Finite Group Databasebeta

← #11711713

Subgroups — #11711713

Order 768.

1291 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 1291 conjugacy classes of subgroups — too many to draw. Only its 101 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
1C22×C4×S4C211yesmaximal, characteristic
2C2×(C2×S4)⋊C4C211yesmaximal, characteristic
3C2×(C2×S4)⋊C4C211yesmaximal, characteristic
4C2×C4⋊SL(2,ℤ/4)C211yesmaximal, characteristic, complemented
5C2×SL(2,ℤ/4)⋊C4C211yesmaximal, characteristic, complemented
6A4×#95C211yesmaximal, characteristic, complemented
7A4⋊#95C211yesmaximal, characteristic, complemented
8#13975—31nomaximal, Sylow
9C23×S4C2211yescharacteristic
10C22×C4×A4C2211yescharacteristic
11C22×C4×A4C2211yescharacteristic
12C22×C4×A4C2211yescharacteristic
13C22×SL(2,ℤ/4)C2211yescharacteristic
14C22×SL(2,ℤ/4)C2211yescharacteristic
15C22×SL(2,ℤ/4)C2211yescharacteristic
16C2×C4×S4—22no—
17C2×C4×S4—22no—
18C2×C4×S4—22no—
19(C2×S4)⋊C4—22no—
20(C2×S4)⋊C4C414yescomplemented
21C4⋊SL(2,ℤ/4)—22no—
22SL(2,ℤ/4)⋊C4—22no—
23#4668—41nomaximal
24C22×C4×D4—31no—
25C2×#386—31no—
26C2×#386—31no—
27C2×#385—31no—
28C2×#385—31no—
29C2×#380—31no—
30C22×#95D311yescharacteristic, complemented
31#1444—31no—
32#1442—31no—
33#1439—31no—
34#1439—31no—
35#1436—31no—
36#1436—31no—
37C22⋊#95—31no—
38C22⋊#95—31no—
39C23×A4C2311yescharacteristic
40C22×S4—21no—
41C22×S4—21no—
42C22×S4—21no—
43C22×S4—21no—
44C22×S4C2×C412yes—
45C22×S4D412yes—
46C22×S4Q812yes—
47C22×C4×D3—41no—
48C2×C4×A4—21no—
49C2×C4×A4—21no—
50C2×C4×A4—21no—
51C2×C4×A4—21no—
52C2×C4×A4—21no—
53C2×C4×A4—21no—
54C2×C4×A4—21no—
55C2×C4×A4C2×C412yescomplemented
56C2×C4×A4D412yes—
57C2×SL(2,ℤ/4)—21no—
58C2×SL(2,ℤ/4)—21no—
59C2×SL(2,ℤ/4)—21no—
60C2×SL(2,ℤ/4)—21no—
61C2×SL(2,ℤ/4)—21no—
62C2×SL(2,ℤ/4)—21no—
63C2×SL(2,ℤ/4)—21no—
64C2×SL(2,ℤ/4)C2×C412yescomplemented
65C2×SL(2,ℤ/4)D412yes—
66C4×S4—28no—
67C2×(C2×D3)⋊C4—41no—
68C2×(C2×D3)⋊C4—41no—
69C2×C4⋊Dic3—41no—
70C2×Dic3⋊C4—41no—
71C3×#95—41no—
72C3⋊#95—41no—
73C23×D4—31no—
74C24×C4—31no—
75C24×C4C2×D311yescharacteristic
76C24×C4C2×D311yescharacteristic
77C24×C4C2×D311yescharacteristic
78C2×C4×D4—62no—
79C2×C4×D4—62no—
80C2×C4×D4—62no—
81C2×C4×D4—62no—
82C2×C4×D4—62no—
83C2×C4×D4—62no—
84C22×C4⋊C4—31no—
85C22×C4⋊C4—31no—
86C22×C4⋊C4—31no—
87C22×C4⋊C4—31no—
88C22×C4⋊C4—31no—
89C22×C22⋊C4—31no—
90C22×C22⋊C4—31no—
91C22×C22⋊C4—31no—
92C22×C22⋊C4—31no—
93C22×C22⋊C4—31no—
94C22×C22⋊C4—31no—
95C22×C22⋊C4—31no—
96C22×C22⋊C4—31no—
97C22×C42—31no—
98#386—34no—
99#386—34no—
100#386—62no—
101#386—62no—
102#385—61no—
103#385—61no—
104#385—61no—
105#385—62no—
