Finite Group Databasebeta

← #612835

Subgroups — #612835

Order 512.

3512 conjugacy classes of subgroups.

The subgroup lattice has 809 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2853C212yesmaximal, complemented
2C2×#2501C211yesmaximal, characteristic
3C22×C4×C4⋊C4C211yesmaximal, characteristic, complemented
4#14912C212yesmaximal, complemented
5#14912C212yesmaximal, complemented
6#14793C214yesmaximal, complemented
7#14785C214yesmaximal, complemented
8#14706C212yesmaximal, complemented
9#14698C211yesmaximal, characteristic
10#14141C212yesmaximal, complemented
11#14137C211yesmaximal, characteristic
12#14130C211yesmaximal, characteristic, complemented
13#14022C212yesmaximal, complemented
14#13981C212yesmaximal, complemented
15#13904C211yesmaximal, characteristic, complemented
16#13884C212yesmaximal, complemented
17C4×#385C211yesmaximal, characteristic, complemented
18C22×#123C2212yes—
19C22×#123C2212yes—
20C22×#121C2211yescharacteristic
21C23×C4⋊C4C2211yescharacteristic
22C23×C4⋊C4C2211yescharacteristic
23C23×C42C2211yescharacteristic
24C23×C42C2212yes—
25#2853—216no—
26#2501—28no—
27C2×#399C2212yes—
28C2×#399C2212yes—
29C2×#390C2212yes—
30C2×#390C2211yescharacteristic
31C2×#390C2212yes—
32C2×#390C2211yescharacteristic
33C2×#389C2212yes—
34C2×#388C2214yes—
35C2×#388C2214yes—
36C2×#387C2214yes—
37C2×#387C2214yes—
38C2×#386C2212yes—
39C2×#386C2212yes—
40C2×#386C2212yes—
41C2×#386C2212yes—
42C2×#385C2212yes—
43C2×#385C2211yescharacteristic
44C2×#385C2211yescharacteristic
45C2×#384C2211yescharacteristic
46C2×#384C2211yescharacteristic
47C2×#381C2212yes—
48C2×#381C2212yes—
49C2×#380C2211yescharacteristic
50C2×C4×C4⋊C4—28no—
51C2×C4×C4⋊C4C2212yes—
52C2×C4×C4⋊C4C2212yes—
53C2×C4×C4⋊C4C2212yes—
54C2×C4×C4⋊C4C2214yes—
55C2×C4×C22⋊C4C2211yescharacteristic
56C2×C4×C22⋊C4C2211yescharacteristic
57C22×#95C2212yes—
58#1445C2214yes—
59#1444C2212yes—
60#1442C2212yes—
61#1442C2214yes—
62#1442C2214yes—
63#1441C2214yes—
64#1441C2214yes—
65#1440C2214yes—
66#1440C2214yes—
67#1439C2214yes—
68#1439C2214yes—
69#1439C2214yes—
70#1437C2214yes—
71#1437C2214yes—
72#1437C2214yes—
73#1436C2214yes—
74#1436C2214yes—
75#1436C2212yes—
76#1436C2212yes—
77C4⋊#95C2212yes—
78C4⋊#95C2212yes—
79C4⋊#95C2212yes—
80C4⋊#95C2212yes—
81C4⋊#95C2212yes—
82C22⋊#95C2212yes—
83C22⋊#95C2211yescharacteristic
84C22⋊#95C2211yescharacteristic
85C4×#95C2212yes—
86C23×D4C2312yes—
87C23×D4C2311yescharacteristic
88C24×C4C2311yescharacteristic
89C24×C4C2312yes—
90C24×C4C2312yes—
91C24×C4C2311yescharacteristic
92C24×C4C2311yescharacteristic
93C2×#123—28no—
94C2×#123—28no—
95C2×#123—28no—
96C2×#123—28no—
97C2×#123—44no—
98C2×#123—44no—
99C2×#121—24no—
100C2×#121—24no—
101C2×#121—24no—
102C22×C4⋊C4—24no—
103C22×C4⋊C4—24no—
104C22×C4⋊C4—24no—
105C22×C4⋊C4—28no—
106C22×C4⋊C4D418yes—
107C22×C4⋊C4C2312yes—
108C22×C4⋊C4C2311yescharacteristic
109C22×C4⋊C4C2312yes—
