Finite Group Databasebeta

← #10733130

Subgroups — #10733130

Order 768.

3134 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#895C212yesmaximal, complemented
2C2×#4991C212yesmaximal, complemented
3C2×#4671C212yesmaximal, complemented
4C2×#4665C212yesmaximal, complemented
5C3×#1444C211yesmaximal, characteristic, complemented
6#71570C212yesmaximal, complemented
7#69426C211yesmaximal, characteristic, complemented
8#69426C211yesmaximal, characteristic, complemented
9(C2×D3)⋊#95C212yesmaximal, complemented
10#15278—31nomaximal, Sylow
11C23×D12C2212yes—
12C23×D12C2211yescharacteristic
13C23×D12C2212yes—
14C23×D12C2211yescharacteristic
15C23×C4×D3C2212yes—
16C22×C3×C4⋊C4C2212yes—
17C22×C3×C4⋊C4C2211yescharacteristic
18C22×(C2×D3)⋊C4C2212yes—
19C22×(C2×D3)⋊C4C2212yes—
20C22×(C2×D3)⋊C4C2212yes—
21C22×(C2×D3)⋊C4C2212yes—
22C22×(C2×D3)⋊C4C2212yes—
23C22×(C2×D3)⋊C4C2212yes—
24C22×(C2×D3)⋊C4C2212yes—
25C2×#895—28no—
26C2×#895—28no—
27C2×#895—28no—
28C2×C3×#95C2212yes—
29C2×C3×#95C2211yescharacteristic
30C2×C3×#95C2211yescharacteristic
31C2×C3⋊#95C2212yes—
32C2×C3⋊#95C2212yes—
33C2×C3⋊#95C2211yescharacteristic
34C2×C3⋊#95C2211yescharacteristic
35#4991—28no—
36#4671—28no—
37#4665—28no—
38C22×#121—32no—
39C2×#394—32no—
40C2×#392—32no—
41C2×#386—32no—
42#1444D311yescharacteristic, complemented
43#1439—32no—
44#1438—31no—
45#1438—31no—
46C22⋊#95—32no—
47C24×D3C2312yes—
48C24×D3C2312yes—
49C23×C3×C4C2312yes—
50C23×C3×C4C2311yescharacteristic
51C23×C3×C4C2311yescharacteristic
52C23×C3×C4C2311yescharacteristic
53C23×C3×C4C2312yes—
54C23×Dic3C2312yes—
55C23×Dic3C2312yes—
56C22×D12—24no—
57C22×D12—24no—
58C22×D12—24no—
59C22×D12—24no—
60C22×D12—24no—
61C22×D12—24no—
62C22×D12—24no—
63C22×D12—24no—
64C22×D12—24no—
65C22×D12—24no—
66C22×D12—24no—
67C22×D12—24no—
68C22×D12—22no—
69C22×D12—42no—
70C22×D12—42no—
71C22×D12—41no—
72C22×D12—41no—
73C22×D12—42no—
74C22×D12—42no—
75C22×D12—42no—
76C22×D12—41no—
77C22×D12—41no—
78C22×D12D418yescomplemented
79C22×D12D414yescomplemented
80C22×C4×D3—24no—
81C22×C4×D3—24no—
82C22×C4×D3—24no—
83C22×C4×D3—24no—
84C22×C4×D3—24no—
85C22×C4×D3—42no—
86C22×C4×D3—42no—
87C2×C3×C4⋊C4—24no—
88C2×C3×C4⋊C4—24no—
89C2×C3×C4⋊C4—24no—
90C2×C3×C4⋊C4—24no—
91C2×C3×C4⋊C4—41no—
92C2×(C2×D3)⋊C4—24no—
93C2×(C2×D3)⋊C4—24no—
94C2×(C2×D3)⋊C4—24no—
95C2×(C2×D3)⋊C4—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—24no—
107C2×(C2×D3)⋊C4—24no—
108C2×(C2×D3)⋊C4—42no—
109C2×(C2×D3)⋊C4—42no—
110C2×(C2×D3)⋊C4—42no—
111C2×(C2×D3)⋊C4—42no—
112C2×(C2×D3)⋊C4D418yescomplemented
113#895—264no—
114C3×#95—24no—
115C3×#95—41no—
116C3×#95D414yescomplemented
117C3⋊#95—24no—
118C3⋊#95—24no—
119C3⋊#95—41no—
120C3⋊#95—41no—
121C23×D4—32no—
122C23×D4—31no—
123C23×D4—32no—
124C23×D4—31no—
125C24×C4—32no—
126C2×#121—68no—
127C2×#121—68no—
128C2×#121—68no—
129C22×C4⋊C4C2×D312yes—
130C22×C4⋊C4C2×D311yescharacteristic
131C22×C22⋊C4—32no—
132C22×C22⋊C4—32no—
133C22×C22⋊C4—32no—
134C22×C22⋊C4—32no—
135C22×C22⋊C4—32no—