106#385—62no—
107#385—61no—
108#380—62no—
109#380—62no—
110C2×#95—31no—
111C2×#95—31no—
112C2×#95—31no—
113C2×#95—31no—
114C2×#95—31no—
115C2×#95—31no—
116C2×#95—31no—
117C2×#95—31no—
118C2×#95—31no—
119C2×#95—31no—
120C2×#95—31no—
121C2×#95—31no—
122C2×#95—31no—
123C2×#95—31no—
124C2×#95—31no—
125C2×#95—31no—
126C23×D3—41no—
127C22×A4C22×C411yescharacteristic
128C22×A4C2×D411yescharacteristic
129C22×A4C2×D411yescharacteristic
130C22×A4C2×D411yescharacteristic
131C22×A4C2×Q811yescharacteristic
132C22×A4#4111yescharacteristic
133C22×A4#4111yescharacteristic
134C2×S4—22no—
135C2×S4—22no—
136C2×S4—22no—
137C2×S4—22no—
138C2×S4—22no—
139C2×S4—22no—
140C2×S4C4⋊C414yescomplemented
141C22×C3×C4—41no—
142C22×C3×C4—41no—
143C22×C3×C4—41no—
144C22×Dic3—41no—
145C22×Dic3—41no—
146C22×Dic3—41no—
147C2×C4×D3—82no—
148C2×C4×D3—82no—
149C2×C4×D3—82no—
150C4×A4—22no—
151C4×A4—22no—
152C4×A4—41no—
153SL(2,ℤ/4)—22no—
154SL(2,ℤ/4)—22no—
155SL(2,ℤ/4)—41no—
156(C2×D3)⋊C4—44no—
157(C2×D3)⋊C4—82no—
158C4⋊Dic3—82no—
159Dic3⋊C4—82no—
160C25—31no—
161C25C22×D311yescharacteristic
162C22×D4—32no—
163C22×D4—32no—
164C22×D4—32no—
165C22×D4—32no—
166C22×D4—32no—
167C22×D4—32no—
168C22×D4—61no—
169C22×D4—61no—
170C22×D4—61no—
171C22×D4—61no—
172C22×D4—61no—
173C22×D4—61no—
174C22×D4—61no—
175C22×D4—61no—
176C23×C4—21no—
177C23×C4—21no—
178C23×C4—21no—
179C23×C4—21no—
180C23×C4—21no—
181C23×C4—21no—
182C23×C4—21no—
183C23×C4—31no—
184C23×C4—31no—
185C23×C4—31no—
186C23×C4—31no—
187C23×C4—31no—
188C23×C4—31no—
189C23×C4—32no—
190C23×C4—32no—
191C23×C4—31no—
192C23×C4—31no—
193C23×C4—31no—
194C23×C4—31no—
195C23×C4—31no—
196C23×C4—31no—
197C23×C4—31no—
198C23×C4—61no—
199C23×C4—62no—
200C23×C4—62no—
201C23×C4—62no—
202C23×C4—61no—
203C23×C4—61no—
204C23×C4—61no—
205C23×C4—61no—
206C23×C4—61no—
207C23×C4—62no—
208C23×C4—61no—
209C23×C4—61no—
210C23×C4—61no—
211C23×C4—121no—
212C23×C4—121no—
213C23×C4C4×D312yescomplemented
214C23×C4D1212yes—
215C4×D4—68no—
216C4×D4—68no—
217C4×D4—68no—
218C4×D4—68no—
219C2×C4⋊C4—62no—
220C2×C4⋊C4—62no—
221C2×C4⋊C4—62no—
222C2×C4⋊C4—62no—
223C2×C4⋊C4—62no—
224C2×C4⋊C4—62no—
225C2×C4⋊C4—62no—
226C2×C4⋊C4—61no—
227C2×C4⋊C4—62no—
228C2×C4⋊C4—61no—
229C2×C4⋊C4—62no—
230C2×C4⋊C4—61no—
231C2×C4⋊C4—61no—
232C2×C4⋊C4—121no—
233C2×C4⋊C4—121no—
234C2×C4⋊C4—121no—
235C2×C4⋊C4—121no—
236C2×C22⋊C4—32no—
237C2×C22⋊C4—34no—
238C2×C22⋊C4—32no—
239C2×C22⋊C4—32no—
240C2×C22⋊C4—32no—
241C2×C22⋊C4—34no—
242C2×C22⋊C4—62no—
243C2×C22⋊C4—62no—
244C2×C22⋊C4—62no—
245C2×C22⋊C4—61no—
246C2×C22⋊C4—61no—
247C2×C22⋊C4—61no—
248C2×C22⋊C4—61no—
249C2×C22⋊C4—62no—
