Finite Group Databasebeta

← #10731732

Subgroups — #10731732

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×#938C211yesmaximal, characteristic, complemented
2C22×#940C211yesmaximal, characteristic, complemented
3C22×#895C211yesmaximal, characteristic, complemented
4C2×C3×#390C211yesmaximal, characteristic, complemented
5C2×#4960C214yesmaximal, complemented
6C2×#4939C211yesmaximal, characteristic, complemented
7C2×C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
8#71563C211yesmaximal, characteristic, complemented
9#71550C214yesmaximal, complemented
10#15124—31nomaximal, Sylow
11C23×C3×D4C2211yescharacteristic
12C23×#67C2214yes—
13C23×#67C2212yes—
14C23×D12C2211yescharacteristic
15C23×D12C2212yes—
16C23×C4×D3C2211yescharacteristic
17C22×C3×C4⋊C4C2211yescharacteristic
18C22×C3×C22⋊C4C2214yes—
19C22×C3×C42C2211yescharacteristic
20C22×#217C2212yes—
21C2×#940—24no—
22C2×#940—24no—
23C2×#940—24no—
24C2×#938—24no—
25C2×#938—24no—
26C2×#938—24no—
27C22×(C2×D3)⋊C4C2212yes—
28C22×(C2×D3)⋊C4C2214yes—
29C22×(C2×D3)⋊C4C2212yes—
30C22×C4⋊Dic3C2211yescharacteristic
31C22×C4×Dic3C2211yescharacteristic
32C2×#895—24no—
33C2×#895—24no—
34C2×#895—24no—
35C3×#390—24no—
36C2×C3⋊#95C2212yes—
37C2×C3⋊#95C2214yes—
38#4960—216no—
39#4939—24no—
40C4×(C2×D3)⋊C4—24no—
41C22×#127—31no—
42C22×#121—31no—
43C22×#121—31no—
44C2×#392—34no—
45C2×#390—31no—
46C2×#390D311yescharacteristic, complemented
47C2×C4×C22⋊C4—31no—
48#1438—34no—
49C4⋊#95—31no—
50C25×C3C2312yes—
51C24×D3C2312yes—
52C24×D3C2311yescharacteristic
53C22×C3×D4—22no—
54C22×C3×D4—22no—
55C22×C3×D4—22no—
56C22×C3×D4—22no—
57C22×C3×D4—22no—
58C22×C3×D4—22no—
59C22×C3×D4D414yescomplemented
60C23×C3×C4C2312yes—
61C23×C3×C4C2312yes—
62C23×C3×C4C2311yescharacteristic
63C22×#67—24no—
64C22×#67—28no—
65C22×#67—24no—
66C22×#67—28no—
67C22×#67—28no—
68C22×#67—24no—
69C22×#67—28no—
70C22×#67—28no—
71C22×#67—28no—
72C22×#67—44no—
73C22×#67—44no—
74C22×#67—44no—
75C23×Dic3C2311yescharacteristic
76C23×Dic3C2312yes—
77C23×Dic3C2312yes—
78C22×D12—24no—
79C22×D12—24no—
80C22×D12—22no—
81C22×D12—22no—
82C22×D12—24no—
83C22×D12—22no—
84C22×D12—22no—
85C22×D12—22no—
86C22×D12—22no—
87C22×D12—28no—
88C22×D12—44no—
89C22×D12D414yescomplemented
90C22×C4×D3—22no—
91C22×C4×D3—22no—
92C22×C4×D3—22no—
93C22×C4×D3—22no—
94C22×C4×D3—22no—
95C22×C4×D3—22no—
96C22×C4×D3D414yescomplemented
97C2×C3×C4⋊C4—22no—
98C2×C3×C4⋊C4—22no—
99C2×C3×C4⋊C4D414yescomplemented
100C2×C3×C22⋊C4—28no—
101C2×C3×C22⋊C4—28no—
102C2×C3×C22⋊C4—44no—
103C2×C3×C42—22no—
104C2×C3×C42—22no—
105C2×C3×C42—22no—
106C2×#217—24no—
107C2×#217—24no—
108C2×#217—24no—
109#940—232no—
110#938—232no—
111C2×(C2×D3)⋊C4—24no—
112C2×(C2×D3)⋊C4—24no—
113C2×(C2×D3)⋊C4—24no—
114C2×(C2×D3)⋊C4—24no—
115C2×(C2×D3)⋊C4—24no—
116C2×(C2×D3)⋊C4—28no—
117C2×(C2×D3)⋊C4—28no—
