Finite Group Databasebeta

← #10726657

Subgroups — #10726657

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×C3×#120C211yesmaximal, characteristic
2C23×#217C211yesmaximal, characteristic, complemented
3C2×#5247C211yesmaximal, characteristic, complemented
4C2×#5222C212yesmaximal, complemented
5C2×#5220C211yesmaximal, characteristic, complemented
6C2×#5220C211yesmaximal, characteristic, complemented
7C2×#4942C211yesmaximal, characteristic, complemented
8#72131C212yesmaximal, complemented
9#71549C212yesmaximal, complemented
10#71547C212yesmaximal, complemented
11#71544C211yesmaximal, characteristic, complemented
12#14725—31nomaximal, Sylow
13C26×C3C2211yescharacteristic
14C23×C3×D4C2211yescharacteristic
15C23×C3×D4C2212yes—
16C24×Dic3C2211yescharacteristic
17C24×Dic3C2211yescharacteristic
18C2×C3×#120—24no—
19C2×C3×#120—24no—
20C2×C3×#120—24no—
21C22×C3×C22⋊C4C2212yes—
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×#217—24no—
24C22×#217—28no—
25C22×#217C2212yes—
26C22×#217C2211yescharacteristic
27C22×#217C2211yescharacteristic
28C22×#217C2212yes—
29C22×#217C2212yes—
30C22×#217C2212yes—
31C22×#217C2211yescharacteristic, complemented
32C22×#217C2212yescomplemented
33C22×#217C2211yescharacteristic, complemented
34C22×Dic3⋊C4C2212yescomplemented
35#5247—24no—
36#5222—28no—
37#5220—24no—
38#5220—24no—
39C2×C3⋊#95C2211yescharacteristic, complemented
40C2×C3⋊#95C2212yescomplemented
41C2×C3⋊#95C2211yescharacteristic, complemented
42C2×C3⋊#95C2212yescomplemented
43C2×C3⋊#95C2212yescomplemented
44C2×C3⋊#95C2212yescomplemented
45#4942—24no—
46C22×#120D311yescharacteristic
47C23×C22⋊C4—31no—
48C2×#394—32no—
49C2×#386—31no—
50C2×#386—31no—
51C2×#380—31no—
52C2×#379—31no—
53#1440—32no—
54#1439—32no—
55#1438—32no—
56C22⋊#95—31no—
57C25×C3—24no—
58C25×C3—22no—
59C25×C3—24no—
60C25×C3—22no—
61C25×C3—22no—
62C25×C3—22no—
63C25×C3—22no—
64C25×C3—22no—
65C25×C3—42no—
66C25×C3—42no—
67C25×C3D414yes—
68C25×C3C2311yescharacteristic
69C25×C3C2312yes—
70C25×C3C2311yescharacteristic
71C22×C3×D4—22no—
72C22×C3×D4—24no—
73C22×C3×D4—24no—
74C22×C3×D4—22no—
75C22×C3×D4—22no—
76C22×C3×D4—22no—
77C22×C3×D4—22no—
78C22×C3×D4—22no—
79C22×C3×D4—24no—
80C22×C3×D4—24no—
81C22×C3×D4—24no—
82C22×C3×D4—42no—
83C22×C3×D4—42no—
84C22×C3×D4D414yes—
85C23×C3×C4C2311yescharacteristic
86C23×C3×C4C2312yes—
87C23×Dic3—22no—
88C23×Dic3—22no—
89C23×Dic3—22no—
90C23×Dic3—24no—
91C23×Dic3—24no—
92C23×Dic3—22no—
93C23×Dic3—22no—
94C23×Dic3—42no—
95C23×Dic3—42no—
96C23×Dic3D414yescomplemented
97C23×Dic3C2311yescharacteristic
98C23×Dic3C2311yescharacteristic
99C23×Dic3C2312yes—
100C23×Dic3C2311yescharacteristic
101C23×Dic3C2312yes—
102C23×Dic3C2311yescharacteristic
103C3×#120—232no—
104C2×C3×C22⋊C4—24no—
105C2×C3×C22⋊C4—22no—
106C2×C3×C22⋊C4—22no—
