Finite Group Databasebeta

← #10731731

Subgroups — #10731731

Order 768.

3822 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#121C211yesmaximal, characteristic, complemented
2C22×#940C211yesmaximal, characteristic, complemented
3C22×#930C211yesmaximal, characteristic, complemented
4C2×#5223C214yesmaximal, complemented
5C2×#5221C211yesmaximal, characteristic, complemented
6C2×C4×#217C211yesmaximal, characteristic, complemented
7C2×#4988C211yesmaximal, characteristic, complemented
8#71563C211yesmaximal, characteristic, complemented
9#71550C214yesmaximal, complemented
10#15124—31nomaximal, Sylow
11C23×C3×D4C2211yescharacteristic
12C23×C3×D4C2212yes—
13C24×C3×C4C2211yescharacteristic
14C23×#67C2212yes—
15C23×#67C2214yes—
16C23×D12C2211yescharacteristic
17C2×C3×#121—24no—
18C2×C3×#121—24no—
19C2×C3×#121—24no—
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2212yes—
22C22×#217C2214yes—
23C22×#217C2212yes—
24C2×#940—24no—
25C2×#940—24no—
26C2×#940—24no—
27C2×#930—24no—
28C2×#930—24no—
29C2×#930—24no—
30C22×(C2×D3)⋊C4C2212yes—
31C22×(C2×D3)⋊C4C2214yes—
32C22×C4⋊Dic3C2211yescharacteristic
33C22×C4×Dic3C2211yescharacteristic
34C22×C4×Dic3C2211yescharacteristic
35#5223—216no—
36#5221—24no—
37C4×#217—24no—
38C2×C3⋊#95C2212yes—
39C2×C3⋊#95C2214yes—
40#4988—24no—
41C22×#127—31no—
42C22×#121—31no—
43C22×#121D311yescharacteristic, complemented
44C2×#392—34no—
45C2×#390—31no—
46C2×#390—31no—
47C2×C4×C22⋊C4—31no—
48#1438—34no—
49C4⋊#95—31no—
50C25×C3C2312yes—
51C25×C3C2311yescharacteristic
52C24×D3C2312yes—
53C22×C3×D4—24no—
54C22×C3×D4—24no—
55C22×C3×D4—28no—
56C22×C3×D4—22no—
57C22×C3×D4—22no—
58C22×C3×D4—22no—
59C22×C3×D4—24no—
60C22×C3×D4—22no—
61C22×C3×D4—22no—
62C22×C3×D4—22no—
63C22×C3×D4—44no—
64C22×C3×D4D414yescomplemented
65C23×C3×C4—22no—
66C23×C3×C4—22no—
67C23×C3×C4—22no—
68C23×C3×C4—22no—
69C23×C3×C4—22no—
70C23×C3×C4—22no—
71C23×C3×C4D414yescomplemented
72C23×C3×C4C2311yescharacteristic
73C23×C3×C4C2312yes—
74C23×C3×C4C2311yescharacteristic
75C22×#67—24no—
76C22×#67—28no—
77C22×#67—24no—
78C22×#67—28no—
79C22×#67—28no—
80C22×#67—24no—
81C22×#67—28no—
82C22×#67—28no—
83C22×#67—28no—
84C22×#67—44no—
85C22×#67—44no—
86C22×#67—44no—
87C23×Dic3C2312yes—
88C23×Dic3C2312yes—
89C23×Dic3C2312yes—
90C22×D12—22no—
91C22×D12—22no—
92C22×D12—22no—
93C22×D12—22no—
94C22×D12—22no—
95C22×D12—22no—
96C22×D12D414yescomplemented
97C3×#121—232no—
98C2×C3×C4⋊C4—22no—
99C2×C3×C4⋊C4—22no—
100C2×C3×C4⋊C4D414yescomplemented
101C2×C3×C22⋊C4—24no—
102C2×C3×C22⋊C4—24no—
103C2×C3×C22⋊C4—24no—
104C2×#217—24no—
105C2×#217—24no—
106C2×#217—28no—
107C2×#217—28no—
108C2×#217—44no—
109C2×#217D418yescomplemented
110#940—232no—
111#930—232no—
112C2×(C2×D3)⋊C4—24no—
113C2×(C2×D3)⋊C4—24no—
114C2×(C2×D3)⋊C4—24no—
115C2×(C2×D3)⋊C4—28no—
116C2×(C2×D3)⋊C4—28no—
117C2×(C2×D3)⋊C4—44no—
118C2×C4⋊Dic3—22no—
119C2×C4⋊Dic3—22no—
