Finite Group Databasebeta

← C2×#24787 #6442881

Subgroups — C2×#24787 #6442881

Order 512.

3194 conjugacy classes of subgroups.

The subgroup lattice has 831 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#468C211yesmaximal, characteristic, complemented
2C22×#465C211yesmaximal, characteristic, complemented
3C22×#435C211yesmaximal, characteristic, complemented
4C23×#107C211yesmaximal, characteristic, complemented
5C2×#2417C211yesmaximal, characteristic, complemented
6C2×#2416C211yesmaximal, characteristic
7#24787C2116yesmaximal, direct product factor
8C2×#2068C211yesmaximal, characteristic, complemented
9C2×#2067C211yesmaximal, characteristic, complemented
10C2×#2036C211yesmaximal, characteristic, complemented
11C2×#2033C211yesmaximal, characteristic, complemented
12C2×#1973C211yesmaximal, characteristic, complemented
13C2×#1943C211yesmaximal, characteristic, complemented
14C2×#1874C211yesmaximal, characteristic, complemented
15C2×#1872C211yesmaximal, characteristic, complemented
16C2×#1809C211yesmaximal, 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×#468—28no—
29C2×#468C2218yescomplemented
30C2×#465—28no—
31C2×#465C2218yescomplemented
32C2×#435—28no—
33C2×#435C2218yescomplemented
34C22×#107—28no—
35C22×#107C2211yescharacteristic
36C22×#107C2211yescharacteristic
37C22×#107C2211yescharacteristic
38C22×#107C2211yescharacteristic
39C22×#107C2218yescomplemented
40C22×#106C2211yescharacteristic
41C22×C4⋊C8C2211yescharacteristic
42C22×#103C2211yescharacteristic
43C22×#103C2211yescharacteristic
44C22×#103C2211yescharacteristic
45C22×#102C2211yescharacteristic
46C22×#102C2211yescharacteristic
47C22×#102C2211yescharacteristic
48C22×C22⋊C8C2211yescharacteristic
49C22×C22⋊C8C2211yescharacteristic
50C22×#97C2211yescharacteristic
51#2417—24no—
52#2417C2218yescomplemented
53#2416—24no—
54#2416C2218yes—
55C2×#398—21no—
56C2×#396—21no—
57C2×#396—21no—
58C2×#394—21no—
59C2×#391C2211yescharacteristic
60C2×#390C2211yescharacteristic
61C2×#389C2211yescharacteristic
62C2×#389C2211yescharacteristic
63C2×#386—21no—
64C2×#386—21no—
65C2×#380—21no—
66C2×#380C2211yescharacteristic
67C2×#380C2211yescharacteristic
68#2068C2218yescomplemented
69#2067C2218yescomplemented
70#2036C2218yescomplemented
71#2033C2218yescomplemented
72#1973C2218yescomplemented
73#1943C2218yescomplemented
74#1874C2218yescomplemented
75#1872C2218yescomplemented
76#1809C2218yescomplemented
77C2×#340C2211yescharacteristic
78C2×#340C2211yescharacteristic
79C2×#340C2211yescharacteristic
80C2×#340C2211yescharacteristic
81C23×Q8C2311yescharacteristic
82C23×D4—21no—
83C23×D4—21no—
84C23×D4D411yescharacteristic
85C23×D4C2311yescharacteristic
86C24×C4—21no—
87C24×C4—21no—
88C24×C4C2311yescharacteristic
89C24×C4C2311yescharacteristic
90C22×SD16—24no—
91C22×SD16—24no—
92C22×SD16—24no—
93C22×SD16C2314yes—
94C22×M16—24no—
95C22×M16—24no—
96C22×M16—24no—
97C22×M16C2314yes—
98C23×C8—24no—
99C23×C8—24no—
100C23×C8D418yescomplemented
101C23×C8C2311yescharacteristic
102C23×C8C2311yescharacteristic
