Finite Group Databasebeta

← D3×#2502 #10964363

Subgroups — D3×#2502 #10964363

Order 768.

3094 conjugacy classes of subgroups.

The subgroup lattice has 646 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×#2502C211yesmaximal, characteristic, complemented
4#82775C211yesmaximal, characteristic, complemented
5#82178C211yesmaximal, characteristic, complemented
6D3×#398C214yesmaximal, complemented
7#77765C214yesmaximal, complemented
8D3×#391C212yesmaximal, complemented
9#76519C212yesmaximal, complemented
10D3×#385C214yesmaximal
11#74460C214yesmaximal, complemented
12D3×#384C212yesmaximal, complemented
13#74329C212yesmaximal, complemented
14C4×D3×C22⋊C4C211yesmaximal, characteristic
15#73517C211yesmaximal, characteristic, complemented
16C2×#2502—31nomaximal, Sylow
17C22×D3×Q8C2211yescharacteristic
18C23×C4×D3C2211yescharacteristic
19C23×C4×D3C2212yes—
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⋊C4C2211yescharacteristic
33C2×D3×C4⋊C4C2212yes—
34C2×D3×C4⋊C4C2212yes—
35C2×D3×C4⋊C4C2212yes—
36C2×D3×C4⋊C4C2218yes—
37C2×D3×C22⋊C4C2212yes—
38C2×D3×C22⋊C4C2212yes—
39C2×#878C2212yes—
40C2×C42×D3C2212yes—
41C3×#398C2214yescomplemented
42C3×#391C2212yescomplemented
43C3×#385C2214yes—
44C3×#384C2212yescomplemented
45C3×C4×C22⋊C4C2211yescharacteristic
46#5229C2212yescomplemented
47#5210C2214yes—
48C4×#217C2211yescharacteristic
49#4989C2218yes—
50#4983C2214yescomplemented
51#4982C2218yescomplemented
52#4981C2214yescomplemented
53#4975C2212yescomplemented
54#4975C2212yescomplemented
55#4975C2218yescomplemented
56#4973C2212yescomplemented
57#4950C2214yes—
58#4946C2214yes—
59Dic3×C22⋊C4C2212yes—
60C4×(C2×D3)⋊C4C2212yes—
61#4935C2212yescomplemented
62#4929C2212yescomplemented
63#4668C2218yes—
64#4666C2212yes—
65D3×#95C2218yes—
66D3×#95C2212yes—
67#4661C2214yescomplemented
68#4657C2218yescomplemented
69#4646C2218yescomplemented
70C22×C22⋊Q8—31no—
71C23×C4⋊C4—31no—
72#2502—34no—
73#2502—32no—
74#2502—34no—
75#2502—32no—
76#2502—31no—
77#2502—31no—
78#2502—31no—
79#2502D311yescharacteristic, direct product factor
80C2×#398—34no—
81C2×#391—32no—
82C2×#385—34no—
83C2×#384—32no—
84C2×C4×C22⋊C4—31no—
85C24×D3C2311yescharacteristic
86C22×C3×Q8C2311yescharacteristic
87C23×C3×C4C2311yescharacteristic
88C23×C3×C4C2312yes—
89C23×Dic3C2311yescharacteristic
90C23×Dic3C2312yes—