118C2×(C2×D3)⋊C4—44no—
119C2×(C2×D3)⋊C4D418yescomplemented
120C2×C4⋊Dic3—22no—
121C2×C4⋊Dic3—22no—
122C2×C4⋊Dic3D414yescomplemented
123C2×C4×Dic3—22no—
124C2×C4×Dic3—22no—
125C2×C4×Dic3D414yescomplemented
126#895—232no—
127C3⋊#95—24no—
128C3⋊#95—28no—
129C23×D4—32no—
130C23×D4—34no—
131C23×D4—31no—
132C23×D4—32no—
133C23×D4C2×D311yescharacteristic
134C24×C4—31no—
135C2×#127—64no—
136C2×#127—64no—
137C2×#127—64no—
138C2×#121—64no—
139C2×#121—64no—
140C2×#121—64no—
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—32no—
149C22×C22⋊C4—34no—
150C22×C22⋊C4C2×D314yes—
151C22×C42—31no—
152C22×C42C2×D311yescharacteristic
153#392—616no—
154#390—24no—
155#390—64no—
156C4×C22⋊C4—64no—
157C2×#95—34no—
158C2×#95—32no—
159C24×C3—22no—
160C24×C3—22no—
161C24×C3—22no—
162C24×C3—24no—
163C24×C3—22no—
164C24×C3—22no—
165C24×C3—24no—
166C24×C3—22no—
167C24×C3—24no—
168C24×C3—24no—
169C24×C3C2×D414yes—
170C24×C3C2411yescharacteristic
171C23×D3—21no—
172C23×D3—21no—
173C23×D3—21no—
174C23×D3—21no—
175C23×D3—21no—
176C23×D3—22no—
177C23×D3—21no—
178C23×D3—22no—
179C23×D3—22no—
180C23×D3—22no—
181C23×D3—22no—
182C23×D3—22no—
183C23×D3—24no—
184C23×D3—22no—
185C23×D3—22no—
186C23×D3—22no—
187C23×D3—24no—
188C23×D3—24no—
189C23×D3—24no—
190C23×D3C2×D414yes—
191C23×D3C2×D414yes—
192C23×D3C2×D412yes—
193C2×C3×D4—28no—
194C2×C3×D4—28no—
195C2×C3×D4—28no—
196C2×C3×D4—44no—
197C2×C3×D4—44no—
198C2×C3×D4—44no—
199C2×C3×D4—44no—
200C22×C3×C4—22no—
201C22×C3×C4—24no—
202C22×C3×C4—22no—
203C22×C3×C4—22no—
204C22×C3×C4—22no—
205C22×C3×C4—22no—
206C22×C3×C4—22no—
207C22×C3×C4—22no—
208C22×C3×C4—22no—
209C22×C3×C4—24no—
210C22×C3×C4C2×D412yes—
211C22×C3×C4C2×D414yes—
212C22×C3×C4C2×D412yes—
213C22×C3×C4C2×D412yes—
214C22×C3×C4C2×D412yes—
215C22×C3×C4C2×D412yes—
216C22×C3×C4C2×D414yes—
217C22×C3×C4C2×D412yes—
218C22×C3×C4#4112yes—
219C2×#67—216no—
220C2×#67—232no—
221C2×#67—416no—
222C2×#67—416no—
223C2×#67—416no—
224C2×#67—416no—
225C2×#67—416no—
226C2×#67—416no—
227C2×#67—416no—
228C2×#67—48no—
229C2×#67—48no—
230C2×#67—416no—
231C22×Dic3—22no—
232C22×Dic3—22no—
233C22×Dic3—22no—
234C22×Dic3—22no—
235C22×Dic3—21no—
236C22×Dic3—24no—
237C22×Dic3—22no—
238C22×Dic3—22no—
239C22×Dic3—21no—
240C22×Dic3—21no—
241C22×Dic3—21no—
242C22×Dic3—21no—
243C22×Dic3—21no—
244C22×Dic3—24no—
245C22×Dic3C2×D414yes—
246C22×Dic3C2×D412yes—
247C22×Dic3C2×D414yes—
248C22×Dic3C2×D414yes—
249C22×Dic3#4114yes—
250C2×D12—216no—
251C2×D12—28no—
252C2×D12—28no—
253C2×D12—28no—
254C2×D12—416no—
255C2×D12—416no—
256C2×D12—48no—
257C2×D12—48no—
258C2×D12—44no—
259C2×D12—44no—
260C2×D12—44no—
261C2×D12—44no—
262C2×C4×D3—28no—
263C2×C4×D3—28no—
264C2×C4×D3—28no—
265C2×C4×D3—44no—
266C2×C4×D3—44no—
267C2×C4×D3—44no—
268C2×C4×D3—44no—
269C3×C4⋊C4—28no—
270C3×C22⋊C4—416no—
271C3×C42—44no—
272#217—216no—
273(C2×D3)⋊C4—216no—
