Finite Group Databasebeta

← #10729039

Subgroups — #10729039

Order 768.

2638 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#938C211yesmaximal, characteristic
2C2×#4956C212yesmaximal, complemented
3C2×#4956C212yesmaximal, complemented
4C2×D3×#95C211yesmaximal, characteristic, complemented
5C3×#1438C211yesmaximal, characteristic, complemented
6#72131C211yesmaximal, characteristic, complemented
7#71549C212yesmaximal, complemented
8#71548C212yesmaximal, complemented
9(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
10#69415C211yesmaximal, characteristic, complemented
11#69412C211yesmaximal, characteristic, complemented
12#14913—31nomaximal, Sylow
13C23×C3×D4C2211yescharacteristic
14C23×#67C2212yes—
15C23×C4×D3C2211yescharacteristic
16C23×C4×D3C2211yescharacteristic
17C23×C4×D3C2211yescharacteristic
18C22×C3×C22⋊C4C2212yes—
19C22×C3×C22⋊C4C2212yes—
20C22×#217C2212yes—
21C22×#217C2212yes—
22C22×#217C2212yes—
23C2×#938—28no—
24C2×#938—24no—
25C22×(C2×D3)⋊C4C2212yes—
26C22×C4⋊Dic3C2211yescharacteristic
27C2×C3×#95C2211yescharacteristic
28C2×C3×#95C2211yescharacteristic
29C2×C3⋊#95C2212yes—
30C2×C3⋊#95C2212yes—
31C2×C3⋊#95C2211yescharacteristic
32C2×C3⋊#95C2211yescharacteristic
33C2×C3⋊#95C2212yes—
34C2×C3⋊#95C2212yes—
35C2×C3⋊#95C2211yescharacteristic
36C2×C3⋊#95C2211yescharacteristic
37C2×C3⋊#95C2212yes—
38#4956—28no—
39#4956—28no—
40D3×#95—24no—
41C22×#121—31no—
42C2×#386—32no—
43C2×#386—32no—
44C22×#95—31no—
45#1442—31no—
46#1442—31no—
47#1440—32no—
48#1440—32no—
49#1438—31no—
50#1438D311yescharacteristic, complemented
51C22⋊#95—31no—
52C25×C3C2312yes—
53C24×D3C2311yescharacteristic
54C22×C3×D4—24no—
55C22×C3×D4—22no—
56C22×C3×D4—22no—
57C22×C3×D4—22no—
58C22×C3×D4—42no—
59C23×C3×C4C2312yes—
60C23×C3×C4C2311yescharacteristic
61C23×C3×C4C2311yescharacteristic
62C23×C3×C4C2311yescharacteristic
63C22×#67—24no—
64C22×#67—24no—
65C22×#67—24no—
66C22×#67—24no—
67C22×#67—24no—
68C22×#67—24no—
69C22×#67D418yes—
70C23×Dic3C2312yes—
71C23×Dic3C2311yescharacteristic
72C23×Dic3C2311yescharacteristic
73C23×Dic3C2312yes—
74C23×Dic3C2311yescharacteristic
75C22×C4×D3—22no—
76C22×C4×D3—22no—
77C22×C4×D3—24no—
78C22×C4×D3—22no—
79C22×C4×D3—22no—
80C22×C4×D3—22no—
81C22×C4×D3—22no—
82C22×C4×D3—22no—
83C22×C4×D3—24no—
84C22×C4×D3—42no—
85C22×C4×D3—42no—
86C22×C4×D3—42no—
87C22×C4×D3—42no—
88C22×C4×D3D414yes—
89C22×C4×D3D414yescomplemented
90C2×C3×C22⋊C4—24no—
91C2×C3×C22⋊C4—24no—
92C2×C3×C22⋊C4—24no—
93C2×C3×C22⋊C4—42no—
94C2×C3×C22⋊C4—42no—
95C2×C3×C22⋊C4—42no—
96C2×#217—24no—
