Finite Group Databasebeta

← #10732245

Subgroups — #10732245

Order 768.

1586 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#380C211yesmaximal, characteristic
2C2×#5212C211yesmaximal, characteristic
3C2×C4×#217C211yesmaximal, characteristic
4C2×#4984C211yesmaximal, characteristic, complemented
5#71563C211yesmaximal, characteristic, complemented
6#71563C211yesmaximal, characteristic, complemented
7#71563C211yesmaximal, characteristic, complemented
8#71549C212yesmaximal
9#71546C212yesmaximal
10#69422C212yesmaximal, complemented
11#69418C212yesmaximal, complemented
12#15183—31nomaximal, Sylow
13C24×C3×C4C2211yescharacteristic
14C22×C3×C4⋊C4C2211yescharacteristic
15C22×C3×C4⋊C4C2211yescharacteristic
16C22×C3×C22⋊C4C2212yes—
17C22×#217C2211yescharacteristic
18C22×#217C2211yescharacteristic
19C22×#217C2212yes—
20C22×C4⋊Dic3C2211yescharacteristic
21C22×C4⋊Dic3C2211yescharacteristic
22C22×C4⋊Dic3C2212yes—
23C22×C4×Dic3C2211yescharacteristic
24C22×C4×Dic3C2211yescharacteristic
25C3×#380—24no—
26C2×C3×#95C2212yes—
27#5212—24no—
28C4×#217—24no—
29C2×C3⋊#95C2211yescharacteristic
30C2×C3⋊#95C2212yes—
31C2×C3⋊#95C2212yes—
32C2×C3⋊#95C2212yes—
33C2×C3⋊#95C2211yescharacteristic
34C2×C3⋊#95C2212yes—
35C2×C3⋊#95C2212yes—
36C2×C3⋊#95C2212yes—
37C2×C3⋊#95C2212yes—
38C2×C3⋊#95C2212yes—
39#4984—24no—
40C2×#389—31no—
41C2×#380—31no—
42C2×#380D311yescharacteristic
43C2×C4×C22⋊C4—31no—
44#1445—32no—
45#1443—32no—
46#1440—32no—
47#1439—32no—
48C4⋊#95—31no—
49C4⋊#95—31no—
50C4⋊#95—31no—
51C25×C3C2311yescharacteristic
52C23×C3×C4—22no—
53C23×C3×C4—22no—
54C23×C3×C4—22no—
55C23×C3×C4—22no—
56C23×C3×C4—22no—
57C23×C3×C4—22no—
58C23×C3×C4D414yes—
59C23×C3×C4C2312yes—
60C23×C3×C4C2311yescharacteristic
61C23×C3×C4C2312yes—
62C23×C3×C4C2311yescharacteristic
63C23×Dic3C2312yes—
64C23×Dic3C2312yes—
65C23×Dic3C2311yescharacteristic
66C23×Dic3C2311yescharacteristic
67C23×Dic3C2311yescharacteristic
68C23×Dic3C2311yescharacteristic
69C2×C3×C4⋊C4—22no—
70C2×C3×C4⋊C4—22no—
71C2×C3×C4⋊C4—22no—
72C2×C3×C4⋊C4—22no—
73C2×C3×C4⋊C4—22no—
74C2×C3×C4⋊C4D414yes—
75C2×C3×C22⋊C4—24no—
76C2×C3×C22⋊C4—24no—
77C2×C3×C22⋊C4—42no—
78C2×#217—22no—
79C2×#217—22no—
80C2×#217—22no—
81C2×#217—22no—
82C2×#217—22no—
83C2×#217—24no—
84C2×#217—42no—
85C2×#217—42no—
86C2×#217Q814yes—
87C2×C4⋊Dic3—22no—
88C2×C4⋊Dic3—22no—
89C2×C4⋊Dic3—24no—
90C2×C4⋊Dic3—22no—
91C2×C4⋊Dic3—22no—
92C2×C4⋊Dic3—22no—
93C2×C4⋊Dic3—22no—
94C2×C4⋊Dic3—24no—
95C2×C4⋊Dic3—42no—
96C2×C4×Dic3—22no—
97C2×C4×Dic3—22no—
98C2×C4×Dic3—22no—
99C2×C4×Dic3—22no—
100C2×C4×Dic3—22no—
101C2×C4×Dic3—22no—
102C3×#95—24no—
103C3⋊#95—22no—
104C3⋊#95—22no—
105C3⋊#95—24no—
106C3⋊#95—24no—
107C3⋊#95—24no—
108C3⋊#95—42no—
