Finite Group Databasebeta

← #656998

Subgroups — #656998

Order 512.

4456 conjugacy classes of subgroups.

The subgroup lattice has 935 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2486C211yesmaximal, characteristic, complemented
2C2×#2352C211yesmaximal, characteristic, complemented
3C2×C4×#120C211yesmaximal, characteristic
4C22×#380C211yesmaximal, characteristic, complemented
5#15687C214yesmaximal, complemented
6#15512C214yesmaximal, complemented
7#15220C212yesmaximal, complemented
8#15181C212yesmaximal, complemented
9#14927C212yesmaximal, complemented
10#14911C212yesmaximal
11#14680C211yesmaximal, characteristic, complemented
12#13992C212yesmaximal, complemented
13#13973C212yesmaximal, complemented
14#13907C211yesmaximal, characteristic, complemented
15#13904C211yesmaximal, characteristic, complemented
16#13903C212yesmaximal, complemented
17#13871C212yesmaximal, complemented
18C25×C4C2211yescharacteristic
19C22×#123C2212yes—
20C22×#120C2211yescharacteristic
21C22×C4×D4C2212yes—
22C22×C4×D4C2211yescharacteristic
23C22×#117C2211yescharacteristic, complemented
24C23×C4⋊C4C2211yescharacteristic
25C23×C4⋊C4C2211yescharacteristic
26C23×C22⋊C4C2212yes—
27#2486—28no—
28C2×#398C2212yescomplemented
29C2×#397C2212yescomplemented
30#2352—28no—
31C4×#120—28no—
32C2×#389C2212yescomplemented
33C2×#389C2212yescomplemented
34C2×#388C2212yescomplemented
35C2×#387C2212yescomplemented
36C2×#386C2212yes—
37C2×#386C2212yes—
38C2×#386C2211yescharacteristic
39C2×#385C2212yes—
40C2×#385C2211yescharacteristic
41C2×#382C2211yescharacteristic, complemented
42C2×#381C2212yes—
43C2×#381C2212yes—
44C2×#381C2212yes—
45C2×#380—28no—
46C2×#380C2212yes—
47C2×#380C2211yescharacteristic
48C2×#380C2214yes—
49C2×#380C2212yes—
50C2×#380C2212yes—
51C2×#380C2211yescharacteristic
52C2×#380C2212yes—
53C2×#380C2212yes—
54C2×#380C2212yescomplemented
55C2×#380C2211yescharacteristic, complemented
56C2×#379C2211yescharacteristic
57C2×#379C2212yes—
58C2×C4×C4⋊C4C2211yescharacteristic, complemented
59C2×C4×C22⋊C4C2212yes—
60C2×C4×C22⋊C4C2211yescharacteristic
61C2×C4×C22⋊C4C2212yes—
62C22×#95C2212yes—
63#1445C2214yescomplemented
64#1443C2214yescomplemented
65#1442C2214yescomplemented
66#1442C2214yescomplemented
67#1441C2214yescomplemented
68#1441C2214yescomplemented
69#1440C2214yescomplemented
70#1439C2214yes—
71#1439C2214yes—
72#1439C2214yes—
73#1439C2214yes—
74#1439C2214yescomplemented
75#1438C2214yes—
76#1438C2214yes—
77#1437C2214yes—
78#1437C2214yes—
79#1436C2214yescomplemented
80C4⋊#95C2212yescomplemented
81C4⋊#95C2212yescomplemented
82C4⋊#95C2212yescomplemented
83#1434C2214yescomplemented
84C22⋊#95C2212yes—
85C22⋊#95C2214yes—
86C22⋊#95C2212yes—
87C26C2311yescharacteristic
88C23×D4C2311yescharacteristic
89C23×D4C2312yes—
90C24×C4—24no—
91C24×C4—28no—
92C24×C4—24no—
93C24×C4—24no—
94C24×C4—44no—
95C24×C4C2312yes—
96C24×C4C2311yescharacteristic
97C24×C4C2312yes—
98C24×C4C2311yescharacteristic
99C24×C4C2312yes—
100C24×C4C2311yescharacteristic
101C24×C4C2312yes—
102C2×#123—28no—
103C2×#123—44no—
104C2×#123—44no—
105C2×#120—24no—
106C2×#120—24no—
107C2×#120—24no—
108C2×C4×D4—24no—
109C2×C4×D4—24no—
110C2×C4×D4—28no—
111C2×C4×D4—28no—
112C2×C4×D4—44no—
113C2×C4×D4D418yes—
114C2×#117—24no—
115C2×#117—44no—
