Finite Group Databasebeta

← D3×#64101 #13176522

Subgroups — D3×#64101 #13176522

Order 1728.

2284 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D3×C3⋊D3C211yesmaximal, characteristic
2#11723933C211yesmaximal, characteristic, complemented
3C3×#64101C211yesmaximal, characteristic, complemented
4C32×D3×C4⋊C4C211yesmaximal, characteristic, complemented
5D3×#3752C212yesmaximal
6D3×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
7#11723469C212yesmaximal, complemented
8#11723466C212yesmaximal, complemented
9C4×D3×C3⋊Dic3C212yesmaximal, complemented
10#11723413C211yesmaximal, characteristic, complemented
11#11723404C211yesmaximal, characteristic, complemented
12C2×#64101—31nomaximal
13D3×#892—34nomaximal
14C22×D3×C3⋊D3C2211yescharacteristic
15C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
16C2×C3×C4×C3⋊D3C2211yescharacteristic
17C2×C32×C4×D3C2212yes—
18C2×C32×C4×D3C2211yescharacteristic
19C2×#6289C2211yescharacteristic
20C2×Dic3×C3⋊D3C2211yescharacteristic
21C2×D3×C3⋊Dic3C2212yes—
22C2×D3×C3⋊Dic3C2211yescharacteristic
23C4×D3×C3⋊D3C418yescomplemented
24C33×C4⋊C4C2211yescharacteristic, complemented
25#88859C2212yes—
26C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic, complemented
27C4×C3⋊(C3⋊Dic3)C2212yescomplemented
28C3×#3752C2212yes—
29C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
30C3×C4×C3⋊Dic3C2212yescomplemented
31C32×C4⋊Dic3C2211yescharacteristic, complemented
32C32×Dic3⋊C4C2212yescomplemented
33Dic3⋊(C3⋊Dic3)C2212yescomplemented
34#88804C2212yes—
35#88803C2212yes—
36Dic3×C3⋊Dic3C2212yescomplemented
37Dic3×C3⋊Dic3C2212yescomplemented
38C22×C4×C3⋊D3—31no—
39C2×C4×D32—34no—
40C2×C32×C4⋊C4—31no—
41C2×#3752—32no—
42C2×C4⋊(C3⋊Dic3)—31no—
43C2×C4×C3⋊Dic3—32no—
44#64101—31no—
45#64101—31no—
46#64101—32no—
47#64101—31no—
48#64101—32no—
49#64101—34no—
50#64101—64no—
51#64101D311yescharacteristic, direct product factor
52C3×#892—34no—
53C3×D3×C4⋊C4D314yescomplemented
54D3×(C2×D3)⋊C4—38no—
55D3×C4⋊Dic3—34no—
56#63878—38no—
57C4×D3×Dic3—38no—
58#63849—34no—
59#63841—34no—
60#63836—38no—
61C22×C3⋊(C3⋊D3)C2311yescharacteristic
62C22×C3×C3⋊D3C2311yescharacteristic
63C22×C32×D3C2311yescharacteristic
64C2×D3×C3⋊D3—22no—
65C2×D3×C3⋊D3—22no—
66C2×D3×C3⋊D3C2×C414yes—
67C2×C33×C4C2312yes—
68C2×C33×C4C2311yescharacteristic
69C2×C3⋊(C3⋊Dic3)C2312yes—
