Finite Group Databasebeta

← #874599

Subgroups — #874599

Order 512.

3652 conjugacy classes of subgroups.

The subgroup lattice has 978 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2503C211yesmaximal, characteristic, complemented
2C2×#2436C211yesmaximal, characteristic, complemented
3C2×#2409C211yesmaximal, characteristic, complemented
4C2×#2416C211yesmaximal, characteristic
5#16882C214yesmaximal, complemented
6#15602C214yesmaximal, complemented
7#15468C214yesmaximal, complemented
8#15237C211yesmaximal, characteristic, complemented
9#15233C211yesmaximal, characteristic, complemented
10#15219C211yesmaximal, characteristic, complemented
11#15217C211yesmaximal, characteristic, complemented
12#15215C211yesmaximal, characteristic, complemented
13#15215C211yesmaximal, characteristic, complemented
14#14708C211yesmaximal, characteristic, complemented
15#14703C211yesmaximal, characteristic, complemented
16#14363C214yesmaximal, complemented
17#14139C211yesmaximal, characteristic, complemented
18#13922C211yesmaximal, characteristic, complemented
19C4×#390C211yesmaximal, characteristic, complemented
20C24×Q8C2211yescharacteristic
21C22×#124C2211yescharacteristic
22C22×#124C2211yescharacteristic
23C22×C22⋊Q8C2211yescharacteristic
24C22×C22⋊Q8C2211yescharacteristic
25C22×#121C2212yes—
26C22×#121C2211yescharacteristic
27C22×#121C2211yescharacteristic
28C22×C4×D4C2211yescharacteristic
29C23×C4⋊C4C2211yescharacteristic
30#2503—28no—
31#2436—28no—
32#2416—28no—
33#2409—28no—
34C2×#400C2214yes—
35C2×#396C2212yes—
36C2×#395C2212yes—
37C2×#394C2212yes—
38C2×#393C2212yes—
39C2×#393C2214yes—
40C2×#391C2211yescharacteristic
41C2×#391C2211yescharacteristic
42C2×#391C2211yescharacteristic
43C2×#391C2211yescharacteristic
44C2×#391C2211yescharacteristic
45C2×#391C2211yescharacteristic
46C2×#391C2211yescharacteristic
47C2×#391C2211yescharacteristic
48C2×#390C2212yes—
49C2×#390C2211yescharacteristic
50C2×#390C2211yescharacteristic
51C2×#390C2211yescharacteristic
52C2×#389C2211yescharacteristic
53C2×#386C2212yes—
54C2×#386C2214yes—
55C2×#386C2212yes—
56C2×#385C2212yes—
57C2×#382C2211yescharacteristic
58C2×#382C2211yescharacteristic
59C2×#381C2214yes—
60C2×#380C2211yescharacteristic
61C2×#380C2211yescharacteristic
62C2×C4×C4⋊C4C2211yescharacteristic
63C2×C4×C22⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2211yescharacteristic
65C2×C4×C22⋊C4C2211yescharacteristic
66C2×C4×C22⋊C4C2211yescharacteristic
67C2×C43C2211yescharacteristic
68#1446C2214yes—
69#1443C2214yes—
70#1443C2214yes—
71#1441C2214yes—
72#1441C2214yes—
73#1440C2214yes—
74#1440C2214yes—
75#1440C2214yes—
76#1439C2214yes—
77#1439C2214yes—
78#1439C2214yes—
79#1438C2214yes—
80#1438C2214yes—
81#1438C2214yes—
82#1437C2214yes—
83#1437C2212yes—
84#1437C2214yes—
85#1437C2212yes—
86#1436C2214yes—
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91C4⋊#95C2212yes—
