Finite Group Databasebeta

← #719818

Subgroups — #719818

Order 512.

4214 conjugacy classes of subgroups.

The subgroup lattice has 909 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2537C211yesmaximal, characteristic, complemented
2C2×#2535C211yesmaximal, characteristic, complemented
3C2×#2428C212yesmaximal, complemented
4C2×#2349C211yesmaximal, characteristic, complemented
5C2×#2328C211yesmaximal, characteristic, complemented
6#16401C212yesmaximal, complemented
7#16260C212yesmaximal, complemented
8#15376C214yesmaximal, complemented
9#15274C214yesmaximal, complemented
10#15220C212yesmaximal, complemented
11#15126C212yesmaximal, complemented
12#14757C212yesmaximal, complemented
13#14735C212yesmaximal, complemented
14#14277C211yesmaximal, characteristic, complemented
15#13970C212yesmaximal, complemented
16#13906C211yesmaximal, characteristic, complemented
17#13847C211yesmaximal, characteristic, complemented
18C22×#127C2211yescharacteristic
19C22×#121C2212yes—
20C22×#121C2212yes—
21C22×#121C2212yes—
22C22×#121C2214yes—
23C22×C4×D4C2211yescharacteristic
24C22×C4×D4C2211yescharacteristic
25C22×C4×D4C2212yes—
26C22×C4×D4C2211yescharacteristic
27#2537—28no—
28#2535—28no—
29#2428—216no—
30C2×#397C2212yes—
31C2×#394C2214yes—
32C2×#394C2214yes—
33C2×#394C2214yes—
34C2×#392C2214yes—
35C2×#392C2212yes—
36#2349—28no—
37#2328—28no—
38C2×#390C2211yescharacteristic
39C2×#390C2211yescharacteristic
40C2×#390C2212yes—
41C2×#389C2212yes—
42C2×#389C2212yes—
43C2×#386C2212yes—
44C2×#386C2214yes—
45C2×#386C2214yes—
46C2×#386C2212yes—
47C2×#386C2212yes—
48C2×#386C2212yes—
49C2×#386C2214yes—
50C2×#385C2214yes—
51C2×#384C2211yescharacteristic
52C2×#382C2211yescharacteristic
53C2×#382C2211yescharacteristic
54C2×#380C2212yes—
55C2×#380C2212yes—
56C2×#380C2212yes—
57C2×#380C2212yes—
58C2×#380C2214yes—
59C2×C4×C4⋊C4C2211yescharacteristic
60C2×C4×C22⋊C4C2212yes—
61C2×C4×C22⋊C4C2212yes—
62C2×#376C2211yescharacteristic
63C22×#95C2212yes—
64#1445C2211yescharacteristic
65#1445C2211yescharacteristic
66#1444C2212yes—
67#1444C2212yes—
68#1443C2214yes—
69#1442C2212yes—
70#1442C2212yes—
71#1441C2214yes—
72#1440C2214yes—
73#1440C2214yes—
74#1439C2212yes—
75#1439C2214yes—
76#1439C2214yes—
77#1439C2212yes—
78#1439C2212yes—
79#1439C2212yes—
80#1439C2214yes—
81#1438C2214yes—
82#1438C2211yescharacteristic
83#1438C2211yescharacteristic
84#1438C2214yes—
85C4⋊#95C2212yes—
86C4⋊#95C2212yes—
87C22⋊#95C2214yes—
88C23×D4C2311yescharacteristic
89C23×D4C2311yescharacteristic
90C23×D4C2314yes—
91C23×D4C2311yescharacteristic
92C23×D4C2314yes—
93C23×D4C2312yes—
94C23×D4C2312yes—
95C24×C4C2312yes—
96C24×C4C2314yes—
97C24×C4C2312yes—
98C24×C4C2312yes—
99C2×#127—24no—
100C2×#127—24no—
101C2×#127D418yescomplemented
102C2×#121—216no—
103C2×#121—28no—
104C2×#121—28no—
105C2×#121—28no—
106C2×#121—28no—
107C2×#121—28no—
108C2×#121—28no—
109C2×#121—48no—
110C2×#121—48no—
111C2×#121—48no—
112C2×#121—44no—
113C2×C4×D4—28no—
114C2×C4×D4—28no—
115C2×C4×D4—24no—
116C2×C4×D4—24no—
117C2×C4×D4—24no—
118C2×C4×D4—24no—