109C3⋊#95—42no—
110C3⋊#95—42no—
111C3⋊#95—42no—
112C3⋊#95—42no—
113C24×C4C2×D311yescharacteristic
114C22×C4⋊C4—31no—
115C22×C4⋊C4—31no—
116C22×C4⋊C4—32no—
117C22×C4⋊C4C2×D311yescharacteristic
118C22×C4⋊C4C2×D311yescharacteristic
119C22×C22⋊C4—31no—
120C22×C22⋊C4—31no—
121C22×C22⋊C4—32no—
122C22×C22⋊C4C2×D312yes—
123C22×C42—31no—
124C22×C42—31no—
125#389—64no—
126#380—24no—
127#380—64no—
128C4×C22⋊C4—64no—
129C2×#95—32no—
130C2×#95—32no—
131C2×#95—31no—
132C2×#95—32no—
133C2×#95—31no—
134C2×#95—32no—
135C2×#95—32no—
136C2×#95—32no—
137C2×#95—32no—
138C2×#95—32no—
139C2×#95C2×D312yes—
140C24×C3—21no—
141C24×C3—21no—
142C24×C3—21no—
143C24×C3—21no—
144C24×C3—21no—
145C24×C3—21no—
146C24×C3—21no—
147C24×C3—21no—
148C24×C3—21no—
149C24×C3—21no—
150C24×C3—21no—
151C24×C3—21no—
152C24×C3C2×D412yes—
153C24×C3C2×Q812yes—
154C24×C3#4112yes—
155C24×C3C2411yescharacteristic
156C22×C3×C4—21no—
157C22×C3×C4—22no—
158C22×C3×C4—22no—
159C22×C3×C4—22no—
160C22×C3×C4—22no—
161C22×C3×C4—21no—
162C22×C3×C4—21no—
163C22×C3×C4—21no—
164C22×C3×C4—21no—
165C22×C3×C4—21no—
166C22×C3×C4—22no—
167C22×C3×C4—22no—
168C22×C3×C4—28no—
169C22×C3×C4—28no—
170C22×C3×C4—28no—
171C22×C3×C4—22no—
172C22×C3×C4—22no—
173C22×C3×C4—22no—
174C22×C3×C4—22no—
175C22×C3×C4—22no—
176C22×C3×C4—22no—
177C22×C3×C4—22no—
178C22×C3×C4—44no—
179C22×C3×C4—44no—
180C22×C3×C4—44no—
181C22×C3×C4—44no—
182C22×C3×C4C2×D412yes—
183C22×C3×C4C2×D412yes—
184C22×C3×C4C2×D414yes—
185C22×C3×C4C2×D412yes—
186C22×C3×C4#4112yes—
187C22×C3×C4#4112yes—
188C22×C3×C4#4112yes—
189C22×C3×C4#4112yes—
190C22×C3×C4#4112yes—
191C22×Dic3—21no—
192C22×Dic3—21no—
193C22×Dic3—21no—
194C22×Dic3—21no—
195C22×Dic3—21no—
196C22×Dic3—21no—
197C22×Dic3—21no—
198C22×Dic3—21no—
199C22×Dic3—21no—
200C22×Dic3—21no—
201C22×Dic3—21no—
202C22×Dic3—21no—
203C22×Dic3—21no—
204C22×Dic3—21no—
205C22×Dic3—21no—
206C22×Dic3—21no—
207C22×Dic3—21no—
208C22×Dic3—21no—
209C22×Dic3—21no—
210C22×Dic3—21no—
211C22×Dic3—21no—
212C22×Dic3—21no—
213C22×Dic3—21no—
214C22×Dic3—21no—
215C22×Dic3—22no—
216C22×Dic3—22no—
217C22×Dic3—22no—
218C22×Dic3—22no—
219C22×Dic3—22no—
220C22×Dic3—22no—
221C22×Dic3—22no—
222C22×Dic3—22no—
223C22×Dic3—22no—
224C22×Dic3—22no—
225C22×Dic3—22no—
226C22×Dic3—22no—
227C22×Dic3—22no—
228C22×Dic3—22no—
229C22×Dic3C2×Q812yes—
230C22×Dic3C2×Q812yes—
231C22×Dic3#4112yes—
232C22×Dic3#4112yes—
233C3×C4⋊C4—28no—
234C3×C4⋊C4—44no—
235C3×C22⋊C4—48no—
236#217—28no—
237#217—28no—
238#217—48no—
239C4⋊Dic3—48no—
240C4⋊Dic3—44no—
241C4⋊Dic3—44no—
242C4×Dic3—44no—
243C4×Dic3—44no—
244C25C22×D311yescharacteristic
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—31no—
252C23×C4—31no—
253C23×C4—31no—
254C23×C4—31no—
