Finite Group Databasebeta

← D3×#4894 #11861071

Subgroups — D3×#4894 #11861071

Order 1152.

980 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#907C212yesmaximal, complemented
2D3×#904C211yesmaximal, characteristic
3#10592593C211yesmaximal, characteristic, complemented
4C3×#4894C211yesmaximal, characteristic, complemented
5C3×D3×#108C211yesmaximal, characteristic, complemented
6D3×#825C212yesmaximal, complemented
7#10590994C212yesmaximal, complemented
8#10590978C212yesmaximal, complemented
9#10590920C211yesmaximal, characteristic, complemented
10#10590918C211yesmaximal, characteristic, complemented
11D3×#815C211yesmaximal, characteristic, complemented
12D3×#444—31nomaximal
13C2×#4894—31nomaximal
14D3×#235C2212yes—
15#64116C2212yescomplemented
16#64113C2211yescharacteristic
17C3×#907C2212yescomplemented
18C3×D3×M16C2212yes—
19C3×#904C2211yescharacteristic
20C2×C3×D3×C8C2211yescharacteristic
21C4×D3×Dic3C2211yescharacteristic
22#63829C2212yes—
23#63817C2212yescomplemented
24#63815C2212yescomplemented
25C2×D3×C3⋊C8C2211yescharacteristic
26#63808C411yescharacteristic, complemented
27#63807C411yescharacteristic, complemented
28#63806C412yescomplemented
29#63805—22no—
30#63804—22no—
31D3×Dic12C411yescharacteristic, complemented
32D3×D24C411yescharacteristic, complemented
33D3×#204C412yescomplemented
34D3×ΓL(1,𝔽25)—22no—
35D32×C8—22no—
36C32×#108C2211yescharacteristic, complemented
37#63652C2212yescomplemented
38#63642C2211yescharacteristic, complemented
39C3×#825C2212yescomplemented
40C3×#822C2212yescomplemented
41C3×#819C2211yescharacteristic, complemented
42C3×#815C2211yescharacteristic, complemented
43#63570C2212yescomplemented
44#63568C2212yescomplemented
45#63555C2211yescharacteristic, complemented
46#63554C2211yescharacteristic, complemented
47D3×#135—31no—
48D3×#131—32no—
49C2×#907—32no—
50C2×#904—31no—
51C3×#444—31no—
52C2×C3×#108—31no—
53#5197—31no—
54#5145—32no—
55C2×#825—32no—
56C2×#815—31no—
57#4894—32no—
58#4894—31no—
59#4894—31no—
60#4894—31no—
61#4894—32no—
62#4894—31no—
63#4894—61no—
64#4894D311yescharacteristic, direct product factor
65D3×#108D311yescharacteristic, complemented
66#4823—32no—
67D3×#104—32no—
68#4717—31no—
69D3×#97—31no—
70#3828C2312yes—
71C3×#235C2312yes—
72C2×C3×C4×D3C2311yescharacteristic
73D3×#67—22no—
74#3804—22no—
75C2×D3×Dic3—21no—
76D3×D12C2×C412yes—
77C4×D32—22no—
78#3799C2×C412yes—
79#3798—22no—
80#3795C2×C412yes—
81D3×Dic6C2×C412yes—
82C32×M16C2312yes—
83C2×C32×C8C2311yescharacteristic
84C4×C3⋊Dic3C2311yescharacteristic
85C2×C3⋊(C3⋊C8)C2311yescharacteristic
86#3746C2×C411yescharacteristic, complemented
87#3745C2×C411yescharacteristic, complemented
88#3744C2×C412yescomplemented
89#3743—22no—
90C8×C3⋊D3—22no—
91C3×C4×Dic3C2311yescharacteristic
92C3×#208C2312yes—
93C2×C3×C3⋊C8C2311yescharacteristic
94C2×C3×C3⋊C8C2311yescharacteristic
95C3×Dic12C2×C411yescharacteristic, complemented
96C3×D24C2×C411yescharacteristic, complemented
97C3×#204C2×C412yescomplemented
98C3×ΓL(1,𝔽25)—22no—
99C3×ΓL(1,𝔽25)—22no—
100C3×D3×C8—22no—
101C3×D3×C8—22no—
102C3×D3×C8C2×C411yescharacteristic
103C3×D3×C8C2×C411yescharacteristic
104C3×D3×C8C2×C411yescharacteristic
105C3×D3×C8C2×C411yescharacteristic
106Dic32—21no—
107#3719C2×C412yescomplemented
108#3717C2×C412yescomplemented
109#3716C2×C412yescomplemented
