Finite Group Databasebeta

← #10727607

Subgroups — #10727607

Order 768.

2578 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×Dic3C211yesmaximal, characteristic, complemented
2C2×C3×#392C211yesmaximal, characteristic
3C2×#5220C212yesmaximal, complemented
4C2×#4953C211yesmaximal, characteristic, complemented
5C2×#4944C211yesmaximal, characteristic, complemented
6#72131C211yesmaximal, characteristic, complemented
7#72131C212yesmaximal, complemented
8#71547C212yesmaximal, complemented
9#71544C212yesmaximal, complemented
10#69423C211yesmaximal, characteristic, complemented
11#69402C211yesmaximal, characteristic, complemented
12#14795—31nomaximal, Sylow
13C23×C3×D4C2211yescharacteristic
14C23×C3×D4C2212yes—
15C24×Dic3C2212yes—
16C22×C3×C22⋊C4C2211yescharacteristic
17C22×C3×C22⋊C4C2212yes—
18C22×#217C2212yes—
19C22×#217C2212yes—
20C22×#217C2212yes—
21C22×#217C2211yescharacteristic
22C22×#217C2212yes—
23C22×#217C2211yescharacteristic
24C2×D4×Dic3—24no—
25C2×D4×Dic3—24no—
26C2×D4×Dic3—24no—
27C22×C4⋊Dic3C2211yescharacteristic
28C22×Dic3⋊C4C2211yescharacteristic
29C22×C4×Dic3C2211yescharacteristic
30C3×#392—24no—
31C2×C3×#95C2211yescharacteristic
32#5220—28no—
33C2×C3⋊#95C2212yes—
34C2×C3⋊#95C2212yes—
35C2×C3⋊#95C2211yescharacteristic
36C2×C3⋊#95C2212yes—
37C2×C3⋊#95C2211yescharacteristic
38C2×C3⋊#95C2211yescharacteristic
39C2×C3⋊#95C2212yes—
40C2×C3⋊#95C2212yes—
41#4953—24no—
42#4944—24no—
43C22×C4×D4—31no—
44C2×#397—31no—
45C2×#392D311yescharacteristic
46C2×#388—31no—
47C2×#386—32no—
48#1445—31no—
49#1439—32no—
50#1438—32no—
51#1438—31no—
52#1434—31no—
53C22⋊#95—32no—
54C25×C3C2311yescharacteristic
55C25×C3C2312yes—
56C22×C3×D4—24no—
57C22×C3×D4—24no—
58C22×C3×D4—24no—
59C22×C3×D4—24no—
60C22×C3×D4—24no—
61C22×C3×D4—24no—
62C22×C3×D4—22no—
63C22×C3×D4—22no—
64C22×C3×D4—24no—
65C22×C3×D4—42no—
66C22×C3×D4—42no—
67C22×C3×D4D414yes—
68C23×C3×C4C2311yescharacteristic
69C23×C3×C4C2312yes—
70C23×C3×C4C2311yescharacteristic
71C23×Dic3—24no—
72C23×Dic3—24no—
73C23×Dic3—24no—
74C23×Dic3—24no—
75C23×Dic3—24no—
76C23×Dic3—42no—
77C23×Dic3—42no—
78C23×Dic3C2312yes—
79C23×Dic3C2311yescharacteristic
80C23×Dic3C2312yes—
81C23×Dic3C2311yescharacteristic
82C23×Dic3C2311yescharacteristic
83C23×Dic3C2311yescharacteristic
84C2×C3×C22⋊C4—24no—
85C2×C3×C22⋊C4—22no—
86C2×C3×C22⋊C4—22no—
87C2×C3×C22⋊C4—22no—
88C2×C3×C22⋊C4—24no—
89C2×C3×C22⋊C4—42no—
90C2×#217—24no—
91C2×#217—22no—
92C2×#217—24no—
93C2×#217—24no—
94C2×#217—22no—
95C2×#217—24no—
96C2×#217—24no—
97C2×#217—24no—
98C2×#217—22no—
99C2×#217—24no—
100C2×#217—24no—
101C2×#217—42no—
102C2×#217—42no—
103C2×#217—42no—
104C2×#217—42no—
