Finite Group Databasebeta

← #517283

Subgroups — #517283

Order 512.

5578 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2848C211yesmaximal, characteristic
2C2×#2329C211yesmaximal, characteristic, complemented
3C23×#95C211yesmaximal, characteristic
4#14693C212yesmaximal
5#14680C211yesmaximal, characteristic
6#14281C211yesmaximal, characteristic, complemented
7#14275C211yesmaximal, characteristic, complemented
8#14265C212yesmaximal, complemented
9#14052C214yesmaximal, complemented
10#14028C214yesmaximal, complemented
11#14004C214yesmaximal, complemented
12#13980C214yesmaximal, complemented
13#13782C212yesmaximal, complemented
14#13778C211yesmaximal, characteristic, complemented
15C4×#379C212yesmaximal
16C25×C4C2211yescharacteristic
17C25×C4C2211yescharacteristic
18C25×C4C2211yescharacteristic
19C22×C22⋊Q8C2211yescharacteristic
20C22×C22⋊Q8C2212yes—
21#2848C4116yescomplemented
22#2329—28no—
23C2×#391C2212yescomplemented
24C2×#389C2212yescomplemented
25C2×#387C2212yescomplemented
26C2×#387C2212yescomplemented
27C2×#385C2212yes—
28C2×#385C2212yes—
29C2×#385C2214yes—
30C2×#385C2214yes—
31C2×#385C2214yes—
32C2×#385C2212yes—
33C2×#380C2211yescharacteristic
34C2×#380C2211yescharacteristic
35C2×#380C2212yes—
36C2×#380C2212yes—
37C2×#380C2211yescharacteristic
38C2×#380C2212yes—
39C2×#379C2212yes—
40C2×#379C2212yes—
41C2×C4×C22⋊C4C2212yes—
42C2×C4×C22⋊C4C2212yes—
43C2×C4×C22⋊C4C2214yes—
44C2×C4×C22⋊C4C2214yes—
45C22×#95—28no—
46C22×#95C2214yes—
47C22×#95C2211yescharacteristic
48C22×#95C2211yescharacteristic
49C22×#95C2214yes—
50C22×#95C2211yescharacteristic
51C22×#95C2211yescharacteristic
52#1446C2212yescomplemented
53#1445C2214yescomplemented
54#1445C2212yescomplemented
55#1444C2212yescomplemented
56#1443C2214yescomplemented
57#1442C2212yescomplemented
58#1442C2214yescomplemented
59#1441C2214yescomplemented
60#1441C2214yescomplemented
61#1441C2214yescomplemented
62#1436C2214yescomplemented
63#1436C2214yescomplemented
64#1436C2214yescomplemented
65#1436C2214yescomplemented
66C4⋊#95C2214yescomplemented
67#1434C2214yescomplemented
68C22⋊#95C2212yes—
69C22⋊#95C2214yes—
70C22⋊#95C2214yes—
71C22⋊#95C2214yes—
72C22⋊#95C2212yes—
73C22⋊#95C2212yes—
74C22⋊#95C2214yes—
75C22⋊#95C2214yes—
76C22⋊#95C2212yes—
77C22⋊#95C2212yes—
78C26C2311yescharacteristic
79C23×Q8C2311yescharacteristic
80C24×C4—24no—
81C24×C4—24no—
82C24×C4—24no—
83C24×C4—24no—
84C24×C4—24no—
85C24×C4—24no—
86C24×C4—24no—
87C24×C4—44no—
88C24×C4—44no—
89C24×C4—44no—
90C24×C4—44no—
91C24×C4—44no—
92C24×C4—44no—
93C24×C4C2×C418yes—
94C24×C4Q818yescomplemented
95C24×C4C2314yes—
96C24×C4C2312yes—
97C24×C4C2312yes—
98C24×C4C2314yes—
99C24×C4C2311yescharacteristic
100C24×C4C2311yescharacteristic
101C24×C4C2311yescharacteristic
102C24×C4C2311yescharacteristic
103C24×C4C2311yescharacteristic
104C24×C4C2311yescharacteristic
105C2×C22⋊Q8—24no—
106C2×C22⋊Q8—24no—
107C2×C22⋊Q8—44no—
108C2×C22⋊Q8—44no—
109C2×C22⋊Q8C2×C418yescomplemented
110C2×C22⋊Q8C2×C4116yescomplemented
111C22×C4⋊C4C2312yes—
112C22×C4⋊C4C2311yescharacteristic
113C22×C4⋊C4C2314yes—
114C22×C4⋊C4C2312yes—
115C22×C4⋊C4C2312yes—
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2312yes—
