Finite Group Databasebeta

← #846065

Subgroups — #846065

Order 512.

4566 conjugacy classes of subgroups.

The subgroup lattice has 905 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2848C212yesmaximal, complemented
2C2×#2542C211yesmaximal, characteristic, complemented
3C2×#2417C212yesmaximal, complemented
4C2×C4×#120C211yesmaximal, characteristic
5#16321C212yesmaximal, complemented
6#16298C212yesmaximal, complemented
7#15392C214yesmaximal, complemented
8#15327C214yesmaximal, complemented
9#15179C212yesmaximal, complemented
10#15178C212yesmaximal, complemented
11#15177C212yesmaximal, complemented
12#14401C212yesmaximal, complemented
13#14357C212yesmaximal
14#13993C212yesmaximal, complemented
15#13872C211yesmaximal, characteristic, complemented
16C25×C4C2211yescharacteristic
17C22×C4⋊Q8C2211yescharacteristic, complemented
18C22×C22⋊Q8C2212yes—
19C22×C22⋊Q8C2212yes—
20C22×C22⋊Q8C2212yes—
21C22×C22⋊Q8C2212yescomplemented
22C22×#120C2211yescharacteristic
23C22×C4×D4C2212yes—
24C22×C4×D4C2211yescharacteristic
25C23×C4⋊C4C2211yescharacteristic, complemented
26#2848—216no—
27#2542—28no—
28#2417—216no—
29C2×#399C2212yes—
30C2×#399C2212yescomplemented
31C2×#398C2214yescomplemented
32C2×#396C2214yes—
33C4×#120—28no—
34C2×#391C2212yescomplemented
35C2×#391C2212yescomplemented
36C2×#390C2212yes—
37C2×#389C2212yescomplemented
38C2×#386C2212yes—
39C2×#386C2214yes—
40C2×#386C2211yescharacteristic
41C2×#386C2212yes—
42C2×#385C2214yes—
43C2×#385C2214yes—
44C2×#385C2214yes—
45C2×#385C2212yes—
46C2×#385C2211yescharacteristic
47C2×#384C2212yescomplemented
48C2×#380C2212yes—
49C2×#380C2212yes—
50C2×#380C2212yes—
51C2×#380C2214yescomplemented
52C2×#380C2211yescharacteristic, complemented
53C2×#379C2214yes—
54C2×#379C2211yescharacteristic
55C2×C4×C4⋊C4C2211yescharacteristic, complemented
56C2×C4×C22⋊C4C2212yes—
57C2×C4×C22⋊C4C2211yescharacteristic
58#1444C2214yescomplemented
59#1444C2214yescomplemented
60#1444C2214yescomplemented
61#1443C2214yescomplemented
62#1442C2214yescomplemented
63#1441C2212yescomplemented
64#1441C2214yescomplemented
65#1440C2214yes—
66#1439C2214yes—
67#1439C2214yes—
68#1439C2212yes—
69#1439C2214yes—
70#1439C2214yes—
71#1439C2214yes—
72#1439C2214yescomplemented
73#1438C2214yes—
74#1437C2214yes—
75#1436C2214yescomplemented
76C4⋊#95C2212yescomplemented
77C4⋊#95C2212yescomplemented
78C22⋊#95C2212yescomplemented
79C26C2311yescharacteristic
80C23×Q8C2312yes—
81C23×D4C2312yes—
82C23×D4C2311yescharacteristic
83C24×C4—28no—
84C24×C4—24no—
85C24×C4—42no—
86C24×C4—44no—
87C24×C4—42no—
88C24×C4C2312yes—
89C24×C4C2311yescharacteristic
90C24×C4C2311yescharacteristic
91C24×C4C2312yes—
92C24×C4C2311yescharacteristic
93C24×C4C2312yes—
94C2×C4⋊Q8—24no—
95C2×C4⋊Q8—42no—
96C2×C4⋊Q8—42no—
97C2×C22⋊Q8—28no—
98C2×C22⋊Q8—28no—
99C2×C22⋊Q8—28no—
100C2×C22⋊Q8—28no—
101C2×C22⋊Q8—28no—
102C2×C22⋊Q8—28no—
103C2×C22⋊Q8—28no—
104C2×C22⋊Q8—44no—
105C2×C22⋊Q8—44no—
106C2×C22⋊Q8—44no—
107C2×C22⋊Q8—44no—
108C2×C22⋊Q8—44no—
109C2×#120—24no—
110C2×#120—24no—
111C2×#120Q818yescomplemented
112C2×C4×D4—28no—
113C2×C4×D4—28no—
114C2×C4×D4—42no—
115C2×C4×D4—42no—
116C2×C4×D4—44no—
117C2×C4×D4D418yes—
118C22×C4⋊C4—28no—
119C22×C4⋊C4—42no—
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2314yes—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2314yes—
