Finite Group Databasebeta

← #945647

Subgroups — #945647

Order 512.

2928 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×#2491C211yesmaximal, characteristic
2C2×#2501C211yesmaximal, characteristic
3C2×#2442C211yesmaximal, characteristic, complemented
4C2×#2660C211yesmaximal, characteristic, complemented
5#17104C214yesmaximal, complemented
6#16543C214yesmaximal, complemented
7#16257C214yesmaximal, complemented
8#15262C214yesmaximal, complemented
9#15244C211yesmaximal, characteristic, complemented
10#15233C211yesmaximal, characteristic, complemented
11#15229C211yesmaximal, characteristic, complemented
12#15219C211yesmaximal, characteristic
13#15143C211yesmaximal, characteristic, complemented
14#15134C211yesmaximal, characteristic, complemented
15#14260C211yesmaximal, characteristic, complemented
16#14048C211yesmaximal, characteristic, complemented
17#13909C211yesmaximal, characteristic, complemented
18#13880C211yesmaximal, characteristic, complemented
19#13842C211yesmaximal, characteristic, complemented
20C22×C4⋊Q8C2211yescharacteristic
21C22×#125C2211yescharacteristic
22C22×#124C2212yes—
23C22×#123C2214yes—
24C22×#121C2211yescharacteristic
25C23×C4⋊C4C2211yescharacteristic
26#2660—28no—
27#2501—28no—
28#2491—28no—
29#2442—28no—
30C2×#400C2212yes—
31C2×#399C2214yes—
32C2×#398C2214yes—
33C2×#398C2212yes—
34C2×#396C2214yes—
35C2×#395C2214yes—
36C2×#395C2214yes—
37C2×#394C2212yes—
38C2×#393C2212yes—
39C2×#390C2211yescharacteristic
40C2×#390C2211yescharacteristic
41C2×#390C2211yescharacteristic
42C2×#390C2211yescharacteristic
43C2×#390C2211yescharacteristic
44C2×#390C2211yescharacteristic
45C2×#389C2211yescharacteristic
46C2×#389C2211yescharacteristic
47C2×#388C2212yes—
48C2×#385C2212yes—
49C2×#385C2214yes—
50C2×#384C2211yescharacteristic
51C2×#384C2211yescharacteristic
52C2×#384C2211yescharacteristic
53C2×#384C2211yescharacteristic
54C2×#382C2211yescharacteristic
55C2×#382C2211yescharacteristic
56C2×#382C2211yescharacteristic
57C2×#380C2211yescharacteristic
58C2×#380C2211yescharacteristic
59C2×#380C2212yes—
60C2×C4×C4⋊C4C2211yescharacteristic
61C2×C4×C4⋊C4C2211yescharacteristic
62C2×C4×C22⋊C4C2211yescharacteristic
63C2×C4×C22⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2211yescharacteristic
65C2×#376C2211yescharacteristic
66#1444C2214yes—
67#1444C2214yes—
68#1443C2212yes—
69#1443C2214yes—
70#1442C2212yes—
71#1441C2214yes—
72#1441C2214yes—
73#1440C2212yes—
74#1440C2214yes—
75#1440C2214yes—
76#1440C2214yes—
77#1439C2212yes—
78#1439C2214yes—
79#1439C2214yes—
80#1439C2214yes—
81#1439C2214yes—
82#1439C2214yes—
83#1439C2214yes—
84#1438C2214yes—
85#1436C2214yes—
86#1436C2214yes—
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91C4⋊#95C2211yescharacteristic
92C4⋊#95C2211yescharacteristic
93C4×#95C2211yescharacteristic
94C4×#95C2211yescharacteristic
95C23×Q8C2312yes—
96C23×D4C2311yescharacteristic
97C23×D4C2312yes—
98C24×C4C2311yescharacteristic
99C24×C4C2312yes—
100C2×C4⋊Q8—24no—
101C2×C4⋊Q8—24no—
102C2×C4⋊Q8—42no—
103C2×#125—24no—
104C2×#125—24no—
105C2×#125—42no—
106C2×#124—28no—
107C2×#124—48no—
108C2×#123—216no—
109C2×#123—48no—
110C2×#123—48no—
111C2×#121—24no—
112C2×#121—24no—
113C2×#121—42no—
114C22×C4⋊C4—24no—
115C22×C4⋊C4—24no—
116C22×C4⋊C4—42no—
