Finite Group Databasebeta

← A4×#67⋊C4 #11923155

Subgroups — A4×#67⋊C4 #11923155

Order 1152.

1190 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×A4×#67C211yesmaximal, characteristic
2C22×Dic3×A4C211yesmaximal, characteristic, complemented
3C2×C4×D3×A4C211yesmaximal, characteristic, complemented
4C3×A4×C22⋊C4C211yesmaximal, characteristic, complemented
5A4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
6A4×Dic3⋊C4C211yesmaximal, characteristic, complemented
7C4×Dic3×A4C211yesmaximal, characteristic, complemented
8C22×#67⋊C4C311yesmaximal, characteristic, complemented
9C4×D4×A4—31nomaximal
10C23×C3×A4C2211yescharacteristic
11C22×D3×A4C2211yescharacteristic
12C2×C3×C4×A4C2211yescharacteristic
13C2×C3×C4×A4C2211yescharacteristic
14A4×#67C414yescomplemented
15C2×Dic3×A4—22no—
16C2×Dic3×A4C2211yescharacteristic
17C2×Dic3×A4C2211yescharacteristic
18C2×Dic3×A4C2211yescharacteristic
19C4×D3×A4—22no—
20C3×#67⋊C4—41nomaximal
21C23×#67C2×C311yescharacteristic
22C24×Dic3C2×C311yescharacteristic, complemented
23C23×C4×D3C2×C311yescharacteristic, complemented
24C2×D4×A4—31no—
25C22×C4×A4—31no—
26C22×C4×A4—31no—
27C22×C3×C22⋊C4C2×C311yescharacteristic, complemented
28C22×(C2×D3)⋊C4C2×C311yescharacteristic, complemented
29C22×Dic3⋊C4C2×C311yescharacteristic, complemented
30C22×C4×Dic3C2×C311yescharacteristic, complemented
31C2×#67⋊C4—31no—
32C2×#67⋊C4—31no—
33C2×#67⋊C4—31no—
34C2×#67⋊C4—31no—
35C2×#67⋊C4—31no—
36C2×#67⋊C4—31no—
37C2×#67⋊C4—31no—
38C2×#67⋊C4—31no—
39A4×C4⋊C4—31no—
40A4×C22⋊C4—21no—
41A4×C22⋊C4—31no—
42A4×C22⋊C4D311yescharacteristic, complemented
43C42×A4—31no—
44C22×C3×A4—21no—
45C22×C3×A4—21no—
46C22×C3×A4C2×C412yescomplemented
47C22×C3×A4C2311yescharacteristic
48C2×D3×A4—21no—
49C2×D3×A4—21no—
50C2×D3×A4C2×C412yescomplemented
51C2×C3×#67—41no—
52C22×C3×Dic3—41no—
53C2×C3×C4×D3—41no—
54C3×C4×A4—21no—
55C3×C4×A4—21no—
56Dic3×A4—21no—
57Dic3×A4C2×C412yescomplemented
58Dic3×A4D412yescomplemented
59C32×C22⋊C4—41no—
60C3×(C2×D3)⋊C4—41no—
61C3×Dic3⋊C4—41no—
62C3×C4×Dic3—41no—
63C22×C4×D4—31noSylow
64C25×C3C22×C311yescharacteristic
65C24×D3C22×C311yescharacteristic
66C23×A4—21no—
67C23×A4—31no—
68C23×A4C2×D311yescharacteristic
69C23×C3×C4C22×C311yescharacteristic
70C23×C3×C4C22×C311yescharacteristic
71C22×#67—31no—
72C22×#67—34no—
73C22×#67—31no—
74C22×#67—31no—
75C22×#67—31no—
76C22×#67C3×C414yescomplemented
77C23×Dic3—22no—
78C23×Dic3—31no—
79C23×Dic3—31no—
80C23×Dic3—31no—
81C23×Dic3—31no—
82C23×Dic3—62no—