91C2×D3×Q8—24no—
92C2×D3×Q8—28no—
93C22×C4×D3—28no—
94C22×C4×D3—28no—
95C22×C4×D3—48no—
96C22×C4×D3D418yes—
97C22×C4×D3C2312yes—
98C22×C4×D3C2314yes—
99C22×C4×D3C2312yes—
100C22×C4×D3C2311yescharacteristic
101C22×C4×D3C2311yescharacteristic
102C22×C4×D3C2311yescharacteristic
103C22×C4×D3C2314yes—
104C22×C4×D3C2314yes—
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×C4⋊C4C2318yes—
115C2×C3×C22⋊C4C2312yes—
116C2×C3×C22⋊C4C2312yes—
117C2×C3×C42C2312yes—
118C2×#217C2312yes—
119C2×#217C2312yes—
120#946—24no—
121C2×(C2×D3)⋊C4C2312yes—
122C2×(C2×D3)⋊C4C2312yes—
123C2×(C2×D3)⋊C4C2314yes—
124C2×C4⋊Dic3—24no—
125C2×C4⋊Dic3C2312yes—
126C2×C4⋊Dic3C2312yes—
127C2×C4⋊Dic3C2311yescharacteristic
128C2×C4⋊Dic3C2312yes—
129C2×C4⋊Dic3C2318yes—
130#924—24no—
131C2×Dic3⋊C4—28no—
132C2×Dic3⋊C4C2314yes—
133C2×Dic3⋊C4C2312yes—
134C2×Dic3⋊C4C2314yes—
135C2×Dic3⋊C4C2312yes—
136C2×Dic3⋊C4C2312yes—
137C2×Dic3⋊C4C2318yes—
138C2×Dic3⋊C4C2318yes—
139C2×C4×Dic3C2314yes—
140C2×C4×Dic3C2312yes—
141#897—24no—
142#896—28no—
143D3×C4⋊C4—28no—
144D3×C4⋊C4—28no—
145D3×C4⋊C4—28no—
146D3×C4⋊C4—28no—
147D3×C4⋊C4—28no—
148D3×C4⋊C4—24no—
149D3×C4⋊C4—416no—
150D3×C22⋊C4—28no—
151D3×C22⋊C4Q8116yescomplemented
152#878—28no—
153C42×D3—28no—
154C3×#95C2318yes—
155C3×#95C2312yes—
156C3⋊#95C2318yes—
157C3⋊#95C2318yes—
158C3⋊#95C2318yes—
159C3⋊#95C2314yes—
160C3⋊#95C2312yes—
161C23×Q8—31no—
162C24×C4—31no—
163C24×C4—32no—
164C2×C22⋊Q8—31no—
165C2×C22⋊Q8—31no—
166C2×C22⋊Q8—32no—
167C2×C22⋊Q8—31no—
168C2×C22⋊Q8—32no—
169C2×C22⋊Q8—68no—
170C2×C22⋊Q8C2×D311yescharacteristic
171C22×C4⋊C4—32no—
172C22×C4⋊C4—31no—
173C22×C4⋊C4—32no—
174C22×C4⋊C4—32no—
175C22×C4⋊C4—32no—
176C22×C4⋊C4—32no—
177C22×C4⋊C4—32no—
178C22×C4⋊C4—31no—
179C22×C4⋊C4—38no—
180C22×C4⋊C4—68no—
181C22×C4⋊C4C2×D311yescharacteristic
182C22×C22⋊C4—32no—
183C22×C22⋊C4—32no—
184C22×C42—32no—
185#398—34no—
186#398—38no—
187#398—34no—
188#398—38no—
189#398—34no—
190#398C2×D314yescomplemented
191#391—32no—
192#391—32no—
193#391—32no—
194#391—38no—
195#391C2×D312yescomplemented
196#385—34no—
197#385—38no—
198#385—34no—
199#385—34no—
200#385—38no—
201#385C2×D314yes—
202#384—38no—
203#384—32no—
204#384—32no—
205#384—32no—
206#384C2×D312yescomplemented
207C4×C22⋊C4—31no—
208C4×C22⋊C4—32no—
209C4×C22⋊C4—32no—
210C4×C22⋊C4—32no—
211C4×C22⋊C4C2×D311yescharacteristic