92#1434C2214yes—
93C22⋊#95C2214yes—
94C22⋊#95C2214yes—
95C23×Q8—24no—
96C23×Q8—24no—
97C23×Q8—24no—
98C23×Q8—42no—
99C23×Q8—42no—
100C23×Q8—42no—
101C23×Q8—42no—
102C23×Q8C2311yescharacteristic
103C23×Q8C2311yescharacteristic
104C23×Q8C2312yes—
105C23×D4C2311yescharacteristic
106C23×D4C2312yes—
107C23×D4C2312yes—
108C23×D4C2311yescharacteristic
109C24×C4C2311yescharacteristic
110C24×C4C2311yescharacteristic
111C24×C4C2312yes—
112C24×C4C2312yes—
113C2×#124—24no—
114C2×#124—24no—
115C2×#124—24no—
116C2×#124—42no—
117C2×#124—42no—
118C2×#124—42no—
119C2×C22⋊Q8—24no—
120C2×C22⋊Q8—24no—
121C2×C22⋊Q8—24no—
122C2×C22⋊Q8—24no—
123C2×C22⋊Q8—42no—
124C2×C22⋊Q8—42no—
125C2×#121—28no—
126C2×#121—216no—
127C2×#121—24no—
128C2×#121—24no—
129C2×#121—24no—
130C2×#121—42no—
131C2×#121—42no—
132C2×#121—42no—
133C2×C4×D4—42no—
134C2×C4×D4—42no—
135C2×C4×D4D418yes—
136C22×C4⋊C4—24no—
137C22×C4⋊C4—24no—
138C22×C4⋊C4—42no—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2311yescharacteristic
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2312yes—
147C22×C4⋊C4C2311yescharacteristic
148C22×C4⋊C4C2312yes—
149C22×C4⋊C4C2311yescharacteristic
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2314yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2312yes—
160C22×C22⋊C4C2314yes—
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2312yes—
163C22×C22⋊C4C2314yes—
164C22×C22⋊C4C2312yes—
165C22×C22⋊C4C2314yes—
166C22×C22⋊C4C2311yescharacteristic
167C22×C22⋊C4C2311yescharacteristic
168C22×C42C2311yescharacteristic
169C22×C42C2311yescharacteristic
170C22×C42C2311yescharacteristic
171C22×C42C2311yescharacteristic
172C22×C42C2311yescharacteristic
173C22×C42C2312yes—
174C22×C42C2312yes—
175#400—216no—
176#396—28no—
177#395—28no—
178#394—28no—
179#393—28no—
180#393—216no—
181#391—24no—
182#391—24no—
183#391—24no—
184#391—24no—
185#391—42no—
186#391—42no—
187#391—42no—
188#391D418yescomplemented
189#390—28no—
190#390—24no—
191#390—42no—
192#390—42no—
193#389—24no—
194#386—28no—
195#386—28no—
196#386—216no—
197#385—28no—
198#382—24no—
199#382—24no—
200#381—216no—
201#380—24no—
202#380—24no—
203C4×C4⋊C4—42no—
204C4×C22⋊C4—24no—
205C4×C22⋊C4—24no—
206C4×C22⋊C4—42no—
207C4×C22⋊C4—42no—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2314yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2314yes—
219C2×#95C2314yes—
220C2×#95C2314yes—
221C2×#95C2314yes—
222C2×#95C2314yes—
223C2×#95C2314yes—
224C2×#95C2314yes—
225C2×#95C2314yes—
226C2×#95C2314yes—
227C2×#95C2312yes—
228C2×#95C2312yes—
229C2×#95C2314yes—
230C2×#95C2312yes—
231C2×#95C2314yes—
232C43—42no—
233C25C2412yes—
234C25C2411yescharacteristic
235C25C2411yescharacteristic
236C22×Q8—22no—
237C22×Q8—22no—
238C22×Q8—22no—
239C22×Q8—24no—
240C22×Q8—24no—
241C22×Q8—22no—
242C22×Q8—24no—
243C22×Q8—22no—
244C22×Q8—22no—
245C22×Q8—22no—
246C22×Q8—22no—
