Finite Group Databasebeta

← D3×#894 #10594607

Subgroups — D3×#894 #10594607

Order 576.

723 conjugacy classes of subgroups.

The subgroup lattice has 531 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×D12C211yesmaximal, characteristic
2C2×C4×D32C211yesmaximal, characteristic, complemented
3#64103C211yesmaximal, characteristic, complemented
4C3×#894C211yesmaximal, characteristic, complemented
5C3×D3×C4⋊C4C211yesmaximal, characteristic, complemented
6D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
7D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
8D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
9#63897C211yesmaximal, characteristic, complemented
10#63890C211yesmaximal, characteristic, complemented
11#63884C211yesmaximal, characteristic, complemented
12D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
13#63854C211yesmaximal, characteristic, complemented
14#63853C211yesmaximal, characteristic, complemented
15#63850C211yesmaximal, characteristic, complemented
16D3×#123—31nomaximal
17C2×#894—31nomaximal
18C22×D32C2211yescharacteristic
19C22×D32C2211yescharacteristic
20C2×C4⋊(C3⋊D3)C2211yescharacteristic
21C2×C4×C3⋊D3C2211yescharacteristic, complemented
22C2×C3×D12C2211yescharacteristic
23C2×C3×C4×D3C2211yescharacteristic
24C2×C3×C4×D3C2211yescharacteristic
25C2×C3×C4×D3C2211yescharacteristic
26C2×C3×C4×D3C2211yescharacteristic, complemented
27C2×#626C2211yescharacteristic
28C2×#626C2211yescharacteristic
29C2×#624C2211yescharacteristic, complemented
30C2×D3×Dic3C2211yescharacteristic
31C2×D3×Dic3C2211yescharacteristic
32C2×D3×Dic3C2211yescharacteristic, complemented
33D3×D12—24no—
34C4×D32—24no—
35C32×C4⋊C4C2211yescharacteristic, complemented
36#3752C2211yescharacteristic, complemented
37#3752C2211yescharacteristic, complemented
38#3752C2211yescharacteristic, complemented
39#3750C2211yescharacteristic, complemented
40C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
41C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
42C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
43C3×C4⋊Dic3C2211yescharacteristic, complemented
44C3×Dic3⋊C4C2211yescharacteristic, complemented
45C3×Dic3⋊C4C2211yescharacteristic, complemented
46C3×Dic3⋊C4C2211yescharacteristic, complemented
47#3724C2211yescharacteristic, complemented
48Dic3⋊Dic3C2211yescharacteristic, complemented
49#3722C2211yescharacteristic, complemented
50#3722C2211yescharacteristic, complemented
51#3722C2211yescharacteristic, complemented
52(C2×D3)⋊Dic3C2211yescharacteristic, complemented
53(C2×D3)⋊Dic3C2211yescharacteristic, complemented
54(C2×D3)⋊Dic3C2211yescharacteristic, complemented
55C2×D3×D4—31no—
56C22×D12—31no—
57C22×C4×D3—31no—
58C22×C4×D3—31no—
59C3×#123—31no—
60C2×C3×C4⋊C4—31no—
61#935—31no—
