Finite Group Databasebeta

← #364487

Subgroups — #364487

Order 512.

2966 conjugacy classes of subgroups.

The subgroup lattice has 837 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#103C211yesmaximal, characteristic, complemented
2C2×#2409C211yesmaximal, characteristic
3C2×D4×C4⋊C4C211yesmaximal, characteristic
4C2×#1872C212yesmaximal, complemented
5C2×#1869C211yesmaximal, characteristic
6C2×#1787C211yesmaximal, characteristic, complemented
7#11050C212yesmaximal, complemented
8#10970C212yesmaximal, complemented
9#10932C212yesmaximal, complemented
10#10730C211yesmaximal, characteristic, complemented
11#10721C211yesmaximal, characteristic, complemented
12C24×Q8C2211yescharacteristic
13C24×C8C2211yescharacteristic
14C22×C22⋊Q8C2212yes—
15C22×C4×D4—21no—
16C22×C4×D4C2211yescharacteristic
17C23×C4⋊C4C2211yescharacteristic
18C23×C4⋊C4C2211yescharacteristic
19C22×#103—28no—
20C22×#103—24no—
21C22×#103C2212yes—
22C22×#103C2212yes—
23C22×#103C2212yes—
24C22×#103C2212yes—
25C22×C22⋊C8C2211yescharacteristic
26C22×C22⋊C8C2212yes—
27#2409—24no—
28#2409C418yescomplemented
29C2×#395—21no—
30C2×#393—21no—
31D4×C4⋊C4—24no—
32D4×C4⋊C4—24no—
33C2×#391C2212yes—
34C2×#389—21no—
35C2×#386—21no—
36C2×#385—21no—
37C2×#385—21no—
38C2×#385—21no—
39C2×#384C2211yescharacteristic
40C2×#380C2211yescharacteristic
41C2×#380C2211yescharacteristic
42C2×#380C2211yescharacteristic
43C2×C4×C4⋊C4C2211yescharacteristic
44#1872—28no—
45#1869—24no—
46#1787—24no—
47C2×#340C2212yes—
48C2×#340C2212yes—
49C2×#340C2212yes—
50C2×#340C2212yes—
51C2×#336C2212yes—
52C23×Q8—21no—
53C23×Q8—22no—
54C23×Q8—24no—
55C23×Q8—24no—
56C23×Q8—22no—
57C23×Q8—22no—
58C23×Q8—22no—
59C23×Q8—22no—
60C23×Q8—42no—
61C23×Q8—42no—
62C23×Q8C2×C414yescomplemented
63C23×Q8C2312yes—
64C23×D4D411yescharacteristic
65C24×C4—21no—
66C24×C4—21no—
67C24×C4—21no—
68C24×C4C2311yescharacteristic
69C24×C4C2311yescharacteristic
70C23×C8—22no—
71C23×C8—24no—
72C23×C8—22no—
73C23×C8—22no—
74C23×C8—42no—
75C23×C8C2312yes—
76C23×C8C2312yes—
77C2×C22⋊Q8—24no—
78C2×C22⋊Q8—24no—
79C2×C22⋊Q8—24no—
80C2×C22⋊Q8—42no—
81C2×C22⋊Q8—42no—
82C2×C22⋊Q8C2×C418yescomplemented
83C2×C4×D4—22no—
84C2×C4×D4—22no—
85C2×C4×D4—22no—
86C2×C4×D4—22no—
87C2×C4×D4—28no—
88C2×C4×D4—44no—
89C2×C4×D4—44no—
90C2×C4×D4C2×C414yes—
91C2×C4×D4D414yes—
92C22×C4⋊C4—24no—
93C22×C4⋊C4—22no—
94C22×C4⋊C4—22no—
95C22×C4⋊C4—21no—
96C22×C4⋊C4—21no—
97C22×C4⋊C4—21no—
98C22×C4⋊C4—21no—
99C22×C4⋊C4—22no—
100C22×C4⋊C4—22no—
101C22×C4⋊C4—24no—
102C22×C4⋊C4—42no—
103C22×C4⋊C4—42no—
104C22×C4⋊C4D411yescharacteristic
105C22×C4⋊C4D414yes—
106C22×C4⋊C4C2312yes—
