Finite Group Databasebeta

← #640979

Subgroups — #640979

Order 512.

4964 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2847C211yesmaximal, characteristic
2C2×#2412C212yesmaximal, complemented
3C2×#2618C211yesmaximal, characteristic, complemented
4C22×#385C211yesmaximal, characteristic, complemented
5C22×#380C211yesmaximal, characteristic, complemented
6#16513C214yesmaximal, complemented
7#16399C212yesmaximal, complemented
8#16261C212yesmaximal, complemented
9#14927C212yesmaximal, complemented
10#14766C212yesmaximal, complemented
11#14747C212yesmaximal, complemented
12#14729C214yesmaximal, complemented
13#14729C212yesmaximal, complemented
14#14339C211yesmaximal, characteristic, complemented
15#14275C211yesmaximal, characteristic, complemented
16#14271C211yesmaximal, characteristic, complemented
17#14134C212yesmaximal, complemented
18C25×C4C2211yescharacteristic
19C22×#123C2212yes—
20C22×#121C2211yescharacteristic
21C22×#121C2211yescharacteristic
22C22×#121C2211yescharacteristic
23C22×#120C2212yes—
24C23×C4⋊C4C2211yescharacteristic
25C23×C4⋊C4C2212yes—
26C23×C4⋊C4C2211yescharacteristic
27C23×C22⋊C4C2212yes—
28C23×C22⋊C4C2211yescharacteristic
29C23×C22⋊C4C2211yescharacteristic
30#2847—28no—
31#2618—28no—
32#2412—216no—
33C2×#398C2212yescomplemented
34C2×#397C2214yes—
35C2×#396C2214yescomplemented
36C2×#396C2214yescomplemented
37C2×#394C2214yes—
38C2×#394C2212yescomplemented
39C2×#386C2212yes—
40C2×#386C2212yes—
41C2×#386C2212yes—
42C2×#386C2212yes—
43C2×#386C2214yes—
44C2×#386C2212yes—
45C2×#386C2212yes—
46C2×#386C2214yes—
47C2×#385—28no—
48C2×#385C2212yes—
49C2×#385C2212yes—
50C2×#385C2212yes—
51C2×#385C2212yes—
52C2×#385C2212yes—
53C2×#381C2212yes—
54C2×#380—28no—
55C2×#380C2211yescharacteristic
56C2×#380C2211yescharacteristic
57C2×#380C2211yescharacteristic
58C2×#380C2211yescharacteristic
59C2×#380C2212yes—
60C2×#380C2212yes—
61C2×#380C2214yes—
62C2×#380C2212yes—
63C2×#380C2211yescharacteristic
64C22×#95C2211yescharacteristic
65C22×#95C2212yes—
66C22×#95C2211yescharacteristic
67#1445C2212yescomplemented
68#1444C2212yescomplemented
69#1442C2212yescomplemented
70#1442C2214yescomplemented
71#1441C2212yescomplemented
72#1441C2214yescomplemented
73#1441C2212yescomplemented
74#1441C2214yescomplemented
75#1441C2214yescomplemented
76#1441C2214yescomplemented
77#1441C2214yescomplemented
78#1440C2214yes—
79#1440C2214yescomplemented
80#1439C2214yescomplemented
81#1439C2214yescomplemented
82#1439C2214yescomplemented
83#1438C2214yes—
84#1438C2212yescomplemented
85C22⋊#95C2212yes—
86C22⋊#95C2212yes—
87C22⋊#95C2214yes—
88C26C2311yescharacteristic
89C23×D4C2312yes—
90C23×D4C2312yes—
91C23×D4C2312yes—
92C23×D4C2311yescharacteristic
93C24×C4—24no—
94C24×C4—24no—
95C24×C4—44no—
96C24×C4—44no—
97C24×C4D418yes—
98C24×C4C2311yescharacteristic
99C24×C4C2311yescharacteristic
100C24×C4C2314yes—
101C24×C4C2311yescharacteristic
102C24×C4C2311yescharacteristic
103C24×C4C2311yescharacteristic
104C24×C4C2311yescharacteristic