105C2×#217—42no—
106C2×#217D414yescomplemented
107D4×Dic3—232no—
108C2×C4⋊Dic3—22no—
109C2×C4⋊Dic3—22no—
110C2×C4⋊Dic3D414yescomplemented
111C2×Dic3⋊C4—22no—
112C2×Dic3⋊C4—42no—
113C2×C4×Dic3—22no—
114C2×C4×Dic3—22no—
115C2×C4×Dic3D414yescomplemented
116C3×#95—22no—
117C3⋊#95—22no—
118C3⋊#95—22no—
119C3⋊#95—24no—
120C3⋊#95—22no—
121C3⋊#95—24no—
122C3⋊#95—24no—
123C3⋊#95—24no—
124C3⋊#95—42no—
125C23×D4C2×D311yescharacteristic
126C23×D4C2×D312yes—
127C24×C4—32no—
128C2×C4×D4—64no—
129C2×C4×D4—64no—
130C2×C4×D4—64no—
131C22×C4⋊C4—31no—
132C22×C4⋊C4—31no—
133C22×C22⋊C4—31no—
134C22×C22⋊C4—32no—
135C22×C22⋊C4—32no—
136C22×C22⋊C4—32no—
137C22×C22⋊C4—32no—
138C22×C22⋊C4—31no—
139C22×C22⋊C4C2×D311yescharacteristic
140C22×C22⋊C4C2×D312yes—
141C22×C42—31no—
142#397—64no—
143#392—24no—
144#388—64no—
145#386—68no—
146C2×#95—32no—
147C2×#95—31no—
148C2×#95—31no—
149C2×#95—32no—
150C2×#95—32no—
151C2×#95—31no—
152C2×#95—32no—
153C2×#95—32no—
154C2×#95C2×D311yescharacteristic
155C24×C3—22no—
156C24×C3—22no—
157C24×C3—22no—
158C24×C3—22no—
159C24×C3—22no—
160C24×C3—22no—
161C24×C3—22no—
162C24×C3—22no—
163C24×C3—22no—
164C24×C3—22no—
165C24×C3—22no—
166C24×C3—22no—
167C24×C3—21no—
168C24×C3—21no—
169C24×C3—21no—
170C24×C3—21no—
171C24×C3—22no—
172C24×C3—22no—
173C24×C3—22no—
174C24×C3—21no—
175C24×C3—22no—
176C24×C3—21no—
177C24×C3C2×D412yes—
178C24×C3C2×D414yes—
179C24×C3#4114yes—
180C24×C3#4114yes—
181C24×C3C2411yescharacteristic
182C2×C3×D4—28no—
183C2×C3×D4—28no—
184C2×C3×D4—216no—
185C2×C3×D4—216no—
186C2×C3×D4—216no—
187C2×C3×D4—28no—
188C2×C3×D4—48no—
189C2×C3×D4—48no—
190C2×C3×D4—48no—
191C2×C3×D4—48no—
192C2×C3×D4—48no—
193C2×C3×D4—48no—
194C22×C3×C4—22no—
195C22×C3×C4—22no—
196C22×C3×C4—22no—
197C22×C3×C4—22no—
198C22×C3×C4—22no—
199C22×C3×C4—22no—
200C22×C3×C4—22no—
201C22×C3×C4—22no—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—22no—
206C22×C3×C4—22no—
207C22×C3×C4C2×D412yes—
208C22×C3×C4C2×D412yes—
209C22×C3×C4C2×D412yes—
210C22×C3×C4#4114yes—
211C22×Dic3—21no—
212C22×Dic3—21no—
213C22×Dic3—21no—
214C22×Dic3—21no—
215C22×Dic3—216no—
216C22×Dic3—21no—
217C22×Dic3—22no—
218C22×Dic3—21no—
219C22×Dic3—21no—
220C22×Dic3—22no—
221C22×Dic3—22no—
222C22×Dic3—22no—
223C22×Dic3—22no—
224C22×Dic3—21no—
225C22×Dic3—22no—
226C22×Dic3—22no—
227C22×Dic3—22no—
228C22×Dic3—22no—
229C22×Dic3—22no—
230C22×Dic3—21no—
231C22×Dic3—22no—
232C22×Dic3—22no—
233C22×Dic3—22no—
234C22×Dic3—22no—
235C22×Dic3—22no—
236C22×Dic3—22no—
237C22×Dic3—21no—
238C22×Dic3—22no—
239C22×Dic3—22no—
240C22×Dic3—21no—
241C22×Dic3—22no—
242C22×Dic3—48no—
243C22×Dic3—48no—
244C22×Dic3—48no—
245C22×Dic3—48no—
