Finite Group Databasebeta

← #663897

Subgroups — #663897

Order 512.

4594 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2483C212yesmaximal, complemented
2C2×D4×C22⋊C4C211yesmaximal, characteristic
3C22×#390C211yesmaximal, characteristic
4#15342C214yesmaximal, complemented
5#15285C214yesmaximal, complemented
6#15138C212yesmaximal, complemented
7#15136C212yesmaximal, complemented
8#14918C212yesmaximal, complemented
9#14727C212yesmaximal, complemented
10#14685C211yesmaximal, characteristic, complemented
11#14130C211yesmaximal, characteristic, complemented
12#14127C212yesmaximal, complemented
13#13977C212yesmaximal, complemented
14#13916C212yesmaximal, complemented
15#13902C211yesmaximal, characteristic
16#13880C211yesmaximal, characteristic, complemented
17C4×#381C211yesmaximal, characteristic, complemented
18C24×D4C2211yescharacteristic
19C22×C4×D4C2211yescharacteristic
20C22×C4×D4C2211yescharacteristic
21C23×C4⋊C4C2211yescharacteristic
22C23×C22⋊C4C2212yes—
23C23×C22⋊C4C2212yes—
24C23×C22⋊C4C2212yes—
25C23×C42C2211yescharacteristic
26#2483—216no—
27C2×#397C2214yescomplemented
28C2×#397C2214yescomplemented
29C2×#397C2214yescomplemented
30D4×C22⋊C4—28no—
31C2×#390—28no—
32C2×#390C2211yescharacteristic
33C2×#390C2212yes—
34C2×#390C2211yescharacteristic
35C2×#390C2212yes—
36C2×#390C2212yes—
37C2×#390C2214yes—
38C2×#390C2212yes—
39C2×#389C2212yescomplemented
40C2×#386C2212yes—
41C2×#386C2212yes—
42C2×#385C2212yes—
43C2×#385C2212yes—
44C2×#385C2212yes—
45C2×#385C2214yescomplemented
46C2×#385C2214yescomplemented
47C2×#384C2212yescomplemented
48C2×#381C2211yescharacteristic
49C2×#381C2212yes—
50C2×#381C2211yescharacteristic
51C2×#381C2214yescomplemented
52C2×#380C2211yescharacteristic
53C2×#380C2211yescharacteristic
54C2×#379C2212yes—
55C2×#379C2212yes—
56C2×#379C2212yes—
57C2×C4×C22⋊C4C2211yescharacteristic
58C2×C4×C22⋊C4C2211yescharacteristic
59#1444C2212yescomplemented
60#1444C2214yescomplemented
61#1442C2212yescomplemented
62#1440C2214yescomplemented
63#1440C2214yescomplemented
64#1440C2214yescomplemented
65#1440C2214yescomplemented
66#1439C2214yescomplemented
67#1439C2214yescomplemented
68#1439C2214yescomplemented
69#1439C2214yescomplemented
70#1439C2214yescomplemented
71#1438C2214yes—
72C4⋊#95C2212yescomplemented
73C4⋊#95C2212yescomplemented
74C4⋊#95C2212yescomplemented
75C4⋊#95C2212yescomplemented
76#1434C2214yescomplemented
77#1434C2212yescomplemented
78#1434C2212yescomplemented
79C22⋊#95C2211yescharacteristic
80C22⋊#95C2212yes—
81C22⋊#95C2212yes—
82C22⋊#95C2211yescharacteristic
83C22⋊#95C2214yescomplemented
84C4×#95C2212yescomplemented
85C4×#95C2212yescomplemented
86C26C2312yes—
87C23×D4—28no—
88C23×D4—24no—
89C23×D4—24no—
90C23×D4—44no—
91C23×D4D418yes—
92C23×D4C2311yescharacteristic
93C23×D4C2312yes—
94C23×D4C2311yescharacteristic
95C24×C4C2311yescharacteristic
96C24×C4C2311yescharacteristic
97C24×C4C2312yes—
98C24×C4C2311yescharacteristic
99C24×C4C2312yes—
100C24×C4C2312yes—
101C2×C4×D4—24no—
102C2×C4×D4—24no—
103C2×C4×D4—28no—
104C2×C4×D4—44no—
105C22×C4⋊C4—24no—
106C22×C4⋊C4—44no—
107C22×C4⋊C4C2312yes—
108C22×C4⋊C4C2311yescharacteristic
109C22×C4⋊C4C2311yescharacteristic
110C22×C4⋊C4C2312yes—
111C22×C4⋊C4C2314yes—
112C22×C4⋊C4C2314yes—
113C22×C4⋊C4C2312yes—
114C22×C4⋊C4C2314yes—
