊C4—182no—
470C4⋊C4—181no—
471C4⋊C4—181no—
472C4⋊C4—181no—
473C4⋊C4—181no—
474C4⋊C4—181no—
475C22⋊C4—61no—
476C22⋊C4—181no—
477C22⋊C4—181no—
478C22⋊C4—181no—
479C22×C3—21no—
480C22×C3—21no—
481C22×C3—21no—
482C22×C3—21no—
483C22×C3—21no—
484C22×C3—22no—
485C22×C3—32no—
486C22×C3—32no—
487C22×C3—32no—
488C22×C3—32no—
489C22×C3—41no—
490C22×C3—41no—
491C22×C3—68no—
492C22×C3—61no—
493C22×C3—61no—
494C22×C3C2×#20412yes—
495C22×C3D3×SD1612yes—
496C22×C3C22×D1211yescharacteristic
497C22×C3C2×D3×D411yescharacteristic
498C2×D3—21no—
499C2×D3—21no—
500C2×D3—28no—
501C2×D3#88612yes—
502C2×D3C2×#20412yes—
503C2×D3C2×#20412yes—
504C2×D3#90912yes—
505C3×C4—21no—
506C3×C4—21no—
507C3×C4—22no—
508C3×C4—32no—
509C3×C4—41no—
510C3×C4—61no—
511C3×C4—122no—
512C3×C4—121no—
513C3×C4—121no—
514C3×C4C2×#23712yes—
515C3×C4D3×#4112yes—
516Dic3—21no—
517Dic3—41no—
518Dic3—42no—
519Dic3—41no—
520Dic3—121no—
521Dic3—122no—
522Dic3—121no—
523Dic3—121no—
524Dic3—122no—
525Dic3—121no—
526Dic3—241no—
527Dic3—242no—
528Dic3—241no—
529Dic3#88612yes—
530C32C2×#48311yescharacteristic, complemented, Sylow
531C23—31no—
532C23—31no—
533C23—34no—
534C23—62no—
535C23—62no—
536C23D3×D1211yescharacteristic
537Q8—62no—
538Q8—182no—
539Q8—362no—
540C2×C4—22no—
541C2×C4—31no—
542C2×C4—34no—
543C2×C4—31no—
544C2×C4—62no—
545C2×C4—62no—
546C2×C4—62no—
547C2×C4—62no—
548C2×C4—61no—
549C2×C4—61no—
550C2×C4—62no—
551C2×C4—122no—
552C2×C4—181no—
553C2×C4—181no—
554C2×C4—182no—
555C2×C4—364no—
556C2×C4—364no—
557C2×C4—362no—
558C2×C4—362no—
559C2×C4—362no—
560C2×C4D3×D1211yescharacteristic
561C2×C4C22×D3211yescharacteristic
562C8—22no—
563C8—62no—
564C2×C3—22no—
565C2×C3—22no—
566C2×C3—21no—
567C2×C3—21no—
568C2×C3—21no—
569C2×C3—34no—
570C2×C3—42no—
571C2×C3—62no—
572C2×C3C2×#88611yescharacteristic
573C2×C3D3×#12311yescharacteristic
574C2×C3C22×#20411yescharacteristic
575C2×C3C2×#90911yescharacteristic
576C2×C3C2×D3×SD1611yescharacteristic
577C2×C3D3×#13711yescharacteristic
578D3—22no—
579D3#472114yesdirect product factor
580C22—21no—
581C22—21no—
582C22—32no—
583C22—32no—
584C22—32no—
585C22—32no—
586C22—68no—
587C22—61no—
588C22—61no—
589C22D3×#20412yes—
590C22C2×D3×D1211yescharacteristic
591C4—21no—
592C4—32no—
593C4—61no—
594C4—122no—
595C4—121no—
596C4—121no—
597C4—362no—
598C4—361no—
599C4—361no—
600C4D3×#23712yes—
601C3—21no—
602C3C2×#472111yescharacteristic, complemented
603C3D3×#48311yescharacteristic, complemented
604C2—22no—
605C2—34no—
606C2—62no—
607C2D3×#88611yescharacteristic
608C2C2×D3×#20411yescharacteristic
609C2D3×#90911yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
prime radicalC23×C3×D3D4
hypercenterC22⋊C8D32
hypocenterC32C2×#483
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
3. #10592420C2semidirect
5. C3×#4721C2semidirect
6. #10591126C2semidirect
7. #10591124C2semidirect
8. #10590675C2semidirect
9. #10590674C2semidirect
10. D3×#817C2semidirect
11. D3×#816C2semidirect
35. #63644C22semidirect
36. #63643C22semidirect
39. C3×#817C22semidirect
40. C3×#816C22semidirect
41. #63573C22semidirect
42. #63573C22semidirect
43. #63567C22semidirect
44. #63566C22semidirect
67. #4721D3direct (N × H)
165. #817C2×D3semidirect
171. #816C2×D3semidirect
439. C3×D3#483semidirect
530. C32C2×#483semidirect
579. D3#4721direct (N × H)
602. C3C2×#4721semidirect
603. C3D3×#483semidirect

Maximal subgroups

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

subgroupindex
C2×D3×C4⋊Dic32
D3×#9242
#105924202
C3×D3×C22⋊C82
C3×#47212
#105911262
#105911242
#105906752
#105906742
D3×#8172
D3×#8162
D3×#4833
C2×#47213