Finite Group Databasebeta

← #10729214

Subgroups — #10729214

Order 768.

2430 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#936C211yesmaximal, characteristic, complemented
2C2×C3×#392C211yesmaximal, characteristic
3C2×#5222C211yesmaximal, characteristic, complemented
4C2×#5221C212yesmaximal, complemented
5C2×#4947C211yesmaximal, characteristic, complemented
6C2×#4945C211yesmaximal, characteristic, complemented
7C2×#4656C211yesmaximal, characteristic, complemented
8#72131C212yesmaximal, complemented
9#71546C212yesmaximal, complemented
10#71545C212yesmaximal, complemented
11Dic3×#95C211yesmaximal, characteristic, complemented
12#14928—31nomaximal, Sylow
13C23×C3×D4C2212yes—
14C23×C3×D4C2211yescharacteristic
15C23×Dic6C2211yescharacteristic
16C22×C3×C22⋊C4C2212yes—
17C22×C3×C22⋊C4C2211yescharacteristic
18C22×#217C2211yescharacteristic
19C22×#217C2212yes—
20C22×#217C2211yescharacteristic
21C22×#217C2212yes—
22C22×#217C2212yes—
23C22×#217C2212yes—
24C22×#217C2212yes—
25C2×#936—28no—
26C2×#936—24no—
27C22×C4⋊Dic3C2212yes—
28C22×Dic3⋊C4C2211yescharacteristic
29C22×C4×Dic3C2212yes—
30C22×C4×Dic3C2211yescharacteristic
31C3×#392—24no—
32C2×C3×#95C2211yescharacteristic
33#5222—24no—
34#5221—28no—
35C2×C3⋊#95C2212yes—
36C2×C3⋊#95C2211yescharacteristic
37C2×C3⋊#95C2212yes—
38C2×C3⋊#95C2212yes—
39C2×C3⋊#95C2211yescharacteristic
40C2×C3⋊#95C2211yescharacteristic
41#4947—24no—
42#4945—24no—
43#4656—24no—
44C22×#124—31no—
45C2×#395—31no—
46C2×#394—31no—
47C2×#393—31no—
48C2×#392D311yescharacteristic
49C2×#390—32no—
50C2×#388—31no—
51#1439—32no—
52#1438—32no—
53#1437—32no—
54C4×#95—31no—
55C25×C3C2312yes—
56C25×C3C2311yescharacteristic
57C22×C3×D4—24no—
58C22×C3×D4—24no—
59C22×C3×D4—24no—
60C22×C3×D4—22no—
61C22×C3×D4—22no—
62C22×C3×D4—24no—
63C22×C3×D4—22no—
64C22×C3×D4—24no—
65C22×C3×D4—24no—
66C22×C3×D4—42no—
67C22×C3×D4—42no—
68C22×C3×D4—42no—
69C23×C3×C4C2311yescharacteristic
70C23×C3×C4C2311yescharacteristic
71C23×C3×C4C2312yes—
72C23×Dic3C2311yescharacteristic
73C23×Dic3C2312yes—
74C23×Dic3C2311yescharacteristic
75C23×Dic3C2312yes—
76C23×Dic3C2311yescharacteristic
77C23×Dic3C2311yescharacteristic
78C22×Dic6—22no—
79C22×Dic6—24no—
80C22×Dic6—22no—
81C22×Dic6—22no—
82C22×Dic6—42no—
83C2×C3×C22⋊C4—22no—
84C2×C3×C22⋊C4—22no—
85C2×C3×C22⋊C4—24no—
86C2×C3×C22⋊C4—22no—
87C2×C3×C22⋊C4—24no—
88C2×C3×C22⋊C4—24no—
89C2×#217—24no—
90C2×#217—22no—
91C2×#217—22no—
92C2×#217—24no—
93C2×#217—24no—
94C2×#217—24no—
95C2×#217—24no—
96C2×#217—22no—
97C2×#217—24no—
98C2×#217—22no—
99C2×#217—24no—
100C2×#217—24no—
101C2×#217—24no—
102C2×#217—24no—
103C2×#217—24no—
104C2×#217—24no—
105C2×#217—42no—
106C2×#217—42no—
107C2×#217—42no—
108C2×#217D418yescomplemented