105C24×C4C2311yescharacteristic
106C24×C4C2311yescharacteristic
107C24×C4C2311yescharacteristic
108C24×C4C2311yescharacteristic
109C2×#123—28no—
110C2×#123—28no—
111C2×#123—44no—
112C2×#121—24no—
113C2×#121—24no—
114C2×#121—24no—
115C2×#121—24no—
116C2×#121—24no—
117C2×#121—44no—
118C2×#121—44no—
119C2×#120—28no—
120C2×#120—28no—
121C2×#120—28no—
122C22×C4⋊C4—24no—
123C22×C4⋊C4—24no—
124C22×C4⋊C4—24no—
125C22×C4⋊C4—24no—
126C22×C4⋊C4—28no—
127C22×C4⋊C4—44no—
128C22×C4⋊C4—44no—
129C22×C4⋊C4—44no—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2314yes—
135C22×C4⋊C4C2314yes—
136C22×C4⋊C4C2314yes—
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2312yes—
142C22×C22⋊C4—24no—
143C22×C22⋊C4—24no—
144C22×C22⋊C4—28no—
145C22×C22⋊C4—24no—
146C22×C22⋊C4—28no—
147C22×C22⋊C4—44no—
148C22×C22⋊C4—44no—
149C22×C22⋊C4D418yescomplemented
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2314yes—
158C22×C22⋊C4C2314yes—
159C22×C22⋊C4C2312yes—
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2314yes—
163C22×C22⋊C4C2314yes—
164C22×C22⋊C4C2312yes—
165C22×C22⋊C4C2312yes—
166C22×C22⋊C4C2314yes—
167#398—28no—
168#397—216no—
169#396—216no—
170#396—48no—
171#394—216no—
172#394—28no—
173#386—28no—
174#386—28no—
175#386—28no—
176#386—28no—
177#386—28no—
178#386—216no—
179#386—48no—
180#386—44no—
181#385—28no—
182#385—28no—
183#385—28no—
184#385—28no—
185#385—28no—
186#381—28no—
187#380—24no—
188#380—24no—
189#380—24no—
190#380—24no—
191#380—28no—
192#380—216no—
193#380—28no—
194#380—28no—
195#380D418yescomplemented
196C2×#95—24no—
197C2×#95—24no—
198C2×#95—28no—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2314yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
218C2×#95C2312yes—
219C25—22no—
220C25—22no—
221C25—22no—
222C25—24no—
223C25—24no—
224C25—22no—
225C25—42no—
226C25—42no—
227C25C2×D414yes—
228C25C2×D414yes—
229C25#4114yes—
230C25C2412yes—
231C25C2411yescharacteristic
232C25C2411yescharacteristic
233C25C2411yescharacteristic
234C22×D4—24no—
235C22×D4—24no—
236C22×D4—24no—
237C22×D4—24no—
238C22×D4—24no—
239C22×D4—24no—
240C22×D4—24no—
241C22×D4—24no—
242C22×D4—24no—
243C22×D4—28no—
244C22×D4—24no—
245C22×D4—28no—
246C22×D4—24no—
247C22×D4—24no—
248C22×D4—24no—
249C22×D4—22no—
250C22×D4—22no—
251C22×D4—22no—
252C22×D4—42no—
253C22×D4—42no—
254C22×D4—44no—
255C22×D4—44no—
256C23×C4—24no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—24no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—24no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—232no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—24no—
279C23×C4—24no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—28no—
283C23×C4—28no—
284C23×C4—28no—
285C23×C4—22no—
286C23×C4—22no—
287C23×C4—22no—
288C23×C4—22no—
289C23×C4—28no—
290C23×C4—416no—
291C23×C4—42no—
292C23×C4—416no—
293C23×C4—42no—
294C23×C4—42no—
295C23×C4—42no—
296C23×C4—42no—
297C23×C4—42no—
298C23×C4—42no—
299C23×C4—42no—
300C23×C4—42no—
301C23×C4—44no—
