Finite Group Databasebeta

← D3×#388 #75824

Subgroups — D3×#388 #75824

Order 384.

928 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×C4⋊C4C211yesmaximal, characteristic, complemented
2C2×D3×C22⋊C4C211yesmaximal, characteristic
3C2×D3×C22⋊C4C211yesmaximal, characteristic
4C2×D3×C22⋊C4C211yesmaximal, characteristic
5C2×C42×D3C211yesmaximal, characteristic, complemented
6C3×#388C211yesmaximal, characteristic, complemented
7#4990C211yesmaximal, characteristic, complemented
8#4951C211yesmaximal, characteristic, complemented
9#4945C211yesmaximal, characteristic, complemented
10#4944C211yesmaximal, characteristic, complemented
11#4940C211yesmaximal, characteristic, complemented
12#4670C211yesmaximal, characteristic, complemented
13#4669C211yesmaximal, characteristic, complemented
14D3×#95C211yesmaximal, characteristic, complemented
15D3×#95C211yesmaximal, characteristic, complemented
16C2×#388—31nomaximal, Sylow
17C24×D3C2211yescharacteristic
18C22×C4×D3C2211yescharacteristic
19C22×C4×D3C2211yescharacteristic
20C22×C4×D3C2211yescharacteristic
21C22×C4×D3C2211yescharacteristic
22C22×C4×D3C2211yescharacteristic
23C22×C4×D3C2211yescharacteristic
24C2×C3×C4⋊C4C2211yescharacteristic, complemented
25C2×C3×C22⋊C4C2211yescharacteristic
26C2×C3×C22⋊C4C2211yescharacteristic
27C2×C3×C22⋊C4C2211yescharacteristic
28C2×C3×C42C2211yescharacteristic, complemented
29C2×#217C2211yescharacteristic
30C2×#217C2211yescharacteristic
31C2×#217C2211yescharacteristic
32C2×(C2×D3)⋊C4C2211yescharacteristic
33C2×(C2×D3)⋊C4C2211yescharacteristic
34C2×(C2×D3)⋊C4C2211yescharacteristic
35C2×(C2×D3)⋊C4C2211yescharacteristic
36C2×(C2×D3)⋊C4C2211yescharacteristic
37C2×(C2×D3)⋊C4C2211yescharacteristic
38C2×C4⋊Dic3C2211yescharacteristic, complemented
39C2×Dic3⋊C4C2211yescharacteristic, complemented
40C2×Dic3⋊C4C2211yescharacteristic, complemented
41C2×C4×Dic3C2211yescharacteristic, complemented
42C2×C4×Dic3C2211yescharacteristic, complemented
43C2×C4×Dic3C2211yescharacteristic, complemented
44D3×C4⋊C4—24no—
45D3×C22⋊C4—24no—
46D3×C22⋊C4—24no—
47D3×C22⋊C4C418yescomplemented
48C42×D3—24no—
49C3×#95C2211yescharacteristic, complemented
50C3×#95C2211yescharacteristic, complemented
51C3⋊#95C2211yescharacteristic, complemented
52C3⋊#95C2211yescharacteristic, complemented
53C3⋊#95C2211yescharacteristic, complemented
54C3⋊#95C2211yescharacteristic, complemented
55C3⋊#95C2211yescharacteristic, complemented
56C3⋊#95C2211yescharacteristic, complemented
57C22×C4⋊C4—31no—
58C22×C22⋊C4—31no—
59C22×C22⋊C4—31no—
60C22×C22⋊C4—31no—
61C22×C42—31no—
62#388—31no—
63#388—31no—
64#388—31no—
65#388—31no—
66#388—31no—
67#388—31no—
68#388—31no—
69#388D311yescharacteristic, direct product factor
70C2×#95—31no—
71C2×#95—31no—
72C24×C3C2311yescharacteristic
73C23×D3—22no—
74C23×D3—22no—
75C23×D3—22no—
76C23×D3—22no—
77C23×D3—22no—
78C23×D3—22no—
79C23×D3C2×C414yes—
80C23×D3C2311yescharacteristic
81C23×D3C2311yescharacteristic
