Finite Group Databasebeta

← #705267

Subgroups — #705267

Order 512.

2604 conjugacy classes of subgroups.

The subgroup lattice has 807 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2497C211yesmaximal, characteristic, complemented
2C2×#2363C211yesmaximal, characteristic
3#16285C214yesmaximal, complemented
4#15424C214yesmaximal, complemented
5#15346C214yesmaximal, complemented
6#15222C211yesmaximal, characteristic, complemented
7#15136C211yesmaximal, characteristic, complemented
8#15130C211yesmaximal, characteristic
9#15130C211yesmaximal, characteristic
10#14819C214yesmaximal, complemented
11#14276C211yesmaximal, characteristic, complemented
12#14049C211yesmaximal, characteristic, complemented
13#14048C211yesmaximal, characteristic, complemented
14#13977C211yesmaximal, characteristic, complemented
15#13939C211yesmaximal, characteristic, complemented
16#13910C211yesmaximal, characteristic, complemented
17#13879C211yesmaximal, characteristic, complemented
18#13842C211yesmaximal, characteristic, complemented
19#13785C211yesmaximal, characteristic, complemented
20C22×#121C2211yescharacteristic
21C22×C4×D4C2211yescharacteristic
22C22×#117C2211yescharacteristic
23#2497—28no—
24C2×#400C2212yes—
25C2×#397C2214yes—
26C2×#396C2212yes—
27C2×#394C2214yes—
28C2×#394C2214yes—
29#2363—28no—
30C2×#390C2211yescharacteristic
31C2×#390C2211yescharacteristic
32C2×#390C2211yescharacteristic
33C2×#390C2211yescharacteristic
34C2×#390C2212yes—
35C2×#390C2211yescharacteristic
36C2×#389C2211yescharacteristic
37C2×#389C2211yescharacteristic
38C2×#389C2211yescharacteristic
39C2×#389C2214yes—
40C2×#388C2212yes—
41C2×#388C2212yes—
42C2×#387C2212yes—
43C2×#387C2214yes—
44C2×#386C2212yes—
45C2×#385C2214yes—
46C2×#384C2211yescharacteristic
47C2×#384C2211yescharacteristic
48C2×#384C2211yescharacteristic
49C2×#384C2211yescharacteristic
50C2×#382C2211yescharacteristic
51C2×#380C2211yescharacteristic
52C2×#380C2211yescharacteristic
53C2×C4×C4⋊C4C2211yescharacteristic
54C2×C4×C4⋊C4C2211yescharacteristic
55C2×C4×C4⋊C4C2211yescharacteristic
56C2×C4×C22⋊C4C2211yescharacteristic
57C2×C4×C22⋊C4C2212yes—
58C2×C4×C22⋊C4C2211yescharacteristic
59C2×C4×C22⋊C4C2211yescharacteristic
60C2×#376C2211yescharacteristic
61#1445C2214yes—
62#1444C2214yes—
63#1443C2212yes—
64#1442C2212yes—
65#1441C2214yes—
66#1441C2214yes—
67#1441C2214yes—
68#1440C2212yes—
69#1440C2214yes—
70#1439C2212yes—
71#1439C2214yes—
72#1439C2214yes—
73#1439C2214yes—
74#1439C2214yes—
75#1439C2214yes—
76#1439C2214yes—
77#1439C2214yes—
78#1437C2214yes—
79#1436C2214yes—
80#1436C2214yes—
81C4⋊#95C2211yescharacteristic
82C4⋊#95C2211yescharacteristic
83C4⋊#95C2211yescharacteristic
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89#1434C2214yes—
90C22⋊#95C2214yes—
91C4×#95C2211yescharacteristic
92C4×#95C2211yescharacteristic
93C23×D4C2311yescharacteristic
94C23×D4C2312yes—
95C24×C4C2311yescharacteristic
96C24×C4C2312yes—
97C2×#121—24no—
98C2×#121—24no—
99C2×#121—24no—
100C2×C4×D4—24no—
101C2×C4×D4—24no—
102C2×C4×D4—42no—
103C2×#117—24no—
104C2×#117—24no—
105C2×#117—42no—
106C22×C4⋊C4C2311yescharacteristic
107C22×C4⋊C4C2311yescharacteristic
108C22×C4⋊C4C2311yescharacteristic
109C22×C4⋊C4C2311yescharacteristic
110C22×C4⋊C4C2311yescharacteristic
111C22×C4⋊C4C2312yes—
112C22×C4⋊C4C2314yes—
113C22×C4⋊C4C2311yescharacteristic
114C22×C4⋊C4C2311yescharacteristic
115C22×C4⋊C4C2314yes—
116C22×C4⋊C4C2312yes—
117C22×C4⋊C4C2312yes—
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2314yes—
