Finite Group Databasebeta

← D3×Dic3×Q16 #11859936

Subgroups — D3×Dic3×Q16 #11859936

Order 1152.

1031 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×Q16C211yesmaximal, characteristic
2D3×Q8×Dic3C212yesmaximal
3Q16×C3⋊Dic3C211yesmaximal, characteristic, complemented
4C3×Dic3×Q16C211yesmaximal, characteristic, complemented
5#10591581C212yesmaximal, complemented
6Dic3×#216C212yesmaximal, complemented
7D3×#835C212yesmaximal
8#10590818C211yesmaximal, characteristic, complemented
9Dic3×Dic12C211yesmaximal, characteristic, complemented
10D3×#818C211yesmaximal, characteristic
11D3×C8×Dic3C211yesmaximal, characteristic
12C2×Dic3×Q16—31nomaximal
13C4×D3×Q16—31nomaximal
14C2×C3×D3×Q8C2212yes—
15C2×C32×Q16C2211yescharacteristic
16Q8×C3⋊Dic3C2212yes—
17C3×Q8×Dic3C2212yes—
18C2×C3×#216C2212yes—
19C3×D3×Q16C418yescomplemented
20C2×C3×Dic12C2211yescharacteristic
21C2×C3×D3×C8C2211yescharacteristic
22D3×C4⋊Dic3—22no—
23D3×C4⋊Dic3C2212yes—
24C4×D3×Dic3—22no—
25C4×D3×Dic3C2211yescharacteristic
26#63843—22no—
27#63843C2212yes—
28Dic3×Dic6—22no—
29Dic3×Dic6C2212yes—
30C2×D3×C3⋊C8C2211yescharacteristic
31#63662C2212yes—
32#63645C2211yescharacteristic
33C8×C3⋊Dic3C2211yescharacteristic
34C3×#835C2212yes—
35C3×#818C2211yescharacteristic
36C3×C8×Dic3C2211yescharacteristic
37#63575C2212yes—
38#63566C2212yes—
39#63565C2212yes—
40#63553C2211yescharacteristic
41Dic3×C3⋊C8C2211yescharacteristic
42C22×C3×Q16—31no—
43C2×Q8×Dic3—32no—
44C2×D3×Q16D311yescharacteristic
45C4×D3×Q8—32no—
46C3×C4×Q16—31no—
47C2×#835—32no—
48Dic3×Q16—31no—
49Dic3×Q16—31no—
50Dic3×Q16—32no—
51Dic3×Q16—32no—
52Dic3×Q16—31no—
53Dic3×Q16—31no—
54Dic3×Q16—61no—
55Dic3×Q16D311yescharacteristic, direct product factor
56C2×#818—31no—
57C2×C8×Dic3—31no—
58C4×#216—32no—
59D3×#107—31no—
60#4873—31no—
61D3×#103—32no—
62#4790—32no—
63C4×Dic12—31no—
64C4×D3×C8—31no—
65C2×C32×Q8C2312yes—
66C3×D3×Q8—24no—
67C3×D3×Q8C2×C418yes—
68C2×C3×C4×D3—22no—
69C2×C3×C4×D3C2311yescharacteristic
70C2×C3×Dic6—22no—
71C2×C3×Dic6C2312yes—
72C2×D3×Dic3—22no—
73C2×D3×Dic3D411yescharacteristic
74C2×D3×Dic3D411yescharacteristic
75C32×Q16C2×C414yescomplemented
76C2×C32×C8C2311yescharacteristic
77C4⋊(C3⋊Dic3)—22no—
78C4⋊(C3⋊Dic3)C2312yes—
79C4×C3⋊Dic3—22no—
80C4×C3⋊Dic3C2311yescharacteristic
81C2×C3⋊(C3⋊C8)C2311yescharacteristic
82C3×#216C2×C418yescomplemented
83C3×C4⋊Dic3—22no—
84C3×C4⋊Dic3C2312yes—
85C3×C4×Dic3—22no—
86C3×C4×Dic3C2311yescharacteristic