109#936—232no—
110C2×C4⋊Dic3—24no—
111C2×C4⋊Dic3—24no—
112C2×C4⋊Dic3—42no—
113C2×Dic3⋊C4—22no—
114C2×Dic3⋊C4—22no—
115C2×Dic3⋊C4—22no—
116C2×C4×Dic3—24no—
117C2×C4×Dic3—24no—
118C2×C4×Dic3—24no—
119C2×C4×Dic3—42no—
120C2×C4×Dic3D414yescomplemented
121C3×#95D414yes—
122C3⋊#95—24no—
123C3⋊#95—24no—
124C3⋊#95—22no—
125C3⋊#95—22no—
126C3⋊#95—24no—
127C3⋊#95D414yescomplemented
128C23×Q8—31no—
129C23×D4C2×D311yescharacteristic
130C23×D4C2×D312yes—
131C2×#124—64no—
132C2×#124—68no—
133C22×C4⋊C4—31no—
134C22×C4⋊C4—32no—
135C22×C22⋊C4—32no—
136C22×C22⋊C4—32no—
137C22×C22⋊C4—31no—
138C22×C22⋊C4—31no—
139C22×C22⋊C4—32no—
140C22×C22⋊C4—32no—
141C22×C22⋊C4—32no—
142C22×C22⋊C4C2×D311yescharacteristic
143C22×C22⋊C4C2×D312yes—
144C22×C42—31no—
145C22×C42—32no—
146#395—64no—
147#394—64no—
148#393—64no—
149#392—24no—
150#390—68no—
151#388—64no—
152C2×#95—31no—
153C2×#95—32no—
154C2×#95—32no—
155C2×#95—32no—
156C2×#95—31no—
157C2×#95—31no—
158C2×#95C2×D311yescharacteristic
159C24×C3—21no—
160C24×C3—21no—
161C24×C3—22no—
162C24×C3—22no—
163C24×C3—22no—
164C24×C3—22no—
165C24×C3—22no—
166C24×C3—21no—
167C24×C3—21no—
168C24×C3—22no—
169C24×C3—22no—
170C24×C3—22no—
171C24×C3—22no—
172C24×C3—22no—
173C24×C3—22no—
174C24×C3—22no—
175C24×C3—22no—
176C24×C3—22no—
177C24×C3—22no—
178C24×C3—22no—
179C24×C3—22no—
180C24×C3—21no—
181C24×C3—22no—
182C24×C3—21no—
183C24×C3C2×D414yes—
184C24×C3#4112yes—
185C24×C3C2411yescharacteristic
186C2×C3×D4—28no—
187C2×C3×D4—216no—
188C2×C3×D4—48no—
189C2×C3×D4—48no—
190C2×C3×D4—48no—
191C2×C3×D4—48no—
192C2×C3×D4—48no—
193C2×C3×D4—48no—
194C2×C3×D4—44no—
195C2×C3×D4—48no—
196C2×C3×D4—48no—
197C2×C3×D4—44no—
198C22×C3×C4—22no—
199C22×C3×C4—22no—
200C22×C3×C4—22no—
201C22×C3×C4—22no—
202C22×C3×C4—22no—
203C22×C3×C4—22no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4—22no—
208C22×C3×C4—22no—
209C22×C3×C4C2×D412yes—
210C22×C3×C4C2×D412yes—
211C22×C3×C4C2×D414yes—
212C22×C3×C4C2×D412yes—
213C22×C3×C4#4114yes—
214C22×C3×C4#4114yes—
215C22×Dic3—22no—
216C22×Dic3—21no—
217C22×Dic3—21no—
218C22×Dic3—21no—
219C22×Dic3—21no—
220C22×Dic3—22no—
221C22×Dic3—22no—
222C22×Dic3—22no—
223C22×Dic3—22no—
224C22×Dic3—21no—
225C22×Dic3—22no—
226C22×Dic3—22no—
227C22×Dic3—22no—
228C22×Dic3—22no—
229C22×Dic3—22no—
230C22×Dic3—21no—
231C22×Dic3—21no—
232C22×Dic3—21no—
233C22×Dic3—22no—
234C22×Dic3—22no—
235C22×Dic3—22no—
236C22×Dic3—22no—
237C22×Dic3—21no—
238C22×Dic3—22no—
239C22×Dic3—21no—
240C22×Dic3—21no—
241C22×Dic3—21no—
242C22×Dic3—21no—
243C22×Dic3—22no—
244C22×Dic3—22no—
245C22×Dic3C2×D414yes—
246C22×Dic3C2×D412yes—
247C22×Dic3C2×D414yes—
248C22×Dic3C2×D412yes—
249C22×Dic3C2×D414yes—
250C22×Dic3#4112yes—
251C2×Dic6—28no—