116C22×C4⋊C4—24no—
117C22×C4⋊C4—24no—
118C22×C4⋊C4—24no—
119C22×C4⋊C4—44no—
120C22×C4⋊C4D418yescomplemented
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2314yes—
131C22×C4⋊C4C2314yes—
132C22×C4⋊C4C2312yes—
133C22×C22⋊C4—28no—
134C22×C22⋊C4—28no—
135C22×C22⋊C4—44no—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2311yescharacteristic
140C22×C22⋊C4C2314yes—
141C22×C22⋊C4C2314yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2311yescharacteristic
146C22×C22⋊C4C2311yescharacteristic
147C22×C22⋊C4C2311yescharacteristic
148C22×C22⋊C4C2314yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2314yes—
151C22×C22⋊C4C2314yes—
152C22×C22⋊C4C2312yes—
153C22×C42C2312yes—
154C22×C42C2311yescharacteristic
155C22×C42C2312yes—
156C22×C42C2312yes—
157#398—28no—
158#397—28no—
159#389—28no—
160#389—44no—
161#388—28no—
162#387—28no—
163#386—24no—
164#386—28no—
165#386—28no—
166#385—28no—
167#385—24no—
168#382—24no—
169#381—28no—
170#381—28no—
171#381—44no—
172#380—24no—
173#380—24no—
174#380—28no—
175#380—28no—
176#380—24no—
177#380—28no—
178#380—28no—
179#380—216no—
180#380—44no—
181#380—44no—
182#379—24no—
183#379—44no—
184C4×C4⋊C4—24no—
185C4×C22⋊C4—28no—
186C4×C22⋊C4—24no—
187C4×C22⋊C4—28no—
188C2×#95—28no—
189C2×#95C2312yes—
190C2×#95C2314yes—
191C2×#95C2314yes—
192C2×#95C2314yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2314yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2314yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2314yes—
211C25—22no—
212C25—24no—
213C25—22no—
214C25—24no—
215C25—22no—
216C25—22no—
217C25—22no—
218C25—22no—
219C25—42no—
220C25—42no—
221C25#4114yes—
222C25C2411yescharacteristic
223C25C2412yes—
224C25C2411yescharacteristic
225C22×D4—24no—
226C22×D4—22no—
227C22×D4—22no—
228C22×D4—24no—
229C22×D4—22no—
230C22×D4—22no—
231C22×D4—22no—
232C22×D4—22no—
233C22×D4—24no—
234C22×D4—24no—
235C22×D4—24no—
236C22×D4—42no—
237C22×D4—42no—
238C22×D4C2×D414yes—
239C23×C4—24no—
240C23×C4—24no—
241C23×C4—232no—
242C23×C4—22no—
243C23×C4—24no—
244C23×C4—24no—
245C23×C4—24no—
246C23×C4—22no—
247C23×C4—24no—
248C23×C4—24no—
249C23×C4—24no—
250C23×C4—22no—
251C23×C4—24no—
252C23×C4—24no—
253C23×C4—24no—
254C23×C4—24no—
255C23×C4—24no—
256C23×C4—24no—
257C23×C4—24no—
258C23×C4—24no—
259C23×C4—24no—
260C23×C4—24no—
261C23×C4—22no—
262C23×C4—24no—
263C23×C4—24no—
264C23×C4—22no—
265C23×C4—24no—
266C23×C4—24no—
267C23×C4—24no—
268C23×C4—24no—
269C23×C4—24no—
270C23×C4—42no—
271C23×C4—42no—
272C23×C4—42no—
273C23×C4—432no—
274C23×C4—432no—
275C23×C4—44no—
276C23×C4—44no—
277C23×C4—416no—
278C23×C4—416no—
279C23×C4C2×D414yes—
280C23×C4C2×D414yes—
281C23×C4C2×D414yes—
282C23×C4C2×D418yes—
283C23×C4#4118yes—
284C23×C4#4114yes—
285C23×C4C2414yes—
286C23×C4C2412yes—
287C23×C4C2412yes—
288C23×C4C2412yes—
289C23×C4C2414yes—
290C23×C4C2411yescharacteristic
291C23×C4C2412yes—
292C23×C4C2411yescharacteristic
293C23×C4C2412yes—
294C23×C4C2411yescharacteristic
295C23×C4C2412yes—
296C23×C4C2412yes—
297C23×C4C2411yescharacteristic
298C23×C4C2411yescharacteristic
299#123—432no—
300#120—232no—
301C4×D4—232no—
302C4×D4—432no—
303#117—416no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—28no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—416no—