107C2×C3×C22⋊C4—24no—
108C2×C3×C22⋊C4—24no—
109C2×C3×C22⋊C4D414yes—
110C2×#217—232no—
111C2×#217—24no—
112C2×#217—24no—
113C2×#217—24no—
114C2×#217—24no—
115C2×#217—24no—
116C2×#217—22no—
117C2×#217—22no—
118C2×#217—22no—
119C2×#217—24no—
120C2×#217—24no—
121C2×#217—24no—
122C2×#217—22no—
123C2×#217—24no—
124C2×#217—22no—
125C2×#217—24no—
126C2×#217—22no—
127C2×#217—22no—
128C2×#217—22no—
129C2×#217—24no—
130C2×#217—24no—
131C2×#217—42no—
132C2×#217—42no—
133C2×#217—42no—
134C2×#217—42no—
135C2×#217D418yescomplemented
136C2×Dic3⋊C4—24no—
137C2×Dic3⋊C4—24no—
138C2×Dic3⋊C4—42no—
139C3⋊#95—24no—
140C3⋊#95—24no—
141C3⋊#95—22no—
142C3⋊#95—22no—
143C3⋊#95—24no—
144C3⋊#95—42no—
145C26C2×D311yescharacteristic
146C23×D4C2×D311yescharacteristic
147C23×D4C2×D312yes—
148C24×C4—31no—
149C24×C4—31no—
150C2×#120—24no—
151C2×#120—24no—
152C2×#120—24no—
153C22×C4⋊C4—32no—
154C22×C22⋊C4—32no—
155C22×C22⋊C4—31no—
156C22×C22⋊C4—32no—
157C22×C22⋊C4—32no—
158C22×C22⋊C4—31no—
159C22×C22⋊C4—31no—
160C22×C22⋊C4—32no—
161C22×C22⋊C4—31no—
162C22×C22⋊C4—32no—
163C22×C22⋊C4—68no—
164C22×C22⋊C4—64no—
165C22×C22⋊C4C2×D312yes—
166C22×C22⋊C4C2×D311yescharacteristic
167#394—68no—
168#386—64no—
169#386—64no—
170#380—64no—
171#379—64no—
172C2×#95—32no—
173C2×#95—32no—
174C2×#95—31no—
175C2×#95—32no—
176C2×#95—31no—
177C2×#95—32no—
178C24×C3—22no—
179C24×C3—22no—
180C24×C3—22no—
181C24×C3—22no—
182C24×C3—28no—
183C24×C3—216no—
184C24×C3—28no—
185C24×C3—216no—
186C24×C3—28no—
187C24×C3—22no—
188C24×C3—22no—
189C24×C3—22no—
190C24×C3—22no—
191C24×C3—22no—
192C24×C3—22no—
193C24×C3—22no—
194C24×C3—22no—
195C24×C3—22no—
196C24×C3—22no—
197C24×C3—22no—
198C24×C3—22no—
199C24×C3—28no—
200C24×C3—28no—
201C24×C3—21no—
202C24×C3—22no—
203C24×C3—21no—
204C24×C3—21no—
205C24×C3—21no—
206C24×C3—21no—
207C24×C3—21no—
208C24×C3—22no—
209C24×C3—22no—
210C24×C3—22no—
211C24×C3—48no—
212C24×C3—48no—
213C24×C3—48no—
214C24×C3—48no—
215C24×C3—48no—
216C24×C3—48no—
217C24×C3—48no—
218C24×C3—48no—
219C24×C3—48no—
220C24×C3—44no—
221C24×C3—44no—
222C24×C3—48no—
223C24×C3—44no—
224C24×C3—44no—
225C24×C3—44no—
226C24×C3—44no—
227C24×C3C2×D414yes—
228C24×C3C2×D412yes—
229C24×C3C2×D412yes—
230C24×C3C2×D414yes—
231C24×C3C2×D412yes—
232C24×C3C2×D412yes—
233C24×C3C2×D412yes—
234C24×C3#4114yes—
235C24×C3#4112yes—
236C24×C3#4112yes—
237C24×C3#4112yes—
238C24×C3C2411yescharacteristic
239C2×C3×D4—216no—
240C2×C3×D4—28no—
241C2×C3×D4—28no—
242C2×C3×D4—28no—
243C2×C3×D4—48no—
244C2×C3×D4—48no—
245C2×C3×D4—48no—
246C2×C3×D4—48no—
247C2×C3×D4—48no—
248C2×C3×D4—44no—
249C2×C3×D4—48no—
250C2×C3×D4—44no—
251C2×C3×D4—44no—
252C2×C3×D4—44no—
253C22×C3×C4—21no—
254C22×C3×C4—22no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—22no—
258C22×C3×C4—22no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—22no—