250C2×C22⋊C4—61no—
251C2×C22⋊C4—61no—
252C2×C22⋊C4—61no—
253C2×C22⋊C4—61no—
254C2×C22⋊C4—61no—
255C2×C22⋊C4—61no—
256C2×C22⋊C4—62no—
257C2×C22⋊C4—61no—
258C2×C22⋊C4—61no—
259C2×C22⋊C4—61no—
260C2×C22⋊C4—62no—
261C2×C22⋊C4—62no—
262C2×C22⋊C4—61no—
263C2×C22⋊C4—61no—
264C2×C22⋊C4—61no—
265C2×C22⋊C4—61no—
266C2×C22⋊C4—61no—
267C2×C22⋊C4—121no—
268C2×C22⋊C4—121no—
269C2×C22⋊C4—121no—
270C2×C22⋊C4—121no—
271C2×C42—62no—
272C2×C42—62no—
273C2×C42—62no—
274#95—34no—
275#95—34no—
276#95—31no—
277#95—31no—
278#95—31no—
279#95—61no—
280#95—62no—
281#95—62no—
282#95—62no—
283#95—62no—
284#95—62no—
285#95—61no—
286#95—62no—
287#95—62no—
288#95—61no—
289#95—121no—
290#95—121no—
291#95S411yescharacteristic, complemented
292C23×C3—41no—
293C22×D3—42no—
294C22×D3—42no—
295C22×D3—42no—
296C22×D3—81no—
297C22×D3—81no—
298C22×D3—81no—
299C22×D3—81no—
300C2×A4C2×C4⋊C411yescharacteristic
301C2×A4C4×D411yescharacteristic
302C2×A4C4×D411yescharacteristic
303C2×A4#12011yescharacteristic
304C2×A4C22⋊Q811yescharacteristic
305C2×A4C22⋊Q811yescharacteristic
306C2×A4#12311yescharacteristic
307S4—24no—
308C2×C3×C4—42no—
309C2×C3×C4—42no—
310C2×C3×C4—81no—
311C2×C3×C4—81no—
312C2×C3×C4—81no—
313C2×C3×C4—81no—
314C2×C3×C4—81no—
315C2×C3×C4—81no—
316C2×C3×C4—81no—
317C2×Dic3—42no—
318C2×Dic3—42no—
319C2×Dic3—81no—
320C2×Dic3—81no—
321C2×Dic3—81no—
322C2×Dic3—81no—
323C2×Dic3—81no—
324C2×Dic3—81no—
325C2×Dic3—81no—
326C4×D3—88no—
327C24—31no—
328C24—31no—
329C24—31no—
330C24—31no—
331C24—31no—
332C24—31no—
333C24—31no—
334C24—31no—
335C24—32no—
336C24—32no—
337C24—32no—
338C24—61no—
339C24—61no—
340C24—61no—
341C24—61no—
342C24—61no—
343C24—61no—
344C24—61no—
345C24—61no—
346C24—61no—
347C24—61no—
348C24—61no—
349C24—61no—
350C24C2×C4×D311yescharacteristic
351C24C2×D1211yescharacteristic
352C24#23511yescharacteristic
353C24D3×D411yescharacteristic
354C24D3×D411yescharacteristic
355C24#23711yescharacteristic
356C24D3×Q811yescharacteristic
357C2×D4—34no—
358C2×D4—34no—
359C2×D4—34no—
360C2×D4—34no—
361C2×D4—62no—
362C2×D4—62no—
363C2×D4—62no—
364C2×D4—62no—
365C2×D4—62no—
366C2×D4—62no—
367C2×D4—62no—
368C2×D4—62no—
369C2×D4—62no—
370C2×D4—62no—
371C2×D4—62no—
372C2×D4—62no—
373C2×D4—62no—
374C2×D4—62no—
375C2×D4—62no—
376C2×D4—62no—
377C2×D4—62no—
378C2×D4—62no—
379C2×D4—62no—
380C2×D4—62no—
381C2×D4—62no—
382C2×D4—62no—
383C2×D4—62no—
384C2×D4—62no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—32no—
388C22×C4—32no—
389C22×C4—32no—
390C22×C4—31no—
391C22×C4—31no—
392C22×C4—32no—
393C22×C4—32no—
394C22×C4—32no—
395C22×C4—32no—
396C22×C4—32no—
