Finite Group Databasebeta

← #10732012

Subgroups — #10732012

Order 768.

2578 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#893C211yesmaximal, characteristic, complemented
2C2×#4960C211yesmaximal, characteristic
3C2×#4956C212yesmaximal, complemented
4C2×#4945C211yesmaximal, characteristic, complemented
5C2×#4672C211yesmaximal, characteristic, complemented
6C3×#1439C211yesmaximal, characteristic, complemented
7#71566C211yesmaximal, characteristic, complemented
8#71550C212yesmaximal, complemented
9#69429C212yesmaximal, complemented
10(C2×D3)⋊#95C212yesmaximal, complemented
11#69403C211yesmaximal, characteristic, complemented
12#15159—31nomaximal, Sylow
13C23×#67C2212yes—
14C23×D12C2211yescharacteristic
15C23×C4×D3C2212yes—
16C22×C3×C4⋊C4C2211yescharacteristic
17C22×C3×C22⋊C4C2211yescharacteristic
18C22×C3×C22⋊C4C2212yes—
19C22×#217C2211yescharacteristic
20C22×#217C2211yescharacteristic
21C22×(C2×D3)⋊C4C2212yes—
22C22×(C2×D3)⋊C4C2212yes—
23C22×(C2×D3)⋊C4C2212yes—
24C22×(C2×D3)⋊C4C2212yes—
25C22×Dic3⋊C4C2211yescharacteristic
26C22×C4×Dic3C2211yescharacteristic
27C2×#893—28no—
28C2×#893—24no—
29C2×C3×#95C2211yescharacteristic
30C2×C3×#95C2212yes—
31C2×C3⋊#95C2212yes—
32C2×C3⋊#95C2212yes—
33C2×C3⋊#95C2211yescharacteristic
34C2×C3⋊#95C2211yescharacteristic
35C2×C3⋊#95C2211yescharacteristic
36C2×C3⋊#95C2212yes—
37C2×C3⋊#95C2212yes—
38#4960—24no—
39#4956—28no—
40#4945—24no—
41#4672—24no—
42C22×C4×D4—31no—
43C2×#394—31no—
44C2×#392—31no—
45C2×#388—31no—
46C2×#386—32no—
47#1441—31no—
48#1440—32no—
49#1439D311yescharacteristic, complemented
50#1438—32no—
51#1434—31no—
52C22⋊#95—32no—
53C25×C3C2311yescharacteristic
54C24×D3C2312yes—
55C23×C3×C4C2311yescharacteristic
56C23×C3×C4C2312yes—
57C23×C3×C4C2312yes—
58C23×C3×C4C2311yescharacteristic
59C22×#67—24no—
60C22×#67—24no—
61C22×#67—24no—
62C22×#67—24no—
63C22×#67—24no—
64C22×#67—42no—
65C22×#67—42no—
66C23×Dic3C2311yescharacteristic
67C23×Dic3C2311yescharacteristic
68C23×Dic3C2312yes—
69C23×Dic3C2311yescharacteristic
70C23×Dic3C2311yescharacteristic
71C22×D12—24no—
72C22×D12—24no—
73C22×D12—22no—
74C22×D12—22no—
75C22×D12D414yes—
76C22×C4×D3—24no—
77C22×C4×D3—24no—
78C22×C4×D3—42no—
79C22×C4×D3—42no—
80C22×C4×D3—42no—
81C22×C4×D3—42no—
82C22×C4×D3D418yescomplemented
83C2×C3×C4⋊C4—24no—
84C2×C3×C4⋊C4—22no—
85C2×C3×C22⋊C4—22no—
86C2×C3×C22⋊C4—24no—
87C2×C3×C22⋊C4—22no—
88C2×C3×C22⋊C4—22no—
89C2×C3×C22⋊C4—42no—
90C2×C3×C22⋊C4—42no—
91C2×#217—22no—
92C2×#217—22no—
93C2×#217—22no—
94C2×#217—22no—
95C2×#217—24no—
96C2×(C2×D3)⋊C4—24no—
97C2×(C2×D3)⋊C4—24no—
98C2×(C2×D3)⋊C4—24no—
99C2×(C2×D3)⋊C4—24no—
100C2×(C2×D3)⋊C4—24no—