302C23×C4—42no—
303C23×C4—42no—
304C23×C4—44no—
305C23×C4—42no—
306C23×C4—44no—
307C23×C4—42no—
308C23×C4—432no—
309C23×C4—432no—
310C23×C4C2×D414yes—
311C23×C4C2×D414yes—
312C23×C4C2×D414yes—
313C23×C4C2×D414yes—
314C23×C4C2×D414yes—
315C23×C4C2×D414yes—
316C23×C4C2×D414yes—
317C23×C4C2×D414yes—
318C23×C4C2×D414yes—
319C23×C4#4114yes—
320C23×C4C2412yes—
321C23×C4C2414yes—
322C23×C4C2412yes—
323C23×C4C2412yes—
324C23×C4C2412yes—
325C23×C4C2412yes—
326C23×C4C2412yes—
327C23×C4C2412yes—
328C23×C4C2414yes—
329C23×C4C2411yescharacteristic
330C23×C4C2411yescharacteristic
331C23×C4C2411yescharacteristic
332C23×C4C2411yescharacteristic
333#123—432no—
334#121—416no—
335#121—416no—
336#121—416no—
337#120—432no—
338C2×C4⋊C4—28no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—28no—
351C2×C4⋊C4—28no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—28no—
356C2×C4⋊C4—28no—
357C2×C4⋊C4—28no—
358C2×C4⋊C4—42no—
359C2×C4⋊C4—42no—
360C2×C4⋊C4—44no—
361C2×C4⋊C4—42no—
362C2×C4⋊C4—42no—
363C2×C4⋊C4—44no—
364C2×C4⋊C4—42no—
365C2×C4⋊C4—42no—
366C2×C4⋊C4—44no—
367C2×C4⋊C4—432no—
368C2×C4⋊C4—416no—
369C2×C4⋊C4—416no—
370C2×C4⋊C4—44no—
371C2×C4⋊C4—44no—
372C2×C4⋊C4C2×D418yes—
373C2×C22⋊C4—232no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—28no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—28no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—28no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—28no—
402C2×C22⋊C4—28no—
403C2×C22⋊C4—24no—
404C2×C22⋊C4—28no—
405C2×C22⋊C4—28no—
406C2×C22⋊C4—28no—
407C2×C22⋊C4—432no—
408C2×C22⋊C4—44no—
409C2×C22⋊C4—44no—
410C2×C22⋊C4—44no—
411C2×C22⋊C4—44no—
412C2×C22⋊C4—416no—
413C2×C22⋊C4—44no—
414C2×C22⋊C4—44no—
415C2×C22⋊C4—44no—
416C2×C22⋊C4—44no—
417C2×C22⋊C4—44no—
418C2×C22⋊C4—44no—
419C2×C22⋊C4—44no—
420C2×C22⋊C4C2×D418yes—
421C2×C22⋊C4C2×D418yes—
422C2×C22⋊C4C2×D418yes—
423#95—28no—
424#95—24no—
425#95—24no—
426#95—24no—
427#95—24no—
428#95—24no—
429#95—28no—
430#95—24no—
431#95—24no—
432#95—24no—
433#95—28no—
434#95—28no—
435#95—28no—
436#95—28no—
437#95—44no—
438#95—44no—
439#95—44no—
440#95—44no—
441#95—44no—
442#95C2×D418yes—
443C24—21no—
444C24—21no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—21no—
449C24—22no—
450C24—21no—
451C24—22no—
452C24—22no—
453C24—28no—
454C24—28no—
455C24—28no—
456C24—216no—
457C24—28no—
458C24—216no—
459C24—28no—
460C24—28no—
461C24—28no—
462C24—28no—
463C24—21no—
464C24—21no—
465C24—21no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—21no—
470C24—22no—
471C24—22no—
472C24—22no—
473C24—22no—
474C24—22no—
475C24—22no—
476C24—24no—
477C24—22no—
478C24—24no—
479C24—24no—
480C24—22no—
481C24—24no—
482C24—44no—
483C24—44no—
484C24—48no—
485C24—48no—
486C24—48no—
487C24—48no—
488C24—48no—
489C24—48no—
490C24—48no—
491C24—48no—
492C24—48no—
493C24—48no—
494C24#121116yes—
495C24C22×D412yes—
496C24C22×D412yes—
497C24C22×D412yes—
498C24C22×D412yes—
499C24C22×D412yes—
500C24C22×D412yes—
501C24C22×D412yes—
502C24C2×#4112yes—