325C2×C4⋊C4—44no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4—44no—
328C2×C4⋊C4—44no—
329C2×C4⋊C4—416no—
330C2×C4⋊C4—44no—
331C2×C4⋊C4—44no—
332C2×C4⋊C4—44no—
333C2×C4⋊C4C2×D414yes—
334C2×C4⋊C4C2×D414yes—
335C2×C4⋊C4C2×D414yes—
336C2×C4⋊C4C2×D418yes—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—22no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—22no—
342C2×C22⋊C4—22no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—22no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—28no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—28no—
352C2×C22⋊C4—28no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—28no—
362C2×C22⋊C4—28no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—28no—
368C2×C22⋊C4—28no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—44no—
377C2×C22⋊C4—44no—
378C2×C22⋊C4—432no—
379C2×C22⋊C4—44no—
380C2×C22⋊C4—44no—
381C2×C22⋊C4—44no—
382C2×C22⋊C4—44no—
383C2×C22⋊C4—44no—
384C2×C22⋊C4C2×D414yes—
385C2×C22⋊C4C2×D414yes—
386C2×C22⋊C4#4114yes—
387C2×C42—22no—
388C2×C42—22no—
389C2×C42—24no—
390C2×C42—24no—
391C2×C42—24no—
392C2×C42—24no—
393C2×C42—24no—
394C2×C42—44no—
395C2×C42—44no—
396C2×C42C2×D414yes—
397#95—28no—
398#95—28no—
399#95—24no—
400#95—24no—
401#95—24no—
402#95—24no—
403#95—24no—
404#95—24no—
405#95—28no—
406#95—24no—
407#95—24no—
408#95—28no—
409#95—24no—
410#95—28no—
411#95—28no—
412#95—28no—
413#95—44no—
414#95—44no—
415#95—44no—
416#95—44no—
417#95—44no—
418#95—44no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—28no—
424C24—28no—
425C24—216no—
426C24—28no—
427C24—216no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—28no—
441C24—28no—
442C24—21no—
443C24—21no—
444C24—22no—
445C24—21no—
446C24—21no—
447C24—21no—
448C24—21no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—48no—
453C24—48no—
454C24—48no—
455C24—48no—
456C24—48no—
457C24—48no—
458C24—48no—
459C24—48no—
460C24—48no—
461C24—44no—
462C24—44no—
463C24—48no—
464C24—44no—
465C24—44no—
466C24—44no—
467C24—44no—
468C24C22×D412yes—
469C24C22×D412yes—
470C24C22×D412yes—
471C24C2×#4114yes—
472C24C2×#4114yes—
473C24C2×#4112yes—
474C24C2×#4112yes—
475C24C2×#4112yes—
476C24H(5,𝔽2)12yes—
477C24H(5,𝔽2)12yes—
478C242−1+414yes—
479C24C2511yescharacteristic
480C2×D4—216no—
481C2×D4—28no—
482C2×D4—28no—
483C2×D4—28no—
484C2×D4—48no—
485C2×D4—48no—
486C2×D4—48no—
487C2×D4—48no—
488C2×D4—48no—
489C2×D4—44no—
490C2×D4—44no—
491C2×D4—48no—
492C2×D4—44no—
493C2×D4—44no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—28no—
497C22×C4—28no—
498C22×C4—216no—
499C22×C4—216no—
500C22×C4—216no—
501C22×C4—28no—
502C22×C4—21no—
503C22×C4—22no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—24no—
524C22×C4—22no—
525C22×C4—24no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—24no—
534C22×C4—22no—
535C22×C4—24no—
536C22×C4—216no—
537C22×C4—28no—
538C22×C4—216no—
539C22×C4—216no—
540C22×C4—216no—
541C22×C4—216no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—24no—
545C22×C4—22no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—22no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—24no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—22no—
565C22×C4—24no—
566C22×C4—24no—
567C22×C4—24no—
