Finite Group Databasebeta

← #627710

Subgroups — #627710

Order 512.

5486 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#539C211yesmaximal, characteristic, complemented
2C2×#2848C211yesmaximal, characteristic, complemented
3C2×#2847C211yesmaximal, characteristic
4C22×#385C211yesmaximal, characteristic, complemented
5#16004C214yesmaximal, complemented
6#15996C214yesmaximal, complemented
7#15951C214yesmaximal, complemented
8#15950C214yesmaximal, complemented
9#14912C212yesmaximal, complemented
10#14911C212yesmaximal, complemented
11#14339C211yesmaximal, characteristic, complemented
12#14281C211yesmaximal, characteristic, complemented
13#14271C211yesmaximal, characteristic, complemented
14#14015C212yesmaximal, complemented
15#13967C212yesmaximal, complemented
16C25×C4C2211yescharacteristic
17C2×#539—28no—
18C2×#539—28no—
19C2×#539—28no—
20C22×#126C2212yescomplemented
21C22×#125C2212yescomplemented
22C22×#123C2212yes—
23C22×#123C2212yescomplemented
24C22×C22⋊Q8C2211yescharacteristic
25C22×C22⋊Q8C2212yes—
26C22×C22⋊Q8C2212yescomplemented
27C22×#121C2211yescharacteristic
28C22×#121C2212yes—
29C22×#120C2212yes—
30C22×C4×D4C2212yes—
31C23×C4⋊C4C2211yescharacteristic
32C23×C4⋊C4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34C23×C22⋊C4C2211yescharacteristic
35#2848—28no—
36#2847—28no—
37C2×#386C2212yes—
38C2×#386C2214yes—
39C2×#386C2212yes—
40C2×#386C2212yes—
41C2×#386C2214yes—
42C2×#385—28no—
43C2×#385C2212yes—
44C2×#385C2214yes—
45C2×#385C2214yes—
46C2×#385C2214yes—
47C2×#385C2214yescomplemented
48C2×#381C2212yes—
49C2×#380C2211yescharacteristic
50C2×#380C2211yescharacteristic
51C2×#380C2212yes—
52C2×#380C2212yes—
53C2×#379C2212yes—
54C22×#95C2211yescharacteristic
55C22×#95C2211yescharacteristic
56#1446C2212yescomplemented
57#1445C2212yescomplemented
58#1445C2212yescomplemented
59#1444C2214yescomplemented
60#1442C2214yescomplemented
61#1441C2214yescomplemented
62#1441C2214yescomplemented
63#1441C2214yescomplemented
64#1441C2214yescomplemented
65#1440C2214yescomplemented
66#1439C2214yes—
67#1439C2214yes—
68#1439C2214yes—
69#1439C2214yescomplemented
70#1439C2214yescomplemented
71#1439C2214yescomplemented
72#1438C2214yes—
73#1438C2214yes—
74#1438C2214yes—
75#1438C2212yescomplemented
76#1437C2214yes—
77#1436C2214yescomplemented
78C22⋊#95C2212yes—
79C22⋊#95C2212yes—
80C22⋊#95C2212yes—
81C26C2311yescharacteristic
82C23×Q8C2311yescharacteristic
83C23×D4C2312yes—
84C23×D4C2314yes—
85C23×D4C2311yescharacteristic
86C24×C4—24no—
87C24×C4—24no—
88C24×C4—24no—
89C24×C4—44no—
90C24×C4—44no—
91C24×C4C2311yescharacteristic
92C24×C4C2311yescharacteristic
93C24×C4C2312yes—
94C24×C4C2312yes—
95C24×C4C2311yescharacteristic
96C24×C4C2312yes—
97C24×C4C2311yescharacteristic
98C24×C4C2311yescharacteristic
99C24×C4C2311yescharacteristic
100#539—2128no—
101C2×#126—28no—
102C2×#126—28no—
103C2×#126—28no—
104C2×#125—28no—
105C2×#125—28no—
106C2×#125—28no—
107C2×#123—28no—
108C2×#123—28no—
109C2×#123—28no—
110C2×#123—28no—
111C2×#123—28no—
112C2×#123—28no—
113C2×C22⋊Q8—28no—
114C2×C22⋊Q8—24no—
115C2×C22⋊Q8—24no—
116C2×C22⋊Q8—28no—
117C2×C22⋊Q8—28no—
118C2×C22⋊Q8—28no—
119C2×C22⋊Q8—44no—
120C2×C22⋊Q8—44no—
121C2×C22⋊Q8D418yescomplemented
122C2×#121—24no—
123C2×#121—24no—
124C2×#121—28no—
