Finite Group Databasebeta

← D3×#5081 #11875026

Subgroups — D3×#5081 #11875026

Order 1152.

813 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×C4⋊Q8C211yesmaximal, characteristic
2D3×#870C211yesmaximal, characteristic
3#10592780C211yesmaximal, characteristic, complemented
4C3×#5081C211yesmaximal, characteristic, complemented
5D3×#808C212yesmaximal
6D3×#807C212yesmaximal
7#10590421C212yesmaximal, complemented
8#10590420C212yesmaximal, complemented
9D3×#803C211yesmaximal, characteristic
10#10590315C211yesmaximal, characteristic, complemented
11#10590305C211yesmaximal, characteristic, complemented
12C2×#5081—31nomaximal
13D3×#501—31nomaximal
14C2×C3×D3×Q8—21no—
15C32×C4⋊Q8C2211yescharacteristic
16#64079C2211yescharacteristic
17C3×#944—21no—
18C3×D3×C4⋊C4—21no—
19C3×D3×C4⋊C4C2212yes—
20C3×#888—21no—
21C3×#888C2212yes—
22C3×C42×D3C2211yescharacteristic
23C3×#870C2211yescharacteristic
24C3×#869C2211yescharacteristic
25D3×C4⋊Dic3C2211yescharacteristic
26D3×C4⋊Dic3C2211yescharacteristic
27D3×Dic3⋊C4—21no—
28D3×Dic3⋊C4—21no—
29#63869C2211yescharacteristic
30#63869C2211yescharacteristic
31#63867—21no—
32#63867—21no—
33C2×D3×C3⋊C8C2212yes—
34#63635C2212yes—
35#63634C2212yes—
36#63630C2211yescharacteristic
37C3×#808C2212yes—
38C3×#807C2212yes—
39C3×#803C2211yescharacteristic
40#63576C2212yes—
41#63575C2212yes—
42#63574C2212yes—
43#63573C2212yes—
44#63554C2212yes—
45C2×C3×C4⋊Q8—31no—
46D3×C4⋊Q8D311yescharacteristic
47D3×#125—31no—
48C2×#870—31no—
49C3×#501—31no—
50#5081—31no—
51#5081—31no—
52#5081—31no—
53#5081—32no—
54#5081—32no—
55#5081—31no—
56#5081—61no—
57#5081D311yescharacteristic, direct product factor
58#5064—31no—
59C2×#808—32no—
60C2×#807—32no—
61C2×#803—31no—
62D3×#107—32no—
63#4876—32no—
64D3×#106—32no—
65#4856—32no—
66D3×#97—31no—
67#4702—31no—
68C2×C32×Q8—21no—
69C3×D3×Q8—44no—
70C2×C3×C4×D3—22no—
71C2×C3×C4×D3D411yescharacteristic
72C2×C3×C4×D3D411yescharacteristic
73C2×C3×C4×D3C2311yescharacteristic
74C2×C3×Dic6—21no—
75C2×C3×Dic6—22no—
76C2×D3×Dic3—21no—
77C2×D3×Dic3—21no—
78C32×C4⋊C4—21no—
79C32×C4⋊C4C2312yes—
80C32×C42C2311yescharacteristic
81C4⋊(C3⋊Dic3)C2311yescharacteristic
82C4⋊(C3⋊Dic3)C2311yescharacteristic
83#3750—21no—
84#3750—21no—
85C2×C3⋊(C3⋊C8)C2312yes—
86C3×C4⋊Dic3—21no—
87C3×C4⋊Dic3C2312yes—
88C3×C4⋊Dic3C2311yescharacteristic
89C3×C4⋊Dic3C2311yescharacteristic