246C22×Dic3—48no—
247C22×Dic3—48no—
248C22×Dic3C2×D412yes—
249C22×Dic3C2×D414yes—
250C22×Dic3C2×D412yes—
251C22×Dic3C2×D412yes—
252C22×Dic3C2×D412yes—
253C22×Dic3#4112yes—
254C3×C22⋊C4—48no—
255C3×C22⋊C4—44no—
256#217—216no—
257#217—28no—
258#217—48no—
259#217—48no—
260#217—44no—
261#217—48no—
262C4⋊Dic3—28no—
263Dic3⋊C4—44no—
264C4×Dic3—28no—
265C25C22×D311yescharacteristic
266C25C22×D312yes—
267C22×D4—24no—
268C22×D4—24no—
269C22×D4—24no—
270C22×D4—24no—
271C22×D4—24no—
272C22×D4—24no—
273C22×D4—22no—
274C22×D4—22no—
275C22×D4—24no—
276C22×D4—42no—
277C22×D4—42no—
278C22×D4#6714yes—
279C23×C4—31no—
280C23×C4—31no—
281C23×C4—31no—
282C23×C4—32no—
283C23×C4—32no—
284C23×C4—31no—
285C23×C4—64no—
286C23×C4—64no—
287C23×C4—64no—
288C23×C4—64no—
289C23×C4—64no—
290C23×C4—122no—
291C23×C4—122no—
292C23×C4C22×D311yescharacteristic
293C23×C4C22×D312yes—
294C23×C4C22×D311yescharacteristic
295C4×D4—632no—
296C2×C4⋊C4—34no—
297C2×C4⋊C4—62no—
298C2×C4⋊C4—62no—
299C2×C4⋊C4—62no—
300C2×C4⋊C4—122no—
301C2×C22⋊C4—24no—
302C2×C22⋊C4—22no—
303C2×C22⋊C4—22no—
304C2×C22⋊C4—24no—
305C2×C22⋊C4—22no—
306C2×C22⋊C4—34no—
307C2×C22⋊C4—42no—
308C2×C22⋊C4—64no—
309C2×C22⋊C4—64no—
310C2×C22⋊C4—62no—
311C2×C22⋊C4—62no—
312C2×C22⋊C4—64no—
313C2×C22⋊C4—64no—
314C2×C22⋊C4—62no—
315C2×C22⋊C4—64no—
316C2×C22⋊C4—64no—
317C2×C22⋊C4—64no—
318C2×C22⋊C4—64no—
319C2×C22⋊C4—122no—
320C2×C22⋊C4—122no—
321C2×C22⋊C4—122no—
322C2×C22⋊C4—122no—
323C2×C22⋊C4—122no—
324C2×C42—34no—
325C2×C42—62no—
326C2×C42—62no—
327#95—22no—
328#95—64no—
329#95—64no—
330#95—62no—
331#95—64no—
332#95—62no—
333#95—62no—
334#95—64no—
335#95—122no—
336C23×C3—24no—
337C23×C3—24no—
338C23×C3—24no—
339C23×C3—24no—
340C23×C3—24no—
341C23×C3—24no—
342C23×C3—24no—
343C23×C3—24no—
344C23×C3—24no—
345C23×C3—24no—
346C23×C3—24no—
347C23×C3—24no—
348C23×C3—24no—
349C23×C3—24no—
350C23×C3—24no—
351C23×C3—24no—
352C23×C3—24no—
353C23×C3—24no—
354C23×C3—22no—
355C23×C3—24no—
356C23×C3—22no—
357C23×C3—22no—
358C23×C3—24no—
359C23×C3—42no—
360C23×C3—42no—
361C23×C3—42no—
362C23×C3—42no—
363C23×C3—42no—
364C23×C3—42no—
365C23×C3—42no—
366C23×C3—42no—
367C23×C3—42no—
368C23×C3—42no—
369C23×C3—42no—
370C23×C3—42no—
371C23×C3—42no—
372C23×C3—42no—
373C23×C3—42no—
374C23×C3—42no—
375C23×C3—41no—
376C23×C3—42no—
377C23×C3—41no—
378C23×C3—42no—
379C23×C3—41no—
380C23×C3—42no—
381C23×C3—41no—
382C23×C3—41no—
383C23×C3—41no—
384C23×C3—42no—
385C23×C3—42no—
386C23×C3—42no—
387C23×C3—41no—
388C23×C3—41no—
389C23×C3—42no—
390C23×C3—42no—
391C23×C3—42no—
392C23×C3—42no—
393C23×C3#12318yes—
394C23×C3C22×D411yescharacteristic
395C23×C3C22×D411yescharacteristic