97C2×#217—24no—
98C2×#217—24no—
99C2×#217—24no—
100C2×#217—24no—
101C2×#217—24no—
102C2×#217—42no—
103C2×#217—42no—
104C2×#217—42no—
105#938—232no—
106C2×(C2×D3)⋊C4—24no—
107C2×(C2×D3)⋊C4—24no—
108C2×(C2×D3)⋊C4—24no—
109C2×C4⋊Dic3—22no—
110C2×C4⋊Dic3—24no—
111C3×#95—22no—
112C3×#95—22no—
113C3⋊#95—22no—
114C3⋊#95—24no—
115C3⋊#95—22no—
116C3⋊#95—22no—
117C3⋊#95—22no—
118C3⋊#95—24no—
119C3⋊#95—24no—
120C3⋊#95—24no—
121C3⋊#95—42no—
122C23×D4—32no—
123C23×D4C2×D311yescharacteristic
124C24×C4—31no—
125C24×C4—31no—
126C24×C4—31no—
127C2×#121—64no—
128C2×#121—68no—
129C22×C4⋊C4—31no—
130C22×C22⋊C4—32no—
131C22×C22⋊C4—32no—
132C22×C22⋊C4—32no—
133C22×C22⋊C4—32no—
134C22×C22⋊C4C2×D312yes—
135C22×C22⋊C4C2×D312yes—
136#386—68no—
137#386—68no—
138C2×#95—31no—
139C2×#95—31no—
140C2×#95—31no—
141C2×#95—31no—
142C2×#95—32no—
143C2×#95—32no—
144C2×#95—32no—
145C2×#95—32no—
146C2×#95—32no—
147C2×#95—64no—
148C2×#95C2×D311yescharacteristic
149C2×#95C2×D311yescharacteristic
150C24×C3—22no—
151C24×C3—22no—
152C24×C3—22no—
153C24×C3—22no—
154C24×C3—22no—
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×C3C2×D414yes—
165C24×C3C2411yescharacteristic
166C23×D3—21no—
167C23×D3—21no—
168C23×D3—21no—
169C23×D3—21no—
170C23×D3—22no—
171C23×D3—22no—
172C23×D3C2×D414yes—
173C23×D3C2×D412yes—
174C23×D3C2×D412yes—
175C23×D3#4112yes—
176C23×D3#4114yes—
177C2×C3×D4—28no—
178C2×C3×D4—48no—
179C2×C3×D4—48no—
180C2×C3×D4—44no—
181C2×C3×D4—44no—
182C22×C3×C4—22no—
183C22×C3×C4—22no—
184C22×C3×C4—21no—
185C22×C3×C4—21no—
186C22×C3×C4—22no—
187C22×C3×C4—21no—
188C22×C3×C4—21no—
189C22×C3×C4—22no—
190C22×C3×C4—22no—
191C22×C3×C4—22no—
192C22×C3×C4—22no—
193C22×C3×C4—22no—
194C22×C3×C4—22no—
195C22×C3×C4—22no—
196C22×C3×C4—22no—
197C22×C3×C4—22no—
198C22×C3×C4—22no—
199C22×C3×C4C2×D412yes—
200C22×C3×C4C2×D412yes—
201C22×C3×C4#4112yes—
202C22×C3×C4#4112yes—
203C22×C3×C4#4112yes—
204C2×#67—216no—
205C2×#67—216no—
206C2×#67—216no—
207C2×#67—48no—
208C2×#67—48no—
209C2×#67—48no—
210C2×#67—48no—
211C22×Dic3—21no—
212C22×Dic3—21no—
213C22×Dic3—22no—
214C22×Dic3—22no—
215C22×Dic3—22no—
216C22×Dic3—22no—
217C22×Dic3—22no—
218C22×Dic3—21no—
219C22×Dic3—21no—
220C22×Dic3—21no—
221C22×Dic3—21no—
222C22×Dic3—22no—
223C22×Dic3—22no—
224C22×Dic3—22no—
225C22×Dic3—22no—
226C22×Dic3—22no—
227C22×Dic3—22no—
228C22×Dic3—22no—
229C22×Dic3—22no—
230C22×Dic3—22no—
231C22×Dic3—22no—
232C22×Dic3—22no—
233C22×Dic3—22no—
234C22×Dic3—22no—
235C22×Dic3—22no—
236C22×Dic3C2×D414yes—
237C22×Dic3C2×D412yes—
238C22×Dic3C2×D412yes—
239C22×Dic3#4112yes—
