Finite Group Databasebeta

← #947090

Subgroups — #947090

Order 512.

2576 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2441C211yesmaximal, characteristic, complemented
2C2×#2422C211yesmaximal, characteristic
3#17092C214yesmaximal, complemented
4#16492C214yesmaximal, complemented
5#16257C214yesmaximal, complemented
6#15306C214yesmaximal, complemented
7#15229C211yesmaximal, characteristic, complemented
8#15197C211yesmaximal, characteristic, complemented
9#15195C211yesmaximal, characteristic, complemented
10#15151C211yesmaximal, characteristic, complemented
11#15145C211yesmaximal, characteristic, complemented
12#15130C211yesmaximal, characteristic
13#14283C211yesmaximal, characteristic, complemented
14#14260C211yesmaximal, characteristic, complemented
15#14136C211yesmaximal, characteristic
16#13977C211yesmaximal, characteristic, complemented
17#13939C211yesmaximal, characteristic, complemented
18#13906C211yesmaximal, characteristic, complemented
19#13842C211yesmaximal, characteristic, complemented
20C22×#125C2211yescharacteristic
21C22×#123C2212yes—
22C22×#121C2211yescharacteristic
23C22×C4×D4C2211yescharacteristic
24C22×#117C2211yescharacteristic
25#2441—28no—
26#2422—28no—
27C2×#399C2212yes—
28C2×#398C2214yes—
29C2×#398C2214yes—
30C2×#397C2212yes—
31C2×#396C2212yes—
32C2×#394C2212yes—
33C2×#394C2214yes—
34C2×#390C2211yescharacteristic
35C2×#390C2211yescharacteristic
36C2×#390C2211yescharacteristic
37C2×#390C2211yescharacteristic
38C2×#390C2211yescharacteristic
39C2×#389C2211yescharacteristic
40C2×#389C2211yescharacteristic
41C2×#389C2211yescharacteristic
42C2×#389C2212yes—
43C2×#387C2212yes—
44C2×#385C2212yes—
45C2×#385C2214yes—
46C2×#384C2211yescharacteristic
47C2×#384C2211yescharacteristic
48C2×#384C2211yescharacteristic
49C2×#384C2211yescharacteristic
50C2×#380C2211yescharacteristic
51C2×#380C2211yescharacteristic
52C2×#380C2214yes—
53C2×C4×C4⋊C4C2211yescharacteristic
54C2×C4×C22⋊C4C2211yescharacteristic
55C2×C4×C22⋊C4C2211yescharacteristic
56C2×C4×C22⋊C4C2211yescharacteristic
57C2×#376C2211yescharacteristic
58#1445C2214yes—
59#1444C2214yes—
60#1443C2212yes—
61#1442C2212yes—
62#1442C2214yes—
63#1442C2214yes—
64#1441C2214yes—
65#1441C2214yes—
66#1441C2214yes—
67#1440C2212yes—
68#1440C2214yes—
69#1440C2214yes—
70#1439C2212yes—
71#1439C2214yes—
72#1439C2214yes—
73#1439C2214yes—
74#1439C2214yes—
75#1439C2214yes—
76#1439C2214yes—
77#1439C2214yes—
78#1438C2214yes—
79#1437C2214yes—
80C4⋊#95C2211yescharacteristic
81C4⋊#95C2211yescharacteristic
82C4⋊#95C2211yescharacteristic
83C4⋊#95C2211yescharacteristic
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90#1434C2214yes—
91C4×#95C2211yescharacteristic
92C4×#95C2211yescharacteristic
93C23×D4C2311yescharacteristic
94C23×D4C2312yes—
95C24×C4C2311yescharacteristic
96C24×C4C2312yes—
97C2×#125—24no—
98C2×#125—24no—
99C2×#125—42no—
100C2×#123—28no—
101C2×#123—48no—
102C2×#121—24no—
103C2×#121—24no—
104C2×#121—42no—
105C2×C4×D4—24no—
106C2×C4×D4—24no—
107C2×C4×D4—42no—
108C2×#117—24no—
109C2×#117—24no—
110C2×#117—42no—
111C22×C4⋊C4C2312yes—
112C22×C4⋊C4C2312yes—
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×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2314yes—
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2314yes—
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2314yes—
134C22×C22⋊C4C2311yescharacteristic
