Finite Group Databasebeta

← C2×C3×#63921 #13174651

Subgroups — C2×C3×#63921 #13174651

Order 1728.

3250 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×D32C211yesmaximal, characteristic
2C22×C3×C4×C3⋊D3C211yesmaximal, characteristic, complemented
3C22×C3×#624C211yesmaximal, characteristic, complemented
4C2×C32×(C2×D3)⋊C4C212yesmaximal, complemented
5C2×C3×(C2×D3)⋊Dic3C212yesmaximal, complemented
6C3×#63921C218yesmaximal, direct product factor
7C2×C3×D3×C22⋊C4—32nomaximal
8C2×#63921C311yesmaximal, characteristic, direct product factor
9C23×C3×C3⋊D3C2211yescharacteristic
10C23×C32×D3C2212yes—
11C22×C3×D32—24no—
12C22×C3×D32—24no—
13C22×C3×D32C418yescomplemented
14C22×C3×D32C2214yes—
15C22×C33×C4C2211yescharacteristic, complemented
16C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
17C2×C3×C4×C3⋊D3—24no—
18C2×C3×C4×C3⋊D3C2214yescomplemented
19C22×C32×Dic3C2212yescomplemented
20C2×C3×#624—24no—
21C2×C3×#624C2214yescomplemented
22C32×(C2×D3)⋊C4C2218yescomplemented
23C3×(C2×D3)⋊Dic3C2218yescomplemented
24C24×C3×D3—32no—
25C23×D32C2×C311yescharacteristic
26C22×C4×C3⋊D3C2×C311yescharacteristic, complemented
27C22×C3×C4×D3—32no—
28C22×C3×C4×D3—32no—
29C22×C3×C4×D3—61no—
30C22×#624C2×C311yescharacteristic, complemented
31C2×C32×C22⋊C4—32no—
32C2×C3×#217—32no—
33C2×C3×(C2×D3)⋊C4—22no—
34C2×C3×(C2×D3)⋊C4—32no—
35C2×C3×(C2×D3)⋊C4D312yescomplemented
36C2×C3×(C2×D3)⋊C4C2×C312yescomplemented
37C3×D3×C22⋊C4—316no—
38C2×(C2×D3)⋊Dic3C2×C312yescomplemented
39#63921C2×C318yesdirect product factor
40C23×C33C2311yescharacteristic
41C22×C3×C3⋊D3C2×C414yes—
42C22×C3×C3⋊D3D414yes—
43C22×C3×C3⋊D3D414yes—
44C22×C3×C3⋊D3C2312yes—
45C22×C32×D3—24no—
46C22×C32×D3—24no—
47C22×C32×D3C2×C418yescomplemented
48C22×C32×D3C2314yes—
49C2×C3×D32—232no—
50C2×C3×D32—28no—
51C2×C3×D32—28no—
52C2×C3×D32C2×C4116yescomplemented
53C2×C33×C4—22no—
54C2×C33×C4C2312yescomplemented
55C2×C3×C3⋊Dic3—22no—
56C2×C3×C3⋊Dic3C2312yescomplemented
57C3×C4×C3⋊D3—28no—
58C2×C32×Dic3—24no—
59C2×C32×Dic3C2314yescomplemented
60C3×#624—28no—
61C22×C3×C22⋊C4—91no—
62C2×D3×C22⋊C4—32no—
63C24×C32—32no—
64C23×C3⋊D3C22×C311yescharacteristic
65C23×C3×D3—22no—
66C23×C3×D3—32no—
67C23×C3×D3—316no—
68C23×C3×D3—38no—
69C23×C3×D3—68no—
70C23×C3×D3—68no—
71C23×C3×D3—61no—
72C23×C3×D3C2×D312yes—
73C23×C3×D3C22×C312yes—
74C22×D32—24no—
75C22×D32—24no—
76C22×D32C3×C418yescomplemented
77C22×D32C22×C314yes—
78C22×C32×C4—21no—
79C22×C32×C4—22no—
80C22×C32×C4—32no—
81C22×C32×C4—41no—
82C22×C32×C4C2×D312yescomplemented
83C22×C32×C4C22×C311yescharacteristic, complemented
84C22×C3⋊Dic3C22×C311yescharacteristic, complemented
