Finite Group Databasebeta

← C2×C3×C4×D3×Dic3 #13174435

Subgroups — C2×C3×C4×D3×Dic3 #13174435

Order 1728.

2498 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×C4×D3C211yesmaximal, characteristic
2C22×C3×D3×Dic3C212yesmaximal
3C2×C3×C4×C3⋊Dic3C211yesmaximal, characteristic, complemented
4C2×C32×C4×Dic3C211yesmaximal, characteristic, complemented
5C2×C3×Dic32C212yesmaximal, complemented
6C3×C4×D3×Dic3C218yesmaximal, direct product factor
7C22×C3×C4×Dic3—31nomaximal
8C2×C3×C42×D3—31nomaximal
9C2×C4×D3×Dic3C311yesmaximal, characteristic, direct product factor
10C23×C32×D3C2211yescharacteristic
11C22×C33×C4C2211yescharacteristic
12C22×C3×C3⋊Dic3C2212yes—
13C22×C32×Dic3C2212yes—
14C22×C32×Dic3C2211yescharacteristic
15C2×C32×C4×D3C418yescomplemented
16C2×C32×C4×D3C2214yes—
17C2×C3×D3×Dic3C4116yesdirect product factor
18C2×C3×D3×Dic3C2218yes—
19C3×C4×C3⋊Dic3C2214yescomplemented
20C32×C4×Dic3C2214yescomplemented
21C3×Dic32C2218yescomplemented
22C23×C32×C4—31no—
23C23×C3×Dic3—32no—
24C22×C3×C4×D3—21no—
25C22×C3×C4×D3—32no—
26C22×C3×C4×D3D311yescharacteristic
27C22×C3×C4×D3C2×C311yescharacteristic
28C22×D3×Dic3C2×C312yes—
29C2×C32×C42—31no—
30C2×C4×C3⋊Dic3C2×C311yescharacteristic, complemented
31C2×C3×C4×Dic3—21no—
32C2×C3×C4×Dic3—31no—
33C2×C3×C4×Dic3—31no—
34C2×C3×C4×Dic3—32no—
35C2×C3×C4×Dic3—32no—
36C2×C3×C4×Dic3—38no—
37C2×C3×C4×Dic3—61no—
38C2×C3×C4×Dic3D311yescharacteristic, direct product factor
39C2×C3×C4×Dic3C2×C311yescharacteristic, complemented
40C3×C42×D3—38no—
41C2×Dic32C2×C312yescomplemented
42C4×D3×Dic3C2×C318yesdirect product factor
43C23×C33C2311yescharacteristic
44C22×C32×D3C2×C418yes—
45C22×C32×D3C2×C414yes—
46C22×C32×D3C2312yes—
47C2×C33×C4C2×C414yescomplemented
48C2×C33×C4C2312yes—
49C2×C3×C3⋊Dic3C2×C418yescomplemented
50C2×C3×C3⋊Dic3C2314yes—
51C2×C32×Dic3C2×C418yescomplemented
52C2×C32×Dic3C2×C414yescomplemented
53C2×C32×Dic3C2314yes—
54C2×C32×Dic3C2312yes—
55C32×C4×D3C2×C4116yescomplemented
56C3×D3×Dic3C2×C4132yesdirect product factor
57C22×C3×C42—91no—
58C22×C4×Dic3—31no—
59C2×C42×D3—31no—
60C24×C32—31no—
61C23×C3×D3—21no—
62C23×C3×D3C2×D311yescharacteristic
63C23×C3×D3C22×C311yescharacteristic
64C22×C32×C4—21no—
65C22×C32×C4—21no—
66C22×C32×C4—21no—
67C22×C32×C4—31no—
68C22×C32×C4—32no—
69C22×C32×C4—38no—
70C22×C32×C4—34no—
71C22×C32×C4—41no—
72C22×C32×C4C2×D311yescharacteristic