396C23×C3C22×D411yescharacteristic
397C23×C3C22×D411yescharacteristic
398C23×C3C2×#4112yes—
399C23×C3C2×#4112yes—
400C23×C3C2×#4112yes—
401C23×C3C2×#4111yescharacteristic
402C23×C3H(5,𝔽2)11yescharacteristic
403C23×C3H(5,𝔽2)12yes—
404C23×C3H(5,𝔽2)11yescharacteristic
405C3×D4—232no—
406C3×D4—432no—
407C2×C3×C4—24no—
408C2×C3×C4—22no—
409C2×C3×C4—22no—
410C2×C3×C4—24no—
411C2×C3×C4—24no—
412C2×C3×C4—24no—
413C2×C3×C4—24no—
414C2×C3×C4—42no—
415C2×C3×C4—42no—
416C2×C3×C4—42no—
417C2×C3×C4—42no—
418C2×C3×C4—41no—
419C2×C3×C4—41no—
420C2×C3×C4—41no—
421C2×C3×C4—42no—
422C2×C3×C4—42no—
423C2×C3×C4#12014yes—
424C2×Dic3—22no—
425C2×Dic3—22no—
426C2×Dic3—22no—
427C2×Dic3—22no—
428C2×Dic3—22no—
429C2×Dic3—22no—
430C2×Dic3—22no—
431C2×Dic3—24no—
432C2×Dic3—22no—
433C2×Dic3—22no—
434C2×Dic3—22no—
435C2×Dic3—24no—
436C2×Dic3—24no—
437C2×Dic3—24no—
438C2×Dic3—432no—
439C2×Dic3—42no—
440C2×Dic3—41no—
441C2×Dic3—41no—
442C2×Dic3—42no—
443C2×Dic3—42no—
444C2×Dic3—42no—
445C2×Dic3—42no—
446C2×Dic3—42no—
447C2×Dic3—42no—
448C2×Dic3—41no—
449C2×Dic3—42no—
450C2×Dic3—42no—
451C2×Dic3—41no—
452C2×Dic3—41no—
453C2×Dic3—42no—
454C2×Dic3—42no—
455C2×Dic3—42no—
456C2×Dic3—42no—
457C2×Dic3—42no—
458C2×Dic3—42no—
459C2×Dic3—42no—
460C2×Dic3#12114yes—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24—22no—
472C24—22no—
473C24—21no—
474C24—21no—
475C24—22no—
476C24—22no—
477C24—22no—
478C24—22no—
479C24—21no—
480C24—21no—
481C24—21no—
482C24—21no—
483C24D3×D412yes—
484C24#23714yes—
485C24#23714yes—
486C24C2×#6714yes—
487C24C23×D311yescharacteristic
488C2×D4—28no—
489C2×D4—216no—
490C2×D4—28no—
491C2×D4—216no—
492C2×D4—216no—
493C2×D4—28no—
494C2×D4—48no—
495C2×D4—48no—
496C2×D4—48no—
497C2×D4—48no—
498C2×D4—48no—
499C2×D4—48no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—21no—
513C22×C4—32no—
514C22×C4—32no—
515C22×C4—32no—
516C22×C4—32no—
517C22×C4—34no—
518C22×C4—32no—
519C22×C4—61no—
520C22×C4—61no—
521C22×C4—61no—
522C22×C4—61no—
523C22×C4—616no—
524C22×C4—61no—
525C22×C4—62no—
526C22×C4—61no—
527C22×C4—62no—
528C22×C4—62no—
529C22×C4—62no—
530C22×C4—62no—
531C22×C4—62no—
532C22×C4—62no—
533C22×C4—61no—
534C22×C4—62no—
535C22×C4—62no—
536C22×C4—61no—
537C22×C4—62no—
538C22×C4—61no—
539C22×C4—62no—
540C22×C4—62no—
541C22×C4—62no—
542C22×C4—62no—
543C22×C4—62no—
544C22×C4—62no—
545C22×C4—61no—
546C22×C4—62no—
547C22×C4—62no—
548C22×C4—61no—
549C22×C4—62no—
550C22×C4—128no—
551C22×C4—128no—
552C22×C4—128no—
553C22×C4—128no—
554C22×C4—128no—
555C22×C4—128no—
556C22×C4D3×D412yes—
557C22×C4D3×D412yes—
558C22×C4#23714yes—
559C22×C4C2×#6712yes—
560C4⋊C4—68no—
561C4⋊C4—124no—
562C22⋊C4—48no—
