Finite Group Databasebeta

← Dic3×#825 #11783882

Subgroups — Dic3×#825 #11783882

Order 1152.

775 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Dic3×#235C211yesmaximal, characteristic
2C2×C3×#825C211yesmaximal, characteristic
3C3×Dic3×M16C211yesmaximal, characteristic, complemented
4C4×Dic32C211yesmaximal, characteristic, complemented
5C2×#63568C211yesmaximal, characteristic
6#10589421C211yesmaximal, characteristic, complemented
7#10589162C211yesmaximal, characteristic, complemented
8Dic3×#104—31nomaximal
9C4×#825—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12#64135C2211yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C2×C3×C4×Dic3C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17Dic3×#67—22no—
18C2×Dic32—22no—
19Dic3×D12C412yescomplemented
20C4×D3×Dic3—21no—
21#63855—21no—
22Dic3×Dic6C412yescomplemented
23C3×#825C414yescomplemented
24C3×#815—21no—
25C3×C8×Dic3—21no—
26#63568C414yescomplemented
27Dic3×#41—31no—
28C4×#235—31no—
29C2×C3×#104—31no—
30C3×C4×M16—31no—
31C2×#837—31no—
32C2×#825—31no—
33C2×#825D311yescharacteristic
34Dic3×M16D311yescharacteristic, complemented
35C42×Dic3—31no—
36C42×Dic3—31no—
37#4555—31no—
38#4555—31no—
39#4555—31no—
40#4555—61no—
41#4523—31no—
42C22×C32×C4C2311yescharacteristic
43C22×C3⋊Dic3—21no—
44C2×C3×#67—21no—
45C22×C3×Dic3—21no—
46C22×C3×Dic3D412yes—
47C3×#235—21no—
48C3×#235—21no—
49C3×#235C2×C412yes—
50C3×#235C2×C412yes—
51C2×C3×D12C2×C411yescharacteristic
52C2×C3×C4×D3—21no—
53C2×C3×Dic6C2×C411yescharacteristic
54C2×D3×Dic3—22no—
55C32×M16—21no—
56C32×M16C2×C412yescomplemented
57C2×C32×C8—21no—
58#3757—21no—
59C4⋊(C3⋊Dic3)C2×C412yes—
60C4×C3⋊Dic3—21no—
61C4×C3⋊Dic3—21no—
62C4×C3⋊Dic3C2×C412yescomplemented
63C3×C4×Dic3—21no—
64C3×C4×Dic3C2×C412yes—
65C3×C4×Dic3C2×C412yescomplemented
66C3×C4×Dic3D411yescharacteristic
67C3×C4×Dic3D411yescharacteristic
68C3×#208—21no—
69C3×#208C2×C412yescomplemented
70C2×C3×C3⋊C8—21no—
71Dic3⋊Dic3—22no—
72(C2×D3)⋊Dic3—22no—
73Dic32—28no—
74Dic32—22no—
75C4×#104—91noSylow
76C2×C3×#41—31no—
77C2×#235C2×D311yescharacteristic
78C2×C3×M16—21no—
79C2×C3×M16—31no—
80C2×C3×M16C2×D311yescharacteristic
81C2×C3×M16C2×D311yescharacteristic
82C2×C3×C42—31no—
83C2×C3×C42—31no—
84Q8×Dic3—32no—
85D4×Dic3—32no—
86D4×Dic3—62no—
87C4×#67—62no—
88#926—31no—
89#926—31no—
90#926—61no—
91#926—61no—
92C2×C4×Dic3—31no—
93C2×C4×Dic3—31no—
94C2×C4×Dic3—61no—
95C2×C4×Dic3—62no—
96C2×C4×Dic3—62no—
97C2×C4×Dic3—61no—
98C2×C4×Dic3C2×D311yescharacteristic
99C2×C4×Dic3C2×D311yescharacteristic
100C2×#208C2×D311yescharacteristic
101C4×D12—32no—
102#872—61no—
103C42×D3—61no—
104C4×Dic6—32no—
105C3×#104—34no—
106C3×#97—61no—
107C3×C4×C8—61no—
108#837—34no—
109#825—34no—
110#825Dic314yesdirect product factor
111#815—21no—
112C8×Dic3—21no—
113C23×C32C2×D411yescharacteristic
114C22×C3×D3—21no—