119C2×C4×D4—24no—
120C2×C4×D4—24no—
121C2×C4×D4—24no—
122C2×C4×D4—24no—
123C2×C4×D4—44no—
124C2×C4×D4D418yescomplemented
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2314yes—
133C22×C4⋊C4C2314yes—
134C22×C4⋊C4C2312yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2314yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2314yes—
140C22×C22⋊C4C2314yes—
141C22×C22⋊C4C2314yes—
142C22×C22⋊C4C2314yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2314yes—
146C22×C22⋊C4C2314yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C42C2312yes—
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157#397—28no—
158#394—216no—
159#394—216no—
160#394—48no—
161#392—216no—
162#392—28no—
163#390—24no—
164#390—28no—
165#390—24no—
166#389—28no—
167#389—28no—
168#386—216no—
169#386—28no—
170#386—28no—
171#386—28no—
172#386—28no—
173#386—216no—
174#386—48no—
175#385—216no—
176#384—24no—
177#382—24no—
178#382D418yescomplemented
179#380—28no—
180#380—28no—
181#380—28no—
182#380—28no—
183#380—48no—
184C4×C4⋊C4—24no—
185C4×C22⋊C4—28no—
186C4×C22⋊C4—44no—
187#376—24no—
188C2×#95—28no—
189C2×#95C2314yes—
190C2×#95C2312yes—
191C2×#95C2314yes—
192C2×#95C2314yes—
193C2×#95C2314yes—
194C2×#95C2311yescharacteristic
195C2×#95C2311yescharacteristic
196C2×#95C2314yes—
197C2×#95C2311yescharacteristic
198C2×#95C2311yescharacteristic
199C2×#95C2312yes—
200C2×#95C2311yescharacteristic
201C2×#95C2312yes—
202C2×#95C2311yescharacteristic
203C2×#95C2312yes—
204C2×#95C2314yes—
205C2×#95C2312yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C25C2412yes—
212C25C2412yes—
213C25C2412yes—
214C22×D4—24no—
215C22×D4—24no—
216C22×D4—24no—
217C22×D4—24no—
218C22×D4—24no—
219C22×D4—28no—
220C22×D4—28no—
221C22×D4—28no—
222C22×D4—28no—
223C22×D4—28no—
224C22×D4—28no—
225C22×D4—22no—
226C22×D4—22no—
227C22×D4—22no—
228C22×D4—22no—
229C22×D4—22no—
230C22×D4—28no—
231C22×D4—22no—
232C22×D4—22no—
233C22×D4—22no—
234C22×D4—22no—
235C22×D4—22no—
236C22×D4—22no—
237C22×D4—22no—
238C22×D4—22no—
239C22×D4—42no—
240C22×D4—44no—
241C22×D4—44no—
242C22×D4—44no—
243C22×D4—44no—
244C22×D4—44no—
245C22×D4—44no—
246C22×D4—44no—
247C22×D4—44no—
248C22×D4—44no—
249C22×D4—44no—
250C22×D4—44no—
251C22×D4C2×D414yes—
252C22×D4C2×D414yes—
253C22×D4C2×D414yes—
254C22×D4C2×D418yes—
255C22×D4C2×D418yes—
256C22×D4#4114yes—
257C23×C4—24no—
258C23×C4—24no—
259C23×C4—28no—
260C23×C4—24no—
261C23×C4—24no—
262C23×C4—24no—
263C23×C4—24no—
264C23×C4—24no—
265C23×C4—24no—
266C23×C4—24no—
267C23×C4—24no—
268C23×C4—28no—
269C23×C4—28no—
270C23×C4—24no—
271C23×C4—24no—
272C23×C4—44no—
273C23×C4—44no—
274C23×C4—44no—
275C23×C4—44no—
276C23×C4—44no—
277C23×C4—44no—
278C23×C4—44no—
279C23×C4—44no—
280C23×C4C2×D418yes—
281C23×C4C2412yes—
282C23×C4C2411yescharacteristic
283C23×C4C2411yescharacteristic
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2414yes—
287C23×C4C2412yes—
288C23×C4C2414yes—
289C23×C4C2411yescharacteristic
290C23×C4C2411yescharacteristic
291C23×C4C2412yes—
292C23×C4C2411yescharacteristic
