Finite Group Databasebeta

← #657012

Subgroups — #657012

Order 512.

4768 conjugacy classes of subgroups.

The subgroup lattice has 963 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2848C211yesmaximal, characteristic, complemented
2C2×#2502C211yesmaximal, characteristic, complemented
3C2×#2487C211yesmaximal, characteristic, complemented
4C2×#2417C211yesmaximal, characteristic, complemented
5C2×C4×#120C211yesmaximal, characteristic
6C22×#380C211yesmaximal, characteristic, complemented
7#15513C214yesmaximal, complemented
8#15505C214yesmaximal, complemented
9#15177C212yesmaximal, complemented
10#15135C212yesmaximal, complemented
11#14946C212yesmaximal, complemented
12#14734C212yesmaximal, complemented
13#13997C212yesmaximal, complemented
14#13995C212yesmaximal
15#13965C212yesmaximal, complemented
16#13906C212yesmaximal, complemented
17C22⋊C4×C4⋊C4C211yesmaximal, characteristic, complemented
18C25×C4C2211yescharacteristic
19C22×C22⋊Q8C2211yescharacteristic
20C22×C22⋊Q8C2212yes—
21C22×C22⋊Q8C2211yescharacteristic, complemented
22C22×#120C2211yescharacteristic
23C22×C4×D4C2211yescharacteristic
24C22×C4×D4C2212yes—
25C23×C4⋊C4C2211yescharacteristic
26C23×C4⋊C4C2211yescharacteristic
27C23×C22⋊C4C2212yes—
28#2848—28no—
29#2502—28no—
30#2487—28no—
31#2417—28no—
32C2×#400C2212yescomplemented
33C2×#399C2214yes—
34C2×#399C2212yescomplemented
35C2×#398C2212yescomplemented
36C2×#398C2214yescomplemented
37C2×#396C2212yescomplemented
38C4×#120—28no—
39C2×#391C2212yescomplemented
40C2×#391C2211yescharacteristic, complemented
41C2×#390C2214yes—
42C2×#389C2211yescharacteristic, complemented
43C2×#389C2212yescomplemented
44C2×#386C2211yescharacteristic
45C2×#386C2212yes—
46C2×#386C2212yes—
47C2×#386C2212yes—
48C2×#385C2212yes—
49C2×#385C2214yes—
50C2×#385C2212yes—
51C2×#385C2211yescharacteristic
52C2×#385C2212yes—
53C2×#385C2212yes—
54C2×#385C2212yes—
55C2×#384C2212yescomplemented
56C2×#380—28no—
57C2×#380C2212yes—
58C2×#380C2212yes—
59C2×#380C2212yes—
60C2×#380C2212yes—
61C2×#380C2214yes—
62C2×#380C2211yescharacteristic
63C2×#380C2212yescomplemented
64C2×#380C2211yescharacteristic, complemented
65C2×#379C2212yes—
66C2×#379C2211yescharacteristic
67C2×C4×C4⋊C4C2212yescomplemented
68C2×C4×C22⋊C4C2212yes—
69C2×C4×C22⋊C4C2212yes—
70C2×C4×C22⋊C4C2211yescharacteristic
71C22×#95C2212yes—
72#1445C2214yescomplemented
73#1445C2214yescomplemented
74#1444C2214yescomplemented
75#1444C2214yescomplemented
76#1439C2214yes—
77#1439C2214yes—
78#1439C2214yes—
79#1439C2214yes—
80#1439C2214yescomplemented
81#1439C2214yescomplemented
82#1438C2214yes—
83#1437C2214yes—
84#1436C2214yescomplemented
85C4⋊#95C2212yescomplemented
86C4⋊#95C2214yescomplemented
87C4⋊#95C2214yescomplemented
88C22⋊#95C2212yes—
89C26C2311yescharacteristic
90C23×Q8C2311yescharacteristic
91C23×D4C2311yescharacteristic
92C23×D4C2312yes—
93C24×C4—24no—
94C24×C4—28no—
95C24×C4—24no—
96C24×C4—24no—
97C24×C4—44no—
98C24×C4C2311yescharacteristic
99C24×C4C2312yes—