503C24C2×#4112yes—
504C24C2×#4112yes—
505C24C2×#4112yes—
506C24H(5,𝔽2)14yes—
507C24H(5,𝔽2)12yes—
508C242−1+414yes—
509C242−1+412yes—
510C24C2511yescharacteristic
511C2×D4—44no—
512C2×D4—44no—
513C2×D4—48no—
514C2×D4—48no—
515C2×D4—48no—
516C2×D4—48no—
517C2×D4—48no—
518C2×D4—48no—
519C2×D4—48no—
520C2×D4—48no—
521C2×D4—416no—
522C2×D4—48no—
523C2×D4—416no—
524C2×D4—48no—
525C2×D4—48no—
526C2×D4—48no—
527C2×D4—48no—
528C2×D4—44no—
529C2×D4—84no—
530C2×D4—84no—
531C2×D4—88no—
532C2×D4—88no—
533C22×C4—216no—
534C22×C4—216no—
535C22×C4—28no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—28no—
544C22×C4—28no—
545C22×C4—28no—
546C22×C4—28no—
547C22×C4—28no—
548C22×C4—28no—
549C22×C4—28no—
550C22×C4—28no—
551C22×C4—21no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—24no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—21no—
560C22×C4—24no—
561C22×C4—24no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—24no—
565C22×C4—24no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—24no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—28no—
572C22×C4—28no—
573C22×C4—28no—
574C22×C4—28no—
575C22×C4—28no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—24no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—24no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—24no—
595C22×C4—22no—
596C22×C4—24no—
597C22×C4—24no—
598C22×C4—24no—
599C22×C4—24no—
600C22×C4—24no—
601C22×C4—24no—
602C22×C4—24no—
603C22×C4—24no—
604C22×C4—22no—
605C22×C4—24no—
606C22×C4—22no—
607C22×C4—24no—
608C22×C4—24no—
609C22×C4—24no—
610C22×C4—44no—
611C22×C4—44no—
612C22×C4—44no—
613C22×C4—44no—
614C22×C4—44no—
615C22×C4—44no—
616C22×C4—44no—
617C22×C4—48no—
618C22×C4—48no—
619C22×C4—48no—
620C22×C4—48no—
621C22×C4—48no—
622C22×C4—48no—
623C22×C4—48no—
624C22×C4—48no—
625C22×C4—48no—
626C22×C4—4128no—
627C22×C4—48no—
628C22×C4—48no—
629C22×C4—416no—
630C22×C4—416no—
631C22×C4—416no—
632C22×C4—44no—
633C22×C4—44no—
634C22×C4—48no—
635C22×C4—44no—
636C22×C4—44no—
637C22×C4—44no—
638C22×C4—44no—
639C22×C4—44no—
640C22×C4—44no—
641C22×C4—44no—
642C22×C4—44no—
643C22×C4—44no—
644C22×C4—416no—
645C22×C4—44no—
646C22×C4—88no—
647C22×C4—88no—
648C22×C4—88no—
649C22×C4—84no—
650C22×C4—84no—
651C22×C4—84no—
652C22×C4—84no—
653C22×C4#121116yes—
654C22×C4C22×D414yes—
655C22×C4C22×D414yes—
656C22×C4C22×D412yes—
657C22×C4C22×D418yes—
658C22×C4C22×D412yes—
659C22×C4C22×D412yes—
660C22×C4C22×D412yes—
661C22×C4C22×D412yes—
662C22×C4C22×D412yes—
663C22×C4C2×#4112yes—
664C22×C4C2×#4112yes—
665C22×C4H(5,𝔽2)14yes—
666C4⋊C4—48no—
667C4⋊C4—416no—
668C4⋊C4—416no—
669C4⋊C4—48no—
670C4⋊C4—48no—
671C4⋊C4—44no—
672C4⋊C4—44no—
673C4⋊C4—48no—
674C4⋊C4—48no—
675C4⋊C4—44no—
676C4⋊C4—48no—
677C4⋊C4—88no—
678C22⋊C4—216no—
679C22⋊C4—216no—
680C22⋊C4—216no—
681C22⋊C4—416no—
682C22⋊C4—416no—
683C22⋊C4—48no—
684C22⋊C4—48no—
685C22⋊C4—48no—
686C22⋊C4—48no—
687C22⋊C4—48no—
688C22⋊C4—48no—
689C22⋊C4—48no—
690C22⋊C4—48no—
691C22⋊C4—48no—
692C22⋊C4—88no—