83C23×Dic3C22×C311yescharacteristic
84C23×Dic3C22×C311yescharacteristic
85C23×Dic3C22×C311yescharacteristic
86C22×C4×D3—22no—
87C22×C4×D3—31no—
88C22×C4×D3—31no—
89C22×C4×D3—31no—
90C22×C4×D3—31no—
91C22×C4×D3—62no—
92D4×A4—34no—
93C2×C4×A4—21no—
94C2×C4×A4—21no—
95C2×C4×A4—31no—
96C2×C4×A4—31no—
97C2×C4×A4—31no—
98C2×C4×A4—62no—
99C2×C4×A4—62no—
100C2×C4×A4C2×D311yescharacteristic
101C2×C4×A4C2×D311yescharacteristic
102C3×C4×D4—121no—
103C2×C3×C22⋊C4—31no—
104C2×C3×C22⋊C4—31no—
105C2×C3×C22⋊C4—31no—
106C2×C3×C22⋊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—
115C2×C4×Dic3—31no—
116C2×C4×Dic3—31no—
117C2×C4×Dic3—31no—
118C2×C4×Dic3—31no—
119#67⋊C4—32no—
120#67⋊C4—32no—
121#67⋊C4—32no—
122#67⋊C4—32no—
123#67⋊C4—32no—
124#67⋊C4—32no—
125#67⋊C4—32no—
126#67⋊C4—31no—
127#67⋊C4—31no—
128#67⋊C4—31no—
129#67⋊C4—31no—
130#67⋊C4—31no—
131#67⋊C4—31no—
132#67⋊C4—31no—
133#67⋊C4A411yescharacteristic, direct product factor
134C23×C32—41no—
135C22×C3×D3—41no—
136C2×C3×A4—22no—
137C2×C3×A4C22×C411yescharacteristic
138C2×C3×A4C2×D411yescharacteristic
139C2×C3×A4#4111yescharacteristic
140D3×A4—22no—
141C2×C32×C4—41no—
142C2×C32×C4—41no—
143C3×#67—44no—
144C2×C3×Dic3—41no—
145C2×C3×Dic3—41no—
146C2×C3×Dic3—41no—
147C2×C3×Dic3—82no—
148C3×C4×D3—82no—
149C23×D4—31no—
150C24×C4—31no—
151C24×C4—31no—
152C2×C4×D4—91no—
153C2×C4×D4—91no—
154C2×C4×D4—91no—
155C2×C4×D4—91no—
156C2×C4×D4—91no—
157C2×C4×D4—91no—
158C2×C4×D4—91no—
159C2×C4×D4—91no—
160C22×C4⋊C4—31no—
161C22×C22⋊C4—31no—
162C22×C22⋊C4C3×D311yescharacteristic, complemented
163C22×C42—31no—
164C24×C3—21no—
165C24×C3—21no—
166C24×C3—31no—
167C24×C3—32no—
168C24×C3—31no—
169C24×C3—61no—
170C24×C3—61no—
171C24×C3C2×C3×C412yescomplemented
172C24×C3C23×C311yescharacteristic
173C23×D3—21no—
174C23×D3—21no—
175C23×D3—31no—
176C23×D3—31no—
177C23×D3—32no—
178C23×D3—61no—
179C23×D3—61no—
180C23×D3C2×C3×C412yescomplemented
181C22×A4—21no—
182C22×A4—21no—
183C22×A4—22no—
184C22×A4—21no—
185C22×A4—32no—
186C22×A4—41no—
187C22×A4—41no—
188C22×A4—61no—
189C22×A4—61no—
190C22×A4C4×D312yescomplemented
191C22×A4C22×D311yescharacteristic
192C2×C3×D4—121no—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—31no—
196C22×C3×C4—31no—
197C22×C3×C4—31no—
198C22×C3×C4—31no—
199C22×C3×C4—61no—
200C22×C3×C4—61no—
201C22×C3×C4—121no—
202C22×C3×C4—121no—
203C2×#67—32no—
204C2×#67—34no—
205C2×#67—34no—
206C2×#67—34no—
207C2×#67—31no—
208C2×#67—31no—
209C2×#67—34no—
210C2×#67—34no—
211C2×#67—34no—
