Finite Group Databasebeta

← #642403

Subgroups — #642403

Order 512.

4942 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2848C211yesmaximal, characteristic, complemented
2C2×#2626C211yesmaximal, characteristic, complemented
3C22×#386C211yesmaximal, characteristic
4C2×#2280C211yesmaximal, characteristic, complemented
5#16513C214yesmaximal, complemented
6#16392C212yesmaximal, complemented
7#16263C212yesmaximal, complemented
8#14890C214yesmaximal, complemented
9#14839C212yesmaximal, complemented
10#14765C212yesmaximal, complemented
11#14727C212yesmaximal, complemented
12#14724C212yesmaximal
13#14338C211yesmaximal, characteristic, complemented
14#14281C211yesmaximal, characteristic, complemented
15#14275C211yesmaximal, characteristic, complemented
16#14044C212yesmaximal, complemented
17#13971C212yesmaximal, complemented
18C24×D4C2211yescharacteristic
19C25×C4C2211yescharacteristic
20C22×C22⋊Q8C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic, complemented
22C22×C22⋊Q8C2211yescharacteristic, complemented
23C22×#117C2212yescomplemented
24C23×C22⋊C4C2211yescharacteristic
25C23×C22⋊C4C2211yescharacteristic
26C23×C22⋊C4C2211yescharacteristic
27#2848—28no—
28#2626—28no—
29C2×#399C2212yescomplemented
30C2×#397C2214yescomplemented
31C2×#396C2214yescomplemented
32C2×#394C2214yes—
33C2×#394C2214yes—
34C2×#393C2212yescomplemented
35C2×#388C2214yescomplemented
36C2×#386—28no—
37C2×#386C2212yes—
38C2×#386C2212yes—
39C2×#386C2212yes—
40C2×#386C2212yes—
41C2×#385C2212yes—
42C2×#385C2212yes—
43C2×#385C2212yes—
44C2×#385C2212yescomplemented
45C2×#385C2212yescomplemented
46#2280—28no—
47C2×#381C2212yescomplemented
48C2×#380C2211yescharacteristic
49C2×#380C2211yescharacteristic
50C2×#380C2211yescharacteristic
51C2×#380C2211yescharacteristic, complemented
52C2×#380C2211yescharacteristic, complemented
53C2×#380C2212yescomplemented
54C2×#379C2212yes—
55C2×#379C2212yes—
56C2×#379C2212yes—
57C2×#379C2212yes—
58C2×C4×C22⋊C4C2212yes—
59C2×C4×C22⋊C4C2212yescomplemented
60C22×#95C2211yescharacteristic
61C22×#95C2211yescharacteristic
62#1446C2212yescomplemented
63#1445C2212yescomplemented
64#1444C2212yescomplemented
65#1442C2214yescomplemented
66#1442C2212yescomplemented
67#1441C2214yescomplemented
68#1441C2214yescomplemented
69#1441C2214yescomplemented
70#1440C2214yescomplemented
71#1440C2214yescomplemented
72#1440C2214yescomplemented
73#1439C2212yescomplemented
74#1439C2214yescomplemented
75#1439C2212yescomplemented
76#1439C2214yescomplemented
77#1439C2214yescomplemented
78#1438C2214yes—
79#1438C2214yes—
80#1437C2214yescomplemented
81#1436C2214yescomplemented
82C4⋊#95C2214yescomplemented
83C22⋊#95C2212yes—
84C22⋊#95C2212yes—
85C22⋊#95C2212yes—
86C22⋊#95C2212yes—
87C26C2311yescharacteristic
88C26C2311yescharacteristic
89C23×Q8C2311yescharacteristic
90C23×D4—24no—
91C23×D4—24no—
92C23×D4—24no—
93C23×D4—44no—
94C23×D4—44no—
95C23×D4C2312yes—