110#3714C2×C412yescomplemented
111#3712—22no—
112#3711—22no—
113#3710—22no—
114D3×C3⋊C8—22no—
115D3×C3⋊C8D412yes—
116D3×C3⋊C8D412yes—
117C2×#444—91noSylow
118D3×#41—32no—
119C2×#235—32no—
120C3×#135—31no—
121C3×#131—32no—
122C2×C3×M16—32no—
123C22×C3×C8—31no—
124#950—32no—
125#948—32no—
126C2×C4×Dic3—31no—
127C22×C3⋊C8—31no—
128#919—31no—
129D3×Q16—31no—
130#916—32no—
131D3×SD16—32no—
132#912—31no—
133D3×D8—31no—
134#907—32no—
135#907—32no—
136#907—32no—
137#907—32no—
138#907—62no—
139#907—62no—
140#907—62no—
141#907—62no—
142#907C2×D312yescomplemented
143D3×M16—62no—
144D3×M16C2×D312yes—
145C2×Dic12—31no—
146#904—32no—
147#904—31no—
148#904—31no—
149#904—31no—
150#904—31no—
151#904—32no—
152#904—61no—
153#904C2×D311yescharacteristic
154C2×D24—31no—
155C2×#204—32no—
156#901—32no—
157#901—62no—
158C2×ΓL(1,𝔽25)—62no—
159C2×D3×C8—31no—
160C2×D3×C8—62no—
161C2×D3×C8—62no—
162C2×D3×C8C2×D311yescharacteristic
163C42×D3—31no—
164C3×#108—21no—
165C3×#108—32no—
166C3×#108—31no—
167C3×#108C2×D311yescharacteristic, complemented
168C3×#108C2×D311yescharacteristic, complemented
169C3×#104—32no—
170C3×#97—31no—
171#837—32no—
172#825—32no—
173#825—32no—
174#825—32no—
175#825—32no—
176#825—62no—
177#825C2×D312yescomplemented
178#822C2×D312yescomplemented
179#819C2×D311yescharacteristic, complemented
180#815—31no—
181#815—31no—
182#815—31no—
183#815—31no—
184#815—31no—
185#815—61no—
186#815C2×D311yescharacteristic, complemented
187#805—32no—
188#803—31no—
189C22×C3×D3#4111yescharacteristic
190C2×D32—22no—
191C2×C32×C4C2411yescharacteristic
192#638—22no—
193C2×C3⋊Dic3—21no—
194C4⋊(C3⋊D3)C22×C412yes—
195C4×C3⋊D3—22no—
196#634C22×C412yes—
197C3×#67—22no—
198C2×C3×Dic3—21no—
199C2×C3×Dic3#4111yescharacteristic
200C3×D12C22×C412yes—
201C3×C4×D3—22no—
202C3×C4×D3C22×C411yescharacteristic
203C3×C4×D3C22×C411yescharacteristic
204C3×C4×D3C2×D411yescharacteristic
205C3×C4×D3C2×D411yescharacteristic
206C3×Dic6C22×C412yes—
207#627—22no—
208#626—22no—
209#626—22no—
210#625—22no—
211#624—22no—
212D3×Dic3—22no—
213D3×Dic3—22no—
214D3×Dic3—42no—
215C32×C8—22no—
216C32×C8C22×C411yescharacteristic
217C32×C8C22×C411yescharacteristic
218C3⋊(C3⋊C8)C2×D412yes—
219C3×C3⋊C8—22no—
220C3×C3⋊C8C22×C411yescharacteristic
221C3×C3⋊C8C22×C411yescharacteristic
222C3×C3⋊C8C2×D412yes—
223C2×#135—91no—
224C2×#131—92no—
225#444—31no—
226#444—91no—
227#444—92no—
228#444—92no—
229#444—91no—
230#444—91no—
231C2×#108—31no—
232C2×#104—92no—
233C2×#97—91no—
234C3×#41—32no—
235C22×C3×C4—31no—
236C2×#67—62no—
237C22×Dic3—61no—
238#239—32no—
239D3×Q8—32no—
240#237—32no—
241#237—62no—
242D3×D4—32no—
243D3×D4—62no—
244#235—32no—
245#235—32no—
246#235—32no—
247#235—32no—
248#235—62no—
249#235—62no—
250#235—62no—
251#235—62no—
252#235C22×D312yes—
253C2×D12—32no—
254C2×C4×D3—62no—
255C2×C4×D3—62no—
256C2×C4×D3—61no—
257C2×C4×D3C22×D311yescharacteristic
258C2×Dic6—32no—
259C3×Q16—31no—
260C3×SD16—32no—
261C3×D8—31no—
262C3×M16—22no—
263C3×M16—32no—
264C3×M16—62no—
265C3×M16—62no—
266C3×M16C22×D312yes—
267C3×M16C22×D312yes—
268C2×C3×C8—21no—
269C2×C3×C8—31no—
270C2×C3×C8—31no—
271C2×C3×C8—31no—
272C2×C3×C8—31no—
273C2×C3×C8—31no—
274C2×C3×C8—31no—
275C2×C3×C8—62no—
276C2×C3×C8—62no—
277C2×C3×C8C22×D311yescharacteristic
278C2×C3×C8C22×D311yescharacteristic
279C3×C42—31no—
280#216—32no—
281#215—32no—
282#214—32no—
