Finite Group Databasebeta

← D3×#2503 #10964474

Subgroups — D3×#2503 #10964474

Order 768.

2918 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×C22⋊Q8C211yesmaximal, characteristic
2C22×D3×C4⋊C4C211yesmaximal, characteristic
3C3×#2503C211yesmaximal, characteristic, complemented
4#82776C211yesmaximal, characteristic, complemented
5#82179C211yesmaximal, characteristic, complemented
6D3×#400C214yesmaximal, complemented
7#78152C214yesmaximal, complemented
8D3×#391C212yesmaximal, complemented
9#76520C212yesmaximal, complemented
10D3×#382C212yesmaximal, complemented
11#74167C212yesmaximal, complemented
12D3×#381C214yesmaximal
13#74079C214yesmaximal, complemented
14C4×D3×C22⋊C4C211yesmaximal, characteristic
15#73518C211yesmaximal, characteristic, complemented
16C2×#2503—31nomaximal, Sylow
17C22×D3×Q8C2211yescharacteristic
18C23×C4×D3C2212yes—
19C23×C4×D3C2211yescharacteristic
20C2×C3×C22⋊Q8C2211yescharacteristic
21C22×C3×C4⋊C4C2211yescharacteristic
22C2×#946C2211yescharacteristic
23C22×C4⋊Dic3C2211yescharacteristic
24C2×#924C2211yescharacteristic
25C22×Dic3⋊C4C2212yes—
26D3×C22⋊Q8—28no—
27C2×#897C2211yescharacteristic
28C2×#896C2212yes—
29C2×D3×C4⋊C4—28no—
30C2×D3×C4⋊C4C2212yes—
31C2×D3×C4⋊C4C2212yes—
32C2×D3×C4⋊C4C2212yes—
33C2×D3×C4⋊C4C2212yes—
34C2×D3×C4⋊C4C2212yes—
35C2×D3×C4⋊C4C2211yescharacteristic
36C2×D3×C22⋊C4C2212yes—
37C2×D3×C22⋊C4C2212yes—
38C2×#878C2212yes—
39C2×C42×D3C2212yes—
40C3×#400C2214yescomplemented
41C3×#391C2212yescomplemented
42C3×#382C2212yescomplemented
43C3×#381C2214yes—
44C3×C4×C22⋊C4C2211yescharacteristic
45#5229C2212yescomplemented
46#5211C2214yes—
47C4×#217C2211yescharacteristic
48#4986C2214yescomplemented
49#4985C2214yescomplemented
50#4977C2212yescomplemented
51#4977C2212yescomplemented
52#4973C2212yescomplemented
53#4943C2214yes—
54#4943C2214yes—
55Dic3×C22⋊C4C2212yes—
56C4×(C2×D3)⋊C4C2212yes—
57#4936C2212yescomplemented
58#4929C2212yescomplemented
59#4666C2212yes—
60#4664C2218yes—
61#4664C2218yes—
62D3×#95C2212yes—
63D3×#95C2218yes—
64D3×#95C2218yes—
65#4660C2218yescomplemented
66#4659C2214yescomplemented
67#4658C2218yescomplemented
68#4650C2218yescomplemented
69#4646C2218yescomplemented
70C22×C22⋊Q8—31no—
71C23×C4⋊C4—31no—
72#2503—34no—
73#2503—32no—
74#2503—32no—
75#2503—34no—
76#2503—31no—
77#2503—31no—
78#2503—31no—
79#2503D311yescharacteristic, direct product factor
