Finite Group Databasebeta

← D3×#5179 #11899600

Subgroups — D3×#5179 #11899600

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
1C2×C3×D3×Q16C211yesmaximal, characteristic, complemented
2D3×#904C211yesmaximal, characteristic
3#10592878C211yesmaximal, characteristic, complemented
4C3×#5179C211yesmaximal, characteristic, complemented
5#10591047C212yesmaximal, complemented
6#10591045C212yesmaximal, complemented
7D3×#829C212yesmaximal, complemented
8D3×#828C212yesmaximal, complemented
9#10590642C211yesmaximal, characteristic, complemented
10#10590636C211yesmaximal, characteristic, complemented
11D3×#812C211yesmaximal, characteristic, complemented
12C2×#5179—31nomaximal
13D3×#510—31nomaximal
14C2×C3×D3×Q8—21no—
15D3×#235—21no—
16C2×C32×Q16C2211yescharacteristic, complemented
17#64113C2211yescharacteristic
18C2×C3×#216—21no—
19C3×D3×Q16—21no—
20C3×D3×Q16—21no—
21C3×D3×Q16C2212yes—
22C3×D3×Q16C2212yescomplemented
23C2×C3×Dic12C2211yescharacteristic, complemented
24C3×#904C2211yescharacteristic
25C2×C3×D3×C8C2211yescharacteristic
26#63829—21no—
27#63808C2211yescharacteristic
28#63807C2211yescharacteristic
29#63806—21no—
30D3×Dic12C2211yescharacteristic
31D3×D24C2211yescharacteristic
32D3×#204—21no—
33#63656C2212yescomplemented
34#63655C2212yescomplemented
35#63639C2211yescharacteristic, complemented
36C3×#829C2212yescomplemented
37C3×#828C2212yescomplemented
38C3×#812C2211yescharacteristic, complemented
39#63551C2212yescomplemented
40#63550C2212yescomplemented
41#63549C2212yescomplemented
42#63547C2212yescomplemented
43#63543C2212yescomplemented
44D3×C3⋊C16C2212yes—
45C22×C3×Q16—31no—
46D3×#135—31no—
47C2×D3×Q16D311yescharacteristic, complemented
48C2×#904—31no—
49C3×#510—31no—
50#5195—31no—
51C2×#829—32no—
52#5179—31no—
53#5179—31no—
54#5179—31no—
55#5179—32no—
56#5179—32no—
57#5179—31no—
58#5179—61no—
59#5179D311yescharacteristic, direct product factor
60C2×#828—32no—
61C2×#812—31no—
62#4918—32no—
63D3×Q32—32no—
64#4915—32no—
65D3×SD32—32no—
66#4909—31no—
67D3×M32—31no—
68C2×C32×Q8—21no—
69#3828—21no—
70C3×D3×Q8—22no—
71C3×D3×Q8—22no—
72C3×D3×Q8—41no—
73C3×D3×Q8—41no—
74C3×#235—21no—
75C2×C3×C4×D3—41no—
76C2×C3×C4×D3D411yescharacteristic
77C2×C3×Dic6—21no—
78C2×C3×Dic6—41no—
79D3×#67—41no—
80#3804—41no—
81D3×D12—21no—
82C4×D32—41no—
83#3799—21no—
84#3798—41no—
85#3795—21no—
86D3×Dic6—21no—
87C32×Q16—21no—
88C32×Q16C2312yes—
89C2×C32×C8C2311yescharacteristic
90#3746C2311yescharacteristic
91#3745C2311yescharacteristic
92#3744—21no—
93C3×#216—22no—
94C3×#216—22no—
95C2×C3×C3⋊C8D411yescharacteristic
96C3×Dic12—21no—
97C3×Dic12C2311yescharacteristic
98C3×Dic12C2312yes—
99C3×D24C2311yescharacteristic
100C3×#204—21no—
101C3×D3×C8D411yescharacteristic
102C3×D3×C8D411yescharacteristic
103C3×D3×C8C2311yescharacteristic
104C3×D3×C8C2311yescharacteristic
105#3719—21no—
106#3717—21no—
107#3716—21no—
108#3714—21no—
109C3⋊(C3⋊C16)C2312yes—
110C3×C3⋊C16C2312yes—
111C2×#510—91noSylow
112C22×C3×Q8—61no—
113D3×#41—61no—
114C2×D3×Q8—21no—
115C2×#235—61no—
116C3×#135—31no—
117C2×C3×Q16—21no—
118C2×C3×Q16—32no—
119C2×C3×Q16—32no—
120C2×C3×Q16—31no—