397C22×C4—32no—
398C22×C4—32no—
399C22×C4—32no—
400C22×C4—32no—
401C22×C4—32no—
402C22×C4—32no—
403C22×C4—31no—
404C22×C4—41no—
405C22×C4—61no—
406C22×C4—61no—
407C22×C4—61no—
408C22×C4—61no—
409C22×C4—61no—
410C22×C4—61no—
411C22×C4—61no—
412C22×C4—61no—
413C22×C4—61no—
414C22×C4—61no—
415C22×C4—61no—
416C22×C4—61no—
417C22×C4—61no—
418C22×C4—61no—
419C22×C4—61no—
420C22×C4—61no—
421C22×C4—61no—
422C22×C4—61no—
423C22×C4—61no—
424C22×C4—61no—
425C22×C4—62no—
426C22×C4—62no—
427C22×C4—61no—
428C22×C4—61no—
429C22×C4—61no—
430C22×C4—61no—
431C22×C4—61no—
432C22×C4—61no—
433C22×C4—61no—
434C22×C4—61no—
435C22×C4—61no—
436C22×C4—61no—
437C22×C4—62no—
438C22×C4—62no—
439C22×C4—62no—
440C22×C4—62no—
441C22×C4—61no—
442C22×C4—61no—
443C22×C4—61no—
444C22×C4—61no—
445C22×C4—61no—
446C22×C4—61no—
447C22×C4—61no—
448C22×C4—61no—
449C22×C4—61no—
450C22×C4—61no—
451C22×C4—61no—
452C22×C4—61no—
453C22×C4—61no—
454C22×C4—61no—
455C22×C4—61no—
456C22×C4—61no—
457C22×C4—61no—
458C22×C4—61no—
459C22×C4—61no—
460C22×C4—61no—
461C22×C4—61no—
462C22×C4—61no—
463C22×C4—61no—
464C22×C4—61no—
465C22×C4—68no—
466C22×C4—61no—
467C22×C4—61no—
468C22×C4—61no—
469C22×C4—61no—
470C22×C4—61no—
471C22×C4—61no—
472C22×C4—61no—
473C22×C4—61no—
474C22×C4—61no—
475C22×C4—61no—
476C22×C4—61no—
477C22×C4—61no—
478C22×C4—61no—
479C22×C4—61no—
480C22×C4—61no—
481C22×C4—61no—
482C22×C4—61no—
483C22×C4—122no—
484C22×C4—122no—
485C22×C4—122no—
486C22×C4—122no—
487C22×C4—122no—
488C22×C4—122no—
489C22×C4—124no—
490C22×C4—122no—
491C22×C4—121no—
492C22×C4—121no—
493C22×C4—124no—
494C22×C4—122no—
495C22×C4—124no—
496C22×C4—122no—
497C22×C4—121no—
498C22×C4C2×S411yescharacteristic
499C22×C4C2×S411yescharacteristic
500C22×C4C2×S411yescharacteristic
501C4⋊C4—68no—
502C4⋊C4—122no—
503C4⋊C4—122no—
504C4⋊C4—124no—
505C4⋊C4—122no—
506C4⋊C4—124no—
507C4⋊C4—122no—
508C22⋊C4—64no—
509C22⋊C4—62no—
510C22⋊C4—62no—
511C22⋊C4—62no—
512C22⋊C4—62no—
513C22⋊C4—62no—
514C22⋊C4—62no—
515C22⋊C4—68no—
516C22⋊C4—62no—
517C22⋊C4—62no—
518C22⋊C4—64no—
519C22⋊C4—122no—
520C22⋊C4—124no—
521C22⋊C4—124no—
522C22⋊C4—122no—
523C22⋊C4—121no—
524C22⋊C4—121no—
525C22⋊C4—121no—
526C22⋊C4—121no—
527C42—68no—
528C22×C3—41no—
529C22×C3—41no—
530C22×C3—41no—
531C22×C3—41no—
532C22×C3—41no—
533C22×C3—41no—
534C22×C3—41no—
535C2×D3—44no—
536C2×D3—82no—
537C2×D3—82no—
538C2×D3—82no—
539C2×D3—82no—
540C2×D3—82no—
541C2×D3—82no—
542A4#38511yescharacteristic, complemented
543C3×C4—82no—
544C3×C4—82no—
545C3×C4—161no—
546Dic3—82no—
547Dic3—82no—
548Dic3—161no—
549C23—31no—
550C23—31no—
551C23—31no—
552C23—31no—
553C23—31no—