80C2×#400—34no—
81C2×#391—32no—
82C2×#382—32no—
83C2×#381—34no—
84C2×C4×C22⋊C4—31no—
85C24×D3C2311yescharacteristic
86C22×C3×Q8C2311yescharacteristic
87C23×C3×C4C2312yes—
88C23×C3×C4C2311yescharacteristic
89C23×Dic3C2312yes—
90C23×Dic3C2311yescharacteristic
91C2×D3×Q8—24no—
92C2×D3×Q8—28no—
93C22×C4×D3—28no—
94C22×C4×D3—28no—
95C22×C4×D3—216no—
96C22×C4×D3D418yes—
97C22×C4×D3C2314yes—
98C22×C4×D3C2314yes—
99C22×C4×D3C2312yes—
100C22×C4×D3C2312yes—
101C22×C4×D3C2314yes—
102C22×C4×D3C2311yescharacteristic
103C22×C4×D3C2311yescharacteristic
104C22×C4×D3C2311yescharacteristic
105C22×C4×D3C2311yescharacteristic
106C22×Dic6C2312yes—
107C22×Dic6C2311yescharacteristic
108C3×C22⋊Q8—24no—
109C2×C3×C4⋊C4—24no—
110C2×C3×C4⋊C4C2312yes—
111C2×C3×C4⋊C4C2311yescharacteristic
112C2×C3×C4⋊C4C2312yes—
113C2×C3×C4⋊C4C2312yes—
114C2×C3×C22⋊C4C2312yes—
115C2×C3×C22⋊C4C2312yes—
116C2×C3×C42C2312yes—
117C2×#217C2312yes—
118C2×#217C2312yes—
119#946—24no—
120C2×(C2×D3)⋊C4C2314yes—
121C2×(C2×D3)⋊C4C2312yes—
122C2×(C2×D3)⋊C4C2312yes—
123C2×C4⋊Dic3—24no—
124C2×C4⋊Dic3C2312yes—
125C2×C4⋊Dic3C2312yes—
126C2×C4⋊Dic3C2312yes—
127C2×C4⋊Dic3C2311yescharacteristic
128#924—24no—
129C2×Dic3⋊C4—28no—
130C2×Dic3⋊C4C2314yes—
131C2×Dic3⋊C4C2312yes—
132C2×Dic3⋊C4C2312yes—
133C2×Dic3⋊C4C2314yes—
134C2×Dic3⋊C4C2312yes—
135C2×C4×Dic3C2314yes—
136C2×C4×Dic3C2312yes—
137#897—24no—
138#896—28no—
139D3×C4⋊C4—28no—
140D3×C4⋊C4—28no—
141D3×C4⋊C4—28no—
142D3×C4⋊C4—28no—
143D3×C4⋊C4—28no—
144D3×C4⋊C4—24no—
145D3×C22⋊C4—28no—
146D3×C22⋊C4—28no—
147#878—28no—
148C42×D3—28no—
149C3×#95C2318yes—
150C3×#95C2318yes—
151C3×#95C2312yes—
152C3⋊#95C2318yes—
153C3⋊#95C2318yes—
154C3⋊#95C2318yes—
155C3⋊#95C2318yes—
156C3⋊#95C2318yes—
157C3⋊#95C2318yes—
158C3⋊#95C2314yes—
159C3⋊#95C2312yes—
160C23×Q8—31no—
161C24×C4—31no—
162C24×C4—32no—
163C2×C22⋊Q8—31no—
164C2×C22⋊Q8—31no—
165C2×C22⋊Q8—32no—
166C2×C22⋊Q8—31no—
167C2×C22⋊Q8—32no—
168C2×C22⋊Q8—68no—
169C2×C22⋊Q8C2×D311yescharacteristic
170C22×C4⋊C4—32no—
171C22×C4⋊C4—31no—
172C22×C4⋊C4—32no—
173C22×C4⋊C4—32no—
174C22×C4⋊C4—32no—
175C22×C4⋊C4—32no—
176C22×C4⋊C4—32no—
177C22×C4⋊C4—31no—
178C22×C4⋊C4—68no—
179C22×C4⋊C4C2×D311yescharacteristic
180C22×C22⋊C4—32no—
181C22×C22⋊C4—32no—
182C22×C42—32no—
183#400—34no—
184#400—34no—
185#400—38no—
186#400—34no—
187#400—38no—