100C24×C4C2311yescharacteristic
101C24×C4C2312yes—
102C24×C4C2311yescharacteristic
103C24×C4C2312yes—
104C24×C4C2312yes—
105C2×C22⋊Q8—24no—
106C2×C22⋊Q8—24no—
107C2×C22⋊Q8—24no—
108C2×C22⋊Q8—28no—
109C2×C22⋊Q8—28no—
110C2×C22⋊Q8—24no—
111C2×C22⋊Q8—44no—
112C2×C22⋊Q8—44no—
113C2×#120—24no—
114C2×#120—24no—
115C2×#120Q818yescomplemented
116C2×C4×D4—24no—
117C2×C4×D4—24no—
118C2×C4×D4—24no—
119C2×C4×D4—28no—
120C2×C4×D4—28no—
121C2×C4×D4—44no—
122C22×C4⋊C4—24no—
123C22×C4⋊C4—24no—
124C22×C4⋊C4—24no—
125C22×C4⋊C4—44no—
126C22×C4⋊C4D418yescomplemented
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2314yes—
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2314yes—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2314yes—
141C22×C4⋊C4C2314yes—
142C22×C4⋊C4C2312yes—
143C22×C22⋊C4—28no—
144C22×C22⋊C4—48no—
145C22×C22⋊C4C2311yescharacteristic
146C22×C22⋊C4C2311yescharacteristic
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2314yes—
150C22×C22⋊C4C2314yes—
151C22×C22⋊C4C2314yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2314yes—
155C22×C22⋊C4C2311yescharacteristic
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2312yes—
160C22×C22⋊C4C2314yes—
161C22×C22⋊C4C2311yescharacteristic
162C22×C42C2311yescharacteristic
163C22×C42C2312yes—
164C22×C42C2314yes—
165#400—28no—
166#399—28no—
167#399—48no—
168#398—28no—
169#398—216no—
170#396—28no—
171#391—24no—
172#391—28no—
173#390—48no—
174#389—24no—
175#389—28no—
176#386—28no—
177#386—28no—
178#386—24no—
179#386—28no—
180#385—28no—
181#385—28no—
182#385—28no—
183#385—28no—
184#385—24no—
185#385—216no—
186#385—28no—
187#384—28no—
188#380—28no—
189#380—28no—
190#380—24no—
191#380—28no—
192#380—28no—
193#380—28no—
194#380—216no—
195#380D418yescomplemented
196#379—28no—
197#379—24no—
198C4×C4⋊C4—44no—
199C4×C22⋊C4—28no—
200C4×C22⋊C4—28no—
201C4×C22⋊C4D418yes—
202C2×#95—28no—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2314yes—
206C2×#95C2312yes—
207C2×#95C2314yes—
208C2×#95C2312yes—
209C2×#95C2314yes—
210C2×#95C2314yes—
211C2×#95C2314yes—
212C2×#95C2312yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2312yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C25—22no—
222C25—24no—
223C25—24no—
224C25—22no—
225C25—22no—
226C25—22no—
227C25—22no—
228C25—22no—
229C25—42no—
230C25—42no—
231C25C2×Q814yes—
232C25C2411yescharacteristic
233C25C2412yes—
234C25C2411yescharacteristic
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8—22no—
238C22×Q8—24no—
239C22×Q8—24no—
240C22×D4—22no—
241C22×D4—22no—
242C22×D4—22no—
243C22×D4—24no—
244C22×D4—22no—
245C22×D4—24no—
246C22×D4—22no—
247C22×D4—22no—
248C22×D4—24no—
249C22×D4—24no—
250C22×D4—42no—
251C22×D4—42no—
252C22×D4C2×Q814yes—
253C22×D4C2×Q818yes—
254C23×C4—24no—
255C23×C4—24no—
256C23×C4—232no—
257C23×C4—22no—
258C23×C4—24no—
259C23×C4—24no—
260C23×C4—24no—
261C23×C4—24no—
262C23×C4—24no—
263C23×C4—24no—
264C23×C4—24no—
265C23×C4—24no—
266C23×C4—24no—
267C23×C4—24no—
268C23×C4—24no—
269C23×C4—24no—