693C22⋊C4—88no—
694C22⋊C4—88no—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—24no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—24no—
705C23—22no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—24no—
710C23—24no—
711C23—24no—
712C23—24no—
713C23—24no—
714C23—24no—
715C23—24no—
716C23—24no—
717C23—24no—
718C23—24no—
719C23—24no—
720C23—24no—
721C23—24no—
722C23—24no—
723C23—24no—
724C23—24no—
725C23—24no—
726C23—24no—
727C23—24no—
728C23—24no—
729C23—232no—
730C23—22no—
731C23—232no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—24no—
737C23—22no—
738C23—24no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—24no—
744C23—24no—
745C23—416no—
746C23—416no—
747C23—432no—
748C23—432no—
749C23—416no—
750C23—432no—
751C23—416no—
752C23—432no—
753C23—416no—
754C23—42no—
755C23—42no—
756C23—42no—
757C23—42no—
758C23—42no—
759C23—42no—
760C23—42no—
761C23—42no—
762C23—42no—
763C23—42no—
764C23—42no—
765C23—42no—
766C23—42no—
767C23—44no—
768C23—42no—
769C23—42no—
770C23—44no—
771C23—42no—
772C23—42no—
773C23—42no—
774C23—42no—
775C23—44no—
776C23—44no—
777C23—44no—
778C23—44no—
779C23—44no—
780C23—44no—
781C23—44no—
782C23—44no—
783C23—44no—
784C23—44no—
785C23C2×#12114yes—
786C23C2×#12114yes—
787C23C2×#12114yes—
788C23C2×#12114yes—
789C23#53414yes—
790C23#53614yes—
791C23#53718yes—
792C23#53714yes—
793C23#53918yes—
794C23D4214yes—
795C23#54714yes—
796C23#54814yes—
797C23#55314yes—
798C23C23×D411yescharacteristic
799C23C23×D411yescharacteristic
800C23C23×D411yescharacteristic
801C23C22×#4111yescharacteristic
802C23C22×#4111yescharacteristic
803C23C2×H(5,𝔽2)12yes—
804C23C2×H(5,𝔽2)12yes—
805C23C2×H(5,𝔽2)11yescharacteristic
806C23C2×2−1+412yes—
807C23C2×2−1+411yescharacteristic
808C23#58512yes—
809D4—88no—
810D4—816no—
811D4—816no—
812D4—816no—
813C2×C4—232no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—24no—
821C2×C4—24no—
822C2×C4—24no—
823C2×C4—24no—
824C2×C4—24no—
825C2×C4—24no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—28no—
832C2×C4—24no—
833C2×C4—24no—
834C2×C4—28no—
835C2×C4—28no—
836C2×C4—28no—
837C2×C4—416no—
838C2×C4—416no—
839C2×C4—416no—
840C2×C4—416no—
841C2×C4—416no—
842C2×C4—416no—
843C2×C4—42no—
844C2×C4—416no—
845C2×C4—42no—
846C2×C4—44no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—44no—
854C2×C4—44no—
855C2×C4—44no—
856C2×C4—44no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—42no—
860C2×C4—42no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—42no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—44no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—44no—
872C2×C4—42no—
873C2×C4—42no—
874C2×C4—44no—
875C2×C4—44no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—42no—
879C2×C4—42no—
880C2×C4—44no—
881C2×C4—44no—
882C2×C4—44no—
883C2×C4—44no—
884C2×C4—44no—
885C2×C4—44no—
886C2×C4—44no—
887C2×C4—44no—
888C2×C4—44no—
889C2×C4—44no—
890C2×C4—44no—
891C2×C4—832no—
892C2×C4—88no—
893C2×C4—88no—
894C2×C4C2×#12114yes—
