Finite Group Databasebeta

← #759339

Subgroups — #759339

Order 512.

4802 conjugacy classes of subgroups.

The subgroup lattice has 813 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2440C212yesmaximal, complemented
2C2×#2437C212yesmaximal
3C22×#380C212yesmaximal
4#16305C212yesmaximal, complemented
5#16303C212yesmaximal, complemented
6#15135C211yesmaximal, characteristic, complemented
7#15131C212yesmaximal, complemented
8#15125C211yesmaximal, characteristic, complemented
9#14758C214yesmaximal, complemented
10#14736C214yesmaximal, complemented
11#14130C212yesmaximal, complemented
12#14127C212yesmaximal
13#13907C212yesmaximal, complemented
14#13880C212yesmaximal, complemented
15C4×#379C211yesmaximal, characteristic
16C25×C4C2211yescharacteristic
17C22×C4⋊Q8C2211yescharacteristic, complemented
18C22×C22⋊Q8C2214yes—
19C23×C4⋊C4C2212yes—
20C23×C4⋊C4C2212yes—
21C23×C22⋊C4C2214yes—
22#2440—216no—
23#2437—216no—
24C2×#399C2212yes—
25C2×#398C2214yescomplemented
26C2×#396C2214yes—
27C2×#395C2214yescomplemented
28C2×#393C2212yes—
29C2×#389C2212yescomplemented
30C2×#389C2212yescomplemented
31C2×#389C2212yescomplemented
32C2×#385C2214yes—
33C2×#385C2214yes—
34C2×#385C2214yes—
35C2×#385C2214yes—
36C2×#384C2212yescomplemented
37C2×#384C2211yescharacteristic, complemented
38C2×#380—216no—
39C2×#380C2212yes—
40C2×#380C2212yes—
41C2×#380C2212yes—
42C2×#380C2214yes—
43C2×#380C2214yes—
44C2×#380C2214yes—
45C2×#380C2212yes—
46C2×#379C2211yescharacteristic
47C2×#379C2211yescharacteristic
48C2×C4×C22⋊C4C2212yes—
49C2×C4×C22⋊C4C2212yes—
50C2×C4×C22⋊C4C2211yescharacteristic
51C2×C4×C22⋊C4C2211yescharacteristic
52C22×#95C2214yes—
53#1446C2212yescomplemented
54#1445C2212yescomplemented
55#1444C2212yescomplemented
56#1444C2214yescomplemented
57#1444C2214yescomplemented
58#1444C2214yescomplemented
59#1442C2212yescomplemented
60#1442C2214yescomplemented
61#1441C2214yescomplemented
62#1441C2214yescomplemented
63#1441C2214yescomplemented
64#1441C2214yescomplemented
65#1439C2212yes—
66#1439C2214yes—
67#1439C2212yes—
68C4⋊#95C2212yescomplemented
69C4⋊#95C2211yescharacteristic, complemented
70C4⋊#95C2212yescomplemented
71C4⋊#95C2211yescharacteristic, complemented
72C22⋊#95C2214yes—
73C22⋊#95C2214yes—
74C22⋊#95C2212yes—
75C22⋊#95C2212yes—
76C22⋊#95C2211yescharacteristic
77C22⋊#95C2211yescharacteristic
78C26C2311yescharacteristic
79C23×Q8C2312yes—
80C24×C4—28no—
81C24×C4—28no—
82C24×C4—42no—
83C24×C4—42no—
84C24×C4Q818yescomplemented
85C24×C4C2311yescharacteristic
86C24×C4C2314yes—
87C24×C4C2314yes—
88C24×C4C2312yes—
89C24×C4C2311yescharacteristic
90C24×C4C2312yes—
91C2×C4⋊Q8—28no—
92C2×C4⋊Q8—42no—
93C2×C22⋊Q8—216no—
