Finite Group Databasebeta

← #10731928

Subgroups — #10731928

Order 768.

1778 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#390C211yesmaximal, characteristic
2C2×#5221C211yesmaximal, characteristic
3C2×#5221C211yesmaximal, characteristic
4C2×#4952C212yesmaximal, complemented
5C2×C4×Dic3⋊C4C211yesmaximal, characteristic, complemented
6#71563C211yesmaximal, characteristic, complemented
7#71563C211yesmaximal, characteristic, complemented
8#71549C212yesmaximal, complemented
9#71548C212yesmaximal, complemented
10#71547C212yesmaximal, complemented
11#71535C211yesmaximal, characteristic, complemented
12#15147—31nomaximal, Sylow
13C23×C3×D4C2211yescharacteristic
14C22×C3×C4⋊C4C2211yescharacteristic
15C22×C3×C22⋊C4C2212yes—
16C22×C3×C22⋊C4C2212yes—
17C22×C3×C42C2211yescharacteristic
18C22×#217C2212yes—
19C22×#217C2212yes—
20C22×#217C2212yes—
21C22×#217C2212yes—
22C22×C4⋊Dic3C2211yescharacteristic
23C22×C4⋊Dic3C2211yescharacteristic
24C22×Dic3⋊C4C2211yescharacteristic
25C22×Dic3⋊C4C2211yescharacteristic
26C22×C4×Dic3C2211yescharacteristic
27C22×C4×Dic3C2211yescharacteristic
28C3×#390—24no—
29#5221—24no—
30#5221—24no—
31C2×C3⋊#95C2212yes—
32C2×C3⋊#95C2212yes—
33C2×C3⋊#95C2211yescharacteristic
34C2×C3⋊#95C2212yes—
35C2×C3⋊#95C2211yescharacteristic
36C2×C3⋊#95C2212yes—
37C2×C3⋊#95C2212yes—
38C2×C3⋊#95C2212yes—
39#4952—28no—
40C4×Dic3⋊C4—24no—
41C2×#397—32no—
42C2×#390—31no—
43C2×#390—31no—
44C2×#390D311yescharacteristic
45C2×C4×C4⋊C4—31no—
46#1440—32no—
47#1440—32no—
48#1439—32no—
49C4⋊#95—31no—
50C4⋊#95—31no—
51C4⋊#95—31no—
52C25×C3C2312yes—
53C22×C3×D4—22no—
54C22×C3×D4—22no—
55C22×C3×D4—22no—
56C22×C3×D4—22no—
57C22×C3×D4—22no—
58C22×C3×D4—22no—
59C22×C3×D4D414yes—
60C23×C3×C4C2312yes—
61C23×C3×C4C2311yescharacteristic
62C23×C3×C4C2311yescharacteristic
63C23×C3×C4C2311yescharacteristic
64C23×Dic3C2312yes—
65C23×Dic3C2312yes—
66C23×Dic3C2311yescharacteristic
67C23×Dic3C2311yescharacteristic
68C23×Dic3C2311yescharacteristic
69C23×Dic3C2311yescharacteristic
70C2×C3×C4⋊C4—22no—
71C2×C3×C4⋊C4—22no—
72C2×C3×C4⋊C4—22no—
73C2×C3×C22⋊C4—24no—
74C2×C3×C22⋊C4—24no—
75C2×C3×C22⋊C4—24no—
76C2×C3×C22⋊C4—24no—
77C2×C3×C22⋊C4—42no—
78C2×C3×C22⋊C4—42no—
79C2×C3×C42—22no—
80C2×C3×C42—22no—
81C2×C3×C42—22no—
82C2×#217—24no—
83C2×#217—24no—
84C2×#217—24no—
85C2×#217—24no—
86C2×#217—24no—
87C2×#217—24no—
88C2×#217—24no—
89C2×#217—24no—
90C2×#217—42no—
91C2×#217—42no—
92C2×#217—42no—
93C2×#217—42no—
94C2×C4⋊Dic3—22no—
95C2×C4⋊Dic3—22no—
96C2×C4⋊Dic3—22no—
97C2×C4⋊Dic3—22no—
98C2×C4⋊Dic3—22no—
99C2×C4⋊Dic3—22no—
100C2×Dic3⋊C4—22no—
101C2×Dic3⋊C4—22no—
102C2×Dic3⋊C4—22no—
103C2×Dic3⋊C4—22no—
104C2×Dic3⋊C4—22no—
