Finite Group Databasebeta

← #846397

Subgroups — #846397

Order 512.

3870 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2563C211yesmaximal, characteristic, complemented
2C2×C4×#120C211yesmaximal, characteristic
3#16481C212yesmaximal, complemented
4#16297C212yesmaximal, complemented
5#16057C214yesmaximal, complemented
6#15506C214yesmaximal, complemented
7#15183C212yesmaximal, complemented
8#15181C212yesmaximal, complemented
9#15125C212yesmaximal, complemented
10#14680C212yesmaximal, complemented
11#14513C212yesmaximal, complemented
12#14357C212yesmaximal
13#13993C212yesmaximal, complemented
14#13872C212yesmaximal, complemented
15#13872C211yesmaximal, characteristic, complemented
16C25×C4C2211yescharacteristic
17C22×C4⋊Q8C2211yescharacteristic, complemented
18C22×#120C2211yescharacteristic
19C22×C4×D4C2212yes—
20C22×C4×D4C2211yescharacteristic
21C23×C4⋊C4C2211yescharacteristic, complemented
22#2563—28no—
23C2×#393C2212yes—
24C2×#393C2214yes—
25C2×#393C2212yescomplemented
26C4×#120—28no—
27C2×#390C2212yes—
28C2×#389C2212yescomplemented
29C2×#386C2212yes—
30C2×#386C2212yes—
31C2×#386C2211yescharacteristic
32C2×#386C2214yes—
33C2×#385C2211yescharacteristic
34C2×#385C2212yes—
35C2×#382C2212yescomplemented
36C2×#380C2212yes—
37C2×#380C2212yes—
38C2×#380C2212yes—
39C2×#380C2212yes—
40C2×#380C2212yes—
41C2×#380C2212yes—
42C2×#380C2212yescomplemented
43C2×#380C2211yescharacteristic, complemented
44C2×#379C2211yescharacteristic
45C2×#379C2214yes—
46C2×C4×C4⋊C4C2211yescharacteristic, complemented
47C2×C4×C22⋊C4C2212yes—
48C2×C4×C22⋊C4C2211yescharacteristic
49#1446C2214yescomplemented
50#1445C2214yescomplemented
51#1443C2214yescomplemented
52#1443C2214yescomplemented
53#1442C2214yescomplemented
54#1442C2214yescomplemented
55#1441C2214yescomplemented
56#1441C2212yescomplemented
57#1440C2214yes—
58#1439C2214yes—
59#1439C2212yes—
60#1439C2214yes—
61#1439C2214yes—
62#1439C2214yes—
63#1439C2214yes—
64#1439C2214yescomplemented
65#1438C2214yes—
66#1437C2214yes—
67#1436C2214yescomplemented
68C4⋊#95C2212yescomplemented
69C4⋊#95C2212yescomplemented
70C4⋊#95C2212yescomplemented
71C4⋊#95C2212yescomplemented
72C22⋊#95C2214yes—
73C22⋊#95C2214yes—
74C22⋊#95C2214yes—
75C22⋊#95C2212yescomplemented
76C22⋊#95C2214yescomplemented
77C26C2311yescharacteristic
78C23×Q8C2312yes—
79C23×D4C2312yes—
80C23×D4C2311yescharacteristic
81C24×C4—24no—
82C24×C4—28no—
83C24×C4—42no—
84C24×C4—44no—
85C24×C4—42no—
86C24×C4C2311yescharacteristic
87C24×C4C2311yescharacteristic
88C24×C4C2312yes—
89C24×C4C2311yescharacteristic
90C24×C4C2312yes—
91C24×C4C2312yes—
