Finite Group Databasebeta

← #759747

Subgroups — #759747

Order 512.

4114 conjugacy classes of subgroups.

The subgroup lattice has 1043 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2537C211yesmaximal, characteristic, complemented
2C2×#2414C212yesmaximal, complemented
3C2×C4×#121C211yesmaximal, characteristic, complemented
4C2×C4×#121C211yesmaximal, characteristic, complemented
5C2×#2285C211yesmaximal, characteristic, complemented
6#16512C214yesmaximal, complemented
7#15220C212yesmaximal, complemented
8#15219C212yesmaximal, complemented
9#15129C212yesmaximal, complemented
10#15123C212yesmaximal, complemented
11#14799C214yesmaximal, complemented
12#14151C211yesmaximal, characteristic, complemented
13#13998C212yesmaximal, complemented
14#13974C212yesmaximal, complemented
15#13906C211yesmaximal, characteristic, complemented
16#13906C211yesmaximal, characteristic, complemented
17#13871C212yesmaximal, complemented
18C22×#121C2211yescharacteristic
19C22×#121C2212yes—
20C22×#121C2212yes—
21C22×#121C2211yescharacteristic
22C22×C4×D4C2212yes—
23C22×C4×D4C2211yescharacteristic
24C22×C4×D4C2211yescharacteristic
25C22×C4×D4C2212yes—
26C22×#117C2212yes—
27C23×C42C2211yescharacteristic
28#2537—28no—
29#2414—216no—
30C2×#394C2214yes—
31C2×#394C2214yes—
32C2×#392C2214yes—
33C4×#121—28no—
34C4×#121—28no—
35C2×#390C2212yes—
36C2×#390C2211yescharacteristic
37C2×#390C2214yes—
38C2×#390C2211yescharacteristic
39C2×#390C2212yes—
40C2×#389C2212yes—
41C2×#389C2211yescharacteristic
42C2×#389C2211yescharacteristic
43C2×#389C2212yes—
44C2×#388C2214yes—
45C2×#388C2212yes—
46C2×#388C2212yes—
47C2×#386C2212yes—
48C2×#386C2212yes—
49#2285—28no—
50C2×#384C2211yescharacteristic
51C2×#384C2211yescharacteristic
52C2×#382C2212yes—
53C2×#380C2212yes—
54C2×#380C2212yes—
55C2×#380C2211yescharacteristic
56C2×#380C2212yes—
57C2×#380C2211yescharacteristic
58C2×#380C2212yes—
59C2×#380C2212yes—
60C2×#380C2212yes—
61C2×#380C2212yes—
62C2×#380C2212yes—
63C2×C4×C4⋊C4C2211yescharacteristic
64C2×C4×C4⋊C4C2211yescharacteristic
65C2×C4×C4⋊C4C2212yes—
66C2×C4×C4⋊C4C2212yes—
67C2×C4×C22⋊C4C2212yes—
68C2×C4×C22⋊C4C2212yes—
69#1443C2214yes—
70#1441C2214yes—
71#1441C2214yes—
72#1440C2214yes—
73#1440C2214yes—
74#1440C2214yes—
75#1439C2214yes—
76#1439C2214yes—
77#1439C2214yes—
78#1439C2214yes—
79#1438C2214yes—
80#1438C2214yes—
81#1438C2214yes—
82#1437C2214yes—
83#1436C2214yes—
84C4⋊#95C2212yes—
85C4⋊#95C2212yes—
86C4⋊#95C2212yes—
87C4⋊#95C2212yes—
88C23×D4C2311yescharacteristic
89C23×D4C2311yescharacteristic
90C23×D4C2312yes—
91C23×D4C2314yes—
92C23×D4C2312yes—
93C24×C4C2312yes—
94C24×C4C2312yes—
95C24×C4C2311yescharacteristic
96C24×C4C2311yescharacteristic
97C24×C4C2311yescharacteristic
98C2×#121—24no—
99C2×#121—24no—
100C2×#121—24no—
101C2×#121—24no—
102C2×#121—28no—
103C2×#121—28no—
104C2×#121—28no—
105C2×#121—28no—
106C2×#121—24no—
107C2×#121—44no—
108C2×#121—44no—
109C2×#121D418yescomplemented
