Finite Group Databasebeta

← C2×#28565 #6459474

Subgroups — C2×#28565 #6459474

Order 512.

2966 conjugacy classes of subgroups.

The subgroup lattice has 819 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#465C211yesmaximal, characteristic, complemented
2C22×#435C211yesmaximal, characteristic, complemented
3C2×#2417C211yesmaximal, characteristic, complemented
4C2×#2416C211yesmaximal, characteristic
5#28565C2116yesmaximal, direct product factor
6C2×#2088C211yesmaximal, characteristic, complemented
7C2×#2077C211yesmaximal, characteristic, complemented
8C2×#2055C211yesmaximal, characteristic, complemented
9C2×#2000C211yesmaximal, characteristic, complemented
10C2×#1936C211yesmaximal, characteristic, complemented
11C2×#1935C211yesmaximal, characteristic, complemented
12C2×#1895C211yesmaximal, characteristic, complemented
13C2×#1894C211yesmaximal, characteristic, complemented
14C2×#1874C211yesmaximal, characteristic, complemented
15C2×#1872C211yesmaximal, characteristic, complemented
16C22×#340C211yesmaximal, characteristic, complemented
17C23×SD16C2211yescharacteristic
18C23×M16C2211yescharacteristic
19C24×C8C2211yescharacteristic
20C22×C22⋊Q8C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C22×#121—21no—
23C22×#121C2211yescharacteristic
24C22×#121C2211yescharacteristic
25C22×C4×D4C2211yescharacteristic
26C23×C4⋊C4C2211yescharacteristic
27C23×C4⋊C4C2211yescharacteristic
28C2×#465—28no—
29C2×#465C2218yescomplemented
30C2×#435—28no—
31C2×#435C2218yescomplemented
32C22×#106C2211yescharacteristic
33C22×C4⋊C8C2211yescharacteristic
34C22×#103C2211yescharacteristic
35C22×#103C2211yescharacteristic
36C22×#103C2211yescharacteristic
37C22×#102C2211yescharacteristic
38C22×#102C2211yescharacteristic
39C22×#102C2211yescharacteristic
40C22×C22⋊C8C2211yescharacteristic
41C22×C22⋊C8C2211yescharacteristic
42C22×#97C2211yescharacteristic
43#2417—24no—
44#2417C2218yescomplemented
45#2416—24no—
46#2416C2218yes—
47C2×#398—21no—
48C2×#396—21no—
49C2×#396—21no—
50C2×#394—21no—
51C2×#391C2211yescharacteristic
52C2×#390C2211yescharacteristic
53C2×#389C2211yescharacteristic
54C2×#389C2211yescharacteristic
55C2×#386—21no—
56C2×#386—21no—
57C2×#380—21no—
58C2×#380C2211yescharacteristic
59C2×#380C2211yescharacteristic
60#2088C2218yescomplemented
61#2077C2218yescomplemented
62#2055C2218yescomplemented
63#2000C2218yescomplemented
64#1936C2218yescomplemented
65#1935C2218yescomplemented
66#1895C2218yescomplemented
67#1894C2218yescomplemented
68#1874C2218yescomplemented
69#1872C2218yescomplemented
70C2×#340C2211yescharacteristic
71C2×#340C2211yescharacteristic
72C2×#340C2211yescharacteristic
73C2×#340C2211yescharacteristic
74C2×#340C2211yescharacteristic
75C2×#340C2211yescharacteristic
76C2×#340C2211yescharacteristic
77C2×#340C2211yescharacteristic
78C2×#340C2218yescomplemented
79C23×Q8C2311yescharacteristic