212C2×#67—34no—
213C2×#67—34no—
214C2×#67—31no—
215C2×#67C2×A411yescharacteristic
216C22×Dic3—21no—
217C22×Dic3—31no—
218C22×Dic3—31no—
219C22×Dic3—31no—
220C22×Dic3—31no—
221C22×Dic3—32no—
222C22×Dic3—32no—
223C22×Dic3—32no—
224C22×Dic3—31no—
225C22×Dic3—31no—
226C22×Dic3—31no—
227C22×Dic3—31no—
228C22×Dic3—31no—
229C22×Dic3—62no—
230C22×Dic3—62no—
231C22×Dic3—62no—
232C22×Dic3—62no—
233C22×Dic3—62no—
234C22×Dic3—62no—
235C22×Dic3—62no—
236C22×Dic3—62no—
237C22×Dic3—61no—
238C22×Dic3C2×C3×C412yescomplemented
239C22×Dic3C3×D412yescomplemented
240C22×Dic3C2×A411yescharacteristic, complemented
241C2×C4×D3—32no—
242C2×C4×D3—31no—
243C2×C4×D3—31no—
244C2×C4×D3—31no—
245C2×C4×D3—62no—
246C2×C4×D3—62no—
247C2×C4×D3—62no—
248C2×C4×D3—62no—
249C2×C4×D3—62no—
250C2×C4×D3—62no—
251C2×C4×D3—62no—
252C2×C4×D3—62no—
253C2×C4×D3C2×A411yescharacteristic, complemented
254C4×A4—21no—
255C4×A4—21no—
256C4×A4—32no—
257C4×A4—32no—
258C4×A4—41no—
259C4×A4—41no—
260C4×A4—61no—
261C3×C4⋊C4—121no—
262C3×C22⋊C4—32no—
263C3×C22⋊C4—31no—
264C3×C22⋊C4—31no—
265C3×C22⋊C4—31no—
266C3×C22⋊C4—41no—
267C3×C22⋊C4—81no—
268C3×C22⋊C4—121no—
269C3×C22⋊C4C2×A411yescharacteristic, complemented
270C3×C42—121no—
271(C2×D3)⋊C4—32no—
272(C2×D3)⋊C4—31no—
273(C2×D3)⋊C4—31no—
274(C2×D3)⋊C4—31no—
275(C2×D3)⋊C4C2×A411yescharacteristic, complemented
276Dic3⋊C4—32no—
277Dic3⋊C4—31no—
278Dic3⋊C4—31no—
279Dic3⋊C4—31no—
280Dic3⋊C4C2×A411yescharacteristic, complemented
281C4×Dic3—32no—
282C4×Dic3—31no—
283C4×Dic3—31no—
284C4×Dic3—31no—
285C4×Dic3C2×A411yescharacteristic, complemented
286C22×C32—42no—
287C22×C32—41no—
288C22×C32—81no—
289C22×C32—81no—
290C2×C3×D3—42no—
291C2×C3×D3—81no—
292C2×C3×D3—81no—
293C3×A4C4×D411yescharacteristic, complemented
294C32×C4—81no—
295C32×C4—81no—
296C3×Dic3—42no—
297C3×Dic3—42no—
298C3×Dic3—81no—
299C25—31no—
300C25C2×C3×D311yescharacteristic
301C22×D4—34no—
302C22×D4—91no—
303C22×D4—91no—
304C22×D4—91no—
305C22×D4—91no—
306C22×D4—94no—
307C23×C4—31no—
308C23×C4—31no—
309C23×C4—31no—
310C23×C4—62no—
311C23×C4—62no—
312C23×C4—91no—
313C23×C4—91no—
314C23×C4—91no—
315C23×C4—91no—
316C23×C4—91no—
317C23×C4—91no—
318C23×C4—91no—
319C23×C4—91no—
320C23×C4—182no—
321C23×C4—182no—
322C23×C4C2×C3×D311yescharacteristic
323C23×C4C2×C3×D311yescharacteristic
324C4×D4—31no—
325C4×D4—91no—
326C4×D4—91no—
327C4×D4—91no—
328C4×D4—91no—
329C4×D4—91no—
330C4×D4—91no—
331C4×D4—92no—
332C4×D4—92no—
333C4×D4—92no—
334C4×D4—92no—
335C4×D4—92no—
336C4×D4—92no—