252C2×Dic6—48no—
253C2×Dic6—48no—
254C2×Dic6—44no—
255C2×Dic6—44no—
256C3×C22⋊C4—48no—
257C3×C22⋊C4—44no—
258#217—216no—
259#217—28no—
260#217—216no—
261#217—48no—
262#217—48no—
263#217—48no—
264#217—44no—
265C4⋊Dic3—48no—
266Dic3⋊C4—44no—
267C4×Dic3—28no—
268C4×Dic3—48no—
269C25C22×D312yes—
270C25C22×D311yescharacteristic
271C22×Q8—64no—
272C22×Q8—62no—
273C22×Q8—62no—
274C22×Q8—62no—
275C22×Q8—122no—
276C22×D4—24no—
277C22×D4—24no—
278C22×D4—24no—
279C22×D4—22no—
280C22×D4—22no—
281C22×D4—24no—
282C22×D4—24no—
283C22×D4—24no—
284C22×D4—22no—
285C22×D4—42no—
286C22×D4—42no—
287C22×D4—42no—
288C23×C4—31no—
289C23×C4—32no—
290C23×C4—31no—
291C23×C4—32no—
292C23×C4—31no—
293C23×C4—31no—
294C23×C4C22×D311yescharacteristic
295C23×C4C22×D311yescharacteristic
296C23×C4C22×D312yes—
297#124—632no—
298C2×C4⋊C4—64no—
299C2×C4⋊C4—62no—
300C2×C4⋊C4—62no—
301C2×C4⋊C4—62no—
302C2×C4⋊C4—64no—
303C2×C4⋊C4—122no—
304C2×C22⋊C4—22no—
305C2×C22⋊C4—22no—
306C2×C22⋊C4—24no—
307C2×C22⋊C4—24no—
308C2×C22⋊C4—24no—
309C2×C22⋊C4—22no—
310C2×C22⋊C4—38no—
311C2×C22⋊C4—64no—
312C2×C22⋊C4—64no—
313C2×C22⋊C4—64no—
314C2×C22⋊C4—64no—
315C2×C22⋊C4—62no—
316C2×C22⋊C4—62no—
317C2×C22⋊C4—64no—
318C2×C22⋊C4—62no—
319C2×C22⋊C4—62no—
320C2×C22⋊C4—64no—
321C2×C22⋊C4—64no—
322C2×C22⋊C4—64no—
323C2×C22⋊C4—64no—
324C2×C22⋊C4—64no—
325C2×C22⋊C4—64no—
326C2×C22⋊C4—64no—
327C2×C22⋊C4—122no—
328C2×C22⋊C4—122no—
329C2×C22⋊C4—122no—
330C2×C42—34no—
331C2×C42—64no—
332C2×C42—64no—
333C2×C42—64no—
334C2×C42—122no—
335#95—34no—
336#95—62no—
337#95—62no—
338#95—64no—
339#95—64no—
340#95—64no—
341#95#6714yes—
342C23×C3—24no—
343C23×C3—22no—
344C23×C3—24no—
345C23×C3—24no—
346C23×C3—24no—
347C23×C3—24no—
348C23×C3—24no—
349C23×C3—22no—
350C23×C3—24no—
351C23×C3—24no—
352C23×C3—22no—
353C23×C3—24no—
354C23×C3—41no—
355C23×C3—42no—
356C23×C3—42no—
357C23×C3—42no—
358C23×C3—42no—
359C23×C3—42no—
360C23×C3—41no—
361C23×C3—42no—
362C23×C3—41no—
363C23×C3—41no—
364C23×C3—42no—
365C23×C3—42no—
366C23×C3—42no—
367C23×C3—42no—
368C23×C3—42no—
369C23×C3—42no—
370C23×C3—42no—
371C23×C3—42no—
372C23×C3—41no—
373C23×C3—42no—
374C23×C3—41no—
375C23×C3—42no—
376C23×C3—42no—
377C23×C3—42no—
378C23×C3—42no—
379C23×C3—42no—
380C23×C3—42no—
381C23×C3—42no—
382C23×C3—42no—
383C23×C3—42no—
384C23×C3—42no—
385C23×C3—42no—
386C23×C3—42no—
387C23×C3—42no—
388C23×C3—42no—
389C23×C3—41no—
390C23×C3—42no—
391C23×C3—42no—
392C23×C3—42no—
393C23×C3—41no—
394C23×C3—42no—
395C23×C3—42no—
396C23×C3—42no—
397C23×C3—42no—
398C23×C3—42no—
399C23×C3—42no—
400C23×C3C22×D411yescharacteristic
401C23×C3C22×D412yes—
402C23×C3C22×D411yescharacteristic
403C23×C3C22×D411yescharacteristic
404C23×C3C2×#4111yescharacteristic
405C23×C3C2×#4112yes—
