Finite Group Databasebeta

← C2×#24654 #6448941

Subgroups — C2×#24654 #6448941

Order 512.

3004 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#463C211yesmaximal, characteristic, complemented
2C22×#431C211yesmaximal, characteristic, complemented
3C2×#2850C211yesmaximal, characteristic, complemented
4C2×C4×#121C211yesmaximal, characteristic, complemented
5#24654C2116yesmaximal, direct product factor
6C2×#2036C211yesmaximal, characteristic, complemented
7C2×#2034C211yesmaximal, characteristic, complemented
8C2×#2000C211yesmaximal, characteristic, complemented
9C2×#1999C211yesmaximal, characteristic
10C2×#1983C211yesmaximal, characteristic, complemented
11C2×#1970C211yesmaximal, characteristic, complemented
12C2×#1968C211yesmaximal, characteristic, complemented
13C2×#1949C211yesmaximal, characteristic, complemented
14C2×#1934C211yesmaximal, characteristic, complemented
15C2×#1933C211yesmaximal, characteristic, complemented
16C2×#1804C211yesmaximal, characteristic, complemented
17C23×SD16C2211yescharacteristic
18C23×D8C2211yescharacteristic
19C22×#124C2211yescharacteristic
20C22×C22⋊Q8C2211yescharacteristic
21C22×#121C2211yescharacteristic
22C22×#121C2211yescharacteristic
23C22×C4×D4—21no—
24C22×C4×D4C2211yescharacteristic
25C23×C42C2211yescharacteristic
26C2×#463—28no—
27C2×#463C2218yescomplemented
28C2×#431—28no—
29C2×#431C2218yescomplemented
30C22×#107C2211yescharacteristic
31C22×#106C2211yescharacteristic
32C22×C4⋊C8C2211yescharacteristic
33C22×C4⋊C8C2211yescharacteristic
34C22×#103C2211yescharacteristic
35C22×#103C2211yescharacteristic
36C22×#103C2211yescharacteristic
37C22×#102C2211yescharacteristic
38C22×#102C2211yescharacteristic
39C22×#102C2211yescharacteristic
40C22×#102C2211yescharacteristic
41C22×#102C2211yescharacteristic
42C22×C22⋊C8C2211yescharacteristic
43C22×C22⋊C8C2211yescharacteristic
44C22×C4×C8C2211yescharacteristic
45C22×C4×C8C2211yescharacteristic
46#2850—24no—
47#2850C2218yescomplemented
48C4×#121—24no—
49C4×#121C2218yescomplemented
50C2×#391C2211yescharacteristic
51C2×#390C2211yescharacteristic
52C2×#390C2211yescharacteristic
53C2×#389C2211yescharacteristic
54C2×#388—21no—
55C2×#388—21no—
56C2×#388—21no—
57C2×#386—21no—
58C2×#386—21no—
59C2×#386—21no—
60C2×#382C2211yescharacteristic
61C2×#380C2211yescharacteristic
62C2×C4×C4⋊C4C2211yescharacteristic
63C2×C4×C22⋊C4—21no—
64#2036C2218yescomplemented
65#2034C2218yescomplemented
66#2000C2218yescomplemented
67#1999C2218yes—
68#1983C2218yescomplemented
69#1970C2218yescomplemented
70#1968C2218yescomplemented
71#1949C2218yescomplemented
72#1934C2218yescomplemented
73#1933C2218yescomplemented
74#1804C2218yescomplemented
75C2×#340C2211yescharacteristic
76C2×#340C2211yescharacteristic
77C2×#340C2211yescharacteristic
78C2×#340C2211yescharacteristic
79C23×Q8C2311yescharacteristic
80C23×D4—21no—
81C23×D4—21no—
82C23×D4C2311yescharacteristic
83C23×D4C2311yescharacteristic
84C24×C4—21no—
85C24×C4D411yescharacteristic
86C24×C4D411yescharacteristic
87C24×C4C2311yescharacteristic
88C22×SD16—24no—
89C22×SD16—24no—
90C22×SD16—42no—
91C22×SD16C2314yes—
92C22×D8—24no—