70C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
71C4×C3⋊(C3⋊D3)C2×C414yescomplemented
72C2×C3×C3⋊Dic3C2312yes—
73C2×C3×C3⋊Dic3C2311yescharacteristic
74C3×C4×C3⋊D3C2×C414yescomplemented
75C2×C32×Dic3C2312yes—
76C2×C32×Dic3C2311yescharacteristic
77C32×C4×D3—24no—
78C32×C4×D3C2×C414yes—
79#6289C2×C414yescomplemented
80Dic3×C3⋊D3C2×C414yescomplemented
81D3×C3⋊Dic3—24no—
82D3×C3⋊Dic3C2×C414yes—
83D3×#117—91no—
84C2×#892—94no—
85C23×C3⋊D3—31no—
86C22×D32—34no—
87C22×C32×C4—31no—
88C22×C32×C4—32no—
89C22×C3⋊Dic3—31no—
90C22×C3⋊Dic3—32no—
91C2×C4×C3⋊D3—31no—
92C2×C4×C3⋊D3—31no—
93C2×C4×C3⋊D3—34no—
94C2×C4×C3⋊D3—31no—
95C2×C4×C3⋊D3—38no—
96C2×C4×C3⋊D3—64no—
97C2×C4×C3⋊D3C2×D311yescharacteristic
98C2×C3×C4×D3—34no—
99C2×C3×C4×D3C2×D318yes—
100C2×C3×C4×D3C2×D314yes—
101C2×#624—34no—
102C2×D3×Dic3—34no—
103C2×D3×Dic3—34no—
104C2×D3×Dic3—38no—
105C4×D32—332no—
106C32×C4⋊C4—24no—
107C32×C4⋊C4—32no—
108C32×C4⋊C4—31no—
109C32×C4⋊C4C2×D314yescomplemented
110C32×C4⋊C4C2×D311yescharacteristic, complemented
111#3752—32no—
112#3752—32no—
113#3752—38no—
114#3752—32no—
115#3752—68no—
116#3752C2×D312yes—
117C4⋊(C3⋊Dic3)—31no—
118C4⋊(C3⋊Dic3)—34no—
119C4⋊(C3⋊Dic3)—32no—
120C4⋊(C3⋊Dic3)—64no—
121C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
122C4×C3⋊Dic3—32no—
123C4×C3⋊Dic3—38no—
124C4×C3⋊Dic3—32no—
125C4×C3⋊Dic3—32no—
126C4×C3⋊Dic3—68no—
127C4×C3⋊Dic3C2×D312yescomplemented
128C3×(C2×D3)⋊C4—38no—
129C3×C4⋊Dic3—34no—
130C3×C4⋊Dic3C2×D314yescomplemented
131C3×Dic3⋊C4C2×D318yescomplemented
132C3×C4×Dic3—38no—
133Dic3⋊Dic3—38no—
134#3722—38no—
135(C2×D3)⋊Dic3—38no—
136Dic32—38no—
137Dic32—38no—
138C22×C33C2411yescharacteristic
139C2×C3⋊(C3⋊D3)—21no—
140C2×C3⋊(C3⋊D3)—21no—
141C2×C3⋊(C3⋊D3)C22×C412yes—
142C2×C3×C3⋊D3—21no—
143C2×C3×C3⋊D3—21no—
144C2×C3×C3⋊D3C22×C412yes—
145C2×C32×D3C22×C412yes—
146C2×C32×D3#4112yes—
147C2×C32×D3#4112yes—
148D3×C3⋊D3—28no—
149C33×C4—22no—
150C33×C4C22×C412yes—
151C3⋊(C3⋊Dic3)—22no—
152C3⋊(C3⋊Dic3)C22×C412yes—
153C3×C3⋊Dic3—22no—
154C3×C3⋊Dic3C22×C412yes—
155C32×Dic3—22no—
156C32×Dic3C22×C412yes—
157C22×C4×D3—94no—
158C22×C4×D3—91no—
159C3×#117—91no—
160C2×C3×C4⋊C4—34no—
161C2×(C2×D3)⋊C4—98no—
162#926—91no—
163C2×C4⋊Dic3—94no—
164C2×C4×Dic3—98no—
165#892—34no—
166#892—98no—
167#892—94no—
168#892—98no—
169#892—94no—
170#892—94no—
171#892—91no—
