Finite Group Databasebeta

← #846790

Subgroups — #846790

Order 512.

5470 conjugacy classes of subgroups.

The subgroup lattice has 891 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2406C211yesmaximal, characteristic, complemented
2C2×#2411C212yesmaximal, complemented
3C2×#2404C212yesmaximal, complemented
4C22×#390C211yesmaximal, characteristic, complemented
5#16556C212yesmaximal, complemented
6#16551C212yesmaximal, complemented
7#15662C212yesmaximal, complemented
8#15630C212yesmaximal, complemented
9#15419C214yesmaximal, complemented
10#14918C212yesmaximal, complemented
11#14911C212yesmaximal, complemented
12#14715C212yesmaximal, complemented
13#14696C212yesmaximal, complemented
14#14534C214yesmaximal, complemented
15#13870C211yesmaximal, characteristic, complemented
16C23×#41C2211yescharacteristic
17C24×D4C2211yescharacteristic
18C22×#123C2212yes—
19C22×#120C2212yes—
20C22×#120C2212yes—
21C22×#117C2211yescharacteristic
22C23×C4⋊C4C2211yescharacteristic
23C23×C22⋊C4C2212yes—
24C23×C22⋊C4C2212yes—
25C23×C42C2211yescharacteristic
26#2411—216no—
27#2406—28no—
28#2404—216no—
29C2×#396C2214yescomplemented
30C2×#395C2211yescharacteristic, complemented
31C2×#395C2211yescharacteristic, complemented
32C2×#394C2211yescharacteristic, complemented
33C2×#394C2214yescomplemented
34C2×#394C2211yescharacteristic, complemented
35C2×#393C2214yescomplemented
36C2×#392C2214yes—
37C2×#392C2214yes—
38C2×#392C2214yescomplemented
39C2×#390—28no—
40C2×#390C2212yes—
41C2×#390C2212yes—
42C2×#390C2212yes—
43C2×#390C2212yes—
44C2×#390C2214yescomplemented
45C2×#388C2214yescomplemented
46C2×#388C2214yescomplemented
47C2×#386C2212yes—
48C2×#386C2212yes—
49C2×#386C2212yes—
50C2×#386C2214yescomplemented
51C2×#386C2214yescomplemented
52C2×#385C2212yes—
53C2×#385C2212yescomplemented
54C2×#385C2212yescomplemented
55C2×#381C2212yes—
56C2×#381C2211yescharacteristic
57C2×#381C2211yescharacteristic
58C2×#379C2212yes—
59C2×#379C2212yes—
60#1441C2212yescomplemented
61#1441C2212yescomplemented
62#1440C2214yescomplemented
63#1440C2214yescomplemented
64#1439C2214yescomplemented
65#1439C2214yescomplemented
66#1439C2214yescomplemented
67#1439C2214yescomplemented
68#1438C2214yes—
69#1438C2214yes—
70#1438C2214yescomplemented
71#1438C2214yescomplemented
72#1437C2214yescomplemented
73#1436C2212yescomplemented
74#1436C2212yescomplemented
75#1436C2214yescomplemented
76#1434C2214yescomplemented
77C22⋊#95C2212yes—
78C22⋊#95C2212yes—
79C26C2312yes—
80C22×#41—28no—
81C22×#41—24no—
82C22×#41—44no—
83C22×#41—42no—
84C22×#41—42no—
85C23×Q8C2311yescharacteristic
86C23×D4—28no—
87C23×D4—24no—
88C23×D4—44no—
89C23×D4—42no—
90C23×D4—42no—
91C23×D4C2312yes—
92C23×D4C2312yes—
93C23×D4C2311yescharacteristic
94C23×D4C2314yes—
95C23×D4C2314yes—
96C23×D4C2312yes—
97C24×C4C2311yescharacteristic
98C24×C4C2311yescharacteristic
99C24×C4C2311yescharacteristic
100C24×C4C2312yes—
101C24×C4C2312yes—
102C2×#123—28no—
103C2×#123—28no—
104C2×#123—44no—
105C2×#120—28no—
106C2×#120—28no—
107C2×#120—28no—
108C2×#120—44no—
109C2×#120—44no—
110C2×#120—44no—
111C2×#117—28no—
112C2×#117—42no—
113C22×C4⋊C4—42no—
114C22×C4⋊C4—42no—
115C22×C4⋊C4D418yescomplemented
116C22×C4⋊C4C2312yes—
117C22×C4⋊C4C2312yes—
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2314yes—
