Finite Group Databasebeta

← #625853

Subgroups — #625853

Order 512.

2862 conjugacy classes of subgroups.

The subgroup lattice has 833 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2485C211yesmaximal, characteristic
2C2×#2487C211yesmaximal, characteristic
3C2×#2317C211yesmaximal, characteristic, complemented
4C2×#2290C211yesmaximal, characteristic
5#15895C214yesmaximal, complemented
6#15383C214yesmaximal
7#15298C214yesmaximal, complemented
8#15294C214yesmaximal, complemented
9#15234C211yesmaximal, characteristic, complemented
10#15233C211yesmaximal, characteristic, complemented
11#15195C211yesmaximal, characteristic, complemented
12#15151C211yesmaximal, 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#13904C211yesmaximal, characteristic, complemented
20C22×C4×D4C2211yescharacteristic
21C22×#117C2211yescharacteristic
22C22×#117C2211yescharacteristic
23C23×C4⋊C4C2211yescharacteristic
24C23×C42C2211yescharacteristic
25#2487—28no—
26#2485—28no—
27C2×#400C2212yes—
28C2×#399C2212yes—
29C2×#398C2214yes—
30C2×#397C2212yes—
31C2×#394C2212yes—
32#2317—28no—
33C2×#389C2214yes—
34C2×#389C2211yescharacteristic
35C2×#389C2211yescharacteristic
36C2×#389C2211yescharacteristic
37C2×#389C2211yescharacteristic
38#2290—28no—
39C2×#388C2212yes—
40C2×#388C2212yes—
41C2×#387C2212yes—
42C2×#387C2212yes—
43C2×#386C2212yes—
44C2×#386C2212yes—
45C2×#385C2214yes—
46C2×#385C2212yes—
47C2×#385C2212yes—
48C2×#384C2211yescharacteristic
49C2×#384C2211yescharacteristic
50C2×#384C2211yescharacteristic
51C2×#382C2211yescharacteristic
52C2×#382C2211yescharacteristic
53C2×#382C2211yescharacteristic
54C2×#381C2214yes—
55C2×#380C2211yescharacteristic
56C2×#380C2211yescharacteristic
57C2×#380C2211yescharacteristic
58C2×#380C2211yescharacteristic
59C2×#380C2211yescharacteristic
60C2×#380C2211yescharacteristic
61C2×#380C2214yes—
62C2×C4×C4⋊C4C2211yescharacteristic
63C2×C4×C22⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2211yescharacteristic
65C2×#376C2211yescharacteristic
66#1445C2214yes—
67#1445C2214yes—
68#1444C2214yes—
69#1443C2214yes—
70#1442C2214yes—
71#1442C2214yes—
72#1442C2214yes—
73#1441C2214yes—
74#1441C2214yes—
75#1441C2214yes—
76#1441C2214yes—
77#1440C2214yes—
78#1440C2214yes—
79#1439C2214yes—
80#1439C2214yes—
81C4⋊#95C2211yescharacteristic
82C4⋊#95C2211yescharacteristic
83C4⋊#95C2214yes—
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91C4⋊#95C2211yescharacteristic
92#1434C2214yes—
93#1434C2214yes—
94C22⋊#95C2214yes—
95C23×D4C2311yescharacteristic
96C24×C4C2311yescharacteristic
97C24×C4C2312yes—
98C24×C4C2311yescharacteristic
99C24×C4C2312yes—
100C2×C4×D4—24no—
101C2×C4×D4—24no—
102C2×C4×D4D418yes—
103C2×#117—24no—
104C2×#117—24no—
105C2×#117—24no—
106C2×#117—24no—
107C2×#117—24no—
108C2×#117D418yes—
109C22×C4⋊C4—24no—
110C22×C4⋊C4—24no—
111C22×C4⋊C4—24no—
112C22×C4⋊C4C2312yes—
113C22×C4⋊C4C2311yescharacteristic
114C22×C4⋊C4C2311yescharacteristic
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2314yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2314yes—
130C22×C4⋊C4C2314yes—
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2311yescharacteristic
136C22×C22⋊C4C2311yescharacteristic
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C42—24no—
144C22×C42—24no—
145C22×C42—24no—
146C22×C42C2312yes—
147C22×C42C2311yescharacteristic
148C22×C42C2312yes—
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153#400—28no—
154#399—28no—
155#398—48no—
156#397—28no—
157#394—28no—
158#389—216no—
159#389—24no—
160#389—24no—
161#389—24no—
162#389—24no—
163#388—28no—
164#388—28no—
165#387—28no—
166#387—28no—
167#386—28no—
168#386—28no—
169#385—28no—
170#385—216no—
171#385—28no—
172#384—24no—
173#384—24no—
174#384—24no—
175#382—24no—
176#382—24no—
177#382—24no—
178#381—48no—
