Finite Group Databasebeta

← #761053

Subgroups — #761053

Order 512.

4910 conjugacy classes of subgroups.

The subgroup lattice has 913 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#386C211yesmaximal, characteristic
2C22×#385C211yesmaximal, characteristic, complemented
3#16885C214yesmaximal, complemented
4#15245C214yesmaximal, complemented
5#15091C212yesmaximal, complemented
6#15026C212yesmaximal, complemented
7#14945C212yesmaximal, complemented
8#14918C212yesmaximal, complemented
9#14020C212yesmaximal, complemented
10#14019C212yesmaximal, complemented
11#13972C212yesmaximal, complemented
12#13971C212yesmaximal, complemented
13#13869C211yesmaximal, characteristic, complemented
14#13869C211yesmaximal, characteristic, complemented
15#13867C211yesmaximal, characteristic
16#13867C211yesmaximal, characteristic
17C4×#379C211yesmaximal, characteristic, complemented
18C24×D4C2211yescharacteristic
19C25×C4C2211yescharacteristic
20C23×C4⋊C4C2211yescharacteristic, complemented
21C23×C4⋊C4C2211yescharacteristic, complemented
22C23×C22⋊C4C2211yescharacteristic
23C23×C22⋊C4C2211yescharacteristic
24C23×C22⋊C4C2211yescharacteristic
25C23×C22⋊C4C2211yescharacteristic
26C23×C22⋊C4C2211yescharacteristic
27C2×#388C2214yescomplemented
28C2×#386—28no—
29C2×#386C2212yes—
30C2×#386C2212yes—
31C2×#386C2212yes—
32C2×#386C2212yes—
33C2×#386C2212yes—
34C2×#386C2212yes—
35C2×#386C2212yes—
36C2×#386C2212yes—
37C2×#385—28no—
38C2×#385C2212yes—
39C2×#385C2212yes—
40C2×#385C2212yescomplemented
41C2×#385C2212yescomplemented
42C2×#381C2212yes—
43C2×#381C2212yes—
44C2×#379C2211yescharacteristic
45C2×#379C2211yescharacteristic
46C2×#379C2212yes—
47C2×#379C2212yes—
48C2×C4×C22⋊C4C2212yes—
49C2×C4×C22⋊C4C2212yescomplemented
50C2×C4×C22⋊C4C2212yescomplemented
51C22×#95C2211yescharacteristic
52C22×#95C2211yescharacteristic
53C22×#95C2211yescharacteristic, complemented
54C22×#95C2211yescharacteristic, complemented
55#1443C2214yescomplemented
56#1443C2214yescomplemented
57#1443C2214yescomplemented
58#1442C2214yescomplemented
59#1442C2214yescomplemented
60#1442C2214yescomplemented
61#1440C2214yescomplemented
62#1440C2214yescomplemented
63#1440C2214yescomplemented
64#1440C2214yescomplemented
65#1440C2214yescomplemented
66#1439C2214yescomplemented
67#1439C2214yescomplemented
68#1439C2214yescomplemented
69#1438C2214yes—
70#1438C2214yes—
71#1437C2214yescomplemented
72#1436C2214yescomplemented
73#1434C2214yescomplemented
74C22⋊#95C2212yes—
75C22⋊#95C2212yes—
76C22⋊#95C2212yes—
77C22⋊#95C2212yes—
78C22⋊#95C2212yes—
79C22⋊#95C2212yescomplemented
80C22⋊#95C2212yescomplemented
81C22⋊#95C2212yescomplemented
82C22⋊#95C2212yescomplemented
83C22⋊#95C2212yescomplemented
84C22⋊#95C2212yescomplemented
85C26C2311yescharacteristic
86C26C2311yescharacteristic
87C23×D4—24no—
88C23×D4—28no—
89C23×D4—24no—
90C23×D4—24no—
91C23×D4—44no—
92C23×D4C2312yes—
93C23×D4C2312yes—
94C24×C4—44no—
95C24×C4—44no—
96C24×C4—44no—
97C24×C4D418yes—
98C24×C4C2311yescharacteristic
99C24×C4C2311yescharacteristic
100C24×C4C2311yescharacteristic
101C24×C4C2311yescharacteristic
102C24×C4C2311yescharacteristic
