Finite Group Databasebeta

← #722869

Subgroups — #722869

Order 512.

3076 conjugacy classes of subgroups.

The subgroup lattice has 797 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2580C211yesmaximal, characteristic, complemented
2C2×#2396C211yesmaximal, characteristic, complemented
3C2×Q8×C4⋊C4C211yesmaximal, characteristic, complemented
4C2×#2324C211yesmaximal, characteristic
5#17071C212yesmaximal, complemented
6#16899C212yesmaximal, complemented
7#15309C214yesmaximal, complemented
8#15305C214yesmaximal, complemented
9#15157C212yesmaximal, complemented
10#15134C212yesmaximal, complemented
11#15131C212yesmaximal, complemented
12#14877C212yesmaximal, complemented
13#14340C211yesmaximal, characteristic, complemented
14#14045C212yesmaximal, complemented
15#13998C212yesmaximal
16#13954C211yesmaximal, characteristic, complemented
17#13906C211yesmaximal, characteristic, complemented
18C22×#121C2211yescharacteristic
19C22×C4×Q8C2211yescharacteristic
20C22×C4×Q8C2212yes—
21C22×C4×D4C2211yescharacteristic
22C22×#117C2211yescharacteristic
23#2580—28no—
24#2396—28no—
25C2×#400C2211yescharacteristic
26C2×#399C2212yes—
27C2×#399C2211yescharacteristic
28C2×#398C2212yes—
29C2×#396C2212yes—
30C2×#396C2214yes—
31C2×#396C2214yes—
32C2×#396C2214yes—
33C2×#395C2211yescharacteristic
34C2×#393C2212yes—
35C2×#393C2211yescharacteristic
36Q8×C4⋊C4—28no—
37#2324—28no—
38C2×#390C2211yescharacteristic
39C2×#390C2212yes—
40C2×#390C2212yes—
41C2×#390C2212yes—
42C2×#390C2214yes—
43C2×#389C2212yes—
44C2×#389C2211yescharacteristic
45C2×#389C2212yes—
46C2×#389C2214yes—
47C2×#389C2212yes—
48C2×#389C2212yes—
49C2×#388C2212yes—
50C2×#386C2212yes—
51C2×#385C2212yes—
52C2×#385C2214yes—
53C2×#384C2211yescharacteristic
54C2×#384C2212yes—
55C2×#382C2211yescharacteristic
56C2×#380C2211yescharacteristic
57C2×#380C2212yes—
58C2×#380C2214yes—
59C2×C4×C4⋊C4C2212yes—
60C2×C4×C4⋊C4C2212yes—
61C2×C4×C4⋊C4C2211yescharacteristic
62C2×C4×C4⋊C4C2211yescharacteristic
63C2×C4×C22⋊C4C2212yes—
64#1444C2214yes—
65#1444C2214yes—
66#1441C2212yes—
67#1441C2214yes—
68#1441C2214yes—
69#1441C2212yes—
70#1441C2214yes—
71#1439C2214yes—
72#1439C2212yes—
73#1439C2214yes—
74#1439C2212yes—
75#1439C2212yes—
76#1439C2214yes—
77#1439C2212yes—
78#1439C2214yes—
79#1438C2214yes—
80#1437C2214yes—
81#1436C2214yes—
82C4⋊#95C2212yes—
83C4⋊#95C2212yes—
84C4⋊#95C2212yes—
85C4⋊#95C2212yes—
86C4⋊#95C2214yes—
87C23×Q8C2311yescharacteristic
88C23×D4C2311yescharacteristic
89C23×D4C2312yes—
90C24×C4C2311yescharacteristic
91C24×C4C2312yes—
92C2×#121—24no—
93C2×#121—24no—
94C2×#121Q818yescomplemented
95C2×C4×Q8—24no—
96C2×C4×Q8—28no—
97C2×C4×Q8—24no—
98C2×C4×Q8—48no—
99C2×C4×Q8D418yescomplemented
100C2×C4×D4—24no—
101C2×C4×D4—24no—
102C2×C4×D4—24no—
103C2×#117—24no—
104C2×#117—24no—
105C2×#117—24no—
106C22×C4⋊C4C2312yes—
107C22×C4⋊C4C2311yescharacteristic
108C22×C4⋊C4C2311yescharacteristic
109C22×C4⋊C4C2311yescharacteristic
110C22×C4⋊C4C2312yes—