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2311yescharacteristic
124C22×C22⋊C4—28no—
125C22×C22⋊C4—28no—
126C22×C22⋊C4—28no—
127C22×C22⋊C4—28no—
128C22×C22⋊C4—44no—
129C22×C22⋊C4—44no—
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2312yes—
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⋊C4C2314yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2314yes—
144C22×C22⋊C4C2314yes—
145C22×C22⋊C4C2314yes—
146C22×C22⋊C4C2314yes—
147C22×C22⋊C4C2314yes—
148C22×C22⋊C4C2314yes—
149C22×C42—24no—
150C22×C42—44no—
151C22×C42C2312yes—
152C22×C42C2312yes—
153C22×C42C2312yes—
154#396—216no—
155#395—24no—
156#395—24no—
157#394—24no—
158#394—24no—
159#394—216no—
160#393—216no—
161#392—216no—
162#392—216no—
163#392—48no—
164#390—28no—
165#390—28no—
166#390—28no—
167#390—28no—
168#390—216no—
169#388—216no—
170#388—48no—
171#386—28no—
172#386—28no—
173#386—216no—
174#386—216no—
175#386D4116yescomplemented
176#385—28no—
177#385—28no—
178#385—28no—
179#381—24no—
180#381—28no—
181#381—42no—
182#379—28no—
183#379—44no—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2311yescharacteristic
189C2×#95C2311yescharacteristic
190C2×#95C2314yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2314yes—
194C2×#95C2312yes—
195C2×#95C2314yes—
196C2×#95C2314yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2314yes—
200C25—24no—
201C25—28no—
202C25—24no—
203C25—24no—
204C25—24no—
205C25—24no—
206C25—24no—
207C25—24no—
208C25—44no—
209C25—44no—
210C25—44no—
211C25C2412yes—
212C25C2414yes—
213C25C2411yescharacteristic
214C2×#41—432no—
215C2×#41—416no—
216C2×#41—416no—
217C2×#41—432no—
218C2×#41—416no—
219C22×Q8—24no—
220C22×Q8—22no—
221C22×Q8—42no—
222C22×Q8—41no—
223C22×Q8—41no—
224C22×D4—232no—
225C22×D4—24no—
226C22×D4—24no—
227C22×D4—28no—
228C22×D4—24no—
229C22×D4—24no—
230C22×D4—24no—
231C22×D4—24no—
232C22×D4—24no—
233C22×D4—28no—
234C22×D4—28no—
235C22×D4—28no—
236C22×D4—28no—
237C22×D4—24no—
238C22×D4—24no—
239C22×D4—22no—
240C22×D4—28no—
241C22×D4—24no—
242C22×D4—28no—
243C22×D4—42no—
244C22×D4—42no—
245C22×D4—42no—
246C22×D4—42no—
247C22×D4—42no—
248C22×D4—42no—
249C22×D4—42no—
250C22×D4—41no—
251C22×D4—41no—
252C22×D4—432no—
253C22×D4—432no—
254C22×D4—416no—
255C22×D4—416no—
256C22×D4—44no—
257C22×D4—44no—
258C22×D4—44no—
259C22×D4—44no—
260C22×D4—44no—
261C22×D4—44no—
262C22×D4—44no—
263C22×D4—44no—
264C22×D4—44no—
265C22×D4C2×D418yes—
266C22×D4#4118yescomplemented
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—24no—
270C23×C4—24no—
271C23×C4—24no—
272C23×C4—24no—
273C23×C4—24no—
274C23×C4—24no—
275C23×C4—24no—
276C23×C4—24no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—24no—
282C23×C4—24no—
283C23×C4—24no—
284C23×C4—44no—
285C23×C4—42no—
286C23×C4—42no—
287C23×C4—42no—
288C23×C4—42no—
289C23×C4—44no—
290C23×C4C2×D414yes—
291C23×C4C2×D414yes—
292C23×C4C2×D414yes—
293C23×C4C2×D418yes—
294C23×C4C2412yes—
295C23×C4C2412yes—
296C23×C4C2414yes—
297C23×C4C2411yescharacteristic
298C23×C4C2411yescharacteristic
299C23×C4C2414yes—
300C23×C4C2414yes—
301C23×C4C2411yescharacteristic
302C23×C4C2411yescharacteristic
303C23×C4C2412yes—
304C23×C4C2411yescharacteristic
305C23×C4C2411yescharacteristic
306#123—432no—
307#120—432no—
308#120—432no—