87C2×C3×C3⋊C8C2311yescharacteristic
88C2×C3×C3⋊C8C2311yescharacteristic
89C3×Dic12C2×C414yescomplemented
90C3×D3×C8C2×C414yes—
91Dic3⋊Dic3—22no—
92Dic3⋊Dic3—22no—
93Dic3⋊Dic3—22no—
94Dic32—22no—
95Dic32—22no—
96Dic32D411yescharacteristic
97Dic32D411yescharacteristic
98D3×C3⋊C8—22no—
99C2×C4×Q16—91noSylow
100C22×C3×Q8—32no—
101C2×D3×Q8C2×D312yes—
102C2×C3×Q16—21no—
103C2×C3×Q16—32no—
104C2×C3×Q16—38no—
105C2×C3×Q16—31no—
106C2×C3×Q16C2×D311yescharacteristic
107C2×C3×Q16C2×D311yescharacteristic
108C22×C3×C8—31no—
109C3×C4×Q8—32no—
110Q8×Dic3—32no—
111Q8×Dic3—32no—
112Q8×Dic3—32no—
113Q8×Dic3—32no—
114Q8×Dic3—62no—
115Q8×Dic3—62no—
116Q8×Dic3—62no—
117Q8×Dic3C2×D312yes—
118C2×#216C2×D312yes—
119C2×C4⋊Dic3—32no—
120C2×C4⋊Dic3—62no—
121C2×C4×Dic3—31no—
122C2×C4×Dic3—62no—
123C22×C3⋊C8—31no—
124D3×Q16Dic318yesdirect product factor
125C2×Dic12C2×D311yescharacteristic
126C2×D3×C8—31no—
127C2×D3×C8C2×D311yescharacteristic
128D3×C4⋊C4—32no—
129D3×C4⋊C4—62no—
130#887—32no—
131#887—62no—
132C42×D3—31no—
133C42×D3—62no—
134C4×Dic6—32no—
135C4×Dic6—62no—
136C3×#107—31no—
137C3×#103—32no—
138C3×C4×C8—31no—
139#835—32no—
140#835—32no—
141#835—32no—
142#835—32no—
143#835—62no—
144#835C2×D312yes—
145#818—31no—
146#818—31no—
147#818—32no—
148#818—61no—
149#818C2×D311yescharacteristic
150#816—32no—
151C8×Dic3—31no—
152C8×Dic3—31no—
153C8×Dic3—31no—
154C8×Dic3—31no—
155C8×Dic3—31no—
156C8×Dic3—61no—
157C8×Dic3C2×D311yescharacteristic
158#810—32no—
159#807—32no—
160C4×C3⋊C8—31no—
161C22×C3×D3C2×D411yescharacteristic
162C32×Q8—22no—
163C32×Q8C22×C414yes—
164C2×C32×C4—22no—
165C2×C32×C4C2411yescharacteristic
166C2×C3⋊Dic3—22no—
167C2×C3⋊Dic3C2×D411yescharacteristic
168C2×C3⋊Dic3C2×D411yescharacteristic
169C2×C3×Dic3—22no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3C2×D411yescharacteristic
172C2×C3×Dic3C2×D411yescharacteristic
173C2×C3×Dic3C2×D411yescharacteristic
174C3×C4×D3—28no—
175C3×C4×D3C22×C412yes—
176C3×C4×D3#4112yes—
177C3×Dic6—22no—
178C3×Dic6—28no—
179C3×Dic6C22×C414yes—
180D3×Dic3—22no—
181D3×Dic3—44no—
182D3×Dic3Q1614yesdirect product factor
183C32×C8C22×C412yes—
184C3⋊(C3⋊C8)—21no—
185C3×C3⋊C8—21no—
186C3×C3⋊C8C22×C412yes—
187C22×Q16—31no—
188C2×C4×Q8—92no—
189C4×Q16—31no—
190C4×Q16—91no—
191C4×Q16—92no—
192C4×Q16—91no—
193C4×Q16—92no—
194C4×Q16—91no—
195C2×#107—91no—
196C2×#103—92no—
197C2×C4×C8—91no—
198C2×C3×Q8—22no—
199C2×C3×Q8—38no—
