Finite Group Databasebeta

← D3×#4681 #11873400

Subgroups — D3×#4681 #11873400

Order 1152.

897 conjugacy classes of subgroups.

The subgroup lattice has 471 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#869C211yesmaximal, characteristic
2D3×#869C211yesmaximal, characteristic
3#10592380C211yesmaximal, characteristic, complemented
4C3×C4×D3×C8C211yesmaximal, characteristic
5C3×#4681C211yesmaximal, characteristic, complemented
6#10590890C214yesmaximal, complemented
7D3×#816C214yesmaximal
8#10590288C211yesmaximal, characteristic, complemented
9#10590287C211yesmaximal, characteristic, complemented
10D3×#487—31nomaximal
11C2×#4681—31nomaximal
12C2×D3×Dic6—21no—
13C2×D3×Dic6C2212yes—
14#64078C2211yescharacteristic
15#64078C2211yescharacteristic
16C2×C3×D3×C8C2212yes—
17C3×C42×D3C2211yescharacteristic
18C3×#869C2211yescharacteristic
19C3×#869C2211yescharacteristic
20#63918—21no—
21#63918—21no—
22#63918—21no—
23#63918C2212yes—
24D3×C4⋊Dic3—21no—
25D3×C4⋊Dic3—21no—
26D3×C4⋊Dic3—21no—
27D3×C4⋊Dic3C2212yes—
28#63866—21no—
29#63866C2212yes—
30C32×C4×C8C2211yescharacteristic
31#63643C2214yes—
32C3×#816C2214yes—
33C3×C8×Dic3C2212yes—
34C3×C4×C3⋊C8C2211yescharacteristic
35#63567C2214yes—
36#63566C2214yes—
37D3×C4⋊Q8—31no—
38D3×C4⋊Q8—31no—
39C2×#869—31no—
40C2×#869—31no—
41C3×#487—31no—
42C2×C3×C4×C8—31no—
43C2×#816—34no—
44#5093—31no—
45#5079—31no—
46D3×#103—34no—
47#4792—34no—
48C4×D3×C8D311yescharacteristic
49#4681—31no—
50#4681—31no—
51#4681—31no—
52#4681—31no—
53#4681—34no—
54#4681—61no—
55#4681D311yescharacteristic, direct product factor
56C2×#634—21no—
57C2×#634C2312yes—
58C2×C3×C4×D3D411yescharacteristic
59C2×C3×C4×D3D411yescharacteristic
60C2×C3×C4×D3C2311yescharacteristic
61C2×C3×Dic6—21no—
62C2×C3×Dic6C2312yes—
63C2×#627—22no—
64C2×#627—22no—
65C2×D3×Dic3—22no—
66C2×D3×Dic3—22no—
67D3×Dic6—28no—
68D3×Dic6—44no—
69C2×C32×C8C2312yes—
70C32×C42C2311yescharacteristic
71C4⋊(C3⋊Dic3)—21no—
72C4⋊(C3⋊Dic3)—21no—
73C4⋊(C3⋊Dic3)—21no—
74C4⋊(C3⋊Dic3)C2312yes—
75C3×C4⋊Dic3—21no—
76C3×C4⋊Dic3—21no—
77C3×C4⋊Dic3—21no—
78C3×C4⋊Dic3C2312yes—
79C3×C4×Dic3D411yescharacteristic
80C3×C4×Dic3D411yescharacteristic
81C3×C4×Dic3C2311yescharacteristic
82C2×C3×C3⋊C8C2312yes—
83C3×D3×C8—24no—
84Dic3⋊Dic3—22no—
85Dic3⋊Dic3—22no—
86Dic3⋊Dic3—22no—
87Dic3⋊Dic3—22no—
88C2×#487—91noSylow
89C2×D3×Q8—32no—
90C2×D3×Q8—61no—
91C22×Dic6—32no—
92C22×Dic6—61no—
93C22×C3×C8—32no—
94C3×C4⋊Q8—31no—
95C3×C4⋊Q8—31no—
96C2×C3×C42—31no—
97#944—32no—
98#944—61no—
99C2×C4⋊Dic3—32no—
100C2×C4⋊Dic3—61no—
101C2×C4⋊Dic3—61no—
102C2×C4⋊Dic3—61no—
103C2×D3×C8C2×D312yes—
