Finite Group Databasebeta

← C3×GL(2,ℤ/4)⋊C4 #11922581

Subgroups — C3×GL(2,ℤ/4)⋊C4 #11922581

Order 1152.

948 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 948 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×GL(2,ℤ/4)C211yesmaximal, characteristic
2C22×C3×SL(2,ℤ/4)C211yesmaximal, characteristic, complemented
3C2×C3×C4×S4C211yesmaximal, characteristic, complemented
4C3×A4×C22⋊C4C211yesmaximal, characteristic, complemented
5C3×(C2×S4)⋊C4C211yesmaximal, characteristic, complemented
6C3×SL(2,ℤ/4)⋊C4C211yesmaximal, characteristic, complemented
7C3×C4×SL(2,ℤ/4)C211yesmaximal, characteristic, complemented
8GL(2,ℤ/4)⋊C4C311yesmaximal, characteristic, direct product factor
9C3×#2358—31nomaximal
10C23×C3×A4C2211yescharacteristic
11C22×C3×S4C2211yescharacteristic
12C2×C3×C4×A4C2211yescharacteristic
13C2×C3×C4×A4C2211yescharacteristic
14C3×GL(2,ℤ/4)C414yescomplemented
15C2×C3×SL(2,ℤ/4)—22no—
16C2×C3×SL(2,ℤ/4)C2211yescharacteristic
17C2×C3×SL(2,ℤ/4)C2211yescharacteristic
18C2×C3×SL(2,ℤ/4)C2211yescharacteristic
19C3×C4×S4—22no—
20C3×#67⋊C4—41nomaximal
21C2×GL(2,ℤ/4)C2×C311yescharacteristic
22C22×SL(2,ℤ/4)C2×C311yescharacteristic, complemented
23C2×C4×S4C2×C311yescharacteristic, complemented
24C2×C3×#120—31no—
25C2×C3×C4×D4—31no—
26C2×C3×C4×D4—31no—
27C22×C3×C22⋊C4—31no—
28C22×C3×C22⋊C4D311yescharacteristic, complemented
29A4×C22⋊C4—21no—
30A4×C22⋊C4C2×C311yescharacteristic, complemented
31(C2×S4)⋊C4C2×C311yescharacteristic, complemented
32SL(2,ℤ/4)⋊C4C2×C311yescharacteristic, complemented
33C4×SL(2,ℤ/4)C2×C311yescharacteristic, complemented
34C3×#390—31no—
35C3×#388—31no—
36C3×#388—31no—
37C3×#386—31no—
38C3×#386—31no—
39C3×#386—31no—
40C3×#385—31no—
41C3×#385—31no—
42C3×C4×C22⋊C4—31no—
43C3×C4×C22⋊C4—31no—
44C22×C3×A4—21no—
45C22×C3×A4—21no—
46C22×C3×A4C2×C412yescomplemented
47C22×C3×A4C2311yescharacteristic
48C2×C3×S4—21no—
49C2×C3×S4—21no—
50C2×C3×S4C2×C412yescomplemented
51C2×C3×#67—41no—
52C22×C3×Dic3—41no—
53C2×C3×C4×D3—41no—
54C3×C4×A4—21no—
55C3×C4×A4—21no—
56C3×SL(2,ℤ/4)—21no—
57C3×SL(2,ℤ/4)C2×C412yescomplemented
58C3×SL(2,ℤ/4)D412yescomplemented
59C32×C22⋊C4—41no—
60C3×(C2×D3)⋊C4—41no—
61C3×Dic3⋊C4—41no—
62C3×C4×Dic3—41no—
63#2358—31noSylow
