Finite Group Databasebeta

← D3×#2133 #10948018

Subgroups — D3×#2133 #10948018

Order 768.

1198 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#536C211yesmaximal, characteristic
2C2×D3×#101C212yesmaximal, complemented
3C3×#2133C211yesmaximal, characteristic, complemented
4#71872C211yesmaximal, characteristic, complemented
5#70128C212yesmaximal, complemented
6#69171C212yesmaximal, complemented
7D3×#356C212yesmaximal, complemented
8#69164C212yesmaximal, complemented
9D3×#355C212yesmaximal, complemented
10C2×#2133—31nomaximal, Sylow
11C2×D3×#41C411yescharacteristic
12C22×D3×Q8C2211yescharacteristic
13C3×#536C2211yescharacteristic
14#5825C411yescharacteristic
15#5816C2211yescharacteristic
16C2×D3×M16—22no—
17#5724C411yescharacteristic
18#5724C2211yescharacteristic
19D3×C4⋊Q8C411yescharacteristic
20D3×C4⋊Q8C2211yescharacteristic
21#5675C411yescharacteristic
22#5675C2211yescharacteristic
23D3×#124C411yescharacteristic
24D3×#124C2211yescharacteristic
25D3×#123—22no—
26#5648—22no—
27#5628—22no—
28D3×C22⋊Q8—22no—
29#5526C411yescharacteristic
30D3×#117C411yescharacteristic
31C2×C3×#101C2212yescomplemented
32C2×#836C2212yescomplemented
33C2×#824—22no—
34D3×#101—22no—
35D3×#101—22no—
36D3×#101C2214yes—
37D3×#101C2214yescomplemented
38C3×#356C2212yescomplemented
39C3×#355C2212yescomplemented
40#4548C2212yescomplemented
41#4542C2212yescomplemented
42#4478C2214yescomplemented
43#4477C2214yescomplemented
44C2×#536—31no—
45C22×#101—32no—
46#2133—32no—
47#2133—32no—
48#2133—32no—
49#2133—31no—
50#2133D311yescharacteristic, direct product factor
51C2×#356—32no—
52C2×#355—32no—
53C2×C3×#41C2×C411yescharacteristic
54C22×C3×Q8C2311yescharacteristic
55D3×#41—42no—
56D3×#41—42no—
57C2×#239C2×C411yescharacteristic
58C2×D3×Q8—42no—
59C2×D3×Q8—42no—
60C2×D3×Q8C2×C411yescharacteristic
61C2×D3×Q8C2×C411yescharacteristic
62C2×D3×Q8C2×C411yescharacteristic
63C2×D3×Q8D412yes—
64C2×D3×Q8D412yes—
65C2×D3×Q8C2311yescharacteristic
66C2×D3×Q8C2311yescharacteristic
67C2×#237—21no—
68C2×#237C2×C411yescharacteristic
69C2×D3×D4—21no—
70C2×D3×D4C2×C411yescharacteristic
71C2×#235—21no—
72C2×#235C2×C411yescharacteristic
73C22×C4×D3—21no—
74C22×C4×D3C2×C411yescharacteristic
75C22×C4×D3D412yes—
76C22×Dic6C2×C411yescharacteristic
77C22×Dic6D412yes—
78C2×C3×M16—22no—
79C3×C4⋊Q8C2×C411yescharacteristic
80C3×C4⋊Q8C2311yescharacteristic
81C3×#124C2×C411yescharacteristic
82C3×#124C2311yescharacteristic
83C3×#123—22no—
84C3×C22⋊Q8—22no—
85C3×#117C2×C411yescharacteristic