283#213—32no—
284C4×Dic3—31no—
285C4×Dic3—31no—
286C4×Dic3—61no—
287C4×Dic3—61no—
288C4×Dic3—61no—
289C4×Dic3C22×D311yescharacteristic
290#208—62no—
291#208C22×D312yes—
292C2×C3⋊C8—31no—
293C2×C3⋊C8—31no—
294C2×C3⋊C8—32no—
295C2×C3⋊C8—32no—
296C2×C3⋊C8—61no—
297C2×C3⋊C8—62no—
298C2×C3⋊C8C22×D311yescharacteristic
299C2×C3⋊C8C22×D311yescharacteristic
300Dic12—32no—
301Dic12—31no—
302Dic12—31no—
303Dic12—61no—
304Dic12C4×D311yescharacteristic, complemented
305D24—32no—
306D24—31no—
307D24—31no—
308D24—61no—
309D24C4×D311yescharacteristic, complemented
310#204—32no—
311#204—32no—
312#204—32no—
313#204—32no—
314#204—62no—
315#204C4×D312yescomplemented
316ΓL(1,𝔽25)—22no—
317ΓL(1,𝔽25)—22no—
318ΓL(1,𝔽25)—62no—
319ΓL(1,𝔽25)—62no—
320ΓL(1,𝔽25)—62no—
321ΓL(1,𝔽25)—62no—
322ΓL(1,𝔽25)—62no—
323ΓL(1,𝔽25)—122no—
324D3×C8—22no—
325D3×C8—22no—
326D3×C8—32no—
327D3×C8—32no—
328D3×C8—62no—
329D3×C8—62no—
330D3×C8—62no—
331D3×C8—62no—
332D3×C8—62no—
333D3×C8—122no—
334D3×C8C4×D311yescharacteristic
335D3×C8C4×D311yescharacteristic
336D3×C8C4×D311yescharacteristic
337D3×C8C4×D311yescharacteristic
338C22×C32C2×#4111yescharacteristic
339C2×C3⋊D3—22no—
340C2×C3×D3—22no—
341C2×C3×D3—22no—
342C2×C3×D3C4×D411yescharacteristic
343C2×C3×D3C4×D411yescharacteristic
344D32—44no—
345C32×C4C23×C411yescharacteristic
346C32×C4C22×D411yescharacteristic
347C3⋊Dic3—22no—
348C3⋊Dic3—41no—
349C3×Dic3—22no—
350C3×Dic3—41no—
351C3×Dic3C4×D411yescharacteristic
352C3×Dic3C4×D411yescharacteristic
353C2×#41—92no—
354#135—31no—
355#135—91no—
356#135—92no—
357#135—91no—
358#135—92no—
359#135—91no—
360C2×Q16—91no—
361C2×SD16—92no—
362C2×D8—91no—
363#131—32no—
364#131—92no—
365#131—92no—
366#131—92no—
367#131—182no—
368#131—182no—
369C2×M16—32no—
370C2×M16—182no—
371C22×C8—31no—
372C22×C8—91no—
373C22×C8—182no—
374C2×C42—91no—
375#108—32no—
376#108—31no—
377#108D3211yescharacteristic, complemented
378#104—32no—
379#104—92no—
380#104—92no—
381#104—92no—
382#97—31no—
383#97—91no—
384#97—91no—
385#97—91no—
386C23×C3—31no—
387C22×D3—62no—
388C22×D3—62no—
389C22×D3#23911yescharacteristic
390C3×Q8—32no—
391C3×D4—32no—
392C3×D4—62no—
393C2×C3×C4—21no—
394C2×C3×C4—31no—
395C2×C3×C4—31no—
396C2×C3×C4—31no—
397C2×C3×C4—31no—
398C2×C3×C4—31no—
399C2×C3×C4—62no—
400C2×C3×C4—61no—
401C2×C3×C4C23×D311yescharacteristic
402C2×C3×C4C23×D311yescharacteristic
403#67—22no—
404#67—62no—
405#67—62no—
406#67—62no—
407#67—62no—
408#67—62no—
409#67—62no—
410#67—122no—
411C2×Dic3—21no—
412C2×Dic3—62no—
413C2×Dic3—62no—
414C2×Dic3—61no—
415C2×Dic3—61no—
416C2×Dic3—121no—
417C2×Dic3—122no—
418C2×Dic3#23911yescharacteristic
419D12—32no—
420D12—32no—
421D12—62no—
422D12—62no—
423D12—62no—
424D12C2×C4×D312yes—
425C4×D3—22no—
426C4×D3—62no—
427C4×D3—62no—
428C4×D3—62no—
429C4×D3—62no—
430C4×D3—62no—
431C4×D3—62no—
432C4×D3—122no—
433C4×D3—122no—
434C4×D3C2×C4×D311yescharacteristic
435C4×D3C2×C4×D311yescharacteristic
436C4×D3D3×D411yescharacteristic
437C4×D3D3×D411yescharacteristic
438Dic6—32no—
439Dic6—32no—
440Dic6—62no—
441Dic6—62no—
442Dic6—62no—
443Dic6C2×C4×D312yes—
444C3×C8—22no—
445C3×C8—22no—
446C3×C8—21no—
447C3×C8—21no—
448C3×C8—31no—
449C3×C8—31no—
450C3×C8—32no—
451C3×C8—42no—
452C3×C8—62no—
453C3×C8C2×C4×D311yescharacteristic
454C3×C8C2×C4×D311yescharacteristic
455C3×C8C2×C4×D311yescharacteristic