104D3×C4⋊C4—32no—
105D3×C4⋊C4—61no—
106D3×C4⋊C4—61no—
107D3×C4⋊C4—61no—
108#888—32no—
109#888—61no—
110#888—61no—
111#888—61no—
112C42×D3C2×D311yescharacteristic
113#869—31no—
114#869—31no—
115#869—32no—
116#869—32no—
117#869—31no—
118#869—31no—
119#869—61no—
120#869—61no—
121#869—61no—
122#869—61no—
123#869—61no—
124#869—61no—
125#869C2×D311yescharacteristic
126#869C2×D311yescharacteristic
127C3×#103—34no—
128C3×C4×C8—21no—
129C3×C4×C8—32no—
130C3×C4×C8—31no—
131C3×C4×C8C2×D311yescharacteristic
132C3×C4×C8C2×D311yescharacteristic
133#835—34no—
134#816—34no—
135#816—34no—
136#816—34no—
137#816—34no—
138#816—64no—
139#816C2×D314yes—
140C8×Dic3C2×D312yes—
141#810—34no—
142C4×C3⋊C8C2×D311yescharacteristic
143C22×C3×D3C2×D411yescharacteristic
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4C2411yescharacteristic
147C2×C3⋊Dic3—22no—
148C2×C3⋊Dic3—22no—
149#634—24no—
150#634—42no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3C2×D411yescharacteristic
154C2×C3×Dic3C2×D411yescharacteristic
155C2×C3×Dic3C2×D411yescharacteristic
156C3×C4×D3SD1614yes—
157C3×C4×D3Q1614yes—
158C3×C4×D3#4114yes—
159C3×Dic6—24no—
160C3×Dic6—42no—
161#627—44no—
162#627—44no—
163D3×Dic3—44no—
164D3×Dic3—44no—
165C32×C8—22no—
166C3×C3⋊C8—22no—
167C2×C4⋊Q8—91no—
168C2×C4⋊Q8—91no—
169#487—31no—
170#487—94no—
171#487—91no—
172#487—91no—
173#487—91no—
174C2×#103—94no—
175C2×C4×C8—31no—
176C2×C3×Q8—32no—
177C2×C3×Q8—61no—
178C22×C3×C4—31no—
179C22×C3×C4—31no—
180C22×C3×C4—31no—
181C22×Dic3—62no—
182C22×Dic3—62no—
183D3×Q8—68no—
184D3×Q8—124no—
185C2×C4×D3—62no—
186C2×C4×D3—62no—
187C2×C4×D3D1211yescharacteristic
188C2×C4×D3D1211yescharacteristic
189C2×C4×D3C22×D311yescharacteristic
190C2×Dic6—21no—
191C2×Dic6—32no—
192C2×Dic6—32no—
193C2×Dic6—62no—
194C2×Dic6—68no—
195C2×Dic6—62no—
196C2×Dic6—62no—
197C2×Dic6—61no—
198C2×Dic6—61no—
199C2×Dic6—62no—
200C2×Dic6—62no—
201C2×Dic6—121no—
202C2×Dic6—124no—
203C2×Dic6C22×D312yes—
204C2×C3×C8—22no—
205C2×C3×C8—32no—
206C2×C3×C8—64no—
207C2×C3×C8C22×D312yes—
208C2×C3×C8C22×D312yes—
209C3×C4⋊C4—32no—
210C3×C4⋊C4—61no—
211C3×C4⋊C4—61no—
212C3×C4⋊C4—61no—
213C3×C42—21no—
214C3×C42—31no—
215C3×C42—31no—
216C3×C42—31no—
217C3×C42C22×D311yescharacteristic
218C3×C42C22×D311yescharacteristic
219C4⋊Dic3—21no—
220C4⋊Dic3—21no—
221C4⋊Dic3—21no—
222C4⋊Dic3—32no—
223C4⋊Dic3—32no—
224C4⋊Dic3—62no—
225C4⋊Dic3—62no—
226C4⋊Dic3—62no—
227C4⋊Dic3—62no—
228C4⋊Dic3—62no—
229C4⋊Dic3—61no—
230C4⋊Dic3—61no—
231C4⋊Dic3—61no—
232C4⋊Dic3—61no—
233C4⋊Dic3—61no—
234C4⋊Dic3—61no—
235C4⋊Dic3—121no—
236C4⋊Dic3—121no—
237C4⋊Dic3—121no—
238C4⋊Dic3C22×D312yes—