172#892—91no—
173#892—184no—
174D3×C4⋊C4—91no—
175D3×C4⋊C4C3⋊D311yescharacteristic, complemented
176D3×C22⋊C4—92no—
177#877—92no—
178#872—92no—
179C42×D3—92no—
180C23×C32—31no—
181C22×C3⋊D3—31no—
182C22×C3⋊D3—34no—
183C22×C3⋊D3—34no—
184C22×C3⋊D3—64no—
185C22×C3⋊D3—62no—
186C22×C3⋊D3—62no—
187C22×C3⋊D3C22×D311yescharacteristic
188C22×C3×D3—34no—
189C22×C3×D3C22×D314yes—
190C2×D32—316no—
191C2×D32—68no—
192C2×D32—68no—
193C2×C32×C4—24no—
194C2×C32×C4—28no—
195C2×C32×C4—31no—
196C2×C32×C4—34no—
197C2×C32×C4—32no—
198C2×C32×C4—64no—
199C2×C32×C4C22×D318yes—
200C2×C32×C4C22×D314yes—
201C2×C32×C4C22×D312yes—
202C2×C32×C4C22×D311yescharacteristic
203C2×C3⋊Dic3—31no—
204C2×C3⋊Dic3—34no—
205C2×C3⋊Dic3—32no—
206C2×C3⋊Dic3—34no—
207C2×C3⋊Dic3—38no—
208C2×C3⋊Dic3—64no—
209C2×C3⋊Dic3—68no—
210C2×C3⋊Dic3—64no—
211C2×C3⋊Dic3C22×D312yes—
212C2×C3⋊Dic3C22×D311yescharacteristic
213C4×C3⋊D3—34no—
214C4×C3⋊D3—34no—
215C4×C3⋊D3—34no—
216C4×C3⋊D3—316no—
217C4×C3⋊D3—616no—
218C4×C3⋊D3C4×D314yescomplemented
219C2×C3×Dic3—34no—
220C2×C3×Dic3—38no—
221C2×C3×Dic3C22×D318yes—
222C2×C3×Dic3C22×D314yes—
223C3×C4×D3—216no—
224C3×C4×D3—316no—
225C3×C4×D3C4×D3116yes—
226#624—316no—
227D3×Dic3—316no—
228D3×Dic3—316no—
229D3×Dic3—616no—
230C2×#117—271noSylow
231C2×C33C23×C411yescharacteristic
232C2×C33C2×#4111yescharacteristic
233C2×C33C2×#4111yescharacteristic
234C3⋊(C3⋊D3)—22no—
235C3×C3⋊D3—22no—
236C32×D3#11714yescomplemented
237C23×D3—94no—
238C23×D3—91no—
239C22×C3×C4—34no—
240C22×C3×C4—38no—
241C22×C3×C4—91no—
242C22×Dic3—94no—
243C22×Dic3—98no—
244C22×Dic3—91no—
245C2×C4×D3—34no—
246C2×C4×D3—932no—
247C2×C4×D3—94no—
248C2×C4×D3—94no—
249C2×C4×D3—91no—
250C2×C4×D3—94no—
251C2×C4×D3—91no—
252C2×C4×D3—91no—
253C2×C4×D3—98no—
254C2×C4×D3—92no—
255C2×C4×D3—184no—
256C2×C4×D3C2×C3⋊D312yes—
257C2×C4×D3C2×C3⋊D311yescharacteristic
258C3×C4⋊C4—24no—
259C3×C4⋊C4—38no—
260C3×C4⋊C4—34no—
261C3×C4⋊C4—91no—
262C3×C4⋊C4D3214yescomplemented
263C3×C4⋊C4C2×C3⋊D311yescharacteristic, complemented
264C3×C22⋊C4—92no—
265C3×C42—92no—
266#217—92no—
267(C2×D3)⋊C4—38no—
268(C2×D3)⋊C4—98no—
269(C2×D3)⋊C4—98no—
270(C2×D3)⋊C4—98no—
271(C2×D3)⋊C4—92no—
272(C2×D3)⋊C4—92no—
273(C2×D3)⋊C4—188no—
274C4⋊Dic3—34no—
275C4⋊Dic3—98no—
276C4⋊Dic3—94no—
277C4⋊Dic3—91no—
278C4⋊Dic3—184no—
279C4⋊Dic3C2×C3⋊D311yescharacteristic, complemented
