Finite Group Databasebeta

← #625852

Subgroups — #625852

Order 512.

2910 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2485C211yesmaximal, characteristic
2C2×#2486C211yesmaximal, characteristic
3C2×#2317C211yesmaximal, characteristic, complemented
4C2×#2290C211yesmaximal, characteristic
5#15929C214yesmaximal, complemented
6#15874C214yesmaximal, complemented
7#15290C214yesmaximal, complemented
8#15269C214yesmaximal
9#15234C211yesmaximal, characteristic, complemented
10#15233C211yesmaximal, characteristic, complemented
11#15196C211yesmaximal, characteristic, complemented
12#15150C211yesmaximal, characteristic, complemented
13#14686C211yesmaximal, characteristic, complemented
14#14682C211yesmaximal, characteristic, complemented
15#14340C211yesmaximal, characteristic, complemented
16#14277C211yesmaximal, characteristic, complemented
17#14276C211yesmaximal, characteristic, complemented
18#13939C211yesmaximal, characteristic, complemented
19#13924C211yesmaximal, characteristic, complemented
20C22×#123C2212yes—
21C22×C4×D4C2211yescharacteristic
22C22×#117C2211yescharacteristic
23C22×#117C2211yescharacteristic
24C23×C4⋊C4C2211yescharacteristic
25C23×C42C2211yescharacteristic
26#2486—28no—
27#2485—28no—
28C2×#398C2212yes—
29C2×#397C2212yes—
30C2×#397C2212yes—
31C2×#397C2214yes—
32C2×#394C2212yes—
33#2317—28no—
34C2×#389C2214yes—
35C2×#389C2211yescharacteristic
36C2×#389C2211yescharacteristic
37C2×#389C2211yescharacteristic
38C2×#389C2211yescharacteristic
39#2290—28no—
40C2×#388C2212yes—
41C2×#388C2212yes—
42C2×#387C2212yes—
43C2×#387C2212yes—
44C2×#386C2212yes—
45C2×#385C2214yes—
46C2×#385C2212yes—
47C2×#384C2211yescharacteristic
48C2×#384C2211yescharacteristic
49C2×#384C2211yescharacteristic
50C2×#382C2211yescharacteristic
51C2×#382C2211yescharacteristic
52C2×#382C2211yescharacteristic
53C2×#381C2212yes—
54C2×#380C2211yescharacteristic
55C2×#380C2211yescharacteristic
56C2×#380C2211yescharacteristic
57C2×#380C2211yescharacteristic
58C2×#380C2211yescharacteristic
59C2×#380C2211yescharacteristic
60C2×#380C2214yes—
61C2×C4×C4⋊C4C2211yescharacteristic
62C2×C4×C22⋊C4C2211yescharacteristic
63C2×C4×C22⋊C4C2211yescharacteristic
64C2×#376C2211yescharacteristic
65#1445C2214yes—
66#1445C2214yes—
67#1444C2214yes—
68#1444C2214yes—
69#1443C2214yes—
70#1442C2214yes—
71#1442C2214yes—
72#1441C2214yes—
73#1441C2214yes—
74#1441C2214yes—
75#1441C2214yes—
76#1441C2214yes—
77#1440C2214yes—
78#1440C2214yes—
79#1439C2214yes—
80C4⋊#95C2214yes—
81C4⋊#95C2211yescharacteristic
82C4⋊#95C2211yescharacteristic
83C4⋊#95C2211yescharacteristic
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91#1434C2214yes—
92#1434C2214yes—
93C22⋊#95C2214yes—
94C22⋊#95C2214yes—
95C23×D4C2311yescharacteristic
96C24×C4C2311yescharacteristic
97C24×C4C2312yes—
98C24×C4C2311yescharacteristic
99C24×C4C2312yes—
100C2×#123—28no—
101C2×#123—48no—
102C2×C4×D4—24no—
103C2×C4×D4—24no—
104C2×C4×D4D418yes—
105C2×#117—24no—
106C2×#117—24no—
107C2×#117—24no—
108C2×#117—24no—
109C2×#117—24no—
110C2×#117D418yes—
111C22×C4⋊C4—24no—
112C22×C4⋊C4—24no—
113C22×C4⋊C4—24no—
114C22×C4⋊C4C2312yes—