105C2×Dic3⋊C4D414yescomplemented
106C2×C4×Dic3—22no—
107C2×C4×Dic3—22no—
108C2×C4×Dic3—22no—
109C2×C4×Dic3—22no—
110C2×C4×Dic3—22no—
111C2×C4×Dic3D414yes—
112C3⋊#95—24no—
113C3⋊#95—22no—
114C3⋊#95—22no—
115C3⋊#95—24no—
116C3⋊#95—24no—
117C3⋊#95—42no—
118C3⋊#95—42no—
119C3⋊#95—42no—
120C23×D4C2×D311yescharacteristic
121C22×C4⋊C4—31no—
122C22×C4⋊C4—31no—
123C22×C4⋊C4—31no—
124C22×C4⋊C4—31no—
125C22×C4⋊C4C2×D311yescharacteristic
126C22×C22⋊C4—32no—
127C22×C22⋊C4—32no—
128C22×C22⋊C4—32no—
129C22×C22⋊C4—32no—
130C22×C22⋊C4C2×D312yes—
131C22×C22⋊C4C2×D312yes—
132C22×C42—31no—
133C22×C42—31no—
134C22×C42C2×D311yescharacteristic
135#397—68no—
136#390—24no—
137#390—64no—
138#390—64no—
139C4×C4⋊C4—64no—
140C2×#95—32no—
141C2×#95—32no—
142C2×#95—32no—
143C2×#95—31no—
144C2×#95—31no—
145C2×#95—32no—
146C2×#95—32no—
147C2×#95—32no—
148C24×C3—22no—
149C24×C3—22no—
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×C3C2×D414yes—
163C24×C3C2411yescharacteristic
164C2×C3×D4—28no—
165C2×C3×D4—28no—
166C2×C3×D4—28no—
167C2×C3×D4—44no—
168C2×C3×D4—44no—
169C2×C3×D4—44no—
170C2×C3×D4—44no—
171C22×C3×C4—21no—
172C22×C3×C4—21no—
173C22×C3×C4—21no—
174C22×C3×C4—21no—
175C22×C3×C4—21no—
176C22×C3×C4—21no—
177C22×C3×C4—21no—
178C22×C3×C4—21no—
179C22×C3×C4—21no—
180C22×C3×C4—21no—
181C22×C3×C4—21no—
182C22×C3×C4—21no—
183C22×C3×C4—22no—
184C22×C3×C4—22no—
185C22×C3×C4—22no—
186C22×C3×C4—22no—
187C22×C3×C4—22no—
188C22×C3×C4—22no—
189C22×C3×C4—22no—
190C22×C3×C4C2×D412yes—
191C22×C3×C4C2×D412yes—
192C22×C3×C4C2×D412yes—
193C22×C3×C4#4112yes—
194C22×C3×C4#4112yes—
195C22×C3×C4#4112yes—
196C22×C3×C4#4112yes—
197C22×C3×C4#4112yes—
198C22×C3×C4#4112yes—
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—21no—
216C22×Dic3—21no—
217C22×Dic3—21no—
218C22×Dic3—21no—
219C22×Dic3—21no—
220C22×Dic3—21no—
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×Dic3—22no—
230C22×Dic3—22no—
231C22×Dic3—22no—
232C22×Dic3—22no—
233C22×Dic3—22no—
234C22×Dic3—22no—
235C22×Dic3C2×D412yes—
236C22×Dic3C2×D412yes—
237C22×Dic3C2×D412yes—
238C22×Dic3C2×D412yes—
239C22×Dic3#4112yes—
240C22×Dic3#4112yes—
241C3×C4⋊C4—44no—
242C3×C22⋊C4—48no—
243C3×C22⋊C4—48no—
244C3×C42—44no—
245#217—48no—
246#217—48no—
247#217—48no—
248#217—48no—
249C4⋊Dic3—44no—
250C4⋊Dic3—44no—
251Dic3⋊C4—28no—
252Dic3⋊C4—28no—
253C4×Dic3—28no—
254C4×Dic3—44no—
255C25C22×D312yes—
256C22×D4—22no—
257C22×D4—22no—
258C22×D4—22no—
259C22×D4—22no—
260C22×D4—22no—
261C22×D4—22no—
262C22×D4#6714yes—
263C23×C4—31no—
264C23×C4—31no—
265C23×C4—31no—
266C23×C4—31no—
267C23×C4—32no—
268C23×C4—32no—
269C23×C4C22×D312yes—
270C23×C4C22×D311yescharacteristic