110C22×C4⋊C4C2312yes—
111C22×C4⋊C4C2312yes—
112C22×C4⋊C4C2312yes—
113C22×C4⋊C4C2312yes—
114C22×C4⋊C4C2312yes—
115C22×C4⋊C4C2314yes—
116C22×C4⋊C4C2312yes—
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2312yes—
121C22×C22⋊C4C2312yes—
122C22×C22⋊C4C2311yescharacteristic
123C22×C22⋊C4C2312yes—
124C22×C22⋊C4C2314yes—
125C22×C22⋊C4C2312yes—
126C22×C22⋊C4C2312yes—
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2314yes—
130C22×C22⋊C4C2311yescharacteristic
131C22×C22⋊C4C2311yescharacteristic
132C22×C22⋊C4C2311yescharacteristic
133C22×C22⋊C4C2314yes—
134C22×C22⋊C4C2314yes—
135C22×C42—24no—
136C22×C42—28no—
137C22×C42—28no—
138C22×C42—28no—
139C22×C42—44no—
140C22×C42C2312yes—
141C22×C42C2311yescharacteristic
142C22×C42C2312yes—
143C22×C42C2311yescharacteristic
144C22×C42C2314yes—
145C22×C42C2314yes—
146C22×C42C2312yes—
147#399—28no—
148#399—28no—
149#390—24no—
150#390—24no—
151#390—28no—
152#390—28no—
153#389—28no—
154#388—216no—
155#388—216no—
156#387—216no—
157#387—216no—
158#386—28no—
159#386—28no—
160#386—44no—
161#386—44no—
162#385—28no—
163#385—24no—
164#385D418yescomplemented
165#384—24no—
166#384—24no—
167#381—28no—
168#381—44no—
169#380—24no—
170C4×C4⋊C4—28no—
171C4×C4⋊C4—28no—
172C4×C4⋊C4—216no—
173C4×C4⋊C4—28no—
174C4×C22⋊C4—24no—
175C4×C22⋊C4—24no—
176C2×#95—28no—
177C2×#95C2311yescharacteristic
178C2×#95C2311yescharacteristic
179C2×#95C2312yes—
180C2×#95C2312yes—
181C2×#95C2312yes—
182C2×#95C2314yes—
183C2×#95C2312yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2314yes—
192C2×#95C2314yes—
193C2×#95C2312yes—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2312yes—
200C25C2412yes—
201C25C2411yescharacteristic
202C22×D4—24no—
203C22×D4—24no—
204C22×D4—24no—
205C22×D4—24no—
206C22×D4—24no—
207C22×D4—24no—
208C22×D4—24no—
209C22×D4—22no—
210C22×D4—22no—
211C22×D4—22no—
212C22×D4—24no—
213C22×D4—24no—
214C23×C4—22no—
215C23×C4—22no—
216C23×C4—24no—
217C23×C4—24no—
218C23×C4—24no—
219C23×C4—24no—
220C23×C4—24no—
221C23×C4—24no—
222C23×C4—22no—
223C23×C4—24no—
224C23×C4—24no—
225C23×C4—24no—
226C23×C4—24no—
227C23×C4—24no—
228C23×C4—28no—
229C23×C4—24no—
230C23×C4—24no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—24no—
234C23×C4—44no—
235C23×C4—42no—
236C23×C4C2×D418yes—
237C23×C4C2×D414yes—
238C23×C4C2×D414yes—
239C23×C4#4114yes—
240C23×C4#4114yes—
241C23×C4C2414yes—
242C23×C4C2412yes—
243C23×C4C2412yes—
244C23×C4C2411yescharacteristic
245C23×C4C2411yescharacteristic
246C23×C4C2412yes—
247C23×C4C2412yes—
248C23×C4C2412yes—
249C23×C4C2411yescharacteristic
250C23×C4C2411yescharacteristic
251C23×C4C2414yes—
252C23×C4C2412yes—
253C23×C4C2411yescharacteristic
254C23×C4C2412yes—
255C23×C4C2411yescharacteristic
256#123—432no—
257#123—432no—
258#121—416no—
259C2×C4⋊C4—232no—
260C2×C4⋊C4—232no—
261C2×C4⋊C4—24no—
262C2×C4⋊C4—24no—
263C2×C4⋊C4—28no—
264C2×C4⋊C4—24no—
