Finite Group Databasebeta

← C2×#24763 #6442975

Subgroups — C2×#24763 #6442975

Order 512.

3002 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#468C211yesmaximal, characteristic, complemented
2C22×#466C211yesmaximal, characteristic
3C22×#463C211yesmaximal, characteristic, complemented
4C22×#424C211yesmaximal, characteristic, complemented
5C2×#2620C211yesmaximal, characteristic, complemented
6C2×#2324C211yesmaximal, characteristic, complemented
7#24763C2116yesmaximal, direct product factor
8C2×#2068C211yesmaximal, characteristic, complemented
9C2×#2067C211yesmaximal, characteristic, complemented
10C2×#2055C211yesmaximal, characteristic, complemented
11C2×#2054C211yesmaximal, characteristic, complemented
12C2×#1983C211yesmaximal, characteristic, complemented
13C2×#1947C211yesmaximal, characteristic, complemented
14C2×#1895C211yesmaximal, characteristic, complemented
15C2×#1892C211yesmaximal, characteristic, complemented
16C2×#1802C211yesmaximal, characteristic, complemented
17C23×SD16C2211yescharacteristic
18C23×D8C2211yescharacteristic
19C23×M16C2211yescharacteristic
20C24×C8C2211yescharacteristic
21C22×#124C2211yescharacteristic
22C22×C22⋊Q8C2211yescharacteristic
23C22×#121C2211yescharacteristic
24C22×#121C2211yescharacteristic
25C22×C4×D4C2211yescharacteristic
26C22×#117C2211yescharacteristic
27C2×#468—28no—
28C2×#468C2218yescomplemented
29C2×#466—28no—
30C2×#466C2218yes—
31C2×#463—28no—
32C2×#463C2218yescomplemented
33C22×#107C2211yescharacteristic
34C22×#107C2211yescharacteristic
35C2×#424—28no—
36C2×#424C2218yescomplemented
37C22×C4⋊C8C2211yescharacteristic
38C22×C4⋊C8C2211yescharacteristic
39C22×C4⋊C8C2211yescharacteristic
40C22×C4⋊C8C2211yescharacteristic
41C22×#103C2211yescharacteristic
42C22×#103C2211yescharacteristic
43C22×#103C2211yescharacteristic
44C22×#102C2211yescharacteristic
45C22×#102C2211yescharacteristic
46C22×#102C2211yescharacteristic
47C22×#102C2211yescharacteristic
48C22×#102C2211yescharacteristic
49#2620—24no—
50#2620C2218yescomplemented
51C2×#396—21no—
52C2×#396—21no—
53C2×#394—21no—
54C2×#394—21no—
55#2324—24no—
56#2324C2218yescomplemented
57C2×#391C2211yescharacteristic
58C2×#390—21no—
59C2×#390C2211yescharacteristic
60C2×#390C2211yescharacteristic
61C2×#389C2211yescharacteristic
62C2×#388—21no—
63C2×#386—21no—
64C2×#385—21no—
65C2×#384C2211yescharacteristic
66C2×#380C2211yescharacteristic
67C2×C4×C4⋊C4C2211yescharacteristic
68#2068C2218yescomplemented
69#2067C2218yescomplemented
70#2055C2218yescomplemented
71#2054C2218yescomplemented
72#1983C2218yescomplemented
73#1947C2218yescomplemented
74#1895C2218yescomplemented
75#1892C2218yescomplemented
76#1802C2218yescomplemented
77C2×#340C2211yescharacteristic
78C2×#340C2211yescharacteristic
79C2×#340C2211yescharacteristic
80C2×#340C2211yescharacteristic
81C23×Q8C2311yescharacteristic
82C23×D4—21no—
83C23×D4—21no—
84C23×D4C2311yescharacteristic
85C23×D4C2311yescharacteristic
86C24×C4—21no—
87C24×C4C2311yescharacteristic
88C22×SD16—24no—
89C22×SD16—24no—
90C22×SD16—42no—