110C2×C4×D4—28no—
111C2×C4×D4—28no—
112C2×C4×D4—28no—
113C2×C4×D4—28no—
114C2×C4×D4—24no—
115C2×C4×D4—24no—
116C2×C4×D4—24no—
117C2×C4×D4—24no—
118C2×C4×D4—24no—
119C2×C4×D4—24no—
120C2×C4×D4—44no—
121C2×C4×D4—44no—
122C2×#117—28no—
123C2×#117—28no—
124C2×#117—44no—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2314yes—
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2314yes—
146C22×C22⋊C4C2314yes—
147C22×C22⋊C4C2314yes—
148C22×C22⋊C4C2314yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2314yes—
151C22×C22⋊C4C2314yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2314yes—
157C22×C42—24no—
158C22×C42—24no—
159C22×C42D418yescomplemented
160C22×C42C2312yes—
161C22×C42C2312yes—
162C22×C42C2314yes—
163C22×C42C2311yescharacteristic
164C22×C42C2311yescharacteristic
165C22×C42C2311yescharacteristic
166C22×C42C2311yescharacteristic
167#394—216no—
168#394—216no—
169#392—216no—
170#390—28no—
171#390—216no—
172#390—24no—
173#390—24no—
174#390—44no—
175#389—28no—
176#389—24no—
177#389—24no—
178#389—44no—
179#388—216no—
180#388—28no—
181#388—28no—
182#386—28no—
183#386—28no—
184#384—24no—
185#384D418yescomplemented
186#382—28no—
187#380—24no—
188#380—24no—
189#380—28no—
190#380—28no—
191#380—28no—
192#380—28no—
193#380—28no—
194#380—28no—
195#380—44no—
196#380—44no—
197C4×C4⋊C4—28no—
198C4×C4⋊C4—28no—
199C4×C4⋊C4—24no—
200C4×C4⋊C4—24no—
201C4×C22⋊C4—28no—
202C4×C22⋊C4—28no—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2312yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
219C25C2412yes—
220C25C2412yes—
221C25C2411yescharacteristic
222C22×D4—24no—
223C22×D4—24no—
224C22×D4—24no—
225C22×D4—24no—
226C22×D4—24no—
227C22×D4—24no—
228C22×D4—28no—
229C22×D4—28no—
230C22×D4—22no—
231C22×D4—22no—
232C22×D4—22no—
233C22×D4—22no—
234C22×D4—28no—
235C22×D4—22no—
236C22×D4—22no—
237C22×D4—24no—
238C22×D4—22no—
239C22×D4—22no—
240C22×D4—22no—
241C22×D4—22no—
242C22×D4—22no—
243C22×D4—22no—
244C22×D4—42no—
245C22×D4—42no—
246C22×D4—42no—
247C22×D4—42no—
248C22×D4—42no—
249C22×D4—42no—
250C22×D4—44no—
251C22×D4—44no—
252C22×D4—44no—
253C22×D4—44no—
254C22×D4C2×D414yes—
255C22×D4C2×D418yes—
256C22×D4#4114yes—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—24no—
270C23×C4—24no—
271C23×C4—24no—
272C23×C4—24no—
273C23×C4—24no—
274C23×C4—24no—
275C23×C4—24no—
276C23×C4—24no—
277C23×C4—24no—
278C23×C4—24no—
279C23×C4—24no—
280C23×C4—24no—
281C23×C4—24no—
282C23×C4—24no—
283C23×C4—41no—
284C23×C4—41no—
285C23×C4—41no—
286C23×C4—41no—
287C23×C4C2×D414yes—
288C23×C4C2×D414yes—
289C23×C4C2×D414yes—
290C23×C4C2×D414yes—
291C23×C4#4114yes—
292C23×C4C2412yes—
293C23×C4C2414yes—
294C23×C4C2412yes—
295C23×C4C2412yes—
296C23×C4C2412yes—
297C23×C4C2411yescharacteristic
298C23×C4C2411yescharacteristic
299C23×C4C2412yes—
300C23×C4C2414yes—
301C23×C4C2412yes—
302C23×C4C2411yescharacteristic
303C23×C4C2411yescharacteristic
304C23×C4C2411yescharacteristic
