Finite Group Databasebeta

← C3×D4×#624 #13174699

Subgroups — C3×D4×#624 #13174699

Order 1728.

2182 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×C3⋊D3C211yesmaximal, characteristic
2C22×C3×#624C212yesmaximal, complemented
3C32×D4×Dic3C212yesmaximal, complemented
4C3×#63974C212yesmaximal, complemented
5C3×#63952C214yesmaximal, complemented
6C3×#63900C211yesmaximal, characteristic, complemented
7C3×#63894C212yesmaximal, complemented
8C3×C4×#624C211yesmaximal, characteristic, complemented
9C3×C4×D3×D4—32nomaximal
10D4×#624C311yesmaximal, characteristic, direct product factor
11C23×C3×C3⋊D3C2212yes—
12C2×C33×D4C2211yescharacteristic
13C2×C3×#638C2212yes—
14C3×D4×C3⋊D3C418yescomplemented
15C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
16C2×C3×C4×C3⋊D3C2211yescharacteristic
17C22×C32×Dic3C2214yescomplemented
18C2×C3×#624—28no—
19C2×C3×#624C2212yes—
20C2×C3×#624C2211yescharacteristic
21C2×C3×#624C2211yescharacteristic
22C2×C3×#624C2214yescomplemented
23C32×#217C2214yescomplemented
24C32×C4⋊Dic3C2212yescomplemented
25C32×C4×Dic3C2212yescomplemented
26C3×#3724C2212yescomplemented
27C3×#3722C2214yescomplemented
28C3×Dic32C2212yescomplemented
29C2×D4×C3⋊D3C2×C311yescharacteristic
30C2×C3×D3×D4—32no—
31C2×C3×D3×D4—61no—
32C22×C3×C4×D3—34no—
33C22×#624C2×C312yescomplemented
34C32×C4×D4—32no—
35C3×D4×Dic3—22no—
36C3×D4×Dic3D312yescomplemented
37C3×D4×Dic3C2×C312yescomplemented
38C3×C4×#67—34no—
39C3×#893—32no—
40C3×D3×C4⋊C4—32no—
41C3×#67⋊C4—34no—
42C3×D3×C22⋊C4—34no—
43C3×C4×D12—32no—
44C3×C42×D3—32no—
45#63974C2×C312yescomplemented
46#63952C2×C314yescomplemented
47#63900C2×C311yescharacteristic, complemented
48#63894C2×C312yescomplemented
49C4×#624C2×C311yescharacteristic, complemented
50C23×C33C2312yes—
51C22×C3×C3⋊D3—24no—
52C22×C3×C3⋊D3—24no—
53C22×C3×C3⋊D3C2×C418yescomplemented
54C22×C3×C3⋊D3C2312yes—
55C22×C3×C3⋊D3C2311yescharacteristic
56C33×D4C2×C414yescomplemented
57C2×C33×C4C2311yescharacteristic
58C3×#638C2×C418yescomplemented
59C2×C3×C3⋊Dic3C2311yescharacteristic
60C3×C4⋊(C3⋊D3)C2×C414yescomplemented
61C3×C4×C3⋊D3C2×C414yescomplemented
62C2×C32×Dic3—28no—
63C2×C32×Dic3C2312yes—
64C2×C32×Dic3C2314yes—
65C2×C32×Dic3C2312yes—
66C3×#624—24no—
67C3×#624—22no—
68C3×#624—28no—
69C3×#624D414yesdirect product factor
70C2×C3×C4×D4—91no—
71C4×D3×D4—32no—
