Finite Group Databasebeta

← A4×#894 #11923168

Subgroups — A4×#894 #11923168

Order 1152.

942 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 942 conjugacy classes of subgroups — too many to draw. Only its 93 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×A4×D12C211yesmaximal, characteristic
2C2×C4×D3×A4C211yesmaximal, characteristic, complemented
3C3×A4×C4⋊C4C211yesmaximal, characteristic, complemented
4A4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
5A4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
6A4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
7A4×Dic3⋊C4C211yesmaximal, characteristic, complemented
8C22×#894C311yesmaximal, characteristic, complemented
9A4×#123—31nomaximal
10C22×D3×A4C2211yescharacteristic
11C22×D3×A4C2211yescharacteristic
12C2×C3×C4×A4C2211yescharacteristic
13C2×C3×C4×A4C2211yescharacteristic
14C2×C3×C4×A4C2211yescharacteristic
15C2×Dic3×A4C2211yescharacteristic
16C2×Dic3×A4C2211yescharacteristic
17A4×D12—22no—
18C4×D3×A4—22no—
19C3×#894—41nomaximal
20C23×D12C2×C311yescharacteristic
21C23×C4×D3C2×C311yescharacteristic, complemented
22C2×D4×A4—31no—
23C22×C4×A4—31no—
24C22×C3×C4⋊C4C2×C311yescharacteristic, complemented
25C22×(C2×D3)⋊C4C2×C311yescharacteristic, complemented
26C22×(C2×D3)⋊C4C2×C311yescharacteristic, complemented
27C22×(C2×D3)⋊C4C2×C311yescharacteristic, complemented
28C22×Dic3⋊C4C2×C311yescharacteristic, complemented
29C2×#894—31no—
30C2×#894—31no—
31C2×#894—31no—
32C2×#894—31no—
33C2×#894—31no—
34C2×#894—31no—
35C2×#894—31no—
36C2×#894—31no—
37A4×C4⋊C4—21no—
38A4×C4⋊C4—31no—
39A4×C4⋊C4D311yescharacteristic, complemented
40A4×C22⋊C4—31no—
41A4×C22⋊C4—31no—
42A4×C22⋊C4—31no—
43C22×C3×A4C2311yescharacteristic
44C2×D3×A4—21no—
45C2×D3×A4—21no—
46C2×D3×A4—21no—
47C2×D3×A4—21no—
48C2×D3×A4—21no—
49C2×D3×A4D412yes—
50C2×C3×D12—41no—
51C2×C3×C4×D3—41no—
52C3×C4×A4—21no—
53C3×C4×A4—21no—
54C3×C4×A4—21no—
55Dic3×A4—21no—
56Dic3×A4—21no—
57C32×C4⋊C4—41no—
58C3×(C2×D3)⋊C4—41no—
59C3×(C2×D3)⋊C4—41no—
60C3×(C2×D3)⋊C4—41no—
61C3×Dic3⋊C4—41no—
62C22×#123—31noSylow
63C24×D3C22×C311yescharacteristic
64C24×D3C22×C311yescharacteristic
65C23×A4—31no—
66C23×A4—31no—
67C23×C3×C4C22×C311yescharacteristic
68C23×C3×C4C22×C311yescharacteristic
69C23×C3×C4C22×C311yescharacteristic
70C23×Dic3C22×C311yescharacteristic
71C23×Dic3C22×C311yescharacteristic
72C22×D12—22no—
73C22×D12—31no—
74C22×D12—31no—
75C22×D12—31no—
76C22×D12—31no—
77C22×D12—62no—
78C22×C4×D3—22no—
79C22×C4×D3—31no—
80C22×C4×D3—31no—
81C22×C4×D3—31no—
82C22×C4×D3—31no—
83C22×C4×D3—62no—
84D4×A4—62no—
85C2×C4×A4—21no—
86C2×C4×A4—21no—
87C2×C4×A4—21no—
88C2×C4×A4—31no—
89C2×C4×A4—31no—
90C2×C4×A4—62no—
