Finite Group Databasebeta

← D3×Dic3×D12 #13170733

Subgroups — D3×Dic3×D12 #13170733

Order 1728.

2010 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×D12C211yesmaximal, characteristic
2C2×D32×Dic3C212yesmaximal, complemented
3#11723691C211yesmaximal, characteristic, complemented
4D12×C3⋊Dic3C211yesmaximal, characteristic, complemented
5Dic3×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
6D3×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
7C3×Dic3×D12C211yesmaximal, characteristic, complemented
8C3×C4×D3×Dic3C211yesmaximal, characteristic, complemented
9#11722928C212yesmaximal, complemented
10Dic3×#626C212yesmaximal, complemented
11D3×(C2×D3)⋊Dic3C212yesmaximal, complemented
12D3×D4×Dic3—31nomaximal
13C2×Dic3×D12—31nomaximal
14C4×D3×D12—31nomaximal
15C22×C3×D32C2212yes—
16C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
17C2×C32×D12C2211yescharacteristic
18C2×C32×C4×D3C2211yescharacteristic
19C2×#6294C2212yescomplemented
20C2×Dic3×C3⋊D3C2212yescomplemented
21C2×D3×C3⋊Dic3C2212yes—
22C2×D3×C3⋊Dic3C2212yescomplemented
23C2×C3×#626C2212yes—
24C2×C3×D3×Dic3C2211yescharacteristic
25C2×C3×D3×Dic3C2211yescharacteristic
26C2×C3×D3×Dic3C2212yescomplemented
27C3×D3×D12C418yescomplemented
28D32×Dic3—28no—
29C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic, complemented
30C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
31C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
32C32×C4×Dic3C2211yescharacteristic, complemented
33#88814C2212yescomplemented
34Dic3⋊(C3⋊Dic3)C2212yescomplemented
35#88803C2212yescomplemented
36(C2×D3)⋊(C3⋊Dic3)C2212yescomplemented
37C3×(C2×D3)⋊Dic3C2212yescomplemented
38C3×Dic32C2211yescharacteristic, complemented
39C3×Dic32C2211yescharacteristic, complemented
40C2×C3×D3×D4—31no—
41C22×C3×D12—31no—
42C22×D3×Dic3—32no—
43C22×D3×Dic3—32no—
44C2×D3×D12D311yescharacteristic
45C2×C4×D32—32no—
46D4×C3⋊Dic3—31no—
47C2×C4⋊(C3⋊Dic3)—31no—
48C4×C4⋊(C3⋊D3)—31no—
49C3×D4×Dic3—31no—
50C2×C3×C4×Dic3—31no—
51C3×C4×D12—31no—
52C3×C42×D3—31no—
53#67⋊Dic3—32no—
54Dic3×#67—32no—
55D3×#217—32no—
56C2×(C2×D3)⋊Dic3—32no—
57D3×(C2×D3)⋊C4—32no—
58C4×#626—32no—
59#63898—31no—
60#63894—31no—
61Dic3×D12—31no—
62Dic3×D12—31no—
63Dic3×D12—32no—
64Dic3×D12—31no—
65Dic3×D12—31no—
66Dic3×D12—31no—
67Dic3×D12—32no—
68Dic3×D12—61no—
69Dic3×D12—61no—
70Dic3×D12D311yescharacteristic, direct product factor
71D3×C4⋊Dic3—31no—
72D3×C4⋊Dic3—31no—
73D3×C4⋊Dic3—61no—
74#63880—32no—
75C4×D3×Dic3D311yescharacteristic, complemented
76C22×C3×C3⋊D3C2312yes—
77C22×C32×D3C2312yes—
78C22×C32×D3C2311yescharacteristic
79C2×C3×D32—24no—
80C2×C3×D32—24no—
81C2×C3×D32C2×C418yescomplemented
82C2×C33×C4C2311yescharacteristic
83C2×C3⋊(C3⋊Dic3)C2312yes—
84C2×C3×C3⋊Dic3C2311yescharacteristic
85C2×C3×C3⋊Dic3C2312yes—