263C22×C3×C4—22no—
264C22×C3×C4—22no—
265C22×C3×C4C2×D412yes—
266C22×C3×C4C2×D414yes—
267C22×Dic3—21no—
268C22×Dic3—21no—
269C22×Dic3—22no—
270C22×Dic3—28no—
271C22×Dic3—28no—
272C22×Dic3—21no—
273C22×Dic3—22no—
274C22×Dic3—22no—
275C22×Dic3—22no—
276C22×Dic3—22no—
277C22×Dic3—21no—
278C22×Dic3—22no—
279C22×Dic3—22no—
280C22×Dic3—22no—
281C22×Dic3—22no—
282C22×Dic3—28no—
283C22×Dic3—22no—
284C22×Dic3—21no—
285C22×Dic3—22no—
286C22×Dic3—21no—
287C22×Dic3—22no—
288C22×Dic3—22no—
289C22×Dic3—22no—
290C22×Dic3—21no—
291C22×Dic3—21no—
292C22×Dic3—21no—
293C22×Dic3—22no—
294C22×Dic3—21no—
295C22×Dic3—22no—
296C22×Dic3—22no—
297C22×Dic3—22no—
298C22×Dic3—22no—
299C22×Dic3—22no—
300C22×Dic3—44no—
301C22×Dic3—48no—
302C22×Dic3—48no—
303C22×Dic3—48no—
304C22×Dic3—48no—
305C22×Dic3—44no—
306C22×Dic3—44no—
307C22×Dic3C2×D412yes—
308C22×Dic3C2×D414yes—
309C22×Dic3C2×D412yes—
310C22×Dic3C2×D414yes—
311C3×C22⋊C4—216no—
312C3×C22⋊C4—28no—
313#217—216no—
314#217—216no—
315#217—48no—
316#217—44no—
317#217—48no—
318#217—44no—
319#217—48no—
320#217—44no—
321#217—44no—
322Dic3⋊C4—48no—
323C25—24no—
324C25—22no—
325C25—24no—
326C25—22no—
327C25—22no—
328C25—22no—
329C25—22no—
330C25—22no—
331C25—42no—
332C25—42no—
333C25#6714yes—
334C25C22×D311yescharacteristic
335C25C22×D312yes—
336C25C22×D311yescharacteristic
337C22×D4—22no—
338C22×D4—22no—
339C22×D4—22no—
340C22×D4—22no—
341C22×D4—24no—
342C22×D4—24no—
343C22×D4—22no—
344C22×D4—22no—
345C22×D4—24no—
346C22×D4—24no—
347C22×D4—24no—
348C22×D4—42no—
349C22×D4—42no—
350C22×D4#6714yes—
351C23×C4—31no—
352C23×C4—32no—
353C23×C4—31no—
354C23×C4—34no—
355C23×C4—32no—
356C23×C4—31no—
357C23×C4—31no—
358C23×C4—64no—
359C23×C4—64no—
360C23×C4—62no—
361C23×C4—62no—
362C23×C4—62no—
363C23×C4—62no—
364C23×C4—62no—
365C23×C4—122no—
366C23×C4—122no—
367C23×C4C22×D312yes—
368C23×C4C22×D311yescharacteristic
369#120—232no—
370C2×C4⋊C4—64no—
371C2×C4⋊C4—64no—
372C2×C4⋊C4—122no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—38no—
379C2×C22⋊C4—64no—
380C2×C22⋊C4—64no—
381C2×C22⋊C4—64no—
382C2×C22⋊C4—64no—
383C2×C22⋊C4—632no—
384C2×C22⋊C4—64no—
385C2×C22⋊C4—62no—
386C2×C22⋊C4—62no—
387C2×C22⋊C4—64no—
388C2×C22⋊C4—64no—
389C2×C22⋊C4—62no—
390C2×C22⋊C4—64no—
391C2×C22⋊C4—64no—
392C2×C22⋊C4—62no—
393C2×C22⋊C4—64no—
394C2×C22⋊C4—64no—
395C2×C22⋊C4—62no—
396C2×C22⋊C4—62no—
397C2×C22⋊C4—62no—
398C2×C22⋊C4—64no—
399C2×C22⋊C4—62no—
400C2×C22⋊C4—122no—
401C2×C22⋊C4—122no—
402C2×C22⋊C4—122no—
403C2×C22⋊C4—122no—
404C2×C22⋊C4#6714yes—
405#95—62no—
406#95—62no—
407#95—64no—
408#95—64no—
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—232no—
428C23×C3—24no—
429C23×C3—24no—
430C23×C3—24no—
431C23×C3—24no—
432C23×C3—24no—
433C23×C3—24no—
434C23×C3—24no—
435C23×C3—24no—