293C23×C4C2411yescharacteristic
294C23×C4C2411yescharacteristic
295#127—232no—
296#121—464no—
297#121—432no—
298#121—432no—
299#121—432no—
300C4×D4—232no—
301C4×D4—432no—
302C4×D4—416no—
303C4×D4—416no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—28no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—28no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4—44no—
325C2×C4⋊C4—44no—
326C2×C4⋊C4—44no—
327C2×C4⋊C4—44no—
328C2×C4⋊C4—44no—
329C2×C4⋊C4—44no—
330C2×C4⋊C4C2×D418yes—
331C2×C4⋊C4C2×D414yes—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—28no—
338C2×C22⋊C4—28no—
339C2×C22⋊C4—28no—
340C2×C22⋊C4—28no—
341C2×C22⋊C4—28no—
342C2×C22⋊C4—28no—
343C2×C22⋊C4—28no—
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—28no—
351C2×C22⋊C4—28no—
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—28no—
360C2×C22⋊C4—28no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—44no—
368C2×C22⋊C4—44no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4—44no—
375C2×C22⋊C4—44no—
376C2×C22⋊C4—44no—
377C2×C22⋊C4—44no—
378C2×C22⋊C4—44no—
379C2×C22⋊C4—44no—
380C2×C22⋊C4—44no—
381C2×C22⋊C4C2×D418yes—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—24no—
385C2×C42—24no—
386C2×C42—22no—
387C2×C42—24no—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42C2×D414yes—
391C2×C42C2×D414yes—
392C2×C42C2×D414yes—
393C2×C42#4114yes—
394#95—22no—
395#95—28no—
396#95—22no—
397#95—22no—
398#95—22no—
399#95—22no—
400#95—24no—
401#95—24no—
402#95—22no—
403#95—28no—
404#95—28no—
405#95—24no—
406#95—24no—
407#95—28no—
408#95—28no—
409#95—42no—
410#95—42no—
411#95—44no—
412#95—44no—
413#95—44no—
414#95C2×D418yes—
415#95C2×D418yes—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—24no—
420C24—24no—
421C24—22no—
422C24—24no—
423C24—24no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—24no—
435C24—22no—
436C24—24no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—24no—
445C24—22no—
446C24—24no—
447C24—22no—
448C24C22×D414yes—
449C24C22×D414yes—
450C24C22×D414yes—
451C24C2×#4114yes—
452C24H(5,𝔽2)14yes—
453C24C2511yescharacteristic
454C2×D4—28no—
455C2×D4—216no—
456C2×D4—216no—
457C2×D4—28no—
458C2×D4—28no—
459C2×D4—28no—
460C2×D4—28no—
461C2×D4—28no—
462C2×D4—28no—
463C2×D4—28no—
464C2×D4—28no—
465C2×D4—28no—
466C2×D4—48no—
467C2×D4—48no—
468C2×D4—44no—
469C2×D4—416no—
470C2×D4—416no—
471C2×D4—416no—
472C2×D4—416no—
473C2×D4—416no—
474C2×D4—416no—
475C2×D4—416no—
476C2×D4—416no—
477C2×D4—416no—
478C2×D4—44no—
479C2×D4—44no—
480C2×D4—44no—
481C2×D4—44no—
482C2×D4—44no—
483C2×D4—88no—
484C2×D4—84no—
485C2×D4—88no—
486C2×D4—84no—
487C2×D4—84no—
488C2×D4—84no—
489C2×D4—88no—
490C2×D4—88no—
491C2×D4—88no—
492C2×D4—88no—
493C2×D4—88no—
494C2×D4—88no—
495C2×D4—88no—
496C2×D4#121116yes—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—24no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—22no—
520C22×C4—24no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—24no—
525C22×C4—216no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—24no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—22no—