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2314yes—
120C22×C4⋊C4C2312yes—
121C22×C22⋊C4C2312yes—
122C22×C22⋊C4C2314yes—
123C22×C22⋊C4C2312yes—
124C22×C22⋊C4C2314yes—
125C22×C22⋊C4C2312yes—
126C22×C22⋊C4C2314yes—
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2314yes—
129C22×C42C2314yes—
130C22×C42C2312yes—
131C22×C42C2312yes—
132#391—28no—
133#389—28no—
134#387—28no—
135#387—28no—
136#385—28no—
137#385—28no—
138#385—48no—
139#385—48no—
140#385C2×C4132yescomplemented
141#385C2×C4116yescomplemented
142#380—24no—
143#380—24no—
144#380—44no—
145#380—44no—
146#380C2×C4116yescomplemented
147#380C2×C418yescomplemented
148#379—28no—
149#379C2×C4116yes—
150C4×C22⋊C4—28no—
151C4×C22⋊C4—28no—
152C4×C22⋊C4—48no—
153C4×C22⋊C4—48no—
154C2×#95—24no—
155C2×#95—24no—
156C2×#95—24no—
157C2×#95—216no—
158C2×#95—216no—
159C2×#95D418yes—
160C2×#95C2312yes—
161C2×#95C2314yes—
162C2×#95C2312yes—
163C2×#95C2314yes—
164C2×#95C2312yes—
165C2×#95C2312yes—
166C2×#95C2312yes—
167C2×#95C2312yes—
168C2×#95C2314yes—
169C2×#95C2312yes—
170C2×#95C2312yes—
171C2×#95C2314yes—
172C2×#95C2314yes—
173C2×#95C2314yes—
174C2×#95C2314yes—
175C2×#95C2314yes—
176C2×#95C2314yes—
177C2×#95C2314yes—
178C2×#95C2314yes—
179C2×#95C2314yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C2×#95C2314yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C25—22no—
187C25—22no—
188C25—22no—
189C25—22no—
190C25—24no—
191C25—24no—
192C25—24no—
193C25—24no—
194C25C22×C414yes—
195C25C2×Q814yes—
196C25#4114yes—
197C25C2411yescharacteristic
198C25C2412yes—
199C22×Q8—22no—
200C22×Q8—22no—
201C22×Q8—42no—
202C22×Q8—42no—
203C22×Q8C22×C414yescomplemented
204C23×C4—232no—
205C23×C4—22no—
206C23×C4—22no—
207C23×C4—22no—
208C23×C4—28no—
209C23×C4—22no—
210C23×C4—22no—
211C23×C4—22no—
212C23×C4—22no—
213C23×C4—22no—
214C23×C4—24no—
215C23×C4—24no—
216C23×C4—28no—
217C23×C4—28no—
218C23×C4—24no—
219C23×C4—24no—
220C23×C4—232no—
221C23×C4—232no—
222C23×C4—28no—
223C23×C4—24no—
224C23×C4—24no—
225C23×C4—28no—
226C23×C4—28no—
227C23×C4—24no—
228C23×C4—24no—
229C23×C4—28no—
230C23×C4—28no—
231C23×C4—28no—
232C23×C4—432no—
233C23×C4—432no—
234C23×C4—42no—
235C23×C4—42no—
236C23×C4—44no—
237C23×C4—44no—
238C23×C4—42no—
239C23×C4—42no—
240C23×C4—42no—
241C23×C4—42no—
242C23×C4—42no—
243C23×C4—42no—
244C23×C4—42no—
245C23×C4—42no—
246C23×C4—42no—
247C23×C4—42no—
248C23×C4—42no—
249C23×C4—42no—
250C23×C4—42no—
251C23×C4—42no—
252C23×C4—44no—
253C23×C4—44no—
254C23×C4—416no—
255C23×C4—416no—
256C23×C4—416no—
257C23×C4—416no—
258C23×C4—416no—
259C23×C4—416no—
260C23×C4—432no—
261C23×C4—432no—
262C23×C4—432no—
263C23×C4—432no—
264C23×C4C22×C418yes—
265C23×C4C22×C418yes—
266C23×C4C22×C414yes—
267C23×C4C22×C414yes—
268C23×C4C2×D414yes—
269C23×C4C2×D414yes—
270C23×C4C2×D414yes—
271C23×C4C2×Q8116yes—
272C23×C4C2×Q814yes—
273C23×C4C2×Q814yes—
274C23×C4#4114yes—
275C23×C4#4114yes—
276C23×C4#4114yes—
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2414yes—
280C23×C4C2412yes—
281C23×C4C2412yes—
282C23×C4C2414yes—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2412yes—
287C23×C4C2411yescharacteristic
288C23×C4C2411yescharacteristic
289C23×C4C2412yes—
290C22⋊Q8—232no—
291C22⋊Q8—432no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—28no—