212C2×#95—32no—
213C2×#95—38no—
214C24×C3C2411yescharacteristic
215C23×D3—24no—
216C23×D3—24no—
217C23×D3C2×D414yes—
218C23×D3C2×Q818yes—
219C23×D3C2411yescharacteristic
220C23×D3C2411yescharacteristic
221C2×C3×Q8—22no—
222C2×C3×Q8—24no—
223C22×C3×C4—24no—
224C22×C3×C4—24no—
225C22×C3×C4—44no—
226C22×C3×C4C2×D414yes—
227C22×C3×C4C2412yes—
228C22×C3×C4C2414yes—
229C22×C3×C4C2412yes—
230C22×C3×C4C2411yescharacteristic
231C22×C3×C4C2414yes—
232C22×C3×C4C2411yescharacteristic
233C22×Dic3—24no—
234C22×Dic3—24no—
235C22×Dic3—44no—
236C22×Dic3C2×D414yes—
237C22×Dic3C2412yes—
238C22×Dic3C2414yes—
239C22×Dic3C2412yes—
240C22×Dic3C2411yescharacteristic
241C22×Dic3C2414yes—
242C22×Dic3C2411yescharacteristic
243D3×Q8—416no—
244C2×C4×D3—28no—
245C2×C4×D3—24no—
246C2×C4×D3—28no—
247C2×C4×D3—24no—
248C2×C4×D3—24no—
249C2×C4×D3—232no—
250C2×C4×D3—24no—
251C2×C4×D3—24no—
252C2×C4×D3—28no—
253C2×C4×D3—28no—
254C2×C4×D3—28no—
255C2×C4×D3—28no—
256C2×C4×D3—216no—
257C2×C4×D3—48no—
258C2×C4×D3—432no—
259C2×C4×D3C2×D414yes—
260C2×C4×D3C2×D414yes—
261C2×C4×D3C2×D414yes—
262C2×C4×D3C2×D414yes—
263C2×C4×D3C2×Q8116yes—
264C2×C4×D3#4118yes—
265C2×Dic6—22no—
266C2×Dic6—24no—
267C2×Dic6—24no—
268C2×Dic6—28no—
269C3×C4⋊C4—24no—
270C3×C4⋊C4—24no—
271C3×C4⋊C4—24no—
272C3×C4⋊C4—22no—
273C3×C4⋊C4—48no—
274C3×C22⋊C4—24no—
275C3×C22⋊C4C2×Q818yescomplemented
276C3×C42—24no—
277#217—24no—
278#217C2×Q818yescomplemented
279(C2×D3)⋊C4—24no—
280(C2×D3)⋊C4—24no—
281(C2×D3)⋊C4C2×Q8116yescomplemented
282C4⋊Dic3—24no—
283C4⋊Dic3—24no—
284C4⋊Dic3—22no—
285C4⋊Dic3—24no—
286C4⋊Dic3—48no—
287Dic3⋊C4—24no—
288Dic3⋊C4—24no—
289Dic3⋊C4—24no—
290Dic3⋊C4—28no—
291Dic3⋊C4—28no—
292Dic3⋊C4—48no—
293Dic3⋊C4—48no—
294C4×Dic3—24no—
295C4×Dic3—28no—
296C25—31no—
297C22×Q8—32no—
298C22×Q8—31no—
299C22×Q8—64no—
300C22×Q8—68no—
301C22×Q8C22×D311yescharacteristic
302C23×C4—31no—
303C23×C4—31no—
304C23×C4—38no—
305C23×C4—34no—
306C23×C4—31no—
307C23×C4—31no—
308C23×C4—31no—
309C23×C4—32no—
310C23×C4—32no—
311C23×C4—32no—
312C23×C4—34no—
313C23×C4—34no—
314C23×C4—68no—
315C23×C4—68no—
316C23×C4—128no—
317C23×C4C22×D311yescharacteristic
318C23×C4C22×D312yes—
319C22⋊Q8—24no—
320C22⋊Q8—68no—
321C22⋊Q8—68no—
322C22⋊Q8—64no—
323C22⋊Q8—64no—
324C22⋊Q8—64no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—34no—
327C2×C4⋊C4—32no—
328C2×C4⋊C4—34no—
