Finite Group Databasebeta

← A4×#939 #11923352

Subgroups — A4×#939 #11923352

Order 1152.

1210 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 1210 conjugacy classes of subgroups — too many to draw. Only its 105 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×D4×A4C211yesmaximal, characteristic, complemented
2C2×A4×#67C211yesmaximal, characteristic, complemented
3C2×A4×#67C211yesmaximal, characteristic, complemented
4C22×Dic3×A4C211yesmaximal, characteristic, complemented
5A4×#217C211yesmaximal, characteristic, complemented
6A4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
7A4×Dic3⋊C4C211yesmaximal, characteristic, complemented
8C22×#939C311yesmaximal, characteristic, complemented
9A4×#121—31nomaximal
10C23×C3×A4C2211yescharacteristic
11C23×C3×A4C2211yescharacteristic
12C22×D3×A4C2211yescharacteristic
13C3×D4×A4—22no—
14C2×C3×C4×A4C2211yescharacteristic
15A4×#67—22no—
16A4×#67—22no—
17C2×Dic3×A4—22no—
18C2×Dic3×A4C2211yescharacteristic
19C2×Dic3×A4C2211yescharacteristic
20C2×Dic3×A4C2211yescharacteristic
21C3×#939—41nomaximal
22C23×C3×D4C2×C311yescharacteristic, complemented
23C23×#67C2×C311yescharacteristic, complemented
24C23×#67C2×C311yescharacteristic, complemented
25C24×Dic3C2×C311yescharacteristic, complemented
26C2×D4×A4—21no—
27C2×D4×A4—31no—
28C2×D4×A4—31no—
29C2×D4×A4D311yescharacteristic, complemented
30C22×C4×A4—31no—
31C22×#217C2×C311yescharacteristic, complemented
32C2×#939—31no—
33C2×#939—31no—
34C2×#939—31no—
35C2×#939—31no—
36C2×#939—31no—
37C2×#939—31no—
38C2×#939—31no—
39C2×#939—31no—
40C22×(C2×D3)⋊C4C2×C311yescharacteristic, complemented
41C22×Dic3⋊C4C2×C311yescharacteristic, complemented
42A4×C4⋊C4—31no—
43A4×C22⋊C4—31no—
44A4×C22⋊C4—31no—
45C22×C3×A4—21no—
46C22×C3×A4—21no—
47C22×C3×A4—21no—
48C22×C3×A4—21no—
49C22×C3×A4—21no—
50C22×C3×A4D412yescomplemented
51C22×C3×A4C2311yescharacteristic
52C2×D3×A4—21no—
53C2×D3×A4—21no—
54C2×D3×A4—21no—
55C2×C32×D4—41no—
56C2×C3×#67—41no—
57C2×C3×#67—41no—
58C22×C3×Dic3—41no—
59C3×C4×A4—21no—
60Dic3×A4—21no—
61Dic3×A4—21no—
62Dic3×A4D412yescomplemented
63C3×#217—41no—
64C3×(C2×D3)⋊C4—41no—
65C3×Dic3⋊C4—41no—
66C22×#121—31noSylow
67C25×C3C22×C311yescharacteristic
68C25×C3C22×C311yescharacteristic
69C24×D3C22×C311yescharacteristic
70C23×A4—21no—
71C23×A4—21no—
72C23×A4—31no—
73C23×A4C2×D311yescharacteristic
74C23×A4C2×D311yescharacteristic
75C22×C3×D4—22no—
76C22×C3×D4—31no—
77C22×C3×D4—31no—
78C22×C3×D4—31no—
79C22×C3×D4—31no—
80C22×C3×D4—62no—
81C23×C3×C4C22×C311yescharacteristic
82C22×#67—22no—
83C22×#67—22no—
84C22×#67—31no—
85C22×#67—31no—
86C22×#67—31no—
87C22×#67—31no—
88C22×#67—31no—
89C22×#67—31no—