86C2×C3×C3⋊Dic3C2311yescharacteristic
87C3×C4⋊(C3⋊D3)C2×C414yescomplemented
88C2×C32×Dic3C2311yescharacteristic
89C2×C32×Dic3C2311yescharacteristic
90C2×C32×Dic3C2311yescharacteristic
91C32×D12C2×C414yescomplemented
92C32×C4×D3C2×C414yescomplemented
93#6294—24no—
94Dic3×C3⋊D3—24no—
95D3×C3⋊Dic3—24no—
96D3×C3⋊Dic3—24no—
97C3×#626C2×C418yescomplemented
98C3×D3×Dic3—22no—
99C3×D3×Dic3—24no—
100C3×D3×Dic3D414yescomplemented
101C2×D4×Dic3—91no—
102C4×D3×D4—91no—
103C2×C4×D12—91no—
104C23×C3×D3—32no—
105C23×C3×D3—32no—
106C22×D32C2×D312yes—
107C2×C32×D4—31no—
108C22×C32×C4—31no—
109C22×C3⋊Dic3—32no—
110C22×C3⋊Dic3—32no—
111C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
112C2×C4×C3⋊D3—32no—
113C2×C3×#67—32no—
114C22×C3×Dic3—31no—
115C22×C3×Dic3—31no—
116C22×C3×Dic3—32no—
117C3×D3×D4—38no—
118C2×C3×D12—21no—
119C2×C3×D12—32no—
120C2×C3×D12—31no—
121C2×C3×D12—31no—
122C2×C3×D12—38no—
123C2×C3×D12—61no—
124C2×C3×D12C2×D311yescharacteristic
125C2×C3×D12C2×D311yescharacteristic
126C2×C3×C4×D3—21no—
127C2×C3×C4×D3—31no—
128C2×C3×C4×D3—32no—
129C2×C3×C4×D3—31no—
130C2×C3×C4×D3C2×D311yescharacteristic
131C2×C3×C4×D3C2×D311yescharacteristic
132C2×#626C2×D312yes—
133C2×#624—32no—
134C2×D3×Dic3—32no—
135C2×D3×Dic3—32no—
136C2×D3×Dic3—32no—
137C2×D3×Dic3—32no—
138C2×D3×Dic3—32no—
139C2×D3×Dic3—32no—
140C2×D3×Dic3—32no—
141C2×D3×Dic3—32no—
142C2×D3×Dic3—68no—
143C2×D3×Dic3—68no—
144C2×D3×Dic3—62no—
145C2×D3×Dic3—62no—
146C2×D3×Dic3—62no—
147C2×D3×Dic3C2×D311yescharacteristic
148C2×D3×Dic3C2×D311yescharacteristic
149C2×D3×Dic3C2×D312yescomplemented
150D3×D12Dic318yesdirect product factor
151C4×D32—68no—
152C32×C42—31no—
153#3757—32no—
154#3752—32no—
155C4⋊(C3⋊Dic3)—31no—
156C4⋊(C3⋊Dic3)—31no—
157C4⋊(C3⋊Dic3)—31no—
158C4⋊(C3⋊Dic3)—32no—
159C4⋊(C3⋊Dic3)—61no—
160C4⋊(C3⋊Dic3)—61no—
161C4⋊(C3⋊Dic3)—61no—
162C4⋊(C3⋊Dic3)—121no—
163C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
164C4×C3⋊Dic3C2×D311yescharacteristic, complemented
165C3×#217—32no—
166C3×(C2×D3)⋊C4—32no—
167C3×C4⋊Dic3—31no—
168C3×C4⋊Dic3—31no—
169C3×C4⋊Dic3—61no—
170C3×C4×Dic3—21no—
171C3×C4×Dic3—31no—
172C3×C4×Dic3—31no—
173C3×C4×Dic3—31no—
174C3×C4×Dic3—31no—
175C3×C4×Dic3—31no—
176C3×C4×Dic3—31no—
177C3×C4×Dic3—61no—
178C3×C4×Dic3C2×D311yescharacteristic, complemented
179C3×C4×Dic3C2×D311yescharacteristic, complemented
180Dic3⋊Dic3—32no—
181Dic3⋊Dic3—32no—
182Dic3⋊Dic3—62no—
183#3722—32no—
184(C2×D3)⋊Dic3—32no—
185(C2×D3)⋊Dic3—32no—
186(C2×D3)⋊Dic3—32no—
187(C2×D3)⋊Dic3—32no—
188(C2×D3)⋊Dic3—32no—
189(C2×D3)⋊Dic3—32no—
190(C2×D3)⋊Dic3—62no—
191(C2×D3)⋊Dic3—62no—
192(C2×D3)⋊Dic3C2×D312yescomplemented
193Dic32C2×D311yescharacteristic, complemented
194Dic32C2×D311yescharacteristic, complemented
195C22×C33C2411yescharacteristic
196C2×C3×C3⋊D3—22no—