121C2×C3×Q16—61no—
122C2×C3×Q16—61no—
123C2×C3×Q16—61no—
124C2×C3×Q16C2×D311yescharacteristic, complemented
125C2×C3×Q16C2×D311yescharacteristic, complemented
126C22×C3×C8—31no—
127#950—61no—
128C2×#216—21no—
129#919—31no—
130D3×Q16—21no—
131D3×Q16—21no—
132D3×Q16—31no—
133D3×Q16C2×D312yes—
134D3×Q16C2×D312yescomplemented
135#916—61no—
136D3×SD16—61no—
137#912—31no—
138D3×D8—31no—
139C2×Dic12—31no—
140C2×Dic12C2×D311yescharacteristic, complemented
141#904—31no—
142#904—31no—
143#904—31no—
144#904—31no—
145#904—61no—
146#904—61no—
147#904—61no—
148#904C2×D311yescharacteristic
149C2×D24—31no—
150C2×#204—61no—
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#828—32no—
164#828—32no—
165#828—32no—
166#828—62no—
167#828C2×D312yescomplemented
168#827—32no—
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×D3D811yescharacteristic
180C2×D32—41no—
181C32×Q8—22no—
182C32×Q8—41no—
183C2×C32×C4—41no—
184C2×C32×C4C2×D411yescharacteristic
185#638—41no—
186C4⋊(C3⋊D3)—21no—
187C4×C3⋊D3—41no—
188#634—21no—
189C3×#67—41no—
190C2×C3×Dic3—41no—
191C2×C3×Dic3D811yescharacteristic
192C3×D12—21no—
193C3×C4×D3—42no—
194C3×C4×D3—42no—
195C3×C4×D3—41no—
196C3×C4×D3D811yescharacteristic
197C3×C4×D3D811yescharacteristic
198C3×C4×D3C2×D411yescharacteristic
199C3×C4×D3C2×D411yescharacteristic
200C3×Dic6—21no—
201C3×Dic6—22no—
202C3×Dic6—41no—
203C3×Dic6—42no—
204C3×Dic6—42no—
205#627—41no—
206#626—41no—
207#626—41no—
208#625—41no—
209#624—41no—
210D3×Dic3—41no—
211D3×Dic3—41no—
212C32×C8C2×D411yescharacteristic
213C32×C8C2411yescharacteristic
214C3×C3⋊C8C2×D411yescharacteristic
215C3×C3⋊C8C2×D411yescharacteristic
216C2×#135—91no—
217C22×Q16—31no—
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—61no—
228C2×C3×Q8—21no—
229C2×C3×Q8—21no—
230C2×C3×Q8—41no—
231C2×C3×Q8—62no—
232C2×C3×Q8—62no—
233C2×C3×Q8—61no—
234C2×C3×Q8—121no—
235C2×C3×Q8—121no—
236C2×C3×Q8—121no—
237C22×C3×C4—31no—
238C22×C3×C4—121no—
239C2×#67—121no—
240#239—61no—
241D3×Q8—22no—
242D3×Q8—22no—
243D3×Q8—41no—
244D3×Q8—41no—
245D3×Q8—61no—
246#237—61no—
247#237—121no—
248D3×D4—61no—
249D3×D4—121no—
250#235—21no—
251#235—61no—
252#235—61no—
253#235—61no—
254#235—61no—
255#235—121no—
256#235—121no—
257#235—121no—
258#235—121no—
259C2×D12—61no—
260C2×C4×D3—41no—
261C2×C4×D3—121no—
262C2×C4×D3—121no—
263C2×C4×D3#6711yescharacteristic
264C2×Dic6—21no—
265C2×Dic6—41no—
266C2×Dic6—61no—
267C3×Q16—21no—
268C3×Q16—21no—
269C3×Q16—22no—
270C3×Q16—32no—
271C3×Q16—31no—
272C3×Q16—41no—
273C3×Q16—62no—
274C3×Q16—62no—
275C3×Q16—61no—
276C3×Q16C22×D312yes—
277C3×Q16C22×D312yes—
278C3×SD16—61no—
279C3×D8—31no—
280C2×C3×C8—21no—
281C2×C3×C8—31no—
282C2×C3×C8—31no—
283C2×C3×C8—31no—
284C2×C3×C8—31no—
285C2×C3×C8—31no—
286C2×C3×C8C22×D311yescharacteristic
287C2×C3×C8C22×D311yescharacteristic
288#216—22no—
289#216—22no—
290#216—61no—
291#215—61no—
292#214—61no—
293#213—61no—
294C2×C3⋊C8#6711yescharacteristic
295Dic12—21no—
296Dic12—31no—
297Dic12—31no—
298Dic12—61no—
299Dic12—61no—
300Dic12C22×D312yes—
301Dic12C22×D311yescharacteristic
302D24—31no—
303D24—31no—
304D24—61no—
305D24—61no—