90C3×Dic3⋊C4—21no—
91C3×Dic3⋊C4—21no—
92C3×Dic3⋊C4—22no—
93C3×Dic3⋊C4—22no—
94C3×C4×Dic3D411yescharacteristic
95C3×C4×Dic3D411yescharacteristic
96C3×C4×Dic3C2311yescharacteristic
97C2×C3×C3⋊C8C2312yes—
98#3724—21no—
99#3724—21no—
100Dic3⋊Dic3—21no—
101Dic3⋊Dic3—21no—
102Dic3⋊Dic3—21no—
103Dic3⋊Dic3—21no—
104D3×C3⋊C8Q818yescomplemented
105C2×#501—91noSylow
106C22×C3×Q8—61no—
107C2×D3×Q8—21no—
108C3×C4⋊Q8—21no—
109C3×C4⋊Q8—32no—
110C3×C4⋊Q8—31no—
111C3×C4⋊Q8—61no—
112C3×C4⋊Q8—61no—
113C3×C4⋊Q8C2×D311yescharacteristic
114C3×C4⋊Q8C2×D311yescharacteristic
115C3×#125—31no—
116C2×C3×C4⋊C4—32no—
117C2×C3×C4⋊C4—61no—
118C2×C3×C42—31no—
119#944—21no—
120C2×C4⋊Dic3—31no—
121C2×C4⋊Dic3—31no—
122C2×Dic3⋊C4—61no—
123C2×Dic3⋊C4—61no—
124C22×C3⋊C8—32no—
125C2×D3×C8—32no—
126D3×C4⋊C4—21no—
127D3×C4⋊C4—31no—
128D3×C4⋊C4—31no—
129D3×C4⋊C4—61no—
130D3×C4⋊C4—61no—
131D3×C4⋊C4C2×D312yes—
132#890—31no—
133#890—31no—
134#889—61no—
135#889—61no—
136#888—21no—
137#888C2×D312yes—
138C42×D3C2×D311yescharacteristic
139#870—31no—
140#870—31no—
141#870—31no—
142#870—31no—
143#870—61no—
144#870—61no—
145#870—61no—
146#870C2×D311yescharacteristic
147#869C2×D311yescharacteristic
148C3×#107—32no—
149C3×#106—32no—
150C3×#97—31no—
151#818—32no—
152#817—32no—
153#815—32no—
154#808—32no—
155#808—32no—
156#808—32no—
157#808—32no—
158#808—32no—
159#808—62no—
160#808C2×D312yes—
161#807—32no—
162#807—32no—
163#807—32no—
164#807—32no—
165#807—32no—
166#807—62no—
167#807C2×D312yes—
168#803—31no—
169#803—31no—
170#803—32no—
171#803—61no—
172#803C2×D311yescharacteristic
173C22×C3×D3C2×D411yescharacteristic
174C32×Q8—42no—
175C2×C32×C4—22no—
176C2×C32×C4C2×D411yescharacteristic
177C2×C32×C4C2×D411yescharacteristic
178C2×C32×C4C2411yescharacteristic
179C2×C3⋊Dic3—21no—
180C2×C3⋊Dic3—21no—
181C2×C3×Dic3—21no—
182C2×C3×Dic3—21no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3C2×D411yescharacteristic
185C2×C3×Dic3C2×D411yescharacteristic
186C2×C3×Dic3C2×D411yescharacteristic
187C3×C4×D3—22no—
188C3×C4×D3—22no—
189C3×C4×D3—44no—
190C3×C4×D3C2×Q814yes—
191C3×Dic6—44no—
192C3×Dic6—42no—
193D3×Dic3—42no—
194D3×Dic3—42no—
195C3⋊(C3⋊C8)C2×Q814yescomplemented
196C3×C3⋊C8C2×Q814yescomplemented
197C2×C4⋊Q8—31no—
198C2×#125—91no—
199#501—31no—
200#501—91no—
201#501—92no—
202#501—92no—
203#501—91no—
204#501—91no—
205C2×#107—92no—
206C2×#106—92no—
207C2×#97—91no—
