Finite Group Databasebeta

← D4×A4×C3⋊D3 #13181460

Subgroups — D4×A4×C3⋊D3 #13181460

Order 1728.

2030 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 2030 conjugacy classes of subgroups — too many to draw. Only its 147 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×A4×C3⋊D3C212yesmaximal, complemented
2C32×D4×A4C211yesmaximal, characteristic, complemented
3A4×#638C212yesmaximal, complemented
4A4×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
5C4×A4×C3⋊D3C211yesmaximal, characteristic, complemented
6C22×D4×C3⋊D3C311yesmaximal, characteristic, complemented
7D3×D4×A4—34nomaximal
8C22×C32×A4C2212yescomplemented
9C2×A4×C3⋊D3—24no—
10C2×A4×C3⋊D3C2211yescharacteristic
11C2×A4×C3⋊D3C2212yescomplemented
12C3×D4×C3⋊D3—41nomaximal
13C32×C4×A4C2211yescharacteristic, complemented
14A4×C3⋊Dic3C2211yescharacteristic, complemented
15C24×C3⋊D3C2×C312yescomplemented
16C22×D3×A4—38no—
17C22×C32×D4C2×C311yescharacteristic, complemented
18C22×#638C2×C312yescomplemented
19C2×D4×C3⋊D3—31no—
20C2×D4×C3⋊D3—32no—
21C2×D4×C3⋊D3—31no—
22C2×D4×C3⋊D3—31no—
23C2×D4×C3⋊D3—31no—
24C2×D4×C3⋊D3—32no—
25C22×C4⋊(C3⋊D3)C2×C311yescharacteristic, complemented
26C22×C4×C3⋊D3C2×C311yescharacteristic, complemented
27C3×D4×A4—24no—
28C3×D4×A4D314yescomplemented
29A4×#67—38no—
30A4×D12—34no—
31C4×D3×A4—34no—
32C22×C3×C3⋊D3—42no—
33C2×C32×A4—22no—
34C2×C32×A4C2311yescharacteristic
35A4×C3⋊D3—22no—
36A4×C3⋊D3D412yesdirect product factor
37C33×D4—41no—
38C3×#638—42no—
39C3×C4⋊(C3⋊D3)—41no—
40C3×C4×C3⋊D3—41no—
41C22×D3×D4—34no—
42C2×D4×A4—91no—
43C24×C32C22×C312yescomplemented
44C23×C3⋊D3—24no—
45C23×C3⋊D3—32no—
46C23×C3⋊D3—32no—
47C23×C3⋊D3—32no—
48C23×C3⋊D3—32no—
49C23×C3⋊D3—64no—
50C23×C3⋊D3C22×C311yescharacteristic
51C23×C3⋊D3C22×C312yescomplemented
52C22×C3×A4—28no—
53C22×C3×A4C2×D318yescomplemented
54C2×D3×A4—34no—
55C2×D3×A4—38no—
56C2×D3×A4—616no—
57C2×C32×D4—31no—
58C2×C32×D4—31no—
59C2×C32×D4—32no—
60C22×C32×C4C22×C311yescharacteristic, complemented
61C2×#638—32no—
62C2×#638—32no—
63C2×#638—32no—
64C2×#638—32no—
65C22×C3⋊Dic3C22×C311yescharacteristic, complemented
66D4×C3⋊D3—34no—
67D4×C3⋊D3—34no—
68D4×C3⋊D3—32no—
69D4×C3⋊D3—32no—
70D4×C3⋊D3—32no—
71D4×C3⋊D3—32no—
72D4×C3⋊D3—31no—
73D4×C3⋊D3—32no—
74D4×C3⋊D3—31no—
75D4×C3⋊D3—31no—
76D4×C3⋊D3A411yescharacteristic, direct product factor
77C2×C4⋊(C3⋊D3)—31no—
78C2×C4⋊(C3⋊D3)—32no—
79C2×C4⋊(C3⋊D3)—31no—
80C2×C4×C3⋊D3—31no—
81C2×C4×C3⋊D3—31no—
82C2×C4×C3⋊D3—31no—
83C2×C4×C3⋊D3—31no—
84C3×D3×D4—124no—
85C3×C4×A4—24no—
86C3×C4×A4C2×D314yescomplemented
87Dic3×A4—34no—
88C22×C33—42no—
89C2×C3×C3⋊D3—41no—
90C2×C3×C3⋊D3—42no—
91C2×C3×C3⋊D3—84no—
92C32×A4C2×D411yescharacteristic, complemented
93C33×C4—41no—
94C3×C3⋊Dic3—41no—
95C24×D3—38no—