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2314yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2314yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2314yes—
134C22×C4⋊C4C2314yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2314yes—
140C22×C22⋊C4C2311yescharacteristic
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2314yes—
145C22×C22⋊C4C2314yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2314yes—
149C22×C22⋊C4C2311yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2312yes—
157#400—28no—
158#399—216no—
159#398—216no—
160#398—28no—
161#396—48no—
162#395—216no—
163#395—48no—
164#394—28no—
165#393—28no—
166#390—24no—
167#390—24no—
168#390—24no—
169#390—24no—
170#390—24no—
171#390—42no—
172#389—24no—
173#389—24no—
174#388—28no—
175#385—28no—
176#385—48no—
177#384—24no—
178#384—24no—
179#384—42no—
180#384D418yes—
181#382—24no—
182#382—24no—
183#382—24no—
184#380—24no—
185#380—24no—
186#380—28no—
187C4×C4⋊C4—24no—
188C4×C4⋊C4—24no—
189C4×C22⋊C4—24no—
190C4×C22⋊C4—24no—
191C4×C22⋊C4D418yes—
192#376—24no—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2314yes—
212C2×#95C2312yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
217C2×#95C2311yescharacteristic
218C2×#95C2311yescharacteristic
219C25C2412yes—
220C25C2411yescharacteristic
221C22×Q8—24no—
222C22×Q8—24no—
223C22×Q8—44no—
224C22×Q8—42no—
225C22×Q8—44no—
226C22×D4—24no—
227C22×D4—28no—
228C22×D4—24no—
229C22×D4—22no—
230C22×D4—22no—
231C22×D4—22no—
232C22×D4—22no—
233C22×D4—22no—
234C22×D4—22no—
235C22×D4—22no—
236C22×D4—42no—
237C22×D4—44no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—24no—
245C23×C4—28no—
246C23×C4—24no—
247C23×C4—42no—
248C23×C4—44no—
249C23×C4C2×D414yes—
250C23×C4C2412yes—
251C23×C4C2412yes—
252C23×C4C2412yes—
253C23×C4C2412yes—
254C23×C4C2412yes—
255C23×C4C2411yescharacteristic
256C23×C4C2411yescharacteristic
257C23×C4C2411yescharacteristic
258C23×C4C2412yes—
259C23×C4C2411yescharacteristic
260C23×C4C2412yes—
261C23×C4C2411yescharacteristic
262C23×C4C2412yes—
263C23×C4C2412yes—
264C23×C4C2412yes—
265C23×C4C2412yes—
266C23×C4C2411yescharacteristic
267C4⋊Q8—416no—
268#125—416no—
269#124—432no—
270#123—464no—
271#121—416no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—24no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—28no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—28no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—28no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—416no—
307C2×C4⋊C4—42no—
308C2×C4⋊C4—42no—
309C2×C4⋊C4—44no—
310C2×C4⋊C4—44no—
311C2×C4⋊C4—44no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—42no—
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⋊C4C2×D414yes—
323C2×C4⋊C4C2×D414yes—
324C2×C4⋊C4C2×D4116yes—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—28no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—28no—
338C2×C22⋊C4—28no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—28no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—28no—
345C2×C22⋊C4—28no—
346C2×C22⋊C4—42no—
347C2×C22⋊C4—44no—
348C2×C22⋊C4—44no—
349C2×C22⋊C4—42no—
350C2×C22⋊C4—44no—
351C2×C22⋊C4—44no—
352C2×C22⋊C4—44no—
353C2×C22⋊C4—44no—
354C2×C22⋊C4—44no—
355C2×C22⋊C4—44no—
356C2×C22⋊C4—44no—
357C2×C22⋊C4—44no—
