Finite Group Databasebeta

← #10826185

Subgroups — #10826185

Order 768.

2414 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D42C211yesmaximal, characteristic, complemented
2C23×#213C211yesmaximal, characteristic, complemented
3C2×#5217C212yesmaximal, complemented
4C2×#5036C211yesmaximal, characteristic, complemented
5#82403C211yesmaximal, characteristic, complemented
6#72128C211yesmaximal, characteristic, complemented
7#71767C212yesmaximal, complemented
8#71684C212yesmaximal, complemented
9#71681C211yesmaximal, characteristic, complemented
10#71613C212yesmaximal, complemented
11#71610C211yesmaximal, characteristic, complemented
12#23848—31nomaximal, Sylow
13C23×C3×D4—21no—
14C23×C3×D4C2211yescharacteristic
15C23×C3×D4C2211yescharacteristic, complemented
16C23×D12C2211yescharacteristic, complemented
17C3×D42—24no—
18C3×D42—24no—
19C2×C3×#127C2211yescharacteristic, complemented
20C2×C3×#121—21no—
21C2×C3×#121C2211yescharacteristic
22C2×C3×#121C2211yescharacteristic, complemented
23C2×C3×#120—21no—
24C2×C3×#120—21no—
25C2×C3×C4×D4C2211yescharacteristic
26C2×C3×C4×D4C2211yescharacteristic, complemented
27C2×#937—21no—
28C22×#213—24no—
29C22×#213—28no—
30C22×#213C2212yes—
31C22×#213C2212yescomplemented
32C22×#213C2212yescomplemented
33C2×#930C2212yescomplemented
34C23×C3⋊C8C2211yescharacteristic, complemented
35#5217—28no—
36C2×#832C2212yescomplemented
37C2×#832C2212yescomplemented
38C2×#832C2212yescomplemented
39#5212C2211yescharacteristic, complemented
40C2×#830C2212yescomplemented
41C2×#830C2211yescharacteristic, complemented
42#5036—24no—
43#4991—21no—
44C2×#809C2212yescomplemented
45#4960—21no—
46#4955—21no—
47#4939C2212yescomplemented
48#4529C2212yescomplemented
49#4524C2212yescomplemented
50C23×D8—31no—
51C2×D42D311yescharacteristic, complemented
52C2×#447—32no—
53C2×#447—31no—
54#2408—31no—
55#2011—32no—
56#1999—32no—
57#1893—31no—
58#1879—32no—
59#1869—31no—
60#1786—31no—
61C25×C3—21no—
62C25×C3—21no—
63C24×D3—21no—
64C22×C3×D4—24no—
65C22×C3×D4—28no—
66C22×C3×D4—21no—
67C22×C3×D4—21no—
68C22×C3×D4—22no—
69C22×C3×D4—22no—
70C22×C3×D4—24no—
71C22×C3×D4—21no—
72C22×C3×D4—21no—
73C22×C3×D4—22no—
74C22×C3×D4—21no—
75C22×C3×D4—21no—
76C22×C3×D4—42no—
77C22×C3×D4—42no—
78C22×C3×D4—44no—
79C22×C3×D4—44no—
80C22×C3×D4D411yescharacteristic
81C22×C3×D4D414yescomplemented
82C22×C3×D4C2311yescharacteristic
83C22×C3×D4C2311yescharacteristic
84C22×C3×D4C2311yescharacteristic
85C23×C3×C4—21no—
86C23×C3×C4C2311yescharacteristic
87C23×C3×C4C2311yescharacteristic
88C22×#67—22no—
89C22×D12—22no—
90C22×D12—24no—
91C22×D12—22no—
92C22×D12—21no—
93C22×D12—42no—
94C22×D12C2312yes—
95C3×#127—22no—
96C3×#127—22no—
97C3×#121—28no—
98C3×#121—22no—
99C3×#121—22no—
100C3×#121—22no—
101C3×#121D414yescomplemented
102C3×#120—28no—
103C3×#120—28no—
104C3×C4×D4—22no—
105C3×C4×D4—22no—
106C3×C4×D4—22no—