93C22×D8—24no—
94C22×D8—42no—
95C22×D8C2314yes—
96C23×C8C2311yescharacteristic
97C23×C8C2311yescharacteristic
98C23×C8C2311yescharacteristic
99C23×C8C2311yescharacteristic
100C2×#124—22no—
101C2×#124—24no—
102C2×#124—24no—
103C2×#124C2314yes—
104C2×C22⋊Q8—22no—
105C2×C22⋊Q8—42no—
106C2×C22⋊Q8—42no—
107C2×C22⋊Q8C2314yes—
108C2×#121—24no—
109C2×#121—22no—
110C2×#121—22no—
111C2×#121—24no—
112C2×#121—42no—
113C2×#121—42no—
114C2×#121C2314yes—
115C2×#121C2314yes—
116C2×C4×D4—28no—
117C2×C4×D4—22no—
118C2×C4×D4—24no—
119C2×C4×D4—24no—
120C2×C4×D4—48no—
121C2×C4×D4C2314yes—
122C22×C4⋊C4—21no—
123C22×C4⋊C4—21no—
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2311yescharacteristic
129C22×C22⋊C4—21no—
130C22×C22⋊C4—21no—
131C22×C22⋊C4—21no—
132C22×C22⋊C4—21no—
133C22×C22⋊C4—21no—
134C22×C22⋊C4—21no—
135C22×C22⋊C4—21no—
136C22×C22⋊C4—21no—
137C22×C22⋊C4—21no—
138C22×C22⋊C4—21no—
139C22×C22⋊C4—21no—
140C22×C42—24no—
141C22×C42—24no—
142C22×C42—21no—
143C22×C42D414yes—
144C22×C42D411yescharacteristic
145C22×C42D411yescharacteristic
146C22×C42C2314yes—
147C22×C42C2311yescharacteristic
148C22×C42C2311yescharacteristic
149#463—232no—
150#431—232no—
151C2×#107—42no—
152C2×#107C2314yes—
153C2×#106—42no—
154C2×#106C2314yes—
155C2×C4⋊C8—24no—
156C2×C4⋊C8D418yescomplemented
157C2×C4⋊C8C2314yes—
158C2×C4⋊C8C2314yes—
159C2×#103—24no—
160C2×#103—24no—
161C2×#103—42no—
162C2×#103C2314yes—
163C2×#103C2314yes—
164C2×#103C2314yes—
165C2×#102—24no—
166C2×#102—24no—
167C2×#102—42no—
168C2×#102—42no—
169C2×#102—42no—
170C2×#102C2314yes—
171C2×#102C2314yes—
172C2×#102C2314yes—
173C2×#102C2314yes—
174C2×#102C2314yes—
175C2×C22⋊C8—24no—
176C2×C22⋊C8—24no—
177C2×C22⋊C8C2314yes—
178C2×C22⋊C8C2314yes—
179C2×C4×C8—24no—
180C2×C4×C8—24no—
181C2×C4×C8C2314yes—
182C2×C4×C8C2314yes—
183#391—22no—
184#391C2314yes—
185#390—22no—
186#390—22no—
187#390C2314yes—
188#390C2314yes—
189#389—22no—
190#389C2314yes—
191#388—28no—
192#388—28no—
193#388—28no—
194#386—28no—
195#386—28no—
196#386—28no—
197#382—22no—
198#382C2314yes—
199#380—22no—
200#380C2314yes—
201C4×C4⋊C4—22no—
202C4×C4⋊C4C2314yes—
203C4×C22⋊C4—28no—
204C2×#95—21no—
205C2×#95—21no—
206C2×#95—21no—
207C2×#95—21no—
208C2×#95—21no—
209C2×#95—21no—
210C2×#95—21no—
211#340C2314yes—
212#340C2314yes—
213#340C2314yes—
214#340C2314yes—
215C25—21no—
216C25—21no—
217C25C2×D411yescharacteristic
218C22×Q8—21no—
219C22×Q8—22no—
220C22×Q8—22no—
221C22×Q8—22no—
222C22×Q8—22no—
223C22×Q8—22no—
224C22×Q8—22no—
225C22×Q8C2412yes—
226C22×D4—28no—
227C22×D4—24no—
228C22×D4—24no—
229C22×D4—22no—
230C22×D4—21no—
231C22×D4—22no—
232C22×D4—21no—
233C22×D4—22no—
234C22×D4—22no—
235C22×D4—22no—
236C22×D4—22no—
237C22×D4—22no—
238C22×D4—22no—
239C22×D4—22no—
240C22×D4—22no—
241C22×D4—22no—
242C22×D4—44no—
243C22×D4—44no—
244C22×D4—44no—
245C22×D4—44no—
246C22×D4—44no—
247C22×D4#4114yes—
248C22×D4C2412yes—
249C22×D4C2412yes—
250C23×C4—24no—
251C23×C4—24no—
252C23×C4—24no—
253C23×C4—21no—
254C23×C4—24no—
255C23×C4—24no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—21no—
263C23×C4—21no—
264C23×C4—21no—
265C23×C4—21no—
266C23×C4—21no—
