Finite Group Databasebeta

← D3×#4690 #11858786

Subgroups — D3×#4690 #11858786

Order 1152.

872 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#872C211yesmaximal, characteristic
2#10592389C211yesmaximal, characteristic, complemented
3C3×#4690C211yesmaximal, characteristic, complemented
4C3×C4×D3×C8C211yesmaximal, characteristic, complemented
5D3×(C2×D3)⋊C8C212yesmaximal
6#10590696C212yesmaximal, complemented
7D3×Dic3⋊C8C212yesmaximal, complemented
8#10590648C212yesmaximal, complemented
9D3×#803C211yesmaximal, characteristic, complemented
10#10590298C211yesmaximal, characteristic, complemented
11#10590264C211yesmaximal, characteristic, complemented
12D3×#433—31nomaximal
13C2×#4690—31nomaximal
14C2×C4×D32C2211yescharacteristic
15#64081C2211yescharacteristic
16C2×C3×D3×C8C2212yes—
17C3×#872C2211yescharacteristic
18C3×C42×D3C2211yescharacteristic
19D3×(C2×D3)⋊C4C412yes—
20#63877C412yes—
21D3×Dic3⋊C4C412yes—
22C4×D3×Dic3C2211yescharacteristic
23#63874C2211yescharacteristic
24#63855C2211yescharacteristic
25#63836C412yes—
26C2×D3×C3⋊C8C2212yes—
27C32×C4×C8C2211yescharacteristic, complemented
28#63647C2212yes—
29#63641C2212yescomplemented
30#63630C2211yescharacteristic, complemented
31C3×(C2×D3)⋊C8C2212yes—
32C3×Dic3⋊C8C2212yescomplemented
33C3×C8×Dic3C2212yescomplemented
34C3×#803C2211yescharacteristic, complemented
35C3×C4×C3⋊C8C2211yescharacteristic, complemented
36#63572C2212yescomplemented
37Dic3⋊(C3⋊C8)C2212yescomplemented
38#63557C2212yes—
39(C2×D3)⋊(C3⋊C8)C2212yes—
40#63554C2212yescomplemented
41D3×#117—31no—
42C2×#872—31no—
43C3×#433—31no—
44C2×C3×C4×C8—31no—
45C2×(C2×D3)⋊C8—32no—
46C2×Dic3⋊C8—32no—
47#5000—31no—
48C2×#803—31no—
49#4840—32no—
50D3×C4⋊C8—32no—
51D3×C22⋊C8—32no—
52#4720—32no—
53#4709—31no—
54D3×#97—31no—
55#4690—31no—
56#4690—31no—
57#4690—31no—
58#4690—32no—
59#4690—32no—
60#4690—31no—
61#4690—61no—
62#4690D311yescharacteristic, direct product factor
63C4×D3×C8D311yescharacteristic, complemented
64C22×D32C2×C411yescharacteristic
65C2×C4×C3⋊D3C2311yescharacteristic
66C2×C3×C4×D3C2×C412yes—
67C2×C3×C4×D3C2311yescharacteristic
68C2×C3×C4×D3C2311yescharacteristic
69C2×#624C2×C411yescharacteristic
70C2×D3×Dic3C2×C411yescharacteristic
71C2×D3×Dic3C2×C411yescharacteristic
72C2×D3×Dic3C2×C412yes—
73C4×D32—24no—
74C2×C32×C8C2312yes—
75C32×C42C2311yescharacteristic