274(C2×D3)⋊C4—216no—
275(C2×D3)⋊C4—416no—
276C4⋊Dic3—28no—
277C4×Dic3—28no—
278C25—31no—
279C25—32no—
280C25C22×D312yes—
281C22×D4—22no—
282C22×D4—22no—
283C22×D4—22no—
284C22×D4—22no—
285C22×D4—22no—
286C22×D4—22no—
287C22×D4—34no—
288C22×D4—64no—
289C22×D4—64no—
290C22×D4—68no—
291C22×D4—64no—
292C22×D4—68no—
293C22×D4—68no—
294C22×D4—68no—
295C22×D4—64no—
296C22×D4—68no—
297C22×D4—64no—
298C22×D4—68no—
299C22×D4—68no—
300C22×D4—62no—
301C22×D4—62no—
302C22×D4—62no—
303C22×D4—62no—
304C22×D4—62no—
305C22×D4—64no—
306C22×D4—62no—
307C22×D4—124no—
308C22×D4—124no—
309C22×D4—124no—
310C22×D4—124no—
311C22×D4D1214yescomplemented
312C23×C4—32no—
313C23×C4—31no—
314C23×C4—32no—
315C23×C4—34no—
316C23×C4—62no—
317C23×C4—62no—
318C23×C4—62no—
319C23×C4—62no—
320C23×C4—62no—
321C23×C4—62no—
322C23×C4C22×D312yes—
323C23×C4C22×D312yes—
324C23×C4C22×D311yescharacteristic
325#127—632no—
326#121—632no—
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—28no—
335C2×C22⋊C4—28no—
336C2×C22⋊C4—38no—
337C2×C22⋊C4—44no—
338C2×C22⋊C4—64no—
339C2×C22⋊C4—64no—
340C2×C22⋊C4—64no—
341C2×C22⋊C4—64no—
342C2×C22⋊C4—64no—
343C2×C22⋊C4—64no—
344C2×C22⋊C4—64no—
345C2×C22⋊C4—64no—
346C2×C22⋊C4—68no—
347C2×C22⋊C4—68no—
348C2×C22⋊C4—124no—
349C2×C42—22no—
350C2×C42—22no—
351C2×C42—22no—
352C2×C42—34no—
353C2×C42—62no—
354C2×C42—62no—
355#95—64no—
356#95—68no—
357C23×C3—24no—
358C23×C3—24no—
359C23×C3—24no—
360C23×C3—28no—
361C23×C3—28no—
362C23×C3—42no—
363C23×C3—44no—
364C23×C3—42no—
365C23×C3—42no—
366C23×C3—42no—
367C23×C3—42no—
368C23×C3—42no—
369C23×C3—44no—
370C23×C3—42no—
371C23×C3—44no—
372C23×C3—42no—
373C23×C3—44no—
374C23×C3—44no—
375C23×C3—44no—
376C23×C3—44no—
377C23×C3—44no—
378C23×C3—44no—
379C23×C3—44no—
380C23×C3C22×D411yescharacteristic
381C23×C3C22×D411yescharacteristic
382C23×C3C22×D411yescharacteristic
383C23×C3C22×D411yescharacteristic
384C23×C3C22×D411yescharacteristic
385C23×C3C22×D412yes—
386C23×C3C22×D411yescharacteristic
387C23×C3C2×#4111yescharacteristic
388C23×C3C2×#4112yes—
389C23×C3H(5,𝔽2)12yes—
390C23×C3H(5,𝔽2)12yes—
391C22×D3—22no—
392C22×D3—22no—
393C22×D3—24no—
394C22×D3—22no—
395C22×D3—22no—
396C22×D3—24no—
397C22×D3—22no—
398C22×D3—22no—
399C22×D3—24no—
400C22×D3—24no—
401C22×D3—24no—
402C22×D3—24no—
403C22×D3—24no—
404C22×D3—24no—
405C22×D3—24no—
406C22×D3—28no—
407C22×D3—28no—
408C22×D3—41no—
409C22×D3—41no—
410C22×D3—41no—
411C22×D3—41no—
412C22×D3—42no—
413C22×D3—42no—
414C22×D3—42no—
415C22×D3—42no—
416C22×D3—42no—
417C22×D3—42no—
418C22×D3—42no—
419C22×D3—42no—
420C22×D3—42no—
421C22×D3—44no—
422C22×D3—42no—
423C22×D3—42no—
424C22×D3—42no—
425C22×D3—44no—
426C22×D3—42no—
427C22×D3—44no—
428C22×D3—42no—
429C22×D3—44no—
430C22×D3—44no—
431C22×D3—44no—
432C22×D3—44no—
433C22×D3—44no—
434C22×D3—44no—
435C22×D3—44no—