107C22×C4⋊C4C2311yescharacteristic
108C22×C4⋊C4C2311yescharacteristic
109C22×C4⋊C4C2311yescharacteristic
110C22×C4⋊C4C2311yescharacteristic
111C22×C22⋊C4—22no—
112C22×C22⋊C4—21no—
113C22×C22⋊C4—21no—
114C22×C22⋊C4—21no—
115C22×C22⋊C4D411yescharacteristic
116C22×C22⋊C4D411yescharacteristic
117C22×C42—21no—
118C22×C42C2311yescharacteristic
119C2×#103—232no—
120C2×#103—24no—
121C2×#103—24no—
122C2×#103—24no—
123C2×#103—24no—
124C2×#103—24no—
125C2×#103—24no—
126C2×#103—24no—
127C2×#103—24no—
128C2×#103—24no—
129C2×#103—42no—
130C2×#103—42no—
131C2×#103D418yescomplemented
132C2×C22⋊C8—24no—
133C2×C22⋊C8—22no—
134C2×C22⋊C8—22no—
135C2×C22⋊C8—22no—
136C2×C22⋊C8—24no—
137C2×C22⋊C8—42no—
138#395—28no—
139#393—28no—
140#391—24no—
141#391C2×C418yescomplemented
142#389—28no—
143#386—28no—
144#385—28no—
145#385—28no—
146#385—28no—
147#384—22no—
148#384—22no—
149#380—22no—
150#380—22no—
151#380—22no—
152#380—22no—
153#380C2×C414yescomplemented
154#380D414yes—
155C4×C4⋊C4—22no—
156C4×C4⋊C4—22no—
157C2×#95—21no—
158C2×#95—22no—
159C2×#95—22no—
160C2×#95—21no—
161C2×#95—21no—
162C2×#95—21no—
163#340—24no—
164#340—24no—
165#340—42no—
166#340—42no—
167#336—24no—
168C25C2×D411yescharacteristic
169C25C2×D411yescharacteristic
170C22×Q8—24no—
171C22×Q8—22no—
172C22×Q8—22no—
173C22×Q8—22no—
174C22×Q8—28no—
175C22×Q8—216no—
176C22×Q8—28no—
177C22×Q8—216no—
178C22×Q8—28no—
179C22×Q8—28no—
180C22×Q8—22no—
181C22×Q8—22no—
182C22×Q8—22no—
183C22×Q8—22no—
184C22×Q8—22no—
185C22×Q8—22no—
186C22×Q8—22no—
187C22×Q8—22no—
188C22×Q8—44no—
189C22×Q8—44no—
190C22×Q8—48no—
191C22×Q8—48no—
192C22×Q8—48no—
193C22×Q8—48no—
194C22×Q8—48no—
195C22×Q8—48no—
196C22×Q8—48no—
197C22×Q8—44no—
198C22×Q8—44no—
199C22×Q8—48no—
200C22×Q8—42no—
201C22×Q8—44no—
202C22×Q8—44no—
203C22×Q8—42no—
204C22×Q8C22×C414yes—
205C22×Q8C2×D414yes—
206C22×Q8#4114yes—
207C22×D4—22no—
208C22×D4—22no—
209C22×D4—22no—
210C22×D4—22no—
211C22×D4C22⋊C414yes—
212C22×D4SD1614yes—
213C22×D4Q1614yes—
214C23×C4—22no—
215C23×C4—22no—
216C23×C4—22no—
217C23×C4—22no—
218C23×C4—22no—
219C23×C4—21no—
220C23×C4—21no—
221C23×C4—21no—
222C23×C4—22no—
223C23×C4—21no—
224C23×C4—21no—
225C23×C4—22no—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—24no—
229C23×C4—22no—
230C23×C4—21no—
231C23×C4—21no—
232C23×C4—21no—
233C23×C4—24no—
234C23×C4—24no—
235C23×C4—44no—
236C23×C4—44no—
237C23×C4—44no—
238C23×C4—44no—
239C23×C4—42no—
240C23×C4—42no—
241C23×C4—42no—
242C23×C4—42no—
243C23×C4—42no—
244C23×C4—42no—
245C23×C4—82no—
246C23×C4—82no—
247C23×C4C22×C412yes—
248C23×C4C22×C412yes—
249C23×C4C2×D411yescharacteristic
250C23×C4C2×D411yescharacteristic