208C2×C3×Q8—21no—
209C2×C3×Q8—21no—
210C2×C3×Q8—41no—
211C2×C3×Q8—62no—
212C2×C3×Q8—61no—
213C2×C3×Q8—124no—
214C22×C3×C4—31no—
215C22×C3×C4—31no—
216C22×C3×C4—31no—
217C22×C3×C4—62no—
218C22×Dic3—61no—
219C22×Dic3—61no—
220D3×Q8—44no—
221C2×C4×D3—22no—
222C2×C4×D3—61no—
223C2×C4×D3—61no—
224C2×C4×D3#6711yescharacteristic
225C2×C4×D3#6711yescharacteristic
226C2×C4×D3C22×D311yescharacteristic
227C2×Dic6—21no—
228C2×Dic6—22no—
229C2×C3×C8—32no—
230C3×C4⋊C4—21no—
231C3×C4⋊C4—21no—
232C3×C4⋊C4—22no—
233C3×C4⋊C4—32no—
234C3×C4⋊C4—31no—
235C3×C4⋊C4—31no—
236C3×C4⋊C4—41no—
237C3×C4⋊C4—62no—
238C3×C4⋊C4—62no—
239C3×C4⋊C4—61no—
240C3×C4⋊C4—61no—
241C3×C4⋊C4—61no—
242C3×C4⋊C4C22×D312yes—
243C3×C4⋊C4C22×D312yes—
244C3×C42—21no—
245C3×C42—31no—
246C3×C42—31no—
247C3×C42—31no—
248C3×C42C22×D311yescharacteristic
249C3×C42C22×D311yescharacteristic
250C4⋊Dic3—21no—
251C4⋊Dic3—31no—
252C4⋊Dic3—31no—
253C4⋊Dic3—31no—
254C4⋊Dic3—31no—
255C4⋊Dic3—61no—
256C4⋊Dic3—61no—
257C4⋊Dic3—61no—
258C4⋊Dic3—61no—
259C4⋊Dic3—61no—
260C4⋊Dic3—61no—
261C4⋊Dic3C22×D311yescharacteristic
262C4⋊Dic3C22×D312yes—
263C4⋊Dic3C22×D311yescharacteristic
264Dic3⋊C4—21no—
265Dic3⋊C4—21no—
266Dic3⋊C4—22no—
267Dic3⋊C4—22no—
268Dic3⋊C4—61no—
269Dic3⋊C4—61no—
270Dic3⋊C4—61no—
271Dic3⋊C4—61no—
272Dic3⋊C4—61no—
273Dic3⋊C4—61no—
274Dic3⋊C4—61no—
275Dic3⋊C4—61no—
276Dic3⋊C4—61no—
277Dic3⋊C4—61no—
278Dic3⋊C4—61no—
279Dic3⋊C4—61no—
280Dic3⋊C4—121no—
281Dic3⋊C4—121no—
282C4×Dic3#6711yescharacteristic
283C4×Dic3#6711yescharacteristic
284C4×Dic3C22×D311yescharacteristic
285C2×C3⋊C8—32no—
286C2×C3⋊C8—32no—
287C2×C3⋊C8—38no—
288C2×C3⋊C8—62no—
289C2×C3⋊C8C22×D312yes—
290D3×C8—38no—
291C22×C32C22×D411yescharacteristic
292C2×C3×D3C4⋊Q812yes—
293C2×C3×D3AGL(1,ℤ/8)12yes—
294C2×C3×D3#13712yes—
295C32×C4—21no—
296C32×C4—21no—
297C32×C4—42no—
298C32×C4C22×Q812yes—
299C3⋊Dic3—41no—
300C3⋊Dic3—41no—
301C3×Dic3—21no—
302C3×Dic3—21no—
303C3×Dic3—41no—
304C3×Dic3—42no—
305C3×Dic3—41no—
306C3×Dic3C4⋊Q812yes—
307C22×Q8—61no—
308C22×C8—92no—
309C4⋊Q8—32no—
310C4⋊Q8—31no—
311C4⋊Q8—61no—
312C4⋊Q8—61no—
313C4⋊Q8D3211yescharacteristic
314#125—31no—
315#125—91no—
316#125—91no—
317#125—91no—
318#125—181no—
319#125—181no—
320C2×C4⋊C4—32no—
321C2×C4⋊C4—61no—
322C2×C4⋊C4—91no—
323C2×C4⋊C4—91no—
324C2×C4⋊C4—181no—
325C2×C4⋊C4—181no—
326C2×C42—31no—
327#107—32no—
328#107—92no—