90C22×#67—31no—
91C22×#67—31no—
92C22×#67—62no—
93C22×#67—62no—
94C23×Dic3—22no—
95C23×Dic3—31no—
96C23×Dic3—31no—
97C23×Dic3—31no—
98C23×Dic3—31no—
99C23×Dic3—62no—
100C23×Dic3C22×C311yescharacteristic
101C23×Dic3C22×C311yescharacteristic
102C23×Dic3C22×C311yescharacteristic
103D4×A4—24no—
104D4×A4—22no—
105D4×A4—62no—
106D4×A4—62no—
107C2×C4×A4—21no—
108C2×C4×A4—31no—
109C2×C4×A4—31no—
110C2×C4×A4—31no—
111C2×C4×A4—62no—
112C2×C4×A4C2×D311yescharacteristic
113C3×#121—121no—
114C2×#217—31no—
115C2×#217—31no—
116C2×#217—31no—
117C2×#217—31no—
118#939—32no—
119#939—32no—
120#939—32no—
121#939—32no—
122#939—32no—
123#939—32no—
124#939—32no—
125#939—31no—
126#939—31no—
127#939—31no—
128#939—31no—
129#939—31no—
130#939—31no—
131#939—31no—
132#939A411yescharacteristic, direct product factor
133C2×(C2×D3)⋊C4—31no—
134C2×(C2×D3)⋊C4—31no—
135C2×(C2×D3)⋊C4—31no—
136C2×(C2×D3)⋊C4—31no—
137C2×Dic3⋊C4—31no—
138C2×Dic3⋊C4—31no—
139C2×Dic3⋊C4—31no—
140C2×Dic3⋊C4—31no—
141C23×C32—41no—
142C23×C32—41no—
143C22×C3×D3—41no—
144C2×C3×A4—22no—
145C2×C3×A4—41no—
146C2×C3×A4C2×D411yescharacteristic
147C2×C3×A4C2×D411yescharacteristic
148C2×C3×A4#4111yescharacteristic
149D3×A4—41no—
150C32×D4—82no—
151C2×C32×C4—41no—
152C3×#67—82no—
153C3×#67—82no—
154C2×C3×Dic3—41no—
155C2×C3×Dic3—41no—
156C2×C3×Dic3—41no—
157C2×C3×Dic3—82no—
158C23×D4—31no—
159C23×D4—31no—
160C23×D4C3×D311yescharacteristic, complemented
161C24×C4—31no—
162C2×#121—91no—
163C2×#121—91no—
164C2×#121—91no—
165C2×#121—91no—
166C2×#121—91no—
167C2×#121—91no—
168C2×#121—91no—
169C2×#121—91no—
170C22×C4⋊C4—31no—
171C22×C22⋊C4—31no—
172C22×C22⋊C4—31no—
173C24×C3—21no—
174C24×C3—21no—
175C24×C3—21no—
176C24×C3—21no—
177C24×C3—21no—
178C24×C3—31no—
179C24×C3—32no—
180C24×C3—31no—
181C24×C3—31no—
182C24×C3—31no—
183C24×C3—61no—
184C24×C3—61no—
185C24×C3—61no—
186C24×C3—61no—
187C24×C3—61no—
188C24×C3C3×D412yescomplemented
189C24×C3C23×C311yescharacteristic
190C23×D3—21no—
191C23×D3—21no—
192C23×D3—21no—
193C23×D3—31no—
194C23×D3—31no—
195C23×D3—61no—
196C23×D3—61no—
197C23×D3—61no—
198C22×A4—21no—
199C22×A4—21no—
200C22×A4—22no—
201C22×A4—21no—
202C22×A4—21no—
203C22×A4—21no—
204C22×A4—22no—
205C22×A4—21no—
206C22×A4—41no—
207C22×A4—41no—
208C22×A4—41no—
209C22×A4—41no—
210C22×A4—61no—
211C22×A4—61no—
212C22×A4—61no—
213C22×A4#6712yescomplemented
214C22×A4C22×D311yescharacteristic
215C2×C3×D4—32no—
216C2×C3×D4—31no—
217C2×C3×D4—31no—
218C2×C3×D4—31no—
219C2×C3×D4—41no—
220C2×C3×D4—62no—
221C2×C3×D4—62no—
222C2×C3×D4—62no—
223C2×C3×D4—62no—
224C2×C3×D4—62no—
225C2×C3×D4—62no—
226C2×C3×D4—62no—
227C2×C3×D4—62no—
228C2×C3×D4—81no—
229C2×C3×D4—121no—
230C2×C3×D4—121no—