136C22×C22⋊C4—32no—
137C22×C22⋊C4—32no—
138#394—68no—
139#392—68no—
140#386—68no—
141C2×#95—32no—
142C2×#95—32no—
143C2×#95—31no—
144C2×#95—31no—
145C2×#95C2×D312yes—
146C2×#95C2×D311yescharacteristic
147C2×#95C2×D311yescharacteristic
148C24×C3C2411yescharacteristic
149C23×D3—22no—
150C23×D3—22no—
151C23×D3—22no—
152C23×D3—22no—
153C23×D3—22no—
154C23×D3—22no—
155C23×D3—22no—
156C23×D3—22no—
157C23×D3—22no—
158C23×D3—22no—
159C23×D3—22no—
160C23×D3—22no—
161C23×D3—22no—
162C23×D3—22no—
163C23×D3—22no—
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×D3C2×D414yes—
176C23×D3C2×D414yes—
177C23×D3C2×D414yes—
178C23×D3C2×D414yes—
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—22no—
188C22×C3×C4—22no—
189C22×C3×C4—22no—
190C22×C3×C4—22no—
191C22×C3×C4—21no—
192C22×C3×C4—21no—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—22no—
197C22×C3×C4—22no—
198C22×C3×C4—22no—
199C22×C3×C4—22no—
200C22×C3×C4—21no—
201C22×C3×C4C2×D412yes—
202C22×C3×C4C2×D414yes—
203C22×C3×C4C2×D412yes—
204C22×C3×C4C2×D414yes—
205C22×C3×C4C2×D414yes—
206C22×C3×C4#4112yes—
207C22×C3×C4#4114yes—
208C22×Dic3—22no—
209C22×Dic3—22no—
210C22×Dic3—22no—
211C22×Dic3—22no—
212C22×Dic3—22no—
213C22×Dic3—22no—
214C22×Dic3—22no—
215C22×Dic3—22no—
216C22×Dic3—22no—
217C22×Dic3—22no—
218C22×Dic3—22no—
219C22×Dic3—22no—
220C22×Dic3—22no—
221C22×Dic3C2×D414yes—
222C2×D12—216no—
223C2×D12—216no—
224C2×D12—216no—
225C2×D12—216no—
226C2×D12—48no—
227C2×D12—44no—
228C2×D12—48no—
229C2×D12—48no—
230C2×D12—48no—
231C2×D12—48no—
232C2×D12—48no—
233C2×D12—48no—
234C2×D12—48no—
235C2×D12—44no—
236C2×D12—44no—
237C2×D12—44no—
238C2×D12—48no—
239C2×D12—48no—
240C2×D12—48no—
241C2×D12—44no—
242C2×D12—48no—
243C2×D12—48no—
244C2×D12—44no—
245C2×D12—48no—
246C2×C4×D3—216no—
247C2×C4×D3—48no—
248C2×C4×D3—48no—
249C2×C4×D3—48no—
250C2×C4×D3—48no—
251C2×C4×D3—48no—
252C2×C4×D3—48no—
253C3×C4⋊C4—216no—
254C3×C4⋊C4—44no—
255(C2×D3)⋊C4—216no—
256(C2×D3)⋊C4—216no—
257(C2×D3)⋊C4—48no—
258(C2×D3)⋊C4—48no—
259(C2×D3)⋊C4—48no—
260(C2×D3)⋊C4—48no—
261(C2×D3)⋊C4—48no—
262C25—32no—
263C25—32no—
264C22×D4—34no—
265C22×D4—38no—
266C22×D4—64no—
267C22×D4—64no—
268C22×D4—64no—
269C22×D4—64no—
270C22×D4—64no—
271C22×D4—64no—
272C22×D4—64no—
273C22×D4—64no—
274C22×D4—64no—
275C22×D4—64no—
276C22×D4—64no—
277C22×D4—64no—
278C22×D4—62no—
279C22×D4—122no—
280C22×D4—122no—
281C22×D4—121no—
282C22×D4—121no—
283C22×D4—122no—
284C22×D4—121no—
285C22×D4—121no—
286C22×D4—122no—
287C22×D4—122no—
288C23×C4—32no—
289C23×C4—32no—
290C23×C4—64no—
291C23×C4—64no—
292C23×C4—64no—
293C23×C4—64no—
294C23×C4—64no—
295C23×C4—122no—
296C23×C4—122no—
297C23×C4C22×D311yescharacteristic
298C23×C4C22×D312yes—
299C23×C4C22×D311yescharacteristic
300C23×C4C22×D311yescharacteristic
301C23×C4C22×D312yes—
302#121—664no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—41no—
308C2×C22⋊C4—38no—
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—64no—
319C2×C22⋊C4—64no—