96C23×D4C2312yes—
97C24×C4—24no—
98C24×C4—24no—
99C24×C4—44no—
100C24×C4—44no—
101C24×C4D418yes—
102C24×C4C2311yescharacteristic
103C24×C4C2311yescharacteristic
104C24×C4C2311yescharacteristic
105C24×C4C2311yescharacteristic
106C24×C4C2311yescharacteristic
107C24×C4C2311yescharacteristic
108C24×C4C2311yescharacteristic
109C24×C4C2311yescharacteristic
110C24×C4C2311yescharacteristic
111C2×C22⋊Q8—24no—
112C2×C22⋊Q8—24no—
113C2×C22⋊Q8—24no—
114C2×C22⋊Q8—24no—
115C2×C22⋊Q8—24no—
116C2×C22⋊Q8—44no—
117C2×C22⋊Q8—44no—
118C2×#117—28no—
119C2×#117—44no—
120C2×#117—44no—
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2314yes—
125C22×C4⋊C4C2314yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2312yes—
131C22×C22⋊C4—24no—
132C22×C22⋊C4—24no—
133C22×C22⋊C4—24no—
134C22×C22⋊C4—24no—
135C22×C22⋊C4—24no—
136C22×C22⋊C4—44no—
137C22×C22⋊C4—44no—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2314yes—
148C22×C22⋊C4C2314yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2314yes—
151C22×C22⋊C4C2314yes—
152C22×C22⋊C4C2314yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2314yes—
157C22×C22⋊C4C2312yes—
158C22×C42C2314yes—
159#399—28no—
160#397—48no—
161#396—216no—
162#394—48no—
163#394—48no—
164#393—28no—
165#388—48no—
166#386—28no—
167#386—28no—
168#386—28no—
169#386—28no—
170#385—28no—
171#385—28no—
172#385—28no—
173#385—28no—
174#385—28no—
175#381—28no—
176#380—24no—
177#380—24no—
178#380—24no—
179#380—24no—
180#380—28no—
181#380D418yescomplemented
182#379—28no—
183#379—28no—
184#379—28no—
185#379—28no—
186C4×C22⋊C4—28no—
187C4×C22⋊C4—28no—
188C2×#95—24no—
189C2×#95—24no—
190C2×#95C2314yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2314yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2314yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2312yes—
210C25—22no—
211C25—22no—
212C25—24no—
213C25—24no—
214C25—22no—
215C25—22no—
216C25—22no—
217C25—22no—
218C25—22no—
219C25—22no—
220C25—22no—
221C25—22no—
222C25—22no—
223C25—22no—
224C25—42no—
225C25—42no—
226C25—42no—
227C25—42no—
228C25—42no—
229C25—42no—
230C25C2×D414yes—
231C25#4114yes—
232C25C2412yes—
233C25C2411yescharacteristic
234C25C2411yescharacteristic
235C25C2411yescharacteristic
236C22×Q8—22no—
237C22×Q8—22no—
238C22×Q8—22no—
239C22×Q8—42no—
240C22×Q8—42no—
241C22×D4—232no—
242C22×D4—24no—
243C22×D4—24no—
244C22×D4—24no—
245C22×D4—24no—
246C22×D4—28no—
247C22×D4—28no—
248C22×D4—24no—
249C22×D4—24no—
250C22×D4—44no—
251C22×D4—44no—
252C22×D4—432no—
253C22×D4—432no—
254C22×D4—416no—
255C22×D4—416no—
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—24no—
265C23×C4—232no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—24no—
273C23×C4—24no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—416no—
281C23×C4—416no—
282C23×C4—42no—
283C23×C4—42no—
284C23×C4—42no—
285C23×C4—42no—
286C23×C4—42no—
287C23×C4—42no—
288C23×C4—42no—
289C23×C4—42no—
290C23×C4—42no—
