Finite Group Databasebeta

← #10727865

Subgroups — #10727865

Order 768.

2278 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#392C211yesmaximal, characteristic
2C2×#5222C212yesmaximal, complemented
3C2×#5221C212yesmaximal, complemented
4C2×#5221C211yesmaximal, characteristic, complemented
5C2×#4948C212yesmaximal, complemented
6C2×#4944C211yesmaximal, characteristic, complemented
7C2×#4649C211yesmaximal, characteristic, complemented
8#72131C211yesmaximal, characteristic, complemented
9#71546C211yesmaximal, characteristic, complemented
10#71545C212yesmaximal, complemented
11#69419C211yesmaximal, characteristic, complemented
12#14815—31nomaximal, Sylow
13C23×C3×D4C2212yes—
14C23×C3×D4C2211yescharacteristic
15C22×C3×C22⋊C4C2212yes—
16C22×C3×C22⋊C4C2211yescharacteristic
17C22×#217C2212yes—
18C22×#217C2212yes—
19C22×#217C2211yescharacteristic
20C22×#217C2212yes—
21C22×#217C2212yes—
22C22×#217C2212yes—
23C22×#217C2211yescharacteristic
24C22×C4⋊Dic3C2212yes—
25C22×C4⋊Dic3C2211yescharacteristic
26C22×Dic3⋊C4C2211yescharacteristic
27C22×Dic3⋊C4C2212yes—
28C22×C4×Dic3C2212yes—
29C22×C4×Dic3C2211yescharacteristic
30C3×#392—24no—
31C2×C3×#95C2211yescharacteristic
32#5222—28no—
33#5221—28no—
34#5221—24no—
35C2×C3⋊#95C2212yes—
36C2×C3⋊#95C2211yescharacteristic
37C2×C3⋊#95C2211yescharacteristic
38C2×C3⋊#95C2211yescharacteristic
39C2×C3⋊#95C2212yes—
40#4948—28no—
41#4944—24no—
42#4649—24no—
43C2×#396—32no—
44C2×#394—32no—
45C2×#392D311yescharacteristic
46C2×#390—32no—
47C2×#390—31no—
48C2×#388—31no—
49C2×C4×C4⋊C4—31no—
50#1444—31no—
51#1439—31no—
52#1438—31no—
53#1437—32no—
54C25×C3C2311yescharacteristic
55C25×C3C2312yes—
56C22×C3×D4—24no—
57C22×C3×D4—24no—
58C22×C3×D4—24no—
59C22×C3×D4—22no—
60C22×C3×D4—24no—
61C22×C3×D4—22no—
62C22×C3×D4—24no—
63C22×C3×D4—24no—
64C22×C3×D4—22no—
65C22×C3×D4—42no—
66C22×C3×D4—42no—
67C22×C3×D4—42no—
68C23×C3×C4C2311yescharacteristic
69C23×C3×C4C2311yescharacteristic
70C23×C3×C4C2312yes—
71C23×Dic3C2311yescharacteristic
72C23×Dic3C2312yes—
73C23×Dic3C2312yes—
74C23×Dic3C2311yescharacteristic
75C23×Dic3C2311yescharacteristic
76C23×Dic3C2311yescharacteristic
77C2×C3×C22⋊C4—22no—
78C2×C3×C22⋊C4—24no—
79C2×C3×C22⋊C4—22no—
80C2×C3×C22⋊C4—24no—
81C2×C3×C22⋊C4—22no—
82C2×C3×C22⋊C4—24no—
83C2×#217—22no—
84C2×#217—22no—
85C2×#217—24no—
86C2×#217—24no—
87C2×#217—22no—
88C2×#217—24no—
89C2×#217—24no—
90C2×#217—24no—
91C2×#217—24no—
92C2×#217—24no—
93C2×#217—24no—
94C2×#217—24no—
95C2×#217—24no—
96C2×#217—24no—
97C2×#217—24no—
98C2×#217—24no—
99C2×#217—42no—
100C2×#217—42no—
101C2×#217—42no—
