Finite Group Databasebeta

← #705319

Subgroups — #705319

Order 512.

2912 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2494C211yesmaximal, characteristic, complemented
2C2×#2339C211yesmaximal, characteristic
3#16379C214yesmaximal, complemented
4#16061C214yesmaximal, complemented
5#15988C214yesmaximal, complemented
6#15241C211yesmaximal, characteristic, complemented
7#15237C211yesmaximal, characteristic, complemented
8#15233C211yesmaximal, characteristic, complemented
9#15233C211yesmaximal, characteristic, complemented
10C22⋊#401C214yesmaximal, complemented
11#14261C211yesmaximal, characteristic, complemented
12#14003C211yesmaximal, characteristic, complemented
13#13979C211yesmaximal, characteristic, complemented
14#13979C211yesmaximal, characteristic, complemented
15#13941C211yesmaximal, characteristic, complemented
16#13937C211yesmaximal, characteristic
17#13937C211yesmaximal, characteristic
18#13842C211yesmaximal, characteristic, complemented
19#13785C211yesmaximal, characteristic, complemented
20C23×#41C2211yescharacteristic
21C22×C4×D4C2211yescharacteristic
22C22×C4×D4C2211yescharacteristic
23#2494—28no—
24C2×#401C2212yes—
25C2×#397C2212yes—
26#2339—28no—
27C2×#391C2211yescharacteristic
28C2×#391C2211yescharacteristic
29C2×#391C2211yescharacteristic
30C2×#391C2211yescharacteristic
31C2×#391C2211yescharacteristic
32C2×#391C2211yescharacteristic
33C2×#390C2211yescharacteristic
34C2×#390C2211yescharacteristic
35C2×#390C2211yescharacteristic
36C2×#390C2211yescharacteristic
37C2×#389C2211yescharacteristic
38C2×#389C2211yescharacteristic
39C2×#388C2212yes—
40C2×#387C2212yes—
41C2×#386C2212yes—
42C2×#386C2212yes—
43C2×#382C2211yescharacteristic
44C2×#382C2211yescharacteristic
45C2×#382C2211yescharacteristic
46C2×#381C2212yes—
47C2×#380C2211yescharacteristic
48C2×#380C2211yescharacteristic
49C2×#380C2211yescharacteristic
50C2×C4×C4⋊C4C2211yescharacteristic
51C2×C4×C4⋊C4C2211yescharacteristic
52C2×C4×C22⋊C4C2211yescharacteristic
53C2×C4×C22⋊C4C2211yescharacteristic
54C2×C4×C22⋊C4C2211yescharacteristic
55C2×#376C2211yescharacteristic
56C22×#95C2212yes—
57#1443C2212yes—
58#1443C2214yes—
59#1443C2214yes—
60#1443C2214yes—
61#1443C2214yes—
62#1443C2214yes—
63#1443C2214yes—
64#1443C2214yes—
65#1442C2212yes—
66#1442C2214yes—
67#1441C2214yes—
68#1440C2212yes—
69#1440C2214yes—
70#1440C2214yes—
71#1439C2212yes—
72#1439C2214yes—
73#1439C2214yes—
74#1439C2214yes—
75#1438C2214yes—
76#1438C2214yes—
77#1437C2214yes—
78C4⋊#95C2211yescharacteristic
79C4⋊#95C2211yescharacteristic
80C4⋊#95C2211yescharacteristic
81C4⋊#95C2211yescharacteristic
82C4⋊#95C2211yescharacteristic
83C4⋊#95C2211yescharacteristic
84#1434C2214yes—
85C22⋊#95C2214yes—
86C22⋊#95C2214yes—
87C22⋊#95C2214yes—
88C22⋊#95C2214yes—
89C22⋊#95C2214yes—
90C22⋊#95C2214yes—
91C4×#95C2211yescharacteristic
92C4×#95C2211yescharacteristic
93C22×#41—24no—
94C22×#41—24no—
95C22×#41—24no—
96C22×#41—24no—
97C22×#41—24no—
98C22×#41—42no—
99C22×#41—42no—
100C23×Q8C2311yescharacteristic
101C23×D4C2312yes—
102C23×D4C2311yescharacteristic
103C24×C4C2311yescharacteristic
104C24×C4C2312yes—
105C24×C4C2312yes—
106C24×C4C2312yes—
107C2×C4×D4—24no—
108C2×C4×D4—24no—
109C2×C4×D4—24no—
110C2×C4×D4—24no—
111C2×C4×D4—42no—
112C2×C4×D4—42no—
113C22×C4⋊C4C2311yescharacteristic
114C22×C4⋊C4C2311yescharacteristic
