Finite Group Databasebeta

← C2×#28610 #6462931

Subgroups — C2×#28610 #6462931

Order 512.

2804 conjugacy classes of subgroups.

The subgroup lattice has 811 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#489C211yesmaximal, characteristic, complemented
2C22×#435C211yesmaximal, characteristic, complemented
3C2×#2547C211yesmaximal, characteristic, complemented
4C2×#2540C211yesmaximal, characteristic
5#28610C2116yesmaximal, direct product factor
6C2×#2036C211yesmaximal, characteristic, complemented
7C2×#2034C211yesmaximal, characteristic, complemented
8C2×#2035C211yesmaximal, characteristic, complemented
9C2×#2033C211yesmaximal, characteristic, complemented
10C2×#1987C211yesmaximal, characteristic, complemented
11C2×#1983C211yesmaximal, characteristic, complemented
12C2×#1895C211yesmaximal, characteristic, complemented
13C2×#1894C211yesmaximal, characteristic, complemented
14C2×#1893C211yesmaximal, characteristic, complemented
15C2×#1892C211yesmaximal, characteristic, complemented
16C2×#1776C211yesmaximal, characteristic, complemented
17C23×M16C2211yescharacteristic
18C24×C8C2211yescharacteristic
19C22×C4⋊Q8C2211yescharacteristic
20C22×#124—21no—
21C22×#124C2211yescharacteristic
22C22×C22⋊Q8C2211yescharacteristic
23C22×C22⋊Q8C2211yescharacteristic
24C22×#121C2211yescharacteristic
25C22×#121C2211yescharacteristic
26C22×C4×D4C2211yescharacteristic
27C2×#489—28no—
28C2×#489C2218yescomplemented
29C2×#435—28no—
30C2×#435C2218yescomplemented
31C22×#107C2211yescharacteristic
32C22×#106C2211yescharacteristic
33C22×C4⋊C8C2211yescharacteristic
34C22×#103C2211yescharacteristic
35C22×#103C2211yescharacteristic
36C22×#103C2211yescharacteristic
37C22×#103C2211yescharacteristic
38C22×#102C2211yescharacteristic
39C22×#102C2211yescharacteristic
40C22×#102C2211yescharacteristic
41C22×#102C2211yescharacteristic
42C22×C22⋊C8C2211yescharacteristic
43C22×C22⋊C8C2211yescharacteristic
44C22×#97C2211yescharacteristic
45#2547—24no—
46#2547C2218yescomplemented
47#2540—24no—
48#2540C2218yes—
49C2×#399—21no—
50C2×#397—21no—
51C2×#397—21no—
52C2×#392—21no—
53C2×#391—21no—
54C2×#390—21no—
55C2×#390—21no—
56C2×#380C2211yescharacteristic
57C2×#380C2211yescharacteristic
58C2×#380C2211yescharacteristic
59C2×#380C2211yescharacteristic
60C2×C4×C4⋊C4C2211yescharacteristic
61C2×C4×C4⋊C4C2211yescharacteristic
62#2036C2218yescomplemented
63#2035C2218yescomplemented
64#2034C2218yescomplemented
65#2033C2218yescomplemented
66#1987C2218yescomplemented
67#1983C2218yescomplemented
68#1895C2218yescomplemented
69#1894C2218yescomplemented
70#1893C2218yescomplemented
71#1892C2218yescomplemented
72#1776C2218yescomplemented
73C2×#340C2211yescharacteristic
74C2×#340C2211yescharacteristic
75C2×#340C2211yescharacteristic
76C2×#340C2211yescharacteristic
77C2×#340C2211yescharacteristic
78C2×#340C2211yescharacteristic
79C23×Q8—21no—
