Finite Group Databasebeta

← #10726664

Subgroups — #10726664

Order 768.

4034 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#937C211yesmaximal, characteristic
2C23×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
3C2×C3×#386C211yesmaximal, characteristic, complemented
4C2×#5220C211yesmaximal, characteristic, complemented
5C2×#4959C212yesmaximal, complemented
6C2×#4955C211yesmaximal, characteristic, complemented
7C2×#4942C211yesmaximal, characteristic, complemented
8#72127C211yesmaximal, characteristic, complemented
9#71550C212yesmaximal, complemented
10#69429C212yesmaximal, complemented
11#69428C212yesmaximal, complemented
12#14725—31nomaximal, Sylow
13C25×D3C2211yescharacteristic
14C23×C3×D4C2211yescharacteristic
15C24×C3×C4C2211yescharacteristic
16C23×#67C2212yes—
17C24×Dic3C2211yescharacteristic
18C22×C3×C22⋊C4C2211yescharacteristic
19C22×C3×C22⋊C4C2212yescomplemented
20C22×#217C2211yescharacteristic
21C22×#217C2211yescharacteristic
22C22×#217C2211yescharacteristic, complemented
23C22×#217C2211yescharacteristic, complemented
24C2×#937—24no—
25C2×#937—24no—
26C2×#937—24no—
27C22×(C2×D3)⋊C4—24no—
28C22×(C2×D3)⋊C4—28no—
29C22×(C2×D3)⋊C4C2212yes—
30C22×(C2×D3)⋊C4C2212yes—
31C22×(C2×D3)⋊C4C2212yes—
32C22×(C2×D3)⋊C4C2212yes—
33C22×(C2×D3)⋊C4C2212yes—
34C22×Dic3⋊C4C2212yescomplemented
35C3×#386—24no—
36C2×C3×#95C2212yescomplemented
37#5220—24no—
38C2×C3⋊#95C2211yescharacteristic, complemented
39C2×C3⋊#95C2211yescharacteristic, complemented
40C2×C3⋊#95C2212yescomplemented
41C2×C3⋊#95C2212yescomplemented
42C2×C3⋊#95C2212yescomplemented
43#4959—28no—
44#4955—24no—
45#4942—24no—
46C22×#120—31no—
47C23×C22⋊C4—31no—
48C2×#394—32no—
49C2×#386—31no—
50C2×#386D311yescharacteristic, complemented
51C2×#380—31no—
52C2×#379—31no—
53#1440—32no—
54#1439—32no—
55#1438—32no—
56C22⋊#95—31no—
57C25×C3C2311yescharacteristic
58C25×C3C2311yescharacteristic
59C24×D3—22no—
60C24×D3—22no—
61C24×D3—24no—
62C24×D3—24no—
63C24×D3—22no—
64C24×D3—22no—
65C24×D3—22no—
66C24×D3—22no—
67C24×D3—42no—
68C24×D3—42no—
69C24×D3D414yes—
70C24×D3C2312yes—
71C22×C3×D4—22no—
72C22×C3×D4—22no—
73C22×C3×D4—22no—
74C22×C3×D4—22no—
75C22×C3×D4—22no—
76C22×C3×D4—22no—
77C22×C3×D4D414yes—
78C23×C3×C4—22no—
79C23×C3×C4—24no—
80C23×C3×C4—22no—
81C23×C3×C4—22no—
82C23×C3×C4—42no—
83C23×C3×C4C2312yes—
84C23×C3×C4C2312yes—
85C23×C3×C4C2311yescharacteristic
86C22×#67—24no—
87C22×#67—24no—
88C22×#67—24no—
89C22×#67—24no—
90C22×#67—24no—
91C22×#67—42no—
92C22×#67—42no—
93C23×Dic3—22no—