73C22×C32×C4C2×D311yescharacteristic
74C22×C32×C4C22×C311yescharacteristic
75C22×C3⋊Dic3C22×C312yes—
76C22×C3×Dic3—22no—
77C22×C3×Dic3—21no—
78C22×C3×Dic3—32no—
79C22×C3×Dic3—32no—
80C22×C3×Dic3—316no—
81C22×C3×Dic3—38no—
82C22×C3×Dic3—62no—
83C22×C3×Dic3C2×D312yes—
84C22×C3×Dic3C2×D311yescharacteristic
85C22×C3×Dic3C22×C312yes—
86C22×C3×Dic3C22×C311yescharacteristic
87C2×C3×C4×D3—28no—
88C2×C3×C4×D3—24no—
89C2×C3×C4×D3—316no—
90C2×C3×C4×D3—38no—
91C2×C3×C4×D3Dic318yesdirect product factor
92C2×C3×C4×D3C3×C418yescomplemented
93C2×C3×C4×D3C2×D314yes—
94C2×C3×C4×D3C22×C314yes—
95C2×D3×Dic3C3×C4116yesdirect product factor
96C2×D3×Dic3C22×C318yes—
97C32×C42—34no—
98C4×C3⋊Dic3C22×C314yescomplemented
99C3×C4×Dic3—24no—
100C3×C4×Dic3—34no—
101C3×C4×Dic3—34no—
102C3×C4×Dic3—38no—
103C3×C4×Dic3—38no—
104C3×C4×Dic3—64no—
105C3×C4×Dic3C2×D314yesdirect product factor
106C3×C4×Dic3C22×C314yescomplemented
107Dic32C22×C318yescomplemented
108C22×C33C22×C414yes—
109C22×C33C22×C412yes—
110C22×C33C2411yescharacteristic
111C2×C32×D3C42116yescomplemented
112C2×C32×D3C22×C418yes—
113C2×C32×D3C22×C414yes—
114C33×C4C22×C414yescomplemented
115C3×C3⋊Dic3C22×C418yescomplemented
116C32×Dic3C22×C418yescomplemented
117C32×Dic3C22×C414yescomplemented
118C23×C3×C4—31no—
119C23×C3×C4—31no—
120C23×C3×C4—61no—
121C23×C3×C4—92no—
122C23×Dic3—32no—
123C22×C4×D3—32no—
124C22×C4×D3C3×D311yescharacteristic
125C2×C3×C42—31no—
126C2×C3×C42—31no—
127C2×C3×C42—61no—
128C2×C3×C42—98no—
129C2×C3×C42—92no—
130C2×C3×C42—91no—
131C2×C4×Dic3—31no—
132C2×C4×Dic3—31no—
133C2×C4×Dic3—32no—
134C2×C4×Dic3—32no—
135C2×C4×Dic3—38no—
136C2×C4×Dic3—61no—
137C2×C4×Dic3C3×D311yescharacteristic, direct product factor
138C42×D3—38no—
139C23×C32—21no—
140C23×C32—21no—
141C23×C32—21no—
142C23×C32—38no—
143C23×C32—34no—
144C23×C32—32no—
145C23×C32—41no—
146C23×C32C22×D311yescharacteristic
147C23×C32C22×D311yescharacteristic
148C23×C32C23×C311yescharacteristic
149C22×C3×D3—28no—
150C22×C3×D3—24no—
151C22×C3×D3—22no—
152C22×C3×D3C4×D318yes—
153C22×C3×D3C2×Dic314yes—
154C22×C3×D3C2×C3×C418yes—
155C22×C3×D3C2×C3×C414yes—
156C22×C3×D3C22×D312yes—
157C22×C3×D3C23×C312yes—
158C2×C32×C4—24no—
159C2×C32×C4—24no—
160C2×C32×C4—24no—
161C2×C32×C4—22no—
162C2×C32×C4—22no—
163C2×C32×C4—22no—
164C2×C32×C4—38no—
165C2×C32×C4—34no—
166C2×C32×C4—32no—
167C2×C32×C4—34no—
168C2×C32×C4—316no—