72C23×C3⋊D3C22×C312yes—
73C23×C3×D3—34no—
74C23×C3×D3—62no—
75C2×C32×D4—21no—
76C2×C32×D4—22no—
77C2×C32×D4—41no—
78C2×C32×D4C2×D312yes—
79C2×C32×D4C22×C311yescharacteristic
80C22×C32×C4—34no—
81C2×#638C22×C312yes—
82D4×C3⋊D3C3×C418yescomplemented
83C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
84C2×C4×C3⋊D3C22×C311yescharacteristic
85C2×C3×#67—34no—
86C2×C3×#67—62no—
87C22×C3×Dic3—24no—
88C22×C3×Dic3C2×D314yescomplemented
89C22×C3×Dic3C22×C314yescomplemented
90C3×D3×D4—316no—
91C3×D3×D4—68no—
92C2×C3×D12—32no—
93C2×C3×D12—61no—
94C2×C3×C4×D3—32no—
95C2×C3×C4×D3—32no—
96C2×C3×C4×D3—32no—
97C2×C3×C4×D3—34no—
98C2×C3×C4×D3—34no—
99C2×C3×C4×D3—34no—
100C2×C3×C4×D3—616no—
101C2×C3×C4×D3—61no—
102C2×#624—28no—
103C2×#624C22×C312yes—
104C2×#624C22×C311yescharacteristic
105C2×#624C22×C311yescharacteristic
106C2×#624C22×C314yescomplemented
107C32×C4⋊C4—32no—
108C32×C22⋊C4—34no—
109C32×C42—32no—
110C3×#217—24no—
111C3×#217C2×D314yescomplemented
112C3×#217C22×C314yescomplemented
113C3×(C2×D3)⋊C4—34no—
114C3×(C2×D3)⋊C4—34no—
115C3×C4⋊Dic3—22no—
116C3×C4⋊Dic3C2×D312yescomplemented
117C3×C4⋊Dic3C22×C312yescomplemented
118C3×Dic3⋊C4—34no—
119C3×C4×Dic3—22no—
120C3×C4×Dic3—32no—
121C3×C4×Dic3—32no—
122C3×C4×Dic3C2×D312yescomplemented
123C3×C4×Dic3C22×C312yescomplemented
124#3724C22×C312yescomplemented
125#3722C22×C314yescomplemented
126Dic32C22×C312yescomplemented
127C22×C33—22no—
128C22×C33—22no—
129C22×C33C22×C414yescomplemented
130C22×C33C2411yescharacteristic
131C2×C3×C3⋊D3—22no—
132C2×C3×C3⋊D3—22no—
133C2×C3×C3⋊D3—216no—
134C2×C3×C3⋊D3C22×C412yes—
135C2×C3×C3⋊D3C22×C414yescomplemented
136C2×C3×C3⋊D3C2×D412yes—
137C2×C3×C3⋊D3#4112yes—
138C33×C4C22×C412yescomplemented
139C3×C3⋊Dic3C22×C412yescomplemented
140C32×Dic3—24no—
141C32×Dic3—22no—
142C32×Dic3C2×D414yescomplemented
143C22×C3×D4—91no—
144C23×C3×C4—92no—
145C2×D3×D4—32no—
146C2×D3×D4—61no—
147C22×C4×D3—34no—
148C3×C4×D4—32no—
149C3×C4×D4—32no—
150C3×C4×D4—62no—
151C3×C4×D4—92no—
152C3×C4×D4—94no—
153C2×C3×C4⋊C4—91no—
154C2×C3×C22⋊C4—92no—
155C2×C3×C42—91no—
156D4×Dic3C3×D312yescomplemented
157C4×#67—34no—
158#893—32no—
159D3×C4⋊C4—32no—
160#67⋊C4—34no—
161D3×C22⋊C4—34no—
162C4×D12—32no—
163C42×D3—32no—
164C23×C32—22no—
165C23×C32—24no—
166C23×C32—42no—
167C23×C32C22×D314yes—
168C23×C32C23×C312yes—
169C22×C3⋊D3—24no—