125C22×C4⋊C4C2314yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2314yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2314yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2311yescharacteristic
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2314yes—
135C22×C22⋊C4C2314yes—
136C22×C22⋊C4C2314yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2314yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2314yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2311yescharacteristic
143C22×C22⋊C4C2314yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2311yescharacteristic
146C22×C22⋊C4C2314yes—
147C22×C22⋊C4C2311yescharacteristic
148C22×C22⋊C4C2311yescharacteristic
149C22×C42C2312yes—
150C22×C42C2311yescharacteristic
151C22×C42C2312yes—
152#399—28no—
153#399—28no—
154#398—216no—
155#396—216no—
156#391—28no—
157#391—44no—
158#390—28no—
159#389—28no—
160#386—24no—
161#386—28no—
162#386—216no—
163#386—28no—
164#385—28no—
165#385—216no—
166#385—24no—
167#385—216no—
168#385—216no—
169#384—28no—
170#380—28no—
171#380—28no—
172#380—216no—
173#380—42no—
174#380D4116yescomplemented
175#379—216no—
176#379—24no—
177C4×C4⋊C4—24no—
178C4×C22⋊C4—24no—
179C4×C22⋊C4—28no—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C2×#95C2314yes—
183C2×#95C2312yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2312yes—
187C2×#95C2314yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2314yes—
191C2×#95C2314yes—
192C2×#95C2314yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2312yes—
196C2×#95C2314yes—
197C25—22no—
198C25—24no—
199C25—22no—
200C25—24no—
201C25—42no—
202C25—41no—
203C25—41no—
204C25—42no—
205C25—41no—
206C25—41no—
207C25C2×Q814yes—
208C25C2411yescharacteristic
209C25C2411yescharacteristic
210C25C2412yes—
211C22×Q8—24no—
212C22×Q8—24no—
213C22×Q8—24no—
214C22×Q8—24no—
215C22×Q8—24no—
216C22×Q8—24no—
217C22×Q8—24no—
218C22×D4—24no—
219C22×D4—24no—
220C22×D4—24no—
221C22×D4—24no—
222C22×D4—41no—
223C22×D4—41no—
224C22×D4—42no—
225C22×D4—41no—
226C22×D4—41no—
227C22×D4—42no—
228C22×D4C2×D414yes—
229C22×D4C2×Q818yes—
230C22×D4C2×Q814yes—
231C22×D4#4114yes—
232C23×C4—24no—
233C23×C4—24no—
234C23×C4—24no—
235C23×C4—24no—
236C23×C4—22no—
237C23×C4—24no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—24no—
241C23×C4—22no—
242C23×C4—24no—
243C23×C4—24no—
244C23×C4—24no—
245C23×C4—24no—
246C23×C4—24no—
247C23×C4—22no—
248C23×C4—24no—
249C23×C4—24no—
250C23×C4—24no—
251C23×C4—24no—
252C23×C4—28no—
253C23×C4—42no—
254C23×C4—42no—
255C23×C4—42no—
256C23×C4—42no—
257C23×C4—41no—
258C23×C4—42no—
259C23×C4—41no—
260C23×C4—432no—
261C23×C4—416no—
262C23×C4—42no—
263C23×C4—44no—
264C23×C4—42no—
265C23×C4—416no—
266C23×C4—432no—
267C23×C4—416no—
268C23×C4C2×D414yes—
269C23×C4C2×D418yes—
270C23×C4C2×D414yes—
271C23×C4C2414yes—
272C23×C4C2414yes—
273C23×C4C2412yes—
274C23×C4C2414yes—
275C23×C4C2411yescharacteristic
276C23×C4C2411yescharacteristic
277C23×C4C2414yes—
278C23×C4C2412yes—
279C23×C4C2411yescharacteristic
280C23×C4C2412yes—
281C23×C4C2411yescharacteristic
282C23×C4C2411yescharacteristic
283C4⋊Q8—416no—
284C22⋊Q8—432no—
285C22⋊Q8—432no—
286C22⋊Q8—432no—
287C22⋊Q8—432no—
288#120—232no—
289C4×D4—416no—
290C4×D4—432no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—28no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—28no—
