Finite Group Databasebeta

← C2×#25500 #6452050

Subgroups — C2×#25500 #6452050

Order 512.

3976 conjugacy classes of subgroups.

The subgroup lattice has 849 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#529C211yesmaximal, characteristic, complemented
2C22×#466C211yesmaximal, characteristic
3C22×#465C211yesmaximal, characteristic, complemented
4C2×#2854C211yesmaximal, characteristic, complemented
5#25500C2116yesmaximal, direct product factor
6C2×#2059C211yesmaximal, characteristic, complemented
7C2×#2042C211yesmaximal, characteristic, complemented
8C2×#2025C211yesmaximal, characteristic, complemented
9C2×#2012C211yesmaximal, characteristic, complemented
10C2×#1893C211yesmaximal, characteristic, complemented
11C2×#1892C211yesmaximal, characteristic, complemented
12C2×#1880C211yesmaximal, characteristic, complemented
13C2×#1879C211yesmaximal, characteristic, complemented
14C2×#1863C211yesmaximal, characteristic, complemented
15C2×#1864C211yesmaximal, characteristic, complemented
16C22×#336C211yesmaximal, characteristic, complemented
17C23×SD16C2211yescharacteristic
18C23×D8C2211yescharacteristic
19C24×C8C2211yescharacteristic
20C24×C8C2211yescharacteristic
21C2×#529—24no—
22C2×#529—28no—
23C2×#529—28no—
24C2×#529C2218yescomplemented
25C22×#126—21no—
26C22×#125C2211yescharacteristic
27C22×#124C2211yescharacteristic
28C22×#123—21no—
29C22×#123—21no—
30C22×C22⋊Q8C2211yescharacteristic
31C22×#121C2211yescharacteristic
32C22×#121C2211yescharacteristic
33C22×C4×Q8C2211yescharacteristic
34C22×C4×D4—21no—
35C22×C4×D4C2211yescharacteristic
36C22×#117—21no—
37C23×C42C2211yescharacteristic
38C2×#466—28no—
39C2×#466C2218yes—
40C2×#465—28no—
41C2×#465C2218yescomplemented
42C22×#107C2211yescharacteristic
43C22×#106C2211yescharacteristic
44C22×#103C2211yescharacteristic
45C22×#103C2211yescharacteristic
46C22×#103C2211yescharacteristic
47C22×#102C2211yescharacteristic
48C22×#102C2211yescharacteristic
49C22×#102C2211yescharacteristic
50C22×#102C2211yescharacteristic
51C22×#102C2211yescharacteristic
52#2854—24no—
53#2854C2218yescomplemented
54C2×#390C2211yescharacteristic
55C2×#390C2211yescharacteristic
56C2×#389C2211yescharacteristic
57C2×#389C2211yescharacteristic
58C2×#388—21no—
59C2×#388—21no—
60C2×#386—21no—
61C2×#380C2211yescharacteristic
62#2059C2218yescomplemented
63#2042C2218yescomplemented
64#2025C2218yescomplemented
65#2012C2218yescomplemented
66#1893C2218yescomplemented
67#1892C2218yescomplemented
68#1880C2218yescomplemented
69#1879C2218yescomplemented
70#1864C2218yescomplemented
71#1863C2218yescomplemented
72C2×#340C2211yescharacteristic
73C2×#340C2211yescharacteristic
74C2×#340C2211yescharacteristic
75C2×#340C2211yescharacteristic