91C22×SD16C2314yes—
92C22×D8—24no—
93C22×D8—24no—
94C22×D8—42no—
95C22×D8C2314yes—
96C22×M16—24no—
97C22×M16—24no—
98C22×M16—42no—
99C22×M16C2314yes—
100C23×C8—24no—
101C23×C8—24no—
102C23×C8—42no—
103C23×C8C2311yescharacteristic
104C23×C8C2311yescharacteristic
105C23×C8C2314yes—
106C23×C8C2311yescharacteristic
107C23×C8C2311yescharacteristic
108C2×#124—22no—
109C2×#124—24no—
110C2×#124—24no—
111C2×#124C2314yes—
112C2×C22⋊Q8—22no—
113C2×C22⋊Q8—24no—
114C2×C22⋊Q8—24no—
115C2×C22⋊Q8C2314yes—
116C2×#121—22no—
117C2×#121—24no—
118C2×#121—22no—
119C2×#121—24no—
120C2×#121—24no—
121C2×#121D418yes—
122C2×#121C2314yes—
123C2×#121C2314yes—
124C2×C4×D4—22no—
125C2×C4×D4—24no—
126C2×C4×D4—24no—
127C2×C4×D4C2314yes—
128C2×#117—24no—
129C2×#117—24no—
130C2×#117D414yes—
131C2×#117C2314yes—
132C22×C4⋊C4—21no—
133C22×C4⋊C4—21no—
134C22×C4⋊C4—21no—
135C22×C4⋊C4—21no—
136C22×C4⋊C4D411yescharacteristic
137C22×C4⋊C4D411yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2311yescharacteristic
143C22×C22⋊C4—21no—
144C22×C22⋊C4—21no—
145C22×C22⋊C4—21no—
146C22×C22⋊C4—21no—
147C22×C22⋊C4—21no—
148C22×C22⋊C4—21no—
149C22×C22⋊C4—21no—
150C22×C22⋊C4—21no—
151C22×C22⋊C4—21no—
152C22×C22⋊C4—21no—
153C22×C22⋊C4—21no—
154C22×C22⋊C4D411yescharacteristic
155C22×C22⋊C4D411yescharacteristic
156C22×C42—21no—
157C22×C42C2311yescharacteristic
158C22×C42C2311yescharacteristic
159#468—232no—
160#466—232no—
161#463—232no—
162C2×#107—24no—
163C2×#107—24no—
164C2×#107C2314yes—
165C2×#107C2314yes—
166#424—232no—
167C2×C4⋊C8—24no—
168C2×C4⋊C8—24no—
169C2×C4⋊C8—24no—
170C2×C4⋊C8D418yescomplemented
171C2×C4⋊C8C2314yes—
172C2×C4⋊C8C2314yes—
173C2×C4⋊C8C2314yes—
174C2×C4⋊C8C2314yes—
175C2×#103—24no—
176C2×#103—24no—
177C2×#103—42no—
178C2×#103C2314yes—
179C2×#103C2314yes—
180C2×#103C2314yes—
181C2×#102—24no—
182C2×#102—24no—
183C2×#102—24no—
184C2×#102—24no—
185C2×#102—42no—
186C2×#102C2314yes—
187C2×#102C2314yes—
188C2×#102C2314yes—
189C2×#102C2314yes—
190C2×#102C2314yes—
191#396—28no—
192#396—28no—
193#394—28no—
194#394—28no—
195#391—22no—
196#391C2314yes—
197#390—28no—
198#390—22no—
199#390—22no—
200#390C2314yes—
201#390C2314yes—
202#389—22no—
203#389C2314yes—
204#388—28no—
205#386—28no—
206#385—28no—
207#384—22no—
208#384C2314yes—
209#380—22no—
210#380C2314yes—
211C4×C4⋊C4—22no—
212C4×C4⋊C4C2314yes—
213C2×#95—21no—
214C2×#95—21no—
215C2×#95—21no—
216C2×#95—21no—
217C2×#95—21no—
218#340C2314yes—
219#340C2314yes—
220#340C2314yes—
221#340C2314yes—
222C25—21no—
223C25—21no—
224C25C2×D411yescharacteristic
225C22×Q8—21no—
226C22×Q8—22no—
227C22×Q8—22no—
228C22×Q8—22no—
229C22×Q8—22no—
230C22×Q8—22no—
231C22×Q8—22no—
232C22×Q8C2412yes—
233C22×D4—28no—
234C22×D4—24no—
235C22×D4—24no—
236C22×D4—22no—
237C22×D4—21no—
238C22×D4—22no—
239C22×D4—22no—
240C22×D4—21no—
241C22×D4—22no—
242C22×D4—22no—
243C22×D4—22no—
244C22×D4—22no—
245C22×D4—22no—
246C22×D4—22no—
247C22×D4—22no—
248C22×D4—22no—
249C22×D4—44no—
250C22×D4—82no—
251C22×D4—82no—
252C22×D4—82no—
253C22×D4—82no—
254C22×D4C2×D414yes—
255C22×D4C2412yes—