231C2×C3×D4C2×A411yescharacteristic, complemented
232C22×C3×C4—21no—
233C22×C3×C4—31no—
234C22×C3×C4—31no—
235C22×C3×C4—61no—
236C22×C3×C4—121no—
237C2×#67—32no—
238C2×#67—32no—
239C2×#67—31no—
240C2×#67—31no—
241C2×#67—31no—
242C2×#67—31no—
243C2×#67—31no—
244C2×#67—31no—
245C2×#67—62no—
246C2×#67—62no—
247C2×#67—62no—
248C2×#67—62no—
249C2×#67—62no—
250C2×#67—62no—
251C2×#67—62no—
252C2×#67—62no—
253C2×#67—62no—
254C2×#67—62no—
255C2×#67—62no—
256C2×#67—62no—
257C2×#67—62no—
258C2×#67—62no—
259C2×#67—62no—
260C2×#67—62no—
261C2×#67C2×A411yescharacteristic, complemented
262C2×#67C2×A411yescharacteristic, complemented
263C22×Dic3—21no—
264C22×Dic3—21no—
265C22×Dic3—31no—
266C22×Dic3—31no—
267C22×Dic3—32no—
268C22×Dic3—32no—
269C22×Dic3—31no—
270C22×Dic3—31no—
271C22×Dic3—31no—
272C22×Dic3—31no—
273C22×Dic3—31no—
274C22×Dic3—31no—
275C22×Dic3—31no—
276C22×Dic3—62no—
277C22×Dic3—62no—
278C22×Dic3—62no—
279C22×Dic3—62no—
280C22×Dic3—62no—
281C22×Dic3—62no—
282C22×Dic3—62no—
283C22×Dic3—62no—
284C22×Dic3—61no—
285C22×Dic3—61no—
286C22×Dic3C3×D412yescomplemented
287C22×Dic3C2×A411yescharacteristic, complemented
288C4×A4—22no—
289C4×A4—21no—
290C4×A4—32no—
291C4×A4—61no—
292C4×A4—61no—
293C3×C4⋊C4—121no—
294C3×C22⋊C4—121no—
295C3×C22⋊C4—121no—
296#217—32no—
297#217—31no—
298#217—31no—
299#217—31no—
300#217C2×A411yescharacteristic, complemented
301(C2×D3)⋊C4—32no—
302(C2×D3)⋊C4—31no—
303(C2×D3)⋊C4—31no—
304(C2×D3)⋊C4—31no—
305(C2×D3)⋊C4C2×A411yescharacteristic, complemented
306Dic3⋊C4—32no—
307Dic3⋊C4—31no—
308Dic3⋊C4—31no—
309Dic3⋊C4—31no—
310Dic3⋊C4C2×A411yescharacteristic, complemented
311C22×C32—42no—
312C22×C32—41no—
313C22×C32—81no—
314C22×C32—81no—
315C22×C32—81no—
316C22×C32—81no—
317C22×C32—81no—
318C2×C3×D3—81no—
319C2×C3×D3—81no—
320C2×C3×D3—81no—
321C3×A4#12111yescharacteristic, complemented
322C32×C4—81no—
323C3×Dic3—42no—
324C3×Dic3—81no—
325C3×Dic3—81no—
326C25—31no—
327C25C2×C3×D311yescharacteristic
328C25C2×C3×D311yescharacteristic
329C22×D4—22no—
330C22×D4—31no—
331C22×D4—31no—
332C22×D4—31no—
333C22×D4—31no—
334C22×D4—62no—
335C22×D4—62no—
336C22×D4—62no—
337C22×D4—91no—
338C22×D4—91no—
339C22×D4—91no—
340C22×D4—91no—
341C22×D4—91no—
342C22×D4—91no—
343C22×D4—91no—
344C22×D4—91no—
345C22×D4—182no—
346C22×D4—182no—
347C23×C4—31no—
348C23×C4—31no—
349C23×C4—31no—
350C23×C4—62no—
351C23×C4—91no—
352C23×C4—91no—
353C23×C4—91no—
354C23×C4—91no—
355C23×C4—182no—
356C23×C4C2×C3×D311yescharacteristic
357#121—31no—
358#121—91no—
359#121—91no—
360#121—91no—
361#121—91no—
362#121—91no—
363#121—91no—
364#121—92no—
365#121—92no—
366#121—92no—
367#121—92no—
368#121—92no—
369#121—92no—
370#121—92no—