305C23×C4C2411yescharacteristic
306#121—232no—
307#121—232no—
308#121—432no—
309#121—432no—
310C4×D4—432no—
311C4×D4—432no—
312C4×D4—416no—
313C4×D4—416no—
314#117—432no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—28no—
347C2×C4⋊C4—42no—
348C2×C4⋊C4—42no—
349C2×C4⋊C4—42no—
350C2×C4⋊C4—42no—
351C2×C4⋊C4—42no—
352C2×C4⋊C4—42no—
353C2×C4⋊C4—44no—
354C2×C4⋊C4—44no—
355C2×C4⋊C4C2×D418yes—
356C2×C4⋊C4C2×D418yes—
357C2×C4⋊C4C2×D414yes—
358C2×C4⋊C4C2×D418yes—
359C2×C4⋊C4#4114yes—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—28no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—28no—
370C2×C22⋊C4—28no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—28no—
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—28no—
382C2×C22⋊C4—28no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—28no—
389C2×C22⋊C4—28no—
390C2×C22⋊C4—28no—
391C2×C22⋊C4—44no—
392C2×C22⋊C4—42no—
393C2×C22⋊C4—42no—
394C2×C22⋊C4—42no—
395C2×C22⋊C4—42no—
396C2×C22⋊C4—44no—
397C2×C22⋊C4—42no—
398C2×C22⋊C4—42no—
399C2×C22⋊C4—42no—
400C2×C22⋊C4—42no—
401C2×C22⋊C4—44no—
402C2×C22⋊C4—44no—
403C2×C22⋊C4—44no—
404C2×C22⋊C4—44no—
405C2×C22⋊C4—44no—
406C2×C22⋊C4—44no—
407C2×C22⋊C4—44no—
408C2×C22⋊C4—44no—
409C2×C22⋊C4—44no—
410C2×C22⋊C4C2×D418yes—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42—232no—
418C2×C42—28no—
419C2×C42—28no—
420C2×C42—24no—
421C2×C42—24no—
422C2×C42—24no—
423C2×C42—24no—
424C2×C42—24no—
425C2×C42—24no—
426C2×C42—44no—
427C2×C42C2×D414yes—
428C2×C42C2×D414yes—
429C2×C42C2×D414yes—
430C2×C42C2×D414yes—
431C2×C42C2×D414yes—
432C2×C42#4114yes—
433#95—24no—
434#95—24no—
435#95—24no—
436#95—24no—
437#95—28no—
438#95—28no—
439#95—24no—
440#95—24no—
441#95—28no—
442#95—28no—
443#95—28no—
444#95—28no—
445#95—44no—
446#95—44no—
447#95—44no—
448#95—44no—
449C24—21no—
450C24—21no—
451C24—21no—
452C24—21no—
453C24—21no—
454C24—21no—
455C24—21no—
456C24—21no—
457C24—21no—
458C24—21no—
459C24—21no—
460C24—21no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24—22no—
472C24—22no—
473C24—22no—
474C24—22no—
475C24—22no—
476C24—22no—
477C24—22no—
478C24—22no—
479C24—22no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24—22no—
485C24—22no—
486C24—22no—
487C24—22no—
488C24—22no—
489C24C22×D414yes—
490C24C22×D412yes—
491C24C22×D412yes—
492C24C2×#4114yes—
493C24C2×#4112yes—
494C24C2511yescharacteristic
495C2×D4—216no—
496C2×D4—216no—
497C2×D4—28no—
498C2×D4—28no—
499C2×D4—28no—
500C2×D4—28no—
501C2×D4—28no—
502C2×D4—28no—
503C2×D4—48no—
504C2×D4—48no—
505C2×D4—48no—
506C2×D4—48no—
507C2×D4—416no—
508C2×D4—416no—
509C2×D4—48no—
510C2×D4—48no—
511C2×D4—48no—
512C2×D4—48no—
513C2×D4—48no—
514C2×D4—48no—
515C2×D4—48no—
516C2×D4—48no—
517C2×D4—416no—
518C2×D4—44no—
519C2×D4—44no—
520C2×D4—44no—
521C2×D4—44no—
522C2×D4—44no—
523C2×D4—44no—
524C2×D4—44no—
525C2×D4—44no—
526C2×D4—88no—
527C2×D4—88no—
528C2×D4—88no—
529C2×D4—88no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—28no—