80C23×Q8C2311yescharacteristic
81C23×D4—21no—
82C23×D4—21no—
83C23×D4D411yescharacteristic
84C23×D4C2311yescharacteristic
85C24×C4C2311yescharacteristic
86C24×C4C2311yescharacteristic
87C22×M16—24no—
88C22×M16—42no—
89C22×M16—42no—
90C22×M16C2314yes—
91C23×C8—24no—
92C23×C8—42no—
93C23×C8—42no—
94C23×C8C2311yescharacteristic
95C23×C8C2311yescharacteristic
96C23×C8C2311yescharacteristic
97C23×C8C2311yescharacteristic
98C23×C8C2314yes—
99C2×C4⋊Q8—22no—
100C2×C4⋊Q8—24no—
101C2×C4⋊Q8—24no—
102C2×C4⋊Q8C2314yes—
103C2×#124—28no—
104C2×#124—22no—
105C2×#124—24no—
106C2×#124—24no—
107C2×#124—48no—
108C2×#124C2314yes—
109C2×C22⋊Q8—22no—
110C2×C22⋊Q8—22no—
111C2×C22⋊Q8—24no—
112C2×C22⋊Q8—24no—
113C2×C22⋊Q8—42no—
114C2×C22⋊Q8—42no—
115C2×C22⋊Q8C2314yes—
116C2×C22⋊Q8C2314yes—
117C2×#121—22no—
118C2×#121—22no—
119C2×#121—24no—
120C2×#121—24no—
121C2×#121—42no—
122C2×#121—42no—
123C2×#121C2314yes—
124C2×#121C2314yes—
125C2×C4×D4—24no—
126C2×C4×D4—24no—
127C2×C4×D4D414yes—
128C2×C4×D4C2314yes—
129C22×C4⋊C4—21no—
130C22×C4⋊C4—21no—
131C22×C4⋊C4—21no—
132C22×C4⋊C4D411yescharacteristic
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C22⋊C4—21no—
140C22×C22⋊C4—21no—
141C22×C22⋊C4—21no—
142C22×C22⋊C4—21no—
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⋊C4D411yescharacteristic
150C22×C22⋊C4D411yescharacteristic
151C22×C42—21no—
152C22×C42—21no—
153C22×C42C2311yescharacteristic
154#489—232no—
155#435—232no—
156C2×#107—24no—
157C2×#107C2314yes—
158C2×#106—24no—
159C2×#106C2314yes—
160C2×C4⋊C8—24no—
161C2×C4⋊C8C2314yes—
162C2×#103—24no—
163C2×#103—24no—
164C2×#103—42no—
165C2×#103—42no—
166C2×#103C2314yes—
167C2×#103C2314yes—
168C2×#103C2314yes—
169C2×#103C2314yes—
170C2×#102—24no—
171C2×#102—24no—
172C2×#102—42no—
173C2×#102—42no—
174C2×#102C2314yes—
175C2×#102C2314yes—
176C2×#102C2314yes—
177C2×#102C2314yes—
178C2×C22⋊C8—24no—
179C2×C22⋊C8—24no—
180C2×C22⋊C8C2314yes—
181C2×C22⋊C8C2314yes—
182C2×#97D418yescomplemented
183C2×#97C2314yes—
184#399—28no—
185#397—28no—
186#397—28no—
187#392—28no—
188#391—28no—
189#390—28no—
190#390—28no—
191#380—22no—
192#380—22no—
193#380—22no—
194#380—22no—
195#380C2314yes—
196#380C2314yes—
197#380C2314yes—
198#380C2314yes—
199C4×C4⋊C4—22no—
200C4×C4⋊C4—22no—
201C4×C4⋊C4C2314yes—
202C4×C4⋊C4C2314yes—
203C2×#95—21no—
204C2×#95—21no—
205C2×#95—21no—
206C2×#95—21no—
207C2×#95—21no—
208C2×#95—21no—
209#340C2314yes—
210#340C2314yes—
211#340C2314yes—
212#340C2314yes—
213#340C2314yes—
214#340C2314yes—
215C25—21no—
216C25C2×D411yescharacteristic
217C25C2×D411yescharacteristic
218C22×Q8—21no—
219C22×Q8—24no—
220C22×Q8—22no—
221C22×Q8—22no—
222C22×Q8—22no—
223C22×Q8—22no—
224C22×Q8—22no—
225C22×Q8—22no—
226C22×Q8—44no—
227C22×Q8—44no—
228C22×Q8—44no—
229C22×Q8C2412yes—
230C22×D4—24no—
231C22×D4—24no—
232C22×D4—24no—
233C22×D4—24no—
234C22×D4—22no—
235C22×D4—21no—