91C2×C4×A4C2×D311yescharacteristic
92C2×C4×A4C2×D311yescharacteristic
93C2×C4×A4C2×D311yescharacteristic
94C3×#123—121no—
95C2×C3×C4⋊C4—31no—
96C2×C3×C4⋊C4—31no—
97C2×C3×C4⋊C4—31no—
98C2×C3×C4⋊C4—31no—
99C2×(C2×D3)⋊C4—31no—
100C2×(C2×D3)⋊C4—31no—
101C2×(C2×D3)⋊C4—31no—
102C2×(C2×D3)⋊C4—31no—
103C2×(C2×D3)⋊C4—31no—
104C2×(C2×D3)⋊C4—31no—
105C2×(C2×D3)⋊C4—31no—
106C2×(C2×D3)⋊C4—31no—
107C2×(C2×D3)⋊C4—31no—
108C2×(C2×D3)⋊C4—31no—
109C2×(C2×D3)⋊C4—31no—
110C2×(C2×D3)⋊C4—31no—
111C2×Dic3⋊C4—31no—
112C2×Dic3⋊C4—31no—
113C2×Dic3⋊C4—31no—
114C2×Dic3⋊C4—31no—
115#894—32no—
116#894—32no—
117#894—32no—
118#894—32no—
119#894—32no—
120#894—32no—
121#894—32no—
122#894—31no—
123#894—31no—
124#894—31no—
125#894—31no—
126#894—31no—
127#894—31no—
128#894—31no—
129#894A411yescharacteristic, direct product factor
130C22×C3×D3—41no—
131C22×C3×D3—41no—
132C2×C3×A4C2×D411yescharacteristic
133C2×C3×A4#4111yescharacteristic
134C2×C3×A4#4111yescharacteristic
135D3×A4—22no—
136D3×A4—41no—
137C2×C32×C4—41no—
138C2×C32×C4—41no—
139C2×C32×C4—41no—
140C2×C3×Dic3—41no—
141C2×C3×Dic3—41no—
142C3×D12—82no—
143C3×C4×D3—82no—
144C23×D4—31no—
145C24×C4—31no—
146C2×#123—91no—
147C2×#123—91no—
148C2×#123—91no—
149C2×#123—91no—
150C2×#123—91no—
151C2×#123—91no—
152C2×#123—91no—
153C2×#123—91no—
154C22×C4⋊C4—31no—
155C22×C4⋊C4C3×D311yescharacteristic, complemented
156C22×C22⋊C4—31no—
157C22×C22⋊C4—31no—
158C22×C22⋊C4—31no—
159C24×C3C23×C311yescharacteristic
160C23×D3—21no—
161C23×D3—21no—
162C23×D3—21no—
163C23×D3—21no—
164C23×D3—21no—
165C23×D3—31no—
166C23×D3—31no—
167C23×D3—32no—
168C23×D3—31no—
169C23×D3—31no—
170C23×D3—61no—
171C23×D3—61no—
172C23×D3—61no—
173C23×D3—61no—
174C23×D3—61no—
175C23×D3C3×D412yes—
176C22×A4—21no—
177C22×A4—32no—
178C22×A4—61no—
179C22×A4—61no—
180C22×A4—61no—
181C22×A4—61no—
182C22×A4—61no—
183C22×A4C22×D311yescharacteristic
184C2×C3×D4—121no—
185C22×C3×C4—21no—
186C22×C3×C4—21no—
187C22×C3×C4—21no—
188C22×C3×C4—31no—
189C22×C3×C4—31no—
190C22×C3×C4—31no—
191C22×C3×C4—31no—
192C22×C3×C4—31no—
193C22×C3×C4—31no—
194C22×C3×C4—61no—
195C22×C3×C4—61no—
196C22×C3×C4—61no—
197C22×C3×C4—121no—
198C22×Dic3—21no—
199C22×Dic3—21no—
200C22×Dic3—31no—
201C22×Dic3—31no—
202C22×Dic3—31no—
203C22×Dic3—31no—
204C22×Dic3—61no—
205C22×Dic3—61no—
206C2×D12—32no—
207C2×D12—31no—
208C2×D12—31no—
209C2×D12—31no—
210C2×D12—62no—
211C2×D12—62no—
212C2×D12—62no—
213C2×D12—62no—
214C2×D12—62no—
215C2×D12—62no—
216C2×D12—62no—
217C2×D12—62no—
218C2×D12C2×A411yescharacteristic
219C2×C4×D3—32no—
220C2×C4×D3—31no—
221C2×C4×D3—31no—
222C2×C4×D3—31no—
223C2×C4×D3—62no—
224C2×C4×D3—62no—
225C2×C4×D3—62no—
226C2×C4×D3—62no—
227C2×C4×D3—62no—
228C2×C4×D3—62no—