125C2×#121—44no—
126C2×#121—44no—
127C2×#121D418yes—
128C2×#120—28no—
129C2×#120—28no—
130C2×#120—44no—
131C2×C4×D4—28no—
132C2×C4×D4—28no—
133C2×C4×D4—28no—
134C22×C4⋊C4—24no—
135C22×C4⋊C4—24no—
136C22×C4⋊C4—24no—
137C22×C4⋊C4—44no—
138C22×C4⋊C4D418yescomplemented
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2314yes—
143C22×C4⋊C4C2314yes—
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2311yescharacteristic
147C22×C4⋊C4C2312yes—
148C22×C4⋊C4C2311yescharacteristic
149C22×C4⋊C4C2312yes—
150C22×C4⋊C4C2312yes—
151C22×C22⋊C4—24no—
152C22×C22⋊C4—24no—
153C22×C22⋊C4—24no—
154C22×C22⋊C4—24no—
155C22×C22⋊C4—44no—
156C22×C22⋊C4C2314yes—
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2312yes—
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2314yes—
163C22×C22⋊C4C2314yes—
164C22×C22⋊C4C2314yes—
165C22×C22⋊C4C2314yes—
166C22×C22⋊C4C2314yes—
167C22×C22⋊C4C2312yes—
168C22×C22⋊C4C2312yes—
169C22×C22⋊C4C2314yes—
170C22×C22⋊C4C2314yes—
171C22×C42C2312yes—
172#386—28no—
173#386—28no—
174#386—216no—
175#386—48no—
176#386—44no—
177#385—216no—
178#385—216no—
179#385—216no—
180#385—28no—
181#385—48no—
182#381—44no—
183#380—24no—
184#380—24no—
185#380—28no—
186#380—28no—
187#379—28no—
188C2×#95—24no—
189C2×#95—24no—
190C2×#95C2314yes—
191C2×#95C2314yes—
192C2×#95C2314yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2314yes—
197C2×#95C2312yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C25—22no—
208C25—22no—
209C25—24no—
210C25—24no—
211C25—22no—
212C25—22no—
213C25—22no—
214C25—22no—
215C25—42no—
216C25—42no—
217C25#4114yes—
218C25C2412yes—
219C25C2412yes—
220C25C2411yescharacteristic
221C22×Q8—22no—
222C22×Q8—22no—
223C22×Q8—42no—
224C22×Q8—42no—
225C22×Q8C2×D414yes—
226C22×D4—24no—
227C22×D4—24no—
228C22×D4—24no—
229C22×D4—24no—
230C22×D4—24no—
231C22×D4—24no—
232C22×D4—28no—
233C22×D4—28no—
234C22×D4—28no—
235C22×D4—28no—
236C22×D4—22no—
237C22×D4—22no—
238C22×D4—44no—
239C22×D4—42no—
240C22×D4—42no—
241C22×D4—44no—
242C22×D4—44no—
243C22×D4C2×D418yes—
244C22×D4C2×D414yes—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—24no—
253C23×C4—24no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—24no—
259C23×C4—24no—
260C23×C4—24no—
261C23×C4—24no—
262C23×C4—24no—
263C23×C4—24no—
264C23×C4—24no—
265C23×C4—24no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—24no—
272C23×C4—24no—
273C23×C4—24no—
274C23×C4—24no—
275C23×C4—42no—
276C23×C4—42no—
277C23×C4—42no—
278C23×C4—42no—
279C23×C4—42no—
280C23×C4—42no—
281C23×C4—42no—
282C23×C4—42no—
283C23×C4—42no—
284C23×C4—42no—
285C23×C4—42no—
286C23×C4—42no—
287C23×C4—42no—
288C23×C4—44no—
289C23×C4—44no—
290C23×C4—416no—
291C23×C4—432no—
292C23×C4—432no—
293C23×C4—416no—
294C23×C4—416no—
295C23×C4C2×D414yes—
296C23×C4C2×D414yes—
297C23×C4C2×D414yes—
298C23×C4C2×D414yes—
299C23×C4C2×D414yes—
300C23×C4#4114yes—
301C23×C4C2414yes—
302C23×C4C2412yes—
303C23×C4C2414yes—
304C23×C4C2412yes—
305C23×C4C2412yes—
306C23×C4C2412yes—
307C23×C4C2412yes—
308C23×C4C2412yes—
309C23×C4C2412yes—
310C23×C4C2412yes—
311C23×C4C2411yescharacteristic
312C23×C4C2411yescharacteristic
313#126—264no—
314#125—264no—
315#123—264no—
316#123—264no—
317C22⋊Q8—264no—
318C22⋊Q8—232no—
319C22⋊Q8—432no—
320#121—232no—
321#121—432no—
