Finite Group Databasebeta

← #847108

Subgroups — #847108

Order 512.

3402 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2709C212yesmaximal
2C2×#2486C211yesmaximal, characteristic, complemented
3C2×C4×#127C211yesmaximal, characteristic
4#16596C212yesmaximal, complemented
5#16563C212yesmaximal, complemented
6#15702C214yesmaximal, complemented
7#15502C214yesmaximal, complemented
8#15129C212yesmaximal, complemented
9#15129C212yesmaximal, complemented
10#15129C212yesmaximal, complemented
11#14699C212yesmaximal, complemented
12#14505C212yesmaximal, complemented
13#13872C212yesmaximal, complemented
14#13872C212yesmaximal, complemented
15#13872C211yesmaximal, characteristic, complemented
16C22×#127C2211yescharacteristic
17C22×#123C2212yes—
18C22×C4×D4C2212yes—
19C22×C4×D4C2212yes—
20C22×C4×D4C2211yescharacteristic
21C22×C4×D4C2211yescharacteristic
22C23×C4⋊C4C2211yescharacteristic
23C23×C4⋊C4C2211yescharacteristic
24#2709—216no—
25#2486—28no—
26C2×#398C2212yes—
27C2×#397C2212yes—
28C2×#394C2214yes—
29C2×#394C2214yes—
30C2×#394C2214yes—
31C4×#127—28no—
32C2×#390C2212yes—
33C2×#390C2212yes—
34C2×#390C2211yescharacteristic
35C2×#390C2211yescharacteristic
36C2×#389C2212yes—
37C2×#389C2212yes—
38C2×#387C2214yes—
39C2×#386C2214yes—
40C2×#386C2214yes—
41C2×#386C2212yes—
42C2×#384C2211yescharacteristic
43C2×#381C2212yes—
44C2×#380C2211yescharacteristic
45C2×#380C2212yes—
46C2×#380C2212yes—
47C2×#380C2211yescharacteristic
48C2×#380C2212yes—
49C2×#380C2212yes—
50C2×#380C2212yes—
51C2×#380C2212yes—
52C2×C43C2211yescharacteristic
53#1441C2214yes—
54#1441C2214yes—
55#1441C2214yes—
56#1441C2214yes—
57#1441C2214yes—
58#1441C2212yes—
59#1440C2214yes—
60#1440C2214yes—
61#1440C2214yes—
62#1440C2214yes—
63#1440C2214yes—
64#1440C2214yes—
65#1439C2212yes—
66#1439C2214yes—
67#1439C2214yes—
68#1436C2214yes—
69#1436C2214yes—
70C4⋊#95C2212yes—
71C4⋊#95C2212yes—
72C4⋊#95C2212yes—
73C4⋊#95C2212yes—
74#1434C2214yes—
75C22⋊#95C2214yes—
76C22⋊#95C2212yes—
77C22⋊#95C2214yes—
78C23×D4C2312yes—
79C23×D4C2312yes—
80C23×D4C2311yescharacteristic
81C23×D4C2311yescharacteristic
82C24×C4C2312yes—
83C24×C4C2311yescharacteristic
84C24×C4C2311yescharacteristic
85C24×C4C2312yes—
86C24×C4C2312yes—
87C2×#127—24no—
88C2×#127—24no—
89C2×#127D418yes—
90C2×#123—28no—
91C2×#123—28no—
92C2×#123—28no—
93C2×C4×D4—28no—
94C2×C4×D4—28no—
95C2×C4×D4—24no—
96C2×C4×D4—28no—
97C2×C4×D4—28no—
98C2×C4×D4—42no—
99C2×C4×D4—42no—
100C2×C4×D4—44no—
101C2×C4×D4—44no—
102C2×C4×D4—42no—
103C2×C4×D4—42no—
104C2×C4×D4D418yes—
105C22×C4⋊C4—24no—
106C22×C4⋊C4—42no—
107C22×C4⋊C4—42no—
108C22×C4⋊C4—42no—
109C22×C4⋊C4—44no—
110C22×C4⋊C4C2314yes—
111C22×C4⋊C4C2314yes—
112C22×C4⋊C4C2312yes—
113C22×C4⋊C4C2312yes—
114C22×C4⋊C4C2312yes—
115C22×C4⋊C4C2312yes—
116C22×C4⋊C4C2312yes—
117C22×C4⋊C4C2312yes—