107C3×C4×D4—22no—
108C2×C3×C4⋊C4D411yescharacteristic
109C2×C3×C4⋊C4C2311yescharacteristic
110C2×C3×C22⋊C4—21no—
111C2×C3×C22⋊C4—21no—
112C2×C3×C22⋊C4—21no—
113C2×C3×C22⋊C4D411yescharacteristic
114C2×C3×C22⋊C4D411yescharacteristic
115C2×C3×C42C2311yescharacteristic
116C2×#217—21no—
117#937—44no—
118C2×#213—232no—
119C2×#213—24no—
120C2×#213—24no—
121C2×#213—24no—
122C2×#213—24no—
123C2×#213—24no—
124C2×#213—24no—
125C2×#213—24no—
126C2×#213—42no—
127C2×#213D418yescomplemented
128#930—24no—
129#930—42no—
130C2×(C2×D3)⋊C4—22no—
131C2×(C2×D3)⋊C4—22no—
132C2×(C2×D3)⋊C4—22no—
133C2×C4⋊Dic3C2312yes—
134C22×C3⋊C8—22no—
135C22×C3⋊C8—24no—
136C22×C3⋊C8C2312yes—
137C22×C3⋊C8C2312yes—
138#832—24no—
139#832—24no—
140#832—42no—
141C3⋊#95—21no—
142#830—22no—
143#830—24no—
144#809—24no—
145C23×D4—21no—
146C23×D4—31no—
147C23×D4C2×D311yescharacteristic
148C23×D4C2×D311yescharacteristic, complemented
149C22×D8—32no—
150C22×D8—32no—
151C22×D8—32no—
152C22×D8—68no—
153C22×D8—64no—
154C23×C8—31no—
155D42—24no—
156D42—24no—
157C2×#127C2×D311yescharacteristic, complemented
158C2×#121—21no—
159C2×#121—32no—
160C2×#121C2×D311yescharacteristic
161C2×#121C2×D311yescharacteristic, complemented
162C2×#120—21no—
163C2×#120—21no—
164C2×#120—61no—
165C2×C4×D4C2×D311yescharacteristic
166C2×C4×D4C2×D311yescharacteristic, complemented
167#447—68no—
168#447—64no—
169C2×#102—32no—
170C2×#102—32no—
171C2×#102—32no—
172C2×#102—32no—
173C2×C22⋊C8—32no—
174C2×C22⋊C8—31no—
175#394—61no—
176#392—61no—
177#390—32no—
178#380—31no—
179#379—61no—
180#340—32no—
181#336—32no—
182C24×C3—21no—
183C24×C3—24no—
184C24×C3—21no—
185C24×C3—21no—
186C24×C3—24no—
187C24×C3—44no—
188C24×C3—44no—
189C24×C3—42no—
190C24×C3—42no—
191C24×C3—42no—
192C24×C3—42no—
193C24×C3—82no—
194C24×C3—82no—
195C24×C3C2×D411yescharacteristic
196C24×C3C2×D411yescharacteristic
197C23×D3—22no—
198C23×D3—44no—
199C23×D3—42no—
200C23×D3—42no—
201C23×D3—42no—
202C23×D3—82no—
203C2×C3×D4—22no—
204C2×C3×D4—22no—
205C2×C3×D4—28no—
206C2×C3×D4—24no—
207C2×C3×D4—24no—
208C2×C3×D4—24no—
209C2×C3×D4—24no—
210C2×C3×D4—24no—
211C2×C3×D4—24no—
212C2×C3×D4—21no—
213C2×C3×D4—22no—
214C2×C3×D4—22no—
215C2×C3×D4—21no—
216C2×C3×D4—21no—
217C2×C3×D4—22no—
218C2×C3×D4—22no—
219C2×C3×D4—22no—
220C2×C3×D4—44no—
221C2×C3×D4—48no—
222C2×C3×D4—44no—
223C2×C3×D4—44no—
224C2×C3×D4—42no—
225C2×C3×D4—48no—
226C2×C3×D4—432no—
227C2×C3×D4—44no—
228C2×C3×D4—42no—
229C2×C3×D4—42no—
230C2×C3×D4—42no—
231C2×C3×D4—42no—
232C2×C3×D4—44no—
233C2×C3×D4—42no—
234C2×C3×D4—82no—
235C2×C3×D4D814yescomplemented
236C2×C3×D4C2×D414yes—
237C2×C3×D4C2×D412yes—
238C2×C3×D4C2×D412yes—
239C2×C3×D4C2×D412yes—
240C22×C3×C4—22no—
241C22×C3×C4—22no—
242C22×C3×C4—24no—
243C22×C3×C4—21no—
244C22×C3×C4—22no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—22no—
248C22×C3×C4—42no—
249C22×C3×C4—42no—