197C2×C3×C3⋊D3—22no—
198C2×C3×C3⋊D3C22×C414yescomplemented
199C2×C32×D3—22no—
200C2×C32×D3—22no—
201C2×C32×D3C22×C412yes—
202C2×C32×D3C22×C414yescomplemented
203C2×C32×D3C2×D412yes—
204C2×C32×D3#4112yes—
205C3×D32—216no—
206C33×C4C22×C412yescomplemented
207C3⋊(C3⋊Dic3)—22no—
208C3×C3⋊Dic3—22no—
209C3×C3⋊Dic3—21no—
210C3×C3⋊Dic3C2×D412yescomplemented
211C32×Dic3—21no—
212C32×Dic3C22×C412yescomplemented
213C32×Dic3C2×D412yescomplemented
214C22×C3×D4—91no—
215C23×Dic3—92no—
216C2×D3×D4—31no—
217C22×D12—31no—
218C22×C4×D3—92no—
219C22×C4×D3—92no—
220C3×C4×D4—91no—
221C2×C3×C42—91no—
222C2×#217—92no—
223D4×Dic3—31no—
224D4×Dic3—91no—
225D4×Dic3—92no—
226D4×Dic3—92no—
227D4×Dic3—91no—
228D4×Dic3—91no—
229D4×Dic3—91no—
230D4×Dic3—181no—
231C4×#67—92no—
232C2×(C2×D3)⋊C4—92no—
233C2×C4⋊Dic3—91no—
234C2×C4⋊Dic3—91no—
235C2×C4⋊Dic3—181no—
236C2×C4×Dic3—31no—
237#893—91no—
238D3×C4⋊C4—91no—
239#67⋊C4—92no—
240D3×C22⋊C4—92no—
241C4×D12—31no—
242C4×D12—91no—
243C4×D12—92no—
244C4×D12—91no—
245C4×D12—91no—
246C4×D12—92no—
247C4×D12—91no—
248C4×D12—181no—
249C42×D3—31no—
250C23×C32—31no—
251C23×C32—32no—
252C22×C3⋊D3C22×D312yes—
253C22×C3×D3—21no—
254C22×C3×D3—22no—
255C22×C3×D3—32no—
256C22×C3×D3—32no—
257C22×C3×D3—38no—
258C22×C3×D3—38no—
259C22×C3×D3—62no—
260C22×C3×D3—64no—
261C22×C3×D3—64no—
262C22×C3×D3—64no—
263C22×C3×D3—64no—
264C22×C3×D3C22×D312yes—
265C22×C3×D3C22×D312yes—
266C22×C3×D3C22×D311yescharacteristic
267C22×C3×D3C22×D311yescharacteristic
268C2×D32—24no—
269C2×D32—24no—
270C2×D32C2×Dic318yescomplemented
271C32×D4—34no—
272C2×C32×C4—21no—
273C2×C32×C4—21no—
274C2×C32×C4—21no—
275C2×C32×C4—31no—
276C2×C32×C4—31no—
277C2×C32×C4—34no—
278C2×C32×C4—31no—
279C2×C32×C4—41no—
280C2×C32×C4C22×D311yescharacteristic
281C2×C32×C4C22×D311yescharacteristic
282C2×C32×C4C22×D311yescharacteristic
283C2×C3⋊Dic3—32no—
284C2×C3⋊Dic3—32no—
285C2×C3⋊Dic3—32no—
286C2×C3⋊Dic3—62no—
287C2×C3⋊Dic3—62no—
288C2×C3⋊Dic3—62no—
289C2×C3⋊Dic3—64no—
290C2×C3⋊Dic3—64no—
291C2×C3⋊Dic3—122no—
292C2×C3⋊Dic3C22×D311yescharacteristic
293C2×C3⋊Dic3C22×D312yes—
294C2×C3⋊Dic3C22×D311yescharacteristic
295C4⋊(C3⋊D3)C2×Dic314yescomplemented
296C4×C3⋊D3—64no—
297C3×#67—38no—
298C2×C3×Dic3—21no—
299C2×C3×Dic3—21no—
300C2×C3×Dic3—21no—
301C2×C3×Dic3—31no—
302C2×C3×Dic3—31no—
303C2×C3×Dic3—34no—
304C2×C3×Dic3—31no—
305C2×C3×Dic3—31no—
306C2×C3×Dic3—32no—
307C2×C3×Dic3—32no—
308C2×C3×Dic3—61no—
309C2×C3×Dic3—61no—
310C2×C3×Dic3—62no—
311C2×C3×Dic3—62no—
312C2×C3×Dic3—64no—
313C2×C3×Dic3C22×D311yescharacteristic
314C2×C3×Dic3C22×D311yescharacteristic
315C2×C3×Dic3C22×D311yescharacteristic
316C2×C3×Dic3C22×D311yescharacteristic
317C2×C3×Dic3C22×D311yescharacteristic
318C2×C3×Dic3C22×D311yescharacteristic
319C3×D12—24no—
320C3×D12—38no—
321C3×D12—34no—