553C22×C4—24no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—24no—
561C22×C4—22no—
562C22×C4—48no—
563C22×C4—48no—
564C22×C4—416no—
565C22×C4—416no—
566C22×C4—416no—
567C22×C4—416no—
568C22×C4—48no—
569C22×C4—48no—
570C22×C4—48no—
571C22×C4—48no—
572C22×C4—48no—
573C22×C4—48no—
574C22×C4—48no—
575C22×C4—48no—
576C22×C4—88no—
577C22×C4—88no—
578C22×C4—88no—
579C22×C4—84no—
580C22×C4—84no—
581C22×C4—88no—
582C22×C4—88no—
583C22×C4—88no—
584C22×C4—88no—
585C22×C4C22×D412yes—
586C22×C4C22×D414yes—
587C22×C4C22×D418yes—
588C22×C4C22×D412yes—
589C22×C4C22×D412yes—
590C22×C4C22×D412yes—
591C22×C4C22×D412yes—
592C22×C4C22×D412yes—
593C22×C4C22×D412yes—
594C22×C4C22×D412yes—
595C22×C4C22×D412yes—
596C22×C4C2×#4112yes—
597C22×C4C2×#4112yes—
598C22×C4C2×#4112yes—
599C22×C4C2×#4112yes—
600C22×C4H(5,𝔽2)14yes—
601C22×C4H(5,𝔽2)12yes—
602C22×C42−1+412yes—
603C4⋊C4—28no—
604C4⋊C4—216no—
605C4⋊C4—48no—
606C4⋊C4—48no—
607C4⋊C4—416no—
608C4⋊C4—44no—
609C4⋊C4—44no—
610C4⋊C4—48no—
611C4⋊C4—84no—
612C4⋊C4—88no—
613C22⋊C4—216no—
614C22⋊C4—216no—
615C22⋊C4—416no—
616C22⋊C4—416no—
617C22⋊C4—416no—
618C22⋊C4—416no—
619C22⋊C4—48no—
620C22⋊C4—48no—
621C22⋊C4—48no—
622C22⋊C4—416no—
623C22⋊C4—48no—
624C22⋊C4—48no—
625C22⋊C4—84no—
626C22⋊C4—84no—
627C22⋊C4—88no—
628C22⋊C4—88no—
629C22⋊C4—84no—
630C22⋊C4—84no—
631C42—28no—
632C42—44no—
633C42—48no—
634C42#121116yescomplemented
635C23—24no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—28no—
642C23—24no—
643C23—24no—
644C23—28no—
645C23—24no—
646C23—24no—
647C23—28no—
648C23—28no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—28no—
655C23—28no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—44no—
665C23—44no—
666C23—44no—
667C23—44no—
668C23—44no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—44no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—44no—
691C23—44no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—44no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—44no—
702C23—44no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—44no—
708C23—44no—
709C23—42no—
710C23—44no—
711C23—42no—
712C23—42no—
713C23—44no—
714C23—42no—
715C23C2×#12118yes—
716C23C23×D411yescharacteristic
717C23C23×D411yescharacteristic
718C23C23×D411yescharacteristic
719C23C22×#4111yescharacteristic
720C23C22×#4111yescharacteristic
721C23C2×H(5,𝔽2)11yescharacteristic
722C23C2×H(5,𝔽2)12yes—
723C23C2×H(5,𝔽2)12yes—
724C23C2×2−1+411yescharacteristic
725C23#58512yes—
726C23#58512yes—
727D4—232no—
728D4—416no—
729D4—416no—
730D4—816no—
731D4—816no—
732D4—832no—
733D4—832no—
734C2×C4—24no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—24no—
745C2×C4—28no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—28no—
752C2×C4—24no—
753C2×C4—28no—
754C2×C4—24no—
755C2×C4—42no—
756C2×C4—44no—
757C2×C4—41no—
758C2×C4—42no—
759C2×C4—44no—
760C2×C4—41no—
761C2×C4—44no—
762C2×C4—42no—
763C2×C4—44no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—44no—