229C2×C4×D3—62no—
230C2×C4×D3—62no—
231C2×C4×D3C2×A411yescharacteristic, complemented
232C4×A4—22no—
233C4×A4—21no—
234C4×A4—21no—
235C4×A4—21no—
236C4×A4—41no—
237C4×A4—41no—
238C4×A4—61no—
239C4×A4—61no—
240C3×C4⋊C4—32no—
241C3×C4⋊C4—31no—
242C3×C4⋊C4—31no—
243C3×C4⋊C4—31no—
244C3×C4⋊C4—41no—
245C3×C4⋊C4—81no—
246C3×C4⋊C4—121no—
247C3×C4⋊C4C2×A411yescharacteristic, complemented
248C3×C22⋊C4—121no—
249C3×C22⋊C4—121no—
250C3×C22⋊C4—121no—
251(C2×D3)⋊C4—32no—
252(C2×D3)⋊C4—32no—
253(C2×D3)⋊C4—32no—
254(C2×D3)⋊C4—31no—
255(C2×D3)⋊C4—31no—
256(C2×D3)⋊C4—31no—
257(C2×D3)⋊C4—31no—
258(C2×D3)⋊C4—31no—
259(C2×D3)⋊C4—31no—
260(C2×D3)⋊C4—31no—
261(C2×D3)⋊C4—31no—
262(C2×D3)⋊C4—31no—
263(C2×D3)⋊C4C2×A411yescharacteristic, complemented
264(C2×D3)⋊C4C2×A411yescharacteristic, complemented
265(C2×D3)⋊C4C2×A411yescharacteristic, complemented
266Dic3⋊C4—32no—
267Dic3⋊C4—31no—
268Dic3⋊C4—31no—
269Dic3⋊C4—31no—
270Dic3⋊C4C2×A411yescharacteristic, complemented
271C22×C32—41no—
272C2×C3×D3—42no—
273C2×C3×D3—81no—
274C2×C3×D3—81no—
275C2×C3×D3—81no—
276C2×C3×D3—81no—
277C2×C3×D3—81no—
278C3×A4#12311yescharacteristic, complemented
279C32×C4—81no—
280C32×C4—81no—
281C32×C4—81no—
282C3×Dic3—81no—
283C3×Dic3—81no—
284C25—31no—
285C25—31no—
286C22×D4—62no—
287C22×D4—91no—
288C22×D4—91no—
289C22×D4—91no—
290C22×D4—91no—
291C22×D4—182no—
292C23×C4—31no—
293C23×C4—31no—
294C23×C4—62no—
295C23×C4—91no—
296C23×C4—91no—
297C23×C4—91no—
298C23×C4—91no—
299C23×C4—182no—
300C23×C4C2×C3×D311yescharacteristic
301C23×C4C2×C3×D311yescharacteristic
302C23×C4C2×C3×D311yescharacteristic
303#123—31no—
304#123—91no—
305#123—91no—
306#123—91no—
307#123—91no—
308#123—91no—
309#123—91no—
310#123—92no—
311#123—92no—
312#123—92no—
313#123—92no—
314#123—92no—
315#123—92no—
316#123—92no—
317#123—91no—
318C2×C4⋊C4—31no—
319C2×C4⋊C4—31no—
320C2×C4⋊C4—31no—
321C2×C4⋊C4—31no—
322C2×C4⋊C4—91no—
323C2×C4⋊C4—91no—
324C2×C4⋊C4—91no—
325C2×C4⋊C4—91no—
326C2×C22⋊C4—91no—
327C2×C22⋊C4—91no—
328C2×C22⋊C4—91no—
329C2×C22⋊C4—91no—
330C2×C22⋊C4—91no—
331C2×C22⋊C4—91no—
332C2×C22⋊C4—91no—
333C2×C22⋊C4—91no—
334C2×C22⋊C4—91no—
335C2×C22⋊C4—91no—
336C2×C22⋊C4—91no—
337C2×C22⋊C4—91no—
338C23×C3—31no—
339C23×C3—31no—
340C23×C3—31no—
341C23×C3—31no—
342C23×C3—121no—
343C23×C3—121no—
344C23×C3C2×C3×D411yescharacteristic
345C23×C3C3×#4111yescharacteristic
346C23×C3C3×#4111yescharacteristic
347C22×D3—22no—
348C22×D3—32no—
349C22×D3—31no—
350C22×D3—32no—
351C22×D3—32no—
352C22×D3—32no—
353C22×D3—31no—
354C22×D3—41no—
355C22×D3—61no—
356C22×D3—61no—
357C22×D3—61no—
358C22×D3—61no—
359C22×D3—61no—
360C22×D3—61no—
361C22×D3—61no—
362C22×D3—61no—
363C22×D3—61no—
364C22×D3—61no—
365C22×D3—64no—