76C2×#336C2211yescharacteristic
77C2×#336C2211yescharacteristic
78C2×#336C2211yescharacteristic
79C2×#336C2211yescharacteristic
80C2×#336C2218yescomplemented
81C23×Q8C2311yescharacteristic
82C23×D4—21no—
83C23×D4—21no—
84C23×D4C2311yescharacteristic
85C23×D4C2311yescharacteristic
86C24×C4—21no—
87C24×C4D411yescharacteristic
88C24×C4D411yescharacteristic
89C24×C4C2311yescharacteristic
90C22×SD16—24no—
91C22×SD16—24no—
92C22×SD16—42no—
93C22×SD16C2314yes—
94C22×D8—24no—
95C22×D8—24no—
96C22×D8—42no—
97C22×D8C2314yes—
98C23×C8—24no—
99C23×C8—24no—
100C23×C8—24no—
101C23×C8—24no—
102C23×C8—42no—
103C23×C8—42no—
104C23×C8C2311yescharacteristic
105C23×C8C2311yescharacteristic
106C23×C8C2314yes—
107C23×C8C2314yes—
108C23×C8C2311yescharacteristic
109C23×C8C2311yescharacteristic
110#529—264no—
111#529—232no—
112#529—232no—
113C2×#126—216no—
114C2×#126—28no—
115C2×#125—24no—
116C2×#125—24no—
117C2×#125—22no—
118C2×#125C2314yes—
119C2×#124—24no—
120C2×#124—24no—
121C2×#124—22no—
122C2×#124C2314yes—
123C2×#123—216no—
124C2×#123—28no—
125C2×#123—28no—
126C2×#123—48no—
127C2×C22⋊Q8—24no—
128C2×C22⋊Q8—22no—
129C2×C22⋊Q8D418yes—
130C2×C22⋊Q8C2314yes—
131C2×#121—24no—
132C2×#121—22no—
133C2×#121—22no—
134C2×#121—24no—
135C2×#121—24no—
136C2×#121D418yes—
137C2×#121C2314yes—
138C2×#121C2314yes—
139C2×C4×Q8—24no—
140C2×C4×Q8—24no—
141C2×C4×Q8—22no—
142C2×C4×Q8C2314yes—
143C2×C4×D4—216no—
144C2×C4×D4—24no—
145C2×C4×D4—28no—
146C2×C4×D4—24no—
147C2×C4×D4—22no—
148C2×C4×D4C2314yes—
149C2×#117—216no—
150C2×#117—28no—
151C22×C4⋊C4—21no—
152C22×C4⋊C4—21no—
153C22×C4⋊C4—21no—
154C22×C4⋊C4—21no—
155C22×C4⋊C4—21no—
156C22×C4⋊C4—21no—
157C22×C4⋊C4C2311yescharacteristic
158C22×C4⋊C4C2311yescharacteristic
159C22×C4⋊C4C2311yescharacteristic
160C22×C4⋊C4C2311yescharacteristic
161C22×C4⋊C4C2311yescharacteristic
162C22×C22⋊C4—21no—
163C22×C22⋊C4—21no—
164C22×C22⋊C4—21no—
165C22×C22⋊C4—21no—
166C22×C22⋊C4—21no—
167C22×C22⋊C4—21no—
168C22×C22⋊C4—21no—
169C22×C22⋊C4—21no—
170C22×C22⋊C4—21no—
171C22×C22⋊C4—21no—
172C22×C22⋊C4—21no—
173C22×C42—24no—
174C22×C42—24no—
175C22×C42—21no—
176C22×C42D414yes—
177C22×C42D411yescharacteristic
178C22×C42D411yescharacteristic
179C22×C42C2314yes—
180C22×C42C2311yescharacteristic
181C22×C42C2311yescharacteristic
182#466—232no—
183#465—232no—
184C2×#107—24no—
185C2×#107C2314yes—
186C2×#106—24no—
187C2×#106C2314yes—
188C2×#103—24no—
189C2×#103—24no—
190C2×#103—42no—
191C2×#103C2314yes—
192C2×#103C2314yes—
193C2×#103C2314yes—
194C2×#102—24no—
195C2×#102—24no—
196C2×#102—24no—
197C2×#102—24no—
198C2×#102—42no—
199C2×#102C2314yes—
200C2×#102C2314yes—
201C2×#102C2314yes—
202C2×#102C2314yes—
203C2×#102C2314yes—
204#390—22no—
205#390—22no—
206#390C2314yes—