103C23×C8C2311yescharacteristic
104C23×C8C2314yes—
105C23×C8C2311yescharacteristic
106C2×C22⋊Q8—22no—
107C2×C22⋊Q8—22no—
108C2×C22⋊Q8—24no—
109C2×C22⋊Q8—24no—
110C2×C22⋊Q8—24no—
111C2×C22⋊Q8—42no—
112C2×C22⋊Q8C2314yes—
113C2×C22⋊Q8C2314yes—
114C2×#121—28no—
115C2×#121—22no—
116C2×#121—22no—
117C2×#121—24no—
118C2×#121—24no—
119C2×#121—24no—
120C2×#121—42no—
121C2×#121—48no—
122C2×#121C2314yes—
123C2×#121C2314yes—
124C2×C4×D4—24no—
125C2×C4×D4—24no—
126C2×C4×D4D414yes—
127C2×C4×D4C2314yes—
128C22×C4⋊C4—24no—
129C22×C4⋊C4—24no—
130C22×C4⋊C4—21no—
131C22×C4⋊C4—21no—
132C22×C4⋊C4—21no—
133C22×C4⋊C4—21no—
134C22×C4⋊C4—21no—
135C22×C4⋊C4—22no—
136C22×C4⋊C4—22no—
137C22×C4⋊C4—21no—
138C22×C4⋊C4—42no—
139C22×C4⋊C4—42no—
140C22×C4⋊C4D411yescharacteristic
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2311yescharacteristic
144C22×C4⋊C4C2311yescharacteristic
145C22×C4⋊C4C2314yes—
146C22×C4⋊C4C2314yes—
147C22×C4⋊C4C2311yescharacteristic
148C22×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
156C22×C22⋊C4—21no—
157C22×C22⋊C4D411yescharacteristic
158C22×C22⋊C4D411yescharacteristic
159C22×C42C2311yescharacteristic
160#468—232no—
161#465—232no—
162#435—232no—
163C2×#107—24no—
164C2×#107—24no—
165C2×#107—24no—
166C2×#107—232no—
167C2×#107D418yescomplemented
168C2×#107C2314yes—
169C2×#107C2314yes—
170C2×#107C2314yes—
171C2×#107C2314yes—
172C2×#106—24no—
173C2×#106C2314yes—
174C2×C4⋊C8—24no—
175C2×C4⋊C8C2314yes—
176C2×#103—24no—
177C2×#103—24no—
178C2×#103—42no—
179C2×#103C2314yes—
180C2×#103C2314yes—
181C2×#103C2314yes—
182C2×#102—24no—
183C2×#102—24no—
184C2×#102—42no—
185C2×#102C2314yes—
186C2×#102C2314yes—
187C2×#102C2314yes—
188C2×C22⋊C8—24no—
189C2×C22⋊C8—24no—
190C2×C22⋊C8C2314yes—
191C2×C22⋊C8C2314yes—
192C2×#97—24no—
193C2×#97C2314yes—
194#398—28no—
195#396—28no—
196#396—28no—
197#394—28no—
198#391—22no—
199#391C2314yes—
200#390—22no—
201#390C2314yes—
202#389—22no—
203#389—22no—
204#389C2314yes—
205#389C2314yes—
206#386—28no—
207#386—28no—
208#380—22no—
209#380—22no—
210#380—28no—
211#380C2314yes—
212#380C2314yes—
213C2×#95—21no—
214C2×#95—21no—
215C2×#95—21no—
216C2×#95—21no—
217C2×#95—21no—
218C2×#95—21no—
219#340C2314yes—
220#340C2314yes—
221#340C2314yes—
222#340C2314yes—
223C25—21no—
224C25C2×D411yescharacteristic
225C25C2×D411yescharacteristic
226C22×Q8—21no—
227C22×Q8—22no—
228C22×Q8—22no—
229C22×Q8—22no—
230C22×Q8—22no—
231C22×Q8—22no—
232C22×Q8—22no—
233C22×Q8C2412yes—
234C22×D4—24no—
235C22×D4—24no—
236C22×D4—24no—
237C22×D4—24no—
238C22×D4—24no—
239C22×D4—22no—
240C22×D4—22no—
241C22×D4—21no—
242C22×D4—22no—
243C22×D4—22no—
244C22×D4—22no—
245C22×D4—22no—
246C22×D4—44no—
247C22×D4—44no—
248C22×D4—44no—
249C22×D4—44no—
250C22×D4—44no—
251C22×D4—82no—
252C22×D4C2×D414yes—
253C22×D4C2412yes—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—21no—
259C23×C4—21no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—21no—
267C23×C4—21no—
268C23×C4—21no—
269C23×C4—21no—
270C23×C4—21no—
271C23×C4—24no—
