Finite Group Databasebeta

← #656994

Subgroups — #656994

Order 512.

5244 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2405C211yesmaximal, characteristic
2C2×D4×C22⋊C4C211yesmaximal, characteristic
3C22×#386C211yesmaximal, characteristic
4C22×#381C211yesmaximal, characteristic, complemented
5#15702C214yesmaximal, complemented
6#15538C214yesmaximal, complemented
7#14945C212yesmaximal, complemented
8#14935C212yesmaximal, complemented
9#14927C212yesmaximal, complemented
10#14918C212yesmaximal, complemented
11#14681C211yesmaximal, characteristic, complemented
12#13972C212yesmaximal, complemented
13#13968C212yesmaximal, complemented
14#13960C212yesmaximal, complemented
15#13877C211yesmaximal, characteristic, complemented
16#13869C211yesmaximal, characteristic, complemented
17#13869C212yesmaximal, complemented
18C24×D4C2211yescharacteristic
19C25×C4C2211yescharacteristic
20C22×#123C2211yescharacteristic
21C22×#123C2211yescharacteristic
22C22×C4×D4C2212yes—
23C23×C22⋊C4C2211yescharacteristic
24C23×C22⋊C4C2212yes—
25C23×C22⋊C4C2211yescharacteristic
26C23×C22⋊C4C2211yescharacteristic
27C23×C22⋊C4C2211yescharacteristic
28#2405—28no—
29C2×#394C2212yes—
30C2×#394C2212yes—
31D4×C22⋊C4—28no—
32C2×#390C2212yes—
33C2×#386—28no—
34C2×#386C2212yes—
35C2×#386C2212yes—
36C2×#386C2212yes—
37C2×#386C2212yes—
38C2×#386C2211yescharacteristic
39C2×#386C2211yescharacteristic
40C2×#386C2212yes—
41C2×#386C2212yes—
42C2×#385C2212yes—
43C2×#385C2212yes—
44C2×#381—28no—
45C2×#381C2212yes—
46C2×#381C2212yes—
47C2×#381C2212yes—
48C2×#381C2212yes—
49C2×#381C2214yescomplemented
50C2×#381C2212yescomplemented
51C2×#380C2211yescharacteristic
52C2×#380C2212yescomplemented
53C2×#379C2211yescharacteristic
54C2×#379C2212yes—
55C2×#379C2211yescharacteristic
56C2×#379C2211yescharacteristic
57C2×C4×C22⋊C4C2211yescharacteristic
58C22×#95C2212yes—
59C22×#95C2212yescomplemented
60C22×#95C2212yescomplemented
61#1443C2214yescomplemented
62#1443C2214yescomplemented
63#1442C2214yescomplemented
64#1441C2214yescomplemented
65#1441C2214yescomplemented
66#1441C2214yescomplemented
67#1440C2214yescomplemented
68#1440C2214yescomplemented
69#1440C2214yescomplemented
70#1440C2214yescomplemented
71#1440C2214yescomplemented
72#1439C2214yescomplemented
73#1439C2214yescomplemented
74#1439C2214yescomplemented
75#1436C2214yescomplemented
76#1434C2214yescomplemented
77C22⋊#95C2212yes—
78C22⋊#95C2212yes—
79C22⋊#95C2212yes—
80C22⋊#95C2212yescomplemented
81C22⋊#95C2214yescomplemented
82C22⋊#95C2214yescomplemented
83C22⋊#95C2212yescomplemented
84C22⋊#95C2212yescomplemented
85C22⋊#95C2214yescomplemented
86C22⋊#95C2212yescomplemented
87C26C2311yescharacteristic
88C26C2311yescharacteristic
89C23×D4—24no—
90C23×D4—24no—
91C23×D4—28no—
92C23×D4—44no—
93C23×D4D418yes—
94C23×D4C2311yescharacteristic
95C23×D4C2311yescharacteristic
96C23×D4C2311yescharacteristic
97C23×D4C2311yescharacteristic
98C24×C4—24no—
99C24×C4—28no—
100C24×C4—24no—
101C24×C4—24no—
102C24×C4—44no—
103C24×C4C2311yescharacteristic
104C24×C4C2312yes—
105C24×C4C2312yes—
106C24×C4C2312yes—
107C24×C4C2311yescharacteristic
108C24×C4C2312yes—
109C24×C4C2311yescharacteristic
110C24×C4C2312yes—
111C24×C4C2312yes—
112C2×#123—24no—
113C2×#123—24no—
114C2×#123—28no—
115C2×#123—44no—
116C2×C4×D4—28no—
117C2×C4×D4—28no—