101C2×(C2×D3)⋊C4—24no—
102C2×(C2×D3)⋊C4—24no—
103C2×(C2×D3)⋊C4—24no—
104C2×(C2×D3)⋊C4—24no—
105C2×(C2×D3)⋊C4—24no—
106C2×(C2×D3)⋊C4—42no—
107C2×(C2×D3)⋊C4—42no—
108C2×Dic3⋊C4—22no—
109C2×Dic3⋊C4—22no—
110C2×Dic3⋊C4—22no—
111C2×C4×Dic3—24no—
112C2×C4×Dic3D414yescomplemented
113#893—232no—
114C3×#95—22no—
115C3×#95—42no—
116C3⋊#95—24no—
117C3⋊#95—22no—
118C3⋊#95—22no—
119C3⋊#95—22no—
120C3⋊#95—24no—
121C3⋊#95—24no—
122C3⋊#95—42no—
123C23×D4—32no—
124C23×D4—31no—
125C24×C4—32no—
126C2×C4×D4—64no—
127C2×C4×D4—68no—
128C22×C4⋊C4—31no—
129C22×C4⋊C4C2×D311yescharacteristic
130C22×C22⋊C4—31no—
131C22×C22⋊C4—31no—
132C22×C22⋊C4—32no—
133C22×C22⋊C4—32no—
134C22×C22⋊C4—32no—
135C22×C22⋊C4—32no—
136C22×C22⋊C4C2×D311yescharacteristic
137C22×C22⋊C4C2×D312yes—
138C22×C42—31no—
139#394—64no—
140#392—64no—
141#388—64no—
142#386—68no—
143C2×#95—31no—
144C2×#95—31no—
145C2×#95—32no—
146C2×#95—32no—
147C2×#95—31no—
148C2×#95—32no—
149C2×#95—32no—
150C2×#95C2×D311yescharacteristic
151C2×#95C2×D312yes—
152C24×C3—21no—
153C24×C3—22no—
154C24×C3—21no—
155C24×C3—21no—
156C24×C3—21no—
157C24×C3—22no—
158C24×C3—22no—
159C24×C3—21no—
160C24×C3—22no—
161C24×C3—21no—
162C24×C3#4112yes—
163C24×C3C2411yescharacteristic
164C23×D3—22no—
165C23×D3—22no—
166C23×D3—22no—
167C23×D3—22no—
168C23×D3—22no—
169C23×D3—22no—
170C23×D3—22no—
171C23×D3—22no—
172C23×D3—22no—
173C23×D3—22no—
174C23×D3—22no—
175C23×D3—22no—
176C23×D3C2×D414yes—
177C23×D3C2×D414yes—
178C23×D3#4114yes—
179C22×C3×C4—22no—
180C22×C3×C4—22no—
181C22×C3×C4—22no—
182C22×C3×C4—22no—
183C22×C3×C4—22no—
184C22×C3×C4—22no—
185C22×C3×C4—22no—
186C22×C3×C4—22no—
187C22×C3×C4—21no—
188C22×C3×C4—22no—
189C22×C3×C4—22no—
190C22×C3×C4—21no—
191C22×C3×C4—22no—
192C22×C3×C4—22no—
193C22×C3×C4—22no—
194C22×C3×C4—22no—
195C22×C3×C4—21no—
196C22×C3×C4—22no—
197C22×C3×C4—22no—
198C22×C3×C4—22no—
199C22×C3×C4C2×D414yes—
200C22×C3×C4C2×D412yes—
201C22×C3×C4C2×D412yes—
202C22×C3×C4#4112yes—
203C2×#67—216no—
204C2×#67—48no—
205C2×#67—48no—
206C2×#67—48no—
207C2×#67—48no—
208C2×#67—48no—
209C2×#67—48no—
210C22×Dic3—22no—
211C22×Dic3—21no—
212C22×Dic3—21no—
213C22×Dic3—22no—
214C22×Dic3—21no—
215C22×Dic3—22no—
216C22×Dic3—22no—
217C22×Dic3—21no—
218C22×Dic3—22no—
219C22×Dic3—21no—
220C22×Dic3—21no—
221C22×Dic3—21no—
222C22×Dic3—21no—
223C22×Dic3—22no—
224C22×Dic3—22no—
225C22×Dic3—21no—
226C22×Dic3—22no—
227C22×Dic3—21no—
228C22×Dic3—22no—
229C22×Dic3—21no—
230C22×Dic3—22no—
231C22×Dic3—21no—
232C22×Dic3—21no—
233C22×Dic3—22no—
234C22×Dic3C2×D412yes—
235C22×Dic3C2×D414yes—
236C22×Dic3C2×D412yes—
237C22×Dic3#4114yes—
238C22×Dic3#4112yes—
239C2×D12—28no—
240C2×D12—28no—
