Finite Group Databasebeta

← #873699

Subgroups — #873699

Order 512.

3388 conjugacy classes of subgroups.

The subgroup lattice has 969 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2850C211yesmaximal, characteristic, complemented
2C2×#2542C211yesmaximal, characteristic, complemented
3C2×#2503C211yesmaximal, characteristic, complemented
4C2×#2416C211yesmaximal, characteristic
5#16369C214yesmaximal, complemented
6#15771C214yesmaximal, complemented
7#15399C214yesmaximal, complemented
8#15243C211yesmaximal, characteristic, complemented
9#15236C211yesmaximal, characteristic, complemented
10#15215C211yesmaximal, characteristic, complemented
11#15215C211yesmaximal, characteristic, complemented
12#15215C211yesmaximal, characteristic, complemented
13#15188C211yesmaximal, characteristic, complemented
14#14702C211yesmaximal, characteristic, complemented
15#14363C214yesmaximal, complemented
16#14139C211yesmaximal, characteristic, complemented
17#14050C211yesmaximal, characteristic, complemented
18#14002C211yesmaximal, characteristic, complemented
19C4×#386C211yesmaximal, characteristic, complemented
20C22×C4⋊Q8C2211yescharacteristic
21C22×#124C2211yescharacteristic
22C22×#124C2211yescharacteristic
23C22×C22⋊Q8C2211yescharacteristic
24C22×C22⋊Q8C2211yescharacteristic
25C22×C22⋊Q8C2211yescharacteristic
26C22×C22⋊Q8C2211yescharacteristic
27C22×#121C2212yes—
28C22×#121C2211yescharacteristic
29C22×#121C2211yescharacteristic
30C22×C4×D4C2211yescharacteristic
31C23×C4⋊C4C2211yescharacteristic
32C23×C42C2211yescharacteristic
33#2850—28no—
34#2542—28no—
35#2503—28no—
36#2416—28no—
37C2×#400C2214yes—
38C2×#399C2212yes—
39C2×#399C2212yes—
40C2×#396C2212yes—
41C2×#394C2212yes—
42C2×#391C2211yescharacteristic
43C2×#391C2211yescharacteristic
44C2×#391C2211yescharacteristic
45C2×#391C2211yescharacteristic
46C2×#391C2211yescharacteristic
47C2×#391C2211yescharacteristic
48C2×#390C2211yescharacteristic
49C2×#390C2212yes—
50C2×#390C2211yescharacteristic
51C2×#390C2211yescharacteristic
52C2×#389C2211yescharacteristic
53C2×#388C2214yes—
54C2×#386C2214yes—
55C2×#386C2212yes—
56C2×#386C2212yes—
57C2×#384C2212yes—
58C2×#382C2211yescharacteristic
59C2×#382C2211yescharacteristic
60C2×#381C2214yes—
61C2×#380C2211yescharacteristic
62C2×C4×C4⋊C4C2211yescharacteristic
63C2×C4×C22⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2211yescharacteristic
65C2×C4×C22⋊C4C2211yescharacteristic
66#1443C2214yes—
67#1442C2214yes—
68#1442C2214yes—
69#1441C2214yes—
70#1441C2214yes—
71#1440C2214yes—
72#1440C2214yes—
73#1439C2214yes—
74#1439C2214yes—
75#1439C2214yes—
76#1439C2214yes—
77#1439C2214yes—
78#1438C2214yes—
79#1438C2214yes—
80#1438C2214yes—
81#1437C2214yes—
82#1437C2212yes—
83#1436C2214yes—
84#1436C2214yes—
85#1436C2212yes—
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C22⋊#95C2214yes—
91C22⋊#95C2214yes—
92C22⋊#95C2212yes—
93C4×#95C2211yescharacteristic
94C4×#95C2211yescharacteristic
95C23×Q8C2311yescharacteristic
96C23×Q8C2311yescharacteristic
97C23×D4C2311yescharacteristic
98C23×D4C2312yes—
99C23×D4C2312yes—
100C23×D4C2311yescharacteristic
101C24×C4C2311yescharacteristic
102C24×C4C2311yescharacteristic
103C24×C4C2312yes—
104C24×C4C2312yes—
105C2×C4⋊Q8—24no—
106C2×C4⋊Q8—42no—
107C2×C4⋊Q8—42no—
108C2×#124—24no—