322C3×D12—34no—
323C3×D12—64no—
324C3×D12C4×D314yescomplemented
325C3×D12C2×Dic314yescomplemented
326C3×C4×D3—24no—
327C3×C4×D3—34no—
328C3×C4×D3—64no—
329C3×C4×D3—62no—
330C3×C4×D3C4×D314yescomplemented
331C3×C4×D3C2×Dic314yescomplemented
332#626C2×Dic318yescomplemented
333#624—64no—
334D3×Dic3—22no—
335D3×Dic3—24no—
336D3×Dic3—64no—
337D3×Dic3—64no—
338D3×Dic3—64no—
339D3×Dic3—64no—
340D3×Dic3—64no—
341D3×Dic3—64no—
342D3×Dic3—64no—
343D3×Dic3—64no—
344D3×Dic3—124no—
345D3×Dic3—124no—
346D3×Dic3—124no—
347D3×Dic3D1214yesdirect product factor
348C2×C4×D4—271noSylow
349C2×C33C23×C411yescharacteristic
350C2×C33C22×D411yescharacteristic
351C2×C33C2×#4111yescharacteristic
352C3×C3⋊D3—24no—
353C32×D3—24no—
354C32×D3C4×D414yescomplemented
355C24×C3—92no—
356C23×D3—32no—
357C23×D3—32no—
358C2×C3×D4—31no—
359C2×C3×D4—31no—
360C2×C3×D4—61no—
361C2×C3×D4—98no—
362C2×C3×D4—92no—
363C2×C3×D4—91no—
364C22×C3×C4—31no—
365C22×C3×C4—31no—
366C22×C3×C4—61no—
367C22×C3×C4—91no—
368C22×C3×C4—91no—
369C22×C3×C4—92no—
370C2×#67—32no—
371C22×Dic3—31no—
372C22×Dic3—31no—
373C22×Dic3—32no—
374C22×Dic3—92no—
375C22×Dic3—92no—
376C22×Dic3—92no—
377C22×Dic3—92no—
378C22×Dic3—92no—
379C22×Dic3—92no—
380C22×Dic3—182no—
381C22×Dic3—182no—
382C22×Dic3—188no—
383D3×D4—38no—
384C2×D12—32no—
385C2×D12—31no—
386C2×D12—31no—
387C2×D12—38no—
388C2×D12—61no—
389C2×D12D3211yescharacteristic
390C2×C4×D3—31no—
391C2×C4×D3—31no—
392C2×C4×D3—32no—
393C2×C4×D3—92no—
394C2×C4×D3—92no—
395C2×C4×D3—92no—
396C2×C4×D3—92no—
397C2×C4×D3—92no—
398C2×C4×D3—92no—
399C2×C4×D3—182no—
400C2×C4×D3—188no—
401C2×C4×D3—188no—
402C2×C4×D3D3211yescharacteristic
403C3×C4⋊C4—91no—
404C3×C22⋊C4—92no—
405C3×C42—31no—
406C3×C42—31no—
407C3×C42—61no—
408C3×C42—91no—
409C3×C42—91no—
410C3×C42—91no—
411#217—32no—
412#217—92no—
413#217—92no—
414#217—92no—
415#217—92no—
416#217—182no—
417(C2×D3)⋊C4—32no—
418(C2×D3)⋊C4—92no—
419(C2×D3)⋊C4—92no—
420(C2×D3)⋊C4—92no—
421(C2×D3)⋊C4—92no—
422(C2×D3)⋊C4—92no—
423(C2×D3)⋊C4—182no—
424C4⋊Dic3—31no—
425C4⋊Dic3—31no—
426C4⋊Dic3—61no—
427C4⋊Dic3—92no—
428C4⋊Dic3—92no—
429C4⋊Dic3—91no—
430C4⋊Dic3—91no—
431C4⋊Dic3—91no—
432C4⋊Dic3—182no—
433C4⋊Dic3—181no—
434C4⋊Dic3—181no—
435C4⋊Dic3—181no—
436C4⋊Dic3—361no—
437Dic3⋊C4—92no—
438C4×Dic3—31no—
439C4×Dic3—31no—
440C4×Dic3—31no—
441C4×Dic3—31no—
442C4×Dic3—31no—
443C4×Dic3—31no—
444C4×Dic3—61no—
445C4×Dic3D3211yescharacteristic, complemented
446C22×C32—21no—
447C22×C32—21no—
448C22×C32—21no—
449C22×C32—32no—
450C22×C32—32no—
451C22×C32—32no—
452C22×C32—34no—
453C22×C32—41no—
454C22×C32—62no—
455C22×C32—62no—
456C22×C32C23×D311yescharacteristic
457C22×C32C23×D311yescharacteristic
458C22×C32C23×D311yescharacteristic
459C2×C3⋊D3—22no—
460C2×C3⋊D3—22no—
461C2×C3⋊D3C22×Dic314yescomplemented