94C2×C22⋊Q8—216no—
95C2×C22⋊Q8—48no—
96C22×C4⋊C4—28no—
97C22×C4⋊C4—28no—
98C22×C4⋊C4—28no—
99C22×C4⋊C4—28no—
100C22×C4⋊C4—44no—
101C22×C4⋊C4—44no—
102C22×C4⋊C4C2312yes—
103C22×C4⋊C4C2312yes—
104C22×C4⋊C4C2314yes—
105C22×C4⋊C4C2314yes—
106C22×C4⋊C4C2314yes—
107C22×C4⋊C4C2314yes—
108C22×C4⋊C4C2312yes—
109C22×C4⋊C4C2314yes—
110C22×C4⋊C4C2312yes—
111C22×C4⋊C4C2312yes—
112C22×C4⋊C4C2314yes—
113C22×C4⋊C4C2314yes—
114C22×C4⋊C4C2312yes—
115C22×C4⋊C4C2312yes—
116C22×C22⋊C4—216no—
117C22×C22⋊C4—216no—
118C22×C22⋊C4—48no—
119C22×C22⋊C4C2314yes—
120C22×C22⋊C4C2314yes—
121C22×C22⋊C4C2314yes—
122C22×C22⋊C4C2314yes—
123C22×C22⋊C4C2312yes—
124C22×C22⋊C4C2312yes—
125C22×C22⋊C4C2312yes—
126C22×C22⋊C4C2312yes—
127C22×C22⋊C4C2311yescharacteristic
128C22×C22⋊C4C2311yescharacteristic
129C22×C22⋊C4C2311yescharacteristic
130C22×C22⋊C4C2311yescharacteristic
131C22×C42C2311yescharacteristic
132C22×C42C2311yescharacteristic
133C22×C42C2312yes—
134#399—28no—
135#398—216no—
136#396—216no—
137#395—216no—
138#393—28no—
139#389—28no—
140#389—28no—
141#389—44no—
142#385—216no—
143#385—216no—
144#385—216no—
145#385—48no—
146#384—28no—
147#384—42no—
148#380—28no—
149#380—28no—
150#380—28no—
151#380—216no—
152#380—216no—
153#380—216no—
154#380D4116yes—
155#379D418yes—
156#379Q818yescomplemented
157C4×C22⋊C4—28no—
158C4×C22⋊C4—28no—
159C4×C22⋊C4—42no—
160C4×C22⋊C4—42no—
161C2×#95—216no—
162C2×#95C2312yes—
163C2×#95C2314yes—
164C2×#95C2312yes—
165C2×#95C2314yes—
166C2×#95C2314yes—
167C2×#95C2312yes—
168C2×#95C2314yes—
169C2×#95C2312yes—
170C2×#95C2312yes—
171C2×#95C2312yes—
172C2×#95C2314yes—
173C2×#95C2314yes—
174C2×#95C2314yes—
175C2×#95C2312yes—
176C2×#95C2312yes—
177C2×#95C2314yes—
178C2×#95C2312yes—
179C2×#95C2311yescharacteristic
180C2×#95C2311yescharacteristic
181C2×#95C2314yes—
182C2×#95C2314yes—
183C2×#95C2314yes—
184C25—24no—
185C25—24no—
186C25—24no—
187C25—24no—
188C25—41no—
189C25—41no—
190C25—41no—
191C25—41no—
192C25C2×D414yes—
193C25C2×Q814yes—
194C25C2×Q814yes—
195C25C2411yescharacteristic
196C25C2412yes—
197C22×Q8—24no—
198C22×Q8—28no—
199C22×Q8—44no—
200C22×Q8—42no—
201C22×Q8—42no—
202C23×C4—24no—
203C23×C4—24no—
204C23×C4—24no—
205C23×C4—24no—
206C23×C4—24no—
207C23×C4—24no—
208C23×C4—264no—
209C23×C4—24no—
210C23×C4—24no—
211C23×C4—24no—
212C23×C4—24no—
213C23×C4—24no—
214C23×C4—24no—
215C23×C4—22no—
216C23×C4—22no—
217C23×C4—28no—
218C23×C4—28no—
219C23×C4—28no—
220C23×C4—28no—
221C23×C4—28no—
222C23×C4—28no—
223C23×C4—28no—
224C23×C4—28no—
225C23×C4—416no—
226C23×C4—41no—
227C23×C4—41no—
228C23×C4—42no—
229C23×C4—42no—
230C23×C4—416no—
231C23×C4—432no—
232C23×C4—416no—
233C23×C4—44no—
234C23×C4—44no—
235C23×C4—44no—