94C23×Dic3—22no—
95C23×Dic3—24no—
96C23×Dic3—42no—
97C23×Dic3D414yescomplemented
98C23×Dic3C2311yescharacteristic
99C23×Dic3C2311yescharacteristic
100C23×Dic3C2311yescharacteristic
101C23×Dic3C2312yes—
102C23×Dic3C2311yescharacteristic
103C2×C3×C22⋊C4—22no—
104C2×C3×C22⋊C4—22no—
105C2×C3×C22⋊C4—22no—
106C2×C3×C22⋊C4—24no—
107C2×C3×C22⋊C4—24no—
108C2×C3×C22⋊C4—42no—
109C2×#217—22no—
110C2×#217—22no—
111C2×#217—22no—
112C2×#217—22no—
113C2×#217—22no—
114C2×#217—24no—
115C2×#217—22no—
116C2×#217—22no—
117C2×#217—42no—
118C2×#217D414yes—
119#937—232no—
120C2×(C2×D3)⋊C4—232no—
121C2×(C2×D3)⋊C4—24no—
122C2×(C2×D3)⋊C4—24no—
123C2×(C2×D3)⋊C4—24no—
124C2×(C2×D3)⋊C4—24no—
125C2×(C2×D3)⋊C4—24no—
126C2×(C2×D3)⋊C4—24no—
127C2×(C2×D3)⋊C4—24no—
128C2×(C2×D3)⋊C4—24no—
129C2×(C2×D3)⋊C4—24no—
130C2×(C2×D3)⋊C4—24no—
131C2×(C2×D3)⋊C4—24no—
132C2×(C2×D3)⋊C4—24no—
133C2×(C2×D3)⋊C4—42no—
134C2×(C2×D3)⋊C4—42no—
135C2×(C2×D3)⋊C4D418yescomplemented
136C2×Dic3⋊C4—24no—
137C2×Dic3⋊C4—24no—
138C2×Dic3⋊C4—42no—
139C3×#95—24no—
140C3⋊#95—24no—
141C3⋊#95—24no—
142C3⋊#95—22no—
143C3⋊#95—22no—
144C3⋊#95—42no—
145C26—31no—
146C23×D4—32no—
147C23×D4C2×D311yescharacteristic
148C24×C4—31no—
149C24×C4C2×D311yescharacteristic
150C2×#120—64no—
151C2×#120—64no—
152C2×#120—64no—
153C22×C4⋊C4—32no—
154C22×C22⋊C4—31no—
155C22×C22⋊C4—32no—
156C22×C22⋊C4—31no—
157C22×C22⋊C4—31no—
158C22×C22⋊C4—32no—
159C22×C22⋊C4—32no—
160C22×C22⋊C4—32no—
161C22×C22⋊C4—31no—
162C22×C22⋊C4—32no—
163C22×C22⋊C4—68no—
164C22×C22⋊C4—64no—
165C22×C22⋊C4C2×D311yescharacteristic
166C22×C22⋊C4C2×D312yescomplemented
167#394—68no—
168#386—24no—
169#386—64no—
170#380—64no—
171#379—64no—
172C2×#95—32no—
173C2×#95—32no—
174C2×#95—31no—
175C2×#95—31no—
176C2×#95—32no—
177C2×#95C2×D312yescomplemented
178C24×C3—22no—
179C24×C3—22no—
180C24×C3—22no—
181C24×C3—22no—
182C24×C3—21no—
183C24×C3—22no—
184C24×C3—21no—
185C24×C3—21no—
186C24×C3—22no—
187C24×C3—21no—
188C24×C3—21no—
189C24×C3—21no—
190C24×C3—22no—
191C24×C3—22no—
192C24×C3C2×D412yes—
193C24×C3C2×D412yes—
194C24×C3C2×D412yes—
195C24×C3C2×D412yes—
196C24×C3C2×D412yes—
197C24×C3#4112yes—
198C24×C3#4112yes—
199C24×C3#4112yes—
200C24×C3C2411yescharacteristic
201C23×D3—28no—
202C23×D3—216no—
203C23×D3—28no—
204C23×D3—28no—
205C23×D3—22no—
206C23×D3—22no—
207C23×D3—22no—
208C23×D3—22no—
209C23×D3—22no—
210C23×D3—22no—
211C23×D3—22no—
212C23×D3—22no—
213C23×D3—22no—
214C23×D3—22no—
215C23×D3—22no—
216C23×D3—22no—
217C23×D3—216no—
218C23×D3—28no—
219C23×D3—28no—
220C23×D3—48no—