96C23×A4—92no—
97C22×C3×D4C3×D314yescomplemented
98C22×#67—38no—
99C2×D3×D4—94no—
100C2×D3×D4—94no—
101C2×D3×D4—94no—
102C2×D3×D4—98no—
103C2×D3×D4—98no—
104C2×D3×D4—94no—
105C22×D12—34no—
106C22×C4×D3—34no—
107D4×A4—24no—
108D4×A4—92no—
109D4×A4—91no—
110D4×A4C3⋊D311yescharacteristic, direct product factor
111C2×C4×A4—91no—
112C23×C32—22no—
113C23×C32—32no—
114C23×C32—32no—
115C23×C32—62no—
116C23×C32C23×C311yescharacteristic
117C22×C3⋊D3—22no—
118C22×C3⋊D3—31no—
119C22×C3⋊D3—31no—
120C22×C3⋊D3—32no—
121C22×C3⋊D3—34no—
122C22×C3⋊D3—32no—
123C22×C3⋊D3—32no—
124C22×C3⋊D3—32no—
125C22×C3⋊D3—32no—
126C22×C3⋊D3—32no—
127C22×C3⋊D3—64no—
128C22×C3⋊D3—64no—
129C22×C3⋊D3—64no—
130C22×C3⋊D3—64no—
131C22×C3⋊D3—64no—
132C22×C3⋊D3—64no—
133C22×C3⋊D3—64no—
134C22×C3⋊D3—64no—
135C22×C3⋊D3—62no—
136C22×C3⋊D3C3×D412yescomplemented
137C22×C3⋊D3C2×A412yescomplemented
138C22×C3×D3—128no—
139C2×C3×A4—24no—
140C2×C3×A4—28no—
141C2×C3×A4—48no—
142C2×C3×A4C22×D314yes—
143D3×A4—38no—
144D3×A4—68no—
145C32×D4—32no—
146C32×D4—32no—
147C32×D4—31no—
148C32×D4—44no—
149C32×D4—84no—
150C32×D4C2×A411yescharacteristic, complemented
151C2×C32×C4—31no—
152C2×C32×C4—31no—
153#638—34no—
154#638—32no—
155#638—32no—
156#638—32no—
157#638C2×A412yescomplemented
158C2×C3⋊Dic3—31no—
159C2×C3⋊Dic3—31no—
160C4⋊(C3⋊D3)—32no—
161C4⋊(C3⋊D3)—32no—
162C4⋊(C3⋊D3)—31no—
163C4⋊(C3⋊D3)C2×A411yescharacteristic, complemented
164C4×C3⋊D3—32no—
165C4×C3⋊D3—31no—
166C4×C3⋊D3—31no—
167C4×C3⋊D3—31no—
168C4×C3⋊D3C2×A411yescharacteristic, complemented
169C3×#67—128no—
170C3×D12—124no—
171C3×C4×D3—124no—
172C23×D4—91noSylow
173C2×C33—41no—
174C2×C33—82no—
175C3×C3⋊D3—42no—
176C3×C3⋊D3—82no—
177C24×C3C2×C3×D318yescomplemented
178C23×D3—34no—
179C23×D3—38no—
180C23×D3—616no—
181C23×D3—98no—
182C23×D3—98no—
183C23×D3—98no—
184C23×D3—98no—
185C23×D3—1816no—
186C22×A4—28no—
187C22×A4—91no—
188C22×A4—92no—
189C22×A4—184no—
190C22×A4C2×C3⋊D312yescomplemented
191C2×C3×D4—34no—
192C2×C3×D4—34no—
193C2×C3×D4—38no—
194C2×C3×D4—361no—
195C22×C3×C4C2×C3×D314yescomplemented
196C2×#67—98no—
197C2×#67—98no—
198C2×#67—98no—
199C2×#67—98no—
200C22×Dic3—34no—
201D3×D4—34no—
202D3×D4—94no—
203D3×D4—94no—
204D3×D4—98no—
205D3×D4—98no—
206D3×D4—98no—
207D3×D4—98no—
208D3×D4—916no—
209D3×D4—916no—
210D3×D4—98no—
211D3×D4—94no—
212C2×D12—94no—
213C2×D12—98no—
214C2×D12—94no—
215C2×C4×D3—94no—
216C2×C4×D3—94no—
217C2×C4×D3—94no—
218C2×C4×D3—94no—
219C4×A4—24no—
220C4×A4—91no—
221C4×A4C2×C3⋊D311yescharacteristic, complemented
222C22×C32—31no—
223C22×C32—31no—
224C22×C32—32no—
225C22×C32—48no—
226C22×C32—62no—
227C22×C32—62no—
228C22×C32—62no—
229C22×C32—62no—
230C22×C32—88no—
231C22×C32C2×C3×D411yescharacteristic, complemented