302C2×C4⋊C4—42no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—44no—
305C2×C4⋊C4—44no—
306C2×C4⋊C4—42no—
307C2×C4⋊C4—42no—
308C2×C4⋊C4—42no—
309C2×C4⋊C4—42no—
310C2×C4⋊C4—44no—
311C2×C4⋊C4—44no—
312C2×C4⋊C4—44no—
313C2×C4⋊C4—44no—
314C2×C4⋊C4C22×C414yescomplemented
315C2×C4⋊C4C22×C418yescomplemented
316C2×C4⋊C4C22×C418yescomplemented
317C2×C4⋊C4C22×C4116yescomplemented
318C2×C22⋊C4—24no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—28no—
323C2×C22⋊C4—28no—
324C2×C22⋊C4—28no—
325C2×C22⋊C4—28no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—28no—
331C2×C22⋊C4—28no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—28no—
335C2×C22⋊C4—28no—
336C2×C22⋊C4—28no—
337C2×C22⋊C4—28no—
338C2×C22⋊C4C22×C418yes—
339C2×C22⋊C4C22×C4116yes—
340C2×C22⋊C4C22×C418yes—
341C2×C22⋊C4C22×C4116yes—
342C2×C42—24no—
343C2×C42—24no—
344C2×C42—28no—
345C2×C42—44no—
346C2×C42—44no—
347C2×C42—44no—
348C2×C42—44no—
349#95—28no—
350#95—24no—
351#95—24no—
352#95—28no—
353#95—24no—
354#95—24no—
355#95—24no—
356#95—24no—
357#95—24no—
358#95—28no—
359#95—24no—
360#95—28no—
361#95—44no—
362#95—44no—
363#95—44no—
364#95—44no—
365#95—44no—
366#95—44no—
367#95—44no—
368#95—44no—
369#95—44no—
370#95—44no—
371#95C22×C4116yescomplemented
372#95C22×C418yescomplemented
373#95C2×D418yes—
374#95C2×D418yes—
375C24—28no—
376C24—28no—
377C24—28no—
378C24—216no—
379C24—216no—
380C24—216no—
381C24—28no—
382C24—216no—
383C24—216no—
384C24—216no—
385C24—28no—
386C24—28no—
387C24—216no—
388C24—216no—
389C24—28no—
390C24—28no—
391C24—28no—
392C24—28no—
393C24—216no—
394C24—216no—
395C24—216no—
396C24—216no—
397C24—22no—
398C24—22no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—22no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24C4×Q8116yes—
410C24C23×C412yes—
411C24C23×C414yes—
412C24C22×D412yes—
413C24C22×Q812yes—
414C24C22×Q814yes—
415C24C2×#4112yes—
416C24C2×#4112yes—
417C24C2×#4114yes—
418C24C2×#4112yes—
419C24C2×#4112yes—
420C24H(5,𝔽2)14yes—
421C24H(5,𝔽2)14yes—
422C24H(5,𝔽2)14yes—
423C242−1+414yes—
424C24C2511yescharacteristic
425C2×Q8—28no—
426C2×Q8—48no—
427C2×Q8—82no—
428C2×Q8—82no—
429C2×Q8—84no—
430C22×C4—24no—
431C22×C4—24no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—232no—
437C22×C4—28no—
438C22×C4—216no—
439C22×C4—216no—
440C22×C4—28no—
441C22×C4—28no—
442C22×C4—28no—
443C22×C4—232no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—24no—
450C22×C4—24no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—24no—
463C22×C4—24no—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4—24no—
467C22×C4—24no—
468C22×C4—24no—
469C22×C4—24no—
470C22×C4—24no—
471C22×C4—24no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—24no—
475C22×C4—24no—
476C22×C4—216no—
477C22×C4—216no—
478C22×C4—232no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—24no—
483C22×C4—24no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—24no—
487C22×C4—22no—
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—48no—
497C22×C4—48no—
498C22×C4—48no—
499C22×C4—48no—
500C22×C4—44no—
501C22×C4—44no—
502C22×C4—44no—
503C22×C4—44no—
504C22×C4—44no—
505C22×C4—44no—
506C22×C4—48no—
507C22×C4—416no—
508C22×C4—48no—