568C22×C4—22no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—24no—
572C22×C4—22no—
573C22×C4—48no—
574C22×C4—48no—
575C22×C4—48no—
576C22×C4—48no—
577C22×C4—48no—
578C22×C4—48no—
579C22×C4—48no—
580C22×C4—48no—
581C22×C4—48no—
582C22×C4—4128no—
583C22×C4—44no—
584C22×C4—44no—
585C22×C4—48no—
586C22×C4—48no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—48no—
590C22×C4—48no—
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—48no—
600C22×C4—88no—
601C22×C4—88no—
602C22×C4#121116yes—
603C22×C4C22×D412yes—
604C22×C4C22×D414yes—
605C22×C4C22×D412yes—
606C22×C4C22×D414yes—
607C22×C4C22×D412yes—
608C22×C4C22×D412yes—
609C22×C4C22×D412yes—
610C22×C4C22×D412yes—
611C22×C4C22×D412yes—
612C22×C4C2×#4114yes—
613C22×C4C2×#4114yes—
614C22×C4C2×#4112yes—
615C22×C4C2×#4112yes—
616C22×C4C2×#4114yes—
617C22×C4H(5,𝔽2)14yes—
618C4⋊C4—28no—
619C4⋊C4—28no—
620C4⋊C4—28no—
621C4⋊C4—48no—
622C4⋊C4—48no—
623C4⋊C4—416no—
624C4⋊C4—48no—
625C4⋊C4—48no—
626C4⋊C4—44no—
627C4⋊C4—44no—
628C4⋊C4—48no—
629C4⋊C4—88no—
630C22⋊C4—216no—
631C22⋊C4—28no—
632C22⋊C4—28no—
633C22⋊C4—28no—
634C22⋊C4—48no—
635C22⋊C4—416no—
636C22⋊C4—416no—
637C22⋊C4—48no—
638C22⋊C4—48no—
639C22⋊C4—48no—
640C22⋊C4—416no—
641C22⋊C4—44no—
642C22⋊C4—48no—
643C22⋊C4—48no—
644C22⋊C4—84no—
645C22⋊C4—88no—
646C22⋊C4—88no—
647C42—28no—
648C42—48no—
649C42—48no—
650C42—84no—
651C23—22no—
652C23—22no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—22no—
658C23—22no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—232no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—24no—
676C23—24no—
677C23—24no—
678C23—24no—
679C23—24no—
680C23—24no—
681C23—24no—
682C23—24no—
683C23—24no—
684C23—24no—
685C23—24no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—24no—
690C23—24no—
691C23—432no—
692C23—432no—
693C23—416no—
694C23—416no—
695C23—416no—
696C23—432no—
697C23—416no—
698C23—432no—
699C23—416no—
700C23—42no—
701C23—416no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—42no—
722C23—42no—
723C23—41no—
724C23—41no—
725C23—42no—
726C23—41no—
727C23—41no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23—42no—
734C23—42no—
735C23C2×#12114yes—
736C23#52514yes—
737C23#53514yes—
738C23#54614yes—
739C23#55014yes—
740C23#55218yes—
741C23#55314yes—
742C23#55514yes—
743C23C23×D411yescharacteristic
744C23C23×D411yescharacteristic
745C23C22×#4111yescharacteristic
746C23C22×#4112yes—
747C23C22×#4111yescharacteristic
748C23C22×#4111yescharacteristic
749C23C2×H(5,𝔽2)12yes—
750C23C2×H(5,𝔽2)11yescharacteristic
751C23C2×H(5,𝔽2)11yescharacteristic
752C23C2×2−1+412yes—
753C23#58512yes—
754D4—432no—
755D4—416no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—232no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—24no—
769C2×C4—22no—
770C2×C4—24no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—432no—
781C2×C4—416no—
782C2×C4—42no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—44no—
800C2×C4—44no—
801C2×C4—42no—
802C2×C4—44no—
803C2×C4—44no—
804C2×C4—416no—
805C2×C4—432no—
806C2×C4—44no—
807C2×C4—42no—
808C2×C4—44no—
809C2×C4—42no—
810C2×C4—44no—
811C2×C4—44no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—44no—
815C2×C4—44no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—44no—
819C2×C4—44no—
820C2×C4—44no—