241C2×D12—216no—
242C2×D12—216no—
243C2×D12—28no—
244C2×C4×D3—216no—
245C2×C4×D3—48no—
246C2×C4×D3—48no—
247C2×C4×D3—48no—
248C2×C4×D3—48no—
249C2×C4×D3—48no—
250C2×C4×D3—48no—
251C3×C4⋊C4—28no—
252C3×C22⋊C4—48no—
253C3×C22⋊C4—44no—
254#217—28no—
255#217—44no—
256(C2×D3)⋊C4—216no—
257(C2×D3)⋊C4—48no—
258(C2×D3)⋊C4—48no—
259(C2×D3)⋊C4—48no—
260Dic3⋊C4—44no—
261C4×Dic3—28no—
262C25—32no—
263C25C22×D311yescharacteristic
264C22×D4—34no—
265C22×D4—64no—
266C22×D4—64no—
267C22×D4—64no—
268C22×D4—64no—
269C22×D4—64no—
270C22×D4—64no—
271C22×D4—64no—
272C22×D4—62no—
273C22×D4—62no—
274C22×D4—122no—
275C22×D4—122no—
276C23×C4—31no—
277C23×C4—31no—
278C23×C4—31no—
279C23×C4—32no—
280C23×C4—38no—
281C23×C4—31no—
282C23×C4—64no—
283C23×C4—64no—
284C23×C4—122no—
285C23×C4—122no—
286C23×C4—122no—
287C23×C4—122no—
288C23×C4C22×D311yescharacteristic
289C23×C4C22×D312yes—
290C23×C4C22×D312yes—
291C23×C4C22×D311yescharacteristic
292C4×D4—632no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—62no—
296C2×C4⋊C4—62no—
297C2×C4⋊C4—62no—
298C2×C22⋊C4—22no—
299C2×C22⋊C4—24no—
300C2×C22⋊C4—22no—
301C2×C22⋊C4—22no—
302C2×C22⋊C4—42no—
303C2×C22⋊C4—42no—
304C2×C22⋊C4—64no—
305C2×C22⋊C4—64no—
306C2×C22⋊C4—62no—
307C2×C22⋊C4—62no—
308C2×C22⋊C4—62no—
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—62no—
319C2×C22⋊C4—122no—
320C2×C22⋊C4—122no—
321C2×C42—34no—
322C2×C42—64no—
323#95—22no—
324#95—42no—
325#95—64no—
326#95—64no—
327#95—62no—
328#95—62no—
329#95—64no—
330#95—62no—
331#95—122no—
332C23×C3—22no—
333C23×C3—24no—
334C23×C3—22no—
335C23×C3—24no—
336C23×C3—22no—
337C23×C3—41no—
338C23×C3—41no—
339C23×C3—42no—
340C23×C3—41no—
341C23×C3—42no—
342C23×C3—42no—
343C23×C3—41no—
344C23×C3—42no—
345C23×C3—42no—
346C23×C3—41no—
347C23×C3—41no—
348C23×C3—42no—
349C23×C3—41no—
350C23×C3—42no—
351C23×C3—42no—
352C23×C3—42no—
353C23×C3—41no—
354C23×C3—42no—
355C23×C3C22×D412yes—
356C23×C3C22×D411yescharacteristic
357C23×C3C22×D411yescharacteristic
358C23×C3C2×#4111yescharacteristic
359C23×C3C2×#4111yescharacteristic
360C23×C3C2×#4112yes—
361C23×C3C2×#4112yes—
362C23×C3C2×#4111yescharacteristic
363C23×C3H(5,𝔽2)12yes—
364C23×C3H(5,𝔽2)11yescharacteristic
365C23×C3H(5,𝔽2)11yescharacteristic
366C22×D3—24no—
367C22×D3—24no—
368C22×D3—24no—
369C22×D3—24no—
370C22×D3—24no—
371C22×D3—24no—
372C22×D3—24no—
373C22×D3—24no—
374C22×D3—24no—
375C22×D3—24no—
376C22×D3—24no—
377C22×D3—24no—
378C22×D3—24no—
379C22×D3—24no—
380C22×D3—24no—
381C22×D3—24no—
382C22×D3—24no—
383C22×D3—24no—
384C22×D3—42no—
385C22×D3—42no—
386C22×D3—42no—
387C22×D3—42no—
388C22×D3—42no—
389C22×D3—42no—
390C22×D3—42no—
391C22×D3—42no—