236C23×C4—44no—
237C23×C4—44no—
238C23×C4—44no—
239C23×C4C2×D418yes—
240C23×C4C2×Q814yes—
241C23×C4C2×Q818yes—
242C23×C4C2×Q814yes—
243C23×C4C2×Q818yes—
244C23×C4#4118yes—
245C23×C4C2414yes—
246C23×C4C2414yes—
247C23×C4C2412yes—
248C23×C4C2411yescharacteristic
249C23×C4C2411yescharacteristic
250C23×C4C2414yes—
251C23×C4C2414yes—
252C23×C4C2411yescharacteristic
253C23×C4C2412yes—
254C23×C4C2411yescharacteristic
255C23×C4C2411yescharacteristic
256C23×C4C2412yes—
257C23×C4C2411yescharacteristic
258C4⋊Q8—416no—
259C22⋊Q8—464no—
260C2×C4⋊C4—24no—
261C2×C4⋊C4—24no—
262C2×C4⋊C4—24no—
263C2×C4⋊C4—24no—
264C2×C4⋊C4—28no—
265C2×C4⋊C4—28no—
266C2×C4⋊C4—24no—
267C2×C4⋊C4—24no—
268C2×C4⋊C4—24no—
269C2×C4⋊C4—28no—
270C2×C4⋊C4—28no—
271C2×C4⋊C4—28no—
272C2×C4⋊C4—28no—
273C2×C4⋊C4—28no—
274C2×C4⋊C4—28no—
275C2×C4⋊C4—28no—
276C2×C4⋊C4—28no—
277C2×C4⋊C4—28no—
278C2×C4⋊C4—24no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—28no—
282C2×C4⋊C4—28no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—432no—
285C2×C4⋊C4—432no—
286C2×C4⋊C4—44no—
287C2×C4⋊C4—44no—
288C2×C4⋊C4—44no—
289C2×C4⋊C4—44no—
290C2×C4⋊C4—44no—
291C2×C4⋊C4—42no—
292C2×C4⋊C4—44no—
293C2×C4⋊C4—44no—
294C2×C4⋊C4—42no—
295C2×C4⋊C4—42no—
296C2×C4⋊C4—42no—
297C2×C4⋊C4—44no—
298C2×C4⋊C4—44no—
299C2×C4⋊C4—44no—
300C2×C4⋊C4C2×D418yes—
301C2×C4⋊C4C2×D418yes—
302C2×C22⋊C4—28no—
303C2×C22⋊C4—24no—
304C2×C22⋊C4—24no—
305C2×C22⋊C4—24no—
306C2×C22⋊C4—24no—
307C2×C22⋊C4—28no—
308C2×C22⋊C4—24no—
309C2×C22⋊C4—24no—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—28no—
313C2×C22⋊C4—28no—
314C2×C22⋊C4—28no—
315C2×C22⋊C4—28no—
316C2×C22⋊C4—28no—
317C2×C22⋊C4—28no—
318C2×C22⋊C4—28no—
319C2×C22⋊C4—464no—
320C2×C22⋊C4—44no—
321C2×C22⋊C4—44no—
322C2×C22⋊C4—41no—
323C2×C22⋊C4—41no—
324C2×C22⋊C4—41no—
325C2×C22⋊C4—41no—
326C2×C22⋊C4—41no—
327C2×C22⋊C4—41no—
328C2×C22⋊C4—41no—
329C2×C22⋊C4—41no—
330C2×C22⋊C4C2×D4116yes—
331C2×C22⋊C4C2×D418yes—
332C2×C22⋊C4C2×D418yes—
333C2×C22⋊C4C2×D414yes—
334C2×C22⋊C4C2×D414yes—
335C2×C22⋊C4C2×Q818yes—
336C2×C22⋊C4C2×Q818yes—
337C2×C22⋊C4C2×Q814yes—
338C2×C22⋊C4C2×Q814yes—
339C2×C42—24no—
340C2×C42—24no—
341C2×C42—24no—
342C2×C42—24no—
343C2×C42—22no—
344C2×C42—22no—
345C2×C42—24no—
346#95—28no—
347#95—28no—
348#95—28no—
349#95—24no—
350#95—24no—
351#95—24no—
352#95—28no—
353#95—28no—
354#95—24no—
355#95—28no—
356#95—28no—
357#95—24no—
358#95—24no—
359#95—42no—
360#95—42no—
361#95—42no—
362#95—41no—
363#95—41no—
364#95—44no—
365#95—44no—
366#95—44no—
367#95C2×D4116yes—
368C24—22no—
369C24—22no—
370C24—22no—
371C24—22no—
372C24—22no—
373C24—22no—
374C24—22no—
375C24—22no—
376C24—216no—
377C24—216no—
378C24—216no—
379C24—216no—