270C23×C4—24no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—24no—
274C23×C4—24no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—24no—
279C23×C4—24no—
280C23×C4—24no—
281C23×C4—24no—
282C23×C4—42no—
283C23×C4—42no—
284C23×C4—42no—
285C23×C4—432no—
286C23×C4—432no—
287C23×C4—44no—
288C23×C4—44no—
289C23×C4—44no—
290C23×C4—44no—
291C23×C4—416no—
292C23×C4—416no—
293C23×C4C2×D414yes—
294C23×C4C2×D414yes—
295C23×C4C2×D414yes—
296C23×C4C2×D418yes—
297C23×C4#4118yes—
298C23×C4C2412yes—
299C23×C4C2411yescharacteristic
300C23×C4C2412yes—
301C23×C4C2411yescharacteristic
302C23×C4C2414yes—
303C23×C4C2414yes—
304C23×C4C2412yes—
305C23×C4C2412yes—
306C23×C4C2412yes—
307C23×C4C2411yescharacteristic
308C23×C4C2412yes—
309C23×C4C2411yescharacteristic
310C23×C4C2412yes—
311C23×C4C2411yescharacteristic
312C22⋊Q8—432no—
313C22⋊Q8—416no—
314C22⋊Q8—416no—
315#120—232no—
316C4×D4—432no—
317C4×D4—416no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—28no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—28no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—28no—
344C2×C4⋊C4—28no—
345C2×C4⋊C4—28no—
346C2×C4⋊C4—416no—
347C2×C4⋊C4—44no—
348C2×C4⋊C4—42no—
349C2×C4⋊C4—44no—
350C2×C4⋊C4—44no—
351C2×C4⋊C4—416no—
352C2×C4⋊C4—44no—
353C2×C4⋊C4—44no—
354C2×C4⋊C4—44no—
355C2×C4⋊C4—44no—
356C2×C4⋊C4—44no—
357C2×C4⋊C4—44no—
358C2×C4⋊C4—44no—
359C2×C4⋊C4C2×D414yes—
360C2×C4⋊C4C2×D414yes—
361C2×C4⋊C4C2×D418yes—
362C2×C4⋊C4C2×D418yes—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—28no—
377C2×C22⋊C4—28no—
378C2×C22⋊C4—28no—
379C2×C22⋊C4—28no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—28no—
382C2×C22⋊C4—28no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—28no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—28no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—28no—
395C2×C22⋊C4—44no—
396C2×C22⋊C4—44no—
397C2×C22⋊C4—44no—
398C2×C22⋊C4—42no—
399C2×C22⋊C4—42no—
400C2×C22⋊C4—42no—
401C2×C22⋊C4—44no—
402C2×C22⋊C4—44no—
403C2×C22⋊C4—432no—
404C2×C22⋊C4—44no—
405C2×C22⋊C4—44no—
406C2×C22⋊C4—44no—
407C2×C22⋊C4C2×D414yes—
408C2×C22⋊C4C2×D418yes—
409C2×C22⋊C4C2×D414yes—
410C2×C22⋊C4C2×Q818yes—
411C2×C22⋊C4C2×Q814yes—
412C2×C22⋊C4#4114yes—
413C2×C42—24no—
414C2×C42—24no—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—28no—
419C2×C42—44no—
420C2×C42—44no—
421C2×C42C2×D418yes—
422#95—28no—
423#95—28no—
424#95—24no—
425#95—24no—
426#95—24no—
427#95—28no—
428#95—28no—
429#95—24no—
430#95—28no—
431#95—28no—
432#95—24no—
433#95—28no—
434#95—24no—
435#95—28no—
436#95—44no—
437#95—44no—
438#95C2×D418yes—
439#95C2×D418yes—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—28no—
445C24—28no—
446C24—216no—
447C24—28no—
448C24—216no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—28no—
462C24—28no—
463C24—21no—
464C24—21no—
465C24—21no—
466C24—22no—
467C24—21no—
468C24—22no—
469C24—22no—
470C24—21no—
471C24—21no—
472C24—22no—
473C24—48no—
474C24—48no—
475C24—48no—
476C24—48no—
477C24—48no—