320C2×C22⋊C4—64no—
321C2×C22⋊C4—64no—
322C2×C22⋊C4—64no—
323C2×C22⋊C4—64no—
324C2×C22⋊C4—64no—
325C2×C22⋊C4—122no—
326C2×C22⋊C4—122no—
327C2×C22⋊C4—122no—
328C2×C22⋊C4—122no—
329#95—24no—
330#95—41no—
331#95—64no—
332#95—64no—
333#95—121no—
334#95—121no—
335#95D1214yescomplemented
336C23×C3C22×D411yescharacteristic
337C23×C3C22×D411yescharacteristic
338C23×C3C22×D412yes—
339C23×C3C22×D412yes—
340C23×C3C2×#4112yes—
341C23×C3C2×#4111yescharacteristic
342C23×C3H(5,𝔽2)11yescharacteristic
343C23×C3H(5,𝔽2)11yescharacteristic
344C23×C3H(5,𝔽2)12yes—
345C23×C3H(5,𝔽2)11yescharacteristic
346C23×C32−1+411yescharacteristic
347C22×D3—24no—
348C22×D3—24no—
349C22×D3—24no—
350C22×D3—24no—
351C22×D3—24no—
352C22×D3—24no—
353C22×D3—24no—
354C22×D3—24no—
355C22×D3—24no—
356C22×D3—24no—
357C22×D3—24no—
358C22×D3—24no—
359C22×D3—24no—
360C22×D3—24no—
361C22×D3—24no—
362C22×D3—24no—
363C22×D3—24no—
364C22×D3—24no—
365C22×D3—24no—
366C22×D3—24no—
367C22×D3—24no—
368C22×D3—24no—
369C22×D3—24no—
370C22×D3—24no—
371C22×D3—24no—
372C22×D3—42no—
373C22×D3—42no—
374C22×D3—42no—
375C22×D3—42no—
376C22×D3—42no—
377C22×D3—42no—
378C22×D3—42no—
379C22×D3—42no—
380C22×D3—42no—
381C22×D3—42no—
382C22×D3—42no—
383C22×D3—42no—
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—42no—
401C22×D3—42no—
402C22×D3—42no—
403C22×D3—42no—
404C22×D3—42no—
405C22×D3—42no—
406C22×D3—42no—
407C22×D3—42no—
408C22×D3—42no—
409C22×D3—42no—
410C22×D3—42no—
411C22×D3—42no—
412C22×D3—42no—
413C22×D3—42no—
414C22×D3—42no—
415C22×D3—42no—
416C22×D3#12018yes—
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—24no—
424C2×C3×C4—24no—
425C2×C3×C4—22no—
426C2×C3×C4—22no—
427C2×C3×C4—22no—
428C2×C3×C4—24no—
429C2×C3×C4—24no—
430C2×C3×C4—24no—
431C2×C3×C4—24no—
432C2×C3×C4—42no—
433C2×C3×C4—42no—
434C2×C3×C4—42no—
435C2×C3×C4—42no—
436C2×C3×C4—41no—
437C2×C3×C4—42no—
438C2×C3×C4—41no—
439C2×C3×C4—41no—
440C2×C3×C4—41no—
441C2×C3×C4—42no—
442C2×C3×C4—42no—
443C2×C3×C4—41no—
444C2×C3×C4—41no—
445C2×C3×C4#12118yescomplemented
446C2×Dic3—24no—
447C2×Dic3—24no—
448C2×Dic3—24no—
449C2×Dic3—42no—
450C2×Dic3—42no—
451C2×Dic3—42no—
452C2×Dic3—42no—
453C2×Dic3—42no—
454C2×Dic3—42no—
455C2×Dic3—42no—
456C2×Dic3—42no—
457C2×Dic3—42no—
458C2×Dic3—42no—
459C2×Dic3—42no—
460D12—432no—
461D12—416no—
462D12—432no—
463D12—416no—
464C4×D3—432no—
465C24—34no—
466C24—34no—
467C24—34no—
468C24—34no—
469C24—62no—
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—62no—
483C24—62no—
484C24—62no—
485C24—62no—
486C24—62no—
487C24—62no—
488C24—62no—
489C24—62no—
490C24—62no—
491C24—62no—
492C24—62no—
493C24—62no—
494C24—62no—
495C24C23×D311yescharacteristic
496C2×D4—616no—
497C2×D4—616no—
498C2×D4—616no—
499C2×D4—616no—
500C2×D4—128no—
501C2×D4—124no—
502C2×D4—128no—
503C2×D4—128no—
504C2×D4—128no—
505C2×D4—128no—
506C2×D4—128no—
507C2×D4—128no—
508C2×D4—128no—
509C2×D4—124no—
510C2×D4—128no—
511C2×D4—124no—
512C2×D4—128no—
513C2×D4—124no—
514C2×D4—124no—