250C22×C3×C4C2×D411yescharacteristic
251C22×C3×C4C2×D411yescharacteristic
252C22×C3×C4C2×D411yescharacteristic
253C22×C3×C4C2×D412yes—
254C22×C3×C4C2×D412yes—
255C22×C3×C4C2×D411yescharacteristic
256C22×C3×C4C2411yescharacteristic
257C2×#67—44no—
258C2×#67—44no—
259C2×#67—82no—
260C22×Dic3—22no—
261C2×D12—28no—
262C2×D12—22no—
263C2×D12—22no—
264C2×D12—22no—
265C2×D12—22no—
266C2×D12—22no—
267C2×D12—48no—
268C2×D12—44no—
269C2×D12—44no—
270C2×D12—42no—
271C2×D12C2×D414yescomplemented
272C3×C4⋊C4—22no—
273C3×C4⋊C4—21no—
274C3×C4⋊C4C2×D412yes—
275C3×C22⋊C4—24no—
276C3×C22⋊C4—24no—
277C3×C22⋊C4—22no—
278C3×C22⋊C4—24no—
279C3×C22⋊C4—22no—
280C3×C42—21no—
281C3×C42—21no—
282#217—42no—
283#213—216no—
284#213—216no—
285#213—48no—
286(C2×D3)⋊C4—44no—
287(C2×D3)⋊C4—44no—
288(C2×D3)⋊C4—82no—
289C4⋊Dic3—22no—
290C4⋊Dic3—22no—
291C2×C3⋊C8—28no—
292C2×C3⋊C8—22no—
293C2×C3⋊C8—22no—
294C2×C3⋊C8—22no—
295C2×C3⋊C8—22no—
296C2×C3⋊C8—22no—
297C2×C3⋊C8C2×D414yescomplemented
298C25—21no—
299C25—21no—
300C25—61no—
301C22×D4—24no—
302C22×D4—28no—
303C22×D4—21no—
304C22×D4—21no—
305C22×D4—22no—
306C22×D4—22no—
307C22×D4—24no—
308C22×D4—21no—
309C22×D4—21no—
310C22×D4—21no—
311C22×D4—22no—
312C22×D4—21no—
313C22×D4—32no—
314C22×D4—42no—
315C22×D4—42no—
316C22×D4—44no—
317C22×D4—44no—
318C22×D4—64no—
319C22×D4—62no—
320C22×D4—62no—
321C22×D4—62no—
322C22×D4—61no—
323C22×D4—122no—
324C22×D4#6711yescharacteristic
325C22×D4#6714yescomplemented
326C22×D4C22×D311yescharacteristic
327C22×D4C22×D311yescharacteristic
328C22×D4C22×D311yescharacteristic
329C23×C4—21no—
330C23×C4C22×D311yescharacteristic
331C23×C4C22×D311yescharacteristic
332C2×D8—38no—
333C2×D8—64no—
334C2×D8—64no—
335C2×D8—632no—
336C2×D8—64no—
337C2×D8—64no—
338C2×D8—64no—
339C2×D8—64no—
340C2×D8—64no—
341C2×D8—122no—
342C22×C8—32no—
343C22×C8—32no—
344C22×C8—64no—
345C22×C8—62no—
346#127—22no—
347#127—22no—
348#121—28no—
349#121—22no—
350#121—22no—
351#121—22no—
352#121—64no—
353#121—122no—
354#121#6714yescomplemented
355#120—28no—
356#120—28no—
357#120—124no—
358C4×D4—22no—
359C4×D4—22no—
360C4×D4—22no—
361C4×D4—22no—
362C2×C4⋊C4—32no—
363C2×C4⋊C4#6711yescharacteristic
364C2×C4⋊C4C22×D311yescharacteristic
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—61no—
369C2×C22⋊C4—62no—
370C2×C22⋊C4—62no—
371C2×C22⋊C4—62no—
372C2×C22⋊C4#6711yescharacteristic
373C2×C22⋊C4#6711yescharacteristic
374C2×C42C22×D311yescharacteristic
375#102—64no—
376#102—64no—
377#102—64no—
378#102—122no—
379C22⋊C8—64no—
380C22⋊C8—62no—
381#95—61no—
382C23×C3—22no—
383C23×C3—22no—
384C23×C3—21no—
385C23×C3—22no—
386C23×C3—22no—
387C23×C3—24no—
388C23×C3—21no—
389C23×C3—22no—
390C23×C3—22no—
391C23×C3—22no—
392C23×C3—48no—
393C23×C3—48no—
394C23×C3—48no—
395C23×C3—41no—
396C23×C3—41no—
397C23×C3—42no—
398C23×C3—42no—
399C23×C3—42no—
400C23×C3—41no—
401C23×C3—41no—
402C23×C3—41no—
403C23×C3—41no—