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2311yescharacteristic
122C22×C22⋊C4C2312yes—
123C22×C22⋊C4C2314yes—
124C22×C22⋊C4C2312yes—
125C22×C22⋊C4C2312yes—
126C22×C22⋊C4C2312yes—
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2314yes—
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2314yes—
131C22×C22⋊C4C2314yes—
132C22×C22⋊C4C2314yes—
133C22×C22⋊C4C2314yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2311yescharacteristic
136C22×C22⋊C4C2311yescharacteristic
137C22×C42C2312yes—
138C22×C42C2311yescharacteristic
139C22×C42C2311yescharacteristic
140C22×C42C2312yes—
141C22×C42C2311yescharacteristic
142#398—28no—
143#397—28no—
144#394—216no—
145#394—216no—
146#394—216no—
147#390—24no—
148#390—24no—
149#390—28no—
150#390—28no—
151#389—28no—
152#389—28no—
153#387—216no—
154#386—216no—
155#386—216no—
156#386—28no—
157#384—24no—
158#381—28no—
159#380—28no—
160#380—24no—
161#380—44no—
162#380—44no—
163#380—44no—
164#380—44no—
165#380—42no—
166#380—44no—
167C2×#95C2314yes—
168C2×#95C2314yes—
169C2×#95C2314yes—
170C2×#95C2312yes—
171C2×#95C2314yes—
172C2×#95C2314yes—
173C2×#95C2314yes—
174C2×#95C2314yes—
175C2×#95C2314yes—
176C2×#95C2314yes—
177C2×#95C2314yes—
178C2×#95C2314yes—
179C2×#95C2314yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C2×#95C2314yes—
183C2×#95C2312yes—
184C2×#95C2314yes—
185C43—24no—
186C25C2412yes—
187C25C2411yescharacteristic
188C25C2411yescharacteristic
189C22×D4—24no—
190C22×D4—24no—
191C22×D4—24no—
192C22×D4—24no—
193C22×D4—22no—
194C22×D4—24no—
195C22×D4—24no—
196C22×D4—22no—
197C22×D4—24no—
198C22×D4—24no—
199C22×D4—41no—
200C22×D4—41no—
201C22×D4—42no—
202C22×D4—42no—
203C22×D4—41no—
204C22×D4—41no—
205C22×D4—41no—
206C22×D4—41no—
207C22×D4—42no—
208C22×D4—42no—
209C22×D4—41no—
210C22×D4—41no—
211C22×D4C2×D418yes—
212C22×D4C2×D418yes—
213C22×D4C2×D414yes—
214C22×D4C2×D414yes—
215C22×D4C2×D414yes—
216C22×D4#4114yes—
217C23×C4—24no—
218C23×C4—24no—
219C23×C4—22no—
220C23×C4—22no—
221C23×C4—22no—
222C23×C4—24no—
223C23×C4—22no—
224C23×C4—24no—
225C23×C4—24no—
226C23×C4—24no—
227C23×C4—24no—
228C23×C4—24no—
229C23×C4—24no—
230C23×C4—24no—
231C23×C4—24no—
232C23×C4—24no—
233C23×C4—24no—
234C23×C4—24no—
235C23×C4—24no—
236C23×C4—42no—
237C23×C4—42no—
238C23×C4—42no—
239C23×C4—44no—
240C23×C4—42no—
241C23×C4—42no—
242C23×C4—42no—
243C23×C4—44no—
244C23×C4C2×D414yes—
245C23×C4C2×D414yes—
246C23×C4C2414yes—
247C23×C4C2414yes—
248C23×C4C2414yes—
249C23×C4C2412yes—
250C23×C4C2414yes—
251C23×C4C2411yescharacteristic
252C23×C4C2411yescharacteristic
253C23×C4C2411yescharacteristic
254C23×C4C2412yes—
255C23×C4C2411yescharacteristic
256C23×C4C2412yes—
257C23×C4C2411yescharacteristic
258#127—232no—
259#123—432no—
260C4×D4—416no—
261C4×D4—432no—
262C4×D4—432no—
263C4×D4—416no—
264C2×C4⋊C4—24no—
265C2×C4⋊C4—24no—