265C2×C4⋊C4—24no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—24no—
271C2×C4⋊C4—24no—
272C2×C4⋊C4—24no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—24no—
278C2×C4⋊C4—24no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—28no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—28no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—42no—
292C2×C4⋊C4—44no—
293C2×C4⋊C4—42no—
294C2×C4⋊C4—42no—
295C2×C4⋊C4—42no—
296C2×C4⋊C4—42no—
297C2×C4⋊C4C2×D414yes—
298C2×C4⋊C4C2×D414yes—
299C2×C4⋊C4C2×D418yes—
300C2×C4⋊C4C2×D418yes—
301C2×C4⋊C4#4118yes—
302C2×C22⋊C4—22no—
303C2×C22⋊C4—22no—
304C2×C22⋊C4—22no—
305C2×C22⋊C4—22no—
306C2×C22⋊C4—22no—
307C2×C22⋊C4—22no—
308C2×C22⋊C4—24no—
309C2×C22⋊C4—22no—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—22no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—28no—
322C2×C22⋊C4—28no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—28no—
328C2×C22⋊C4—28no—
329C2×C22⋊C4—28no—
330C2×C22⋊C4—28no—
331C2×C22⋊C4—28no—
332C2×C22⋊C4—44no—
333C2×C22⋊C4—42no—
334C2×C22⋊C4—42no—
335C2×C22⋊C4—42no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4—44no—
338C2×C22⋊C4—44no—
339C2×C22⋊C4—44no—
340C2×C22⋊C4—44no—
341C2×C22⋊C4C2×D414yes—
342C2×C22⋊C4C2×D414yes—
343C2×C22⋊C4#4114yes—
344C2×C42—232no—
345C2×C42—24no—
346C2×C42—24no—
347C2×C42—24no—
348C2×C42—24no—
349C2×C42—24no—
350C2×C42—22no—
351C2×C42—22no—
352C2×C42—28no—
353C2×C42—28no—
354C2×C42—28no—
355C2×C42—28no—
356C2×C42—24no—
357C2×C42—24no—
358C2×C42—24no—
359C2×C42—24no—
360C2×C42—24no—
361C2×C42—44no—
362C2×C42—44no—
363C2×C42—432no—
364C2×C42#4118yes—
365#95—28no—
366#95—28no—
367#95—22no—
368#95—22no—
369#95—28no—
370#95—28no—
371#95—28no—
372#95—28no—
373#95—28no—
374#95—24no—
375#95—24no—
376#95—24no—
377#95—24no—
378#95—24no—
379#95—28no—
380#95—24no—
381#95—44no—
382#95—42no—
383#95—44no—
384#95—44no—
385#95—44no—
386#95—44no—
387#95C2×D418yes—
388C24—22no—
389C24—22no—
390C24—22no—
391C24—22no—
392C24—22no—
393C24—22no—
394C24—24no—
395C24—24no—
396C24—22no—
397C24—22no—
398C24—22no—
399C24—22no—
400C24—22no—
401C24—24no—
402C24—24no—
403C24C22×D412yes—
404C24C22×D412yes—
405C24C2×#4112yes—
406C24C2×#4112yes—
407C24C2×#4112yes—
408C24H(5,𝔽2)12yes—
409C24H(5,𝔽2)12yes—
410C24C2511yescharacteristic
411C2×D4—48no—
412C2×D4—48no—
413C2×D4—48no—
414C2×D4—48no—
415C2×D4—48no—
416C2×D4—48no—
417C2×D4—48no—
418C2×D4—44no—
419C2×D4—44no—
420C2×D4—44no—
421C2×D4—48no—
422C2×D4—48no—
423C22×C4—28no—
424C22×C4—28no—
425C22×C4—216no—
426C22×C4—28no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—28no—
434C22×C4—28no—
435C22×C4—216no—
436C22×C4—216no—
437C22×C4—216no—
438C22×C4—28no—
439C22×C4—216no—
440C22×C4—216no—
441C22×C4—216no—
442C22×C4—216no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—24no—