406C23×C3C2×#4112yes—
407C23×C3C2×#4111yescharacteristic
408C23×C3H(5,𝔽2)12yes—
409C23×C3H(5,𝔽2)11yescharacteristic
410C23×C32−1+411yescharacteristic
411C3×D4—416no—
412C3×D4—432no—
413C2×C3×C4—22no—
414C2×C3×C4—24no—
415C2×C3×C4—22no—
416C2×C3×C4—24no—
417C2×C3×C4—24no—
418C2×C3×C4—24no—
419C2×C3×C4—24no—
420C2×C3×C4—24no—
421C2×C3×C4—24no—
422C2×C3×C4—24no—
423C2×C3×C4—42no—
424C2×C3×C4—41no—
425C2×C3×C4—41no—
426C2×C3×C4—41no—
427C2×C3×C4—42no—
428C2×C3×C4#12418yescomplemented
429C2×C3×C4#12714yes—
430C2×Dic3—22no—
431C2×Dic3—22no—
432C2×Dic3—24no—
433C2×Dic3—24no—
434C2×Dic3—22no—
435C2×Dic3—24no—
436C2×Dic3—22no—
437C2×Dic3—22no—
438C2×Dic3—22no—
439C2×Dic3—24no—
440C2×Dic3—24no—
441C2×Dic3—24no—
442C2×Dic3—24no—
443C2×Dic3—22no—
444C2×Dic3—24no—
445C2×Dic3—22no—
446C2×Dic3—42no—
447C2×Dic3—41no—
448C2×Dic3—42no—
449C2×Dic3—42no—
450C2×Dic3—42no—
451C2×Dic3—42no—
452C2×Dic3—41no—
453C2×Dic3—42no—
454C2×Dic3—42no—
455C2×Dic3—42no—
456C2×Dic3—42no—
457C2×Dic3—41no—
458C2×Dic3—41no—
459C2×Dic3—42no—
460C2×Dic3—41no—
461C2×Dic3—41no—
462C2×Dic3—41no—
463C2×Dic3—42no—
464C2×Dic3—42no—
465C2×Dic3#12014yes—
466Dic6—416no—
467C24—21no—
468C24—21no—
469C24—22no—
470C24—22no—
471C24—22no—
472C24—22no—
473C24—22no—
474C24—22no—
475C24—22no—
476C24—22no—
477C24—22no—
478C24—22no—
479C24—22no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24—21no—
485C24—22no—
486C24—21no—
487C24—21no—
488C24—22no—
489C24—22no—
490C24—21no—
491C24D3×D414yes—
492C24#23712yes—
493C24C23×D311yescharacteristic
494C2×Q8—68no—
495C2×Q8—128no—
496C2×Q8—128no—
497C2×Q8—124no—
498C2×Q8—124no—
499C2×D4—28no—
500C2×D4—216no—
501C2×D4—48no—
502C2×D4—48no—
503C2×D4—48no—
504C2×D4—48no—
505C2×D4—48no—
506C2×D4—48no—
507C2×D4—44no—
508C2×D4—48no—
509C2×D4—48no—
510C2×D4—44no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—21no—
522C22×C4—32no—
523C22×C4—34no—
524C22×C4—34no—
525C22×C4—32no—
526C22×C4—34no—
527C22×C4—32no—
528C22×C4—62no—
529C22×C4—61no—
530C22×C4—61no—
531C22×C4—61no—
532C22×C4—62no—
533C22×C4—62no—
534C22×C4—62no—
535C22×C4—61no—
536C22×C4—62no—
537C22×C4—62no—
538C22×C4—62no—
539C22×C4—62no—
540C22×C4—62no—
541C22×C4—61no—
542C22×C4—61no—
543C22×C4—62no—
544C22×C4—62no—
545C22×C4—61no—
546C22×C4—62no—
547C22×C4—62no—
548C22×C4—61no—
549C22×C4—62no—
550C22×C4—61no—
551C22×C4—61no—
552C22×C4—62no—
553C22×C4—61no—
554C22×C4—62no—
555C22×C4—61no—
556C22×C4—62no—
557C22×C4—61no—
558C22×C4D3×D412yes—
559C22×C4D3×D412yes—
560C22×C4#23714yes—
561C22×C4#23714yes—
562C22×C4C2×#6714yes—
563C22×C4C2×#6712yes—
564C4⋊C4—128no—
565C4⋊C4—124no—
566C22⋊C4—48no—
567C22⋊C4—44no—
568C22⋊C4—616no—
569C22⋊C4—616no—
570C22⋊C4—68no—
571C22⋊C4—124no—
572C22⋊C4—128no—