85C2×C4×C3⋊D3—24no—
86C2×C4×C3⋊D3C22×C314yescomplemented
87C22×C3×Dic3—22no—
88C22×C3×Dic3—32no—
89C22×C3×Dic3—61no—
90C22×C3×Dic3C2×D312yescomplemented
91C22×C3×Dic3C22×C312yescomplemented
92C2×C3×C4×D3—38no—
93C2×C3×C4×D3—38no—
94C2×C3×C4×D3—68no—
95C2×C3×C4×D3—68no—
96C2×C3×C4×D3—64no—
97C2×C3×C4×D3—68no—
98C2×#624—24no—
99C2×#624C22×C314yescomplemented
100C32×C22⋊C4—38no—
101C3×#217—38no—
102C3×(C2×D3)⋊C4—28no—
103C3×(C2×D3)⋊C4—38no—
104C3×(C2×D3)⋊C4C2×D318yescomplemented
105C3×(C2×D3)⋊C4C22×C318yescomplemented
106(C2×D3)⋊Dic3C22×C318yescomplemented
107C22×C33C22×C412yes—
108C22×C33C2×D412yes—
109C22×C33C2×D412yes—
110C22×C33C2411yescharacteristic
111C2×C3×C3⋊D3C22⋊C4116yescomplemented
112C2×C3×C3⋊D3C22×C414yes—
113C2×C3×C3⋊D3C2×D414yes—
114C2×C3×C3⋊D3C2×D414yes—
115C2×C32×D3—216no—
116C2×C32×D3—24no—
117C2×C32×D3—24no—
118C2×C32×D3C22×C418yescomplemented
119C3×D32—232no—
120C33×C4—22no—
121C3×C3⋊Dic3—22no—
122C32×Dic3—24no—
123C25×C3—91no—
124C24×D3—32no—
125C23×C3×C4—91no—
126C23×C3×C4—91no—
127C22×C4×D3—32no—
128C22×C4×D3—32no—
129C22×C4×D3—61no—
130C2×C3×C22⋊C4—32no—
131C2×C3×C22⋊C4—32no—
132C2×C3×C22⋊C4—62no—
133C2×C3×C22⋊C4—98no—
134C2×C3×C22⋊C4—92no—
135C2×#217—32no—
136C2×(C2×D3)⋊C4—32no—
137C2×(C2×D3)⋊C4C3×D312yescomplemented
138D3×C22⋊C4—316no—
139C23×C32—21no—
140C23×C32—22no—
141C23×C32—38no—
142C23×C32—34no—
143C23×C32—41no—
144C23×C32—64no—
145C23×C32—64no—
146C23×C32C22×D312yes—
147C23×C32C23×C311yescharacteristic
148C22×C3⋊D3C2×C3×C414yes—
149C22×C3⋊D3C3×D414yes—
150C22×C3⋊D3C3×D414yes—
151C22×C3⋊D3C23×C312yes—
152C22×C3×D3—24no—
153C22×C3×D3—24no—
154C22×C3×D3—24no—
155C22×C3×D3—24no—
156C22×C3×D3—28no—
157C22×C3×D3—24no—
158C22×C3×D3—38no—
159C22×C3×D3—38no—
160C22×C3×D3—38no—
161C22×C3×D3—34no—
162C22×C3×D3—332no—
163C22×C3×D3—44no—
164C22×C3×D3—44no—
165C22×C3×D3—64no—
166C22×C3×D3—64no—
167C22×C3×D3—64no—
168C22×C3×D3—62no—
169C22×C3×D3—664no—
170C22×C3×D3—616no—
171C22×C3×D3—616no—
172C22×C3×D3C4×D318yescomplemented
173C22×C3×D3C2×C3×C418yescomplemented
174C22×C3×D3C22×D314yes—
175C22×C3×D3C23×C314yes—
176C2×D32—232no—
177C2×D32—28no—
178C2×D32—28no—
179C2×D32C2×C3×C4116yescomplemented
180C2×C32×C4—22no—
181C2×C32×C4—24no—
182C2×C32×C4—24no—
183C2×C32×C4—22no—
184C2×C32×C4—24no—
185C2×C32×C4—34no—
186C2×C32×C4—42no—
187C2×C32×C4—44no—
188C2×C32×C4—44no—
189C2×C32×C4—64no—
190C2×C32×C4C22×D314yescomplemented
191C2×C32×C4C23×C312yescomplemented
192C2×C3⋊Dic3—22no—
193C2×C3⋊Dic3C23×C312yescomplemented
194C4×C3⋊D3—28no—
195C2×C3×Dic3—24no—
196C2×C3×Dic3—24no—
197C2×C3×Dic3—24no—
