Finite Group Databasebeta

← D3×#4702 #11875032

Subgroups — D3×#4702 #11875032

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
1D3×#870C211yesmaximal, characteristic
2D3×#869C211yesmaximal, characteristic
3#10592401C211yesmaximal, characteristic, complemented
4C3×D3×#97C211yesmaximal, characteristic
5C3×#4702C211yesmaximal, characteristic, complemented
6#10590894C212yesmaximal, complemented
7#10590892C212yesmaximal, complemented
8D3×#818C212yesmaximal
9D3×#817C212yesmaximal
10#10590306C211yesmaximal, characteristic, complemented
11#10590305C211yesmaximal, characteristic, complemented
12D3×#501—31nomaximal
13C2×#4702—31nomaximal
14C2×D3×Dic6—21no—
15#64079C2211yescharacteristic
16#64078C2211yescharacteristic
17C2×C3×D3×C8C2212yes—
18C3×C42×D3C2211yescharacteristic
19C3×#870C2211yescharacteristic
20C3×#869C2211yescharacteristic
21#63918—21no—
22#63918C2212yes—
23D3×C4⋊Dic3—21no—
24D3×C4⋊Dic3C2212yes—
25D3×C4⋊Dic3C2211yescharacteristic
26D3×C4⋊Dic3C2211yescharacteristic
27D3×Dic3⋊C4—21no—
28D3×Dic3⋊C4—21no—
29#63869C2211yescharacteristic
30#63869C2211yescharacteristic
31#63867—21no—
32#63867—21no—
33#63866—21no—
34C32×#97C2211yescharacteristic
35#63645C2212yes—
36#63644C2212yes—
37C3×#818C2212yes—
38C3×#817C2212yes—
39C3×#815C2212yes—
40C3×#803C2211yescharacteristic
41#63575C2212yes—
42#63575C2212yes—
43#63573C2212yes—
44#63573C2212yes—
45D3×C4⋊Q8—31no—
46D3×#125—31no—
47C2×#870—31no—
48C2×#869—31no—
49C3×#501—31no—
50C2×C3×#97—31no—
51C2×#818—32no—
52C2×#817—32no—
53#5081—31no—
54#5064—31no—
55D3×#107—32no—
56#4876—32no—
57D3×#106—32no—
58#4856—32no—
59D3×#97D311yescharacteristic
60#4702—31no—
61#4702—31no—
62#4702—31no—
63#4702—31no—
64#4702—32no—
65#4702—32no—
66#4702—61no—
67#4702D311yescharacteristic, direct product factor
68C2×#634—21no—
69C2×C3×C4×D3D411yescharacteristic
70C2×C3×C4×D3D411yescharacteristic
71C2×C3×C4×D3C2311yescharacteristic
72C2×C3×Dic6—21no—
73C2×#627—22no—
74C2×D3×Dic3—22no—
75C2×D3×Dic3—21no—
76C2×D3×Dic3—21no—
77D3×Dic6—44no—
78C2×C32×C8C2312yes—
79C32×C42C2311yescharacteristic
80C4⋊(C3⋊Dic3)—21no—
81C4⋊(C3⋊Dic3)C2312yes—
82C4⋊(C3⋊Dic3)C2311yescharacteristic
83C4⋊(C3⋊Dic3)C2311yescharacteristic
84#3750—21no—
85#3750—21no—
86C3×C4⋊Dic3—21no—
87C3×C4⋊Dic3C2311yescharacteristic
88C3×C4⋊Dic3C2312yes—
89C3×C4⋊Dic3C2311yescharacteristic
90C3×Dic3⋊C4—21no—
91C3×Dic3⋊C4—21no—
92C3×C4×Dic3D411yescharacteristic
93C3×C4×Dic3D411yescharacteristic
94C3×C4×Dic3C2311yescharacteristic
95C2×C3×C3⋊C8C2312yes—
96C3×D3×C8Q818yescomplemented
97#3724—21no—
98#3724—21no—
99Dic3⋊Dic3—22no—
100Dic3⋊Dic3—22no—
101Dic3⋊Dic3—21no—
102Dic3⋊Dic3—21no—
103Dic3⋊Dic3—21no—
104Dic3⋊Dic3—21no—
105C2×#501—91noSylow
106C2×D3×Q8—61no—
107C22×Dic6—61no—
108C22×C3×C8—32no—
109C3×C4⋊Q8—31no—
110C3×#125—31no—
111C2×C3×C42—31no—
112#944—61no—
113C2×C4⋊Dic3—32no—
114C2×C4⋊Dic3—31no—