271C23×C4C22×D311yescharacteristic
272C23×C4C22×D311yescharacteristic
273C2×C4⋊C4—22no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—34no—
277C2×C4⋊C4—62no—
278C2×C4⋊C4—62no—
279C2×C4⋊C4—62no—
280C2×C4⋊C4—62no—
281C2×C4⋊C4—62no—
282C2×C4⋊C4—62no—
283C2×C4⋊C4—62no—
284C2×C4⋊C4—62no—
285C2×C4⋊C4—62no—
286C2×C4⋊C4—62no—
287C2×C4⋊C4—62no—
288C2×C22⋊C4—24no—
289C2×C22⋊C4—24no—
290C2×C22⋊C4—24no—
291C2×C22⋊C4—24no—
292C2×C22⋊C4—42no—
293C2×C22⋊C4—42no—
294C2×C22⋊C4—64no—
295C2×C22⋊C4—64no—
296C2×C22⋊C4—64no—
297C2×C22⋊C4—64no—
298C2×C22⋊C4—64no—
299C2×C22⋊C4—64no—
300C2×C22⋊C4—64no—
301C2×C22⋊C4—64no—
302C2×C22⋊C4—122no—
303C2×C22⋊C4—122no—
304C2×C22⋊C4—122no—
305C2×C22⋊C4—122no—
306C2×C42—22no—
307C2×C42—22no—
308C2×C42—22no—
309C2×C42—34no—
310C2×C42—62no—
311C2×C42—62no—
312C2×C42—62no—
313C2×C42—62no—
314C2×C42—62no—
315#95—62no—
316#95—62no—
317#95—64no—
318#95—64no—
319#95—64no—
320#95—122no—
321#95—122no—
322#95—122no—
323C23×C3—24no—
324C23×C3—24no—
325C23×C3—24no—
326C23×C3—24no—
327C23×C3—24no—
328C23×C3—24no—
329C23×C3—24no—
330C23×C3—42no—
331C23×C3—42no—
332C23×C3—42no—
333C23×C3—42no—
334C23×C3—42no—
335C23×C3—42no—
336C23×C3—42no—
337C23×C3—42no—
338C23×C3—42no—
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×C3C22×D411yescharacteristic
359C23×C3C22×D411yescharacteristic
360C23×C3C22×D411yescharacteristic
361C23×C3C2×#4111yescharacteristic
362C23×C3C2×#4111yescharacteristic
363C23×C3C2×#4111yescharacteristic
364C23×C3C2×#4111yescharacteristic
365C23×C3C2×#4111yescharacteristic
366C23×C3C2×#4111yescharacteristic
367C23×C3C2×#4111yescharacteristic
368C23×C3C2×#4111yescharacteristic
369C23×C3H(5,𝔽2)11yescharacteristic
370C23×C3H(5,𝔽2)11yescharacteristic
371C23×C3H(5,𝔽2)11yescharacteristic
372C23×C32−1+411yescharacteristic
373C3×D4—416no—
374C2×C3×C4—22no—
375C2×C3×C4—22no—
376C2×C3×C4—22no—
377C2×C3×C4—22no—
378C2×C3×C4—22no—
379C2×C3×C4—22no—
380C2×C3×C4—41no—
381C2×C3×C4—41no—
382C2×C3×C4—41no—
383C2×C3×C4—41no—
384C2×C3×C4—41no—
385C2×C3×C4—41no—
386C2×C3×C4—41no—
387C2×C3×C4—41no—
388C2×C3×C4—42no—
389C2×C3×C4—42no—
390C2×C3×C4—42no—
391C2×C3×C4—42no—
392C2×C3×C4—42no—
393C2×C3×C4—42no—
394C2×C3×C4—42no—
395C2×C3×C4#12114yes—
396C2×C3×C4#12314yes—
397C2×C3×C4#12314yes—
398C2×C3×C4#12314yes—
399C2×C3×C4#12414yes—
400C2×C3×C4#12614yes—
401C2×C3×C4#12614yes—
402C2×Dic3—22no—
403C2×Dic3—22no—
404C2×Dic3—22no—
405C2×Dic3—22no—
406C2×Dic3—22no—
407C2×Dic3—22no—
408C2×Dic3—22no—
409C2×Dic3—22no—
410C2×Dic3—22no—
411C2×Dic3—22no—
412C2×Dic3—22no—
413C2×Dic3—22no—
414C2×Dic3—22no—
415C2×Dic3—22no—
416C2×Dic3—22no—
417C2×Dic3—41no—
418C2×Dic3—41no—
419C2×Dic3—41no—
420C2×Dic3—41no—
