Finite Group Databasebeta

← #10727612

Subgroups — #10727612

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×C3×C4×D4C211yesmaximal, characteristic, complemented
2C2×#5223C211yesmaximal, characteristic
3C2×#5213C212yesmaximal, complemented
4C2×#4992C211yesmaximal, characteristic, complemented
5C2×#4940C211yesmaximal, characteristic, complemented
6#72131C211yesmaximal, characteristic, complemented
7#72127C212yesmaximal, complemented
8#71569C211yesmaximal, characteristic, complemented
9#71550C212yesmaximal, complemented
10#71547C212yesmaximal, complemented
11#71534C211yesmaximal, characteristic, complemented
12#14795—31nomaximal, Sylow
13C23×C3×D4C2211yescharacteristic
14C24×C3×C4C2212yes—
15C23×#67C2212yes—
16C2×C3×C4×D4—24no—
17C2×C3×C4×D4—24no—
18C2×C3×C4×D4—24no—
19C22×C3×C4⋊C4C2211yescharacteristic
20C22×C3×C22⋊C4C2212yes—
21C22×C3×C42C2211yescharacteristic
22C22×#217C2212yes—
23C22×#217C2212yes—
24C22×#217C2212yes—
25C22×(C2×D3)⋊C4C2211yescharacteristic
26C22×(C2×D3)⋊C4C2212yes—
27C22×(C2×D3)⋊C4C2211yescharacteristic
28C22×(C2×D3)⋊C4C2211yescharacteristic
29C22×Dic3⋊C4C2211yescharacteristic
30#5223—24no—
31#5213—28no—
32C2×C3⋊#95C2211yescharacteristic
33C2×C3⋊#95C2212yes—
34C2×C3⋊#95C2212yes—
35C2×C3⋊#95C2212yes—
36C2×C3⋊#95C2211yescharacteristic
37C2×C3⋊#95C2212yes—
38C2×C3⋊#95C2211yescharacteristic
39C2×C3⋊#95C2211yescharacteristic
40C2×C3⋊#95C2212yes—
41#4992—24no—
42#4940—24no—
43C22×C4×D4D311yescharacteristic, complemented
44C2×#397—31no—
45C2×#392—31no—
46C2×#388—31no—
47C2×#386—32no—
48#1445—31no—
49#1439—32no—
50#1438—31no—
51#1438—32no—
52#1434—31no—
53C22⋊#95—32no—
54C25×C3C2312yes—
55C24×D3C2311yescharacteristic
56C22×C3×D4—24no—
57C22×C3×D4—24no—
58C22×C3×D4—22no—
59C22×C3×D4—22no—
60C22×C3×D4D414yes—
61C23×C3×C4—24no—
62C23×C3×C4—24no—
63C23×C3×C4—24no—
64C23×C3×C4—24no—
65C23×C3×C4—24no—
66C23×C3×C4—42no—
67C23×C3×C4—42no—
68C23×C3×C4C2312yes—
69C23×C3×C4C2311yescharacteristic
70C23×C3×C4C2311yescharacteristic
71C23×C3×C4C2311yescharacteristic
72C22×#67—24no—
73C22×#67—24no—
74C22×#67—24no—
75C22×#67—24no—
76C22×#67—24no—
77C22×#67—42no—
78C22×#67—42no—
79C23×Dic3C2312yes—
80C23×Dic3C2311yescharacteristic
81C23×Dic3C2311yescharacteristic
82C23×Dic3C2311yescharacteristic
83C23×Dic3C2312yes—
84C3×C4×D4—232no—
85C2×C3×C4⋊C4—22no—
86C2×C3×C4⋊C4—22no—
87C2×C3×C4⋊C4D414yescomplemented
88C2×C3×C22⋊C4—24no—
89C2×C3×C22⋊C4—24no—
90C2×C3×C22⋊C4—24no—
91C2×C3×C42—22no—
92C2×C3×C42—22no—
93C2×C3×C42D414yescomplemented