436C23×C3—24no—
437C23×C3—24no—
438C23×C3—24no—
439C23×C3—24no—
440C23×C3—24no—
441C23×C3—24no—
442C23×C3—24no—
443C23×C3—24no—
444C23×C3—24no—
445C23×C3—24no—
446C23×C3—22no—
447C23×C3—22no—
448C23×C3—22no—
449C23×C3—24no—
450C23×C3—24no—
451C23×C3—432no—
452C23×C3—432no—
453C23×C3—416no—
454C23×C3—416no—
455C23×C3—416no—
456C23×C3—416no—
457C23×C3—432no—
458C23×C3—432no—
459C23×C3—416no—
460C23×C3—42no—
461C23×C3—42no—
462C23×C3—42no—
463C23×C3—42no—
464C23×C3—42no—
465C23×C3—42no—
466C23×C3—42no—
467C23×C3—42no—
468C23×C3—42no—
469C23×C3—42no—
470C23×C3—42no—
471C23×C3—42no—
472C23×C3—42no—
473C23×C3—42no—
474C23×C3—42no—
475C23×C3—42no—
476C23×C3—416no—
477C23×C3—41no—
478C23×C3—41no—
479C23×C3—41no—
480C23×C3—42no—
481C23×C3—41no—
482C23×C3—42no—
483C23×C3—41no—
484C23×C3—41no—
485C23×C3—41no—
486C23×C3—42no—
487C23×C3—41no—
488C23×C3—42no—
489C23×C3—42no—
490C23×C3—42no—
491C23×C3—42no—
492C23×C3—42no—
493C23×C3—42no—
494C23×C3—42no—
495C23×C3#12014yes—
496C23×C3#12114yes—
497C23×C3#12118yes—
498C23×C3#12114yes—
499C23×C3#12114yes—
500C23×C3#12314yes—
501C23×C3#12314yes—
502C23×C3#12414yes—
503C23×C3C22×D411yescharacteristic
504C23×C3C22×D412yes—
505C23×C3C22×D411yescharacteristic
506C23×C3C22×D411yescharacteristic
507C23×C3C22×D411yescharacteristic
508C23×C3C2×#4111yescharacteristic
509C23×C3C2×#4111yescharacteristic
510C23×C3C2×#4111yescharacteristic
511C23×C3C2×#4112yes—
512C23×C3H(5,𝔽2)12yes—
513C23×C3H(5,𝔽2)12yes—
514C3×D4—432no—
515C3×D4—416no—
516C2×C3×C4—22no—
517C2×C3×C4—24no—
518C2×C3×C4—22no—
519C2×C3×C4—22no—
520C2×C3×C4—24no—
521C2×C3×C4—24no—
522C2×C3×C4—41no—
523C2×C3×C4—41no—
524C2×C3×C4—42no—
525C2×C3×C4—41no—
526C2×C3×C4—41no—
527C2×C3×C4—42no—
528C2×C3×C4—42no—
529C2×C3×C4—42no—
530C2×Dic3—22no—
531C2×Dic3—22no—
532C2×Dic3—24no—
533C2×Dic3—24no—
534C2×Dic3—24no—
535C2×Dic3—22no—
536C2×Dic3—22no—
537C2×Dic3—22no—
538C2×Dic3—24no—
539C2×Dic3—24no—
540C2×Dic3—416no—
541C2×Dic3—416no—
542C2×Dic3—42no—
543C2×Dic3—42no—
544C2×Dic3—42no—
545C2×Dic3—42no—
546C2×Dic3—42no—
547C2×Dic3—42no—
548C2×Dic3—42no—
549C2×Dic3—41no—
550C2×Dic3—41no—
551C2×Dic3—42no—
552C2×Dic3—41no—
553C2×Dic3—42no—
554C2×Dic3—41no—
555C2×Dic3—42no—
556C2×Dic3—42no—
557C2×Dic3—42no—
558C2×Dic3—41no—
559C2×Dic3—41no—
560C2×Dic3—42no—
561C2×Dic3—42no—
562C2×Dic3—42no—
563C2×Dic3—42no—
564C2×Dic3—42no—
565C2×Dic3#12014yescomplemented
566C24—22no—
567C24—22no—
568C24—22no—
569C24—22no—
570C24—28no—
571C24—28no—
572C24—216no—
573C24—216no—
574C24—28no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—22no—
579C24—22no—
580C24—22no—
581C24—22no—
582C24—22no—
583C24—22no—
584C24—22no—
585C24—22no—
586C24—22no—
587C24—28no—
588C24—28no—
589C24—22no—
590C24—21no—
591C24—21no—
592C24—21no—
593C24—21no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—21no—