509C22×C4—48no—
510C22×C4—48no—
511C22×C4—48no—
512C22×C4—416no—
513C22×C4—416no—
514C22×C4—48no—
515C22×C4—48no—
516C22×C4—48no—
517C22×C4—48no—
518C22×C4—416no—
519C22×C4—416no—
520C22×C4—48no—
521C22×C4—48no—
522C22×C4—48no—
523C22×C4—48no—
524C22×C4—416no—
525C22×C4—416no—
526C22×C4—416no—
527C22×C4—416no—
528C22×C4—4128no—
529C22×C4—4128no—
530C22×C4—4128no—
531C22×C4—48no—
532C22×C4—48no—
533C22×C4—416no—
534C22×C4—44no—
535C22×C4—44no—
536C22×C4—44no—
537C22×C4—44no—
538C22×C4—44no—
539C22×C4—44no—
540C22×C4—48no—
541C22×C4—48no—
542C22×C4—48no—
543C22×C4—416no—
544C22×C4C4×D4116yes—
545C22×C4C22⋊Q8116yescomplemented
546C22×C4C23×C414yes—
547C22×C4C23×C418yes—
548C22×C4C23×C414yes—
549C22×C4C23×C414yes—
550C22×C4C23×C412yes—
551C22×C4C23×C412yes—
552C22×C4C22×D414yes—
553C22×C4C22×D412yes—
554C22×C4C22×D412yes—
555C22×C4C22×D414yes—
556C22×C4C22×Q814yes—
557C22×C4C22×Q814yes—
558C22×C4C2×#4114yes—
559C22×C4C2×#4112yes—
560C22×C4C2×#4112yes—
561C22×C4C2×#4114yes—
562C4⋊C4—28no—
563C4⋊C4—216no—
564C4⋊C4—48no—
565C4⋊C4—416no—
566C4⋊C4—82no—
567C4⋊C4—82no—
568C4⋊C4—84no—
569C4⋊C4—84no—
570C4⋊C4—84no—
571C4⋊C4—88no—
572C22⋊C4—216no—
573C22⋊C4—216no—
574C22⋊C4—232no—
575C22⋊C4—232no—
576C22⋊C4—48no—
577C22⋊C4—48no—
578C22⋊C4—416no—
579C22⋊C4—416no—
580C42—84no—
581C42—84no—
582C42—88no—
583C23—232no—
584C23—232no—
585C23—232no—
586C23—232no—
587C23—232no—
588C23—264no—
589C23—232no—
590C23—264no—
591C23—264no—
592C23—264no—
593C23—24no—
594C23—24no—
595C23—24no—
596C23—24no—
597C23—24no—
598C23—24no—
599C23—24no—
600C23—24no—
601C23—24no—
602C23—24no—
603C23—24no—
604C23—24no—
605C23—24no—
606C23—24no—
607C23—24no—
608C23—24no—
609C23—24no—
610C23—24no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—24no—
615C23—24no—
616C23—24no—
617C23—22no—
618C23—24no—
619C23—24no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—24no—
626C23—24no—
627C23—24no—
628C23—24no—
629C23—24no—
630C23—24no—
631C23—24no—
632C23—24no—
633C23—24no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—232no—
638C23C2×C4×D414yes—
639C23C2×C4×Q818yes—
640C23C2×C4×Q814yes—
641C23C4×#4114yes—
642C23#51818yes—
643C23#52018yes—
644C23C2×C22⋊Q814yes—
645C23#52514yes—
646C23#52914yes—
647C23#53314yes—
648C23#53818yes—
649C23#53918yes—
650C23#54318yes—
651C23#54418yes—
652C23C24×C411yescharacteristic
653C23C23×D411yescharacteristic
654C23C23×Q811yescharacteristic
655C23C22×#4111yescharacteristic
656C23C22×#4111yescharacteristic
657C23C22×#4111yescharacteristic
658C23C22×#4111yescharacteristic
659C23C2×H(5,𝔽2)12yes—
660C23C2×H(5,𝔽2)12yes—
661C23C2×H(5,𝔽2)12yes—
662C23C2×2−1+412yes—
663Q8—88no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—28no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—28no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—28no—
680C2×C4—28no—
681C2×C4—28no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—28no—
685C2×C4—28no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—28no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—28no—
693C2×C4—416no—
694C2×C4—416no—
695C2×C4—432no—
696C2×C4—432no—
697C2×C4—464no—
698C2×C4—416no—
699C2×C4—416no—
700C2×C4—416no—
701C2×C4—416no—
702C2×C4—464no—
703C2×C4—44no—