239Dic3⋊C4—62no—
240Dic3⋊C4—62no—
241Dic3⋊C4—62no—
242Dic3⋊C4—62no—
243C4×Dic3D1211yescharacteristic
244C4×Dic3D1211yescharacteristic
245C4×Dic3C22×D311yescharacteristic
246C2×C3⋊C8C22×D312yes—
247D3×C8—24no—
248C22×C32C22×D411yescharacteristic
249C2×C3×D3#12412yes—
250C2×C3×D3C2×SD1612yes—
251C2×C3×D3C2×Q1612yes—
252C32×C4C2×SD1612yes—
253C32×C4C2×Q1612yes—
254C32×C4C2×#4112yes—
255C3⋊Dic3—42no—
256C3⋊Dic3—42no—
257C3×Dic3—42no—
258C3×Dic3—42no—
259C3×Dic3#12412yes—
260C3×Dic3C2×SD1612yes—
261C3×Dic3C2×Q1612yes—
262C22×Q8—92no—
263C22×Q8—181no—
264C22×C8—32no—
265C4⋊Q8—31no—
266C4⋊Q8—31no—
267C4⋊Q8—92no—
268C4⋊Q8—92no—
269C4⋊Q8—91no—
270C4⋊Q8—91no—
271C4⋊Q8—181no—
272C4⋊Q8—181no—
273C4⋊Q8—181no—
274C4⋊Q8—181no—
275C2×C4⋊C4—92no—
276C2×C4⋊C4—181no—
277C2×C4⋊C4—181no—
278C2×C4⋊C4—181no—
279C2×C42—31no—
280#103—34no—
281#103—94no—
282#103—94no—
283#103—94no—
284C4×C8—32no—
285C4×C8—31no—
286C4×C8D3211yescharacteristic
287C23×C3—31no—
288C22×D3C2×D1211yescharacteristic
289C3×Q8—64no—
290C3×Q8—122no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—31no—
295C2×C3×C4—31no—
296C2×C3×C4—31no—
297C2×C3×C4—34no—
298C2×C3×C4—34no—
299C2×C3×C4—34no—
300C2×C3×C4—62no—
301C2×C3×C4—62no—
302C2×C3×C4C2×D1211yescharacteristic
303C2×C3×C4C2×D1211yescharacteristic
304C2×C3×C4D3×D411yescharacteristic
305C2×C3×C4D3×D411yescharacteristic
306C2×C3×C4C23×D311yescharacteristic
307C2×C3×C4C23×D311yescharacteristic
308C2×Dic3—22no—
309C2×Dic3—22no—
310C2×Dic3—62no—
311C2×Dic3—62no—
312C2×Dic3—62no—
313C2×Dic3—62no—
314C2×Dic3—122no—
315C2×Dic3—122no—
316C2×Dic3—124no—
317C2×Dic3—124no—
318C2×Dic3C2×D1211yescharacteristic
319C2×Dic3C2×D1211yescharacteristic
320C2×Dic3C2×D1211yescharacteristic
321C4×D3—124no—
322C4×D3—124no—
323C4×D3#20414yes—
324C4×D3Dic1214yes—
325C4×D3#23514yes—
326Dic6—24no—
327Dic6—42no—
328Dic6—64no—
329Dic6—64no—
330Dic6—124no—
331Dic6—124no—
332Dic6—124no—
333Dic6—122no—
334Dic6—122no—
335Dic6—124no—
336Dic6—124no—
337Dic6—242no—
338C3×C8—22no—
339C3×C8—22no—
340C3×C8—42no—
341C3×C8—62no—
342C3⋊C8—22no—
343C2×C32C2×#12411yescharacteristic
344C2×C32C22×SD1611yescharacteristic
345C2×C32C22×Q1611yescharacteristic
346C3×D3#48714yescomplemented
347C2×Q8—32no—
348C2×Q8—61no—
349C2×Q8—92no—
350C2×Q8—182no—
351C2×Q8—182no—
352C2×Q8—188no—
353C2×Q8—181no—
354C2×Q8—364no—
355C22×C4—31no—
356C22×C4—31no—
357C22×C4—31no—
358C22×C4—182no—
359C22×C4—182no—
360C2×C8—32no—
361C2×C8—64no—
362C2×C8C2×D3212yes—
363C4⋊C4—32no—
364C4⋊C4—61no—
365C4⋊C4—61no—
366C4⋊C4—61no—
367C4⋊C4—92no—
368C4⋊C4—182no—
369C4⋊C4—182no—
370C4⋊C4—182no—