421C2×Dic3—41no—
422C2×Dic3—41no—
423C2×Dic3—41no—
424C2×Dic3—41no—
425C2×Dic3—41no—
426C2×Dic3—41no—
427C2×Dic3—41no—
428C2×Dic3—41no—
429C2×Dic3—42no—
430C2×Dic3—42no—
431C2×Dic3—42no—
432C2×Dic3—42no—
433C2×Dic3—42no—
434C2×Dic3—42no—
435C2×Dic3—42no—
436C2×Dic3—42no—
437C2×Dic3—42no—
438C2×Dic3—42no—
439C2×Dic3—42no—
440C2×Dic3—42no—
441C2×Dic3—42no—
442C2×Dic3—42no—
443C2×Dic3#12114yes—
444C24—22no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24C2×#6714yes—
459C24C23×D311yescharacteristic
460C2×D4—28no—
461C2×D4—28no—
462C2×D4—28no—
463C2×D4—44no—
464C2×D4—44no—
465C2×D4—44no—
466C2×D4—44no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—32no—
487C22×C4—32no—
488C22×C4—32no—
489C22×C4—32no—
490C22×C4—32no—
491C22×C4—32no—
492C22×C4—61no—
493C22×C4—61no—
494C22×C4—61no—
495C22×C4—61no—
496C22×C4—61no—
497C22×C4—61no—
498C22×C4—61no—
499C22×C4—61no—
500C22×C4—61no—
501C22×C4—61no—
502C22×C4—61no—
503C22×C4—61no—
504C22×C4—61no—
505C22×C4—61no—
506C22×C4—61no—
507C22×C4—61no—
508C22×C4—61no—
509C22×C4—61no—
510C22×C4—61no—
511C22×C4—61no—
512C22×C4—61no—
513C22×C4—61no—
514C22×C4—62no—
515C22×C4—62no—
516C22×C4—62no—
517C22×C4—62no—
518C22×C4—62no—
519C22×C4—62no—
520C22×C4—62no—
521C22×C4—62no—
522C22×C4—62no—
523C22×C4—62no—
524C22×C4—62no—
525C22×C4—62no—
526C22×C4—62no—
527C22×C4—62no—
528C22×C4#23512yes—
529C22×C4#23512yes—
530C22×C4D3×D412yes—
531C22×C4D3×D412yes—
532C22×C4#23712yes—
533C22×C4#23712yes—
534C22×C4#23712yes—
535C22×C4#23712yes—
536C22×C4C2×#6712yes—
537C4⋊C4—44no—
538C4⋊C4—68no—
539C4⋊C4—68no—
540C4⋊C4—124no—
541C4⋊C4—124no—
542C22⋊C4—48no—
543C22⋊C4—48no—
544C22⋊C4—128no—
545C22⋊C4—128no—
546C22⋊C4—128no—
547C22⋊C4—128no—
548C42—44no—
549C42—68no—
550C42—124no—
551C22×C3—44no—
552C22×C3—44no—
553C22×C3—44no—
554C22×C3—44no—
555C22×C3—44no—
556C22×C3—44no—
557C22×C3—44no—
558C22×C3—82no—
559C22×C3—82no—
560C22×C3—82no—
561C22×C3—82no—
562C22×C3—82no—
563C22×C3—82no—
564C22×C3—82no—
565C22×C3—82no—
566C22×C3C2×#12111yescharacteristic
567C22×C3C2×#12111yescharacteristic
568C22×C3C2×#12311yescharacteristic
569C22×C3C2×#12311yescharacteristic
570C22×C3C2×#12311yescharacteristic
571C22×C3#52511yescharacteristic
572C22×C3C2×#12411yescharacteristic
573C22×C3C2×#12611yescharacteristic
574C22×C3C2×#12611yescharacteristic
575C22×C3#52911yescharacteristic
576C22×C3#52911yescharacteristic
577C22×C3#53211yescharacteristic
578C22×C3#53211yescharacteristic
579C22×C3#53511yescharacteristic
580C22×C3#53711yescharacteristic
581C22×C3#54011yescharacteristic
582C22×C3#54011yescharacteristic
583C22×C3#54211yescharacteristic
584C22×C3#54211yescharacteristic