478C24—48no—
479C24—48no—
480C24—48no—
481C24—48no—
482C24—44no—
483C24—44no—
484C24—48no—
485C24—44no—
486C24—44no—
487C24—44no—
488C24—44no—
489C24C22×D412yes—
490C24C22×D412yes—
491C24C22×D412yes—
492C24C22×Q812yes—
493C24C22×Q814yes—
494C24C22×Q812yes—
495C24C2×#4114yes—
496C24C2×#4112yes—
497C24H(5,𝔽2)14yes—
498C242−1+412yes—
499C242−1+412yes—
500C24C2511yescharacteristic
501C2×Q8—44no—
502C2×Q8—44no—
503C2×Q8—44no—
504C2×Q8—48no—
505C2×Q8—48no—
506C2×D4—28no—
507C2×D4—28no—
508C2×D4—28no—
509C2×D4—216no—
510C2×D4—216no—
511C2×D4—48no—
512C2×D4—48no—
513C2×D4—48no—
514C2×D4—48no—
515C2×D4—48no—
516C2×D4—44no—
517C2×D4—44no—
518C2×D4—44no—
519C2×D4—44no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—28no—
527C22×C4—28no—
528C22×C4—216no—
529C22×C4—216no—
530C22×C4—216no—
531C22×C4—28no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—22no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—24no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—21no—
543C22×C4—24no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—24no—
548C22×C4—24no—
549C22×C4—24no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—24no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—24no—
563C22×C4—22no—
564C22×C4—216no—
565C22×C4—216no—
566C22×C4—216no—
567C22×C4—216no—
568C22×C4—21no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—24no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—24no—
585C22×C4—24no—
586C22×C4—24no—
587C22×C4—24no—
588C22×C4—22no—
589C22×C4—24no—
590C22×C4—22no—
591C22×C4—24no—
592C22×C4—22no—
593C22×C4—24no—
594C22×C4—24no—
595C22×C4—48no—
596C22×C4—48no—
597C22×C4—48no—
598C22×C4—48no—
599C22×C4—48no—
600C22×C4—48no—
601C22×C4—48no—
602C22×C4—48no—
603C22×C4—48no—
604C22×C4—4128no—
605C22×C4—44no—
606C22×C4—44no—
607C22×C4—48no—
608C22×C4—48no—
609C22×C4—48no—
610C22×C4—48no—
611C22×C4—48no—
612C22×C4—48no—
613C22×C4—48no—
614C22×C4—48no—
615C22×C4—44no—
616C22×C4—44no—
617C22×C4—44no—
618C22×C4—48no—
619C22×C4—48no—
620C22×C4—88no—
621C22×C4—88no—
622C22×C4—88no—
623C22×C4—88no—
624C22×C4#127116yes—
625C22×C4C22×D414yes—
626C22×C4C22×D414yes—
627C22×C4C22×D418yes—
628C22×C4C22×D414yes—
629C22×C4C22×D414yes—
630C22×C4C22×D412yes—
631C22×C4C22×D412yes—
632C22×C4C22×D412yes—
633C22×C4C22×D412yes—
634C22×C4C22×D412yes—
635C22×C4C22×D412yes—
636C22×C4C22×Q812yes—
637C22×C4C22×Q814yes—
638C22×C4C2×#4114yes—
639C22×C4C2×#4114yes—
640C22×C4C2×#4114yes—
641C22×C4H(5,𝔽2)14yes—
642C4⋊C4—28no—
643C4⋊C4—28no—
644C4⋊C4—216no—
645C4⋊C4—48no—
646C4⋊C4—48no—
647C4⋊C4—416no—
648C4⋊C4—48no—
649C4⋊C4—48no—
650C4⋊C4—48no—
651C4⋊C4—44no—
652C4⋊C4—44no—
653C4⋊C4—48no—
654C4⋊C4—88no—
655C4⋊C4—84no—
656C4⋊C4—88no—
657C4⋊C4—88no—
658C22⋊C4—28no—
659C22⋊C4—216no—
660C22⋊C4—216no—
661C22⋊C4—48no—
662C22⋊C4—416no—
663C22⋊C4—48no—
664C22⋊C4—416no—
665C22⋊C4—416no—
666C22⋊C4—48no—
667C22⋊C4—416no—
668C22⋊C4—48no—
669C22⋊C4—44no—
670C22⋊C4—48no—
671C22⋊C4—44no—
672C22⋊C4—84no—
673C22⋊C4—88no—