92C2×C4⋊Q8—24no—
93C2×C4⋊Q8—42no—
94C2×C4⋊Q8—42no—
95C2×#120—24no—
96C2×#120—24no—
97C2×#120Q818yescomplemented
98C2×C4×D4—28no—
99C2×C4×D4—28no—
100C2×C4×D4—42no—
101C2×C4×D4—42no—
102C2×C4×D4—44no—
103C2×C4×D4D418yes—
104C22×C4⋊C4—42no—
105C22×C4⋊C4—44no—
106C22×C4⋊C4C2312yes—
107C22×C4⋊C4C2312yes—
108C22×C4⋊C4C2312yes—
109C22×C4⋊C4C2312yes—
110C22×C4⋊C4C2312yes—
111C22×C4⋊C4C2312yes—
112C22×C4⋊C4C2312yes—
113C22×C4⋊C4C2314yes—
114C22×C4⋊C4C2311yescharacteristic
115C22×C22⋊C4C2312yes—
116C22×C22⋊C4C2312yes—
117C22×C22⋊C4C2312yes—
118C22×C22⋊C4C2312yes—
119C22×C22⋊C4C2311yescharacteristic
120C22×C22⋊C4C2314yes—
121C22×C22⋊C4C2314yes—
122C22×C22⋊C4C2314yes—
123C22×C22⋊C4C2314yes—
124C22×C22⋊C4C2314yes—
125C22×C22⋊C4C2314yes—
126C22×C22⋊C4C2314yes—
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2311yescharacteristic
129C22×C22⋊C4C2311yescharacteristic
130C22×C22⋊C4C2311yescharacteristic
131C22×C42C2312yes—
132C22×C42C2311yescharacteristic
133C22×C42C2312yes—
134#393—28no—
135#393—28no—
136#393—48no—
137#390—28no—
138#389—44no—
139#386—24no—
140#386—28no—
141#386—28no—
142#386—48no—
143#385—28no—
144#385—24no—
145#382—28no—
146#380—28no—
147#380—28no—
148#380—28no—
149#380—44no—
150#380—44no—
151#380—44no—
152#380—44no—
153#380—42no—
154#379—24no—
155#379—48no—
156C4×C4⋊C4—24no—
157C4×C22⋊C4—24no—
158C4×C22⋊C4—28no—
159C2×#95C2312yes—
160C2×#95C2314yes—
161C2×#95C2314yes—
162C2×#95C2314yes—
163C2×#95C2314yes—
164C2×#95C2312yes—
165C2×#95C2312yes—
166C2×#95C2312yes—
167C2×#95C2314yes—
168C2×#95C2314yes—
169C2×#95C2314yes—
170C2×#95C2314yes—
171C2×#95C2314yes—
172C2×#95C2314yes—
173C2×#95C2314yes—
174C2×#95C2314yes—
175C2×#95C2314yes—
176C2×#95C2314yes—
177C2×#95C2314yes—
178C2×#95C2314yes—
179C2×#95C2312yes—
180C25—22no—
181C25—22no—
182C25—24no—
183C25—24no—
184C25—42no—
185C25—41no—
186C25—41no—
187C25—42no—
188C25—41no—
189C25—41no—
190C25C2×Q814yes—
191C25C2411yescharacteristic
192C25C2411yescharacteristic
193C25C2412yes—
194C22×Q8—24no—
195C22×Q8—42no—
196C22×Q8—42no—
197C22×Q8—44no—
198C22×Q8—44no—
199C22×D4—24no—
200C22×D4—24no—
201C22×D4—24no—
202C22×D4—24no—
203C22×D4—41no—
204C22×D4—41no—
205C22×D4—42no—
206C22×D4—41no—
207C22×D4—41no—
208C22×D4—42no—
209C22×D4C2×D414yes—
210C22×D4C2×Q818yes—
211C22×D4C2×Q814yes—
212C22×D4#4114yes—
213C23×C4—24no—
214C23×C4—24no—
215C23×C4—24no—
216C23×C4—24no—
217C23×C4—22no—
218C23×C4—24no—
219C23×C4—22no—
220C23×C4—22no—
221C23×C4—24no—
222C23×C4—22no—
223C23×C4—24no—
224C23×C4—24no—
225C23×C4—24no—
226C23×C4—24no—
227C23×C4—22no—
228C23×C4—24no—
229C23×C4—24no—