115C2×C32×C4C22×C411yescharacteristic
116C2×C32×C4C22×C411yescharacteristic
117C2×C32×C4C22×C411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4#4111yescharacteristic
120C2×C32×C4#4111yescharacteristic
121C2×C3⋊Dic3—24no—
122C2×C3⋊Dic3—22no—
123C2×C3⋊Dic3—22no—
124C3×#67—22no—
125C3×#67—22no—
126C2×C3×Dic3—24no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—22no—
129C2×C3×Dic3—24no—
130C2×C3×Dic3C22⋊C412yes—
131C2×C3×Dic3C22⋊C412yes—
132C3×D12—21no—
133C3×D12C4212yescomplemented
134C3×C4×D3—22no—
135C3×C4×D3—22no—
136C3×Dic6—21no—
137C3×Dic6C4212yescomplemented
138D3×Dic3—44no—
139C32×C8—22no—
140C3×C3⋊C8—22no—
141C4×#41—91no—
142C2×#104—31no—
143C2×#104—91no—
144C4×M16—31no—
145C43—91no—
146#339—91no—
147#339—91no—
148C3×#41—32no—
149C3×#41—32no—
150C3×#41—61no—
151C3×#41—61no—
152C2×C3×Q8—31no—
153C2×C3×D4—31no—
154C2×C3×D4—61no—
155C22×C3×C4—21no—
156C22×C3×C4—32no—
157C22×C3×C4—61no—
158C22×C3×C4—61no—
159C22×C3×C4C22×D311yescharacteristic
160C22×C3×C4C22×D311yescharacteristic
161C2×#67—21no—
162C22×Dic3—21no—
163C22×Dic3—61no—
164C22×Dic3—61no—
165C22×Dic3—62no—
166C22×Dic3—121no—
167C22×Dic3D1212yes—
168#235—21no—
169#235—21no—
170#235C4×D312yes—
171#235C2×Dic312yes—
172C2×D12C4×D311yescharacteristic
173C2×C4×D3—21no—
174C2×C4×D3—62no—
175C2×Dic6C4×D311yescharacteristic
176C3×M16—21no—
177C3×M16—21no—
178C3×M16—22no—
179C3×M16—32no—
180C3×M16—41no—
181C3×M16—61no—
182C3×M16C4×D312yescomplemented
183C3×M16C2×Dic312yescomplemented
184C2×C3×C8—21no—
185C2×C3×C8—21no—
186C2×C3×C8—41no—
187C2×C3×C8—61no—
188C3×C42—32no—
189C3×C42—31no—
190C3×C42—31no—
191C3×C42—32no—
192C3×C42—61no—
193#217—61no—
194#217—61no—
195#217—62no—
196#217—121no—
197(C2×D3)⋊C4—62no—
198C4⋊Dic3—32no—
199C4⋊Dic3—32no—
200C4⋊Dic3—62no—
201C4⋊Dic3—62no—
202Dic3⋊C4—62no—
203C4×Dic3—21no—
204C4×Dic3—32no—
205C4×Dic3—32no—
206C4×Dic3—62no—
207C4×Dic3—62no—
208C4×Dic3—68no—
209C4×Dic3—68no—
210C4×Dic3—61no—
211C4×Dic3—61no—
212C4×Dic3—61no—
213C4×Dic3—61no—
214C4×Dic3—62no—
215C4×Dic3—121no—
216C4×Dic3—121no—
217C4×Dic3C4×D312yes—
218C4×Dic3C2×Dic312yescomplemented
219C4×Dic3#6711yescharacteristic
220C4×Dic3#6711yescharacteristic
221#208—21no—
222#208C4×D312yescomplemented
223C2×C3⋊C8—21no—
224C22×C32—22no—
225C22×C32C2×C22⋊C411yescharacteristic
226C22×C32C4×D411yescharacteristic
227C22×C32C4×D411yescharacteristic
228C2×C3×D3—22no—
229C2×C3×D3—42no—
230C32×C4C2×C4211yescharacteristic
231C32×C4#11711yescharacteristic
232C32×C4C4×D411yescharacteristic
233C32×C4C4×D411yescharacteristic
234C3⋊Dic3—24no—
235C3⋊Dic3—42no—
236C3×Dic3—24no—
237C3×Dic3—22no—
238C3×Dic3—22no—
239C3×Dic3#10414yescomplemented
240C2×#41—31no—
241C2×M16—31no—
242C2×M16D3211yescharacteristic
243C4×Q8—92no—
244C4×D4—92no—
245C4×D4—182no—
246#117—91no—
247#117—181no—
248C2×C42—31no—
249C2×C42—31no—
250C2×C42—91no—
251C2×C42—181no—