62#929—31no—
63C2×(C2×D3)⋊C4—31no—
64C2×(C2×D3)⋊C4—31no—
65C2×(C2×D3)⋊C4—31no—
66C2×Dic3⋊C4—31no—
67#894—31no—
68#894—31no—
69#894—31no—
70#894—31no—
71#894—31no—
72#894—31no—
73#894—31no—
74#894—31no—
75#894—31no—
76#894—61no—
77#894D311yescharacteristic, direct product factor
78D3×C4⋊C4—31no—
79D3×C4⋊C4D311yescharacteristic, complemented
80#886—31no—
81#883—31no—
82#883—31no—
83D3×C22⋊C4—31no—
84D3×C22⋊C4—31no—
85D3×C22⋊C4—31no—
86C22×C3⋊D3C2311yescharacteristic
87C22×C3⋊D3C2311yescharacteristic
88C22×C3×D3C2311yescharacteristic
89C22×C3×D3C2311yescharacteristic
90C22×C3×D3C2311yescharacteristic
91C2×D32—22no—
92C2×D32—22no—
93C2×D32—22no—
94C2×D32—22no—
95C2×D32—22no—
96C2×D32D414yes—
97C2×C32×C4C2311yescharacteristic
98C2×C32×C4C2311yescharacteristic
99C2×C32×C4C2311yescharacteristic
100C2×C3⋊Dic3C2311yescharacteristic
101C2×C3⋊Dic3C2311yescharacteristic
102C4⋊(C3⋊D3)—22no—
103C4×C3⋊D3—22no—
104C2×C3×Dic3C2311yescharacteristic
105C2×C3×Dic3C2311yescharacteristic
106C2×C3×Dic3C2311yescharacteristic
107C2×C3×Dic3C2311yescharacteristic
108C2×C3×Dic3C2311yescharacteristic
109C3×D12—22no—
110C3×C4×D3—22no—
111C3×C4×D3—22no—
112C3×C4×D3—22no—
113C3×C4×D3—22no—
114#626—22no—
115#626—22no—
116#624—22no—
117D3×Dic3—22no—
118D3×Dic3—22no—
119D3×Dic3—22no—
120C2×#123—91noSylow
121C23×D3—31no—
122C23×D3—31no—
123C23×D3—31no—
124C23×D3—31no—
125C2×C3×D4—31no—
126C22×C3×C4—31no—
127C22×C3×C4—31no—
128C22×C3×C4—31no—
129C22×C3×C4—31no—
130C2×#67—31no—
131C2×#67—31no—
132C22×Dic3—31no—
133C22×Dic3—31no—
134C22×Dic3—31no—
135D3×D4—64no—
136C2×D12—31no—
137C2×D12—31no—
138C2×D12—31no—
139C2×D12—31no—
140C2×D12—61no—
141C2×D12—64no—
142C2×D12C2×D311yescharacteristic
143C2×C4×D3—31no—
144C2×C4×D3—31no—
145C2×C4×D3—31no—
146C2×C4×D3—31no—
147C2×C4×D3—31no—
148C2×C4×D3—31no—
149C2×C4×D3—31no—
150C2×C4×D3—61no—
151C2×C4×D3—64no—
152C2×C4×D3—64no—
153C2×C4×D3C2×D311yescharacteristic
154C2×C4×D3C2×D311yescharacteristic
155C2×C4×D3C2×D311yescharacteristic
156C2×C4×D3C2×D311yescharacteristic, complemented
157C3×C4⋊C4—21no—
158C3×C4⋊C4—31no—
159C3×C4⋊C4—31no—
160C3×C4⋊C4—31no—
161C3×C4⋊C4—31no—
162C3×C4⋊C4C2×D311yescharacteristic, complemented
163C3×C4⋊C4C2×D311yescharacteristic, complemented
164C3×C22⋊C4—31no—
165C3×C22⋊C4—31no—
166C3×C22⋊C4—31no—
167#217—31no—
168#217—31no—
169#217—31no—
170(C2×D3)⋊C4—31no—
171(C2×D3)⋊C4—31no—
172(C2×D3)⋊C4—31no—
173(C2×D3)⋊C4—31no—
174(C2×D3)⋊C4—31no—
175(C2×D3)⋊C4—31no—
176(C2×D3)⋊C4—31no—
177(C2×D3)⋊C4—31no—
178(C2×D3)⋊C4—31no—
179(C2×D3)⋊C4—31no—
180(C2×D3)⋊C4—31no—
181(C2×D3)⋊C4—31no—
182(C2×D3)⋊C4—31no—
183(C2×D3)⋊C4—31no—
184(C2×D3)⋊C4—31no—
185(C2×D3)⋊C4—61no—
186(C2×D3)⋊C4—61no—
187(C2×D3)⋊C4—61no—
188(C2×D3)⋊C4C2×D311yescharacteristic, complemented