366C22×D3—62no—
367C22×D3—62no—
368C22×D3—61no—
369C22×D3—61no—
370C22×D3—61no—
371C22×D3—61no—
372C22×D3—62no—
373C22×D3—61no—
374C22×D3—61no—
375C22×D3—61no—
376C22×D3—61no—
377C22×D3—61no—
378C22×D3—61no—
379C22×D3—122no—
380C22×D3—121no—
381C22×D3—121no—
382C22×D3—121no—
383C22×D3C22×A411yescharacteristic
384C22×D3C22×A411yescharacteristic
385C2×A4—21no—
386C2×A4—21no—
387C2×A4—21no—
388C2×A4—62no—
389C2×A4—121no—
390C2×A4#23511yescharacteristic
391C2×A4D3×D411yescharacteristic
392C2×A4#23911yescharacteristic
393C3×D4—242no—
394C2×C3×C4—31no—
395C2×C3×C4—31no—
396C2×C3×C4—31no—
397C2×C3×C4—41no—
398C2×C3×C4—41no—
399C2×C3×C4—41no—
400C2×C3×C4—61no—
401C2×C3×C4—61no—
402C2×C3×C4—61no—
403C2×C3×C4—61no—
404C2×C3×C4—61no—
405C2×C3×C4—61no—
406C2×C3×C4—61no—
407C2×C3×C4—61no—
408C2×C3×C4—61no—
409C2×C3×C4—61no—
410C2×C3×C4—61no—
411C2×C3×C4—61no—
412C2×C3×C4—81no—
413C2×C3×C4—81no—
414C2×C3×C4—81no—
415C2×C3×C4—121no—
416C2×C3×C4—121no—
417C2×C3×C4—242no—
418C2×C3×C4C22×A411yescharacteristic
419C2×C3×C4C22×A411yescharacteristic
420C2×C3×C4C22×A411yescharacteristic
421C2×Dic3—31no—
422C2×Dic3—31no—
423C2×Dic3—61no—
424C2×Dic3—61no—
425C2×Dic3—61no—
426C2×Dic3—61no—
427C2×Dic3—61no—
428C2×Dic3—61no—
429C2×Dic3—61no—
430C2×Dic3—61no—
431C2×Dic3C22×A411yescharacteristic
432C2×Dic3C22×A411yescharacteristic
433D12—22no—
434D12—62no—
435D12—62no—
436D12—64no—
437D12—62no—
438C4×D3—22no—
439C4×D3—62no—
440C4×D3—62no—
441C4×D3—64no—
442C4×D3—62no—
443C2×C32—41no—
444C2×C32—41no—
445C2×C32—41no—
446C3×D3—82no—
447C3×D3—161no—
448C24—32no—
449C24—61no—
450C24—61no—
451C24—61no—
452C24—61no—
453C24—61no—
454C24—91no—
455C24—91no—
456C24—91no—
457C24—92no—
458C24—91no—
459C24—181no—
460C24—181no—
461C24—181no—
462C24—181no—
463C24—181no—
464C24C22×C3×D311yescharacteristic
465C2×D4—31no—
466C2×D4—91no—
467C2×D4—91no—
468C2×D4—92no—
469C2×D4—91no—
470C2×D4—182no—
471C2×D4—182no—
472C2×D4—182no—
473C2×D4—182no—
474C2×D4—182no—
475C2×D4—182no—
476C2×D4—182no—
477C2×D4—182no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—31no—
482C22×C4—31no—
483C22×C4—31no—
484C22×C4—31no—
485C22×C4—31no—
486C22×C4—31no—
487C22×C4—31no—
488C22×C4—61no—
489C22×C4—61no—
490C22×C4—61no—
491C22×C4—61no—
492C22×C4—61no—
493C22×C4—91no—
494C22×C4—91no—
495C22×C4—91no—
496C22×C4—91no—
497C22×C4—92no—
498C22×C4—91no—
499C22×C4—91no—
500C22×C4—91no—
501C22×C4—182no—
502C22×C4—182no—
503C22×C4—182no—
504C22×C4—182no—
505C22×C4—182no—
506C22×C4—182no—
507C22×C4—182no—
508C22×C4—182no—
509C22×C4—181no—
510C22×C4—181no—
511C4⋊C4—32no—
512C4⋊C4—31no—
513C4⋊C4—31no—
514C4⋊C4—31no—
515C4⋊C4—31no—
516C4⋊C4—91no—
517C4⋊C4—91no—
518C4⋊C4—92no—
519C4⋊C4—91no—