82C22×C3×C4C2311yescharacteristic
83C22×C3×C4C2311yescharacteristic
84C22×C3×C4C2311yescharacteristic
85C22×C3×C4C2311yescharacteristic
86C22×C3×C4C2311yescharacteristic
87C22×C3×C4C2311yescharacteristic
88C22×Dic3C2311yescharacteristic
89C22×Dic3C2311yescharacteristic
90C22×Dic3C2311yescharacteristic
91C22×Dic3C2311yescharacteristic
92C22×Dic3C2311yescharacteristic
93C22×Dic3C2311yescharacteristic
94C2×C4×D3—22no—
95C2×C4×D3—22no—
96C2×C4×D3—22no—
97C2×C4×D3—22no—
98C2×C4×D3—22no—
99C2×C4×D3—22no—
100C2×C4×D3—22no—
101C2×C4×D3—22no—
102C2×C4×D3—22no—
103C2×C4×D3—22no—
104C2×C4×D3—22no—
105C2×C4×D3—22no—
106C2×C4×D3—22no—
107C2×C4×D3—22no—
108C2×C4×D3C2×C414yes—
109C2×C4×D3C2×C414yes—
110C2×C4×D3D414yes—
111C2×C4×D3D414yes—
112C3×C4⋊C4—22no—
113C3×C22⋊C4—22no—
114C3×C22⋊C4—22no—
115C3×C22⋊C4C2×C414yescomplemented
116C3×C42—22no—
117#217—22no—
118#217—22no—
119#217C2×C414yescomplemented
120(C2×D3)⋊C4—22no—
121(C2×D3)⋊C4—22no—
122(C2×D3)⋊C4—22no—
123(C2×D3)⋊C4—22no—
124(C2×D3)⋊C4C2×C414yescomplemented
125(C2×D3)⋊C4C2×C414yescomplemented
126C4⋊Dic3—22no—
127Dic3⋊C4—22no—
128Dic3⋊C4—22no—
129C4×Dic3—22no—
130C4×Dic3—22no—
131C4×Dic3—22no—
132C25—31no—
133C23×C4—31no—
134C23×C4—31no—
135C23×C4—31no—
136C23×C4—31no—
137C23×C4—31no—
138C23×C4—31no—
139C2×C4⋊C4—31no—
140C2×C4⋊C4—31no—
141C2×C4⋊C4—31no—
142C2×C4⋊C4—64no—
143C2×C4⋊C4C2×D311yescharacteristic, complemented
144C2×C22⋊C4—31no—
145C2×C22⋊C4—31no—
146C2×C22⋊C4—31no—
147C2×C22⋊C4—38no—
148C2×C22⋊C4—31no—
149C2×C22⋊C4—31no—
150C2×C22⋊C4—31no—
151C2×C22⋊C4—31no—
152C2×C22⋊C4—31no—
153C2×C22⋊C4—31no—
154C2×C22⋊C4—64no—
155C2×C22⋊C4—64no—
156C2×C22⋊C4C2×D311yescharacteristic
157C2×C22⋊C4C2×D311yescharacteristic
158C2×C22⋊C4C2×D311yescharacteristic
159C2×C42—31no—
160C2×C42—31no—
161C2×C42—31no—
162C2×C42—64no—
163C2×C42C2×D311yescharacteristic, complemented
164#95—31no—
165#95—31no—
166#95—31no—
167#95—31no—
168#95—31no—
169#95—31no—
170#95C2×D311yescharacteristic, complemented
171#95C2×D311yescharacteristic, complemented
172C23×C3—21no—
173C23×C3—21no—
174C23×C3—21no—
175C23×C3—21no—
176C23×C3—21no—
177C23×C3—21no—
178C23×C3C22×C412yes—
179C23×C3C2411yescharacteristic
180C22×D3—21no—
181C22×D3—21no—
182C22×D3—21no—
183C22×D3—21no—
184C22×D3—21no—
185C22×D3—21no—
186C22×D3—28no—
187C22×D3—28no—
188C22×D3—28no—
189C22×D3—44no—
190C22×D3—44no—
191C22×D3—44no—
192C22×D3—44no—
193C22×D3C22×C412yes—
194C22×D3C22×C412yes—
195C22×D3C2×D412yes—
196C22×D3C2×D412yes—
197C22×D3#4112yes—
198C22×D3#4112yes—
199C22×D3#4112yes—
200C22×D3#4112yes—
201C2×C3×C4—21no—
202C2×C3×C4—21no—
203C2×C3×C4—21no—
204C2×C3×C4—21no—
205C2×C3×C4—21no—
206C2×C3×C4—21no—
207C2×C3×C4—21no—
208C2×C3×C4—21no—
209C2×C3×C4—21no—
210C2×C3×C4—21no—
211C2×C3×C4—21no—
212C2×C3×C4—21no—
213C2×C3×C4—21no—
214C2×C3×C4—21no—
215C2×C3×C4C22×C412yes—
216C2×C3×C4C22×C412yes—
217C2×C3×C4C2×D412yes—
218C2×C3×C4C2×D412yes—
219C2×Dic3—21no—
220C2×Dic3—21no—
221C2×Dic3—21no—
222C2×Dic3—21no—