371#121—91no—
372C2×C4⋊C4—91no—
373C2×C4⋊C4—91no—
374C2×C4⋊C4—91no—
375C2×C4⋊C4—91no—
376C2×C22⋊C4—91no—
377C2×C22⋊C4—91no—
378C2×C22⋊C4—91no—
379C2×C22⋊C4—91no—
380C2×C22⋊C4—91no—
381C2×C22⋊C4—91no—
382C2×C22⋊C4—91no—
383C2×C22⋊C4—91no—
384C23×C3—22no—
385C23×C3—31no—
386C23×C3—31no—
387C23×C3—31no—
388C23×C3—31no—
389C23×C3—32no—
390C23×C3—32no—
391C23×C3—32no—
392C23×C3—32no—
393C23×C3—31no—
394C23×C3—31no—
395C23×C3—41no—
396C23×C3—41no—
397C23×C3—41no—
398C23×C3—61no—
399C23×C3—61no—
400C23×C3—61no—
401C23×C3—61no—
402C23×C3—61no—
403C23×C3—61no—
404C23×C3—61no—
405C23×C3—61no—
406C23×C3—61no—
407C23×C3—61no—
408C23×C3—62no—
409C23×C3—61no—
410C23×C3—61no—
411C23×C3—62no—
412C23×C3—62no—
413C23×C3—61no—
414C23×C3—61no—
415C23×C3—64no—
416C23×C3—61no—
417C23×C3—61no—
418C23×C3—61no—
419C23×C3—61no—
420C23×C3—61no—
421C23×C3—61no—
422C23×C3—81no—
423C23×C3—81no—
424C23×C3—121no—
425C23×C3—121no—
426C23×C3—121no—
427C23×C3—121no—
428C23×C3—122no—
429C23×C3C2×C3×D411yescharacteristic
430C23×C3C2×C3×D411yescharacteristic
431C23×C3C3×#4111yescharacteristic
432C23×C3C22×A411yescharacteristic
433C23×C3C22×A411yescharacteristic
434C22×D3—31no—
435C22×D3—41no—
436C22×D3—61no—
437C22×D3—61no—
438C22×D3—61no—
439C22×D3—61no—
440C22×D3—61no—
441C22×D3—61no—
442C22×D3—61no—
443C22×D3—61no—
444C22×D3—61no—
445C22×D3—61no—
446C22×D3—61no—
447C22×D3—61no—
448C22×D3—122no—
449C22×D3—121no—
450C22×D3—121no—
451C22×D3—121no—
452C22×D3C22×A411yescharacteristic
453C2×A4—22no—
454C2×A4—21no—
455C2×A4—21no—
456C2×A4—21no—
457C2×A4—42no—
458C2×A4—42no—
459C2×A4—41no—
460C2×A4—121no—
461C2×A4D3×D411yescharacteristic
462C2×A4#23711yescharacteristic
463C2×A4C2×#6711yescharacteristic
464C3×D4—22no—
465C3×D4—62no—
466C3×D4—62no—
467C3×D4—64no—
468C3×D4—62no—
469C3×D4—82no—
470C3×D4—84no—
471C3×D4—242no—
472C3×D4—242no—
473C2×C3×C4—31no—
474C2×C3×C4—41no—
475C2×C3×C4—61no—
476C2×C3×C4—61no—
477C2×C3×C4—61no—
478C2×C3×C4—61no—
479C2×C3×C4—81no—
480C2×C3×C4—121no—
481C2×C3×C4—121no—
482C2×C3×C4—121no—
483C2×C3×C4—242no—
484C2×C3×C4C22×A411yescharacteristic
485#67—22no—
486#67—22no—
487#67—62no—
488#67—62no—
489#67—62no—
490#67—64no—
491#67—62no—
492#67—64no—
493#67—62no—
494#67—62no—
495C2×Dic3—22no—
496C2×Dic3—32no—
497C2×Dic3—31no—
498C2×Dic3—32no—
499C2×Dic3—32no—
500C2×Dic3—32no—
501C2×Dic3—31no—
502C2×Dic3—31no—
503C2×Dic3—62no—
504C2×Dic3—61no—
505C2×Dic3—61no—
506C2×Dic3—61no—
507C2×Dic3—61no—
508C2×Dic3—62no—
509C2×Dic3—64no—
510C2×Dic3—62no—
511C2×Dic3—61no—
512C2×Dic3—61no—
513C2×Dic3—61no—
514C2×Dic3—61no—
515C2×Dic3C22×A411yescharacteristic
516C2×Dic3C22×A411yescharacteristic
517C2×Dic3C22×A411yescharacteristic