456C3×C8C2×C4×D311yescharacteristic
457C3⋊C8—22no—
458C3⋊C8—32no—
459C3⋊C8—32no—
460C3⋊C8—62no—
461C3⋊C8C2×C4×D311yescharacteristic
462C3⋊C8C2×C4×D311yescharacteristic
463C3⋊C8D3×D412yes—
464C2×C32—21no—
465C2×C32C2×C4×D411yescharacteristic
466C3⋊D3—42no—
467C3×D3—21no—
468C3×D3—42no—
469C3×D3#44412yescomplemented
470#41—32no—
471#41—92no—
472#41—92no—
473#41—92no—
474#41—182no—
475#41—182no—
476C2×Q8—92no—
477C2×D4—92no—
478C2×D4—182no—
479C22×C4—31no—
480C22×C4—182no—
481C22×C4—181no—
482Q16—31no—
483Q16—92no—
484Q16—91no—
485SD16—32no—
486SD16—92no—
487SD16—92no—
488SD16—92no—
489D8—31no—
490D8—92no—
491D8—91no—
492M16—32no—
493M16—62no—
494M16—62no—
495M16—182no—
496M16—182no—
497M16—182no—
498M16C2×D3212yes—
499C2×C8—31no—
500C2×C8—31no—
501C2×C8—31no—
502C2×C8—31no—
503C2×C8—31no—
504C2×C8—31no—
505C2×C8—62no—
506C2×C8—62no—
507C2×C8—92no—
508C2×C8—92no—
509C2×C8—91no—
510C2×C8—182no—
511C2×C8—182no—
512C2×C8—182no—
513C2×C8C2×D3211yescharacteristic
514C42—31no—
515C42—91no—
516C42—181no—
517C22×C3—21no—
518C22×C3—31no—
519C22×C3—31no—
520C22×C3—62no—
521C22×C3—62no—
522C22×C3C2×#23911yescharacteristic
523C22×C3D3×#4111yescharacteristic
524C2×D3—22no—
525C2×D3—22no—
526C2×D3—62no—
527C2×D3—62no—
528C2×D3—122no—
529C2×D3—124no—
530C2×D3—124no—
531C2×D3#89311yescharacteristic
532C2×D3#89311yescharacteristic
533C3×C4—21no—
534C3×C4—21no—
535C3×C4—31no—
536C3×C4—31no—
537C3×C4—62no—
538C3×C4—121no—
539C3×C4C22×C4×D311yescharacteristic
540C3×C4C22×C4×D311yescharacteristic
541C3×C4C2×D3×D411yescharacteristic
542C3×C4C2×D3×D411yescharacteristic
543Dic3—22no—
544Dic3—41no—
545Dic3—62no—
546Dic3—62no—
547Dic3—122no—
548Dic3—121no—
549Dic3—121no—
550Dic3—241no—
551Dic3#89311yescharacteristic
552Dic3#89311yescharacteristic
553C32C2×#44411yescharacteristic, complemented, Sylow
554C23—31no—
555C23—182no—
556Q8—32no—
557Q8—92no—
558Q8—182no—
559D4—32no—
560D4—62no—
561D4—92no—
562D4—182no—
563D4—182no—
564D4—182no—
565D4—182no—
566C2×C4—31no—
567C2×C4—31no—
568C2×C4—31no—
569C2×C4—31no—
570C2×C4—31no—
571C2×C4—62no—
572C2×C4—61no—
573C2×C4—182no—
574C2×C4—182no—
575C2×C4—182no—
576C2×C4—182no—
577C2×C4—181no—
578C2×C4—362no—
579C2×C4C22×D3211yescharacteristic
580C8—22no—
581C8—31no—
582C8—31no—
583C8—32no—
584C8—62no—
585C8—92no—
586C8C4×D3211yescharacteristic
587C8C4×D3211yescharacteristic
588C2×C3—21no—
589C2×C3—21no—
590C2×C3—21no—
591C2×C3—32no—
592C2×C3—41no—
593C2×C3—61no—
594C2×C3—122no—
595C2×C3C2×#89311yescharacteristic
596C2×C3C4×D3×D411yescharacteristic
597D3—21no—
598D3—42no—
599D3—122no—
600D3—122no—
601D3—242no—
602D3#489412yesdirect product factor
603C22—31no—
604C22—31no—
605C22—62no—
606C22—62no—
607C22—182no—
608C22—364no—
609C22D3×#23911yescharacteristic
610C4—31no—
611C4—31no—
612C4—62no—
613C4—121no—
614C4—182no—
615C4—361no—
616C4C2×C4×D3211yescharacteristic
617C4D32×D411yescharacteristic
618C3—21no—
619C3C2×#489411yescharacteristic, complemented
620C3D3×#44411yescharacteristic, complemented
621C2—21no—
622C2—32no—
623C2—61no—
624C2—122no—
625C2—362no—
626C2D3×#89311yescharacteristic
subgroupG/H
centerC4D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#108C22
socleC2×C32C2×C4×D4
prime radicalD3×#904C2
cosocleC2×C32×C4C24
hypercenter#108D32
hypocenterC32C2×#444
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ #108