291C23×C4—42no—
292C23×C4—42no—
293C23×C4—42no—
294C23×C4—42no—
295C23×C4—432no—
296C23×C4—432no—
297C23×C4C2×D414yes—
298C23×C4C2×D414yes—
299C23×C4C2×D414yes—
300C23×C4C2×D414yes—
301C23×C4C2×D414yes—
302C23×C4C2×D414yes—
303C23×C4C2×D414yes—
304C23×C4#4114yes—
305C23×C4#4114yes—
306C23×C4C2412yes—
307C23×C4C2412yes—
308C23×C4C2412yes—
309C23×C4C2412yes—
310C23×C4C2414yes—
311C23×C4C2412yes—
312C23×C4C2412yes—
313C23×C4C2414yes—
314C23×C4C2411yescharacteristic
315C23×C4C2412yes—
316C23×C4C2411yescharacteristic
317C23×C4C2411yescharacteristic
318C23×C4C2411yescharacteristic
319C22⋊Q8—416no—
320C22⋊Q8—416no—
321C22⋊Q8—416no—
322#117—432no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—28no—
335C2×C4⋊C4—28no—
336C2×C4⋊C4—28no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4—42no—
339C2×C4⋊C4—42no—
340C2×C4⋊C4—42no—
341C2×C4⋊C4—42no—
342C2×C4⋊C4—42no—
343C2×C4⋊C4—44no—
344C2×C4⋊C4—44no—
345C2×C4⋊C4—44no—
346C2×C4⋊C4—44no—
347C2×C4⋊C4—44no—
348C2×C4⋊C4C2×D418yescomplemented
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—24no—
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—28no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—28no—
367C2×C22⋊C4—28no—
368C2×C22⋊C4—28no—
369C2×C22⋊C4—28no—
370C2×C22⋊C4—28no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—28no—
379C2×C22⋊C4—28no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—28no—
383C2×C22⋊C4—28no—
384C2×C22⋊C4—28no—
385C2×C22⋊C4—28no—
386C2×C22⋊C4—44no—
387C2×C22⋊C4—44no—
388C2×C22⋊C4—44no—
389C2×C22⋊C4—44no—
390C2×C22⋊C4—44no—
391C2×C22⋊C4—44no—
392C2×C22⋊C4—44no—
393C2×C22⋊C4—44no—
394C2×C22⋊C4—416no—
395C2×C22⋊C4—416no—
396C2×C22⋊C4—416no—
397C2×C22⋊C4—44no—
398C2×C22⋊C4—44no—
399C2×C22⋊C4—44no—
400C2×C22⋊C4—44no—
401C2×C22⋊C4—44no—
402C2×C22⋊C4—44no—
403C2×C22⋊C4C2×D418yes—
404C2×C42—28no—
405C2×C42—28no—
406C2×C42—44no—
407#95—24no—
408#95—24no—
409#95—24no—
410#95—24no—
411#95—28no—
412#95—24no—
413#95—24no—
414#95—24no—
415#95—24no—
416#95—28no—
417#95—28no—
418#95—44no—
419#95—44no—
420#95—44no—
421#95—44no—
422#95—44no—
423#95—44no—
424#95—44no—
425#95—44no—
426#95C2×D418yescomplemented
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—216no—
432C24—216no—
433C24—28no—
434C24—28no—
435C24—28no—
436C24—21no—
437C24—21no—
438C24—21no—
439C24—21no—
440C24—21no—
441C24—21no—
442C24—21no—
443C24—21no—
444C24—22no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—21no—
449C24—21no—
450C24—21no—
451C24—21no—
452C24—22no—
453C24—22no—
454C24—28no—
455C24—28no—
456C24—28no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—24no—
462C24—24no—
463C24—24no—
464C24—22no—
465C24—22no—
466C24—24no—
467C24—28no—
468C24—28no—
469C24—44no—
470C24—44no—
471C24—48no—
472C24—48no—
473C24—48no—
474C24—48no—
475C24—48no—
476C24—48no—
477C24—48no—
478C24—48no—
479C24—48no—
480C24—48no—
481C24—48no—
482C24—48no—
483C24—44no—
484C24—44no—
485C24—44no—