109C2×#124—42no—
110C2×#124—42no—
111C2×#124—42no—
112C2×#124—42no—
113C2×#124—42no—
114C2×C22⋊Q8—24no—
115C2×C22⋊Q8—24no—
116C2×C22⋊Q8—24no—
117C2×C22⋊Q8—24no—
118C2×C22⋊Q8—24no—
119C2×C22⋊Q8—24no—
120C2×C22⋊Q8—24no—
121C2×C22⋊Q8—24no—
122C2×C22⋊Q8—42no—
123C2×C22⋊Q8—42no—
124C2×C22⋊Q8—42no—
125C2×C22⋊Q8—42no—
126C2×#121—28no—
127C2×#121—216no—
128C2×#121—24no—
129C2×#121—24no—
130C2×#121—24no—
131C2×#121—42no—
132C2×#121—42no—
133C2×#121—42no—
134C2×C4×D4—42no—
135C2×C4×D4—42no—
136C2×C4×D4D418yes—
137C22×C4⋊C4—24no—
138C22×C4⋊C4—24no—
139C22×C4⋊C4—42no—
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2312yes—
147C22×C4⋊C4C2312yes—
148C22×C4⋊C4C2311yescharacteristic
149C22×C4⋊C4C2311yescharacteristic
150C22×C4⋊C4C2311yescharacteristic
151C22×C4⋊C4C2312yes—
152C22×C4⋊C4C2312yes—
153C22×C4⋊C4C2311yescharacteristic
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2312yes—
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2312yes—
163C22×C22⋊C4C2314yes—
164C22×C22⋊C4C2312yes—
165C22×C22⋊C4C2312yes—
166C22×C22⋊C4C2314yes—
167C22×C22⋊C4C2312yes—
168C22×C22⋊C4C2314yes—
169C22×C22⋊C4C2314yes—
170C22×C22⋊C4C2311yescharacteristic
171C22×C22⋊C4C2311yescharacteristic
172C22×C42—24no—
173C22×C42—42no—
174C22×C42—42no—
175C22×C42C2311yescharacteristic
176C22×C42C2311yescharacteristic
177C22×C42C2311yescharacteristic
178C22×C42C2311yescharacteristic
179C22×C42C2311yescharacteristic
180C22×C42C2312yes—
181C22×C42C2312yes—
182#400—216no—
183#399—28no—
184#399—28no—
185#396—28no—
186#394—28no—
187#391—24no—
188#391—24no—
189#391—24no—
190#391—42no—
191#391—42no—
192#391—42no—
193#390—28no—
194#390—24no—
195#390—24no—
196#390—24no—
197#389—24no—
198#388—216no—
199#386—28no—
200#386—28no—
201#386—216no—
202#384—28no—
203#382—24no—
204#382D418yescomplemented
205#381—216no—
206#380—24no—
207C4×C4⋊C4—24no—
208C4×C22⋊C4—24no—
209C4×C22⋊C4—42no—
210C4×C22⋊C4—42no—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2314yes—
222C2×#95C2312yes—
223C2×#95C2314yes—
224C2×#95C2314yes—
225C2×#95C2314yes—
226C2×#95C2314yes—
227C2×#95C2312yes—
228C2×#95C2314yes—
229C2×#95C2314yes—
230C2×#95C2312yes—
231C2×#95C2314yes—
232C2×#95C2314yes—
233C25C2412yes—
234C25C2411yescharacteristic
235C25C2411yescharacteristic
236C22×Q8—22no—
237C22×Q8—22no—
238C22×Q8—22no—
239C22×Q8—22no—
240C22×Q8—22no—
241C22×Q8—22no—
242C22×Q8—22no—
243C22×Q8—22no—
244C22×Q8—22no—
245C22×Q8—22no—
246C22×Q8—22no—
247C22×Q8—22no—
248C22×Q8—22no—
249C22×Q8—22no—
250C22×D4—24no—
251C22×D4—24no—
252C22×D4—28no—
253C22×D4—28no—
254C22×D4—22no—
255C22×D4—22no—
256C22×D4—24no—
257C22×D4—22no—
258C22×D4—22no—
259C22×D4—22no—
260C22×D4—22no—
261C22×D4—22no—
262C22×D4—41no—
263C22×D4—41no—
264C22×D4—42no—
265C22×D4—42no—
266C22×D4—42no—
267C22×D4—42no—
268C22×D4—44no—
269C22×D4—44no—
270C22×D4C2×D414yes—
271C22×D4#4118yes—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—24no—
285C23×C4—24no—
286C23×C4—28no—
287C23×C4—24no—
288C23×C4—24no—
289C23×C4—24no—
290C23×C4—42no—
291C23×C4—42no—
292C23×C4—42no—
293C23×C4—42no—
294C23×C4—42no—
295C23×C4—44no—
296C23×C4C2×D414yes—
297C23×C4C2×D414yes—
298C23×C4C2412yes—
299C23×C4C2412yes—
300C23×C4C2412yes—
301C23×C4C2412yes—
302C23×C4C2412yes—
303C23×C4C2412yes—
304C23×C4C2412yes—
305C23×C4C2411yescharacteristic