120C2×C4⋊Dic3D414yescomplemented
121C2×C4×Dic3—22no—
122C2×C4×Dic3—22no—
123C2×C4×Dic3—22no—
124C2×C4×Dic3—22no—
125C2×C4×Dic3—22no—
126C2×C4×Dic3D414yescomplemented
127C3⋊#95—24no—
128C3⋊#95—28no—
129C23×D4—32no—
130C23×D4—34no—
131C23×D4—31no—
132C23×D4C2×D311yescharacteristic
133C23×D4C2×D312yes—
134C24×C4C2×D311yescharacteristic
135C2×#127—64no—
136C2×#127—64no—
137C2×#127—64no—
138C2×#121—24no—
139C2×#121—24no—
140C2×#121—24no—
141C2×#121—64no—
142C2×#121—64no—
143C2×#121—64no—
144C22×C4⋊C4—31no—
145C22×C4⋊C4C2×D311yescharacteristic
146C22×C22⋊C4—32no—
147C22×C22⋊C4—32no—
148C22×C22⋊C4—34no—
149C22×C22⋊C4—34no—
150C22×C22⋊C4C2×D312yes—
151C22×C42—31no—
152C22×C42—31no—
153#392—616no—
154#390—64no—
155#390—64no—
156C4×C22⋊C4—64no—
157C2×#95—34no—
158C2×#95—32no—
159C24×C3—21no—
160C24×C3—21no—
161C24×C3—21no—
162C24×C3—21no—
163C24×C3—21no—
164C24×C3—22no—
165C24×C3—21no—
166C24×C3—22no—
167C24×C3—22no—
168C24×C3—22no—
169C24×C3—24no—
170C24×C3—22no—
171C24×C3—22no—
172C24×C3—22no—
173C24×C3—22no—
174C24×C3—24no—
175C24×C3—22no—
176C24×C3—24no—
177C24×C3—24no—
178C24×C3C2×D414yes—
179C24×C3C2×D414yes—
180C24×C3C2×D412yes—
181C24×C3C2411yescharacteristic
182C23×D3—22no—
183C23×D3—22no—
184C23×D3—22no—
185C23×D3—24no—
186C23×D3—22no—
187C23×D3—22no—
188C23×D3—22no—
189C23×D3—24no—
190C23×D3—24no—
191C23×D3—24no—
192C23×D3C2×D414yes—
193C2×C3×D4—216no—
194C2×C3×D4—28no—
195C2×C3×D4—28no—
196C2×C3×D4—28no—
197C2×C3×D4—416no—
198C2×C3×D4—416no—
199C2×C3×D4—48no—
200C2×C3×D4—48no—
201C2×C3×D4—44no—
202C2×C3×D4—44no—
203C2×C3×D4—44no—
204C2×C3×D4—44no—
205C22×C3×C4—21no—
206C22×C3×C4—24no—
207C22×C3×C4—21no—
208C22×C3×C4—21no—
209C22×C3×C4—21no—
210C22×C3×C4—21no—
211C22×C3×C4—22no—
212C22×C3×C4—22no—
213C22×C3×C4—21no—
214C22×C3×C4—24no—
215C22×C3×C4—28no—
216C22×C3×C4—28no—
217C22×C3×C4—28no—
218C22×C3×C4—44no—
219C22×C3×C4—44no—
220C22×C3×C4—44no—
221C22×C3×C4—44no—
222C22×C3×C4C2×D412yes—
223C22×C3×C4C2×D412yes—
224C22×C3×C4C2×D412yes—
225C22×C3×C4C2×D412yes—
226C22×C3×C4C2×D414yes—
227C22×C3×C4C2×D412yes—
228C22×C3×C4C2×D412yes—
229C22×C3×C4C2×D412yes—
230C22×C3×C4#4112yes—
231C2×#67—216no—
232C2×#67—232no—
233C2×#67—416no—
234C2×#67—416no—
235C2×#67—416no—
236C2×#67—416no—
237C2×#67—416no—
238C2×#67—416no—
239C2×#67—416no—
240C2×#67—48no—
241C2×#67—48no—
242C2×#67—416no—
243C22×Dic3—22no—
244C22×Dic3—22no—
245C22×Dic3—22no—
246C22×Dic3—22no—
247C22×Dic3—22no—
248C22×Dic3—24no—
249C22×Dic3—22no—
250C22×Dic3—22no—
251C22×Dic3—22no—
252C22×Dic3—22no—
253C22×Dic3—22no—
254C22×Dic3—22no—
255C22×Dic3—22no—
256C22×Dic3—24no—
257C22×Dic3C2×D414yes—
258C22×Dic3C2×D414yes—
259C22×Dic3C2×D414yes—
260C22×Dic3C2×D414yes—
261C22×Dic3#4114yes—
262C2×D12—28no—
263C2×D12—28no—
264C2×D12—28no—
265C2×D12—44no—
266C2×D12—44no—
267C2×D12—44no—
268C2×D12—44no—
269C3×C4⋊C4—28no—
270C3×C22⋊C4—216no—