337C4×D4—92no—
338C4×D4—91no—
339C2×C4⋊C4—91no—
340C2×C4⋊C4—91no—
341C2×C4⋊C4—91no—
342C2×C4⋊C4—91no—
343C2×C22⋊C4—31no—
344C2×C22⋊C4—31no—
345C2×C22⋊C4—31no—
346C2×C22⋊C4—31no—
347C2×C22⋊C4—91no—
348C2×C22⋊C4—91no—
349C2×C22⋊C4—91no—
350C2×C22⋊C4—91no—
351C2×C42—91no—
352C2×C42—91no—
353C2×C42—91no—
354C2×C42—91no—
355C23×C3—22no—
356C23×C3—31no—
357C23×C3—31no—
358C23×C3—31no—
359C23×C3—31no—
360C23×C3—32no—
361C23×C3—32no—
362C23×C3—32no—
363C23×C3—32no—
364C23×C3—31no—
365C23×C3—41no—
366C23×C3—61no—
367C23×C3—61no—
368C23×C3—61no—
369C23×C3—61no—
370C23×C3—62no—
371C23×C3—61no—
372C23×C3—61no—
373C23×C3—62no—
374C23×C3—62no—
375C23×C3—61no—
376C23×C3—61no—
377C23×C3—64no—
378C23×C3—81no—
379C23×C3—121no—
380C23×C3C22×C3×C411yescharacteristic
381C23×C3C2×C3×D411yescharacteristic
382C23×C3C3×#4111yescharacteristic
383C23×C3C22×A411yescharacteristic
384C22×D3—22no—
385C22×D3—32no—
386C22×D3—31no—
387C22×D3—32no—
388C22×D3—32no—
389C22×D3—32no—
390C22×D3—61no—
391C22×D3—61no—
392C22×D3—61no—
393C22×D3—61no—
394C22×D3—64no—
395C22×D3—61no—
396C22×D3—61no—
397C22×D3—62no—
398C22×D3—62no—
399C22×D3—61no—
400C22×D3—61no—
401C22×D3—62no—
402C22×D3C22×A411yescharacteristic
403C2×A4—22no—
404C2×A4—21no—
405C2×A4—21no—
406C2×A4—21no—
407C2×A4—42no—
408C2×A4—62no—
409C2×A4C2×C4×D311yescharacteristic
410C2×A4D3×D411yescharacteristic
411C2×A4#23711yescharacteristic
412C3×D4—124no—
413C2×C3×C4—31no—
414C2×C3×C4—31no—
415C2×C3×C4—41no—
416C2×C3×C4—41no—
417C2×C3×C4—61no—
418C2×C3×C4—61no—
419C2×C3×C4—61no—
420C2×C3×C4—61no—
421C2×C3×C4—61no—
422C2×C3×C4—61no—
423C2×C3×C4—61no—
424C2×C3×C4—61no—
425C2×C3×C4—81no—
426C2×C3×C4—81no—
427C2×C3×C4—121no—
428C2×C3×C4—121no—
429C2×C3×C4—121no—
430C2×C3×C4—242no—
431C2×C3×C4—242no—
432C2×C3×C4C22×A411yescharacteristic
433C2×C3×C4C22×A411yescharacteristic
434#67—38no—
435#67—34no—
436#67—34no—
437#67—34no—
438#67C4×A414yescomplemented
439C2×Dic3—22no—
440C2×Dic3—32no—
441C2×Dic3—32no—
442C2×Dic3—31no—
443C2×Dic3—31no—
444C2×Dic3—32no—
445C2×Dic3—32no—
446C2×Dic3—32no—
447C2×Dic3—32no—
448C2×Dic3—32no—
449C2×Dic3—32no—
450C2×Dic3—31no—
451C2×Dic3—62no—
452C2×Dic3—61no—
453C2×Dic3—61no—
454C2×Dic3—62no—
455C2×Dic3—64no—
456C2×Dic3—62no—
457C2×Dic3—61no—
458C2×Dic3—61no—
459C2×Dic3C22×A411yescharacteristic
460C2×Dic3C22×A411yescharacteristic
461C2×Dic3C22×A411yescharacteristic
462C4×D3—22no—
463C4×D3—62no—
464C4×D3—62no—
465C4×D3—64no—
466C4×D3—62no—
467C2×C32—41no—
468C2×C32—41no—
469C2×C32—41no—