170C22×C3⋊D3—24no—
171C22×C3⋊D3C2×C3×C418yescomplemented
172C22×C3⋊D3C23×C312yes—
173C22×C3⋊D3C23×C311yescharacteristic
174C22×C3×D3—32no—
175C22×C3×D3—316no—
176C22×C3×D3—34no—
177C22×C3×D3—61no—
178C22×C3×D3—68no—
179C22×C3×D3—62no—
180C22×C3×D3—68no—
181C22×C3×D3—68no—
182C22×C3×D3—124no—
183C22×C3×D3—124no—
184C32×D4—24no—
185C32×D4—28no—
186C32×D4—44no—
187C32×D4C4×D318yescomplemented
188C32×D4C2×C3×C414yescomplemented
189C2×C32×C4—21no—
190C2×C32×C4—22no—
191C2×C32×C4—32no—
192C2×C32×C4—32no—
193C2×C32×C4—34no—
194C2×C32×C4—41no—
195C2×C32×C4—68no—
196C2×C32×C4C22×D312yes—
197C2×C32×C4C23×C311yescharacteristic
198#638C2×C3×C418yescomplemented
199C2×C3⋊Dic3C23×C311yescharacteristic
200C4⋊(C3⋊D3)C2×C3×C414yescomplemented
201C4×C3⋊D3C2×C3×C414yescomplemented
202C3×#67—316no—
203C3×#67—68no—
204C2×C3×Dic3—28no—
205C2×C3×Dic3—28no—
206C2×C3×Dic3—22no—
207C2×C3×Dic3—22no—
208C2×C3×Dic3—24no—
209C2×C3×Dic3—32no—
210C2×C3×Dic3—48no—
211C2×C3×Dic3—61no—
212C2×C3×Dic3C22×D312yes—
213C2×C3×Dic3C22×D314yes—
214C2×C3×Dic3C22×D312yes—
215C2×C3×Dic3C23×C312yes—
216C2×C3×Dic3C23×C314yes—
217C2×C3×Dic3C23×C312yes—
218C3×D12—38no—
219C3×D12—64no—
220C3×C4×D3—38no—
221C3×C4×D3—38no—
222C3×C4×D3—64no—
223C3×C4×D3—68no—
224C3×C4×D3—64no—
225C3×C4×D3—68no—
226C3×C4×D3—68no—
227#624—24no—
228#624—22no—
229#624—28no—
230#624C3×D414yesdirect product factor
231C2×C4×D4—91noSylow
232C2×C33—24no—
233C2×C33C23×C411yescharacteristic
234C2×C33C22×D411yescharacteristic
235C2×C33C2×#4111yescharacteristic
236C3×C3⋊D3—24no—
237C3×C3⋊D3C4×D414yescomplemented
238C24×C3—92no—
239C23×D3—34no—
240C23×D3—62no—
241C2×C3×D4—22no—
242C2×C3×D4—21no—
243C2×C3×D4—41no—
244C2×C3×D4—92no—
245C2×C3×D4—98no—
246C2×C3×D4—91no—
247C2×C3×D4D3211yescharacteristic
248C2×C3×D4C2×C3×D312yes—
249C22×C3×C4—34no—
250C22×C3×C4—34no—
251C22×C3×C4—64no—
252C22×C3×C4—91no—
253C22×C3×C4—91no—
254C22×C3×C4—92no—
255C22×C3×C4—94no—
256C22×C3×C4—91no—
257C22×C3×C4—188no—
258C2×#67—34no—
259C2×#67—62no—
260C22×Dic3C2×C3×D314yescomplemented
261D3×D4—316no—
262D3×D4—68no—
263C2×D12—32no—
264C2×D12—61no—
265C2×C4×D3—32no—
266C2×C4×D3—32no—
267C2×C4×D3—32no—
268C2×C4×D3—34no—
269C2×C4×D3—34no—
270C2×C4×D3—34no—
271C2×C4×D3—61no—
272C2×C4×D3—616no—
273C3×C4⋊C4—32no—
274C3×C4⋊C4—32no—
275C3×C4⋊C4—62no—
276C3×C4⋊C4—92no—
277C3×C22⋊C4—34no—
278C3×C22⋊C4—34no—