86#947C2×C411yescharacteristic
87#947C2311yescharacteristic
88#946—22no—
89#944C2×C411yescharacteristic
90#944C2×C411yescharacteristic
91#944C2×C411yescharacteristic
92#944C2311yescharacteristic
93#936C2×C411yescharacteristic
94#936C2×C411yescharacteristic
95#935—22no—
96#929—22no—
97#926C2×C411yescharacteristic
98#924—22no—
99C2×#208—22no—
100D3×M16—24no—
101D3×M16—24no—
102D3×M16—42no—
103D3×M16—42no—
104C2×ΓL(1,𝔽25)—42no—
105C2×D3×C8—42no—
106#897—22no—
107#896—22no—
108#896—22no—
109#894—22no—
110#894—22no—
111#892—21no—
112D3×C4⋊C4—22no—
113D3×C4⋊C4—21no—
114D3×C4⋊C4—22no—
115#888—22no—
116#888—22no—
117#886—22no—
118#885—22no—
119#885—22no—
120#883—22no—
121#883—22no—
122D3×C22⋊C4—21no—
123D3×C22⋊C4—22no—
124D3×C22⋊C4—22no—
125#878—22no—
126#878—22no—
127#877—21no—
128#875C2×C411yescharacteristic
129#875C2×C411yescharacteristic
130#872C2×C411yescharacteristic
131#872C2×C411yescharacteristic
132C42×D3C2×C411yescharacteristic
133C42×D3C2×C411yescharacteristic
134#869C2×C411yescharacteristic
135#869C2×C411yescharacteristic
136C3×#101—22no—
137C3×#101C2314yes—
138#836—22no—
139#836C2314yes—
140#824—24no—
141#824—24no—
142C22×#41—31no—
143C23×Q8—31no—
144C22×M16—62no—
145#536—31no—
146#536—31no—
147#536—31no—
148#536—31no—
149#536—31no—
150#536—31no—
151#536—31no—
152#536—62no—
153#536—62no—
154#536C2×D311yescharacteristic
155C2×C4⋊Q8—31no—
156C2×C4⋊Q8—31no—
157C2×#124—31no—
158C2×#124—31no—
159C2×#123—62no—
160C2×C22⋊Q8—62no—
161C2×#117—31no—
162C2×#101—32no—
163C2×#101—34no—
164C2×#101—34no—
165C2×#101—62no—
166C2×#101—62no—
167C2×#101—62no—
168C2×#101C2×D312yescomplemented
169#356—32no—
170#356—34no—
171#356C2×D312yescomplemented
172#355—32no—
173#355—34no—
174#355C2×D312yescomplemented
175C23×D3—21no—
176C23×D3C22⋊C411yescharacteristic
177C3×#41—42no—
178C2×C3×Q8—42no—
179C2×C3×Q8C22×C411yescharacteristic
180C2×C3×Q8C22×C411yescharacteristic
181C2×C3×Q8C2×D412yes—
182C2×C3×Q8C2411yescharacteristic
183C2×C3×D4—21no—
184C2×C3×D4C22×C411yescharacteristic
185C22×C3×C4—21no—
186C22×C3×C4C22×C411yescharacteristic
187C22×C3×C4C2×D412yes—
188C2×#67—21no—
189C2×#67—21no—
190C2×#67—21no—
191C22×Dic3—21no—
192C22×Dic3C22⋊C411yescharacteristic
193C22×Dic3C22⋊C412yes—
194#239—42no—
195D3×Q8—41no—
196D3×Q8—41no—
197D3×Q8—42no—
198D3×Q8—42no—
199D3×Q8—42no—
200D3×Q8—42no—
201D3×Q8—42no—
202D3×Q8—41no—
203D3×Q8—42no—
204D3×Q8—41no—
205D3×Q8—41no—
206D3×Q8—41no—
207#237—42no—
208#237—44no—
209D3×D4—41no—
210D3×D4—41no—
211D3×D4—42no—