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2314yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2314yes—
132C22×C4⋊C4C2314yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2311yescharacteristic
140C22×C22⋊C4C2311yescharacteristic
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C42—24no—
146C22×C42—24no—
147C22×C42—24no—
148C22×C42C2312yes—
149C22×C42C2311yescharacteristic
150C22×C42C2312yes—
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155#398—28no—
156#397—28no—
157#397—28no—
158#397—48no—
159#394—28no—
160#389—216no—
161#389—24no—
162#389—24no—
163#389—24no—
164#389—24no—
165#388—28no—
166#388—28no—
167#387—28no—
168#387—28no—
169#386—28no—
170#385—28no—
171#385—216no—
172#384—24no—
173#384—24no—
174#384—24no—
175#382—24no—
176#382—24no—
177#382—24no—
178#381—28no—
179#380—24no—
180#380—24no—
181#380—24no—
182#380—24no—
183#380—24no—
184#380—24no—
185#380—48no—
186C4×C4⋊C4—24no—
187C4×C22⋊C4—24no—
188C4×C22⋊C4—24no—
189#376—24no—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2312yes—
203C2×#95C2314yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2314yes—
210C2×#95C2314yes—
211C2×#95C2314yes—
212C2×#95C2314yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
218C25C2411yescharacteristic
219C25C2411yescharacteristic
220C22×D4—22no—
221C22×D4—22no—
222C22×D4—24no—
223C22×D4—42no—
224C22×D4C2×D414yes—
225C23×C4—22no—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—24no—
230C23×C4—22no—
231C23×C4—22no—
232C23×C4—24no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—24no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—24no—
239C23×C4—24no—
240C23×C4—24no—
241C23×C4—24no—
242C23×C4—24no—
243C23×C4—42no—
244C23×C4—42no—
245C23×C4—44no—
246C23×C4—44no—
247C23×C4C2×D414yes—
248C23×C4C2×D414yes—
249C23×C4C2×D414yes—
250C23×C4#4114yes—
251C23×C4C2412yes—
252C23×C4C2412yes—
253C23×C4C2412yes—
254C23×C4C2412yes—
255C23×C4C2412yes—
256C23×C4C2412yes—
257C23×C4C2412yes—
258C23×C4C2412yes—
259C23×C4C2412yes—
260C23×C4C2411yescharacteristic
261C23×C4C2412yes—
262C23×C4C2411yescharacteristic
263C23×C4C2411yescharacteristic
264C23×C4C2412yes—
265C23×C4C2411yescharacteristic
266C23×C4C2412yes—
267C23×C4C2411yescharacteristic
268#123—432no—
269C4×D4—232no—
270#117—232no—
271#117—416no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—24no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—28no—
309C2×C4⋊C4—28no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—28no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4—44no—
314C2×C4⋊C4—44no—
315C2×C4⋊C4—44no—
316C2×C4⋊C4—416no—
317C2×C4⋊C4—44no—
318C2×C4⋊C4—44no—
319C2×C4⋊C4—44no—
320C2×C4⋊C4—44no—
321C2×C4⋊C4—44no—
322C2×C4⋊C4—44no—
323C2×C4⋊C4—44no—
324C2×C4⋊C4C2×D418yes—
325C2×C4⋊C4C2×D414yes—
326C2×C22⋊C4—22no—
327C2×C22⋊C4—22no—
328C2×C22⋊C4—22no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—22no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—28no—
341C2×C22⋊C4—28no—
342C2×C22⋊C4—28no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—42no—
349C2×C22⋊C4—42no—
350C2×C22⋊C4—44no—
351C2×C22⋊C4—44no—
352C2×C22⋊C4—44no—
353C2×C22⋊C4C2×D418yes—
354C2×C22⋊C4C2×D414yes—
355C2×C22⋊C4C2×D414yes—
356C2×C42—22no—
357C2×C42—22no—