267C23×C4—24no—
268C23×C4—42no—
269C23×C4—44no—
270C23×C4—44no—
271C23×C4—44no—
272C23×C4C2×D412yes—
273C23×C4C2×D414yes—
274C23×C4C2×D411yescharacteristic
275C23×C4C2×D414yes—
276C23×C4C2×D411yescharacteristic
277C23×C4C2×D411yescharacteristic
278C23×C4C2×D411yescharacteristic
279C23×C4C2×D411yescharacteristic
280C23×C4C2412yes—
281C23×C4C2411yescharacteristic
282C2×SD16—28no—
283C2×SD16—28no—
284C2×SD16—44no—
285C2×SD16—416no—
286C2×D8—28no—
287C2×D8—28no—
288C2×D8—44no—
289C2×D8—416no—
290C22×C8—22no—
291C22×C8—22no—
292C22×C8—22no—
293C22×C8—22no—
294C22×C8—22no—
295C22×C8—22no—
296C22×C8—22no—
297C22×C8—22no—
298C22×C8—22no—
299C22×C8—22no—
300C22×C8C2×D414yes—
301C22×C8C2×D414yes—
302C22×C8C2412yes—
303C22×C8C2412yes—
304C22×C8C2412yes—
305C22×C8C2412yes—
306#124—28no—
307#124—28no—
308#124—48no—
309C22⋊Q8—44no—
310C22⋊Q8—44no—
311C22⋊Q8—48no—
312#121—216no—
313#121—28no—
314#121—28no—
315#121—44no—
316#121—44no—
317#121—48no—
318C4×D4—28no—
319C4×D4—28no—
320C4×D4—432no—
321C4×D4—48no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—44no—
339C2×C4⋊C4—44no—
340C2×C4⋊C4#4114yes—
341C2×C4⋊C4C2412yes—
342C2×C4⋊C4C2412yes—
343C2×C4⋊C4C2412yes—
344C2×C4⋊C4C2412yes—
345C2×C4⋊C4C2412yes—
346C2×C22⋊C4—28no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
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⋊C4—44no—
365C2×C22⋊C4—44no—
366C2×C22⋊C4—44no—
367C2×C22⋊C4—44no—
368C2×C42—24no—
369C2×C42—24no—
370C2×C42—22no—
371C2×C42—22no—
372C2×C42—216no—
373C2×C42—28no—
374C2×C42—28no—
375C2×C42—24no—
376C2×C42—44no—
377C2×C42C2×D414yes—
378C2×C42C2×D414yes—
379C2×C42C2×D412yes—
380C2×C42C2×D412yes—
381C2×C42C2×D414yes—
382C2×C42#4114yes—
383C2×C42C2412yes—
384C2×C42C2412yes—
385#107—44no—
386#106—44no—
387C4⋊C8—28no—
388C4⋊C8C2×D4116yescomplemented
389#103—28no—
390#103—28no—
391#103—44no—
392#102—28no—
393#102—28no—
394#102—44no—
395#102—44no—
396#102—44no—
397C22⋊C8—28no—
398C22⋊C8—28no—
399C4×C8—28no—
400C4×C8—28no—
401#95—24no—
402#95—24no—
403#95—24no—
404#95—24no—
405#95—24no—
406#95—24no—
407#95—24no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—24no—
415C24—22no—
416C24—22no—
417C24—42no—
418C24—42no—
419C24—42no—
420C24—42no—
421C24—42no—
422C24—42no—
423C24—42no—
424C24—42no—
425C24—42no—
426C24—42no—
427C24—42no—
428C24—42no—
429C24—42no—
430C24#13514yes—
431C24C22×D412yes—
432C24C22×D411yescharacteristic
433C2×Q8—22no—
434C2×Q8—22no—
435C2×Q8—22no—
436C2×Q8—22no—
437C2×Q8—22no—
438C2×Q8—22no—
439C2×Q8—42no—
440C2×Q8—42no—
441C2×Q8—42no—
442C2×Q8—44no—
443C2×Q8—44no—
444C2×Q8—44no—
445C2×Q8—44no—
446C2×D4—216no—
447C2×D4—24no—
448C2×D4—28no—
449C2×D4—28no—
450C2×D4—22no—
451C2×D4—22no—
452C2×D4—22no—
453C2×D4—22no—
454C2×D4—22no—
455C2×D4—22no—
456C2×D4—22no—
457C2×D4—22no—
458C2×D4—22no—
459C2×D4—22no—
460C2×D4—22no—
461C2×D4—48no—
462C2×D4—432no—
463C2×D4—48no—
464C2×D4—48no—
465C2×D4—48no—
466C2×D4—48no—
467C2×D4—42no—
468C2×D4—42no—
469C2×D4—42no—
470C2×D4—42no—
471C2×D4—42no—
472C2×D4—44no—
473C2×D4—44no—
474C2×D4—44no—
475C2×D4—44no—
476C2×D4—44no—
477C2×D4—44no—
478C2×D4—816no—
