Finite Group Databasebeta

← #626840

Subgroups — #626840

Order 512.

4506 conjugacy classes of subgroups.

The subgroup lattice has 801 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#543C211yesmaximal, characteristic
2C2×#2857C211yesmaximal, characteristic, complemented
3C2×#2659C211yesmaximal, characteristic, complemented
4C2×#2626C211yesmaximal, characteristic
5#15671C212yesmaximal, complemented
6#15614C214yesmaximal, complemented
7#15466C212yesmaximal, complemented
8#15430C212yesmaximal, complemented
9#15276C214yesmaximal, complemented
10#15265C212yesmaximal, complemented
11#14758C214yesmaximal, complemented
12#14702C211yesmaximal, characteristic, complemented
13#14281C211yesmaximal, characteristic, complemented
14#13877C214yesmaximal
15C2×#1437C211yesmaximal, characteristic
16C2×#543—28no—
17C2×#543—28no—
18C2×#543—28no—
19C22×C4⋊Q8C2211yescharacteristic, complemented
20C22×C22⋊Q8C2211yescharacteristic
21C22×C22⋊Q8C2212yes—
22C22×C22⋊Q8C2212yes—
23C22×C22⋊Q8C2212yes—
24C22×C22⋊Q8C2212yes—
25C22×C22⋊Q8C2212yes—
26C22×C22⋊Q8C2211yescharacteristic
27C22×C22⋊Q8C2211yescharacteristic
28C23×C22⋊C4C2212yes—
29C23×C22⋊C4C2211yescharacteristic
30C23×C22⋊C4C2212yes—
31C23×C42C2211yescharacteristic
32#2857—28no—
33#2659—28no—
34#2626—28no—
35C2×#399C2212yes—
36C2×#398C2212yescomplemented
37C2×#398C2212yescomplemented
38C2×#396C2214yes—
39C2×#395C2212yescomplemented
40C2×#395C2212yescomplemented
41C2×#395C2214yescomplemented
42C2×#393C2212yes—
43C2×#391C2211yescharacteristic, complemented
44C2×#391C2211yescharacteristic, complemented
45C2×#391C2212yescomplemented
46C2×#389C2214yescomplemented
47C2×#385C2212yes—
48C2×#385C2214yes—
49C2×#385C2214yes—
50C2×#384C2211yescharacteristic, complemented
51C2×#380C2214yes—
52C2×#380C2214yes—
53C2×#380C2211yescharacteristic
54C2×#379C2212yes—
55C22×#95C2211yescharacteristic
56C22×#95C2212yes—
57#1446C2214yescomplemented
58#1446C2212yescomplemented
59#1445C2212yescomplemented
60#1444C2214yescomplemented
61#1444C2214yescomplemented
62#1444C2214yescomplemented
63#1441C2214yescomplemented
64#1441C2214yescomplemented
65#1441C2214yescomplemented
66#1441C2214yescomplemented
67#1439C2214yes—
68#1439C2214yes—
69#1439C2214yes—
70#1439C2214yes—
71#1437C2212yes—
72#1437C2212yes—
73#1437C2214yes—
74#1436C2212yescomplemented
75#1436C2212yescomplemented
76C4⋊#95C2212yescomplemented
77C22⋊#95C2214yes—
78C22⋊#95C2214yes—
79C22⋊#95C2214yes—
80C22⋊#95C2214yes—
81C26C2311yescharacteristic
82C23×Q8C2311yescharacteristic
83C23×Q8C2312yes—
84C23×Q8C2311yescharacteristic
85C23×Q8C2311yescharacteristic
86C24×C4C2312yes—
87C24×C4C2312yes—
88C24×C4C2312yes—
89C24×C4C2311yescharacteristic
90C24×C4C2312yes—
91C24×C4C2311yescharacteristic
92#543—2128no—
93C2×C4⋊Q8—24no—
94C2×C4⋊Q8—44no—
95C2×C22⋊Q8—28no—
96C2×C22⋊Q8—28no—
97C2×C22⋊Q8—28no—
98C2×C22⋊Q8—24no—
99C2×C22⋊Q8—24no—
100C2×C22⋊Q8—24no—