198C2×C3×Dic3—34no—
199C2×C3×Dic3—44no—
200C2×C3×Dic3—62no—
201C2×C3×Dic3—64no—
202C2×C3×Dic3—64no—
203C2×C3×Dic3C22×D314yescomplemented
204C2×C3×Dic3C23×C314yescomplemented
205C3×C4×D3—616no—
206C3×C4×D3—616no—
207C3×C4×D3—616no—
208#624—28no—
209C22×C22⋊C4—91noSylow
210C2×C33C2×C22⋊C414yescomplemented
211C2×C33C23×C411yescharacteristic
212C2×C33C22×D411yescharacteristic
213C2×C33C22×D411yescharacteristic
214C3×C3⋊D3C2×C22⋊C418yescomplemented
215C32×D3—28no—
216C24×C3—32no—
217C24×C3—32no—
218C24×C3—62no—
219C24×C3—98no—
220C24×C3—94no—
221C24×C3—91no—
222C24×C3—184no—
223C24×C3—184no—
224C23×D3—32no—
225C23×D3—316no—
226C23×D3—38no—
227C23×D3—61no—
228C23×D3—68no—
229C23×D3—68no—
230C23×D3C2×C3×D312yes—
231C22×C3×C4—21no—
232C22×C3×C4—22no—
233C22×C3×C4—32no—
234C22×C3×C4—32no—
235C22×C3×C4—41no—
236C22×C3×C4—62no—
237C22×C3×C4—94no—
238C22×C3×C4—91no—
239C22×C3×C4—94no—
240C22×C3×C4—184no—
241C22×C3×C4—184no—
242C22×C3×C4D3211yescharacteristic, complemented
243C22×C3×C4C2×C3×D312yescomplemented
244C22×Dic3—32no—
245C22×Dic3—61no—
246C22×Dic3C2×C3×D312yescomplemented
247C2×C4×D3—38no—
248C2×C4×D3—38no—
249C2×C4×D3—64no—
250C2×C4×D3—68no—
251C2×C4×D3—68no—
252C2×C4×D3—68no—
253C3×C22⋊C4—38no—
254C3×C22⋊C4—38no—
255C3×C22⋊C4—68no—
256C3×C22⋊C4—98no—
257#217—38no—
258(C2×D3)⋊C4—38no—
259(C2×D3)⋊C4C2×C3×D318yescomplemented
260C22×C32—21no—
261C22×C32—22no—
262C22×C32—22no—
263C22×C32—22no—
264C22×C32—22no—
265C22×C32—24no—
266C22×C32—24no—
267C22×C32—24no—
268C22×C32—38no—
269C22×C32—42no—
270C22×C32—42no—
271C22×C32—42no—
272C22×C32—41no—
273C22×C32—616no—
274C22×C32—64no—
275C22×C32—64no—
276C22×C32C2×C4×D314yes—
277C22×C32D3×D414yes—
278C22×C32D3×D414yes—
279C22×C32C22×C3×C412yes—
280C22×C32C2×C3×D412yes—
281C22×C32C2×C3×D412yes—
282C22×C32C23×D312yes—
283C22×C32C24×C311yescharacteristic
284C2×C3⋊D3C3×C22⋊C4116yescomplemented
285C2×C3⋊D3C22×C3×C414yes—
286C2×C3⋊D3C2×C3×D414yes—
287C2×C3⋊D3C2×C3×D414yes—
288C2×C3×D3—216no—
289C2×C3×D3—216no—
290C2×C3×D3—24no—
291C2×C3×D3—24no—
292C2×C3×D3—24no—
293C2×C3×D3—24no—
294C2×C3×D3—28no—
295C2×C3×D3—332no—
296C2×C3×D3—38no—
297C2×C3×D3—38no—
298C2×C3×D3—38no—
299C2×C3×D3—416no—
300C2×C3×D3—44no—
301C2×C3×D3—44no—
302C2×C3×D3—616no—
303C2×C3×D3—64no—
304C2×C3×D3—64no—
305C2×C3×D3—64no—
306C2×C3×D3—664no—
307C2×C3×D3C2×C4×D318yescomplemented
308C2×C3×D3C22×C3×C418yescomplemented
309D32—232no—
310C32×C4—22no—
311C32×C4—24no—
312C32×C4—24no—
313C32×C4—44no—
314C32×C4—44no—
315C32×C4—64no—
316C3⋊Dic3—22no—
317C3×Dic3—24no—
318C3×Dic3—24no—
319C3×Dic3—44no—
320C3×Dic3—64no—
321C3×Dic3—64no—
322C25—91no—
