Finite Group Databasebeta

← D3×#4531 #11783137

Subgroups — D3×#4531 #11783137

Order 1152.

855 conjugacy classes of subgroups.

The subgroup lattice has 667 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×#117C211yesmaximal, characteristic
2D3×#926C211yesmaximal, characteristic
3C2×D3×#208C211yesmaximal, characteristic
4#10589397C211yesmaximal, characteristic, complemented
5C3×#4531C211yesmaximal, characteristic, complemented
6#10589158C211yesmaximal, characteristic, complemented
7#10589157C211yesmaximal, characteristic, complemented
8C2×#4531—31nomaximal
9D3×H(3,ℤ/4)—31nomaximal
10C22×C3×C4×D3C2211yescharacteristic
11C32×#117C2211yescharacteristic
12#64135C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C3×#926C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×#892—21no—
18C3×D3×C4⋊C4—21no—
19C3×D3×C22⋊C4—21no—
20C3×#877—21no—
21C3×#872C412yescomplemented
22C3×C42×D3C412yescomplemented
23D3×#217—21no—
24#63955—21no—
25D3×C4⋊Dic3—21no—
26C4×D3×Dic3C412yescomplemented
27#63855C412yescomplemented
28#63841—21no—
29C2×#3711C412yescomplemented
30D3×#208—21no—
31D3×#208—21no—
32D3×#208—21no—
33D3×#208—21no—
34C2×D3×C3⋊C8C412yescomplemented
35C2×C3×#117—31no—
36C2×#926—31no—
37C22×#208—31no—
38C2×D3×M16—31no—
39D3×#117—31no—
40D3×#117D311yescharacteristic
41C3×H(3,ℤ/4)—31no—
42#4557—31no—
43#4531—31no—
44#4531—31no—
45#4531—31no—
46#4531—31no—
47#4531—31no—
48#4531—61no—
49#4531D311yescharacteristic, direct product factor
50C23×C3×D3D411yescharacteristic
51C22×C32×C4C2311yescharacteristic
52C22×C3×Dic3D411yescharacteristic
53C2×C3×C4×D3—22no—
54C2×C3×C4×D3C2×C411yescharacteristic
55C2×C3×C4×D3C2×C411yescharacteristic
56C2×C3×C4×D3C2×C411yescharacteristic
57C2×C3×C4×D3C2×C411yescharacteristic
58C2×C3×C4×D3C2×C411yescharacteristic
59C2×C3×C4×D3C2×C411yescharacteristic
60C2×C3×C4×D3D411yescharacteristic
61C2×C3×C4×D3D411yescharacteristic
62C2×C3×C4×D3D411yescharacteristic
63C2×C3×C4×D3D411yescharacteristic
64C2×C3×C4×D3Q811yescharacteristic
65C2×C3×C4×D3Q811yescharacteristic
66C2×D3×Dic3—22no—
67C32×C4⋊C4—21no—
68C32×C22⋊C4—21no—
69C32×C42C2×C412yescomplemented
70#3757—21no—
71C4⋊(C3⋊Dic3)—21no—
72C4×C3⋊Dic3C2×C412yescomplemented
73#3748—21no—
74#3748—21no—
75C2×C3⋊(C3⋊C8)C2×C412yescomplemented
76C3×#217—21no—
77C3×#217—21no—
78C3×(C2×D3)⋊C4—22no—
79C3×C4⋊Dic3—21no—
80C3×C4⋊Dic3—21no—
81C3×Dic3⋊C4—22no—