236C22×D4—22no—
237C22×D4—22no—
238C22×D4—22no—
239C22×D4—22no—
240C22×D4—22no—
241C22×D4—42no—
242C22×D4—44no—
243C22×D4—44no—
244C22×D4—44no—
245C22×D4—44no—
246C22×D4—82no—
247C22×D4—82no—
248C22×D4C2×D414yes—
249C22×D4C2412yes—
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—22no—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—21no—
265C23×C4—21no—
266C23×C4—21no—
267C23×C4—21no—
268C23×C4—21no—
269C23×C4C2×D412yes—
270C23×C4C2×D412yes—
271C23×C4C2×D411yescharacteristic
272C23×C4C2×D411yescharacteristic
273C23×C4C2×D411yescharacteristic
274C23×C4C2×D411yescharacteristic
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2411yescharacteristic
278C2×M16—28no—
279C2×M16—44no—
280C2×M16—44no—
281C2×M16—416no—
282C22×C8—22no—
283C22×C8—22no—
284C22×C8—22no—
285C22×C8—22no—
286C22×C8—22no—
287C22×C8—22no—
288C22×C8—22no—
289C22×C8—22no—
290C22×C8—22no—
291C22×C8—22no—
292C22×C8—28no—
293C22×C8—44no—
294C22×C8—44no—
295C22×C8—416no—
296C22×C8C2×D414yes—
297C22×C8C2×D414yes—
298C22×C8C2412yes—
299C22×C8C2412yes—
300C22×C8C2412yes—
301C22×C8C2412yes—
302C4⋊Q8—28no—
303C4⋊Q8—28no—
304C4⋊Q8—48no—
305#124—28no—
306#124—28no—
307#124—432no—
308#124—48no—
309C22⋊Q8—28no—
310C22⋊Q8—28no—
311C22⋊Q8—44no—
312C22⋊Q8—44no—
313C22⋊Q8—48no—
314C22⋊Q8—48no—
315#121—28no—
316#121—28no—
317#121—44no—
318#121—44no—
319#121—48no—
320#121—48no—
321C4×D4—216no—
322C4×D4—28no—
323C4×D4—28no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
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—24no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—44no—
345C2×C4⋊C4—44no—
346C2×C4⋊C4—44no—
347C2×C4⋊C4C2×D414yes—
348C2×C4⋊C4#4114yes—
349C2×C4⋊C4#4114yes—
350C2×C4⋊C4C2412yes—
351C2×C4⋊C4C2412yes—
352C2×C4⋊C4C2412yes—
353C2×C4⋊C4C2412yes—
354C2×C4⋊C4C2412yes—
355C2×C4⋊C4C2412yes—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—44no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4—44no—
375C2×C22⋊C4—44no—
376C2×C22⋊C4—44no—
377C2×C22⋊C4—44no—
378C2×C22⋊C4C2×D414yes—
379C2×C22⋊C4C2×D414yes—
380C2×C42—24no—
381C2×C42—24no—
382C2×C42—44no—
383C2×C42—82no—
384C2×C42C2×D412yes—
385C2×C42C2×D414yes—
386C2×C42#4114yes—
387C2×C42C2412yes—
388#107—28no—
389#106—28no—
390C4⋊C8—28no—
391#103—28no—
392#103—28no—
393#103—44no—
394#103—44no—
395#102—28no—
396#102—28no—
397#102—44no—
398#102—44no—
399C22⋊C8—28no—
400C22⋊C8—28no—
401#97C2×D4116yescomplemented
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—22no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—42no—
423C24—42no—
424C24—42no—
425C24—42no—
426C24—42no—
427C24—42no—
428C24—42no—
429C24AGL(1,ℤ/8)14yes—
430C24C22×D412yes—
431C24C22×D412yes—
432C24C22×D411yescharacteristic
433C2×Q8—22no—
434C2×Q8—22no—
435C2×Q8—22no—
436C2×Q8—22no—
437C2×Q8—22no—
438C2×Q8—22no—
439C2×Q8—48no—
440C2×Q8—48no—
441C2×Q8—42no—
442C2×Q8—48no—
443C2×Q8—42no—