598C24—21no—
599C24—48no—
600C24—48no—
601C24—48no—
602C24—48no—
603C24—48no—
604C24—48no—
605C24—48no—
606C24—48no—
607C24—48no—
608C24—44no—
609C24—44no—
610C24—48no—
611C24—44no—
612C24—44no—
613C24—44no—
614C24—44no—
615C24D3×D414yes—
616C24D3×D412yes—
617C24#23714yes—
618C24#23712yes—
619C24#23712yes—
620C24#23712yes—
621C24C2×#6712yes—
622C24C2×#6714yes—
623C24C2×#6712yes—
624C24C2×#6712yes—
625C24C2×#6712yes—
626C24C23×D311yescharacteristic
627C2×D4—216no—
628C2×D4—28no—
629C2×D4—28no—
630C2×D4—28no—
631C2×D4—48no—
632C2×D4—48no—
633C2×D4—48no—
634C2×D4—48no—
635C2×D4—48no—
636C2×D4—44no—
637C2×D4—44no—
638C2×D4—44no—
639C2×D4—48no—
640C2×D4—44no—
641C22×C4—21no—
642C22×C4—22no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—32no—
654C22×C4—34no—
655C22×C4—34no—
656C22×C4—32no—
657C22×C4—68no—
658C22×C4—61no—
659C22×C4—62no—
660C22×C4—61no—
661C22×C4—68no—
662C22×C4—68no—
663C22×C4—62no—
664C22×C4—62no—
665C22×C4—62no—
666C22×C4—61no—
667C22×C4—62no—
668C22×C4—62no—
669C22×C4—62no—
670C22×C4—62no—
671C22×C4—61no—
672C22×C4—62no—
673C22×C4—61no—
674C22×C4—62no—
675C22×C4—61no—
676C22×C4—62no—
677C22×C4—62no—
678C22×C4—61no—
679C22×C4—62no—
680C22×C4—61no—
681C22×C4—62no—
682C22×C4—62no—
683C22×C4—62no—
684C22×C4—62no—
685C22×C4—62no—
686C22×C4—62no—
687C22×C4—61no—
688C22×C4—61no—
689C22×C4—62no—
690C22×C4—124no—
691C22×C4—128no—
692C22×C4—128no—
693C22×C4—128no—
694C22×C4—128no—
695C22×C4—124no—
696C22×C4—124no—
697C22×C4C2×#6712yes—
698C22×C4C2×#6714yes—
699C4⋊C4—128no—
700C22⋊C4—216no—
701C22⋊C4—28no—
702C22⋊C4—616no—
703C22⋊C4—616no—
704C22⋊C4—124no—
705C22⋊C4—128no—
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—28no—
722C22×C3—28no—
723C22×C3—28no—
724C22×C3—464no—
725C22×C3—44no—
726C22×C3—44no—
727C22×C3—44no—
728C22×C3—44no—
729C22×C3—44no—
730C22×C3—44no—
731C22×C3—44no—
732C22×C3—44no—
733C22×C3—44no—
734C22×C3—44no—
735C22×C3—44no—
736C22×C3—44no—
737C22×C3—42no—
738C22×C3—42no—
739C22×C3—44no—
740C22×C3—44no—
741C22×C3—42no—
742C22×C3—81no—
743C22×C3—81no—
744C22×C3—81no—
745C22×C3—81no—
746C22×C3—82no—
747C22×C3—82no—
748C22×C3#39418yescomplemented
749C22×C3C2×#12011yescharacteristic
750C22×C3C2×#12011yescharacteristic
751C22×C3C2×#12111yescharacteristic
752C22×C3C2×#12111yescharacteristic
753C22×C3C2×#12112yes—
754C22×C3C2×#12111yescharacteristic
755C22×C3C2×#12311yescharacteristic
756C22×C3C2×#12311yescharacteristic
757C22×C3#52511yescharacteristic
758C22×C3#52512yes—
759C22×C3C2×#12411yescharacteristic
760C22×C3#53412yes—
761C22×C3#53411yescharacteristic
762C22×C3#53511yescharacteristic
763C22×C3#53812yes—
764C22×C3D4212yes—
765C22×C3D4212yes—
766C22×C3#54612yes—
767C22×C3#54612yes—
768C22×C3#54612yes—
769C22×C3#54612yes—
770C22×C3#55112yes—