169C2×C32×C4—44no—
170C2×C32×C4—42no—
171C2×C32×C4C4×D314yescomplemented
172C2×C32×C4C2×Dic314yescomplemented
173C2×C32×C4C2×C3×C414yescomplemented
174C2×C32×C4C22×D312yes—
175C2×C32×C4C22×D312yes—
176C2×C32×C4C23×C312yes—
177C2×C3⋊Dic3C2×C3×C418yescomplemented
178C2×C3⋊Dic3C23×C314yes—
179C2×C3×Dic3—28no—
180C2×C3×Dic3—24no—
181C2×C3×Dic3—24no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—38no—
184C2×C3×Dic3—38no—
185C2×C3×Dic3—34no—
186C2×C3×Dic3—34no—
187C2×C3×Dic3—332no—
188C2×C3×Dic3—64no—
189C2×C3×Dic3—68no—
190C2×C3×Dic3C4×D318yesdirect product factor
191C2×C3×Dic3C2×Dic314yescomplemented
192C2×C3×Dic3C2×C3×C418yescomplemented
193C2×C3×Dic3C2×C3×C414yescomplemented
194C2×C3×Dic3C22×D314yes—
195C2×C3×Dic3C22×D312yes—
196C2×C3×Dic3C23×C312yes—
197C2×C3×Dic3C23×C314yes—
198C3×C4×D3—216no—
199C3×C4×D3—332no—
200C3×C4×D3C2×Dic3116yesdirect product factor
201C3×C4×D3C2×C3×C4116yescomplemented
202D3×Dic3C2×C3×C4132yesdirect product factor
203C22×C42—91noSylow
204C2×C33C2×C4214yescomplemented
205C2×C33C23×C412yes—
206C2×C33C23×C411yescharacteristic
207C32×D3C2×C4218yescomplemented
208C24×C3—31no—
209C24×C3—31no—
210C24×C3—61no—
211C23×D3C2×C3×D311yescharacteristic
212C22×C3×C4—21no—
213C22×C3×C4—21no—
214C22×C3×C4—21no—
215C22×C3×C4—32no—
216C22×C3×C4—31no—
217C22×C3×C4—31no—
218C22×C3×C4—32no—
219C22×C3×C4—38no—
220C22×C3×C4—38no—
221C22×C3×C4—34no—
222C22×C3×C4—34no—
223C22×C3×C4—41no—
224C22×C3×C4—68no—
225C22×C3×C4—64no—
226C22×C3×C4—62no—
227C22×C3×C4—61no—
228C22×C3×C4—98no—
229C22×C3×C4—916no—
230C22×C3×C4—92no—
231C22×C3×C4D3211yescharacteristic
232C22×C3×C4C2×C3×D311yescharacteristic
233C22×C3×C4C2×C3×D311yescharacteristic
234C22×Dic3—32no—
235C22×Dic3—32no—
236C22×Dic3—316no—
237C22×Dic3—38no—
238C22×Dic3—62no—
239C22×Dic3C2×C3×D312yes—
240C22×Dic3C2×C3×D311yescharacteristic
241C2×C4×D3—316no—
242C2×C4×D3—38no—
243C2×C4×D3C3×Dic318yesdirect product factor
244C2×C4×D3C2×C3×D314yes—
245C3×C42—34no—
246C3×C42—34no—
247C3×C42—64no—
248C3×C42—98no—
249C3×C42—94no—
250C4×Dic3—34no—
251C4×Dic3—34no—
252C4×Dic3—38no—
253C4×Dic3—38no—
254C4×Dic3—64no—
255C4×Dic3C2×C3×D314yesdirect product factor
256C22×C32—21no—
257C22×C32—21no—
258C22×C32—21no—
259C22×C32—24no—
260C22×C32—22no—
261C22×C32—24no—
262C22×C32—22no—
263C22×C32—24no—
264C22×C32—22no—
265C22×C32—316no—
266C22×C32—38no—
267C22×C32—34no—