94C2×#217—24no—
95C2×#217—24no—
96C2×#217—24no—
97C2×#217—24no—
98C2×#217—24no—
99C2×#217—42no—
100C2×#217—42no—
101C2×#217—42no—
102C2×#217—42no—
103C2×(C2×D3)⋊C4—22no—
104C2×(C2×D3)⋊C4—22no—
105C2×(C2×D3)⋊C4—24no—
106C2×(C2×D3)⋊C4—22no—
107C2×(C2×D3)⋊C4—22no—
108C2×(C2×D3)⋊C4—22no—
109C2×(C2×D3)⋊C4—24no—
110C2×(C2×D3)⋊C4—22no—
111C2×(C2×D3)⋊C4—42no—
112C2×(C2×D3)⋊C4—42no—
113C2×(C2×D3)⋊C4D414yescomplemented
114C2×Dic3⋊C4—22no—
115C2×Dic3⋊C4—42no—
116C3⋊#95—22no—
117C3⋊#95—22no—
118C3⋊#95—24no—
119C3⋊#95—22no—
120C3⋊#95—24no—
121C3⋊#95—22no—
122C3⋊#95—24no—
123C3⋊#95—24no—
124C3⋊#95—42no—
125C23×D4—32no—
126C23×D4C2×D311yescharacteristic
127C24×C4C2×D312yes—
128C2×C4×D4—24no—
129C2×C4×D4—24no—
130C2×C4×D4—24no—
131C22×C4⋊C4—31no—
132C22×C4⋊C4C2×D311yescharacteristic
133C22×C22⋊C4—31no—
134C22×C22⋊C4—31no—
135C22×C22⋊C4—32no—
136C22×C22⋊C4—32no—
137C22×C22⋊C4—32no—
138C22×C22⋊C4—32no—
139C22×C22⋊C4—31no—
140C22×C22⋊C4C2×D312yes—
141C22×C42C2×D311yescharacteristic
142#397—64no—
143#392—64no—
144#388—64no—
145#386—68no—
146C2×#95—31no—
147C2×#95—32no—
148C2×#95—31no—
149C2×#95—31no—
150C2×#95—32no—
151C2×#95—32no—
152C2×#95—31no—
153C2×#95—32no—
154C2×#95—32no—
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×C3C2×D414yes—
168C24×C3#4114yes—
169C24×C3#4114yes—
170C24×C3C2411yescharacteristic
171C23×D3—21no—
172C23×D3—21no—
173C23×D3—21no—
174C23×D3—21no—
175C23×D3—22no—
176C23×D3—22no—
177C23×D3—22no—
178C23×D3—21no—
179C23×D3—22no—
180C23×D3—21no—
181C23×D3C2×D412yes—
182C2×C3×D4—28no—
183C2×C3×D4—28no—
184C2×C3×D4—216no—
185C2×C3×D4—216no—
186C2×C3×D4—28no—
187C22×C3×C4—21no—
188C22×C3×C4—21no—
189C22×C3×C4—22no—
190C22×C3×C4—22no—
191C22×C3×C4—21no—
192C22×C3×C4—21no—
193C22×C3×C4—216no—
194C22×C3×C4—22no—
195C22×C3×C4—21no—
196C22×C3×C4—21no—
197C22×C3×C4—22no—
198C22×C3×C4—22no—
199C22×C3×C4—22no—
200C22×C3×C4—22no—
201C22×C3×C4—22no—
202C22×C3×C4—22no—
203C22×C3×C4—22no—
204C22×C3×C4—48no—
205C22×C3×C4—48no—
206C22×C3×C4—48no—
207C22×C3×C4—48no—
208C22×C3×C4—48no—
209C22×C3×C4—48no—
210C22×C3×C4C2×D412yes—
211C22×C3×C4C2×D414yes—
212C22×C3×C4C2×D412yes—
213C22×C3×C4C2×D412yes—
214C22×C3×C4C2×D412yes—
215C22×C3×C4C2×D412yes—
216C22×C3×C4C2×D412yes—
217C22×C3×C4#4112yes—
218C2×#67—216no—
219C2×#67—48no—
220C2×#67—48no—
221C2×#67—48no—
222C2×#67—48no—
223C2×#67—48no—
224C2×#67—48no—
225C22×Dic3—22no—
226C22×Dic3—21no—
227C22×Dic3—22no—
228C22×Dic3—21no—
229C22×Dic3—22no—
230C22×Dic3—22no—