212D3×D4—42no—
213#235—44no—
214#235—42no—
215C2×D12—21no—
216C2×D12C22×C411yescharacteristic
217C2×C4×D3—22no—
218C2×C4×D3—22no—
219C2×C4×D3—22no—
220C2×C4×D3—22no—
221C2×C4×D3—22no—
222C2×C4×D3—22no—
223C2×C4×D3—21no—
224C2×C4×D3—21no—
225C2×C4×D3—21no—
226C2×C4×D3—21no—
227C2×C4×D3—21no—
228C2×C4×D3—42no—
229C2×C4×D3—42no—
230C2×C4×D3C22⋊C412yes—
231C2×C4×D3C22⋊C412yes—
232C2×C4×D3C22⋊C411yescharacteristic
233C2×C4×D3C22⋊C411yescharacteristic
234C2×C4×D3C22×C411yescharacteristic
235C2×C4×D3C22×C411yescharacteristic
236C2×C4×D3C2×D412yes—
237C2×C4×D3C2×D412yes—
238C2×Dic6—21no—
239C2×Dic6—42no—
240C2×Dic6—42no—
241C2×Dic6—42no—
242C2×Dic6C22⋊C412yes—
243C2×Dic6C22⋊C412yes—
244C2×Dic6C22⋊C412yes—
245C2×Dic6C22×C411yescharacteristic
246C2×Dic6C22×C411yescharacteristic
247C2×Dic6C22×C411yescharacteristic
248C2×Dic6C2×D412yes—
249C2×Dic6C2×D412yes—
250C3×M16—24no—
251C3×M16—42no—
252C2×C3×C8—42no—
253C3×C4⋊C4—22no—
254C3×C4⋊C4—21no—
255C3×C4⋊C4—22no—
256C3×C22⋊C4—21no—
257C3×C22⋊C4—22no—
258C3×C22⋊C4—22no—
259C3×C42C22×C411yescharacteristic
260C3×C42C22×C411yescharacteristic
261#217—21no—
262#217—22no—
263#217—22no—
264(C2×D3)⋊C4—21no—
265(C2×D3)⋊C4—21no—
266(C2×D3)⋊C4—22no—
267(C2×D3)⋊C4—22no—
268(C2×D3)⋊C4—22no—
269(C2×D3)⋊C4—22no—
270C4⋊Dic3—21no—
271C4⋊Dic3—22no—
272C4⋊Dic3—22no—
273Dic3⋊C4—22no—
274Dic3⋊C4—22no—
275Dic3⋊C4—21no—
276Dic3⋊C4—21no—
277Dic3⋊C4—22no—
278Dic3⋊C4—22no—
279C4×Dic3—21no—
280C4×Dic3—21no—
281C4×Dic3C22×C411yescharacteristic
282C4×Dic3C22×C411yescharacteristic
283#208—24no—
284#208—42no—
285C2×C3⋊C8—42no—
286ΓL(1,𝔽25)—44no—
287ΓL(1,𝔽25)—44no—
288D3×C8—44no—
289D3×C8—44no—
290C2×#41—31no—
291C2×#41—31no—
292C2×#41—31no—
293C2×#41—61no—
294C2×#41—61no—
295C2×#41—122no—
296C2×#41—122no—
297C2×#41C4×D311yescharacteristic
298C22×Q8—31no—
299C22×Q8—31no—
300C22×Q8—32no—
301C22×Q8—32no—
302C22×Q8—31no—
303C22×Q8—31no—
304C22×Q8—31no—
305C22×Q8—32no—
306C22×Q8—31no—
307C22×Q8—122no—
308C22×Q8—122no—
309C22×Q8C22×D311yescharacteristic
310C22×D4—31no—
311C22×D4—61no—
312C23×C4—31no—
313C23×C4—32no—
314C23×C4—61no—
315C2×M16—22no—
316C2×M16—64no—
317C2×M16—64no—
318C2×M16—62no—
319C2×M16—122no—
320C2×M16—122no—
321C2×M16—122no—
322C22×C8—122no—
323C4⋊Q8—31no—
324C4⋊Q8—31no—
325C4⋊Q8—31no—
326C4⋊Q8—31no—
327C4⋊Q8—31no—
328C4⋊Q8—31no—
329C4⋊Q8—62no—
330C4⋊Q8—62no—
331C4⋊Q8C4×D311yescharacteristic
332C4⋊Q8C22×D311yescharacteristic
333#124—31no—
334#124—31no—
335#124—31no—
336#124—31no—
337#124—31no—
338#124—31no—