392C22×D3—42no—
393C22×D3—42no—
394C22×D3—42no—
395C22×D3—42no—
396C22×D3—42no—
397C22×D3—42no—
398C22×D3—42no—
399C22×D3—42no—
400C22×D3#12118yes—
401C2×C3×C4—22no—
402C2×C3×C4—24no—
403C2×C3×C4—22no—
404C2×C3×C4—24no—
405C2×C3×C4—24no—
406C2×C3×C4—24no—
407C2×C3×C4—24no—
408C2×C3×C4—42no—
409C2×C3×C4—42no—
410C2×C3×C4—42no—
411C2×C3×C4—42no—
412C2×C3×C4—42no—
413C2×C3×C4—41no—
414C2×C3×C4—42no—
415C2×C3×C4—41no—
416C2×C3×C4—42no—
417C2×C3×C4—41no—
418C2×C3×C4—42no—
419C2×C3×C4—42no—
420C2×C3×C4—42no—
421C2×C3×C4—42no—
422C2×C3×C4—42no—
423C2×C3×C4—42no—
424C2×C3×C4#12114yes—
425#67—432no—
426C2×Dic3—24no—
427C2×Dic3—24no—
428C2×Dic3—22no—
429C2×Dic3—22no—
430C2×Dic3—22no—
431C2×Dic3—22no—
432C2×Dic3—22no—
433C2×Dic3—24no—
434C2×Dic3—22no—
435C2×Dic3—22no—
436C2×Dic3—24no—
437C2×Dic3—24no—
438C2×Dic3—22no—
439C2×Dic3—41no—
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—41no—
450C2×Dic3—41no—
451C2×Dic3—42no—
452C2×Dic3—41no—
453C2×Dic3—42no—
454C2×Dic3#12014yes—
455D12—232no—
456C4×D3—432no—
457C24—21no—
458C24—21no—
459C24—22no—
460C24—21no—
461C24—21no—
462C24—22no—
463C24—21no—
464C24—22no—
465C24—22no—
466C24—21no—
467C24—34no—
468C24—34no—
469C24—34no—
470C24—62no—
471C24—62no—
472C24—62no—
473C24—62no—
474C24—62no—
475C24—62no—
476C24—62no—
477C24—62no—
478C24—62no—
479C24—62no—
480C24—62no—
481C24—62no—
482C24#23912yes—
483C24C23×D311yescharacteristic
484C2×D4—616no—
485C2×D4—68no—
486C2×D4—68no—
487C2×D4—616no—
488C2×D4—616no—
489C2×D4—68no—
490C2×D4—128no—
491C2×D4—128no—
492C2×D4—128no—
493C2×D4—128no—
494C2×D4—128no—
495C2×D4—128no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—32no—
517C22×C4—34no—
518C22×C4—32no—
519C22×C4—34no—
520C22×C4—32no—
521C22×C4—616no—
522C22×C4—62no—
523C22×C4—61no—
524C22×C4—61no—
525C22×C4—61no—
526C22×C4—62no—
527C22×C4—61no—
528C22×C4—62no—
529C22×C4—62no—
530C22×C4—61no—
531C22×C4—61no—
532C22×C4—62no—
533C22×C4—61no—
534C22×C4—61no—
535C22×C4—62no—
536C22×C4—62no—
537C22×C4—61no—
538C22×C4—62no—
539C22×C4—61no—
540C22×C4—62no—
541C22×C4—61no—
542C22×C4—62no—
543C22×C4—61no—
544C22×C4—61no—
545C22×C4—62no—
546C22×C4—128no—
547C22×C4—128no—
548C22×C4—128no—
549C22×C4—128no—
550C22×C4—128no—
551C22×C4—128no—
552C22×C4#23512yes—
553C22×C4D3×D414yes—
554C22×C4D3×D412yes—
555C22×C4D3×D412yes—
556C4⋊C4—28no—
557C4⋊C4—124no—
558C22⋊C4—48no—
559C22⋊C4—44no—
560C22⋊C4—616no—
561C22⋊C4—68no—
562C22⋊C4—124no—
563C22⋊C4—128no—
564C22⋊C4—128no—
565C22⋊C4—128no—
566C42—68no—
567C22×C3—42no—
568C22×C3—44no—
569C22×C3—42no—
570C22×C3—44no—
571C22×C3—42no—
572C22×C3—81no—
573C22×C3—82no—
574C22×C3—81no—
575C22×C3—81no—
576C22×C3—82no—