102C2×#217D414yescomplemented
103C2×C4⋊Dic3—24no—
104C2×C4⋊Dic3—22no—
105C2×C4⋊Dic3—24no—
106C2×C4⋊Dic3—42no—
107C2×C4⋊Dic3—42no—
108C2×Dic3⋊C4—24no—
109C2×Dic3⋊C4—24no—
110C2×Dic3⋊C4—22no—
111C2×Dic3⋊C4—24no—
112C2×Dic3⋊C4D418yescomplemented
113C2×C4×Dic3—22no—
114C2×C4×Dic3—22no—
115C2×C4×Dic3—24no—
116C2×C4×Dic3—24no—
117C2×C4×Dic3—42no—
118C2×C4×Dic3D414yescomplemented
119C3×#95D414yes—
120C3⋊#95—22no—
121C3⋊#95—22no—
122C3⋊#95—24no—
123C3⋊#95—22no—
124C3⋊#95—24no—
125C23×D4C2×D312yes—
126C23×D4C2×D311yescharacteristic
127C22×C4⋊C4—32no—
128C22×C4⋊C4—31no—
129C22×C4⋊C4—32no—
130C22×C4⋊C4—31no—
131C22×C22⋊C4—31no—
132C22×C22⋊C4—31no—
133C22×C22⋊C4—32no—
134C22×C22⋊C4—32no—
135C22×C22⋊C4—32no—
136C22×C22⋊C4—32no—
137C22×C22⋊C4—32no—
138C22×C22⋊C4C2×D312yes—
139C22×C22⋊C4C2×D311yescharacteristic
140C22×C42—31no—
141C22×C42—32no—
142#396—68no—
143#394—68no—
144#392—24no—
145#390—64no—
146#390—68no—
147#388—64no—
148C4×C4⋊C4—64no—
149C2×#95—32no—
150C2×#95—32no—
151C2×#95—31no—
152C2×#95—31no—
153C2×#95—31no—
154C2×#95C2×D311yescharacteristic
155C24×C3—21no—
156C24×C3—22no—
157C24×C3—22no—
158C24×C3—22no—
159C24×C3—22no—
160C24×C3—22no—
161C24×C3—21no—
162C24×C3—22no—
163C24×C3—21no—
164C24×C3—22no—
165C24×C3—22no—
166C24×C3—21no—
167C24×C3—22no—
168C24×C3—22no—
169C24×C3—22no—
170C24×C3—22no—
171C24×C3—22no—
172C24×C3—22no—
173C24×C3—22no—
174C24×C3—22no—
175C24×C3—21no—
176C24×C3—22no—
177C24×C3—21no—
178C24×C3—22no—
179C24×C3C2×D412yes—
180C24×C3#4114yes—
181C24×C3C2411yescharacteristic
182C2×C3×D4—28no—
183C2×C3×D4—216no—
184C2×C3×D4—48no—
185C2×C3×D4—48no—
186C2×C3×D4—48no—
187C2×C3×D4—48no—
188C2×C3×D4—48no—
189C2×C3×D4—48no—
190C2×C3×D4—44no—
191C2×C3×D4—48no—
192C2×C3×D4—44no—
193C2×C3×D4—48no—
194C22×C3×C4—22no—
195C22×C3×C4—22no—
196C22×C3×C4—22no—
197C22×C3×C4—22no—
198C22×C3×C4—22no—
199C22×C3×C4—22no—
200C22×C3×C4—21no—
201C22×C3×C4—22no—
202C22×C3×C4—21no—
203C22×C3×C4—22no—
204C22×C3×C4—21no—
205C22×C3×C4C2×D412yes—
206C22×C3×C4C2×D414yes—
207C22×C3×C4C2×D412yes—
208C22×C3×C4C2×D414yes—
209C22×C3×C4#4112yes—
210C22×C3×C4#4114yes—
211C22×Dic3—21no—
212C22×Dic3—21no—
213C22×Dic3—21no—
214C22×Dic3—21no—
215C22×Dic3—22no—
216C22×Dic3—21no—
217C22×Dic3—21no—
218C22×Dic3—22no—
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—21no—
229C22×Dic3—22no—
230C22×Dic3—22no—
231C22×Dic3—22no—
232C22×Dic3—22no—
233C22×Dic3—22no—
234C22×Dic3—22no—
235C22×Dic3—22no—
236C22×Dic3—22no—
237C22×Dic3—22no—
238C22×Dic3—21no—
239C22×Dic3—21no—
240C22×Dic3C2×D414yes—
241C22×Dic3C2×D412yes—