221C23×D3—48no—
222C23×D3—48no—
223C23×D3—48no—
224C23×D3—48no—
225C23×D3—48no—
226C23×D3—48no—
227C23×D3—48no—
228C23×D3—48no—
229C23×D3—44no—
230C23×D3—44no—
231C23×D3—48no—
232C23×D3—44no—
233C23×D3—44no—
234C23×D3—44no—
235C23×D3—44no—
236C23×D3C2×D414yes—
237C23×D3C2×D414yes—
238C23×D3#4114yes—
239C2×C3×D4—28no—
240C2×C3×D4—28no—
241C2×C3×D4—28no—
242C2×C3×D4—44no—
243C2×C3×D4—44no—
244C2×C3×D4—44no—
245C2×C3×D4—44no—
246C22×C3×C4—28no—
247C22×C3×C4—21no—
248C22×C3×C4—22no—
249C22×C3×C4—22no—
250C22×C3×C4—22no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—22no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—22no—
258C22×C3×C4—22no—
259C22×C3×C4—22no—
260C22×C3×C4—22no—
261C22×C3×C4—22no—
262C22×C3×C4—22no—
263C22×C3×C4—22no—
264C22×C3×C4—22no—
265C22×C3×C4—22no—
266C22×C3×C4—48no—
267C22×C3×C4—48no—
268C22×C3×C4—44no—
269C22×C3×C4—44no—
270C22×C3×C4C2×D414yes—
271C22×C3×C4C2×D412yes—
272C2×#67—216no—
273C2×#67—48no—
274C2×#67—48no—
275C2×#67—48no—
276C2×#67—48no—
277C2×#67—48no—
278C2×#67—48no—
279C22×Dic3—21no—
280C22×Dic3—21no—
281C22×Dic3—22no—
282C22×Dic3—28no—
283C22×Dic3—21no—
284C22×Dic3—22no—
285C22×Dic3—22no—
286C22×Dic3—22no—
287C22×Dic3—22no—
288C22×Dic3—21no—
289C22×Dic3—22no—
290C22×Dic3—22no—
291C22×Dic3—22no—
292C22×Dic3—22no—
293C22×Dic3—28no—
294C22×Dic3—22no—
295C22×Dic3—21no—
296C22×Dic3—21no—
297C22×Dic3—21no—
298C22×Dic3—21no—
299C22×Dic3—22no—
300C22×Dic3—21no—
301C22×Dic3—21no—
302C22×Dic3—22no—
303C22×Dic3—22no—
304C22×Dic3—44no—
305C22×Dic3—48no—
306C22×Dic3—48no—
307C22×Dic3C2×D414yes—
308C22×Dic3C2×D412yes—
309C22×Dic3C2×D412yes—
310C22×Dic3C2×D414yes—
311C3×C22⋊C4—48no—
312C3×C22⋊C4—44no—
313#217—28no—
314#217—44no—
315#217—44no—
316#217—44no—
317(C2×D3)⋊C4—216no—
318(C2×D3)⋊C4—216no—
319(C2×D3)⋊C4—216no—
320(C2×D3)⋊C4—48no—
321(C2×D3)⋊C4—48no—
322Dic3⋊C4—48no—
323C25—32no—
324C25—34no—
325C25—64no—
326C25—64no—
327C25—62no—
328C25—62no—
329C25—62no—
330C25—62no—
331C25—62no—
332C25—62no—
333C25—122no—
334C25—122no—
335C25C22×D311yescharacteristic
336C25C22×D311yescharacteristic
337C22×D4—22no—
338C22×D4—22no—
339C22×D4—22no—
340C22×D4—22no—
341C22×D4—22no—
342C22×D4—22no—
343C22×D4—64no—
344C22×D4—64no—
345C22×D4—64no—
346C22×D4—64no—
347C22×D4—64no—
348C22×D4—122no—
349C22×D4—122no—
350C22×D4#6714yes—
351C23×C4—22no—
352C23×C4—24no—
353C23×C4—22no—
354C23×C4—22no—
355C23×C4—31no—
356C23×C4—31no—
357C23×C4—32no—
358C23×C4—34no—
359C23×C4—31no—
360C23×C4—31no—
361C23×C4—42no—
362C23×C4—64no—
363C23×C4—62no—