255C23×C4—32no—
256C23×C4—32no—
257C23×C4D1214yes—
258C23×C4C22×D312yes—
259C23×C4C22×D311yescharacteristic
260C23×C4C22×D312yes—
261C23×C4C22×D311yescharacteristic
262C2×C4⋊C4—22no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—64no—
268C2×C4⋊C4—62no—
269C2×C4⋊C4—62no—
270C2×C4⋊C4—62no—
271C2×C4⋊C4—62no—
272C2×C4⋊C4—62no—
273C2×C4⋊C4—64no—
274C2×C4⋊C4—62no—
275C2×C4⋊C4—122no—
276C2×C4⋊C4#6714yes—
277C2×C22⋊C4—24no—
278C2×C22⋊C4—24no—
279C2×C22⋊C4—34no—
280C2×C22⋊C4—42no—
281C2×C22⋊C4—62no—
282C2×C22⋊C4—62no—
283C2×C22⋊C4—62no—
284C2×C22⋊C4—62no—
285C2×C22⋊C4—62no—
286C2×C22⋊C4—64no—
287C2×C22⋊C4—122no—
288C2×C22⋊C4—122no—
289C2×C42—62no—
290C2×C42—62no—
291C2×C42—62no—
292C2×C42—62no—
293C2×C42—62no—
294C2×C42—62no—
295#95—24no—
296#95—64no—
297#95—62no—
298#95—62no—
299#95—64no—
300#95—64no—
301#95—122no—
302#95—122no—
303#95—122no—
304#95—122no—
305#95—122no—
306C23×C3—22no—
307C23×C3—22no—
308C23×C3—22no—
309C23×C3—22no—
310C23×C3—22no—
311C23×C3—22no—
312C23×C3—22no—
313C23×C3—22no—
314C23×C3—22no—
315C23×C3—22no—
316C23×C3—22no—
317C23×C3—22no—
318C23×C3—22no—
319C23×C3—22no—
320C23×C3—22no—
321C23×C3—22no—
322C23×C3—22no—
323C23×C3—22no—
324C23×C3—41no—
325C23×C3—41no—
326C23×C3—41no—
327C23×C3—41no—
328C23×C3—41no—
329C23×C3—41no—
330C23×C3—41no—
331C23×C3—41no—
332C23×C3—41no—
333C23×C3—41no—
334C23×C3—41no—
335C23×C3—41no—
336C23×C3—41no—
337C23×C3—41no—
338C23×C3—41no—
339C23×C3—41no—
340C23×C3C22⋊Q814yes—
341C23×C3C22×D411yescharacteristic
342C23×C3C22×D411yescharacteristic
343C23×C3C22×Q811yescharacteristic
344C23×C3C2×#4111yescharacteristic
345C23×C3C2×#4111yescharacteristic
346C23×C3C2×#4111yescharacteristic
347C23×C3C2×#4111yescharacteristic
348C23×C3C2×#4111yescharacteristic
349C23×C3C2×#4111yescharacteristic
350C23×C3C2×#4111yescharacteristic
351C23×C3C2×#4111yescharacteristic
352C23×C3H(5,𝔽2)11yescharacteristic
353C23×C3H(5,𝔽2)11yescharacteristic
354C23×C3H(5,𝔽2)11yescharacteristic
355C23×C32−1+411yescharacteristic
356C2×C3×C4—22no—
357C2×C3×C4—24no—
358C2×C3×C4—22no—
359C2×C3×C4—22no—
360C2×C3×C4—24no—
361C2×C3×C4—24no—
362C2×C3×C4—41no—
363C2×C3×C4—41no—
364C2×C3×C4—41no—
365C2×C3×C4—41no—
366C2×C3×C4—42no—
367C2×C3×C4—42no—
368C2×C3×C4—42no—
369C2×C3×C4—42no—
370C2×C3×C4—416no—
371C2×C3×C4—42no—
372C2×C3×C4—42no—
373C2×C3×C4—42no—
374C2×C3×C4—42no—
375C2×C3×C4—42no—
376C2×C3×C4—42no—
377C2×C3×C4—42no—
378C2×C3×C4#12114yes—
379C2×C3×C4#12314yes—
380C2×C3×C4#12314yes—
381C2×C3×C4#12314yes—
382C2×C3×C4#12414yes—
383C2×C3×C4#12614yes—
384C2×C3×C4#12614yes—
385C2×Dic3—22no—
386C2×Dic3—22no—
387C2×Dic3—22no—
388C2×Dic3—22no—
389C2×Dic3—22no—
390C2×Dic3—22no—
391C2×Dic3—22no—
392C2×Dic3—22no—
393C2×Dic3—22no—