380C24—216no—
381C24—216no—
382C24—22no—
383C24—22no—
384C24—22no—
385C24—21no—
386C24—21no—
387C24—22no—
388C24—21no—
389C24—21no—
390C24—44no—
391C24—44no—
392C24—44no—
393C24—44no—
394C24—44no—
395C24—44no—
396C24—44no—
397C24—48no—
398C24—44no—
399C24—48no—
400C24—48no—
401C24—48no—
402C24—48no—
403C24—48no—
404C24—44no—
405C24—44no—
406C24C4⋊Q8116yescomplemented
407C24C22×D412yes—
408C24C22×D414yes—
409C24C22×D414yes—
410C24C22×Q812yes—
411C24C22×Q812yes—
412C24C22×Q814yes—
413C24C22×Q814yes—
414C24C2×#4114yes—
415C24H(5,𝔽2)14yes—
416C242−1+414yes—
417C24C2511yescharacteristic
418C2×Q8—416no—
419C2×Q8—48no—
420C2×Q8—88no—
421C2×Q8—84no—
422C2×Q8—84no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—216no—
428C22×C4—216no—
429C22×C4—216no—
430C22×C4—216no—
431C22×C4—216no—
432C22×C4—216no—
433C22×C4—216no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—24no—
440C22×C4—24no—
441C22×C4—24no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—24no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—24no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—24no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—24no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—24no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—24no—
478C22×C4—216no—
479C22×C4—216no—
480C22×C4—216no—
481C22×C4—28no—
482C22×C4—24no—
483C22×C4—24no—
484C22×C4—24no—
485C22×C4—24no—
486C22×C4—24no—
487C22×C4—24no—
488C22×C4—24no—
489C22×C4—24no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—44no—
497C22×C4—48no—
498C22×C4—44no—
499C22×C4—48no—
500C22×C4—44no—
501C22×C4—4128no—
502C22×C4—48no—
503C22×C4—48no—
504C22×C4—48no—
505C22×C4—48no—
506C22×C4—416no—
507C22×C4—416no—
508C22×C4—416no—
509C22×C4—416no—
510C22×C4—416no—
511C22×C4—416no—
512C22×C4—44no—
513C22×C4—48no—
514C22×C4—44no—
515C22×C4—416no—
516C22×C4—416no—
517C22×C4—88no—
518C22×C4—88no—
519C22×C4—88no—
520C22×C4—88no—
521C22×C4—88no—
522C22×C4—88no—
523C22×C4C22⋊Q8132yescomplemented
524C22×C4C22×D412yes—
525C22×C4C22×D418yes—
526C22×C4C22×D414yes—
527C22×C4C22×D412yes—
528C22×C4C22×D418yes—
529C22×C4C22×D414yes—
530C22×C4C22×D414yes—
531C22×C4C22×Q812yes—
532C22×C4C22×Q814yes—
533C22×C4C22×Q812yes—
534C22×C4C22×Q812yes—
535C22×C4C22×Q814yes—
536C22×C4C22×Q812yes—
537C22×C4C2×#4114yes—
538C22×C4C2×#4114yes—
539C22×C4H(5,𝔽2)12yes—
540C22×C4H(5,𝔽2)12yes—
541C4⋊C4—216no—
542C4⋊C4—216no—
543C4⋊C4—416no—
544C4⋊C4—416no—
545C4⋊C4—416no—
546C4⋊C4—416no—
547C4⋊C4—416no—
548C4⋊C4—48no—
549C4⋊C4—48no—
550C4⋊C4—48no—
551C4⋊C4—88no—
552C4⋊C4—88no—
553C4⋊C4—84no—
554C4⋊C4—84no—
555C22⋊C4—232no—
556C22⋊C4—216no—
557C22⋊C4—216no—
558C22⋊C4—216no—