358C2×C22⋊C4—44no—
359C2×C22⋊C4—44no—
360C2×C22⋊C4C2×D414yes—
361C2×C22⋊C4C2×D414yes—
362C2×C42—22no—
363C2×C42—22no—
364C2×C42—22no—
365C2×C42—22no—
366C2×C42—22no—
367C2×C42—22no—
368C2×C42—22no—
369C2×C42—22no—
370C2×C42—24no—
371C2×C42—22no—
372C2×C42—22no—
373C2×C42—22no—
374C2×C42—22no—
375C2×C42—22no—
376C2×C42—22no—
377C2×C42—44no—
378C2×C42C2×D414yes—
379C2×C42C2×D414yes—
380C2×C42C2×D414yes—
381C2×C42#4114yes—
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—24no—
396#95—24no—
397#95—28no—
398#95—24no—
399#95—24no—
400#95—42no—
401#95—44no—
402#95—44no—
403#95—44no—
404#95—44no—
405#95—44no—
406#95C2×D414yes—
407#95C2×D414yes—
408C24—21no—
409C24—21no—
410C24—22no—
411C24—21no—
412C24—22no—
413C24—21no—
414C24—21no—
415C24—21no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—24no—
421C24—24no—
422C24—22no—
423C24—24no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—24no—
428C24C22×D412yes—
429C24H(5,𝔽2)14yes—
430C24C2511yescharacteristic
431C2×Q8—48no—
432C2×Q8—48no—
433C2×Q8—88no—
434C2×Q8—84no—
435C2×Q8—88no—
436C2×D4—48no—
437C2×D4—416no—
438C2×D4—48no—
439C2×D4—44no—
440C2×D4—44no—
441C2×D4—44no—
442C2×D4—44no—
443C2×D4—44no—
444C2×D4—44no—
445C2×D4—44no—
446C2×D4—84no—
447C2×D4—88no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—24no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—24no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—21no—
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—21no—
488C22×C4—21no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—28no—
503C22×C4—28no—
504C22×C4—28no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—24no—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—22no—
520C22×C4—24no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—24no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—48no—
531C22×C4—416no—
532C22×C4—44no—
533C22×C4—44no—
534C22×C4—44no—
535C22×C4—44no—
536C22×C4—48no—
537C22×C4—84no—
538C22×C4—88no—
539C22×C4C22×D414yes—
540C22×C4C22×D412yes—
541C22×C4C22×D412yes—
542C22×C4C22×D412yes—
543C22×C4C22×D412yes—
544C22×C4C22×D414yes—
545C22×C4C22×D412yes—
546C22×C4C22×D414yes—
547C22×C4C22×D412yes—
548C22×C4C22×D412yes—
549C22×C4C2×#4114yes—
550C22×C4C2×#4112yes—
551C22×C4H(5,𝔽2)14yes—
552C22×C4H(5,𝔽2)12yes—
553C22×C42−1+414yes—
554C22×C42−1+412yes—
555C22×C42−1+412yes—
556C22×C42−1+412yes—
557C4⋊C4—28no—
558C4⋊C4—28no—
559C4⋊C4—416no—
560C4⋊C4—48no—
561C4⋊C4—48no—
562C4⋊C4—416no—
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—88no—
572C4⋊C4—84no—
573C4⋊C4—84no—
574C4⋊C4—88no—
575C22⋊C4—216no—
576C22⋊C4—216no—
577C22⋊C4—28no—
578C22⋊C4—44no—
579C22⋊C4—48no—
580C22⋊C4—416no—
581C22⋊C4—48no—
582C22⋊C4—416no—
583C22⋊C4—48no—
584C22⋊C4—48no—
585C22⋊C4—48no—
586C22⋊C4—48no—
587C22⋊C4—88no—
588C22⋊C4—84no—
589C22⋊C4—88no—
590C42—28no—
591C42—28no—
592C42—28no—
593C42—28no—
594C42—48no—
595C42—44no—
596C42—44no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—24no—
602C23—24no—
603C23—22no—
604C23—22no—
605C23—24no—
606C23—24no—
607C23—24no—
608C23—24no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—42no—
613C23—42no—
614C23—41no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—44no—
628C23—44no—
629C23—44no—