486C24—48no—
487C24—44no—
488C24—48no—
489C24—44no—
490C24—44no—
491C24—44no—
492C24—44no—
493C24—44no—
494C24—44no—
495C24—44no—
496C24—44no—
497C24—84no—
498C24—84no—
499C24—84no—
500C24—84no—
501C24—84no—
502C24—84no—
503C24—84no—
504C24—84no—
505C24C22×D412yes—
506C24C22×D412yes—
507C24C22×D412yes—
508C24C22×D412yes—
509C24C2×#4114yes—
510C24C2×#4112yes—
511C24C2×#4112yes—
512C24C2×#4112yes—
513C24H(5,𝔽2)14yes—
514C24H(5,𝔽2)14yes—
515C242−1+412yes—
516C242−1+412yes—
517C24C2511yescharacteristic
518C2×Q8—44no—
519C2×Q8—44no—
520C2×Q8—44no—
521C2×Q8—84no—
522C2×Q8—84no—
523C2×D4—216no—
524C2×D4—216no—
525C2×D4—416no—
526C2×D4—416no—
527C2×D4—416no—
528C2×D4—416no—
529C2×D4—4128no—
530C2×D4—48no—
531C2×D4—48no—
532C2×D4—48no—
533C2×D4—48no—
534C22×C4—216no—
535C22×C4—216no—
536C22×C4—28no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—28no—
545C22×C4—28no—
546C22×C4—28no—
547C22×C4—28no—
548C22×C4—28no—
549C22×C4—21no—
550C22×C4—22no—
551C22×C4—24no—
552C22×C4—21no—
553C22×C4—22no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—24no—
558C22×C4—24no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—28no—
564C22×C4—28no—
565C22×C4—28no—
566C22×C4—28no—
567C22×C4—28no—
568C22×C4—24no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—24no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—24no—
587C22×C4—24no—
588C22×C4—24no—
589C22×C4—24no—
590C22×C4—24no—
591C22×C4—24no—
592C22×C4—24no—
593C22×C4—24no—
594C22×C4—24no—
595C22×C4—24no—
596C22×C4—24no—
597C22×C4—24no—
598C22×C4—24no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—24no—
602C22×C4—24no—
603C22×C4—24no—
604C22×C4—24no—
605C22×C4—44no—
606C22×C4—44no—
607C22×C4—44no—
608C22×C4—44no—
609C22×C4—44no—
610C22×C4—44no—
611C22×C4—44no—
612C22×C4—48no—
613C22×C4—48no—
614C22×C4—48no—
615C22×C4—48no—
616C22×C4—48no—
617C22×C4—48no—
618C22×C4—48no—
619C22×C4—48no—
620C22×C4—48no—
621C22×C4—4128no—
622C22×C4—48no—
623C22×C4—48no—
624C22×C4—44no—
625C22×C4—44no—
626C22×C4—48no—
627C22×C4—44no—
628C22×C4—44no—
629C22×C4—44no—
630C22×C4—44no—
631C22×C4—44no—
632C22×C4—44no—
633C22×C4—84no—
634C22×C4—84no—
635C22×C4—84no—
636C22×C4—84no—
637C22×C4#121116yes—
638C22×C4C22×D412yes—
639C22×C4C22×D418yes—
640C22×C4C22×D412yes—
641C22×C4C22×D412yes—
642C22×C4C22×D412yes—
643C22×C4C22×D412yes—
644C22×C4C22×D412yes—
645C22×C4C2×#4114yes—
646C22×C4C2×#4112yes—
647C22×C4C2×#4112yes—
648C22×C4H(5,𝔽2)14yes—
649C4⋊C4—48no—
650C4⋊C4—48no—
651C4⋊C4—44no—
652C4⋊C4—44no—
653C4⋊C4—48no—
654C4⋊C4—44no—
655C4⋊C4—48no—
656C4⋊C4—48no—
657C4⋊C4—88no—
658C4⋊C4—88no—
659C22⋊C4—216no—
660C22⋊C4—416no—
661C22⋊C4—416no—
662C22⋊C4—48no—
663C22⋊C4—48no—
664C22⋊C4—416no—
665C22⋊C4—48no—
666C22⋊C4—48no—
667C22⋊C4—48no—
668C22⋊C4—48no—
669C22⋊C4—48no—
670C22⋊C4—48no—
671C22⋊C4—48no—
672C22⋊C4—48no—
673C22⋊C4—48no—
674C22⋊C4—48no—
675C22⋊C4—48no—
676C22⋊C4—88no—
677C22⋊C4—88no—
678C22⋊C4—88no—