240C2×C4×D3—28no—
241C2×C4×D3—28no—
242C2×C4×D3—28no—
243C2×C4×D3—28no—
244C2×C4×D3—44no—
245C2×C4×D3—48no—
246C2×C4×D3—48no—
247C2×C4×D3—48no—
248C2×C4×D3—48no—
249C2×C4×D3—48no—
250C2×C4×D3—44no—
251C2×C4×D3—44no—
252C2×C4×D3—44no—
253C2×C4×D3—48no—
254C2×C4×D3—44no—
255C3×C22⋊C4—48no—
256C3×C22⋊C4—48no—
257#217—216no—
258#217—48no—
259#217—48no—
260(C2×D3)⋊C4—48no—
261C4⋊Dic3—28no—
262C25—31no—
263C25C22×D312yes—
264C22×D4—24no—
265C22×D4—22no—
266C22×D4—22no—
267C22×D4—22no—
268C22×D4—38no—
269C22×D4—42no—
270C22×D4—64no—
271C22×D4—64no—
272C22×D4—64no—
273C22×D4—64no—
274C22×D4—64no—
275C22×D4—64no—
276C23×C4—31no—
277C23×C4—31no—
278C23×C4—31no—
279C23×C4—32no—
280C23×C4—34no—
281C23×C4—34no—
282C23×C4—32no—
283C23×C4—62no—
284C23×C4—64no—
285C23×C4—62no—
286C23×C4—62no—
287C23×C4—62no—
288C23×C4—64no—
289C23×C4—62no—
290C23×C4—62no—
291C23×C4—62no—
292C23×C4—122no—
293C23×C4—122no—
294C23×C4—122no—
295C23×C4—122no—
296C23×C4C22×D312yes—
297C23×C4C22×D311yescharacteristic
298C23×C4C22×D311yescharacteristic
299C23×C4C22×D311yescharacteristic
300#121—632no—
301C2×C4⋊C4—64no—
302C2×C4⋊C4—62no—
303C2×C22⋊C4—24no—
304C2×C22⋊C4—24no—
305C2×C22⋊C4—24no—
306C2×C22⋊C4—42no—
307C2×C22⋊C4—42no—
308C2×C22⋊C4—42no—
309C2×C22⋊C4—64no—
310C2×C22⋊C4—64no—
311C2×C22⋊C4—64no—
312C2×C22⋊C4—64no—
313C2×C22⋊C4—64no—
314C2×C22⋊C4—64no—
315C2×C22⋊C4—64no—
316C2×C22⋊C4—64no—
317C2×C22⋊C4—64no—
318C2×C22⋊C4—122no—
319C2×C22⋊C4—122no—
320C2×C22⋊C4—122no—
321#95—22no—
322#95—22no—
323#95—62no—
324#95—62no—
325#95—64no—
326#95—64no—
327#95—64no—
328#95—62no—
329#95—62no—
330#95—64no—
331#95—122no—
332C23×C3—24no—
333C23×C3—24no—
334C23×C3—24no—
335C23×C3—24no—
336C23×C3—24no—
337C23×C3—24no—
338C23×C3—24no—
339C23×C3—42no—
340C23×C3—42no—
341C23×C3—42no—
342C23×C3—42no—
343C23×C3—42no—
344C23×C3—42no—
345C23×C3—42no—
346C23×C3—42no—
347C23×C3—42no—
348C23×C3—42no—
349C23×C3—42no—
350C23×C3—42no—
351C23×C3—42no—
352C23×C3—42no—
353C23×C3—42no—
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×C3C22×D411yescharacteristic
368C23×C3C22×D412yes—
369C23×C3C22×D411yescharacteristic
370C23×C3C2×#4111yescharacteristic
371C23×C3C2×#4111yescharacteristic
372C23×C3C2×#4111yescharacteristic
373C23×C3C2×#4111yescharacteristic
374C23×C3C2×#4112yes—
375C23×C3C2×#4111yescharacteristic
376C23×C3H(5,𝔽2)12yes—
377C23×C3H(5,𝔽2)12yes—
378C22×D3—22no—
379C22×D3—22no—
380C22×D3—22no—
381C22×D3—22no—
382C22×D3—22no—
383C22×D3—22no—
384C22×D3—22no—
385C22×D3—24no—
386C22×D3—22no—
387C22×D3—24no—
388C22×D3—24no—