518C2×C32—41no—
519C2×C32—41no—
520C2×C32—41no—
521C2×C32—82no—
522C2×C32—161no—
523C3×D3—161no—
524C24—21no—
525C24—21no—
526C24—21no—
527C24—21no—
528C24—21no—
529C24—31no—
530C24—32no—
531C24—31no—
532C24—31no—
533C24—31no—
534C24—61no—
535C24—61no—
536C24—61no—
537C24—61no—
538C24—61no—
539C24—61no—
540C24—61no—
541C24—61no—
542C24—91no—
543C24—91no—
544C24—181no—
545C24—181no—
546C24—181no—
547C24C3×#6712yescomplemented
548C24C22×C3×D311yescharacteristic
549C2×D4—32no—
550C2×D4—31no—
551C2×D4—31no—
552C2×D4—31no—
553C2×D4—31no—
554C2×D4—31no—
555C2×D4—62no—
556C2×D4—62no—
557C2×D4—62no—
558C2×D4—62no—
559C2×D4—62no—
560C2×D4—62no—
561C2×D4—62no—
562C2×D4—62no—
563C2×D4—91no—
564C2×D4—91no—
565C2×D4—91no—
566C2×D4—91no—
567C2×D4—92no—
568C2×D4—92no—
569C2×D4—91no—
570C2×D4—91no—
571C2×D4—182no—
572C2×D4—182no—
573C2×D4—182no—
574C2×D4—182no—
575C2×D4—182no—
576C2×D4—182no—
577C2×D4—182no—
578C2×D4—182no—
579C2×D4—182no—
580C2×D4—182no—
581C2×D4—182no—
582C2×D4—182no—
583C2×D4—182no—
584C2×D4—182no—
585C2×D4—182no—
586C2×D4—182no—
587C2×D4D3×A411yescharacteristic, complemented
588C22×C4—21no—
589C22×C4—31no—
590C22×C4—31no—
591C22×C4—31no—
592C22×C4—32no—
593C22×C4—61no—
594C22×C4—61no—
595C22×C4—61no—
596C22×C4—91no—
597C22×C4—91no—
598C22×C4—91no—
599C22×C4—91no—
600C22×C4—91no—
601C22×C4—91no—
602C22×C4—92no—
603C22×C4—92no—
604C22×C4—91no—
605C22×C4—91no—
606C22×C4—91no—
607C22×C4—182no—
608C22×C4—182no—
609C22×C4—182no—
610C22×C4—182no—
611C22×C4—182no—
612C22×C4—182no—
613C22×C4—182no—
614C22×C4—182no—
615C22×C4—181no—
616C22×C4—181no—
617C4⋊C4—31no—
618C4⋊C4—91no—
619C4⋊C4—91no—
620C4⋊C4—92no—
621C4⋊C4—91no—
622C22⋊C4—31no—
623C22⋊C4—31no—
624C22⋊C4—91no—
625C22⋊C4—91no—
626C22⋊C4—91no—
627C22⋊C4—91no—
628C22⋊C4—92no—
629C22⋊C4—92no—
630C22⋊C4—91no—
631C22⋊C4—91no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—31no—
638C22×C3—31no—
639C22×C3—31no—
640C22×C3—32no—
641C22×C3—31no—
642C22×C3—31no—
643C22×C3—31no—
644C22×C3—31no—
645C22×C3—31no—
646C22×C3—31no—
647C22×C3—32no—
648C22×C3—42no—
649C22×C3—41no—
650C22×C3—62no—
651C22×C3—62no—
652C22×C3—62no—
653C22×C3—62no—
654C22×C3—62no—
655C22×C3—62no—
656C22×C3—62no—
657C22×C3—62no—
658C22×C3—61no—
659C22×C3—61no—
660C22×C3—61no—
661C22×C3—61no—
662C22×C3—61no—
663C22×C3—81no—
664C22×C3—81no—
665C22×C3—81no—
666C22×C3—81no—
667C22×C3—81no—
668C22×C3—82no—
669C22×C3—82no—
670C22×C3—81no—
671C22×C3—121no—
672C22×C3—121no—
673C22×C3—121no—
674C22×C3—121no—
675C22×C3—121no—
676C22×C3—121no—
677C22×C3—121no—
678C22×C3—121no—
679C22×C3—161no—
680C22×C3—161no—
681C22×C3—161no—
682C22×C3—161no—
683C22×C3—241no—
684C22×C3—241no—