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2312yes—
122C22×C22⋊C4C2312yes—
123C22×C22⋊C4C2312yes—
124C22×C22⋊C4C2312yes—
125C22×C22⋊C4C2312yes—
126C22×C22⋊C4C2314yes—
127C22×C22⋊C4C2314yes—
128C22×C22⋊C4C2314yes—
129C22×C22⋊C4C2314yes—
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2311yescharacteristic
134C22×C22⋊C4C2311yescharacteristic
135C22×C42C2311yescharacteristic
136C22×C42C2311yescharacteristic
137C22×C42C2311yescharacteristic
138C22×C42C2311yescharacteristic
139C22×C42C2311yescharacteristic
140C22×C42C2311yescharacteristic
141C22×C42C2312yes—
142#401—28no—
143#397—28no—
144#391—24no—
145#391—24no—
146#391—24no—
147#391—24no—
148#391—42no—
149#391—42no—
150#390—24no—
151#390—24no—
152#390—24no—
153#390—24no—
154#389—24no—
155#389—24no—
156#388—28no—
157#387—28no—
158#386—28no—
159#386—28no—
160#382—24no—
161#382—42no—
162#382—42no—
163#381—28no—
164#380—24no—
165#380—24no—
166#380—24no—
167C4×C4⋊C4—24no—
168C4×C4⋊C4—42no—
169C4×C22⋊C4—42no—
170C4×C22⋊C4—42no—
171C4×C22⋊C4D418yes—
172#376—42no—
173C2×#95—28no—
174C2×#95C2312yes—
175C2×#95C2312yes—
176C2×#95C2312yes—
177C2×#95C2312yes—
178C2×#95C2312yes—
179C2×#95C2312yes—
180C2×#95C2312yes—
181C2×#95C2314yes—
182C2×#95C2314yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2312yes—
207C2×#95C2311yescharacteristic
208C2×#95C2311yescharacteristic
209C25C2411yescharacteristic
210C25C2412yes—
211C2×#41—232no—
212C2×#41—416no—
213C2×#41—416no—
214C2×#41—416no—
215C2×#41—416no—
216C2×#41—416no—
217C2×#41—416no—
218C22×Q8—22no—
219C22×Q8—22no—
220C22×Q8—22no—
221C22×Q8—22no—
222C22×Q8—22no—
223C22×Q8—22no—
224C22×Q8#4114yes—
225C22×D4—24no—
226C22×D4—24no—
227C22×D4—24no—
228C22×D4—24no—
229C22×D4—22no—
230C22×D4—22no—
231C22×D4—24no—
232C22×D4—22no—
233C22×D4—22no—
234C22×D4—42no—
235C22×D4—42no—
236C22×D4#4114yes—
237C22×D4#4114yes—
238C22×D4#4114yes—
239C23×C4—24no—
240C23×C4—24no—
241C23×C4—24no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—24no—
249C23×C4—24no—
250C23×C4—24no—
251C23×C4—24no—
252C23×C4—24no—
253C23×C4—24no—
254C23×C4—42no—
255C23×C4—42no—
256C23×C4—42no—
257C23×C4—42no—
258C23×C4—44no—
259C23×C4—44no—
260C23×C4—44no—
261C23×C4—44no—
262C23×C4C2×D414yes—
263C23×C4C2412yes—
264C23×C4C2412yes—
265C23×C4C2412yes—
266C23×C4C2412yes—
267C23×C4C2412yes—
268C23×C4C2412yes—
269C23×C4C2412yes—
270C23×C4C2412yes—
271C23×C4C2412yes—
272C23×C4C2412yes—
273C23×C4C2411yescharacteristic
274C23×C4C2411yescharacteristic
275C23×C4C2411yescharacteristic
276C23×C4C2411yescharacteristic
277C23×C4C2411yescharacteristic
278C23×C4C2412yes—
279C23×C4C2411yescharacteristic
280C4×D4—416no—
281C4×D4—416no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
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—22no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—44no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—42no—
305C2×C4⋊C4—42no—
306C2×C4⋊C4—44no—
307C2×C22⋊C4—24no—
308C2×C22⋊C4—24no—
309C2×C22⋊C4—24no—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—28no—
315C2×C22⋊C4—28no—
316C2×C22⋊C4—28no—
317C2×C22⋊C4—28no—
318C2×C22⋊C4—42no—
319C2×C22⋊C4—42no—
320C2×C22⋊C4—44no—
321C2×C22⋊C4—42no—
322C2×C22⋊C4—42no—
323C2×C22⋊C4—42no—
324C2×C22⋊C4—42no—
325C2×C22⋊C4—42no—
326C2×C22⋊C4—42no—
327C2×C22⋊C4—42no—
328C2×C22⋊C4—42no—
329C2×C22⋊C4—44no—
330C2×C22⋊C4—44no—
331C2×C22⋊C4—44no—