394C2×Dic3—22no—
395C2×Dic3—22no—
396C2×Dic3—22no—
397C2×Dic3—41no—
398C2×Dic3—41no—
399C2×Dic3—41no—
400C2×Dic3—41no—
401C2×Dic3—41no—
402C2×Dic3—41no—
403C2×Dic3—41no—
404C2×Dic3—41no—
405C2×Dic3—41no—
406C2×Dic3—41no—
407C2×Dic3—41no—
408C2×Dic3—41no—
409C2×Dic3—41no—
410C2×Dic3—41no—
411C2×Dic3—41no—
412C2×Dic3—41no—
413C2×Dic3—42no—
414C2×Dic3—42no—
415C2×Dic3—42no—
416C2×Dic3—42no—
417C2×Dic3—42no—
418C2×Dic3—42no—
419C2×Dic3—42no—
420C2×Dic3—42no—
421C2×Dic3—42no—
422C2×Dic3—42no—
423C2×Dic3—42no—
424C2×Dic3—42no—
425C2×Dic3—42no—
426C2×Dic3—42no—
427C24—21no—
428C24—21no—
429C24—21no—
430C24—21no—
431C24—21no—
432C24—21no—
433C24—21no—
434C24—21no—
435C24—21no—
436C24—21no—
437C24—21no—
438C24—21no—
439C24C2×D1212yes—
440C24#23712yes—
441C24D3×Q812yes—
442C24C23×D311yescharacteristic
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—28no—
456C22×C4—28no—
457C22×C4—28no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—32no—
466C22×C4—32no—
467C22×C4—32no—
468C22×C4—32no—
469C22×C4—44no—
470C22×C4—44no—
471C22×C4—44no—
472C22×C4—44no—
473C22×C4—61no—
474C22×C4—61no—
475C22×C4—61no—
476C22×C4—61no—
477C22×C4—61no—
478C22×C4—61no—
479C22×C4—61no—
480C22×C4—61no—
481C22×C4—61no—
482C22×C4—61no—
483C22×C4—61no—
484C22×C4—61no—
485C22×C4—61no—
486C22×C4—61no—
487C22×C4—61no—
488C22×C4—61no—
489C22×C4—61no—
490C22×C4—61no—
491C22×C4—61no—
492C22×C4—61no—
493C22×C4—61no—
494C22×C4—61no—
495C22×C4—61no—
496C22×C4—61no—
497C22×C4—62no—
498C22×C4—62no—
499C22×C4—62no—
500C22×C4—62no—
501C22×C4—62no—
502C22×C4—62no—
503C22×C4—62no—
504C22×C4—62no—
505C22×C4—62no—
506C22×C4—62no—
507C22×C4—62no—
508C22×C4—62no—
509C22×C4—62no—
510C22×C4—62no—
511C22×C4C2×D1212yes—
512C22×C4C2×D1212yes—
513C22×C4#23512yes—
514C22×C4#23712yes—
515C22×C4#23712yes—
516C22×C4#23712yes—
517C22×C4#23712yes—
518C22×C4C2×#6714yes—
519C22×C4C2×#6712yes—
520C4⋊C4—28no—
521C4⋊C4—44no—
522C4⋊C4—128no—
523C4⋊C4—124no—
524C4⋊C4—124no—
525C22⋊C4—48no—
526C22⋊C4—68no—
527C22⋊C4—68no—
528C22⋊C4—128no—
529C42—124no—
530C42—124no—
531C22×C3—24no—
532C22×C3—24no—
533C22×C3—24no—
534C22×C3—42no—
535C22×C3—42no—
536C22×C3—42no—
537C22×C3—42no—
538C22×C3—42no—
539C22×C3—42no—
540C22×C3—42no—
541C22×C3—42no—
542C22×C3—42no—
543C22×C3—42no—
544C22×C3—42no—
545C22×C3—42no—
546C22×C3C2×#12111yescharacteristic
547C22×C3C2×C22⋊Q811yescharacteristic
548C22×C3C2×#12311yescharacteristic
549C22×C3C2×#12311yescharacteristic
550C22×C3C2×#12311yescharacteristic
551C22×C3#52511yescharacteristic
552C22×C3C2×#12411yescharacteristic
553C22×C3C2×#12611yescharacteristic
554C22×C3C2×#12611yescharacteristic
555C22×C3#52911yescharacteristic
556C22×C3#52911yescharacteristic