188#400C2×D314yescomplemented
189#391—32no—
190#391—32no—
191#391—32no—
192#391—38no—
193#391C2×D312yescomplemented
194#382—32no—
195#382—32no—
196#382—32no—
197#382—38no—
198#382C2×D312yescomplemented
199#381—34no—
200#381—34no—
201#381—34no—
202#381—38no—
203#381—38no—
204#381C2×D314yes—
205C4×C22⋊C4—31no—
206C4×C22⋊C4—32no—
207C4×C22⋊C4—32no—
208C4×C22⋊C4—32no—
209C4×C22⋊C4C2×D311yescharacteristic
210C2×#95—32no—
211C2×#95—38no—
212C2×#95—38no—
213C24×C3C2411yescharacteristic
214C23×D3—24no—
215C23×D3—24no—
216C23×D3C2×D414yes—
217C23×D3#4118yes—
218C23×D3C2411yescharacteristic
219C23×D3C2411yescharacteristic
220C2×C3×Q8—22no—
221C2×C3×Q8—24no—
222C22×C3×C4—24no—
223C22×C3×C4—24no—
224C22×C3×C4—28no—
225C22×C3×C4C2×D414yes—
226C22×C3×C4C2414yes—
227C22×C3×C4C2414yes—
228C22×C3×C4C2412yes—
229C22×C3×C4C2412yes—
230C22×C3×C4C2411yescharacteristic
231C22×C3×C4C2411yescharacteristic
232C22×Dic3—24no—
233C22×Dic3—24no—
234C22×Dic3—28no—
235C22×Dic3C2×D414yes—
236C22×Dic3C2414yes—
237C22×Dic3C2412yes—
238C22×Dic3C2414yes—
239C22×Dic3C2412yes—
240C22×Dic3C2411yescharacteristic
241C22×Dic3C2411yescharacteristic
242D3×Q8—416no—
243C2×C4×D3—24no—
244C2×C4×D3—24no—
245C2×C4×D3—24no—
246C2×C4×D3—232no—
247C2×C4×D3—24no—
248C2×C4×D3—24no—
249C2×C4×D3—28no—
250C2×C4×D3—28no—
251C2×C4×D3—28no—
252C2×C4×D3—28no—
253C2×C4×D3—216no—
254C2×C4×D3—216no—
255C2×C4×D3—28no—
256C2×C4×D3—28no—
257C2×C4×D3—28no—
258C2×C4×D3—432no—
259C2×C4×D3C2×D414yes—
260C2×C4×D3C2×D414yes—
261C2×C4×D3C2×D414yes—
262C2×C4×D3C2×D414yes—
263C2×C4×D3#4118yes—
264C2×Dic6—22no—
265C2×Dic6—24no—
266C2×Dic6—24no—
267C2×Dic6—28no—
268C3×C4⋊C4—24no—
269C3×C4⋊C4—24no—
270C3×C4⋊C4—24no—
271C3×C4⋊C4—22no—
272C3×C22⋊C4—24no—
273C3×C22⋊C4—24no—
274C3×C42—24no—
275#217—24no—
276#217—24no—
277(C2×D3)⋊C4—24no—
278(C2×D3)⋊C4—24no—
279(C2×D3)⋊C4—28no—
280C4⋊Dic3—24no—
281C4⋊Dic3—24no—
282C4⋊Dic3—22no—
283C4⋊Dic3—24no—
284Dic3⋊C4—24no—
285Dic3⋊C4—24no—
286Dic3⋊C4—24no—
287Dic3⋊C4—28no—
288Dic3⋊C4—28no—
289C4×Dic3—24no—
290C4×Dic3—28no—
291C25—31no—
292C22×Q8—32no—
293C22×Q8—31no—
294C22×Q8—64no—
295C22×Q8—68no—
296C22×Q8C22×D311yescharacteristic
297C23×C4—31no—
298C23×C4—31no—
299C23×C4—38no—
300C23×C4—31no—
301C23×C4—31no—
302C23×C4—31no—
303C23×C4—32no—
304C23×C4—32no—
305C23×C4—32no—
306C23×C4—34no—
307C23×C4—34no—
308C23×C4—34no—
309C23×C4—68no—