436C22×D3#12714yescomplemented
437C3×D4—416no—
438C2×C3×C4—24no—
439C2×C3×C4—24no—
440C2×C3×C4—24no—
441C2×C3×C4—24no—
442C2×C3×C4—28no—
443C2×C3×C4—42no—
444C2×C3×C4—42no—
445C2×C3×C4—42no—
446C2×C3×C4—42no—
447C2×C3×C4—44no—
448C2×C3×C4—42no—
449C2×C3×C4—42no—
450C2×C3×C4#12014yes—
451C2×C3×C4#12014yes—
452C2×C3×C4#12014yes—
453C2×C3×C4#12114yes—
454C2×C3×C4#12114yes—
455C2×C3×C4#12114yes—
456C2×C3×C4#12714yes—
457#67—464no—
458#67—432no—
459C2×Dic3—24no—
460C2×Dic3—24no—
461C2×Dic3—24no—
462C2×Dic3—24no—
463C2×Dic3—24no—
464C2×Dic3—24no—
465C2×Dic3—24no—
466C2×Dic3—22no—
467C2×Dic3—22no—
468C2×Dic3—22no—
469C2×Dic3—28no—
470C2×Dic3—41no—
471C2×Dic3—41no—
472C2×Dic3—41no—
473C2×Dic3—41no—
474C2×Dic3—42no—
475C2×Dic3—42no—
476C2×Dic3—44no—
477C2×Dic3#12118yescomplemented
478D12—432no—
479D12—416no—
480C4×D3—416no—
481C24—22no—
482C24—24no—
483C24—22no—
484C24—22no—
485C24—22no—
486C24—22no—
487C24—24no—
488C24—24no—
489C24—24no—
490C24—22no—
491C24—34no—
492C24—32no—
493C24—34no—
494C24—61no—
495C24—61no—
496C24—61no—
497C24—61no—
498C24—61no—
499C24—62no—
500C24—62no—
501C24—62no—
502C24—61no—
503C24—62no—
504C24—62no—
505C24—62no—
506C24—64no—
507C24—62no—
508C24—62no—
509C24—64no—
510C24—64no—
511C24—64no—
512C24—62no—
513C24C2×D1214yes—
514C24C23×D311yescharacteristic
515C2×D4—28no—
516C2×D4—28no—
517C2×D4—28no—
518C2×D4—44no—
519C2×D4—44no—
520C2×D4—44no—
521C2×D4—44no—
522C2×D4—616no—
523C2×D4—616no—
524C2×D4—632no—
525C2×D4—68no—
526C2×D4—68no—
527C2×D4—68no—
528C2×D4—1216no—
529C2×D4—1216no—
530C2×D4—128no—
531C2×D4—1216no—
532C2×D4—128no—
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—22no—
547C22×C4—24no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—24no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—34no—
557C22×C4—34no—
558C22×C4—34no—
559C22×C4—32no—
560C22×C4—34no—
561C22×C4—62no—
562C22×C4—62no—
563C22×C4—62no—
564C22×C4—62no—
565C22×C4—61no—
566C22×C4—62no—
567C22×C4—61no—
568C22×C4—61no—
569C22×C4—64no—
570C22×C4—61no—
571C22×C4—61no—
572C22×C4—62no—
573C22×C4—64no—
574C22×C4—61no—
575C22×C4—68no—
576C22×C4—68no—
577C22×C4—68no—
578C22×C4—124no—
579C22×C4—124no—
580C22×C4—124no—
581C22×C4—124no—
582C22×C4C2×D1212yes—
583C22×C4#23512yes—
584C22×C4D3×D414yes—
585C22×C4D3×D412yes—
586C22×C4D3×D412yes—
587C22×C4D3×D412yes—
588C22×C4D3×D412yes—
589C22×C4C2×#6714yes—
590C22×C4C2×#6712yes—
591C4⋊C4—28no—
592C4⋊C4—68no—
593C22⋊C4—416no—
594C22⋊C4—616no—
595C22⋊C4—616no—
596C22⋊C4—616no—
597C22⋊C4—1216no—
598C42—44no—
599C42—68no—
600C22×C3—44no—
601C22×C3—48no—
602C22×C3—48no—
603C22×C3—44no—
604C22×C3—44no—
605C22×C3—82no—
606C22×C3—82no—
607C22×C3—84no—
608C22×C3—82no—
609C22×C3—82no—
610C22×C3—84no—
611C22×C3C2×#12011yescharacteristic
612C22×C3C2×#12011yescharacteristic
613C22×C3C2×#12011yescharacteristic