520C4⋊C4D3×A411yescharacteristic, complemented
521C22⋊C4—31no—
522C22⋊C4—31no—
523C22⋊C4—31no—
524C22⋊C4—91no—
525C22⋊C4—91no—
526C22⋊C4—91no—
527C22⋊C4—91no—
528C22⋊C4—91no—
529C22⋊C4—91no—
530C22⋊C4—92no—
531C22⋊C4—92no—
532C22⋊C4—92no—
533C22⋊C4—91no—
534C22⋊C4—91no—
535C22⋊C4—91no—
536C22×C3—31no—
537C22×C3—31no—
538C22×C3—31no—
539C22×C3—32no—
540C22×C3—31no—
541C22×C3—31no—
542C22×C3—31no—
543C22×C3—31no—
544C22×C3—31no—
545C22×C3—31no—
546C22×C3—41no—
547C22×C3—81no—
548C22×C3—122no—
549C22×C3—241no—
550C22×C3—241no—
551C22×C3—241no—
552C22×C3—241no—
553C22×C3—241no—
554C22×C3C3×#12311yescharacteristic, complemented
555C22×C3C23×A411yescharacteristic
556C2×D3—21no—
557C2×D3—21no—
558C2×D3—21no—
559C2×D3—21no—
560C2×D3—21no—
561C2×D3—32no—
562C2×D3—62no—
563C2×D3—62no—
564C2×D3—62no—
565C2×D3—62no—
566C2×D3—62no—
567C2×D3—62no—
568C2×D3—61no—
569C2×D3—61no—
570C2×D3—62no—
571C2×D3—62no—
572C2×D3—61no—
573C2×D3—61no—
574C2×D3—61no—
575C2×D3—121no—
576C2×D3—121no—
577C2×D3—121no—
578C2×D3—121no—
579C2×D3—121no—
580C2×D3—121no—
581C2×D3—121no—
582C2×D3—121no—
583C2×D3D4×A412yes—
584A4—21no—
585A4#89411yescharacteristic, direct product factor
586C3×C4—21no—
587C3×C4—21no—
588C3×C4—21no—
589C3×C4—61no—
590C3×C4—61no—
591C3×C4—61no—
592C3×C4—81no—
593C3×C4—81no—
594C3×C4—81no—
595C3×C4—82no—
596C3×C4—161no—
597C3×C4—161no—
598C3×C4—241no—
599C3×C4—241no—
600Dic3—21no—
601Dic3—21no—
602Dic3—61no—
603Dic3—61no—
604C32—41noSylow
605C23—31no—
606C23—31no—
607C23—31no—
608C23—31no—
609C23—31no—
610C23—31no—
611C23—62no—
612C23—92no—
613C23—92no—
614C23—92no—
615C23—92no—
616C23—91no—
617C23—91no—
618C23—121no—
619C23—181no—
620C23—181no—
621C23—181no—
622C23—181no—
623C23—181no—
624C23—181no—
625C23—181no—
626C23—181no—
627C23—181no—
628C23—181no—
629C23—182no—
630C23—182no—
631C23—182no—
632C23—181no—
633C23—181no—
634C23—181no—
635C23—181no—
636C23—184no—
637C23—181no—
638C23—181no—
639C23—181no—
640C23—181no—
641C23—181no—
642C23—181no—
643C23—361no—
644C23—361no—
645C23—361no—
646C23—362no—
647C23C3×#23511yescharacteristic
648C23C3×D3×D411yescharacteristic
649C23C3×#23911yescharacteristic
650D4—62no—
651D4—182no—
652D4—182no—
653D4—182no—
654D4—184no—
655C2×C4—31no—
656C2×C4—31no—
657C2×C4—31no—
658C2×C4—31no—
659C2×C4—31no—
660C2×C4—61no—
661C2×C4—61no—
662C2×C4—61no—
663C2×C4—61no—
664C2×C4—61no—
665C2×C4—61no—
666C2×C4—62no—
667C2×C4—61no—
668C2×C4—61no—
669C2×C4—61no—
670C2×C4—61no—
671C2×C4—61no—
672C2×C4—61no—
673C2×C4—91no—
674C2×C4—91no—
675C2×C4—182no—
676C2×C4—182no—
677C2×C4—181no—
678C2×C4—181no—
679C2×C4—181no—
680C2×C4—182no—
681C2×C4—181no—
682C2×C4—184no—
683C2×C4—181no—
684C2×C4—181no—
685C2×C4—181no—