247C22×Q8—22no—
248C22×Q8—22no—
249C22×Q8—22no—
250C22×Q8—22no—
251C22×Q8—42no—
252C22×Q8—42no—
253C22×Q8—42no—
254C22×Q8—42no—
255C22×Q8—416no—
256C22×Q8—416no—
257C22×Q8—416no—
258C22×Q8—416no—
259C22×Q8—416no—
260C22×Q8—416no—
261C22×Q8—416no—
262C22×Q8C2×D414yes—
263C22×Q8#4114yes—
264C22×D4—24no—
265C22×D4—24no—
266C22×D4—28no—
267C22×D4—28no—
268C22×D4—22no—
269C22×D4—22no—
270C22×D4—24no—
271C22×D4—22no—
272C22×D4—22no—
273C22×D4—22no—
274C22×D4—22no—
275C22×D4—22no—
276C22×D4—41no—
277C22×D4—41no—
278C22×D4—42no—
279C22×D4—42no—
280C22×D4—42no—
281C22×D4—42no—
282C22×D4—44no—
283C22×D4—44no—
284C22×D4C2×D414yes—
285C22×D4#4118yes—
286C23×C4—22no—
287C23×C4—22no—
288C23×C4—22no—
289C23×C4—22no—
290C23×C4—22no—
291C23×C4—22no—
292C23×C4—22no—
293C23×C4—22no—
294C23×C4—22no—
295C23×C4—22no—
296C23×C4—22no—
297C23×C4—22no—
298C23×C4—24no—
299C23×C4—24no—
300C23×C4—28no—
301C23×C4—24no—
302C23×C4—24no—
303C23×C4—24no—
304C23×C4—42no—
305C23×C4—42no—
306C23×C4—42no—
307C23×C4—42no—
308C23×C4—42no—
309C23×C4—44no—
310C23×C4C2×D414yes—
311C23×C4C2×D414yes—
312C23×C4C2412yes—
313C23×C4C2412yes—
314C23×C4C2412yes—
315C23×C4C2412yes—
316C23×C4C2412yes—
317C23×C4C2412yes—
318C23×C4C2412yes—
319C23×C4C2411yescharacteristic
320C23×C4C2411yescharacteristic
321C23×C4C2411yescharacteristic
322C23×C4C2412yes—
323C23×C4C2412yes—
324C23×C4C2412yes—
325C23×C4C2412yes—
326C23×C4C2411yescharacteristic
327C23×C4C2411yescharacteristic
328#124—416no—
329#124—416no—
330C22⋊Q8—416no—
331C22⋊Q8—416no—
332#121—416no—
333#121—416no—
334#121—432no—
335C4×D4—416no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—28no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—416no—
360C2×C4⋊C4—42no—
361C2×C4⋊C4—42no—
362C2×C4⋊C4—41no—
363C2×C4⋊C4—41no—
364C2×C4⋊C4—42no—
365C2×C4⋊C4—42no—
366C2×C4⋊C4—42no—
367C2×C4⋊C4C2×D414yes—
368C2×C4⋊C4C2×D414yes—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—28no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—28no—
384C2×C22⋊C4—28no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—28no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—28no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—28no—
394C2×C22⋊C4—42no—
395C2×C22⋊C4—42no—
396C2×C22⋊C4—44no—
397C2×C22⋊C4—41no—
398C2×C22⋊C4—41no—
399C2×C22⋊C4—41no—
400C2×C22⋊C4—41no—
401C2×C22⋊C4—42no—
402C2×C22⋊C4—42no—
403C2×C22⋊C4—42no—
404C2×C22⋊C4—42no—
405C2×C22⋊C4—42no—
406C2×C22⋊C4—44no—
407C2×C22⋊C4—44no—
408C2×C22⋊C4—44no—
409C2×C22⋊C4—42no—
410C2×C22⋊C4—42no—
411C2×C22⋊C4—44no—
412C2×C22⋊C4—44no—
413C2×C22⋊C4—44no—
414C2×C22⋊C4—44no—
415C2×C22⋊C4—44no—
416C2×C22⋊C4—44no—
417C2×C22⋊C4C2×D414yes—
418C2×C22⋊C4C2×D414yes—
419C2×C42—22no—
420C2×C42—22no—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42—24no—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—22no—
430C2×C42—22no—
431C2×C42—22no—