80C23×D4—21no—
81C23×D4—21no—
82C23×D4D411yescharacteristic
83C23×D4C2311yescharacteristic
84C24×C4—21no—
85C24×C4—21no—
86C24×C4C2311yescharacteristic
87C24×C4C2311yescharacteristic
88C22×SD16—24no—
89C22×SD16—42no—
90C22×SD16—42no—
91C22×SD16C2314yes—
92C22×M16—24no—
93C22×M16—42no—
94C22×M16—42no—
95C22×M16C2314yes—
96C23×C8—42no—
97C23×C8—42no—
98C23×C8D418yescomplemented
99C23×C8C2311yescharacteristic
100C23×C8C2311yescharacteristic
101C23×C8C2311yescharacteristic
102C23×C8C2311yescharacteristic
103C23×C8C2314yes—
104C2×C22⋊Q8—22no—
105C2×C22⋊Q8—22no—
106C2×C22⋊Q8—24no—
107C2×C22⋊Q8—24no—
108C2×C22⋊Q8—24no—
109C2×C22⋊Q8—42no—
110C2×C22⋊Q8C2314yes—
111C2×C22⋊Q8C2314yes—
112C2×#121—28no—
113C2×#121—22no—
114C2×#121—22no—
115C2×#121—24no—
116C2×#121—24no—
117C2×#121—24no—
118C2×#121—42no—
119C2×#121—48no—
120C2×#121C2314yes—
121C2×#121C2314yes—
122C2×C4×D4—24no—
123C2×C4×D4—24no—
124C2×C4×D4D414yes—
125C2×C4×D4C2314yes—
126C22×C4⋊C4—24no—
127C22×C4⋊C4—24no—
128C22×C4⋊C4—21no—
129C22×C4⋊C4—21no—
130C22×C4⋊C4—21no—
131C22×C4⋊C4—21no—
132C22×C4⋊C4—21no—
133C22×C4⋊C4—22no—
134C22×C4⋊C4—22no—
135C22×C4⋊C4—21no—
136C22×C4⋊C4—42no—
137C22×C4⋊C4—42no—
138C22×C4⋊C4D411yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2314yes—
144C22×C4⋊C4C2314yes—
145C22×C4⋊C4C2311yescharacteristic
146C22×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
155C22×C22⋊C4D411yescharacteristic
156C22×C22⋊C4D411yescharacteristic
157C22×C42C2311yescharacteristic
158#465—232no—
159#435—232no—
160C2×#106—24no—
161C2×#106C2314yes—
162C2×C4⋊C8—24no—
163C2×C4⋊C8C2314yes—
164C2×#103—24no—
165C2×#103—24no—
166C2×#103—42no—
167C2×#103C2314yes—
168C2×#103C2314yes—
169C2×#103C2314yes—
170C2×#102—24no—
171C2×#102—24no—
172C2×#102—42no—
173C2×#102C2314yes—
174C2×#102C2314yes—
175C2×#102C2314yes—
176C2×C22⋊C8—24no—
177C2×C22⋊C8—24no—
178C2×C22⋊C8C2314yes—
179C2×C22⋊C8C2314yes—
180C2×#97—24no—
181C2×#97C2314yes—
182#398—28no—
183#396—28no—
184#396—28no—
185#394—28no—
186#391—22no—
187#391C2314yes—
188#390—22no—
189#390C2314yes—
190#389—22no—
191#389—22no—
192#389C2314yes—
193#389C2314yes—
194#386—28no—
195#386—28no—
196#380—22no—
197#380—22no—
198#380—28no—
199#380C2314yes—
200#380C2314yes—
201C2×#95—21no—
202C2×#95—21no—
203C2×#95—21no—
204C2×#95—21no—
205C2×#95—21no—
206C2×#95—21no—
207#340C2314yes—
208#340C2314yes—
209#340C2314yes—
210#340C2314yes—
211#340C2314yes—
212#340C2314yes—
213#340C2314yes—
214#340C2314yes—
215C25—21no—
216C25C2×D411yescharacteristic
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—24no—
227C22×D4—24no—
228C22×D4—24no—
229C22×D4—24no—
230C22×D4—24no—
231C22×D4—22no—
232C22×D4—21no—
233C22×D4—22no—
234C22×D4—22no—
235C22×D4—22no—
236C22×D4—22no—
237C22×D4—22no—
238C22×D4—44no—
239C22×D4—44no—
240C22×D4—44no—
241C22×D4—44no—
242C22×D4—44no—
243C22×D4—82no—
244C22×D4C2×D414yes—