82C3×C4×Dic3—22no—
83C3×C4×Dic3C2×C412yescomplemented
84C3×C4×Dic3C2×C412yescomplemented
85C3×#208—21no—
86C3×#208—21no—
87C2×C3×C3⋊C8C2×C412yescomplemented
88Dic3⋊Dic3—22no—
89(C2×D3)⋊Dic3—22no—
90Dic32—22no—
91#3711—22no—
92#3711—22no—
93D3×C3⋊C8—22no—
94D3×C3⋊C8—22no—
95C2×H(3,ℤ/4)—91noSylow
96C23×C3×C4—31no—
97C22×C4×D3C2×D311yescharacteristic
98C2×C3×M16—31no—
99C3×#117—21no—
100C3×#117—31no—
101C3×#117—31no—
102C3×#117—32no—
103C3×#117—61no—
104C3×#117—61no—
105C3×#117C2×D311yescharacteristic
106C3×#117C2×D311yescharacteristic
107C2×C3×C4⋊C4—61no—
108C2×C3×C22⋊C4—61no—
109C2×C3×C42—32no—
110C2×#217—61no—
111#926—31no—
112#926—31no—
113#926—32no—
114#926—61no—
115#926—61no—
116#926—61no—
117#926C2×D311yescharacteristic
118#926C2×D311yescharacteristic
119C2×C4⋊Dic3—61no—
120C2×C4×Dic3—32no—
121C2×#208—31no—
122C2×#208—31no—
123C2×#208—32no—
124C2×#208—61no—
125C2×#208—61no—
126C2×#208—61no—
127C2×#208—61no—
128C2×#208—61no—
129C2×#208C2×D311yescharacteristic
130C22×C3⋊C8—32no—
131D3×M16—61no—
132D3×M16—61no—
133D3×M16—61no—
134D3×M16—61no—
135C2×ΓL(1,𝔽25)—32no—
136C2×D3×C8—32no—
137#892—21no—
138#892—61no—
139D3×C4⋊C4—21no—
140D3×C4⋊C4—61no—
141D3×C22⋊C4—21no—
142D3×C22⋊C4—61no—
143#877—21no—
144#877—61no—
145#872—32no—
146#872Dic312yescomplemented
147C42×D3—32no—
148C42×D3Dic312yescomplemented
149C23×C32C2×D411yescharacteristic
150C22×C3×D3—42no—
151C22×C3×D3C22⋊C411yescharacteristic
152C22×C3×D3C22⋊C411yescharacteristic
153C22×C3×D3C22⋊C411yescharacteristic
154C22×C3×D3C22⋊C411yescharacteristic
155C22×C3×D3C4⋊C411yescharacteristic
156C22×C3×D3C4⋊C411yescharacteristic
157C2×C32×C4—22no—
158C2×C32×C4C22×C411yescharacteristic
159C2×C32×C4C22×C411yescharacteristic
160C2×C32×C4C22×C411yescharacteristic
161C2×C32×C4C2×D411yescharacteristic
162C2×C32×C4C2×D411yescharacteristic
163C2×C32×C4C2×Q811yescharacteristic
164C2×C3⋊Dic3—22no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3C22⋊C411yescharacteristic
168C2×C3×Dic3C22⋊C411yescharacteristic
169C2×C3×Dic3C22⋊C411yescharacteristic
170C2×C3×Dic3C22⋊C411yescharacteristic
171C2×C3×Dic3C4⋊C411yescharacteristic
172C2×C3×Dic3C4⋊C411yescharacteristic
173C3×C4×D3—44no—
174C3×C4×D3C4211yescharacteristic
175C3×C4×D3C4211yescharacteristic
176C3×C4×D3C4211yescharacteristic
177C3×C4×D3C4211yescharacteristic
178C3×C4×D3C22⋊C411yescharacteristic
179C3×C4×D3C22⋊C411yescharacteristic