447C22×C4—24no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—24no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—24no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—24no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—24no—
489C22×C4—24no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—22no—
497C22×C4—24no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—24no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—24no—
508C22×C4—22no—
509C22×C4—24no—
510C22×C4—416no—
511C22×C4—48no—
512C22×C4—48no—
513C22×C4—416no—
514C22×C4—48no—
515C22×C4—44no—
516C22×C4—48no—
517C22×C4—48no—
518C22×C4—48no—
519C22×C4—44no—
520C22×C4—48no—
521C22×C4—48no—
522C22×C4#123116yes—
523C22×C4C22×D414yes—
524C22×C4C22×D412yes—
525C22×C4C22×D414yes—
526C22×C4C22×D414yes—
527C22×C4C22×D412yes—
528C22×C4C22×D412yes—
529C22×C4C22×D414yes—
530C22×C4C22×D412yes—
531C22×C4C2×#4112yes—
532C22×C4C2×#4114yes—
533C22×C4C2×#4118yes—
534C22×C4C2×#4112yes—
535C22×C4C2×#4112yes—
536C22×C4C2×#4112yes—
537C22×C4C2×#4114yes—
538C22×C4C2×#4112yes—
539C22×C4C2×#4112yes—
540C22×C4C2×#4114yes—
541C22×C4C2×#4114yes—
542C22×C42−1+414yes—
543C4⋊C4—216no—
544C4⋊C4—216no—
545C4⋊C4—28no—
546C4⋊C4—28no—
547C4⋊C4—216no—
548C4⋊C4—216no—
549C4⋊C4—416no—
550C4⋊C4—48no—
551C4⋊C4—48no—
552C4⋊C4—48no—
553C4⋊C4—48no—
554C4⋊C4—48no—
555C4⋊C4—44no—
556C4⋊C4—48no—
557C22⋊C4—28no—
558C22⋊C4—28no—
559C22⋊C4—28no—
560C22⋊C4—416no—
561C22⋊C4—48no—
562C22⋊C4—48no—
563C22⋊C4—48no—
564C22⋊C4—48no—
565C22⋊C4—44no—
566C22⋊C4—48no—
567C22⋊C4—48no—
568C22⋊C4—416no—
569C22⋊C4—88no—
570C22⋊C4—88no—
571C42—216no—
572C42—216no—
573C42—416no—
574C42—416no—
575C42—44no—
576C42—44no—
577C42—48no—
578C23—22no—
579C23—22no—
580C23—24no—
581C23—24no—
582C23—24no—
583C23—24no—
584C23—24no—
585C23—24no—
586C23—24no—
587C23—22no—
588C23—22no—
589C23—24no—
590C23—24no—
591C23—24no—
592C23—24no—
593C23—24no—
594C23—42no—
595C23—42no—
596C23—42no—
597C23—44no—
598C23—44no—
599C23—42no—
600C23—42no—
601C23—44no—
602C23—42no—
603C23—42no—
604C23—44no—
605C23—42no—
606C23—44no—
607C23—44no—
608C23—42no—
609C23—44no—
610C23—42no—
611C23—42no—
612C23—44no—
613C23—44no—
614C23—44no—
615C23—44no—
616C23—44no—
617C23C2×#12314yes—
618C23#53214yes—
619C23#54014yes—
620C23D4214yes—
621C23#54614yes—
622C23#55014yes—
623C23#55914yes—
624C23C23×D411yescharacteristic
625C23C23×D411yescharacteristic
626C23C22×#4111yescharacteristic
627C23C22×#4111yescharacteristic
628C23C22×#4112yes—
629C23C22×#4112yes—
630C23C22×#4111yescharacteristic
631C23C2×H(5,𝔽2)11yescharacteristic
632C23C2×H(5,𝔽2)11yescharacteristic
633C23C2×2−1+412yes—
634C23#58512yes—
635D4—816no—
636D4—88no—
637C2×C4—232no—
638C2×C4—22no—
639C2×C4—24no—
640C2×C4—22no—
641C2×C4—24no—
642C2×C4—24no—
643C2×C4—24no—
644C2×C4—24no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—232no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—28no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—24no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—24no—