585C22×C3D4211yescharacteristic
586C22×C3#54611yescharacteristic
587C22×C3#54611yescharacteristic
588C22×C3#54711yescharacteristic
589C22×C3#54711yescharacteristic
590C22×C3#55011yescharacteristic
591C22×C3#55011yescharacteristic
592C22×C3#55311yescharacteristic
593C22×C3#55311yescharacteristic
594C22×C3#55511yescharacteristic
595C22×C3#55611yescharacteristic
596C22×C3#55611yescharacteristic
597C22×C3#55911yescharacteristic
598C22×C3#55911yescharacteristic
599C22×C3#55911yescharacteristic
600C22×C3#55911yescharacteristic
601C3×C4—42no—
602C3×C4—42no—
603C3×C4—82no—
604C3×C4#39718yescomplemented
605Dic3—24no—
606Dic3—42no—
607Dic3—42no—
608Dic3—42no—
609Dic3—82no—
610Dic3—82no—
611C23—24no—
612C23—24no—
613C23—24no—
614C23—24no—
615C23—24no—
616C23—24no—
617C23—24no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23C2×#23511yescharacteristic
647C23C2×#23511yescharacteristic
648C23C2×D3×D411yescharacteristic
649C23C2×D3×D411yescharacteristic
650C23C2×#23711yescharacteristic
651C23C2×#23711yescharacteristic
652C23C2×#23711yescharacteristic
653C23C2×#23711yescharacteristic
654C23#100411yescharacteristic
655C23#100411yescharacteristic
656C23D3×#4111yescharacteristic
657C23D3×#4111yescharacteristic
658C23#100911yescharacteristic
659C23#101011yescharacteristic
660C23C22×#6711yescharacteristic
661D4—416no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—34no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—62no—
685C2×C4—62no—
686C2×C4—62no—
687C2×C4—62no—
688C2×C4—62no—
689C2×C4—62no—
690C2×C4—62no—
691C2×C4—62no—
692C2×C4—62no—
693C2×C4—62no—
694C2×C4—62no—
695C2×C4—62no—
696C2×C4—62no—
697C2×C4—62no—
698C2×C4—62no—
699C2×C4—121no—
700C2×C4—121no—
701C2×C4—121no—
702C2×C4—121no—
703C2×C4—121no—
704C2×C4—121no—
705C2×C4—121no—
706C2×C4—121no—
707C2×C4—121no—
708C2×C4—121no—
709C2×C4—121no—
710C2×C4—121no—
711C2×C4—122no—
712C2×C4—122no—
713C2×C4—122no—
714C2×C4—122no—
715C2×C4—122no—
716C2×C4—122no—
717C2×C4—122no—
718C2×C4—122no—
719C2×C4—122no—
720C2×C4—122no—
721C2×C4—122no—
722C2×C4—122no—
723C2×C4—122no—
724C2×C4—122no—
725C2×C4#87914yes—
726C2×C4#87914yes—
727C2×C4#88314yes—
728C2×C4#88514yes—
729C2×C4#92914yes—
730C2×C4#93514yes—
731C2×C4#93914yes—
732C2×C3—84no—
733C2×C3C2×#39711yescharacteristic
734C2×C3#244511yescharacteristic
735C2×C3#244511yescharacteristic
736C2×C3#244711yescharacteristic
737C2×C3#244711yescharacteristic
738C2×C3#251211yescharacteristic
739C2×C3#251211yescharacteristic
740C2×C3#251311yescharacteristic
741C2×C3#251311yescharacteristic
742C2×C3#253511yescharacteristic
743C2×C3#253711yescharacteristic
744C2×C3#254811yescharacteristic
745C2×C3#259211yescharacteristic
