Finite Group Databasebeta

← #637369

Subgroups — #637369

Order 512.

3162 conjugacy classes of subgroups.

The subgroup lattice has 825 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2851C211yesmaximal, characteristic, complemented
2C2×#2562C211yesmaximal, characteristic, complemented
3C2×C4×#121C211yesmaximal, characteristic
4C2×#2285C211yesmaximal, characteristic, complemented
5#16567C212yesmaximal, complemented
6#16519C212yesmaximal, complemented
7#16400C212yesmaximal, complemented
8#16261C212yesmaximal
9#15181C212yesmaximal, complemented
10#15131C212yesmaximal, complemented
11#15131C212yesmaximal, complemented
12#15129C212yesmaximal, complemented
13#14890C214yesmaximal, complemented
14#14310C214yesmaximal, complemented
15#14160C211yesmaximal, characteristic, complemented
16#13954C211yesmaximal, characteristic, complemented
17#13905C211yesmaximal, characteristic, complemented
18C22×#125C2211yescharacteristic
19C22×#121C2211yescharacteristic
20C22×C4×D4C2211yescharacteristic
21C22×C4×D4C2212yes—
22C22×#117C2212yes—
23C23×C42C2211yescharacteristic
24#2851—28no—
25#2562—28no—
26C2×#400C2212yes—
27C2×#396C2214yes—
28C2×#396C2214yes—
29C2×#394C2212yes—
30C2×#394C2214yes—
31C4×#121—28no—
32C2×#390C2211yescharacteristic
33C2×#389C2211yescharacteristic
34C2×#389C2211yescharacteristic
35C2×#389C2211yescharacteristic
36C2×#389C2212yes—
37C2×#389C2212yes—
38C2×#388C2214yes—
39C2×#388C2212yes—
40C2×#387C2212yes—
41C2×#387C2212yes—
42C2×#386C2212yes—
43C2×#385C2212yes—
44C2×#385C2212yes—
45#2285—28no—
46C2×#384C2212yes—
47C2×#382C2211yescharacteristic
48C2×#382C2212yes—
49C2×#380C2211yescharacteristic
50C2×#380C2211yescharacteristic
51C2×#380C2211yescharacteristic
52C2×#380C2212yes—
53C2×#380C2212yes—
54C2×#380C2212yes—
55C2×#380C2212yes—
56C2×#380C2212yes—
57C2×#380C2212yes—
58C2×C4×C4⋊C4C2211yescharacteristic
59C2×C4×C4⋊C4C2211yescharacteristic
60C2×C4×C4⋊C4C2212yes—
61C2×C4×C4⋊C4C2211yescharacteristic
62C2×C4×C22⋊C4C2212yes—
63#1445C2212yes—
64#1444C2212yes—
65#1444C2212yes—
66#1442C2214yes—
67#1441C2214yes—
68#1441C2214yes—
69#1441C2212yes—
70#1441C2214yes—
71#1441C2214yes—
72#1441C2214yes—
73#1441C2212yes—
74#1440C2214yes—
75#1440C2214yes—
76#1439C2214yes—
77#1439C2214yes—
78#1439C2214yes—
79#1439C2214yes—
80#1438C2214yes—
81#1438C2212yes—
82#1437C2214yes—
83#1436C2214yes—
84C4⋊#95C2212yes—
85C4⋊#95C2212yes—
86C4⋊#95C2214yes—
87C23×D4C2312yes—
88C23×D4C2311yescharacteristic
89C24×C4C2312yes—
90C24×C4C2311yescharacteristic
91C24×C4C2311yescharacteristic
92C24×C4C2311yescharacteristic
93C2×#125—24no—
94C2×#125—24no—
95C2×#125—24no—
96C2×#121—24no—
97C2×#121—28no—
98C2×C4×D4—28no—
99C2×C4×D4—24no—
100C2×C4×D4—24no—
101C2×C4×D4—24no—
102C2×C4×D4—44no—
103C2×C4×D4—44no—
104C2×#117—28no—
105C2×#117—44no—
106C2×#117—44no—
107C22×C4⋊C4C2312yes—
108C22×C4⋊C4C2312yes—
109C22×C4⋊C4C2312yes—
110C22×C4⋊C4C2311yescharacteristic
111C22×C4⋊C4C2311yescharacteristic
112C22×C4⋊C4C2311yescharacteristic
113C22×C4⋊C4C2311yescharacteristic
114C22×C4⋊C4C2312yes—
115C22×C4⋊C4C2312yes—
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2314yes—
119C22×C4⋊C4C2314yes—
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2314yes—
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2314yes—
125C22×C22⋊C4C2312yes—
126C22×C22⋊C4C2312yes—