462C2×C3×D3—22no—
463C2×C3×D3—22no—
464C2×C3×D3—22no—
465C2×C3×D3—22no—
466C2×C3×D3—22no—
467C2×C3×D3—22no—
468C2×C3×D3—22no—
469C2×C3×D3—24no—
470C2×C3×D3—34no—
471C2×C3×D3—34no—
472C2×C3×D3—42no—
473C2×C3×D3—42no—
474C2×C3×D3—64no—
475C2×C3×D3—616no—
476C2×C3×D3—62no—
477C2×C3×D3—62no—
478C2×C3×D3—62no—
479C2×C3×D3—62no—
480C2×C3×D3—616no—
481C2×C3×D3—122no—
482C2×C3×D3—122no—
483C2×C3×D3C2×C4×D312yes—
484C2×C3×D3C2×C4×D314yescomplemented
485C2×C3×D3C2×D1212yes—
486C2×C3×D3#23512yes—
487C2×C3×D3D3×D412yes—
488C2×C3×D3#23712yes—
489C2×C3×D3C22×Dic312yes—
490C2×C3×D3C22×Dic314yescomplemented
491D32—216no—
492C32×C4—22no—
493C32×C4—22no—
494C32×C4—22no—
495C32×C4—32no—
496C32×C4—32no—
497C32×C4—42no—
498C32×C4—61no—
499C32×C4C2×C4×D312yescomplemented
500C32×C4C2×C4×D312yescomplemented
501C32×C4C22×Dic312yescomplemented
502C3⋊Dic3—21no—
503C3⋊Dic3—22no—
504C3⋊Dic3—62no—
505C3⋊Dic3—62no—
506C3⋊Dic3—62no—
507C3⋊Dic3—122no—
508C3⋊Dic3—122no—
509C3⋊Dic3—122no—
510C3⋊Dic3—242no—
511C3⋊Dic3C2×D1212yescomplemented
512C3×Dic3—21no—
513C3×Dic3—21no—
514C3×Dic3—22no—
515C3×Dic3—22no—
516C3×Dic3—32no—
517C3×Dic3—32no—
518C3×Dic3—41no—
519C3×Dic3—62no—
520C3×Dic3—62no—
521C3×Dic3—62no—
522C3×Dic3—61no—
523C3×Dic3—61no—
524C3×Dic3—122no—
525C3×Dic3—121no—
526C3×Dic3C2×C4×D312yescomplemented
527C3×Dic3C2×D1212yescomplemented
528C3×Dic3D3×D412yescomplemented
529C3×Dic3C22×Dic312yescomplemented
530C22×D4—91no—
531C23×C4—272no—
532C4×D4—91no—
533C4×D4—271no—
534C4×D4—272no—
535C4×D4—271no—
536C4×D4—272no—
537C4×D4—271no—
538C2×C4⋊C4—271no—
539C2×C22⋊C4—272no—
540C2×C42—91no—
541C33C2×C4×D411yescharacteristic, complemented, Sylow
542C23×C3—31no—
543C23×C3—31no—
544C23×C3—32no—
545C23×C3—32no—
546C23×C3—61no—
547C23×C3—62no—
548C23×C3—98no—
549C23×C3—92no—
550C23×C3—184no—
551C23×C3—184no—
552C22×D3—32no—
553C22×D3—32no—
554C22×D3—38no—
555C22×D3—38no—
556C22×D3—62no—
557C22×D3—64no—
558C22×D3—64no—
559C22×D3—64no—
560C22×D3—64no—
561C22×D3C2×D3212yes—
562C22×D3C2×D3211yescharacteristic
563C3×D4—34no—
564C3×D4—34no—
565C3×D4—64no—
566C3×D4—98no—
567C3×D4—94no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—31no—
572C2×C3×C4—31no—
573C2×C3×C4—31no—
574C2×C3×C4—31no—
575C2×C3×C4—34no—
576C2×C3×C4—34no—
577C2×C3×C4—31no—
578C2×C3×C4—31no—
579C2×C3×C4—41no—
580C2×C3×C4—64no—
581C2×C3×C4—61no—
582C2×C3×C4—61no—
583C2×C3×C4—61no—
584C2×C3×C4—94no—
585C2×C3×C4—91no—
586C2×C3×C4—92no—
587C2×C3×C4—91no—
588C2×C3×C4—184no—
589C2×C3×C4—182no—
590C2×C3×C4C2×D3211yescharacteristic
591C2×C3×C4C2×D3211yescharacteristic
592C2×C3×C4C2×D3211yescharacteristic
593#67—38no—
594C2×Dic3—31no—
595C2×Dic3—31no—
596C2×Dic3—34no—
597C2×Dic3—31no—
598C2×Dic3—31no—
599C2×Dic3—32no—
600C2×Dic3—32no—
601C2×Dic3—61no—
602C2×Dic3—61no—
603C2×Dic3—62no—