115C2×C4⋊Dic3—31no—
116C2×C4⋊Dic3—61no—
117C2×Dic3⋊C4—61no—
118C2×Dic3⋊C4—61no—
119C2×D3×C8C2×D312yes—
120D3×C4⋊C4—31no—
121D3×C4⋊C4—32no—
122D3×C4⋊C4—31no—
123D3×C4⋊C4—61no—
124D3×C4⋊C4—61no—
125D3×C4⋊C4—61no—
126#890—31no—
127#890—31no—
128#889—61no—
129#889—61no—
130#888—32no—
131#888—61no—
132C42×D3C2×D311yescharacteristic
133#870—31no—
134#870—31no—
135#870—31no—
136#870—31no—
137#870—61no—
138#870—61no—
139#870—61no—
140#870C2×D311yescharacteristic
141#869—31no—
142#869—31no—
143#869—32no—
144#869—61no—
145#869—61no—
146#869—61no—
147#869C2×D311yescharacteristic
148C3×#107—32no—
149C3×#106—32no—
150C3×#97—21no—
151C3×#97—32no—
152C3×#97—31no—
153C3×#97C2×D311yescharacteristic
154C3×#97C2×D311yescharacteristic
155#818—32no—
156#818—32no—
157#818—32no—
158#818—32no—
159#818—62no—
160#818C2×D312yes—
161#817—32no—
162#817—32no—
163#817—32no—
164#817—32no—
165#817—62no—
166#817C2×D312yes—
167#815C2×D312yes—
168#808—32no—
169#808—32no—
170#807—32no—
171#807—32no—
172#803C2×D311yescharacteristic
173C22×C3×D3C2×D411yescharacteristic
174C2×C32×C4C2×D411yescharacteristic
175C2×C32×C4C2×D411yescharacteristic
176C2×C32×C4C2411yescharacteristic
177C2×C3⋊Dic3—21no—
178C2×C3⋊Dic3—21no—
179C2×C3⋊Dic3—22no—
180#634—42no—
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×D3C2×Q814yes—
190C3×Dic6—42no—
191#627—44no—
192D3×Dic3—44no—
193D3×Dic3—42no—
194D3×Dic3—42no—
195C32×C8C2×Q814yescomplemented
196C3×C3⋊C8C2×Q814yescomplemented
197C2×C4⋊Q8—91no—
198C2×#125—91no—
199#501—31no—
200#501—92no—
201#501—92no—
202#501—91no—
203#501—91no—
204#501—91no—
205C2×#107—92no—
206C2×#106—92no—
207C2×#97—31no—
208C2×C3×Q8—61no—
209C22×C3×C4—31no—
210C22×C3×C4—31no—
211C22×C3×C4—31no—
212C22×Dic3—61no—
213C22×Dic3—61no—
214C22×Dic3—62no—
215D3×Q8—124no—
216C2×C4×D3—61no—
217C2×C4×D3—61no—
218C2×C4×D3—62no—
219C2×C4×D3D1211yescharacteristic
220C2×C4×D3D1211yescharacteristic
221C2×C4×D3C22×D311yescharacteristic
222C2×Dic6—21no—
223C2×Dic6—62no—
224C2×Dic6—61no—
225C2×Dic6—61no—
226C2×Dic6—62no—
227C2×Dic6—121no—
228C2×Dic6—124no—
229C2×C3×C8—22no—
230C2×C3×C8—32no—
231C2×C3×C8—38no—
232C2×C3×C8C22×D312yes—
233C2×C3×C8C22×D312yes—
234C3×C4⋊C4—31no—
235C3×C4⋊C4—32no—
236C3×C4⋊C4—31no—
237C3×C4⋊C4—61no—
238C3×C4⋊C4—61no—
239C3×C4⋊C4—61no—
240C3×C42—21no—
241C3×C42—31no—
242C3×C42—31no—
243C3×C42—31no—
244C3×C42C22×D311yescharacteristic
245C3×C42C22×D311yescharacteristic
246C4⋊Dic3—21no—
247C4⋊Dic3—31no—
248C4⋊Dic3—32no—
249C4⋊Dic3—31no—
250C4⋊Dic3—31no—
251C4⋊Dic3—32no—
252C4⋊Dic3—31no—
253C4⋊Dic3—61no—
254C4⋊Dic3—62no—
255C4⋊Dic3—61no—
256C4⋊Dic3—62no—
257C4⋊Dic3—62no—
258C4⋊Dic3—61no—
259C4⋊Dic3—61no—
260C4⋊Dic3—61no—
261C4⋊Dic3—61no—
262C4⋊Dic3—61no—
263C4⋊Dic3—61no—
264C4⋊Dic3—121no—
265C4⋊Dic3C22×D311yescharacteristic
266C4⋊Dic3C22×D312yes—
267C4⋊Dic3C22×D311yescharacteristic
268Dic3⋊C4—21no—