223C2×Dic3—21no—
224C2×Dic3—21no—
225C2×Dic3—21no—
226C2×Dic3—21no—
227C2×Dic3—21no—
228C2×Dic3—21no—
229C2×Dic3—21no—
230C2×Dic3—21no—
231C2×Dic3—21no—
232C2×Dic3—21no—
233C2×Dic3C22×C412yes—
234C2×Dic3C22×C412yes—
235C2×Dic3C2×D412yes—
236C2×Dic3C2×D412yes—
237C4×D3—28no—
238C4×D3—28no—
239C4×D3—28no—
240C4×D3—28no—
241C4×D3—44no—
242C4×D3—44no—
243C24—31no—
244C24—34no—
245C24—31no—
246C24—62no—
247C24—62no—
248C24—62no—
249C24—62no—
250C24—62no—
251C24—62no—
252C24C22×D311yescharacteristic
253C22×C4—31no—
254C22×C4—31no—
255C22×C4—31no—
256C22×C4—31no—
257C22×C4—34no—
258C22×C4—34no—
259C22×C4—34no—
260C22×C4—34no—
261C22×C4—31no—
262C22×C4—31no—
263C22×C4—62no—
264C22×C4—62no—
265C22×C4—62no—
266C22×C4—62no—
267C22×C4—62no—
268C22×C4—62no—
269C22×C4—62no—
270C22×C4—62no—
271C22×C4—62no—
272C22×C4—62no—
273C22×C4—62no—
274C22×C4—62no—
275C22×C4—62no—
276C22×C4—62no—
277C22×C4C22×D311yescharacteristic
278C22×C4C22×D311yescharacteristic
279C22×C4C22×D311yescharacteristic
280C22×C4C22×D311yescharacteristic
281C22×C4C22×D311yescharacteristic
282C22×C4C22×D311yescharacteristic
283C4⋊C4—22no—
284C4⋊C4—62no—
285C4⋊C4—62no—
286C4⋊C4—62no—
287C22⋊C4—22no—
288C22⋊C4—22no—
289C22⋊C4—34no—
290C22⋊C4—34no—
291C22⋊C4—34no—
292C22⋊C4—62no—
293C22⋊C4—62no—
294C22⋊C4—62no—
295C22⋊C4—62no—
296C22⋊C4—62no—
297C22⋊C4—62no—
298C22⋊C4C4×D314yescomplemented
299C42—22no—
300C42—62no—
301C42—62no—
302C42—62no—
303C22×C3—22no—
304C22×C3—22no—
305C22×C3—22no—
306C22×C3—41no—
307C22×C3—41no—
308C22×C3—41no—
309C22×C3—41no—
310C22×C3C23×C411yescharacteristic
311C22×C3C22×D411yescharacteristic
312C22×C3C22×D411yescharacteristic
313C22×C3C2×#4111yescharacteristic
314C22×C3C2×#4111yescharacteristic
315C22×C3C2×#4111yescharacteristic
316C22×C3C2×#4111yescharacteristic
317C2×D3—22no—
318C2×D3—22no—
319C2×D3—22no—
320C2×D3—41no—
321C2×D3—41no—
322C2×D3—41no—
323C2×D3—41no—
324C2×D3—416no—
325C2×D3#11714yes—
326C2×D3C4×D414yes—
327C2×D3C4×D414yes—
328C2×D3#12114yes—
329C2×D3#12314yes—
330C2×D3#12414yes—
331C2×D3#12614yes—
332C3×C4—22no—
333C3×C4—22no—
334C3×C4—22no—
335C3×C4—22no—
336C3×C4—41no—
337C3×C4—41no—
338Dic3—22no—
339Dic3—22no—
340Dic3—22no—
341Dic3—22no—
342Dic3—41no—
343Dic3—41no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—21no—
348C23—21no—
349C23—21no—
350C23—32no—
351C23—32no—
352C23—32no—
353C23—32no—
354C23—32no—
355C23—32no—
356C23—32no—
357C23—32no—
358C23—68no—
359C23—68no—
360C23—68no—
361C23—61no—
362C23—61no—
363C23—61no—
364C23—61no—
365C23—61no—
366C23—61no—
367C23—124no—
368C23—124no—
369C23—124no—
370C23—124no—
371C23C2×C4×D312yes—
372C23C23×D311yescharacteristic
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—32no—
388C2×C4—32no—
389C2×C4—32no—
390C2×C4—32no—
391C2×C4—68no—
392C2×C4—68no—
393C2×C4—68no—
394C2×C4—68no—
395C2×C4—61no—
396C2×C4—61no—
397C2×C4—61no—
398C2×C4—61no—
399C2×C4—61no—
400C2×C4—61no—
401C2×C4—61no—
402C2×C4—61no—
403C2×C4—61no—