364C23×C4—62no—
365C23×C4—122no—
366C23×C4C22×D312yes—
367C23×C4C22×D312yes—
368C23×C4C22×D311yescharacteristic
369#120—632no—
370C2×C4⋊C4—64no—
371C2×C4⋊C4—64no—
372C2×C4⋊C4—122no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—34no—
379C2×C22⋊C4—38no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—64no—
382C2×C22⋊C4—64no—
383C2×C22⋊C4—64no—
384C2×C22⋊C4—64no—
385C2×C22⋊C4—64no—
386C2×C22⋊C4—64no—
387C2×C22⋊C4—632no—
388C2×C22⋊C4—62no—
389C2×C22⋊C4—62no—
390C2×C22⋊C4—64no—
391C2×C22⋊C4—64no—
392C2×C22⋊C4—64no—
393C2×C22⋊C4—64no—
394C2×C22⋊C4—64no—
395C2×C22⋊C4—64no—
396C2×C22⋊C4—62no—
397C2×C22⋊C4—62no—
398C2×C22⋊C4—64no—
399C2×C22⋊C4—62no—
400C2×C22⋊C4—62no—
401C2×C22⋊C4—62no—
402C2×C22⋊C4—122no—
403C2×C22⋊C4—122no—
404C2×C22⋊C4—122no—
405#95—24no—
406#95—64no—
407#95—62no—
408#95—62no—
409#95—64no—
410#95—122no—
411C23×C3—22no—
412C23×C3—24no—
413C23×C3—22no—
414C23×C3—24no—
415C23×C3—22no—
416C23×C3—24no—
417C23×C3—22no—
418C23×C3—24no—
419C23×C3—24no—
420C23×C3—24no—
421C23×C3—24no—
422C23×C3—24no—
423C23×C3—24no—
424C23×C3—24no—
425C23×C3—24no—
426C23×C3—24no—
427C23×C3—22no—
428C23×C3—22no—
429C23×C3—22no—
430C23×C3—24no—
431C23×C3—24no—
432C23×C3—41no—
433C23×C3—42no—
434C23×C3—41no—
435C23×C3—41no—
436C23×C3—41no—
437C23×C3—41no—
438C23×C3—42no—
439C23×C3—41no—
440C23×C3—41no—
441C23×C3—42no—
442C23×C3—41no—
443C23×C3—42no—
444C23×C3—42no—
445C23×C3—42no—
446C23×C3—42no—
447C23×C3—42no—
448C23×C3—42no—
449C23×C3—42no—
450C23×C3#12014yes—
451C23×C3#12114yes—
452C23×C3#12114yes—
453C23×C3#12114yes—
454C23×C3#12314yes—
455C23×C3#12314yes—
456C23×C3#12414yes—
457C23×C3C22×D411yescharacteristic
458C23×C3C22×D411yescharacteristic
459C23×C3C22×D412yes—
460C23×C3C22×D411yescharacteristic
461C23×C3C22×D411yescharacteristic
462C23×C3C2×#4111yescharacteristic
463C23×C3C2×#4111yescharacteristic
464C23×C3C2×#4111yescharacteristic
465C23×C3C2×#4112yes—
466C23×C3H(5,𝔽2)12yes—
467C23×C3H(5,𝔽2)12yes—
468C22×D3—232no—
469C22×D3—24no—
470C22×D3—24no—
471C22×D3—24no—
472C22×D3—24no—
473C22×D3—24no—
474C22×D3—24no—
475C22×D3—24no—
476C22×D3—24no—
477C22×D3—24no—
478C22×D3—24no—
479C22×D3—24no—
480C22×D3—24no—
481C22×D3—24no—
482C22×D3—24no—
483C22×D3—24no—
484C22×D3—24no—
485C22×D3—24no—
486C22×D3—24no—
487C22×D3—432no—
488C22×D3—432no—
489C22×D3—416no—
490C22×D3—416no—
491C22×D3—416no—
492C22×D3—416no—
493C22×D3—432no—
494C22×D3—432no—
495C22×D3—416no—
496C22×D3—42no—
497C22×D3—42no—
498C22×D3—42no—
499C22×D3—42no—
500C22×D3—42no—
501C22×D3—42no—