306C23×C4C2411yescharacteristic
307C23×C4C2411yescharacteristic
308C23×C4C2412yes—
309C23×C4C2412yes—
310C23×C4C2412yes—
311C23×C4C2412yes—
312C23×C4C2411yescharacteristic
313C23×C4C2411yescharacteristic
314C4⋊Q8—416no—
315#124—416no—
316#124—416no—
317C22⋊Q8—416no—
318C22⋊Q8—416no—
319C22⋊Q8—416no—
320C22⋊Q8—416no—
321#121—416no—
322#121—416no—
323#121—432no—
324C4×D4—416no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—28no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—416no—
352C2×C4⋊C4—42no—
353C2×C4⋊C4—41no—
354C2×C4⋊C4—41no—
355C2×C4⋊C4—42no—
356C2×C4⋊C4—42no—
357C2×C4⋊C4—42no—
358C2×C4⋊C4—42no—
359C2×C4⋊C4—42no—
360C2×C4⋊C4—42no—
361C2×C4⋊C4—42no—
362C2×C4⋊C4—42no—
363C2×C4⋊C4C2×D414yes—
364C2×C4⋊C4C2×D414yes—
365C2×C4⋊C4C2×D414yes—
366C2×C4⋊C4#4114yes—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—28no—
373C2×C22⋊C4—24no—
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—28no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—28no—
385C2×C22⋊C4—28no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—28no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—28no—
392C2×C22⋊C4—44no—
393C2×C22⋊C4—42no—
394C2×C22⋊C4—42no—
395C2×C22⋊C4—41no—
396C2×C22⋊C4—41no—
397C2×C22⋊C4—41no—
398C2×C22⋊C4—41no—
399C2×C22⋊C4—42no—
400C2×C22⋊C4—42no—
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—44no—
410C2×C22⋊C4—44no—
411C2×C22⋊C4—42no—
412C2×C22⋊C4—42no—
413C2×C22⋊C4—44no—
414C2×C22⋊C4—44no—
415C2×C22⋊C4—44no—
416C2×C22⋊C4C2×D414yes—
417C2×C22⋊C4C2×D414yes—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—22no—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42—24no—
424C2×C42—24no—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—22no—
430C2×C42—22no—
431C2×C42—22no—
432C2×C42—22no—
433C2×C42—416no—
434C2×C42—42no—
435C2×C42—42no—
436C2×C42—44no—
437C2×C42C2×D414yes—
438C2×C42C2×D414yes—
439#95—24no—
440#95—24no—
441#95—24no—
442#95—28no—
443#95—28no—
444#95—28no—
445#95—28no—
446#95—24no—
447#95—24no—
448#95—24no—
449#95—24no—
450#95—44no—
451#95—44no—
452#95—44no—
453#95—44no—
454#95—42no—
455#95—42no—
456#95—42no—
457#95—44no—
458#95—44no—
459#95—44no—
460#95C2×D4116yes—
461C24—21no—
462C24—21no—
463C24—21no—
464C24—21no—
465C24—21no—
466C24—21no—
467C24—21no—
468C24—21no—
469C24—21no—
470C24—21no—
471C24—21no—
472C24—21no—
473C24—22no—
474C24—22no—
475C24—22no—
476C24—22no—
477C24—22no—
478C24—22no—
479C24—22no—
480C24—22no—
481C24—22no—
482C24—24no—
483C24—22no—
484C24—22no—
485C24—22no—
486C24—22no—
487C24—24no—
488C24—24no—
489C24—24no—
490C24C22×D412yes—
491C24C22×D412yes—
492C24C2×#4114yes—
493C24C2×#4114yes—
494C24C2511yescharacteristic
495C2×Q8—44no—
496C2×Q8—44no—
497C2×Q8—44no—
498C2×Q8—44no—
499C2×Q8—44no—
500C2×Q8—44no—
501C2×Q8—44no—
502C2×Q8—44no—
503C2×Q8—44no—
504C2×Q8—44no—
505C2×Q8—44no—
506C2×Q8—44no—
507C2×Q8—44no—
508C2×Q8—44no—
509C2×D4—44no—
510C2×D4—44no—
511C2×D4—48no—
512C2×D4—48no—
513C2×D4—48no—
514C2×D4—416no—
515C2×D4—48no—
516C2×D4—48no—
517C2×D4—48no—
518C2×D4—48no—
519C2×D4—44no—
520C2×D4—44no—
521C2×D4—44no—
522C2×D4—44no—
523C2×D4—44no—
524C2×D4—44no—
525C2×D4—44no—
526C2×D4—84no—
527C2×D4—88no—
528C2×D4—88no—
529C2×D4—88no—
530C2×D4#124116yescomplemented
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—24no—