268C22×C32—42no—
269C22×C32—44no—
270C22×C32—41no—
271C22×C32C2×C4×D314yes—
272C22×C32C2×C4×D314yes—
273C22×C32C2×C4×D312yes—
274C22×C32C22×Dic312yes—
275C22×C32C22×C3×C414yes—
276C22×C32C22×C3×C412yes—
277C22×C32C23×D311yescharacteristic
278C22×C32C23×D311yescharacteristic
279C22×C32C24×C311yescharacteristic
280C2×C3×D3—216no—
281C2×C3×D3—28no—
282C2×C3×D3—24no—
283C2×C3×D3C4×Dic3116yesdirect product factor
284C2×C3×D3C3×C42116yescomplemented
285C2×C3×D3C2×C4×D318yes—
286C2×C3×D3C22×Dic314yes—
287C2×C3×D3C22×C3×C418yes—
288C2×C3×D3C22×C3×C414yes—
289C32×C4—24no—
290C32×C4—24no—
291C32×C4—24no—
292C32×C4—38no—
293C32×C4—34no—
294C32×C4—44no—
295C32×C4C2×C4×D314yescomplemented
296C32×C4C22×Dic314yescomplemented
297C32×C4C22×C3×C414yescomplemented
298C3⋊Dic3C22×C3×C418yescomplemented
299C3×Dic3—28no—
300C3×Dic3—24no—
301C3×Dic3—38no—
302C3×Dic3—38no—
303C3×Dic3—68no—
304C3×Dic3C2×C4×D318yesdirect product factor
305C3×Dic3C22×Dic314yescomplemented
306C3×Dic3C22×C3×C418yescomplemented
307C3×Dic3C22×C3×C414yescomplemented
308C23×C4—31no—
309C23×C4—92no—
310C2×C42—31no—
311C2×C42—98no—
312C2×C42—92no—
313C2×C42—91no—
314C33C22×C4211yescharacteristic, complemented, Sylow
315C23×C3—21no—
316C23×C3—21no—
317C23×C3—21no—
318C23×C3—32no—
319C23×C3—32no—
320C23×C3—38no—
321C23×C3—34no—
322C23×C3—38no—
323C23×C3—34no—
324C23×C3—41no—
325C23×C3—62no—
326C23×C3—64no—
327C23×C3—68no—
328C23×C3C2×D3211yescharacteristic
329C23×C3C22×C3×D311yescharacteristic
330C23×C3C22×C3×D311yescharacteristic
331C22×D3C3×C4×D318yes—
332C22×D3C2×C3×Dic314yes—
333C22×D3C22×C3×D312yes—
334C2×C3×C4—24no—
335C2×C3×C4—24no—
336C2×C3×C4—24no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—22no—
340C2×C3×C4—34no—
341C2×C3×C4—32no—
342C2×C3×C4—32no—
343C2×C3×C4—34no—
344C2×C3×C4—38no—
345C2×C3×C4—34no—
346C2×C3×C4—38no—
347C2×C3×C4—34no—
348C2×C3×C4—316no—
349C2×C3×C4—316no—
350C2×C3×C4—44no—
351C2×C3×C4—42no—
352C2×C3×C4—616no—
353C2×C3×C4—64no—
354C2×C3×C4—68no—
355C2×C3×C4—62no—
356C2×C3×C4—64no—
357C2×C3×C4—932no—
358C2×C3×C4—94no—
359C2×C3×C4—98no—
360C2×C3×C4D3×Dic314yesdirect product factor
361C2×C3×C4C3×C4×D314yescomplemented
362C2×C3×C4C2×C3×Dic314yescomplemented
363C2×C3×C4C2×D3212yes—
364C2×C3×C4C22×C3×D312yes—
365C2×C3×C4C22×C3×D312yes—
366C2×Dic3—34no—
367C2×Dic3—34no—
368C2×Dic3—38no—
369C2×Dic3—38no—
370C2×Dic3—332no—