339#124—62no—
340#124—62no—
341#124C4×D311yescharacteristic
342#124C22×D311yescharacteristic
343#123—22no—
344#123—62no—
345#123—62no—
346#123—62no—
347#123—62no—
348#123—62no—
349#123—62no—
350#123—62no—
351C22⋊Q8—22no—
352C22⋊Q8—62no—
353C22⋊Q8—62no—
354C22⋊Q8—62no—
355C22⋊Q8—62no—
356C22⋊Q8—62no—
357C22⋊Q8—62no—
358C22⋊Q8—62no—
359#117—31no—
360#117—31no—
361#117—31no—
362#117—61no—
363#117—61no—
364#117C4×D311yescharacteristic
365C2×C4⋊C4—61no—
366C2×C4⋊C4—62no—
367C2×C4⋊C4—62no—
368C2×C22⋊C4—62no—
369C2×C22⋊C4—62no—
370C2×C22⋊C4—61no—
371C2×C42—31no—
372C2×C42—31no—
373#101—22no—
374#101—34no—
375#101—64no—
376#101—64no—
377#101—62no—
378#101C22×D314yes—
379C23×C3—21no—
380C23×C3C2×C22⋊C411yescharacteristic
381C22×D3—21no—
382C22×D3—42no—
383C22×D3—44no—
384C22×D3—41no—
385C22×D3—41no—
386C22×D3#9912yes—
387C22×D3#9912yes—
388C22×D3C2×C22⋊C411yescharacteristic
389C22×D3C2×C22⋊C411yescharacteristic
390C3×Q8—41no—
391C3×Q8—42no—
392C3×Q8—41no—
393C3×Q8—41no—
394C3×D4—41no—
395C3×D4—42no—
396C2×C3×C4—22no—
397C2×C3×C4—22no—
398C2×C3×C4—22no—
399C2×C3×C4—21no—
400C2×C3×C4—21no—
401C2×C3×C4—21no—
402C2×C3×C4—42no—
403C2×C3×C4C2×C22⋊C412yes—
404C2×C3×C4C2×C22⋊C411yescharacteristic
405C2×C3×C4C23×C411yescharacteristic
406C2×C3×C4C22×D412yes—
407#67—42no—
408#67—42no—
409#67—42no—
410C2×Dic3—22no—
411C2×Dic3—22no—
412C2×Dic3—22no—
413C2×Dic3—21no—
414C2×Dic3—21no—
415C2×Dic3—21no—
416C2×Dic3—42no—
417C2×Dic3C2×C22⋊C411yescharacteristic
418C2×Dic3C2×C22⋊C411yescharacteristic
419C2×Dic3C2×C22⋊C412yes—
420C2×Dic3C2×C22⋊C412yes—
421D12—41no—
422D12—42no—
423C4×D3—22no—
424C4×D3—22no—
425C4×D3—22no—
426C4×D3—22no—
427C4×D3—21no—
428C4×D3—21no—
429C4×D3—22no—
430C4×D3—22no—
431C4×D3—22no—
432C4×D3—22no—
433C4×D3—22no—
434C4×D3—21no—
435C4×D3—21no—
436C4×D3—22no—
437C4×D3—42no—
438C4×D3—42no—
439C4×D3—42no—
440C4×D3—42no—
441C4×D3—41no—
442C4×D3—41no—
443Dic6—42no—
444Dic6—42no—
445Dic6—42no—
446Dic6—41no—
447Dic6—41no—
448Dic6—42no—
449Dic6—42no—
450Dic6—42no—
451Dic6—41no—
452C3×C8—44no—
453C3⋊C8—44no—
454C24—31no—
455C24—61no—
456#41—42no—
457#41—122no—
458#41—124no—
459#41—124no—
460#41—122no—
461#41—122no—
462C2×Q8—32no—
463C2×Q8—32no—
464C2×Q8—32no—
465C2×Q8—31no—
466C2×Q8—31no—
467C2×Q8—32no—
468C2×Q8—32no—
469C2×Q8—31no—
470C2×Q8—42no—
471C2×Q8—61no—
472C2×Q8—122no—
473C2×Q8—122no—
474C2×Q8—122no—
475C2×Q8—121no—
476C2×Q8—122no—
477C2×Q8—122no—
478C2×Q8—122no—
479C2×Q8—121no—
480C2×Q8—122no—
481C2×Q8—122no—
482C2×Q8—121no—