685C22×C3—241no—
686C22×C3C3×#12111yescharacteristic, complemented
687C22×C3D4×A412yescomplemented
688C22×C3C23×A411yescharacteristic
689C2×D3—21no—
690C2×D3—21no—
691C2×D3—21no—
692C2×D3—61no—
693C2×D3—61no—
694C2×D3—61no—
695C2×D3—121no—
696C2×D3—121no—
697C2×D3—121no—
698C2×D3—121no—
699C2×D3—121no—
700C2×D3—121no—
701C2×D3—121no—
702C2×D3—121no—
703A4—21no—
704A4#93911yescharacteristic, direct product factor
705C3×C4—21no—
706C3×C4—61no—
707C3×C4—81no—
708C3×C4—82no—
709C3×C4—122no—
710C3×C4—241no—
711C3×C4—241no—
712Dic3—21no—
713Dic3—21no—
714Dic3—32no—
715Dic3—61no—
716Dic3—61no—
717Dic3D4×A412yescomplemented
718C32—41noSylow
719C23—22no—
720C23—31no—
721C23—31no—
722C23—31no—
723C23—31no—
724C23—32no—
725C23—32no—
726C23—32no—
727C23—32no—
728C23—31no—
729C23—31no—
730C23—31no—
731C23—41no—
732C23—61no—
733C23—61no—
734C23—61no—
735C23—61no—
736C23—61no—
737C23—61no—
738C23—61no—
739C23—61no—
740C23—61no—
741C23—61no—
742C23—62no—
743C23—61no—
744C23—61no—
745C23—62no—
746C23—62no—
747C23—61no—
748C23—61no—
749C23—64no—
750C23—61no—
751C23—61no—
752C23—61no—
753C23—61no—
754C23—61no—
755C23—61no—
756C23—91no—
757C23—121no—
758C23—121no—
759C23—121no—
760C23—122no—
761C23—121no—
762C23—181no—
763C23—181no—
764C23—181no—
765C23—181no—
766C23—181no—
767C23—181no—
768C23—181no—
769C23—181no—
770C23—181no—
771C23—181no—
772C23—181no—
773C23—181no—
774C23—361no—
775C23—361no—
776C23—361no—
777C23—362no—
778C23C3×D3×D411yescharacteristic
779C23C3×#23711yescharacteristic
780C23C2×C3×#6711yescharacteristic
781C23C2×D3×A411yescharacteristic
782C23C2×D3×A411yescharacteristic
783D4—22no—
784D4—62no—
785D4—62no—
786D4—62no—
787D4—64no—
788D4—62no—
789D4—62no—
790D4—182no—
791D4—182no—
792D4—182no—
793D4—182no—
794D4—184no—
795D4—182no—
796D4—184no—
797D4—182no—
798C2×C4—31no—
799C2×C4—31no—
800C2×C4—31no—
801C2×C4—31no—
802C2×C4—61no—
803C2×C4—61no—
804C2×C4—62no—
805C2×C4—61no—
806C2×C4—61no—
807C2×C4—92no—
808C2×C4—92no—
809C2×C4—92no—
810C2×C4—91no—
811C2×C4—92no—
812C2×C4—91no—
813C2×C4—91no—
814C2×C4—182no—
815C2×C4—182no—
816C2×C4—181no—
817C2×C4—181no—
818C2×C4—181no—
819C2×C4—181no—
820C2×C4—182no—
821C2×C4—184no—
822C2×C4—181no—
823C2×C4—181no—
824C2×C4—181no—
825C2×C4—181no—
826C2×C4C2×D3×A411yescharacteristic
827C2×C3—22no—
828C2×C3—31no—
829C2×C3—31no—
830C2×C3—31no—
831C2×C3—31no—
832C2×C3—41no—
833C2×C3—41no—
834C2×C3—41no—
835C2×C3—41no—
836C2×C3—62no—
837C2×C3—82no—
838C2×C3—81no—
839C2×C3—81no—
840C2×C3—81no—
841C2×C3—121no—
842C2×C3—162no—
843C2×C3—161no—
844C2×C3—162no—
845C2×C3—481no—
846C2×C3C2×D4×A411yescharacteristic
847C2×C3C2×D4×A411yescharacteristic
848C2×C3A4×#4111yescharacteristic