310C23×C4—68no—
311C23×C4—616no—
312C23×C4C22×D312yes—
313C23×C4C22×D311yescharacteristic
314C22⋊Q8—24no—
315C22⋊Q8—68no—
316C22⋊Q8—68no—
317C22⋊Q8—64no—
318C22⋊Q8—64no—
319C22⋊Q8—64no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—34no—
322C2×C4⋊C4—32no—
323C2×C4⋊C4—34no—
324C2×C4⋊C4—32no—
325C2×C4⋊C4—32no—
326C2×C4⋊C4—31no—
327C2×C4⋊C4—32no—
328C2×C4⋊C4—32no—
329C2×C4⋊C4—32no—
330C2×C4⋊C4—68no—
331C2×C4⋊C4—68no—
332C2×C4⋊C4—68no—
333C2×C4⋊C4—68no—
334C2×C4⋊C4—64no—
335C2×C4⋊C4—68no—
336C2×C4⋊C4—68no—
337C2×C4⋊C4—64no—
338C2×C4⋊C4C22×D312yes—
339C2×C4⋊C4C22×D312yes—
340C2×C4⋊C4C22×D311yescharacteristic
341C2×C4⋊C4C22×D312yes—
342C2×C22⋊C4—32no—
343C2×C22⋊C4—32no—
344C2×C22⋊C4—32no—
345C2×C22⋊C4—32no—
346C2×C22⋊C4—34no—
347C2×C22⋊C4—68no—
348C2×C22⋊C4—68no—
349C2×C22⋊C4C22×D312yes—
350C2×C22⋊C4C22×D312yes—
351C2×C42—34no—
352C2×C42—32no—
353C2×C42—68no—
354C2×C42C22×D312yes—
355#95—34no—
356#95—32no—
357#95—38no—
358#95—38no—
359#95—38no—
360#95—38no—
361#95—38no—
362#95—38no—
363#95C22×D312yes—
364#95C22×D318yes—
365#95C22×D318yes—
366C23×C3—22no—
367C23×C3—22no—
368C23×C3C22×D412yes—
369C23×C3C2×#4114yes—
370C23×C3C2511yescharacteristic
371C22×D3—22no—
372C22×D3—22no—
373C22×D3—28no—
374C22×D3—28no—
375C22×D3—232no—
376C22×D3#124116yes—
377C22×D3C22×D412yes—
378C22×D3C22×D412yes—
379C22×D3C2×#4114yes—
380C22×D3C2×#4114yes—
381C22×D3C2×#4114yes—
382C22×D32−1+414yes—
383C3×Q8—44no—
384C2×C3×C4—22no—
385C2×C3×C4—28no—
386C2×C3×C4—24no—
387C2×C3×C4—22no—
388C2×C3×C4—22no—
389C2×C3×C4—24no—
390C2×C3×C4—24no—
391C2×C3×C4—24no—
392C2×C3×C4—28no—
393C2×C3×C4—24no—
394C2×C3×C4—24no—
395C2×C3×C4—48no—
396C2×C3×C4C22×D412yes—
397C2×C3×C4C22×D412yes—
398C2×C3×C4C2×#4114yes—
399C2×Dic3—22no—
400C2×Dic3—28no—
401C2×Dic3—22no—
402C2×Dic3—24no—
403C2×Dic3—22no—
404C2×Dic3—24no—
405C2×Dic3—24no—
406C2×Dic3—24no—
407C2×Dic3—28no—
408C2×Dic3—24no—
409C2×Dic3—24no—
410C2×Dic3—48no—
411C2×Dic3C22×D412yes—
412C2×Dic3C22×D412yes—
413C2×Dic3C2×#4114yes—
414C4×D3—28no—
415C4×D3—28no—
416C4×D3—28no—
417C4×D3—48no—
418C4×D3—416no—
419C4×D3—416no—
420C4×D3—48no—
421C4×D3—416no—
422C4×D3#123116yes—
423Dic6—44no—
424Dic6—48no—
425C24—31no—
426C24—34no—
427C24—38no—
428C24—31no—
429C24—64no—
430C24—64no—
431C24C23×D311yescharacteristic
432C2×Q8—22no—
433C2×Q8—24no—
434C2×Q8—64no—
435C2×Q8—68no—