483C2×Q8—121no—
484C2×Q8—122no—
485C2×Q8—121no—
486C2×Q8—121no—
487C2×Q8C2×C4×D311yescharacteristic
488C2×Q8C2×C4×D311yescharacteristic
489C2×Q8D3×D412yes—
490C2×Q8C23×D311yescharacteristic
491C2×D4—21no—
492C2×D4—31no—
493C2×D4—61no—
494C2×D4—61no—
495C2×D4—61no—
496C2×D4—61no—
497C2×D4—121no—
498C2×D4—121no—
499C2×D4—122no—
500C2×D4—122no—
501C2×D4C2×C4×D311yescharacteristic
502C22×C4—21no—
503C22×C4—31no—
504C22×C4—32no—
505C22×C4—32no—
506C22×C4—31no—
507C22×C4—31no—
508C22×C4—32no—
509C22×C4—31no—
510C22×C4—31no—
511C22×C4—32no—
512C22×C4—32no—
513C22×C4—61no—
514C22×C4—62no—
515C22×C4—62no—
516C22×C4—62no—
517C22×C4—62no—
518C22×C4—62no—
519C22×C4—62no—
520C22×C4—61no—
521C22×C4—61no—
522C22×C4—61no—
523C22×C4—61no—
524C22×C4—61no—
525C22×C4—122no—
526C22×C4—122no—
527C22×C4C2×C4×D311yescharacteristic
528C22×C4D3×D412yes—
529M16—24no—
530M16—42no—
531M16—64no—
532M16—124no—
533M16—124no—
534M16—122no—
535C2×C8—42no—
536C2×C8—124no—
537C2×C8—124no—
538C2×C8—122no—
539C4⋊C4—21no—
540C4⋊C4—22no—
541C4⋊C4—22no—
542C4⋊C4—61no—
543C4⋊C4—61no—
544C4⋊C4—62no—
545C4⋊C4—62no—
546C4⋊C4—62no—
547C4⋊C4—62no—
548C4⋊C4—61no—
549C4⋊C4—62no—
550C4⋊C4—62no—
551C22⋊C4—21no—
552C22⋊C4—22no—
553C22⋊C4—22no—
554C22⋊C4—62no—
555C22⋊C4—62no—
556C22⋊C4—61no—
557C22⋊C4—61no—
558C22⋊C4—62no—
559C22⋊C4—62no—
560C22⋊C4—61no—
561C22⋊C4—62no—
562C22⋊C4—62no—
563C42—31no—
564C42—31no—
565C42—61no—
566C42—61no—
567C42C2×C4×D311yescharacteristic
568C42C2×C4×D311yescharacteristic
569C22×C3—41no—
570C22×C3—42no—
571C22×C3—41no—
572C22×C3C2×#9912yes—
573C22×C3C22×C22⋊C411yescharacteristic
574C2×D3—22no—
575C2×D3—24no—
576C2×D3—42no—
577C2×D3—41no—
578C2×D3—42no—
579C2×D3—41no—
580C2×D3—82no—
581C2×D3—82no—
582C2×D3C2×#9911yescharacteristic
583C2×D3C2×#9912yes—
584C2×D3C2×#9911yescharacteristic
585C3×C4—22no—
586C3×C4—21no—
587C3×C4—21no—
588C3×C4—22no—
589C3×C4—41no—
590C3×C4—41no—
591C3×C4—41no—
592Dic3—21no—
593Dic3—21no—
594Dic3—22no—
595Dic3—22no—
596Dic3—41no—
597Dic3—41no—
598Dic3—41no—
599C23—21no—
600C23—31no—
601C23—32no—
602C23—31no—
603C23—32no—
604C23—61no—
605C23—121no—
606C23—121no—
607C23—122no—
608C23—124no—
609C23D3×C22⋊C411yescharacteristic
610Q8—41no—
611Q8—42no—
612Q8—41no—
613Q8—41no—
614Q8—122no—
615Q8—122no—
616Q8—122no—
617Q8—122no—
618Q8—122no—
619Q8—121no—
620Q8—121no—
621Q8—121no—
622Q8—122no—
623D4—41no—
624D4—42no—
625D4—121no—
626D4—122no—
627D4—122no—
628D4—122no—
629D4—122no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—31no—