242C22×Dic3C2×D412yes—
243C22×Dic3C2×D412yes—
244C22×Dic3C2×D412yes—
245C22×Dic3C2×D414yes—
246C22×Dic3#4112yes—
247C3×C22⋊C4—44no—
248C3×C22⋊C4—48no—
249#217—28no—
250#217—48no—
251#217—48no—
252#217—48no—
253#217—48no—
254#217—44no—
255#217—48no—
256C4⋊Dic3—48no—
257C4⋊Dic3—44no—
258Dic3⋊C4—216no—
259Dic3⋊C4—44no—
260C4×Dic3—28no—
261C4×Dic3—48no—
262C25C22×D311yescharacteristic
263C25C22×D312yes—
264C22×D4—24no—
265C22×D4—24no—
266C22×D4—24no—
267C22×D4—22no—
268C22×D4—24no—
269C22×D4—24no—
270C22×D4—22no—
271C22×D4—22no—
272C22×D4—24no—
273C22×D4—42no—
274C22×D4—42no—
275C22×D4—42no—
276C23×C4—31no—
277C23×C4—31no—
278C23×C4—31no—
279C23×C4—32no—
280C23×C4—32no—
281C23×C4—31no—
282C23×C4C22×D311yescharacteristic
283C23×C4C22×D312yes—
284C23×C4C22×D311yescharacteristic
285C2×C4⋊C4—38no—
286C2×C4⋊C4—64no—
287C2×C4⋊C4—64no—
288C2×C4⋊C4—62no—
289C2×C4⋊C4—64no—
290C2×C4⋊C4—64no—
291C2×C4⋊C4—62no—
292C2×C4⋊C4—64no—
293C2×C4⋊C4—122no—
294C2×C4⋊C4—122no—
295C2×C22⋊C4—22no—
296C2×C22⋊C4—24no—
297C2×C22⋊C4—22no—
298C2×C22⋊C4—24no—
299C2×C22⋊C4—22no—
300C2×C22⋊C4—24no—
301C2×C22⋊C4—34no—
302C2×C22⋊C4—62no—
303C2×C22⋊C4—62no—
304C2×C22⋊C4—62no—
305C2×C22⋊C4—64no—
306C2×C22⋊C4—64no—
307C2×C22⋊C4—64no—
308C2×C22⋊C4—64no—
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—
321C2×C42—34no—
322C2×C42—62no—
323C2×C42—62no—
324C2×C42—64no—
325C2×C42—64no—
326C2×C42—122no—
327#95—62no—
328#95—64no—
329#95—62no—
330#95—64no—
331#95—62no—
332#95#6714yes—
333C23×C3—22no—
334C23×C3—24no—
335C23×C3—24no—
336C23×C3—24no—
337C23×C3—24no—
338C23×C3—24no—
339C23×C3—22no—
340C23×C3—24no—
341C23×C3—24no—
342C23×C3—22no—
343C23×C3—24no—
344C23×C3—24no—
345C23×C3—42no—
346C23×C3—41no—
347C23×C3—42no—
348C23×C3—42no—
349C23×C3—42no—
350C23×C3—42no—
351C23×C3—41no—
352C23×C3—42no—
353C23×C3—42no—
354C23×C3—42no—
355C23×C3—42no—
356C23×C3—41no—
357C23×C3—41no—
358C23×C3—42no—
359C23×C3—42no—
360C23×C3—42no—
361C23×C3—42no—
362C23×C3—42no—
363C23×C3—41no—
364C23×C3—41no—
365C23×C3—42no—
366C23×C3—42no—
367C23×C3—42no—
368C23×C3—42no—
369C23×C3—42no—
370C23×C3—42no—
371C23×C3—42no—
372C23×C3—42no—
373C23×C3—42no—
374C23×C3—42no—
375C23×C3—42no—
376C23×C3—42no—
377C23×C3—42no—
378C23×C3—42no—
379C23×C3—42no—
380C23×C3—41no—
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×C3C22×D411yescharacteristic
392C23×C3C22×D411yescharacteristic
393C23×C3C22×D412yes—
394C23×C3C22×D411yescharacteristic
395C23×C3C2×#4112yes—
396C23×C3C2×#4111yescharacteristic
397C23×C3C2×#4112yes—
398C23×C3C2×#4111yescharacteristic
399C23×C3H(5,𝔽2)12yes—