502C22×D3—42no—
503C22×D3—42no—
504C22×D3—42no—
505C22×D3—42no—
506C22×D3—42no—
507C22×D3—42no—
508C22×D3—42no—
509C22×D3—42no—
510C22×D3—42no—
511C22×D3—42no—
512C22×D3—416no—
513C22×D3#12118yes—
514C3×D4—416no—
515C2×C3×C4—24no—
516C2×C3×C4—22no—
517C2×C3×C4—22no—
518C2×C3×C4—22no—
519C2×C3×C4—24no—
520C2×C3×C4—24no—
521C2×C3×C4—416no—
522C2×C3×C4—42no—
523C2×C3×C4—41no—
524C2×C3×C4—41no—
525C2×C3×C4—41no—
526C2×C3×C4—41no—
527C2×C3×C4—42no—
528C2×C3×C4—42no—
529C2×C3×C4—42no—
530C2×C3×C4—42no—
531C2×C3×C4—42no—
532C2×C3×C4—42no—
533C2×C3×C4—42no—
534C2×C3×C4—42no—
535C2×C3×C4—42no—
536C2×C3×C4—42no—
537#67—432no—
538C2×Dic3—22no—
539C2×Dic3—22no—
540C2×Dic3—24no—
541C2×Dic3—24no—
542C2×Dic3—22no—
543C2×Dic3—24no—
544C2×Dic3—22no—
545C2×Dic3—22no—
546C2×Dic3—24no—
547C2×Dic3—24no—
548C2×Dic3—416no—
549C2×Dic3—42no—
550C2×Dic3—42no—
551C2×Dic3—42no—
552C2×Dic3—42no—
553C2×Dic3—42no—
554C2×Dic3—42no—
555C2×Dic3—41no—
556C2×Dic3—42no—
557C2×Dic3—41no—
558C2×Dic3—41no—
559C2×Dic3—41no—
560C2×Dic3—42no—
561C2×Dic3—42no—
562C2×Dic3—41no—
563C2×Dic3—41no—
564C2×Dic3—42no—
565C2×Dic3#12014yescomplemented
566C24—22no—
567C24—22no—
568C24—22no—
569C24—22no—
570C24—21no—
571C24—21no—
572C24—22no—
573C24—21no—
574C24—21no—
575C24—21no—
576C24—21no—
577C24—22no—
578C24—22no—
579C24—22no—
580C24—34no—
581C24—34no—
582C24—34no—
583C24—616no—
584C24—68no—
585C24—68no—
586C24—616no—
587C24—68no—
588C24—62no—
589C24—62no—
590C24—62no—
591C24—62no—
592C24—62no—
593C24—62no—
594C24—62no—
595C24—62no—
596C24—62no—
597C24—62no—
598C24—62no—
599C24—62no—
600C24—68no—
601C24—68no—
602C24—128no—
603C24—128no—
604C24—128no—
605C24—128no—
606C24—128no—
607C24—128no—
608C24—128no—
609C24—128no—
610C24—128no—
611C24—124no—
612C24—128no—
613C24—124no—
614C24—124no—
615C24—124no—
616C24—124no—
617C24—124no—
618C24#23512yes—
619C24#23512yes—
620C24D3×D412yes—
621C24D3×D412yes—
622C24D3×D412yes—
623C24#23712yes—
624C24C2×#6712yes—
625C24C2×#6712yes—
626C24C23×D311yescharacteristic
627C2×D4—28no—
628C2×D4—28no—
629C2×D4—28no—
630C2×D4—44no—
631C2×D4—44no—
632C2×D4—44no—
633C2×D4—44no—
634C2×D4—616no—
635C2×D4—128no—
636C2×D4—128no—
637C2×D4—128no—
638C2×D4—128no—
639C2×D4—128no—
640C2×D4—128no—
641C22×C4—28no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—22no—
650C22×C4—21no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—32no—
662C22×C4—34no—
663C22×C4—34no—
664C22×C4—32no—
665C22×C4—48no—
666C22×C4—48no—
667C22×C4—44no—
668C22×C4—44no—
669C22×C4—68no—