189(C2×D3)⋊C4C2×D311yescharacteristic, complemented
190(C2×D3)⋊C4C2×D311yescharacteristic, complemented
191C4⋊Dic3—31no—
192C4⋊Dic3C2×D311yescharacteristic, complemented
193Dic3⋊C4—31no—
194Dic3⋊C4—31no—
195Dic3⋊C4—31no—
196Dic3⋊C4—31no—
197Dic3⋊C4—31no—
198Dic3⋊C4—61no—
199Dic3⋊C4C2×D311yescharacteristic, complemented
200Dic3⋊C4C2×D311yescharacteristic, complemented
201Dic3⋊C4C2×D311yescharacteristic, complemented
202C22×C32C2411yescharacteristic
203C2×C3⋊D3—21no—
204C2×C3⋊D3—21no—
205C2×C3⋊D3—21no—
206C2×C3⋊D3—21no—
207C2×C3⋊D3—21no—
208C2×C3⋊D3C2×D412yes—
209C2×C3×D3—21no—
210C2×C3×D3—21no—
211C2×C3×D3—21no—
212C2×C3×D3—21no—
213C2×C3×D3—21no—
214C2×C3×D3C2×D412yes—
215C2×C3×D3C2×D412yes—
216C2×C3×D3#4112yes—
217C2×C3×D3#4112yes—
218D32—28no—
219D32—44no—
220C32×C4—21no—
221C32×C4—21no—
222C32×C4—21no—
223C3⋊Dic3—21no—
224C3⋊Dic3—21no—
225C3×Dic3—21no—
226C3×Dic3—21no—
227C3×Dic3—21no—
228C3×Dic3—21no—
229C3×Dic3—21no—
230C22×D4—91no—
231C23×C4—91no—
232#123—31no—
233#123—91no—
234#123—91no—
235#123—91no—
236#123—91no—
237#123—91no—
238#123—91no—
239#123—91no—
240C2×C4⋊C4—31no—
241C2×C4⋊C4—91no—
242C2×C22⋊C4—91no—
243C2×C22⋊C4—91no—
244C2×C22⋊C4—91no—
245C23×C3—31no—
246C23×C3—31no—
247C23×C3—31no—
248C22×D3—31no—
249C22×D3—31no—
250C22×D3—34no—
251C22×D3—34no—
252C22×D3—31no—
253C22×D3—31no—
254C22×D3—61no—
255C22×D3—61no—
256C22×D3—62no—
257C22×D3—62no—
258C22×D3—62no—
259C22×D3—62no—
260C22×D3—62no—
261C22×D3—62no—
262C22×D3—62no—
263C22×D3—62no—
264C22×D3—62no—
265C22×D3—62no—
266C22×D3C22×D311yescharacteristic
267C22×D3C22×D311yescharacteristic
268C22×D3C22×D311yescharacteristic
269C3×D4—62no—
270C2×C3×C4—21no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—31no—
274C2×C3×C4—31no—
275C2×C3×C4—31no—
276C2×C3×C4—31no—
277C2×C3×C4—31no—
278C2×C3×C4—62no—
279C2×C3×C4—62no—
280C2×C3×C4—62no—
281C2×C3×C4—62no—
282C2×C3×C4C22×D311yescharacteristic
283C2×C3×C4C22×D311yescharacteristic
284C2×C3×C4C22×D311yescharacteristic
285C2×C3×C4C22×D311yescharacteristic
286C2×C3×C4C22×D311yescharacteristic
287C2×C3×C4C22×D311yescharacteristic
288#67—62no—
289#67—62no—
290C2×Dic3—31no—
291C2×Dic3—31no—
292C2×Dic3—31no—
293C2×Dic3—31no—
294C2×Dic3—61no—
295C2×Dic3—61no—
296C2×Dic3—62no—
297C2×Dic3—62no—
298C2×Dic3—62no—
299C2×Dic3C22×D311yescharacteristic
300C2×Dic3C22×D311yescharacteristic
301C2×Dic3C22×D311yescharacteristic
302C2×Dic3C22×D311yescharacteristic
303C2×Dic3C22×D311yescharacteristic
304D12—22no—
305D12—62no—
306D12—62no—
307D12—62no—
308D12—62no—
309D12—122no—
310C4×D3—22no—
311C4×D3—22no—
312C4×D3—22no—
313C4×D3—22no—
314C4×D3—62no—
315C4×D3—62no—
316C4×D3—62no—
317C4×D3—62no—
318C4×D3—62no—
319C4×D3—62no—
320C4×D3—62no—
321C4×D3—122no—
322C2×C32C22×D411yescharacteristic