111C22×C4⋊C4C2312yes—
112C22×C4⋊C4C2312yes—
113C22×C4⋊C4C2312yes—
114C22×C4⋊C4C2314yes—
115C22×C4⋊C4C2312yes—
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2314yes—
119C22×C4⋊C4C2314yes—
120C22×C4⋊C4C2314yes—
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2314yes—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2311yescharacteristic
126C22×C22⋊C4C2314yes—
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2311yescharacteristic
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2311yescharacteristic
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2314yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2314yes—
138C22×C22⋊C4C2314yes—
139C22×C22⋊C4C2314yes—
140C22×C42C2311yescharacteristic
141C22×C42C2312yes—
142C22×C42C2314yes—
143C22×C42C2312yes—
144C22×C42C2312yes—
145C22×C42C2311yescharacteristic
146#400—24no—
147#399—28no—
148#399—24no—
149#398—28no—
150#396—28no—
151#396—48no—
152#396—48no—
153#396—48no—
154#395—24no—
155#393—28no—
156#393—24no—
157#390—24no—
158#390—28no—
159#390—28no—
160#390—48no—
161#390—44no—
162#389—24no—
163#389—28no—
164#389—28no—
165#389—28no—
166#389—216no—
167#389—44no—
168#388—28no—
169#386—28no—
170#385—216no—
171#385—28no—
172#384—28no—
173#384—24no—
174#382—24no—
175#380—24no—
176#380—48no—
177#380—44no—
178C4×C4⋊C4—28no—
179C4×C4⋊C4—28no—
180C4×C4⋊C4—24no—
181C4×C4⋊C4D418yes—
182C4×C22⋊C4—28no—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2311yescharacteristic
186C2×#95C2314yes—
187C2×#95C2312yes—
188C2×#95C2311yescharacteristic
189C2×#95C2312yes—
190C2×#95C2314yes—
191C2×#95C2312yes—
192C2×#95C2314yes—
193C2×#95C2312yes—
194C2×#95C2314yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2312yes—
203C25C2411yescharacteristic
204C25C2412yes—
205C22×Q8—22no—
206C22×Q8—22no—
207C22×Q8—24no—
208C22×Q8—24no—
209C22×Q8C2×D414yes—
210C22×D4—22no—
211C22×D4—22no—
212C22×D4—24no—
213C22×D4—22no—
214C22×D4—22no—
215C22×D4—24no—
216C22×D4—22no—
217C22×D4—22no—
218C22×D4—44no—
219C22×D4—44no—
220C22×D4C2×Q814yes—
221C22×D4C2×Q818yes—
222C23×C4—22no—
223C23×C4—22no—
224C23×C4—22no—
225C23×C4—22no—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—24no—
229C23×C4—24no—
230C23×C4—24no—
231C23×C4—44no—
232C23×C4—44no—
233C23×C4C2×Q814yes—
234C23×C4C2411yescharacteristic
235C23×C4C2414yes—
236C23×C4C2414yes—
237C23×C4C2412yes—
238C23×C4C2411yescharacteristic
239C23×C4C2412yes—
240C23×C4C2412yes—
241C23×C4C2412yes—
242C23×C4C2411yescharacteristic
243C23×C4C2412yes—
244C23×C4C2411yescharacteristic
245C23×C4C2411yescharacteristic
246C23×C4C2412yes—
247C23×C4C2412yes—
248C23×C4C2411yescharacteristic
249#121—232no—
250C4×Q8—232no—
251C4×Q8—432no—
252C4×D4—416no—
253#117—416no—
254C2×C4⋊C4—24no—
255C2×C4⋊C4—22no—
256C2×C4⋊C4—24no—
257C2×C4⋊C4—22no—
258C2×C4⋊C4—22no—
259C2×C4⋊C4—22no—
260C2×C4⋊C4—22no—
261C2×C4⋊C4—22no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—28no—
267C2×C4⋊C4—24no—
268C2×C4⋊C4—24no—