559C22⋊C4—216no—
560C22⋊C4—44no—
561C22⋊C4—44no—
562C22⋊C4—44no—
563C22⋊C4—44no—
564C22⋊C4—416no—
565C22⋊C4—416no—
566C22⋊C4—416no—
567C42—44no—
568C42—48no—
569C42—44no—
570C23—24no—
571C23—24no—
572C23—24no—
573C23—24no—
574C23—24no—
575C23—24no—
576C23—24no—
577C23—24no—
578C23—24no—
579C23—24no—
580C23—24no—
581C23—24no—
582C23—24no—
583C23—24no—
584C23—24no—
585C23—24no—
586C23—24no—
587C23—24no—
588C23—24no—
589C23—24no—
590C23—24no—
591C23—24no—
592C23—24no—
593C23—24no—
594C23—24no—
595C23—24no—
596C23—24no—
597C23—24no—
598C23—24no—
599C23—22no—
600C23—24no—
601C23—22no—
602C23—24no—
603C23—264no—
604C23—24no—
605C23—24no—
606C23—24no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—416no—
612C23—416no—
613C23—416no—
614C23—416no—
615C23—416no—
616C23—416no—
617C23—416no—
618C23—432no—
619C23—432no—
620C23—432no—
621C23—41no—
622C23—42no—
623C23—41no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—41no—
630C23—41no—
631C23C2×C22⋊Q818yes—
632C23C2×C4⋊Q814yes—
633C23C2×C4⋊Q818yes—
634C23#54418yes—
635C23D4218yes—
636C23#54718yes—
637C23D4×Q818yes—
638C23#55418yes—
639C23C23×D412yes—
640C23C23×D411yescharacteristic
641C23C23×Q811yescharacteristic
642C23C23×Q811yescharacteristic
643C23C22×#4112yes—
644C23C2×H(5,𝔽2)11yescharacteristic
645C23C2×H(5,𝔽2)11yescharacteristic
646C23C2×H(5,𝔽2)12yes—
647C23C2×2−1+412yes—
648C23#58511yescharacteristic
649C23#58511yescharacteristic
650Q8—816no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—264no—
658C2×C4—24no—
659C2×C4—22no—
660C2×C4—28no—
661C2×C4—28no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—28no—
665C2×C4—28no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—28no—
673C2×C4—28no—
674C2×C4—22no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—24no—
680C2×C4—416no—
681C2×C4—432no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—44no—
685C2×C4—41no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—44no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—42no—
694C2×C4—44no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—44no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—44no—
704C2×C4—44no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—44no—
708C2×C4—41no—
709C2×C4—44no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—416no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—44no—
721C2×C4—44no—
722C2×C4—44no—
723C2×C4—44no—
724C2×C4—44no—
725C2×C4—44no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—832no—
729C2×C4—832no—
730C2×C4C2×C22⋊Q818yes—
731C2×C4C2×C22⋊Q818yes—
732C2×C4#54314yes—
733C2×C4D4214yes—
734C2×C4#54618yes—
735C2×C4#55114yes—
736C22—28no—
737C22—28no—
738C22—28no—