371C2×Dic3—68no—
372C2×Dic3—64no—
373C2×Dic3C3×C4×D318yesdirect product factor
374C2×Dic3C2×C3×Dic314yescomplemented
375C2×Dic3C22×C3×D314yes—
376C2×Dic3C22×C3×D312yes—
377C4×D3—332no—
378C4×D3C2×C3×Dic3116yesdirect product factor
379C2×C32—24no—
380C2×C32—22no—
381C2×C32—21no—
382C2×C32—22no—
383C2×C32—21no—
384C2×C32—22no—
385C2×C32—21no—
386C2×C32—24no—
387C2×C32—24no—
388C2×C32—38no—
389C2×C32—44no—
390C2×C32—41no—
391C2×C32—42no—
392C2×C32C42×D314yescomplemented
393C2×C32C2×C4×Dic314yescomplemented
394C2×C32C2×C3×C4214yescomplemented
395C2×C32C22×C4×D312yes—
396C2×C32C22×C4×D312yes—
397C2×C32C22×C4×D311yescharacteristic
398C2×C32C23×Dic311yescharacteristic
399C2×C32C23×C3×C412yes—
400C2×C32C23×C3×C411yescharacteristic
401C3×D3—28no—
402C3×D3C2×C4×Dic318yesdirect product factor
403C3×D3C2×C3×C4218yescomplemented
404C24—31no—
405C22×C4—32no—
406C22×C4—31no—
407C22×C4—38no—
408C22×C4—34no—
409C22×C4—98no—
410C22×C4—916no—
411C22×C4—92no—
412C22×C4C3×D3211yescharacteristic
413C42—34no—
414C42—98no—
415C42—94no—
416C22×C3—21no—
417C22×C3—21no—
418C22×C3—21no—
419C22×C3—24no—
420C22×C3—24no—
421C22×C3—24no—
422C22×C3—22no—
423C22×C3—22no—
424C22×C3—22no—
425C22×C3—38no—
426C22×C3—34no—
427C22×C3—38no—
428C22×C3—34no—
429C22×C3—316no—
430C22×C3—316no—
431C22×C3—41no—
432C22×C3—44no—
433C22×C3—42no—
434C22×C3—64no—
435C22×C3—616no—
436C22×C3—68no—
437C22×C3C4×D3214yes—
438C22×C3C2×D3×Dic312yes—
439C22×C3C2×C3×C4×D314yes—
440C22×C3C2×C3×C4×D314yes—
441C22×C3C2×C3×C4×D312yes—
442C22×C3C22×C3×Dic312yes—
443C22×C3C22×D3211yescharacteristic
444C22×C3C23×C3×D311yescharacteristic
445C22×C3C23×C3×D311yescharacteristic
446C2×D3C3×C4×Dic3116yesdirect product factor
447C2×D3C2×C3×C4×D318yes—
448C2×D3C22×C3×Dic314yes—
449C3×C4—24no—
450C3×C4—24no—
451C3×C4—24no—
452C3×C4—38no—
453C3×C4—34no—
454C3×C4—38no—
455C3×C4—34no—
456C3×C4—44no—
457C3×C4—64no—
458C3×C4—68no—
459C3×C4—98no—
460C3×C4C2×D3×Dic314yesdirect product factor
461C3×C4C2×C3×C4×D314yescomplemented
462C3×C4C22×C3×Dic314yescomplemented
463Dic3—38no—
464Dic3—38no—
465Dic3—68no—
466Dic3C2×C3×C4×D318yesdirect product factor
467Dic3C22×C3×Dic314yescomplemented
468C32—21no—
469C32—21no—
470C32—21no—
471C32—41no—
472C32C2×C42×D311yescharacteristic, complemented
473C32C22×C4×Dic311yescharacteristic, complemented
474C32C22×C3×C4211yescharacteristic, complemented
475C23—32no—