180C3×C4×D3C22⋊C411yescharacteristic
181C3×C4×D3C22⋊C411yescharacteristic
182C3×C4×D3C4⋊C411yescharacteristic
183C3×C4×D3C4⋊C411yescharacteristic
184C3×C4×D3C4⋊C411yescharacteristic
185C3×C4×D3C4⋊C411yescharacteristic
186C3×C4×D3C4⋊C411yescharacteristic
187C3×C4×D3C4⋊C411yescharacteristic
188C3×C4×D3C4⋊C411yescharacteristic
189C3×C4×D3C4⋊C411yescharacteristic
190D3×Dic3—44no—
191C3⋊(C3⋊C8)—22no—
192C3×C3⋊C8—22no—
193C22×M16—91no—
194C2×#117—31no—
195C2×#117—91no—
196H(3,ℤ/4)—31no—
197H(3,ℤ/4)—91no—
198H(3,ℤ/4)—91no—
199H(3,ℤ/4)—91no—
200C24×C3—31no—
201C23×D3#6711yescharacteristic
202C22×C3×C4—21no—
203C22×C3×C4—31no—
204C22×C3×C4—31no—
205C22×C3×C4—31no—
206C22×C3×C4—31no—
207C22×C3×C4—31no—
208C22×C3×C4—31no—
209C22×C3×C4—31no—
210C22×C3×C4—31no—
211C22×C3×C4—31no—
212C22×C3×C4—31no—
213C22×C3×C4—31no—
214C22×C3×C4—31no—
215C22×C3×C4—31no—
216C22×C3×C4—62no—
217C22×C3×C4C22×D311yescharacteristic
218C22×C3×C4C22×D311yescharacteristic
219C22×Dic3—62no—
220C22×Dic3#6711yescharacteristic
221C2×C4×D3—22no—
222C2×C4×D3—62no—
223C2×C4×D3Dic611yescharacteristic
224C2×C4×D3Dic611yescharacteristic
225C2×C4×D3C4×D311yescharacteristic
226C2×C4×D3C4×D311yescharacteristic
227C2×C4×D3C4×D311yescharacteristic
228C2×C4×D3C4×D311yescharacteristic
229C2×C4×D3D1211yescharacteristic
230C2×C4×D3D1211yescharacteristic
231C2×C4×D3C2×Dic311yescharacteristic
232C2×C4×D3C2×Dic311yescharacteristic
233C2×C4×D3#6711yescharacteristic
234C2×C4×D3#6711yescharacteristic
235C3×M16—61no—
236C3×M16—61no—
237C2×C3×C8—32no—
238C3×C4⋊C4—21no—
239C3×C4⋊C4—21no—
240C3×C4⋊C4—41no—
241C3×C4⋊C4—62no—
242C3×C4⋊C4—61no—
243C3×C4⋊C4—61no—
244C3×C22⋊C4—21no—
245C3×C22⋊C4—21no—
246C3×C22⋊C4—41no—
247C3×C22⋊C4—62no—
248C3×C22⋊C4—61no—
249C3×C22⋊C4—61no—
250C3×C42—22no—
251C3×C42—32no—
252C3×C42—32no—
253C3×C42—62no—
254C3×C42C4×D312yescomplemented
255C3×C42C2×Dic312yescomplemented
256#217—21no—
257#217—21no—
258#217—62no—
259#217—61no—
260#217—61no—
261#217—121no—
262(C2×D3)⋊C4—22no—
263(C2×D3)⋊C4—62no—
264C4⋊Dic3—21no—
265C4⋊Dic3—21no—
266C4⋊Dic3—62no—
267C4⋊Dic3—61no—
268C4⋊Dic3—61no—
269C4⋊Dic3—121no—
270Dic3⋊C4—22no—
271Dic3⋊C4—62no—
272C4×Dic3—22no—
273C4×Dic3—32no—
274C4×Dic3—32no—
275C4×Dic3—62no—
276C4×Dic3—62no—
277C4×Dic3—62no—
278C4×Dic3C4×D312yescomplemented
279C4×Dic3C2×Dic312yescomplemented
280#208—21no—
281#208—21no—
282#208—62no—
283#208—62no—
284#208—61no—