554C23—31no—
555C23—31no—
556C23—31no—
557C23—31no—
558C23—31no—
559C23—31no—
560C23—31no—
561C23—31no—
562C23—31no—
563C23—31no—
564C23—31no—
565C23—31no—
566C23—31no—
567C23—31no—
568C23—31no—
569C23—31no—
570C23—31no—
571C23—31no—
572C23—31no—
573C23—31no—
574C23—31no—
575C23—31no—
576C23—31no—
577C23—31no—
578C23—31no—
579C23—31no—
580C23—31no—
581C23—31no—
582C23—31no—
583C23—31no—
584C23—34no—
585C23—61no—
586C23—61no—
587C23—61no—
588C23—61no—
589C23—61no—
590C23—61no—
591C23—61no—
592C23—62no—
593C23—62no—
594C23—62no—
595C23—62no—
596C23—62no—
597C23—62no—
598C23—62no—
599C23—62no—
600C23—62no—
601C23—62no—
602C23—62no—
603C23—62no—
604C23—62no—
605C23—62no—
606C23—62no—
607C23—62no—
608C23—62no—
609C23—62no—
610C23—121no—
611C23—121no—
612C23—121no—
613C23—121no—
614C23—121no—
615C23—121no—
616C23—121no—
617C23—121no—
618C23—121no—
619C23—121no—
620C23—121no—
621C23—121no—
622C23—121no—
623C23—121no—
624C23—121no—
625C23—121no—
626C23C4×D1211yescharacteristic
627C23#67⋊C411yescharacteristic
628C23#88211yescharacteristic
629C23#88311yescharacteristic
630C23D3×C4⋊C411yescharacteristic
631C23#89611yescharacteristic
632C23#89711yescharacteristic
633C23C22×S411yescharacteristic
634D4—64no—
635D4—64no—
636D4—64no—
637D4—64no—
638D4—64no—
639D4—64no—
640D4—64no—
641D4—64no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—34no—
650C2×C4—32no—
651C2×C4—32no—
652C2×C4—62no—
653C2×C4—62no—
654C2×C4—62no—
655C2×C4—62no—
656C2×C4—62no—
657C2×C4—62no—
658C2×C4—62no—
659C2×C4—62no—
660C2×C4—62no—
661C2×C4—62no—
662C2×C4—62no—
663C2×C4—62no—
664C2×C4—62no—
665C2×C4—62no—
666C2×C4—61no—
667C2×C4—61no—
668C2×C4—61no—
669C2×C4—61no—
670C2×C4—62no—
671C2×C4—62no—
672C2×C4—62no—
673C2×C4—62no—
674C2×C4—62no—
675C2×C4—62no—
676C2×C4—62no—
677C2×C4—62no—
678C2×C4—62no—
679C2×C4—62no—
680C2×C4—62no—
681C2×C4—62no—
682C2×C4—62no—
683C2×C4—62no—
684C2×C4—62no—
685C2×C4—62no—
686C2×C4—62no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—62no—
690C2×C4—61no—
691C2×C4—128no—
692C2×C4—121no—
693C2×C4—121no—
694C2×C4—121no—
695C2×C4—121no—
696C2×C4—121no—
697C2×C4—121no—
698C2×C4—121no—
699C2×C4—121no—
700C2×C4—128no—
701C2×C4—121no—
702C2×C4—121no—
703C2×C4—121no—
704C2×C4—121no—
705C2×C4—121no—
706C2×C4—121no—
707C2×C4—121no—
708C2×C4—121no—
709C2×C4—121no—
710C2×C4—121no—
711C2×C4—121no—
712C2×C4—121no—
713C2×C4—121no—
714C2×C4—121no—
715C2×C4—121no—
716C2×C4—121no—
717C2×C4—121no—
718C2×C4—121no—
719C2×C4—121no—
720C2×C4—121no—
721C2×C4—121no—
722C2×C4—121no—
723C2×C4—121no—
724C2×C4—121no—
725C2×C4—121no—
726C2×C4—121no—
727C2×C4—121no—