101C2×C22⋊Q8—24no—
102C2×C22⋊Q8—24no—
103C2×C22⋊Q8—24no—
104C2×C22⋊Q8—24no—
105C2×C22⋊Q8—28no—
106C2×C22⋊Q8—28no—
107C2×C22⋊Q8—28no—
108C2×C22⋊Q8—28no—
109C2×C22⋊Q8—28no—
110C2×C22⋊Q8—28no—
111C2×C22⋊Q8—28no—
112C2×C22⋊Q8—28no—
113C2×C22⋊Q8—28no—
114C2×C22⋊Q8—28no—
115C2×C22⋊Q8—28no—
116C2×C22⋊Q8—28no—
117C2×C22⋊Q8D418yes—
118C2×C22⋊Q8D418yes—
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2314yes—
125C22×C4⋊C4C2314yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2314yes—
131C22×C4⋊C4C2314yes—
132C22×C4⋊C4C2314yes—
133C22×C4⋊C4C2312yes—
134C22×C22⋊C4—28no—
135C22×C22⋊C4—24no—
136C22×C22⋊C4—24no—
137C22×C22⋊C4—28no—
138C22×C22⋊C4—28no—
139C22×C22⋊C4—44no—
140C22×C22⋊C4—44no—
141C22×C22⋊C4D418yes—
142C22×C22⋊C4Q8116yescomplemented
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2314yes—
152C22×C22⋊C4C2314yes—
153C22×C22⋊C4C2314yes—
154C22×C22⋊C4C2314yes—
155C22×C42—24no—
156C22×C42—44no—
157C22×C42C2311yescharacteristic
158C22×C42C2312yes—
159C22×C42C2311yescharacteristic
160#399—28no—
161#398—28no—
162#398—28no—
163#396—216no—
164#395—28no—
165#395—28no—
166#395—48no—
167#393—28no—
168#391—24no—
169#391—24no—
170#391—44no—
171#389—216no—
172#385—28no—
173#385—48no—
174#385—48no—
175#384—24no—
176#380—24no—
177#380—216no—
178#380—216no—
179#379—28no—
180C2×#95—24no—
181C2×#95—44no—
182C2×#95C2314yes—
183C2×#95C2312yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C2×#95C2314yes—
191C2×#95C2314yes—
192C2×#95C2314yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C25—22no—
201C25—22no—
202C25—24no—
203C25—42no—
204C25—42no—
205C25—42no—
206C25—42no—
207C25C2×D414yes—
208C25C2×Q818yes—
209C25C2412yes—
210C25C2411yescharacteristic
211C22×Q8—24no—
212C22×Q8—24no—
213C22×Q8—24no—
214C22×Q8—22no—
215C22×Q8—22no—
216C22×Q8—22no—
217C22×Q8—22no—
218C22×Q8—22no—
219C22×Q8—22no—
220C22×Q8—22no—
221C22×Q8—42no—
222C22×Q8—42no—
223C22×Q8—42no—
224C22×Q8—42no—
225C22×Q8—42no—
226C22×Q8—42no—
227C22×Q8—44no—
228C22×Q8—44no—
229C22×Q8C2×D414yes—
230C22×Q8C2×D414yes—
231C23×C4—24no—
232C23×C4—24no—
233C23×C4—24no—
234C23×C4—24no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—24no—
238C23×C4—24no—
239C23×C4—24no—
240C23×C4—24no—
241C23×C4—24no—
242C23×C4—24no—
243C23×C4—24no—
244C23×C4—24no—
245C23×C4—42no—
246C23×C4—42no—
247C23×C4—42no—
248C23×C4—42no—
249C23×C4—42no—
250C23×C4—42no—
251C23×C4—42no—
252C23×C4—42no—
253C23×C4—42no—
254C23×C4—42no—
255C23×C4—44no—
256C23×C4—44no—
257C23×C4—44no—
258C23×C4—44no—
259C23×C4C2×D414yes—
260C23×C4C2×D414yes—
261C23×C4C2×D414yes—
262C23×C4C2×D414yes—
263C23×C4C2×Q818yes—
264C23×C4C2×Q818yes—
265C23×C4C2412yes—
266C23×C4C2412yes—
267C23×C4C2414yes—
268C23×C4C2412yes—
269C23×C4C2412yes—
270C23×C4C2412yes—
271C23×C4C2412yes—
272C23×C4C2412yes—
273C23×C4C2414yes—
274C23×C4C2412yes—
275C23×C4C2411yescharacteristic
276C23×C4C2411yescharacteristic