545C22×C4—22no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—21no—
560C22×C4—22no—
561C22×C4—21no—
562C22×C4—22no—
563C22×C4—24no—
564C22×C4—22no—
565C22×C4—24no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—24no—
569C22×C4—24no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—24no—
573C22×C4—22no—
574C22×C4—28no—
575C22×C4—28no—
576C22×C4—28no—
577C22×C4—28no—
578C22×C4—28no—
579C22×C4—28no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—24no—
592C22×C4—24no—
593C22×C4—22no—
594C22×C4—22no—
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—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—24no—
615C22×C4—24no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—48no—
619C22×C4—48no—
620C22×C4—48no—
621C22×C4—48no—
622C22×C4—48no—
623C22×C4—48no—
624C22×C4—416no—
625C22×C4—48no—
626C22×C4—48no—
627C22×C4—44no—
628C22×C4—44no—
629C22×C4—44no—
630C22×C4—44no—
631C22×C4—44no—
632C22×C4—44no—
633C22×C4—44no—
634C22×C4—44no—
635C22×C4—48no—
636C22×C4—84no—
637C22×C4—88no—
638C22×C4C22×D414yes—
639C22×C4C22×D412yes—
640C22×C4C22×D414yes—
641C22×C4C22×D414yes—
642C22×C4C22×D412yes—
643C22×C4C22×D412yes—
644C22×C4C22×D412yes—
645C22×C4C22×D412yes—
646C22×C4C22×D412yes—
647C22×C4C2×#4114yes—
648C22×C4C2×#4114yes—
649C22×C4C2×#4112yes—
650C22×C4H(5,𝔽2)12yes—
651C22×C4H(5,𝔽2)12yes—
652C22×C4H(5,𝔽2)12yes—
653C22×C4H(5,𝔽2)12yes—
654C22×C42−1+414yes—
655C4⋊C4—28no—
656C4⋊C4—28no—
657C4⋊C4—28no—
658C4⋊C4—44no—
659C4⋊C4—48no—
660C4⋊C4—48no—
661C4⋊C4—48no—
662C4⋊C4—48no—
663C4⋊C4—48no—
664C4⋊C4—48no—
665C4⋊C4—48no—
666C4⋊C4—48no—
667C4⋊C4—44no—
668C4⋊C4—44no—
669C22⋊C4—44no—
670C22⋊C4—44no—
671C22⋊C4—416no—
672C22⋊C4—48no—
673C22⋊C4—48no—
674C22⋊C4—48no—
675C22⋊C4—48no—
676C22⋊C4—48no—
677C22⋊C4—48no—
678C22⋊C4—48no—
679C22⋊C4—48no—
680C22⋊C4—416no—
681C22⋊C4—48no—
682C22⋊C4—416no—
683C22⋊C4—48no—
684C22⋊C4—48no—
685C22⋊C4—84no—
686C22⋊C4—88no—
687C42—28no—
688C42—28no—
689C42—48no—
690C42—48no—
691C42—44no—
692C42—44no—
693C42—44no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—24no—
703C23—24no—
704C23—24no—
705C23—24no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—24no—
711C23—24no—
712C23—24no—
713C23—24no—
714C23—24no—
715C23—24no—
716C23—24no—
717C23—24no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—41no—
729C23—41no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23—42no—
734C23—42no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—42no—
744C23—42no—
745C23—42no—
746C23—44no—
747C23—44no—
748C23—44no—
749C23—42no—
750C23—42no—
751C23—44no—
752C23—44no—
753C23—44no—
754C23—44no—
755C23—44no—
756C23—42no—
757C23—44no—
758C23—44no—
759C23—44no—
760C23—44no—
761C23C2×#12414yes—
762C23C2×#12414yes—
763C23C23×D411yescharacteristic
764C23C23×D411yescharacteristic
765C23C22×#4112yes—
766C23C22×#4111yescharacteristic
767C23C2×H(5,𝔽2)11yescharacteristic
768C23C2×H(5,𝔽2)11yescharacteristic
769C23C2×H(5,𝔽2)11yescharacteristic
770C23C2×H(5,𝔽2)11yescharacteristic
771C23C2×2−1+412yes—
772C23#58512yes—
773C23#58512yes—
774Q8—88no—
775Q8—88no—
776D4—416no—
777D4—816no—
778D4—816no—
779D4—88no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—24no—
783C2×C4—24no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—22no—
790C2×C4—24no—