323C23×C4—91no—
324C23×C4—91no—
325C2×C22⋊C4—32no—
326C2×C22⋊C4—98no—
327C2×C22⋊C4—92no—
328C33C22×C22⋊C411yescharacteristic, complemented, Sylow
329C23×C3—22no—
330C23×C3—21no—
331C23×C3—34no—
332C23×C3—34no—
333C23×C3—38no—
334C23×C3—38no—
335C23×C3—41no—
336C23×C3—64no—
337C23×C3—68no—
338C23×C3—64no—
339C23×C3—64no—
340C23×C3—64no—
341C23×C3—64no—
342C23×C3—916no—
343C23×C3—92no—
344C23×C3—94no—
345C23×C3—94no—
346C23×C3—94no—
347C23×C3—124no—
348C23×C3—124no—
349C23×C3—188no—
350C23×C3—188no—
351C23×C3—1832no—
352C23×C3C2×D3211yescharacteristic
353C23×C3C22×C3×D312yes—
354C22×D3—24no—
355C22×D3—24no—
356C22×D3—34no—
357C22×D3—38no—
358C22×D3—38no—
359C22×D3—38no—
360C22×D3—332no—
361C22×D3—64no—
362C22×D3—64no—
363C22×D3—64no—
364C22×D3—62no—
365C22×D3—664no—
366C22×D3—616no—
367C22×D3—616no—
368C22×D3C3×C4×D318yescomplemented
369C22×D3C22×C3×D314yes—
370C2×C3×C4—24no—
371C2×C3×C4—22no—
372C2×C3×C4—24no—
373C2×C3×C4—22no—
374C2×C3×C4—24no—
375C2×C3×C4—34no—
376C2×C3×C4—34no—
377C2×C3×C4—44no—
378C2×C3×C4—44no—
379C2×C3×C4—42no—
380C2×C3×C4—64no—
381C2×C3×C4—64no—
382C2×C3×C4—64no—
383C2×C3×C4—92no—
384C2×C3×C4—124no—
385C2×C3×C4—188no—
386C2×C3×C4—188no—
387C2×C3×C4—182no—
388C2×C3×C4C2×D3212yescomplemented
389C2×C3×C4C22×C3×D314yescomplemented
390C2×Dic3—24no—
391C2×Dic3—34no—
392C2×Dic3—62no—
393C2×Dic3—64no—
394C2×Dic3—64no—
395C2×Dic3C22×C3×D314yescomplemented
396C4×D3—616no—
397C4×D3—616no—
398C4×D3—616no—
399C2×C32—28no—
400C2×C32—21no—
401C2×C32—21no—
402C2×C32—21no—
403C2×C32—22no—
404C2×C32—22no—
405C2×C32—22no—
406C2×C32—24no—
407C2×C32—44no—
408C2×C32—41no—
409C2×C32—41no—
410C2×C32—41no—
411C2×C32—68no—
412C2×C32D3×C22⋊C418yescomplemented
413C2×C32C2×C3×C22⋊C414yescomplemented
414C2×C32C22×C4×D312yes—
415C2×C32C2×D3×D412yes—
416C2×C32C2×D3×D412yes—
417C2×C32C23×C3×C411yescharacteristic
418C2×C32C22×C3×D411yescharacteristic
419C2×C32C22×C3×D411yescharacteristic
420C3⋊D3C2×C3×C22⋊C418yescomplemented
421C3×D3—28no—
422C3×D3—28no—
423C3×D3—316no—
424C3×D3—48no—
425C3×D3—68no—
426C24—32no—
427C24—94no—
428C24—98no—
429C24—91no—
430C24—184no—
431C24—184no—
432C22×C4—32no—
433C22×C4—94no—
434C22×C4—91no—
435C22×C4—94no—
436C22×C4—184no—
437C22×C4—184no—
438C22×C4C3×D3211yescharacteristic, complemented
439C22⋊C4—38no—
440C22⋊C4—98no—
441C22×C3—21no—
442C22×C3—22no—
443C22×C3—22no—
444C22×C3—24no—
445C22×C3—24no—
446C22×C3—22no—
447C22×C3—22no—
448C22×C3—24no—
449C22×C3—38no—
450C22×C3—38no—
451C22×C3—41no—
452C22×C3—42no—
453C22×C3—42no—
454C22×C3—42no—
455C22×C3—68no—
456C22×C3—616no—
457C22×C3—64no—
458C22×C3—64no—