277C23×C4C2412yes—
278C4⋊Q8—416no—
279C22⋊Q8—264no—
280C22⋊Q8—264no—
281C22⋊Q8—264no—
282C22⋊Q8—264no—
283C22⋊Q8—264no—
284C22⋊Q8—232no—
285C22⋊Q8—232no—
286C22⋊Q8—416no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—28no—
311C2×C4⋊C4—28no—
312C2×C4⋊C4—28no—
313C2×C4⋊C4—28no—
314C2×C4⋊C4—28no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—28no—
317C2×C4⋊C4—28no—
318C2×C4⋊C4—44no—
319C2×C4⋊C4—44no—
320C2×C4⋊C4—42no—
321C2×C4⋊C4—44no—
322C2×C4⋊C4—44no—
323C2×C4⋊C4—44no—
324C2×C4⋊C4—44no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—44no—
327C2×C4⋊C4—44no—
328C2×C4⋊C4C2×D414yes—
329C2×C4⋊C4C2×D418yes—
330C2×C4⋊C4C2×D418yes—
331C2×C4⋊C4C2×D414yes—
332C2×C22⋊C4—264no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—232no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—28no—
349C2×C22⋊C4—28no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—28no—
355C2×C22⋊C4—28no—
356C2×C22⋊C4—28no—
357C2×C22⋊C4—432no—
358C2×C22⋊C4—44no—
359C2×C22⋊C4—44no—
360C2×C22⋊C4—44no—
361C2×C22⋊C4—44no—
362C2×C22⋊C4—44no—
363C2×C22⋊C4—44no—
364C2×C22⋊C4C2×D418yes—
365C2×C22⋊C4C2×D418yes—
366C2×C22⋊C4C2×D418yes—
367C2×C22⋊C4C2×D418yes—
368C2×C22⋊C4C2×Q8116yes—
369C2×C22⋊C4C2×Q8116yes—
370C2×C42—22no—
371C2×C42—24no—
372C2×C42—24no—
373C2×C42—22no—
374C2×C42—24no—
375C2×C42—416no—
376C2×C42—42no—
377C2×C42—42no—
378#95—24no—
379#95—24no—
380#95—28no—
381#95—28no—
382#95—24no—
383#95—28no—
384#95—28no—
385#95—28no—
386#95—28no—
387#95—28no—
388#95—28no—
389#95—44no—
390#95—44no—
391#95—44no—
392#95—44no—
393#95—44no—
394#95—44no—
395#95—44no—
396C24—22no—
397C24—22no—
398C24—22no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24—24no—
403C24—24no—
404C24—24no—
405C24—24no—
406C24—24no—
407C24—28no—
408C24—28no—
409C24—216no—
410C24—216no—
411C24—48no—
412C24—48no—
413C24—48no—
414C24—48no—
415C24—48no—
416C24—48no—
417C24—82no—
418C24—82no—
419C24—84no—
420C24—84no—
421C24—82no—
422C24—82no—
423C24—84no—
424C24—84no—
425C24—84no—
426C24—84no—
427C24C4⋊Q8116yescomplemented
428C24C22×D414yes—
429C24C22×D412yes—
430C24C22×D412yes—
431C24C22×D412yes—
432C24C22×Q818yes—
433C24C22×Q814yes—
434C242−1+414yes—
435C24C2511yescharacteristic
436C2×Q8—216no—
437C2×Q8—28no—
438C2×Q8—28no—
439C2×Q8—44no—
440C2×Q8—44no—
441C2×Q8—48no—
442C2×Q8—44no—
443C2×Q8—44no—
444C2×Q8—44no—
445C2×Q8—82no—
446C2×Q8—82no—
447C2×Q8—84no—
448C2×Q8—84no—
449C2×Q8—84no—
450C2×Q8—84no—
451C2×Q8—84no—
452C2×Q8—88no—
453C2×Q8—88no—
454C2×Q8—84no—
455C2×Q8—84no—
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—216no—
465C22×C4—22no—
466C22×C4—24no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—24no—
478C22×C4—24no—
479C22×C4—24no—
480C22×C4—24no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—24no—
484C22×C4—24no—
485C22×C4—24no—
486C22×C4—24no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—24no—