791C2×C4—22no—
792C2×C4—24no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—24no—
796C2×C4—28no—
797C2×C4—24no—
798C2×C4—28no—
799C2×C4—24no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—24no—
803C2×C4—28no—
804C2×C4—24no—
805C2×C4—432no—
806C2×C4—42no—
807C2×C4—41no—
808C2×C4—42no—
809C2×C4—41no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—44no—
823C2×C4—42no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—44no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—44no—
833C2×C4—416no—
834C2×C4—416no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—44no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—42no—
860C2×C4—44no—
861C2×C4—44no—
862C2×C4—42no—
863C2×C4—44no—
864C2×C4—42no—
865C2×C4—42no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—42no—
873C2×C4—816no—
874C2×C4C2×#12414yes—
875C2×C4#53414yes—
876C2×C4#53514yes—
877C2×C4#54014yes—
878C2×C4D4214yes—
879C2×C4#54614yes—
880C2×C4#55014yes—
881C2×C4#56014yes—
882C22—24no—
883C22—24no—
884C22—24no—
885C22—24no—
886C22—24no—
887C22—24no—
888C22—42no—
889C22—42no—
890C22—44no—
891C22—44no—
892C22—42no—
893C22—42no—
894C22—44no—
895C22—44no—
896C22—42no—
897C22—42no—
898C22—44no—
899C22—44no—
900C22—42no—
901C22—42no—
902C22—44no—
903C22—44no—
904C22—82no—
905C22—82no—
906C22—84no—
907C22—82no—
908C22—84no—
909C22—82no—
910C22—84no—
911C22—82no—
912C22—82no—
913C22—82no—
914C22—84no—
915C22C22×#12411yescharacteristic
916C22C2×#53411yescharacteristic
917C22C2×#53511yescharacteristic
918C22#344911yescharacteristic
919C22C2×#54011yescharacteristic
920C22C2×D4211yescharacteristic
921C22C2×#54611yescharacteristic
922C22C2×#55011yescharacteristic
923C22D4×#4112yes—
924C22#348212yes—
925C22#348912yes—
926C22#349911yescharacteristic
927C22#350011yescharacteristic
928C22#350512yes—
929C22#350512yes—
930C22#351412yes—
931C22#352012yes—
932C22#352112yes—
933C22C2×#56011yescharacteristic
934C22#353912yes—
935C22#354112yes—
936C22#354712yes—
937C22#355412yes—
938C4—24no—
939C4—44no—
940C4—42no—
941C4—44no—
942C4—42no—
943C4—42no—
944C4—44no—
945C4—44no—
946C4—44no—
947C4—82no—
948C4—82no—
949C4—82no—
950C4—82no—
951C4—82no—
952C4—82no—
953C4#267318yes—
954C2—44no—
955C2—44no—
956C2—162no—
957C2#3501911yescharacteristic
958C2D4×#12411yescharacteristic
959C2#3630311yescharacteristic
960C2#3738811yescharacteristic
961C2#3768011yescharacteristic
962C2#3809211yescharacteristic
963C2#3988712yes—
964C2#4021712yes—
965C2#4561612yes—
966C2C2×#267311yescharacteristic
967C2#5905412yes—
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×#2850C2semidirect
2. C2×#2542C2semidirect
3. C2×#2503C2semidirect
5. #16369C2semidirect
6. #15771C2semidirect
7. #15399C2semidirect
8. #15243C2semidirect
9. #15236C2semidirect
10. #15215C2semidirect
11. #15215C2semidirect
12. #15215C2semidirect
13. #15188C2semidirect
14. #14702C2semidirect
15. #14363C2semidirect
16. #14139C2semidirect
17. #14050C2semidirect
18. #14002C2semidirect
19. C4×#386C2semidirect
204. #382D4semidirect
530. C2×D4#124semidirect

Maximal subgroups

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

subgroupindex
C2×#28502
C2×#25422
C2×#25032
C2×#24162
#163692
#157712
#153992
#152432
#152362
#152152
#151882
#147022
#143632
#141392
#140502
#140022
C4×#3862