300C2×C4⋊C4—28no—
301C2×C4⋊C4—28no—
302C2×C4⋊C4—28no—
303C2×C4⋊C4—28no—
304C2×C4⋊C4—28no—
305C2×C4⋊C4—28no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—28no—
311C2×C4⋊C4—416no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4—41no—
314C2×C4⋊C4—41no—
315C2×C4⋊C4—42no—
316C2×C4⋊C4—44no—
317C2×C4⋊C4—44no—
318C2×C4⋊C4—44no—
319C2×C4⋊C4—44no—
320C2×C4⋊C4—44no—
321C2×C4⋊C4—42no—
322C2×C4⋊C4—42no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—44no—
326C2×C4⋊C4—44no—
327C2×C4⋊C4C2×D418yes—
328C2×C4⋊C4C2×D418yes—
329C2×C4⋊C4C2×D414yes—
330C2×C22⋊C4—22no—
331C2×C22⋊C4—22no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—28no—
337C2×C22⋊C4—28no—
338C2×C22⋊C4—28no—
339C2×C22⋊C4—28no—
340C2×C22⋊C4—22no—
341C2×C22⋊C4—28no—
342C2×C22⋊C4—28no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—28no—
347C2×C22⋊C4—28no—
348C2×C22⋊C4—28no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—28no—
351C2×C22⋊C4—28no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—44no—
354C2×C22⋊C4—44no—
355C2×C22⋊C4—42no—
356C2×C22⋊C4—44no—
357C2×C22⋊C4—44no—
358C2×C22⋊C4—41no—
359C2×C22⋊C4—41no—
360C2×C22⋊C4—41no—
361C2×C22⋊C4—41no—
362C2×C22⋊C4—41no—
363C2×C22⋊C4—41no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—44no—
367C2×C22⋊C4—44no—
368C2×C22⋊C4—44no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4C2×D414yes—
374C2×C22⋊C4C2×D414yes—
375C2×C22⋊C4C2×D4116yes—
376C2×C22⋊C4C2×Q814yes—
377C2×C22⋊C4C2×Q818yes—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—24no—
381C2×C42—24no—
382C2×C42—24no—
383C2×C42—24no—
384C2×C42—42no—
385C2×C42—42no—
386C2×C42C2×D414yes—
387#95—24no—
388#95—24no—
389#95—24no—
390#95—24no—
391#95—28no—
392#95—28no—
393#95—28no—
394#95—28no—
395#95—28no—
396#95—28no—
397#95—44no—
398#95—44no—
399#95—44no—
400#95—42no—
401#95—44no—
402#95—44no—
403#95C2×D4116yes—
404C24—22no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—21no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—21no—
416C24—21no—
417C24—21no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—21no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—21no—
428C24—21no—
429C24—22no—
430C24—21no—
431C24—22no—
432C24—28no—
433C24—216no—
434C24—44no—
435C24—48no—
436C24—44no—
437C24—44no—
438C24—48no—
439C24—48no—
440C24—48no—
441C24—48no—
442C24—48no—
443C24—44no—
444C24—44no—
445C24—48no—
446C24—44no—
447C24—48no—
448C24—44no—
449C24—44no—
450C24—48no—
451C24—48no—
452C24—44no—
453C24—48no—
454C24—44no—
455C24C22×D412yes—
456C24C22×D412yes—
457C24C22×D414yes—
458C24C22×Q812yes—
459C24C22×Q812yes—
460C24C22×Q814yes—
461C24C2×#4112yes—
462C24C2×#4112yes—
463C242−1+414yes—
464C24C2511yescharacteristic
465C2×Q8—48no—
466C2×Q8—48no—
467C2×Q8—48no—
468C2×Q8—48no—
469C2×Q8—48no—
470C2×Q8—48no—
471C2×Q8—48no—
472C2×D4—216no—
473C2×D4—216no—
474C2×D4—44no—
475C2×D4—44no—
476C2×D4—44no—
477C2×D4—44no—
478C2×D4—48no—
479C2×D4—44no—
480C2×D4—44no—
481C2×D4—48no—
482C2×D4—48no—
483C2×D4—48no—
484C2×D4—48no—
485C2×D4C22⋊Q8116yescomplemented
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—22no—
498C22×C4—24no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—24no—
505C22×C4—24no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—24no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—24no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—28no—