476C23—38no—
477C23—34no—
478C23C2×C3×D3211yescharacteristic
479C2×C4—34no—
480C2×C4—32no—
481C2×C4—38no—
482C2×C4—34no—
483C2×C4—316no—
484C2×C4—932no—
485C2×C4—94no—
486C2×C4—98no—
487C2×C4C3×D3×Dic314yesdirect product factor
488C2×C4C2×C3×D3212yes—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—24no—
493C2×C3—24no—
494C2×C3—24no—
495C2×C3—22no—
496C2×C3—22no—
497C2×C3—22no—
498C2×C3—38no—
499C2×C3—38no—
500C2×C3—41no—
501C2×C3—44no—
502C2×C3—42no—
503C2×C3—68no—
504C2×C3C4×D3×Dic314yesdirect product factor
505C2×C3C3×C42×D314yescomplemented
506C2×C3C2×C3×C4×Dic314yescomplemented
507C2×C3C2×C4×D3212yes—
508C2×C3C22×D3×Dic311yescharacteristic
509C2×C3C22×C3×C4×D311yescharacteristic
510C2×C3C22×C3×C4×D312yes—
511C2×C3C22×C3×C4×D312yes—
512C2×C3C23×C3×Dic311yescharacteristic
513D3C2×C3×C4×Dic318yesdirect product factor
514C22—34no—
515C22—316no—
516C22—38no—
517C22C3×C4×D3214yes—
518C22C2×C3×D3×Dic312yes—
519C22C22×C3×D3211yescharacteristic
520C4—34no—
521C4—38no—
522C4—98no—
523C4C2×C3×D3×Dic314yesdirect product factor
524C3—21no—
525C3—21no—
526C3—21no—
527C3—41no—
528C3C2×C4×D3×Dic311yescharacteristic, direct product factor
529C3C2×C3×C42×D311yescharacteristic, complemented
530C3C22×C3×C4×Dic311yescharacteristic, complemented
531C2—38no—
532C2C3×C4×D3×Dic314yesdirect product factor
533C2C2×C3×C4×D3212yes—
534C2C22×C3×D3×Dic311yescharacteristic
subgroupG/H
center, hypercenterC22×C3×C4D32
commutator, hypocenterC32C22×C3×C42
FrattiniC22C22×C3×D32
FittingC22×C33×C4C22
socleC23×C33C23
prime radicalC23×C32×D3C22
cosocleC22×C32C24×C3
LCSG ▷ C32
UCSC1 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
3. C2×C3×C4×C3⋊Dic3C2semidirect
4. C2×C32×C4×Dic3C2semidirect
5. C2×C3×Dic32C2semidirect
6. C3×C4×D3×Dic3C2direct (N × H)
9. C2×C4×D3×Dic3C3direct (N × H)
15. C2×C32×C4×D3C4semidirect
17. C2×C3×D3×Dic3C4direct (N × H)
19. C3×C4×C3⋊Dic3C22semidirect
20. C32×C4×Dic3C22semidirect
21. C3×Dic32C22semidirect
30. C2×C4×C3⋊Dic3C2×C3semidirect
38. C2×C3×C4×Dic3D3direct (N × H)
39. C2×C3×C4×Dic3C2×C3semidirect
41. C2×Dic32C2×C3semidirect
42. C4×D3×Dic3C2×C3direct (N × H)
47. C2×C33×C4C2×C4semidirect
49. C2×C3×C3⋊Dic3C2×C4semidirect
51. C2×C32×Dic3C2×C4semidirect
52. C2×C32×Dic3C2×C4semidirect
55. C32×C4×D3C2×C4semidirect
56. C3×D3×Dic3C2×C4direct (N × H)
91. C2×C3×C4×D3Dic3direct (N × H)
92. C2×C3×C4×D3C3×C4semidirect