245C22×D4C2412yes—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—21no—
251C23×C4—21no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—21no—
259C23×C4—21no—
260C23×C4—21no—
261C23×C4—21no—
262C23×C4—21no—
263C23×C4—24no—
264C23×C4—24no—
265C23×C4—44no—
266C23×C4—44no—
267C23×C4—44no—
268C23×C4—44no—
269C23×C4—82no—
270C23×C4—82no—
271C23×C4C2×D412yes—
272C23×C4C2×D411yescharacteristic
273C23×C4C2×D411yescharacteristic
274C23×C4C2×D411yescharacteristic
275C23×C4C2×D412yes—
276C23×C4C2×D411yescharacteristic
277C23×C4C2×D414yes—
278C23×C4#4114yes—
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2411yescharacteristic
282C2×SD16—28no—
283C2×SD16—44no—
284C2×SD16—44no—
285C2×SD16—416no—
286C2×M16—28no—
287C2×M16—44no—
288C2×M16—44no—
289C2×M16—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×C8—416no—
301C22×C8—44no—
302C22×C8—44no—
303C22×C8C2×D414yes—
304C22×C8C2×D414yes—
305C22×C8C2×D4116yescomplemented
306C22×C8C2412yes—
307C22×C8C2412yes—
308C22×C8C2412yes—
309C22×C8C2412yes—
310C22⋊Q8—28no—
311C22⋊Q8—28no—
312C22⋊Q8—28no—
313C22⋊Q8—44no—
314C22⋊Q8—48no—
315C22⋊Q8—48no—
316#121—28no—
317#121—28no—
318#121—28no—
319#121—44no—
320#121—48no—
321#121—432no—
322#121—48no—
323C4×D4—216no—
324C4×D4—28no—
325C4×D4—28no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—28no—
340C2×C4⋊C4—28no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—44no—
352C2×C4⋊C4—44no—
353C2×C4⋊C4—48no—
354C2×C4⋊C4—48no—
355C2×C4⋊C4—44no—
356C2×C4⋊C4—44no—
357C2×C4⋊C4—44no—
358C2×C4⋊C4—44no—
359C2×C4⋊C4—44no—
360C2×C4⋊C4—82no—
361C2×C4⋊C4C2×D414yes—
362C2×C4⋊C4#4114yes—
363C2×C4⋊C4#4114yes—
364C2×C4⋊C4C2412yes—
365C2×C4⋊C4C2412yes—
366C2×C4⋊C4C2412yes—
367C2×C4⋊C4C2412yes—
368C2×C4⋊C4C2412yes—
369C2×C4⋊C4C2412yes—
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—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—44no—
381C2×C22⋊C4—44no—
382C2×C22⋊C4—44no—
383C2×C22⋊C4—44no—
384C2×C22⋊C4—44no—
385C2×C22⋊C4—44no—
386C2×C22⋊C4—82no—
387C2×C22⋊C4—82no—
388C2×C22⋊C4C2×D414yes—
389C2×C22⋊C4C2×D414yes—
390C2×C42—22no—
391C2×C42—22no—
392C2×C42C2×D412yes—
393C2×C42C2412yes—
394#106—28no—
395C4⋊C8—28no—
396#103—28no—
397#103—28no—
398#103—44no—
399#102—28no—
400#102—28no—
401#102—44no—
402C22⋊C8—28no—
403C22⋊C8—28no—
404#97—28no—
405#95—24no—
406#95—24no—
407#95—24no—
408#95—24no—
409#95—24no—
410#95—24no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—42no—
424C24—42no—
425C24—42no—
426C24—42no—
427C24—42no—
428C24—42no—
429C24—42no—
430C24#12114yes—
431C24AGL(1,ℤ/8)14yes—
432C24#13714yes—
433C24C22×D412yes—
434C24C22×D412yes—
435C24C22×D411yescharacteristic
436C2×Q8—22no—
437C2×Q8—22no—
438C2×Q8—22no—
439C2×Q8—22no—
440C2×Q8—22no—
441C2×Q8—22no—
442C2×Q8—42no—
443C2×Q8—42no—
444C2×Q8—42no—
445C2×Q8—44no—
446C2×Q8—44no—
447C2×Q8—44no—
448C2×Q8—44no—
449C2×D4—28no—
450C2×D4—28no—
451C2×D4—28no—
452C2×D4—22no—