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×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2312yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
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
268C4×D4—232no—
269#117—232no—
270#117—416no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—24no—
273C2×C4⋊C4—24no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—28no—
306C2×C4⋊C4—28no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—28no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—44no—
313C2×C4⋊C4—416no—
314C2×C4⋊C4—44no—
315C2×C4⋊C4—44no—
316C2×C4⋊C4—44no—
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⋊C4C2×D418yes—
324C2×C4⋊C4C2×D414yes—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—22no—
327C2×C22⋊C4—22no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—22no—
331C2×C22⋊C4—24no—
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—28no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—42no—
346C2×C22⋊C4—42no—
347C2×C22⋊C4—44no—
348C2×C22⋊C4—44no—
349C2×C22⋊C4—44no—
350C2×C22⋊C4—44no—
351C2×C22⋊C4—44no—
352C2×C22⋊C4C2×D418yes—
353C2×C22⋊C4C2×D414yes—
354C2×C22⋊C4C2×D414yes—
355C2×C42—22no—
356C2×C42—22no—
357C2×C42—22no—
358C2×C42—22no—
359C2×C42—24no—
360C2×C42—24no—
361C2×C42—22no—
362C2×C42—22no—
363C2×C42—24no—
364C2×C42—24no—
365C2×C42—24no—
366C2×C42—24no—
367C2×C42—22no—
368C2×C42—22no—
369C2×C42—22no—
370C2×C42—22no—
371C2×C42—416no—
372C2×C42C2×D414yes—
373C2×C42C2×D414yes—
374C2×C42C2×D414yes—
375C2×C42#4114yes—
376C2×C42#4114yes—
377#95—24no—
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—28no—
389#95—28no—
390#95—24no—
391#95—24no—
392#95—24no—
393#95—24no—
394#95—28no—
395#95—28no—
396#95—28no—
397#95—28no—
398#95—44no—
399#95—44no—
400#95—44no—
401#95—44no—
402#95—44no—
403#95—44no—
404#95—44no—
405C24—21no—
406C24—21no—
407C24—21no—
408C24—21no—
409C24—21no—
410C24—21no—
411C24—22no—
412C24—22no—
413C24—21no—
414C24—21no—
415C24—21no—
416C24—21no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24C22×D412yes—
423C24C22×D412yes—
424C24C22×D412yes—
425C24C2×#4112yes—
426C242−1+414yes—
427C24C2511yescharacteristic
428C2×D4—28no—
429C2×D4—28no—
430C2×D4—44no—
431C2×D4—48no—
432C2×D4—48no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—28no—
442C22×C4—28no—
443C22×C4—28no—
444C22×C4—28no—
445C22×C4—28no—
446C22×C4—28no—
447C22×C4—216no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—28no—
475C22×C4—28no—
476C22×C4—28no—
477C22×C4—22no—
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—24no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—24no—
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—48no—
525C22×C4—48no—
526C22×C4—48no—
527C22×C4—48no—
528C22×C4—48no—
529C22×C4—48no—
530C22×C4—44no—
531C22×C4—44no—
532C22×C4—44no—
533C22×C4—44no—
534C22×C4—416no—
535C22×C4—48no—
536C22×C4—88no—
537C22×C4—84no—
538C22×C4—84no—
539C22×C4#121116yes—
540C22×C4C22×D412yes—
541C22×C4C22×D412yes—
542C22×C4C22×D414yes—
543C22×C4C22×D412yes—
544C22×C4C22×D412yes—
545C22×C4C22×D412yes—
546C22×C4C22×D414yes—
547C22×C4C22×D412yes—
548C22×C4C22×D412yes—
549C22×C4C2×#4112yes—
550C22×C4C2×#4114yes—
551C22×C4C2×#4114yes—
552C22×C4C2×#4112yes—
553C22×C4C2×#4112yes—
554C22×C4C2×#4112yes—
555C22×C4H(5,𝔽2)14yes—
556C22×C42−1+412yes—
557C22×C42−1+412yes—
558C4⋊C4—28no—
559C4⋊C4—216no—
560C4⋊C4—48no—
561C4⋊C4—48no—
562C4⋊C4—48no—
563C4⋊C4—44no—
564C4⋊C4—44no—
565C4⋊C4—44no—
566C4⋊C4—44no—
567C4⋊C4—44no—
568C4⋊C4—44no—
569C4⋊C4—44no—
570C4⋊C4—44no—
571C4⋊C4—88no—
572C4⋊C4—88no—
573C4⋊C4—88no—
574C4⋊C4—84no—
575C4⋊C4—84no—
576C4⋊C4—84no—
577C22⋊C4—28no—
578C22⋊C4—28no—
579C22⋊C4—216no—
580C22⋊C4—48no—
581C22⋊C4—48no—
582C22⋊C4—48no—
583C22⋊C4—48no—
584C22⋊C4—48no—
585C22⋊C4—84no—
586C22⋊C4—84no—
587C22⋊C4—84no—
588C22⋊C4—84no—
589C42—28no—