269Dic3⋊C4—21no—
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—62no—
279Dic3⋊C4—62no—
280Dic3⋊C4—61no—
281Dic3⋊C4—61no—
282Dic3⋊C4—61no—
283Dic3⋊C4—61no—
284Dic3⋊C4—121no—
285Dic3⋊C4—121no—
286C4×Dic3D1211yescharacteristic
287C4×Dic3D1211yescharacteristic
288C4×Dic3C22×D311yescharacteristic
289C2×C3⋊C8C22×D312yes—
290D3×C8Dic618yescomplemented
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×C4C22×Q812yes—
298C3⋊Dic3—42no—
299C3⋊Dic3—41no—
300C3⋊Dic3—41no—
301C3×Dic3—21no—
302C3×Dic3—21no—
303C3×Dic3—42no—
304C3×Dic3—41no—
305C3×Dic3—41no—
306C3×Dic3C4⋊Q812yes—
307C22×Q8—181no—
308C22×C8—32no—
309C4⋊Q8—31no—
310C4⋊Q8—92no—
311C4⋊Q8—91no—
312C4⋊Q8—181no—
313C4⋊Q8—181no—
314#125—31no—
315#125—91no—
316#125—91no—
317#125—91no—
318#125—181no—
319#125—181no—
320C2×C4⋊C4—91no—
321C2×C4⋊C4—91no—
322C2×C4⋊C4—92no—
323C2×C4⋊C4—181no—
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—32no—
336#97—31no—
337#97D3211yescharacteristic
338C23×C3—31no—
339C22×D3C2×D1211yescharacteristic
340C3×Q8—122no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—31no—
345C2×C3×C4—34no—
346C2×C3×C4—31no—
347C2×C3×C4—31no—
348C2×C3×C4—62no—
349C2×C3×C4—62no—
350C2×C3×C4—61no—
351C2×C3×C4—61no—
352C2×C3×C4—62no—
353C2×C3×C4C2×D1211yescharacteristic
354C2×C3×C4C2×D1211yescharacteristic
355C2×C3×C4D3×D411yescharacteristic
356C2×C3×C4D3×D411yescharacteristic
357C2×C3×C4C23×D311yescharacteristic
358C2×C3×C4C23×D311yescharacteristic
359C2×Dic3—21no—
360C2×Dic3—21no—
361C2×Dic3—22no—
362C2×Dic3—61no—
363C2×Dic3—61no—
364C2×Dic3—62no—
365C2×Dic3—61no—
366C2×Dic3—61no—
367C2×Dic3—62no—
368C2×Dic3—121no—
369C2×Dic3—121no—
370C2×Dic3—122no—
371C2×Dic3—124no—
372C2×Dic3—122no—
373C2×Dic3—122no—
374C2×Dic3C2×D1211yescharacteristic
375C2×Dic3C2×D1211yescharacteristic
376C2×Dic3C2×D1211yescharacteristic
377C4×D3—22no—
378C4×D3—22no—
379C4×D3—122no—
380C4×D3—124no—
381C4×D3—122no—
382C4×D3C2×Dic614yes—
383Dic6—42no—
384Dic6—124no—
385Dic6—124no—
386Dic6—122no—
387Dic6—122no—
388Dic6—242no—
389C3×C8—24no—
390C3×C8—34no—
391C3×C8C2×Dic614yescomplemented
392C3×C8D3×Q814yescomplemented
393C3⋊C8C2×Dic614yescomplemented
394C2×C32C2×C4⋊Q811yescharacteristic
395C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
396C2×C32C2×#13711yescharacteristic
397C3×D3#50114yescomplemented
398C2×Q8—61no—
399C2×Q8—182no—
400C2×Q8—181no—
401C2×Q8—364no—
402C22×C4—31no—
403C22×C4—31no—
404C22×C4—31no—
405C22×C4—181no—
406C22×C4—181no—
407C22×C4—182no—
408C2×C8—32no—
409C2×C8—38no—
410C2×C8C2×D3212yes—
411C4⋊C4—31no—
412C4⋊C4—32no—
413C4⋊C4—31no—
414C4⋊C4—61no—
415C4⋊C4—61no—
416C4⋊C4—61no—
417C4⋊C4—91no—
418C4⋊C4—92no—
419C4⋊C4—91no—
420C4⋊C4—181no—
421C4⋊C4—181no—
422C4⋊C4—182no—
423C4⋊C4—181no—
424C4⋊C4—181no—
425C4⋊C4—181no—
426C4⋊C4—181no—
427C4⋊C4—182no—
428C4⋊C4—181no—
429C4⋊C4—181no—
430C4⋊C4—181no—
431C42—31no—