563C22⋊C4—44no—
564C22⋊C4—68no—
565C22⋊C4—616no—
566C22⋊C4—128no—
567C22⋊C4—128no—
568C22⋊C4—124no—
569C22⋊C4—128no—
570C42—68no—
571C22×C3—28no—
572C22×C3—28no—
573C22×C3—28no—
574C22×C3—44no—
575C22×C3—44no—
576C22×C3—44no—
577C22×C3—44no—
578C22×C3—44no—
579C22×C3—44no—
580C22×C3—44no—
581C22×C3—44no—
582C22×C3—44no—
583C22×C3—44no—
584C22×C3—44no—
585C22×C3—44no—
586C22×C3—42no—
587C22×C3—42no—
588C22×C3—44no—
589C22×C3—44no—
590C22×C3—42no—
591C22×C3—81no—
592C22×C3—81no—
593C22×C3—81no—
594C22×C3—81no—
595C22×C3—82no—
596C22×C3—82no—
597C22×C3C2×#12011yescharacteristic
598C22×C3C2×#12111yescharacteristic
599C22×C3C2×#12312yes—
600C22×C3#52511yescharacteristic
601C22×C3#52511yescharacteristic
602C22×C3#52512yes—
603C22×C3#52512yes—
604C22×C3#52912yes—
605C22×C3#53211yescharacteristic
606C22×C3#53511yescharacteristic
607C22×C3#53511yescharacteristic
608C22×C3#53812yes—
609C22×C3#53812yes—
610C22×C3D4211yescharacteristic
611C22×C3D4211yescharacteristic
612C22×C3#54612yes—
613C22×C3#54611yescharacteristic
614C22×C3#54612yes—
615C22×C3#54611yescharacteristic
616C22×C3#55012yes—
617C22×C3#55112yes—
618C22×C3#55312yes—
619C22×C3#55312yes—
620C3×C4—24no—
621C3×C4—44no—
622C3×C4—81no—
623Dic3—24no—
624Dic3—44no—
625Dic3—42no—
626Dic3—42no—
627Dic3—81no—
628Dic3—82no—
629C23—24no—
630C23—24no—
631C23—24no—
632C23—24no—
633C23—24no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—22no—
648C23—24no—
649C23—24no—
650C23—22no—
651C23—22no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—41no—
669C23—41no—
670C23—42no—
671C23—42no—
672C23—41no—
673C23—42no—
674C23—41no—
675C23—41no—
676C23—42no—
677C23—41no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—41no—
683C23—41no—
684C23—42no—
685C23—42no—
686C23#93518yes—
687C23C2×D3×D411yescharacteristic
688C23C2×D3×D411yescharacteristic
689C23C2×D3×D411yescharacteristic
690C23C2×#23712yes—
691C23C2×#23712yes—
692C23C2×#23712yes—
693C23#100412yes—
694C23#100411yescharacteristic
695C23D3×#4111yescharacteristic
696C23#100911yescharacteristic
697C23C22×#6711yescharacteristic
698D4—232no—
699D4—432no—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—34no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—42no—
715C2×C4—41no—
716C2×C4—42no—
717C2×C4—62no—
718C2×C4—62no—
719C2×C4—62no—
720C2×C4—62no—
721C2×C4—62no—
722C2×C4—62no—
723C2×C4—62no—
724C2×C4—62no—
725C2×C4—62no—
726C2×C4—64no—
727C2×C4—64no—
728C2×C4—62no—
729C2×C4—64no—
730C2×C4—64no—
731C2×C4—1232no—
732C2×C4—121no—
733C2×C4—122no—
734C2×C4—122no—
735C2×C4—122no—
736C2×C4—122no—
737C2×C4—121no—
738C2×C4—122no—
739C2×C4—122no—
740C2×C4—122no—
741C2×C4—121no—