118C2×C4×D4—44no—
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2314yes—
123C22×C22⋊C4—24no—
124C22×C22⋊C4—24no—
125C22×C22⋊C4—28no—
126C22×C22⋊C4—24no—
127C22×C22⋊C4—24no—
128C22×C22⋊C4—28no—
129C22×C22⋊C4—24no—
130C22×C22⋊C4—44no—
131C22×C22⋊C4—44no—
132C22×C22⋊C4—44no—
133C22×C22⋊C4—44no—
134C22×C22⋊C4D418yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2311yescharacteristic
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2311yescharacteristic
142C22×C22⋊C4C2311yescharacteristic
143C22×C22⋊C4C2311yescharacteristic
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2314yes—
146C22×C22⋊C4C2314yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2311yescharacteristic
149C22×C22⋊C4C2311yescharacteristic
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2312yes—
159C22×C42C2312yes—
160#394—28no—
161#394—28no—
162#390—28no—
163#386—24no—
164#386—24no—
165#386—28no—
166#386—28no—
167#386—28no—
168#386—28no—
169#386—28no—
170#386—28no—
171#385—28no—
172#385—44no—
173#381—28no—
174#381—28no—
175#381—28no—
176#381—216no—
177#381—44no—
178#381—44no—
179#380—24no—
180#380—44no—
181#379—24no—
182#379—28no—
183#379—24no—
184#379—24no—
185C4×C22⋊C4—24no—
186C2×#95—28no—
187C2×#95—28no—
188C2×#95—28no—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2314yes—
192C2×#95C2314yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2312yes—
199C2×#95C2314yes—
200C2×#95C2312yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C25—24no—
211C25—24no—
212C25—24no—
213C25—24no—
214C25—24no—
215C25—22no—
216C25—24no—
217C25—22no—
218C25—24no—
219C25—44no—
220C25—42no—
221C25—44no—
222C25C2×D414yes—
223C25C2×D414yes—
224C25C2×D414yes—
225C25#4114yes—
226C25C2411yescharacteristic
227C25C2411yescharacteristic
228C25C2411yescharacteristic
229C25C2411yescharacteristic
230C25C2411yescharacteristic
231C22×D4—22no—
232C22×D4—22no—
233C22×D4—24no—
234C22×D4—232no—
235C22×D4—22no—
236C22×D4—22no—
237C22×D4—22no—
238C22×D4—22no—
239C22×D4—22no—
240C22×D4—22no—
241C22×D4—24no—
242C22×D4—24no—
243C22×D4—24no—
244C22×D4—232no—
245C22×D4—24no—
246C22×D4—42no—
247C22×D4—42no—
248C22×D4—416no—
249C22×D4—432no—
250C22×D4—432no—
251C22×D4C2×D414yes—
252C22×D4C2×D414yes—
253C22×D4C2×D414yes—
254C22×D4C2×D414yes—
255C22×D4#4118yes—
256C23×C4—232no—
257C23×C4—24no—
258C23×C4—24no—
259C23×C4—24no—
260C23×C4—24no—
261C23×C4—22no—
262C23×C4—24no—
263C23×C4—24no—
264C23×C4—22no—
265C23×C4—24no—
266C23×C4—24no—
267C23×C4—24no—
268C23×C4—24no—
269C23×C4—28no—
270C23×C4—28no—
271C23×C4—24no—
272C23×C4—24no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—24no—
277C23×C4—24no—
278C23×C4—22no—
279C23×C4—24no—
280C23×C4—24no—
281C23×C4—24no—
282C23×C4—24no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—24no—
286C23×C4—24no—
287C23×C4—24no—
288C23×C4—24no—
289C23×C4—44no—
290C23×C4—44no—
291C23×C4—42no—
292C23×C4—44no—
293C23×C4—44no—
294C23×C4—44no—
295C23×C4—42no—
296C23×C4—44no—
297C23×C4—44no—
298C23×C4—44no—
299C23×C4—44no—
300C23×C4—432no—
301C23×C4—432no—
302C23×C4—416no—
303C23×C4—416no—
304C23×C4C2×D414yes—
305C23×C4C2×D418yes—
306C23×C4#4118yes—
307C23×C4C2412yes—
308C23×C4C2412yes—
309C23×C4C2412yes—
310C23×C4C2412yes—
311C23×C4C2414yes—
312C23×C4C2412yes—
313C23×C4C2412yes—
314C23×C4C2412yes—
315C23×C4C2412yes—