271#217—216no—
272#217—416no—
273(C2×D3)⋊C4—216no—
274(C2×D3)⋊C4—416no—
275C4⋊Dic3—28no—
276C4×Dic3—28no—
277C4×Dic3—44no—
278C25—32no—
279C25C22×D312yes—
280C25C22×D311yescharacteristic
281C22×D4—24no—
282C22×D4—24no—
283C22×D4—28no—
284C22×D4—22no—
285C22×D4—22no—
286C22×D4—22no—
287C22×D4—22no—
288C22×D4—24no—
289C22×D4—22no—
290C22×D4—22no—
291C22×D4—34no—
292C22×D4—44no—
293C22×D4—64no—
294C22×D4—68no—
295C22×D4—68no—
296C22×D4—68no—
297C22×D4—64no—
298C22×D4—68no—
299C22×D4—64no—
300C22×D4—68no—
301C22×D4—68no—
302C22×D4—62no—
303C22×D4—62no—
304C22×D4—62no—
305C22×D4—62no—
306C22×D4—62no—
307C22×D4—62no—
308C22×D4—124no—
309C22×D4—124no—
310C22×D4—124no—
311C22×D4#6714yescomplemented
312C23×C4—22no—
313C23×C4—22no—
314C23×C4—22no—
315C23×C4—22no—
316C23×C4—22no—
317C23×C4—22no—
318C23×C4—32no—
319C23×C4—32no—
320C23×C4—32no—
321C23×C4#6714yescomplemented
322C23×C4C22×D311yescharacteristic
323C23×C4C22×D312yes—
324C23×C4C22×D311yescharacteristic
325#127—632no—
326#121—232no—
327#121—632no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—34no—
331C2×C4⋊C4—62no—
332C2×C4⋊C4—62no—
333C2×C4⋊C4#6714yescomplemented
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—38no—
338C2×C22⋊C4—64no—
339C2×C22⋊C4—64no—
340C2×C22⋊C4—64no—
341C2×C22⋊C4—64no—
342C2×C22⋊C4—64no—
343C2×C22⋊C4—68no—
344C2×C22⋊C4—68no—
345C2×C22⋊C4—68no—
346C2×C22⋊C4—68no—
347C2×C22⋊C4—124no—
348C2×C22⋊C4—124no—
349C2×C42—34no—
350C2×C42—62no—
351C2×C42—62no—
352C2×C42—62no—
353C2×C42—62no—
354C2×C42—62no—
355#95—64no—
356#95—68no—
357C23×C3—22no—
358C23×C3—22no—
359C23×C3—24no—
360C23×C3—22no—
361C23×C3—22no—
362C23×C3—24no—
363C23×C3—22no—
364C23×C3—22no—
365C23×C3—24no—
366C23×C3—24no—
367C23×C3—24no—
368C23×C3—24no—
369C23×C3—24no—
370C23×C3—24no—
371C23×C3—24no—
372C23×C3—28no—
373C23×C3—28no—
374C23×C3—41no—
375C23×C3—41no—
376C23×C3—41no—
377C23×C3—41no—
378C23×C3—42no—
379C23×C3—42no—
380C23×C3—42no—
381C23×C3—42no—
382C23×C3—42no—
383C23×C3—42no—
384C23×C3—42no—
385C23×C3—44no—
386C23×C3—42no—
387C23×C3—42no—
388C23×C3—42no—
389C23×C3—42no—
390C23×C3—42no—
391C23×C3—44no—
392C23×C3—44no—
393C23×C3—42no—
394C23×C3—42no—
395C23×C3—44no—
396C23×C3—44no—
397C23×C3—44no—
398C23×C3—44no—
399C23×C3—44no—
400C23×C3—44no—
401C23×C3—44no—
402C23×C3#12714yescomplemented
403C23×C3C22×D411yescharacteristic
404C23×C3C22×D411yescharacteristic
405C23×C3C22×D411yescharacteristic
406C23×C3C22×D412yes—
407C23×C3C22×D411yescharacteristic
408C23×C3C22×D411yescharacteristic
409C23×C3C22×D411yescharacteristic
410C23×C3C2×#4111yescharacteristic
411C23×C3C2×#4112yes—
412C23×C3H(5,𝔽2)12yes—
413C23×C3H(5,𝔽2)12yes—
414C22×D3—24no—
415C22×D3—24no—
416C22×D3—24no—
417C22×D3—28no—
418C22×D3—28no—
419C22×D3—42no—
420C22×D3—42no—
421C22×D3—42no—
422C22×D3—44no—
423C22×D3—42no—
424C22×D3—42no—
425C22×D3—42no—
426C22×D3—44no—
427C22×D3—42no—