557C22×C3#53311yescharacteristic
558C22×C3#53311yescharacteristic
559C22×C3#53511yescharacteristic
560C22×C3#53711yescharacteristic
561C22×C3#54011yescharacteristic
562C22×C3#54011yescharacteristic
563C22×C3#54211yescharacteristic
564C22×C3#54211yescharacteristic
565C22×C3#54611yescharacteristic
566C22×C3#54611yescharacteristic
567C22×C3D4×Q811yescharacteristic
568C22×C3#55011yescharacteristic
569C22×C3#55211yescharacteristic
570C22×C3#55211yescharacteristic
571C22×C3#55311yescharacteristic
572C22×C3#55311yescharacteristic
573C22×C3#55311yescharacteristic
574C22×C3#55311yescharacteristic
575C22×C3#55411yescharacteristic
576C22×C3#55411yescharacteristic
577C22×C3#55411yescharacteristic
578C22×C3#55511yescharacteristic
579C22×C3#55511yescharacteristic
580C22×C3#55611yescharacteristic
581C3×C4—42no—
582C3×C4—44no—
583C3×C4—82no—
584C3×C4#39718yes—
585Dic3—42no—
586Dic3—42no—
587Dic3—42no—
588Dic3—42no—
589Dic3—82no—
590Dic3—82no—
591C23—22no—
592C23—22no—
593C23—22no—
594C23—22no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23#89714yes—
626C23C22×D1211yescharacteristic
627C23C2×#23511yescharacteristic
628C23C2×#23711yescharacteristic
629C23C2×#23711yescharacteristic
630C23C2×#23711yescharacteristic
631C23C2×#23711yescharacteristic
632C23C2×#23711yescharacteristic
633C23#100411yescharacteristic
634C23C2×D3×Q811yescharacteristic
635C23#100711yescharacteristic
636C23D3×#4111yescharacteristic
637C23D3×#4111yescharacteristic
638C23#100911yescharacteristic
639C23#100911yescharacteristic
640C23C22×#6711yescharacteristic
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—24no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—416no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—62no—
664C2×C4—62no—
665C2×C4—62no—
666C2×C4—62no—
667C2×C4—62no—
668C2×C4—62no—
669C2×C4—62no—
670C2×C4—62no—
671C2×C4—62no—
672C2×C4—62no—
673C2×C4—62no—
674C2×C4—62no—
675C2×C4—121no—
676C2×C4—121no—
677C2×C4—121no—
678C2×C4—121no—
679C2×C4—121no—
680C2×C4—121no—
681C2×C4—121no—
682C2×C4—121no—
683C2×C4—121no—
684C2×C4—121no—
685C2×C4—121no—
686C2×C4—121no—
687C2×C4—121no—
688C2×C4—121no—
689C2×C4—121no—
690C2×C4—121no—
691C2×C4—122no—
692C2×C4—122no—
693C2×C4—122no—
694C2×C4—122no—
695C2×C4—122no—
696C2×C4—122no—
697C2×C4—122no—
698C2×C4—122no—
699C2×C4—122no—
700C2×C4—122no—
701C2×C4—122no—
702C2×C4—122no—
703C2×C4—122no—
704C2×C4—122no—
705C2×C4#87914yes—
706C2×C4#87914yes—
707C2×C4#88614yes—
708C2×C4#88614yes—
709C2×C4#93014yes—
710C2×C4#93514yes—
711C2×C4#93614yes—
712C2×C3—44no—
713C2×C3C2×#39711yescharacteristic
714C2×C3#241411yescharacteristic
715C2×C3#241711yescharacteristic
716C2×C3#242011yescharacteristic
717C2×C3#242311yescharacteristic
