Finite Group Databasebeta

← D3×#5195 #11899598

Subgroups — D3×#5195 #11899598

Order 1152.

761 conjugacy classes of subgroups.

The subgroup lattice has 615 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×#135C211yesmaximal, characteristic
2C2×D3×Dic12C211yesmaximal, characteristic, complemented
3#10592894C211yesmaximal, characteristic, complemented
4C3×#5195C211yesmaximal, characteristic, complemented
5#10591042C212yesmaximal, complemented
6D3×#829C212yesmaximal, complemented
7#10591028C212yesmaximal, complemented
8D3×#827C212yesmaximal, complemented
9#10590638C211yesmaximal, characteristic, complemented
10#10590636C211yesmaximal, characteristic, complemented
11D3×#812C211yesmaximal, characteristic, complemented
12C2×#5195—31nomaximal
13D3×#510—31nomaximal
14C3×D3×#41—21no—
15C2×D3×Dic6—21no—
16C32×#135C2211yescharacteristic
17C2×#3746C2211yescharacteristic, complemented
18C3×#950—21no—
19C3×#919C2211yescharacteristic
20C3×D3×Q16C2211yescharacteristic
21C3×#916—21no—
22C3×D3×SD16—21no—
23C3×#912C2211yescharacteristic
24C3×D3×D8C2211yescharacteristic
25C2×C3×Dic12C2211yescharacteristic, complemented
26C3×#904C2211yescharacteristic
27C2×C3×D3×C8C2211yescharacteristic
28C2×#3719—21no—
29D3×Dic12—21no—
30D3×Dic12—21no—
31D3×Dic12C2212yes—
32D3×Dic12C2212yescomplemented
33#63656C2212yescomplemented
34#63654C2212yescomplemented
35#63639C2211yescharacteristic, complemented
36C3×#829C2212yescomplemented
37C3×#827C2212yescomplemented
38C3×#812C2211yescharacteristic, complemented
39#63551C2212yescomplemented
40#63550C2212yescomplemented
41#63548C2212yescomplemented
42#63547C2212yescomplemented
43#63543C2212yescomplemented
44D3×C3⋊C16C2212yes—
45C2×C3×#135—31no—
46D3×#135D311yescharacteristic
47C2×D3×Q16—31no—
48C22×Dic12—31no—
49C3×#510—31no—
50#5195—31no—
51#5195—31no—
52#5195—31no—
53#5195—32no—
54#5195—32no—
55#5195—31no—
56#5195—61no—
57#5195D311yescharacteristic, direct product factor
58C2×#829—32no—
59#5179—31no—
60C2×#827—32no—
61C2×#812—31no—
62#4918—32no—
63D3×Q32—32no—
64#4915—32no—
65D3×SD32—32no—
66#4909—31no—
67D3×M32—31no—
68C32×#41—21no—
69C2×#634—21no—
70C3×#239—21no—
71C3×D3×Q8—21no—
72C3×#237—21no—
73C3×#237—41no—
74C3×D3×D4—21no—
75C3×D3×D4—41no—
76C3×#235—21no—
77C3×#235—41no—
78C2×C3×C4×D3—41no—
79C2×C3×C4×D3D411yescharacteristic
80C2×C3×Dic6—21no—
81C2×#627—41no—
82C2×D3×Dic3—41no—
83D3×Dic6—22no—
84D3×Dic6—22no—
85D3×Dic6—41no—
86D3×Dic6—41no—
87C32×Q16C2311yescharacteristic
88C32×SD16—21no—
89C32×D8C2311yescharacteristic
90C2×C32×C8C2311yescharacteristic
91#3746—21no—
92#3746C2312yes—
93C3×#216—21no—
94C3×#215—21no—
95C3×#214—21no—
96C3×#213—21no—
97C2×C3×C3⋊C8D411yescharacteristic
98C3×Dic12—21no—
99C3×Dic12C2311yescharacteristic
100C3×Dic12C2312yes—
101C3×D24C2311yescharacteristic
102C3×#204—21no—
103C3×D3×C8D411yescharacteristic
104C3×D3×C8D411yescharacteristic
105C3×D3×C8C2311yescharacteristic
106C3×D3×C8C2311yescharacteristic
107#3719—22no—
108#3719—22no—
109C3⋊(C3⋊C16)C2312yes—
110C3×C3⋊C16C2312yes—
111C2×#510—91noSylow
112C2×C3×#41—61no—
113D3×#41—21no—
114C2×D3×Q8—61no—
115C22×Dic6—61no—
116C3×#135—21no—
117C3×#135—31no—
118C3×#135—31no—
119C3×#135—31no—
120C3×#135—61no—
121C3×#135—61no—