285#208—61no—
286#208—61no—
287#208—61no—
288#208—121no—
289#208—121no—
290C2×C3⋊C8—32no—
291C2×C3⋊C8—32no—
292C2×C3⋊C8—62no—
293C2×C3⋊C8—62no—
294C2×C3⋊C8—62no—
295C2×C3⋊C8C4×D312yescomplemented
296ΓL(1,𝔽25)—62no—
297ΓL(1,𝔽25)—62no—
298D3×C8—62no—
299D3×C8—62no—
300C22×C32—41no—
301C22×C32C2×C22⋊C411yescharacteristic
302C22×C32C2×C22⋊C411yescharacteristic
303C22×C32C2×C4⋊C411yescharacteristic
304C2×C3×D3—22no—
305C2×C3×D3—22no—
306C2×C3×D3—22no—
307C2×C3×D3—41no—
308C2×C3×D3—41no—
309C2×C3×D3—41no—
310C2×C3×D3#9511yescharacteristic
311C2×C3×D3#9511yescharacteristic
312C2×C3×D3#9511yescharacteristic
313C2×C3×D3#9511yescharacteristic
314C32×C4—42no—
315C32×C4C2×C4211yescharacteristic
316C32×C4C2×C22⋊C411yescharacteristic
317C32×C4C2×C4⋊C411yescharacteristic
318C32×C4C2×C4⋊C411yescharacteristic
319C3⋊Dic3—42no—
320C3×Dic3—42no—
321C3×Dic3—42no—
322C3×Dic3#9511yescharacteristic
323C3×Dic3#9511yescharacteristic
324C3×Dic3#9511yescharacteristic
325C3×Dic3#9511yescharacteristic
326C23×C4—31no—
327C2×M16—31no—
328C2×M16—92no—
329C2×M16—91no—
330C2×M16—181no—
331C2×M16—181no—
332C2×M16—181no—
333C2×M16—181no—
334C22×C8—92no—
335#117—31no—
336#117—31no—
337#117—32no—
338#117—61no—
339#117—61no—
340#117—92no—
341#117—91no—
342#117—181no—
343#117—181no—
344#117D3211yescharacteristic
345C2×C4⋊C4—61no—
346C2×C4⋊C4—181no—
347C2×C22⋊C4—61no—
348C2×C22⋊C4—181no—
349C2×C42—32no—
350C2×C42—92no—
351C23×C3—21no—
352C23×C3—31no—
353C23×C3—31no—
354C23×C3—31no—
355C23×C3—31no—
356C23×C3—31no—
357C23×C3—31no—
358C23×C3—122no—
359C23×C3D3×D411yescharacteristic
360C23×C3C2×#6711yescharacteristic
361C22×D3—42no—
362C22×D3Dic3⋊C411yescharacteristic
363C22×D3Dic3⋊C411yescharacteristic
364C22×D3(C2×D3)⋊C411yescharacteristic
365C22×D3(C2×D3)⋊C411yescharacteristic
366C22×D3#21711yescharacteristic
367C22×D3#21711yescharacteristic
368C2×C3×C4—22no—
369C2×C3×C4—22no—
370C2×C3×C4—21no—
371C2×C3×C4—21no—
372C2×C3×C4—21no—
373C2×C3×C4—21no—
374C2×C3×C4—21no—
375C2×C3×C4—21no—
376C2×C3×C4—31no—
377C2×C3×C4—31no—
378C2×C3×C4—31no—
379C2×C3×C4—31no—
380C2×C3×C4—31no—
381C2×C3×C4—31no—
382C2×C3×C4—31no—
383C2×C3×C4—31no—
384C2×C3×C4—31no—
385C2×C3×C4—31no—
386C2×C3×C4—31no—
387C2×C3×C4—31no—
388C2×C3×C4—31no—
389C2×C3×C4—31no—
390C2×C3×C4—31no—
391C2×C3×C4—31no—
392C2×C3×C4—31no—
393C2×C3×C4—31no—
394C2×C3×C4—31no—
395C2×C3×C4—31no—
396C2×C3×C4—31no—
397C2×C3×C4—31no—