200C2×C3×Q8—32no—
201C2×C3×Q8—62no—
202C2×C3×Q8—64no—
203C2×C3×Q8C22×D312yes—
204C2×C3×Q8C22×D312yes—
205C22×C3×C4—31no—
206C22×C3×C4—62no—
207C22×Dic3—31no—
208C22×Dic3—31no—
209C22×Dic3—62no—
210D3×Q8—24no—
211D3×Q8C2×Dic318yes—
212C2×C4×D3—22no—
213C2×C4×D3—31no—
214C2×C4×D3—31no—
215C2×C4×D3—62no—
216C2×C4×D3C22×D311yescharacteristic
217C2×Dic6—22no—
218C2×Dic6C22×D312yes—
219C3×Q16—24no—
220C3×Q16—38no—
221C3×Q16—34no—
222C3×Q16C4×D314yescomplemented
223C3×Q16C2×Dic314yescomplemented
224C2×C3×C8—21no—
225C2×C3×C8—31no—
226C2×C3×C8—34no—
227C2×C3×C8—31no—
228C2×C3×C8C22×D311yescharacteristic
229C2×C3×C8C22×D311yescharacteristic
230C3×C4⋊C4—32no—
231C3×C4⋊C4—62no—
232C3×C42—31no—
233C3×C42—62no—
234#216C2×Dic318yescomplemented
235C4⋊Dic3—22no—
236C4⋊Dic3—32no—
237C4⋊Dic3—32no—
238C4⋊Dic3—62no—
239C4⋊Dic3—62no—
240C4⋊Dic3—62no—
241C4⋊Dic3—62no—
242C4⋊Dic3—62no—
243C4⋊Dic3—62no—
244C4⋊Dic3—122no—
245C4⋊Dic3C22×D312yes—
246Dic3⋊C4—62no—
247Dic3⋊C4—62no—
248Dic3⋊C4—62no—
249C4×Dic3—22no—
250C4×Dic3—31no—
251C4×Dic3—31no—
252C4×Dic3—31no—
253C4×Dic3—31no—
254C4×Dic3—31no—
255C4×Dic3—31no—
256C4×Dic3—61no—
257C4×Dic3—62no—
258C4×Dic3—62no—
259C4×Dic3—62no—
260C4×Dic3—62no—
261C4×Dic3—62no—
262C4×Dic3—62no—
263C4×Dic3—122no—
264C4×Dic3C22×D311yescharacteristic
265C2×C3⋊C8—31no—
266C2×C3⋊C8—31no—
267C2×C3⋊C8—61no—
268C2×C3⋊C8—62no—
269C2×C3⋊C8C22×D311yescharacteristic
270C2×C3⋊C8C22×D311yescharacteristic
271Dic12C2×Dic314yescomplemented
272D3×C8—62no—
273D3×C8C2×Dic314yes—
274C22×C32C22×D411yescharacteristic
275C2×C3×D3C4×D412yes—
276C2×C3×D3C2×Q1612yes—
277C2×C3×D3#13512yes—
278C32×C4—24no—
279C32×C4C23×C411yescharacteristic
280C32×C4C2×#4111yescharacteristic
281C3⋊Dic3—21no—
282C3⋊Dic3—42no—
283C3⋊Dic3C2×Q1612yescomplemented
284C3×Dic3—24no—
285C3×Dic3—21no—
286C3×Dic3—42no—
287C3×Dic3C4×D412yes—
288C3×Dic3C2×Q1612yescomplemented
289C22×Q8—32no—
290C2×Q16—32no—
291C2×Q16—38no—
292C2×Q16—31no—
293C2×Q16D3211yescharacteristic
294C22×C8—31no—
295C22×C8—91no—
296C4×Q8—32no—
297C4×Q8—92no—
298C4×Q8—92no—
299C4×Q8—92no—
300C4×Q8—182no—
301C4×Q8—182no—
302C2×C4⋊C4—92no—
303C2×C4⋊C4—182no—
304C2×C42—91no—
305C2×C42—182no—
306#107—31no—
307#107—92no—
308#107—91no—
309#103—32no—
310#103—92no—
311#103—92no—
312#103—92no—
313C4×C8—31no—
314C4×C8—91no—
315C4×C8—91no—
316C4×C8—91no—
317C23×C3—31no—
318C22×D3D3×D411yescharacteristic
319C3×Q8—22no—
320C3×Q8—22no—
321C3×Q8—24no—