371C4⋊C4—182no—
372C4⋊C4—181no—
373C4⋊C4—181no—
374C4⋊C4—181no—
375C42—31no—
376C42—31no—
377C42—31no—
378C42C2×D3211yescharacteristic
379C22×C3—21no—
380C22×C3—32no—
381C22×C3—32no—
382C22×C3—32no—
383C22×C3C22×D1211yescharacteristic
384C22×C3C2×D3×D411yescharacteristic
385C2×D3#87512yes—
386C2×D3C2×#20412yes—
387C2×D3C2×Dic1212yes—
388C3×C4—22no—
389C3×C4—22no—
390C3×C4—22no—
391C3×C4—32no—
392C3×C4—32no—
393C3×C4—32no—
394C3×C4—122no—
395C3×C4—122no—
396C3×C4C2×#20412yes—
397C3×C4C2×Dic1212yes—
398C3×C4D3×SD1612yes—
399C3×C4D3×Q1612yes—
400C3×C4C2×#23512yes—
401C3×C4D3×#4112yes—
402Dic3—42no—
403Dic3—42no—
404Dic3—122no—
405Dic3—122no—
406Dic3—122no—
407Dic3—122no—
408Dic3—242no—
409Dic3—242no—
410Dic3#87512yes—
411Dic3C2×#20412yes—
412Dic3C2×Dic1212yes—
413C32C2×#48711yescharacteristic, complemented, Sylow
414C23—31no—
415Q8—64no—
416Q8—122no—
417Q8—184no—
418Q8—364no—
419Q8—364no—
420Q8—362no—
421C2×C4—31no—
422C2×C4—31no—
423C2×C4—31no—
424C2×C4—34no—
425C2×C4—34no—
426C2×C4—34no—
427C2×C4—62no—
428C2×C4—62no—
429C2×C4—182no—
430C2×C4—182no—
431C2×C4—364no—
432C2×C4—364no—
433C2×C4D3×D1211yescharacteristic
434C2×C4D3×D1211yescharacteristic
435C2×C4C22×D3211yescharacteristic
436C8—22no—
437C8—62no—
438C2×C3—21no—
439C2×C3—21no—
440C2×C3—21no—
441C2×C3—34no—
442C2×C3C2×#87511yescharacteristic
443C2×C3D3×#12411yescharacteristic
444C2×C3C22×#20411yescharacteristic
445C2×C3C22×Dic1211yescharacteristic
446C2×C3C2×D3×SD1611yescharacteristic
447C2×C3C2×D3×Q1611yescharacteristic
448D3#468114yesdirect product factor
449C22—32no—
450C22—32no—
451C22—32no—
452C22C2×D3×D1211yescharacteristic
453C4—32no—
454C4—32no—
455C4—32no—
456C4—122no—
457C4—122no—
458C4—362no—
459C4—362no—
460C4D3×#20412yes—
461C4D3×Dic1212yes—
462C4D3×#23512yes—
463C3—21no—
464C3C2×#468111yescharacteristic, complemented
465C3D3×#48711yescharacteristic, complemented
466C2—34no—
467C2D3×#87511yescharacteristic
468C2C2×D3×#20411yescharacteristic
469C2C2×D3×Dic1211yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenterC4×C8D32
hypocenterC32C2×#487
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
3. #10592380C2semidirect
5. C3×#4681C2semidirect
6. #10590890C2semidirect
8. #10590288C2semidirect
9. #10590287C2semidirect
55. #4681D3direct (N × H)
346. C3×D3#487semidirect
413. C32C2×#487semidirect
448. D3#4681direct (N × H)
464. C3C2×#4681semidirect
465. C3D3×#487semidirect

Maximal subgroups

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

subgroupindex
D3×#8692
#105923802
C3×C4×D3×C82
C3×#46812
#105908902
D3×#8162
#105902882
#105902872
D3×#4873
C2×#46813