232C22×C32C22×A412yescomplemented
233C2×C3⋊D3—24no—
234C2×C3⋊D3—32no—
235C2×C3⋊D3—31no—
236C2×C3⋊D3—32no—
237C2×C3⋊D3—32no—
238C2×C3⋊D3—32no—
239C2×C3⋊D3—32no—
240C2×C3⋊D3—64no—
241C2×C3⋊D3—62no—
242C2×C3⋊D3—62no—
243C2×C3⋊D3—64no—
244C2×C3⋊D3—68no—
245C2×C3⋊D3—64no—
246C2×C3⋊D3—62no—
247C2×C3⋊D3—62no—
248C2×C3⋊D3C22×A411yescharacteristic
249C2×C3⋊D3C22×A412yescomplemented
250C2×C3×D3—124no—
251C2×C3×D3—128no—
252C2×C3×D3—2416no—
253C3×A4—24no—
254C3×A4D3×D414yescomplemented
255C32×C4—31no—
256C32×C4—44no—
257C32×C4—84no—
258C32×C4C22×A411yescharacteristic, complemented
259C3⋊Dic3—31no—
260C3⋊Dic3C22×A411yescharacteristic, complemented
261C3×Dic3—124no—
262C25—92no—
263C22×D4—92no—
264C22×D4—91no—
265C22×D4—271no—
266C22×D4—271no—
267C22×D4—271no—
268C22×D4—271no—
269C22×D4—272no—
270C22×D4—272no—
271C22×D4C3×C3⋊D311yescharacteristic, complemented
272C23×C4—91no—
273C33—41noSylow
274C23×C3—28no—
275C23×C3—38no—
276C23×C3—38no—
277C23×C3—68no—
278C23×C3—362no—
279C23×C3C22×C3×D314yes—
280C22×D3—38no—
281C22×D3—38no—
282C22×D3—68no—
283C22×D3—94no—
284C22×D3—98no—
285C22×D3—98no—
286C22×D3—98no—
287C22×D3—94no—
288C22×D3—98no—
289C22×D3—916no—
290C22×D3—98no—
291C22×D3—98no—
292C22×D3—1816no—
293C22×D3—1816no—
294C22×D3—1816no—
295C22×D3—1816no—
296C22×D3—1816no—
297C22×D3—1816no—
298C22×D3—1816no—
299C22×D3—1816no—
300C22×D3—188no—
301C2×A4—22no—
302C2×A4—24no—
303C2×A4—48no—
304C2×A4—92no—
305C2×A4—182no—
306C2×A4C22×C3⋊D311yescharacteristic
307C3×D4—38no—
308C3×D4—38no—
309C3×D4—34no—
310C3×D4—41no—
311C3×D4—84no—
312C3×D4—361no—
313C3×D4—362no—
314C3×D4D3×A414yescomplemented
315C2×C3×C4—34no—
316C2×C3×C4—34no—
317C2×C3×C4—361no—
318#67—38no—
319#67—98no—
320#67—98no—
321#67—916no—
322#67—98no—
323C2×Dic3—94no—
324C2×Dic3—94no—
325D12—34no—
326D12—98no—
327D12—98no—
328D12—94no—
329C4×D3—34no—
330C4×D3—94no—
331C4×D3—94no—
332C4×D3—98no—
333C4×D3—94no—
334C2×C32—22no—
335C2×C32—31no—
336C2×C32—31no—
337C2×C32—44no—
338C2×C32—62no—
339C2×C32—88no—
340C2×C32—84no—
341C2×C32—168no—
342C2×C32C23×A411yescharacteristic
343C3⋊D3—22no—
344C3⋊D3—32no—
345C3⋊D3—62no—
346C3⋊D3D4×A412yesdirect product factor
347C3×D3—128no—
348C3×D3—248no—
349C24—91no—
350C24—92no—
351C24—184no—
352C24—272no—
353C24—272no—
354C24—272no—
355C24—272no—
356C24—544no—
357C24C2×C3×C3⋊D312yescomplemented
358C2×D4—31no—
359C2×D4—31no—
360C2×D4—32no—
361C2×D4—91no—
362C2×D4—271no—
363C2×D4—271no—
364C2×D4—272no—
365C2×D4—271no—
366C2×D4—272no—
367C2×D4—271no—
368C2×D4—272no—
369C2×D4—272no—
370C2×D4—272no—
371C2×D4—274no—
372C2×D4—274no—
373C2×D4—272no—
374C2×D4—272no—
375C2×D4—271no—
376C2×D4—272no—
377C2×D4—272no—
378C2×D4—272no—
379C22×C4—91no—
380C22×C4—271no—
381C22×C4—271no—
382C22×C4—271no—