251C23×C4C2×D412yes—
252C23×C4C2×D411yescharacteristic
253C23×C4C2×D411yescharacteristic
254C23×C4C2×D412yes—
255C23×C4C2×D412yes—
256C23×C4C2×D412yes—
257C23×C4#4112yes—
258C23×C4#4112yes—
259C23×C4C2411yescharacteristic
260C22×C8—28no—
261C22×C8—22no—
262C22×C8—22no—
263C22×C8—22no—
264C22×C8—22no—
265C22×C8—22no—
266C22×C8—22no—
267C22×C8—22no—
268C22×C8—22no—
269C22×C8—22no—
270C22×C8—22no—
271C22×C8—22no—
272C22×C8—22no—
273C22×C8—22no—
274C22×C8—48no—
275C22×C8—48no—
276C22×C8—44no—
277C22×C8—44no—
278C22×C8C2×D414yes—
279C22⋊Q8—216no—
280C22⋊Q8—48no—
281C22⋊Q8—48no—
282C22⋊Q8—48no—
283C4×D4—28no—
284C4×D4—28no—
285C4×D4—28no—
286C4×D4—28no—
287C4×D4—432no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—28no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—28no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—44no—
313C2×C4⋊C4—48no—
314C2×C4⋊C4—48no—
315C2×C4⋊C4—44no—
316C2×C4⋊C4—44no—
317C2×C4⋊C4—44no—
318C2×C4⋊C4—44no—
319C2×C4⋊C4—44no—
320C2×C4⋊C4—42no—
321C2×C4⋊C4—42no—
322C2×C4⋊C4—44no—
323C2×C4⋊C4—82no—
324C2×C4⋊C4C22⋊C414yes—
325C2×C4⋊C4C22×C414yes—
326C2×C4⋊C4C2×D412yes—
327C2×C4⋊C4C2×D412yes—
328C2×C4⋊C4C2×D412yes—
329C2×C4⋊C4C2×D414yes—
330C2×C4⋊C4C2×D412yes—
331C2×C22⋊C4—22no—
332C2×C22⋊C4—22no—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—28no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—44no—
340C2×C22⋊C4—44no—
341C2×C22⋊C4—42no—
342C2×C22⋊C4—42no—
343C2×C22⋊C4—42no—
344C2×C22⋊C4—42no—
345C2×C22⋊C4—42no—
346C2×C22⋊C4—42no—
347C2×C22⋊C4C22⋊C414yes—
348C2×C22⋊C4C22⋊C414yes—
349C2×C42—21no—
350C2×C42—21no—
351C2×C42—21no—
352C2×C42—21no—
353C2×C42—24no—
354C2×C42—42no—
355C2×C42—42no—
356C2×C42C22×C412yes—
357C2×C42C2×D412yes—
358#103—216no—
359#103—216no—
360#103—48no—
361#103—48no—
362C22⋊C8—48no—
363C22⋊C8—44no—
364#95—24no—
365#95—24no—
366#95—24no—
367#95—28no—
368#95—28no—
369#95—24no—
370C24—22no—
371C24—22no—
372C24—22no—
373C24—22no—
374C24—21no—
375C24—21no—
376C24—22no—
377C24—22no—
378C24—21no—
379C24—21no—
380C24—22no—
381C24—22no—
382C24C2×C22⋊C412yes—
383C24C2×C22⋊C412yes—
384C24#12012yes—
385C24#12312yes—
386C24C2×SD1612yes—
387C24C2×SD1612yes—
388C24C2×Q1612yes—
389C24C2×Q1612yes—
390C24AGL(1,ℤ/8)12yes—
391C24#13712yes—
392C24C22×D411yescharacteristic
393C2×Q8—24no—
394C2×Q8—24no—
395C2×Q8—24no—
396C2×Q8—232no—
397C2×Q8—24no—
398C2×Q8—24no—
399C2×Q8—24no—
400C2×Q8—24no—
401C2×Q8—24no—
402C2×Q8—24no—
403C2×Q8—24no—
404C2×Q8—24no—
405C2×Q8—24no—
406C2×Q8—24no—
407C2×Q8—24no—
408C2×Q8—24no—
409C2×Q8—416no—
410C2×Q8—432no—
411C2×Q8—48no—
412C2×Q8—48no—
413C2×Q8—416no—
414C2×Q8—416no—