770C2×C4—44no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—44no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—42no—
778C2×C4—44no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—42no—
787C2×C4—41no—
788C2×C4—44no—
789C2×C4—42no—
790C2×C4—41no—
791C2×C4—44no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—41no—
795C2×C4—42no—
796C2×C4—44no—
797C2×C4—41no—
798C2×C4—42no—
799C2×C4—44no—
800C2×C4—44no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—816no—
808C2×C4—816no—
809C2×C4—832no—
810C2×C4—816no—
811C2×C4C2×#12114yes—
812C2×C4C2×#12114yes—
813C2×C4C2×#12114yes—
814C2×C4C2×#12114yes—
815C2×C4#53714yes—
816C2×C4D4214yes—
817C2×C4#54714yes—
818C2×C4#54814yes—
819C2×C4#55314yes—
820C22—28no—
821C22—28no—
822C22—28no—
823C22—48no—
824C22—48no—
825C22—48no—
826C22—44no—
827C22—44no—
828C22—44no—
829C22—44no—
830C22—48no—
831C22—44no—
832C22—44no—
833C22—44no—
834C22—44no—
835C22—48no—
836C22—44no—
837C22—44no—
838C22—48no—
839C22—44no—
840C22—44no—
841C22—44no—
842C22—44no—
843C22—84no—
844C22—82no—
845C22—82no—
846C22—82no—
847C22—82no—
848C22—82no—
849C22—82no—
850C22—82no—
851C22—82no—
852C22—82no—
853C22—82no—
854C22—82no—
855C22—82no—
856C22—84no—
857C22C22×#12111yescharacteristic
858C22C22×#12111yescharacteristic
859C22C2×#53711yescharacteristic
860C22#346012yes—
861C22C2×D4211yescharacteristic
862C22C2×#54711yescharacteristic
863C22C2×#54811yescharacteristic
864C22C2×#55311yescharacteristic
865C22#348412yes—
866C22#348411yescharacteristic
867C22#348512yes—
868C22#348511yescharacteristic
869C22#348812yes—
870C22#348812yes—
871C22#349412yes—
872C22#349811yescharacteristic
873C22#350011yescharacteristic
874C22#351912yes—
875C22#352112yes—
876C22#354212yes—
877C22#354212yes—
878C22#354712yes—
879C22#355912yes—
880C4—24no—
881C4—24no—
882C4—42no—
883C4—44no—
884C4—48no—
885C4—42no—
886C4—44no—
887C4—84no—
888C4—82no—
889C4—82no—
890C4—81no—
891C4—82no—
892C4—81no—
893C4#241618yes—
894C2—48no—
895C2—84no—
896C2—84no—
897C2C2×#241611yescharacteristic
898C2#3525611yescharacteristic
899C2#3551411yescharacteristic
900C2#3569111yescharacteristic
901C2#3600911yescharacteristic
902C2#3776412yes—
903C2#3926212yes—
904C2#4242411yescharacteristic
905C2#4264611yescharacteristic
906C2#4493212yes—
907C2#4504212yes—
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×#2537C2semidirect
2. C2×#2535C2semidirect
3. C2×#2428C2semidirect
4. C2×#2349C2semidirect
5. C2×#2328C2semidirect
6. #16401C2semidirect
7. #16260C2semidirect
8. #15376C2semidirect
9. #15274C2semidirect
10. #15220C2semidirect
11. #15126C2semidirect
12. #14757C2semidirect
13. #14735C2semidirect
14. #14277C2semidirect
15. #13970C2semidirect
16. #13906C2semidirect
17. #13847C2semidirect
101. C2×#127D4semidirect
124. C2×C4×D4D4semidirect
178. #382D4semidirect
634. C42#121semidirect

Maximal subgroups

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

subgroupindex
C2×#25372
C2×#25352
C2×#24282
C2×#23492
C2×#23282
#164012
#162602
#153762
#152742
#152202
#151262
#147572
#147352
#142772
#139702
#139062
#138472