590C42—28no—
591C42—48no—
592C42—48no—
593C42—44no—
594C42—44no—
595C42#123116yes—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—24no—
603C23—22no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—24no—
610C23—24no—
611C23—24no—
612C23—24no—
613C23—24no—
614C23—24no—
615C23—24no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—24no—
621C23—24no—
622C23—41no—
623C23—41no—
624C23—42no—
625C23—41no—
626C23—41no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23C2×#12114yes—
641C23#53614yes—
642C23C23×D411yescharacteristic
643C23C23×D411yescharacteristic
644C23C22×#4111yescharacteristic
645C23C22×#4111yescharacteristic
646C23C22×#4111yescharacteristic
647C23C2×H(5,𝔽2)12yes—
648C23C2×2−1+411yescharacteristic
649C23C2×2−1+411yescharacteristic
650C23C2×2−1+412yes—
651C23#58512yes—
652C23#58512yes—
653D4—416no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—24no—
661C2×C4—24no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—232no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—432no—
683C2×C4—42no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—42no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—42no—
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—416no—
700C2×C4—42no—
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—44no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—44no—
720C2×C4—44no—
721C2×C4—44no—
722C2×C4—42no—
723C2×C4—44no—
724C2×C4—44no—
725C2×C4—44no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—44no—
741C2×C4—44no—
742C2×C4—42no—
743C2×C4—44no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—44no—
747C2×C4—816no—
748C2×C4C2×#12114yes—
749C2×C4C2×#12114yes—
750C2×C4C2×#12318yes—
751C2×C4C2×#12314yes—
752C2×C4#53614yes—
753C2×C4#54714yes—
754C2×C4#54714yes—
755C2×C4#55214yes—
756C2×C4#55214yes—
757C22—24no—
758C22—24no—
759C22—24no—
760C22—24no—
761C22—24no—
762C22—24no—
763C22—44no—
764C22—44no—
765C22—44no—
766C22—44no—
767C22—44no—
768C22—44no—
769C22—42no—
770C22—44no—
771C22—44no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22C22×#12111yescharacteristic
780C22C22×#12311yescharacteristic
781C22C2×#53611yescharacteristic
782C22C2×#53611yescharacteristic
783C22#344911yescharacteristic
784C22#346012yes—
785C22C2×#54711yescharacteristic
786C22C2×#54711yescharacteristic
787C22C2×#55211yescharacteristic
788C22C2×#55211yescharacteristic
789C22#348812yes—
790C22#348912yes—
791C22#349212yes—
792C22#349312yes—
793C22#349412yes—
794C22#349512yes—
795C22#349512yes—
796C22#349811yescharacteristic
797C22#350011yescharacteristic
798C22#354712yes—
799C22#355212yes—
800C22#356312yes—
801C22#356512yes—
802C4—28no—
803C4—24no—
804C4—42no—
805C4—44no—
806C4—44no—
807C4—42no—
808C4—42no—
809C4—82no—
810C4—82no—
811C4—82no—
812C4—82no—
813C4—82no—
814C4—82no—
815C4—82no—
816C4—82no—
817C4—82no—
818C4#248618yes—
819C2—44no—
820C2—44no—
821C2C2×#248611yescharacteristic
822C2#3525611yescharacteristic
823C2#3530611yescharacteristic
824C2#3551612yes—
825C2#3727912yes—
826C2#3786211yescharacteristic
827C2#3786511yescharacteristic
828C2#3786911yescharacteristic
829C2#3787011yescharacteristic
830C2#3793712yes—
831C2#3793812yes—
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. #15895C2semidirect
7. #15298C2semidirect
8. #15294C2semidirect
9. #15234C2semidirect
10. #15233C2semidirect
11. #15195C2semidirect
12. #15151C2semidirect
13. #14686C2semidirect
14. #14682C2semidirect
15. #14340C2semidirect
16. #14277C2semidirect
17. #14276C2semidirect
18. #13939C2semidirect
19. #13904C2semidirect

Maximal subgroups

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

subgroupindex
C2×#24852
C2×#24872
C2×#23172
C2×#22902
#158952
#153832
#152982
#152942
#152342
#152332
#151952
#151512
#146862
#146822
#143402
#142772
#142762
#139392
#139042