637C2×C4—32no—
638C2×C4—32no—
639C2×C4—31no—
640C2×C4—42no—
641C2×C4—62no—
642C2×C4—62no—
643C2×C4—62no—
644C2×C4—62no—
645C2×C4—61no—
646C2×C4—61no—
647C2×C4—61no—
648C2×C4—61no—
649C2×C4—62no—
650C2×C4—62no—
651C2×C4—62no—
652C2×C4—62no—
653C2×C4—62no—
654C2×C4—62no—
655C2×C4—62no—
656C2×C4—62no—
657C2×C4—62no—
658C2×C4—61no—
659C2×C4—61no—
660C2×C4—61no—
661C2×C4—122no—
662C2×C4—122no—
663C2×C4—121no—
664C2×C4—121no—
665C2×C4—122no—
666C2×C4—122no—
667C2×C4—122no—
668C2×C4D3×C22⋊C412yes—
669C2×C4D3×C22⋊C411yescharacteristic
670C2×C4C22×C4×D311yescharacteristic
671C2×C4C2×D3×D412yes—
672C8—44no—
673C8—124no—
674C2×C3—21no—
675C2×C3—22no—
676C2×C3—81no—
677C2×C3C22×#9911yescharacteristic
678D3—21no—
679D3—22no—
680D3—81no—
681D3#213312yesdirect product factor
682C22—31no—
683C22—31no—
684C22—32no—
685C22—41no—
686C22—42no—
687C22—41no—
688C22—62no—
689C22—64no—
690C22—121no—
691C22—122no—
692C22—122no—
693C22—121no—
694C22—242no—
695C22—242no—
696C22D3×#9912yes—
697C22C2×D3×C22⋊C411yescharacteristic
698C4—22no—
699C4—21no—
700C4—22no—
701C4—21no—
702C4—41no—
703C4—41no—
704C4—41no—
705C4—61no—
706C4—61no—
707C4—62no—
708C4—62no—
709C4—121no—
710C4—121no—
711C4—121no—
712C3C2×#213311yescharacteristic, complemented, Sylow
713C2—21no—
714C2—22no—
715C2—32no—
716C2—61no—
717C2—62no—
718C2—81no—
719C2—241no—
720C2C2×D3×#9911yescharacteristic
subgroupG/H
centerC2C2×D3×#99
commutatorC2×C3×C4C23×C4
FrattiniC2×Q8C23×D3
FittingC3×#2133C2
socleC2×C3C22×#99
prime radicalC2×D3×#41C4
cosocleC2×C3×Q8C24
hypercenter#2133D3
hypocenterC3C2×#2133
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2 ◁ C23 ◁ C22×Q8 ◁ #2133

Complements

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

NH ≅ G/Ntype
2. C2×D3×#101C2semidirect
3. C3×#2133C2semidirect
4. #71872C2semidirect
5. #70128C2semidirect
6. #69171C2semidirect
7. D3×#356C2semidirect
8. #69164C2semidirect
9. D3×#355C2semidirect
31. C2×C3×#101C22semidirect
32. C2×#836C22semidirect
37. D3×#101C22semidirect
38. C3×#356C22semidirect
39. C3×#355C22semidirect
40. #4548C22semidirect
41. #4542C22semidirect
42. #4478C22semidirect
43. #4477C22semidirect
50. #2133D3direct (N × H)
168. C2×#101C2×D3semidirect
171. #356C2×D3semidirect
174. #355C2×D3semidirect
681. D3#2133direct (N × H)
712. C3C2×#2133semidirect

Maximal subgroups

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

subgroupindex
D3×#5362
C2×D3×#1012
C3×#21332
#718722
#701282
#691712
D3×#3562
#691642
D3×#3552
C2×#21333