231C22×Dic3—22no—
232C22×Dic3—22no—
233C22×Dic3—22no—
234C22×Dic3—22no—
235C22×Dic3—21no—
236C22×Dic3—21no—
237C22×Dic3—22no—
238C22×Dic3—21no—
239C22×Dic3—22no—
240C22×Dic3—21no—
241C22×Dic3—22no—
242C22×Dic3—22no—
243C22×Dic3—22no—
244C22×Dic3—22no—
245C22×Dic3—22no—
246C22×Dic3—21no—
247C22×Dic3—22no—
248C22×Dic3—22no—
249C22×Dic3—22no—
250C22×Dic3—21no—
251C22×Dic3—22no—
252C22×Dic3C2×D412yes—
253C22×Dic3#4114yes—
254C3×C4⋊C4—28no—
255C3×C22⋊C4—216no—
256C3×C42—28no—
257#217—48no—
258#217—48no—
259#217—48no—
260(C2×D3)⋊C4—28no—
261(C2×D3)⋊C4—48no—
262(C2×D3)⋊C4—44no—
263(C2×D3)⋊C4—44no—
264Dic3⋊C4—44no—
265C25—31no—
266C25C22×D312yes—
267C22×D4—24no—
268C22×D4—24no—
269C22×D4—22no—
270C22×D4—22no—
271C22×D4—64no—
272C22×D4—64no—
273C22×D4—64no—
274C22×D4—64no—
275C22×D4—64no—
276C22×D4—122no—
277C22×D4—122no—
278C22×D4#6714yes—
279C23×C4—24no—
280C23×C4—24no—
281C23×C4—24no—
282C23×C4—24no—
283C23×C4—24no—
284C23×C4—31no—
285C23×C4—32no—
286C23×C4—31no—
287C23×C4—32no—
288C23×C4—31no—
289C23×C4—42no—
290C23×C4—42no—
291C23×C4C22×D311yescharacteristic
292C23×C4C22×D312yes—
293C23×C4C22×D311yescharacteristic
294C23×C4C22×D311yescharacteristic
295C4×D4—232no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—62no—
299C2×C4⋊C4—122no—
300C2×C4⋊C4#6714yescomplemented
301C2×C22⋊C4—24no—
302C2×C22⋊C4—24no—
303C2×C22⋊C4—24no—
304C2×C22⋊C4—34no—
305C2×C22⋊C4—62no—
306C2×C22⋊C4—62no—
307C2×C22⋊C4—64no—
308C2×C22⋊C4—64no—
309C2×C22⋊C4—64no—
310C2×C22⋊C4—64no—
311C2×C22⋊C4—64no—
312C2×C22⋊C4—64no—
313C2×C22⋊C4—62no—
314C2×C22⋊C4—62no—
315C2×C22⋊C4—62no—
316C2×C22⋊C4—64no—
317C2×C22⋊C4—62no—
318C2×C22⋊C4—122no—
319C2×C22⋊C4—122no—
320C2×C22⋊C4—122no—
321C2×C22⋊C4—122no—
322C2×C22⋊C4—122no—
323C2×C22⋊C4—122no—
324C2×C42—22no—
325C2×C42—22no—
326C2×C42#6714yescomplemented
327#95—64no—
328#95—64no—
329#95—64no—
330#95—62no—
331#95—62no—
332#95—62no—
333#95—64no—
334#95—62no—
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—42no—
355C23×C3—42no—
356C23×C3—42no—
357C23×C3—42no—
358C23×C3—42no—
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#12318yes—
371C23×C3C22×D411yescharacteristic
372C23×C3C22×D411yescharacteristic
373C23×C3C22×D411yescharacteristic
374C23×C3C22×D411yescharacteristic
375C23×C3C2×#4112yes—
376C23×C3C2×#4112yes—
377C23×C3C2×#4111yescharacteristic
378C23×C3C2×#4112yes—
379C23×C3H(5,𝔽2)11yescharacteristic
380C23×C3H(5,𝔽2)11yescharacteristic
381C23×C3H(5,𝔽2)12yes—
382C22×D3—22no—
383C22×D3—24no—
384C22×D3—22no—