490C22×C4—22no—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—216no—
498C22×C4—216no—
499C22×C4—28no—
500C22×C4—216no—
501C22×C4—216no—
502C22×C4—24no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—24no—
510C22×C4—24no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—44no—
520C22×C4—44no—
521C22×C4—48no—
522C22×C4—48no—
523C22×C4—48no—
524C22×C4—48no—
525C22×C4—48no—
526C22×C4—48no—
527C22×C4—48no—
528C22×C4—48no—
529C22×C4—48no—
530C22×C4—48no—
531C22×C4—84no—
532C22×C4—84no—
533C22×C4—88no—
534C22×C4—88no—
535C22×C4—84no—
536C22×C4—84no—
537C22×C4—84no—
538C22×C4—84no—
539C22×C4—88no—
540C22×C4—88no—
541C22×C4—84no—
542C22×C4—82no—
543C22×C4—82no—
544C22×C4—84no—
545C22×C4—84no—
546C22×C4#120116yes—
547C22×C4C22×D414yes—
548C22×C4C22×D414yes—
549C22×C4C22×D414yes—
550C22×C4C22×D414yes—
551C22×C4C22×D414yes—
552C22×C4C22×D412yes—
553C22×C4C22×D412yes—
554C22×C4C22×D412yes—
555C22×C4C22×D412yes—
556C22×C4C22×D412yes—
557C22×C4C22×D412yes—
558C22×C4C22×Q818yes—
559C22×C4C22×Q814yes—
560C22×C4C22×Q814yes—
561C22×C4H(5,𝔽2)14yes—
562C22×C4H(5,𝔽2)14yes—
563C4⋊C4—216no—
564C4⋊C4—216no—
565C4⋊C4—216no—
566C4⋊C4—216no—
567C4⋊C4—28no—
568C4⋊C4—28no—
569C4⋊C4—216no—
570C4⋊C4—416no—
571C4⋊C4—416no—
572C4⋊C4—44no—
573C4⋊C4—48no—
574C4⋊C4—84no—
575C4⋊C4—88no—
576C4⋊C4—88no—
577C4⋊C4—88no—
578C22⋊C4—216no—
579C22⋊C4—216no—
580C22⋊C4—216no—
581C22⋊C4—216no—
582C22⋊C4—216no—
583C22⋊C4—216no—
584C22⋊C4—232no—
585C22⋊C4—416no—
586C22⋊C4—48no—
587C22⋊C4—48no—
588C22⋊C4—88no—
589C22⋊C4—88no—
590C42—28no—
591C42—48no—
592C42—44no—
593C23—24no—
594C23—24no—
595C23—22no—
596C23—22no—
597C23—24no—
598C23—24no—
599C23—24no—
600C23—24no—
601C23—22no—
602C23—22no—
603C23—24no—
604C23—24no—
605C23—24no—
606C23—24no—
607C23—24no—
608C23—24no—
609C23—24no—
610C23—24no—
611C23—28no—
612C23—28no—
613C23—28no—
614C23—28no—
615C23—28no—
616C23—28no—
617C23—28no—
618C23—28no—
619C23—232no—
620C23—432no—
621C23—42no—
622C23—42no—
623C23—44no—
624C23—44no—
625C23—42no—
626C23—42no—
627C23—44no—
628C23—44no—
629C23—44no—
630C23—44no—
631C23—88no—
632C23—816no—
633C23—816no—
634C23—816no—
635C23—88no—
636C23—816no—
637C23—816no—
638C23C2×#12014yes—
639C23C2×C4⋊Q818yes—
640C23C2×C4⋊Q814yes—
641C23#53614yes—
642C23D4×Q818yes—
643C23D4×Q818yes—
644C23C23×D411yescharacteristic
645C23C23×D411yescharacteristic
646C23C23×D411yescharacteristic
647C23C23×Q812yes—
648C23C2×H(5,𝔽2)12yes—
649C23C2×H(5,𝔽2)12yes—
650C23C2×2−1+412yes—
651C23#58512yes—
652C23#58512yes—
653Q8—88no—
654Q8—88no—
655Q8—88no—
656Q8—816no—
657C2×C4—24no—
658C2×C4—24no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—28no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—28no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—28no—
683C2×C4—28no—
684C2×C4—28no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—28no—
689C2×C4—416no—