115C22×C22⋊C4—28no—
116C22×C22⋊C4—28no—
117C22×C22⋊C4—28no—
118C22×C22⋊C4—28no—
119C22×C22⋊C4—28no—
120C22×C22⋊C4—48no—
121C22×C22⋊C4—44no—
122C22×C22⋊C4—44no—
123C22×C22⋊C4C2312yes—
124C22×C22⋊C4C2312yes—
125C22×C22⋊C4C2311yescharacteristic
126C22×C22⋊C4C2312yes—
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2314yes—
130C22×C22⋊C4C2314yes—
131C22×C22⋊C4C2314yes—
132C22×C22⋊C4C2314yes—
133C22×C22⋊C4C2314yes—
134C22×C22⋊C4C2314yes—
135C22×C22⋊C4C2311yescharacteristic
136C22×C22⋊C4C2311yescharacteristic
137C22×C22⋊C4C2311yescharacteristic
138C22×C22⋊C4C2314yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2314yes—
142C22×C22⋊C4C2312yes—
143C22×C42—24no—
144C22×C42—24no—
145C22×C42—24no—
146C22×C42C2312yes—
147C22×C42C2312yes—
148C22×C42C2311yescharacteristic
149C22×C42C2311yescharacteristic
150C22×C42C2312yes—
151#397—216no—
152#397—216no—
153#397—48no—
154#390—24no—
155#390—24no—
156#390—28no—
157#390—216no—
158#390—28no—
159#390—28no—
160#390—44no—
161#389—44no—
162#386—28no—
163#386—28no—
164#385—28no—
165#385—28no—
166#385—216no—
167#385—48no—
168#385—44no—
169#384—44no—
170#381—28no—
171#381—24no—
172#381—216no—
173#381D418yescomplemented
174#380—24no—
175#380—24no—
176#379—28no—
177#379—28no—
178#379—28no—
179C4×C22⋊C4—24no—
180C4×C22⋊C4—24no—
181C2×#95C2312yes—
182C2×#95C2314yes—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2311yescharacteristic
193C2×#95C2311yescharacteristic
194C2×#95C2312yes—
195C2×#95C2314yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C25—28no—
204C25—24no—
205C25—24no—
206C25—24no—
207C25—24no—
208C25—24no—
209C25—24no—
210C25—44no—
211C25—44no—
212C25—44no—
213C25C2×D418yes—
214C25C2412yes—
215C25C2412yes—
216C25C2411yescharacteristic
217C22×D4—28no—
218C22×D4—232no—
219C22×D4—232no—
220C22×D4—22no—
221C22×D4—22no—
222C22×D4—24no—
223C22×D4—24no—
224C22×D4—22no—
225C22×D4—24no—
226C22×D4—22no—
227C22×D4—24no—
228C22×D4—24no—
229C22×D4—416no—
230C22×D4—432no—
231C22×D4—432no—
232C22×D4—44no—
233C22×D4C2×D414yes—
234C22×D4C2×D418yes—
235C22×D4C2×D414yes—
236C22×D4#4118yes—
237C23×C4—24no—
238C23×C4—24no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—24no—
247C23×C4—24no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—24no—
251C23×C4—24no—
252C23×C4—28no—
253C23×C4—24no—
254C23×C4—24no—
255C23×C4—24no—
256C23×C4—24no—
257C23×C4—42no—
258C23×C4—42no—
259C23×C4—42no—
260C23×C4—44no—
261C23×C4—44no—
262C23×C4—44no—
263C23×C4—44no—
264C23×C4—44no—
265C23×C4C2×D414yes—
266C23×C4C2×D414yes—
267C23×C4#4114yes—
268C23×C4#4114yes—
269C23×C4C2414yes—
270C23×C4C2411yescharacteristic
271C23×C4C2411yescharacteristic
272C23×C4C2412yes—
273C23×C4C2414yes—
274C23×C4C2412yes—
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2411yescharacteristic
278C23×C4C2411yescharacteristic
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2411yescharacteristic
282C23×C4C2411yescharacteristic
283C4×D4—416no—
284C4×D4—416no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—28no—
297C2×C4⋊C4—28no—
298C2×C4⋊C4—44no—
299C2×C4⋊C4—416no—
300C2×C4⋊C4—44no—
301C2×C4⋊C4—44no—
302C2×C4⋊C4—44no—
303C2×C4⋊C4—44no—
304C2×C4⋊C4—44no—
305C2×C4⋊C4—44no—
306C2×C4⋊C4—44no—
307C2×C22⋊C4—22no—
308C2×C22⋊C4—22no—
309C2×C22⋊C4—22no—
310C2×C22⋊C4—22no—
311C2×C22⋊C4—22no—