436C2×Q8—62no—
437C2×Q8—64no—
438C2×Q8—1216no—
439C22×C4—24no—
440C22×C4—24no—
441C22×C4—28no—
442C22×C4—31no—
443C22×C4—34no—
444C22×C4—38no—
445C22×C4—34no—
446C22×C4—31no—
447C22×C4—34no—
448C22×C4—34no—
449C22×C4—34no—
450C22×C4—34no—
451C22×C4—32no—
452C22×C4—32no—
453C22×C4—34no—
454C22×C4—64no—
455C22×C4—632no—
456C22×C4—64no—
457C22×C4—68no—
458C22×C4—64no—
459C22×C4—64no—
460C22×C4—68no—
461C22×C4—68no—
462C22×C4—68no—
463C22×C4—616no—
464C22×C4—616no—
465C22×C4—68no—
466C22×C4—68no—
467C22×C4—68no—
468C22×C4—64no—
469C22×C4—64no—
470C22×C4—64no—
471C22×C4—68no—
472C22×C4—1232no—
473C22×C4D3×D414yes—
474C22×C4C23×D314yes—
475C22×C4C23×D312yes—
476C22×C4C23×D312yes—
477C22×C4C23×D314yes—
478C22×C4C23×D311yescharacteristic
479C22×C4C23×D311yescharacteristic
480C4⋊C4—24no—
481C4⋊C4—24no—
482C4⋊C4—22no—
483C4⋊C4—24no—
484C4⋊C4—68no—
485C4⋊C4—68no—
486C4⋊C4—64no—
487C4⋊C4—64no—
488C4⋊C4—64no—
489C4⋊C4—64no—
490C4⋊C4—64no—
491C4⋊C4—64no—
492C4⋊C4—62no—
493C22⋊C4—24no—
494C22⋊C4—24no—
495C22⋊C4—64no—
496C22⋊C4—64no—
497C22⋊C4—68no—
498C22⋊C4—64no—
499C22⋊C4—64no—
500C42—24no—
501C42—68no—
502C42—64no—
503C22×C3—22no—
504C22×C3—22no—
505C22×C3—28no—
506C22×C3C2×#12414yes—
507C22×C3C23×D411yescharacteristic
508C22×C3C22×#4112yes—
509C22×C3C22×#4112yes—
510C22×C3C2×2−1+412yes—
511C2×D3—22no—
512C2×D3—22no—
513C2×D3—28no—
514C2×D3—232no—
515C2×D3C2×#12314yes—
516C2×D3C2×#12414yes—
517C2×D3C2×#12414yes—
518C2×D3#53614yes—
519C2×D3#552116yes—
520C3×C4—22no—
521C3×C4—42no—
522C3×C4—44no—
523C3×C4—42no—
524C3×C4—44no—
525C3×C4C2×#12314yes—
526Dic3—22no—
527Dic3—42no—
528Dic3—44no—
529Dic3—42no—
530Dic3—44no—
531Dic3C2×#12314yes—
532C23—22no—
533C23—22no—
534C23—32no—
535C23—34no—
536C23—34no—
537C23—34no—
538C23—316no—
539C23—32no—
540C23—34no—
541C23—68no—
542C23—632no—
543C23—68no—
544C23—62no—
545C23—62no—
546C23C2×D3×D412yes—
547C23D3×#4114yes—
548C23C24×D311yescharacteristic
549Q8—44no—
550Q8—128no—
551Q8—124no—
552C2×C4—22no—
553C2×C4—28no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—28no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—32no—
564C2×C4—34no—
565C2×C4—316no—
566C2×C4—32no—
567C2×C4—48no—
568C2×C4—68no—
569C2×C4—68no—
570C2×C4—68no—
571C2×C4—62no—
572C2×C4—68no—
573C2×C4—62no—
574C2×C4—62no—
575C2×C4—64no—
576C2×C4—64no—
577C2×C4—64no—
578C2×C4—68no—
579C2×C4—64no—