358C2×C42—22no—
359C2×C42—22no—
360C2×C42—24no—
361C2×C42—24no—
362C2×C42—22no—
363C2×C42—22no—
364C2×C42—24no—
365C2×C42—24no—
366C2×C42—24no—
367C2×C42—24no—
368C2×C42—22no—
369C2×C42—22no—
370C2×C42—22no—
371C2×C42—22no—
372C2×C42—416no—
373C2×C42C2×D414yes—
374C2×C42C2×D414yes—
375C2×C42C2×D414yes—
376C2×C42#4114yes—
377C2×C42#4114yes—
378#95—24no—
379#95—24no—
380#95—24no—
381#95—24no—
382#95—24no—
383#95—24no—
384#95—24no—
385#95—24no—
386#95—24no—
387#95—24no—
388#95—24no—
389#95—24no—
390#95—24no—
391#95—28no—
392#95—28no—
393#95—24no—
394#95—24no—
395#95—28no—
396#95—28no—
397#95—44no—
398#95—44no—
399#95—44no—
400#95—44no—
401#95—44no—
402#95—44no—
403#95—44no—
404#95—44no—
405#95—44no—
406C24—21no—
407C24—21no—
408C24—21no—
409C24—21no—
410C24—21no—
411C24—21no—
412C24—22no—
413C24—22no—
414C24—21no—
415C24—21no—
416C24—21no—
417C24—21no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24C22×D412yes—
424C24C22×D412yes—
425C24C22×D412yes—
426C24C2×#4112yes—
427C24H(5,𝔽2)14yes—
428C24C2511yescharacteristic
429C2×D4—28no—
430C2×D4—28no—
431C2×D4—44no—
432C2×D4—48no—
433C2×D4—48no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—28no—
443C22×C4—28no—
444C22×C4—28no—
445C22×C4—28no—
446C22×C4—28no—
447C22×C4—28no—
448C22×C4—216no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—28no—
476C22×C4—28no—
477C22×C4—28no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—24no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—48no—
526C22×C4—48no—
527C22×C4—48no—
528C22×C4—48no—
529C22×C4—48no—
530C22×C4—48no—
531C22×C4—44no—
532C22×C4—44no—
533C22×C4—44no—
534C22×C4—44no—
535C22×C4—48no—
536C22×C4—48no—
537C22×C4—48no—
538C22×C4—88no—
539C22×C4—88no—
540C22×C4#121116yes—
541C22×C4C22×D412yes—
542C22×C4C22×D412yes—
543C22×C4C22×D414yes—
544C22×C4C22×D412yes—
545C22×C4C22×D412yes—
546C22×C4C22×D412yes—
547C22×C4C22×D414yes—
548C22×C4C22×D412yes—
549C22×C4C22×D412yes—
550C22×C4C2×#4112yes—
551C22×C4C2×#4114yes—
552C22×C4C2×#4114yes—
553C22×C4C2×#4112yes—
554C22×C4C2×#4112yes—
555C22×C4C2×#4112yes—
556C22×C42−1+414yes—
557C22×C42−1+412yes—
558C22×C42−1+412yes—
559C4⋊C4—28no—
560C4⋊C4—216no—
561C4⋊C4—48no—
562C4⋊C4—48no—
563C4⋊C4—48no—
564C4⋊C4—48no—
565C4⋊C4—48no—
566C4⋊C4—44no—
567C4⋊C4—44no—
568C4⋊C4—44no—
569C4⋊C4—44no—
570C4⋊C4—44no—
571C4⋊C4—44no—
572C4⋊C4—44no—
573C4⋊C4—44no—
574C4⋊C4—88no—
575C4⋊C4—88no—
576C4⋊C4—88no—
577C4⋊C4—84no—
578C22⋊C4—28no—
579C22⋊C4—28no—
580C22⋊C4—216no—
581C22⋊C4—48no—
582C22⋊C4—48no—
583C22⋊C4—48no—
584C22⋊C4—48no—
585C22⋊C4—48no—
586C22⋊C4—48no—
587C22⋊C4—48no—
588C22⋊C4—84no—
589C22⋊C4—84no—
590C42—28no—
591C42—28no—
592C42—48no—
593C42—48no—
594C42—44no—
595C42—44no—
596C42#123116yescomplemented
597C23—22no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—24no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—24no—
611C23—24no—
612C23—24no—
613C23—24no—
614C23—24no—
615C23—24no—
616C23—24no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—24no—
622C23—24no—
623C23—41no—
624C23—41no—
625C23—42no—
626C23—41no—
627C23—41no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23C2×#12114yes—
642C23#53514yes—
643C23C23×D411yescharacteristic