312C2×C22⋊C4—22no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—28no—
318C2×C22⋊C4—28no—
319C2×C22⋊C4—28no—
320C2×C22⋊C4—28no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—22no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—28no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—22no—
329C2×C22⋊C4—28no—
330C2×C22⋊C4—28no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—22no—
333C2×C22⋊C4—28no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—28no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—28no—
338C2×C22⋊C4—28no—
339C2×C22⋊C4—28no—
340C2×C22⋊C4—28no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—28no—
344C2×C22⋊C4—28no—
345C2×C22⋊C4—432no—
346C2×C22⋊C4—42no—
347C2×C22⋊C4—42no—
348C2×C22⋊C4—44no—
349C2×C22⋊C4—44no—
350C2×C22⋊C4—44no—
351C2×C22⋊C4—44no—
352C2×C22⋊C4—44no—
353C2×C22⋊C4—44no—
354C2×C22⋊C4—44no—
355C2×C22⋊C4—432no—
356C2×C22⋊C4—432no—
357C2×C22⋊C4—44no—
358C2×C22⋊C4—44no—
359C2×C22⋊C4—44no—
360C2×C22⋊C4—44no—
361C2×C22⋊C4—44no—
362C2×C22⋊C4—44no—
363C2×C22⋊C4C2×D414yes—
364C2×C22⋊C4C2×D414yes—
365C2×C22⋊C4#4114yes—
366C2×C42—22no—
367C2×C42—22no—
368C2×C42—24no—
369C2×C42—24no—
370C2×C42—24no—
371C2×C42—24no—
372C2×C42—24no—
373C2×C42—24no—
374C2×C42—24no—
375C2×C42—24no—
376C2×C42—24no—
377C2×C42—24no—
378C2×C42—24no—
379C2×C42—416no—
380#95—22no—
381#95—22no—
382#95—24no—
383#95—28no—
384#95—28no—
385#95—28no—
386#95—28no—
387#95—24no—
388#95—24no—
389#95—24no—
390#95—24no—
391#95—24no—
392#95—28no—
393#95—24no—
394#95—42no—
395#95—42no—
396#95—44no—
397#95—44no—
398#95—44no—
399#95—44no—
400#95C2×D418yescomplemented
401#95C2×D418yescomplemented
402C24—22no—
403C24—22no—
404C24—22no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—24no—
411C24—22no—
412C24—24no—
413C24—22no—
414C24—24no—
415C24—216no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—24no—
421C24—24no—
422C24—22no—
423C24—24no—
424C24—22no—
425C24—24no—
426C24—216no—
427C24—216no—
428C24—216no—
429C24—48no—
430C24—48no—
431C24—48no—
432C24—416no—
433C24—416no—
434C24—416no—
435C24—416no—
436C24—416no—
437C24—416no—
438C24—48no—
439C24—48no—
440C24—48no—
441C24—48no—
442C24—88no—
443C24—88no—
444C24—88no—
445C24—88no—
446C24—88no—
447C24—88no—
448C24C22×D414yes—
449C24C22×D414yes—
450C24C22×D412yes—
451C24C22×D412yes—
452C24C2×#4118yes—
453C24C2×#4112yes—
454C24C2×#4112yes—
455C24C2×#4112yes—
456C24H(5,𝔽2)12yes—
457C242−1+412yes—
458C24C2511yescharacteristic
459C2×D4—216no—
460C2×D4—28no—
461C2×D4—216no—
462C2×D4—28no—
463C2×D4—28no—
464C2×D4—28no—
465C2×D4—28no—
466C2×D4—216no—
467C2×D4—216no—
468C2×D4—4128no—
469C2×D4—48no—
470C2×D4—416no—
471C2×D4—416no—
472C2×D4—48no—
473C2×D4—48no—
474C2×D4#123116yes—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—28no—
478C22×C4—28no—
479C22×C4—216no—
480C22×C4—216no—
481C22×C4—28no—
482C22×C4—28no—
483C22×C4—28no—
484C22×C4—28no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—24no—
519C22×C4—22no—
520C22×C4—24no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—24no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—24no—
529C22×C4—22no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—22no—
534C22×C4—24no—
535C22×C4—24no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—24no—
541C22×C4—24no—