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2314yes—
129C22×C22⋊C4C2314yes—
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2314yes—
132C22×C22⋊C4C2314yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2314yes—
137C22×C42—24no—
138C22×C42—24no—
139C22×C42D418yes—
140C22×C42C2312yes—
141C22×C42C2311yescharacteristic
142C22×C42C2311yescharacteristic
143C22×C42C2311yescharacteristic
144C22×C42C2312yes—
145C22×C42C2312yes—
146C22×C42C2311yescharacteristic
147#400—28no—
148#396—216no—
149#396—48no—
150#394—28no—
151#394—48no—
152#390—24no—
153#389—24no—
154#389—24no—
155#389—24no—
156#389—44no—
157#389—44no—
158#388—216no—
159#388—28no—
160#387—28no—
161#387—28no—
162#386—28no—
163#385—28no—
164#385—28no—
165#384—28no—
166#382—24no—
167#382—28no—
168#380—24no—
169#380—24no—
170#380—24no—
171#380—28no—
172#380—28no—
173#380—28no—
174#380—28no—
175#380—44no—
176#380—44no—
177C4×C4⋊C4—28no—
178C4×C4⋊C4—24no—
179C4×C4⋊C4—24no—
180C4×C4⋊C4D418yescomplemented
181C4×C22⋊C4—28no—
182C2×#95C2314yes—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2314yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2312yes—
204C25C2412yes—
205C25C2411yescharacteristic
206C22×D4—24no—
207C22×D4—24no—
208C22×D4—24no—
209C22×D4—24no—
210C22×D4—24no—
211C22×D4—22no—
212C22×D4—22no—
213C22×D4—24no—
214C22×D4—22no—
215C22×D4—42no—
216C22×D4—42no—
217C22×D4—42no—
218C23×C4—22no—
219C23×C4—22no—
220C23×C4—22no—
221C23×C4—22no—
222C23×C4—22no—
223C23×C4—22no—
224C23×C4—22no—
225C23×C4—22no—
226C23×C4—24no—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—24no—
230C23×C4—24no—
231C23×C4—24no—
232C23×C4—24no—
233C23×C4—24no—
234C23×C4—24no—
235C23×C4—24no—
236C23×C4—24no—
237C23×C4—24no—
238C23×C4—42no—
239C23×C4C2×D414yes—
240C23×C4C2×D414yes—
241C23×C4C2×D414yes—
242C23×C4C2412yes—
243C23×C4C2412yes—
244C23×C4C2412yes—
245C23×C4C2412yes—
246C23×C4C2412yes—
247C23×C4C2414yes—
248C23×C4C2412yes—
249C23×C4C2414yes—
250C23×C4C2411yescharacteristic
251C23×C4C2412yes—
252C23×C4C2411yescharacteristic
253C23×C4C2411yescharacteristic
254C23×C4C2411yescharacteristic
255C23×C4C2411yescharacteristic
256C23×C4C2411yescharacteristic
257#125—416no—
258#121—232no—
259C4×D4—432no—
260C4×D4—416no—
261#117—432no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—24no—
264C2×C4⋊C4—24no—
265C2×C4⋊C4—24no—
266C2×C4⋊C4—28no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—24no—
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—24no—
277C2×C4⋊C4—24no—
278C2×C4⋊C4—28no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—28no—
291C2×C4⋊C4—28no—
292C2×C4⋊C4—28no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—28no—
300C2×C4⋊C4—44no—
301C2×C4⋊C4—42no—
302C2×C4⋊C4—44no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—42no—
305C2×C4⋊C4—44no—
306C2×C4⋊C4—44no—
307C2×C4⋊C4—44no—
308C2×C4⋊C4—44no—
309C2×C4⋊C4—44no—
310C2×C4⋊C4C2×D418yes—
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—24no—
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—28no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—28no—
330C2×C22⋊C4—28no—
331C2×C22⋊C4—44no—
332C2×C22⋊C4—44no—
333C2×C22⋊C4—44no—
334C2×C22⋊C4—42no—
335C2×C22⋊C4—42no—
336C2×C22⋊C4—42no—
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#4118yes—
346C2×C42—22no—
347C2×C42—22no—
348C2×C42—22no—
349C2×C42—22no—
350C2×C42—22no—