103C24×C4C2311yescharacteristic
104C24×C4C2311yescharacteristic
105C24×C4C2311yescharacteristic
106C24×C4C2311yescharacteristic
107C24×C4C2311yescharacteristic
108C24×C4C2311yescharacteristic
109C24×C4C2311yescharacteristic
110C24×C4C2311yescharacteristic
111C22×C4⋊C4—24no—
112C22×C4⋊C4—24no—
113C22×C4⋊C4—44no—
114C22×C4⋊C4—44no—
115C22×C4⋊C4C2312yes—
116C22×C4⋊C4C2312yes—
117C22×C4⋊C4C2312yes—
118C22×C4⋊C4C2312yes—
119C22×C22⋊C4—24no—
120C22×C22⋊C4—28no—
121C22×C22⋊C4—24no—
122C22×C22⋊C4—24no—
123C22×C22⋊C4—24no—
124C22×C22⋊C4—24no—
125C22×C22⋊C4—24no—
126C22×C22⋊C4—24no—
127C22×C22⋊C4—44no—
128C22×C22⋊C4—44no—
129C22×C22⋊C4—44no—
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2314yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2314yes—
148C22×C22⋊C4C2314yes—
149C22×C22⋊C4C2314yes—
150C22×C42C2314yes—
151#388—48no—
152#386—28no—
153#386—28no—
154#386—28no—
155#386—28no—
156#386—28no—
157#386—28no—
158#386—44no—
159#386—44no—
160#385—28no—
161#385—28no—
162#385—28no—
163#385—28no—
164#381—28no—
165#381—44no—
166#379—24no—
167#379—24no—
168#379—28no—
169#379—44no—
170C4×C22⋊C4—44no—
171C4×C22⋊C4—44no—
172C4×C22⋊C4—44no—
173C2×#95—24no—
174C2×#95—24no—
175C2×#95—24no—
176C2×#95—24no—
177C2×#95C2314yes—
178C2×#95C2314yes—
179C2×#95C2314yes—
180C2×#95C2314yes—
181C2×#95C2312yes—
182C2×#95C2312yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2314yes—
190C2×#95C2314yes—
191C2×#95C2314yes—
192C2×#95C2314yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C25—24no—
201C25—24no—
202C25—24no—
203C25—24no—
204C25—22no—
205C25—24no—
206C25—22no—
207C25—22no—
208C25—24no—
209C25—24no—
210C25—42no—
211C25—42no—
212C25—42no—
213C25—42no—
214C25—42no—
215C25C2×D414yes—
216C25#4114yes—
217C25#4114yes—
218C25C2412yes—
219C25C2411yescharacteristic
220C25C2411yescharacteristic
221C25C2411yescharacteristic
222C22×D4—232no—
223C22×D4—24no—
224C22×D4—24no—
225C22×D4—24no—
226C22×D4—24no—
227C22×D4—24no—
228C22×D4—24no—
229C22×D4—24no—
230C22×D4—24no—
231C22×D4—24no—
232C22×D4—24no—
233C22×D4—24no—
234C22×D4—42no—
235C22×D4—42no—
236C22×D4—432no—
237C22×D4—432no—
238C22×D4—416no—
239C22×D4—416no—
240C22×D4#4118yes—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—24no—
245C23×C4—24no—
246C23×C4—24no—
247C23×C4—24no—
248C23×C4—24no—
249C23×C4—24no—
250C23×C4—24no—
251C23×C4—24no—
252C23×C4—24no—
253C23×C4—24no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—24no—
263C23×C4—24no—
264C23×C4—24no—
265C23×C4—24no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—24no—
269C23×C4—24no—
270C23×C4—416no—
271C23×C4—42no—
272C23×C4—416no—
273C23×C4—416no—
274C23×C4—42no—
275C23×C4—42no—
276C23×C4—42no—
277C23×C4—42no—
278C23×C4—42no—
279C23×C4—42no—
280C23×C4—42no—
281C23×C4—42no—
282C23×C4—42no—
283C23×C4—42no—
284C23×C4—42no—
285C23×C4—42no—
286C23×C4—42no—
287C23×C4—42no—
288C23×C4—42no—
289C23×C4—42no—
290C23×C4—42no—
291C23×C4—42no—
292C23×C4—42no—
293C23×C4—464no—
294C23×C4C2×D414yes—
295C23×C4C2×D414yes—
296C23×C4C2×D414yes—
297C23×C4C2×D414yes—
298C23×C4C2×D414yes—
299C23×C4C2×D414yes—
300C23×C4C2414yes—
301C23×C4C2414yes—
302C23×C4C2412yes—
303C23×C4C2412yes—