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2314yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2314yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2314yes—
144C22×C22⋊C4C2311yescharacteristic
145C22×C42C2311yescharacteristic
146C22×C42C2311yescharacteristic
147C22×C42C2311yescharacteristic
148C22×C42C2311yescharacteristic
149C22×C42C2312yes—
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152#399—28no—
153#398—48no—
154#398—48no—
155#397—28no—
156#396—28no—
157#394—28no—
158#394—48no—
159#390—24no—
160#390—24no—
161#390—24no—
162#390—42no—
163#390—42no—
164#389—24no—
165#389—24no—
166#389—24no—
167#389—28no—
168#387—28no—
169#385—28no—
170#385—48no—
171#384—24no—
172#384—24no—
173#384—42no—
174#384—42no—
175#380—24no—
176#380—24no—
177#380—48no—
178C4×C4⋊C4—42no—
179C4×C22⋊C4—42no—
180C4×C22⋊C4—42no—
181C4×C22⋊C4D418yes—
182#376—42no—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2314yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2312yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2311yescharacteristic
208C2×#95C2311yescharacteristic
209C25C2411yescharacteristic
210C25C2412yes—
211C22×D4—24no—
212C22×D4—24no—
213C22×D4—22no—
214C22×D4—22no—
215C22×D4—22no—
216C22×D4—22no—
217C22×D4—22no—
218C22×D4—22no—
219C22×D4—42no—
220C22×D4—44no—
221C22×D4—44no—
222C22×D4#4114yes—
223C23×C4—22no—
224C23×C4—22no—
225C23×C4—22no—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—24no—
230C23×C4—24no—
231C23×C4—28no—
232C23×C4—42no—
233C23×C4—44no—
234C23×C4C2×D414yes—
235C23×C4C2412yes—
236C23×C4C2412yes—
237C23×C4C2412yes—
238C23×C4C2412yes—
239C23×C4C2412yes—
240C23×C4C2412yes—
241C23×C4C2412yes—
242C23×C4C2412yes—
243C23×C4C2411yescharacteristic
244C23×C4C2411yescharacteristic
245C23×C4C2411yescharacteristic
246C23×C4C2411yescharacteristic
247C23×C4C2412yes—
248C23×C4C2412yes—
249C23×C4C2412yes—
250C23×C4C2411yescharacteristic
251C23×C4C2411yescharacteristic
252#125—416no—
253#123—432no—
254#121—416no—
255C4×D4—416no—
256#117—416no—
257C2×C4⋊C4—22no—
258C2×C4⋊C4—22no—
259C2×C4⋊C4—22no—
260C2×C4⋊C4—22no—
261C2×C4⋊C4—22no—
262C2×C4⋊C4—24no—
263C2×C4⋊C4—24no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—24no—
266C2×C4⋊C4—24no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—24no—
270C2×C4⋊C4—24no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—28no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—28no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—28no—
293C2×C4⋊C4—44no—
294C2×C4⋊C4—44no—
295C2×C4⋊C4—42no—
296C2×C4⋊C4—42no—
297C2×C4⋊C4—42no—
298C2×C4⋊C4—44no—
299C2×C4⋊C4—44no—
300C2×C4⋊C4—44no—
301C2×C4⋊C4—44no—
302C2×C4⋊C4—44no—
303C2×C4⋊C4—44no—
304C2×C4⋊C4—44no—
305C2×C4⋊C4—44no—
306C2×C4⋊C4#4114yes—
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—24no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—28no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—28no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—28no—
323C2×C22⋊C4—28no—
324C2×C22⋊C4—42no—
325C2×C22⋊C4—42no—
326C2×C22⋊C4—42no—
327C2×C22⋊C4—44no—
328C2×C22⋊C4—42no—
329C2×C22⋊C4—42no—
330C2×C22⋊C4—42no—
331C2×C22⋊C4—44no—
332C2×C22⋊C4—44no—
333C2×C22⋊C4—42no—
334C2×C22⋊C4—42no—
335C2×C22⋊C4—44no—
336C2×C22⋊C4—44no—
337C2×C22⋊C4—44no—
338C2×C22⋊C4—44no—
339C2×C22⋊C4—44no—
340C2×C22⋊C4—44no—
341C2×C22⋊C4—44no—
342C2×C22⋊C4—44no—
343C2×C22⋊C4—44no—
344C2×C22⋊C4C2×D414yes—
345C2×C22⋊C4C2×D414yes—
346C2×C42—22no—
347C2×C42—22no—
348C2×C42—22no—
349C2×C42—22no—
350C2×C42—24no—
351C2×C42—24no—
352C2×C42—22no—
353C2×C42—22no—