404C23×C3—42no—
405C23×C3—42no—
406C23×C3—48no—
407C23×C3—84no—
408C23×C3—88no—
409C23×C3—88no—
410C23×C3—88no—
411C23×C3—84no—
412C23×C3—88no—
413C23×C3#12012yes—
414C23×C3C2×D812yes—
415C23×C3C2×D812yescomplemented
416C23×C3AGL(1,ℤ/8)12yes—
417C23×C3C22×D411yescharacteristic
418C22×D3—24no—
419C22×D3—48no—
420C22×D3—42no—
421C22×D3—42no—
422C22×D3—42no—
423C22×D3—42no—
424C22×D3—42no—
425C22×D3—42no—
426C22×D3—88no—
427C22×D3—88no—
428C22×D3—84no—
429C22×D3—84no—
430C3×D4—28no—
431C3×D4—22no—
432C3×D4—22no—
433C3×D4—22no—
434C3×D4—24no—
435C3×D4—24no—
436C3×D4—48no—
437C3×D4—48no—
438C3×D4—48no—
439C3×D4—48no—
440C3×D4—48no—
441C3×D4—41no—
442C3×D4—41no—
443C3×D4—42no—
444C3×D4—84no—
445C3×D4#12014yescomplemented
446C2×C3×C4—21no—
447C2×C3×C4—22no—
448C2×C3×C4—21no—
449C2×C3×C4—22no—
450C2×C3×C4—22no—
451C2×C3×C4—24no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
454C2×C3×C4—22no—
455C2×C3×C4—22no—
456C2×C3×C4—22no—
457C2×C3×C4—48no—
458C2×C3×C4—41no—
459C2×C3×C4—41no—
460C2×C3×C4—41no—
461C2×C3×C4—41no—
462C2×C3×C4—42no—
463C2×C3×C4#12012yes—
464C2×C3×C4C2×D812yescomplemented
465C2×C3×C4C22×D412yes—
466C2×C3×C4C22×D411yescharacteristic
467C2×C3×C4C22×D411yescharacteristic
468C2×C3×C4H(5,𝔽2)12yes—
469#67—88no—
470C2×Dic3—42no—
471C2×Dic3—42no—
472C2×Dic3—42no—
473D12—24no—
474D12—24no—
475D12—48no—
476D12—42no—
477D12—42no—
478C3⋊C8—24no—
479C3⋊C8—42no—
480C24—21no—
481C24—24no—
482C24—21no—
483C24—21no—
484C24—24no—
485C24—44no—
486C24—44no—
487C24—42no—
488C24—42no—
489C24—42no—
490C24—42no—
491C24—62no—
492C24—82no—
493C24—82no—
494C24—124no—
495C24—122no—
496C24—122no—
497C24—122no—
498C24—242no—
499C24C2×#6711yescharacteristic
500C24C2×#6711yescharacteristic
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—28no—
504C2×D4—24no—
505C2×D4—24no—
506C2×D4—24no—
507C2×D4—24no—
508C2×D4—24no—
509C2×D4—24no—
510C2×D4—22no—
511C2×D4—22no—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4—22no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—34no—
519C2×D4—44no—
520C2×D4—48no—
521C2×D4—44no—
522C2×D4—44no—
523C2×D4—42no—
524C2×D4—48no—
525C2×D4—432no—
526C2×D4—44no—
527C2×D4—42no—
528C2×D4—42no—
529C2×D4—42no—
530C2×D4—42no—
531C2×D4—44no—
532C2×D4—42no—
533C2×D4—68no—
534C2×D4—62no—
535C2×D4—62no—
536C2×D4—62no—
537C2×D4—62no—
538C2×D4—62no—
539C2×D4—82no—
540C2×D4—128no—
541C2×D4—124no—
542C2×D4—124no—
543C2×D4—124no—
544C2×D4—124no—
545C2×D4—122no—
546C2×D4—242no—
547C2×D4#21314yescomplemented
548C2×D4D3×D414yes—
549C2×D4C2×#6712yes—
550C2×D4C2×#6712yes—
551C2×D4C2×#6712yes—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—24no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—62no—
563C22×C4C2×#6711yescharacteristic
564C22×C4C2×#6711yescharacteristic
565C22×C4C2×#6711yescharacteristic
566C22×C4C2×#6711yescharacteristic
567C22×C4C2×#6712yes—