661C2×C4—24no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—28no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—28no—
672C2×C4—432no—
673C2×C4—416no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—44no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—44no—
689C2×C4—432no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—44no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—44no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—44no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—42no—
719C2×C4—44no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—44no—
723C2×C4—42no—
724C2×C4—44no—
725C2×C4—42no—
726C2×C4—44no—
727C2×C4—42no—
728C2×C4C2×#12314yes—
729C2×C4C2×#12314yes—
730C2×C4#52514yes—
731C2×C4#52514yes—
732C2×C4#52918yes—
733C2×C4#52918yes—
734C2×C4#54718yes—
735C22—24no—
736C22—24no—
737C22—24no—
738C22—28no—
739C22—24no—
740C22—24no—
741C22—24no—
742C22—28no—
743C22—28no—
744C22—28no—
745C22—82no—
746C22—82no—
747C22—82no—
748C22—84no—
749C22—82no—
750C22—82no—
751C22—82no—
752C22—82no—
753C22—84no—
754C22—84no—
755C22—84no—
756C22#244518yes—
757C22C22×#12311yescharacteristic
758C22C2×#52511yescharacteristic
759C22C2×#52511yescharacteristic
760C22C2×#52912yes—
761C22C2×#52912yes—
762C22C2×#53211yescharacteristic
763C22C2×#54011yescharacteristic
764C22#346112yes—
765C22C2×D4211yescharacteristic
766C22C2×#54611yescharacteristic
767C22C2×#54712yes—
768C22C2×#55011yescharacteristic
769C22D4×#4112yes—
770C22#347512yes—
771C22C2×#55911yescharacteristic
772C22#348212yes—
773C22#348611yescharacteristic
774C22#348711yescharacteristic
775C22#349212yes—
776C22#349412yes—
777C22#350712yes—
778C22#351312yes—
779C22#352212yes—
780C4—28no—
781C4—24no—
782C4—42no—
783C4—48no—
784C4—42no—
785C4—42no—
786C4—42no—
787C4—44no—
788C4—44no—
789C4—44no—
790C4—44no—
791C4—84no—
792C4—82no—
793C4—82no—
794C4#285318yescomplemented
795C2—28no—
796C2—162no—
797C2C2×#244511yescharacteristic
798C2#3476312yes—
799C2#3518211yescharacteristic
800C2#3522912yes—
801C2#3610211yescharacteristic
802C2#3610311yescharacteristic
803C2#3611712yes—
804C2#3642211yescharacteristic
805C2#3642611yescharacteristic
806C2#3648712yes—
807C2C2×#285311yescharacteristic
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×#2853C2semidirect
3. C22×C4×C4⋊C4C2semidirect
4. #14912C2semidirect
5. #14912C2semidirect
6. #14793C2semidirect
7. #14785C2semidirect
8. #14706C2semidirect
10. #14141C2semidirect
12. #14130C2semidirect
13. #14022C2semidirect
14. #13981C2semidirect
15. #13904C2semidirect
16. #13884C2semidirect
17. C4×#385C2semidirect
164. #385D4semidirect
794. C4#2853semidirect

Maximal subgroups

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

subgroupindex
C2×#28532
C2×#25012
C22×C4×C4⋊C42
#149122
#147932
#147852
#147062
#146982
#141412
#141372
#141302
#140222
#139812
#139042
#138842
C4×#3852