Finite Group Databasebeta

← #945656

Subgroups — #945656

Order 512.

2704 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2504C211yesmaximal, characteristic
2C2×#2491C211yesmaximal, characteristic
3C2×#2442C211yesmaximal, characteristic, complemented
4C2×#2660C211yesmaximal, characteristic, complemented
5#17127C214yesmaximal, complemented
6#16536C214yesmaximal, complemented
7#16286C214yesmaximal, complemented
8#15311C214yesmaximal, complemented
9#15244C211yesmaximal, characteristic, complemented
10#15230C211yesmaximal, characteristic, complemented
11#15229C211yesmaximal, characteristic, complemented
12#15222C211yesmaximal, characteristic, complemented
13#15150C211yesmaximal, characteristic, complemented
14#15130C211yesmaximal, characteristic
15#14260C211yesmaximal, characteristic, complemented
16#14050C211yesmaximal, characteristic, complemented
17#13909C211yesmaximal, characteristic, complemented
18#13881C211yesmaximal, characteristic, complemented
19#13842C211yesmaximal, characteristic, complemented
20C22×C4⋊Q8C2211yescharacteristic
21C22×#125C2211yescharacteristic
22C22×#124C2212yes—
23C22×#121C2211yescharacteristic
24C23×C4⋊C4C2211yescharacteristic
25#2660—28no—
26#2504—28no—
27#2491—28no—
28#2442—28no—
29C2×#400C2212yes—
30C2×#398C2214yes—
31C2×#398C2212yes—
32C2×#397C2214yes—
33C2×#397C2214yes—
34C2×#395C2214yes—
35C2×#394C2212yes—
36C2×#394C2214yes—
37C2×#393C2212yes—
38C2×#390C2211yescharacteristic
39C2×#390C2211yescharacteristic
40C2×#390C2211yescharacteristic
41C2×#390C2211yescharacteristic
42C2×#390C2211yescharacteristic
43C2×#390C2211yescharacteristic
44C2×#389C2211yescharacteristic
45C2×#389C2211yescharacteristic
46C2×#388C2212yes—
47C2×#386C2214yes—
48C2×#385C2212yes—
49C2×#384C2211yescharacteristic
50C2×#384C2211yescharacteristic
51C2×#382C2211yescharacteristic
52C2×#382C2211yescharacteristic
53C2×#382C2211yescharacteristic
54C2×#382C2211yescharacteristic
55C2×#382C2211yescharacteristic
56C2×#380C2211yescharacteristic
57C2×#380C2211yescharacteristic
58C2×#380C2212yes—
59C2×C4×C4⋊C4C2211yescharacteristic
60C2×C4×C4⋊C4C2211yescharacteristic
61C2×C4×C22⋊C4C2211yescharacteristic
62C2×C4×C22⋊C4C2211yescharacteristic
63C2×C4×C22⋊C4C2211yescharacteristic
64C2×#376C2211yescharacteristic
65#1446C2214yes—
66#1445C2214yes—
67#1443C2212yes—
68#1443C2214yes—
69#1442C2212yes—
70#1442C2214yes—
71#1441C2214yes—
72#1441C2214yes—
73#1440C2212yes—
74#1440C2214yes—
75#1439C2212yes—
76#1439C2214yes—
77#1439C2214yes—
78#1439C2214yes—
79#1439C2214yes—
80#1439C2214yes—
81#1439C2214yes—
82#1439C2214yes—
83#1439C2214yes—
84#1436C2214yes—
85#1436C2214yes—
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91C4⋊#95C2211yescharacteristic
92C22⋊#95C2214yes—
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×#121—24no—
109C2×#121—24no—
110C2×#121—42no—
111C22×C4⋊C4—24no—
112C22×C4⋊C4—24no—
113C22×C4⋊C4—42no—
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⋊C4C2312yes—
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2314yes—
126C22×C4⋊C4C2314yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2311yescharacteristic
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2314yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2314yes—
141C22×C22⋊C4C2314yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2314yes—