400C23×C3H(5,𝔽2)11yescharacteristic
401C23×C32−1+411yescharacteristic
402C3×D4—416no—
403C3×D4—432no—
404C2×C3×C4—22no—
405C2×C3×C4—24no—
406C2×C3×C4—22no—
407C2×C3×C4—24no—
408C2×C3×C4—24no—
409C2×C3×C4—24no—
410C2×C3×C4—24no—
411C2×C3×C4—24no—
412C2×C3×C4—24no—
413C2×C3×C4—24no—
414C2×C3×C4—41no—
415C2×C3×C4—42no—
416C2×C3×C4—41no—
417C2×C3×C4—41no—
418C2×C3×C4—42no—
419C2×C3×C4#12114yes—
420C2×C3×C4#12118yes—
421C2×Dic3—22no—
422C2×Dic3—22no—
423C2×Dic3—24no—
424C2×Dic3—22no—
425C2×Dic3—24no—
426C2×Dic3—22no—
427C2×Dic3—22no—
428C2×Dic3—22no—
429C2×Dic3—22no—
430C2×Dic3—22no—
431C2×Dic3—24no—
432C2×Dic3—22no—
433C2×Dic3—24no—
434C2×Dic3—24no—
435C2×Dic3—24no—
436C2×Dic3—42no—
437C2×Dic3—41no—
438C2×Dic3—41no—
439C2×Dic3—42no—
440C2×Dic3—42no—
441C2×Dic3—42no—
442C2×Dic3—42no—
443C2×Dic3—42no—
444C2×Dic3—41no—
445C2×Dic3—41no—
446C2×Dic3—42no—
447C2×Dic3—42no—
448C2×Dic3—41no—
449C2×Dic3—42no—
450C2×Dic3—42no—
451C2×Dic3—42no—
452C2×Dic3—42no—
453C2×Dic3—42no—
454C2×Dic3—42no—
455C2×Dic3#12114yes—
456C2×Dic3#12714yes—
457C24—22no—
458C24—21no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—21no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24—22no—
472C24—22no—
473C24—21no—
474C24—22no—
475C24—22no—
476C24—21no—
477C24—22no—
478C24—21no—
479C24—21no—
480C24—22no—
481C24D3×D412yes—
482C24#23714yes—
483C24C23×D311yescharacteristic
484C2×D4—28no—
485C2×D4—216no—
486C2×D4—48no—
487C2×D4—48no—
488C2×D4—48no—
489C2×D4—48no—
490C2×D4—48no—
491C2×D4—48no—
492C2×D4—44no—
493C2×D4—48no—
494C2×D4—44no—
495C2×D4—48no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—32no—
508C22×C4—32no—
509C22×C4—32no—
510C22×C4—34no—
511C22×C4—32no—
512C22×C4—34no—
513C22×C4—32no—
514C22×C4—61no—
515C22×C4—61no—
516C22×C4—62no—
517C22×C4—61no—
518C22×C4—61no—
519C22×C4—61no—
520C22×C4—61no—
521C22×C4—61no—
522C22×C4—62no—
523C22×C4—62no—
524C22×C4—62no—
525C22×C4—62no—
526C22×C4—62no—
527C22×C4—62no—
528C22×C4—62no—
529C22×C4—61no—
530C22×C4—62no—
531C22×C4—61no—
532C22×C4—62no—
533C22×C4—62no—
534C22×C4—62no—
535C22×C4—62no—
536C22×C4—62no—
537C22×C4—62no—
538C22×C4—61no—
539C22×C4—62no—
540C22×C4—62no—
541C22×C4—62no—
542C22×C4—61no—
543C22×C4D3×D412yes—
544C22×C4D3×D414yes—
545C22×C4#23712yes—
546C22×C4#23714yes—
547C22×C4C2×#6712yes—
548C22×C4C2×#6714yes—
549C4⋊C4—616no—
550C4⋊C4—128no—
551C4⋊C4—124no—
552C4⋊C4—124no—
553C22⋊C4—44no—
554C22⋊C4—48no—
555C22⋊C4—68no—
556C22⋊C4—124no—
557C22⋊C4—128no—
558C22⋊C4—128no—
559C22⋊C4—128no—
560C22⋊C4—128no—
561C22⋊C4—128no—
562C42—68no—
563C42—128no—
564C22×C3—42no—