746C2×C3#262411yescharacteristic
747C2×C3#285411yescharacteristic
748C22—44no—
749C22—44no—
750C22—44no—
751C22—44no—
752C22—44no—
753C22—44no—
754C22—44no—
755C22—82no—
756C22—82no—
757C22—82no—
758C22—82no—
759C22—82no—
760C22—82no—
761C22—82no—
762C22—82no—
763C22C2×#87911yescharacteristic
764C22C2×#87911yescharacteristic
765C22C2×#88311yescharacteristic
766C22C2×#88511yescharacteristic
767C22#554211yescharacteristic
768C22#554811yescharacteristic
769C22#555311yescharacteristic
770C22#555711yescharacteristic
771C22#555911yescharacteristic
772C22#555911yescharacteristic
773C22#556111yescharacteristic
774C22#556211yescharacteristic
775C22D3×#12111yescharacteristic
776C22#560611yescharacteristic
777C22#560711yescharacteristic
778C22#560811yescharacteristic
779C22#561111yescharacteristic
780C22#561411yescharacteristic
781C22#561611yescharacteristic
782C22#561811yescharacteristic
783C22#567111yescharacteristic
784C22#568011yescharacteristic
785C22#568111yescharacteristic
786C22#568211yescharacteristic
787C22#571311yescharacteristic
788C22#571611yescharacteristic
789C22#571811yescharacteristic
790C22#571911yescharacteristic
791C22C2×#92911yescharacteristic
792C22C2×#93511yescharacteristic
793C22D4×#6711yescharacteristic
794C22C2×#93911yescharacteristic
795C22#580611yescharacteristic
796C22#582411yescharacteristic
797C22#582911yescharacteristic
798C4—42no—
799C4—42no—
800C4—64no—
801C4—82no—
802C4—122no—
803C4—122no—
804C4—122no—
805C4—242no—
806C4—242no—
807C4#495218yescomplemented
808C3#1514711yescharacteristic, complemented, Sylow
809C2—84no—
810C2#7633711yescharacteristic
811C2#7633811yescharacteristic
812C2#7634011yescharacteristic
813C2#7634111yescharacteristic
814C2#7635311yescharacteristic
815C2#7636511yescharacteristic
816C2#7645811yescharacteristic
817C2#7647511yescharacteristic
818C2C2×#495211yescharacteristic
819C2#8235811yescharacteristic
820C2#8235911yescharacteristic
821C2#8266611yescharacteristic
822C2#8266711yescharacteristic
823C2#8296211yescharacteristic
824C2#8317611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#390C2
prime radicalC23×C3×D4C22
hypercenterC2×#390D3
hypocenterC3#15147
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
4. C2×#4952C2semidirect
5. C2×C4×Dic3⋊C4C2semidirect
6. #71563C2semidirect
7. #71563C2semidirect
8. #71549C2semidirect
9. #71548C2semidirect
10. #71547C2semidirect
11. #71535C2semidirect
105. C2×Dic3⋊C4D4semidirect
604. C3×C4#397semidirect
807. C4#4952semidirect
808. C3#15147semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#3902
C2×#52212
C2×#49522
C2×C4×Dic3⋊C42
#715632
#715492
#715482
#715472
#715352
#151473