389C22×D3—24no—
390C22×D3—24no—
391C22×D3—24no—
392C22×D3—24no—
393C22×D3—24no—
394C22×D3—24no—
395C22×D3—24no—
396C22×D3#12014yes—
397C22×D3#12118yes—
398C22×D3#12114yes—
399C22×D3#12318yes—
400C22×D3#12414yes—
401C3×D4—416no—
402C2×C3×C4—22no—
403C2×C3×C4—22no—
404C2×C3×C4—24no—
405C2×C3×C4—24no—
406C2×C3×C4—22no—
407C2×C3×C4—22no—
408C2×C3×C4—24no—
409C2×C3×C4—24no—
410C2×C3×C4—41no—
411C2×C3×C4—41no—
412C2×C3×C4—41no—
413C2×C3×C4—41no—
414C2×C3×C4—42no—
415C2×C3×C4—42no—
416C2×C3×C4—42no—
417C2×C3×C4—42no—
418C2×C3×C4—42no—
419C2×C3×C4—42no—
420C2×C3×C4—42no—
421C2×C3×C4—42no—
422C2×C3×C4—42no—
423C2×C3×C4#12314yes—
424#67—432no—
425C2×Dic3—24no—
426C2×Dic3—22no—
427C2×Dic3—22no—
428C2×Dic3—24no—
429C2×Dic3—22no—
430C2×Dic3—24no—
431C2×Dic3—22no—
432C2×Dic3—24no—
433C2×Dic3—22no—
434C2×Dic3—24no—
435C2×Dic3—41no—
436C2×Dic3—42no—
437C2×Dic3—42no—
438C2×Dic3—42no—
439C2×Dic3—42no—
440C2×Dic3—41no—
441C2×Dic3—41no—
442C2×Dic3—41no—
443C2×Dic3—42no—
444C2×Dic3—42no—
445C2×Dic3—42no—
446C2×Dic3—42no—
447C2×Dic3—42no—
448C2×Dic3—42no—
449C2×Dic3—42no—
450C2×Dic3—42no—
451C2×Dic3—42no—
452C2×Dic3—42no—
453C2×Dic3—42no—
454C4×D3—416no—
455C4×D3—416no—
456C4×D3—416no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24—32no—
472C24—34no—
473C24—32no—
474C24—34no—
475C24—32no—
476C24—61no—
477C24—61no—
478C24—61no—
479C24—62no—
480C24—62no—
481C24—61no—
482C24D3×D414yes—
483C24C23×D311yescharacteristic
484C2×D4—28no—
485C2×D4—48no—
486C2×D4—48no—
487C2×D4—44no—
488C2×D4—44no—
489C2×D4—616no—
490C2×D4—616no—
491C2×D4—616no—
492C2×D4—128no—
493C2×D4—128no—
494C2×D4—128no—
495C2×D4—128no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—32no—
514C22×C4—32no—
515C22×C4—34no—
516C22×C4—32no—
517C22×C4—68no—
518C22×C4—68no—
519C22×C4—68no—
520C22×C4—61no—
521C22×C4—61no—
522C22×C4—61no—
523C22×C4—62no—
524C22×C4—62no—
525C22×C4—62no—
526C22×C4—62no—
527C22×C4—62no—
528C22×C4—61no—
529C22×C4—61no—
530C22×C4—62no—
531C22×C4—62no—
532C22×C4—62no—
533C22×C4—62no—
534C22×C4—61no—
535C22×C4—62no—
536C22×C4—62no—
537C22×C4—62no—
538C22×C4—68no—
539C22×C4—62no—
540C22×C4—62no—
541C22×C4—62no—
542C22×C4—62no—
543C22×C4—62no—
544C22×C4—62no—
545C22×C4—62no—
546C22×C4—124no—
547C22×C4—128no—
548C22×C4—128no—
549C22×C4—128no—
550C22×C4—128no—
551C22×C4—128no—
552C22×C4—124no—
553C22×C4—124no—
554C22×C4—124no—
555C22×C4—124no—
556C22×C4—128no—
557C22×C4#23512yes—
558C22×C4D3×D412yes—
559C22×C4D3×D412yes—
560C22×C4#23712yes—
561C22×C4#23712yes—
562C4⋊C4—68no—
563C22⋊C4—48no—
564C22⋊C4—48no—
565C22⋊C4—616no—