470C2×C32—82no—
471C3×D3—82no—
472C24—21no—
473C24—21no—
474C24—31no—
475C24—32no—
476C24—31no—
477C24—32no—
478C24—61no—
479C24—61no—
480C24—61no—
481C24—61no—
482C24—91no—
483C24—91no—
484C24—92no—
485C24—181no—
486C24—181no—
487C24C3×C4×D312yescomplemented
488C24C22×C3×D311yescharacteristic
489C2×D4—31no—
490C2×D4—91no—
491C2×D4—94no—
492C2×D4—94no—
493C2×D4—91no—
494C2×D4—92no—
495C2×D4—94no—
496C2×D4—94no—
497C2×D4—94no—
498C2×D4—91no—
499C2×D4—94no—
500C2×D4—94no—
501C2×D4—94no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—31no—
505C22×C4—31no—
506C22×C4—31no—
507C22×C4—31no—
508C22×C4—31no—
509C22×C4—31no—
510C22×C4—32no—
511C22×C4—32no—
512C22×C4—61no—
513C22×C4—61no—
514C22×C4—61no—
515C22×C4—91no—
516C22×C4—91no—
517C22×C4—91no—
518C22×C4—91no—
519C22×C4—91no—
520C22×C4—91no—
521C22×C4—91no—
522C22×C4—92no—
523C22×C4—91no—
524C22×C4—91no—
525C22×C4—92no—
526C22×C4—92no—
527C22×C4—92no—
528C22×C4—91no—
529C22×C4—91no—
530C22×C4—91no—
531C22×C4—182no—
532C22×C4—182no—
533C22×C4—182no—
534C22×C4—182no—
535C22×C4—182no—
536C22×C4—182no—
537C22×C4—182no—
538C22×C4—182no—
539C22×C4—182no—
540C22×C4—182no—
541C22×C4—182no—
542C22×C4—182no—
543C22×C4—182no—
544C22×C4—182no—
545C22×C4—182no—
546C22×C4—182no—
547C22×C4—181no—
548C4⋊C4—31no—
549C4⋊C4—91no—
550C4⋊C4—91no—
551C4⋊C4—92no—
552C4⋊C4—91no—
553C22⋊C4—32no—
554C22⋊C4—31no—
555C22⋊C4—31no—
556C22⋊C4—31no—
557C22⋊C4—31no—
558C22⋊C4—91no—
559C22⋊C4—91no—
560C22⋊C4—92no—
561C22⋊C4—91no—
562C22⋊C4D3×A411yescharacteristic, complemented
563C42—31no—
564C42—91no—
565C42—91no—
566C42—92no—
567C42—91no—
568C22×C3—21no—
569C22×C3—21no—
570C22×C3—31no—
571C22×C3—31no—
572C22×C3—31no—
573C22×C3—32no—
574C22×C3—31no—
575C22×C3—31no—
576C22×C3—31no—
577C22×C3—31no—
578C22×C3—31no—
579C22×C3—31no—
580C22×C3—32no—
581C22×C3—42no—
582C22×C3—41no—
583C22×C3—62no—
584C22×C3—62no—
585C22×C3—62no—
586C22×C3—62no—
587C22×C3—62no—
588C22×C3—62no—
589C22×C3—62no—
590C22×C3—62no—
591C22×C3—61no—
592C22×C3—61no—
593C22×C3—81no—
594C22×C3—81no—
595C22×C3—82no—
596C22×C3—81no—
597C22×C3—122no—
598C22×C3—161no—
599C22×C3—161no—
600C22×C3—241no—
601C22×C3—241no—
602C22×C3C3×C4×D411yescharacteristic, complemented
603C22×C3C2×C4×A412yescomplemented
604C22×C3C23×A411yescharacteristic
605C2×D3—21no—
606C2×D3—21no—
607C2×D3—32no—
608C2×D3—62no—
609C2×D3—62no—
610C2×D3—62no—
611C2×D3—62no—
612C2×D3—62no—
613C2×D3—62no—
614C2×D3—61no—
615C2×D3—61no—
616C2×D3—62no—
617C2×D3—62no—