539C22×C4—28no—
540C22×C4—28no—
541C22×C4—28no—
542C22×C4—28no—
543C22×C4—28no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—24no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—22no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—24no—
558C22×C4—24no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—24no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—24no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
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—22no—
579C22×C4—22no—
580C22×C4—24no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—24no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—24no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
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—24no—
602C22×C4—24no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—24no—
611C22×C4—24no—
612C22×C4—22no—
613C22×C4—44no—
614C22×C4—44no—
615C22×C4—44no—
616C22×C4—44no—
617C22×C4—44no—
618C22×C4—44no—
619C22×C4—44no—
620C22×C4—44no—
621C22×C4—44no—
622C22×C4—44no—
623C22×C4—48no—
624C22×C4—48no—
625C22×C4—48no—
626C22×C4—48no—
627C22×C4—48no—
628C22×C4—48no—
629C22×C4—48no—
630C22×C4—48no—
631C22×C4—48no—
632C22×C4—48no—
633C22×C4—48no—
634C22×C4—48no—
635C22×C4—48no—
636C22×C4—48no—
637C22×C4#121116yescomplemented
638C22×C4C22×D412yes—
639C22×C4C22×D414yes—
640C22×C4C22×D418yes—
641C22×C4C22×D412yes—
642C22×C4C22×D412yes—
643C22×C4C22×D412yes—
644C22×C4C22×D412yes—
645C22×C4C22×D412yes—
646C22×C4C22×D412yes—
647C22×C4C22×D412yes—
648C22×C4C22×D412yes—
649C22×C4C22×D412yes—
650C22×C4C22×D412yes—
651C22×C4C2×#4114yes—
652C22×C4C2×#4112yes—
653C22×C4C2×#4112yes—
654C22×C4C2×#4112yes—
655C22×C4C2×#4112yes—
656C22×C4C2×#4112yes—
657C22×C4C2×#4112yes—
658C22×C4C2×#4112yes—
659C22×C4H(5,𝔽2)12yes—
660C22×C4H(5,𝔽2)12yes—
661C22×C4H(5,𝔽2)12yes—
662C22×C42−1+412yes—
663C4⋊C4—28no—
664C4⋊C4—28no—
665C4⋊C4—216no—
666C4⋊C4—216no—
667C4⋊C4—48no—
668C4⋊C4—48no—
669C4⋊C4—48no—
670C4⋊C4—48no—
671C4⋊C4—44no—
672C4⋊C4—44no—
673C4⋊C4—44no—
674C4⋊C4—44no—
675C4⋊C4—48no—
676C4⋊C4—48no—
677C4⋊C4—88no—
678C22⋊C4—216no—
679C22⋊C4—216no—
680C22⋊C4—416no—
681C22⋊C4—416no—
682C22⋊C4—416no—
683C22⋊C4—416no—
684C22⋊C4—48no—
685C22⋊C4—48no—
686C22⋊C4—48no—
687C22⋊C4—48no—
688C22⋊C4—48no—
689C22⋊C4—48no—
690C22⋊C4—48no—
691C22⋊C4—48no—
692C22⋊C4—88no—
693C22⋊C4—88no—
694C22⋊C4—88no—
695C42—28no—
696C42—28no—
697C42—28no—
698C42—416no—
699C42—48no—
700C42—48no—
701C42#121116yes—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—24no—
721C23—24no—
722C23—24no—
723C23—24no—
724C23—24no—
725C23—24no—
726C23—24no—
727C23—24no—
728C23—24no—
729C23—24no—
730C23—24no—
731C23—24no—
732C23—24no—
733C23—24no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—42no—
751C23—42no—
752C23—42no—
753C23—42no—
754C23—42no—
755C23—42no—
756C23—42no—
757C23—42no—
758C23—42no—
759C23—42no—
760C23—42no—
761C23—42no—