679C42—416no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—24no—
685C23—24no—
686C23—24no—
687C23—24no—
688C23—24no—
689C23—24no—
690C23—24no—
691C23—24no—
692C23—24no—
693C23—24no—
694C23—24no—
695C23—24no—
696C23—232no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
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—28no—
723C23—24no—
724C23—24no—
725C23—28no—
726C23—416no—
727C23—416no—
728C23—416no—
729C23—416no—
730C23—416no—
731C23—432no—
732C23—432no—
733C23—432no—
734C23—432no—
735C23—416no—
736C23—416no—
737C23—416no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—42no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—42no—
751C23—42no—
752C23—42no—
753C23—42no—
754C23—42no—
755C23—42no—
756C23—42no—
757C23—42no—
758C23—42no—
759C23—416no—
760C23—42no—
761C23—42no—
762C23—42no—
763C23—42no—
764C23—42no—
765C23—44no—
766C23—42no—
767C23—42no—
768C23—44no—
769C23—44no—
770C23—44no—
771C23—44no—
772C23—44no—
773C23—44no—
774C23—44no—
775C23—44no—
776C23—44no—
777C23—816no—
778C23—816no—
779C23—88no—
780C23—816no—
781C23—88no—
782C23—816no—
783C23—88no—
784C23—88no—
785C23C2×#12114yes—
786C23#52514yes—
787C23#53414yes—
788C23#53514yes—
789C23#53614yes—
790C23#54714yes—
791C23#54814yes—
792C23#55214yes—
793C23#55614yes—
794C23C23×D411yescharacteristic
795C23C23×D411yescharacteristic
796C23C22×#4111yescharacteristic
797C23C22×#4111yescharacteristic
798C23C22×#4111yescharacteristic
799C23C2×H(5,𝔽2)12yes—
800C23C2×H(5,𝔽2)12yes—
801C23C2×H(5,𝔽2)12yes—
802C23C2×2−1+411yescharacteristic
803C23C2×2−1+411yescharacteristic
804C23#58512yes—
805Q8—88no—
806D4—432no—
807D4—432no—
808C2×C4—232no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—24no—
816C2×C4—24no—
817C2×C4—24no—
818C2×C4—24no—
819C2×C4—24no—
820C2×C4—24no—
821C2×C4—22no—
822C2×C4—24no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—28no—
826C2×C4—28no—
827C2×C4—28no—
828C2×C4—28no—
829C2×C4—416no—
830C2×C4—416no—
831C2×C4—416no—
832C2×C4—416no—
833C2×C4—416no—
834C2×C4—416no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—44no—
838C2×C4—42no—
839C2×C4—44no—
840C2×C4—42no—
841C2×C4—44no—
842C2×C4—44no—
843C2×C4—44no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—42no—
860C2×C4—42no—
861C2×C4—42no—
862C2×C4—44no—
863C2×C4—44no—
864C2×C4—44no—
865C2×C4—44no—
866C2×C4—44no—
867C2×C4—44no—
868C2×C4—44no—
869C2×C4—44no—
870C2×C4—44no—
871C2×C4—44no—
872C2×C4—44no—
873C2×C4—44no—
874C2×C4—44no—
875C2×C4—44no—
876C2×C4—44no—
877C2×C4—44no—
878C2×C4—44no—
879C2×C4—44no—
880C2×C4—44no—
881C2×C4—88no—
882C2×C4—88no—
883C2×C4C2×#12114yes—
884C2×C4C2×#12114yes—
885C2×C4#53414yes—
886C22—24no—
887C22—28no—
888C22—24no—
889C22—28no—
890C22—24no—
891C22—28no—
892C22—28no—
893C22—24no—
894C22—24no—
895C22—24no—
896C22—24no—
897C22—24no—
898C22—24no—
899C22—24no—
900C22—24no—
901C22—24no—
902C22—464no—
903C22—42no—
904C22—42no—
905C22—44no—
906C22—44no—