279C3×C22⋊C4—64no—
280C3×C22⋊C4—94no—
281C3×C42—32no—
282C3×C42—32no—
283C3×C42—62no—
284C3×C42—92no—
285#217C2×C3×D314yescomplemented
286(C2×D3)⋊C4—34no—
287(C2×D3)⋊C4—34no—
288C4⋊Dic3C2×C3×D312yescomplemented
289Dic3⋊C4—34no—
290C4×Dic3—32no—
291C4×Dic3—32no—
292C4×Dic3C2×C3×D312yescomplemented
293C22×C32—24no—
294C22×C32—24no—
295C22×C32—22no—
296C22×C32—22no—
297C22×C32—21no—
298C22×C32—22no—
299C22×C32—24no—
300C22×C32—28no—
301C22×C32—41no—
302C22×C32—44no—
303C22×C32—44no—
304C22×C32—42no—
305C22×C32—42no—
306C22×C32—44no—
307C22×C32—82no—
308C22×C32—82no—
309C22×C32C2×C4×D318yescomplemented
310C22×C32C22×C3×C414yescomplemented
311C22×C32C23×D312yes—
312C22×C32C24×C311yescharacteristic
313C2×C3⋊D3—22no—
314C2×C3⋊D3—22no—
315C2×C3⋊D3—216no—
316C2×C3⋊D3C22×C3×C412yes—
317C2×C3⋊D3C22×C3×C414yescomplemented
318C2×C3⋊D3C2×C3×D412yes—
319C2×C3⋊D3C3×#4112yes—
320C2×C3×D3—34no—
321C2×C3×D3—34no—
322C2×C3×D3—34no—
323C2×C3×D3—38no—
324C2×C3×D3—62no—
325C2×C3×D3—62no—
326C2×C3×D3—62no—
327C2×C3×D3—64no—
328C2×C3×D3—632no—
329C2×C3×D3—64no—
330C2×C3×D3—64no—
331C2×C3×D3—1216no—
332C2×C3×D3—122no—
333C2×C3×D3—122no—
334C32×C4—22no—
335C32×C4—24no—
336C32×C4—34no—
337C32×C4—42no—
338C32×C4—64no—
339C32×C4—62no—
340C32×C4C2×C4×D314yescomplemented
341C32×C4C22×C3×C412yescomplemented
342C3⋊Dic3C22×C3×C412yescomplemented
343C3×Dic3—24no—
344C3×Dic3—22no—
345C3×Dic3—24no—
346C3×Dic3—22no—
347C3×Dic3—24no—
348C3×Dic3—34no—
349C3×Dic3—42no—
350C3×Dic3—44no—
351C3×Dic3—62no—
352C3×Dic3D3×D414yescomplemented
353C3×Dic3C2×C3×D414yescomplemented
354C22×D4—91no—
355C23×C4—92no—
356C4×D4—32no—
357C4×D4—92no—
358C4×D4—94no—
359C2×C4⋊C4—91no—
360C2×C22⋊C4—92no—
361C2×C42—91no—
362C33C2×C4×D411yescharacteristic, complemented, Sylow
363C23×C3—24no—
364C23×C3—22no—
365C23×C3—42no—
366C23×C3—91no—
367C23×C3—92no—
368C23×C3—98no—
369C23×C3—184no—
370C23×C3—184no—
371C23×C3C2×D3212yes—
372C23×C3C22×C3×D314yes—
373C22×D3—32no—
374C22×D3—34no—
375C22×D3—316no—
376C22×D3—61no—
377C22×D3—68no—
378C22×D3—62no—
379C22×D3—68no—
380C22×D3—68no—
381C22×D3—124no—
382C22×D3—124no—
383C3×D4—28no—
384C3×D4—24no—
385C3×D4—44no—
386C3×D4—98no—
387C3×D4—94no—
388C3×D4#62414yesdirect product factor
389C3×D4C3×C4×D318yescomplemented
390C2×C3×C4—22no—
391C2×C3×C4—21no—
392C2×C3×C4—32no—
393C2×C3×C4—32no—