618C2×D3C2×C4×A412yescomplemented
619A4—21no—
620A4#67⋊C411yescharacteristic, direct product factor
621C3×C4—21no—
622C3×C4—21no—
623C3×C4—61no—
624C3×C4—61no—
625C3×C4—81no—
626C3×C4—81no—
627C3×C4—122no—
628C3×C4—122no—
629C3×C4—161no—
630C3×C4—161no—
631C3×C4—241no—
632Dic3—21no—
633Dic3—32no—
634Dic3—32no—
635Dic3—61no—
636Dic3C2×C4×A412yescomplemented
637Dic3D4×A412yescomplemented
638C32—41noSylow
639C23—22no—
640C23—31no—
641C23—31no—
642C23—31no—
643C23—31no—
644C23—32no—
645C23—32no—
646C23—32no—
647C23—32no—
648C23—31no—
649C23—31no—
650C23—61no—
651C23—61no—
652C23—61no—
653C23—61no—
654C23—62no—
655C23—61no—
656C23—61no—
657C23—62no—
658C23—62no—
659C23—61no—
660C23—61no—
661C23—64no—
662C23—62no—
663C23—92no—
664C23—92no—
665C23—92no—
666C23—92no—
667C23—91no—
668C23—181no—
669C23—181no—
670C23—181no—
671C23—181no—
672C23—182no—
673C23—181no—
674C23—181no—
675C23—182no—
676C23—182no—
677C23—181no—
678C23—181no—
679C23—184no—
680C23C2×C3×C4×D311yescharacteristic
681C23C3×D3×D411yescharacteristic
682C23C3×#23711yescharacteristic
683C23C2×D3×A411yescharacteristic
684D4—34no—
685D4—94no—
686D4—94no—
687D4—98no—
688D4—94no—
689C2×C4—31no—
690C2×C4—31no—
691C2×C4—31no—
692C2×C4—31no—
693C2×C4—31no—
694C2×C4—62no—
695C2×C4—61no—
696C2×C4—61no—
697C2×C4—61no—
698C2×C4—61no—
699C2×C4—62no—
700C2×C4—61no—
701C2×C4—61no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—92no—
705C2×C4—92no—
706C2×C4—92no—
707C2×C4—92no—
708C2×C4—92no—
709C2×C4—92no—
710C2×C4—91no—
711C2×C4—91no—
712C2×C4—92no—
713C2×C4—92no—
714C2×C4—91no—
715C2×C4—182no—
716C2×C4—182no—
717C2×C4—182no—
718C2×C4—182no—
719C2×C4—182no—
720C2×C4—184no—
721C2×C4—181no—
722C2×C4—181no—
723C2×C4—182no—
724C2×C4—184no—
725C2×C4—181no—
726C2×C4—181no—
727C2×C4C2×D3×A411yescharacteristic
728C2×C4C2×D3×A411yescharacteristic
729C2×C3—22no—
730C2×C3—31no—
731C2×C3—31no—
732C2×C3—31no—
733C2×C3—31no—
734C2×C3—41no—
735C2×C3—41no—
736C2×C3—41no—
737C2×C3—62no—
738C2×C3—82no—
739C2×C3—81no—
740C2×C3—81no—
741C2×C3—81no—
742C2×C3—162no—
743C2×C3—242no—
744C2×C3C22×C4×A411yescharacteristic
745C2×C3C2×D4×A411yescharacteristic
746C2×C3A4×#4111yescharacteristic
747D3—22no—
748D3—62no—
749C22—21no—
750C22—21no—
751C22—31no—
752C22—31no—
753C22—31no—
754C22—32no—
755C22—31no—
756C22—31no—
757C22—31no—
758C22—31no—
759C22—31no—
760C22—31no—
761C22—32no—
762C22—32no—
763C22—62no—
764C22—62no—
765C22—62no—
766C22—62no—
767C22—62no—
768C22—62no—
769C22—62no—
770C22—62no—
771C22—61no—