76#3752C2×C412yes—
77#3750C2×C412yes—
78C4×C3⋊Dic3C2311yescharacteristic
79C2×C3⋊(C3⋊C8)C2312yes—
80C3×(C2×D3)⋊C4C2×C412yes—
81C3×Dic3⋊C4C2×C412yes—
82C3×C4×Dic3C2×C412yes—
83C3×C4×Dic3C2311yescharacteristic
84C3×C4×Dic3C2311yescharacteristic
85C2×C3×C3⋊C8C2312yes—
86C2×C3×C3⋊C8C2312yes—
87C3×D3×C8—24no—
88#3724C2×C412yes—
89Dic3⋊Dic3C2×C412yes—
90#3722C2×C412yes—
91(C2×D3)⋊Dic3C2×C412yes—
92Dic32C2×C412yes—
93D3×C3⋊C8—24no—
94C2×#433—91noSylow
95C22×C4×D3—31no—
96C22×C4×D3—31no—
97C22×C3×C8—32no—
98C3×#117—31no—
99C2×C3×C42—31no—
100C2×(C2×D3)⋊C4—32no—
101#926—31no—
102C2×Dic3⋊C4—32no—
103C2×C4×Dic3—31no—
104C22×C3⋊C8—32no—
105C2×D3×C8—32no—
106C2×D3×C8C2×D312yes—
107#892—32no—
108D3×C4⋊C4—32no—
109D3×C22⋊C4—32no—
110#877—32no—
111#872—31no—
112#872—31no—
113#872—31no—
114#872—32no—
115#872—32no—
116#872—31no—
117#872—31no—
118#872—61no—
119#872C2×D311yescharacteristic
120C42×D3—31no—
121C42×D3C2×D311yescharacteristic
122C3×C4⋊C8—32no—
123C3×C22⋊C8—32no—
124C3×#97—31no—
125C3×C4×C8—21no—
126C3×C4×C8—32no—
127C3×C4×C8—31no—
128C3×C4×C8C2×D311yescharacteristic, complemented
129C3×C4×C8C2×D311yescharacteristic, complemented
130#830—32no—
131(C2×D3)⋊C8—32no—
132(C2×D3)⋊C8—32no—
133(C2×D3)⋊C8—32no—
134(C2×D3)⋊C8—32no—
135(C2×D3)⋊C8—32no—
136(C2×D3)⋊C8—62no—
137(C2×D3)⋊C8C2×D312yes—
138#815—32no—
139Dic3⋊C8—32no—
140Dic3⋊C8—32no—
141Dic3⋊C8—32no—
142Dic3⋊C8—32no—
143Dic3⋊C8—32no—
144Dic3⋊C8—62no—
145Dic3⋊C8C2×D312yescomplemented
146C8×Dic3C2×D312yescomplemented
147C4⋊(C3⋊C8)—32no—
148#803—31no—
149#803—31no—
150#803—32no—
151#803—61no—
152#803C2×D311yescharacteristic, complemented
153C4×C3⋊C8C2×D311yescharacteristic, complemented
154C22×C3⋊D3C22×C411yescharacteristic
155C22×C3×D3C22×C411yescharacteristic
156C22×C3×D3C22×C411yescharacteristic
157C2×D32—22no—
158C2×D32—24no—
159C2×C32×C4C22×C412yes—
160C2×C32×C4C2411yescharacteristic
161C2×C3⋊Dic3C22×C412yes—
162C2×C3⋊Dic3C22×C411yescharacteristic
163C4×C3⋊D3—22no—
164C2×C3×Dic3C22×C412yes—
165C2×C3×Dic3C22×C412yes—
166C2×C3×Dic3C22×C411yescharacteristic
167C2×C3×Dic3C22×C411yescharacteristic
168C3×C4×D3—24no—
169C3×C4×D3—22no—
170C3×C4×D3#4114yes—
171#624—22no—
172D3×Dic3—22no—
173D3×Dic3—24no—
174D3×Dic3—22no—
175C32×C8—22no—
176C3⋊(C3⋊C8)—22no—
177C3×C3⋊C8—22no—
178C3×C3⋊C8—22no—
179C2×#117—91no—
180#433—31no—
181#433—91no—
182#433—92no—
183#433—92no—