256C22×D4C2412yes—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—21no—
262C23×C4—21no—
263C23×C4—21no—
264C23×C4—21no—
265C23×C4—21no—
266C23×C4—21no—
267C23×C4—24no—
268C23×C4—44no—
269C23×C4—82no—
270C23×C4—82no—
271C23×C4C2×D411yescharacteristic
272C23×C4C2×D411yescharacteristic
273C23×C4C2×D412yes—
274C23×C4C2×D411yescharacteristic
275C23×C4C2×D411yescharacteristic
276C23×C4C2×D411yescharacteristic
277C23×C4C2×D414yes—
278C23×C4#4114yes—
279C23×C4C2412yes—
280C23×C4C2411yescharacteristic
281C2×SD16—28no—
282C2×SD16—28no—
283C2×SD16—44no—
284C2×SD16—416no—
285C2×D8—28no—
286C2×D8—28no—
287C2×D8—44no—
288C2×D8—416no—
289C2×M16—28no—
290C2×M16—28no—
291C2×M16—44no—
292C2×M16—416no—
293C22×C8—22no—
294C22×C8—22no—
295C22×C8—22no—
296C22×C8—22no—
297C22×C8—22no—
298C22×C8—22no—
299C22×C8—28no—
300C22×C8—22no—
301C22×C8—22no—
302C22×C8—22no—
303C22×C8—22no—
304C22×C8—28no—
305C22×C8—44no—
306C22×C8—416no—
307C22×C8C2×D414yes—
308C22×C8C2×D414yes—
309C22×C8C2412yes—
310C22×C8C2412yes—
311C22×C8C2412yes—
312C22×C8C2412yes—
313#124—28no—
314#124—28no—
315#124—48no—
316C22⋊Q8—28no—
317C22⋊Q8—28no—
318C22⋊Q8—48no—
319#121—216no—
320#121—28no—
321#121—28no—
322#121—28no—
323#121—48no—
324#121C2×D4116yes—
325C4×D4—28no—
326C4×D4—28no—
327C4×D4—48no—
328#117—216no—
329#117—28no—
330#117—28no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—44no—
352C2×C4⋊C4—82no—
353C2×C4⋊C4—82no—
354C2×C4⋊C4—82no—
355C2×C4⋊C4C2×D414yes—
356C2×C4⋊C4C2×D414yes—
357C2×C4⋊C4C2×D414yes—
358C2×C4⋊C4C2412yes—
359C2×C4⋊C4C2412yes—
360C2×C4⋊C4C2412yes—
361C2×C4⋊C4C2412yes—
362C2×C4⋊C4C2412yes—
363C2×C22⋊C4—28no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—44no—
378C2×C22⋊C4—44no—
379C2×C22⋊C4—44no—
380C2×C22⋊C4—44no—
381C2×C22⋊C4—44no—
382C2×C22⋊C4—82no—
383C2×C22⋊C4—82no—
384C2×C22⋊C4—82no—
385C2×C22⋊C4—82no—
386C2×C22⋊C4—82no—
387C2×C22⋊C4C2×D414yes—
388C2×C22⋊C4C2×D414yes—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42—24no—
392C2×C42—82no—
393C2×C42C2×D412yes—
394C2×C42C2×D412yes—
395C2×C42C2×D414yes—
396C2×C42#4114yes—
397C2×C42C2412yes—
398C2×C42C2412yes—
399#107—28no—
400#107—28no—
401C4⋊C8—28no—
402C4⋊C8—28no—
403C4⋊C8—28no—
404C4⋊C8C2×D4116yescomplemented
405#103—28no—
406#103—28no—
407#103—44no—
408#102—28no—
409#102—28no—
410#102—28no—
411#102—28no—
412#102—44no—
413#95—24no—
414#95—24no—
415#95—24no—
416#95—24no—
417#95—24no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—24no—
425C24—22no—
426C24—22no—
427C24—42no—
428C24—42no—
429C24—42no—
430C24—42no—
431C24—42no—
432C24—42no—
433C24—42no—
434C24—42no—
435C24—42no—
436C24—42no—
437C24—42no—
438C24—42no—
439C24—42no—
440C24#12114yes—
441C24C22×D412yes—
442C24C22×D411yescharacteristic
443C2×Q8—22no—
444C2×Q8—22no—
445C2×Q8—22no—
446C2×Q8—22no—
447C2×Q8—22no—
448C2×Q8—22no—
449C2×Q8—42no—
450C2×Q8—42no—
451C2×Q8—42no—
452C2×Q8—44no—
453C2×Q8—44no—
454C2×Q8—44no—
455C2×Q8—44no—
456C2×D4—216no—
457C2×D4—24no—
458C2×D4—28no—
459C2×D4—28no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—48no—