323C2×C32C2×#4111yescharacteristic
324C2×C32C2×#4111yescharacteristic
325C3⋊D3—22no—
326C3⋊D3—41no—
327C3×D3—22no—
328C3×D3—41no—
329C3×D3#12314yescomplemented
330C24—91no—
331C24—91no—
332C2×D4—31no—
333C2×D4—91no—
334C2×D4—91no—
335C2×D4—91no—
336C2×D4—184no—
337C22×C4—31no—
338C22×C4—31no—
339C22×C4—31no—
340C22×C4—31no—
341C22×C4—91no—
342C22×C4—91no—
343C22×C4—91no—
344C22×C4—91no—
345C22×C4—91no—
346C22×C4—184no—
347C4⋊C4—31no—
348C4⋊C4—31no—
349C4⋊C4—31no—
350C4⋊C4—31no—
351C4⋊C4—91no—
352C4⋊C4—91no—
353C4⋊C4—91no—
354C4⋊C4D3211yescharacteristic, complemented
355C22⋊C4—31no—
356C22⋊C4—31no—
357C22⋊C4—31no—
358C22⋊C4—91no—
359C22⋊C4—91no—
360C22⋊C4—91no—
361C22⋊C4—91no—
362C22⋊C4—91no—
363C22⋊C4—91no—
364C22⋊C4—91no—
365C22⋊C4—91no—
366C22⋊C4—91no—
367C22×C3—21no—
368C22×C3—32no—
369C22×C3—32no—
370C22×C3—32no—
371C22×C3—32no—
372C22×C3—61no—
373C22×C3—61no—
374C22×C3—61no—
375C22×C3—61no—
376C22×C3—61no—
377C22×C3C23×D311yescharacteristic
378C22×C3C23×D311yescharacteristic
379C2×D3—21no—
380C2×D3—21no—
381C2×D3—21no—
382C2×D3—21no—
383C2×D3—21no—
384C2×D3—32no—
385C2×D3—32no—
386C2×D3—62no—
387C2×D3—68no—
388C2×D3—61no—
389C2×D3—61no—
390C2×D3—61no—
391C2×D3—61no—
392C2×D3—68no—
393C2×D3—61no—
394C2×D3—61no—
395C2×D3—61no—
396C2×D3—61no—
397C2×D3—61no—
398C2×D3—61no—
399C2×D3—121no—
400C2×D3—121no—
401C2×D3—121no—
402C2×D3—121no—
403C2×D3—121no—
404C2×D3—124no—
405C2×D3—124no—
406C2×D3#23512yes—
407C2×D3D3×D412yes—
408C2×D3D3×D412yes—
409C2×D3#23912yes—
410C3×C4—21no—
411C3×C4—21no—
412C3×C4—21no—
413C3×C4—21no—
414C3×C4—21no—
415C3×C4—21no—
416C3×C4—41no—
417C3×C4—41no—
418C3×C4—41no—
419C3×C4—61no—
420C3×C4—61no—
421C3×C4—61no—
422C3×C4—61no—
423C3×C4—61no—
424Dic3—21no—
425Dic3—21no—
426Dic3—21no—
427Dic3—21no—
428Dic3—21no—
429Dic3—61no—
430Dic3—61no—
431Dic3—61no—
432Dic3—61no—
433Dic3—121no—
434Dic3—121no—
435C32C2×#12311yescharacteristic, complemented, Sylow
436C23—31no—
437C23—31no—
438C23—31no—
439C23—94no—
440C23—91no—
441C23—91no—
442C23—182no—
443C23—182no—
444C23—182no—
445C23—182no—
446C23—182no—
447D4—62no—
448D4—182no—
449D4—182no—
450D4—182no—
451C2×C4—31no—
452C2×C4—31no—
453C2×C4—31no—
454C2×C4—31no—
455C2×C4—31no—
456C2×C4—62no—
457C2×C4—62no—
458C2×C4—62no—
459C2×C4—62no—
460C2×C4—91no—
461C2×C4—91no—
462C2×C4—182no—
463C2×C4—182no—
464C2×C4—182no—
465C2×C4—182no—
466C2×C4—182no—
467C2×C4C2×D3211yescharacteristic
468C2×C4C2×D3211yescharacteristic
469C2×C4C2×D3211yescharacteristic
470C2×C3—21no—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3—34no—
474C2×C3—62no—
475C2×C3—121no—
476C2×C3C2×#23511yescharacteristic
477C2×C3C2×D3×D411yescharacteristic
478C2×C3C2×D3×D411yescharacteristic
479C2×C3C2×#23911yescharacteristic
480C2×C3D3×#4111yescharacteristic