453C2×D4—22no—
454C2×D4—22no—
455C2×D4—22no—
456C2×D4—22no—
457C2×D4—22no—
458C2×D4—48no—
459C2×D4—416no—
460C2×D4—48no—
461C2×D4—48no—
462C2×D4—48no—
463C2×D4—48no—
464C2×D4—42no—
465C2×D4—44no—
466C2×D4—44no—
467C2×D4—42no—
468C2×D4—42no—
469C2×D4—44no—
470C2×D4—44no—
471C2×D4—84no—
472C2×D4—816no—
473C2×D4—816no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—28no—
477C22×C4—28no—
478C22×C4—24no—
479C22×C4—24no—
480C22×C4—28no—
481C22×C4—28no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—24no—
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—48no—
514C22×C4—48no—
515C22×C4—42no—
516C22×C4—42no—
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—48no—
533C22×C4—48no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—84no—
541C22×C4—84no—
542C22×C4—816no—
543C22×C4—816no—
544C22×C4#12114yes—
545C22×C4#12118yes—
546C22×C4C22×D412yes—
547C22×C4C22×D412yes—
548C22×C4C22×D412yes—
549C22×C4C22×D412yes—
550C22×C4C22×D414yes—
551C22×C4C22×D411yescharacteristic
552C22×C4C22×D412yes—
553C22×C4C2×#4114yes—
554C22×C4C2×#4112yes—
555C22×C4C2×#4112yes—
556C22×C4C2×#4112yes—
557C22×C4H(5,𝔽2)12yes—
558C22×C4H(5,𝔽2)12yes—
559C22×C4C2511yescharacteristic
560SD16—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—24no—
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—22no—
592C4⋊C4—48no—
593C4⋊C4—48no—
594C4⋊C4—48no—
595C4⋊C4—48no—
596C4⋊C4—42no—
597C4⋊C4—42no—
598C4⋊C4—48no—
599C4⋊C4—42no—
600C4⋊C4—42no—
601C4⋊C4—84no—
602C4⋊C4C2×#4114yes—
603C4⋊C4C2×#4114yes—
604C22⋊C4—28no—
605C22⋊C4—28no—
606C22⋊C4—48no—
607C22⋊C4—48no—
608C22⋊C4—48no—
609C22⋊C4—48no—
610C22⋊C4—48no—
611C22⋊C4—48no—
612C22⋊C4—84no—
613C22⋊C4—84no—
614C42—24no—
615C42—22no—
616C42—22no—
617C23—22no—
618C23—22no—
619C23—28no—
620C23—28no—
621C23—28no—
622C23—28no—
623C23—28no—
624C23—28no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—44no—
635C23—44no—
636C23—44no—
637C23—44no—
638C23—44no—
639C23—44no—
640C23—44no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—84no—
649C23—84no—
650C23—84no—
651C23—84no—
652C23—84no—
653C23—84no—
654C23—84no—
655C23#468116yes—
656C23C2×#12114yes—
657C23C2×#12112yes—
658C23#54612yes—
659C23#54612yes—
660C23C2×AGL(1,ℤ/8)14yes—
661C23C2×AGL(1,ℤ/8)12yes—
662C23C2×#13714yes—
663C23C2×#13712yes—
664C23#57712yes—
665C23#57712yes—
666C23C23×D411yescharacteristic
667Q8—42no—
668Q8—42no—
669Q8—42no—
670Q8—42no—
671Q8—84no—
672D4—416no—
673D4—42no—
674D4—42no—
675D4—42no—
676D4—42no—
677D4—816no—
678D4—816no—
679D4—84no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—28no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—216no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—48no—
700C2×C4—44no—
701C2×C4—48no—
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—42no—
711C2×C4—42no—
712C2×C4—48no—
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—816no—