316C23×C4C2411yescharacteristic
317C23×C4C2414yes—
318C23×C4C2411yescharacteristic
319#123—416no—
320#123—416no—
321C4×D4—432no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—28no—
327C2×C4⋊C4—42no—
328C2×C4⋊C4—44no—
329C2×C4⋊C4—44no—
330C2×C4⋊C4—44no—
331C2×C4⋊C4—44no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—28no—
339C2×C22⋊C4—28no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—22no—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—22no—
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—28no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—28no—
367C2×C22⋊C4—28no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—416no—
374C2×C22⋊C4—416no—
375C2×C22⋊C4—44no—
376C2×C22⋊C4—44no—
377C2×C22⋊C4—44no—
378C2×C22⋊C4—44no—
379C2×C22⋊C4—44no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—44no—
382C2×C22⋊C4—432no—
383C2×C22⋊C4—416no—
384C2×C22⋊C4—416no—
385C2×C22⋊C4—44no—
386C2×C22⋊C4—44no—
387C2×C22⋊C4—44no—
388C2×C22⋊C4—44no—
389C2×C22⋊C4—44no—
390C2×C22⋊C4C2×D414yes—
391C2×C22⋊C4C2×D414yes—
392C2×C22⋊C4C2×D418yes—
393C2×C42—24no—
394C2×C42—24no—
395C2×C42—42no—
396#95—28no—
397#95—28no—
398#95—28no—
399#95—28no—
400#95—28no—
401#95—28no—
402#95—24no—
403#95—24no—
404#95—24no—
405#95—24no—
406#95—28no—
407#95—28no—
408#95—44no—
409#95—44no—
410#95—44no—
411#95—44no—
412#95—44no—
413#95—44no—
414#95—44no—
415#95—44no—
416#95—44no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—24no—
422C24—24no—
423C24—28no—
424C24—28no—
425C24—28no—
426C24—28no—
427C24—216no—
428C24—216no—
429C24—216no—
430C24—216no—
431C24—21no—
432C24—22no—
433C24—22no—
434C24—21no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—24no—
441C24—24no—
442C24—28no—
443C24—21no—
444C24—22no—
445C24—21no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—24no—
450C24—28no—
451C24—216no—
452C24—48no—
453C24—48no—
454C24—48no—
455C24—44no—
456C24—48no—
457C24—416no—
458C24—416no—
459C24—416no—
460C24—416no—
461C24—48no—
462C24—48no—
463C24—416no—
464C24—416no—
465C24—44no—
466C24—44no—
467C24—48no—
468C24—84no—
469C24—84no—
470C24—88no—
471C24—88no—
472C24#121116yes—
473C24C22×D412yes—
474C24C22×D412yes—
475C24C22×D412yes—
476C24C22×D412yes—
477C24C22×D412yes—
478C24C22×D412yes—
479C24C22×D412yes—
480C24C22×D412yes—
481C24C2×#4112yes—
482C24C2×#4114yes—
483C24C2×#4112yes—
484C24C2×#4112yes—
485C24C2×#4114yes—
486C24C2×#4114yes—
487C24H(5,𝔽2)14yes—
488C24H(5,𝔽2)14yes—
489C24C2511yescharacteristic
490C2×D4—28no—
491C2×D4—28no—
492C2×D4—216no—
493C2×D4—216no—
494C2×D4—28no—
495C2×D4—28no—
496C2×D4—28no—
497C2×D4—28no—
498C2×D4—28no—
499C2×D4—28no—
500C2×D4—28no—
501C2×D4—44no—
502C2×D4—44no—
503C2×D4—48no—
504C2×D4—48no—
505C2×D4—4128no—
506C2×D4—48no—
507C2×D4—48no—
508C2×D4—48no—
509C2×D4—48no—
510C2×D4#123116yes—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—216no—
515C22×C4—216no—
516C22×C4—28no—
517C22×C4—216no—
518C22×C4—216no—
519C22×C4—216no—
520C22×C4—24no—
521C22×C4—21no—
522C22×C4—24no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—21no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—24no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—216no—
539C22×C4—28no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—24no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—24no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—24no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—24no—