398C2×C3×C4—42no—
399C2×C3×C4—62no—
400C2×C3×C4—62no—
401C2×C3×C4—124no—
402C2×C3×C4C2×Dic611yescharacteristic
403C2×C3×C4C2×C4×D311yescharacteristic
404C2×C3×C4C2×C4×D311yescharacteristic
405C2×C3×C4C2×C4×D311yescharacteristic
406C2×C3×C4C2×C4×D311yescharacteristic
407C2×C3×C4C2×C4×D311yescharacteristic
408C2×C3×C4C2×D1211yescharacteristic
409C2×C3×C4D3×D411yescharacteristic
410C2×C3×C4D3×D411yescharacteristic
411C2×C3×C4D3×Q811yescharacteristic
412C2×C3×C4C22×Dic311yescharacteristic
413C2×C3×C4C2×#6711yescharacteristic
414C2×Dic3—22no—
415C2×Dic3—22no—
416C2×Dic3—62no—
417C2×Dic3—62no—
418C2×Dic3—122no—
419C2×Dic3—124no—
420C2×Dic3Dic3⋊C411yescharacteristic
421C2×Dic3Dic3⋊C411yescharacteristic
422C2×Dic3(C2×D3)⋊C411yescharacteristic
423C2×Dic3(C2×D3)⋊C411yescharacteristic
424C2×Dic3#21711yescharacteristic
425C2×Dic3#21711yescharacteristic
426C4×D3—44no—
427C4×D3—124no—
428C4×D3C4×Dic311yescharacteristic
429C4×D3C4×Dic311yescharacteristic
430C4×D3C4×Dic311yescharacteristic
431C4×D3C4×Dic311yescharacteristic
432C4×D3Dic3⋊C411yescharacteristic
433C4×D3Dic3⋊C411yescharacteristic
434C4×D3Dic3⋊C411yescharacteristic
435C4×D3Dic3⋊C411yescharacteristic
436C4×D3C4⋊Dic311yescharacteristic
437C4×D3C4⋊Dic311yescharacteristic
438C4×D3C4⋊Dic311yescharacteristic
439C4×D3C4⋊Dic311yescharacteristic
440C4×D3(C2×D3)⋊C411yescharacteristic
441C4×D3(C2×D3)⋊C411yescharacteristic
442C4×D3(C2×D3)⋊C411yescharacteristic
443C4×D3(C2×D3)⋊C411yescharacteristic
444C3×C8—62no—
445C3⋊C8—22no—
446C3⋊C8—62no—
447C3⋊C8—62no—
448C3⋊C8—122no—
449C2×C32—21no—
450C2×C32—21no—
451C2×C32—21no—
452C2×C32C2×#9511yescharacteristic
453C3×D3—21no—
454C3×D3—21no—
455C3×D3—21no—
456C3×D3H(3,ℤ/4)12yescomplemented
457C24—31no—
458C22×C4—31no—
459C22×C4—31no—
460C22×C4—31no—
461C22×C4—31no—
462C22×C4—31no—
463C22×C4—31no—
464C22×C4—31no—
465C22×C4—31no—
466C22×C4—31no—
467C22×C4—31no—
468C22×C4—31no—
469C22×C4—31no—
470C22×C4—31no—
471C22×C4—62no—
472C22×C4—182no—
473C22×C4C2×D3211yescharacteristic
474M16—61no—
475M16—61no—
476M16—182no—
477M16—182no—
478M16—181no—
479M16—181no—
480C2×C8—32no—
481C2×C8—92no—
482C2×C8—182no—
483C2×C8—182no—
484C4⋊C4—21no—
485C4⋊C4—62no—
486C4⋊C4—61no—
487C4⋊C4—61no—
488C4⋊C4—182no—
489C4⋊C4—181no—
490C22⋊C4—21no—
491C22⋊C4—62no—
492C22⋊C4—61no—
493C22⋊C4—61no—
494C22⋊C4—182no—
495C22⋊C4—181no—
496C42—32no—
497C42—32no—
498C42—62no—