772C22—61no—
773C22—61no—
774C22—61no—
775C22—92no—
776C22—182no—
777C22—182no—
778C22—182no—
779C22—182no—
780C22—182no—
781C22—182no—
782C22—182no—
783C22—182no—
784C22—181no—
785C22—181no—
786C22C3×#67⋊C411yescharacteristic, complemented
787C22C4×D3×A412yescomplemented
788C22C22×D3×A411yescharacteristic
789C4—21no—
790C4—21no—
791C4—32no—
792C4—32no—
793C4—61no—
794C4—61no—
795C4—61no—
796C4—92no—
797C4—92no—
798C4—181no—
799C3—41no—
800C3—81no—
801C3C4×D4×A411yescharacteristic, complemented
802C2—22no—
803C2—31no—
804C2—31no—
805C2—31no—
806C2—31no—
807C2—62no—
808C2—62no—
809C2—182no—
810C2C2×C4×D3×A411yescharacteristic
811C2D3×D4×A411yescharacteristic
812C2A4×#23711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×A4
commutatorC23×C3C22×C3×C4
FittingC22×C3×C22⋊C4C2×C3
socle, cosocleC24×C3C23×C3
prime radicalC2×A4×#67C2
hypercenterC22⋊C4D3×A4
hypocenterC22×C3C3×C4×D4
LCSG ▷ C23×C3 ▷ C22×C3
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×Dic3×A4C2semidirect
3. C2×C4×D3×A4C2semidirect
4. C3×A4×C22⋊C4C2semidirect
5. A4×(C2×D3)⋊C4C2semidirect
6. A4×Dic3⋊C4C2semidirect
7. C4×Dic3×A4C2semidirect
8. C22×#67⋊C4C3semidirect
14. A4×#67C4semidirect
22. C24×Dic3C2×C3semidirect
23. C23×C4×D3C2×C3semidirect
27. C22×C3×C22⋊C4C2×C3semidirect
28. C22×(C2×D3)⋊C4C2×C3semidirect
29. C22×Dic3⋊C4C2×C3semidirect
30. C22×C4×Dic3C2×C3semidirect
42. A4×C22⋊C4D3semidirect
46. C22×C3×A4C2×C4semidirect
50. C2×D3×A4C2×C4semidirect
57. Dic3×A4C2×C4semidirect
58. Dic3×A4D4semidirect
76. C22×#67C3×C4semidirect
133. #67⋊C4A4direct (N × H)
162. C22×C22⋊C4C3×D3semidirect
171. C24×C3C2×C3×C4semidirect
180. C23×D3C2×C3×C4semidirect
190. C22×A4C4×D3semidirect
238. C22×Dic3C2×C3×C4semidirect
239. C22×Dic3C3×D4semidirect
240. C22×Dic3C2×A4semidirect
253. C2×C4×D3C2×A4semidirect
269. C3×C22⋊C4C2×A4semidirect
275. (C2×D3)⋊C4C2×A4semidirect
280. Dic3⋊C4C2×A4semidirect
285. C4×Dic3C2×A4semidirect
293. C3×A4C4×D4semidirect
438. #67C4×A4semidirect
487. C24C3×C4×D3semidirect
562. C22⋊C4D3×A4semidirect
602. C22×C3C3×C4×D4semidirect
603. C22×C3C2×C4×A4semidirect
618. C2×D3C2×C4×A4semidirect
620. A4#67⋊C4direct (N × H)
636. Dic3C2×C4×A4semidirect
637. Dic3D4×A4semidirect
786. C22C3×#67⋊C4semidirect
787. C22C4×D3×A4semidirect
801. C3C4×D4×A4semidirect

Maximal subgroups

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

subgroupindex
C2×A4×#672
C22×Dic3×A42
C2×C4×D3×A42
C3×A4×C22⋊C42
A4×(C2×D3)⋊C42
A4×Dic3⋊C42
C4×Dic3×A42
C22×#67⋊C43
C4×D4×A43
C3×#67⋊C44