64C25×C3C2×D311yescharacteristic
65C23×A4—21no—
66C23×A4C22×C311yescharacteristic
67C22×S4C22×C311yescharacteristic
68C22×C3×D4—31no—
69C22×C3×D4—31no—
70C22×C3×D4—31no—
71C23×C3×C4—31no—
72C23×C3×C4—31no—
73C23×C3×C4—31no—
74C23×C3×C4C2×D311yescharacteristic
75C23×C3×C4C2×D311yescharacteristic
76C2×C4×A4—21no—
77C2×C4×A4—21no—
78C2×C4×A4C22×C311yescharacteristic
79C2×C4×A4C22×C311yescharacteristic
80GL(2,ℤ/4)C3×C414yescomplemented
81C2×SL(2,ℤ/4)—22no—
82C2×SL(2,ℤ/4)C22×C311yescharacteristic
83C2×SL(2,ℤ/4)C22×C311yescharacteristic
84C2×SL(2,ℤ/4)C22×C311yescharacteristic
85C4×S4—22no—
86C3×#120—34no—
87C3×#120—34no—
88C3×C4×D4—62no—
89C3×C4×D4—62no—
90C3×C4×D4—61no—
91C3×C4×D4—61no—
92C3×C4×D4—61no—
93C3×C4×D4—61no—
94C2×C3×C4⋊C4—31no—
95C2×C3×C4⋊C4—31no—
96C2×C3×C4⋊C4—31no—
97C2×C3×C22⋊C4—31no—
98C2×C3×C22⋊C4—31no—
99C2×C3×C22⋊C4—31no—
100C2×C3×C22⋊C4—31no—
101C2×C3×C22⋊C4—31no—
102C2×C3×C22⋊C4—31no—
103C2×C3×C22⋊C4—31no—
104C2×C3×C22⋊C4—31no—
105C2×C3×C22⋊C4—31no—
106C2×C3×C22⋊C4—31no—
107C2×C3×C22⋊C4—31no—
108C2×C3×C22⋊C4—31no—
109C2×C3×C22⋊C4—31no—
110C2×C3×C22⋊C4—31no—
111C2×C3×C22⋊C4—62no—
112C2×C3×C22⋊C4—62no—
113C2×C3×C42—31no—
114C2×C3×C42—31no—
115C2×C3×C42—31no—
116#67⋊C4—41no—
117C3×#95—31no—
118C3×#95—31no—
119C3×#95—31no—
120C3×#95—31no—
121C3×#95—31no—
122C3×#95—31no—
123C23×C32—41no—
124C22×C3×D3—41no—
125C2×C3×A4—22no—
126C2×C3×A4C22×C411yescharacteristic
127C2×C3×A4C2×D411yescharacteristic
128C2×C3×A4#4111yescharacteristic
129C3×S4—22no—
130C2×C32×C4—41no—
131C2×C32×C4—41no—
132C3×#67—44no—
133C2×C3×Dic3—41no—
134C2×C3×Dic3—41no—
135C2×C3×Dic3—41no—
136C2×C3×Dic3—82no—
137C3×C4×D3—82no—
138C2×#120—31no—
139C2×C4×D4—31no—
140C2×C4×D4—31no—
141C22×C22⋊C4—31no—
142C22×C22⋊C4C3×D311yescharacteristic, complemented
143#390—31no—
144#388—31no—
145#388—31no—
146#386—31no—
147#386—31no—
148#386—31no—
149#385—31no—
150#385—31no—
151C4×C22⋊C4—31no—
152C4×C22⋊C4—31no—
153C24×C3—21no—
154C24×C3—21no—
155C24×C3—31no—
156C24×C3—31no—
157C24×C3—32no—
158C24×C3—31no—
159C24×C3—61no—
160C24×C3—61no—
161C24×C3C4×D312yescomplemented
162C24×C3C22×D311yescharacteristic
163C22×A4—21no—
164C22×A4—21no—
165C22×A4—22no—
166C22×A4—21no—
167C22×A4—41no—
168C22×A4—41no—
169C22×A4C2×C3×C412yescomplemented