527C22×C4—28no—
528C22×C4—216no—
529C22×C4—216no—
530C22×C4—216no—
531C22×C4—216no—
532C22×C4—216no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—22no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—22no—
548C22×C4—24no—
549C22×C4—22no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—48no—
555C22×C4—44no—
556C22×C4—48no—
557C22×C4—48no—
558C22×C4—48no—
559C22×C4—48no—
560C22×C4—48no—
561C22×C4—48no—
562C22×C4—48no—
563C22×C4—416no—
564C22×C4—44no—
565C22×C4—48no—
566C22×C4—48no—
567C22×C4—44no—
568C22×C4—4128no—
569C22×C4—48no—
570C22×C4—48no—
571C22×C4—48no—
572C22×C4—48no—
573C22×C4—44no—
574C22×C4—48no—
575C22×C4—44no—
576C22×C4—44no—
577C22×C4—44no—
578C22×C4—48no—
579C22×C4—88no—
580C22×C4—84no—
581C22×C4—84no—
582C22×C4C22×D412yes—
583C22×C4C22×D418yes—
584C22×C4C22×D418yes—
585C22×C4C22×D412yes—
586C22×C4C22×D414yes—
587C22×C4C22×D412yes—
588C22×C4C22×D412yes—
589C22×C4C22×D412yes—
590C22×C4C22×D414yes—
591C22×C4C22×Q814yes—
592C22×C4C22×Q812yes—
593C22×C4C2×#4112yes—
594C22×C4H(5,𝔽2)12yes—
595C22×C4H(5,𝔽2)12yes—
596C22×C4H(5,𝔽2)14yes—
597C4⋊C4—216no—
598C4⋊C4—216no—
599C4⋊C4—44no—
600C4⋊C4—48no—
601C4⋊C4—48no—
602C4⋊C4—416no—
603C4⋊C4—416no—
604C4⋊C4—416no—
605C4⋊C4—416no—
606C4⋊C4—48no—
607C4⋊C4—48no—
608C4⋊C4—48no—
609C4⋊C4—88no—
610C22⋊C4—28no—
611C22⋊C4—216no—
612C22⋊C4—416no—
613C22⋊C4—44no—
614C22⋊C4—44no—
615C22⋊C4—416no—
616C22⋊C4—416no—
617C22⋊C4—48no—
618C22⋊C4—48no—
619C22⋊C4—48no—
620C22⋊C4—416no—
621C22⋊C4—416no—
622C22⋊C4—416no—
623C22⋊C4—44no—
624C22⋊C4—416no—
625C22⋊C4—84no—
626C42—28no—
627C42—48no—
628C42—48no—
629C23—24no—
630C23—22no—
631C23—22no—
632C23—24no—
633C23—22no—
634C23—22no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—22no—
652C23—22no—
653C23—24no—
654C23—22no—
655C23—22no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—416no—
672C23—432no—
673C23—432no—
674C23—416no—
675C23—416no—
676C23—432no—
677C23—416no—
678C23—416no—
679C23—416no—
680C23—432no—
681C23—416no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—41no—
688C23—42no—
689C23—41no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—41no—
701C23—42no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—41no—
710C23—42no—
711C23—41no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23C2×C22⋊Q814yes—
719C23C2×C22⋊Q814yes—
720C23D4×Q818yes—
721C23C23×D411yescharacteristic
722C23C23×D412yes—
723C23C23×Q811yescharacteristic
724C23C22×#4111yescharacteristic
725C23C2×H(5,𝔽2)11yescharacteristic
726C23C2×H(5,𝔽2)11yescharacteristic
727C23C2×H(5,𝔽2)12yes—
728C23C2×2−1+412yes—
729C23#58511yescharacteristic
730C23#58511yescharacteristic
731C23#58512yes—
732Q8—816no—
733D4—416no—
734D4—432no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—24no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—24no—
746C2×C4—28no—
747C2×C4—28no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—28no—
754C2×C4—28no—
755C2×C4—28no—
756C2×C4—28no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—432no—
760C2×C4—416no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—44no—
766C2×C4—42no—
767C2×C4—41no—
768C2×C4—42no—
769C2×C4—41no—
770C2×C4—44no—
771C2×C4—42no—
772C2×C4—44no—
773C2×C4—44no—
774C2×C4—42no—
775C2×C4—44no—
776C2×C4—42no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—42no—