207#390C2314yes—
208#389—22no—
209#389—22no—
210#389C2314yes—
211#389C2314yes—
212#388—28no—
213#388—28no—
214#386—28no—
215#380—22no—
216#380C2314yes—
217C2×#95—21no—
218C2×#95—21no—
219C2×#95—21no—
220#340C2314yes—
221#340C2314yes—
222#340C2314yes—
223#340C2314yes—
224#336C2314yes—
225#336C2314yes—
226#336C2314yes—
227#336C2314yes—
228C25—21no—
229C25—21no—
230C25C2×D411yescharacteristic
231C22×Q8—22no—
232C22×Q8—21no—
233C22×Q8—22no—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8C2×D414yes—
238C22×Q8C2412yes—
239C22×D4—28no—
240C22×D4—24no—
241C22×D4—24no—
242C22×D4—21no—
243C22×D4—22no—
244C22×D4—22no—
245C22×D4—22no—
246C22×D4—21no—
247C22×D4—22no—
248C22×D4—22no—
249C22×D4—22no—
250C22×D4—22no—
251C22×D4—22no—
252C22×D4—22no—
253C22×D4—22no—
254C22×D4—22no—
255C22×D4—44no—
256C22×D4—44no—
257C22×D4—44no—
258C22×D4—44no—
259C22×D4—44no—
260C22×D4C2×D414yes—
261C22×D4C2412yes—
262C22×D4C2412yes—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—28no—
268C23×C4—24no—
269C23×C4—24no—
270C23×C4—24no—
271C23×C4—24no—
272C23×C4—21no—
273C23×C4—21no—
274C23×C4—21no—
275C23×C4—24no—
276C23×C4—24no—
277C23×C4—21no—
278C23×C4—21no—
279C23×C4—21no—
280C23×C4—42no—
281C23×C4—44no—
282C23×C4—44no—
283C23×C4C2×D414yes—
284C23×C4C2×D411yescharacteristic
285C23×C4C2×D411yescharacteristic
286C23×C4C2×D411yescharacteristic
287C23×C4C2×D414yes—
288C23×C4C2×D412yes—
289C23×C4C2×D411yescharacteristic
290C23×C4C2×D414yes—
291C23×C4C2×D414yes—
292C23×C4C2×D411yescharacteristic
293C23×C4C2412yes—
294C23×C4C2411yescharacteristic
295C2×SD16—28no—
296C2×SD16—28no—
297C2×SD16—44no—
298C2×SD16—416no—
299C2×D8—28no—
300C2×D8—28no—
301C2×D8—44no—
302C2×D8—416no—
303C22×C8—22no—
304C22×C8—22no—
305C22×C8—22no—
306C22×C8—22no—
307C22×C8—22no—
308C22×C8—22no—
309C22×C8—28no—
310C22×C8—28no—
311C22×C8—22no—
312C22×C8—22no—
313C22×C8—22no—
314C22×C8—22no—
315C22×C8—28no—
316C22×C8—28no—
317C22×C8—44no—
318C22×C8—44no—
319C22×C8—416no—
320C22×C8—416no—
321C22×C8#4114yes—
322C22×C8#4114yes—
323C22×C8C2412yes—
324C22×C8C2412yes—
325C22×C8C2412yes—
326C22×C8C2412yes—
327#126—264no—
328#125—216no—
329#125—28no—
330#125—28no—
331#124—216no—
332#124—28no—
333#124—28no—
334#123—264no—
335#123—432no—
336C22⋊Q8—216no—
337C22⋊Q8—28no—
338C22⋊Q8C2×D4116yes—
339#121—216no—
340#121—28no—
341#121—28no—
342#121—28no—
343#121—48no—
344#121C2×D4116yes—
345C4×Q8—216no—
346C4×Q8—28no—
347C4×Q8—28no—
348C4×D4—264no—
349C4×D4—216no—
350C4×D4—28no—
351C4×D4—28no—
352#117—264no—
353C2×C4⋊C4—28no—
354C2×C4⋊C4—28no—
355C2×C4⋊C4—28no—
356C2×C4⋊C4—28no—
357C2×C4⋊C4—24no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—24no—
372C2×C4⋊C4—24no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—44no—