170C22×A4C23×C311yescharacteristic
171C2×S4—21no—
172C2×S4—21no—
173C2×S4C2×C3×C412yescomplemented
174C2×C3×D4—32no—
175C2×C3×D4—34no—
176C2×C3×D4—32no—
177C2×C3×D4—34no—
178C2×C3×D4—61no—
179C2×C3×D4—61no—
180C2×C3×D4—61no—
181C2×C3×D4—62no—
182C2×C3×D4—61no—
183C2×C3×D4—61no—
184C2×C3×D4—61no—
185C2×C3×D4—121no—
186C2×C3×D4—121no—
187C22×C3×C4—21no—
188C22×C3×C4—21no—
189C22×C3×C4—31no—
190C22×C3×C4—31no—
191C22×C3×C4—31no—
192C22×C3×C4—31no—
193C22×C3×C4—31no—
194C22×C3×C4—31no—
195C22×C3×C4—31no—
196C22×C3×C4—31no—
197C22×C3×C4—31no—
198C22×C3×C4—31no—
199C22×C3×C4—31no—
200C22×C3×C4—62no—
201C22×C3×C4—62no—
202C22×C3×C4—62no—
203C22×C3×C4—61no—
204C22×C3×C4—61no—
205C22×C3×C4—61no—
206C22×C3×C4—61no—
207C22×C3×C4—62no—
208C22×C3×C4—61no—
209C22×C3×C4—61no—
210C22×C3×C4—121no—
211C22×C3×C4—121no—
212C22×C3×C4—121no—
213C2×#67—41no—
214C22×Dic3—41no—
215C2×C4×D3—41no—
216C4×A4—21no—
217C4×A4—21no—
218C4×A4—41no—
219C4×A4—41no—
220SL(2,ℤ/4)—21no—
221SL(2,ℤ/4)C2×C3×C412yescomplemented
222SL(2,ℤ/4)C3×D412yescomplemented
223C3×C4⋊C4—62no—
224C3×C4⋊C4—61no—
225C3×C4⋊C4—61no—
226C3×C4⋊C4—121no—
227C3×C22⋊C4—32no—
228C3×C22⋊C4—32no—
229C3×C22⋊C4—34no—
230C3×C22⋊C4—34no—
231C3×C22⋊C4—32no—
232C3×C22⋊C4—32no—
233C3×C22⋊C4—31no—
234C3×C22⋊C4—31no—
235C3×C22⋊C4—31no—
236C3×C22⋊C4—41no—
237C3×C22⋊C4—61no—
238C3×C22⋊C4—62no—
239C3×C22⋊C4—62no—
240C3×C22⋊C4—62no—
241C3×C22⋊C4—61no—
242C3×C22⋊C4—61no—
243C3×C22⋊C4—61no—
244C3×C22⋊C4—61no—
245C3×C22⋊C4—81no—
246C3×C22⋊C4—121no—
247C3×C22⋊C4S411yescharacteristic, complemented
248C3×C42—62no—
249C3×C42—61no—
250C3×C42—61no—
251C3×C42—121no—
252(C2×D3)⋊C4—41no—
253Dic3⋊C4—41no—
254C4×Dic3—41no—
255C22×C32—42no—
256C22×C32—41no—
257C22×C32—81no—
258C22×C32—81no—
259C2×C3×D3—42no—
260C2×C3×D3—81no—
261C2×C3×D3—81no—
262C3×A4C4×D411yescharacteristic, complemented
263C32×C4—81no—
264C32×C4—81no—
265C3×Dic3—42no—
266C3×Dic3—42no—
267C3×Dic3—81no—
268C25C2×C3×D311yescharacteristic
269C22×D4—31no—
270C22×D4—31no—
271C22×D4—31no—
272C23×C4—31no—
273C23×C4—31no—
274C23×C4—31no—
275C23×C4C2×C3×D311yescharacteristic
276C23×C4C2×C3×D311yescharacteristic
277#120—34no—
278#120—34no—
279C4×D4—62no—
280C4×D4—62no—
281C4×D4—61no—
282C4×D4—61no—