266C2×C4⋊C4—24no—
267C2×C4⋊C4—24no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—28no—
270C2×C4⋊C4—28no—
271C2×C4⋊C4—24no—
272C2×C4⋊C4—28no—
273C2×C4⋊C4—24no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—28no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—24no—
278C2×C4⋊C4—28no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—28no—
288C2×C4⋊C4—42no—
289C2×C4⋊C4—42no—
290C2×C4⋊C4—42no—
291C2×C4⋊C4—44no—
292C2×C4⋊C4—41no—
293C2×C4⋊C4—41no—
294C2×C4⋊C4—42no—
295C2×C4⋊C4—42no—
296C2×C4⋊C4—41no—
297C2×C4⋊C4—41no—
298C2×C4⋊C4—416no—
299C2×C4⋊C4—416no—
300C2×C4⋊C4C2×D414yes—
301C2×C22⋊C4—24no—
302C2×C22⋊C4—24no—
303C2×C22⋊C4—24no—
304C2×C22⋊C4—28no—
305C2×C22⋊C4—28no—
306C2×C22⋊C4—24no—
307C2×C22⋊C4—24no—
308C2×C22⋊C4—28no—
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—28no—
317C2×C22⋊C4—28no—
318C2×C22⋊C4—28no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—28no—
321C2×C22⋊C4—28no—
322C2×C22⋊C4—41no—
323C2×C22⋊C4—41no—
324C2×C22⋊C4—41no—
325C2×C22⋊C4—41no—
326C2×C22⋊C4—42no—
327C2×C22⋊C4—42no—
328C2×C22⋊C4—42no—
329C2×C22⋊C4—42no—
330C2×C22⋊C4—42no—
331C2×C22⋊C4—42no—
332C2×C22⋊C4—42no—
333C2×C22⋊C4—44no—
334C2×C22⋊C4—44no—
335C2×C22⋊C4—44no—
336C2×C22⋊C4—44no—
337C2×C22⋊C4—44no—
338C2×C22⋊C4—42no—
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—24no—
347C2×C42—22no—
348C2×C42—22no—
349C2×C42—22no—
350C2×C42—22no—
351C2×C42—24no—
352C2×C42—24no—
353C2×C42—22no—
354C2×C42—24no—
355C2×C42—42no—
356C2×C42—41no—
357C2×C42—41no—
358C2×C42C2×D414yes—
359C2×C42C2×D414yes—
360C2×C42#4118yes—
361#95—28no—
362#95—24no—
363#95—28no—
364#95—28no—
365#95—28no—
366#95—28no—
367#95—28no—
368#95—28no—
369#95—44no—
370#95—44no—
371#95—44no—
372#95—44no—
373#95—42no—
374#95—44no—
375#95—44no—
376#95—44no—
377#95—44no—
378#95—44no—
379C24—22no—
380C24—22no—
381C24—21no—
382C24—22no—
383C24—21no—
384C24—21no—
385C24—21no—
386C24—22no—
387C24—22no—
388C24—22no—
389C24—21no—
390C24—22no—
391C24—21no—
392C24—21no—
393C24—21no—
394C24—22no—
395C24—22no—
396C24—22no—
397C24—22no—
398C24—22no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—22no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24C22×D414yes—
410C24C22×D412yes—
411C24C22×D412yes—
412C24C22×D412yes—
413C24C22×D412yes—
414C24C2×#4112yes—
415C24C2×#4112yes—
416C24C2511yescharacteristic
417C2×D4—216no—
418C2×D4—216no—
419C2×D4—28no—
420C2×D4—216no—
421C2×D4—216no—
422C2×D4—44no—
423C2×D4—44no—
424C2×D4—44no—
425C2×D4—44no—
426C2×D4—48no—
427C2×D4—48no—
428C2×D4—44no—
429C2×D4—44no—
430C2×D4—44no—
431C2×D4—44no—
432C2×D4—48no—
433C2×D4—48no—
434C2×D4—48no—
435C2×D4—48no—
436C2×D4—48no—
437C2×D4—48no—
438C2×D4—48no—
439C2×D4—48no—
440C2×D4—44no—
441C2×D4—44no—
442C2×D4—44no—
443C2×D4—44no—
444C2×D4#121116yes—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—28no—