849D3—41no—
850D3—121no—
851C22—21no—
852C22—21no—
853C22—21no—
854C22—21no—
855C22—21no—
856C22—31no—
857C22—31no—
858C22—31no—
859C22—32no—
860C22—31no—
861C22—31no—
862C22—31no—
863C22—31no—
864C22—31no—
865C22—31no—
866C22—32no—
867C22—62no—
868C22—62no—
869C22—62no—
870C22—62no—
871C22—62no—
872C22—62no—
873C22—62no—
874C22—62no—
875C22—61no—
876C22—61no—
877C22—61no—
878C22—61no—
879C22—61no—
880C22—61no—
881C22—61no—
882C22—61no—
883C22—121no—
884C22—121no—
885C22—121no—
886C22—121no—
887C22—121no—
888C22—121no—
889C22—121no—
890C22—121no—
891C22—181no—
892C22—181no—
893C22—181no—
894C22—361no—
895C22—361no—
896C22—361no—
897C22—361no—
898C22—361no—
899C22—361no—
900C22—361no—
901C22—361no—
902C22C3×#93911yescharacteristic, complemented
903C22A4×#6712yescomplemented
904C22C22×D3×A411yescharacteristic
905C4—21no—
906C4—32no—
907C4—61no—
908C4—61no—
909C4—61no—
910C4—92no—
911C4—181no—
912C4—181no—
913C3—41no—
914C3—81no—
915C3A4×#12111yescharacteristic, complemented
916C2—22no—
917C2—31no—
918C2—31no—
919C2—31no—
920C2—31no—
921C2—41no—
922C2—62no—
923C2—121no—
924C2—121no—
925C2—361no—
926C2D3×D4×A411yescharacteristic
927C2A4×#23711yescharacteristic
928C2C2×A4×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×A4
commutator, socle, cosocleC24×C3C23×C3
FittingC23×C3×D4C2×C3
hypercenterC2×D4D3×A4
hypocenterC22×C3C3×#121
LCSG ▷ C24×C3 ▷ C22×C3
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×D4×A4C2semidirect
2. C2×A4×#67C2semidirect
3. C2×A4×#67C2semidirect
4. C22×Dic3×A4C2semidirect
5. A4×#217C2semidirect
6. A4×(C2×D3)⋊C4C2semidirect
7. A4×Dic3⋊C4C2semidirect
8. C22×#939C3semidirect
22. C23×C3×D4C2×C3semidirect
23. C23×#67C2×C3semidirect
24. C23×#67C2×C3semidirect
25. C24×Dic3C2×C3semidirect
29. C2×D4×A4D3semidirect
31. C22×#217C2×C3semidirect
40. C22×(C2×D3)⋊C4C2×C3semidirect
41. C22×Dic3⋊C4C2×C3semidirect
50. C22×C3×A4D4semidirect
62. Dic3×A4D4semidirect
132. #939A4direct (N × H)
160. C23×D4C3×D3semidirect
188. C24×C3C3×D4semidirect
213. C22×A4#67semidirect
231. C2×C3×D4C2×A4semidirect
261. C2×#67C2×A4semidirect
262. C2×#67C2×A4semidirect
286. C22×Dic3C3×D4semidirect
287. C22×Dic3C2×A4semidirect
300. #217C2×A4semidirect
305. (C2×D3)⋊C4C2×A4semidirect
310. Dic3⋊C4C2×A4semidirect
321. C3×A4#121semidirect
547. C24C3×#67semidirect
587. C2×D4D3×A4semidirect
686. C22×C3C3×#121semidirect
687. C22×C3D4×A4semidirect
704. A4#939direct (N × H)
717. Dic3D4×A4semidirect
902. C22C3×#939semidirect
903. C22A4×#67semidirect
915. C3A4×#121semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D4×A42
C2×A4×#672
C22×Dic3×A42
A4×#2172
A4×(C2×D3)⋊C42
A4×Dic3⋊C42
C22×#9393
A4×#1213
C3×#9394