481C2×C3D3×#4111yescharacteristic
482D3—22no—
483D3—41no—
484D3—62no—
485D3—62no—
486D3—122no—
487D3—121no—
488D3—121no—
489D3—241no—
490D3#89414yesdirect product factor
491C22—32no—
492C22—32no—
493C22—32no—
494C22—32no—
495C22—61no—
496C22—61no—
497C22—61no—
498C22—61no—
499C22—61no—
500C22—92no—
501C22—188no—
502C22—181no—
503C22—181no—
504C22—181no—
505C22—181no—
506C22—181no—
507C22—364no—
508C22C22×D3211yescharacteristic
509C4—21no—
510C4—21no—
511C4—21no—
512C4—61no—
513C4—61no—
514C4—61no—
515C4—61no—
516C4—61no—
517C4—181no—
518C4—181no—
519C3—21no—
520C3C2×#89411yescharacteristic, complemented
521C3D3×#12311yescharacteristic, complemented
522C2—34no—
523C2—62no—
524C2—121no—
525C2—182no—
526C2—361no—
527C2D3×#23511yescharacteristic
528C2D32×D411yescharacteristic
529C2D3×#23911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D32
commutator, socle, cosocleC22×C32C24
FittingC32×C4⋊C4C22
prime radicalC2×D3×D12C2
hypercenterC4⋊C4D32
hypocenterC32C2×#123
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×D32C2semidirect
3. #64103C2semidirect
4. C3×#894C2semidirect
5. C3×D3×C4⋊C4C2semidirect
6. D3×(C2×D3)⋊C4C2semidirect
7. D3×(C2×D3)⋊C4C2semidirect
8. D3×(C2×D3)⋊C4C2semidirect
9. #63897C2semidirect
10. #63890C2semidirect
11. #63884C2semidirect
12. D3×Dic3⋊C4C2semidirect
13. #63854C2semidirect
14. #63853C2semidirect
15. #63850C2semidirect
21. C2×C4×C3⋊D3C22semidirect
26. C2×C3×C4×D3C22semidirect
29. C2×#624C22semidirect
32. C2×D3×Dic3C22semidirect
35. C32×C4⋊C4C22semidirect
36. #3752C22semidirect
37. #3752C22semidirect
38. #3752C22semidirect
39. #3750C22semidirect
40. C3×(C2×D3)⋊C4C22semidirect
41. C3×(C2×D3)⋊C4C22semidirect
42. C3×(C2×D3)⋊C4C22semidirect
43. C3×C4⋊Dic3C22semidirect
44. C3×Dic3⋊C4C22semidirect
45. C3×Dic3⋊C4C22semidirect
46. C3×Dic3⋊C4C22semidirect
47. #3724C22semidirect
48. Dic3⋊Dic3C22semidirect
49. #3722C22semidirect
50. #3722C22semidirect
51. #3722C22semidirect
52. (C2×D3)⋊Dic3C22semidirect
53. (C2×D3)⋊Dic3C22semidirect
54. (C2×D3)⋊Dic3C22semidirect
77. #894D3direct (N × H)
79. D3×C4⋊C4D3semidirect
156. C2×C4×D3C2×D3semidirect
162. C3×C4⋊C4C2×D3semidirect
163. C3×C4⋊C4C2×D3semidirect
188. (C2×D3)⋊C4C2×D3semidirect
189. (C2×D3)⋊C4C2×D3semidirect
190. (C2×D3)⋊C4C2×D3semidirect
192. C4⋊Dic3C2×D3semidirect
199. Dic3⋊C4C2×D3semidirect
200. Dic3⋊C4C2×D3semidirect
201. Dic3⋊C4C2×D3semidirect
329. C3×D3#123semidirect
354. C4⋊C4D32semidirect
435. C32C2×#123semidirect
490. D3#894direct (N × H)
520. C3C2×#894semidirect
521. C3D3×#123semidirect

Maximal subgroups

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

subgroupindex
C2×D3×D122
C2×C4×D322
#641032
C3×#8942
C3×D3×C4⋊C42
D3×(C2×D3)⋊C42
#638972
#638902
#638842
D3×Dic3⋊C42
#638542
#638532
#638502
D3×#1233
C2×#8943