394C2×C3×C4—32no—
395C2×C3×C4—34no—
396C2×C3×C4—32no—
397C2×C3×C4—34no—
398C2×C3×C4—41no—
399C2×C3×C4—62no—
400C2×C3×C4—62no—
401C2×C3×C4—64no—
402C2×C3×C4—68no—
403C2×C3×C4—68no—
404C2×C3×C4—94no—
405C2×C3×C4—91no—
406C2×C3×C4—94no—
407C2×C3×C4—128no—
408C2×C3×C4—188no—
409C2×C3×C4—182no—
410C2×C3×C4—184no—
411C2×C3×C4C2×D3211yescharacteristic
412C2×C3×C4C22×C3×D312yes—
413#67—316no—
414#67—68no—
415C2×Dic3—28no—
416C2×Dic3—32no—
417C2×Dic3—61no—
418C2×Dic3C22×C3×D312yes—
419C2×Dic3C22×C3×D314yes—
420C2×Dic3C22×C3×D312yes—
421D12—38no—
422D12—64no—
423C4×D3—38no—
424C4×D3—38no—
425C4×D3—64no—
426C4×D3—68no—
427C4×D3—64no—
428C4×D3—68no—
429C4×D3—68no—
430C2×C32—28no—
431C2×C32—24no—
432C2×C32—21no—
433C2×C32—21no—
434C2×C32—21no—
435C2×C32—22no—
436C2×C32—22no—
437C2×C32—22no—
438C2×C32—41no—
439C2×C32—41no—
440C2×C32—41no—
441C2×C32—44no—
442C2×C32—48no—
443C2×C32—84no—
444C2×C32C22×C4×D312yes—
445C2×C32C2×D3×D412yes—
446C2×C32D3×#4112yes—
447C2×C32C23×C3×C411yescharacteristic
448C2×C32C22×C3×D411yescharacteristic
449C2×C32C2×C3×#4111yescharacteristic
450C3⋊D3—24no—
451C3⋊D3C3×C4×D414yescomplemented
452C3×D3—38no—
453C3×D3—64no—
454C3×D3—68no—
455C3×D3—124no—
456C24—92no—
457C2×D4—92no—
458C2×D4—98no—
459C2×D4—91no—
460C2×D4C3×D3211yescharacteristic
461C22×C4—34no—
462C22×C4—91no—
463C22×C4—91no—
464C22×C4—92no—
465C22×C4—94no—
466C22×C4—91no—
467C22×C4—188no—
468C4⋊C4—32no—
469C4⋊C4—92no—
470C22⋊C4—34no—
471C22⋊C4—94no—
472C42—32no—
473C42—92no—
474C22×C3—22no—
475C22×C3—22no—
476C22×C3—24no—
477C22×C3—24no—
478C22×C3—21no—
479C22×C3—22no—
480C22×C3—24no—
481C22×C3—28no—
482C22×C3—44no—
483C22×C3—42no—
484C22×C3—42no—
485C22×C3—44no—
486C22×C3—41no—
487C22×C3—44no—
488C22×C3—82no—
489C22×C3—82no—
490C22×C3—92no—
491C22×C3—92no—
492C22×C3—92no—
493C22×C3—94no—
494C22×C3—1816no—
495C22×C3—182no—
496C22×C3—182no—
497C22×C3C2×#62414yescomplemented
498C22×C3C2×C3×C4×D318yescomplemented
499C22×C3C22×D3211yescharacteristic
500C22×C3C23×C3×D312yes—
501C2×D3—34no—
502C2×D3—34no—
503C2×D3—34no—
504C2×D3—38no—
505C2×D3—62no—
506C2×D3—62no—
507C2×D3—62no—
508C2×D3—64no—
509C2×D3—632no—
510C2×D3—64no—
511C2×D3—64no—
512C2×D3—1216no—
513C2×D3—122no—
514C2×D3—122no—
515C3×C4—22no—
516C3×C4—24no—
517C3×C4—34no—
518C3×C4—34no—
519C3×C4—42no—
520C3×C4—64no—
521C3×C4—64no—
522C3×C4—62no—