771C22×C3#55112yes—
772C3×C4—42no—
773C3×C4—44no—
774Dic3—24no—
775Dic3—44no—
776Dic3—42no—
777Dic3—81no—
778Dic3—81no—
779Dic3—82no—
780C23—24no—
781C23—24no—
782C23—24no—
783C23—24no—
784C23—24no—
785C23—24no—
786C23—22no—
787C23—24no—
788C23—24no—
789C23—24no—
790C23—22no—
791C23—22no—
792C23—24no—
793C23—24no—
794C23—22no—
795C23—24no—
796C23—232no—
797C23—24no—
798C23—24no—
799C23—24no—
800C23—24no—
801C23—24no—
802C23—24no—
803C23—24no—
804C23—24no—
805C23—24no—
806C23—24no—
807C23—24no—
808C23—24no—
809C23—24no—
810C23—24no—
811C23—24no—
812C23—24no—
813C23—24no—
814C23—24no—
815C23—22no—
816C23—24no—
817C23—22no—
818C23—24no—
819C23—22no—
820C23—432no—
821C23—432no—
822C23—416no—
823C23—416no—
824C23—432no—
825C23—432no—
826C23—416no—
827C23—416no—
828C23—416no—
829C23—416no—
830C23—42no—
831C23—42no—
832C23—42no—
833C23—42no—
834C23—42no—
835C23—42no—
836C23—42no—
837C23—42no—
838C23—42no—
839C23—42no—
840C23—42no—
841C23—42no—
842C23—42no—
843C23—42no—
844C23—42no—
845C23—42no—
846C23—41no—
847C23—41no—
848C23—41no—
849C23—42no—
850C23—41no—
851C23—42no—
852C23—42no—
853C23—42no—
854C23—42no—
855C23—41no—
856C23—42no—
857C23—42no—
858C23—41no—
859C23—41no—
860C23—42no—
861C23—42no—
862C23—41no—
863C23—42no—
864C23#93514yes—
865C23#93514yes—
866C23#93614yes—
867C23#93814yes—
868C23#93918yes—
869C23#93914yes—
870C23#93914yes—
871C23#95314yes—
872C23C2×D3×D411yescharacteristic
873C23C2×D3×D412yes—
874C23C2×#23711yescharacteristic
875C23C2×#23711yescharacteristic
876C23C2×#23711yescharacteristic
877C23C2×#23712yes—
878C23#100412yes—
879C23#100412yes—
880C23C22×#6711yescharacteristic
881C23C22×#6711yescharacteristic
882C23C22×#6711yescharacteristic
883D4—432no—
884D4—416no—
885C2×C4—22no—
886C2×C4—24no—
887C2×C4—22no—
888C2×C4—24no—
889C2×C4—22no—
890C2×C4—24no—
891C2×C4—34no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—42no—
896C2×C4—41no—
897C2×C4—42no—
898C2×C4—42no—
899C2×C4—42no—
900C2×C4—62no—
901C2×C4—64no—
902C2×C4—62no—
903C2×C4—64no—
904C2×C4—62no—
905C2×C4—64no—
906C2×C4—64no—
907C2×C4—62no—
908C2×C4—62no—
909C2×C4—64no—
910C2×C4—1216no—
911C2×C4—1216no—
912C2×C4—122no—
913C2×C4—122no—
914C2×C4—122no—
915C2×C4—122no—
916C2×C4—122no—
917C2×C4—122no—
918C2×C4—122no—
919C2×C4—122no—
920C2×C4—122no—
921C2×C4—121no—
922C2×C4—121no—
923C2×C4—122no—
924C2×C4—122no—
925C2×C4—122no—
926C2×C4—122no—
927C2×C4—122no—
928C2×C4—122no—
929C2×C4—121no—
930C2×C4—122no—
931C2×C4—121no—
932C2×C4—121no—
933C2×C4—121no—
934C2×C4—122no—
935C2×C3—28no—
936C2×C3—48no—
937C2×C3—82no—
938C2×C3C2×#39411yescharacteristic
939C2×C3#240811yescharacteristic
940C2×C3#241012yes—
941C2×C3#241011yescharacteristic
942C2×C3#241111yescharacteristic
943C2×C3#241212yes—
944C2×C3#241812yes—
945C2×C3#247212yes—