184#433—91no—
185#433—91no—
186C2×C4⋊C8—92no—
187C2×C22⋊C8—92no—
188C2×#97—91no—
189C2×C4×C8—31no—
190C23×D3—31no—
191C23×D3—31no—
192C22×C3×C4—31no—
193C22×C3×C4—32no—
194C22×C3×C4—31no—
195C22×Dic3—31no—
196C22×Dic3—32no—
197C22×Dic3—31no—
198C2×C4×D3—32no—
199C2×C4×D3—31no—
200C2×C4×D3—31no—
201C2×C4×D3—31no—
202C2×C4×D3—31no—
203C2×C4×D3—31no—
204C2×C4×D3—31no—
205C2×C4×D3—61no—
206C2×C4×D3—64no—
207C2×C4×D3—64no—
208C2×C4×D3C4×D312yes—
209C2×C4×D3C22×D311yescharacteristic
210C2×C4×D3C22×D311yescharacteristic
211C2×C3×C8—22no—
212C2×C3×C8—32no—
213C2×C3×C8—32no—
214C2×C3×C8—64no—
215C2×C3×C8C22×D312yes—
216C2×C3×C8C22×D312yes—
217C3×C4⋊C4—32no—
218C3×C22⋊C4—32no—
219C3×C42—21no—
220C3×C42—32no—
221C3×C42—31no—
222C3×C42—31no—
223C3×C42C22×D311yescharacteristic
224C3×C42C22×D311yescharacteristic
225#217—32no—
226(C2×D3)⋊C4—32no—
227(C2×D3)⋊C4—32no—
228(C2×D3)⋊C4—32no—
229(C2×D3)⋊C4—32no—
230(C2×D3)⋊C4—32no—
231(C2×D3)⋊C4—62no—
232(C2×D3)⋊C4C4×D312yes—
233C4⋊Dic3—32no—
234Dic3⋊C4—32no—
235Dic3⋊C4—32no—
236Dic3⋊C4—32no—
237Dic3⋊C4—32no—
238Dic3⋊C4—32no—
239Dic3⋊C4—62no—
240Dic3⋊C4C4×D312yes—
241C4×Dic3—31no—
242C4×Dic3—31no—
243C4×Dic3—32no—
244C4×Dic3—32no—
245C4×Dic3—61no—
246C4×Dic3C4×D312yes—
247C4×Dic3C22×D311yescharacteristic
248C4×Dic3C22×D311yescharacteristic
249C2×C3⋊C8—32no—
250C2×C3⋊C8—32no—
251C2×C3⋊C8—62no—
252C2×C3⋊C8—64no—
253C2×C3⋊C8C22×D312yes—
254C2×C3⋊C8C22×D312yes—
255D3×C8—24no—
256D3×C8—64no—
257C22×C32C23×C411yescharacteristic
258C2×C3⋊D3—21no—
259C2×C3⋊D3—22no—
260C2×C3×D3—21no—
261C2×C3×D3—22no—
262C2×C3×D3#11712yes—
263C2×C3×D3#13114yes—
264D32—44no—
265C32×C4—22no—
266C32×C4C2×#4112yes—
267C3⋊Dic3—21no—
268C3⋊Dic3—22no—
269C3×Dic3—21no—
270C3×Dic3—22no—
271C3×Dic3—22no—
272C3×Dic3#11712yes—
273C23×C4—91no—
274C22×C8—32no—
275C22×C8—92no—
276#117—31no—
277#117—91no—
278#117—92no—
279#117—92no—
280#117—91no—
281#117—91no—
282C2×C4⋊C4—92no—
283C2×C22⋊C4—92no—
284C2×C42—31no—
285C2×C42—91no—
286C4⋊C8—32no—
287C4⋊C8—92no—
288C4⋊C8—92no—
289C4⋊C8—92no—
290C22⋊C8—32no—
291C22⋊C8—92no—
292C22⋊C8—92no—
293C22⋊C8—92no—
294#97—31no—
295#97—92no—
296#97—91no—
297C4×C8—32no—
298C4×C8—31no—
299C4×C8D3211yescharacteristic, complemented
300C23×C3—31no—
301C23×C3—31no—
302C22×D3—31no—
303C22×D3—31no—
304C22×D3—61no—
305C22×D3—62no—
306C22×D3—64no—
307C22×D3—62no—