280Dic3⋊C4—92no—
281Dic3⋊C4C2×C3⋊D312yescomplemented
282C4×Dic3—38no—
283C4×Dic3—98no—
284C4×Dic3—98no—
285C4×Dic3—98no—
286C4×Dic3—92no—
287C4×Dic3—92no—
288C4×Dic3—92no—
289C4×Dic3—188no—
290C22×C32—24no—
291C22×C32—32no—
292C22×C32—32no—
293C22×C32—32no—
294C22×C32C23×D314yes—
295C22×C32C23×D311yescharacteristic
296C2×C3⋊D3—21no—
297C2×C3⋊D3—21no—
298C2×C3⋊D3—32no—
299C2×C3⋊D3—38no—
300C2×C3⋊D3—68no—
301C2×C3⋊D3—68no—
302C2×C3⋊D3—61no—
303C2×C3⋊D3—61no—
304C2×C3⋊D3—64no—
305C2×C3⋊D3—64no—
306C2×C3⋊D3—124no—
307C2×C3⋊D3—124no—
308C2×C3⋊D3C2×C4×D312yes—
309C2×C3×D3—38no—
310C2×C3×D3—64no—
311C2×C3×D3—64no—
312C2×C3×D3C2×C4×D318yes—
313C2×C3×D3#23718yes—
314C2×C3×D3#23918yes—
315D32—632no—
316C32×C4—22no—
317C32×C4—28no—
318C32×C4—28no—
319C32×C4—32no—
320C32×C4—48no—
321C32×C4—62no—
322C32×C4C2×C4×D318yes—
323C32×C4C2×C4×D312yes—
324C3⋊Dic3—22no—
325C3⋊Dic3—32no—
326C3⋊Dic3—38no—
327C3⋊Dic3—68no—
328C3⋊Dic3—62no—
329C3⋊Dic3—68no—
330C3⋊Dic3—128no—
331C3⋊Dic3C2×C4×D312yes—
332C3×Dic3—28no—
333C3×Dic3—38no—
334C3×Dic3—68no—
335C3×Dic3C2×C4×D318yes—
336C23×C4—271no—
337#117—91no—
338#117—272no—
339#117—272no—
340#117—271no—
341#117—271no—
342#117—271no—
343C2×C4⋊C4—31no—
344C2×C4⋊C4—271no—
345C2×C22⋊C4—272no—
346C2×C42—272no—
347C33C2×#11711yescharacteristic, complemented, Sylow
348C23×C3—34no—
349C23×C3—91no—
350C22×D3—34no—
351C22×D3—916no—
352C22×D3—94no—
353C22×D3—91no—
354C22×D3—94no—
355C22×D3—184no—
356C22×D3—188no—
357C22×D3—188no—
358C22×D3—182no—
359C22×D3—182no—
360C22×D3C22×C3⋊D311yescharacteristic
361C2×C3×C4—24no—
362C2×C3×C4—28no—
363C2×C3×C4—34no—
364C2×C3×C4—316no—
365C2×C3×C4—38no—
366C2×C3×C4—616no—
367C2×C3×C4—91no—
368C2×C3×C4—94no—
369C2×C3×C4—92no—
370C2×C3×C4C2×D3218yes—
371C2×C3×C4C2×D3214yes—
372C2×C3×C4C22×C3⋊D312yes—
373C2×C3×C4C22×C3⋊D311yescharacteristic
374C2×Dic3—34no—
375C2×Dic3—38no—
376C2×Dic3—916no—
377C2×Dic3—94no—
378C2×Dic3—91no—
379C2×Dic3—94no—
380C2×Dic3—98no—
381C2×Dic3—92no—
382C2×Dic3—184no—
383C2×Dic3—188no—
384C2×Dic3—1816no—
385C2×Dic3C22×C3⋊D312yes—
386C2×Dic3C22×C3⋊D311yescharacteristic
387C4×D3—24no—
388C4×D3—316no—
389C4×D3—916no—
390C4×D3—916no—
391C4×D3—94no—
392C4×D3—916no—
393C4×D3—94no—
394C4×D3—94no—
395C4×D3—1816no—
396C4×D3—184no—
397C4×D3C4×C3⋊D314yes—
398C2×C32—24no—
399C2×C32—24no—