718C2×C3#248511yescharacteristic
719C2×C3#248711yescharacteristic
720C2×C3#249011yescharacteristic
721C2×C3#249211yescharacteristic
722C2×C3#249411yescharacteristic
723C2×C3#249511yescharacteristic
724C2×C3#249711yescharacteristic
725C2×C3#249711yescharacteristic
726C2×C3#262411yescharacteristic
727C2×C3#285511yescharacteristic
728C22—24no—
729C22—24no—
730C22—24no—
731C22—42no—
732C22—42no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22C2×#87911yescharacteristic
744C22C2×#87911yescharacteristic
745C22C2×#88611yescharacteristic
746C22C2×#88611yescharacteristic
747C22C2×#89711yescharacteristic
748C22#551011yescharacteristic
749C22#551111yescharacteristic
750C22#551311yescharacteristic
751C22#552411yescharacteristic
752C22#552511yescharacteristic
753C22#553011yescharacteristic
754C22#553211yescharacteristic
755C22#560011yescharacteristic
756C22#560011yescharacteristic
757C22#561411yescharacteristic
758C22#561611yescharacteristic
759C22#561811yescharacteristic
760C22#561811yescharacteristic
761C22#561911yescharacteristic
762C22#561911yescharacteristic
763C22#562211yescharacteristic
764C22#562211yescharacteristic
765C22#563511yescharacteristic
766C22#563511yescharacteristic
767C22#563911yescharacteristic
768C22#564111yescharacteristic
769C22#564311yescharacteristic
770C22#564311yescharacteristic
771C22C2×#93011yescharacteristic
772C22C2×#93511yescharacteristic
773C22C2×#93611yescharacteristic
774C22#580611yescharacteristic
775C22Q8×#6711yescharacteristic
776C22#582911yescharacteristic
777C22#583411yescharacteristic
778C4—42no—
779C4—44no—
780C4—82no—
781C4—122no—
782C4—122no—
783C4—122no—
784C4—122no—
785C4—242no—
786C4—242no—
787C4#495318yes—
788C3#1518311yescharacteristic, complemented, Sylow
789C2—44no—
790C2#7391811yescharacteristic
791C2#7392111yescharacteristic
792C2#7392411yescharacteristic
793C2#7392511yescharacteristic
794C2#7400011yescharacteristic
795C2#7402611yescharacteristic
796C2#7402811yescharacteristic
797C2#7403311yescharacteristic
798C2C2×#495311yescharacteristic
799C2#8219411yescharacteristic
800C2#8227611yescharacteristic
801C2#8264311yescharacteristic
802C2#8266111yescharacteristic
803C2#8275411yescharacteristic
804C2#8277311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#380C2
prime radicalC25×C3C23
hypercenterC2×#380D3
hypocenterC3#15183
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
4. C2×#4984C2semidirect
5. #71563C2semidirect
6. #71563C2semidirect
7. #71563C2semidirect
10. #69422C2semidirect
11. #69418C2semidirect
788. C3#15183semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#3802
C2×#52122
C2×C4×#2172
C2×#49842
#715632
#715492
#715462
#694222
#694182
#151833