415C2×Q8—416no—
416C2×Q8—432no—
417C2×Q8—416no—
418C2×Q8—42no—
419C2×Q8—42no—
420C2×Q8—42no—
421C2×Q8—42no—
422C2×Q8—42no—
423C2×Q8—42no—
424C2×Q8—42no—
425C2×Q8—42no—
426C2×Q8—42no—
427C2×Q8—42no—
428C2×Q8—42no—
429C2×Q8—42no—
430C2×Q8—48no—
431C2×Q8C4×D418yescomplemented
432C2×D4—28no—
433C2×D4—28no—
434C2×D4—28no—
435C2×D4—28no—
436C2×D4—28no—
437C2×D4—28no—
438C2×D4#103116yescomplemented
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—24no—
446C22×C4—24no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—24no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—24no—
453C22×C4—24no—
454C22×C4—24no—
455C22×C4—24no—
456C22×C4—24no—
457C22×C4—24no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—24no—
466C22×C4—24no—
467C22×C4—22no—
468C22×C4—24no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—24no—
475C22×C4—24no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—24no—
479C22×C4—24no—
480C22×C4—24no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—416no—
485C22×C4—48no—
486C22×C4—48no—
487C22×C4—48no—
488C22×C4—48no—
489C22×C4—416no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—41no—
495C22×C4—41no—
496C22×C4—42no—
497C22×C4—48no—
498C22×C4—41no—
499C22×C4—41no—
500C22×C4—42no—
501C22×C4—41no—
502C22×C4—41no—
503C22×C4—42no—
504C22×C4—42no—
505C22×C4—42no—
506C22×C4—42no—
507C22×C4—42no—
508C22×C4—48no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—41no—
515C22×C4—41no—
516C22×C4—41no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—41no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—48no—
528C22×C4—84no—
529C22×C4—84no—
530C22×C4—88no—
531C22×C4—88no—
532C22×C4—88no—
533C22×C4—88no—
534C22×C4C2×C22⋊C412yes—
535C22×C4C2×C22⋊C412yes—
536C22×C4C2×C22⋊C412yes—
537C22×C4C2×C22⋊C412yes—
538C22×C4C4×D414yes—
539C22×C4C4×D414yes—
540C22×C4#12012yes—
541C22×C4#12114yes—
542C22×C4#12114yes—
543C22×C4#12312yes—
544C22×C4C2×SD1612yes—
545C22×C4C2×Q1612yes—
546C22×C4C23×C411yescharacteristic
547C22×C4C22×D411yescharacteristic
548C22×C4C22×D412yes—
549C22×C4C22×D411yescharacteristic
550C22×C4C22×D411yescharacteristic
551C22×C4C2×#4111yescharacteristic
552C22×C4C2×#4111yescharacteristic
553C22×C4C2×#4112yes—
554C22×C4H(5,𝔽2)12yes—
555C22×C4H(5,𝔽2)12yes—
556C2×C8—24no—
557C2×C8—24no—
558C2×C8—24no—
559C2×C8—416no—
560C2×C8—42no—
561C2×C8—42no—
562C2×C8—42no—
563C2×C8—42no—
564C2×C8—42no—
565C2×C8—42no—
566C2×C8—42no—
567C2×C8—42no—
568C2×C8—42no—
569C2×C8—42no—
570C2×C8—42no—
571C4⋊C4—22no—
572C4⋊C4—24no—
573C4⋊C4—28no—
574C4⋊C4—24no—
575C4⋊C4—24no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—24no—