895C2×C4C2×#12114yes—
896C2×C4#53414yes—
897C22—28no—
898C22—28no—
899C22—28no—
900C22—28no—
901C22—24no—
902C22—24no—
903C22—28no—
904C22—28no—
905C22—24no—
906C22—24no—
907C22—24no—
908C22—24no—
909C22—24no—
910C22—24no—
911C22—24no—
912C22—28no—
913C22—28no—
914C22—24no—
915C22—24no—
916C22—24no—
917C22—24no—
918C22—24no—
919C22—24no—
920C22—464no—
921C22—44no—
922C22—44no—
923C22—42no—
924C22—44no—
925C22—42no—
926C22—42no—
927C22—44no—
928C22—42no—
929C22—84no—
930C22—84no—
931C22—82no—
932C22—84no—
933C22—82no—
934C22—82no—
935C22—82no—
936C22—82no—
937C22—84no—
938C22—82no—
939C22—82no—
940C22#241618yes—
941C22#261818yescomplemented
942C22C22×#12111yescharacteristic
943C22C22×#12111yescharacteristic
944C22C2×#53411yescharacteristic
945C22C2×#53411yescharacteristic
946C22C2×#53611yescharacteristic
947C22C2×#53712yes—
948C22C2×#53711yescharacteristic
949C22#344911yescharacteristic
950C22C2×#53912yes—
951C22C2×D4211yescharacteristic
952C22C2×#54711yescharacteristic
953C22C2×#54811yescharacteristic
954C22C2×#55311yescharacteristic
955C22#348412yes—
956C22#348912yes—
957C22#349012yes—
958C22#349512yes—
959C22#349612yes—
960C22#350512yes—
961C22#353412yes—
962C22#353512yes—
963C22#353612yes—
964C22#353812yes—
965C4—24no—
966C4—24no—
967C4—24no—
968C4—48no—
969C4—44no—
970C4—42no—
971C4—44no—
972C4—84no—
973C4—82no—
974C4—82no—
975C4—82no—
976C4—82no—
977C4—82no—
978C2—28no—
979C2—28no—
980C2—44no—
981C2—162no—
982C2C2×#261811yescharacteristic
983C2C2×#241611yescharacteristic
984C2#3498111yescharacteristic
985C2#3500011yescharacteristic
986C2#3530611yescharacteristic
987C2#3744211yescharacteristic
988C2#3745211yescharacteristic
989C2#3767312yes—
990C2#3770212yes—
991C2#3786112yes—
992C2#3789012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2847C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2412C2semidirect
3. C2×#2618C2semidirect
4. C22×#385C2semidirect
5. C22×#380C2semidirect
6. #16513C2semidirect
7. #16399C2semidirect
8. #16261C2semidirect
9. #14927C2semidirect
10. #14766C2semidirect
11. #14747C2semidirect
12. #14729C2semidirect
13. #14729C2semidirect
14. #14339C2semidirect
15. #14275C2semidirect
16. #14271C2semidirect
17. #14134C2semidirect
33. C2×#398C22semidirect
35. C2×#396C22semidirect
36. C2×#396C22semidirect
38. C2×#394C22semidirect
67. #1445C22semidirect
68. #1444C22semidirect
69. #1442C22semidirect
70. #1442C22semidirect
71. #1441C22semidirect
72. #1441C22semidirect
73. #1441C22semidirect
74. #1441C22semidirect
75. #1441C22semidirect
76. #1441C22semidirect
77. #1441C22semidirect
79. #1440C22semidirect
80. #1439C22semidirect
81. #1439C22semidirect
82. #1439C22semidirect
84. #1438C22semidirect
149. C22×C22⋊C4D4semidirect
195. #380D4semidirect
941. C22#2618semidirect

Maximal subgroups

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

subgroupindex
C2×#28472
C2×#24122
C2×#26182
C22×#3852
C22×#3802
#165132
#163992
#162612
#149272
#147662
#147472
#147292
#143392
#142752
#142712
#141342