739C22—28no—
740C22—28no—
741C22—28no—
742C22—28no—
743C22—28no—
744C22—28no—
745C22—28no—
746C22—28no—
747C22—28no—
748C22—28no—
749C22—28no—
750C22—28no—
751C22—24no—
752C22—464no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—44no—
760C22—44no—
761C22—44no—
762C22#2440116yescomplemented
763C22C22×C22⋊Q812yes—
764C22C22×C4⋊Q811yescharacteristic
765C22C2×#54311yescharacteristic
766C22C2×#54412yes—
767C22#345811yescharacteristic
768C22C2×D4211yescharacteristic
769C22C2×D4212yes—
770C22C2×#54612yes—
771C22C2×#54712yes—
772C22C2×D4×Q812yes—
773C22C2×#55111yescharacteristic
774C22C2×#55412yes—
775C22#348812yes—
776C22#348912yes—
777C22#349412yes—
778C22#349512yes—
779C22#349611yescharacteristic
780C22#349611yescharacteristic
781C22#350111yescharacteristic
782C22#350111yescharacteristic
783C22#353612yes—
784C22#353711yescharacteristic
785C22#353811yescharacteristic
786C4—28no—
787C4—42no—
788C4—42no—
789C4—42no—
790C4—48no—
791C4—42no—
792C4—42no—
793C4—44no—
794C4—48no—
795C4—44no—
796C4—84no—
797C4—84no—
798C4#243718yescomplemented
799C2—216no—
800C2—44no—
801C2C2×#243711yescharacteristic
802C2C2×#244012yes—
803C2#3500211yescharacteristic
804C2#3525312yes—
805C2#3747711yescharacteristic
806C2#5899711yescharacteristic
807C2#5899811yescharacteristic
808C2#5901512yes—
809C2#5901612yes—
810C2#5919811yescharacteristic
811C2#5919911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC26C23
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×#2440C2semidirect
4. #16305C2semidirect
5. #16303C2semidirect
6. #15135C2semidirect
7. #15131C2semidirect
8. #15125C2semidirect
9. #14758C2semidirect
10. #14736C2semidirect
11. #14130C2semidirect
13. #13907C2semidirect
14. #13880C2semidirect
17. C22×C4⋊Q8C22semidirect
25. C2×#398C22semidirect
27. C2×#395C22semidirect
29. C2×#389C22semidirect
30. C2×#389C22semidirect
31. C2×#389C22semidirect
36. C2×#384C22semidirect
37. C2×#384C22semidirect
53. #1446C22semidirect
54. #1445C22semidirect
55. #1444C22semidirect
56. #1444C22semidirect
57. #1444C22semidirect
58. #1444C22semidirect
59. #1442C22semidirect
60. #1442C22semidirect
61. #1441C22semidirect
62. #1441C22semidirect
63. #1441C22semidirect
64. #1441C22semidirect
68. C4⋊#95C22semidirect
69. C4⋊#95C22semidirect
70. C4⋊#95C22semidirect
71. C4⋊#95C22semidirect
84. C24×C4Q8semidirect
156. #379Q8semidirect
406. C24C4⋊Q8semidirect
523. C22×C4C22⋊Q8semidirect
762. C22#2440semidirect
798. C4#2437semidirect

Maximal subgroups

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

subgroupindex
C2×#24402
C2×#24372
C22×#3802
#163052
#163032
#151352
#151312
#151252
#147582
#147362
#141302
#141272
#139072
#138802
C4×#3792