762C23—42no—
763C23—42no—
764C23—42no—
765C23—42no—
766C23—42no—
767C23—42no—
768C23—42no—
769C23—42no—
770C23—42no—
771C23—42no—
772C23—42no—
773C23—42no—
774C23—42no—
775C23—42no—
776C23—42no—
777C23—42no—
778C23—42no—
779C23—42no—
780C23—42no—
781C23—42no—
782C23—42no—
783C23—42no—
784C23—42no—
785C23—42no—
786C23—42no—
787C23—42no—
788C23—42no—
789C23—42no—
790C23—42no—
791C23—42no—
792C23—42no—
793C23—42no—
794C23—42no—
795C23—42no—
796C23—42no—
797C23—42no—
798C23—42no—
799C23—42no—
800C23—42no—
801C23—42no—
802C23—42no—
803C23—42no—
804C23—42no—
805C23—42no—
806C23C2×#12114yes—
807C23C23×D411yescharacteristic
808C23C23×D411yescharacteristic
809C23C23×D411yescharacteristic
810C23C22×#4111yescharacteristic
811C23C22×#4111yescharacteristic
812C23C22×#4111yescharacteristic
813C23C22×#4111yescharacteristic
814C23C2×H(5,𝔽2)11yescharacteristic
815C23C2×H(5,𝔽2)11yescharacteristic
816C23C2×H(5,𝔽2)11yescharacteristic
817C23C2×2−1+411yescharacteristic
818C23#58511yescharacteristic
819C23#58511yescharacteristic
820C23#58511yescharacteristic
821C23#58511yescharacteristic
822D4—432no—
823D4—432no—
824D4—416no—
825D4—416no—
826D4—832no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—232no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—24no—
843C2×C4—22no—
844C2×C4—24no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—28no—
849C2×C4—28no—
850C2×C4—24no—
851C2×C4—24no—
852C2×C4—28no—
853C2×C4—24no—
854C2×C4—24no—
855C2×C4—416no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—42no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—42no—
863C2×C4—44no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—42no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—44no—
872C2×C4—42no—
873C2×C4—42no—
874C2×C4—44no—
875C2×C4—44no—
876C2×C4—416no—
877C2×C4—42no—
878C2×C4—42no—
879C2×C4—42no—
880C2×C4—42no—
881C2×C4—42no—
882C2×C4—42no—
883C2×C4—42no—
884C2×C4—42no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—44no—
890C2×C4—42no—
891C2×C4—42no—
892C2×C4—42no—
893C2×C4—42no—
894C2×C4—44no—
895C2×C4—42no—
896C2×C4—44no—
897C2×C4—42no—
898C2×C4—42no—
899C2×C4—42no—
900C2×C4—44no—
901C2×C4—42no—
902C2×C4—44no—
903C2×C4—42no—
904C2×C4—42no—
905C2×C4—42no—
906C2×C4—44no—
907C2×C4—42no—
908C2×C4—44no—
909C2×C4—42no—
910C2×C4—42no—
911C2×C4—42no—
912C2×C4—816no—
913C2×C4—816no—
914C2×C4C2×#12114yes—
915C2×C4C2×#12114yes—
916C2×C4C2×#12114yes—
917C2×C4C2×#12114yes—
918C2×C4C2×#12114yes—
919C2×C4#52514yes—
920C2×C4#53514yes—
921C2×C4#53714yes—
922C2×C4D4214yes—
923C2×C4#54614yes—
924C2×C4#54714yes—
925C2×C4#54814yes—
926C2×C4#55014yes—
927C2×C4#55314yes—
928C2×C4#55314yes—
929C2×C4#55514yes—
930C22—24no—
931C22—24no—
932C22—24no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22—42no—
945C22—44no—
946C22—44no—
947C22—44no—
948C22—44no—
949C22—44no—
950C22—44no—
951C22—44no—
952C22—44no—
953C22—44no—
954C22—44no—
955C22—44no—
956C22—44no—
957C22—44no—