230C23×C4—24no—
231C23×C4—24no—
232C23×C4—24no—
233C23×C4—41no—
234C23×C4—42no—
235C23×C4—41no—
236C23×C4—42no—
237C23×C4—42no—
238C23×C4—42no—
239C23×C4—42no—
240C23×C4—432no—
241C23×C4—416no—
242C23×C4—42no—
243C23×C4—44no—
244C23×C4—42no—
245C23×C4—44no—
246C23×C4—416no—
247C23×C4—432no—
248C23×C4—416no—
249C23×C4C2×D414yes—
250C23×C4C2×D414yes—
251C23×C4#4118yes—
252C23×C4C2414yes—
253C23×C4C2414yes—
254C23×C4C2414yes—
255C23×C4C2412yes—
256C23×C4C2414yes—
257C23×C4C2411yescharacteristic
258C23×C4C2411yescharacteristic
259C23×C4C2411yescharacteristic
260C23×C4C2412yes—
261C23×C4C2412yes—
262C23×C4C2411yescharacteristic
263C23×C4C2411yescharacteristic
264C4⋊Q8—416no—
265#120—232no—
266C4×D4—416no—
267C4×D4—432no—
268C2×C4⋊C4—24no—
269C2×C4⋊C4—24no—
270C2×C4⋊C4—24no—
271C2×C4⋊C4—24no—
272C2×C4⋊C4—24no—
273C2×C4⋊C4—24no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—24no—
278C2×C4⋊C4—24no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—42no—
284C2×C4⋊C4—44no—
285C2×C4⋊C4—41no—
286C2×C4⋊C4—41no—
287C2×C4⋊C4—42no—
288C2×C4⋊C4—42no—
289C2×C4⋊C4—42no—
290C2×C4⋊C4—416no—
291C2×C4⋊C4—44no—
292C2×C4⋊C4—44no—
293C2×C4⋊C4—44no—
294C2×C4⋊C4C2×D414yes—
295C2×C22⋊C4—22no—
296C2×C22⋊C4—22no—
297C2×C22⋊C4—24no—
298C2×C22⋊C4—24no—
299C2×C22⋊C4—24no—
300C2×C22⋊C4—22no—
301C2×C22⋊C4—24no—
302C2×C22⋊C4—24no—
303C2×C22⋊C4—24no—
304C2×C22⋊C4—24no—
305C2×C22⋊C4—24no—
306C2×C22⋊C4—28no—
307C2×C22⋊C4—28no—
308C2×C22⋊C4—28no—
309C2×C22⋊C4—24no—
310C2×C22⋊C4—28no—
311C2×C22⋊C4—28no—
312C2×C22⋊C4—28no—
313C2×C22⋊C4—28no—
314C2×C22⋊C4—42no—
315C2×C22⋊C4—41no—
316C2×C22⋊C4—41no—
317C2×C22⋊C4—41no—
318C2×C22⋊C4—41no—
319C2×C22⋊C4—41no—
320C2×C22⋊C4—41no—
321C2×C22⋊C4—42no—
322C2×C22⋊C4—42no—
323C2×C22⋊C4—44no—
324C2×C22⋊C4—44no—
325C2×C22⋊C4—44no—
326C2×C22⋊C4—44no—
327C2×C22⋊C4—42no—
328C2×C22⋊C4—44no—
329C2×C22⋊C4—44no—
330C2×C22⋊C4—44no—
331C2×C22⋊C4—44no—
332C2×C22⋊C4—44no—
333C2×C22⋊C4—42no—
334C2×C22⋊C4—44no—
335C2×C22⋊C4—44no—
336C2×C22⋊C4—44no—
337C2×C22⋊C4—44no—
338C2×C22⋊C4—44no—
339C2×C22⋊C4C2×D414yes—
340C2×C22⋊C4C2×D414yes—
341C2×C22⋊C4C2×Q814yes—
342C2×C22⋊C4C2×Q818yes—
343C2×C42—22no—
344C2×C42—22no—
345C2×C42—24no—
346C2×C42—24no—
347C2×C42—24no—
348C2×C42—24no—
349C2×C42—42no—
350C2×C42—42no—
351C2×C42C2×D414yes—
352#95—24no—
353#95—24no—
354#95—24no—
355#95—24no—
356#95—28no—
357#95—28no—
358#95—28no—
359#95—28no—
360#95—44no—
361#95—44no—
362#95—42no—
363#95—44no—
364#95—44no—
365#95—44no—
366#95—44no—
367#95—44no—
368#95—44no—
369#95—44no—
370#95—44no—
371#95—44no—
372#95—44no—
373C24—22no—
374C24—22no—