614C22×C3C2×#12111yescharacteristic
615C22×C3C2×#12111yescharacteristic
616C22×C3C2×#12111yescharacteristic
617C22×C3C2×#12112yes—
618C22×C3C2×#12711yescharacteristic
619C22×C3C2×#12711yescharacteristic
620C22×C3#53211yescharacteristic
621C22×C3#53212yes—
622C22×C3#53511yescharacteristic
623C22×C3#53511yescharacteristic
624C22×C3#53512yes—
625C22×C3#54012yes—
626C22×C3D4212yes—
627C22×C3D4212yes—
628C22×C3D4212yes—
629C22×C3D4212yes—
630C22×C3#54612yes—
631C22×C3#54612yes—
632C22×C3#55012yes—
633C22×C3#55012yes—
634C2×D3—24no—
635C2×D3—24no—
636C2×D3—24no—
637C2×D3—42no—
638C2×D3—42no—
639C2×D3—44no—
640C2×D3—44no—
641C2×D3—44no—
642C2×D3—42no—
643C2×D3—42no—
644C2×D3—44no—
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—44no—
657C3×C4—44no—
658C3×C4#39218yescomplemented
659Dic3—28no—
660Dic3—42no—
661Dic3—44no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—28no—
666C23—28no—
667C23—34no—
668C23—42no—
669C23—42no—
670C23—44no—
671C23—42no—
672C23—42no—
673C23—44no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—44no—
678C23—42no—
679C23—44no—
680C23—44no—
681C23—44no—
682C23—44no—
683C23—44no—
684C23—44no—
685C23—44no—
686C23—62no—
687C23—62no—
688C23—62no—
689C23—64no—
690C23—62no—
691C23—62no—
692C23—62no—
693C23—64no—
694C23—64no—
695C23—64no—
696C23—64no—
697C23—64no—
698C23—68no—
699C23—68no—
700C23—64no—
701C23—64no—
702C23—64no—
703C23—122no—
704C23—121no—
705C23—121no—
706C23—121no—
707C23—121no—
708C23—122no—
709C23—122no—
710C23—122no—
711C23—122no—
712C23—122no—
713C23—122no—
714C23—122no—
715C23—122no—
716C23—122no—
717C23—122no—
718C23—122no—
719C23—122no—
720C23—124no—
721C23—122no—
722C23—124no—
723C23—124no—
724C23—124no—
725C23—124no—
726C23—124no—
727C23—124no—
728C23—124no—
729C23—124no—
730C23—124no—
731C23C22×D1211yescharacteristic
732C23C2×#23511yescharacteristic
733C23C2×D3×D411yescharacteristic
734C23C2×D3×D411yescharacteristic
735C23C2×D3×D412yes—
736C23C2×D3×D411yescharacteristic
737C23C2×D3×D411yescharacteristic
738C23#100412yes—
739C23D3×#4112yes—
740C23#100912yes—
741C23C22×#6711yescharacteristic
742D4—416no—
743D4—1232no—
744D4—1264no—
745D4—1232no—
746D4—1216no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—28no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—38no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—44no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—64no—
761C2×C4—64no—
762C2×C4—64no—
763C2×C4—64no—
764C2×C4—64no—
765C2×C4—64no—
766C2×C4—62no—
767C2×C4—64no—
768C2×C4—62no—
769C2×C4—62no—
770C2×C4—68no—
771C2×C4—122no—
772C2×C4—122no—
773C2×C4—121no—
774C2×C4—121no—
775C2×C4—121no—
776C2×C4—121no—
777C2×C4—124no—
778C2×C4—1216no—
779C2×C4#88214yes—
780C2×C4#88214yes—
781C2×C4#88414yes—
782C2×C4#88414yes—
783C2×C4#93014yes—
784C2×C4#93714yes—
785C2×C4#94014yes—