283C4×D4—61no—
284C4×D4—61no—
285C2×C4⋊C4—31no—
286C2×C4⋊C4—31no—
287C2×C4⋊C4—31no—
288C2×C22⋊C4—31no—
289C2×C22⋊C4—31no—
290C2×C22⋊C4—31no—
291C2×C22⋊C4—31no—
292C2×C22⋊C4—31no—
293C2×C22⋊C4—31no—
294C2×C22⋊C4—31no—
295C2×C22⋊C4—31no—
296C2×C22⋊C4—31no—
297C2×C22⋊C4—31no—
298C2×C22⋊C4—31no—
299C2×C22⋊C4—31no—
300C2×C22⋊C4—31no—
301C2×C22⋊C4—31no—
302C2×C22⋊C4—62no—
303C2×C22⋊C4—62no—
304C2×C42—31no—
305C2×C42—31no—
306C2×C42—31no—
307#95—31no—
308#95—31no—
309#95—31no—
310#95—31no—
311#95—31no—
312#95—31no—
313C23×C3—22no—
314C23×C3—31no—
315C23×C3—31no—
316C23×C3—31no—
317C23×C3—31no—
318C23×C3—32no—
319C23×C3—32no—
320C23×C3—32no—
321C23×C3—31no—
322C23×C3—32no—
323C23×C3—41no—
324C23×C3—61no—
325C23×C3—61no—
326C23×C3—61no—
327C23×C3—61no—
328C23×C3—61no—
329C23×C3—62no—
330C23×C3—61no—
331C23×C3—61no—
332C23×C3—61no—
333C23×C3—62no—
334C23×C3—62no—
335C23×C3—61no—
336C23×C3—61no—
337C23×C3—61no—
338C23×C3—61no—
339C23×C3—61no—
340C23×C3—61no—
341C23×C3—61no—
342C23×C3—81no—
343C23×C3—122no—
344C23×C3C2×C4×D311yescharacteristic
345C23×C3D3×D411yescharacteristic
346C23×C3#23711yescharacteristic
347C23×C3C2×S411yescharacteristic
348C22×D3—41no—
349C2×A4—22no—
350C2×A4—21no—
351C2×A4—21no—
352C2×A4—21no—
353C2×A4—42no—
354C2×A4C22×C3×C411yescharacteristic
355C2×A4C2×C3×D411yescharacteristic
356C2×A4C3×#4111yescharacteristic
357S4—22no—
358C3×D4—62no—
359C3×D4—62no—
360C3×D4—62no—
361C3×D4—64no—
362C3×D4—62no—
363C3×D4—64no—
364C3×D4—124no—
365C2×C3×C4—32no—
366C2×C3×C4—32no—
367C2×C3×C4—32no—
368C2×C3×C4—32no—
369C2×C3×C4—32no—
370C2×C3×C4—31no—
371C2×C3×C4—31no—
372C2×C3×C4—41no—
373C2×C3×C4—41no—
374C2×C3×C4—61no—
375C2×C3×C4—61no—
376C2×C3×C4—61no—
377C2×C3×C4—61no—
378C2×C3×C4—61no—
379C2×C3×C4—61no—
380C2×C3×C4—61no—
381C2×C3×C4—61no—
382C2×C3×C4—61no—
383C2×C3×C4—61no—
384C2×C3×C4—61no—
385C2×C3×C4—61no—
386C2×C3×C4—61no—
387C2×C3×C4—61no—
388C2×C3×C4—61no—
389C2×C3×C4—61no—
390C2×C3×C4—61no—
391C2×C3×C4—61no—
392C2×C3×C4—61no—
393C2×C3×C4—61no—
394C2×C3×C4—61no—
395C2×C3×C4—61no—
396C2×C3×C4—61no—
397C2×C3×C4—61no—
398C2×C3×C4—81no—
399C2×C3×C4—81no—
400C2×C3×C4—122no—
401C2×C3×C4—122no—
402C2×C3×C4—122no—
403C2×C3×C4—124no—
404C2×C3×C4—122no—