459C22×C3—64no—
460C22×C3—64no—
461C22×C3—616no—
462C22×C3—94no—
463C22×C3—94no—
464C22×C3—94no—
465C22×C3—916no—
466C22×C3—124no—
467C22×C3—1216no—
468C22×C3—124no—
469C22×C3—1832no—
470C22×C3C4×D3212yes—
471C22×C3#380212yes—
472C22×C3#381112yes—
473C22×C3C2×C3×C4×D314yes—
474C22×C3C3×D3×D414yes—
475C22×C3C3×D3×D414yes—
476C22×C3C22×D3211yescharacteristic
477C22×C3C23×C3×D312yes—
478C2×D3—216no—
479C2×D3—24no—
480C2×D3—24no—
481C2×D3—332no—
482C2×D3—38no—
483C2×D3—38no—
484C2×D3—38no—
485C2×D3—64no—
486C2×D3—616no—
487C2×D3—64no—
488C2×D3—64no—
489C2×D3—664no—
490C2×D3C2×C3×C4×D318yescomplemented
491C3×C4—24no—
492C3×C4—22no—
493C3×C4—24no—
494C3×C4—44no—
495C3×C4—44no—
496C3×C4—64no—
497C3×C4—64no—
498C3×C4—124no—
499C3×C4—182no—
500Dic3—24no—
501Dic3—64no—
502Dic3—64no—
503C32—21no—
504C32—22no—
505C32—41no—
506C32C2×D3×C22⋊C412yescomplemented
507C32C22×C3×C22⋊C411yescharacteristic, complemented
508C23—34no—
509C23—38no—
510C23—64no—
511C23—64no—
512C23—916no—
513C23—92no—
514C23—94no—
515C23—94no—
516C23—94no—
517C23—188no—
518C23—1832no—
519C23—188no—
520C23C2×C3×D3211yescharacteristic
521C2×C4—22no—
522C2×C4—34no—
523C2×C4—64no—
524C2×C4—92no—
525C2×C4—188no—
526C2×C4—188no—
527C2×C4—182no—
528C2×C4C2×C3×D3212yescomplemented
529C2×C3—21no—
530C2×C3—22no—
531C2×C3—24no—
532C2×C3—28no—
533C2×C3—21no—
534C2×C3—22no—
535C2×C3—22no—
536C2×C3—21no—
537C2×C3—41no—
538C2×C3—44no—
539C2×C3—41no—
540C2×C3—41no—
541C2×C3—68no—
542C2×C3—68no—
543C2×C3—98no—
544C2×C3—128no—
545C2×C3#6392114yesdirect product factor
546C2×C3C3×D3×C22⋊C418yescomplemented
547C2×C3C2×C4×D3211yescharacteristic
548C2×C3C2×#380211yescharacteristic
549C2×C3C2×#381111yescharacteristic
550C2×C3C22×C3×C4×D312yes—
551C2×C3C2×C3×D3×D412yes—
552C2×C3C2×C3×D3×D412yes—
553D3—28no—
554D3—316no—
555D3—68no—
556C22—38no—
557C22—64no—
558C22—616no—
559C22—64no—
560C22—94no—
561C22—916no—
562C22—94no—
563C22—94no—
564C22—1832no—
565C22C3×C4×D3212yes—
566C22C3×#380212yes—
567C22C3×#381112yes—
568C22C22×C3×D3211yescharacteristic
569C4—22no—
570C4—64no—
571C4—182no—
572C3—21no—
573C3—22no—
574C3—41no—
575C3C2×#6392111yescharacteristic, direct product factor
576C3C2×C3×D3×C22⋊C412yescomplemented
577C2—68no—
578C2—98no—
579C2C3×#6392114yesdirect product factor
580C2C2×C3×C4×D3211yescharacteristic
581C2C2×C3×#380211yescharacteristic
582C2C2×C3×#381111yescharacteristic
subgroupG/H
centerC23×C3C2×D32
commutatorC2×C32C23×C3×C4
FrattiniC22C22×C3×D32
FittingC22×C33×C4C22
socleC23×C33C23
prime radicalC23×C3×D32C2
cosocleC22×C32C24×C3
hypercenterC22×C3×C4D32