308C22×D3—64no—
309C22×D3C2×C4×D311yescharacteristic
310C22×D3C2×C4×D311yescharacteristic
311C2×C3×C4—21no—
312C2×C3×C4—22no—
313C2×C3×C4—31no—
314C2×C3×C4—34no—
315C2×C3×C4—32no—
316C2×C3×C4—32no—
317C2×C3×C4—31no—
318C2×C3×C4—64no—
319C2×C3×C4—62no—
320C2×C3×C4C2×C4×D312yes—
321C2×C3×C4C2×C4×D312yes—
322C2×C3×C4C23×D311yescharacteristic
323C2×C3×C4C23×D311yescharacteristic
324C2×Dic3—32no—
325C2×Dic3—32no—
326C2×Dic3—31no—
327C2×Dic3—31no—
328C2×Dic3—62no—
329C2×Dic3—61no—
330C2×Dic3—62no—
331C2×Dic3—64no—
332C2×Dic3—62no—
333C2×Dic3C2×C4×D312yes—
334C2×Dic3C2×C4×D312yes—
335C2×Dic3C2×C4×D311yescharacteristic
336C2×Dic3C2×C4×D311yescharacteristic
337C4×D3—24no—
338C4×D3—22no—
339C4×D3—62no—
340C4×D3—62no—
341C4×D3—62no—
342C4×D3—64no—
343C4×D3—62no—
344C4×D3—62no—
345C4×D3—62no—
346C4×D3—122no—
347C4×D3#23514yes—
348C3×C8—22no—
349C3×C8—22no—
350C3×C8—42no—
351C3×C8—62no—
352C3×C8—62no—
353C3⋊C8—22no—
354C3⋊C8—22no—
355C3⋊C8—62no—
356C3⋊C8—62no—
357C3⋊C8—122no—
358C2×C32C2×#11711yescharacteristic
359C2×C32C2×#13112yes—
360C3⋊D3—41no—
361C3×D3—41no—
362C3×D3#43314yescomplemented
363C24—91no—
364C22×C4—31no—
365C22×C4—31no—
366C22×C4—32no—
367C22×C4—91no—
368C22×C4—92no—
369C22×C4—91no—
370C22×C4—91no—
371C22×C4—91no—
372C22×C4—184no—
373C2×C8—32no—
374C2×C8—32no—
375C2×C8—64no—
376C2×C8—92no—
377C2×C8—184no—
378C2×C8C2×D3212yes—
379C4⋊C4—32no—
380C4⋊C4—92no—
381C4⋊C4—92no—
382C4⋊C4—92no—
383C22⋊C4—32no—
384C22⋊C4—92no—
385C22⋊C4—92no—
386C22⋊C4—92no—
387C42—31no—
388C42—31no—
389C42—32no—
390C42—92no—
391C42—91no—
392C42C2×D3211yescharacteristic
393C22×C3—21no—
394C22×C3—34no—
395C22×C3—32no—
396C22×C3—61no—
397C22×C3—62no—
398C22×C3C22×C4×D311yescharacteristic
399C22×C3C22×C4×D311yescharacteristic
400C2×D3—22no—
401C2×D3—21no—
402C2×D3—61no—
403C2×D3—62no—
404C2×D3—62no—
405C2×D3—61no—
406C2×D3—121no—
407C2×D3—122no—
408C2×D3—124no—
409C2×D3—124no—
410C2×D3#87212yes—
411C2×D3#90114yes—
412C3×C4—22no—
413C3×C4—22no—
414C3×C4—22no—
415C3×C4—32no—
416C3×C4—42no—
417C3×C4—61no—
418C3×C4—62no—
419C3×C4—62no—
420C3×C4C2×#23512yes—
421C3×C4D3×#4112yes—
422Dic3—22no—
423Dic3—22no—
424Dic3—21no—
425Dic3—61no—
426Dic3—62no—
427Dic3—62no—
428Dic3—61no—
429Dic3—121no—
430Dic3—122no—
431Dic3#87212yes—
432C32C2×#43311yescharacteristic, complemented, Sylow
433C23—31no—
434C23—31no—
435C23—91no—
436C23—182no—