385C22×D3—22no—
386C22×D3—24no—
387C22×D3—41no—
388C22×D3—42no—
389C22×D3—41no—
390C22×D3—42no—
391C22×D3—41no—
392C22×D3—42no—
393C22×D3—41no—
394C22×D3—41no—
395C22×D3—41no—
396C22×D3—42no—
397C22×D3—42no—
398C22×D3—42no—
399C22×D3—41no—
400C22×D3—41no—
401C22×D3—42no—
402C22×D3—42no—
403C22×D3—42no—
404C22×D3—42no—
405C3×D4—232no—
406C2×C3×C4—22no—
407C2×C3×C4—24no—
408C2×C3×C4—22no—
409C2×C3×C4—22no—
410C2×C3×C4—24no—
411C2×C3×C4—22no—
412C2×C3×C4—22no—
413C2×C3×C4—22no—
414C2×C3×C4—22no—
415C2×C3×C4—22no—
416C2×C3×C4—22no—
417C2×C3×C4—24no—
418C2×C3×C4—22no—
419C2×C3×C4—22no—
420C2×C3×C4—24no—
421C2×C3×C4—24no—
422C2×C3×C4—432no—
423C2×C3×C4—42no—
424C2×C3×C4—42no—
425C2×C3×C4—42no—
426C2×C3×C4—42no—
427C2×C3×C4—42no—
428C2×C3×C4—42no—
429C2×C3×C4#12014yes—
430C2×C3×C4#12114yes—
431#67—432no—
432C2×Dic3—22no—
433C2×Dic3—24no—
434C2×Dic3—24no—
435C2×Dic3—24no—
436C2×Dic3—24no—
437C2×Dic3—42no—
438C2×Dic3—41no—
439C2×Dic3—41no—
440C2×Dic3—42no—
441C2×Dic3—42no—
442C2×Dic3—42no—
443C2×Dic3—42no—
444C2×Dic3—41no—
445C2×Dic3—41no—
446C2×Dic3—42no—
447C2×Dic3—42no—
448C2×Dic3—41no—
449C2×Dic3—41no—
450C2×Dic3—41no—
451C2×Dic3—41no—
452C2×Dic3—42no—
453C2×Dic3—42no—
454C2×Dic3—42no—
455C2×Dic3—42no—
456C2×Dic3—42no—
457C2×Dic3—42no—
458C2×Dic3—42no—
459C2×Dic3—42no—
460C2×Dic3—42no—
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—32no—
474C24—62no—
475C24—62no—
476C24—61no—
477C24—61no—
478C24—61no—
479C24—62no—
480C24—62no—
481C24—61no—
482C24—61no—
483C24—61no—
484C24#23514yes—
485C24#23514yes—
486C24C2×#6714yes—
487C24C23×D311yescharacteristic
488C2×D4—216no—
489C2×D4—28no—
490C2×D4—28no—
491C2×D4—216no—
492C2×D4—28no—
493C2×D4—616no—
494C2×D4—128no—
495C2×D4—128no—
496C2×D4—128no—
497C2×D4—128no—
498C2×D4—128no—
499C2×D4—128no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—216no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—32no—
518C22×C4—34no—
519C22×C4—48no—
520C22×C4—48no—
521C22×C4—48no—
522C22×C4—48no—
523C22×C4—48no—
524C22×C4—48no—
525C22×C4—62no—
526C22×C4—62no—
527C22×C4—62no—
528C22×C4—62no—
529C22×C4—61no—
530C22×C4—62no—
531C22×C4—62no—
532C22×C4—62no—
533C22×C4—61no—
534C22×C4—62no—
535C22×C4—62no—
536C22×C4—62no—
537C22×C4—62no—
538C22×C4—62no—
539C22×C4—61no—
540C22×C4—62no—
541C22×C4—61no—
542C22×C4—62no—
543C22×C4—62no—
544C22×C4—62no—
545C22×C4—62no—
546C22×C4—62no—
547C22×C4—62no—
548C22×C4—61no—
549C22×C4—61no—
550C22×C4—61no—
551C22×C4—61no—
552C22×C4D3×D412yes—
553C22×C4#23712yes—