432C2×C42—22no—
433C2×C42—24no—
434C2×C42—42no—
435C2×C42—42no—
436C2×C42—42no—
437C2×C42—42no—
438C2×C42C2×D414yes—
439C2×C42C2×D414yes—
440#95—24no—
441#95—24no—
442#95—24no—
443#95—24no—
444#95—28no—
445#95—28no—
446#95—28no—
447#95—24no—
448#95—24no—
449#95—24no—
450#95—28no—
451#95—24no—
452#95—24no—
453#95—44no—
454#95—44no—
455#95—44no—
456#95—44no—
457#95—42no—
458#95—42no—
459#95—42no—
460#95—44no—
461#95—44no—
462#95—44no—
463#95C2×D4116yes—
464C24—21no—
465C24—21no—
466C24—21no—
467C24—21no—
468C24—21no—
469C24—21no—
470C24—21no—
471C24—21no—
472C24—21no—
473C24—21no—
474C24—21no—
475C24—21no—
476C24—22no—
477C24—22no—
478C24—22no—
479C24—22no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24—22no—
485C24—24no—
486C24—22no—
487C24—22no—
488C24—22no—
489C24—22no—
490C24—24no—
491C24—24no—
492C24—24no—
493C24C22×D412yes—
494C24C22×D412yes—
495C24C2×#4114yes—
496C24C2×#4114yes—
497C24C2511yescharacteristic
498C2×Q8—28no—
499C2×Q8—28no—
500C2×Q8—28no—
501C2×Q8—28no—
502C2×Q8—28no—
503C2×Q8—28no—
504C2×Q8—48no—
505C2×Q8—48no—
506C2×Q8—48no—
507C2×Q8—48no—
508C2×Q8—48no—
509C2×Q8—48no—
510C2×Q8—4128no—
511C2×Q8—48no—
512C2×Q8—44no—
513C2×Q8—44no—
514C2×Q8—44no—
515C2×Q8—44no—
516C2×Q8—44no—
517C2×Q8—44no—
518C2×Q8—44no—
519C2×Q8—44no—
520C2×D4—44no—
521C2×D4—44no—
522C2×D4—48no—
523C2×D4—48no—
524C2×D4—48no—
525C2×D4—416no—
526C2×D4—48no—
527C2×D4—48no—
528C2×D4—48no—
529C2×D4—48no—
530C2×D4—44no—
531C2×D4—44no—
532C2×D4—44no—
533C2×D4—44no—
534C2×D4—44no—
535C2×D4—44no—
536C2×D4—44no—
537C2×D4—84no—
538C2×D4—88no—
539C2×D4—88no—
540C2×D4—88no—
541C2×D4#124116yescomplemented
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—22no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—21no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—24no—
556C22×C4—21no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—21no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—21no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—24no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—28no—
590C22×C4—28no—
591C22×C4—28no—
592C22×C4—28no—
593C22×C4—28no—
594C22×C4—28no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—24no—
606C22×C4—22no—
607C22×C4—24no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—24no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—24no—
622C22×C4—22no—
623C22×C4—24no—
624C22×C4—24no—
625C22×C4—24no—
626C22×C4—24no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—48no—
630C22×C4—48no—
631C22×C4—48no—
632C22×C4—48no—
633C22×C4—48no—
634C22×C4—48no—
635C22×C4—416no—
636C22×C4—48no—
637C22×C4—48no—
638C22×C4—44no—
639C22×C4—44no—
640C22×C4—44no—
641C22×C4—44no—
642C22×C4—44no—
643C22×C4—44no—
644C22×C4—44no—
645C22×C4—44no—
646C22×C4—48no—
647C22×C4—84no—
648C22×C4—88no—
649C22×C4C22×D412yes—
650C22×C4C22×D414yes—
651C22×C4C22×D414yes—
652C22×C4C22×D412yes—