322C3×Q8—34no—
323C3×Q8—42no—
324C3×Q8—68no—
325C3×Q8—62no—
326C3×Q8C2×C4×D314yes—
327C3×Q8C22×Dic314yes—
328C2×C3×C4—22no—
329C2×C3×C4—22no—
330C2×C3×C4—21no—
331C2×C3×C4—31no—
332C2×C3×C4—31no—
333C2×C3×C4—32no—
334C2×C3×C4—32no—
335C2×C3×C4—31no—
336C2×C3×C4—42no—
337C2×C3×C4—68no—
338C2×C3×C4—62no—
339C2×C3×C4—62no—
340C2×C3×C4C23×D311yescharacteristic
341C2×C3×C4C23×D311yescharacteristic
342C2×Dic3—22no—
343C2×Dic3—22no—
344C2×Dic3—31no—
345C2×Dic3—31no—
346C2×Dic3—34no—
347C2×Dic3—31no—
348C2×Dic3—31no—
349C2×Dic3—61no—
350C2×Dic3—61no—
351C2×Dic3—62no—
352C2×Dic3—62no—
353C2×Dic3—62no—
354C2×Dic3—122no—
355C2×Dic3—124no—
356C2×Dic3D3×D411yescharacteristic
357C2×Dic3D3×D411yescharacteristic
358C2×Dic3D3×D411yescharacteristic
359C4×D3—28no—
360C4×D3—34no—
361C4×D3—62no—
362C4×D3—124no—
363C4×D3#23712yes—
364C4×D3C22×Dic312yes—
365Dic6—22no—
366Dic6—28no—
367Dic6C22×Dic314yes—
368C3×C8—22no—
369C3×C8—32no—
370C3×C8—61no—
371C3×C8C2×C4×D312yes—
372C3×C8C22×Dic312yes—
373C3⋊C8—21no—
374C3⋊C8—61no—
375C3⋊C8—61no—
376C3⋊C8—121no—
377C3⋊C8C22×Dic312yes—
378C2×C32C2×C4×D411yescharacteristic
379C2×C32C22×Q1611yescharacteristic
380C2×C32C2×#13511yescharacteristic
381C3×D3C4×Q1614yescomplemented
382C2×Q8—38no—
383C2×Q8—32no—
384C2×Q8—62no—
385C2×Q8—64no—
386C2×Q8C2×D3212yes—
387C22×C4—31no—
388C22×C4—62no—
389C22×C4—91no—
390C22×C4—91no—
391C22×C4—182no—
392Q16—38no—
393Q16—34no—
394Q16D3×Dic314yesdirect product factor
395C2×C8—31no—
396C2×C8—34no—
397C2×C8—31no—
398C2×C8—91no—
399C2×C8—182no—
400C2×C8C2×D3211yescharacteristic
401C4⋊C4—32no—
402C4⋊C4—62no—
403C4⋊C4—92no—
404C4⋊C4—182no—
405C4⋊C4—182no—
406C4⋊C4—182no—
407C4⋊C4—182no—
408C42—31no—
409C42—62no—
410C42—91no—
411C42—91no—
412C42—91no—
413C42—182no—
414C42—182no—
415C42—182no—
416C22×C3—21no—
417C22×C3—32no—
418C22×C3—32no—
419C22×C3—32no—
420C22×C3C2×D3×D411yescharacteristic
421C22×C3C2×D3×D411yescharacteristic
422C2×D3D3×Q1612yes—
423C2×D3#91912yes—
424C2×D3D4×Dic312yes—
425C3×C4—24no—
426C3×C4—24no—
427C3×C4—21no—
428C3×C4—21no—
429C3×C4—32no—
430C3×C4—32no—
431C3×C4—44no—
432C3×C4—61no—
433C3×C4—64no—
434C3×C4—122no—
435C3×C4C22×C4×D311yescharacteristic
436C3×C4C2×#23711yescharacteristic
437C3×C4D3×#4111yescharacteristic
438C3×C4C23×Dic311yescharacteristic
439Dic3—21no—
440Dic3—24no—
441Dic3—32no—
442Dic3—32no—
443Dic3—42no—
444Dic3—62no—
445Dic3—61no—
446Dic3—61no—
447Dic3—121no—
448Dic3—122no—