375C24—22no—
376C24—22no—
377C24—22no—
378C24—22no—
379C24—22no—
380C24—21no—
381C24—22no—
382C24—22no—
383C24—22no—
384C24—22no—
385C24—22no—
386C24—21no—
387C24—22no—
388C24—21no—
389C24—21no—
390C24—22no—
391C24—21no—
392C24—22no—
393C24—22no—
394C24—22no—
395C24—22no—
396C24—22no—
397C24—21no—
398C24—21no—
399C24—22no—
400C24—21no—
401C24—28no—
402C24—216no—
403C24—48no—
404C24—44no—
405C24—44no—
406C24—48no—
407C24—44no—
408C24—48no—
409C24—48no—
410C24—48no—
411C24—48no—
412C24—44no—
413C24—44no—
414C24—48no—
415C24—44no—
416C24—48no—
417C24—44no—
418C24—44no—
419C24—48no—
420C24—48no—
421C24—44no—
422C24—44no—
423C24—48no—
424C24C22×D412yes—
425C24C22×D412yes—
426C24C22×Q812yes—
427C24C22×Q812yes—
428C24C22×Q814yes—
429C24C2×#4112yes—
430C24C2×#4112yes—
431C24C2×#4114yes—
432C24H(5,𝔽2)14yes—
433C24C2511yescharacteristic
434C2×Q8—48no—
435C2×Q8—88no—
436C2×Q8—84no—
437C2×Q8—84no—
438C2×Q8—88no—
439C2×D4—216no—
440C2×D4—216no—
441C2×D4—44no—
442C2×D4—44no—
443C2×D4—44no—
444C2×D4—44no—
445C2×D4—48no—
446C2×D4—44no—
447C2×D4—44no—
448C2×D4—48no—
449C2×D4—48no—
450C2×D4—48no—
451C2×D4—48no—
452C2×D4C22⋊Q8116yes—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—28no—
482C22×C4—28no—
483C22×C4—216no—
484C22×C4—216no—
485C22×C4—216no—
486C22×C4—216no—
487C22×C4—216no—
488C22×C4—24no—
489C22×C4—22no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—24no—
498C22×C4—24no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—24no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—24no—
510C22×C4—24no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—48no—
524C22×C4—44no—
525C22×C4—48no—
526C22×C4—48no—
527C22×C4—48no—
528C22×C4—48no—
529C22×C4—48no—
530C22×C4—48no—
531C22×C4—44no—
532C22×C4—48no—
533C22×C4—44no—
534C22×C4—48no—
535C22×C4—4128no—
536C22×C4—48no—
537C22×C4—48no—
538C22×C4—48no—
539C22×C4—48no—
540C22×C4—48no—
541C22×C4—44no—
542C22×C4—44no—
543C22×C4—44no—
544C22×C4—44no—
545C22×C4—48no—
546C22×C4—48no—
547C22×C4—84no—
548C22×C4—88no—
549C22×C4—84no—
550C22×C4—88no—
551C22×C4C22×D412yes—
552C22×C4C22×D412yes—
553C22×C4C22×D412yes—
554C22×C4C22×D412yes—
555C22×C4C22×D412yes—
556C22×C4C22×Q814yes—
557C22×C4C22×Q812yes—
558C22×C4C2×#4114yes—
559C22×C4C2×#4112yes—
560C22×C4C2×#4114yes—
561C22×C4H(5,𝔽2)12yes—
562C22×C4H(5,𝔽2)12yes—
563C22×C4H(5,𝔽2)14yes—
564C4⋊C4—44no—
565C4⋊C4—48no—
566C4⋊C4—48no—
567C4⋊C4—48no—
568C4⋊C4—48no—
569C4⋊C4—48no—
570C4⋊C4—48no—
571C4⋊C4—48no—
572C4⋊C4—88no—
573C22⋊C4—28no—
574C22⋊C4—216no—
575C22⋊C4—44no—
576C22⋊C4—44no—
577C22⋊C4—48no—
578C22⋊C4—48no—
579C22⋊C4—48no—