272C23×C4—24no—
273C23×C4—44no—
274C23×C4—44no—
275C23×C4—44no—
276C23×C4—44no—
277C23×C4—82no—
278C23×C4—82no—
279C23×C4C2×D412yes—
280C23×C4C2×D411yescharacteristic
281C23×C4C2×D411yescharacteristic
282C23×C4C2×D411yescharacteristic
283C23×C4C2×D412yes—
284C23×C4C2×D411yescharacteristic
285C23×C4C2×D414yes—
286C23×C4#4114yes—
287C23×C4C2412yes—
288C23×C4C2412yes—
289C23×C4C2411yescharacteristic
290C2×SD16—28no—
291C2×SD16—28no—
292C2×SD16—28no—
293C2×SD16—416no—
294C2×M16—28no—
295C2×M16—28no—
296C2×M16—28no—
297C2×M16—416no—
298C22×C8—22no—
299C22×C8—22no—
300C22×C8—232no—
301C22×C8—28no—
302C22×C8—28no—
303C22×C8—22no—
304C22×C8—22no—
305C22×C8—22no—
306C22×C8—22no—
307C22×C8—22no—
308C22×C8—22no—
309C22×C8C2×D414yes—
310C22×C8C2×D414yes—
311C22×C8C2×D414yes—
312C22×C8C2×D4116yescomplemented
313C22×C8#4114yes—
314C22×C8C2412yes—
315C22×C8C2412yes—
316C22×C8C2412yes—
317C22×C8C2412yes—
318C22⋊Q8—28no—
319C22⋊Q8—28no—
320C22⋊Q8—28no—
321C22⋊Q8—44no—
322C22⋊Q8—48no—
323C22⋊Q8—48no—
324#121—28no—
325#121—28no—
326#121—28no—
327#121—44no—
328#121—48no—
329#121—432no—
330#121—48no—
331C4×D4—216no—
332C4×D4—28no—
333C4×D4—28no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
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—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—28no—
348C2×C4⋊C4—28no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—24no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—44no—
360C2×C4⋊C4—44no—
361C2×C4⋊C4—48no—
362C2×C4⋊C4—48no—
363C2×C4⋊C4—44no—
364C2×C4⋊C4—44no—
365C2×C4⋊C4—44no—
366C2×C4⋊C4—44no—
367C2×C4⋊C4—44no—
368C2×C4⋊C4—82no—
369C2×C4⋊C4C2×D414yes—
370C2×C4⋊C4C2×D414yes—
371C2×C4⋊C4C2×D414yes—
372C2×C4⋊C4C2412yes—
373C2×C4⋊C4C2412yes—
374C2×C4⋊C4C2412yes—
375C2×C4⋊C4C2412yes—
376C2×C4⋊C4C2412yes—
377C2×C4⋊C4C2412yes—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—44no—
389C2×C22⋊C4—44no—
390C2×C22⋊C4—44no—
391C2×C22⋊C4—44no—
392C2×C22⋊C4—44no—
393C2×C22⋊C4—44no—
394C2×C22⋊C4—82no—
395C2×C22⋊C4—82no—
396C2×C22⋊C4C2×D414yes—
397C2×C22⋊C4C2×D414yes—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42C2×D412yes—
401C2×C42C2412yes—
402#107—28no—
403#107—28no—
404#107—28no—
405#107C2×D4116yescomplemented
406#106—28no—
407C4⋊C8—28no—
408#103—28no—
409#103—28no—
410#103—44no—
411#102—28no—
412#102—28no—
413#102—44no—
414C22⋊C8—28no—
415C22⋊C8—28no—
416#97—28no—
417#95—24no—
418#95—24no—
419#95—24no—
420#95—24no—
421#95—24no—
422#95—24no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—42no—
436C24—42no—
437C24—42no—
438C24—42no—
439C24—42no—
440C24—42no—
441C24—42no—
442C24#12114yes—
443C24AGL(1,ℤ/8)14yes—
444C24#13714yes—
445C24C22×D412yes—
446C24C22×D412yes—
447C24C22×D411yescharacteristic
448C2×Q8—22no—
449C2×Q8—22no—
450C2×Q8—22no—
451C2×Q8—22no—
452C2×Q8—22no—
453C2×Q8—22no—
454C2×Q8—42no—
455C2×Q8—42no—
456C2×Q8—42no—
457C2×Q8—44no—
458C2×Q8—44no—
459C2×Q8—44no—
460C2×Q8—44no—
461C2×D4—28no—
462C2×D4—28no—
463C2×D4—28no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—48no—