383C22×C4—271no—
384C22×C4C2×C3×C3⋊D311yescharacteristic, complemented
385C22×C3—34no—
386C22×C3—34no—
387C22×C3—38no—
388C22×C3—42no—
389C22×C3—68no—
390C22×C3—68no—
391C22×C3—68no—
392C22×C3—68no—
393C22×C3—88no—
394C22×C3—361no—
395C22×C3—362no—
396C22×C3—724no—
397C22×C3C3×D3×D414yescomplemented
398C22×C3C2×D3×A418yescomplemented
399C2×D3—34no—
400C2×D3—38no—
401C2×D3—616no—
402C2×D3—98no—
403C2×D3—98no—
404C2×D3—98no—
405C2×D3—94no—
406C2×D3—98no—
407C2×D3—98no—
408C2×D3—1816no—
409C2×D3—1816no—
410C2×D3—188no—
411C2×D3—188no—
412C2×D3—1816no—
413C2×D3—1832no—
414C2×D3—188no—
415C2×D3—188no—
416A4—24no—
417A4D4×C3⋊D311yescharacteristic, direct product factor
418C3×C4—34no—
419C3×C4—41no—
420C3×C4—84no—
421C3×C4—361no—
422C3×C4C2×D3×A414yescomplemented
423Dic3—34no—
424Dic3—94no—
425C32—44no—
426C32—84no—
427C32C2×D4×A411yescharacteristic, complemented
428C23—22no—
429C23—32no—
430C23—32no—
431C23—62no—
432C23—92no—
433C23—92no—
434C23—182no—
435C23—271no—
436C23—272no—
437C23—272no—
438C23—272no—
439C23—271no—
440C23—272no—
441C23—274no—
442C23—272no—
443C23—272no—
444C23—542no—
445C23—544no—
446C23—544no—
447C23—544no—
448C23—544no—
449C23—544no—
450C23—544no—
451C23—544no—
452C23—544no—
453C23C22×C3×C3⋊D311yescharacteristic
454D4—32no—
455D4—32no—
456D4—31no—
457D4—92no—
458D4—91no—
459D4—272no—
460D4—272no—
461D4—272no—
462D4—272no—
463D4—274no—
464D4—272no—
465D4—271no—
466D4A4×C3⋊D311yescharacteristic, direct product factor
467C2×C4—31no—
468C2×C4—31no—
469C2×C4—91no—
470C2×C4—271no—
471C2×C4—271no—
472C2×C4—272no—
473C2×C4—271no—
474C2×C4—271no—
475C2×C4—271no—
476C2×C3—28no—
477C2×C3—34no—
478C2×C3—34no—
479C2×C3—41no—
480C2×C3—68no—
481C2×C3—82no—
482C2×C3—84no—
483C2×C3—168no—
484C2×C3—362no—
485C2×C3—722no—
486C2×C3C22×D3×A414yes—
487D3—38no—
488D3—68no—
489D3—98no—
490D3—188no—
491C22—31no—
492C22—31no—
493C22—32no—
494C22—62no—
495C22—62no—
496C22—62no—
497C22—62no—
498C22—91no—
499C22—92no—
500C22—184no—
501C22—272no—
502C22—272no—
503C22—272no—
504C22—272no—
505C22—271no—
506C22—272no—
507C22—544no—
508C22—542no—
509C22—542no—
510C22—542no—
511C22—542no—
512C22—544no—
513C22—544no—
514C22—548no—
515C22C3×D4×C3⋊D311yescharacteristic, complemented
516C22C2×A4×C3⋊D312yescomplemented
517C4—31no—
518C4—91no—
519C4—271no—
520C4C2×A4×C3⋊D311yescharacteristic, complemented
521C3—41no—
522C3—84no—
523C3D3×D4×A414yescomplemented
524C2—22no—
525C2—31no—
526C2—31no—
527C2—62no—
528C2—92no—
529C2—182no—
530C2—272no—
531C2—542no—
532C2C22×A4×C3⋊D311yescharacteristic
subgroupG/H
center, FrattiniC2C22×A4×C3⋊D3
commutator, socle, cosocleC23×C32C23×C3
FittingC22×C32×D4C2×C3
hypercenterD4A4×C3⋊D3
hypocenterC22×C32C2×C3×D4
LCSG ▷ C23×C32 ▷ C22×C32
UCSC1 ◁ C2 ◁ D4