121C22×C4⋊C4C2312yes—
122C22×C22⋊C4C2312yes—
123C22×C22⋊C4C2312yes—
124C22×C22⋊C4C2312yes—
125C22×C22⋊C4C2314yes—
126C22×C22⋊C4C2312yes—
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2311yescharacteristic
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2314yes—
133C22×C22⋊C4C2314yes—
134C22×C22⋊C4C2314yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2311yescharacteristic
137C22×C42C2311yescharacteristic
138C22×C42C2311yescharacteristic
139C22×C42C2311yescharacteristic
140C22×C42C2312yes—
141C22×C42C2311yescharacteristic
142C22×C42C2311yescharacteristic
143C22×C42C2311yescharacteristic
144C22×C42C2312yes—
145C22×C42C2312yes—
146#400—28no—
147#397—48no—
148#396—28no—
149#394—48no—
150#394—48no—
151#390—24no—
152#390—24no—
153#390—28no—
154#390—24no—
155#390—24no—
156#390—42no—
157#389—24no—
158#389—24no—
159#389—24no—
160#389—48no—
161#388—28no—
162#388—28no—
163#387—28no—
164#387—48no—
165#386—28no—
166#385—48no—
167#384—24no—
168#384—24no—
169#384—24no—
170#384—24no—
171#382—42no—
172#380—24no—
173#380—24no—
174C4×C4⋊C4—24no—
175C4×C4⋊C4—24no—
176C4×C4⋊C4—24no—
177C4×C22⋊C4—24no—
178C4×C22⋊C4—28no—
179C4×C22⋊C4—42no—
180C4×C22⋊C4D418yes—
181#376—42no—
182C2×#95C2314yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2314yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2314yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2312yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2312yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
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—24no—
218C22×D4—22no—
219C22×D4—22no—
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—42no—
232C23×C4—44no—
233C23×C4—44no—
234C23×C4C2×D414yes—
235C23×C4C2412yes—
236C23×C4C2412yes—
237C23×C4C2412yes—
238C23×C4C2412yes—
239C23×C4C2412yes—
240C23×C4C2412yes—
241C23×C4C2411yescharacteristic
242C23×C4C2411yescharacteristic
243C23×C4C2411yescharacteristic
244C23×C4C2411yescharacteristic
245C23×C4C2412yes—
246C23×C4C2412yes—
247C23×C4C2412yes—
248C23×C4C2412yes—
249C23×C4C2412yes—
250C23×C4C2411yescharacteristic
251C23×C4C2411yescharacteristic
252#121—232no—
253C4×D4—416no—
254#117—416no—
255C2×C4⋊C4—22no—
256C2×C4⋊C4—22no—
257C2×C4⋊C4—22no—
258C2×C4⋊C4—24no—
259C2×C4⋊C4—22no—
260C2×C4⋊C4—24no—
261C2×C4⋊C4—24no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—24no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—28no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—22no—
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—28no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—28no—
285C2×C4⋊C4—28no—
286C2×C4⋊C4—44no—
287C2×C4⋊C4—44no—
288C2×C4⋊C4—44no—
289C2×C4⋊C4—44no—
290C2×C4⋊C4—44no—
291C2×C4⋊C4—44no—
292C2×C4⋊C4—44no—
293C2×C4⋊C4—44no—
294C2×C4⋊C4—44no—
295C2×C4⋊C4—44no—
296C2×C4⋊C4#4114yes—
297C2×C4⋊C4#4114yes—
298C2×C22⋊C4—24no—
299C2×C22⋊C4—24no—
300C2×C22⋊C4—24no—
301C2×C22⋊C4—24no—
302C2×C22⋊C4—24no—
303C2×C22⋊C4—28no—
304C2×C22⋊C4—24no—
305C2×C22⋊C4—24no—
306C2×C22⋊C4—24no—
307C2×C22⋊C4—24no—
308C2×C22⋊C4—24no—
309C2×C22⋊C4—24no—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—28no—
312C2×C22⋊C4—28no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—28no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—28no—
318C2×C22⋊C4—28no—
319C2×C22⋊C4—42no—
320C2×C22⋊C4—42no—
321C2×C22⋊C4—42no—
322C2×C22⋊C4—42no—
323C2×C22⋊C4—42no—
324C2×C22⋊C4—42no—
325C2×C22⋊C4—44no—
326C2×C22⋊C4—44no—
327C2×C22⋊C4—44no—