742C2×C4—122no—
743C2×C4—122no—
744C2×C4—122no—
745C2×C4—121no—
746C2×C4—122no—
747C2×C4—122no—
748C2×C4—121no—
749C2×C4—122no—
750C2×C4—122no—
751C2×C4—122no—
752C2×C4—122no—
753C2×C4#93714yes—
754C2×C3—48no—
755C2×C3—82no—
756C2×C3#239211yescharacteristic
757C2×C3#240811yescharacteristic
758C2×C3#241812yes—
759C2×C3#243111yescharacteristic
760C2×C3#244412yes—
761C2×C3#245612yes—
762C2×C3#246712yes—
763C2×C3#253511yescharacteristic
764C2×C3#260311yescharacteristic
765C2×C3#263111yescharacteristic
766C2×C3#284911yescharacteristic
767C22—28no—
768C22—28no—
769C22—28no—
770C22—44no—
771C22—44no—
772C22—44no—
773C22—44no—
774C22—44no—
775C22—44no—
776C22—44no—
777C22—44no—
778C22—44no—
779C22—44no—
780C22—44no—
781C22—44no—
782C22—42no—
783C22—44no—
784C22—42no—
785C22—44no—
786C22—42no—
787C22—82no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22—82no—
792C22—81no—
793C22#558612yes—
794C22#558611yescharacteristic
795C22#558612yes—
796C22#558611yescharacteristic
797C22#558712yes—
798C22#559112yes—
799C22#559312yes—
800C22#560012yes—
801C22#560112yes—
802C22D3×#12111yescharacteristic
803C22#560711yescharacteristic
804C22#560911yescharacteristic
805C22#561211yescharacteristic
806C22#561712yes—
807C22#561812yes—
808C22#571511yescharacteristic
809C22#571611yescharacteristic
810C22#571812yes—
811C22C2×#93512yes—
812C22C2×#93711yescharacteristic
813C22D4×#6711yescharacteristic
814C22#580612yes—
815C22#582911yescharacteristic
816C4—24no—
817C4—44no—
818C4—64no—
819C4—81no—
820C4—122no—
821C4—124no—
822C4—122no—
823C4—242no—
824C4—241no—
825C3#1479511yescharacteristic, complemented, Sylow
826C2—48no—
827C2—82no—
828C2#7666611yescharacteristic
829C2#7667512yes—
830C2#7668412yes—
831C2#7668611yescharacteristic
832C2#7669511yescharacteristic
833C2#7670011yescharacteristic
834C2#8258512yes—
835C2#8260211yescharacteristic
836C2#8264011yescharacteristic
837C2#8265612yes—
838C2#8318711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
Fitting, prime radicalC2×C3×#392C2
hypercenterC2×#392D3
hypocenterC3#14795
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C22×D4×Dic3C2semidirect
3. C2×#5220C2semidirect
4. C2×#4953C2semidirect
5. C2×#4944C2semidirect
6. #72131C2semidirect
7. #72131C2semidirect
8. #71547C2semidirect
9. #71544C2semidirect
10. #69423C2semidirect
11. #69402C2semidirect
106. C2×#217D4semidirect
110. C2×C4⋊Dic3D4semidirect
115. C2×C4×Dic3D4semidirect
825. C3#14795semidirect

Maximal subgroups

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

subgroupindex
C22×D4×Dic32
C2×C3×#3922
C2×#52202
C2×#49532
C2×#49442
#721312
#715472
#715442
#694232
#694022
#147953