557C22×C4—24no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—24no—
566C22×C4—24no—
567C22×C4—24no—
568C22×C4—24no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—24no—
572C22×C4—24no—
573C22×C4—24no—
574C22×C4—24no—
575C22×C4—24no—
576C22×C4—24no—
577C22×C4—44no—
578C22×C4—48no—
579C22×C4—48no—
580C22×C4—416no—
581C22×C4—416no—
582C22×C4—416no—
583C22×C4—416no—
584C22×C4—48no—
585C22×C4—48no—
586C22×C4—48no—
587C22×C4—48no—
588C22×C4—48no—
589C22×C4—48no—
590C22×C4—4128no—
591C22×C4—48no—
592C22×C4—48no—
593C22×C4—48no—
594C22×C4—48no—
595C22×C4—48no—
596C22×C4—48no—
597C22×C4—48no—
598C22×C4—48no—
599C22×C4—48no—
600C22×C4—44no—
601C22×C4—44no—
602C22×C4—44no—
603C22×C4—44no—
604C22×C4—48no—
605C22×C4—48no—
606C22×C4—48no—
607C22×C4—84no—
608C22×C4—88no—
609C22×C4—88no—
610C22×C4—88no—
611C22×C4—84no—
612C22×C4—84no—
613C22×C4—88no—
614C22×C4—88no—
615C22×C4—88no—
616C22×C4C22×D412yes—
617C22×C4C22×D414yes—
618C22×C4C22×D414yes—
619C22×C4C22×D412yes—
620C22×C4C2×#4118yes—
621C22×C4C2×#4114yes—
622C4⋊C4—48no—
623C4⋊C4—48no—
624C4⋊C4—48no—
625C4⋊C4—88no—
626C22⋊C4—28no—
627C22⋊C4—28no—
628C22⋊C4—48no—
629C22⋊C4—416no—
630C22⋊C4—416no—
631C22⋊C4—48no—
632C22⋊C4—48no—
633C22⋊C4—48no—
634C22⋊C4—48no—
635C22⋊C4—48no—
636C22⋊C4—48no—
637C22⋊C4—44no—
638C22⋊C4—48no—
639C22⋊C4—44no—
640C22⋊C4—48no—
641C22⋊C4—44no—
642C22⋊C4—44no—
643C22⋊C4—48no—
644C22⋊C4—48no—
645C22⋊C4—84no—
646C22⋊C4—84no—
647C22⋊C4—84no—
648C22⋊C4—84no—
649C22⋊C4—84no—
650C42—48no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—28no—
660C23—28no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—28no—
668C23—28no—
669C23—28no—
670C23—28no—
671C23—28no—
672C23—28no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—232no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—24no—
681C23—24no—
682C23—24no—
683C23—24no—
684C23—24no—
685C23—24no—
686C23—24no—
687C23—28no—
688C23—24no—
689C23—24no—
690C23—24no—
691C23—24no—
692C23—28no—
693C23—232no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—24no—
698C23—24no—
699C23—416no—
700C23—432no—
701C23—464no—
702C23—432no—
703C23—432no—
704C23—432no—
705C23—416no—
706C23—432no—
707C23—41no—
708C23—41no—
709C23—42no—
710C23—44no—
711C23—42no—
712C23—42no—
713C23—44no—
714C23—44no—
715C23—44no—
716C23—44no—
717C23—44no—
718C23—41no—
719C23—41no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—44no—
724C23—42no—
725C23—42no—
726C23—44no—
727C23—44no—
728C23—44no—
729C23—416no—
730C23—88no—
731C23—816no—
732C23—832no—
733C23—816no—
734C23—816no—
735C23C2×#12114yes—
736C23C2×#12114yes—
737C23C2×#12114yes—
738C23C2×#12314yes—
739C23C2×#12314yes—
740C23#52514yes—
741C23#53414yes—
742C23#53414yes—
743C23#54618yes—
744C23#54618yes—
745C23#55118yes—
746C23#55118yes—
747C23C23×D411yescharacteristic
748C23C23×D411yescharacteristic
749C23C22×#4111yescharacteristic
750C23C22×#4112yes—
751C23C22×#4112yes—
752C23C2×H(5,𝔽2)12yes—
753C23C2×H(5,𝔽2)12yes—
754C23#58514yes—
755D4—232no—
756D4—416no—
757D4—416no—
758D4—416no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—28no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—22no—
769C2×C4—24no—
770C2×C4—28no—
771C2×C4—24no—