306D24C22×D311yescharacteristic
307#204—21no—
308#204—61no—
309#204—61no—
310#204—61no—
311#204—61no—
312#204—121no—
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×C32C2×D811yescharacteristic
323C2×C3⋊D3—41no—
324C2×C3×D3—22no—
325C2×C3×D3—41no—
326C2×C3×D3C2×D811yescharacteristic
327C2×C3×D3C2×D811yescharacteristic
328D32—82no—
329C32×C4—42no—
330C32×C4C2×D811yescharacteristic
331C32×C4C22×D411yescharacteristic
332C3⋊Dic3—41no—
333C3×Dic3—41no—
334C3×Dic3—42no—
335C3×Dic3C2×D811yescharacteristic
336C3×Dic3C2×D811yescharacteristic
337C2×#41—181no—
338C22×Q8—61no—
339#135—31no—
340#135—91no—
341#135—91no—
342#135—91no—
343#135—181no—
344#135—181no—
345C2×Q16—32no—
346C2×Q16—32no—
347C2×Q16—31no—
348C2×Q16—61no—
349C2×Q16—61no—
350C2×Q16—61no—
351C2×Q16—91no—
352C2×Q16D3211yescharacteristic, complemented
353C2×SD16—181no—
354C2×D8—91no—
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—
369C22×D3—121no—
370C22×D3—121no—
371C22×D3#21311yescharacteristic
372C3×Q8—22no—
373C3×Q8—22no—
374C3×Q8—42no—
375C3×Q8—41no—
376C3×Q8—41no—
377C3×Q8—62no—
378C3×Q8—61no—
379C3×Q8—81no—
380C3×Q8—122no—
381C3×Q8—122no—
382C3×Q8—121no—
383C3×D4—61no—
384C3×D4—121no—
385C2×C3×C4—21no—
386C2×C3×C4—31no—
387C2×C3×C4—31no—
388C2×C3×C4—31no—
389C2×C3×C4—31no—
390C2×C3×C4—31no—
391C2×C3×C4—41no—
392C2×C3×C4—41no—
393C2×C3×C4—81no—
394C2×C3×C4—122no—
395C2×C3×C4—122no—
396C2×C3×C4—121no—
397C2×C3×C4—121no—
398C2×C3×C4D3×D411yescharacteristic
399C2×C3×C4C2×#6711yescharacteristic
400#67—41no—
401#67—121no—
402#67—121no—
403#67—121no—
404#67—121no—
405#67—121no—
406#67—121no—
407#67—241no—
408C2×Dic3—41no—
409C2×Dic3—121no—
410C2×Dic3—121no—
411C2×Dic3#21311yescharacteristic
412D12—21no—
413D12—61no—
414D12—61no—
415D12—121no—
416D12—121no—
417D12—121no—
418C4×D3—42no—
419C4×D3—42no—
420C4×D3—41no—
421C4×D3—121no—
422C4×D3—121no—
423C4×D3—121no—
424C4×D3—121no—
425C4×D3—121no—
426C4×D3—121no—
427C4×D3—241no—
428C4×D3#21311yescharacteristic
429C4×D3#21311yescharacteristic
430C4×D3C2×#6711yescharacteristic
431C4×D3C2×#6711yescharacteristic
432Dic6—21no—
433Dic6—22no—
434Dic6—41no—
435Dic6—42no—
436Dic6—42no—
437Dic6—61no—
438Dic6—61no—
439Dic6—121no—
440Dic6—121no—
441Dic6—121no—
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×C32C22×D811yescharacteristic
454C3⋊D3—81no—
455C3×D3—21no—
456C3×D3—81no—
457C3×D3#51012yescomplemented
458#41—61no—
459#41—181no—
460#41—181no—
461#41—181no—
462#41—361no—
463#41—361no—
464C2×Q8—21no—
465C2×Q8—62no—
466C2×Q8—62no—
467C2×Q8—61no—
468C2×Q8—121no—
469C2×Q8—121no—
470C2×Q8—121no—
471C2×Q8—181no—
472C2×D4—181no—
473C2×D4—361no—
474C22×C4—31no—
475C22×C4—121no—
476C22×C4—361no—
477Q16—21no—
478Q16—32no—
479Q16—31no—
480Q16—62no—
481Q16—62no—
482Q16—61no—
483Q16—91no—
484Q16—181no—
485Q16C2×D3212yes—
486SD16—61no—
487SD16—181no—
488SD16—181no—
489SD16—181no—
490D8—31no—
491D8—91no—
492D8—181no—
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—62no—
505C22×C3—121no—
506C22×C3D3×D811yescharacteristic
507C22×C3C2×#21311yescharacteristic
508C2×D3—22no—
509C2×D3—41no—
510C2×D3—121no—
511C2×D3—121no—
512C2×D3—241no—
513C2×D3—242no—