122C3×#135C2×D311yescharacteristic
123C3×#135C2×D311yescharacteristic
124C2×C3×Q16—31no—
125C2×C3×Q16—31no—
126C2×C3×SD16—61no—
127C2×C3×D8—31no—
128C22×C3×C8—31no—
129#950—21no—
130C2×#216—61no—
131#919C2×D311yescharacteristic
132D3×Q16—32no—
133D3×Q16—32no—
134D3×Q16—61no—
135D3×Q16—61no—
136D3×Q16C2×D311yescharacteristic
137#916—21no—
138D3×SD16—21no—
139#912C2×D311yescharacteristic
140D3×D8C2×D311yescharacteristic
141C2×Dic12—31no—
142C2×Dic12—31no—
143C2×Dic12—32no—
144C2×Dic12—32no—
145C2×Dic12—61no—
146C2×Dic12—61no—
147C2×Dic12—61no—
148C2×Dic12—61no—
149C2×Dic12C2×D311yescharacteristic, complemented
150#904C2×D311yescharacteristic
151C2×D3×C8C2×D311yescharacteristic
152C3×Q32—32no—
153C3×SD32—32no—
154C3×M32—31no—
155#829—32no—
156#829—32no—
157#829—32no—
158#829—32no—
159#829—32no—
160#829—62no—
161#829C2×D312yescomplemented
162#828—32no—
163#827—32no—
164#827—32no—
165#827—32no—
166#827—32no—
167#827—62no—
168#827C2×D312yescomplemented
169#812—31no—
170#812—31no—
171#812—32no—
172#812—61no—
173#812C2×D311yescharacteristic, complemented
174C2×C3⋊C16—32no—
175Dic24—32no—
176#800—32no—
177#798—32no—
178D3×C16—32no—
179C22×C3×D3—41no—
180C22×C3×D3D811yescharacteristic
181C32×Q8—21no—
182C32×D4—21no—
183C32×D4—41no—
184C2×C32×C4—41no—
185C2×C32×C4C2×D411yescharacteristic
186C2×C3⋊Dic3—41no—
187#634—22no—
188#634—41no—
189C3×#67—41no—
190C3×#67—41no—
191C3×#67—41no—
192C2×C3×Dic3—41no—
193C2×C3×Dic3—41no—
194C2×C3×Dic3D811yescharacteristic
195C3×D12—21no—
196C3×D12—41no—
197C3×C4×D3—41no—
198C3×C4×D3—41no—
199C3×C4×D3—41no—
200C3×C4×D3D811yescharacteristic
201C3×C4×D3D811yescharacteristic
202C3×C4×D3C2×D411yescharacteristic
203C3×C4×D3C2×D411yescharacteristic
204C3×Dic6—22no—
205C3×Dic6—21no—
206C3×Dic6—41no—
207C3×Dic6—41no—
208#627—42no—
209#627—42no—
210D3×Dic3—42no—
211D3×Dic3—42no—
212C32×C8C2×D411yescharacteristic
213C32×C8C2411yescharacteristic
214C3×C3⋊C8C2×D411yescharacteristic
215C3×C3⋊C8C2×D411yescharacteristic
216C2×#135—31no—
217C22×Q16—91no—
218#510—31no—
219#510—91no—
220#510—92no—
221#510—92no—
222#510—91no—
223#510—91no—
224C2×Q32—92no—
225C2×SD32—92no—
226C2×M32—91no—
227C3×#41—21no—
228C3×#41—21no—
229C3×#41—41no—
230C3×#41—61no—
231C3×#41—61no—
232C3×#41—61no—
233C3×#41—121no—
234C3×#41—121no—
235C2×C3×Q8—61no—
236C2×C3×Q8—61no—
237C2×C3×D4—61no—
238C2×C3×D4—121no—
239C22×C3×C4—31no—
240C22×C3×C4—121no—
241C22×Dic3—121no—
242#239—21no—
243D3×Q8—21no—
244D3×Q8—62no—
245D3×Q8—62no—
246D3×Q8—121no—
247D3×Q8—121no—
248#237—21no—
249#237—41no—
250D3×D4—21no—
251D3×D4—41no—
252#235—21no—
253#235—41no—
254C2×C4×D3—41no—
255C2×C4×D3—121no—
256C2×C4×D3#6711yescharacteristic
257C2×Dic6—21no—
258C2×Dic6—62no—
259C2×Dic6—62no—
260C2×Dic6—61no—
261C2×Dic6—61no—
262C2×Dic6—121no—
263C2×Dic6—121no—
264C2×Dic6—121no—
265C2×Dic6—121no—
266C2×Dic6—121no—
267C3×Q16—21no—
268C3×Q16—32no—
269C3×Q16—31no—
270C3×Q16—61no—
271C3×Q16—61no—
272C3×Q16C22×D311yescharacteristic
273C3×Q16C22×D311yescharacteristic
274C3×SD16—21no—
275C3×SD16—21no—
276C3×SD16—41no—
277C3×SD16—61no—
278C3×SD16—61no—
279C3×SD16—61no—
280C3×D8—21no—
281C3×D8—31no—
282C3×D8—61no—
283C3×D8C22×D311yescharacteristic
284C3×D8C22×D311yescharacteristic