542C22×C4—22no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—24no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—24no—
549C22×C4—22no—
550C22×C4—24no—
551C22×C4—48no—
552C22×C4—48no—
553C22×C4—48no—
554C22×C4—48no—
555C22×C4—416no—
556C22×C4—44no—
557C22×C4—44no—
558C22×C4—44no—
559C22×C4—44no—
560C22×C4—44no—
561C22×C4—44no—
562C22×C4—48no—
563C22×C4—48no—
564C22×C4—48no—
565C22×C4—48no—
566C22×C4—48no—
567C22×C4—88no—
568C22×C4—84no—
569C22×C4—84no—
570C22×C4—88no—
571C22×C4—88no—
572C22×C4—88no—
573C22×C4—88no—
574C22×C4#123116yes—
575C22×C4C22×D414yes—
576C22×C4C22×D412yes—
577C22×C4C22×D414yes—
578C22×C4C22×D412yes—
579C22×C4C22×D412yes—
580C22×C4C22×D412yes—
581C22×C4C2×#4114yes—
582C22×C4C2×#4112yes—
583C22×C4C2×#4112yes—
584C22×C4C2×#4112yes—
585C22×C4C2×#4114yes—
586C22×C4C2×#4112yes—
587C22×C4H(5,𝔽2)14yes—
588C22×C4H(5,𝔽2)14yes—
589C4⋊C4—48no—
590C4⋊C4—44no—
591C4⋊C4—48no—
592C4⋊C4—44no—
593C4⋊C4—48no—
594C4⋊C4—88no—
595C4⋊C4—88no—
596C4⋊C4—88no—
597C22⋊C4—28no—
598C22⋊C4—28no—
599C22⋊C4—28no—
600C22⋊C4—416no—
601C22⋊C4—416no—
602C22⋊C4—48no—
603C22⋊C4—48no—
604C22⋊C4—416no—
605C22⋊C4—416no—
606C22⋊C4—416no—
607C22⋊C4—416no—
608C22⋊C4—48no—
609C22⋊C4—48no—
610C22⋊C4—48no—
611C22⋊C4—48no—
612C22⋊C4—44no—
613C22⋊C4—88no—
614C22⋊C4—88no—
615C22⋊C4—84no—
616C22⋊C4—84no—
617C42—48no—
618C42—48no—
619C42—44no—
620C42—44no—
621C42—48no—
622C23—22no—
623C23—22no—
624C23—24no—
625C23—24no—
626C23—24no—
627C23—24no—
628C23—22no—
629C23—22no—
630C23—24no—
631C23—24no—
632C23—24no—
633C23—24no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—28no—
643C23—28no—
644C23—28no—
645C23—28no—
646C23—24no—
647C23—24no—
648C23—28no—
649C23—28no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—432no—
658C23—432no—
659C23—432no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—44no—
665C23—44no—
666C23—44no—
667C23—44no—
668C23—44no—
669C23—44no—
670C23—42no—
671C23—432no—
672C23—42no—
673C23—42no—
674C23—44no—
675C23—44no—
676C23—44no—
677C23—42no—
678C23—44no—
679C23—44no—
680C23—44no—
681C23—44no—
682C23—44no—
683C23—44no—
684C23—44no—
685C23—44no—
686C23—44no—
687C23—816no—
688C23—816no—
689C23—816no—
690C23—832no—
691C23—832no—
692C23—832no—
693C23—832no—
694C23C2×#12318yes—
695C23C2×#12314yes—
696C23#53214yes—
697C23#54214yes—
698C23D4214yes—
699C23#54714yes—
700C23#54714yes—
701C23#55314yes—
702C23C23×D411yescharacteristic
703C23C23×D411yescharacteristic
704C23C22×#4111yescharacteristic
705C23C22×#4111yescharacteristic
706C23C22×#4112yes—
707C23C22×#4111yescharacteristic
708C23C2×H(5,𝔽2)12yes—
709C23C2×H(5,𝔽2)11yescharacteristic
710C23C2×H(5,𝔽2)12yes—
711C23C2×2−1+411yescharacteristic
712C23#58512yes—
713D4—232no—
714D4—432no—
715D4—416no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—232no—
721C2×C4—24no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—416no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—416no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—41no—
749C2×C4—42no—
750C2×C4—41no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—41no—
762C2×C4—42no—
763C2×C4—44no—
764C2×C4—41no—
765C2×C4—42no—
766C2×C4—44no—
767C2×C4—44no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—44no—
773C2×C4—44no—
774C2×C4—44no—
775C2×C4—44no—
776C2×C4—42no—
777C2×C4—44no—