523C3×C4—64no—
524C3×C4—62no—
525C3×C4—92no—
526C3×C4—124no—
527C3×C4—122no—
528C3×C4C2×#62412yescomplemented
529C3×C4C2×C3×C4×D314yescomplemented
530Dic3—24no—
531Dic3—22no—
532Dic3—34no—
533Dic3—62no—
534Dic3C3×D3×D414yescomplemented
535C32—22no—
536C32—21no—
537C32—41no—
538C32C4×D3×D412yescomplemented
539C32C2×C3×C4×D411yescharacteristic, complemented
540C23—91no—
541C23—92no—
542C23—98no—
543C23—184no—
544C23—184no—
545C23C2×C3×D3212yes—
546D4—98no—
547D4—94no—
548D4C3×#62414yesdirect product factor
549C2×C4—32no—
550C2×C4—32no—
551C2×C4—34no—
552C2×C4—68no—
553C2×C4—94no—
554C2×C4—91no—
555C2×C4—94no—
556C2×C4—188no—
557C2×C4—184no—
558C2×C4—182no—
559C2×C4C2×C3×D3211yescharacteristic
560C2×C3—28no—
561C2×C3—24no—
562C2×C3—21no—
563C2×C3—22no—
564C2×C3—22no—
565C2×C3—21no—
566C2×C3—22no—
567C2×C3—21no—
568C2×C3—44no—
569C2×C3—48no—
570C2×C3—41no—
571C2×C3—41no—
572C2×C3—41no—
573C2×C3—84no—
574C2×C3—94no—
575C2×C3—184no—
576C2×C3D32×D411yescharacteristic
577C2×C3#6431211yescharacteristic
578C2×C3C22×#62411yescharacteristic
579C2×C3C22×C3×C4×D312yes—
580C2×C3C2×C3×D3×D412yes—
581C2×C3C3×D3×#4112yes—
582D3—38no—
583D3—64no—
584D3—68no—
585D3—124no—
586C22—22no—
587C22—22no—
588C22—92no—
589C22—92no—
590C22—92no—
591C22—94no—
592C22—1816no—
593C22—182no—
594C22—182no—
595C22C2×C3×#62414yescomplemented
596C22C22×C3×D3211yescharacteristic
597C4—34no—
598C4—64no—
599C4—62no—
600C4—92no—
601C4C2×C3×#62412yescomplemented
602C3—21no—
603C3—22no—
604C3—41no—
605C3D4×#62411yescharacteristic, direct product factor
606C3C3×C4×D3×D412yescomplemented
607C2—24no—
608C2—94no—
609C2—184no—
610C2C3×D32×D411yescharacteristic
611C2C3×#6431211yescharacteristic
612C2C22×C3×#62411yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutatorC2×C32C23×C3×C4
FrattiniC22C22×C3×D32
FittingC2×C33×D4C22
socleC22×C33C24
prime radicalC2×C3×D4×C3⋊D3C2
cosocleC22×C32C24×C3
hypercenterC2×C3×D4D32
hypocenterC32C2×C3×C4×D4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
2. C22×C3×#624C2semidirect
3. C32×D4×Dic3C2semidirect
4. C3×#63974C2semidirect
5. C3×#63952C2semidirect
6. C3×#63900C2semidirect
7. C3×#63894C2semidirect
8. C3×C4×#624C2semidirect
10. D4×#624C3direct (N × H)
14. C3×D4×C3⋊D3C4semidirect
17. C22×C32×Dic3C22semidirect
22. C2×C3×#624C22semidirect
23. C32×#217C22semidirect
24. C32×C4⋊Dic3C22semidirect