514C2×D3—242no—
515C2×D3C2×#21311yescharacteristic
516C2×D3C2×#21311yescharacteristic
517C3×C4—21no—
518C3×C4—21no—
519C3×C4—31no—
520C3×C4—31no—
521C3×C4—42no—
522C3×C4—42no—
523C3×C4—82no—
524C3×C4—122no—
525C3×C4—121no—
526C3×C4D3×D811yescharacteristic
527C3×C4C2×#21311yescharacteristic
528C3×C4C2×D3×D411yescharacteristic
529C3×C4C22×#6711yescharacteristic
530Dic3—41no—
531Dic3—42no—
532Dic3—121no—
533Dic3—121no—
534Dic3—241no—
535Dic3C2×#21311yescharacteristic
536Dic3C2×#21311yescharacteristic
537C32C2×#51011yescharacteristic, complemented, Sylow
538C23—31no—
539C23—361no—
540Q8—22no—
541Q8—41no—
542Q8—61no—
543Q8—62no—
544Q8—122no—
545Q8—122no—
546Q8—121no—
547Q8—181no—
548Q8—361no—
549D4—61no—
550D4—121no—
551D4—181no—
552D4—361no—
553D4—361no—
554D4—361no—
555D4—361no—
556C2×C4—31no—
557C2×C4—31no—
558C2×C4—31no—
559C2×C4—31no—
560C2×C4—31no—
561C2×C4—41no—
562C2×C4—122no—
563C2×C4—122no—
564C2×C4—121no—
565C2×C4—121no—
566C2×C4—361no—
567C2×C4—361no—
568C2×C4—361no—
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—241no—
582C2×C3C2×D3×D811yescharacteristic
583C2×C3C22×#21311yescharacteristic
584D3—21no—
585D3—81no—
586D3—241no—
587D3—241no—
588D3—481no—
589D3#517912yesdirect product factor
590C22—31no—
591C22—31no—
592C22—62no—
593C22—121no—
594C22—361no—
595C22—722no—
596C22D3×#21311yescharacteristic
597C4—31no—
598C4—31no—
599C4—42no—
600C4—122no—
601C4—121no—
602C4—361no—
603C4D3×#21311yescharacteristic
604C4C2×D3×#6711yescharacteristic
605C3—21no—
606C3D3×#51011yescharacteristic, complemented
607C3C2×#517911yescharacteristic, complemented
608C2—21no—
609C2—32no—
610C2—61no—
611C2—241no—
612C2—721no—
613C2C2×D3×#21311yescharacteristic
subgroupG/H
centerC2C2×D3×#213
commutator, cosocleC32×C8C24
FrattiniC8C22×D32
FittingC2×C32×Q16C22
socleC2×C32C22×D8
prime radicalD3×#904C2
hypercenterC2×Q16D32
hypocenterC32C2×#510
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
1. C2×C3×D3×Q16C2semidirect
3. #10592878C2semidirect
4. C3×#5179C2semidirect
5. #10591047C2semidirect
6. #10591045C2semidirect
7. D3×#829C2semidirect
8. D3×#828C2semidirect
9. #10590642C2semidirect
10. #10590636C2semidirect
11. D3×#812C2semidirect
16. C2×C32×Q16C22semidirect
22. C3×D3×Q16C22semidirect
23. C2×C3×Dic12C22semidirect
33. #63656C22semidirect
34. #63655C22semidirect
35. #63639C22semidirect
36. C3×#829C22semidirect
37. C3×#828C22semidirect
38. C3×#812C22semidirect
39. #63551C22semidirect
40. #63550C22semidirect
41. #63549C22semidirect
42. #63547C22semidirect
43. #63543C22semidirect
47. C2×D3×Q16D3semidirect
59. #5179D3direct (N × H)
124. C2×C3×Q16C2×D3semidirect
125. C2×C3×Q16C2×D3semidirect
134. D3×Q16C2×D3semidirect
140. C2×Dic12C2×D3semidirect
161. #829C2×D3semidirect
167. #828C2×D3semidirect
173. #812C2×D3semidirect
352. C2×Q16D32semidirect
457. C3×D3#510semidirect
537. C32C2×#510semidirect
589. D3#5179direct (N × H)
606. C3D3×#510semidirect
607. C3C2×#5179semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×Q162
D3×#9042
#105928782
C3×#51792
#105910472
#105910452
D3×#8292
D3×#8282
#105906422
#105906362
D3×#8122
C2×#51793
D3×#5103