579C4⋊C4—24no—
580C4⋊C4—48no—
581C4⋊C4—416no—
582C4⋊C4—48no—
583C4⋊C4—48no—
584C4⋊C4—41no—
585C4⋊C4—41no—
586C4⋊C4—41no—
587C4⋊C4—41no—
588C4⋊C4—42no—
589C4⋊C4—42no—
590C4⋊C4—42no—
591C4⋊C4—84no—
592C4⋊C4#12014yes—
593C22⋊C4—28no—
594C22⋊C4—28no—
595C22⋊C4—416no—
596C22⋊C4—48no—
597C22⋊C4—48no—
598C22⋊C4—48no—
599C42—22no—
600C42—22no—
601C42—22no—
602C42—22no—
603C42—48no—
604C23—24no—
605C23—24no—
606C23—24no—
607C23—22no—
608C23—22no—
609C23—24no—
610C23—22no—
611C23—24no—
612C23—22no—
613C23—24no—
614C23—24no—
615C23—24no—
616C23—24no—
617C23—24no—
618C23—24no—
619C23—24no—
620C23—22no—
621C23—22no—
622C23—24no—
623C23—22no—
624C23—24no—
625C23—22no—
626C23—22no—
627C23—24no—
628C23—24no—
629C23—24no—
630C23—24no—
631C23—22no—
632C23—42no—
633C23—41no—
634C23—41no—
635C23—42no—
636C23—41no—
637C23—42no—
638C23—41no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23#38614yes—
643C23C2×#10314yes—
644C23C2×#10314yescomplemented
645C23#41714yes—
646C23#45014yes—
647C23#45114yes—
648C23#48314yes—
649C23#48414yes—
650C23C22×C22⋊C411yescharacteristic
651C23C2×#12011yescharacteristic
652C23C2×#12311yescharacteristic
653C23D4212yes—
654C23#54612yes—
655C23C22×SD1611yescharacteristic
656C23C22×Q1611yescharacteristic
657C23C2×AGL(1,ℤ/8)11yescharacteristic
658C23C2×#13711yescharacteristic
659C23#57712yes—
660C23#57812yes—
661Q8—28no—
662Q8—28no—
663Q8—432no—
664Q8—44no—
665Q8—44no—
666Q8—44no—
667Q8—44no—
668Q8—44no—
669Q8—44no—
670D4—232no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—24no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—24no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—24no—
682C2×C4—28no—
683C2×C4—24no—
684C2×C4—28no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—28no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—432no—
694C2×C4—42no—
695C2×C4—44no—
696C2×C4—41no—
697C2×C4—44no—
698C2×C4—41no—
699C2×C4—44no—
700C2×C4—42no—
701C2×C4—44no—
702C2×C4—44no—
703C2×C4—42no—
704C2×C4—41no—
705C2×C4—42no—
706C2×C4—44no—
707C2×C4—41no—
708C2×C4—44no—
709C2×C4—44no—
710C2×C4—42no—
711C2×C4—44no—
712C2×C4—42no—
713C2×C4—44no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—816no—
729C2×C4—816no—
730C2×C4—82no—
731C2×C4—82no—
732C2×C4—82no—
733C2×C4—82no—
734C2×C4—82no—
735C2×C4—82no—
736C2×C4—82no—
737C2×C4—82no—
738C2×C4—82no—
739C2×C4—82no—
740C2×C4#38614yes—
741C2×C4C2×#10314yescomplemented
742C2×C4C2×C4×D411yescharacteristic
743C2×C4C2×C4×D411yescharacteristic
744C2×C4C2×C4×D412yes—
745C2×C4#51812yes—
746C2×C4C2×#12011yescharacteristic
747C2×C4C2×#12111yescharacteristic
748C2×C4C2×#12111yescharacteristic