25. C32×C4×Dic3C22semidirect
26. C3×#3724C22semidirect
27. C3×#3722C22semidirect
28. C3×Dic32C22semidirect
33. C22×#624C2×C3semidirect
36. C3×D4×Dic3D3semidirect
37. C3×D4×Dic3C2×C3semidirect
45. #63974C2×C3semidirect
46. #63952C2×C3semidirect
47. #63900C2×C3semidirect
48. #63894C2×C3semidirect
49. C4×#624C2×C3semidirect
53. C22×C3×C3⋊D3C2×C4semidirect
56. C33×D4C2×C4semidirect
58. C3×#638C2×C4semidirect
60. C3×C4⋊(C3⋊D3)C2×C4semidirect
61. C3×C4×C3⋊D3C2×C4semidirect
69. C3×#624D4direct (N × H)
82. D4×C3⋊D3C3×C4semidirect
88. C22×C3×Dic3C2×D3semidirect
89. C22×C3×Dic3C22×C3semidirect
106. C2×#624C22×C3semidirect
111. C3×#217C2×D3semidirect
112. C3×#217C22×C3semidirect
116. C3×C4⋊Dic3C2×D3semidirect
117. C3×C4⋊Dic3C22×C3semidirect
122. C3×C4×Dic3C2×D3semidirect
123. C3×C4×Dic3C22×C3semidirect
124. #3724C22×C3semidirect
125. #3722C22×C3semidirect
126. Dic32C22×C3semidirect
129. C22×C33C22×C4semidirect
135. C2×C3×C3⋊D3C22×C4semidirect
138. C33×C4C22×C4semidirect
139. C3×C3⋊Dic3C22×C4semidirect
142. C32×Dic3C2×D4semidirect
156. D4×Dic3C3×D3semidirect
171. C22×C3⋊D3C2×C3×C4semidirect
187. C32×D4C4×D3semidirect
188. C32×D4C2×C3×C4semidirect
198. #638C2×C3×C4semidirect
200. C4⋊(C3⋊D3)C2×C3×C4semidirect
201. C4×C3⋊D3C2×C3×C4semidirect
230. #624C3×D4direct (N × H)
237. C3×C3⋊D3C4×D4semidirect
260. C22×Dic3C2×C3×D3semidirect
285. #217C2×C3×D3semidirect
288. C4⋊Dic3C2×C3×D3semidirect
292. C4×Dic3C2×C3×D3semidirect
309. C22×C32C2×C4×D3semidirect
310. C22×C32C22×C3×C4semidirect
317. C2×C3⋊D3C22×C3×C4semidirect
340. C32×C4C2×C4×D3semidirect
341. C32×C4C22×C3×C4semidirect
342. C3⋊Dic3C22×C3×C4semidirect
352. C3×Dic3D3×D4semidirect
353. C3×Dic3C2×C3×D4semidirect
362. C33C2×C4×D4semidirect
388. C3×D4#624direct (N × H)
389. C3×D4C3×C4×D3semidirect
451. C3⋊D3C3×C4×D4semidirect
497. C22×C3C2×#624semidirect
498. C22×C3C2×C3×C4×D3semidirect
528. C3×C4C2×#624semidirect
529. C3×C4C2×C3×C4×D3semidirect
534. Dic3C3×D3×D4semidirect
538. C32C4×D3×D4semidirect
539. C32C2×C3×C4×D4semidirect
548. D4C3×#624direct (N × H)
595. C22C2×C3×#624semidirect
601. C4C2×C3×#624semidirect
605. C3D4×#624direct (N × H)
606. C3C3×C4×D3×D4semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D4×C3⋊D32
C22×C3×#6242
C32×D4×Dic32
C3×#639742
C3×#639522
C3×#639002
C3×#638942
C3×C4×#6242
C3×C4×D3×D43
D4×#6243