444C2×Q8—42no—
445C2×Q8—44no—
446C2×Q8—44no—
447C2×Q8—44no—
448C2×Q8—44no—
449C2×Q8—816no—
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—44no—
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—84no—
473C2×D4—816no—
474C2×D4—816no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—24no—
482C22×C4—24no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—24no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
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—42no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—44no—
517C22×C4—44no—
518C22×C4—44no—
519C22×C4—44no—
520C22×C4—44no—
521C22×C4—44no—
522C22×C4—44no—
523C22×C4—44no—
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—42no—
539C22×C4#12114yes—
540C22×C4#12114yes—
541C22×C4C22×D412yes—
542C22×C4C22×D412yes—
543C22×C4C22×D412yes—
544C22×C4C22×D412yes—
545C22×C4C22×D411yescharacteristic
546C22×C4C22×D412yes—
547C22×C4C2×#4112yes—
548C22×C4C2×#4112yes—
549C22×C4C2×#4112yes—
550C22×C4H(5,𝔽2)12yes—
551C22×C4H(5,𝔽2)12yes—
552C22×C4C2511yescharacteristic
553M16—416no—
554C2×C8—28no—
555C2×C8—28no—
556C2×C8—22no—
557C2×C8—22no—
558C2×C8—22no—
559C2×C8—22no—
560C2×C8—22no—
561C2×C8—22no—
562C2×C8—22no—
563C2×C8—22no—
564C2×C8—22no—
565C2×C8—22no—
566C2×C8—416no—
567C2×C8—44no—
568C2×C8—44no—
569C2×C8C22×D414yes—
570C2×C8C22×D414yes—
571C4⋊C4—28no—
572C4⋊C4—24no—
573C4⋊C4—24no—
574C4⋊C4—22no—
575C4⋊C4—22no—
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—48no—
585C4⋊C4—48no—
586C4⋊C4—42no—
587C4⋊C4—42no—
588C4⋊C4—48no—
589C4⋊C4—42no—
590C4⋊C4—42no—
591C4⋊C4C2×#4114yes—
592C4⋊C4C2×#4114yes—
593C22⋊C4—28no—
594C22⋊C4—28no—
595C22⋊C4—48no—
596C22⋊C4—48no—
597C22⋊C4—48no—
598C22⋊C4—48no—
599C22⋊C4—48no—
600C22⋊C4—48no—
601C22⋊C4—48no—
602C22⋊C4—48no—
603C22⋊C4—48no—
604C22⋊C4—48no—
605C42—48no—
606C42—84no—
607C42#12118yes—
608C42C22×D414yes—
609C42C2×#4114yes—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—28no—
614C23—28no—
615C23—28no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—44no—
627C23—44no—
628C23—44no—
629C23—44no—
630C23—44no—
631C23—44no—
632C23—44no—
633C23—44no—
634C23—44no—
635C23—44no—
636C23—44no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—84no—
645C23—84no—
646C23—84no—
647C23—84no—
648C23—84no—
649C23—84no—
650C23—84no—
651C23C2×#12112yes—
652C23#54612yes—
653C23#54612yes—
654C23C2×AGL(1,ℤ/8)14yes—
655C23C2×AGL(1,ℤ/8)12yes—
656C23#57512yes—
657C23#57712yes—
658C23#57812yes—
659C23C23×D411yescharacteristic
660Q8—42no—
661Q8—42no—
662Q8—42no—
663Q8—42no—
664Q8—816no—
665Q8—84no—
666D4—416no—
667D4—42no—
668D4—42no—
669D4—42no—
670D4—42no—
671D4—816no—
672D4—816no—
673D4—84no—
674C2×C4—28no—
675C2×C4—28no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—48no—
689C2×C4—48no—
690C2×C4—44no—
691C2×C4—44no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—48no—