351C2×C42—22no—
352C2×C42—232no—
353C2×C42—24no—
354C2×C42—24no—
355C2×C42—24no—
356C2×C42—24no—
357C2×C42—42no—
358C2×C42—42no—
359C2×C42—42no—
360C2×C42—42no—
361C2×C42C2×D414yes—
362C2×C42C2×D414yes—
363C2×C42C2×D414yes—
364C2×C42C2×D418yes—
365C2×C42C2×D414yes—
366C2×C42C2×D414yes—
367C2×C42#4114yes—
368#95—24no—
369#95—24no—
370#95—28no—
371#95—24no—
372#95—24no—
373#95—24no—
374#95—24no—
375#95—28no—
376#95—28no—
377#95—24no—
378#95—24no—
379#95—24no—
380#95—24no—
381#95—28no—
382#95—44no—
383#95—44no—
384#95—44no—
385#95—44no—
386#95—44no—
387#95—44no—
388#95—44no—
389#95C2×D418yes—
390C24—21no—
391C24—21no—
392C24—22no—
393C24—21no—
394C24—22no—
395C24—22no—
396C24—21no—
397C24—22no—
398C24—22no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—22no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24C22×D412yes—
413C24C2×#4114yes—
414C24H(5,𝔽2)12yes—
415C242−1+412yes—
416C24C2511yescharacteristic
417C2×D4—28no—
418C2×D4—216no—
419C2×D4—48no—
420C2×D4—48no—
421C2×D4—48no—
422C2×D4—48no—
423C2×D4—44no—
424C2×D4—48no—
425C2×D4—48no—
426C2×D4—48no—
427C2×D4—48no—
428C2×D4—44no—
429C22×C4—28no—
430C22×C4—28no—
431C22×C4—28no—
432C22×C4—28no—
433C22×C4—28no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—28no—
448C22×C4—28no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—24no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—24no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—22no—
461C22×C4—24no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—24no—
465C22×C4—28no—
466C22×C4—28no—
467C22×C4—28no—
468C22×C4—28no—
469C22×C4—28no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—24no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—24no—
481C22×C4—24no—
482C22×C4—24no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—24no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—24no—
510C22×C4—24no—
511C22×C4—24no—
512C22×C4—22no—
513C22×C4—44no—
514C22×C4—48no—
515C22×C4—48no—
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×C4C22×D412yes—
526C22×C4C22×D418yes—
527C22×C4C22×D412yes—
528C22×C4C22×D412yes—
529C22×C4C22×D412yes—
530C22×C4C22×D412yes—
531C22×C4C22×D412yes—
532C22×C4C22×D412yes—
533C22×C4C22×D412yes—
534C22×C4C22×D412yes—
535C22×C4C2×#4114yes—
536C22×C4C2×#4112yes—
537C22×C4C2×#4112yes—
538C22×C4C2×#4114yes—
539C22×C4C2×#4112yes—
540C22×C4H(5,𝔽2)12yes—
541C22×C4H(5,𝔽2)14yes—
542C22×C42−1+412yes—
543C22×C42−1+414yes—
544C4⋊C4—28no—
545C4⋊C4—216no—
546C4⋊C4—416no—
547C4⋊C4—416no—
548C4⋊C4—44no—
549C4⋊C4—48no—
550C4⋊C4—44no—
551C4⋊C4—48no—
552C4⋊C4—48no—
553C4⋊C4—44no—
554C4⋊C4—44no—
555C4⋊C4—48no—
556C4⋊C4—44no—
557C4⋊C4—44no—
558C4⋊C4—48no—
559C4⋊C4—48no—
560C4⋊C4—88no—
561C4⋊C4—88no—
562C22⋊C4—216no—
563C22⋊C4—416no—
564C22⋊C4—416no—
565C22⋊C4—48no—
566C22⋊C4—48no—
567C22⋊C4—48no—
568C22⋊C4—48no—
569C22⋊C4—48no—
570C22⋊C4—48no—
571C22⋊C4—88no—
572C22⋊C4—88no—
573C22⋊C4—88no—
574C42—28no—
575C42—28no—
576C42—28no—
577C42—48no—
578C42—48no—
579C42—48no—
580C42#121116yes—
581C23—22no—
582C23—22no—
583C23—22no—
584C23—22no—
585C23—22no—
586C23—22no—
587C23—22no—
588C23—22no—
589C23—22no—
590C23—22no—
591C23—24no—
592C23—24no—
593C23—24no—
594C23—24no—
595C23—24no—
596C23—24no—
597C23—24no—
598C23—24no—
599C23—24no—
600C23—24no—
601C23—24no—
602C23—42no—
603C23—42no—
604C23—42no—