554C22×C4C2×#6714yes—
555C22×C4C2×#6712yes—
556C22×C4C2×#6712yes—
557C22×C4C2×#6712yes—
558C22×C4C2×#6712yes—
559C22×C4C2×#6712yes—
560C4⋊C4—28no—
561C4⋊C4—124no—
562C22⋊C4—216no—
563C22⋊C4—68no—
564C22⋊C4—128no—
565C22⋊C4—124no—
566C22⋊C4—128no—
567C22⋊C4—128no—
568C22⋊C4—128no—
569C22⋊C4—124no—
570C42—28no—
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×C3C2×#12011yescharacteristic
587C22×C3C2×#12111yescharacteristic
588C22×C3C2×#12312yes—
589C22×C3#52511yescharacteristic
590C22×C3#52511yescharacteristic
591C22×C3#52512yes—
592C22×C3#52512yes—
593C22×C3#52912yes—
594C22×C3#53211yescharacteristic
595C22×C3#53511yescharacteristic
596C22×C3#53511yescharacteristic
597C22×C3#53812yes—
598C22×C3#53812yes—
599C22×C3D4211yescharacteristic
600C22×C3D4211yescharacteristic
601C22×C3#54612yes—
602C22×C3#54611yescharacteristic
603C22×C3#54611yescharacteristic
604C22×C3#54612yes—
605C22×C3#55012yes—
606C22×C3#55112yes—
607C22×C3#55312yes—
608C22×C3#55312yes—
609C2×D3—42no—
610C2×D3—42no—
611C2×D3—44no—
612C2×D3—44no—
613C2×D3—42no—
614C2×D3—81no—
615C2×D3—81no—
616C2×D3—81no—
617C2×D3—81no—
618C2×D3—82no—
619C2×D3—82no—
620C3×C4—24no—
621C3×C4—24no—
622C3×C4—44no—
623C3×C4—42no—
624Dic3—44no—
625Dic3—42no—
626Dic3—81no—
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—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—62no—
664C23—62no—
665C23—62no—
666C23—64no—
667C23—64no—
668C23—122no—
669C23—121no—
670C23—122no—
671C23—121no—
672C23—122no—
673C23—122no—
674C23—121no—
675C23—121no—
676C23—121no—
677C23—122no—
678C23—122no—
679C23—122no—
680C23—122no—
681C23—122no—
682C23—121no—
683C23—121no—
684C23—122no—
685C23—121no—
686C23#92918yes—
687C23C2×#23512yes—
688C23C2×#23512yes—
689C23C2×D3×D411yescharacteristic
690C23C2×#23711yescharacteristic
691C23#100411yescharacteristic
692C23#100411yescharacteristic
693C23D3×#4112yes—
694C23#100912yes—
695C23C22×#6711yescharacteristic
696C23C22×#6711yescharacteristic
697C23C22×#6711yescharacteristic
698D4—232no—
699D4—1232no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—432no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—62no—
724C2×C4—64no—
725C2×C4—64no—
726C2×C4—64no—
727C2×C4—64no—
728C2×C4—122no—
729C2×C4—121no—
730C2×C4—122no—
731C2×C4—122no—
732C2×C4—122no—
733C2×C4—122no—
734C2×C4—121no—
735C2×C4—122no—
736C2×C4—121no—
737C2×C4—122no—
738C2×C4—122no—
739C2×C4—122no—
740C2×C4—121no—
741C2×C4—122no—
742C2×C4—122no—
743C2×C4—122no—
744C2×C4—122no—