309#117—416no—
310C2×C4⋊C4—28no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—28no—
316C2×C4⋊C4—416no—
317C2×C4⋊C4—41no—
318C2×C4⋊C4—41no—
319C2×C4⋊C4—41no—
320C2×C4⋊C4—41no—
321C2×C4⋊C4—41no—
322C2×C4⋊C4—41no—
323C2×C4⋊C4—41no—
324C2×C4⋊C4—41no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4—42no—
328C2×C4⋊C4—44no—
329C2×C4⋊C4—44no—
330C2×C4⋊C4C2×D414yes—
331C2×C4⋊C4C2×D414yes—
332C2×C4⋊C4C2×D414yes—
333C2×C4⋊C4C2×D414yes—
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—28no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—28no—
346C2×C22⋊C4—28no—
347C2×C22⋊C4—28no—
348C2×C22⋊C4—28no—
349C2×C22⋊C4—28no—
350C2×C22⋊C4—28no—
351C2×C22⋊C4—28no—
352C2×C22⋊C4—28no—
353C2×C22⋊C4—28no—
354C2×C22⋊C4—28no—
355C2×C22⋊C4—28no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—28no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—28no—
362C2×C22⋊C4—28no—
363C2×C22⋊C4—28no—
364C2×C22⋊C4—28no—
365C2×C22⋊C4—28no—
366C2×C22⋊C4—44no—
367C2×C22⋊C4—44no—
368C2×C22⋊C4—44no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4—44no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—44no—
378C2×C22⋊C4—432no—
379C2×C22⋊C4—432no—
380C2×C22⋊C4—44no—
381C2×C22⋊C4—44no—
382C2×C22⋊C4—44no—
383C2×C22⋊C4—44no—
384C2×C22⋊C4—44no—
385C2×C22⋊C4—44no—
386C2×C22⋊C4—44no—
387C2×C22⋊C4—44no—
388C2×C22⋊C4—44no—
389C2×C22⋊C4C2×D418yes—
390C2×C22⋊C4C2×D4116yescomplemented
391C2×C42—28no—
392C2×C42—24no—
393C2×C42—24no—
394C2×C42—28no—
395C2×C42—42no—
396C2×C42—42no—
397C2×C42—42no—
398C2×C42—416no—
399#95—24no—
400#95—28no—
401#95—28no—
402#95—22no—
403#95—22no—
404#95—24no—
405#95—24no—
406#95—28no—
407#95—28no—
408#95—28no—
409#95—28no—
410#95—44no—
411#95—42no—
412#95—42no—
413#95—44no—
414#95C2×D4116yescomplemented
415C24—22no—
416C24—22no—
417C24—24no—
418C24—216no—
419C24—24no—
420C24—22no—
421C24—24no—
422C24—24no—
423C24—22no—
424C24—24no—
425C24—24no—
426C24—24no—
427C24—24no—
428C24—24no—
429C24—22no—
430C24—24no—
431C24—24no—
432C24—24no—
433C24—24no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—24no—
438C24—24no—
439C24—24no—
440C24—24no—
441C24—24no—
442C24—24no—
443C24—416no—
444C24—416no—
445C24—416no—
446C24—416no—
447C24—416no—
448C24—416no—
449C24—48no—
450C24—48no—
451C24—48no—
452C24—48no—
453C24—48no—
454C24—48no—
455C24—48no—
456C24—48no—
457C24—48no—
458C24—48no—
459C24—88no—
460C24—88no—
461C24—88no—
462C24—88no—
463C24—88no—
464C24—88no—
465C24C22×D414yes—
466C24C22×D412yes—
467C24C22×D414yes—
468C24C2×#4118yes—
469C24H(5,𝔽2)12yes—
470C24H(5,𝔽2)12yes—
471C24H(5,𝔽2)14yes—
472C24C2511yescharacteristic
473#41—4128no—
474C2×Q8—48no—
475C2×Q8—44no—
476C2×Q8—44no—
477C2×Q8—48no—
478C2×Q8—44no—
479C2×D4—216no—
480C2×D4—216no—
481C2×D4—216no—
482C2×D4—216no—
483C2×D4—216no—
484C2×D4—48no—
485C2×D4—48no—
486C2×D4—416no—
487C2×D4—416no—
488C2×D4—48no—
489C2×D4—4128no—
490C2×D4—48no—
491C2×D4—48no—
492C2×D4—48no—
493C2×D4—48no—
494C2×D4—48no—
495C2×D4—44no—
496C2×D4—416no—
497C2×D4—416no—
498C2×D4—44no—
499C2×D4—48no—
500C2×D4—44no—
501C2×D4—48no—
502C2×D4—48no—
503C2×D4—48no—
504C2×D4—48no—
505C2×D4—416no—
506C2×D4—416no—
507C2×D4—416no—
508C2×D4—48no—
509C2×D4—88no—
510C2×D4—88no—
511C2×D4—88no—
512C2×D4—88no—
513C2×D4—88no—
514C2×D4—88no—
515C2×D4—88no—