332C2×C22⋊C4—44no—
333C2×C22⋊C4—44no—
334C2×C22⋊C4—44no—
335C2×C22⋊C4—44no—
336C2×C22⋊C4—44no—
337C2×C22⋊C4—44no—
338C2×C22⋊C4—44no—
339C2×C22⋊C4C2×D414yes—
340C2×C22⋊C4C2×D414yes—
341C2×C42—22no—
342C2×C42—22no—
343C2×C42—22no—
344C2×C42—22no—
345C2×C42—22no—
346C2×C42—22no—
347C2×C42—22no—
348C2×C42—22no—
349C2×C42—22no—
350C2×C42—22no—
351C2×C42—22no—
352C2×C42—22no—
353C2×C42—22no—
354C2×C42—22no—
355C2×C42—22no—
356C2×C42—22no—
357C2×C42—24no—
358C2×C42—44no—
359C2×C42C2×D414yes—
360C2×C42C2×D414yes—
361#95—24no—
362#95—24no—
363#95—24no—
364#95—24no—
365#95—24no—
366#95—24no—
367#95—24no—
368#95—24no—
369#95—24no—
370#95—24no—
371#95—24no—
372#95—24no—
373#95—28no—
374#95—28no—
375#95—42no—
376#95—42no—
377#95—42no—
378#95—42no—
379#95—44no—
380#95—44no—
381#95—44no—
382#95—44no—
383#95—44no—
384#95—44no—
385#95—42no—
386#95—42no—
387#95—42no—
388#95—42no—
389#95—42no—
390#95—44no—
391#95—44no—
392#95—44no—
393#95—44no—
394#95C2×D414yes—
395#95C2×D414yes—
396C24—22no—
397C24—22no—
398C24—22no—
399C24—22no—
400C24—24no—
401C24—24no—
402C24—24no—
403C24—24no—
404C24—21no—
405C24—21no—
406C24—21no—
407C24—21no—
408C24—21no—
409C24—21no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24C22×D412yes—
415C24C2×#4114yes—
416C24C2×#4114yes—
417C24C2×#4114yes—
418C24C2511yescharacteristic
419#41—4128no—
420C2×Q8—28no—
421C2×Q8—28no—
422C2×Q8—28no—
423C2×Q8—44no—
424C2×Q8—44no—
425C2×Q8—44no—
426C2×Q8—44no—
427C2×D4—216no—
428C2×D4—28no—
429C2×D4—28no—
430C2×D4—28no—
431C2×D4—28no—
432C2×D4—28no—
433C2×D4—28no—
434C2×D4—48no—
435C2×D4—48no—
436C2×D4—48no—
437C2×D4—48no—
438C2×D4—48no—
439C2×D4—48no—
440C2×D4#126116yes—
441C22×C4—216no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—28no—
471C22×C4—28no—
472C22×C4—28no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
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—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—24no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—22no—
520C22×C4—24no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—24no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—48no—
532C22×C4—48no—
533C22×C4—48no—
534C22×C4—48no—
535C22×C4—48no—
536C22×C4—48no—
537C22×C4—48no—
538C22×C4—48no—
539C22×C4—48no—
540C22×C4—48no—
541C22×C4—44no—
542C22×C4—44no—
543C22×C4—44no—
544C22×C4—44no—
545C22×C4—84no—
546C22×C4—84no—
547C22×C4—88no—
548C22×C4—88no—
549C22×C4—88no—
550C22×C4—88no—
551C22×C4C22×D412yes—
552C22×C4C22×D412yes—
553C22×C4C22×D412yes—
554C22×C4C22×D412yes—
555C22×C4C22×D412yes—
556C22×C4C22×D412yes—
557C22×C4C2×#4114yes—
558C22×C4C2×#4112yes—
559C22×C4C2×#4112yes—
560C22×C4C2×#4112yes—
561C22×C4C2×#4112yes—
562C22×C4H(5,𝔽2)12yes—
563C22×C4H(5,𝔽2)12yes—
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—84no—
573C22⋊C4—44no—
574C22⋊C4—44no—
575C22⋊C4—48no—
576C22⋊C4—48no—
577C22⋊C4—48no—
578C22⋊C4—48no—
579C22⋊C4—48no—
580C22⋊C4—84no—
581C22⋊C4—84no—
582C22⋊C4—88no—
583C22⋊C4—88no—
584C22⋊C4—88no—
585C22⋊C4—88no—
586C42—28no—
587C42—28no—
588C42—44no—
589C42—44no—
590C42—44no—
591C42—44no—
592C42—84no—
593C23—24no—
594C23—24no—
595C23—24no—
596C23—24no—
597C23—24no—
598C23—24no—
599C23—28no—
600C23—28no—
601C23—28no—
602C23—28no—
603C23—28no—
604C23—28no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—22no—
612C23—42no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—44no—