565C22×C3—44no—
566C22×C3—44no—
567C22×C3—42no—
568C22×C3—44no—
569C22×C3—44no—
570C22×C3—44no—
571C22×C3—44no—
572C22×C3—44no—
573C22×C3—44no—
574C22×C3—42no—
575C22×C3—44no—
576C22×C3—82no—
577C22×C3—81no—
578C22×C3—82no—
579C22×C3—81no—
580C22×C3—81no—
581C22×C3—82no—
582C22×C3—82no—
583C22×C3—82no—
584C22×C3—82no—
585C22×C3—82no—
586C22×C3—81no—
587C22×C3—82no—
588C22×C3—82no—
589C22×C3—82no—
590C22×C3C2×#12111yescharacteristic
591C22×C3C2×#12112yes—
592C22×C3C2×#12111yescharacteristic
593C22×C3#52511yescharacteristic
594C22×C3#52512yes—
595C22×C3#52912yes—
596C22×C3C2×#12711yescharacteristic
597C22×C3#53211yescharacteristic
598C22×C3#53212yes—
599C22×C3#53511yescharacteristic
600C22×C3#53711yescharacteristic
601C22×C3#53812yes—
602C22×C3#54212yes—
603C22×C3D4211yescharacteristic
604C22×C3D4212yes—
605C22×C3#54612yes—
606C22×C3#54612yes—
607C22×C3#54711yescharacteristic
608C22×C3#54811yescharacteristic
609C22×C3#54812yes—
610C22×C3#55012yes—
611C22×C3#55112yes—
612C22×C3#55311yescharacteristic
613C3×C4—24no—
614C3×C4—28no—
615C3×C4—81no—
616Dic3—24no—
617Dic3—24no—
618Dic3—44no—
619Dic3—42no—
620Dic3—81no—
621Dic3—82no—
622C23—22no—
623C23—24no—
624C23—24no—
625C23—24no—
626C23—24no—
627C23—24no—
628C23—24no—
629C23—24no—
630C23—24no—
631C23—24no—
632C23—22no—
633C23—22no—
634C23—42no—
635C23—41no—
636C23—41no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—41no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—41no—
650C23—42no—
651C23—42no—
652C23—41no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—41no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—41no—
677C23—42no—
678C23—42no—
679C23—41no—
680C23C2×D3×D411yescharacteristic
681C23C2×D3×D412yes—
682C23C2×D3×D411yescharacteristic
683C23C2×#23712yes—
684C23C2×#23711yescharacteristic
685C23C2×#23712yes—
686C23#100411yescharacteristic
687C23#100412yes—
688C23D3×#4111yescharacteristic
689C23#101011yescharacteristic
690C23C22×#6711yescharacteristic
691D4—416no—
692D4—432no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—24no—
703C2×C4—34no—
704C2×C4—34no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—42no—
708C2×C4—41no—
709C2×C4—42no—
710C2×C4—62no—
711C2×C4—64no—
712C2×C4—62no—
713C2×C4—62no—
714C2×C4—64no—
715C2×C4—62no—
716C2×C4—62no—
717C2×C4—62no—
718C2×C4—62no—
719C2×C4—62no—
720C2×C4—64no—
721C2×C4—64no—
722C2×C4—64no—
723C2×C4—64no—
724C2×C4—62no—
725C2×C4—121no—
726C2×C4—122no—
727C2×C4—122no—
728C2×C4—122no—
729C2×C4—121no—
730C2×C4—122no—
731C2×C4—122no—
732C2×C4—121no—
733C2×C4—122no—
734C2×C4—121no—