400C2×C32—24no—
401C2×C32—34no—
402C2×C32C22×C4×D314yes—
403C2×C32C22×C4×D311yescharacteristic
404C2×C32C2×#23714yes—
405C2×C32C2×#23914yes—
406C2×C32D3×#4111yescharacteristic
407C2×C32D3×#4111yescharacteristic
408C3⋊D3—22no—
409C3⋊D3—62no—
410C3⋊D3—68no—
411C3⋊D3—128no—
412C3×D3—68no—
413C3×D3#892116yescomplemented
414C24—271no—
415C22×C4—31no—
416C22×C4—32no—
417C22×C4—91no—
418C22×C4—271no—
419C22×C4—278no—
420C22×C4—271no—
421C22×C4—271no—
422C22×C4—272no—
423C22×C4—271no—
424C4⋊C4—32no—
425C4⋊C4—31no—
426C4⋊C4—91no—
427C4⋊C4—272no—
428C4⋊C4—271no—
429C4⋊C4D3×C3⋊D311yescharacteristic, complemented
430C22⋊C4—92no—
431C22⋊C4—272no—
432C22⋊C4—272no—
433C22⋊C4—272no—
434C42—92no—
435C42—272no—
436C42—272no—
437C42—272no—
438C22×C3—24no—
439C22×C3—38no—
440C22×C3—38no—
441C22×C3—38no—
442C22×C3—92no—
443C22×C3—181no—
444C22×C3—181no—
445C22×C3C22×D3214yes—
446C22×C3C23×C3⋊D311yescharacteristic
447C2×D3—38no—
448C2×D3—64no—
449C2×D3—64no—
450C2×D3—98no—
451C2×D3—92no—
452C2×D3—188no—
453C2×D3—1832no—
454C2×D3—184no—
455C2×D3—184no—
456C2×D3—181no—
457C2×D3—181no—
458C2×D3—188no—
459C2×D3—364no—
460C2×D3—364no—
461C2×D3C2×C4×C3⋊D312yes—
462C2×D3#383012yes—
463C2×D3#383212yes—
464C3×C4—28no—
465C3×C4—22no—
466C3×C4—28no—
467C3×C4—38no—
468C3×C4—48no—
469C3×C4—68no—
470C3×C4—92no—
471C3×C4—182no—
472C3×C4C4×D3218yes—
473C3×C4C2×C4×C3⋊D312yes—
474Dic3—22no—
475Dic3—38no—
476Dic3—68no—
477Dic3—98no—
478Dic3—92no—
479Dic3—188no—
480Dic3—188no—
481Dic3—182no—
482Dic3—368no—
483Dic3C2×C4×C3⋊D312yes—
484C32—24no—
485C32C2×#89214yescomplemented
486C32D3×#11711yescharacteristic, complemented
487C23—31no—
488C23—91no—
489C23—274no—
490C23—271no—
491C23—542no—
492C23—542no—
493C2×C4—31no—
494C2×C4—34no—
495C2×C4—32no—
496C2×C4—64no—
497C2×C4—91no—
498C2×C4—94no—
499C2×C4—92no—
500C2×C4—274no—
501C2×C4—274no—
502C2×C4—274no—
503C2×C4—271no—
504C2×C4—274no—
505C2×C4—272no—
506C2×C4—544no—
507C2×C4C2×D3×C3⋊D312yes—
508C2×C4C2×D3×C3⋊D311yescharacteristic
509C2×C3—24no—
510C2×C3—24no—
511C2×C3—24no—
512C2×C3—316no—
513C2×C3—182no—
514C2×C3C2×C4×D3214yes—
515C2×C3D3×#23714yes—
516C2×C3D3×#23914yes—
517C2×C3C22×C4×C3⋊D311yescharacteristic
518C2×C3C2×#383011yescharacteristic
519C2×C3C2×#383211yescharacteristic
520D3—68no—
521D3—188no—
522D3—182no—
523D3—368no—
524D3#6410114yesdirect product factor