580C22⋊C4—44no—
581C22⋊C4—88no—
582C22⋊C4—88no—
583C22⋊C4—88no—
584C22⋊C4—84no—
585C22⋊C4—88no—
586C22⋊C4—88no—
587C22⋊C4—88no—
588C22⋊C4—88no—
589C42—28no—
590C42—48no—
591C42—48no—
592C23—24no—
593C23—22no—
594C23—22no—
595C23—22no—
596C23—22no—
597C23—24no—
598C23—24no—
599C23—24no—
600C23—24no—
601C23—24no—
602C23—24no—
603C23—24no—
604C23—24no—
605C23—24no—
606C23—24no—
607C23—24no—
608C23—24no—
609C23—24no—
610C23—24no—
611C23—24no—
612C23—24no—
613C23—24no—
614C23—24no—
615C23—22no—
616C23—22no—
617C23—24no—
618C23—22no—
619C23—22no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—24no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—24no—
629C23—24no—
630C23—24no—
631C23—24no—
632C23—24no—
633C23—24no—
634C23—432no—
635C23—416no—
636C23—432no—
637C23—416no—
638C23—416no—
639C23—416no—
640C23—416no—
641C23—416no—
642C23—416no—
643C23—432no—
644C23—432no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—41no—
652C23—41no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—41no—
664C23—41no—
665C23—42no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—42no—
670C23—42no—
671C23—41no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23C2×C22⋊Q814yes—
682C23C2×C22⋊Q814yes—
683C23#55418yes—
684C23C23×D411yescharacteristic
685C23C23×Q811yescharacteristic
686C23C22×#4111yescharacteristic
687C23C22×#4112yes—
688C23C2×H(5,𝔽2)11yescharacteristic
689C23C2×H(5,𝔽2)11yescharacteristic
690C23C2×H(5,𝔽2)12yes—
691C23C2×H(5,𝔽2)12yes—
692C23#58511yescharacteristic
693C23#58511yescharacteristic
694C23#58512yes—
695Q8—816no—
696D4—416no—
697D4—432no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—432no—
717C2×C4—416no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—42no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—42no—
735C2×C4—416no—
736C2×C4—416no—
737C2×C4—432no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—42no—
741C2×C4—44no—
742C2×C4—42no—
743C2×C4—44no—
744C2×C4—44no—
745C2×C4—42no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—44no—
749C2×C4—44no—
750C2×C4—42no—
751C2×C4—44no—
752C2×C4—44no—
753C2×C4—42no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—44no—
762C2×C4—42no—
763C2×C4—44no—
764C2×C4—44no—
765C2×C4—44no—
766C2×C4—44no—
767C2×C4—44no—
768C2×C4—44no—
769C2×C4—44no—
770C2×C4—42no—
771C2×C4—44no—
772C2×C4—44no—
773C2×C4—816no—
774C2×C4C2×C22⋊Q814yes—
775C2×C4#53414yes—
776C2×C4#53818yes—
777C2×C4#54618yes—
778C2×C4#55114yes—
779C2×C4H(3,𝔽4)14yes—
780C22—28no—
781C22—28no—
782C22—28no—
783C22—28no—
784C22—28no—
785C22—24no—
786C22—24no—
787C22—464no—