577C22×C3—81no—
578C22×C3C2×#12011yescharacteristic
579C22×C3C2×#12111yescharacteristic
580C22×C3C2×#12112yes—
581C22×C3#52511yescharacteristic
582C22×C3#52512yes—
583C22×C3#52511yescharacteristic
584C22×C3#52512yes—
585C22×C3#53212yes—
586C22×C3#53211yescharacteristic
587C22×C3#53412yes—
588C22×C3#53412yes—
589C22×C3#53511yescharacteristic
590C22×C3#53511yescharacteristic
591C22×C3#54612yes—
592C22×C3#54611yescharacteristic
593C22×C3#54611yescharacteristic
594C22×C3#55112yes—
595C22×C3#55112yes—
596C22×C3#55312yes—
597C22×C3#55312yes—
598C22×C3#55311yescharacteristic
599C22×C3#55311yescharacteristic
600C22×C3#55912yes—
601C2×D3—28no—
602C2×D3—28no—
603C2×D3—28no—
604C2×D3—44no—
605C2×D3—44no—
606C2×D3—44no—
607C2×D3—44no—
608C2×D3—44no—
609C2×D3—44no—
610C2×D3—44no—
611C2×D3—44no—
612C2×D3—44no—
613C2×D3—44no—
614C2×D3—44no—
615C2×D3—44no—
616C3×C4—24no—
617C3×C4—44no—
618C3×C4—82no—
619C3×C4—81no—
620Dic3—24no—
621Dic3—42no—
622Dic3—44no—
623Dic3—42no—
624Dic3—81no—
625C23—24no—
626C23—22no—
627C23—22no—
628C23—24no—
629C23—22no—
630C23—38no—
631C23—41no—
632C23—42no—
633C23—42no—
634C23—41no—
635C23—42no—
636C23—42no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—42no—
641C23—42no—
642C23—41no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—41no—
647C23—42no—
648C23—41no—
649C23—64no—
650C23—64no—
651C23—64no—
652C23—64no—
653C23—64no—
654C23—64no—
655C23—64no—
656C23—64no—
657C23—64no—
658C23—64no—
659C23—64no—
660C23—64no—
661C23—64no—
662C23—64no—
663C23—64no—
664C23—64no—
665C23—64no—
666C23—64no—
667C23—122no—
668C23—122no—
669C23—122no—
670C23—122no—
671C23—122no—
672C23—122no—
673C23—122no—
674C23—122no—
675C23—122no—
676C23—122no—
677C23—122no—
678C23—122no—
679C23—122no—
680C23—122no—
681C23—122no—
682C23—122no—
683C23C2×#23511yescharacteristic
684C23C2×D3×D411yescharacteristic
685C23C2×D3×D412yes—
686C23C2×D3×D411yescharacteristic
687C23#100412yes—
688C23#100411yescharacteristic
689C23C2×#23911yescharacteristic
690C23D3×#4112yes—
691C23D3×#4111yescharacteristic
692C23D3×#4112yes—
693C23#100911yescharacteristic
694D4—632no—
695D4—1232no—
696C2×C4—22no—
697C2×C4—24no—
698C2×C4—22no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—34no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—41no—
711C2×C4—42no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—62no—
721C2×C4—64no—
722C2×C4—64no—
723C2×C4—62no—
724C2×C4—62no—
725C2×C4—64no—
726C2×C4—62no—
727C2×C4—62no—
728C2×C4—62no—
729C2×C4—64no—
730C2×C4—62no—
731C2×C4—62no—
732C2×C4—64no—
733C2×C4—1232no—
734C2×C4—122no—
735C2×C4—122no—
736C2×C4—121no—
737C2×C4—121no—
738C2×C4—122no—