515C2×D4—128no—
516C2×D4—128no—
517C2×D4—128no—
518C2×D4—128no—
519C2×D4—124no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—22no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—34no—
543C22×C4—616no—
544C22×C4—62no—
545C22×C4—62no—
546C22×C4—62no—
547C22×C4—62no—
548C22×C4—62no—
549C22×C4—62no—
550C22×C4—62no—
551C22×C4—62no—
552C22×C4—62no—
553C22×C4—62no—
554C22×C4—62no—
555C22×C4—62no—
556C22×C4—62no—
557C22×C4—128no—
558C22×C4—128no—
559C22×C4—128no—
560C22×C4—128no—
561C22×C4—128no—
562C22×C4—128no—
563C22×C4C2×D1212yes—
564C22×C4C2×D1214yes—
565C22×C4D3×D414yes—
566C22×C4D3×D412yes—
567C22×C4D3×D414yes—
568C22×C4#23912yes—
569C22×C4#23914yes—
570C4⋊C4—216no—
571C4⋊C4—44no—
572C22⋊C4—616no—
573C22⋊C4—616no—
574C22⋊C4—128no—
575C22⋊C4—128no—
576C22⋊C4—128no—
577C22⋊C4—128no—
578C22⋊C4—128no—
579C22×C3C2×#12012yes—
580C22×C3C2×#12112yes—
581C22×C3#53212yes—
582C22×C3#53412yes—
583C22×C3#53411yescharacteristic
584C22×C3#53711yescharacteristic
585C22×C3#53712yes—
586C22×C3#53811yescharacteristic
587C22×C3#54012yes—
588C22×C3D4211yescharacteristic
589C22×C3D4211yescharacteristic
590C22×C3D4212yes—
591C22×C3D4211yescharacteristic
592C22×C3D4212yes—
593C22×C3#54612yes—
594C22×C3#54612yes—
595C22×C3#54612yes—
596C22×C3#54712yes—
597C22×C3#54711yescharacteristic
598C22×C3#55011yescharacteristic
599C22×C3#55511yescharacteristic
600C22×C3#56011yescharacteristic
601C22×C3#56211yescharacteristic
602C2×D3—28no—
603C2×D3—28no—
604C2×D3—28no—
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—
616C2×D3—44no—
617C2×D3—44no—
618C2×D3—44no—
619C2×D3—44no—
620C2×D3—44no—
621C2×D3—44no—
622C2×D3—44no—
623C2×D3—44no—
624C2×D3—82no—
625C2×D3—82no—
626C2×D3—82no—
627C2×D3—82no—
628C2×D3—82no—
629C2×D3—82no—
630C2×D3—82no—
631C2×D3—82no—
632C3×C4—28no—
633C3×C4—42no—
634C3×C4—44no—
635C3×C4—42no—
636C3×C4—42no—
637Dic3—44no—
638Dic3—82no—
639C23—38no—
640C23—64no—
641C23—64no—
642C23—64no—
643C23—64no—
644C23—64no—
645C23—64no—
646C23—64no—
647C23—64no—
648C23—64no—
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—122no—
666C23—122no—
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—
683C23—122no—
684C23—122no—
685C23—122no—
686C23—122no—
687C23—122no—
688C23—122no—
689C23—122no—
690C23—122no—
691C23—122no—
692C23—122no—
693C23—122no—
694C23—122no—
695C23—122no—
696C23—122no—
697C23—122no—
698C23—122no—
699C23—122no—
700C23—122no—
701C23—122no—
702C23—122no—
703C23—122no—
704C23—122no—
705C23—122no—
706C23—122no—
707C23—122no—
708C23—122no—
709C23C22×D1211yescharacteristic
710C23C2×D3×D412yes—
711C23C2×D3×D412yes—
712C23C2×D3×D411yescharacteristic
713C23#100411yescharacteristic
714C23C2×#23911yescharacteristic
715C23C2×#23912yes—
716C23#100711yescharacteristic
717C23#100911yescharacteristic
718C23#100912yes—
719C23#100911yescharacteristic
720D4—1232no—
721D4—1216no—
722D4—1232no—
723D4—1216no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—22no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—42no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—42no—