Complements

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

NH ≅ G/Ntype
1. C22×A4×C3⋊D3C2semidirect
2. C32×D4×A4C2semidirect
3. A4×#638C2semidirect
4. A4×C4⋊(C3⋊D3)C2semidirect
5. C4×A4×C3⋊D3C2semidirect
6. C22×D4×C3⋊D3C3semidirect
8. C22×C32×A4C22semidirect
11. C2×A4×C3⋊D3C22semidirect
13. C32×C4×A4C22semidirect
14. A4×C3⋊Dic3C22semidirect
15. C24×C3⋊D3C2×C3semidirect
17. C22×C32×D4C2×C3semidirect
18. C22×#638C2×C3semidirect
25. C22×C4⋊(C3⋊D3)C2×C3semidirect
26. C22×C4×C3⋊D3C2×C3semidirect
28. C3×D4×A4D3semidirect
36. A4×C3⋊D3D4direct (N × H)
43. C24×C32C22×C3semidirect
51. C23×C3⋊D3C22×C3semidirect
53. C22×C3×A4C2×D3semidirect
60. C22×C32×C4C22×C3semidirect
65. C22×C3⋊Dic3C22×C3semidirect
76. D4×C3⋊D3A4direct (N × H)
86. C3×C4×A4C2×D3semidirect
92. C32×A4C2×D4semidirect
97. C22×C3×D4C3×D3semidirect
110. D4×A4C3⋊D3direct (N × H)
136. C22×C3⋊D3C3×D4semidirect
137. C22×C3⋊D3C2×A4semidirect
150. C32×D4C2×A4semidirect
157. #638C2×A4semidirect
163. C4⋊(C3⋊D3)C2×A4semidirect
168. C4×C3⋊D3C2×A4semidirect
177. C24×C3C2×C3×D3semidirect
190. C22×A4C2×C3⋊D3semidirect
195. C22×C3×C4C2×C3×D3semidirect
221. C4×A4C2×C3⋊D3semidirect
231. C22×C32C2×C3×D4semidirect
232. C22×C32C22×A4semidirect
249. C2×C3⋊D3C22×A4semidirect
254. C3×A4D3×D4semidirect
258. C32×C4C22×A4semidirect
260. C3⋊Dic3C22×A4semidirect
271. C22×D4C3×C3⋊D3semidirect
314. C3×D4D3×A4semidirect
346. C3⋊D3D4×A4direct (N × H)
357. C24C2×C3×C3⋊D3semidirect
384. C22×C4C2×C3×C3⋊D3semidirect
397. C22×C3C3×D3×D4semidirect
398. C22×C3C2×D3×A4semidirect
417. A4D4×C3⋊D3direct (N × H)
422. C3×C4C2×D3×A4semidirect
427. C32C2×D4×A4semidirect
466. D4A4×C3⋊D3direct (N × H)
515. C22C3×D4×C3⋊D3semidirect
516. C22C2×A4×C3⋊D3semidirect
520. C4C2×A4×C3⋊D3semidirect
523. C3D3×D4×A4semidirect

Maximal subgroups

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

subgroupindex
C22×A4×C3⋊D32
C32×D4×A42
A4×#6382
A4×C4⋊(C3⋊D3)2
C4×A4×C3⋊D32
C22×D4×C3⋊D33
D3×D4×A43
C3×D4×C3⋊D34