269C2×C4⋊C4—24no—
270C2×C4⋊C4—24no—
271C2×C4⋊C4—24no—
272C2×C4⋊C4—24no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—28no—
278C2×C4⋊C4—24no—
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—28no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—28no—
289C2×C4⋊C4—28no—
290C2×C4⋊C4—28no—
291C2×C4⋊C4—42no—
292C2×C4⋊C4—42no—
293C2×C4⋊C4—44no—
294C2×C4⋊C4—44no—
295C2×C4⋊C4—44no—
296C2×C4⋊C4—44no—
297C2×C4⋊C4—44no—
298C2×C4⋊C4—44no—
299C2×C4⋊C4—44no—
300C2×C4⋊C4—44no—
301C2×C4⋊C4—44no—
302C2×C4⋊C4—44no—
303C2×C4⋊C4—44no—
304C2×C4⋊C4—44no—
305C2×C4⋊C4C2×D418yes—
306C2×C4⋊C4C2×D414yes—
307C2×C4⋊C4C2×D414yes—
308C2×C4⋊C4C2×D414yes—
309C2×C4⋊C4C2×Q814yes—
310C2×C4⋊C4#4114yes—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—22no—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—22no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—28no—
322C2×C22⋊C4—22no—
323C2×C22⋊C4—22no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—28no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—28no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—28no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—28no—
335C2×C22⋊C4—42no—
336C2×C22⋊C4—44no—
337C2×C22⋊C4—44no—
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⋊C4C2×Q818yes—
350C2×C42—24no—
351C2×C42—24no—
352C2×C42—22no—
353C2×C42—22no—
354C2×C42—28no—
355C2×C42—24no—
356C2×C42—22no—
357C2×C42—24no—
358C2×C42—28no—
359C2×C42—24no—
360C2×C42—44no—
361C2×C42—44no—
362C2×C42C2×D418yes—
363C2×C42C2×D418yes—
364C2×C42C2×D414yes—
365C2×C42C2×D414yes—
366C2×C42#4114yes—
367#95—24no—
368#95—24no—
369#95—28no—
370#95—24no—
371#95—22no—
372#95—22no—
373#95—24no—
374#95—24no—
375#95—24no—
376#95—24no—
377#95—28no—
378#95—24no—
379#95—28no—
380#95—28no—
381#95—44no—
382#95—44no—
383#95—44no—
384#95—44no—
385#95—44no—
386#95C2×D418yes—
387C24—21no—
388C24—22no—
389C24—22no—
390C24—21no—
391C24—21no—
392C24—22no—
393C24—22no—
394C24—21no—
395C24—22no—
396C24—24no—
397C24—24no—
398C24—22no—
399C24—21no—
400C24—22no—
401C24—22no—
402C24—24no—
403C24—21no—
404C24—22no—
405C24—24no—
406C24—22no—
407C24C22×Q814yes—
408C24C22×Q812yes—
409C24C2511yescharacteristic
410C2×Q8—28no—
411C2×Q8—28no—
412C2×Q8—216no—
413C2×Q8—28no—
414C2×Q8—216no—
415C2×D4—28no—
416C2×D4—216no—
417C2×D4—28no—
418C2×D4—28no—
419C2×D4—416no—
420C2×D4—44no—
421C2×D4—44no—
422C2×D4—44no—
423C2×D4—44no—
424C2×D4—84no—
425C2×D4—84no—
426C2×D4—88no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—24no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—24no—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—24no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—24no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—28no—
460C22×C4—28no—
461C22×C4—28no—
462C22×C4—22no—
463C22×C4—24no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—24no—
470C22×C4—21no—
471C22×C4—24no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—22no—