786C2×C3—84no—
787C2×C3C2×#39211yescharacteristic
788C2×C3#240812yes—
789C2×C3#242812yes—
790C2×C3#242812yes—
791C2×C3#243111yescharacteristic
792C2×C3#243111yescharacteristic
793C2×C3#243311yescharacteristic
794C2×C3#243311yescharacteristic
795C2×C3#254112yes—
796C2×C3#261911yescharacteristic
797C2×C3#285611yescharacteristic
798D3—44no—
799D3—84no—
800C22—44no—
801C22—44no—
802C22—48no—
803C22—44no—
804C22—48no—
805C22—64no—
806C22—64no—
807C22—64no—
808C22—82no—
809C22—84no—
810C22—82no—
811C22—82no—
812C22—82no—
813C22—84no—
814C22—122no—
815C22—122no—
816C22—124no—
817C22—124no—
818C22—122no—
819C22—122no—
820C22—124no—
821C22—124no—
822C22—124no—
823C22—128no—
824C22—128no—
825C22—124no—
826C22—124no—
827C22—242no—
828C22—242no—
829C22—242no—
830C22—242no—
831C22—244no—
832C22—244no—
833C22C2×#88211yescharacteristic
834C22C2×#88211yescharacteristic
835C22C2×#88411yescharacteristic
836C22C2×#88411yescharacteristic
837C22#554812yes—
838C22D4×D1212yes—
839C22#555412yes—
840C22#556212yes—
841C22#559912yes—
842C22D3×#12112yes—
843C22#560712yes—
844C22#560912yes—
845C22#566811yescharacteristic
846C22#567411yescharacteristic
847C22#567612yes—
848C22D3×#12711yescharacteristic
849C22#571511yescharacteristic
850C22#571712yes—
851C22C2×#93011yescharacteristic
852C22C2×#93711yescharacteristic
853C22D4×#6712yes—
854C22C2×#94011yescharacteristic
855C22#583412yes—
856C4—44no—
857C4—44no—
858C4—68no—
859C4—124no—
860C4—122no—
861C4#496018yescomplemented
862C3#1512411yescharacteristic, complemented, Sylow
863C2—84no—
864C2—124no—
865C2—244no—
866C2#7631311yescharacteristic
867C2#7631411yescharacteristic
868C2#7643612yes—
869C2#7644412yes—
870C2#7645611yescharacteristic
871C2#7647611yescharacteristic
872C2C2×#496011yescharacteristic
873C2#8240912yes—
874C2#8266912yes—
875C2#8295811yescharacteristic
876C2#8317511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#390C2
hypercenterC2×#390D3
hypocenterC3#15124
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
1. C22×#938C2semidirect
2. C22×#940C2semidirect
3. C22×#895C2semidirect
4. C2×C3×#390C2semidirect
5. C2×#4960C2semidirect
6. C2×#4939C2semidirect
7. C2×C4×(C2×D3)⋊C4C2semidirect
8. #71563C2semidirect
9. #71550C2semidirect
46. C2×#390D3semidirect
59. C22×C3×D4D4semidirect
89. C22×D12D4semidirect
96. C22×C4×D3D4semidirect
99. C2×C3×C4⋊C4D4semidirect
119. C2×(C2×D3)⋊C4D4semidirect
122. C2×C4⋊Dic3D4semidirect
125. C2×C4×Dic3D4semidirect
311. C22×D4D12semidirect
333. C2×C4⋊C4#67semidirect
436. C22×D3#127semidirect
477. C2×Dic3#121semidirect
658. C3×C4#392semidirect
861. C4#4960semidirect
862. C3#15124semidirect

Maximal subgroups

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

subgroupindex
C22×#9382
C22×#9402
C22×#8952
C2×C3×#3902
C2×#49602
C2×#49392
C2×C4×(C2×D3)⋊C42
#715632
#715502
#151243