405C2×C3×C4C2×S411yescharacteristic
406C2×C3×C4C2×S411yescharacteristic
407#67—44no—
408C2×Dic3—41no—
409C2×Dic3—41no—
410C2×Dic3—41no—
411C2×Dic3—82no—
412C4×D3—82no—
413C2×C32—41no—
414C2×C32—41no—
415C2×C32—41no—
416C2×C32—82no—
417C3×D3—82no—
418C24—21no—
419C24—21no—
420C24—31no—
421C24—31no—
422C24—32no—
423C24—31no—
424C24—61no—
425C24—61no—
426C24C3×C4×D312yescomplemented
427C24C22×C3×D311yescharacteristic
428C2×D4—32no—
429C2×D4—34no—
430C2×D4—32no—
431C2×D4—34no—
432C2×D4—61no—
433C2×D4—61no—
434C2×D4—61no—
435C2×D4—62no—
436C2×D4—61no—
437C2×D4—61no—
438C2×D4—61no—
439C2×D4—121no—
440C2×D4—121no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—31no—
444C22×C4—31no—
445C22×C4—31no—
446C22×C4—31no—
447C22×C4—31no—
448C22×C4—31no—
449C22×C4—31no—
450C22×C4—31no—
451C22×C4—31no—
452C22×C4—31no—
453C22×C4—31no—
454C22×C4—62no—
455C22×C4—62no—
456C22×C4—62no—
457C22×C4—61no—
458C22×C4—61no—
459C22×C4—61no—
460C22×C4—61no—
461C22×C4—62no—
462C22×C4—61no—
463C22×C4—61no—
464C22×C4—121no—
465C22×C4—121no—
466C22×C4—121no—
467C4⋊C4—62no—
468C4⋊C4—61no—
469C4⋊C4—61no—
470C4⋊C4—121no—
471C22⋊C4—32no—
472C22⋊C4—32no—
473C22⋊C4—34no—
474C22⋊C4—34no—
475C22⋊C4—31no—
476C22⋊C4—32no—
477C22⋊C4—32no—
478C22⋊C4—31no—
479C22⋊C4—31no—
480C22⋊C4—61no—
481C22⋊C4—62no—
482C22⋊C4—62no—
483C22⋊C4—62no—
484C22⋊C4—61no—
485C22⋊C4—61no—
486C22⋊C4—61no—
487C22⋊C4—61no—
488C22⋊C4—121no—
489C22⋊C4C3×S411yescharacteristic, complemented
490C42—62no—
491C42—61no—
492C42—61no—
493C42—121no—
494C22×C3—21no—
495C22×C3—21no—
496C22×C3—31no—
497C22×C3—31no—
498C22×C3—31no—
499C22×C3—31no—
500C22×C3—31no—
501C22×C3—31no—
502C22×C3—31no—
503C22×C3—31no—
504C22×C3—31no—
505C22×C3—32no—
506C22×C3—41no—
507C22×C3—42no—
508C22×C3—62no—
509C22×C3—62no—
510C22×C3—62no—
511C22×C3—62no—
512C22×C3—61no—
513C22×C3—62no—
514C22×C3—62no—
515C22×C3—62no—
516C22×C3—62no—
517C22×C3—61no—
518C22×C3—61no—
519C22×C3—62no—
520C22×C3—81no—
521C22×C3—81no—
522C22×C3—81no—
523C22×C3—82no—
524C22×C3—121no—
525C22×C3—121no—
526C22×C3—121no—
527C22×C3—121no—
528C22×C3—121no—
529C22×C3—121no—
530C22×C3—161no—
531C22×C3—161no—
532C22×C3#67⋊C411yescharacteristic, complemented
533C22×C3C4×S412yescomplemented
534C22×C3C22×S411yescharacteristic