252C2×C42—182no—
253#104—34no—
254#104—94no—
255#97—61no—
256C4×C8—61no—
257C23×C3—21no—
258C23×C3—61no—
259C23×C3C2×D1211yescharacteristic
260C23×C3D3×D411yescharacteristic
261C22×D3—21no—
262C3×Q8—32no—
263C3×Q8—61no—
264C3×D4—32no—
265C3×D4—62no—
266C3×D4—62no—
267C3×D4—61no—
268C2×C3×C4—21no—
269C2×C3×C4—21no—
270C2×C3×C4—21no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—21no—
274C2×C3×C4—32no—
275C2×C3×C4—32no—
276C2×C3×C4—64no—
277C2×C3×C4—64no—
278C2×C3×C4—62no—
279C2×C3×C4—61no—
280C2×C3×C4—62no—
281C2×C3×C4—62no—
282C2×C3×C4C2×C4×D311yescharacteristic
283C2×C3×C4C2×C4×D311yescharacteristic
284C2×C3×C4C2×C4×D311yescharacteristic
285C2×C3×C4C2×C4×D311yescharacteristic
286C2×C3×C4C2×C4×D311yescharacteristic
287C2×C3×C4#23511yescharacteristic
288C2×C3×C4#23511yescharacteristic
289C2×C3×C4D3×D411yescharacteristic
290C2×C3×C4#23711yescharacteristic
291C2×C3×C4#23711yescharacteristic
292C2×C3×C4C22×Dic311yescharacteristic
293C2×C3×C4C2×#6711yescharacteristic
294#67—22no—
295#67—22no—
296C2×Dic3—24no—
297C2×Dic3—21no—
298C2×Dic3—22no—
299C2×Dic3—24no—
300C2×Dic3—64no—
301C2×Dic3—64no—
302C2×Dic3—62no—
303C2×Dic3—62no—
304C2×Dic3—62no—
305C2×Dic3—62no—
306C2×Dic3—122no—
307C2×Dic3—124no—
308C2×Dic3—122no—
309C2×Dic3—124no—
310C2×Dic3(C2×D3)⋊C412yes—
311C2×Dic3(C2×D3)⋊C412yes—
312D12—21no—
313D12C4×Dic312yescomplemented
314C4×D3—22no—
315C4×D3—22no—
316C4×D3—124no—
317Dic6—21no—
318Dic6C4×Dic312yescomplemented
319C3×C8—22no—
320C3×C8—22no—
321C3×C8—42no—
322C3×C8—62no—
323C3⋊C8—22no—
324C2×C32—21no—
325C2×C32—21no—
326C2×C32C4×C22⋊C411yescharacteristic
327C2×C32C2×#10412yes—
328C3×D3—42no—
329#41—32no—
330#41—32no—
331#41—61no—
332#41—61no—
333C2×Q8—31no—
334C2×D4—31no—
335C2×D4—61no—
336C22×C4—32no—
337C22×C4—61no—
338C22×C4—61no—
339C22×C4—182no—
340C22×C4—181no—
341C22×C4C2×D3211yescharacteristic
342M16—21no—
343M16—32no—
344M16—61no—
345M16D3×Dic312yescomplemented
346C2×C8—21no—
347C2×C8—61no—
348C4⋊C4—92no—
349C4⋊C4—182no—
350C22⋊C4—182no—
351C22⋊C4—181no—
352C42—32no—
353C42—31no—
354C42—31no—
355C42—32no—
356C42—61no—
357C42—92no—
358C42—182no—
359C42—188no—
360C42—181no—
361C42—181no—
362C22×C3—22no—
363C22×C3—22no—
364C22×C3—21no—
365C22×C3—21no—
366C22×C3—21no—
367C22×C3—42no—
368C22×C3—62no—
369C22×C3—122no—
370C22×C3C4×D1211yescharacteristic
371C22×C3C4×D1211yescharacteristic
372C22×C3D3×C22⋊C411yescharacteristic
373C22×C3#67⋊C411yescharacteristic
374C22×C3C2×(C2×D3)⋊C411yescharacteristic
375C22×C3D4×Dic311yescharacteristic
376C2×D3—22no—
377C2×D3—42no—
378C3×C4—21no—
379C3×C4—21no—
380C3×C4—21no—
381C3×C4—21no—
382C3×C4—34no—
383C3×C4—64no—
384C3×C4—62no—
385C3×C4—62no—
386C3×C4C42×D311yescharacteristic
387C3×C4#87211yescharacteristic
388C3×C4#87711yescharacteristic
389C3×C4#67⋊C411yescharacteristic
390C3×C4C2×C4×Dic311yescharacteristic
391C3×C4C4×#6711yescharacteristic