749C2×C4#52512yes—
750C2×C4#52511yescharacteristic
751C2×C4#53411yescharacteristic
752C2×C4#53511yescharacteristic
753C2×C4#53812yes—
754C2×C4D4212yes—
755C2×C4D4212yes—
756C2×C4#54612yes—
757C2×C4#54612yes—
758C2×C4#54612yes—
759C2×C4#55112yes—
760C8—44no—
761C8—82no—
762C22—28no—
763C22—28no—
764C22—24no—
765C22—24no—
766C22—24no—
767C22—28no—
768C22—28no—
769C22—24no—
770C22—24no—
771C22—24no—
772C22—28no—
773C22—24no—
774C22—44no—
775C22—44no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—44no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22#187218yescomplemented
784C22C2×#38611yescharacteristic
785C22D4×C22⋊C412yes—
786C22#240311yescharacteristic
787C22#240411yescharacteristic
788C22#241812yes—
789C22C22×#10311yescharacteristic
790C22C2×#41711yescharacteristic
791C22#289812yes—
792C22C2×#45011yescharacteristic
793C22C2×#45111yescharacteristic
794C22#300911yescharacteristic
795C22#301111yescharacteristic
796C22C2×#48311yescharacteristic
797C22C2×#48411yescharacteristic
798C22#309712yes—
799C22#326512yes—
800C22#327012yes—
801C22D4×SD1612yes—
802C22D4×Q1612yes—
803C22#329812yes—
804C22#329912yes—
805C22#330812yes—
806C22#331612yes—
807C4—24no—
808C4—24no—
809C4—44no—
810C4—42no—
811C4—48no—
812C4—42no—
813C4—82no—
814C4—82no—
815C4—84no—
816C4—82no—
817C4C4×#12011yescharacteristic
818C4#232111yescharacteristic
819C4#235812yes—
820C4#240811yescharacteristic
821C4#242412yes—
822C4#253411yescharacteristic
823C2—28no—
824C2—44no—
825C2#1396711yescharacteristic
826C2C2×#187211yescharacteristic
827C2#2091311yescharacteristic
828C2D4×#10312yes—
829C2#2242112yes—
830C2#2384911yescharacteristic
831C2#2385611yescharacteristic
832C2#2396111yescharacteristic
833C2#2397011yescharacteristic
834C2#2486312yes—
835C2#2486712yes—
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC23×D4D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C22×C4×D4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C23×#103C2semidirect
4. C2×#1872C2semidirect
6. C2×#1787C2semidirect
7. #11050C2semidirect
8. #10970C2semidirect
9. #10932C2semidirect
10. #10730C2semidirect
11. #10721C2semidirect
28. #2409C4semidirect
62. C23×Q8C2×C4semidirect
82. C2×C22⋊Q8C2×C4semidirect
131. C2×#103D4semidirect
141. #391C2×C4semidirect
153. #380C2×C4semidirect
431. C2×Q8C4×D4semidirect
438. C2×D4#103semidirect
644. C23C2×#103semidirect
741. C2×C4C2×#103semidirect
783. C22#1872semidirect

Maximal subgroups

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

subgroupindex
C23×#1032
C2×#24092
C2×D4×C4⋊C42
C2×#18722
C2×#18692
C2×#17872
#110502
#109702
#109322
#107302
#107212