304C23×C4C2412yes—
305C23×C4C2412yes—
306C23×C4C2411yescharacteristic
307C23×C4C2411yescharacteristic
308C23×C4C2411yescharacteristic
309C23×C4C2412yes—
310C23×C4C2412yes—
311C23×C4C2412yes—
312C23×C4C2411yescharacteristic
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—28no—
318C2×C4⋊C4—44no—
319C2×C4⋊C4—44no—
320C2×C4⋊C4—44no—
321C2×C4⋊C4—416no—
322C2×C4⋊C4—416no—
323C2×C22⋊C4—232no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—28no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—28no—
359C2×C22⋊C4—28no—
360C2×C22⋊C4—28no—
361C2×C22⋊C4—28no—
362C2×C22⋊C4—44no—
363C2×C22⋊C4—44no—
364C2×C22⋊C4—44no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4—42no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—416no—
373C2×C22⋊C4—416no—
374C2×C22⋊C4—416no—
375C2×C22⋊C4—416no—
376C2×C22⋊C4—44no—
377C2×C22⋊C4—44no—
378C2×C22⋊C4—44no—
379C2×C22⋊C4—44no—
380C2×C22⋊C4—44no—
381C2×C22⋊C4—44no—
382C2×C22⋊C4—44no—
383C2×C22⋊C4#4118yes—
384C2×C42—28no—
385C2×C42—44no—
386C2×C42—44no—
387#95—24no—
388#95—24no—
389#95—24no—
390#95—24no—
391#95—24no—
392#95—24no—
393#95—24no—
394#95—24no—
395#95—28no—
396#95—28no—
397#95—28no—
398#95—28no—
399#95—44no—
400#95—44no—
401#95—44no—
402#95—44no—
403#95—44no—
404#95—44no—
405#95—44no—
406#95—44no—
407#95—44no—
408#95—44no—
409#95—44no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—28no—
419C24—28no—
420C24—28no—
421C24—28no—
422C24—216no—
423C24—216no—
424C24—216no—
425C24—216no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—28no—
433C24—22no—
434C24—24no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—24no—
439C24—24no—
440C24—22no—
441C24—22no—
442C24—24no—
443C24—44no—
444C24—44no—
445C24—48no—
446C24—48no—
447C24—416no—
448C24—416no—
449C24—416no—
450C24—416no—
451C24—48no—
452C24—48no—
453C24—416no—
454C24—416no—
455C24—44no—
456C24—44no—
457C24—44no—
458C24—44no—
459C24—44no—
460C24—44no—
461C24—48no—
462C24—48no—
463C24—84no—
464C24—84no—
465C24—88no—
466C24—88no—
467C24#124116yes—
468C24C22×D412yes—
469C24C22×D412yes—
470C24C22×D412yes—
471C24C2×#4114yes—
472C24C2×#4112yes—
473C24C2×#4112yes—
474C24C2×#4114yes—
475C24C2×#4114yes—
476C24C2×#4112yes—
477C24C2×#4112yes—
478C24C2×#4112yes—
479C24C2×#4112yes—
480C24H(5,𝔽2)14yes—
481C24H(5,𝔽2)14yes—
482C24C2511yescharacteristic
483C2×D4—216no—
484C2×D4—216no—
485C2×D4—216no—
486C2×D4—216no—
487C2×D4—48no—
488C2×D4—48no—
489C2×D4—48no—
490C2×D4—48no—
491C2×D4—4128no—
492C2×D4—48no—
493C2×D4—48no—
494C2×D4—48no—
495C2×D4—48no—
496C2×D4—48no—
497C2×D4—48no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—28no—
501C22×C4—28no—
502C22×C4—28no—
503C22×C4—28no—
504C22×C4—28no—
505C22×C4—28no—
506C22×C4—28no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—24no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—24no—
530C22×C4—28no—
531C22×C4—28no—
532C22×C4—28no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—24no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—24no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—24no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—24no—
558C22×C4—24no—
559C22×C4—24no—