744C2×C4—41no—
745C2×C4—42no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—64no—
753C2×C4—64no—
754C2×C4—64no—
755C2×C4—1232no—
756C2×C4—122no—
757C2×C4—122no—
758C2×C4—122no—
759C2×C4—122no—
760C2×C4—122no—
761C2×C4—122no—
762C2×C4—122no—
763C2×C4—122no—
764C2×C4—122no—
765C2×C4—122no—
766C2×C4—122no—
767C2×C4#89518yescomplemented
768C2×C3#240311yescharacteristic
769C2×C3#241012yes—
770C2×C3#242812yes—
771C2×C3#243012yes—
772C2×C3#253711yescharacteristic
773C2×C3#255511yescharacteristic
774C2×C3#266811yescharacteristic
775C2×C3#267112yes—
776C2×C3#267511yescharacteristic
777C2×C3#268211yescharacteristic
778C2×C3#269911yescharacteristic
779D3—48no—
780D3—84no—
781C22—68no—
782C22—68no—
783C22—68no—
784C22—124no—
785C22—124no—
786C22—124no—
787C22—124no—
788C22—124no—
789C22—124no—
790C22—124no—
791C22—124no—
792C22—124no—
793C22—124no—
794C22—124no—
795C22—124no—
796C22—124no—
797C22—124no—
798C22—124no—
799C22—124no—
800C22—124no—
801C22—124no—
802C22—124no—
803C22—242no—
804C22—242no—
805C22—242no—
806C22—242no—
807C22—242no—
808C22—242no—
809C22—242no—
810C22—242no—
811C22C2×#89512yes—
812C22#551011yescharacteristic
813C22D4×D1211yescharacteristic
814C22D4×D1212yes—
815C22#557711yescharacteristic
816C22D3×#12012yes—
817C22#559011yescharacteristic
818C22#560511yescharacteristic
819C22#560912yes—
820C22#562912yes—
821C22#563012yes—
822C22#563012yes—
823C22#563012yes—
824C22#564411yescharacteristic
825C22#565312yes—
826C22#566611yescharacteristic
827C22#569712yes—
828C22#570011yescharacteristic
829C22#571711yescharacteristic
830C22#572512yes—
831C22#572612yes—
832C22#572611yescharacteristic
833C22#573411yescharacteristic
834C4—28no—
835C4—42no—
836C4—42no—
837C4—42no—
838C4—44no—
839C4—124no—
840C4—242no—
841C3#1527811yescharacteristic, complemented, Sylow
842C2—128no—
843C2—244no—
844C2#7436811yescharacteristic
845C2#7460112yes—
846C2#7463011yescharacteristic
847C2#7622012yes—
848C2#7626011yescharacteristic
849C2#7675311yescharacteristic
850C2#7718711yescharacteristic
851C2#7725012yes—
852C2#7796712yes—
853C2#7797811yescharacteristic
854C2#7811211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1444C2
hypercenter#1444D3
hypocenterC3#15278
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
1. C22×#895C2semidirect
2. C2×#4991C2semidirect
3. C2×#4671C2semidirect
4. C2×#4665C2semidirect
5. C3×#1444C2semidirect
6. #71570C2semidirect
7. #69426C2semidirect
8. #69426C2semidirect
9. (C2×D3)⋊#95C2semidirect
42. #1444D3semidirect
78. C22×D12D4semidirect
79. C22×D12D4semidirect
112. C2×(C2×D3)⋊C4D4semidirect
116. C3×#95D4semidirect
335. #95D12semidirect
445. C2×C3×C4#121semidirect
767. C2×C4#895semidirect
841. C3#15278semidirect

Maximal subgroups

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

subgroupindex
C22×#8952
C2×#49912
C2×#46712
C2×#46652
C3×#14442
#715702
#694262
(C2×D3)⋊#952
#152783