449Dic3—122no—
450Dic3—242no—
451Dic3D3×Q1612yesdirect product factor
452Dic3D4×Dic312yes—
453C32C2×C4×Q1611yescharacteristic, complemented, Sylow
454C23—31no—
455Q8—22no—
456Q8—34no—
457Q8—68no—
458Q8—62no—
459Q8C2×D3×Dic314yes—
460C2×C4—22no—
461C2×C4—31no—
462C2×C4—31no—
463C2×C4—32no—
464C2×C4—32no—
465C2×C4—31no—
466C2×C4—68no—
467C2×C4—62no—
468C2×C4—62no—
469C2×C4—94no—
470C2×C4—91no—
471C2×C4—91no—
472C2×C4—182no—
473C2×C4—182no—
474C2×C4—364no—
475C2×C4C22×D3211yescharacteristic
476C8—32no—
477C8—61no—
478C8—181no—
479C8C2×D3×Dic312yes—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—34no—
484C2×C3C4×D3×D411yescharacteristic
485C2×C3C2×D3×Q1611yescharacteristic
486C2×C3C2×D3×Q1611yescharacteristic
487C2×C3C2×#91911yescharacteristic
488C2×C3D3×#13511yescharacteristic
489C2×C3C2×D4×Dic311yescharacteristic
490D3Dic3×Q1614yesdirect product factor
491C22—32no—
492C22—32no—
493C22—32no—
494C22D32×D411yescharacteristic
495C4—24no—
496C4—32no—
497C4—32no—
498C4—64no—
499C4—61no—
500C4—92no—
501C4—122no—
502C4—181no—
503C4—362no—
504C4D3×#23711yescharacteristic
505C4C22×D3×Dic311yescharacteristic
506C3—21no—
507C3C4×D3×Q1611yescharacteristic, complemented
508C3C2×Dic3×Q1611yescharacteristic, complemented
509C2—34no—
510C2D32×Q1611yescharacteristic
511C2D3×#91911yescharacteristic
512C2D3×D4×Dic311yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
cosocleC2×C32×C4C24
hypercenterC2×Q16D32
hypocenterC32C2×C4×Q16
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
3. Q16×C3⋊Dic3C2semidirect
4. C3×Dic3×Q16C2semidirect
5. #10591581C2semidirect
6. Dic3×#216C2semidirect
8. #10590818C2semidirect
9. Dic3×Dic12C2semidirect
19. C3×D3×Q16C4semidirect
55. Dic3×Q16D3direct (N × H)
75. C32×Q16C2×C4semidirect
82. C3×#216C2×C4semidirect
89. C3×Dic12C2×C4semidirect
124. D3×Q16Dic3direct (N × H)
182. D3×Dic3Q16direct (N × H)
222. C3×Q16C4×D3semidirect
223. C3×Q16C2×Dic3semidirect
234. #216C2×Dic3semidirect
271. Dic12C2×Dic3semidirect
283. C3⋊Dic3C2×Q16semidirect
288. C3×Dic3C2×Q16semidirect
381. C3×D3C4×Q16semidirect
394. Q16D3×Dic3direct (N × H)
451. Dic3D3×Q16direct (N × H)
453. C32C2×C4×Q16semidirect
490. D3Dic3×Q16direct (N × H)
507. C3C4×D3×Q16semidirect
508. C3C2×Dic3×Q16semidirect

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×Q8×Dic32
Q16×C3⋊Dic32
C3×Dic3×Q162
#105915812
Dic3×#2162
D3×#8352
#105908182
Dic3×Dic122
D3×#8182
D3×C8×Dic32
C2×Dic3×Q163
C4×D3×Q163