573C22⋊C4—128no—
574C22⋊C4—128no—
575C42—68no—
576C42—128no—
577C22×C3—42no—
578C22×C3—44no—
579C22×C3—42no—
580C22×C3—44no—
581C22×C3—44no—
582C22×C3—44no—
583C22×C3—44no—
584C22×C3—44no—
585C22×C3—44no—
586C22×C3—44no—
587C22×C3—42no—
588C22×C3—44no—
589C22×C3—82no—
590C22×C3—81no—
591C22×C3—82no—
592C22×C3—82no—
593C22×C3—81no—
594C22×C3—81no—
595C22×C3—81no—
596C22×C3—82no—
597C22×C3—82no—
598C22×C3—82no—
599C22×C3—82no—
600C22×C3—82no—
601C22×C3—82no—
602C22×C3—82no—
603C22×C3C2×#12011yescharacteristic
604C22×C3#52512yes—
605C22×C3#52511yescharacteristic
606C22×C3C2×#12412yes—
607C22×C3C2×#12711yescharacteristic
608C22×C3#53211yescharacteristic
609C22×C3#53211yescharacteristic
610C22×C3#53212yes—
611C22×C3#53212yes—
612C22×C3#53511yescharacteristic
613C22×C3#53711yescharacteristic
614C22×C3#53812yes—
615C22×C3#54212yes—
616C22×C3D4212yes—
617C22×C3D4212yes—
618C22×C3#54611yescharacteristic
619C22×C3#54612yes—
620C22×C3#54611yescharacteristic
621C22×C3#54712yes—
622C22×C3#54811yescharacteristic
623C22×C3#54811yescharacteristic
624C22×C3#55112yes—
625C22×C3#55512yes—
626C3×C4—24no—
627C3×C4—28no—
628C3×C4—81no—
629Dic3—24no—
630Dic3—42no—
631Dic3—44no—
632Dic3—42no—
633Dic3—44no—
634Dic3—81no—
635C23—24no—
636C23—22no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—22no—
645C23—22no—
646C23—24no—
647C23—41no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—41no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—41no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—41no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—41no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—41no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—41no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—41no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23C2×D3×D411yescharacteristic
694C23C2×D3×D411yescharacteristic
695C23C2×D3×D412yes—
696C23C2×#23712yes—
697C23C2×#23712yes—
698C23C2×#23711yescharacteristic
699C23#100412yes—
700C23#100411yescharacteristic
701C23D3×#4111yescharacteristic
702C23#101011yescharacteristic
703C23C22×#6711yescharacteristic
704Q8—1216no—
705D4—416no—
706D4—432no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—34no—
718C2×C4—41no—
719C2×C4—42no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—41no—
723C2×C4—62no—
724C2×C4—64no—
725C2×C4—62no—
726C2×C4—64no—
727C2×C4—62no—
728C2×C4—64no—
729C2×C4—64no—
730C2×C4—62no—
731C2×C4—62no—
732C2×C4—64no—
733C2×C4—64no—
734C2×C4—64no—
735C2×C4—62no—
736C2×C4—62no—
737C2×C4—62no—
738C2×C4—64no—
739C2×C4—122no—
740C2×C4—121no—
741C2×C4—122no—
742C2×C4—121no—
743C2×C4—122no—
744C2×C4—122no—
745C2×C4—122no—
746C2×C4—122no—
747C2×C4—122no—