568C22×C4C2×#6712yes—
569C22×C4C23×D311yescharacteristic
570D8—616no—
571D8—616no—
572D8—128no—
573C2×C8—34no—
574C2×C8—68no—
575C2×C8—62no—
576C2×C8—62no—
577C2×C8—62no—
578C2×C8—62no—
579C2×C8—62no—
580C4⋊C4—22no—
581C4⋊C4—21no—
582C4⋊C4—62no—
583C4⋊C4—62no—
584C4⋊C4C2×#6712yes—
585C22⋊C4—24no—
586C22⋊C4—24no—
587C22⋊C4—22no—
588C22⋊C4—24no—
589C22⋊C4—22no—
590C22⋊C4—124no—
591C22⋊C4—122no—
592C22⋊C4—124no—
593C22⋊C4—242no—
594C42—21no—
595C42—21no—
596C22×C3—22no—
597C22×C3—22no—
598C22×C3—24no—
599C22×C3—24no—
600C22×C3—24no—
601C22×C3—22no—
602C22×C3—24no—
603C22×C3—41no—
604C22×C3—42no—
605C22×C3—41no—
606C22×C3—42no—
607C22×C3—42no—
608C22×C3—44no—
609C22×C3—44no—
610C22×C3—42no—
611C22×C3—42no—
612C22×C3—42no—
613C22×C3—42no—
614C22×C3—42no—
615C22×C3—42no—
616C22×C3—816no—
617C22×C3—816no—
618C22×C3—82no—
619C22×C3—82no—
620C22×C3—82no—
621C22×C3—82no—
622C22×C3#44714yescomplemented
623C22×C3C2×#12011yescharacteristic
624C22×C3D4212yes—
625C22×C3C22×D811yescharacteristic
626C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
627C22×C3#57612yes—
628C2×D3—44no—
629C2×D3—44no—
630C2×D3—44no—
631C2×D3—816no—
632C2×D3—82no—
633C2×D3—82no—
634C2×D3—82no—
635C2×D3—82no—
636C3×C4—22no—
637C3×C4—22no—
638C3×C4—41no—
639C3×C4—42no—
640C3×C4—41no—
641C3×C4C2×#12011yescharacteristic
642C3×C4#53411yescharacteristic
643C3×C4D4212yes—
644Dic3—82no—
645C23—22no—
646C23—22no—
647C23—21no—
648C23—22no—
649C23—24no—
650C23—22no—
651C23—21no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—48no—
656C23—48no—
657C23—48no—
658C23—41no—
659C23—41no—
660C23—42no—
661C23—48no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—64no—
671C23—84no—
672C23—88no—
673C23—88no—
674C23—88no—
675C23—84no—
676C23—88no—
677C23—128no—
678C23—122no—
679C23—122no—
680C23—122no—
681C23—122no—
682C23—122no—
683C23—122no—
684C23—248no—
685C23—248no—
686C23—244no—
687C23—244no—
688C23C2×#21312yes—
689C23C2×#21312yescomplemented
690C23#93212yes—
691C23#95312yes—
692C23C22×#6711yescharacteristic
693D4—28no—
694D4—22no—
695D4—24no—
696D4—24no—
697D4—22no—
698D4—22no—
699D4—48no—
700D4—48no—
701D4—48no—
702D4—48no—
703D4—48no—
704D4—41no—
705D4—42no—
706D4—41no—
707D4—64no—
708D4—64no—
709D4—84no—
710D4—128no—
711D4—122no—
712D4—122no—
713D4—248no—
714D4#93714yescomplemented
715C2×C4—21no—
716C2×C4—22no—
717C2×C4—21no—
718C2×C4—22no—
719C2×C4—24no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—22no—
726C2×C4—48no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—42no—
731C2×C4—41no—
732C2×C4—122no—
733C2×C4—122no—
734C2×C4—122no—
735C2×C4C2×#21312yescomplemented
736C2×C4#95312yes—
737C2×C4C2×D3×D412yes—
738C2×C4#100412yes—
739C2×C4C22×#6711yescharacteristic
740C2×C4C22×#6711yescharacteristic
741C8—64no—
742C8—122no—
743C2×C3—24no—
744C2×C3—42no—
745C2×C3—44no—
746C2×C3—82no—
747C2×C3—82no—
748C2×C3#240311yescharacteristic