471C2×D4—416no—
472C2×D4—48no—
473C2×D4—48no—
474C2×D4—48no—
475C2×D4—48no—
476C2×D4—44no—
477C2×D4—42no—
478C2×D4—44no—
479C2×D4—42no—
480C2×D4—42no—
481C2×D4—44no—
482C2×D4—44no—
483C2×D4—84no—
484C2×D4—816no—
485C2×D4—816no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—28no—
489C22×C4—28no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—28no—
493C22×C4—28no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—48no—
526C22×C4—48no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—44no—
532C22×C4—44no—
533C22×C4—44no—
534C22×C4—44no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—48no—
545C22×C4—48no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—84no—
553C22×C4—84no—
554C22×C4—816no—
555C22×C4—816no—
556C22×C4#12114yes—
557C22×C4#12118yes—
558C22×C4C22×D412yes—
559C22×C4C22×D412yes—
560C22×C4C22×D412yes—
561C22×C4C22×D412yes—
562C22×C4C22×D414yes—
563C22×C4C22×D412yes—
564C22×C4C22×D411yescharacteristic
565C22×C4C22×D412yes—
566C22×C4C2×#4114yes—
567C22×C4C2×#4112yes—
568C22×C4C2×#4112yes—
569C22×C4H(5,𝔽2)12yes—
570C22×C42−1+412yes—
571C22×C4C2511yescharacteristic
572SD16—416no—
573M16—416no—
574C2×C8—28no—
575C2×C8—22no—
576C2×C8—22no—
577C2×C8—232no—
578C2×C8—22no—
579C2×C8—22no—
580C2×C8—22no—
581C2×C8—22no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—44no—
585C2×C8—44no—
586C2×C8#121116yescomplemented
587C2×C8C22×D414yes—
588C2×C8C22×D414yes—
589C2×C8C22×D414yes—
590C2×C8C2×#4114yes—
591C4⋊C4—28no—
592C4⋊C4—24no—
593C4⋊C4—24no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—22no—
604C4⋊C4—48no—
605C4⋊C4—48no—
606C4⋊C4—48no—
607C4⋊C4—48no—
608C4⋊C4—42no—
609C4⋊C4—42no—
610C4⋊C4—48no—
611C4⋊C4—42no—
612C4⋊C4—42no—
613C4⋊C4—84no—
614C4⋊C4C22×D414yes—
615C4⋊C4C22×D414yes—
616C22⋊C4—28no—
617C22⋊C4—28no—
618C22⋊C4—48no—
619C22⋊C4—48no—
620C22⋊C4—48no—
621C22⋊C4—48no—
622C22⋊C4—48no—
623C22⋊C4—48no—
624C22⋊C4—84no—
625C22⋊C4—84no—
626C42—24no—
627C42—22no—
628C42—22no—
629C23—28no—
630C23—28no—
631C23—28no—
632C23—22no—
633C23—22no—
634C23—28no—
635C23—28no—
636C23—28no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—44no—
647C23—44no—
648C23—44no—
649C23—44no—
650C23—44no—
651C23—44no—
652C23—44no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—84no—
661C23—84no—
662C23—84no—
663C23—84no—
664C23—84no—
665C23—84no—
666C23—84no—
667C23#468116yescomplemented
668C23C2×#12114yes—
669C23C2×#12112yes—
670C23D4212yes—
671C23#54712yes—
672C23C2×AGL(1,ℤ/8)14yes—
673C23C2×AGL(1,ℤ/8)12yes—
674C23C2×#13714yes—
675C23C2×#13712yes—
676C23#57612yes—
677C23#57812yes—
678C23C23×D411yescharacteristic
679Q8—42no—
680Q8—42no—
681Q8—42no—
682Q8—42no—
683Q8—84no—
684D4—416no—
685D4—42no—
686D4—42no—
687D4—42no—
688D4—42no—
689D4—816no—
690D4—816no—
691D4—84no—
692C2×C4—28no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—216no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—44no—
712C2×C4—48no—
713C2×C4—48no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—48no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—816no—