329C2×C4⋊C4—32no—
330C2×C4⋊C4—32no—
331C2×C4⋊C4—31no—
332C2×C4⋊C4—32no—
333C2×C4⋊C4—32no—
334C2×C4⋊C4—32no—
335C2×C4⋊C4—38no—
336C2×C4⋊C4—38no—
337C2×C4⋊C4—38no—
338C2×C4⋊C4—68no—
339C2×C4⋊C4—68no—
340C2×C4⋊C4—68no—
341C2×C4⋊C4—68no—
342C2×C4⋊C4—64no—
343C2×C4⋊C4—68no—
344C2×C4⋊C4—68no—
345C2×C4⋊C4—64no—
346C2×C4⋊C4—1216no—
347C2×C4⋊C4C22×D312yes—
348C2×C4⋊C4C22×D312yes—
349C2×C4⋊C4C22×D311yescharacteristic
350C2×C4⋊C4C22×D312yes—
351C2×C4⋊C4C22×D318yes—
352C2×C22⋊C4—32no—
353C2×C22⋊C4—34no—
354C2×C22⋊C4—316no—
355C2×C22⋊C4—32no—
356C2×C22⋊C4—32no—
357C2×C22⋊C4—32no—
358C2×C22⋊C4—68no—
359C2×C22⋊C4C22×D312yes—
360C2×C22⋊C4C22×D312yes—
361C2×C42—34no—
362C2×C42—32no—
363C2×C42—68no—
364C2×C42C22×D312yes—
365#95—32no—
366#95—34no—
367#95—38no—
368#95—38no—
369#95—38no—
370#95C22×D312yes—
371#95C22×D318yes—
372C23×C3—22no—
373C23×C3—22no—
374C23×C3C22×D412yes—
375C23×C3C22×Q814yes—
376C23×C3C2511yescharacteristic
377C22×D3—22no—
378C22×D3—22no—
379C22×D3—28no—
380C22×D3—28no—
381C22×D3—232no—
382C22×D3C4⋊Q8116yes—
383C22×D3C22×D412yes—
384C22×D3C22×D412yes—
385C22×D3C22×Q814yes—
386C22×D3C22×Q814yes—
387C22×D3C2×#4114yes—
388C22×D3H(5,𝔽2)14yes—
389C3×Q8—44no—
390C2×C3×C4—24no—
391C2×C3×C4—22no—
392C2×C3×C4—24no—
393C2×C3×C4—28no—
394C2×C3×C4—24no—
395C2×C3×C4—22no—
396C2×C3×C4—22no—
397C2×C3×C4—24no—
398C2×C3×C4—24no—
399C2×C3×C4—28no—
400C2×C3×C4—48no—
401C2×C3×C4C22×D412yes—
402C2×C3×C4C22×D412yes—
403C2×C3×C4C22×Q818yes—
404C2×C3×C4C2×#4114yes—
405C2×Dic3—24no—
406C2×Dic3—22no—
407C2×Dic3—24no—
408C2×Dic3—28no—
409C2×Dic3—22no—
410C2×Dic3—24no—
411C2×Dic3—22no—
412C2×Dic3—24no—
413C2×Dic3—24no—
414C2×Dic3—28no—
415C2×Dic3—48no—
416C2×Dic3C22×D412yes—
417C2×Dic3C22×D412yes—
418C2×Dic3C22×Q818yes—
419C2×Dic3C2×#4114yes—
420C4×D3—28no—
421C4×D3—232no—
422C4×D3—28no—
423C4×D3—28no—
424C4×D3—416no—
425C4×D3—48no—
426C4×D3—48no—
427C4×D3—416no—
428C4×D3#123116yes—
429Dic6—44no—
430Dic6—48no—
431C24—31no—
432C24—34no—
433C24—38no—
434C24—31no—
435C24—64no—
436C24—64no—
437C24C23×D311yescharacteristic
438C2×Q8—22no—
439C2×Q8—24no—
440C2×Q8—64no—
441C2×Q8—68no—
442C2×Q8—62no—
443C2×Q8—64no—
444C2×Q8—1216no—
445C22×C4—24no—
446C22×C4—24no—
447C22×C4—31no—
448C22×C4—34no—
449C22×C4—38no—
450C22×C4—34no—
451C22×C4—34no—
452C22×C4—31no—
453C22×C4—34no—
454C22×C4—34no—