686C2×C4—181no—
687C2×C4C2×D3×A411yescharacteristic
688C2×C4C2×D3×A411yescharacteristic
689C2×C4C2×D3×A411yescharacteristic
690C2×C3—31no—
691C2×C3—31no—
692C2×C3—31no—
693C2×C3—31no—
694C2×C3—41no—
695C2×C3—41no—
696C2×C3—41no—
697C2×C3—81no—
698C2×C3—81no—
699C2×C3—81no—
700C2×C3—242no—
701C2×C3—481no—
702C2×C3C2×D4×A411yescharacteristic
703C2×C3A4×#4111yescharacteristic
704C2×C3A4×#4111yescharacteristic
705D3—22no—
706D3—41no—
707D3—62no—
708D3—121no—
709C22—31no—
710C22—31no—
711C22—31no—
712C22—32no—
713C22—31no—
714C22—31no—
715C22—31no—
716C22—31no—
717C22—31no—
718C22—31no—
719C22—32no—
720C22—61no—
721C22—61no—
722C22—61no—
723C22—61no—
724C22—61no—
725C22—92no—
726C22—182no—
727C22—182no—
728C22—182no—
729C22—182no—
730C22—182no—
731C22—182no—
732C22—182no—
733C22—182no—
734C22—181no—
735C22—181no—
736C22—181no—
737C22—181no—
738C22—181no—
739C22—361no—
740C22—361no—
741C22—361no—
742C22—361no—
743C22—361no—
744C22—361no—
745C22—361no—
746C22—361no—
747C22C3×#89411yescharacteristic, complemented
748C22C22×D3×A411yescharacteristic
749C4—21no—
750C4—21no—
751C4—21no—
752C4—61no—
753C4—61no—
754C4—61no—
755C4—61no—
756C4—61no—
757C4—181no—
758C4—181no—
759C3—41no—
760C3—81no—
761C3A4×#12311yescharacteristic, complemented
762C2—31no—
763C2—31no—
764C2—31no—
765C2—31no—
766C2—62no—
767C2—121no—
768C2—182no—
769C2—361no—
770C2A4×#23511yescharacteristic
771C2D3×D4×A411yescharacteristic
772C2A4×#23911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×A4
commutator, socle, cosocleC24×C3C23×C3
FittingC22×C3×C4⋊C4C2×C3
prime radicalC2×A4×D12C2
hypercenterC4⋊C4D3×A4
hypocenterC22×C3C3×#123
LCSG ▷ C24×C3 ▷ C22×C3
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×D3×A4C2semidirect
3. C3×A4×C4⋊C4C2semidirect
4. A4×(C2×D3)⋊C4C2semidirect
5. A4×(C2×D3)⋊C4C2semidirect
6. A4×(C2×D3)⋊C4C2semidirect
7. A4×Dic3⋊C4C2semidirect
8. C22×#894C3semidirect
21. C23×C4×D3C2×C3semidirect
24. C22×C3×C4⋊C4C2×C3semidirect
25. C22×(C2×D3)⋊C4C2×C3semidirect
26. C22×(C2×D3)⋊C4C2×C3semidirect
27. C22×(C2×D3)⋊C4C2×C3semidirect
28. C22×Dic3⋊C4C2×C3semidirect
39. A4×C4⋊C4D3semidirect
129. #894A4direct (N × H)
155. C22×C4⋊C4C3×D3semidirect
231. C2×C4×D3C2×A4semidirect
247. C3×C4⋊C4C2×A4semidirect
263. (C2×D3)⋊C4C2×A4semidirect
264. (C2×D3)⋊C4C2×A4semidirect
265. (C2×D3)⋊C4C2×A4semidirect
270. Dic3⋊C4C2×A4semidirect
278. C3×A4#123semidirect
520. C4⋊C4D3×A4semidirect
554. C22×C3C3×#123semidirect
585. A4#894direct (N × H)
747. C22C3×#894semidirect
761. C3A4×#123semidirect

Maximal subgroups

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

subgroupindex
C2×A4×D122
C2×C4×D3×A42
C3×A4×C4⋊C42
A4×(C2×D3)⋊C42
A4×Dic3⋊C42
C22×#8943
A4×#1233
C3×#8944