322#120—432no—
323C4×D4—264no—
324C2×C4⋊C4—232no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—28no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—28no—
348C2×C4⋊C4—28no—
349C2×C4⋊C4—28no—
350C2×C4⋊C4—44no—
351C2×C4⋊C4—42no—
352C2×C4⋊C4—42no—
353C2×C4⋊C4—44no—
354C2×C4⋊C4—42no—
355C2×C4⋊C4—42no—
356C2×C4⋊C4—416no—
357C2×C4⋊C4C2×D418yes—
358C2×C4⋊C4C2×D418yes—
359C2×C4⋊C4C2×D414yes—
360C2×C4⋊C4C2×D418yes—
361C2×C4⋊C4C2×D414yes—
362C2×C22⋊C4—232no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—28no—
369C2×C22⋊C4—28no—
370C2×C22⋊C4—24no—
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—24no—
380C2×C22⋊C4—28no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—28no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—28no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—28no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—28no—
390C2×C22⋊C4—28no—
391C2×C22⋊C4—28no—
392C2×C22⋊C4—28no—
393C2×C22⋊C4—28no—
394C2×C22⋊C4—28no—
395C2×C22⋊C4—28no—
396C2×C22⋊C4—44no—
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⋊C4—416no—
404C2×C22⋊C4—44no—
405C2×C22⋊C4—44no—
406C2×C22⋊C4—44no—
407C2×C22⋊C4C2×D418yes—
408C2×C22⋊C4C2×D418yes—
409C2×C42—24no—
410C2×C42—24no—
411C2×C42—24no—
412#95—24no—
413#95—24no—
414#95—28no—
415#95—28no—
416#95—24no—
417#95—28no—
418#95—24no—
419#95—28no—
420#95—44no—
421#95—44no—
422#95—44no—
423#95—44no—
424#95—44no—
425#95—44no—
426#95—44no—
427#95—44no—
428#95—44no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—28no—
434C24—28no—
435C24—216no—
436C24—28no—
437C24—216no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—28no—
451C24—28no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—24no—
457C24—24no—
458C24—22no—
459C24—22no—
460C24—24no—
461C24—24no—
462C24—48no—
463C24—48no—
464C24—48no—
465C24—48no—
466C24—48no—
467C24—48no—
468C24—48no—
469C24—48no—
470C24—48no—
471C24—44no—
472C24—48no—
473C24—44no—
474C24—44no—
475C24—44no—
476C24—44no—
477C24—44no—
478C24C22×D414yes—
479C24C22×D412yes—
480C24C22×D412yes—
481C24C22×D412yes—
482C24C2×#4114yes—
483C24C2×#4112yes—
484C24C2×#4112yes—
485C24H(5,𝔽2)14yes—
486C24H(5,𝔽2)12yes—
487C242−1+414yes—
488C242−1+412yes—
489C24C2511yescharacteristic
490C2×Q8—28no—
491C2×Q8—48no—
492C2×Q8—84no—
493C2×Q8—82no—
494C2×Q8—82no—
495C2×D4—216no—
496C2×D4—216no—
497C2×D4—216no—
498C2×D4—28no—
499C2×D4—48no—
500C2×D4—48no—
501C2×D4—48no—
502C2×D4—48no—
503C2×D4—48no—
504C2×D4—416no—
505C2×D4—416no—
506C2×D4—416no—
507C2×D4—416no—
508C2×D4—84no—
509C2×D4—82no—
510C2×D4—82no—
511C2×D4—88no—
512C2×D4—88no—
513C2×D4—88no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—28no—
519C22×C4—216no—
520C22×C4—216no—
521C22×C4—28no—
522C22×C4—28no—
523C22×C4—28no—
524C22×C4—28no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—24no—
549C22×C4—24no—
550C22×C4—24no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—24no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—24no—
558C22×C4—24no—
559C22×C4—216no—
560C22×C4—28no—
561C22×C4—22no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—24no—
566C22×C4—24no—
567C22×C4—24no—
568C22×C4—24no—
569C22×C4—22no—
570C22×C4—24no—
571C22×C4—24no—
572C22×C4—24no—
573C22×C4—24no—
574C22×C4—24no—
575C22×C4—22no—