499C42—92no—
500C42—182no—
501C42D3×Dic312yescomplemented
502C22×C3—21no—
503C22×C3—21no—
504C22×C3—21no—
505C22×C3—31no—
506C22×C3—31no—
507C22×C3—31no—
508C22×C3—31no—
509C22×C3—41no—
510C22×C3—41no—
511C22×C3—62no—
512C22×C3—62no—
513C22×C3—62no—
514C22×C3—81no—
515C22×C3—121no—
516C22×C3—121no—
517C22×C3—121no—
518C22×C3D3×C22⋊C411yescharacteristic
519C22×C3D3×C22⋊C411yescharacteristic
520C22×C3D3×C4⋊C411yescharacteristic
521C22×C3C2×Dic3⋊C411yescharacteristic
522C22×C3C2×(C2×D3)⋊C411yescharacteristic
523C22×C3C2×#21711yescharacteristic
524C2×D3—22no—
525C2×D3—22no—
526C2×D3—22no—
527C2×D3—41no—
528C2×D3—41no—
529C2×D3—41no—
530C2×D3C3⋊#9511yescharacteristic
531C2×D3C3⋊#9511yescharacteristic
532C2×D3C3⋊#9511yescharacteristic
533C2×D3C3⋊#9511yescharacteristic
534C3×C4—21no—
535C3×C4—21no—
536C3×C4—21no—
537C3×C4—21no—
538C3×C4—31no—
539C3×C4—31no—
540C3×C4—31no—
541C3×C4—31no—
542C3×C4—42no—
543C3×C4—42no—
544C3×C4—82no—
545C3×C4—122no—
546C3×C4—122no—
547C3×C4C42×D311yescharacteristic
548C3×C4D3×C22⋊C411yescharacteristic
549C3×C4D3×C4⋊C411yescharacteristic
550C3×C4D3×C4⋊C411yescharacteristic
551C3×C4C2×C4×Dic311yescharacteristic
552C3×C4C2×Dic3⋊C411yescharacteristic
553C3×C4C2×C4⋊Dic311yescharacteristic
554C3×C4C2×(C2×D3)⋊C411yescharacteristic
555Dic3—42no—
556Dic3—42no—
557Dic3—122no—
558Dic3—122no—
559Dic3—242no—
560Dic3C3⋊#9511yescharacteristic
561Dic3C3⋊#9511yescharacteristic
562Dic3C3⋊#9511yescharacteristic
563Dic3C3⋊#9511yescharacteristic
564C32C2×H(3,ℤ/4)11yescharacteristic, complemented, Sylow
565C23—31no—
566C23—31no—
567C23—31no—
568C23—31no—
569C23—31no—
570C23—31no—
571C23—122no—
572C23D3×#6711yescharacteristic
573C2×C4—22no—
574C2×C4—31no—
575C2×C4—31no—
576C2×C4—31no—
577C2×C4—31no—
578C2×C4—31no—
579C2×C4—31no—
580C2×C4—31no—
581C2×C4—31no—
582C2×C4—31no—
583C2×C4—31no—
584C2×C4—31no—
585C2×C4—31no—
586C2×C4—31no—
587C2×C4—31no—
588C2×C4—31no—
589C2×C4—31no—
590C2×C4—31no—
591C2×C4—31no—
592C2×C4—31no—
593C2×C4—31no—
594C2×C4—31no—
595C2×C4—31no—
596C2×C4—62no—
597C2×C4—62no—
598C2×C4—124no—
599C2×C4—182no—
600C2×C4—364no—
601C2×C4D3×Dic611yescharacteristic
602C2×C4C4×D3211yescharacteristic
603C2×C4C4×D3211yescharacteristic
604C2×C4D3×D1211yescharacteristic
605C2×C4C2×D3×Dic311yescharacteristic
606C2×C4D3×#6711yescharacteristic
607C8—62no—
608C8—182no—
609C2×C3—21no—
610C2×C3—21no—
611C2×C3—21no—