455C22×C4—34no—
456C22×C4—316no—
457C22×C4—32no—
458C22×C4—34no—
459C22×C4—32no—
460C22×C4—44no—
461C22×C4—64no—
462C22×C4—632no—
463C22×C4—68no—
464C22×C4—68no—
465C22×C4—64no—
466C22×C4—64no—
467C22×C4—64no—
468C22×C4—68no—
469C22×C4—68no—
470C22×C4—68no—
471C22×C4—616no—
472C22×C4—68no—
473C22×C4—64no—
474C22×C4—64no—
475C22×C4—64no—
476C22×C4—128no—
477C22×C4—1232no—
478C22×C4—124no—
479C22×C4D3×D414yes—
480C22×C4C23×D312yes—
481C22×C4C23×D314yes—
482C22×C4C23×D312yes—
483C22×C4C23×D311yescharacteristic
484C22×C4C23×D314yes—
485C22×C4C23×D311yescharacteristic
486C4⋊C4—24no—
487C4⋊C4—24no—
488C4⋊C4—22no—
489C4⋊C4—24no—
490C4⋊C4—48no—
491C4⋊C4—68no—
492C4⋊C4—68no—
493C4⋊C4—64no—
494C4⋊C4—64no—
495C4⋊C4—64no—
496C4⋊C4—64no—
497C4⋊C4—64no—
498C4⋊C4—64no—
499C4⋊C4—62no—
500C4⋊C4—128no—
501C4⋊C4—128no—
502C4⋊C4—128no—
503C22⋊C4—24no—
504C22⋊C4—38no—
505C22⋊C4—316no—
506C22⋊C4—64no—
507C22⋊C4—64no—
508C22⋊C4—64no—
509C22⋊C4D3×Q818yescomplemented
510C42—24no—
511C42—68no—
512C42—64no—
513C22×C3—22no—
514C22×C3—22no—
515C22×C3—28no—
516C22×C3C2×C4⋊Q814yes—
517C22×C3C23×D411yescharacteristic
518C22×C3C23×Q812yes—
519C22×C3C22×#4112yes—
520C22×C3C2×H(5,𝔽2)12yes—
521C2×D3—22no—
522C2×D3—22no—
523C2×D3—28no—
524C2×D3—232no—
525C2×D3C2×#12314yes—
526C2×D3C2×C4⋊Q814yes—
527C2×D3C2×C4⋊Q814yes—
528C2×D3#53514yes—
529C2×D3#554116yes—
530C3×C4—22no—
531C3×C4—28no—
532C3×C4—42no—
533C3×C4—44no—
534C3×C4—42no—
535C3×C4C2×#12314yes—
536Dic3—22no—
537Dic3—28no—
538Dic3—42no—
539Dic3—44no—
540Dic3—42no—
541Dic3C2×#12314yes—
542C23—22no—
543C23—22no—
544C23—32no—
545C23—34no—
546C23—34no—
547C23—34no—
548C23—32no—
549C23—34no—
550C23—316no—
551C23—68no—
552C23—68no—
553C23—632no—
554C23—62no—
555C23—62no—
556C23C2×D3×D412yes—
557C23C2×D3×Q814yes—
558C23C24×D311yescharacteristic
559Q8—44no—
560Q8—128no—
561Q8—124no—
562C2×C4—24no—
563C2×C4—22no—
564C2×C4—24no—
565C2×C4—28no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—28no—
572C2×C4—32no—
573C2×C4—34no—
574C2×C4—316no—
575C2×C4—32no—
576C2×C4—38no—
577C2×C4—48no—
578C2×C4—68no—
579C2×C4—68no—
580C2×C4—632no—
581C2×C4—68no—
582C2×C4—64no—
583C2×C4—62no—
584C2×C4—64no—
585C2×C4—68no—
586C2×C4—62no—
587C2×C4—62no—
588C2×C4—64no—
589C2×C4—64no—
590C2×C4—64no—
591C2×C4—68no—
592C2×C4—1216no—
593C2×C4—128no—
594C2×C4—128no—
595C2×C4—1216no—