604C2×Dic3—62no—
605C2×Dic3—64no—
606C2×Dic3—92no—
607C2×Dic3—92no—
608C2×Dic3—92no—
609C2×Dic3—182no—
610C2×Dic3—182no—
611C2×Dic3—182no—
612C2×Dic3—184no—
613C2×Dic3—184no—
614C2×Dic3—184no—
615C2×Dic3—184no—
616C2×Dic3—184no—
617C2×Dic3—184no—
618C2×Dic3—362no—
619C2×Dic3—364no—
620C2×Dic3—364no—
621C2×Dic3C2×D3211yescharacteristic
622C2×Dic3C2×D3211yescharacteristic
623C2×Dic3C2×D3211yescharacteristic
624D12—38no—
625D12—34no—
626D12—34no—
627D12—64no—
628D12D3×Dic314yesdirect product factor
629C4×D3—34no—
630C4×D3—64no—
631C4×D3—62no—
632C4×D3—184no—
633C4×D3—184no—
634C4×D3—184no—
635C4×D3—184no—
636C4×D3—184no—
637C4×D3—184no—
638C4×D3—364no—
639C4×D3D3×Dic314yescomplemented
640C2×C32—21no—
641C2×C32—21no—
642C2×C32—21no—
643C2×C32—21no—
644C2×C32—21no—
645C2×C32—21no—
646C2×C32—21no—
647C2×C32—21no—
648C2×C32—21no—
649C2×C32—34no—
650C2×C32—41no—
651C2×C32—41no—
652C2×C32—41no—
653C2×C32—64no—
654C2×C32C22×C4×D311yescharacteristic
655C2×C32C22×C4×D311yescharacteristic
656C2×C32C22×D1211yescharacteristic
657C2×C32C2×#23511yescharacteristic
658C2×C32C2×D3×D411yescharacteristic
659C2×C32C2×D3×D411yescharacteristic
660C2×C32C2×#23711yescharacteristic
661C2×C32D3×#4111yescharacteristic
662C2×C32C23×Dic311yescharacteristic
663C3⋊D3—24no—
664C3×D3—24no—
665C3×D3—24no—
666C3×D3—24no—
667C3×D3—44no—
668C3×D3—64no—
669C3×D3—64no—
670C3×D3—124no—
671C3×D3C4×D1214yescomplemented
672C3×D3D4×Dic314yescomplemented
673C24—92no—
674C2×D4—31no—
675C2×D4—98no—
676C2×D4—92no—
677C2×D4—91no—
678C22×C4—31no—
679C22×C4—91no—
680C22×C4—91no—
681C22×C4—92no—
682C22×C4—272no—
683C22×C4—272no—
684C22×C4—272no—
685C22×C4—272no—
686C22×C4—548no—
687C4⋊C4—91no—
688C4⋊C4—272no—
689C4⋊C4—271no—
690C22⋊C4—92no—
691C22⋊C4—272no—
692C22⋊C4—272no—
693C22⋊C4—272no—
694C42—31no—
695C42—91no—
696C42—91no—
697C42—91no—
698C22×C3—21no—
699C22×C3—21no—
700C22×C3—21no—
701C22×C3—32no—
702C22×C3—32no—
703C22×C3—32no—
704C22×C3—32no—
705C22×C3—32no—
706C22×C3—32no—
707C22×C3—34no—
708C22×C3—34no—
709C22×C3—41no—
710C22×C3—62no—
711C22×C3—62no—
712C22×C3—62no—
713C22×C3—64no—
714C22×C3—62no—
715C22×C3—62no—
716C22×C3—62no—
717C22×C3—62no—
718C22×C3—94no—
719C22×C3—122no—
720C22×C3—122no—
721C22×C3—1816no—
722C22×C3—182no—
723C22×C3—182no—
724C22×C3C22×D3211yescharacteristic
725C22×C3C22×D3211yescharacteristic
726C22×C3C22×D3211yescharacteristic
727C2×D3—22no—
728C2×D3—22no—
729C2×D3—34no—
730C2×D3—34no—
731C2×D3—64no—
732C2×D3—616no—
733C2×D3—62no—
734C2×D3—62no—
735C2×D3—62no—
736C2×D3—62no—
737C2×D3—616no—
738C2×D3—122no—
739C2×D3—122no—
740C2×D3#379512yes—
741C2×D3D3×D1212yes—
742C2×D3C2×D3×Dic312yes—
743C2×D3C2×D3×Dic314yescomplemented
744C3×C4—22no—
745C3×C4—22no—
746C3×C4—22no—
747C3×C4—32no—
748C3×C4—32no—
749C3×C4—32no—
750C3×C4—32no—