745C2×C4—122no—
746C2×C4—121no—
747C2×C4—121no—
748C2×C4—121no—
749C2×C4—122no—
750C2×C4—122no—
751C2×C4—121no—
752C2×C4#93814yes—
753C2×C4#95314yes—
754C2×C3—48no—
755C2×C3#239211yescharacteristic
756C2×C3#240811yescharacteristic
757C2×C3#241812yes—
758C2×C3#243111yescharacteristic
759C2×C3#244412yes—
760C2×C3#245612yes—
761C2×C3#246712yes—
762C2×C3#253511yescharacteristic
763C2×C3#260311yescharacteristic
764C2×C3#263111yescharacteristic
765C2×C3#284911yescharacteristic
766D3—82no—
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—122no—
783C22—122no—
784C22—124no—
785C22—124no—
786C22—122no—
787C22—241no—
788C22—241no—
789C22—242no—
790C22—242no—
791C22—241no—
792C22—241no—
793C22#553812yes—
794C22#554012yes—
795C22#554712yes—
796C22#555012yes—
797C22#555612yes—
798C22#556012yes—
799C22#556012yes—
800C22#556512yes—
801C22C2×#92912yes—
802C22#579112yes—
803C22#579111yescharacteristic
804C22#579111yescharacteristic
805C22C2×#93811yescharacteristic
806C22D4×#6711yescharacteristic
807C22D4×#6711yescharacteristic
808C22#580511yescharacteristic
809C22#580611yescharacteristic
810C22#580611yescharacteristic
811C22#582912yes—
812C22#583011yescharacteristic
813C22#583211yescharacteristic
814C22#583412yes—
815C22C2×#95311yescharacteristic
816C4—24no—
817C4—24no—
818C4—44no—
819C4—42no—
820C4—124no—
821C4—122no—
822C4—241no—
823C4—242no—
824C4—241no—
825C3#1479511yescharacteristic, complemented, Sylow
826C2—48no—
827C2—242no—
828C2#8235712yes—
829C2#8237012yes—
830C2#8239011yescharacteristic
831C2#8240111yescharacteristic
832C2#8240412yes—
833C2#8241112yes—
834C2#8241511yescharacteristic
835C2#8242111yescharacteristic
836C2#8403311yescharacteristic
837C2#8405311yescharacteristic
838C2#8409211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC22×C3×C4×D4C2
prime radicalC2×#5223C2
hypercenterC22×C4×D4D3
hypocenterC3#14795
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×C3×C4×D4C2semidirect
3. C2×#5213C2semidirect
4. C2×#4992C2semidirect
5. C2×#4940C2semidirect
6. #72131C2semidirect
7. #72127C2semidirect
8. #71569C2semidirect
9. #71550C2semidirect
10. #71547C2semidirect
11. #71534C2semidirect
43. C22×C4×D4D3semidirect
87. C2×C3×C4⋊C4D4semidirect
93. C2×C3×C42D4semidirect
113. C2×(C2×D3)⋊C4D4semidirect
300. C2×C4⋊C4#67semidirect
326. C2×C42#67semidirect
825. C3#14795semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C4×D42
C2×#52232
C2×#52132
C2×#49922
C2×#49402
#721312
#721272
#715692
#715502
#715472
#715342
#147953