472C2×D4—42no—
473C2×D4—42no—
474C2×D4—42no—
475C2×D4—42no—
476C2×D4—42no—
477C2×D4—44no—
478C2×D4—44no—
479C2×D4—44no—
480C2×D4—44no—
481C2×D4—44no—
482C2×D4—44no—
483C2×D4—816no—
484C2×D4—84no—
485C2×D4—84no—
486C2×D4—84no—
487C2×D4—84no—
488C2×D4—816no—
489C2×D4C22×D414yes—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—28no—
499C22×C4—28no—
500C22×C4—28no—
501C22×C4—28no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—24no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—48no—
537C22×C4—84no—
538C22×C4—84no—
539C22×C4—816no—
540C22×C4#12114yes—
541C22×C4#12114yes—
542C22×C4#12114yes—
543C22×C4#12118yes—
544C22×C4C22×D412yes—
545C22×C4C22×D412yes—
546C22×C4C22×D412yes—
547C22×C4C22×D412yes—
548C22×C4C22×D412yes—
549C22×C4C22×D414yes—
550C22×C4C22×D411yescharacteristic
551C22×C4C22×D412yes—
552C22×C4C22×D412yes—
553C22×C4C2×#4114yes—
554C22×C4C2×#4112yes—
555C22×C4C2×#4112yes—
556C22×C4H(5,𝔽2)12yes—
557C22×C42−1+412yes—
558C22×C4C2511yescharacteristic
559SD16—416no—
560D8—416no—
561M16—416no—
562C2×C8—28no—
563C2×C8—28no—
564C2×C8—22no—
565C2×C8—22no—
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8—22no—
570C2×C8—22no—
571C2×C8—22no—
572C2×C8—22no—
573C2×C8—22no—
574C2×C8—416no—
575C2×C8—44no—
576C2×C8—44no—
577C2×C8C22×D414yes—
578C2×C8C22×D414yes—
579C4⋊C4—28no—
580C4⋊C4—28no—
581C4⋊C4—24no—
582C4⋊C4—22no—
583C4⋊C4—22no—
584C4⋊C4—22no—
585C4⋊C4—22no—
586C4⋊C4—22no—
587C4⋊C4—22no—
588C4⋊C4—22no—
589C4⋊C4—22no—
590C4⋊C4—22no—
591C4⋊C4—42no—
592C4⋊C4—42no—
593C4⋊C4—42no—
594C4⋊C4—48no—
595C4⋊C4—42no—
596C4⋊C4—84no—
597C4⋊C4—84no—
598C4⋊C4—84no—
599C4⋊C4C22×D414yes—
600C22⋊C4—216no—
601C22⋊C4—28no—
602C22⋊C4—28no—
603C22⋊C4—48no—
604C22⋊C4—48no—
605C22⋊C4—48no—
606C22⋊C4—48no—
607C22⋊C4—48no—
608C22⋊C4—84no—
609C22⋊C4—84no—
610C22⋊C4—84no—
611C22⋊C4—84no—
612C22⋊C4—84no—
613C42—24no—
614C42—22no—
615C42—22no—
616C42—84no—
617C42#12118yes—
618C42C22×D414yes—
619C42C2×#4114yes—
620C23—22no—
621C23—28no—
622C23—22no—
623C23—28no—
624C23—28no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—24no—
630C23—44no—
631C23—44no—
632C23—44no—
633C23—44no—
634C23—42no—
635C23—48no—
636C23—42no—
637C23—48no—
638C23—48no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—84no—
651C23—84no—
652C23—84no—
653C23—84no—
654C23—84no—
655C23—84no—
656C23—84no—
657C23—84no—
658C23—84no—
659C23—84no—
660C23—84no—
661C23C2×#12114yes—
662C23C2×#12112yes—
663C23C2×#12112yes—
664C23#53712yes—
665C23#57612yes—
666C23#57612yes—
667C23#57712yes—
668C23#57812yes—
669C23C23×D411yescharacteristic
670Q8—42no—
671Q8—42no—
672Q8—42no—
673Q8—42no—
674Q8—84no—
675D4—24no—
676D4—24no—
677D4—48no—
678D4—42no—
679D4—42no—
680D4—42no—
681D4—42no—
682D4—42no—
683D4—42no—
684D4—816no—
685D4—816no—
686D4—84no—
687C2×C4—22no—
688C2×C4—28no—
689C2×C4—22no—
690C2×C4—28no—
691C2×C4—28no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—216no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—24no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—48no—