617C23—44no—
618C23—44no—
619C23—44no—
620C23—44no—
621C23—44no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23C2×#12618yes—
639C23C23×D411yescharacteristic
640C23C22×#4111yescharacteristic
641C23C22×#4111yescharacteristic
642C23C22×#4111yescharacteristic
643C23C22×#4111yescharacteristic
644C23C2×H(5,𝔽2)11yescharacteristic
645C23C2×H(5,𝔽2)11yescharacteristic
646C23#58512yes—
647C23#58512yes—
648C23#58512yes—
649C23#58512yes—
650Q8—416no—
651D4—232no—
652D4—432no—
653C2×C4—22no—
654C2×C4—24no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—432no—
672C2×C4—41no—
673C2×C4—42no—
674C2×C4—41no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—416no—
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—42no—
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—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—44no—
724C2×C4—44no—
725C2×C4—44no—
726C2×C4—42no—
727C2×C4—42no—
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—44no—
738C2×C4—44no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—44no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—44no—
747C2×C4—816no—
748C2×C4—816no—
749C2×C4#52514yes—
750C2×C4C2×#12614yes—
751C2×C4#53814yes—
752C2×C4#54614yes—
753C2×C4#54614yes—
754C2×C4#55114yes—
755C2×C4#55114yes—
756C22—28no—
757C22—216no—
758C22—48no—
759C22—44no—
760C22—44no—
761C22—48no—
762C22—44no—
763C22—48no—
764C22—44no—
765C22—44no—
766C22—44no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—82no—
775C22—82no—
776C22—82no—
777C22—82no—
778C22C2×#52511yescharacteristic
779C22C22×#12611yescharacteristic
780C22#344911yescharacteristic
781C22#344911yescharacteristic
782C22C2×#53811yescharacteristic
783C22C2×#54611yescharacteristic
784C22C2×#54611yescharacteristic
785C22C2×#55111yescharacteristic
786C22C2×#55111yescharacteristic
787C22#350011yescharacteristic
788C22#350011yescharacteristic
789C22#352112yes—
790C22#352112yes—
791C22#352112yes—
792C22#352112yes—
793C22#352112yes—
794C22#352112yes—
795C22#352412yes—
796C22#352412yes—
797C22#353912yes—
798C22#353912yes—
799C22#354012yes—
800C22#355112yes—
801C4—42no—
802C4—42no—
803C4—44no—
804C4—42no—
805C4—42no—
806C4—42no—
807C4—82no—
808C4—82no—
809C4—82no—
810C4—82no—
811C4—82no—
812C4—82no—
813C4—82no—
814C4—82no—
815C4—82no—
816C4—82no—
817C4#248018yes—
818C2—48no—
819C2—82no—
820C2C2×#248011yescharacteristic
821C2#3521111yescharacteristic
822C2#3562311yescharacteristic
823C2#3605312yes—
824C2#3809211yescharacteristic
825C2#3809211yescharacteristic
826C2#3809411yescharacteristic
827C2#3894711yescharacteristic
828C2#4276012yes—
829C2#4523412yes—
830C2#4540112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC23×#41C22
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×#2494C2semidirect
3. #16379C2semidirect
4. #16061C2semidirect
5. #15988C2semidirect
6. #15241C2semidirect
7. #15237C2semidirect
8. #15233C2semidirect
9. #15233C2semidirect
10. C22⋊#401C2semidirect
11. #14261C2semidirect
12. #14003C2semidirect
13. #13979C2semidirect
14. #13979C2semidirect
15. #13941C2semidirect
18. #13842C2semidirect
19. #13785C2semidirect

Maximal subgroups

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

subgroupindex
C2×#24942
C2×#23392
#163792
#160612
#159882
#152412
#152372
#152332
C22⋊#4012
#142612
#140032
#139792
#139412
#139372
#138422
#137852