479C2×D4C2×#4114yes—
480C22×C4—232no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—28no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—28no—
491C22×C4—28no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—24no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—28no—
498C22×C4—24no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—28no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—44no—
514C22×C4—416no—
515C22×C4—48no—
516C22×C4—48no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—44no—
520C22×C4—44no—
521C22×C4—44no—
522C22×C4—44no—
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—42no—
537C22×C4—42no—
538C22×C4—48no—
539C22×C4—816no—
540C22×C4#12114yes—
541C22×C4#12114yes—
542C22×C4#13514yes—
543C22×C4AGL(1,ℤ/8)14yes—
544C22×C4C22×D412yes—
545C22×C4C22×D412yes—
546C22×C4C22×D412yes—
547C22×C4C22×D412yes—
548C22×C4C22×D412yes—
549C22×C4C22×D411yescharacteristic
550C22×C4C22×D412yes—
551C22×C4C2×#4112yes—
552C22×C4C2×#4112yes—
553C22×C4C2×#4112yes—
554C22×C4H(5,𝔽2)12yes—
555C22×C4H(5,𝔽2)12yes—
556C22×C4C2511yescharacteristic
557SD16—416no—
558D8—416no—
559C2×C8—28no—
560C2×C8—28no—
561C2×C8—22no—
562C2×C8—22no—
563C2×C8—22no—
564C2×C8—22no—
565C2×C8—22no—
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8—22no—
570C2×C8—22no—
571C2×C8—44no—
572C2×C8—44no—
573C2×C8C22×D414yes—
574C2×C8C22×D414yes—
575C4⋊C4—24no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—22no—
579C4⋊C4—22no—
580C4⋊C4—22no—
581C4⋊C4—22no—
582C4⋊C4—22no—
583C4⋊C4—22no—
584C4⋊C4—22no—
585C4⋊C4—48no—
586C4⋊C4—42no—
587C4⋊C4—42no—
588C4⋊C4—42no—
589C4⋊C4—42no—
590C4⋊C4—48no—
591C4⋊C4C2×#4114yes—
592C22⋊C4—216no—
593C22⋊C4—48no—
594C22⋊C4—48no—
595C22⋊C4—48no—
596C22⋊C4—48no—
597C22⋊C4—48no—
598C22⋊C4—48no—
599C22⋊C4—48no—
600C22⋊C4—48no—
601C22⋊C4—48no—
602C22⋊C4—48no—
603C42—24no—
604C42—28no—
605C42—28no—
606C42—22no—
607C42—22no—
608C42—48no—
609C42#12118yes—
610C42C22×D414yes—
611C42C2×#4114yes—
612C23—28no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—28no—
617C23—28no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—24no—
622C23—44no—
623C23—44no—
624C23—44no—
625C23—44no—
626C23—48no—
627C23—48no—
628C23—42no—
629C23—48no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—84no—
643C23—84no—
644C23—84no—
645C23—84no—
646C23—84no—
647C23—84no—
648C23—84no—
649C23—84no—
650C23—84no—
651C23—84no—
652C23—84no—
653C23C2×#12112yes—
654C23#52512yes—
655C23#53512yes—
656C23C2×#13514yes—
657C23C2×#13512yes—
658C23C2×#13512yes—
659C23C2×AGL(1,ℤ/8)12yes—
660C23#57512yes—
661C23C23×D411yescharacteristic
662Q8—42no—
663Q8—42no—
664Q8—42no—
665Q8—42no—
666Q8—84no—
667D4—24no—
668D4—24no—
669D4—432no—
670D4—48no—
671D4—42no—
672D4—42no—
673D4—42no—
674D4—42no—
675D4—42no—
676D4—42no—
677D4—816no—
678D4—84no—
679C2×C4—232no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—28no—
683C2×C4—28no—
684C2×C4—28no—
685C2×C4—28no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—416no—
697C2×C4—48no—
698C2×C4—44no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—48no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