670C22×C4—61no—
671C22×C4—61no—
672C22×C4—62no—
673C22×C4—68no—
674C22×C4—61no—
675C22×C4—61no—
676C22×C4—62no—
677C22×C4—62no—
678C22×C4—62no—
679C22×C4—62no—
680C22×C4—62no—
681C22×C4—62no—
682C22×C4—62no—
683C22×C4—62no—
684C22×C4—61no—
685C22×C4—61no—
686C22×C4—61no—
687C22×C4—61no—
688C22×C4—62no—
689C22×C4—61no—
690C22×C4—61no—
691C22×C4—62no—
692C22×C4—62no—
693C22×C4—62no—
694C22×C4—124no—
695C22×C4—128no—
696C22×C4—128no—
697C22×C4D3×D414yes—
698C22×C4C2×#6712yes—
699C4⋊C4—128no—
700C22⋊C4—48no—
701C22⋊C4—44no—
702C22⋊C4—616no—
703C22⋊C4—616no—
704C22⋊C4—616no—
705C22⋊C4—68no—
706C22⋊C4—124no—
707C22⋊C4—128no—
708C22⋊C4—128no—
709C22⋊C4—124no—
710C22⋊C4—124no—
711C22×C3—24no—
712C22×C3—24no—
713C22×C3—24no—
714C22×C3—24no—
715C22×C3—28no—
716C22×C3—24no—
717C22×C3—28no—
718C22×C3—28no—
719C22×C3—28no—
720C22×C3—24no—
721C22×C3—42no—
722C22×C3—42no—
723C22×C3—44no—
724C22×C3—44no—
725C22×C3—42no—
726C22×C3—81no—
727C22×C3—81no—
728C22×C3—81no—
729C22×C3—81no—
730C22×C3—82no—
731C22×C3—82no—
732C22×C3#39418yescomplemented
733C22×C3C2×#12011yescharacteristic
734C22×C3C2×#12011yescharacteristic
735C22×C3C2×#12111yescharacteristic
736C22×C3C2×#12111yescharacteristic
737C22×C3C2×#12111yescharacteristic
738C22×C3C2×#12112yes—
739C22×C3C2×#12311yescharacteristic
740C22×C3C2×#12311yescharacteristic
741C22×C3#52511yescharacteristic
742C22×C3#52512yes—
743C22×C3C2×#12411yescharacteristic
744C22×C3#53411yescharacteristic
745C22×C3#53412yes—
746C22×C3#53511yescharacteristic
747C22×C3#53812yes—
748C22×C3D4212yes—
749C22×C3D4212yes—
750C22×C3#54612yes—
751C22×C3#54612yes—
752C22×C3#54612yes—
753C22×C3#54612yes—
754C22×C3#55112yes—
755C22×C3#55112yes—
756C2×D3—28no—
757C2×D3—28no—
758C2×D3—28no—
759C2×D3—464no—
760C2×D3—44no—
761C2×D3—44no—
762C2×D3—44no—
763C2×D3—44no—
764C2×D3—44no—
765C2×D3—44no—
766C2×D3—44no—
767C2×D3—44no—
768C2×D3—44no—
769C2×D3—44no—
770C2×D3—44no—
771C2×D3—44no—
772C3×C4—42no—
773C3×C4—44no—
774C3×C4—82no—
775Dic3—24no—
776Dic3—42no—
777Dic3—44no—
778Dic3—81no—
779Dic3—81no—
780C23—22no—
781C23—22no—
782C23—24no—
783C23—24no—
784C23—24no—
785C23—24no—
786C23—24no—
787C23—24no—
788C23—24no—
789C23—22no—
790C23—24no—
791C23—22no—
792C23—24no—
793C23—24no—
794C23—24no—
795C23—24no—
796C23—22no—
797C23—22no—
798C23—24no—
799C23—22no—
800C23—24no—
801C23—38no—
802C23—41no—
803C23—41no—
804C23—42no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—42no—
810C23—42no—
811C23—42no—
812C23—42no—
813C23—41no—
814C23—42no—
815C23—41no—
816C23—42no—