709C2×C4—44no—
710C2×C4—44no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—816no—
729C2×C4—84no—
730C2×C4—84no—
731C2×C4—84no—
732C2×C4—84no—
733C2×C4—84no—
734C2×C4C2×#12114yes—
735C2×C4C2×#12114yes—
736C2×C4C2×#12114yes—
737C2×C4C2×#12112yes—
738C2×C4C2×#12112yes—
739C2×C4#53712yes—
740C2×C4D4214yes—
741C2×C4#54714yes—
742C2×C4#54814yes—
743C2×C4#55314yes—
744C2×C4C23×D411yescharacteristic
745C2×C4C23×D411yescharacteristic
746C2×C4C22×#4111yescharacteristic
747C2×C4C22×#4111yescharacteristic
748C2×C4C2×H(5,𝔽2)11yescharacteristic
749C2×C4C2×2−1+411yescharacteristic
750C8—24no—
751C8—24no—
752C8—42no—
753C8—42no—
754C22—24no—
755C22—24no—
756C22—24no—
757C22—42no—
758C22—42no—
759C22—416no—
760C22—42no—
761C22—42no—
762C22—44no—
763C22—44no—
764C22—44no—
765C22—82no—
766C22—82no—
767C22—816no—
768C22—82no—
769C22—82no—
770C22—82no—
771C22—82no—
772C22—82no—
773C22—82no—
774C22—82no—
775C22—82no—
776C22—82no—
777C22—168no—
778C22#241614yes—
779C22#304114yes—
780C22#304614yes—
781C22#306114yes—
782C22#306214yes—
783C22#325714yes—
784C22#326214yes—
785C22C22×#12111yescharacteristic
786C22C22×#12111yescharacteristic
787C22C2×#53711yescharacteristic
788C22C2×#57611yescharacteristic
789C22C2×#57611yescharacteristic
790C22C2×#57711yescharacteristic
791C22C2×#57811yescharacteristic
792C4—24no—
793C4—24no—
794C4—24no—
795C4—44no—
796C4—42no—
797C4—42no—
798C4—82no—
799C4—82no—
800C4—82no—
801C4—82no—
802C4—82no—
803C4#241614yes—
804C4C2×D4211yescharacteristic
805C4C2×#54711yescharacteristic
806C4C2×#54811yescharacteristic
807C4C2×#55311yescharacteristic
808C2—44no—
809C2—84no—
810C2—162no—
811C2#2476318yesdirect product factor
812C2C2×#241611yescharacteristic
813C2C2×#304111yescharacteristic
814C2C2×#304611yescharacteristic
815C2C2×#306111yescharacteristic
816C2C2×#306211yescharacteristic
817C2C2×#325711yescharacteristic
818C2C2×#326211yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#466C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C22×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#468C2semidirect
3. C22×#463C2semidirect
4. C22×#424C2semidirect
5. C2×#2620C2semidirect
6. C2×#2324C2semidirect
7. #24763C2direct (N × H)
8. C2×#2068C2semidirect
9. C2×#2067C2semidirect
10. C2×#2055C2semidirect
11. C2×#2054C2semidirect
12. C2×#1983C2semidirect
13. C2×#1947C2semidirect
14. C2×#1895C2semidirect
15. C2×#1892C2semidirect
16. C2×#1802C2semidirect
28. C2×#468C22semidirect
32. C2×#463C22semidirect
36. C2×#424C22semidirect
50. #2620C22semidirect
56. #2324C22semidirect
68. #2068C22semidirect
69. #2067C22semidirect
70. #2055C22semidirect
71. #2054C22semidirect
72. #1983C22semidirect
73. #1947C22semidirect
74. #1895C22semidirect
75. #1892C22semidirect
76. #1802C22semidirect
170. C2×C4⋊C8D4semidirect
404. C4⋊C8C2×D4semidirect
811. C2#24763direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4682
C22×#4662
C22×#4632
C22×#4242
C2×#26202
C2×#23242
#247632
C2×#20682
C2×#20672
C2×#20552
C2×#20542
C2×#19832
C2×#19472
C2×#18952
C2×#18922
C2×#18022