516C2×D4—88no—
517C2×D4—88no—
518C22×C4—216no—
519C22×C4—216no—
520C22×C4—28no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—28no—
528C22×C4—28no—
529C22×C4—28no—
530C22×C4—28no—
531C22×C4—216no—
532C22×C4—216no—
533C22×C4—216no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—21no—
549C22×C4—24no—
550C22×C4—24no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—22no—
564C22×C4—24no—
565C22×C4—24no—
566C22×C4—24no—
567C22×C4—24no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—24no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—24no—
574C22×C4—24no—
575C22×C4—24no—
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—24no—
581C22×C4—24no—
582C22×C4—24no—
583C22×C4—24no—
584C22×C4—24no—
585C22×C4—416no—
586C22×C4—48no—
587C22×C4—48no—
588C22×C4—48no—
589C22×C4—48no—
590C22×C4—48no—
591C22×C4—48no—
592C22×C4—48no—
593C22×C4—416no—
594C22×C4—48no—
595C22×C4—48no—
596C22×C4—48no—
597C22×C4—48no—
598C22×C4—44no—
599C22×C4—44no—
600C22×C4—44no—
601C22×C4—44no—
602C22×C4C22×D418yes—
603C22×C4C22×D418yes—
604C22×C4C22×D412yes—
605C22×C4C22×D412yes—
606C22×C4C22×D414yes—
607C22×C4C22×D412yes—
608C22×C4C22×D412yes—
609C22×C4C22×D412yes—
610C22×C4C22×D412yes—
611C22×C4C2×#4114yes—
612C22×C4H(5,𝔽2)14yes—
613C4⋊C4—44no—
614C4⋊C4—44no—
615C4⋊C4—44no—
616C4⋊C4—44no—
617C4⋊C4—48no—
618C4⋊C4—48no—
619C4⋊C4—48no—
620C4⋊C4—88no—
621C22⋊C4—216no—
622C22⋊C4—416no—
623C22⋊C4—416no—
624C22⋊C4—416no—
625C22⋊C4—416no—
626C22⋊C4—416no—
627C22⋊C4—416no—
628C22⋊C4—416no—
629C22⋊C4—48no—
630C22⋊C4—48no—
631C22⋊C4—416no—
632C22⋊C4—48no—
633C22⋊C4—48no—
634C22⋊C4—48no—
635C22⋊C4—48no—
636C22⋊C4—88no—
637C22⋊C4—88no—
638C22⋊C4—88no—
639C22⋊C4—88no—
640C42—48no—
641C42—48no—
642C42—48no—
643C23—22no—
644C23—22no—
645C23—28no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—28no—
650C23—28no—
651C23—28no—
652C23—24no—
653C23—24no—
654C23—28no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—28no—
659C23—28no—
660C23—28no—
661C23—28no—
662C23—28no—
663C23—28no—
664C23—28no—
665C23—28no—
666C23—432no—
667C23—432no—
668C23—432no—
669C23—42no—
670C23—42no—
671C23—44no—
672C23—44no—
673C23—42no—
674C23—42no—
675C23—44no—
676C23—44no—
677C23—44no—
678C23—44no—
679C23—44no—
680C23—42no—
681C23—44no—
682C23—44no—
683C23—44no—
684C23—42no—
685C23—42no—
686C23—44no—
687C23—44no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—44no—
695C23—44no—
696C23—44no—
697C23—44no—
698C23—44no—
699C23—44no—
700C23—44no—
701C23—42no—
702C23—44no—
703C23—44no—
704C23—44no—
705C23—44no—
706C23—44no—
707C23—44no—
708C23—44no—
709C23—44no—
710C23—44no—
711C23—44no—
712C23—44no—
713C23—44no—
714C23—44no—
715C23—832no—
716C23—832no—
717C23—832no—
718C23—832no—
719C23—816no—
720C23—816no—
721C23—816no—
722C23—816no—
723C23#53414yes—
724C23#53518yes—
725C23D4214yes—
726C23D4218yes—
727C23#56014yes—
728C23C23×D411yescharacteristic
729C23C23×D412yes—
730C23C22×#4112yes—
731C23C2×H(5,𝔽2)11yescharacteristic
732C23C2×H(5,𝔽2)11yescharacteristic
733C23C2×H(5,𝔽2)12yes—
734C23C2×H(5,𝔽2)12yes—
735C23#58514yes—
736Q8—416no—
737D4—432no—
738D4—432no—
739D4—416no—
740D4—432no—
741D4—832no—
742D4—832no—
743C2×C4—232no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—24no—
757C2×C4—28no—