392C3×C4C4×#6711yescharacteristic
393C3×C4D4×Dic311yescharacteristic
394Dic3—24no—
395Dic3—22no—
396Dic3—22no—
397Dic3—64no—
398Dic3—64no—
399Dic3—124no—
400Dic3—122no—
401Dic3—122no—
402Dic3—242no—
403Dic3#82514yesdirect product factor
404C32C4×#10411yescharacteristic, complemented, Sylow
405C23—61no—
406C23D3×D1211yescharacteristic
407Q8—32no—
408Q8—61no—
409D4—32no—
410D4—62no—
411D4—62no—
412D4—61no—
413C2×C4—32no—
414C2×C4—32no—
415C2×C4—64no—
416C2×C4—64no—
417C2×C4—62no—
418C2×C4—61no—
419C2×C4—62no—
420C2×C4—62no—
421C2×C4—184no—
422C2×C4—182no—
423C2×C4—182no—
424C2×C4—364no—
425C2×C4#379511yescharacteristic
426C2×C4C4×D3211yescharacteristic
427C2×C4C4×D3211yescharacteristic
428C2×C4C2×D3×Dic311yescharacteristic
429C2×C4#380411yescharacteristic
430C2×C4D3×#6711yescharacteristic
431C8—22no—
432C8—62no—
433C2×C3—21no—
434C2×C3—21no—
435C2×C3—21no—
436C2×C3—21no—
437C2×C3—22no—
438C2×C3—21no—
439C2×C3—41no—
440C2×C3—41no—
441C2×C3—122no—
442C2×C3D3×#10412yes—
443C2×C3C4×(C2×D3)⋊C411yescharacteristic
444C2×C3Dic3×C22⋊C411yescharacteristic
445C2×C3C2×#82512yes—
446D3—42no—
447C22—22no—
448C22—62no—
449C22—122no—
450C22#6388011yescharacteristic
451C22Dic3×D1211yescharacteristic
452C22D3×(C2×D3)⋊C411yescharacteristic
453C4—34no—
454C4—64no—
455C4—62no—
456C4—62no—
457C4—184no—
458C4—362no—
459C4C4×D3×Dic311yescharacteristic
460C4#6387711yescharacteristic
461C4#6387911yescharacteristic
462C4Dic3×#6711yescharacteristic
463C3—21no—
464C3C4×#82511yescharacteristic, complemented
465C3Dic3×#10411yescharacteristic, complemented
466C2—21no—
467C2—21no—
468C2—122no—
469C2D3×#82512yes—
470C2Dic3×(C2×D3)⋊C411yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC32×C4C2×C42
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32C2×C22⋊C4
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32C4×#104
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
3. C3×Dic3×M16C2semidirect
4. C4×Dic32C2semidirect
6. #10589421C2semidirect
7. #10589162C2semidirect
19. Dic3×D12C4semidirect
22. Dic3×Dic6C4semidirect
23. C3×#825C4semidirect
26. #63568C4semidirect
34. Dic3×M16D3semidirect
56. C32×M16C2×C4semidirect
62. C4×C3⋊Dic3C2×C4semidirect
65. C3×C4×Dic3C2×C4semidirect
69. C3×#208C2×C4semidirect
110. #825Dic3direct (N × H)
133. C3×D12C42semidirect
137. C3×Dic6C42semidirect
182. C3×M16C4×D3semidirect
183. C3×M16C2×Dic3semidirect
218. C4×Dic3C2×Dic3semidirect
222. #208C4×D3semidirect
239. C3×Dic3#104semidirect
313. D12C4×Dic3semidirect
318. Dic6C4×Dic3semidirect
345. M16D3×Dic3semidirect
403. Dic3#825direct (N × H)
404. C32C4×#104semidirect
464. C3C4×#825semidirect
465. C3Dic3×#104semidirect

Maximal subgroups

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

subgroupindex
Dic3×#2352
C2×C3×#8252
C3×Dic3×M162
C4×Dic322
C2×#635682
#105894212
#105891622
Dic3×#1043
C4×#8253