751C3×C4—42no—
752C3×C4—62no—
753C3×C4—62no—
754C3×C4—61no—
755C3×C4—61no—
756C3×C4—92no—
757C3×C4—121no—
758C3×C4—182no—
759C3×C4—181no—
760C3×C4C4×D3212yescomplemented
761C3×C4C2×D3×Dic312yescomplemented
762C3×C4C2×D3×Dic312yescomplemented
763Dic3—21no—
764Dic3—32no—
765Dic3—32no—
766Dic3—62no—
767Dic3—61no—
768Dic3—62no—
769Dic3—61no—
770Dic3—62no—
771Dic3—122no—
772Dic3—121no—
773Dic3—182no—
774Dic3—182no—
775Dic3—182no—
776Dic3—362no—
777Dic3—362no—
778Dic3—362no—
779Dic3—722no—
780Dic3D3×D1212yesdirect product factor
781Dic3C2×D3×Dic312yescomplemented
782C32—21no—
783C32—21no—
784C32—21no—
785C32—41no—
786C32C2×C4×D1211yescharacteristic, complemented
787C32C4×D3×D411yescharacteristic, complemented
788C32C2×D4×Dic311yescharacteristic, complemented
789C23—31no—
790C23—32no—
791C23—98no—
792C23—92no—
793C23—184no—
794C23—184no—
795D4—34no—
796D4—98no—
797D4—94no—
798C2×C4—31no—
799C2×C4—31no—
800C2×C4—34no—
801C2×C4—31no—
802C2×C4—94no—
803C2×C4—91no—
804C2×C4—91no—
805C2×C4—92no—
806C2×C4—184no—
807C2×C4—182no—
808C2×C4—272no—
809C2×C4—544no—
810C2×C4—544no—
811C2×C4—544no—
812C2×C4—544no—
813C2×C4D3311yescharacteristic
814C2×C3—21no—
815C2×C3—21no—
816C2×C3—21no—
817C2×C3—21no—
818C2×C3—21no—
819C2×C3—21no—
820C2×C3—21no—
821C2×C3—21no—
822C2×C3—21no—
823C2×C3—34no—
824C2×C3—34no—
825C2×C3—41no—
826C2×C3—41no—
827C2×C3—41no—
828C2×C3—64no—
829C2×C3—64no—
830C2×C3—64no—
831C2×C3—124no—
832C2×C3—184no—
833C2×C3C2×#379511yescharacteristic
834C2×C3C2×C4×D3211yescharacteristic
835C2×C3C2×D3×D1211yescharacteristic
836C2×C3C2×D3×D1211yescharacteristic
837C2×C3D3×#23511yescharacteristic
838C2×C3D32×D411yescharacteristic
839C2×C3D3×#23711yescharacteristic
840C2×C3C22×D3×Dic311yescharacteristic
841C2×C3C22×D3×Dic311yescharacteristic
842D3—24no—
843D3—64no—
844D3—64no—
845D3—124no—
846D3Dic3×D1214yesdirect product factor
847C22—32no—
848C22—32no—
849C22—32no—
850C22—34no—
851C22—62no—
852C22—62no—
853C22—94no—
854C22—1816no—
855C22—182no—
856C22—182no—
857C22C2×D3311yescharacteristic
858C4—32no—
859C4—32no—
860C4—61no—
861C4—92no—
862C4—181no—
863C4—182no—
864C4—542no—
865C4D32×Dic312yescomplemented
866C3—21no—
867C3—21no—
868C3—21no—
869C3—41no—
870C3C4×D3×D1211yescharacteristic, complemented
871C3C2×Dic3×D1211yescharacteristic, complemented
872C3D3×D4×Dic311yescharacteristic, complemented
873C2—34no—
874C2—64no—
875C2—184no—
876C2D3×#379511yescharacteristic
877C2D32×D1211yescharacteristic
878C2C2×D32×Dic311yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutatorC2×C33C23×C4
FittingC2×C33×C4C23
socle, cosocleC22×C33C24
prime radicalC2×C3×D3×D12C2
hypercenterC2×C4D33
hypocenterC33C2×C4×D4
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C2×D32×Dic3C2semidirect
3. #11723691C2semidirect
4. D12×C3⋊Dic3C2semidirect