285C2×C3×C8—21no—
286C2×C3×C8—31no—
287C2×C3×C8—31no—
288C2×C3×C8—31no—
289C2×C3×C8—31no—
290C2×C3×C8—31no—
291C2×C3×C8C22×D311yescharacteristic
292C2×C3×C8C22×D311yescharacteristic
293#216—21no—
294#216—62no—
295#216—62no—
296#215—21no—
297#214—21no—
298#213—21no—
299C2×C3⋊C8#6711yescharacteristic
300Dic12—21no—
301Dic12—32no—
302Dic12—32no—
303Dic12—62no—
304Dic12—62no—
305Dic12—62no—
306Dic12—61no—
307Dic12—61no—
308Dic12—121no—
309Dic12C22×D311yescharacteristic
310Dic12C22×D312yes—
311D24C22×D311yescharacteristic
312#204—21no—
313D3×C8#6711yescharacteristic
314D3×C8#6711yescharacteristic
315D3×C8C22×D311yescharacteristic
316D3×C8C22×D311yescharacteristic
317C3×C16—32no—
318C3⋊C16—32no—
319C3⋊C16—32no—
320C3⋊C16—62no—
321C3⋊C16C22×D312yes—
322C22×C32—41no—
323C22×C32C2×D811yescharacteristic
324C2×C3×D3—22no—
325C2×C3×D3—41no—
326C2×C3×D3—82no—
327C2×C3×D3C2×D811yescharacteristic
328C2×C3×D3C2×D811yescharacteristic
329C32×C4—41no—
330C32×C4C2×D811yescharacteristic
331C32×C4C22×D411yescharacteristic
332C3⋊Dic3—42no—
333C3×Dic3—42no—
334C3×Dic3—41no—
335C3×Dic3C2×D811yescharacteristic
336C3×Dic3C2×D811yescharacteristic
337C2×#41—61no—
338C22×Q8—181no—
339#135—31no—
340#135—31no—
341#135—31no—
342#135—61no—
343#135—61no—
344#135D3211yescharacteristic
345C2×Q16—31no—
346C2×Q16—31no—
347C2×Q16—92no—
348C2×Q16—92no—
349C2×Q16—91no—
350C2×Q16—181no—
351C2×Q16—181no—
352C2×Q16—181no—
353C2×SD16—61no—
354C2×D8—31no—
355C22×C8—31no—
356Q32—32no—
357Q32—92no—
358Q32—92no—
359Q32—92no—
360SD32—32no—
361SD32—92no—
362SD32—92no—
363SD32—92no—
364M32—31no—
365M32—92no—
366M32—91no—
367C2×C16—92no—
368C23×C3—31no—
369C23×C3—121no—
370C22×D3—41no—
371C22×D3#21311yescharacteristic
372C3×Q8—21no—
373C3×Q8—21no—
374C3×Q8—41no—
375C3×Q8—61no—
376C3×Q8—62no—
377C3×Q8—121no—
378C3×Q8—121no—
379C3×D4—21no—
380C3×D4—21no—
381C3×D4—41no—
382C3×D4—41no—
383C3×D4—41no—
384C3×D4—61no—
385C3×D4—81no—
386C3×D4—121no—
387C3×D4—121no—
388C3×D4—121no—
389C3×D4—121no—
390C2×C3×C4—21no—
391C2×C3×C4—31no—
392C2×C3×C4—31no—
393C2×C3×C4—31no—
394C2×C3×C4—31no—
395C2×C3×C4—31no—
396C2×C3×C4—41no—
397C2×C3×C4—41no—
398C2×C3×C4—81no—
399C2×C3×C4—121no—
400C2×C3×C4—121no—
401C2×C3×C4—121no—
402C2×C3×C4—121no—
403C2×C3×C4—121no—
404C2×C3×C4D3×D411yescharacteristic
405C2×C3×C4C2×#6711yescharacteristic
406#67—41no—
407#67—41no—
408#67—41no—
409C2×Dic3—41no—
410C2×Dic3—41no—
411C2×Dic3—122no—
412C2×Dic3—122no—
413C2×Dic3—121no—
414C2×Dic3—121no—
415C2×Dic3—241no—
416C2×Dic3#21311yescharacteristic
417D12—21no—
418D12—41no—
419C4×D3—41no—
420C4×D3—41no—
421C4×D3—41no—
422C4×D3—122no—
423C4×D3—122no—
424C4×D3#21311yescharacteristic
425C4×D3#21311yescharacteristic
426C4×D3C2×#6711yescharacteristic
427C4×D3C2×#6711yescharacteristic
428Dic6—22no—
429Dic6—21no—
430Dic6—41no—
431Dic6—41no—
432Dic6—62no—
433Dic6—62no—
434Dic6—122no—
435Dic6—122no—
436Dic6—122no—
437Dic6—121no—
438Dic6—121no—
439Dic6—122no—
440Dic6—122no—
441Dic6—241no—
442C3×C8—21no—
443C3×C8—21no—
444C3×C8—31no—
445C3×C8—31no—
446C3×C8D3×D411yescharacteristic
447C3×C8C2×#6711yescharacteristic
448C3×C8C23×D311yescharacteristic
449C3×C8C23×D311yescharacteristic
450C3⋊C8C2×#6711yescharacteristic