674C22⋊C4C22⋊Q8116yescomplemented
675C42—216no—
676C42—44no—
677C42—88no—
678C23—22no—
679C23—22no—
680C23—24no—
681C23—24no—
682C23—24no—
683C23—24no—
684C23—22no—
685C23—22no—
686C23—24no—
687C23—24no—
688C23—24no—
689C23—24no—
690C23—24no—
691C23—24no—
692C23—24no—
693C23—24no—
694C23—232no—
695C23—24no—
696C23—24no—
697C23—24no—
698C23—24no—
699C23—24no—
700C23—24no—
701C23—24no—
702C23—24no—
703C23—24no—
704C23—24no—
705C23—24no—
706C23—24no—
707C23—24no—
708C23—24no—
709C23—24no—
710C23—24no—
711C23—24no—
712C23—24no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—24no—
717C23—24no—
718C23—432no—
719C23—432no—
720C23—416no—
721C23—416no—
722C23—416no—
723C23—432no—
724C23—416no—
725C23—432no—
726C23—416no—
727C23—42no—
728C23—42no—
729C23—42no—
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—416no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—42no—
749C23—42no—
750C23—41no—
751C23—41no—
752C23—42no—
753C23—41no—
754C23—41no—
755C23—42no—
756C23—42no—
757C23—42no—
758C23—42no—
759C23—42no—
760C23—42no—
761C23—42no—
762C23C2×C22⋊Q814yes—
763C23C2×#12714yes—
764C23#53614yes—
765C23#54714yes—
766C23#54714yes—
767C23D4×Q814yes—
768C23D4×Q814yes—
769C23#55418yes—
770C23C23×D411yescharacteristic
771C23C23×D411yescharacteristic
772C23C23×D411yescharacteristic
773C23C23×Q811yescharacteristic
774C23C22×#4111yescharacteristic
775C23C22×#4112yes—
776C23C2×H(5,𝔽2)12yes—
777C23C2×H(5,𝔽2)12yes—
778C23C2×2−1+411yescharacteristic
779C23C2×2−1+411yescharacteristic
780C23#58512yes—
781Q8—88no—
782D4—432no—
783D4—416no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—24no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—24no—
790C2×C4—24no—
791C2×C4—24no—
792C2×C4—24no—
793C2×C4—24no—
794C2×C4—232no—
795C2×C4—22no—
796C2×C4—24no—
797C2×C4—24no—
798C2×C4—24no—
799C2×C4—24no—
800C2×C4—24no—
801C2×C4—28no—
802C2×C4—24no—
803C2×C4—24no—
804C2×C4—28no—
805C2×C4—24no—
806C2×C4—24no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—24no—
810C2×C4—24no—
811C2×C4—28no—
812C2×C4—24no—
813C2×C4—432no—
814C2×C4—416no—
815C2×C4—41no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—41no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—44no—
824C2×C4—44no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—44no—
828C2×C4—44no—
829C2×C4—44no—
830C2×C4—42no—
831C2×C4—44no—
832C2×C4—44no—
833C2×C4—44no—
834C2×C4—42no—
835C2×C4—432no—
836C2×C4—41no—
837C2×C4—42no—
838C2×C4—41no—
839C2×C4—42no—
840C2×C4—41no—
841C2×C4—42no—
842C2×C4—44no—
843C2×C4—42no—
844C2×C4—41no—
845C2×C4—42no—
846C2×C4—44no—
847C2×C4—42no—
848C2×C4—44no—
849C2×C4—44no—
850C2×C4—42no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—42no—
854C2×C4—44no—
855C2×C4—42no—
856C2×C4—44no—
857C2×C4—44no—
858C2×C4—44no—
859C2×C4—42no—
860C2×C4—44no—
861C2×C4—44no—
862C2×C4—44no—
863C2×C4—816no—
864C2×C4—816no—
865C2×C4—88no—
866C2×C4C2×C22⋊Q818yes—
867C2×C4#52514yes—
868C2×C4C2×#12714yes—
869C2×C4C2×#12714yes—
870C2×C4#53414yes—
871C2×C4#54618yes—