728C2×C4—121no—
729C2×C4—121no—
730C2×C4—121no—
731C2×C4—121no—
732C2×C4—121no—
733C2×C4C4×S412yescomplemented
734C2×C4C4⋊S412yes—
735C2×C3—41no—
736C2×C3—41no—
737C2×C3—41no—
738C2×C3—41no—
739C2×C3—41no—
740C2×C3—41no—
741C2×C3—41no—
742D3—84no—
743C22—31no—
744C22—31no—
745C22—31no—
746C22—31no—
747C22—31no—
748C22—31no—
749C22—31no—
750C22—31no—
751C22—31no—
752C22—31no—
753C22—31no—
754C22—31no—
755C22—31no—
756C22—31no—
757C22—31no—
758C22—31no—
759C22—31no—
760C22—31no—
761C22—31no—
762C22—31no—
763C22—31no—
764C22—31no—
765C22—31no—
766C22—31no—
767C22—31no—
768C22—31no—
769C22—31no—
770C22—31no—
771C22—31no—
772C22—31no—
773C22—31no—
774C22—31no—
775C22—31no—
776C22—31no—
777C22—31no—
778C22—61no—
779C22—61no—
780C22—61no—
781C22—61no—
782C22—61no—
783C22—61no—
784C22—61no—
785C22—64no—
786C22—64no—
787C22—64no—
788C22—122no—
789C22—122no—
790C22—122no—
791C22—122no—
792C22—122no—
793C22—122no—
794C22—122no—
795C22—122no—
796C22—122no—
797C22—122no—
798C22—122no—
799C22—122no—
800C22#466811yescharacteristic, complemented
801C22C2×C4×S411yescharacteristic
802C22C2×C4⋊S411yescharacteristic
803C22#591211yescharacteristic
804C22D4×S411yescharacteristic
805C22D4×S411yescharacteristic
806C22#591411yescharacteristic
807C22Q8×S411yescharacteristic
808C4—22no—
809C4—22no—
810C4—41no—
811C4—64no—
812C4—62no—
813C4—62no—
814C4—122no—
815C4—122no—
816C4—122no—
817C4—122no—
818C4—121no—
819C4—241no—
820C4—241no—
821C3—41noSylow
822C2—31no—
823C2—31no—
824C2—31no—
825C2—31no—
826C2—31no—
827C2—31no—
828C2—31no—
829C2—31no—
830C2—124no—
831C2C4×C4⋊S411yescharacteristic
832C2GL(2,ℤ/4)⋊C411yescharacteristic
833C2#8529711yescharacteristic
834C2#8529811yescharacteristic
835C2C4⋊C4×S411yescharacteristic
836C2#8531111yescharacteristic
837C2#8531211yescharacteristic
subgroupG/H
center, FrattiniC23C22×S4
commutatorC22×A4C22×C4
FittingC22×#95D3
socleC25C22×D3
prime radicalC23×S4C22
cosocleC23×A4C23
hypercenter#95S4
hypocenterA4#385
LCSG ▷ C22×A4 ▷ A4
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
4. C2×C4⋊SL(2,ℤ/4)C2semidirect
5. C2×SL(2,ℤ/4)⋊C4C2semidirect
6. A4×#95C2semidirect
7. A4⋊#95C2semidirect
20. (C2×S4)⋊C4C4semidirect
30. C22×#95D3semidirect
55. C2×C4×A4C2×C4semidirect
64. C2×SL(2,ℤ/4)C2×C4semidirect
140. C2×S4C4⋊C4semidirect
213. C23×C4C4×D3semidirect
291. #95S4semidirect
542. A4#385semidirect
733. C2×C4C4×S4semidirect
800. C22#4668semidirect

Maximal subgroups

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

subgroupindex
C22×C4×S42
C2×(C2×S4)⋊C42
C2×C4⋊SL(2,ℤ/4)2
C2×SL(2,ℤ/4)⋊C42
A4×#952
A4⋊#952
#139753
#46684