780C2×C4—41no—
781C2×C4—44no—
782C2×C4—41no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—42no—
786C2×C4—416no—
787C2×C4—416no—
788C2×C4—432no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—44no—
796C2×C4—44no—
797C2×C4—44no—
798C2×C4—44no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—44no—
802C2×C4—42no—
803C2×C4—44no—
804C2×C4—44no—
805C2×C4—44no—
806C2×C4—42no—
807C2×C4—44no—
808C2×C4—42no—
809C2×C4—44no—
810C2×C4—816no—
811C2×C4C2×C22⋊Q814yes—
812C2×C4#53414yes—
813C2×C4#53518yes—
814C2×C4D4218yes—
815C2×C4D4214yes—
816C2×C4#56014yes—
817C22—28no—
818C22—28no—
819C22—24no—
820C22—24no—
821C22—28no—
822C22—28no—
823C22—28no—
824C22—464no—
825C22—44no—
826C22—44no—
827C22—44no—
828C22—44no—
829C22—42no—
830C22—42no—
831C22—44no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—44no—
836C22—42no—
837C22—42no—
838C22—44no—
839C22—42no—
840C22—44no—
841C22—44no—
842C22—44no—
843C22—42no—
844C22—44no—
845C22—42no—
846C22—44no—
847C22—44no—
848C22—44no—
849C22—44no—
850C22—44no—
851C22—44no—
852C22—42no—
853C22—42no—
854C22—44no—
855C22C22×C22⋊Q811yescharacteristic
856C22C2×#53411yescharacteristic
857C22C2×#53512yes—
858C22#344911yescharacteristic
859C22C2×D4212yes—
860C22C2×D4211yescharacteristic
861C22C2×D4×Q812yes—
862C22D4×#4112yes—
863C22#348512yes—
864C22#348912yes—
865C22#348912yes—
866C22#350111yescharacteristic
867C22#350111yescharacteristic
868C22#350112yes—
869C22#350511yescharacteristic
870C22#350511yescharacteristic
871C22#352012yes—
872C22C2×#56011yescharacteristic
873C22#353811yescharacteristic
874C22#353912yes—
875C22#354011yescharacteristic
876C22#354112yes—
877C22#354112yes—
878C4—24no—
879C4—48no—
880C4—42no—
881C4—42no—
882C4—44no—
883C4—48no—
884C4—44no—
885C4—42no—
886C4—82no—
887C4—84no—
888C4—84no—
889C4#266918yes—
890C2—44no—
891C2—48no—
892C2—44no—
893C2#3501011yescharacteristic
894C2D4×C22⋊Q812yes—
895C2#3737411yescharacteristic
896C2#3765612yes—
897C2#3959412yes—
898C2#3988712yes—
899C2#4549311yescharacteristic
900C2#4562211yescharacteristic
901C2C2×#266911yescharacteristic
902C2#5899811yescharacteristic
903C2#5900011yescharacteristic
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×#2542C2semidirect
3. C2×#2417C2semidirect
5. #16321C2semidirect
6. #16298C2semidirect
7. #15392C2semidirect
8. #15327C2semidirect
9. #15179C2semidirect
10. #15178C2semidirect
11. #15177C2semidirect
12. #14401C2semidirect
14. #13993C2semidirect
15. #13872C2semidirect
17. C22×C4⋊Q8C22semidirect
21. C22×C22⋊Q8C22semidirect
25. C23×C4⋊C4C22semidirect
30. C2×#399C22semidirect
31. C2×#398C22semidirect
34. C2×#391C22semidirect
35. C2×#391C22semidirect
37. C2×#389C22semidirect
47. C2×#384C22semidirect
51. C2×#380C22semidirect
52. C2×#380C22semidirect
55. C2×C4×C4⋊C4C22semidirect
58. #1444C22semidirect
59. #1444C22semidirect
60. #1444C22semidirect
61. #1443C22semidirect
62. #1442C22semidirect
63. #1441C22semidirect
64. #1441C22semidirect
72. #1439C22semidirect
75. #1436C22semidirect
76. C4⋊#95C22semidirect
77. C4⋊#95C22semidirect
78. C22⋊#95C22semidirect
111. C2×#120Q8semidirect
174. #380D4semidirect
485. C2×D4C22⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#28482
C2×#25422
C2×#24172
C2×C4×#1202
#163212
#162982
#153922
#153272
#151792
#151782
#151772
#144012
#143572
#139932
#138722