735C2×C4—122no—
736C2×C4—122no—
737C2×C4—122no—
738C2×C4—122no—
739C2×C4—122no—
740C2×C4—122no—
741C2×C4—122no—
742C2×C4—122no—
743C2×C4—121no—
744C2×C4#93814yes—
745C2×C4#93818yes—
746C2×C3—84no—
747C2×C3—82no—
748C2×C3#239211yescharacteristic
749C2×C3#241111yescharacteristic
750C2×C3#241611yescharacteristic
751C2×C3#242412yes—
752C2×C3#242612yes—
753C2×C3#246112yes—
754C2×C3#254011yescharacteristic
755C2×C3#254111yescharacteristic
756C2×C3#255412yes—
757C2×C3#266211yescharacteristic
758C2×C3#285611yescharacteristic
759C22—42no—
760C22—44no—
761C22—44no—
762C22—44no—
763C22—44no—
764C22—42no—
765C22—44no—
766C22—44no—
767C22—44no—
768C22—44no—
769C22—42no—
770C22—44no—
771C22—82no—
772C22—81no—
773C22—82no—
774C22—82no—
775C22—82no—
776C22—81no—
777C22—82no—
778C22—82no—
779C22—81no—
780C22—82no—
781C22—82no—
782C22—82no—
783C22—81no—
784C22—82no—
785C22#558612yes—
786C22#558611yescharacteristic
787C22#558712yes—
788C22#559012yes—
789C22#559112yes—
790C22#559211yescharacteristic
791C22#559312yes—
792C22#559812yes—
793C22#559912yes—
794C22#560012yes—
795C22#560312yes—
796C22D3×#12111yescharacteristic
797C22#560811yescharacteristic
798C22#561111yescharacteristic
799C22#561411yescharacteristic
800C22D3×#12711yescharacteristic
801C22#571611yescharacteristic
802C22#571612yes—
803C22C2×#93811yescharacteristic
804C22C2×#93812yes—
805C22D4×#6711yescharacteristic
806C22#580612yes—
807C22#583111yescharacteristic
808C4—24no—
809C4—28no—
810C4—64no—
811C4—64no—
812C4—81no—
813C4—122no—
814C4—124no—
815C4—241no—
816C4—242no—
817C3#1481511yescharacteristic, complemented, Sylow
818C2—82no—
819C2—84no—
820C2#7666611yescharacteristic
821C2#7668012yes—
822C2#7668711yescharacteristic
823C2#7668811yescharacteristic
824C2#7668912yes—
825C2#7670911yescharacteristic
826C2#8258311yescharacteristic
827C2#8258612yes—
828C2#8264111yescharacteristic
829C2#8264612yes—
830C2#8319211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
Fitting, prime radicalC2×C3×#392C2
hypercenterC2×#392D3
hypocenterC3#14815
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
2. C2×#5222C2semidirect
3. C2×#5221C2semidirect
4. C2×#5221C2semidirect
5. C2×#4948C2semidirect
6. C2×#4944C2semidirect
7. C2×#4649C2semidirect
8. #72131C2semidirect
9. #71546C2semidirect
10. #71545C2semidirect
11. #69419C2semidirect
102. C2×#217D4semidirect
112. C2×Dic3⋊C4D4semidirect
118. C2×C4×Dic3D4semidirect
817. C3#14815semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#3922
C2×#52222
C2×#52212
C2×#49482
C2×#49442
C2×#46492
#721312
#715462
#715452
#694192
#148153