821C2×C4—44no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—44no—
826C2×C4—44no—
827C2×C4—42no—
828C2×C4—44no—
829C2×C4—44no—
830C2×C4—42no—
831C2×C4—44no—
832C2×C4—44no—
833C2×C4—44no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—44no—
837C2×C4—816no—
838C2×C4—816no—
839C2×C4C2×#12114yes—
840C2×C4C2×#12114yes—
841C2×C4#52514yes—
842C2×C4#53414yes—
843C2×C4#54618yes—
844C2×C4#55118yes—
845C22—24no—
846C22—24no—
847C22—24no—
848C22—28no—
849C22—28no—
850C22—24no—
851C22—28no—
852C22—24no—
853C22—28no—
854C22—24no—
855C22—28no—
856C22—28no—
857C22—28no—
858C22—464no—
859C22—44no—
860C22—44no—
861C22—44no—
862C22—44no—
863C22—44no—
864C22—44no—
865C22—44no—
866C22—44no—
867C22—44no—
868C22—44no—
869C22—44no—
870C22—44no—
871C22—42no—
872C22—42no—
873C22—44no—
874C22—42no—
875C22—44no—
876C22—81no—
877C22—82no—
878C22—81no—
879C22—82no—
880C22—81no—
881C22—81no—
882C22#241418yes—
883C22C22×#12111yescharacteristic
884C22C2×#52511yescharacteristic
885C22C2×#52511yescharacteristic
886C22C2×#53411yescharacteristic
887C22C2×#53511yescharacteristic
888C22C2×#54612yes—
889C22C2×#54611yescharacteristic
890C22C2×#55011yescharacteristic
891C22C2×#55112yes—
892C22C2×#55212yes—
893C22C2×#55311yescharacteristic
894C22C2×#55511yescharacteristic
895C22#347512yes—
896C22#348511yescharacteristic
897C22#348611yescharacteristic
898C22#348912yes—
899C22#349212yes—
900C22#349412yes—
901C22#349512yes—
902C22#350512yes—
903C22#352012yes—
904C22#353612yes—
905C22#354212yes—
906C4—24no—
907C4—42no—
908C4—44no—
909C4—44no—
910C4—44no—
911C4—42no—
912C4—44no—
913C4—42no—
914C4—84no—
915C4—82no—
916C4—84no—
917C4—82no—
918C4—82no—
919C4#253418yes—
920C2—28no—
921C2—48no—
922C2—82no—
923C2C2×#241411yescharacteristic
924C2C2×#253411yescharacteristic
925C2#3563311yescharacteristic
926C2#3615612yes—
927C2#3616311yescharacteristic
928C2#3651711yescharacteristic
929C2#3783912yes—
930C2#3913311yescharacteristic
931C2#3946611yescharacteristic
932C2#5919712yes—
933C2#5920312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#120C22
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×#2486C2semidirect
2. C2×#2352C2semidirect
4. C22×#380C2semidirect
5. #15687C2semidirect
6. #15512C2semidirect
7. #15220C2semidirect
8. #15181C2semidirect
9. #14927C2semidirect
11. #14680C2semidirect
12. #13992C2semidirect
13. #13973C2semidirect
14. #13907C2semidirect
15. #13904C2semidirect
16. #13903C2semidirect
17. #13871C2semidirect
23. C22×#117C22semidirect
28. C2×#398C22semidirect
29. C2×#397C22semidirect
32. C2×#389C22semidirect
33. C2×#389C22semidirect
34. C2×#388C22semidirect
35. C2×#387C22semidirect
41. C2×#382C22semidirect
54. C2×#380C22semidirect
55. C2×#380C22semidirect
58. C2×C4×C4⋊C4C22semidirect
63. #1445C22semidirect
64. #1443C22semidirect
65. #1442C22semidirect
66. #1442C22semidirect
67. #1441C22semidirect
68. #1441C22semidirect
69. #1440C22semidirect
74. #1439C22semidirect
79. #1436C22semidirect
80. C4⋊#95C22semidirect
81. C4⋊#95C22semidirect
82. C4⋊#95C22semidirect
83. #1434C22semidirect
120. C22×C4⋊C4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#24862
C2×#23522
C2×C4×#1202
C22×#3802
#156872
#155122
#152202
#151812
#149272
#149112
#146802
#139922
#139732
#139072
#139042
#139032
#138712