377C2×C4⋊C4—44no—
378C2×C4⋊C4C2×D414yes—
379C2×C4⋊C4C2×D414yes—
380C2×C4⋊C4C2412yes—
381C2×C4⋊C4C2412yes—
382C2×C4⋊C4C2412yes—
383C2×C4⋊C4C2412yes—
384C2×C4⋊C4C2412yes—
385C2×C22⋊C4—28no—
386C2×C22⋊C4—28no—
387C2×C22⋊C4—28no—
388C2×C22⋊C4—28no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—28no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—44no—
402C2×C22⋊C4—44no—
403C2×C22⋊C4—44no—
404C2×C22⋊C4—44no—
405C2×C22⋊C4—44no—
406C2×C22⋊C4—44no—
407C2×C42—28no—
408C2×C42—24no—
409C2×C42—24no—
410C2×C42—216no—
411C2×C42—24no—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—22no—
416C2×C42—28no—
417C2×C42—28no—
418C2×C42C2×D414yes—
419C2×C42C2×D412yes—
420C2×C42C2×D412yes—
421C2×C42C2×D414yes—
422C2×C42C2412yes—
423C2×C42C2412yes—
424#107—28no—
425#106—28no—
426#103—28no—
427#103—28no—
428#103—44no—
429#102—28no—
430#102—28no—
431#102—28no—
432#102—28no—
433#102—44no—
434#95—24no—
435#95—24no—
436#95—24no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—24no—
442C24—22no—
443C24—22no—
444C24—42no—
445C24—42no—
446C24—42no—
447C24—42no—
448C24—42no—
449C24—42no—
450C24—42no—
451C24—42no—
452C24—42no—
453C24—42no—
454C24—42no—
455C24—42no—
456C24—42no—
457C24#12014yes—
458C24#13514yes—
459C24AGL(1,ℤ/8)14yes—
460C24C22×D412yes—
461C24C22×D411yescharacteristic
462C2×Q8—24no—
463C2×Q8—22no—
464C2×Q8—28no—
465C2×Q8—28no—
466C2×Q8—22no—
467C2×Q8—22no—
468C2×Q8—22no—
469C2×Q8—22no—
470C2×Q8—42no—
471C2×Q8—42no—
472C2×Q8—44no—
473C2×Q8—44no—
474C2×Q8C22×D414yes—
475C2×D4—216no—
476C2×D4—24no—
477C2×D4—28no—
478C2×D4—28no—
479C2×D4—22no—
480C2×D4—22no—
481C2×D4—22no—
482C2×D4—22no—
483C2×D4—22no—
484C2×D4—22no—
485C2×D4—22no—
486C2×D4—22no—
487C2×D4—22no—
488C2×D4—22no—
489C2×D4—22no—
490C2×D4—48no—
491C2×D4—48no—
492C2×D4—432no—
493C2×D4—48no—
494C2×D4—48no—
495C2×D4—48no—
496C2×D4—42no—
497C2×D4—42no—
498C2×D4—42no—
499C2×D4—42no—
500C2×D4—42no—
501C2×D4—44no—
502C2×D4—44no—
503C2×D4—44no—
504C2×D4—44no—
505C2×D4—44no—
506C2×D4—44no—
507C2×D4—816no—
508C2×D4C22×D414yes—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—28no—
516C22×C4—28no—
517C22×C4—28no—
518C22×C4—28no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—216no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—28no—
528C22×C4—28no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—28no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—28no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—28no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—44no—
548C22×C4—416no—
549C22×C4—432no—
550C22×C4—48no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—416no—
558C22×C4—48no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4#12014yes—