739C2×C4—122no—
740C2×C4—121no—
741C2×C4—122no—
742C2×C4—122no—
743C2×C4—121no—
744C2×C4—121no—
745C2×C4—121no—
746C2×C4—122no—
747C2×C4—121no—
748C2×C4—122no—
749C2×C4#88414yes—
750C2×C3—82no—
751C2×C3#238811yescharacteristic
752C2×C3#253412yes—
753C2×C3#253511yescharacteristic
754C2×C3#254312yes—
755C2×C3#254411yescharacteristic
756C2×C3#259811yescharacteristic
757C2×C3#260012yes—
758C2×C3#260212yes—
759C2×C3#260311yescharacteristic
760C2×C3#261311yescharacteristic
761C2×C3#284711yescharacteristic
762D3—48no—
763C22—44no—
764C22—44no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—68no—
769C22—68no—
770C22—68no—
771C22—81no—
772C22—82no—
773C22—82no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—124no—
778C22—124no—
779C22—124no—
780C22—124no—
781C22—124no—
782C22—124no—
783C22—124no—
784C22—124no—
785C22—124no—
786C22—124no—
787C22—124no—
788C22—124no—
789C22C2×#88411yescharacteristic
790C22#551411yescharacteristic
791C22#553011yescharacteristic
792C22#554712yes—
793C22#555912yes—
794C22D3×#12011yescharacteristic
795C22#558912yes—
796C22D3×#12112yes—
797C22#560512yes—
798C22#560711yescharacteristic
799C22#561212yes—
800C22#561211yescharacteristic
801C22#562712yes—
802C22#562711yescharacteristic
803C22#563011yescharacteristic
804C22#563712yes—
805C22#565611yescharacteristic
806C22#566112yes—
807C22#566112yes—
808C22#566811yescharacteristic
809C22#566812yes—
810C22#570512yes—
811C22#571511yescharacteristic
812C4—24no—
813C4—44no—
814C4—64no—
815C4—81no—
816C4—82no—
817C4—124no—
818C4—122no—
819C4—122no—
820C4—241no—
821C3#1515911yescharacteristic, complemented, Sylow
822C2—82no—
823C2—128no—
824C2#7393311yescharacteristic
825C2#7461712yes—
826C2#7493511yescharacteristic
827C2#7564612yes—
828C2#7635011yescharacteristic
829C2#7676011yescharacteristic
830C2#7677711yescharacteristic
831C2#7712012yes—
832C2#7742112yes—
833C2#7753611yescharacteristic
834C2#7804411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1439C2
prime radicalC2×#4960C2
hypercenter#1439D3
hypocenterC3#15159
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
1. C22×#893C2semidirect
3. C2×#4956C2semidirect
4. C2×#4945C2semidirect
5. C2×#4672C2semidirect
6. C3×#1439C2semidirect
7. #71566C2semidirect
8. #71550C2semidirect
9. #69429C2semidirect
10. (C2×D3)⋊#95C2semidirect
11. #69403C2semidirect
49. #1439D3semidirect
82. C22×C4×D3D4semidirect
112. C2×C4×Dic3D4semidirect
821. C3#15159semidirect

Maximal subgroups

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

subgroupindex
C22×#8932
C2×#49602
C2×#49562
C2×#49452
C2×#46722
C3×#14392
#715662
#715502
#694292
(C2×D3)⋊#952
#694032
#151593