404C2×C4—61no—
405C2×C4—61no—
406C2×C4—61no—
407C2×C4—61no—
408C2×C4—61no—
409C2×C4—124no—
410C2×C4—124no—
411C2×C4C2×C4×D312yes—
412C2×C4C2×C4×D312yes—
413C2×C4D3×D412yes—
414C2×C4D3×D412yes—
415C2×C3—42no—
416C2×C3C2×#11711yescharacteristic
417C2×C3C2×C4×D411yescharacteristic
418C2×C3C2×C4×D411yescharacteristic
419C2×C3C2×#12111yescharacteristic
420C2×C3C2×#12311yescharacteristic
421C2×C3C2×#12411yescharacteristic
422C2×C3C2×#12611yescharacteristic
423D3—42no—
424D3#38818yesdirect product factor
425C22—22no—
426C22—22no—
427C22—22no—
428C22—34no—
429C22—34no—
430C22—34no—
431C22—34no—
432C22—34no—
433C22—34no—
434C22—34no—
435C22—41no—
436C22—41no—
437C22—41no—
438C22—41no—
439C22—62no—
440C22—62no—
441C22—62no—
442C22—1216no—
443C22—121no—
444C22—121no—
445C22—121no—
446C22—121no—
447C22C22×C4×D311yescharacteristic
448C22C2×D3×D411yescharacteristic
449C22C2×D3×D411yescharacteristic
450C22D3×#4111yescharacteristic
451C22D3×#4111yescharacteristic
452C22D3×#4111yescharacteristic
453C22D3×#4111yescharacteristic
454C4—22no—
455C4—22no—
456C4—22no—
457C4—22no—
458C4—41no—
459C4—41no—
460C4—62no—
461C4—62no—
462C4—62no—
463C4—62no—
464C4—121no—
465C4—121no—
466C3C2×#38811yescharacteristic, complemented, Sylow
467C2—38no—
468C2—42no—
469C2—122no—
470C2D3×#11711yescharacteristic
471C2C4×D3×D411yescharacteristic
472C2C4×D3×D411yescharacteristic
473C2D3×#12111yescharacteristic
474C2D3×#12311yescharacteristic
475C2D3×#12411yescharacteristic
476C2D3×#12611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutatorC22×C3C23×C4
FittingC3×#388C2
socle, cosocleC23×C3C24
prime radicalC24×D3C22
hypercenter#388D3
hypocenterC3C2×#388
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×D3×C4⋊C4C2semidirect
5. C2×C42×D3C2semidirect
6. C3×#388C2semidirect
7. #4990C2semidirect
8. #4951C2semidirect
9. #4945C2semidirect
10. #4944C2semidirect
11. #4940C2semidirect
12. #4670C2semidirect
13. #4669C2semidirect
14. D3×#95C2semidirect
15. D3×#95C2semidirect
24. C2×C3×C4⋊C4C22semidirect
28. C2×C3×C42C22semidirect
38. C2×C4⋊Dic3C22semidirect
39. C2×Dic3⋊C4C22semidirect
40. C2×Dic3⋊C4C22semidirect
41. C2×C4×Dic3C22semidirect
42. C2×C4×Dic3C22semidirect
43. C2×C4×Dic3C22semidirect
47. D3×C22⋊C4C4semidirect
49. C3×#95C22semidirect
50. C3×#95C22semidirect
51. C3⋊#95C22semidirect
52. C3⋊#95C22semidirect
53. C3⋊#95C22semidirect
54. C3⋊#95C22semidirect
55. C3⋊#95C22semidirect
56. C3⋊#95C22semidirect
69. #388D3direct (N × H)
115. C3×C22⋊C4C2×C4semidirect
119. #217C2×C4semidirect
124. (C2×D3)⋊C4C2×C4semidirect
125. (C2×D3)⋊C4C2×C4semidirect
143. C2×C4⋊C4C2×D3semidirect
163. C2×C42C2×D3semidirect
170. #95C2×D3semidirect
171. #95C2×D3semidirect
298. C22⋊C4C4×D3semidirect
424. D3#388direct (N × H)
466. C3C2×#388semidirect

Maximal subgroups

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

subgroupindex
C2×D3×C4⋊C42
C2×D3×C22⋊C42
C2×C42×D32
C3×#3882
#49902
#49512
#49452
#49442
#49402
#46702
#46692
D3×#952
C2×#3883