472C22×C4—28no—
473C22×C4—216no—
474C22×C4—216no—
475C22×C4—24no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—24no—
479C22×C4—24no—
480C22×C4—24no—
481C22×C4—22no—
482C22×C4—24no—
483C22×C4—24no—
484C22×C4—24no—
485C22×C4—24no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—24no—
489C22×C4—24no—
490C22×C4—24no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—24no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—24no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—24no—
510C22×C4—48no—
511C22×C4—48no—
512C22×C4—44no—
513C22×C4—44no—
514C22×C4—44no—
515C22×C4—44no—
516C22×C4—48no—
517C22×C4—48no—
518C22×C4—48no—
519C22×C4—48no—
520C22×C4—48no—
521C22×C4—48no—
522C22×C4—48no—
523C22×C4—48no—
524C22×C4—48no—
525C22×C4—48no—
526C22×C4—48no—
527C22×C4—84no—
528C22×C4—84no—
529C22×C4—88no—
530C22×C4—84no—
531C22×C4—84no—
532C22×C4—84no—
533C22×C4—84no—
534C22×C4—88no—
535C22×C4C22×D412yes—
536C22×C4C22×D412yes—
537C22×C4C22×D412yes—
538C22×C4C22×D412yes—
539C22×C4C22×D412yes—
540C22×C4C22×D414yes—
541C22×C4C22×D412yes—
542C22×C4C2×#4114yes—
543C22×C4C2×#4112yes—
544C22×C4C2×#4114yes—
545C22×C4C2×#4114yes—
546C22×C4H(5,𝔽2)12yes—
547C22×C4H(5,𝔽2)12yes—
548C22×C4H(5,𝔽2)14yes—
549C22×C42−1+414yes—
550C4⋊C4—44no—
551C4⋊C4—48no—
552C4⋊C4—48no—
553C4⋊C4—48no—
554C4⋊C4—44no—
555C4⋊C4—48no—
556C4⋊C4—416no—
557C4⋊C4—48no—
558C4⋊C4—48no—
559C4⋊C4—48no—
560C4⋊C4—416no—
561C4⋊C4—48no—
562C22⋊C4—44no—
563C22⋊C4—44no—
564C22⋊C4—48no—
565C22⋊C4—48no—
566C22⋊C4—48no—
567C22⋊C4—48no—
568C22⋊C4—48no—
569C22⋊C4—48no—
570C22⋊C4—416no—
571C22⋊C4—84no—
572C22⋊C4—88no—
573C22⋊C4—88no—
574C22⋊C4—88no—
575C22⋊C4—88no—
576C22⋊C4—88no—
577C42—28no—
578C42—28no—
579C42—216no—
580C42—48no—
581C42—44no—
582C23—22no—
583C23—22no—
584C23—22no—
585C23—22no—
586C23—24no—
587C23—24no—
588C23—24no—
589C23—24no—
590C23—24no—
591C23—24no—
592C23—24no—
593C23—24no—
594C23—24no—
595C23—22no—
596C23—24no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—24no—
605C23—24no—
606C23—24no—
607C23—24no—
608C23—24no—
609C23—24no—
610C23—24no—
611C23—24no—
612C23—24no—
613C23—42no—
614C23—42no—
615C23—41no—
616C23—41no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—41no—
622C23—41no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—42no—
631C23—41no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23C2×#12114yes—
662C23C2×#12114yes—
663C23C23×D411yescharacteristic
664C23C23×D411yescharacteristic
665C23C22×#4111yescharacteristic
666C23C22×#4112yes—
667C23C2×H(5,𝔽2)11yescharacteristic
668C23C2×H(5,𝔽2)11yescharacteristic
669C23C2×H(5,𝔽2)12yes—
670C23C2×2−1+412yes—
671C23#58511yescharacteristic
672C23#58511yescharacteristic
673C23#58512yes—
674D4—416no—
675D4—432no—
676D4—432no—
677D4—416no—