479C22×C4—24no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—24no—
484C22×C4—24no—
485C22×C4—24no—
486C22×C4—24no—
487C22×C4—24no—
488C22×C4—24no—
489C22×C4—22no—
490C22×C4—24no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—24no—
498C22×C4—416no—
499C22×C4—44no—
500C22×C4—44no—
501C22×C4—44no—
502C22×C4—44no—
503C22×C4—48no—
504C22×C4—88no—
505C22×C4—84no—
506C22×C4—84no—
507C22×C4C22×D414yes—
508C22×C4C22×D414yes—
509C22×C4C22×D412yes—
510C22×C4C22×D412yes—
511C22×C4C22×D412yes—
512C22×C4C22×D412yes—
513C22×C4C22×D414yes—
514C22×C4C22×D414yes—
515C22×C4C22×D412yes—
516C22×C4C22×D412yes—
517C22×C4C22×Q812yes—
518C22×C4C22×Q814yes—
519C22×C4C22×Q812yes—
520C22×C4C2×#4112yes—
521C22×C4C2×#4112yes—
522C22×C4C2×#4114yes—
523C22×C4C2×#4112yes—
524C22×C4C2×#4112yes—
525C22×C4H(5,𝔽2)14yes—
526C22×C4H(5,𝔽2)14yes—
527C22×C4H(5,𝔽2)12yes—
528C22×C42−1+414yes—
529C22×C42−1+412yes—
530C4⋊C4—216no—
531C4⋊C4—28no—
532C4⋊C4—28no—
533C4⋊C4—48no—
534C4⋊C4—48no—
535C4⋊C4—416no—
536C4⋊C4—48no—
537C4⋊C4—44no—
538C4⋊C4—44no—
539C4⋊C4—44no—
540C4⋊C4—48no—
541C4⋊C4—48no—
542C4⋊C4—48no—
543C4⋊C4—84no—
544C4⋊C4—84no—
545C4⋊C4—88no—
546C4⋊C4—88no—
547C4⋊C4—88no—
548C4⋊C4—88no—
549C4⋊C4C22⋊Q8116yes—
550C22⋊C4—216no—
551C22⋊C4—48no—
552C22⋊C4—44no—
553C22⋊C4—44no—
554C22⋊C4—48no—
555C22⋊C4—48no—
556C22⋊C4—416no—
557C22⋊C4—84no—
558C22⋊C4—88no—
559C22⋊C4—84no—
560C22⋊C4—84no—
561C22⋊C4—88no—
562C22⋊C4—88no—
563C22⋊C4—88no—
564C42—216no—
565C42—48no—
566C42—416no—
567C42—44no—
568C42—48no—
569C42#121116yes—
570C23—24no—
571C23—22no—
572C23—22no—
573C23—24no—
574C23—22no—
575C23—24no—
576C23—24no—
577C23—28no—
578C23—24no—
579C23—28no—
580C23—41no—
581C23—42no—
582C23—42no—
583C23—44no—
584C23—41no—
585C23—42no—
586C23—41no—
587C23—42no—
588C23—41no—
589C23—42no—
590C23—42no—
591C23—41no—
592C23—42no—
593C23—41no—
594C23—42no—
595C23—44no—
596C23—42no—
597C23—44no—
598C23—41no—
599C23—42no—
600C23—42no—
601C23—41no—
602C23—44no—
603C23—42no—
604C23—42no—
605C23—44no—
606C23—44no—
607C23—42no—
608C23—44no—
609C23—42no—
610C23—42no—
611C23—44no—
612C23—42no—
613C23—44no—
614C23—42no—
615C23—44no—
616C23C23×D411yescharacteristic
617C23C23×D411yescharacteristic
618C23C23×Q811yescharacteristic
619C23C22×#4111yescharacteristic
620C23C22×#4111yescharacteristic
621C23C2×H(5,𝔽2)11yescharacteristic
622C23C2×H(5,𝔽2)12yes—
623C23C2×H(5,𝔽2)12yes—
624C23C2×2−1+411yescharacteristic
625C23C2×2−1+412yes—
626C23#58512yes—
627Q8—232no—
628D4—416no—
629D4—816no—
630C2×C4—24no—
631C2×C4—24no—
632C2×C4—24no—
633C2×C4—24no—
634C2×C4—22no—
635C2×C4—24no—
636C2×C4—22no—
637C2×C4—24no—
638C2×C4—24no—
639C2×C4—24no—
640C2×C4—24no—
641C2×C4—24no—
642C2×C4—22no—
643C2×C4—24no—
644C2×C4—22no—
645C2×C4—28no—
646C2×C4—24no—
647C2×C4—28no—
648C2×C4—24no—
649C2×C4—22no—
650C2×C4—24no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—41no—
661C2×C4—42no—
662C2×C4—41no—
663C2×C4—42no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—44no—