749C2×C3C2×#44711yescharacteristic
750C2×C3#300811yescharacteristic
751C2×C3#326412yes—
752C2×C3D4×D812yes—
753D3—84no—
754C22—24no—
755C22—24no—
756C22—22no—
757C22—22no—
758C22—24no—
759C22—22no—
760C22—24no—
761C22—42no—
762C22—44no—
763C22—44no—
764C22—42no—
765C22—41no—
766C22—41no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—816no—
775C22—816no—
776C22—82no—
777C22—82no—
778C22—82no—
779C22—82no—
780C22—124no—
781C22—124no—
782C22—124no—
783C22—2416no—
784C22—242no—
785C22—242no—
786C22—242no—
787C22—242no—
788C22#521714yescomplemented
789C22C22×#21311yescharacteristic
790C22C2×#93211yescharacteristic
791C22D4×#6712yes—
792C22#583512yes—
793C22C2×#95311yescharacteristic
794C4—22no—
795C4—22no—
796C4—42no—
797C4—41no—
798C4—41no—
799C4—242no—
800C4C2×#93711yescharacteristic
801C4D4×#6712yes—
802C4#580411yescharacteristic
803C3#2384811yescharacteristic, complemented, Sylow
804C2—24no—
805C2—42no—
806C2—44no—
807C2—82no—
808C2—82no—
809C2—244no—
810C2#8348812yes—
811C2D4×#21312yes—
812C2C2×#521711yescharacteristic
813C2#8405211yescharacteristic
814C2#8410111yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×D42C2
socleC23×C3C22×D4
hypercenterC2×D42D3
hypocenterC3#23848
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×D42

Complements

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

NH ≅ G/Ntype
1. C2×C3×D42C2semidirect
2. C23×#213C2semidirect
3. C2×#5217C2semidirect
4. C2×#5036C2semidirect
5. #82403C2semidirect
6. #72128C2semidirect
7. #71767C2semidirect
8. #71684C2semidirect
9. #71681C2semidirect
10. #71613C2semidirect
11. #71610C2semidirect
15. C23×C3×D4C22semidirect
16. C23×D12C22semidirect
19. C2×C3×#127C22semidirect
22. C2×C3×#121C22semidirect
26. C2×C3×C4×D4C22semidirect
31. C22×#213C22semidirect
32. C22×#213C22semidirect
33. C2×#930C22semidirect
34. C23×C3⋊C8C22semidirect
36. C2×#832C22semidirect
37. C2×#832C22semidirect
38. C2×#832C22semidirect
39. #5212C22semidirect
40. C2×#830C22semidirect
41. C2×#830C22semidirect
44. C2×#809C22semidirect
47. #4939C22semidirect
48. #4529C22semidirect
49. #4524C22semidirect
51. C2×D42D3semidirect
81. C22×C3×D4D4semidirect
101. C3×#121D4semidirect
127. C2×#213D4semidirect
148. C23×D4C2×D3semidirect
157. C2×#127C2×D3semidirect
161. C2×#121C2×D3semidirect
166. C2×C4×D4C2×D3semidirect
235. C2×C3×D4D8semidirect
271. C2×D12C2×D4semidirect
297. C2×C3⋊C8C2×D4semidirect
325. C22×D4#67semidirect
354. #121#67semidirect
415. C23×C3C2×D8semidirect
445. C3×D4#120semidirect
464. C2×C3×C4C2×D8semidirect
547. C2×D4#213semidirect
622. C22×C3#447semidirect
689. C23C2×#213semidirect
714. D4#937semidirect
735. C2×C4C2×#213semidirect
788. C22#5217semidirect
803. C3#23848semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D422
C23×#2132
C2×#52172
C2×#50362
#824032
#721282
#717672
#716842
#716812
#716132
#716102
#238483