451C3⋊C8C2×#6711yescharacteristic
452C2×C32—21no—
453C2×C32—81no—
454C2×C32C22×D811yescharacteristic
455C3×D3—21no—
456C3×D3—81no—
457C3×D3#51012yescomplemented
458#41—21no—
459#41—61no—
460#41—61no—
461#41—61no—
462#41—121no—
463#41—121no—
464C2×Q8—61no—
465C2×Q8—61no—
466C2×Q8—182no—
467C2×Q8—182no—
468C2×Q8—181no—
469C2×Q8—361no—
470C2×Q8—361no—
471C2×Q8—361no—
472C2×D4—61no—
473C2×D4—121no—
474C22×C4—31no—
475C22×C4—121no—
476C22×C4—361no—
477Q16—32no—
478Q16—31no—
479Q16—61no—
480Q16—61no—
481Q16—92no—
482Q16—182no—
483Q16—182no—
484Q16—181no—
485Q16C2×D3211yescharacteristic
486SD16—21no—
487SD16—61no—
488SD16—61no—
489SD16—61no—
490D8—31no—
491D8—61no—
492D8C2×D3211yescharacteristic
493C2×C8—31no—
494C2×C8—31no—
495C2×C8—31no—
496C2×C8—31no—
497C2×C8—31no—
498C2×C8C2×D3211yescharacteristic
499C16—32no—
500C16—92no—
501C22×C3—21no—
502C22×C3—31no—
503C22×C3—31no—
504C22×C3—41no—
505C22×C3—41no—
506C22×C3—62no—
507C22×C3—81no—
508C22×C3—121no—
509C22×C3—242no—
510C22×C3D3×D811yescharacteristic
511C22×C3C2×#21311yescharacteristic
512C2×D3—22no—
513C2×D3—41no—
514C2×D3—82no—
515C2×D3C2×#21311yescharacteristic
516C2×D3C2×#21311yescharacteristic
517C3×C4—21no—
518C3×C4—21no—
519C3×C4—31no—
520C3×C4—31no—
521C3×C4—41no—
522C3×C4—41no—
523C3×C4—81no—
524C3×C4—121no—
525C3×C4—122no—
526C3×C4D3×D811yescharacteristic
527C3×C4C2×#21311yescharacteristic
528C3×C4C2×D3×D411yescharacteristic
529C3×C4C22×#6711yescharacteristic
530Dic3—42no—
531Dic3—41no—
532Dic3—122no—
533Dic3—122no—
534Dic3—242no—
535Dic3C2×#21311yescharacteristic
536Dic3C2×#21311yescharacteristic
537C32C2×#51011yescharacteristic, complemented, Sylow
538C23—31no—
539C23—121no—
540Q8—21no—
541Q8—61no—
542Q8—62no—
543Q8—121no—
544Q8—121no—
545Q8—182no—
546Q8—362no—
547Q8—362no—
548Q8—361no—
549D4—21no—
550D4—41no—
551D4—61no—
552D4—121no—
553D4—121no—
554D4—121no—
555D4—121no—
556C2×C4—31no—
557C2×C4—31no—
558C2×C4—31no—
559C2×C4—31no—
560C2×C4—31no—
561C2×C4—41no—
562C2×C4—121no—
563C2×C4—121no—
564C2×C4—121no—
565C2×C4—121no—
566C2×C4—121no—
567C2×C4—362no—
568C2×C4—362no—
569C2×C4—361no—
570C2×C4D3×#6711yescharacteristic
571C8—31no—
572C8—31no—
573C8D3×#6711yescharacteristic
574C8C22×D3211yescharacteristic
575C2×C3—21no—
576C2×C3—21no—
577C2×C3—21no—
578C2×C3—32no—
579C2×C3—41no—
580C2×C3—61no—
581C2×C3—81no—
582C2×C3—81no—
583C2×C3—161no—
584C2×C3—241no—
585C2×C3C2×D3×D811yescharacteristic
586C2×C3C22×#21311yescharacteristic
587D3—21no—
588D3—81no—
589D3#519512yesdirect product factor
590C22—31no—
591C22—31no—
592C22—41no—
593C22—62no—
594C22—121no—
595C22—242no—
596C22D3×#21311yescharacteristic
597C4—31no—
598C4—31no—
599C4—41no—
600C4—121no—
601C4—122no—
602C4—362no—
603C4D3×#21311yescharacteristic
604C4C2×D3×#6711yescharacteristic
605C3—21no—
606C3D3×#51011yescharacteristic, complemented
607C3C2×#519511yescharacteristic, complemented
608C2—21no—
609C2—32no—
610C2—61no—
611C2—81no—
612C2—241no—
613C2C2×D3×#21311yescharacteristic
subgroupG/H
centerC2C2×D3×#213
commutator, cosocleC32×C8C24
FrattiniC8C22×D32
FittingC32×#135C22
socleC2×C32C22×D8
prime radicalC3×D3×#135C2
hypercenter#135D32
hypocenterC32C2×#510
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #135