758C2×C4—28no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—28no—
766C2×C4—28no—
767C2×C4—28no—
768C2×C4—28no—
769C2×C4—432no—
770C2×C4—432no—
771C2×C4—416no—
772C2×C4—416no—
773C2×C4—42no—
774C2×C4—44no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—42no—
784C2×C4—41no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—42no—
794C2×C4—44no—
795C2×C4—44no—
796C2×C4—44no—
797C2×C4—42no—
798C2×C4—44no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—44no—
803C2×C4—44no—
804C2×C4—42no—
805C2×C4—42no—
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#52514yes—
815C2×C4#53514yes—
816C22—28no—
817C22—216no—
818C22—24no—
819C22—28no—
820C22—28no—
821C22—24no—
822C22—28no—
823C22—44no—
824C22—48no—
825C22—48no—
826C22—48no—
827C22—48no—
828C22—48no—
829C22—44no—
830C22—48no—
831C22—48no—
832C22—44no—
833C22—48no—
834C22—48no—
835C22—864no—
836C22—82no—
837C22—84no—
838C22—84no—
839C22—84no—
840C22—82no—
841C22—84no—
842C22—84no—
843C22—84no—
844C22—82no—
845C22—84no—
846C22—84no—
847C22—82no—
848C22—84no—
849C22—84no—
850C22#266918yes—
851C22C2×#52511yescharacteristic
852C22C2×#53411yescharacteristic
853C22C2×#53512yes—
854C22C2×#53511yescharacteristic
855C22C2×D4212yes—
856C22C2×D4211yescharacteristic
857C22D4×#4114yes—
858C22#348712yes—
859C22#349012yes—
860C22#349012yes—
861C22#349614yes—
862C22#351314yes—
863C22C2×#56011yescharacteristic
864C22#354214yes—
865C22#354512yes—
866C22#354512yes—
867C4—24no—
868C4—24no—
869C4—42no—
870C4—42no—
871C4—42no—
872C4—42no—
873C4—44no—
874C4—48no—
875C4—48no—
876C4—82no—
877C4—84no—
878C4—82no—
879C2—28no—
880C2—84no—
881C2—88no—
882C2#3505011yescharacteristic
883C2#3610212yes—
884C2#3718711yescharacteristic
885C2#3842014yes—
886C2#3933912yes—
887C2#4633512yes—
888C2C2×#266911yescharacteristic
889C2#5981412yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
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×#2406C2semidirect
2. C2×#2411C2semidirect
3. C2×#2404C2semidirect
4. C22×#390C2semidirect
5. #16556C2semidirect
6. #16551C2semidirect
7. #15662C2semidirect
8. #15630C2semidirect
9. #15419C2semidirect
10. #14918C2semidirect
11. #14911C2semidirect
12. #14715C2semidirect
13. #14696C2semidirect
14. #14534C2semidirect
15. #13870C2semidirect
29. C2×#396C22semidirect
30. C2×#395C22semidirect
31. C2×#395C22semidirect
32. C2×#394C22semidirect
33. C2×#394C22semidirect
34. C2×#394C22semidirect
35. C2×#393C22semidirect
38. C2×#392C22semidirect
44. C2×#390C22semidirect
45. C2×#388C22semidirect
46. C2×#388C22semidirect
50. C2×#386C22semidirect
51. C2×#386C22semidirect
53. C2×#385C22semidirect
54. C2×#385C22semidirect
60. #1441C22semidirect
61. #1441C22semidirect
62. #1440C22semidirect
63. #1440C22semidirect
64. #1439C22semidirect
65. #1439C22semidirect
66. #1439C22semidirect
67. #1439C22semidirect
70. #1438C22semidirect
71. #1438C22semidirect
72. #1437C22semidirect
73. #1436C22semidirect
74. #1436C22semidirect
75. #1436C22semidirect
76. #1434C22semidirect
115. C22×C4⋊C4D4semidirect
175. #386D4semidirect
266. C22×D4#41semidirect
390. C2×C22⋊C4C2×D4semidirect
414. #95C2×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#24062
C2×#24112
C2×#24042
C22×#3902
#165562
#165512
#156622
#156302
#154192
#149182
#149112
#147152
#146962
#145342
#138702