354C2×C42—22no—
355C2×C42—22no—
356C2×C42—22no—
357C2×C42—22no—
358C2×C42—22no—
359C2×C42—22no—
360C2×C42—22no—
361C2×C42—22no—
362C2×C42—22no—
363C2×C42—22no—
364C2×C42—42no—
365C2×C42C2×D414yes—
366C2×C42C2×D414yes—
367#95—24no—
368#95—24no—
369#95—24no—
370#95—24no—
371#95—24no—
372#95—28no—
373#95—24no—
374#95—24no—
375#95—24no—
376#95—24no—
377#95—44no—
378#95—44no—
379#95—42no—
380#95—42no—
381#95—42no—
382#95—42no—
383#95—42no—
384#95—44no—
385#95—44no—
386#95—44no—
387#95—44no—
388#95—44no—
389#95—44no—
390#95—44no—
391#95C2×D414yes—
392#95C2×D414yes—
393C24—22no—
394C24—21no—
395C24—22no—
396C24—21no—
397C24—24no—
398C24—22no—
399C24—22no—
400C24—21no—
401C24—22no—
402C24—24no—
403C24—21no—
404C24—22no—
405C24—22no—
406C24—24no—
407C24—21no—
408C24—21no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—24no—
413C24C22×D412yes—
414C24C2×#4114yes—
415C24C2511yescharacteristic
416C2×D4—28no—
417C2×D4—28no—
418C2×D4—28no—
419C2×D4—48no—
420C2×D4—48no—
421C2×D4—44no—
422C2×D4—44no—
423C2×D4—44no—
424C2×D4—44no—
425C2×D4—84no—
426C2×D4—88no—
427C2×D4—88no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—24no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—24no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—28no—
466C22×C4—28no—
467C22×C4—28no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
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—24no—
482C22×C4—24no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—24no—
489C22×C4—24no—
490C22×C4—22no—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—24no—
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—22no—
507C22×C4—24no—
508C22×C4—22no—
509C22×C4—24no—
510C22×C4—24no—
511C22×C4—22no—
512C22×C4—48no—
513C22×C4—416no—
514C22×C4—44no—
515C22×C4—44no—
516C22×C4—44no—
517C22×C4—44no—
518C22×C4—48no—
519C22×C4—84no—
520C22×C4—88no—
521C22×C4C22×D412yes—
522C22×C4C22×D412yes—
523C22×C4C22×D412yes—
524C22×C4C22×D412yes—
525C22×C4C22×D412yes—
526C22×C4C22×D412yes—
527C22×C4C2×#4114yes—
528C22×C4C2×#4112yes—
529C22×C4C2×#4112yes—
530C22×C4H(5,𝔽2)14yes—
531C22×C4H(5,𝔽2)14yes—
532C22×C4H(5,𝔽2)12yes—
533C22×C4H(5,𝔽2)12yes—
534C22×C42−1+414yes—
535C22×C42−1+412yes—
536C22×C42−1+412yes—
537C4⋊C4—28no—
538C4⋊C4—48no—
539C4⋊C4—48no—
540C4⋊C4—48no—
541C4⋊C4—48no—
542C4⋊C4—48no—
543C4⋊C4—48no—
544C4⋊C4—48no—
545C4⋊C4—44no—
546C4⋊C4—44no—
547C4⋊C4—44no—
548C4⋊C4—44no—
549C4⋊C4—44no—
550C4⋊C4—44no—
551C4⋊C4—84no—
552C4⋊C4—84no—
553C4⋊C4—84no—
554C4⋊C4—88no—
555C4⋊C4—88no—
556C22⋊C4—28no—
557C22⋊C4—44no—
558C22⋊C4—416no—
559C22⋊C4—48no—
560C22⋊C4—48no—
561C22⋊C4—48no—
562C22⋊C4—48no—
563C22⋊C4—48no—
564C22⋊C4—48no—
565C22⋊C4—48no—
566C22⋊C4—48no—
567C22⋊C4—88no—
568C22⋊C4—84no—
569C22⋊C4—88no—
570C22⋊C4—88no—
571C42—28no—
572C42—28no—
573C42—48no—
574C42—44no—
575C42—44no—
576C42—44no—
577C42—44no—
578C23—22no—
579C23—22no—
580C23—22no—
581C23—24no—
582C23—22no—
583C23—24no—
584C23—22no—
585C23—24no—
586C23—22no—
587C23—22no—
588C23—28no—
589C23—28no—
590C23—42no—
591C23—42no—
592C23—42no—
593C23—41no—
594C23—41no—
595C23—42no—
596C23—42no—
597C23—41no—
598C23—42no—
599C23—42no—
600C23—42no—
601C23—42no—
602C23—44no—
603C23—42no—
604C23—44no—
605C23—42no—
606C23—41no—
607C23—42no—
608C23—44no—
609C23—42no—
610C23—42no—
611C23—44no—
612C23—42no—
613C23—44no—
614C23—42no—
615C23—44no—
616C23—42no—
617C23—42no—
618C23—44no—
619C23—44no—
620C23—42no—
621C23—44no—
622C23—44no—
623C23—42no—