580C2×C4—64no—
581C2×C4—64no—
582C2×C4—1216no—
583C2×C4—1216no—
584C2×C4—128no—
585C2×C4—1216no—
586C2×C4—128no—
587C2×C4—128no—
588C2×C4C2×D3×D412yes—
589C2×C4C2×D3×D412yes—
590C2×C4D3×#4114yes—
591C2×C3—24no—
592C2×C3C22×#12311yescharacteristic
593C2×C3C22×#12411yescharacteristic
594C2×C3C2×#53611yescharacteristic
595C2×C3C2×#55214yes—
596D3—24no—
597D3#250318yesdirect product factor
598C22—28no—
599C22—22no—
600C22—22no—
601C22—34no—
602C22—316no—
603C22—34no—
604C22—34no—
605C22—34no—
606C22—632no—
607C22—68no—
608C22—62no—
609C22—62no—
610C22D3×#12414yes—
611C22C22×D3×D411yescharacteristic
612C22C2×D3×#4112yes—
613C22C2×D3×#4112yes—
614C22D3×2−1+412yes—
615C4—22no—
616C4—34no—
617C4—44no—
618C4—44no—
619C4—42no—
620C4—42no—
621C4—62no—
622C4—124no—
623C4—124no—
624C4—122no—
625C4—122no—
626C4D3×#12314yes—
627C3C2×#250311yescharacteristic, complemented, Sylow
628C2—24no—
629C2—38no—
630C2—64no—
631C2C2×D3×#12311yescharacteristic
632C2C2×D3×#12411yescharacteristic
633C2D3×#53611yescharacteristic
634C2D3×#55214yes—
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2503C2
prime radicalC24×D3C23
hypercenter#2503D3
hypocenterC3C2×#2503
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2503

Complements

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

NH ≅ G/Ntype
3. C3×#2503C2semidirect
4. #82776C2semidirect
5. #82179C2semidirect
6. D3×#400C2semidirect
7. #78152C2semidirect
8. D3×#391C2semidirect
9. #76520C2semidirect
10. D3×#382C2semidirect
11. #74167C2semidirect
13. #74079C2semidirect
15. #73518C2semidirect
40. C3×#400C22semidirect
41. C3×#391C22semidirect
42. C3×#382C22semidirect
45. #5229C22semidirect
48. #4986C22semidirect
49. #4985C22semidirect
50. #4977C22semidirect
51. #4977C22semidirect
52. #4973C22semidirect
57. #4936C22semidirect
58. #4929C22semidirect
65. #4660C22semidirect
66. #4659C22semidirect
67. #4658C22semidirect
68. #4650C22semidirect
69. #4646C22semidirect
79. #2503D3direct (N × H)
188. #400C2×D3semidirect
193. #391C2×D3semidirect
198. #382C2×D3semidirect
597. D3#2503direct (N × H)
627. C3C2×#2503semidirect

Maximal subgroups

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

subgroupindex
C2×D3×C22⋊Q82
C22×D3×C4⋊C42
C3×#25032
#827762
#821792
D3×#4002
#781522
D3×#3912
#765202
D3×#3822
#741672
D3×#3812
#740792
C4×D3×C22⋊C42
#735182
C2×#25033