437C23—184no—
438C2×C4—31no—
439C2×C4—34no—
440C2×C4—32no—
441C2×C4—32no—
442C2×C4—31no—
443C2×C4—64no—
444C2×C4—62no—
445C2×C4—92no—
446C2×C4—91no—
447C2×C4—182no—
448C2×C4—182no—
449C2×C4—182no—
450C2×C4—184no—
451C2×C4—182no—
452C2×C4C4×D3212yes—
453C2×C4C22×D3211yescharacteristic
454C8—22no—
455C8—62no—
456C8—62no—
457C8—182no—
458C2×C3—22no—
459C2×C3—21no—
460C2×C3—34no—
461C2×C3—121no—
462C2×C3C2×#87211yescharacteristic
463C2×C3D3×#11711yescharacteristic
464C2×C3C2×#90112yes—
465C2×C3D3×#13112yes—
466D3—41no—
467D3—121no—
468D3—121no—
469D3—241no—
470D3#469014yesdirect product factor
471C22—34no—
472C22—32no—
473C22—62no—
474C22—61no—
475C22—182no—
476C22—181no—
477C22—364no—
478C22C2×C4×D3211yescharacteristic
479C4—22no—
480C4—32no—
481C4—62no—
482C4—62no—
483C4—61no—
484C4—182no—
485C4—181no—
486C4D3×#23512yes—
487C3—21no—
488C3C2×#469011yescharacteristic, complemented
489C3D3×#43311yescharacteristic, complemented
490C2—34no—
491C2—121no—
492C2—361no—
493C2D3×#87211yescharacteristic
494C2D3×#90112yes—
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC32×C4×C8C22
prime radicalC22×D32C2×C4
cosocleC2×C32×C4C24
hypercenterC4×C8D32
hypocenterC32C2×#433
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. #10592389C2semidirect
3. C3×#4690C2semidirect
4. C3×C4×D3×C8C2semidirect
6. #10590696C2semidirect
7. D3×Dic3⋊C8C2semidirect
8. #10590648C2semidirect
9. D3×#803C2semidirect
10. #10590298C2semidirect
11. #10590264C2semidirect
27. C32×C4×C8C22semidirect
29. #63641C22semidirect
30. #63630C22semidirect
32. C3×Dic3⋊C8C22semidirect
33. C3×C8×Dic3C22semidirect
34. C3×#803C22semidirect
35. C3×C4×C3⋊C8C22semidirect
36. #63572C22semidirect
37. Dic3⋊(C3⋊C8)C22semidirect
40. #63554C22semidirect
62. #4690D3direct (N × H)
63. C4×D3×C8D3semidirect
128. C3×C4×C8C2×D3semidirect
129. C3×C4×C8C2×D3semidirect
145. Dic3⋊C8C2×D3semidirect
146. C8×Dic3C2×D3semidirect
152. #803C2×D3semidirect
153. C4×C3⋊C8C2×D3semidirect
299. C4×C8D32semidirect
362. C3×D3#433semidirect
432. C32C2×#433semidirect
470. D3#4690direct (N × H)
488. C3C2×#4690semidirect
489. C3D3×#433semidirect

Maximal subgroups

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

subgroupindex
D3×#8722
#105923892
C3×#46902
C3×C4×D3×C82
D3×(C2×D3)⋊C82
#105906962
D3×Dic3⋊C82
#105906482
D3×#8032
#105902982
#105902642
D3×#4333
C2×#46903