644C23C23×D411yescharacteristic
645C23C22×#4111yescharacteristic
646C23C22×#4111yescharacteristic
647C23C22×#4111yescharacteristic
648C23C2×H(5,𝔽2)12yes—
649C23C2×2−1+411yescharacteristic
650C23C2×2−1+411yescharacteristic
651C23C2×2−1+412yes—
652C23#58512yes—
653C23#58512yes—
654D4—416no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—24no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—232no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—432no—
684C2×C4—42no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—42no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—416no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—44no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—44no—
723C2×C4—44no—
724C2×C4—44no—
725C2×C4—42no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—44no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—42no—
747C2×C4—44no—
748C2×C4—816no—
749C2×C4C2×#12114yes—
750C2×C4C2×#12114yes—
751C2×C4C2×#12318yes—
752C2×C4C2×#12314yes—
753C2×C4#53614yes—
754C2×C4#54714yes—
755C2×C4#54714yes—
756C2×C4#55214yes—
757C2×C4#55214yes—
758C22—24no—
759C22—24no—
760C22—24no—
761C22—24no—
762C22—24no—
763C22—24no—
764C22—44no—
765C22—44no—
766C22—44no—
767C22—44no—
768C22—44no—
769C22—44no—
770C22—44no—
771C22—44no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22C22×#12111yescharacteristic
781C22C22×#12311yescharacteristic
782C22C2×#53511yescharacteristic
783C22C2×#53611yescharacteristic
784C22#344911yescharacteristic
785C22#346112yes—
786C22C2×#54711yescharacteristic
787C22C2×#54711yescharacteristic
788C22C2×#55211yescharacteristic
789C22C2×#55211yescharacteristic
790C22#348812yes—
791C22#348912yes—
792C22#349212yes—
793C22#349312yes—
794C22#349412yes—
795C22#349412yes—
796C22#349512yes—
797C22#349911yescharacteristic
798C22#350011yescharacteristic
799C22#354412yes—
800C22#355512yes—
801C22#355912yes—
802C22#356512yes—
803C4—28no—
804C4—24no—
805C4—42no—
806C4—44no—
807C4—44no—
808C4—42no—
809C4—42no—
810C4—82no—
811C4—82no—
812C4—82no—
813C4—82no—
814C4—82no—
815C4—82no—
816C4—82no—
817C4—82no—
818C4—82no—
819C4#248618yes—
820C2—44no—
821C2—44no—
822C2C2×#248611yescharacteristic
823C2#3525211yescharacteristic
824C2#3530811yescharacteristic
825C2#3551612yes—
826C2#3728112yes—
827C2#3786311yescharacteristic
828C2#3786411yescharacteristic
829C2#3786811yescharacteristic
830C2#3787111yescharacteristic
831C2#3793612yes—
832C2#3793912yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC23×D4C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C2×#2317C2semidirect
5. #15929C2semidirect
6. #15874C2semidirect
7. #15290C2semidirect
9. #15234C2semidirect
10. #15233C2semidirect
11. #15196C2semidirect
12. #15150C2semidirect
13. #14686C2semidirect
14. #14682C2semidirect
15. #14340C2semidirect
16. #14277C2semidirect
17. #14276C2semidirect
18. #13939C2semidirect
19. #13924C2semidirect
596. C42#123semidirect

Maximal subgroups

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

subgroupindex
C2×#24852
C2×#24862
C2×#23172
C2×#22902
#159292
#158742
#152902
#152692
#152342
#152332
#151962
#151502
#146862
#146822
#143402
#142772
#142762
#139392
#139242