705C2×C4—48no—
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—84no—
722C2×C4—84no—
723C2×C4—84no—
724C2×C4—84no—
725C2×C4—84no—
726C2×C4C2×#12114yes—
727C2×C4C2×#12114yes—
728C2×C4C2×#12112yes—
729C2×C4#53214yes—
730C2×C4#53514yes—
731C2×C4#54612yes—
732C2×C4#54612yes—
733C2×C4#55914yes—
734C2×C4#55914yes—
735C2×C4C23×D411yescharacteristic
736C2×C4C22×#4111yescharacteristic
737C2×C4C22×#4111yescharacteristic
738C2×C4C22×#4111yescharacteristic
739C2×C4C2×H(5,𝔽2)11yescharacteristic
740C2×C4C2×H(5,𝔽2)11yescharacteristic
741C8—24no—
742C8—24no—
743C8—42no—
744C8—42no—
745C22—24no—
746C22—24no—
747C22—24no—
748C22—42no—
749C22—42no—
750C22—416no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—88no—
761C22—82no—
762C22—82no—
763C22—82no—
764C22—82no—
765C22—82no—
766C22—82no—
767C22—82no—
768C22—168no—
769C22#254414yes—
770C22#305514yes—
771C22#306314yes—
772C22#330614yes—
773C22#330814yes—
774C22#331114yes—
775C22#331314yes—
776C22C22×#12111yescharacteristic
777C22C2×#54611yescharacteristic
778C22C2×#54611yescharacteristic
779C22C22×AGL(1,ℤ/8)11yescharacteristic
780C22C2×#57511yescharacteristic
781C22C2×#57711yescharacteristic
782C22C2×#57811yescharacteristic
783C4—24no—
784C4—24no—
785C4—42no—
786C4—42no—
787C4—44no—
788C4—44no—
789C4—82no—
790C4—82no—
791C4—82no—
792C4—82no—
793C4—82no—
794C4#254414yes—
795C4C2×#53211yescharacteristic
796C4C2×#53511yescharacteristic
797C4C2×#55911yescharacteristic
798C4C2×#55911yescharacteristic
799C2—44no—
800C2—82no—
801C2—162no—
802C2#2861018yesdirect product factor
803C2C2×#254411yescharacteristic
804C2C2×#305511yescharacteristic
805C2C2×#306311yescharacteristic
806C2C2×#330611yescharacteristic
807C2C2×#330811yescharacteristic
808C2C2×#331111yescharacteristic
809C2C2×#331311yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#2540C2
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×#489C2semidirect
2. C22×#435C2semidirect
3. C2×#2547C2semidirect
5. #28610C2direct (N × H)
6. C2×#2036C2semidirect
7. C2×#2034C2semidirect
8. C2×#2035C2semidirect
9. C2×#2033C2semidirect
10. C2×#1987C2semidirect
11. C2×#1983C2semidirect
12. C2×#1895C2semidirect
13. C2×#1894C2semidirect
14. C2×#1893C2semidirect
15. C2×#1892C2semidirect
16. C2×#1776C2semidirect
28. C2×#489C22semidirect
30. C2×#435C22semidirect
46. #2547C22semidirect
62. #2036C22semidirect
63. #2035C22semidirect
64. #2034C22semidirect
65. #2033C22semidirect
66. #1987C22semidirect
67. #1983C22semidirect
68. #1895C22semidirect
69. #1894C22semidirect
70. #1893C22semidirect
71. #1892C22semidirect
72. #1776C22semidirect
182. C2×#97D4semidirect
401. #97C2×D4semidirect
802. C2#28610direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4892
C22×#4352
C2×#25472
C2×#25402
#286102
C2×#20362
C2×#20342
C2×#20352
C2×#20332
C2×#19872
C2×#19832
C2×#18952
C2×#18942
C2×#18932
C2×#18922
C2×#17762