566C22⋊C4—128no—
567C22⋊C4—128no—
568C22⋊C4—128no—
569C22×C3—44no—
570C22×C3—44no—
571C22×C3—44no—
572C22×C3—44no—
573C22×C3—44no—
574C22×C3—44no—
575C22×C3—44no—
576C22×C3—82no—
577C22×C3—82no—
578C22×C3—82no—
579C22×C3—82no—
580C22×C3—82no—
581C22×C3—82no—
582C22×C3—82no—
583C22×C3—82no—
584C22×C3C2×#12011yescharacteristic
585C22×C3C2×#12111yescharacteristic
586C22×C3C2×#12112yes—
587C22×C3C2×#12312yes—
588C22×C3C2×#12311yescharacteristic
589C22×C3#52511yescharacteristic
590C22×C3C2×#12411yescharacteristic
591C22×C3#52911yescharacteristic
592C22×C3#52911yescharacteristic
593C22×C3#53211yescharacteristic
594C22×C3#53211yescharacteristic
595C22×C3#53411yescharacteristic
596C22×C3#53412yes—
597C22×C3#53511yescharacteristic
598C22×C3#53812yes—
599C22×C3#54612yes—
600C22×C3#54612yes—
601C22×C3#54612yes—
602C22×C3#54612yes—
603C22×C3#55312yes—
604C22×C3#55312yes—
605C22×C3#55312yes—
606C22×C3#55312yes—
607C2×D3—24no—
608C2×D3—24no—
609C2×D3—24no—
610C2×D3—24no—
611C2×D3—24no—
612C2×D3—28no—
613C2×D3—28no—
614C2×D3—24no—
615C2×D3—28no—
616C2×D3—28no—
617C2×D3#39418yes—
618C3×C4—24no—
619C3×C4—42no—
620C3×C4—42no—
621C3×C4—82no—
622Dic3—42no—
623Dic3—44no—
624Dic3—42no—
625Dic3—42no—
626Dic3—82no—
627C23—24no—
628C23—24no—
629C23—24no—
630C23—24no—
631C23—24no—
632C23—24no—
633C23—24no—
634C23—38no—
635C23—34no—
636C23—34no—
637C23—38no—
638C23—34no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
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—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—64no—
668C23—62no—
669C23—62no—
670C23—62no—
671C23—62no—
672C23—64no—
673C23—62no—
674C23—62no—
675C23—64no—
676C23—62no—
677C23—64no—
678C23—64no—
679C23—64no—
680C23—62no—
681C23—64no—
682C23—64no—
683C23—64no—
684C23—64no—
685C23C2×#23511yescharacteristic
686C23C2×D3×D412yes—
687C23C2×D3×D411yescharacteristic
688C23C2×D3×D411yescharacteristic
689C23C2×#23711yescharacteristic
690C23C2×#23711yescharacteristic
691C23#100412yes—
692C23#100412yes—
693C23D3×#4111yescharacteristic
694C23D3×#4112yes—
695C23D3×#4111yescharacteristic
696D4—416no—
697D4—1232no—
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—64no—
720C2×C4—62no—
721C2×C4—62no—
722C2×C4—64no—
723C2×C4—64no—
724C2×C4—62no—
725C2×C4—62no—
726C2×C4—64no—
727C2×C4—62no—
728C2×C4—64no—
729C2×C4—1216no—
730C2×C4—1216no—
731C2×C4—1216no—
732C2×C4—122no—
733C2×C4—122no—
734C2×C4—121no—
735C2×C4—121no—
736C2×C4—122no—
737C2×C4—121no—
738C2×C4—121no—
739C2×C4—122no—
740C2×C4—122no—
741C2×C4—122no—
742C2×C4—122no—