329#107—92no—
330#107—92no—
331#106—32no—
332#106—92no—
333#106—92no—
334#106—92no—
335#97—31no—
336#97—92no—
337#97—91no—
338C23×C3—31no—
339C22×D3C2×#6711yescharacteristic
340C3×Q8—42no—
341C3×Q8—42no—
342C3×Q8—82no—
343C3×Q8—122no—
344C3×Q8—124no—
345C2×C3×C4—22no—
346C2×C3×C4—22no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—31no—
351C2×C3×C4—34no—
352C2×C3×C4—31no—
353C2×C3×C4—31no—
354C2×C3×C4—42no—
355C2×C3×C4—62no—
356C2×C3×C4—62no—
357C2×C3×C4—62no—
358C2×C3×C4—61no—
359C2×C3×C4—61no—
360C2×C3×C4—124no—
361C2×C3×C4D3×D411yescharacteristic
362C2×C3×C4D3×D411yescharacteristic
363C2×C3×C4C2×#6711yescharacteristic
364C2×C3×C4C2×#6711yescharacteristic
365C2×C3×C4C23×D311yescharacteristic
366C2×C3×C4C23×D311yescharacteristic
367C2×Dic3—21no—
368C2×Dic3—21no—
369C2×Dic3—22no—
370C2×Dic3—61no—
371C2×Dic3—61no—
372C2×Dic3—61no—
373C2×Dic3—61no—
374C2×Dic3—121no—
375C2×Dic3—121no—
376C2×Dic3—122no—
377C2×Dic3—122no—
378C2×Dic3C2×#6711yescharacteristic
379C2×Dic3C2×#6711yescharacteristic
380C2×Dic3C2×#6711yescharacteristic
381C4×D3—22no—
382C4×D3—22no—
383C4×D3—44no—
384C4×D3—122no—
385C4×D3—122no—
386C4×D3D3×Q814yes—
387Dic6—44no—
388Dic6—42no—
389C3×C8—34no—
390C3⋊C8—34no—
391C3⋊C8—34no—
392C3⋊C8—64no—
393C3⋊C8D3×Q814yescomplemented
394C2×C32C2×C4⋊Q811yescharacteristic
395C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
396C2×C32C2×#13711yescharacteristic
397C3×D3#50114yescomplemented
398C2×Q8—21no—
399C2×Q8—62no—
400C2×Q8—61no—
401C2×Q8—124no—
402C22×C4—31no—
403C22×C4—31no—
404C22×C4—31no—
405C22×C4—62no—
406C22×C4—181no—
407C22×C4—181no—
408C2×C8—32no—
409C2×C8—98no—
410C2×C8—92no—
411C4⋊C4—21no—
412C4⋊C4—31no—
413C4⋊C4—32no—
414C4⋊C4—31no—
415C4⋊C4—62no—
416C4⋊C4—62no—
417C4⋊C4—61no—
418C4⋊C4—61no—
419C4⋊C4—61no—
420C4⋊C4—91no—
421C4⋊C4—91no—
422C4⋊C4—181no—
423C4⋊C4—181no—
424C4⋊C4—181no—
425C4⋊C4—181no—
426C4⋊C4—181no—
427C4⋊C4—181no—
428C4⋊C4—181no—
429C4⋊C4—181no—
430C4⋊C4C2×D3212yes—
431C42—31no—
432C42—31no—
433C42—31no—
434C42C2×D3211yescharacteristic
435C22×C3—21no—
436C22×C3—32no—
437C22×C3—32no—
438C22×C3—32no—
439C22×C3C2×D3×D411yescharacteristic
440C22×C3C22×#6711yescharacteristic
441C2×D3#93212yes—
442C2×D3#94212yes—
443C2×D3#94412yes—
444C3×C4—21no—
445C3×C4—21no—
446C3×C4—21no—
447C3×C4—21no—
448C3×C4—22no—
449C3×C4—32no—
450C3×C4—41no—
451C3×C4—41no—