596C2×C4—128no—
597C2×C4C2×D3×D412yes—
598C2×C4C2×D3×D412yes—
599C2×C4C2×D3×Q818yes—
600C2×C4D3×#4114yes—
601C2×C3—24no—
602C2×C3C22×#12311yescharacteristic
603C2×C3C22×C4⋊Q811yescharacteristic
604C2×C3C2×#53511yescharacteristic
605C2×C3C2×#55414yes—
606D3—24no—
607D3#250218yesdirect product factor
608C22—22no—
609C22—28no—
610C22—22no—
611C22—34no—
612C22—316no—
613C22—34no—
614C22—34no—
615C22—34no—
616C22—632no—
617C22—62no—
618C22—68no—
619C22—62no—
620C22D3×C4⋊Q814yes—
621C22C22×D3×D411yescharacteristic
622C22C22×D3×Q812yes—
623C22C2×D3×#4112yes—
624C22D3×H(5,𝔽2)12yes—
625C4—28no—
626C4—22no—
627C4—34no—
628C4—44no—
629C4—42no—
630C4—42no—
631C4—68no—
632C4—62no—
633C4—124no—
634C4—122no—
635C4—122no—
636C4D3×#12314yes—
637C3C2×#250211yescharacteristic, complemented, Sylow
638C2—24no—
639C2—38no—
640C2—64no—
641C2C2×D3×#12311yescharacteristic
642C2C2×D3×C4⋊Q811yescharacteristic
643C2D3×#53511yescharacteristic
644C2D3×#55414yes—
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2502C2
prime radicalC24×D3C23
hypercenter#2502D3
hypocenterC3C2×#2502
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2502

Complements

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

NH ≅ G/Ntype
3. C3×#2502C2semidirect
4. #82775C2semidirect
5. #82178C2semidirect
6. D3×#398C2semidirect
7. #77765C2semidirect
8. D3×#391C2semidirect
9. #76519C2semidirect
11. #74460C2semidirect
12. D3×#384C2semidirect
13. #74329C2semidirect
15. #73517C2semidirect
41. C3×#398C22semidirect
42. C3×#391C22semidirect
44. C3×#384C22semidirect
46. #5229C22semidirect
50. #4983C22semidirect
51. #4982C22semidirect
52. #4981C22semidirect
53. #4975C22semidirect
54. #4975C22semidirect
55. #4975C22semidirect
56. #4973C22semidirect
61. #4935C22semidirect
62. #4929C22semidirect
67. #4661C22semidirect
68. #4657C22semidirect
69. #4646C22semidirect
79. #2502D3direct (N × H)
151. D3×C22⋊C4Q8semidirect
190. #398C2×D3semidirect
195. #391C2×D3semidirect
206. #384C2×D3semidirect
275. C3×C22⋊C4C2×Q8semidirect
278. #217C2×Q8semidirect
281. (C2×D3)⋊C4C2×Q8semidirect
509. C22⋊C4D3×Q8semidirect
607. D3#2502direct (N × H)
637. C3C2×#2502semidirect

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×#25022
#827752
#821782
D3×#3982
#777652
D3×#3912
#765192
D3×#3852
#744602
D3×#3842
#743292
C4×D3×C22⋊C42
#735172
C2×#25023