hypocenterC32C22×C3×C22⋊C4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C23×C3 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
2. C22×C3×C4×C3⋊D3C2semidirect
3. C22×C3×#624C2semidirect
4. C2×C32×(C2×D3)⋊C4C2semidirect
5. C2×C3×(C2×D3)⋊Dic3C2semidirect
6. C3×#63921C2direct (N × H)
8. C2×#63921C3direct (N × H)
13. C22×C3×D32C4semidirect
15. C22×C33×C4C22semidirect
16. C22×C3×C3⋊Dic3C22semidirect
18. C2×C3×C4×C3⋊D3C22semidirect
19. C22×C32×Dic3C22semidirect
21. C2×C3×#624C22semidirect
22. C32×(C2×D3)⋊C4C22semidirect
23. C3×(C2×D3)⋊Dic3C22semidirect
26. C22×C4×C3⋊D3C2×C3semidirect
30. C22×#624C2×C3semidirect
35. C2×C3×(C2×D3)⋊C4D3semidirect
36. C2×C3×(C2×D3)⋊C4C2×C3semidirect
38. C2×(C2×D3)⋊Dic3C2×C3semidirect
39. #63921C2×C3direct (N × H)
47. C22×C32×D3C2×C4semidirect
52. C2×C3×D32C2×C4semidirect
54. C2×C33×C4C23semidirect
56. C2×C3×C3⋊Dic3C23semidirect
59. C2×C32×Dic3C23semidirect
76. C22×D32C3×C4semidirect
82. C22×C32×C4C2×D3semidirect
83. C22×C32×C4C22×C3semidirect
84. C22×C3⋊Dic3C22×C3semidirect
86. C2×C4×C3⋊D3C22×C3semidirect
90. C22×C3×Dic3C2×D3semidirect
91. C22×C3×Dic3C22×C3semidirect
99. C2×#624C22×C3semidirect
104. C3×(C2×D3)⋊C4C2×D3semidirect
105. C3×(C2×D3)⋊C4C22×C3semidirect
106. (C2×D3)⋊Dic3C22×C3semidirect
111. C2×C3×C3⋊D3C22⋊C4semidirect
118. C2×C32×D3C22×C4semidirect
137. C2×(C2×D3)⋊C4C3×D3semidirect
172. C22×C3×D3C4×D3semidirect
173. C22×C3×D3C2×C3×C4semidirect
179. C2×D32C2×C3×C4semidirect
190. C2×C32×C4C22×D3semidirect
191. C2×C32×C4C23×C3semidirect
193. C2×C3⋊Dic3C23×C3semidirect
203. C2×C3×Dic3C22×D3semidirect
204. C2×C3×Dic3C23×C3semidirect
210. C2×C33C2×C22⋊C4semidirect
214. C3×C3⋊D3C2×C22⋊C4semidirect
242. C22×C3×C4D32semidirect
243. C22×C3×C4C2×C3×D3semidirect
246. C22×Dic3C2×C3×D3semidirect
259. (C2×D3)⋊C4C2×C3×D3semidirect
284. C2×C3⋊D3C3×C22⋊C4semidirect
307. C2×C3×D3C2×C4×D3semidirect
308. C2×C3×D3C22×C3×C4semidirect
328. C33C22×C22⋊C4semidirect
368. C22×D3C3×C4×D3semidirect
388. C2×C3×C4C2×D32semidirect
389. C2×C3×C4C22×C3×D3semidirect
395. C2×Dic3C22×C3×D3semidirect
412. C2×C32D3×C22⋊C4semidirect
413. C2×C32C2×C3×C22⋊C4semidirect
420. C3⋊D3C2×C3×C22⋊C4semidirect
438. C22×C4C3×D32semidirect
490. C2×D3C2×C3×C4×D3semidirect
506. C32C2×D3×C22⋊C4semidirect
507. C32C22×C3×C22⋊C4semidirect
528. C2×C4C2×C3×D32semidirect
545. C2×C3#63921direct (N × H)
546. C2×C3C3×D3×C22⋊C4semidirect
575. C3C2×#63921direct (N × H)
576. C3C2×C3×D3×C22⋊C4semidirect
579. C2C3×#63921direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×D322
C22×C3×C4×C3⋊D32
C22×C3×#6242
C2×C32×(C2×D3)⋊C42
C2×C3×(C2×D3)⋊Dic32
C3×#639212
C2×C3×D3×C22⋊C43
C2×#639213