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—24no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—42no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—42no—
712C2×C4—416no—
713C2×C4—416no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—42no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—44no—
725C2×C4—44no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—42no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—44no—
742C2×C4—44no—
743C2×C4—42no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—44no—
749C2×C4—816no—
750C2×C4—816no—
751C2×C4—816no—
752C2×C4C2×#12114yes—
753C2×C4#53414yes—
754C2×C4#54018yes—
755C2×C4#54618yes—
756C2×C4#54718yes—
757C2×C4#55914yes—
758C2×C4#56014yes—
759C22—28no—
760C22—28no—
761C22—24no—
762C22—24no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—44no—
768C22—44no—
769C22—44no—
770C22—44no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—44no—
776C22—44no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—44no—
782C22—44no—
783C22—44no—
784C22—44no—
785C22—44no—
786C22—44no—
787C22—44no—
788C22—82no—
789C22—82no—
790C22—82no—
791C22—82no—
792C22—82no—
793C22—82no—
794C22—82no—
795C22—82no—
796C22C22×#12111yescharacteristic
797C22C2×#53411yescharacteristic
798C22#344911yescharacteristic
799C22C2×#54012yes—
800C22C2×#54612yes—
801C22C2×#54712yes—
802C22#347512yes—
803C22C2×#55911yescharacteristic
804C22#348912yes—
805C22#349612yes—
806C22#349611yescharacteristic
807C22#349611yescharacteristic
808C22#350511yescharacteristic
809C22#350511yescharacteristic
810C22#350712yes—
811C22#351212yes—
812C22#352012yes—
813C22C2×#56011yescharacteristic
814C22#354712yes—
815C22#354712yes—
816C22#355011yescharacteristic
817C22#355111yescharacteristic
818C22#355112yes—
819C4—28no—
820C4—24no—
821C4—42no—
822C4—44no—
823C4—42no—
824C4—42no—
825C4—84no—
826C4—82no—
827C4—84no—
828C4—84no—
829C4—84no—
830C4#270918yescomplemented
831C2—44no—
832C2—44no—
833C2—84no—
834C2#3500011yescharacteristic
835C2#3615312yes—
836C2#3737611yescharacteristic
837C2#3937812yes—
838C2#3946312yes—
839C2#3999812yes—
840C2#4632811yescharacteristic
841C2#4634211yescharacteristic
842C2C2×#270911yescharacteristic
843C2#5982711yescharacteristic
844C2#5986511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#127C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#2486C2semidirect
4. #16596C2semidirect
5. #16563C2semidirect
6. #15702C2semidirect
7. #15502C2semidirect
8. #15129C2semidirect
9. #15129C2semidirect
10. #15129C2semidirect
11. #14699C2semidirect
12. #14505C2semidirect
13. #13872C2semidirect
14. #13872C2semidirect
15. #13872C2semidirect
830. C4#2709semidirect

Maximal subgroups

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

subgroupindex
C2×#27092
C2×#24862
C2×C4×#1272
#165962
#165632
#157022
#155022
#151292
#146992
#145052
#138722