907C22—42no—
908C22—44no—
909C22—44no—
910C22—42no—
911C22—44no—
912C22—44no—
913C22—44no—
914C22—44no—
915C22—42no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—44no—
920C22—48no—
921C22—48no—
922C22—44no—
923C22—44no—
924C22—832no—
925C22—82no—
926C22—84no—
927C22—82no—
928C22—84no—
929C22—82no—
930C22—82no—
931C22#241518yes—
932C22C22×#12111yescharacteristic
933C22C2×#52511yescharacteristic
934C22C2×#53411yescharacteristic
935C22C2×#53411yescharacteristic
936C22C2×#53511yescharacteristic
937C22C2×#53611yescharacteristic
938C22#344911yescharacteristic
939C22#345912yes—
940C22#346012yes—
941C22C2×#54711yescharacteristic
942C22C2×#54811yescharacteristic
943C22C2×#55211yescharacteristic
944C22C2×#55611yescharacteristic
945C22#348412yes—
946C22#348812yes—
947C22#349012yes—
948C22#349012yes—
949C22#349012yes—
950C22#349412yes—
951C22#353512yes—
952C22#353512yes—
953C22#353612yes—
954C22#353612yes—
955C4—24no—
956C4—24no—
957C4—24no—
958C4—48no—
959C4—42no—
960C4—44no—
961C4—82no—
962C4—82no—
963C4—84no—
964C4—82no—
965C4—82no—
966C4—82no—
967C4—82no—
968C2—28no—
969C2—44no—
970C2—44no—
971C2—84no—
972C2#3456211yescharacteristic
973C2C2×#241511yescharacteristic
974C2#3498111yescharacteristic
975C2#3505011yescharacteristic
976C2#3525211yescharacteristic
977C2#3744111yescharacteristic
978C2#3745111yescharacteristic
979C2#3775212yes—
980C2#3776112yes—
981C2#3793212yes—
982C2#3795712yes—
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×#2848C2semidirect
2. C2×#2626C2semidirect
4. C2×#2280C2semidirect
5. #16513C2semidirect
6. #16392C2semidirect
7. #16263C2semidirect
8. #14890C2semidirect
9. #14839C2semidirect
10. #14765C2semidirect
11. #14727C2semidirect
13. #14338C2semidirect
14. #14281C2semidirect
15. #14275C2semidirect
16. #14044C2semidirect
17. #13971C2semidirect
21. C22×C22⋊Q8C22semidirect
22. C22×C22⋊Q8C22semidirect
23. C22×#117C22semidirect
29. C2×#399C22semidirect
30. C2×#397C22semidirect
31. C2×#396C22semidirect
34. C2×#393C22semidirect
35. C2×#388C22semidirect
44. C2×#385C22semidirect
45. C2×#385C22semidirect
47. C2×#381C22semidirect
51. C2×#380C22semidirect
52. C2×#380C22semidirect
53. C2×#380C22semidirect
59. C2×C4×C22⋊C4C22semidirect
62. #1446C22semidirect
63. #1445C22semidirect
64. #1444C22semidirect
65. #1442C22semidirect
66. #1442C22semidirect
67. #1441C22semidirect
68. #1441C22semidirect
69. #1441C22semidirect
70. #1440C22semidirect
71. #1440C22semidirect
72. #1440C22semidirect
73. #1439C22semidirect
74. #1439C22semidirect
75. #1439C22semidirect
76. #1439C22semidirect
77. #1439C22semidirect
80. #1437C22semidirect
81. #1436C22semidirect
82. C4⋊#95C22semidirect
181. #380D4semidirect
348. C2×C4⋊C4C2×D4semidirect
426. #95C2×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#28482
C2×#26262
C22×#3862
C2×#22802
#165132
#163922
#162632
#148902
#148392
#147652
#147272
#147242
#143382
#142812
#142752
#140442
#139712