Complements

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

NH ≅ G/Ntype
2. C2×D3×Dic12C2semidirect
3. #10592894C2semidirect
4. C3×#5195C2semidirect
5. #10591042C2semidirect
6. D3×#829C2semidirect
7. #10591028C2semidirect
8. D3×#827C2semidirect
9. #10590638C2semidirect
10. #10590636C2semidirect
11. D3×#812C2semidirect
17. C2×#3746C22semidirect
25. C2×C3×Dic12C22semidirect
32. D3×Dic12C22semidirect
33. #63656C22semidirect
34. #63654C22semidirect
35. #63639C22semidirect
36. C3×#829C22semidirect
37. C3×#827C22semidirect
38. C3×#812C22semidirect
39. #63551C22semidirect
40. #63550C22semidirect
41. #63548C22semidirect
42. #63547C22semidirect
43. #63543C22semidirect
57. #5195D3direct (N × H)
149. C2×Dic12C2×D3semidirect
161. #829C2×D3semidirect
168. #827C2×D3semidirect
173. #812C2×D3semidirect
457. C3×D3#510semidirect
537. C32C2×#510semidirect
589. D3#5195direct (N × H)
606. C3D3×#510semidirect
607. C3C2×#5195semidirect

Maximal subgroups

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

subgroupindex
C3×D3×#1352
C2×D3×Dic122
#105928942
C3×#51952
#105910422
D3×#8292
#105910282
D3×#8272
#105906382
#105906362
D3×#8122
C2×#51953
D3×#5103