560C22×C4—24no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—24no—
566C22×C4—24no—
567C22×C4—44no—
568C22×C4—44no—
569C22×C4—44no—
570C22×C4—44no—
571C22×C4—44no—
572C22×C4—44no—
573C22×C4—44no—
574C22×C4—44no—
575C22×C4—44no—
576C22×C4—44no—
577C22×C4—44no—
578C22×C4—416no—
579C22×C4—416no—
580C22×C4—416no—
581C22×C4—416no—
582C22×C4—48no—
583C22×C4—48no—
584C22×C4—416no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—416no—
588C22×C4—416no—
589C22×C4—44no—
590C22×C4—4128no—
591C22×C4—416no—
592C22×C4—44no—
593C22×C4—44no—
594C22×C4—44no—
595C22×C4—44no—
596C22×C4—44no—
597C22×C4—44no—
598C22×C4—44no—
599C22×C4—44no—
600C22×C4—44no—
601C22×C4—44no—
602C22×C4—44no—
603C22×C4—44no—
604C22×C4—44no—
605C22×C4—44no—
606C22×C4—44no—
607C22×C4—48no—
608C22×C4—48no—
609C22×C4—84no—
610C22×C4—84no—
611C22×C4—88no—
612C22×C4—88no—
613C22×C4C22×D412yes—
614C22×C4C22×D412yes—
615C22×C4C22×D412yes—
616C22×C4C22×D412yes—
617C22×C4C2×#4114yes—
618C22×C4C2×#4114yes—
619C22×C4C2×#4114yes—
620C22×C4H(5,𝔽2)14yes—
621C4⋊C4—48no—
622C4⋊C4—48no—
623C4⋊C4—48no—
624C4⋊C4—48no—
625C22⋊C4—216no—
626C22⋊C4—216no—
627C22⋊C4—416no—
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—48no—
638C22⋊C4—48no—
639C22⋊C4—48no—
640C22⋊C4—48no—
641C22⋊C4—48no—
642C22⋊C4—88no—
643C22⋊C4—88no—
644C22⋊C4—88no—
645C42—88no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—28no—
659C23—28no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—28no—
665C23—28no—
666C23—28no—
667C23—28no—
668C23—28no—
669C23—28no—
670C23—232no—
671C23—232no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—24no—
679C23—24no—
680C23—24no—
681C23—24no—
682C23—24no—
683C23—24no—
684C23—24no—
685C23—24no—
686C23—24no—
687C23—28no—
688C23—28no—
689C23—416no—
690C23—416no—
691C23—416no—
692C23—464no—
693C23—464no—
694C23—416no—
695C23—416no—
696C23—416no—
697C23—416no—
698C23—416no—
699C23—44no—
700C23—44no—
701C23—44no—
702C23—44no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—44no—
712C23—44no—
713C23—44no—
714C23—44no—
715C23—44no—
716C23—44no—
717C23—44no—
718C23—44no—
719C23—44no—
720C23—44no—
721C23—832no—
722C23—832no—
723C23—88no—
724C23—88no—
725C23—88no—
726C23—88no—
727C23#52514yes—
728C23#52514yes—
729C23C2×#12414yes—
730C23C2×#12414yes—
731C23C2×#12414yes—
732C23#53414yes—
733C23#53414yes—
734C23#55118yes—
735C23#55118yes—
736C23#55318yes—
737C23#55318yes—
738C23C23×D411yescharacteristic
739C23C22×#4112yes—
740C23C22×#4112yes—
741C23C22×#4111yescharacteristic
742C23C22×#4111yescharacteristic
743C23C2×H(5,𝔽2)12yes—
744C23C2×H(5,𝔽2)12yes—
745C23C2×H(5,𝔽2)12yes—
746C23#58512yes—
747D4—432no—
748D4—432no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—28no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—28no—
767C2×C4—28no—
768C2×C4—416no—
769C2×C4—416no—
770C2×C4—416no—
771C2×C4—416no—
772C2×C4—416no—
773C2×C4—416no—
774C2×C4—416no—
775C2×C4—416no—
776C2×C4—416no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—44no—
803C2×C4—44no—
804C2×C4—44no—
805C2×C4—44no—
806C2×C4—44no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—44no—
810C2×C4—44no—