743C2×C4—122no—
744C2×C4—122no—
745C2×C4—122no—
746C2×C4—122no—
747C2×C4—122no—
748C2×C4—122no—
749C2×C4—122no—
750C2×C4—122no—
751C2×C4#88314yes—
752C2×C3—84no—
753C2×C3C2×#39411yescharacteristic
754C2×C3#240411yescharacteristic
755C2×C3#240511yescharacteristic
756C2×C3#244412yes—
757C2×C3#244412yes—
758C2×C3#250411yescharacteristic
759C2×C3#254312yes—
760C2×C3#254312yes—
761C2×C3#259111yescharacteristic
762C2×C3#261711yescharacteristic
763C2×C3#285411yescharacteristic
764D3—28no—
765C22—38no—
766C22—44no—
767C22—44no—
768C22—44no—
769C22—44no—
770C22—44no—
771C22—44no—
772C22—44no—
773C22—64no—
774C22—68no—
775C22—64no—
776C22—64no—
777C22—68no—
778C22—68no—
779C22—64no—
780C22—64no—
781C22—68no—
782C22—64no—
783C22—82no—
784C22—82no—
785C22—82no—
786C22—82no—
787C22—82no—
788C22—82no—
789C22—82no—
790C22—82no—
791C22C2×#88311yescharacteristic
792C22#549012yes—
793C22#554811yescharacteristic
794C22#555711yescharacteristic
795C22#555812yes—
796C22D3×#12011yescharacteristic
797C22#558911yescharacteristic
798C22#558912yes—
799C22#559112yes—
800C22#559112yes—
801C22D3×#12112yes—
802C22D3×#12111yescharacteristic
803C22#560611yescharacteristic
804C22#561012yes—
805C22#561312yes—
806C22#561412yes—
807C22#561412yes—
808C22D3×#12312yes—
809C22#566112yes—
810C22D3×#12411yescharacteristic
811C22#568011yescharacteristic
812C22#571511yescharacteristic
813C22#571611yescharacteristic
814C4—24no—
815C4—42no—
816C4—42no—
817C4—82no—
818C4—124no—
819C4—122no—
820C4—122no—
821C4—122no—
822C4—242no—
823C3#1491311yescharacteristic, complemented, Sylow
824C2—68no—
825C2—84no—
826C2#7385311yescharacteristic
827C2#7489712yes—
828C2#7490212yes—
829C2#7633611yescharacteristic
830C2#7647511yescharacteristic
831C2#7675411yescharacteristic
832C2#7675912yes—
833C2#7676111yescharacteristic
834C2D3×#39411yescharacteristic
835C2#7711812yes—
836C2#7712111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1438C2
prime radicalC22×#938C2
hypercenter#1438D3
hypocenterC3#14913
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
2. C2×#4956C2semidirect
3. C2×#4956C2semidirect
4. C2×D3×#95C2semidirect
5. C3×#1438C2semidirect
6. #72131C2semidirect
7. #71549C2semidirect
8. #71548C2semidirect
9. (C2×D3)⋊#95C2semidirect
10. #69415C2semidirect
11. #69412C2semidirect
50. #1438D3semidirect
89. C22×C4×D3D4semidirect
823. C3#14913semidirect

Maximal subgroups

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

subgroupindex
C22×#9382
C2×#49562
C2×D3×#952
C3×#14382
#721312
#715492
#715482
(C2×D3)⋊#952
#694152
#694122
#149133