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—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—816no—
722C2×C4—84no—
723C2×C4—84no—
724C2×C4—84no—
725C2×C4—84no—
726C2×C4—84no—
727C2×C4C2×#12114yes—
728C2×C4C2×#12114yes—
729C2×C4C2×#12112yes—
730C2×C4#52512yes—
731C2×C4#53512yes—
732C2×C4#54614yes—
733C2×C4#55014yes—
734C2×C4#55314yes—
735C2×C4#55514yes—
736C2×C4C2×#13514yes—
737C2×C4C2×AGL(1,ℤ/8)14yes—
738C2×C4C23×D411yescharacteristic
739C2×C4C22×#4111yescharacteristic
740C2×C4C22×#4111yescharacteristic
741C2×C4C22×#4111yescharacteristic
742C2×C4C2×H(5,𝔽2)11yescharacteristic
743C2×C4C2×H(5,𝔽2)11yescharacteristic
744C8—24no—
745C8—24no—
746C8—42no—
747C8—42no—
748C22—24no—
749C22—24no—
750C22—24no—
751C22—42no—
752C22—416no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—44no—
757C22—44no—
758C22—44no—
759C22—82no—
760C22—82no—
761C22—816no—
762C22—82no—
763C22—82no—
764C22—82no—
765C22—82no—
766C22—82no—
767C22—82no—
768C22—82no—
769C22—82no—
770C22—82no—
771C22—168no—
772C22#241414yes—
773C22#305014yes—
774C22#305514yes—
775C22#310214yes—
776C22#310514yes—
777C22#320714yes—
778C22#321114yes—
779C22C22×#12111yescharacteristic
780C22C2×#52511yescharacteristic
781C22C2×#53511yescharacteristic
782C22C22×#13511yescharacteristic
783C22C22×#13511yescharacteristic
784C22C22×AGL(1,ℤ/8)11yescharacteristic
785C22C2×#57511yescharacteristic
786C4—24no—
787C4—24no—
788C4—24no—
789C4—24no—
790C4—44no—
791C4—42no—
792C4—82no—
793C4—82no—
794C4—82no—
795C4—82no—
796C4—82no—
797C4#241414yes—
798C4C2×#54611yescharacteristic
799C4C2×#55011yescharacteristic
800C4C2×#55311yescharacteristic
801C4C2×#55511yescharacteristic
802C2—44no—
803C2—84no—
804C2—162no—
805C2#2465418yesdirect product factor
806C2C2×#241411yescharacteristic
807C2C2×#305011yescharacteristic
808C2C2×#305511yescharacteristic
809C2C2×#310211yescharacteristic
810C2C2×#310511yescharacteristic
811C2C2×#321111yescharacteristic
812C2C2×#320711yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#1999C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C23×C42 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#463C2semidirect
2. C22×#431C2semidirect
3. C2×#2850C2semidirect
4. C2×C4×#121C2semidirect
5. #24654C2direct (N × H)
6. C2×#2036C2semidirect
7. C2×#2034C2semidirect
8. C2×#2000C2semidirect
10. C2×#1983C2semidirect
11. C2×#1970C2semidirect
12. C2×#1968C2semidirect
13. C2×#1949C2semidirect
14. C2×#1934C2semidirect
15. C2×#1933C2semidirect
16. C2×#1804C2semidirect
27. C2×#463C22semidirect
29. C2×#431C22semidirect
47. #2850C22semidirect
49. C4×#121C22semidirect
64. #2036C22semidirect
65. #2034C22semidirect
66. #2000C22semidirect
68. #1983C22semidirect
69. #1970C22semidirect
70. #1968C22semidirect
71. #1949C22semidirect
72. #1934C22semidirect
73. #1933C22semidirect
74. #1804C22semidirect
156. C2×C4⋊C8D4semidirect
388. C4⋊C8C2×D4semidirect
805. C2#24654direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4632
C22×#4312
C2×#28502
C2×C4×#1212
#246542
C2×#20362
C2×#20342
C2×#20002
C2×#19992
C2×#19832
C2×#19702
C2×#19682
C2×#19492
C2×#19342
C2×#19332
C2×#18042