525C22—32no—
526C22—32no—
527C22—32no—
528C22—92no—
529C22—181no—
530C22—181no—
531C22—272no—
532C22—548no—
533C22—541no—
534C22—541no—
535C22C22×D3×C3⋊D311yescharacteristic
536C4—22no—
537C4—32no—
538C4—62no—
539C4—92no—
540C4—182no—
541C4—272no—
542C4—542no—
543C4C4×D3×C3⋊D312yes—
544C3—24no—
545C3D3×#89214yescomplemented
546C3C2×#6410111yescharacteristic, complemented
547C2—34no—
548C2—182no—
549C2—542no—
550C2C2×C4×D3×C3⋊D311yescharacteristic
551C2D3×#383011yescharacteristic
552C2D3×#383211yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutatorC2×C33C23×C4
FittingC33×C4⋊C4C22
socle, cosocleC22×C33C24
prime radicalC22×D3×C3⋊D3C22
hypercenterC4⋊C4D3×C3⋊D3
hypocenterC33C2×#117
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #11723933C2semidirect
3. C3×#64101C2semidirect
4. C32×D3×C4⋊C4C2semidirect
6. D3×C4⋊(C3⋊Dic3)C2semidirect
7. #11723469C2semidirect
8. #11723466C2semidirect
9. C4×D3×C3⋊Dic3C2semidirect
10. #11723413C2semidirect
11. #11723404C2semidirect
23. C4×D3×C3⋊D3C4semidirect
24. C33×C4⋊C4C22semidirect
26. C4⋊(C3⋊(C3⋊Dic3))C22semidirect
27. C4×C3⋊(C3⋊Dic3)C22semidirect
29. C3×C4⋊(C3⋊Dic3)C22semidirect
30. C3×C4×C3⋊Dic3C22semidirect
31. C32×C4⋊Dic3C22semidirect
32. C32×Dic3⋊C4C22semidirect
33. Dic3⋊(C3⋊Dic3)C22semidirect
36. Dic3×C3⋊Dic3C22semidirect
37. Dic3×C3⋊Dic3C22semidirect
51. #64101D3direct (N × H)
53. C3×D3×C4⋊C4D3semidirect
71. C4×C3⋊(C3⋊D3)C2×C4semidirect
74. C3×C4×C3⋊D3C2×C4semidirect
79. #6289C2×C4semidirect
80. Dic3×C3⋊D3C2×C4semidirect
109. C32×C4⋊C4C2×D3semidirect
110. C32×C4⋊C4C2×D3semidirect
121. C4⋊(C3⋊Dic3)C2×D3semidirect
127. C4×C3⋊Dic3C2×D3semidirect
130. C3×C4⋊Dic3C2×D3semidirect
131. C3×Dic3⋊C4C2×D3semidirect
175. D3×C4⋊C4C3⋊D3semidirect
218. C4×C3⋊D3C4×D3semidirect
236. C32×D3#117semidirect
262. C3×C4⋊C4D32semidirect
263. C3×C4⋊C4C2×C3⋊D3semidirect
279. C4⋊Dic3C2×C3⋊D3semidirect
281. Dic3⋊C4C2×C3⋊D3semidirect
347. C33C2×#117semidirect
413. C3×D3#892semidirect
429. C4⋊C4D3×C3⋊D3semidirect
485. C32C2×#892semidirect
486. C32D3×#117semidirect
524. D3#64101direct (N × H)
545. C3D3×#892semidirect
546. C3C2×#64101semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D3×C3⋊D32
#117239332
C3×#641012
C32×D3×C4⋊C42
D3×#37522
D3×C4⋊(C3⋊Dic3)2
#117234692
#117234662
C4×D3×C3⋊Dic32
#117234132
#117234042
C2×#641013
D3×#8923