624C23C23×D411yescharacteristic
625C23C22×#4111yescharacteristic
626C23C22×#4111yescharacteristic
627C23C2×H(5,𝔽2)12yes—
628C23C2×H(5,𝔽2)11yescharacteristic
629C23C2×H(5,𝔽2)11yescharacteristic
630C23C2×H(5,𝔽2)12yes—
631C23C2×2−1+411yescharacteristic
632C23C2×2−1+411yescharacteristic
633C23C2×2−1+412yes—
634C23#58512yes—
635D4—416no—
636D4—816no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—24no—
640C2×C4—24no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—24no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—24no—
655C2×C4—28no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—42no—
662C2×C4—41no—
663C2×C4—42no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—41no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—44no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—416no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
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—44no—
704C2×C4—44no—
705C2×C4—42no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—44no—
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—44no—
718C2×C4—44no—
719C2×C4—42no—
720C2×C4—44no—
721C2×C4—44no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—816no—
728C2×C4#53514yes—
729C2×C4#53614yes—
730C2×C4#53914yes—
731C2×C4#54214yes—
732C2×C4#54614yes—
733C2×C4#54614yes—
734C2×C4#55214yes—
735C2×C4#56214yes—
736C22—42no—
737C22—42no—
738C22—48no—
739C22—42no—
740C22—44no—
741C22—42no—
742C22—44no—
743C22—42no—
744C22—42no—
745C22—44no—
746C22—42no—
747C22—48no—
748C22—82no—
749C22—82no—
750C22—82no—
751C22—84no—
752C22—82no—
753C22—82no—
754C22—84no—
755C22—82no—
756C22—82no—
757C22—82no—
758C22C2×#53511yescharacteristic
759C22C2×#53611yescharacteristic
760C22#344911yescharacteristic
761C22C2×#53911yescharacteristic
762C22C2×#54211yescharacteristic
763C22C2×#54611yescharacteristic
764C22C2×#54611yescharacteristic
765C22C2×#55211yescharacteristic
766C22#349811yescharacteristic
767C22#349911yescharacteristic
768C22#351512yes—
769C22#351712yes—
770C22#351912yes—
771C22#352012yes—
772C22C2×#56211yescharacteristic
773C22#353712yes—
774C22#354112yes—
775C22#354212yes—
776C22#354412yes—
777C22#354712yes—
778C22#354712yes—
779C22#354812yes—
780C22#355212yes—
781C4—24no—
782C4—42no—
783C4—44no—
784C4—44no—
785C4—44no—
786C4—42no—
787C4—42no—
788C4—42no—
789C4—82no—
790C4—82no—
791C4—82no—
792C4—82no—
793C4—82no—
794C4—82no—
795C4—82no—
796C4—82no—
797C4#268718yes—
798C2—82no—
799C2—84no—
800C2#3730311yescharacteristic
801C2#3763411yescharacteristic
802C2#3808011yescharacteristic
803C2#3808811yescharacteristic
804C2#3808911yescharacteristic
805C2#3895111yescharacteristic
806C2#4255412yes—
807C2#4257712yes—
808C2#4503012yes—
809C2C2×#268711yescharacteristic
810C2#5310112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#121C22
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×#2441C2semidirect
3. #17092C2semidirect
4. #16492C2semidirect
5. #16257C2semidirect
6. #15306C2semidirect
7. #15229C2semidirect
8. #15197C2semidirect
9. #15195C2semidirect
10. #15151C2semidirect
11. #15145C2semidirect
13. #14283C2semidirect
14. #14260C2semidirect
16. #13977C2semidirect
17. #13939C2semidirect
18. #13906C2semidirect
19. #13842C2semidirect

Maximal subgroups

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

subgroupindex
C2×#24412
C2×#24222
#170922
#164922
#162572
#153062
#152292
#151972
#151952
#151512
#151452
#151302
#142832
#142602
#141362
#139772
#139392
#139062
#138422