5. Dic3×C4⋊(C3⋊D3)C2semidirect
6. D3×C4⋊(C3⋊Dic3)C2semidirect
7. C3×Dic3×D12C2semidirect
8. C3×C4×D3×Dic3C2semidirect
9. #11722928C2semidirect
10. Dic3×#626C2semidirect
11. D3×(C2×D3)⋊Dic3C2semidirect
19. C2×#6294C22semidirect
20. C2×Dic3×C3⋊D3C22semidirect
22. C2×D3×C3⋊Dic3C22semidirect
26. C2×C3×D3×Dic3C22semidirect
27. C3×D3×D12C4semidirect
29. C4⋊(C3⋊(C3⋊Dic3))C22semidirect
30. C3×C4⋊(C3⋊Dic3)C22semidirect
31. C3×C4×C3⋊Dic3C22semidirect
32. C32×C4×Dic3C22semidirect
33. #88814C22semidirect
34. Dic3⋊(C3⋊Dic3)C22semidirect
35. #88803C22semidirect
36. (C2×D3)⋊(C3⋊Dic3)C22semidirect
37. C3×(C2×D3)⋊Dic3C22semidirect
38. C3×Dic32C22semidirect
39. C3×Dic32C22semidirect
70. Dic3×D12D3direct (N × H)
75. C4×D3×Dic3D3semidirect
81. C2×C3×D32C2×C4semidirect
87. C3×C4⋊(C3⋊D3)C2×C4semidirect
91. C32×D12C2×C4semidirect
92. C32×C4×D3C2×C4semidirect
97. C3×#626C2×C4semidirect
100. C3×D3×Dic3D4semidirect
149. C2×D3×Dic3C2×D3semidirect
150. D3×D12Dic3direct (N × H)
163. C4⋊(C3⋊Dic3)C2×D3semidirect
164. C4×C3⋊Dic3C2×D3semidirect
178. C3×C4×Dic3C2×D3semidirect
179. C3×C4×Dic3C2×D3semidirect
192. (C2×D3)⋊Dic3C2×D3semidirect
193. Dic32C2×D3semidirect
194. Dic32C2×D3semidirect
198. C2×C3×C3⋊D3C22×C4semidirect
202. C2×C32×D3C22×C4semidirect
206. C33×C4C22×C4semidirect
210. C3×C3⋊Dic3C2×D4semidirect
212. C32×Dic3C22×C4semidirect
213. C32×Dic3C2×D4semidirect
270. C2×D32C2×Dic3semidirect
295. C4⋊(C3⋊D3)C2×Dic3semidirect
324. C3×D12C4×D3semidirect
325. C3×D12C2×Dic3semidirect
330. C3×C4×D3C4×D3semidirect
331. C3×C4×D3C2×Dic3semidirect
332. #626C2×Dic3semidirect
347. D3×Dic3D12direct (N × H)
354. C32×D3C4×D4semidirect
445. C4×Dic3D32semidirect
461. C2×C3⋊D3C22×Dic3semidirect
484. C2×C3×D3C2×C4×D3semidirect
490. C2×C3×D3C22×Dic3semidirect
499. C32×C4C2×C4×D3semidirect
500. C32×C4C2×C4×D3semidirect
501. C32×C4C22×Dic3semidirect
511. C3⋊Dic3C2×D12semidirect
526. C3×Dic3C2×C4×D3semidirect
527. C3×Dic3C2×D12semidirect
528. C3×Dic3D3×D4semidirect
529. C3×Dic3C22×Dic3semidirect
541. C33C2×C4×D4semidirect
628. D12D3×Dic3direct (N × H)
639. C4×D3D3×Dic3semidirect
671. C3×D3C4×D12semidirect
672. C3×D3D4×Dic3semidirect
743. C2×D3C2×D3×Dic3semidirect
760. C3×C4C4×D32semidirect
761. C3×C4C2×D3×Dic3semidirect
762. C3×C4C2×D3×Dic3semidirect
780. Dic3D3×D12direct (N × H)
781. Dic3C2×D3×Dic3semidirect
786. C32C2×C4×D12semidirect
787. C32C4×D3×D4semidirect
788. C32C2×D4×Dic3semidirect
846. D3Dic3×D12direct (N × H)
865. C4D32×Dic3semidirect
870. C3C4×D3×D12semidirect
871. C3C2×Dic3×D12semidirect
872. C3D3×D4×Dic3semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×D122
C2×D32×Dic32
#117236912
D12×C3⋊Dic32
Dic3×C4⋊(C3⋊D3)2
D3×C4⋊(C3⋊Dic3)2
C3×Dic3×D122
C3×C4×D3×Dic32
#117229282
Dic3×#6262
D3×(C2×D3)⋊Dic32
D3×D4×Dic33
C2×Dic3×D123
C4×D3×D123