95. C2×D3×Dic3C3×C4direct (N × H)
98. C4×C3⋊Dic3C22×C3semidirect
105. C3×C4×Dic3C2×D3direct (N × H)
106. C3×C4×Dic3C22×C3semidirect
107. Dic32C22×C3semidirect
111. C2×C32×D3C42semidirect
114. C33×C4C22×C4semidirect
115. C3×C3⋊Dic3C22×C4semidirect
116. C32×Dic3C22×C4semidirect
117. C32×Dic3C22×C4semidirect
137. C2×C4×Dic3C3×D3direct (N × H)
171. C2×C32×C4C4×D3semidirect
172. C2×C32×C4C2×Dic3semidirect
173. C2×C32×C4C2×C3×C4semidirect
177. C2×C3⋊Dic3C2×C3×C4semidirect
190. C2×C3×Dic3C4×D3direct (N × H)
191. C2×C3×Dic3C2×Dic3semidirect
192. C2×C3×Dic3C2×C3×C4semidirect
193. C2×C3×Dic3C2×C3×C4semidirect
200. C3×C4×D3C2×Dic3direct (N × H)
201. C3×C4×D3C2×C3×C4semidirect
202. D3×Dic3C2×C3×C4direct (N × H)
204. C2×C33C2×C42semidirect
207. C32×D3C2×C42semidirect
243. C2×C4×D3C3×Dic3direct (N × H)
255. C4×Dic3C2×C3×D3direct (N × H)
283. C2×C3×D3C4×Dic3direct (N × H)
284. C2×C3×D3C3×C42semidirect
295. C32×C4C2×C4×D3semidirect
296. C32×C4C22×Dic3semidirect
297. C32×C4C22×C3×C4semidirect
298. C3⋊Dic3C22×C3×C4semidirect
304. C3×Dic3C2×C4×D3direct (N × H)
305. C3×Dic3C22×Dic3semidirect
306. C3×Dic3C22×C3×C4semidirect
307. C3×Dic3C22×C3×C4semidirect
314. C33C22×C42semidirect
360. C2×C3×C4D3×Dic3direct (N × H)
361. C2×C3×C4C3×C4×D3semidirect
362. C2×C3×C4C2×C3×Dic3semidirect
373. C2×Dic3C3×C4×D3direct (N × H)
374. C2×Dic3C2×C3×Dic3semidirect
378. C4×D3C2×C3×Dic3direct (N × H)
392. C2×C32C42×D3semidirect
393. C2×C32C2×C4×Dic3semidirect
394. C2×C32C2×C3×C42semidirect
402. C3×D3C2×C4×Dic3direct (N × H)
403. C3×D3C2×C3×C42semidirect
446. C2×D3C3×C4×Dic3direct (N × H)
460. C3×C4C2×D3×Dic3direct (N × H)
461. C3×C4C2×C3×C4×D3semidirect
462. C3×C4C22×C3×Dic3semidirect
466. Dic3C2×C3×C4×D3direct (N × H)
467. Dic3C22×C3×Dic3semidirect
472. C32C2×C42×D3semidirect
473. C32C22×C4×Dic3semidirect
474. C32C22×C3×C42semidirect
487. C2×C4C3×D3×Dic3direct (N × H)
504. C2×C3C4×D3×Dic3direct (N × H)
505. C2×C3C3×C42×D3semidirect
506. C2×C3C2×C3×C4×Dic3semidirect
513. D3C2×C3×C4×Dic3direct (N × H)
523. C4C2×C3×D3×Dic3direct (N × H)
528. C3C2×C4×D3×Dic3direct (N × H)
529. C3C2×C3×C42×D3semidirect
530. C3C22×C3×C4×Dic3semidirect
532. C2C3×C4×D3×Dic3direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C32×C4×D32
C22×C3×D3×Dic32
C2×C3×C4×C3⋊Dic32
C2×C32×C4×Dic32
C2×C3×Dic322
C3×C4×D3×Dic32
C22×C3×C4×Dic33
C2×C3×C42×D33
C2×C4×D3×Dic33