653C22×C4C22×D414yes—
654C22×C4C22×D412yes—
655C22×C4C22×D412yes—
656C22×C4C22×D412yes—
657C22×C4C22×D412yes—
658C22×C4C2×#4114yes—
659C22×C4C2×#4114yes—
660C22×C4C2×#4112yes—
661C22×C4H(5,𝔽2)12yes—
662C22×C4H(5,𝔽2)12yes—
663C22×C4H(5,𝔽2)12yes—
664C22×C4H(5,𝔽2)12yes—
665C22×C42−1+414yes—
666C4⋊C4—28no—
667C4⋊C4—44no—
668C4⋊C4—48no—
669C4⋊C4—48no—
670C4⋊C4—48no—
671C4⋊C4—48no—
672C4⋊C4—48no—
673C4⋊C4—44no—
674C4⋊C4—44no—
675C4⋊C4—44no—
676C4⋊C4—44no—
677C22⋊C4—44no—
678C22⋊C4—44no—
679C22⋊C4—48no—
680C22⋊C4—416no—
681C22⋊C4—48no—
682C22⋊C4—48no—
683C22⋊C4—48no—
684C22⋊C4—48no—
685C22⋊C4—48no—
686C22⋊C4—48no—
687C22⋊C4—48no—
688C22⋊C4—416no—
689C22⋊C4—48no—
690C22⋊C4—48no—
691C22⋊C4—48no—
692C22⋊C4—84no—
693C22⋊C4—88no—
694C22⋊C4—88no—
695C42—28no—
696C42—28no—
697C42—48no—
698C42—48no—
699C42—44no—
700C42—44no—
701C42—44no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—24no—
711C23—24no—
712C23—24no—
713C23—24no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—24no—
719C23—24no—
720C23—24no—
721C23—24no—
722C23—24no—
723C23—24no—
724C23—24no—
725C23—24no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—42no—
733C23—42no—
734C23—42no—
735C23—42no—
736C23—41no—
737C23—41no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—42no—
744C23—42no—
745C23—42no—
746C23—42no—
747C23—42no—
748C23—42no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23—42no—
753C23—42no—
754C23—44no—
755C23—44no—
756C23—44no—
757C23—42no—
758C23—42no—
759C23—44no—
760C23—44no—
761C23—44no—
762C23—44no—
763C23—44no—
764C23—42no—
765C23—44no—
766C23—44no—
767C23—44no—
768C23—44no—
769C23C2×#12414yes—
770C23C2×#12414yes—
771C23C23×D411yescharacteristic
772C23C23×D411yescharacteristic
773C23C22×#4112yes—
774C23C22×#4111yescharacteristic
775C23C2×H(5,𝔽2)11yescharacteristic
776C23C2×H(5,𝔽2)11yescharacteristic
777C23C2×H(5,𝔽2)11yescharacteristic
778C23C2×H(5,𝔽2)11yescharacteristic
779C23C2×2−1+412yes—
780C23#58512yes—
781C23#58512yes—
782Q8—432no—
783Q8—416no—
784Q8—416no—
785D4—416no—
786D4—816no—
787D4—816no—
788D4—88no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—24no—
792C2×C4—24no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—24no—
797C2×C4—24no—
798C2×C4—22no—
799C2×C4—24no—
800C2×C4—24no—
801C2×C4—22no—
802C2×C4—24no—
803C2×C4—24no—
804C2×C4—24no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—24no—
808C2×C4—24no—
809C2×C4—28no—
810C2×C4—24no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—24no—
814C2×C4—24no—
815C2×C4—24no—
816C2×C4—432no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—42no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—41no—
828C2×C4—42no—
829C2×C4—41no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—44no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—416no—
847C2×C4—416no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—42no—