672C2×C4—44no—
673C2×C4—42no—
674C2×C4—416no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—44no—
680C2×C4—42no—
681C2×C4—44no—
682C2×C4—42no—
683C2×C4—44no—
684C2×C4—44no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—44no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—44no—
691C2×C4—42no—
692C2×C4—41no—
693C2×C4—42no—
694C2×C4—44no—
695C2×C4—41no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—44no—
699C2×C4—42no—
700C2×C4—44no—
701C2×C4—44no—
702C2×C4—42no—
703C2×C4—44no—
704C2×C4—42no—
705C2×C4—44no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—42no—
710C2×C4—44no—
711C2×C4—816no—
712C2×C4C2×#12114yes—
713C2×C4C2×#12114yes—
714C2×C4C2×#12114yes—
715C2×C4C2×C22⋊Q818yes—
716C2×C4C2×C22⋊Q814yes—
717C2×C4#53718yes—
718C2×C4#53714yes—
719C2×C4D4×Q814yes—
720C2×C4#55014yes—
721C2×C4#55414yes—
722C2×C4#55614yes—
723C22—44no—
724C22—48no—
725C22—42no—
726C22—44no—
727C22—42no—
728C22—44no—
729C22—44no—
730C22—42no—
731C22—44no—
732C22—48no—
733C22—81no—
734C22—82no—
735C22—82no—
736C22—84no—
737C22—81no—
738C22—82no—
739C22—81no—
740C22—82no—
741C22—82no—
742C22—81no—
743C22—82no—
744C22—84no—
745C22C22×#12111yescharacteristic
746C22C22×C22⋊Q811yescharacteristic
747C22C2×#53711yescharacteristic
748C22C2×#53712yes—
749C22C2×D4×Q811yescharacteristic
750C22C2×#55011yescharacteristic
751C22C2×#55411yescharacteristic
752C22C2×#55611yescharacteristic
753C22#348411yescharacteristic
754C22#348611yescharacteristic
755C22#348812yes—
756C22#349212yes—
757C22#349811yescharacteristic
758C22#350011yescharacteristic
759C22#350112yes—
760C22#350312yes—
761C22#350612yes—
762C22#351412yes—
763C22#352212yes—
764C22#354312yes—
765C22#354812yes—
766C22#355412yes—
767C22#355512yes—
768C4—28no—
769C4—24no—
770C4—28no—
771C4—24no—
772C4—42no—
773C4—44no—
774C4—44no—
775C4—44no—
776C4—81no—
777C4—84no—
778C4—81no—
779C4—82no—
780C4—82no—
781C4—84no—
782C4#253818yes—
783C2—82no—
784C2—84no—
785C2C2×#253811yescharacteristic
786C2#3522311yescharacteristic
787C2#3553311yescharacteristic
788C2#3570211yescharacteristic
789C2#3574811yescharacteristic
790C2#3913712yes—
791C2#3959812yes—
792C2#4242511yescharacteristic
793C2#4279511yescharacteristic
794C2#4490812yes—
795C2#4491112yes—
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×#2580C2semidirect
2. C2×#2396C2semidirect
3. C2×Q8×C4⋊C4C2semidirect
5. #17071C2semidirect
6. #16899C2semidirect
7. #15309C2semidirect
8. #15305C2semidirect
9. #15157C2semidirect
10. #15134C2semidirect
11. #15131C2semidirect
12. #14877C2semidirect
13. #14340C2semidirect
14. #14045C2semidirect
16. #13954C2semidirect
17. #13906C2semidirect
94. C2×#121Q8semidirect
99. C2×C4×Q8D4semidirect

Maximal subgroups

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

subgroupindex
C2×#25802
C2×#23962
C2×Q8×C4⋊C42
C2×#23242
#170712
#168992
#153092
#153052
#151572
#151342
#151312
#148772
#143402
#140452
#139982
#139542
#139062