144C22×C22⋊C4C2311yescharacteristic
145C22×C42C2311yescharacteristic
146C22×C42C2311yescharacteristic
147C22×C42C2311yescharacteristic
148C22×C42C2311yescharacteristic
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2312yes—
152#400—28no—
153#398—216no—
154#398—28no—
155#397—216no—
156#397—48no—
157#395—216no—
158#394—28no—
159#394—48no—
160#393—28no—
161#390—24no—
162#390—24no—
163#390—24no—
164#390—24no—
165#390—24no—
166#390—42no—
167#389—24no—
168#389—24no—
169#388—28no—
170#386—216no—
171#385—28no—
172#384—24no—
173#384—24no—
174#382—24no—
175#382—24no—
176#382—24no—
177#382—42no—
178#382D418yes—
179#380—24no—
180#380—24no—
181#380—28no—
182C4×C4⋊C4—24no—
183C4×C4⋊C4—24no—
184C4×C22⋊C4—24no—
185C4×C22⋊C4—24no—
186C4×C22⋊C4D418yes—
187#376—24no—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2314yes—
192C2×#95C2312yes—
193C2×#95C2314yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2314yes—
211C2×#95C2314yes—
212C2×#95C2314yes—
213C2×#95C2311yescharacteristic
214C2×#95C2314yes—
215C2×#95C2311yescharacteristic
216C25C2412yes—
217C25C2411yescharacteristic
218C22×Q8—24no—
219C22×Q8—24no—
220C22×Q8—44no—
221C22×Q8—42no—
222C22×Q8—44no—
223C22×D4—24no—
224C22×D4—28no—
225C22×D4—24no—
226C22×D4—22no—
227C22×D4—22no—
228C22×D4—22no—
229C22×D4—22no—
230C22×D4—22no—
231C22×D4—22no—
232C22×D4—22no—
233C22×D4—42no—
234C22×D4—44no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—24no—
242C23×C4—24no—
243C23×C4—42no—
244C23×C4—44no—
245C23×C4—44no—
246C23×C4C2×D414yes—
247C23×C4C2412yes—
248C23×C4C2412yes—
249C23×C4C2412yes—
250C23×C4C2412yes—
251C23×C4C2412yes—
252C23×C4C2412yes—
253C23×C4C2412yes—
254C23×C4C2411yescharacteristic
255C23×C4C2411yescharacteristic
256C23×C4C2411yescharacteristic
257C23×C4C2412yes—
258C23×C4C2411yescharacteristic
259C23×C4C2412yes—
260C23×C4C2411yescharacteristic
261C23×C4C2412yes—
262C23×C4C2412yes—
263C23×C4C2411yescharacteristic
264C4⋊Q8—416no—
265#125—416no—
266#124—432no—
267#121—416no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—22no—
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—24no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—24no—
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—24no—
297C2×C4⋊C4—28no—
298C2×C4⋊C4—28no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—416no—
301C2×C4⋊C4—42no—
302C2×C4⋊C4—42no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—42no—
305C2×C4⋊C4—42no—
306C2×C4⋊C4—42no—
307C2×C4⋊C4—44no—
308C2×C4⋊C4—44no—
309C2×C4⋊C4—44no—
310C2×C4⋊C4—44no—
311C2×C4⋊C4—44no—
312C2×C4⋊C4—44no—
313C2×C4⋊C4C2×D414yes—
314C2×C4⋊C4C2×D414yes—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—28no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—28no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—28no—
330C2×C22⋊C4—28no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—28no—
333C2×C22⋊C4—42no—
334C2×C22⋊C4—42no—
335C2×C22⋊C4—42no—
336C2×C22⋊C4—44no—
337C2×C22⋊C4—42no—
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⋊C4—44no—
345C2×C22⋊C4—44no—
346C2×C22⋊C4—44no—
347C2×C22⋊C4—44no—
348C2×C22⋊C4—44no—
349C2×C22⋊C4—44no—
350C2×C22⋊C4C2×D414yes—
351C2×C22⋊C4C2×D414yes—
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—24no—
361C2×C42—22no—
362C2×C42—22no—
363C2×C42—22no—
364C2×C42—22no—
365C2×C42—22no—
366C2×C42—22no—
367C2×C42—44no—