748C2×C4—122no—
749C2×C4—122no—
750C2×C4—121no—
751C2×C4—121no—
752C2×C4—122no—
753C2×C4—122no—
754C2×C4—121no—
755C2×C4—121no—
756C2×C4—122no—
757C2×C4—121no—
758C2×C4#93618yescomplemented
759C2×C4#94014yes—
760C2×C3—82no—
761C2×C3—84no—
762C2×C3#238811yescharacteristic
763C2×C3#243011yescharacteristic
764C2×C3#243311yescharacteristic
765C2×C3#246112yes—
766C2×C3#247212yes—
767C2×C3#249112yes—
768C2×C3#254011yescharacteristic
769C2×C3#255512yes—
770C2×C3#261011yescharacteristic
771C2×C3#266211yescharacteristic
772C2×C3#285811yescharacteristic
773C22—44no—
774C22—42no—
775C22—44no—
776C22—44no—
777C22—44no—
778C22—42no—
779C22—44no—
780C22—44no—
781C22—44no—
782C22—44no—
783C22—44no—
784C22—42no—
785C22—82no—
786C22—82no—
787C22—82no—
788C22—82no—
789C22—81no—
790C22—82no—
791C22—82no—
792C22—81no—
793C22—81no—
794C22—82no—
795C22—82no—
796C22—82no—
797C22—82no—
798C22—81no—
799C22#558612yes—
800C22#558712yes—
801C22D3×#12011yescharacteristic
802C22#559012yes—
803C22#559112yes—
804C22#559211yescharacteristic
805C22#559312yes—
806C22#559612yes—
807C22#559811yescharacteristic
808C22#560312yes—
809C22#560611yescharacteristic
810C22#560811yescharacteristic
811C22#561112yes—
812C22#561211yescharacteristic
813C22#561612yes—
814C22#571611yescharacteristic
815C22#571612yes—
816C22#571611yescharacteristic
817C22C2×#93612yes—
818C22D4×#6712yes—
819C22C2×#94011yescharacteristic
820C22#580611yescharacteristic
821C22#583111yescharacteristic
822C4—24no—
823C4—28no—
824C4—64no—
825C4—81no—
826C4—122no—
827C4—124no—
828C4—124no—
829C4—122no—
830C4—241no—
831C3#1492811yescharacteristic, complemented, Sylow
832C2—82no—
833C2—84no—
834C2#7666511yescharacteristic
835C2#7668012yes—
836C2#7669012yes—
837C2#7669611yescharacteristic
838C2#7670911yescharacteristic
839C2#7675711yescharacteristic
840C2#8258811yescharacteristic
841C2#8258912yes—
842C2#8266212yes—
843C2#8266811yescharacteristic
844C2#8318411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
Fitting, prime radicalC2×C3×#392C2
hypercenterC2×#392D3
hypocenterC3#14928
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C22×#936C2semidirect
3. C2×#5222C2semidirect
4. C2×#5221C2semidirect
5. C2×#4947C2semidirect
6. C2×#4945C2semidirect
7. C2×#4656C2semidirect
8. #72131C2semidirect
9. #71546C2semidirect
10. #71545C2semidirect
11. Dic3×#95C2semidirect
108. C2×#217D4semidirect
120. C2×C4×Dic3D4semidirect
127. C3⋊#95D4semidirect
428. C2×C3×C4#124semidirect
758. C2×C4#936semidirect
831. C3#14928semidirect

Maximal subgroups

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

subgroupindex
C22×#9362
C2×C3×#3922
C2×#52222
C2×#52212
C2×#49472
C2×#49452
C2×#46562
#721312
#715462
#715452
Dic3×#952
#149283