569C22×C4#12018yes—
570C22×C4#13514yes—
571C22×C4C22×D412yes—
572C22×C4C22×D412yes—
573C22×C4C22×D412yes—
574C22×C4C22×D412yes—
575C22×C4C22×D414yes—
576C22×C4C22×D414yes—
577C22×C4C22×D412yes—
578C22×C4C22×D411yescharacteristic
579C22×C4C22×D412yes—
580C22×C4C22×D412yes—
581C22×C4C2×#4112yes—
582C22×C4C2×#4112yes—
583C22×C4H(5,𝔽2)12yes—
584C22×C42−1+412yes—
585C22×C4C2511yescharacteristic
586SD16—416no—
587D8—416no—
588C2×C8—28no—
589C2×C8—28no—
590C2×C8—22no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—22no—
594C2×C8—22no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—22no—
598C2×C8—22no—
599C2×C8—22no—
600C2×C8—416no—
601C2×C8—416no—
602C2×C8—44no—
603C2×C8—44no—
604C2×C8C2×#4114yes—
605C2×C8C2×#4114yes—
606C4⋊C4—216no—
607C4⋊C4—216no—
608C4⋊C4—216no—
609C4⋊C4—216no—
610C4⋊C4—24no—
611C4⋊C4—24no—
612C4⋊C4—22no—
613C4⋊C4—22no—
614C4⋊C4—22no—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—22no—
618C4⋊C4—22no—
619C4⋊C4—22no—
620C4⋊C4—48no—
621C4⋊C4—48no—
622C4⋊C4—42no—
623C4⋊C4—42no—
624C4⋊C4—42no—
625C4⋊C4C22×D414yes—
626C4⋊C4C22×D414yes—
627C22⋊C4—216no—
628C22⋊C4—216no—
629C22⋊C4—216no—
630C22⋊C4—216no—
631C22⋊C4—216no—
632C22⋊C4—48no—
633C22⋊C4—48no—
634C22⋊C4—48no—
635C22⋊C4—48no—
636C22⋊C4—48no—
637C22⋊C4—48no—
638C42—216no—
639C42—28no—
640C42—24no—
641C42—24no—
642C42—28no—
643C42—22no—
644C42—22no—
645C42—22no—
646C42—22no—
647C23—28no—
648C23—28no—
649C23—22no—
650C23—22no—
651C23—28no—
652C23—28no—
653C23—28no—
654C23—28no—
655C23—22no—
656C23—22no—
657C23—24no—
658C23—42no—
659C23—42no—
660C23—48no—
661C23—48no—
662C23—48no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—84no—
675C23—84no—
676C23—84no—
677C23—84no—
678C23—84no—
679C23—84no—
680C23—84no—
681C23—84no—
682C23—84no—
683C23—84no—
684C23—84no—
685C23#449116yes—
686C23C2×#12014yes—
687C23C2×#12012yes—
688C23#53212yes—
689C23#53712yes—
690C23C2×#13514yes—
691C23C2×#13512yes—
692C23C2×#13512yes—
693C23C2×AGL(1,ℤ/8)14yes—
694C23C2×AGL(1,ℤ/8)12yes—
695C23#57512yes—
696C23C23×D411yescharacteristic
697Q8—24no—
698Q8—24no—
699Q8—48no—
700Q8—42no—
701Q8—42no—
702D4—24no—
703D4—24no—
704D4—432no—
705D4—48no—
706D4—42no—
707D4—42no—
708D4—42no—
709D4—42no—
710D4—42no—
711D4—42no—
712D4—816no—
713D4—84no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—28no—
718C2×C4—28no—
719C2×C4—22no—
720C2×C4—216no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—416no—
738C2×C4—432no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—48no—
742C2×C4—416no—
743C2×C4—44no—
744C2×C4—44no—
745C2×C4—48no—
746C2×C4—44no—
747C2×C4—48no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—84no—
762C2×C4—84no—
763C2×C4—84no—
764C2×C4C2×#12014yes—
765C2×C4C2×#12012yes—