958C22—44no—
959C22—82no—
960C22—82no—
961C22—82no—
962C22—82no—
963C22—82no—
964C22—82no—
965C22—82no—
966C22—82no—
967C22—82no—
968C22—82no—
969C22—82no—
970C22—82no—
971C22—82no—
972C22—82no—
973C22—82no—
974C22—82no—
975C22C22×#12111yescharacteristic
976C22C22×#12111yescharacteristic
977C22C2×#52511yescharacteristic
978C22C2×#53511yescharacteristic
979C22C2×#53711yescharacteristic
980C22#344911yescharacteristic
981C22#344911yescharacteristic
982C22C2×D4211yescharacteristic
983C22C2×#54611yescharacteristic
984C22C2×#54711yescharacteristic
985C22C2×#54811yescharacteristic
986C22C2×#55011yescharacteristic
987C22D4×#4111yescharacteristic
988C22D4×#4111yescharacteristic
989C22C2×#55311yescharacteristic
990C22C2×#55311yescharacteristic
991C22C2×#55511yescharacteristic
992C22#347511yescharacteristic
993C22#347511yescharacteristic
994C22#348511yescharacteristic
995C22#348711yescharacteristic
996C22#349311yescharacteristic
997C22#349311yescharacteristic
998C22#349611yescharacteristic
999C22#349611yescharacteristic
1000C22#350611yescharacteristic
1001C22#350611yescharacteristic
1002C22#351411yescharacteristic
1003C22#351511yescharacteristic
1004C22#351711yescharacteristic
1005C22#351811yescharacteristic
1006C22#354611yescharacteristic
1007C22#354611yescharacteristic
1008C22#354711yescharacteristic
1009C22#354711yescharacteristic
1010C4—24no—
1011C4—24no—
1012C4—42no—
1013C4—44no—
1014C4—44no—
1015C4—42no—
1016C4—48no—
1017C4—82no—
1018C4—82no—
1019C4—82no—
1020C4—84no—
1021C4—82no—
1022C4#241418yescomplemented
1023C4#241618yes—
1024C2—44no—
1025C2—84no—
1026C2—84no—
1027C2C2×#241611yescharacteristic
1028C2C2×#241411yescharacteristic
1029C2#3493511yescharacteristic
1030C2#3515011yescharacteristic
1031C2#3516511yescharacteristic
1032C2#3518911yescharacteristic
1033C2#3762111yescharacteristic
1034C2#5903411yescharacteristic
1035C2#5903511yescharacteristic
1036C2#5905011yescharacteristic
1037C2#5905111yescharacteristic
1038C2#5921211yescharacteristic
1039C2#5921311yescharacteristic
1040C2#5922811yescharacteristic
1041C2#5922911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
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×#2537C2semidirect
2. C2×#2414C2semidirect
3. C2×C4×#121C2semidirect
4. C2×C4×#121C2semidirect
5. C2×#2285C2semidirect
6. #16512C2semidirect
7. #15220C2semidirect
8. #15219C2semidirect
9. #15129C2semidirect
10. #15123C2semidirect
11. #14799C2semidirect
12. #14151C2semidirect
13. #13998C2semidirect
14. #13974C2semidirect
15. #13906C2semidirect
16. #13906C2semidirect
17. #13871C2semidirect
109. C2×#121D4semidirect
159. C22×C42D4semidirect
185. #384D4semidirect
637. C22×C4#121semidirect
1022. C4#2414semidirect

Maximal subgroups

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

subgroupindex
C2×#25372
C2×#24142
C2×C4×#1212
C2×#22852
#165122
#152202
#152192
#151292
#151232
#147992
#141512
#139982
#139742
#139062
#138712