368C2×C42C2×D414yes—
369C2×C42C2×D414yes—
370C2×C42C2×D414yes—
371C2×C42#4114yes—
372#95—24no—
373#95—24no—
374#95—24no—
375#95—24no—
376#95—24no—
377#95—24no—
378#95—24no—
379#95—24no—
380#95—24no—
381#95—28no—
382#95—28no—
383#95—24no—
384#95—24no—
385#95—24no—
386#95—44no—
387#95—42no—
388#95—42no—
389#95—44no—
390#95—42no—
391#95—42no—
392#95—44no—
393#95—44no—
394#95—44no—
395#95—44no—
396#95—44no—
397#95C2×D414yes—
398#95C2×D414yes—
399#95C2×D4116yes—
400C24—21no—
401C24—21no—
402C24—21no—
403C24—21no—
404C24—21no—
405C24—21no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—24no—
413C24—22no—
414C24—22no—
415C24—22no—
416C24—22no—
417C24—24no—
418C24—24no—
419C24—24no—
420C24C22×D412yes—
421C24H(5,𝔽2)14yes—
422C24C2511yescharacteristic
423C2×Q8—48no—
424C2×Q8—48no—
425C2×Q8—88no—
426C2×Q8—84no—
427C2×Q8—88no—
428C2×D4—48no—
429C2×D4—416no—
430C2×D4—48no—
431C2×D4—44no—
432C2×D4—44no—
433C2×D4—44no—
434C2×D4—44no—
435C2×D4—44no—
436C2×D4—44no—
437C2×D4—44no—
438C2×D4—84no—
439C2×D4—88no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—24no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—24no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—24no—
480C22×C4—22no—
481C22×C4—24no—
482C22×C4—28no—
483C22×C4—28no—
484C22×C4—28no—
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—22no—
500C22×C4—24no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—24no—
505C22×C4—24no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—24no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—24no—
519C22×C4—22no—
520C22×C4—24no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—48no—
525C22×C4—44no—
526C22×C4—44no—
527C22×C4—44no—
528C22×C4—44no—
529C22×C4—48no—
530C22×C4—88no—
531C22×C4—84no—
532C22×C4—88no—
533C22×C4C22×D412yes—
534C22×C4C22×D412yes—
535C22×C4C22×D414yes—
536C22×C4C22×D414yes—
537C22×C4C22×D414yes—
538C22×C4C22×D412yes—
539C22×C4C22×D412yes—
540C22×C4C22×D412yes—
541C22×C4C22×D412yes—
542C22×C4C22×D412yes—
543C22×C4C2×#4114yes—
544C22×C4C2×#4112yes—
545C22×C4H(5,𝔽2)12yes—
546C22×C42−1+412yes—
547C22×C42−1+412yes—
548C22×C42−1+412yes—
549C4⋊C4—28no—
550C4⋊C4—28no—
551C4⋊C4—48no—
552C4⋊C4—48no—
553C4⋊C4—48no—
554C4⋊C4—48no—
555C4⋊C4—48no—
556C4⋊C4—44no—
557C4⋊C4—44no—
558C4⋊C4—44no—
559C4⋊C4—44no—
560C4⋊C4—44no—
561C4⋊C4—88no—
562C4⋊C4—88no—
563C4⋊C4—84no—
564C4⋊C4—84no—
565C22⋊C4—28no—
566C22⋊C4—44no—
567C22⋊C4—48no—
568C22⋊C4—48no—
569C22⋊C4—48no—
570C22⋊C4—48no—
571C22⋊C4—48no—
572C22⋊C4—48no—
573C22⋊C4—48no—
574C22⋊C4—48no—
575C22⋊C4—88no—
576C22⋊C4—88no—
577C22⋊C4—84no—
578C22⋊C4—88no—
579C22⋊C4—88no—
580C42—28no—
581C42—28no—
582C42—28no—
583C42—28no—
584C42—48no—
585C42—44no—
586C42—44no—
587C23—22no—
588C23—22no—
589C23—22no—
590C23—22no—
591C23—24no—
592C23—24no—
593C23—22no—
594C23—22no—
595C23—24no—
596C23—24no—
597C23—24no—
598C23—24no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—42no—
603C23—42no—
604C23—41no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—42no—
617C23—44no—
618C23—44no—
619C23—44no—
620C23—44no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—44no—
625C23—44no—
626C23—44no—
627C23—44no—
628C23—44no—
629C23—44no—
630C23—44no—
631C23—44no—
632C23#53514yes—
633C23C23×D411yescharacteristic
634C23C23×D411yescharacteristic
635C23C22×#4111yescharacteristic