535C2×D3—42no—
536C2×D3—81no—
537C2×D3—81no—
538A4—21no—
539A4C3×C4×D411yescharacteristic, complemented
540C3×C4—21no—
541C3×C4—21no—
542C3×C4—62no—
543C3×C4—62no—
544C3×C4—62no—
545C3×C4—62no—
546C3×C4—61no—
547C3×C4—62no—
548C3×C4—61no—
549C3×C4—81no—
550C3×C4—81no—
551C3×C4—121no—
552C3×C4—121no—
553C3×C4—161no—
554C3×C4—161no—
555Dic3—42no—
556Dic3—42no—
557Dic3—81no—
558C32—41noSylow
559C23—22no—
560C23—31no—
561C23—31no—
562C23—31no—
563C23—31no—
564C23—32no—
565C23—31no—
566C23—32no—
567C23—32no—
568C23—32no—
569C23—61no—
570C23—61no—
571C23—61no—
572C23—61no—
573C23—61no—
574C23—62no—
575C23—61no—
576C23—61no—
577C23—61no—
578C23—62no—
579C23—62no—
580C23—61no—
581C23—61no—
582C23—61no—
583C23—61no—
584C23—61no—
585C23—61no—
586C23—61no—
587C23—122no—
588C23C2×C3×C4×D311yescharacteristic
589C23C3×D3×D411yescharacteristic
590C23C3×#23711yescharacteristic
591C23C2×C3×S411yescharacteristic
592D4—62no—
593D4—62no—
594D4—62no—
595D4—64no—
596D4—62no—
597D4—64no—
598D4—124no—
599C2×C4—32no—
600C2×C4—32no—
601C2×C4—32no—
602C2×C4—32no—
603C2×C4—32no—
604C2×C4—31no—
605C2×C4—31no—
606C2×C4—61no—
607C2×C4—61no—
608C2×C4—61no—
609C2×C4—61no—
610C2×C4—61no—
611C2×C4—61no—
612C2×C4—61no—
613C2×C4—61no—
614C2×C4—61no—
615C2×C4—61no—
616C2×C4—61no—
617C2×C4—61no—
618C2×C4—61no—
619C2×C4—61no—
620C2×C4—61no—
621C2×C4—61no—
622C2×C4—61no—
623C2×C4—61no—
624C2×C4—61no—
625C2×C4—61no—
626C2×C4—61no—
627C2×C4—61no—
628C2×C4—61no—
629C2×C4—61no—
630C2×C4—122no—
631C2×C4—122no—
632C2×C4—122no—
633C2×C4—124no—
634C2×C4—122no—
635C2×C4C2×C3×S411yescharacteristic
636C2×C4C2×C3×S411yescharacteristic
637C2×C3—22no—
638C2×C3—31no—
639C2×C3—31no—
640C2×C3—31no—
641C2×C3—31no—
642C2×C3—41no—
643C2×C3—41no—
644C2×C3—41no—
645C2×C3—62no—
646C2×C3—82no—
647C2×C3—81no—
648C2×C3—81no—
649C2×C3—81no—
650C2×C3—122no—
651C2×C3—162no—
652C2×C3C2×C4×S411yescharacteristic
653C2×C3D4×S411yescharacteristic
654C2×C3#591411yescharacteristic
655D3—82no—
656C22—21no—
657C22—21no—
658C22—31no—
659C22—31no—
660C22—31no—
661C22—31no—
662C22—31no—
663C22—31no—
664C22—31no—
665C22—31no—
666C22—31no—
667C22—32no—
668C22—62no—
669C22—62no—
670C22—62no—
671C22—62no—
672C22—61no—
673C22—62no—
674C22—62no—