811C2×C4—44no—
812C2×C4—44no—
813C2×C4—44no—
814C2×C4—44no—
815C2×C4—44no—
816C2×C4—44no—
817C2×C4—44no—
818C2×C4—44no—
819C2×C4—44no—
820C2×C4—44no—
821C2×C4—44no—
822C2×C4—44no—
823C2×C4—44no—
824C2×C4—88no—
825C2×C4—88no—
826C2×C4—88no—
827C2×C4—88no—
828C2×C4#53414yes—
829C22—24no—
830C22—24no—
831C22—24no—
832C22—24no—
833C22—24no—
834C22—24no—
835C22—216no—
836C22—216no—
837C22—24no—
838C22—24no—
839C22—216no—
840C22—216no—
841C22—24no—
842C22—24no—
843C22—24no—
844C22—24no—
845C22—24no—
846C22—24no—
847C22—24no—
848C22—464no—
849C22—42no—
850C22—42no—
851C22—48no—
852C22—48no—
853C22—42no—
854C22—42no—
855C22—44no—
856C22—44no—
857C22—48no—
858C22—48no—
859C22—44no—
860C22—832no—
861C22—82no—
862C22—82no—
863C22—84no—
864C22—82no—
865C22—84no—
866C22—82no—
867C22#256118yes—
868C22#259118yes—
869C22C2×#52511yescharacteristic
870C22C2×#52511yescharacteristic
871C22C22×#12411yescharacteristic
872C22C2×#53411yescharacteristic
873C22C2×#53411yescharacteristic
874C22C2×#53411yescharacteristic
875C22#344911yescharacteristic
876C22C2×#55112yes—
877C22C2×#55112yes—
878C22C2×#55312yes—
879C22C2×#55312yes—
880C22#348114yes—
881C22#350512yes—
882C22#350512yes—
883C22#351314yes—
884C22#351314yes—
885C22#353214yes—
886C4—24no—
887C4—44no—
888C4—42no—
889C4—42no—
890C4—42no—
891C4—44no—
892C4—44no—
893C4—82no—
894C4—82no—
895C4—84no—
896C4—82no—
897C4—84no—
898C4—82no—
899C2—28no—
900C2—28no—
901C2—44no—
902C2—84no—
903C2C2×#256111yescharacteristic
904C2C2×#259111yescharacteristic
905C2#3495611yescharacteristic
906C2#3501911yescharacteristic
907C2#3506211yescharacteristic
908C2#3506211yescharacteristic
909C2#3743611yescharacteristic
910C2#5985014yes—
911C2#5985114yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC24×D4C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C22×#385C2semidirect
3. #16885C2semidirect
4. #15245C2semidirect
5. #15091C2semidirect
6. #15026C2semidirect
7. #14945C2semidirect
8. #14918C2semidirect
9. #14020C2semidirect
10. #14019C2semidirect
11. #13972C2semidirect
12. #13971C2semidirect
13. #13869C2semidirect
14. #13869C2semidirect
17. C4×#379C2semidirect
20. C23×C4⋊C4C22semidirect
21. C23×C4⋊C4C22semidirect
27. C2×#388C22semidirect
40. C2×#385C22semidirect
41. C2×#385C22semidirect
49. C2×C4×C22⋊C4C22semidirect
50. C2×C4×C22⋊C4C22semidirect
53. C22×#95C22semidirect
54. C22×#95C22semidirect
55. #1443C22semidirect
56. #1443C22semidirect
57. #1443C22semidirect
58. #1442C22semidirect
59. #1442C22semidirect
60. #1442C22semidirect
61. #1440C22semidirect
62. #1440C22semidirect
63. #1440C22semidirect
64. #1440C22semidirect
65. #1440C22semidirect
66. #1439C22semidirect
67. #1439C22semidirect
68. #1439C22semidirect
71. #1437C22semidirect
72. #1436C22semidirect
73. #1434C22semidirect
79. C22⋊#95C22semidirect
80. C22⋊#95C22semidirect
81. C22⋊#95C22semidirect
82. C22⋊#95C22semidirect
83. C22⋊#95C22semidirect
84. C22⋊#95C22semidirect

Maximal subgroups

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

subgroupindex
C22×#3862
C22×#3852
#168852
#152452
#150912
#150262
#149452
#149182
#140202
#140192
#139722
#139712
#138692
#138672
C4×#3792