636C23C2×H(5,𝔽2)12yes—
637C23C2×H(5,𝔽2)11yescharacteristic
638C23C2×2−1+411yescharacteristic
639C23C2×2−1+411yescharacteristic
640C23C2×2−1+411yescharacteristic
641C23#58512yes—
642C23#58512yes—
643C23#58512yes—
644Q8—816no—
645D4—816no—
646D4—88no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—24no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—24no—
662C2×C4—24no—
663C2×C4—28no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—22no—
668C2×C4—28no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—42no—
673C2×C4—41no—
674C2×C4—42no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—41no—
686C2×C4—44no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—44no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—416no—
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—44no—
714C2×C4—44no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—44no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—44no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—42no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—42no—
733C2×C4—44no—
734C2×C4—42no—
735C2×C4—44no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—816no—
739C2×C4#53614yes—
740C2×C4#53614yes—
741C2×C4#54214yes—
742C2×C4D4214yes—
743C2×C4#54714yes—
744C2×C4#54814yes—
745C2×C4#56314yes—
746C22—24no—
747C22—24no—
748C22—24no—
749C22—44no—
750C22—42no—
751C22—44no—
752C22—42no—
753C22—42no—
754C22—44no—
755C22—44no—
756C22—42no—
757C22—84no—
758C22—82no—
759C22—82no—
760C22—84no—
761C22—82no—
762C22—82no—
763C22—82no—
764C22—84no—
765C22—84no—
766C22—82no—
767C22—82no—
768C22C2×#53511yescharacteristic
769C22C2×#53611yescharacteristic
770C22C2×#53611yescharacteristic
771C22#344911yescharacteristic
772C22C2×#54211yescharacteristic
773C22C2×D4211yescharacteristic
774C22C2×#54711yescharacteristic
775C22C2×#54811yescharacteristic
776C22#348812yes—
777C22#349312yes—
778C22#349412yes—
779C22#350011yescharacteristic
780C22#350011yescharacteristic
781C22#350012yes—
782C22C2×#56311yescharacteristic
783C22#355812yes—
784C22#355912yes—
785C22#355912yes—
786C22#355912yes—
787C22#356212yes—
788C22#356512yes—
789C22#356512yes—
790C22#356512yes—
791C4—44no—
792C4—42no—
793C4—44no—
794C4—42no—
795C4—42no—
796C4—44no—
797C4—44no—
798C4—42no—
799C4—42no—
800C4—82no—
801C4—82no—
802C4—82no—
803C4—82no—
804C4—82no—
805C4—82no—
806C4—82no—
807C4#267418yes—
808C2—44no—
809C2—162no—
810C2#3742311yescharacteristic
811C2#3753911yescharacteristic
812C2#3767711yescharacteristic
813C2#3786411yescharacteristic
814C2#3787111yescharacteristic
815C2#3935711yescharacteristic
816C2#4269312yes—
817C2#4294412yes—
818C2#4515912yes—
819C2C2×#267411yescharacteristic
820C2#5300312yes—
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. #17127C2semidirect
6. #16536C2semidirect
7. #16286C2semidirect
8. #15311C2semidirect
9. #15244C2semidirect
10. #15230C2semidirect
11. #15229C2semidirect
12. #15222C2semidirect
13. #15150C2semidirect
15. #14260C2semidirect
16. #14050C2semidirect
17. #13909C2semidirect
18. #13881C2semidirect
19. #13842C2semidirect

Maximal subgroups

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

subgroupindex
C2×#25042
C2×#24912
C2×#24422
C2×#26602
#171272
#165362
#162862
#153112
#152442
#152302
#152292
#152222
#151502
#151302
#142602
#140502
#139092
#138812
#138422