675C22—62no—
676C22—62no—
677C22—61no—
678C22—61no—
679C22—62no—
680C22—121no—
681C22—121no—
682C22—121no—
683C22—121no—
684C22—121no—
685C22—121no—
686C22C3×#67⋊C411yescharacteristic, complemented
687C22C3×C4×S412yescomplemented
688C22C22×C3×S411yescharacteristic
689C4—21no—
690C4—21no—
691C4—62no—
692C4—62no—
693C4—62no—
694C4—62no—
695C4—61no—
696C4—62no—
697C4—61no—
698C4—121no—
699C4—121no—
700C3—41no—
701C3—81no—
702C3GL(2,ℤ/4)⋊C411yescharacteristic, direct product factor
703C2—22no—
704C2—31no—
705C2—31no—
706C2—31no—
707C2—31no—
708C2—62no—
709C2—122no—
710C2C2×C3×C4×S411yescharacteristic
711C2C3×D4×S411yescharacteristic
712C2C3×#591411yescharacteristic
subgroupG/H
centerC22×C3C22×S4
commutatorC2×A4C22×C3×C4
FrattiniC22C22×C3×S4
FittingC22×C3×C22⋊C4D3
socleC24×C3C22×D3
prime radicalC2×C3×GL(2,ℤ/4)C2
cosocleC22×A4C23×C3
hypercenterC3×C22⋊C4S4
hypocenterA4C3×C4×D4
LCSG ▷ C2×A4 ▷ A4
UCSC1 ◁ C22×C3 ◁ C3×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C3×SL(2,ℤ/4)C2semidirect
3. C2×C3×C4×S4C2semidirect
4. C3×A4×C22⋊C4C2semidirect
5. C3×(C2×S4)⋊C4C2semidirect
6. C3×SL(2,ℤ/4)⋊C4C2semidirect
7. C3×C4×SL(2,ℤ/4)C2semidirect
8. GL(2,ℤ/4)⋊C4C3direct (N × H)
14. C3×GL(2,ℤ/4)C4semidirect
22. C22×SL(2,ℤ/4)C2×C3semidirect
23. C2×C4×S4C2×C3semidirect
28. C22×C3×C22⋊C4D3semidirect
30. A4×C22⋊C4C2×C3semidirect
31. (C2×S4)⋊C4C2×C3semidirect
32. SL(2,ℤ/4)⋊C4C2×C3semidirect
33. C4×SL(2,ℤ/4)C2×C3semidirect
46. C22×C3×A4C2×C4semidirect
50. C2×C3×S4C2×C4semidirect
57. C3×SL(2,ℤ/4)C2×C4semidirect
58. C3×SL(2,ℤ/4)D4semidirect
80. GL(2,ℤ/4)C3×C4semidirect
142. C22×C22⋊C4C3×D3semidirect
161. C24×C3C4×D3semidirect
169. C22×A4C2×C3×C4semidirect
173. C2×S4C2×C3×C4semidirect
221. SL(2,ℤ/4)C2×C3×C4semidirect
222. SL(2,ℤ/4)C3×D4semidirect
247. C3×C22⋊C4S4semidirect
262. C3×A4C4×D4semidirect
426. C24C3×C4×D3semidirect
489. C22⋊C4C3×S4semidirect
532. C22×C3#67⋊C4semidirect
533. C22×C3C4×S4semidirect
539. A4C3×C4×D4semidirect
686. C22C3×#67⋊C4semidirect
687. C22C3×C4×S4semidirect
702. C3GL(2,ℤ/4)⋊C4direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×GL(2,ℤ/4)2
C22×C3×SL(2,ℤ/4)2
C2×C3×C4×S42
C3×A4×C22⋊C42
C3×(C2×S4)⋊C42
C3×SL(2,ℤ/4)⋊C42
C3×C4×SL(2,ℤ/4)2
GL(2,ℤ/4)⋊C43
C3×#23583
C3×#67⋊C44