Complements

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

NH ≅ G/Ntype
1. D3×#907C2semidirect
3. #10592593C2semidirect
4. C3×#4894C2semidirect
5. C3×D3×#108C2semidirect
6. D3×#825C2semidirect
7. #10590994C2semidirect
8. #10590978C2semidirect
9. #10590920C2semidirect
10. #10590918C2semidirect
11. D3×#815C2semidirect
15. #64116C22semidirect
17. C3×#907C22semidirect
23. #63817C22semidirect
24. #63815C22semidirect
26. #63808C4semidirect
27. #63807C4semidirect
28. #63806C4semidirect
31. D3×Dic12C4semidirect
32. D3×D24C4semidirect
33. D3×#204C4semidirect
36. C32×#108C22semidirect
37. #63652C22semidirect
38. #63642C22semidirect
39. C3×#825C22semidirect
40. C3×#822C22semidirect
41. C3×#819C22semidirect
42. C3×#815C22semidirect
43. #63570C22semidirect
44. #63568C22semidirect
45. #63555C22semidirect
46. #63554C22semidirect
64. #4894D3direct (N × H)
65. D3×#108D3semidirect
86. #3746C2×C4semidirect
87. #3745C2×C4semidirect
88. #3744C2×C4semidirect
95. C3×Dic12C2×C4semidirect
96. C3×D24C2×C4semidirect
97. C3×#204C2×C4semidirect
107. #3719C2×C4semidirect
108. #3717C2×C4semidirect
109. #3716C2×C4semidirect
110. #3714C2×C4semidirect
142. #907C2×D3semidirect
167. C3×#108C2×D3semidirect
168. C3×#108C2×D3semidirect
177. #825C2×D3semidirect
178. #822C2×D3semidirect
179. #819C2×D3semidirect
186. #815C2×D3semidirect
304. Dic12C4×D3semidirect
309. D24C4×D3semidirect
315. #204C4×D3semidirect
377. #108D32semidirect
469. C3×D3#444semidirect
553. C32C2×#444semidirect
602. D3#4894direct (N × H)
619. C3C2×#4894semidirect
620. C3D3×#444semidirect

Maximal subgroups

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

subgroupindex
D3×#9072
D3×#9042
#105925932
C3×#48942
C3×D3×#1082
D3×#8252
#105909942
#105909782
#105909202
#105909182
D3×#8152
D3×#4443
C2×#48943