766C2×C4#53212yes—
767C2×C4#53712yes—
768C2×C4#54614yes—
769C2×C4#54614yes—
770C2×C4#54714yes—
771C2×C4#54714yes—
772C2×C4C2×#13514yes—
773C2×C4C23×D411yescharacteristic
774C2×C4C23×D411yescharacteristic
775C2×C4C22×#4111yescharacteristic
776C2×C4C22×#4111yescharacteristic
777C2×C4C2×H(5,𝔽2)11yescharacteristic
778C2×C4C2×2−1+411yescharacteristic
779C8—24no—
780C8—24no—
781C8—42no—
782C8—42no—
783C22—24no—
784C22—232no—
785C22—24no—
786C22—24no—
787C22—24no—
788C22—24no—
789C22—24no—
790C22—44no—
791C22—44no—
792C22—44no—
793C22—82no—
794C22—816no—
795C22—82no—
796C22—82no—
797C22—82no—
798C22—82no—
799C22—82no—
800C22—82no—
801C22—82no—
802C22—82no—
803C22—82no—
804C22—82no—
805C22—168no—
806C22#243014yes—
807C22C2×#44918yes—
808C22C2×#44914yes—
809C22#300214yes—
810C22#316814yes—
811C22#318014yes—
812C22#324714yes—
813C22#325014yes—
814C22C22×#12011yescharacteristic
815C22C2×#53211yescharacteristic
816C22C2×#53711yescharacteristic
817C22C22×#13511yescharacteristic
818C22C22×#13511yescharacteristic
819C22C22×AGL(1,ℤ/8)11yescharacteristic
820C22C2×#57511yescharacteristic
821C4—24no—
822C4—24no—
823C4—44no—
824C4—42no—
825C4—42no—
826C4—44no—
827C4—42no—
828C4—44no—
829C4—82no—
830C4—82no—
831C4—82no—
832C4#243014yes—
833C4C2×#54611yescharacteristic
834C4C2×#54611yescharacteristic
835C4C2×#54711yescharacteristic
836C4C2×#54711yescharacteristic
837C2—28no—
838C2—84no—
839C2—162no—
840C2#2550018yesdirect product factor
841C2C2×#243011yescharacteristic
842C2C22×#44911yescharacteristic
843C2C2×#300211yescharacteristic
844C2C2×#316811yescharacteristic
845C2C2×#318011yescharacteristic
846C2C2×#324711yescharacteristic
847C2C2×#325011yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#466C2
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×#529C2semidirect
3. C22×#465C2semidirect
4. C2×#2854C2semidirect
5. #25500C2direct (N × H)
6. C2×#2059C2semidirect
7. C2×#2042C2semidirect
8. C2×#2025C2semidirect
9. C2×#2012C2semidirect
10. C2×#1893C2semidirect
11. C2×#1892C2semidirect
12. C2×#1880C2semidirect
13. C2×#1879C2semidirect
14. C2×#1863C2semidirect
15. C2×#1864C2semidirect
16. C22×#336C2semidirect
24. C2×#529C22semidirect
41. C2×#465C22semidirect
53. #2854C22semidirect
62. #2059C22semidirect
63. #2042C22semidirect
64. #2025C22semidirect
65. #2012C22semidirect
66. #1893C22semidirect
67. #1892C22semidirect
68. #1880C22semidirect
69. #1879C22semidirect
70. #1864C22semidirect
71. #1863C22semidirect
80. C2×#336C22semidirect
840. C2#25500direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#5292
C22×#4662
C22×#4652
C2×#28542
#255002
C2×#20592
C2×#20422
C2×#20252
C2×#20122
C2×#18932
C2×#18922
C2×#18802
C2×#18792
C2×#18632
C2×#18642
C22×#3362