612C2×C3—21no—
613C2×C3—21no—
614C2×C3—21no—
615C2×C3—21no—
616C2×C3—32no—
617C2×C3—41no—
618C2×C3—41no—
619C2×C3—41no—
620C2×C3—61no—
621C2×C3—61no—
622C2×C3—61no—
623C2×C3D3×#9511yescharacteristic
624C2×C3C2×C3⋊#9511yescharacteristic
625D3—21no—
626D3—21no—
627D3—21no—
628D3#453112yesdirect product factor
629C22—31no—
630C22—31no—
631C22—31no—
632C22—31no—
633C22—41no—
634C22—62no—
635C22—62no—
636C22—62no—
637C22—121no—
638C22—121no—
639C22—121no—
640C22D3×Dic3⋊C411yescharacteristic
641C22D3×(C2×D3)⋊C411yescharacteristic
642C22D3×#21711yescharacteristic
643C4—31no—
644C4—31no—
645C4—31no—
646C4—31no—
647C4—42no—
648C4—122no—
649C4—122no—
650C4—362no—
651C4C4×D3×Dic311yescharacteristic
652C4D3×Dic3⋊C411yescharacteristic
653C4D3×C4⋊Dic311yescharacteristic
654C4D3×(C2×D3)⋊C411yescharacteristic
655C3—21no—
656C3D3×H(3,ℤ/4)11yescharacteristic, complemented
657C3C2×#453111yescharacteristic, complemented
658C2—21no—
659C2—21no—
660C2—21no—
661C2—32no—
662C2—61no—
663C2—61no—
664C2—61no—
665C2D3×C3⋊#9511yescharacteristic
subgroupG/H
centerC4C4×D3×Dic3
commutatorC32×C4C2×C42
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC2×C32C2×#95
prime radicalC23×C3×D3D4
cosocleC22×C32×C4C23
hypercenter#117D32
hypocenterC32C2×H(3,ℤ/4)
LCSG ▷ C32×C4 ▷ C32
UCSC1 ◁ C4 ◁ #117

Complements

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

NH ≅ G/Ntype
4. #10589397C2semidirect
5. C3×#4531C2semidirect
6. #10589158C2semidirect
7. #10589157C2semidirect
21. C3×#872C4semidirect
22. C3×C42×D3C4semidirect
26. C4×D3×Dic3C4semidirect
27. #63855C4semidirect
29. C2×#3711C4semidirect
34. C2×D3×C3⋊C8C4semidirect
49. #4531D3direct (N × H)
69. C32×C42C2×C4semidirect
72. C4×C3⋊Dic3C2×C4semidirect
75. C2×C3⋊(C3⋊C8)C2×C4semidirect
83. C3×C4×Dic3C2×C4semidirect
84. C3×C4×Dic3C2×C4semidirect
87. C2×C3×C3⋊C8C2×C4semidirect
146. #872Dic3semidirect
148. C42×D3Dic3semidirect
254. C3×C42C4×D3semidirect
255. C3×C42C2×Dic3semidirect
278. C4×Dic3C4×D3semidirect
279. C4×Dic3C2×Dic3semidirect
295. C2×C3⋊C8C4×D3semidirect
456. C3×D3H(3,ℤ/4)semidirect
501. C42D3×Dic3semidirect
564. C32C2×H(3,ℤ/4)semidirect
628. D3#4531direct (N × H)
656. C3D3×H(3,ℤ/4)semidirect
657. C3C2×#4531semidirect

Maximal subgroups

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

subgroupindex
C3×D3×#1172
D3×#9262
C2×D3×#2082
#105893972
C3×#45312
#105891582
#105891572
C2×#45313
D3×H(3,ℤ/4)3