452C3×C4—42no—
453C3×C4—42no—
454C3×C4—61no—
455C3×C4—61no—
456C3×C4—82no—
457C3×C4—122no—
458C3×C4—121no—
459C3×C4—121no—
460C3×C4C2×D3×Q812yes—
461C3×C4C2×D3×Q812yes—
462Dic3—21no—
463Dic3—21no—
464Dic3—41no—
465Dic3—41no—
466Dic3—42no—
467Dic3—121no—
468Dic3—121no—
469Dic3—121no—
470Dic3—121no—
471Dic3—241no—
472Dic3—241no—
473Dic3#94412yes—
474C32C2×#50111yescharacteristic, complemented, Sylow
475C23—31no—
476Q8—42no—
477Q8—122no—
478Q8—124no—
479C2×C4—22no—
480C2×C4—31no—
481C2×C4—34no—
482C2×C4—31no—
483C2×C4—31no—
484C2×C4—62no—
485C2×C4—62no—
486C2×C4—62no—
487C2×C4—61no—
488C2×C4—61no—
489C2×C4—124no—
490C2×C4—181no—
491C2×C4—181no—
492C2×C4—362no—
493C2×C4—362no—
494C2×C4D3×#6711yescharacteristic
495C2×C4D3×#6711yescharacteristic
496C2×C4C22×D3211yescharacteristic
497C8—34no—
498C8—94no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3—34no—
503C2×C3D3×C4⋊Q811yescharacteristic
504C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
505C2×C3D3×#13711yescharacteristic
506C2×C3C2×#93211yescharacteristic
507C2×C3C2×#94211yescharacteristic
508C2×C3C2×#94411yescharacteristic
509D3#508114yesdirect product factor
510C22—32no—
511C22—32no—
512C22—32no—
513C22C2×D3×#6711yescharacteristic
514C4—21no—
515C4—21no—
516C4—32no—
517C4—42no—
518C4—61no—
519C4—61no—
520C4—122no—
521C4—121no—
522C4—121no—
523C4—361no—
524C4—361no—
525C4D32×Q812yes—
526C3—21no—
527C3D3×#50111yescharacteristic, complemented
528C3C2×#508111yescharacteristic, complemented
529C2—34no—
530C2D3×#93211yescharacteristic
531C2D3×#94211yescharacteristic
532C2D3×#94411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenterC4⋊Q8D32
hypocenterC32C2×#501
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. #10592780C2semidirect
4. C3×#5081C2semidirect
7. #10590421C2semidirect
8. #10590420C2semidirect
10. #10590315C2semidirect
11. #10590305C2semidirect
57. #5081D3direct (N × H)
104. D3×C3⋊C8Q8semidirect
195. C3⋊(C3⋊C8)C2×Q8semidirect
196. C3×C3⋊C8C2×Q8semidirect
393. C3⋊C8D3×Q8semidirect
397. C3×D3#501semidirect
474. C32C2×#501semidirect
509. D3#5081direct (N × H)
527. C3D3×#501semidirect
528. C3C2×#5081semidirect

Maximal subgroups

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

subgroupindex
C3×D3×C4⋊Q82
D3×#8702
#105927802
C3×#50812
D3×#8082
D3×#8072
#105904212
#105904202
D3×#8032
#105903152
#105903052
C2×#50813
D3×#5013