328C2×C22⋊C4—44no—
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⋊C4C2×D414yes—
336C2×C22⋊C4C2×D414yes—
337C2×C42—22no—
338C2×C42—22no—
339C2×C42—22no—
340C2×C42—22no—
341C2×C42—22no—
342C2×C42—22no—
343C2×C42—24no—
344C2×C42—24no—
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—24no—
355C2×C42—24no—
356C2×C42—42no—
357C2×C42—44no—
358C2×C42—44no—
359C2×C42C2×D414yes—
360C2×C42C2×D414yes—
361C2×C42#4114yes—
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—28no—
373#95—24no—
374#95—28no—
375#95—28no—
376#95—24no—
377#95—24no—
378#95—44no—
379#95—42no—
380#95—42no—
381#95—42no—
382#95—44no—
383#95—44no—
384#95—44no—
385#95—44no—
386#95—44no—
387#95C2×D414yes—
388#95C2×D414yes—
389C24—22no—
390C24—21no—
391C24—21no—
392C24—22no—
393C24—22no—
394C24—22no—
395C24—21no—
396C24—21no—
397C24—24no—
398C24—24no—
399C24—22no—
400C24—22no—
401C24—21no—
402C24—22no—
403C24—22no—
404C24—24no—
405C24—21no—
406C24—22no—
407C24—22no—
408C24—24no—
409C24C22×D412yes—
410C24C2×#4114yes—
411C24C2511yescharacteristic
412C2×D4—216no—
413C2×D4—28no—
414C2×D4—28no—
415C2×D4—28no—
416C2×D4—44no—
417C2×D4—44no—
418C2×D4—44no—
419C2×D4—44no—
420C2×D4—88no—
421C2×D4—84no—
422C2×D4—84no—
423C2×D4—88no—
424C22×C4—21no—
425C22×C4—22no—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—24no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—24no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—24no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—24no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—28no—
472C22×C4—28no—
473C22×C4—28no—
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—24no—
489C22×C4—24no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—24no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—24no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—24no—
505C22×C4—24no—
506C22×C4—48no—
507C22×C4—48no—
508C22×C4—44no—
509C22×C4—44no—
510C22×C4—44no—
511C22×C4—44no—
512C22×C4—84no—
513C22×C4—88no—
514C22×C4—88no—
515C22×C4C22×D412yes—
516C22×C4C22×D412yes—
517C22×C4C22×D412yes—
518C22×C4C22×D412yes—
519C22×C4C22×D412yes—
520C22×C4C22×D412yes—
521C22×C4C2×#4114yes—
522C22×C4C2×#4114yes—
523C22×C4C2×#4114yes—
524C22×C4C2×#4112yes—
525C22×C4C2×#4112yes—
526C22×C4C2×#4112yes—
527C22×C4C2×#4112yes—
528C22×C4H(5,𝔽2)14yes—
529C22×C4H(5,𝔽2)14yes—
530C22×C4H(5,𝔽2)12yes—
531C22×C42−1+414yes—
532C22×C42−1+412yes—
533C4⋊C4—216no—
534C4⋊C4—28no—
535C4⋊C4—28no—
536C4⋊C4—416no—
537C4⋊C4—48no—
538C4⋊C4—44no—
539C4⋊C4—44no—
540C4⋊C4—44no—
541C4⋊C4—44no—
542C4⋊C4—44no—
543C4⋊C4—84no—
544C4⋊C4—84no—
545C4⋊C4—84no—
546C4⋊C4—84no—
547C4⋊C4—88no—
548C4⋊C4—88no—
549C22⋊C4—216no—
550C22⋊C4—28no—
551C22⋊C4—44no—
552C22⋊C4—48no—
553C22⋊C4—48no—
554C22⋊C4—416no—
555C22⋊C4—48no—
556C22⋊C4—48no—
557C22⋊C4—48no—
558C22⋊C4—88no—
559C22⋊C4—84no—
560C22⋊C4—88no—
561C22⋊C4—84no—
562C22⋊C4—84no—
563C22⋊C4—88no—
564C42—28no—
565C42—28no—
566C42—28no—
567C42—48no—
568C42—44no—
569C42—44no—
570C42—44no—
571C42—84no—
572C42—84no—
573C23—24no—
574C23—22no—
575C23—24no—
576C23—22no—
577C23—22no—
578C23—24no—
579C23—22no—
580C23—22no—
581C23—22no—
582C23—22no—
583C23—28no—
584C23—28no—
585C23—41no—
586C23—42no—
587C23—42no—
588C23—41no—
589C23—42no—
590C23—42no—
591C23—41no—
592C23—42no—
593C23—41no—
594C23—42no—
595C23—44no—
596C23—42no—
597C23—42no—
598C23—44no—
599C23—42no—
600C23—42no—
601C23—44no—
602C23—42no—
603C23—42no—
604C23—44no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—44no—