788C22—44no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—44no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—44no—
797C22—42no—
798C22—44no—
799C22—42no—
800C22—42no—
801C22—42no—
802C22—44no—
803C22—44no—
804C22—44no—
805C22—44no—
806C22—42no—
807C22—44no—
808C22—42no—
809C22—44no—
810C22—44no—
811C22—44no—
812C22—44no—
813C22—44no—
814C22—44no—
815C22—44no—
816C22—44no—
817C22—44no—
818C22C22×C22⋊Q811yescharacteristic
819C22C2×#53411yescharacteristic
820C22#344911yescharacteristic
821C22C2×#53812yes—
822C22C2×#54612yes—
823C22C2×#55111yescharacteristic
824C22C2×#55412yes—
825C22#347512yes—
826C22#348812yes—
827C22#349312yes—
828C22#349412yes—
829C22#350112yes—
830C22#350111yescharacteristic
831C22#350111yescharacteristic
832C22#350511yescharacteristic
833C22#350511yescharacteristic
834C22#351912yes—
835C22C2×H(3,𝔽4)11yescharacteristic
836C22#353711yescharacteristic
837C22#354011yescharacteristic
838C22#354012yes—
839C22#354212yes—
840C22#354212yes—
841C4—24no—
842C4—44no—
843C4—42no—
844C4—42no—
845C4—44no—
846C4—42no—
847C4—84no—
848C4—84no—
849C4—84no—
850C4—82no—
851C4—84no—
852C4#268418yes—
853C2—44no—
854C2—48no—
855C2—44no—
856C2#3501011yescharacteristic
857C2#3615412yes—
858C2#3726911yescharacteristic
859C2#3784512yes—
860C2#3960512yes—
861C2#3993312yes—
862C2#4549411yescharacteristic
863C2#4564511yescharacteristic
864C2C2×#268411yescharacteristic
865C2#5919911yescharacteristic
866C2#5920111yescharacteristic
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×#2563C2semidirect
3. #16481C2semidirect
4. #16297C2semidirect
5. #16057C2semidirect
6. #15506C2semidirect
7. #15183C2semidirect
8. #15181C2semidirect
9. #15125C2semidirect
10. #14680C2semidirect
11. #14513C2semidirect
13. #13993C2semidirect
14. #13872C2semidirect
15. #13872C2semidirect
17. C22×C4⋊Q8C22semidirect
21. C23×C4⋊C4C22semidirect
25. C2×#393C22semidirect
28. C2×#389C22semidirect
35. C2×#382C22semidirect
42. C2×#380C22semidirect
43. C2×#380C22semidirect
46. C2×C4×C4⋊C4C22semidirect
49. #1446C22semidirect
50. #1445C22semidirect
51. #1443C22semidirect
52. #1443C22semidirect
53. #1442C22semidirect
54. #1442C22semidirect
55. #1441C22semidirect
56. #1441C22semidirect
64. #1439C22semidirect
67. #1436C22semidirect
68. C4⋊#95C22semidirect
69. C4⋊#95C22semidirect
70. C4⋊#95C22semidirect
71. C4⋊#95C22semidirect
75. C22⋊#95C22semidirect
76. C22⋊#95C22semidirect
97. C2×#120Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#25632
C2×C4×#1202
#164812
#162972
#160572
#155062
#151832
#151812
#151252
#146802
#145132
#143572
#139932
#138722