704C2×C4—44no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—44no—
720C2×C4—44no—
721C2×C4—44no—
722C2×C4—44no—
723C2×C4—44no—
724C2×C4—44no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—44no—
742C2×C4C2×C4×D414yes—
743C2×C4C2×C4×D414yes—
744C2×C4C2×C22⋊Q818yes—
745C22—2128no—
746C22—28no—
747C22—28no—
748C22—24no—
749C22—28no—
750C22—24no—
751C22—28no—
752C22—24no—
753C22—28no—
754C22—24no—
755C22—28no—
756C22—28no—
757C22—28no—
758C22—28no—
759C22—24no—
760C22—28no—
761C22—24no—
762C22—28no—
763C22—28no—
764C22—28no—
765C22—28no—
766C22—28no—
767C22—28no—
768C22—28no—
769C22—28no—
770C22C4×C22⋊Q818yes—
771C22#2329116yescomplemented
772C22C22×C4×D411yescharacteristic
773C22C22×C4×Q811yescharacteristic
774C22C2×C4×#4111yescharacteristic
775C22C2×#51812yes—
776C22C2×#52012yes—
777C22C22×C22⋊Q811yescharacteristic
778C22C2×#52511yescharacteristic
779C22C2×#52911yescharacteristic
780C22C2×#53311yescharacteristic
781C22C2×#53812yes—
782C22C2×#53912yes—
783C22C2×#54312yes—
784C22C2×#54412yes—
785C22#348411yescharacteristic
786C22#348411yescharacteristic
787C22#348411yescharacteristic
788C22#348611yescharacteristic
789C22#349012yes—
790C22#349012yes—
791C22#349012yes—
792C22#349212yes—
793C22#349212yes—
794C22#349212yes—
795C4—24no—
796C4—24no—
797C4—28no—
798C4—44no—
799C4—44no—
800C4—44no—
801C4—44no—
802C4—48no—
803C4—44no—
804C4—44no—
805C4—82no—
806C4—82no—
807C4—84no—
808C2—216no—
809C2—28no—
810C2C2×C4×C22⋊Q811yescharacteristic
811C2C2×#232912yes—
812C2#3419811yescharacteristic
813C2#3420011yescharacteristic
814C2#3421812yes—
815C2#3498211yescharacteristic
816C2#3498811yescharacteristic
817C2#3498911yescharacteristic
818C2#3499712yes—
819C2#3505212yes—
820C2#3522411yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC26C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#2329C2semidirect
6. #14281C2semidirect
7. #14275C2semidirect
8. #14265C2semidirect
9. #14052C2semidirect
10. #14028C2semidirect
11. #14004C2semidirect
12. #13980C2semidirect
13. #13782C2semidirect
14. #13778C2semidirect
21. #2848C4semidirect
23. C2×#391C22semidirect
24. C2×#389C22semidirect
25. C2×#387C22semidirect
26. C2×#387C22semidirect
52. #1446C22semidirect
53. #1445C22semidirect
54. #1445C22semidirect
55. #1444C22semidirect
56. #1443C22semidirect
57. #1442C22semidirect
58. #1442C22semidirect
59. #1441C22semidirect
60. #1441C22semidirect
61. #1441C22semidirect
62. #1436C22semidirect
63. #1436C22semidirect
64. #1436C22semidirect
65. #1436C22semidirect
66. C4⋊#95C22semidirect
67. #1434C22semidirect
94. C24×C4Q8semidirect
109. C2×C22⋊Q8C2×C4semidirect
110. C2×C22⋊Q8C2×C4semidirect
140. #385C2×C4semidirect
141. #385C2×C4semidirect
146. #380C2×C4semidirect
147. #380C2×C4semidirect
203. C22×Q8C22×C4semidirect
314. C2×C4⋊C4C22×C4semidirect
315. C2×C4⋊C4C22×C4semidirect
316. C2×C4⋊C4C22×C4semidirect
317. C2×C4⋊C4C22×C4semidirect
371. #95C22×C4semidirect
372. #95C22×C4semidirect
545. C22×C4C22⋊Q8semidirect
771. C22#2329semidirect

Maximal subgroups

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

subgroupindex
C2×#28482
C2×#23292
C23×#952
#146932
#146802
#142812
#142752
#142652
#140522
#140282
#140042
#139802
#137822
#137782
C4×#3792