946C2×C3#253411yescharacteristic
947C2×C3#261711yescharacteristic
948C2×C3#284711yescharacteristic
949C22—28no—
950C22—24no—
951C22—24no—
952C22—28no—
953C22—28no—
954C22—28no—
955C22—24no—
956C22—24no—
957C22—24no—
958C22—24no—
959C22—28no—
960C22—28no—
961C22—28no—
962C22—464no—
963C22—44no—
964C22—44no—
965C22—44no—
966C22—44no—
967C22—44no—
968C22—44no—
969C22—44no—
970C22—44no—
971C22—44no—
972C22—44no—
973C22—44no—
974C22—44no—
975C22—42no—
976C22—44no—
977C22—42no—
978C22—44no—
979C22—42no—
980C22—81no—
981C22—82no—
982C22—82no—
983C22—81no—
984C22—81no—
985C22—81no—
986C22#522218yescomplemented
987C22#558611yescharacteristic
988C22#558612yes—
989C22#558712yes—
990C22#558712yes—
991C22D3×#12011yescharacteristic
992C22#558911yescharacteristic
993C22#559112yes—
994C22#559112yes—
995C22#559211yescharacteristic
996C22#559312yes—
997C22C2×#93511yescharacteristic
998C22C2×#93511yescharacteristic
999C22C2×#93611yescharacteristic
1000C22C2×#93811yescharacteristic
1001C22D4×#6712yes—
1002C22D4×#6712yes—
1003C22C2×#93911yescharacteristic
1004C22C2×#93911yescharacteristic
1005C22C2×#93912yes—
1006C22#580412yes—
1007C22#580612yes—
1008C22#580612yes—
1009C22C2×#95311yescharacteristic
1010C4—42no—
1011C4—44no—
1012C4—64no—
1013C4—124no—
1014C4—122no—
1015C4—242no—
1016C4—241no—
1017C4—241no—
1018C3#1472511yescharacteristic, complemented, Sylow
1019C2—28no—
1020C2—48no—
1021C2—82no—
1022C2#8258211yescharacteristic
1023C2#8258311yescharacteristic
1024C2#8258412yes—
1025C2#8258512yes—
1026C2#8258912yes—
1027C2#8259011yescharacteristic
1028C2#8259211yescharacteristic
1029C2#8260111yescharacteristic
1030C2#8260511yescharacteristic
1031C2C2×#522211yescharacteristic
1032C2#8404812yes—
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
Fitting, prime radicalC22×C3×#120C2
hypercenterC22×#120D3
hypocenterC3#14725
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22×#120

Complements

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

NH ≅ G/Ntype
2. C23×#217C2semidirect
3. C2×#5247C2semidirect
4. C2×#5222C2semidirect
5. C2×#5220C2semidirect
6. C2×#5220C2semidirect
7. C2×#4942C2semidirect
8. #72131C2semidirect
9. #71549C2semidirect
10. #71547C2semidirect
11. #71544C2semidirect
31. C22×#217C22semidirect
32. C22×#217C22semidirect
33. C22×#217C22semidirect
34. C22×Dic3⋊C4C22semidirect
39. C2×C3⋊#95C22semidirect
40. C2×C3⋊#95C22semidirect
41. C2×C3⋊#95C22semidirect
42. C2×C3⋊#95C22semidirect
43. C2×C3⋊#95C22semidirect
44. C2×C3⋊#95C22semidirect
96. C23×Dic3D4semidirect
135. C2×#217D4semidirect
565. C2×Dic3#120semidirect
748. C22×C3#394semidirect
986. C22#5222semidirect
1018. C3#14725semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#1202
C23×#2172
C2×#52472
C2×#52222
C2×#52202
C2×#49422
#721312
#715492
#715472
#715442
#147253