817C23—42no—
818C23—42no—
819C23—42no—
820C23—632no—
821C23—64no—
822C23—64no—
823C23—64no—
824C23—64no—
825C23—64no—
826C23—64no—
827C23—64no—
828C23—64no—
829C23—64no—
830C23—64no—
831C23—64no—
832C23—64no—
833C23—64no—
834C23—64no—
835C23—64no—
836C23—64no—
837C23—64no—
838C23—64no—
839C23—1232no—
840C23—1232no—
841C23—1216no—
842C23—1216no—
843C23—1216no—
844C23—1216no—
845C23—1216no—
846C23—1232no—
847C23—1232no—
848C23—122no—
849C23—122no—
850C23—1216no—
851C23—122no—
852C23—122no—
853C23—122no—
854C23—122no—
855C23—122no—
856C23—122no—
857C23—122no—
858C23—122no—
859C23—122no—
860C23—122no—
861C23—122no—
862C23—122no—
863C23—122no—
864C23—122no—
865C23#88314yes—
866C23#88414yes—
867C23#88414yes—
868C23#88514yes—
869C23#92914yes—
870C23#93714yes—
871C23#93914yes—
872C23C2×#23511yescharacteristic
873C23C2×#23511yescharacteristic
874C23C2×D3×D411yescharacteristic
875C23C2×D3×D411yescharacteristic
876C23C2×D3×D411yescharacteristic
877C23C2×D3×D412yes—
878C23C2×#23711yescharacteristic
879C23#100412yes—
880C23D3×#4112yes—
881C23#100912yes—
882C23C22×#6711yescharacteristic
883D4—416no—
884D4—1232no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—24no—
888C2×C4—22no—
889C2×C4—24no—
890C2×C4—24no—
891C2×C4—34no—
892C2×C4—416no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—42no—
898C2×C4—42no—
899C2×C4—42no—
900C2×C4—42no—
901C2×C4—42no—
902C2×C4—42no—
903C2×C4—42no—
904C2×C4—42no—
905C2×C4—42no—
906C2×C4—42no—
907C2×C4—42no—
908C2×C4—62no—
909C2×C4—62no—
910C2×C4—64no—
911C2×C4—64no—
912C2×C4—62no—
913C2×C4—62no—
914C2×C4—64no—
915C2×C4—62no—
916C2×C4—64no—
917C2×C4—64no—
918C2×C4—1216no—
919C2×C4—122no—
920C2×C4—122no—
921C2×C4—122no—
922C2×C4—122no—
923C2×C4—122no—
924C2×C4—122no—
925C2×C4—121no—
926C2×C4—121no—
927C2×C4—121no—
928C2×C4—121no—
929C2×C4—122no—
930C2×C4—122no—
931C2×C4—121no—
932C2×C4—121no—
933C2×C4—122no—
934C2×C4—122no—
935C2×C3—28no—
936C2×C3—82no—
937C2×C3C2×#39411yescharacteristic
938C2×C3#240811yescharacteristic
939C2×C3#241012yes—
940C2×C3#241011yescharacteristic
941C2×C3#241111yescharacteristic
942C2×C3#241212yes—
943C2×C3#241812yes—
944C2×C3#247212yes—
945C2×C3#253411yescharacteristic
946C2×C3#261711yescharacteristic
947C2×C3#284711yescharacteristic
948D3—48no—
949C22—28no—
950C22—24no—
951C22—24no—
952C22—28no—
953C22—24no—
954C22—24no—
955C22—24no—
956C22—24no—
957C22—28no—
958C22—28no—
959C22—44no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—44no—
964C22—68no—
965C22—68no—
966C22—68no—
967C22—81no—