730C2×C4—84no—
731C2×C4—84no—
732C2×C4—84no—
733C2×C4—84no—
734C2×C4—84no—
735C2×C4C2×#12114yes—
736C2×C4C2×#12112yes—
737C2×C4#53214yes—
738C2×C4#53414yes—
739C2×C4#54612yes—
740C2×C4#54612yes—
741C2×C4#55314yes—
742C2×C4#55314yes—
743C2×C4C23×D411yescharacteristic
744C2×C4C22×#4111yescharacteristic
745C2×C4C22×#4111yescharacteristic
746C2×C4C22×#4111yescharacteristic
747C2×C4C2×H(5,𝔽2)11yescharacteristic
748C2×C4C2×H(5,𝔽2)11yescharacteristic
749C8—24no—
750C8—24no—
751C8—42no—
752C8—42no—
753C22—24no—
754C22—24no—
755C22—232no—
756C22—24no—
757C22—24no—
758C22—24no—
759C22—24no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—88no—
768C22—82no—
769C22—82no—
770C22—82no—
771C22—82no—
772C22—82no—
773C22—82no—
774C22—82no—
775C22—168no—
776C22#254314yes—
777C22C2×#46818yes—
778C22C2×#46814yes—
779C22#306014yes—
780C22#330614yes—
781C22#331014yes—
782C22#331614yes—
783C22#332014yes—
784C22C22×#12111yescharacteristic
785C22C2×#54611yescharacteristic
786C22C2×#54611yescharacteristic
787C22C22×AGL(1,ℤ/8)11yescharacteristic
788C22C22×#13711yescharacteristic
789C22C2×#57711yescharacteristic
790C22C2×#57711yescharacteristic
791C4—24no—
792C4—42no—
793C4—42no—
794C4—42no—
795C4—44no—
796C4—44no—
797C4—82no—
798C4—82no—
799C4—82no—
800C4—82no—
801C4—82no—
802C4#254314yes—
803C4C2×#53211yescharacteristic
804C4C2×#53411yescharacteristic
805C4C2×#55311yescharacteristic
806C4C2×#55311yescharacteristic
807C2—28no—
808C2—82no—
809C2—162no—
810C2#2856518yesdirect product factor
811C2C2×#254311yescharacteristic
812C2C22×#46811yescharacteristic
813C2C2×#306011yescharacteristic
814C2C2×#330611yescharacteristic
815C2C2×#331011yescharacteristic
816C2C2×#331611yescharacteristic
817C2C2×#332011yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#2416C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C22×C4×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#465C2semidirect
2. C22×#435C2semidirect
3. C2×#2417C2semidirect
5. #28565C2direct (N × H)
6. C2×#2088C2semidirect
7. C2×#2077C2semidirect
8. C2×#2055C2semidirect
9. C2×#2000C2semidirect
10. C2×#1936C2semidirect
11. C2×#1935C2semidirect
12. C2×#1895C2semidirect
13. C2×#1894C2semidirect
14. C2×#1874C2semidirect
15. C2×#1872C2semidirect
16. C22×#340C2semidirect
29. C2×#465C22semidirect
31. C2×#435C22semidirect
44. #2417C22semidirect
60. #2088C22semidirect
61. #2077C22semidirect
62. #2055C22semidirect
63. #2000C22semidirect
64. #1936C22semidirect
65. #1935C22semidirect
66. #1895C22semidirect
67. #1894C22semidirect
68. #1874C22semidirect
69. #1872C22semidirect
78. C2×#340C22semidirect
98. C23×C8D4semidirect
305. C22×C8C2×D4semidirect
810. C2#28565direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4652
C22×#4352
C2×#24172
C2×#24162
#285652
C2×#20882
C2×#20772
C2×#20552
C2×#20002
C2×#19362
C2×#19352
C2×#18952
C2×#18942
C2×#18742
C2×#18722
C22×#3402