772C2×C4—28no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—416no—
776C2×C4—432no—
777C2×C4—432no—
778C2×C4—44no—
779C2×C4—44no—
780C2×C4—44no—
781C2×C4—42no—
782C2×C4—44no—
783C2×C4—42no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—432no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—44no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—44no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—44no—
804C2×C4—44no—
805C2×C4—44no—
806C2×C4—44no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
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—44no—
825C2×C4—44no—
826C2×C4—816no—
827C2×C4—816no—
828C2×C4—88no—
829C2×C4—816no—
830C2×C4—88no—
831C2×C4C2×#12314yes—
832C22—24no—
833C22—28no—
834C22—28no—
835C22—216no—
836C22—216no—
837C22—24no—
838C22—24no—
839C22—24no—
840C22—28no—
841C22—28no—
842C22—28no—
843C22—28no—
844C22—28no—
845C22—28no—
846C22—24no—
847C22—28no—
848C22—24no—
849C22—24no—
850C22—24no—
851C22—464no—
852C22—42no—
853C22—44no—
854C22—48no—
855C22—48no—
856C22—42no—
857C22—44no—
858C22—44no—
859C22—44no—
860C22—44no—
861C22—44no—
862C22—44no—
863C22—42no—
864C22—44no—
865C22—42no—
866C22—42no—
867C22—44no—
868C22—832no—
869C22—84no—
870C22—82no—
871C22—82no—
872C22#241218yes—
873C22#253418yes—
874C22C22×#12111yescharacteristic
875C22C22×#12311yescharacteristic
876C22C2×#52511yescharacteristic
877C22C2×#53411yescharacteristic
878C22C2×#53411yescharacteristic
879C22C2×#54612yes—
880C22C2×#54612yes—
881C22C2×#55112yes—
882C22C2×#55112yes—
883C22#347514yes—
884C22#348512yes—
885C22#348512yes—
886C22#349112yes—
887C22#349414yes—
888C22#351314yes—
889C22#353414yes—
890C4—24no—
891C4—48no—
892C4—42no—
893C4—44no—
894C4—44no—
895C4—82no—
896C4—82no—
897C4—82no—
898C4—82no—
899C4—82no—
900C4—84no—
901C4—82no—
902C2—28no—
903C2—28no—
904C2—44no—
905C2—44no—
906C2—82no—
907C2C2×#241211yescharacteristic
908C2C2×#253411yescharacteristic
909C2#3544711yescharacteristic
910C2#3615512yes—
911C2#3634012yes—
912C2#3783412yes—
913C2#3802212yes—
914C2#5919514yes—
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
4. C22×#381C2semidirect
5. #15702C2semidirect
6. #15538C2semidirect
7. #14945C2semidirect
8. #14935C2semidirect
9. #14927C2semidirect
10. #14918C2semidirect
11. #14681C2semidirect
12. #13972C2semidirect
13. #13968C2semidirect
14. #13960C2semidirect
15. #13877C2semidirect
16. #13869C2semidirect
17. #13869C2semidirect
49. C2×#381C22semidirect
50. C2×#381C22semidirect
52. C2×#380C22semidirect
59. C22×#95C22semidirect
60. C22×#95C22semidirect
61. #1443C22semidirect
62. #1443C22semidirect
63. #1442C22semidirect
64. #1441C22semidirect
65. #1441C22semidirect
66. #1441C22semidirect
67. #1440C22semidirect
68. #1440C22semidirect
69. #1440C22semidirect
70. #1440C22semidirect
71. #1440C22semidirect
72. #1439C22semidirect
73. #1439C22semidirect
74. #1439C22semidirect
75. #1436C22semidirect
76. #1434C22semidirect
80. C22⋊#95C22semidirect
81. C22⋊#95C22semidirect
82. C22⋊#95C22semidirect
83. C22⋊#95C22semidirect
84. C22⋊#95C22semidirect
85. C22⋊#95C22semidirect
86. C22⋊#95C22semidirect

Maximal subgroups

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

subgroupindex
C2×#24052
C2×D4×C22⋊C42
C22×#3862
C22×#3812
#157022
#155382
#149452
#149352
#149272
#149182
#146812
#139722
#139682
#139602
#138772
#138692