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—48no—
581C22×C4—48no—
582C22×C4—44no—
583C22×C4—44no—
584C22×C4—48no—
585C22×C4—48no—
586C22×C4—48no—
587C22×C4—48no—
588C22×C4—48no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—48no—
592C22×C4—48no—
593C22×C4—48no—
594C22×C4—48no—
595C22×C4—48no—
596C22×C4—48no—
597C22×C4—48no—
598C22×C4—48no—
599C22×C4—44no—
600C22×C4—44no—
601C22×C4—48no—
602C22×C4—44no—
603C22×C4—4128no—
604C22×C4—44no—
605C22×C4—44no—
606C22×C4—44no—
607C22×C4—44no—
608C22×C4—44no—
609C22×C4—48no—
610C22×C4—48no—
611C22×C4—44no—
612C22×C4—44no—
613C22×C4—44no—
614C22×C4—84no—
615C22×C4—88no—
616C22×C4—84no—
617C22×C4—84no—
618C22×C4—84no—
619C22×C4—88no—
620C22×C4—84no—
621C22×C4—84no—
622C22×C4#120116yes—
623C22×C4C22×D414yes—
624C22×C4C22×D414yes—
625C22×C4C22×D414yes—
626C22×C4C22×D414yes—
627C22×C4C22×D414yes—
628C22×C4C22×D412yes—
629C22×C4C22×D412yes—
630C22×C4C22×D412yes—
631C22×C4C22×D412yes—
632C22×C4C22×D412yes—
633C22×C4C22×D412yes—
634C22×C4C2×#4114yes—
635C22×C4H(5,𝔽2)14yes—
636C4⋊C4—216no—
637C4⋊C4—216no—
638C4⋊C4—216no—
639C4⋊C4—216no—
640C4⋊C4—216no—
641C4⋊C4—28no—
642C4⋊C4—216no—
643C4⋊C4—28no—
644C4⋊C4—416no—
645C4⋊C4—416no—
646C4⋊C4—48no—
647C4⋊C4—48no—
648C22⋊C4—232no—
649C22⋊C4—216no—
650C22⋊C4—216no—
651C22⋊C4—216no—
652C22⋊C4—216no—
653C22⋊C4—216no—
654C22⋊C4—416no—
655C22⋊C4—416no—
656C22⋊C4—416no—
657C22⋊C4—416no—
658C22⋊C4—416no—
659C22⋊C4—416no—
660C22⋊C4—48no—
661C22⋊C4—48no—
662C22⋊C4—88no—
663C42—216no—
664C23—24no—
665C23—24no—
666C23—22no—
667C23—22no—
668C23—24no—
669C23—24no—
670C23—22no—
671C23—22no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—24no—
676C23—24no—
677C23—24no—
678C23—24no—
679C23—24no—
680C23—232no—
681C23—24no—
682C23—24no—
683C23—24no—
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—24no—
697C23—24no—
698C23—24no—
699C23—24no—
700C23—24no—
701C23—24no—
702C23—28no—
703C23—28no—
704C23—432no—
705C23—432no—
706C23—416no—
707C23—416no—
708C23—416no—
709C23—416no—
710C23—432no—
711C23—432no—
712C23—416no—
713C23—416no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—44no—
733C23—44no—
734C23—42no—
735C23—42no—
736C23—44no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—44no—
742C23—44no—
743C23—44no—
744C23—44no—
745C23—44no—
746C23—44no—
747C23—44no—
748C23C2×#12014yes—
749C23#52514yes—
750C23#53714yes—
751C23#53918yescomplemented
752C23#54614yes—
753C23#54714yes—
754C23#54814yes—
755C23#55014yes—
756C23C23×D411yescharacteristic
757C23C23×D411yescharacteristic
758C23C23×D411yescharacteristic
759C23C22×#4111yescharacteristic
760C23C22×#4111yescharacteristic
761C23C2×H(5,𝔽2)11yescharacteristic
762C23C2×H(5,𝔽2)12yes—
763C23C2×H(5,𝔽2)12yes—
764C23C2×2−1+411yescharacteristic
765C23C2×2−1+412yes—
766C23#58512yes—
767Q8—88no—
768D4—432no—
769D4—88no—
770D4—832no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—24no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—24no—
783C2×C4—24no—
784C2×C4—24no—
785C2×C4—24no—
786C2×C4—24no—
787C2×C4—28no—
788C2×C4—24no—
789C2×C4—24no—
790C2×C4—24no—
791C2×C4—24no—
792C2×C4—28no—
793C2×C4—24no—
794C2×C4—24no—
795C2×C4—24no—
796C2×C4—28no—
797C2×C4—416no—
798C2×C4—432no—
799C2×C4—432no—
800C2×C4—416no—
801C2×C4—416no—