428C22×D3—44no—
429C22×D3—42no—
430C22×D3—44no—
431C22×D3—44no—
432C22×D3—44no—
433C22×D3—44no—
434C22×D3—44no—
435C22×D3—44no—
436C22×D3—44no—
437C3×D4—432no—
438C3×D4—416no—
439C2×C3×C4—22no—
440C2×C3×C4—22no—
441C2×C3×C4—24no—
442C2×C3×C4—22no—
443C2×C3×C4—28no—
444C2×C3×C4—41no—
445C2×C3×C4—41no—
446C2×C3×C4—41no—
447C2×C3×C4—41no—
448C2×C3×C4—42no—
449C2×C3×C4—42no—
450C2×C3×C4—44no—
451C2×C3×C4—416no—
452C2×C3×C4#12014yes—
453C2×C3×C4#12014yes—
454C2×C3×C4#12014yes—
455C2×C3×C4#12114yes—
456C2×C3×C4#12114yes—
457C2×C3×C4#12114yes—
458C2×C3×C4#12714yes—
459#67—464no—
460#67—432no—
461C2×Dic3—24no—
462C2×Dic3—24no—
463C2×Dic3—24no—
464C2×Dic3—24no—
465C2×Dic3—24no—
466C2×Dic3—24no—
467C2×Dic3—24no—
468C2×Dic3—24no—
469C2×Dic3—24no—
470C2×Dic3—24no—
471C2×Dic3—28no—
472C2×Dic3—42no—
473C2×Dic3—42no—
474C2×Dic3—42no—
475C2×Dic3—42no—
476C2×Dic3—44no—
477C2×Dic3—42no—
478C2×Dic3—42no—
479C2×Dic3#12118yescomplemented
480D12—416no—
481C24—21no—
482C24—21no—
483C24—21no—
484C24—21no—
485C24—22no—
486C24—22no—
487C24—22no—
488C24—21no—
489C24—21no—
490C24—22no—
491C24—24no—
492C24—22no—
493C24—22no—
494C24—22no—
495C24—24no—
496C24—24no—
497C24—24no—
498C24—22no—
499C24—22no—
500C24—34no—
501C24—62no—
502C24—64no—
503C24—62no—
504C24—62no—
505C24—64no—
506C24—64no—
507C24—64no—
508C24—62no—
509C24—62no—
510C24—62no—
511C24D3×D414yes—
512C24C2×#6714yes—
513C24C2×#6712yes—
514C24C23×D311yescharacteristic
515C2×D4—216no—
516C2×D4—28no—
517C2×D4—28no—
518C2×D4—28no—
519C2×D4—416no—
520C2×D4—416no—
521C2×D4—48no—
522C2×D4—48no—
523C2×D4—44no—
524C2×D4—44no—
525C2×D4—44no—
526C2×D4—44no—
527C2×D4—616no—
528C2×D4—632no—
529C2×D4—68no—
530C2×D4—68no—
531C2×D4—68no—
532C2×D4—1216no—
533C2×D4—1216no—
534C2×D4—1216no—
535C2×D4—1216no—
536C2×D4—1216no—
537C2×D4—1216no—
538C2×D4—1216no—
539C2×D4—1216no—
540C2×D4—128no—
541C2×D4—128no—
542C2×D4—124no—
543C2×D4—124no—
544C2×D4—124no—
545C2×D4—124no—
546C22×C4—21no—
547C22×C4—24no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—24no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—28no—
557C22×C4—28no—
558C22×C4—28no—
559C22×C4—34no—
560C22×C4—34no—
561C22×C4—34no—
562C22×C4—34no—
563C22×C4—34no—
564C22×C4—44no—
565C22×C4—44no—
566C22×C4—44no—
567C22×C4—44no—
568C22×C4—62no—
569C22×C4—62no—
570C22×C4—62no—
571C22×C4—62no—
572C22×C4—62no—
573C22×C4—64no—
574C22×C4—62no—
575C22×C4—62no—
576C22×C4—62no—
577C22×C4—62no—
578C22×C4—62no—
579C22×C4—64no—
580C22×C4—62no—
581C22×C4—62no—
582C22×C4D3×D412yes—
583C22×C4D3×D412yes—
584C22×C4D3×D412yes—
585C22×C4#23712yes—
586C22×C4C2×#6712yes—
587C22×C4C2×#6714yes—
588C22×C4C2×#6712yes—
589C22×C4C2×#6712yes—
590C22×C4C2×#6712yes—
591C4⋊C4—28no—
592C4⋊C4—68no—
593C22⋊C4—216no—
594C22⋊C4—616no—
595C22⋊C4—616no—
596C22⋊C4—1216no—
597C22⋊C4—1216no—
598C42—68no—
599C42—124no—
600C22×C3—24no—
601C22×C3—24no—
602C22×C3—24no—