690C2×C4—432no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—44no—
696C2×C4—44no—
697C2×C4—44no—
698C2×C4—44no—
699C2×C4—44no—
700C2×C4—44no—
701C2×C4—44no—
702C2×C4—44no—
703C2×C4—44no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—44no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—44no—
721C2×C4—44no—
722C2×C4—44no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—44no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—88no—
730C2×C4—816no—
731C2×C4—816no—
732C2×C4—816no—
733C2×C4C2×#12014yes—
734C2×C4C2×#12014yes—
735C2×C4#54318yescomplemented
736C22—24no—
737C22—28no—
738C22—28no—
739C22—28no—
740C22—24no—
741C22—28no—
742C22—28no—
743C22—28no—
744C22—28no—
745C22—216no—
746C22—44no—
747C22—48no—
748C22—48no—
749C22—48no—
750C22—44no—
751C22—48no—
752C22—48no—
753C22—832no—
754C22#243418yes—
755C22C22×#12011yescharacteristic
756C22C22×C4⋊Q811yescharacteristic
757C22C2×#53611yescharacteristic
758C22C2×#54312yes—
759C22#345812yes—
760C22C2×D4×Q812yes—
761C22C2×D4×Q812yes—
762C22#348411yescharacteristic
763C22#348511yescharacteristic
764C22#348812yes—
765C22#349612yes—
766C22#349612yes—
767C22#349612yes—
768C22#349811yescharacteristic
769C22#350011yescharacteristic
770C22#350112yes—
771C22#350112yes—
772C22#353512yes—
773C22#353612yes—
774C22#356112yes—
775C22#356412yes—
776C4—24no—
777C4—24no—
778C4—28no—
779C4—44no—
780C4—44no—
781C4—44no—
782C4—44no—
783C4—44no—
784C4—44no—
785C4—48no—
786C4—82no—
787C4—84no—
788C4—82no—
789C2—28no—
790C2—48no—
791C2C2×#243411yescharacteristic
792C2#3500212yes—
793C2#3534711yescharacteristic
794C2#3551311yescharacteristic
795C2#3674012yes—
796C2#3768412yes—
797C2#3768812yes—
798C2#3936412yes—
799C2#3936712yes—
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
2. C2×#2857C2semidirect
3. C2×#2659C2semidirect
5. #15671C2semidirect
6. #15614C2semidirect
7. #15466C2semidirect
8. #15430C2semidirect
9. #15276C2semidirect
10. #15265C2semidirect
11. #14758C2semidirect
12. #14702C2semidirect
13. #14281C2semidirect
19. C22×C4⋊Q8C22semidirect
36. C2×#398C22semidirect
37. C2×#398C22semidirect
39. C2×#395C22semidirect
40. C2×#395C22semidirect
41. C2×#395C22semidirect
43. C2×#391C22semidirect
44. C2×#391C22semidirect
45. C2×#391C22semidirect
46. C2×#389C22semidirect
50. C2×#384C22semidirect
57. #1446C22semidirect
58. #1446C22semidirect
59. #1445C22semidirect
60. #1444C22semidirect
61. #1444C22semidirect
62. #1444C22semidirect
63. #1441C22semidirect
64. #1441C22semidirect
65. #1441C22semidirect
66. #1441C22semidirect
74. #1436C22semidirect
75. #1436C22semidirect
76. C4⋊#95C22semidirect
142. C22×C22⋊C4Q8semidirect
427. C24C4⋊Q8semidirect
735. C2×C4#543semidirect

Maximal subgroups

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

subgroupindex
C22×#5432
C2×#28572
C2×#26592
C2×#26262
#156712
#156142
#154662
#154302
#152762
#152652
#147582
#147022
#142812
#138772
C2×#14372