432C42—31no—
433C42—31no—
434C42C2×D3211yescharacteristic
435C22×C3—21no—
436C22×C3—32no—
437C22×C3—32no—
438C22×C3—32no—
439C22×C3C22×D1211yescharacteristic
440C22×C3C2×D3×D411yescharacteristic
441C2×D3#86912yes—
442C2×D3#90812yes—
443C2×D3#90912yes—
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—61no—
453C3×C4—61no—
454C3×C4—122no—
455C3×C4—121no—
456C3×C4—121no—
457C3×C4C22×Dic612yes—
458C3×C4C2×D3×Q812yes—
459Dic3—21no—
460Dic3—21no—
461Dic3—42no—
462Dic3—41no—
463Dic3—41no—
464Dic3—122no—
465Dic3—121no—
466Dic3—121no—
467Dic3—122no—
468Dic3—121no—
469Dic3—121no—
470Dic3—242no—
471Dic3—241no—
472Dic3—241no—
473Dic3#86912yes—
474C32C2×#50111yescharacteristic, complemented, Sylow
475C23—31no—
476Q8—122no—
477Q8—362no—
478Q8—364no—
479C2×C4—31no—
480C2×C4—34no—
481C2×C4—31no—
482C2×C4—31no—
483C2×C4—62no—
484C2×C4—62no—
485C2×C4—61no—
486C2×C4—61no—
487C2×C4—62no—
488C2×C4—181no—
489C2×C4—181no—
490C2×C4—182no—
491C2×C4—364no—
492C2×C4—362no—
493C2×C4—362no—
494C2×C4D3×D1211yescharacteristic
495C2×C4D3×D1211yescharacteristic
496C2×C4C22×D3211yescharacteristic
497C8—34no—
498C8D3×Dic614yescomplemented
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3—34no—
503C2×C3C2×#86911yescharacteristic
504C2×C3D3×C4⋊Q811yescharacteristic
505C2×C3C2×#90811yescharacteristic
506C2×C3C2×#90911yescharacteristic
507C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
508C2×C3D3×#13711yescharacteristic
509D3#470214yesdirect product factor
510C22—32no—
511C22—32no—
512C22—32no—
513C22C2×D3×D1211yescharacteristic
514C4—21no—
515C4—21no—
516C4—32no—
517C4—61no—
518C4—61no—
519C4—122no—
520C4—121no—
521C4—121no—
522C4—362no—
523C4—361no—
524C4—361no—
525C4C2×D3×Dic612yes—
526C3—21no—
527C3C2×#470211yescharacteristic, complemented
528C3D3×#50111yescharacteristic, complemented
529C2—34no—
530C2D3×#86911yescharacteristic
531C2D3×#90811yescharacteristic
532C2D3×#90911yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#97C22
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenter#97D32
hypocenterC32C2×#501
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
3. #10592401C2semidirect
5. C3×#4702C2semidirect
6. #10590894C2semidirect
7. #10590892C2semidirect
10. #10590306C2semidirect
11. #10590305C2semidirect
67. #4702D3direct (N × H)
96. C3×D3×C8Q8semidirect
195. C32×C8C2×Q8semidirect
196. C3×C3⋊C8C2×Q8semidirect
290. D3×C8Dic6semidirect
391. C3×C8C2×Dic6semidirect
392. C3×C8D3×Q8semidirect
393. C3⋊C8C2×Dic6semidirect
397. C3×D3#501semidirect
474. C32C2×#501semidirect
498. C8D3×Dic6semidirect
509. D3#4702direct (N × H)
527. C3C2×#4702semidirect
528. C3D3×#501semidirect

Maximal subgroups

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

subgroupindex
D3×#8702
D3×#8692
#105924012
C3×D3×#972
C3×#47022
#105908942
#105908922
D3×#8182
D3×#8172
#105903062
#105903052
D3×#5013
C2×#47023