802C2×C4—416no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—44no—
817C2×C4—44no—
818C2×C4—44no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—44no—
825C2×C4—44no—
826C2×C4—42no—
827C2×C4—44no—
828C2×C4—44no—
829C2×C4—44no—
830C2×C4—44no—
831C2×C4—42no—
832C2×C4—44no—
833C2×C4—44no—
834C2×C4—42no—
835C2×C4—44no—
836C2×C4—44no—
837C2×C4—44no—
838C2×C4—44no—
839C2×C4—44no—
840C2×C4—44no—
841C2×C4—44no—
842C2×C4—44no—
843C2×C4—44no—
844C2×C4—44no—
845C2×C4—88no—
846C2×C4—816no—
847C2×C4—88no—
848C2×C4C2×#12014yes—
849C2×C4C2×#12014yes—
850C22—24no—
851C22—28no—
852C22—28no—
853C22—24no—
854C22—24no—
855C22—24no—
856C22—28no—
857C22—28no—
858C22—24no—
859C22—24no—
860C22—28no—
861C22—28no—
862C22—28no—
863C22—464no—
864C22—44no—
865C22—44no—
866C22—44no—
867C22—44no—
868C22—44no—
869C22—44no—
870C22—44no—
871C22—44no—
872C22—44no—
873C22—44no—
874C22—44no—
875C22—44no—
876C22—44no—
877C22—48no—
878C22—44no—
879C22—48no—
880C22—44no—
881C22—84no—
882C22—82no—
883C22—82no—
884C22—84no—
885C22—82no—
886C22—82no—
887C22#240718yes—
888C22C22×#12011yescharacteristic
889C22C2×#52511yescharacteristic
890C22C2×#53711yescharacteristic
891C22C2×#53912yes—
892C22#345912yes—
893C22C2×#54611yescharacteristic
894C22C2×#54711yescharacteristic
895C22C2×#54811yescharacteristic
896C22C2×#55011yescharacteristic
897C22#348412yes—
898C22#348412yes—
899C22#348411yescharacteristic
900C22#348411yescharacteristic
901C22#348611yescharacteristic
902C22#348711yescharacteristic
903C22#348912yes—
904C22#348912yes—
905C22#349212yes—
906C22#350512yes—
907C22#353412yes—
908C22#353512yes—
909C22#353612yes—
910C22#353812yes—
911C4—24no—
912C4—24no—
913C4—44no—
914C4—44no—
915C4—44no—
916C4—44no—
917C4—44no—
918C4—44no—
919C4—44no—
920C4—84no—
921C4—82no—
922C4—84no—
923C2—28no—
924C2—48no—
925C2—84no—
926C2C2×#240711yescharacteristic
927C2#3498711yescharacteristic
928C2#3498911yescharacteristic
929C2#3534611yescharacteristic
930C2#3565911yescharacteristic
931C2#3671911yescharacteristic
932C2#3672211yescharacteristic
933C2#3769212yes—
934C2#3770212yes—
935C2#3776012yes—
936C2#3776812yes—
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
1. C22×#539C2semidirect
2. C2×#2848C2semidirect
4. C22×#385C2semidirect
5. #16004C2semidirect
6. #15996C2semidirect
7. #15951C2semidirect
8. #15950C2semidirect
9. #14912C2semidirect
10. #14911C2semidirect
11. #14339C2semidirect
12. #14281C2semidirect
13. #14271C2semidirect
14. #14015C2semidirect
15. #13967C2semidirect
20. C22×#126C22semidirect
21. C22×#125C22semidirect
23. C22×#123C22semidirect
26. C22×C22⋊Q8C22semidirect
47. C2×#385C22semidirect
56. #1446C22semidirect
57. #1445C22semidirect
58. #1445C22semidirect
59. #1444C22semidirect
60. #1442C22semidirect
61. #1441C22semidirect
62. #1441C22semidirect
63. #1441C22semidirect
64. #1441C22semidirect
65. #1440C22semidirect
69. #1439C22semidirect
70. #1439C22semidirect
71. #1439C22semidirect
75. #1438C22semidirect
77. #1436C22semidirect
121. C2×C22⋊Q8D4semidirect
138. C22×C4⋊C4D4semidirect
751. C23#539semidirect

Maximal subgroups

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

subgroupindex
C22×#5392
C2×#28482
C2×#28472
C22×#3852
#160042
#159962
#159512
#159502
#149122
#149112
#143392
#142812
#142712
#140152
#139672