872C2×C4#54618yes—
873C22—24no—
874C22—24no—
875C22—28no—
876C22—24no—
877C22—28no—
878C22—28no—
879C22—24no—
880C22—24no—
881C22—28no—
882C22—24no—
883C22—28no—
884C22—28no—
885C22—28no—
886C22—464no—
887C22—44no—
888C22—44no—
889C22—44no—
890C22—44no—
891C22—44no—
892C22—44no—
893C22—44no—
894C22—44no—
895C22—44no—
896C22—44no—
897C22—44no—
898C22—44no—
899C22—44no—
900C22—42no—
901C22—44no—
902C22—42no—
903C22—42no—
904C22—81no—
905C22—81no—
906C22—81no—
907C22—82no—
908C22—82no—
909C22—81no—
910C22#254218yes—
911C22C22×C22⋊Q811yescharacteristic
912C22C2×#52511yescharacteristic
913C22C22×#12711yescharacteristic
914C22C2×#53411yescharacteristic
915C22C2×#53611yescharacteristic
916C22C2×#54612yes—
917C22C2×#54612yes—
918C22C2×#54711yescharacteristic
919C22C2×#54711yescharacteristic
920C22C2×D4×Q811yescharacteristic
921C22C2×D4×Q811yescharacteristic
922C22C2×#55412yes—
923C22#347512yes—
924C22#348411yescharacteristic
925C22#348711yescharacteristic
926C22#348812yes—
927C22#348812yes—
928C22#349212yes—
929C22#349512yes—
930C22#350112yes—
931C22#351912yes—
932C22#353612yes—
933C22#354112yes—
934C4—24no—
935C4—28no—
936C4—44no—
937C4—44no—
938C4—44no—
939C4—42no—
940C4—48no—
941C4—44no—
942C4—81no—
943C4—82no—
944C4—81no—
945C4—82no—
946C4—84no—
947C4#253918yes—
948C2—28no—
949C2—48no—
950C2—82no—
951C2C2×#253911yescharacteristic
952C2C2×#254211yescharacteristic
953C2#3556511yescharacteristic
954C2#3615412yes—
955C2#3642711yescharacteristic
956C2#3654611yescharacteristic
957C2#3783812yes—
958C2#3891611yescharacteristic
959C2#3959511yescharacteristic
960C2#5901612yes—
961C2#5902112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#120C22
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×#2848C2semidirect
2. C2×#2502C2semidirect
3. C2×#2487C2semidirect
4. C2×#2417C2semidirect
6. C22×#380C2semidirect
7. #15513C2semidirect
8. #15505C2semidirect
9. #15177C2semidirect
10. #15135C2semidirect
11. #14946C2semidirect
12. #14734C2semidirect
13. #13997C2semidirect
15. #13965C2semidirect
16. #13906C2semidirect
17. C22⋊C4×C4⋊C4C2semidirect
21. C22×C22⋊Q8C22semidirect
32. C2×#400C22semidirect
34. C2×#399C22semidirect
35. C2×#398C22semidirect
36. C2×#398C22semidirect
37. C2×#396C22semidirect
39. C2×#391C22semidirect
40. C2×#391C22semidirect
42. C2×#389C22semidirect
43. C2×#389C22semidirect
55. C2×#384C22semidirect
63. C2×#380C22semidirect
64. C2×#380C22semidirect
67. C2×C4×C4⋊C4C22semidirect
72. #1445C22semidirect
73. #1445C22semidirect
74. #1444C22semidirect
75. #1444C22semidirect
80. #1439C22semidirect
81. #1439C22semidirect
84. #1436C22semidirect
85. C4⋊#95C22semidirect
86. C4⋊#95C22semidirect
87. C4⋊#95C22semidirect
115. C2×#120Q8semidirect
126. C22×C4⋊C4D4semidirect
195. #380D4semidirect
674. C22⋊C4C22⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#28482
C2×#25022
C2×#24872
C2×#24172
C2×C4×#1202
C22×#3802
#155132
#155052
#151772
#151352
#149462
#147342
#139972
#139952
#139652
#139062
C22⋊C4×C4⋊C42