860C2×C4—42no—
861C2×C4—44no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—44no—
865C2×C4—42no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—44no—
871C2×C4—44no—
872C2×C4—44no—
873C2×C4—42no—
874C2×C4—42no—
875C2×C4—44no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—42no—
879C2×C4—44no—
880C2×C4—42no—
881C2×C4—44no—
882C2×C4—816no—
883C2×C4C2×#12414yes—
884C2×C4#53414yes—
885C2×C4#53514yes—
886C2×C4#53814yes—
887C2×C4D4214yes—
888C2×C4#54614yes—
889C2×C4#54614yes—
890C2×C4#56014yes—
891C22—24no—
892C22—24no—
893C22—24no—
894C22—24no—
895C22—24no—
896C22—24no—
897C22—42no—
898C22—42no—
899C22—44no—
900C22—44no—
901C22—42no—
902C22—42no—
903C22—44no—
904C22—44no—
905C22—42no—
906C22—42no—
907C22—44no—
908C22—44no—
909C22—44no—
910C22—44no—
911C22—42no—
912C22—42no—
913C22—82no—
914C22—82no—
915C22—84no—
916C22—82no—
917C22—84no—
918C22—82no—
919C22—84no—
920C22—84no—
921C22—82no—
922C22—82no—
923C22—82no—
924C22C22×#12411yescharacteristic
925C22C2×#53411yescharacteristic
926C22C2×#53511yescharacteristic
927C22#344911yescharacteristic
928C22C2×#53811yescharacteristic
929C22C2×D4211yescharacteristic
930C22C2×#54611yescharacteristic
931C22C2×#54611yescharacteristic
932C22D4×#4112yes—
933C22#348212yes—
934C22#349712yes—
935C22#349911yescharacteristic
936C22#350011yescharacteristic
937C22#350512yes—
938C22#350512yes—
939C22#351412yes—
940C22#352012yes—
941C22#352412yes—
942C22C2×#56011yescharacteristic
943C22#354112yes—
944C22#354712yes—
945C22#355112yes—
946C22#356112yes—
947C4—24no—
948C4—44no—
949C4—42no—
950C4—44no—
951C4—42no—
952C4—42no—
953C4—44no—
954C4—44no—
955C4—44no—
956C4—82no—
957C4—82no—
958C4—82no—
959C4—82no—
960C4—82no—
961C4—82no—
962C4#267818yes—
963C2—44no—
964C2—44no—
965C2—162no—
966C2#3501911yescharacteristic
967C2D4×#12411yescharacteristic
968C2#3630311yescharacteristic
969C2#3738811yescharacteristic
970C2#3894811yescharacteristic
971C2#3935611yescharacteristic
972C2#3995012yes—
973C2#4010412yes—
974C2#4568712yes—
975C2C2×#267811yescharacteristic
976C2#5981312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2416C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2503C2semidirect
2. C2×#2436C2semidirect
3. C2×#2409C2semidirect
5. #16882C2semidirect
6. #15602C2semidirect
7. #15468C2semidirect
8. #15237C2semidirect
9. #15233C2semidirect
10. #15219C2semidirect
11. #15217C2semidirect
12. #15215C2semidirect
13. #15215C2semidirect
14. #14708C2semidirect
15. #14703C2semidirect
16. #14363C2semidirect
17. #14139C2semidirect
18. #13922C2semidirect
19. C4×#390C2semidirect
188. #391D4semidirect
541. C2×D4#124semidirect

Maximal subgroups

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

subgroupindex
C2×#25032
C2×#24362
C2×#24092
C2×#24162
#168822
#156022
#154682
#152372
#152332
#152192
#152172
#152152
#147082
#147032
#143632
#141392
#139222
C4×#3902