609C23—42no—
610C23—44no—
611C23—42no—
612C23—44no—
613C23—44no—
614C23—42no—
615C23—42no—
616C23—44no—
617C23—44no—
618C23—42no—
619C23C23×D411yescharacteristic
620C23C22×#4111yescharacteristic
621C23C22×#4111yescharacteristic
622C23C22×#4111yescharacteristic
623C23C22×#4111yescharacteristic
624C23C2×H(5,𝔽2)11yescharacteristic
625C23C2×H(5,𝔽2)12yes—
626C23C2×H(5,𝔽2)12yes—
627C23C2×2−1+412yes—
628C23C2×2−1+411yescharacteristic
629C23#58512yes—
630D4—416no—
631D4—816no—
632C2×C4—22no—
633C2×C4—24no—
634C2×C4—22no—
635C2×C4—24no—
636C2×C4—22no—
637C2×C4—24no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—24no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—28no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—28no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—42no—
662C2×C4—41no—
663C2×C4—42no—
664C2×C4—41no—
665C2×C4—42no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—44no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—44no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—416no—
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—44no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—44no—
708C2×C4—42no—
709C2×C4—44no—
710C2×C4—42no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—42no—
716C2×C4—44no—
717C2×C4—42no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—816no—
723C2×C4#52514yes—
724C2×C4#52914yes—
725C2×C4#53614yes—
726C2×C4#53914yes—
727C2×C4#54614yes—
728C2×C4#54714yes—
729C2×C4#55314yes—
730C2×C4#55614yes—
731C22—42no—
732C22—48no—
733C22—42no—
734C22—44no—
735C22—48no—
736C22—44no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—44no—
741C22—42no—
742C22—42no—
743C22—82no—
744C22—82no—
745C22—82no—
746C22—82no—
747C22—84no—
748C22—82no—
749C22—82no—
750C22—82no—
751C22—82no—
752C22—84no—
753C22C2×#52511yescharacteristic
754C22C2×#52911yescharacteristic
755C22C2×#53611yescharacteristic
756C22#344911yescharacteristic
757C22C2×#53911yescharacteristic
758C22C2×#54611yescharacteristic
759C22C2×#54711yescharacteristic
760C22C2×#55311yescharacteristic
761C22C2×#55611yescharacteristic
762C22#349212yes—
763C22#349412yes—
764C22#349811yescharacteristic
765C22#349811yescharacteristic
766C22#351412yes—
767C22#351512yes—
768C22#351812yes—
769C22#351912yes—
770C22#351912yes—
771C22#352212yes—
772C22#354212yes—
773C22#354712yes—
774C22#354812yes—
775C22#355212yes—
776C4—24no—
777C4—42no—
778C4—42no—
779C4—44no—
780C4—44no—
781C4—44no—
782C4—44no—
783C4—42no—
784C4—44no—
785C4—42no—
786C4—82no—
787C4—82no—
788C4—82no—
789C4—82no—
790C4—82no—
791C4—82no—
792C4#246618yes—
793C2—82no—
794C2—84no—
795C2C2×#246611yescharacteristic
796C2#3520011yescharacteristic
797C2#3553711yescharacteristic
798C2#3594712yes—
799C2#3786211yescharacteristic
800C2#3786911yescharacteristic
801C2#3809011yescharacteristic
802C2#3895211yescharacteristic
803C2#4257712yes—
804C2#4497512yes—
805C2#4504012yes—
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×#2497C2semidirect
3. #16285C2semidirect
4. #15424C2semidirect
5. #15346C2semidirect
6. #15222C2semidirect
7. #15136C2semidirect
10. #14819C2semidirect
11. #14276C2semidirect
12. #14049C2semidirect
13. #14048C2semidirect
14. #13977C2semidirect
15. #13939C2semidirect
16. #13910C2semidirect
17. #13879C2semidirect
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×#24972
C2×#23632
#162852
#154242
#153462
#152222
#151362
#151302
#148192
#142762
#140492
#140482
#139772
#139392
#139102
#138792
#138422
#137852