778C2×C4—41no—
779C2×C4—42no—
780C2×C4—41no—
781C2×C4—42no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—42no—
795C2×C4—816no—
796C2×C4—816no—
797C2×C4—816no—
798C2×C4C2×#12314yes—
799C2×C4C2×#12314yes—
800C2×C4C2×#12314yes—
801C2×C4#53414yes—
802C2×C4#55118yes—
803C2×C4#55118yes—
804C22—24no—
805C22—28no—
806C22—28no—
807C22—24no—
808C22—28no—
809C22—28no—
810C22—24no—
811C22—24no—
812C22—24no—
813C22—24no—
814C22—28no—
815C22—28no—
816C22—28no—
817C22—44no—
818C22—48no—
819C22—44no—
820C22—48no—
821C22—48no—
822C22—48no—
823C22—44no—
824C22—44no—
825C22—44no—
826C22—44no—
827C22—44no—
828C22—44no—
829C22—44no—
830C22—44no—
831C22—44no—
832C22—864no—
833C22—84no—
834C22—84no—
835C22—84no—
836C22—84no—
837C22#242218yes—
838C22C22×#12311yescharacteristic
839C22C22×#12311yescharacteristic
840C22C2×#53211yescharacteristic
841C22C2×#53411yescharacteristic
842C22C2×#54211yescharacteristic
843C22C2×D4211yescharacteristic
844C22C2×#54711yescharacteristic
845C22C2×#54711yescharacteristic
846C22D4×#4112yes—
847C22C2×#55112yes—
848C22C2×#55112yes—
849C22C2×#55311yescharacteristic
850C22#348112yes—
851C22#348411yescharacteristic
852C22#348511yescharacteristic
853C22#349412yes—
854C22#349412yes—
855C22#349812yes—
856C22#351312yes—
857C22#351412yes—
858C22#352012yes—
859C22#354312yes—
860C22#356112yes—
861C4—24no—
862C4—44no—
863C4—44no—
864C4—44no—
865C4—42no—
866C4—44no—
867C4—42no—
868C4—81no—
869C4—81no—
870C4—84no—
871C4—82no—
872C4—84no—
873C4—82no—
874C4#248318yescomplemented
875C2—28no—
876C2—48no—
877C2—84no—
878C2C2×#242211yescharacteristic
879C2C2×#248311yescharacteristic
880C2#3554011yescharacteristic
881C2D4×#12311yescharacteristic
882C2#3623711yescharacteristic
883C2#3626412yes—
884C2#3805412yes—
885C2#3891811yescharacteristic
886C2#3933611yescharacteristic
887C2#5920812yes—
888C2#5927312yes—
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
1. C2×#2483C2semidirect
4. #15342C2semidirect
5. #15285C2semidirect
6. #15138C2semidirect
7. #15136C2semidirect
8. #14918C2semidirect
9. #14727C2semidirect
10. #14685C2semidirect
11. #14130C2semidirect
12. #14127C2semidirect
13. #13977C2semidirect
14. #13916C2semidirect
16. #13880C2semidirect
17. C4×#381C2semidirect
27. C2×#397C22semidirect
28. C2×#397C22semidirect
29. C2×#397C22semidirect
39. C2×#389C22semidirect
45. C2×#385C22semidirect
46. C2×#385C22semidirect
47. C2×#384C22semidirect
51. C2×#381C22semidirect
59. #1444C22semidirect
60. #1444C22semidirect
61. #1442C22semidirect
62. #1440C22semidirect
63. #1440C22semidirect
64. #1440C22semidirect
65. #1440C22semidirect
66. #1439C22semidirect
67. #1439C22semidirect
68. #1439C22semidirect
69. #1439C22semidirect
70. #1439C22semidirect
72. C4⋊#95C22semidirect
73. C4⋊#95C22semidirect
74. C4⋊#95C22semidirect
75. C4⋊#95C22semidirect
76. #1434C22semidirect
77. #1434C22semidirect
78. #1434C22semidirect
83. C22⋊#95C22semidirect
84. C4×#95C22semidirect
85. C4×#95C22semidirect
173. #381D4semidirect
400. #95C2×D4semidirect
401. #95C2×D4semidirect
874. C4#2483semidirect

Maximal subgroups

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

subgroupindex
C2×#24832
C2×D4×C22⋊C42
C22×#3902
#153422
#152852
#151382
#151362
#149182
#147272
#146852
#141302
#141272
#139772
#139162
#139022
#138802
C4×#3812