968C22—81no—
969C22—82no—
970C22—81no—
971C22—81no—
972C22—82no—
973C22—1264no—
974C22—124no—
975C22—124no—
976C22—124no—
977C22—124no—
978C22—124no—
979C22—124no—
980C22—124no—
981C22—124no—
982C22—124no—
983C22—124no—
984C22—124no—
985C22—124no—
986C22#495918yescomplemented
987C22C2×#88311yescharacteristic
988C22C2×#88411yescharacteristic
989C22C2×#88411yescharacteristic
990C22C2×#88511yescharacteristic
991C22#554712yes—
992C22#555012yes—
993C22#555612yes—
994C22#556012yes—
995C22D3×#12011yescharacteristic
996C22#559112yes—
997C22#559211yescharacteristic
998C22D3×#12112yes—
999C22#560512yes—
1000C22#560912yes—
1001C22#561012yes—
1002C22#565311yescharacteristic
1003C22#565611yescharacteristic
1004C22#565812yes—
1005C22C2×#92911yescharacteristic
1006C22C2×#93711yescharacteristic
1007C22D4×#6712yes—
1008C22C2×#93911yescharacteristic
1009C22#582912yes—
1010C4—44no—
1011C4—42no—
1012C4—64no—
1013C4—82no—
1014C4—124no—
1015C4—122no—
1016C4—241no—
1017C4—241no—
1018C3#1472511yescharacteristic, complemented, Sylow
1019C2—28no—
1020C2—82no—
1021C2—128no—
1022C2#7472712yes—
1023C2#7488711yescharacteristic
1024C2#7488911yescharacteristic
1025C2#7489012yes—
1026C2#7490511yescharacteristic
1027C2#7493511yescharacteristic
1028C2C2×#495911yescharacteristic
1029C2#8240412yes—
1030C2#8258211yescharacteristic
1031C2#8270212yes—
1032C2#8290011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#386C2
prime radicalC22×#937C2
hypercenterC2×#386D3
hypocenterC3#14725
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C23×(C2×D3)⋊C4C2semidirect
3. C2×C3×#386C2semidirect
4. C2×#5220C2semidirect
5. C2×#4959C2semidirect
6. C2×#4955C2semidirect
7. C2×#4942C2semidirect
8. #72127C2semidirect
9. #71550C2semidirect
10. #69429C2semidirect
11. #69428C2semidirect
19. C22×C3×C22⋊C4C22semidirect
22. C22×#217C22semidirect
23. C22×#217C22semidirect
34. C22×Dic3⋊C4C22semidirect
36. C2×C3×#95C22semidirect
38. C2×C3⋊#95C22semidirect
39. C2×C3⋊#95C22semidirect
40. C2×C3⋊#95C22semidirect
41. C2×C3⋊#95C22semidirect
42. C2×C3⋊#95C22semidirect
50. C2×#386D3semidirect
97. C23×Dic3D4semidirect
135. C2×(C2×D3)⋊C4D4semidirect
166. C22×C22⋊C4C2×D3semidirect
177. C2×#95C2×D3semidirect
565. C2×Dic3#120semidirect
732. C22×C3#394semidirect
986. C22#4959semidirect
1018. C3#14725semidirect

Maximal subgroups

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

subgroupindex
C22×#9372
C23×(C2×D3)⋊C42
C2×C3×#3862
C2×#52202
C2×#49592
C2×#49552
C2×#49422
#721272
#715502
#694292
#694282
#147253