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—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23#53714yes—
639C23C23×D411yescharacteristic
640C23C23×D411yescharacteristic
641C23C22×#4111yescharacteristic
642C23C22×#4112yes—
643C23C2×H(5,𝔽2)12yes—
644C23C2×H(5,𝔽2)11yescharacteristic
645C23C2×H(5,𝔽2)11yescharacteristic
646C23C2×2−1+412yes—
647C23C2×2−1+411yescharacteristic
648C23C2×2−1+411yescharacteristic
649C23#58512yes—
650D4—416no—
651D4—432no—
652C2×C4—232no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—24no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—28no—
678C2×C4—28no—
679C2×C4—28no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—416no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—44no—
692C2×C4—44no—
693C2×C4—416no—
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—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—44no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—44no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—44no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—44no—
735C2×C4—42no—
736C2×C4—44no—
737C2×C4—816no—
738C2×C4C2×#12114yes—
739C2×C4C2×#12114yes—
740C2×C4C2×#12114yes—
741C2×C4#52514yes—
742C2×C4#53514yes—
743C2×C4#53614yes—
744C2×C4#53714yes—
745C2×C4#53718yes—
746C2×C4#54218yes—
747C22—24no—
748C22—24no—
749C22—24no—
750C22—42no—
751C22—44no—
752C22—42no—
753C22—44no—
754C22—44no—
755C22—42no—
756C22—44no—
757C22—42no—
758C22—44no—
759C22—44no—
760C22—44no—
761C22—44no—
762C22—44no—
763C22—44no—
764C22—44no—
765C22—82no—
766C22—82no—
767C22—82no—
768C22—82no—
769C22—82no—
770C22—82no—
771C22—82no—
772C22—82no—
773C22C22×#12111yescharacteristic
774C22C2×#52511yescharacteristic
775C22C2×#53511yescharacteristic
776C22C2×#53611yescharacteristic
777C22C2×#53712yes—
778C22C2×#53711yescharacteristic
779C22C2×#53711yescharacteristic
780C22#344911yescharacteristic
781C22C2×#54212yes—
782C22D4×#4112yes—
783C22#347512yes—
784C22#348411yescharacteristic
785C22#348611yescharacteristic
786C22#349211yescharacteristic
787C22#349211yescharacteristic
788C22#350912yes—
789C22#351112yes—
790C22#351912yes—
791C22#352012yes—
792C22#354612yes—
793C22#354712yes—
794C22#355912yes—
795C22#356312yes—
796C4—24no—
797C4—24no—
798C4—24no—
799C4—24no—
800C4—42no—
801C4—44no—
802C4—48no—
803C4—82no—
804C4—82no—
805C4—82no—
806C4—84no—
807C4—82no—
808C4—82no—
809C4—82no—
810C4#262018yes—
811C2—44no—
812C2—84no—
813C2C2×#262011yescharacteristic
814C2#3473711yescharacteristic
815C2#3522311yescharacteristic
816C2#3523611yescharacteristic
817C2#3529711yescharacteristic
818C2#3754911yescharacteristic
819C2#3762111yescharacteristic
820C2#3985212yes—
821C2#3987812yes—
822C2#3990212yes—
823C2#3992412yes—
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×#2851C2semidirect
2. C2×#2562C2semidirect
4. C2×#2285C2semidirect
5. #16567C2semidirect
6. #16519C2semidirect
7. #16400C2semidirect
9. #15181C2semidirect
10. #15131C2semidirect
11. #15131C2semidirect
12. #15129C2semidirect
13. #14890C2semidirect
14. #14310C2semidirect
15. #14160C2semidirect
16. #13954C2semidirect
17. #13905C2semidirect
180. C4×C4⋊C4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#28512
C2×#25622
C2×C4×#1212
C2×#22852
#165672
#165192
#164002
#162612
#151812
#151312
#151292
#148902
#143102
#141602
#139542
#139052