603C22×C3—42no—
604C22×C3—42no—
605C22×C3—44no—
606C22×C3—44no—
607C22×C3—44no—
608C22×C3—42no—
609C22×C3—42no—
610C22×C3—44no—
611C22×C3—44no—
612C22×C3—48no—
613C22×C3—48no—
614C22×C3—44no—
615C22×C3—44no—
616C22×C3—82no—
617C22×C3—82no—
618C22×C3—84no—
619C22×C3—82no—
620C22×C3—82no—
621C22×C3—84no—
622C22×C3C2×#12011yescharacteristic
623C22×C3C2×#12011yescharacteristic
624C22×C3C2×#12011yescharacteristic
625C22×C3C2×#12111yescharacteristic
626C22×C3C2×#12111yescharacteristic
627C22×C3C2×#12111yescharacteristic
628C22×C3C2×#12112yes—
629C22×C3C2×#12711yescharacteristic
630C22×C3C2×#12711yescharacteristic
631C22×C3#53211yescharacteristic
632C22×C3#53212yes—
633C22×C3#53511yescharacteristic
634C22×C3#53511yescharacteristic
635C22×C3#53512yes—
636C22×C3#54012yes—
637C22×C3D4212yes—
638C22×C3D4212yes—
639C22×C3D4212yes—
640C22×C3D4212yes—
641C22×C3#54612yes—
642C22×C3#54612yes—
643C22×C3#55012yes—
644C22×C3#55012yes—
645C2×D3—44no—
646C2×D3—48no—
647C2×D3—48no—
648C2×D3—44no—
649C2×D3—44no—
650C2×D3—82no—
651C2×D3—82no—
652C2×D3—84no—
653C2×D3—82no—
654C2×D3—82no—
655C2×D3—84no—
656C3×C4—42no—
657C3×C4—44no—
658C3×C4#39218yescomplemented
659Dic3—28no—
660Dic3—44no—
661Dic3—44no—
662C23—22no—
663C23—24no—
664C23—24no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—28no—
676C23—24no—
677C23—28no—
678C23—24no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—44no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—44no—
699C23—44no—
700C23—44no—
701C23—44no—
702C23—44no—
703C23—44no—
704C23—44no—
705C23—44no—
706C23—44no—
707C23—64no—
708C23—64no—
709C23—64no—
710C23—68no—
711C23—68no—
712C23—124no—
713C23—124no—
714C23—122no—
715C23—122no—
716C23—122no—
717C23—122no—
718C23—122no—
719C23—124no—
720C23—122no—
721C23—122no—
722C23—124no—
723C23—122no—
724C23—124no—
725C23—124no—
726C23—124no—
727C23—124no—
728C23—124no—
729C23—124no—
730C23#94014yescomplemented
731C23C2×D3×D411yescharacteristic
732C23C2×D3×D411yescharacteristic
733C23C2×D3×D411yescharacteristic
734C23C2×D3×D412yes—
735C23C2×#23711yescharacteristic
736C23#100412yes—
737C23D3×#4112yes—
738C23#100912yes—
739C23C22×#6711yescharacteristic
740C23C22×#6711yescharacteristic
741C23C22×#6711yescharacteristic
742D4—432no—
743D4—416no—
744D4—1264no—
745D4—1232no—
746D4—1216no—
747C2×C4—22no—
748C2×C4—28no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—24no—
752C2×C4—38no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—44no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—416no—
761C2×C4—64no—
762C2×C4—64no—
763C2×C4—64no—
764C2×C4—64no—
765C2×C4—64no—
766C2×C4—64no—
767C2×C4—64no—
768C2×C4—64no—
769C2×C4—64no—
770C2×C4—64no—
771C2×C4—68no—
772C2×C4—122no—
773C2×C4—122no—
774C2×C4—122no—
775C2×C4—122no—
776C2×C4—122no—
777C2×C4—122no—
778C2×C4—124no—
779C2×C4#93714yes—
780C2×C4#93714yes—
781C2×C4#93814yes—