741C2×C4—816no—
742C2×C4—84no—
743C2×C4—84no—
744C2×C4—84no—
745C2×C4—84no—
746C2×C4—84no—
747C2×C4C2×#12114yes—
748C2×C4C2×#12114yes—
749C2×C4C2×#12112yes—
750C2×C4#53714yes—
751C2×C4D4212yes—
752C2×C4#54712yes—
753C2×C4#54814yes—
754C2×C4#55314yes—
755C2×C4C23×D411yescharacteristic
756C2×C4C23×D411yescharacteristic
757C2×C4C22×#4111yescharacteristic
758C2×C4C22×#4111yescharacteristic
759C2×C4C2×H(5,𝔽2)11yescharacteristic
760C2×C4C2×2−1+411yescharacteristic
761C8—24no—
762C8—42no—
763C8—42no—
764C8C2×#12118yescomplemented
765C22—24no—
766C22—24no—
767C22—24no—
768C22—24no—
769C22—24no—
770C22—24no—
771C22—232no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—88no—
780C22—82no—
781C22—82no—
782C22—82no—
783C22—82no—
784C22—82no—
785C22—82no—
786C22—82no—
787C22—168no—
788C22#241614yes—
789C22C2×#46814yes—
790C22C2×#46818yescomplemented
791C22#306114yes—
792C22#326414yes—
793C22#327014yes—
794C22#334314yes—
795C22#334614yes—
796C22C22×#12111yescharacteristic
797C22C2×D4211yescharacteristic
798C22C2×#54711yescharacteristic
799C22C22×AGL(1,ℤ/8)11yescharacteristic
800C22C22×#13711yescharacteristic
801C22C2×#57611yescharacteristic
802C22C2×#57811yescharacteristic
803C4—24no—
804C4—42no—
805C4—42no—
806C4—44no—
807C4—44no—
808C4—42no—
809C4—82no—
810C4—82no—
811C4—82no—
812C4—82no—
813C4—82no—
814C4#241614yes—
815C4C22×#12111yescharacteristic
816C4C2×#53711yescharacteristic
817C4C2×#54811yescharacteristic
818C4C2×#55311yescharacteristic
819C2—28no—
820C2—82no—
821C2—162no—
822C2#2478718yesdirect product factor
823C2C2×#241611yescharacteristic
824C2C22×#46811yescharacteristic
825C2C2×#306111yescharacteristic
826C2C2×#326411yescharacteristic
827C2C2×#327011yescharacteristic
828C2C2×#334311yescharacteristic
829C2C2×#334611yescharacteristic
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×#468C2semidirect
2. C22×#465C2semidirect
3. C22×#435C2semidirect
4. C23×#107C2semidirect
5. C2×#2417C2semidirect
7. #24787C2direct (N × H)
8. C2×#2068C2semidirect
9. C2×#2067C2semidirect
10. C2×#2036C2semidirect
11. C2×#2033C2semidirect
12. C2×#1973C2semidirect
13. C2×#1943C2semidirect
14. C2×#1874C2semidirect
15. C2×#1872C2semidirect
16. C2×#1809C2semidirect
29. C2×#468C22semidirect
31. C2×#465C22semidirect
33. C2×#435C22semidirect
39. C22×#107C22semidirect
52. #2417C22semidirect
68. #2068C22semidirect
69. #2067C22semidirect
70. #2036C22semidirect
71. #2033C22semidirect
72. #1973C22semidirect
73. #1943C22semidirect
74. #1874C22semidirect
75. #1872C22semidirect
76. #1809C22semidirect
100. C23×C8D4semidirect
167. C2×#107D4semidirect
312. C22×C8C2×D4semidirect
405. #107C2×D4semidirect
586. C2×C8#121semidirect
667. C23#468semidirect
764. C8C2×#121semidirect
790. C22C2×#468semidirect
822. C2#24787direct (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×#4652
C22×#4352
C23×#1072
C2×#24172
C2×#24162
#247872
C2×#20682
C2×#20672
C2×#20362
C2×#20332
C2×#19732
C2×#19432
C2×#18742
C2×#18722
C2×#18092