630C23—44no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—44no—
635C23—44no—
636C23—44no—
637C23—44no—
638C23—44no—
639C23—44no—
640C23—44no—
641C23—44no—
642C23#53514yes—
643C23C23×D411yescharacteristic
644C23C23×D411yescharacteristic
645C23C22×#4111yescharacteristic
646C23C2×H(5,𝔽2)12yes—
647C23C2×H(5,𝔽2)11yescharacteristic
648C23C2×H(5,𝔽2)12yes—
649C23C2×2−1+411yescharacteristic
650C23C2×2−1+411yescharacteristic
651C23C2×2−1+411yescharacteristic
652C23C2×2−1+412yes—
653C23#58512yes—
654Q8—816no—
655D4—816no—
656D4—88no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—24no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—28no—
675C2×C4—28no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—41no—
691C2×C4—42no—
692C2×C4—41no—
693C2×C4—42no—
694C2×C4—41no—
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—41no—
707C2×C4—42no—
708C2×C4—44no—
709C2×C4—44no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—416no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—44no—
743C2×C4—44no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—816no—
749C2×C4#53614yes—
750C2×C4#53614yes—
751C2×C4#54214yes—
752C2×C4D4214yes—
753C2×C4#54714yes—
754C2×C4#54814yes—
755C2×C4#56314yes—
756C22—24no—
757C22—24no—
758C22—24no—
759C22—44no—
760C22—44no—
761C22—44no—
762C22—42no—
763C22—42no—
764C22—44no—
765C22—42no—
766C22—42no—
767C22—84no—
768C22—82no—
769C22—84no—
770C22—84no—
771C22—82no—
772C22—82no—
773C22—82no—
774C22—84no—
775C22—82no—
776C22—82no—
777C22—82no—
778C22C2×#53511yescharacteristic
779C22C2×#53611yescharacteristic
780C22C2×#53611yescharacteristic
781C22#344911yescharacteristic
782C22C2×#54211yescharacteristic
783C22C2×D4211yescharacteristic
784C22C2×#54711yescharacteristic
785C22C2×#54811yescharacteristic
786C22#348412yes—
787C22#349212yes—
788C22#349412yes—
789C22#349712yes—
790C22#349811yescharacteristic
791C22#349911yescharacteristic
792C22C2×#56311yescharacteristic
793C22#354312yes—
794C22#354412yes—
795C22#354412yes—
796C22#354712yes—
797C22#355212yes—
798C22#355912yes—
799C22#355912yes—
800C22#356112yes—
801C4—44no—
802C4—44no—
803C4—44no—
804C4—42no—
805C4—44no—
806C4—44no—
807C4—42no—
808C4—44no—
809C4—42no—
810C4—42no—
811C4—42no—
812C4—82no—
813C4—82no—
814C4—82no—
815C4—82no—
816C4—82no—
817C4#267418yes—
818C2—44no—
819C2—162no—
820C2#3730311yescharacteristic
821C2#3753911yescharacteristic
822C2#3767411yescharacteristic
823C2#3786311yescharacteristic
824C2#3786911yescharacteristic
825C2#3935611yescharacteristic
826C2#4242312yes—
827C2#4251412yes—
828C2#4487812yes—
829C2C2×#267411yescharacteristic
830C2#5303912yes—
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
3. C2×#2442C2semidirect
4. C2×#2660C2semidirect
5. #17104C2semidirect
6. #16543C2semidirect
7. #16257C2semidirect
8. #15262C2semidirect
9. #15244C2semidirect
10. #15233C2semidirect
11. #15229C2semidirect
13. #15143C2semidirect
14. #15134C2semidirect
15. #14260C2semidirect
16. #14048C2semidirect
17. #13909C2semidirect
18. #13880C2semidirect
19. #13842C2semidirect

Maximal subgroups

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

subgroupindex
C2×#24912
C2×#25012
C2×#24422
C2×#26602
#171042
#165432
#162572
#152622
#152442
#152332
#152292
#152192
#151432
#151342
#142602
#140482
#139092
#138802
#138422