782C2×C4#93914yes—
783C2×C4#93914yes—
784C2×C4#94014yes—
785C2×C4#95314yes—
786C2×C3—44no—
787C2×C3—84no—
788C2×C3C2×#39211yescharacteristic
789C2×C3#240812yes—
790C2×C3#242812yes—
791C2×C3#242812yes—
792C2×C3#243111yescharacteristic
793C2×C3#243111yescharacteristic
794C2×C3#243311yescharacteristic
795C2×C3#243311yescharacteristic
796C2×C3#254112yes—
797C2×C3#261911yescharacteristic
798C2×C3#285611yescharacteristic
799D3—84no—
800C22—24no—
801C22—24no—
802C22—24no—
803C22—42no—
804C22—42no—
805C22—44no—
806C22—44no—
807C22—44no—
808C22—42no—
809C22—44no—
810C22—42no—
811C22—44no—
812C22—44no—
813C22—44no—
814C22—48no—
815C22—48no—
816C22—82no—
817C22—84no—
818C22—82no—
819C22—82no—
820C22—84no—
821C22—82no—
822C22—124no—
823C22—128no—
824C22—128no—
825C22—124no—
826C22—124no—
827C22—242no—
828C22—242no—
829C22—242no—
830C22—244no—
831C22—244no—
832C22—242no—
833C22#559612yes—
834C22#559912yes—
835C22D3×#12112yes—
836C22#560712yes—
837C22#560912yes—
838C22#560912yes—
839C22#561212yes—
840C22#561912yes—
841C22C2×#93711yescharacteristic
842C22C2×#93711yescharacteristic
843C22C2×#93811yescharacteristic
844C22D4×#6712yes—
845C22D4×#6712yes—
846C22C2×#93911yescharacteristic
847C22C2×#93911yescharacteristic
848C22C2×#94011yescharacteristic
849C22C2×#94011yescharacteristic
850C22#580511yescharacteristic
851C22#582912yes—
852C22#583011yescharacteristic
853C22#583211yescharacteristic
854C22#583412yes—
855C22C2×#95311yescharacteristic
856C4—44no—
857C4—42no—
858C4—68no—
859C4—124no—
860C4—124no—
861C4#522318yescomplemented
862C3#1512411yescharacteristic, complemented, Sylow
863C2—44no—
864C2—84no—
865C2—244no—
866C2#8264012yes—
867C2#8264812yes—
868C2#8264912yes—
869C2#8265211yescharacteristic
870C2#8265311yescharacteristic
871C2#8266912yes—
872C2#8267611yescharacteristic
873C2#8270011yescharacteristic
874C2#8404911yescharacteristic
875C2C2×#522311yescharacteristic
876C2#8409211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC22×C3×#121C2
hypercenterC22×#121D3
hypocenterC3#15124
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C22×C3×#121C2semidirect
2. C22×#940C2semidirect
3. C22×#930C2semidirect
4. C2×#5223C2semidirect
5. C2×#5221C2semidirect
6. C2×C4×#217C2semidirect
7. C2×#4988C2semidirect
8. #71563C2semidirect
9. #71550C2semidirect
43. C22×#121D3semidirect
64. C22×C3×D4D4semidirect
71. C23×C3×C4D4semidirect
96. C22×D12D4semidirect
100. C2×C3×C4⋊C4D4semidirect
109. C2×#217D4semidirect
120. C2×C4⋊Dic3D4semidirect
126. C2×C4×Dic3D4semidirect
311. C22×D4#67semidirect
321. C23×C4#67semidirect
333. C2×C4⋊C4#67semidirect
402. C23×C3#127semidirect
479. C2×Dic3#121semidirect
658. C3×C4#392semidirect
730. C23#940semidirect
861. C4#5223semidirect
862. C3#15124semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#1212
C22×#9402
C22×#9302
C2×#52232
C2×#52212
C2×C4×#2172
C2×#49882
#715632
#715502
#151243