Finite Group Databasebeta

← C2×#6629007 #72280452

Subgroups — C2×#6629007 #72280452

Order 1024.

52439 conjugacy classes of subgroups.

The subgroup lattice has 1146 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C25×M16C211yesmaximal, characteristic, complemented
2C22×#3055C213yesmaximal, complemented
3C2×#36614C211yesmaximal, characteristic, complemented
4C22×#2847C211yesmaximal, characteristic, complemented
5#6629007C2132yesmaximal, direct product factor
6C2×#32936C216yesmaximal, complemented
7C2×#32935C216yesmaximal, complemented
8C2×#32930C212yesmaximal, complemented
9C2×#32929C212yesmaximal, complemented
10C2×#20973C213yesmaximal, complemented
11C2×#20971C213yesmaximal, complemented
12C2×#20661C213yesmaximal, complemented
13C26×C4C2211yescharacteristic
14C23×AGL(1,ℤ/8)C2211yescharacteristic, complemented
15C24×M16—248no—
16C24×M16C2213yes—
17C24×M16C2213yes—
18C24×M16C2216yescomplemented
19C24×M16C22116yescomplemented
20C25×C8C2212yescomplemented
21C22×#525C2213yes—
22C23×#121C2213yes—
23C23×#120—21no—
24C2×#3055—248no—
25C2×#3055C22148yescomplemented
26C22×#469C2216yescomplemented
27C22×#468C2216yescomplemented
28C22×#466C2216yescomplemented
29C22×#465C2216yescomplemented
30C22×#428C2213yescomplemented
31C22×#417C2213yescomplemented
32C22×#418C2213yescomplemented
33#36614—28no—
34#36614C22116yescomplemented
35C2×#2849—23no—
36C2×#2848C2211yescharacteristic, complemented
37C2×#2848C2213yescomplemented
38C2×#2847—28no—
39C2×#2847—21no—
40C2×#2847—23no—
41C2×#2847C2212yes—
42C2×#2847C2216yes—
43C2×#2847C22116yescomplemented
44C2×#2847C2211yescharacteristic, complemented
45C2×#2847C2213yescomplemented
46C2×#2846—21no—
47C2×C4×#120—21no—
48C2×C4×#120—23no—
49C22×#386—23no—
50C2×#2280C2213yes—
51C22×#380C2213yes—
52#32936C22196yescomplemented
53#32935C22196yescomplemented
54#32930C22132yescomplemented
55#32929C22132yescomplemented
56#20973C22148yescomplemented
57#20971C22148yescomplemented
58C2×#1895C22112yescomplemented
59C2×#1895C2216yescomplemented
60C2×#1894C2216yescomplemented
61C2×#1893C2216yescomplemented
62C2×#1893C2216yescomplemented
63C2×#1893C2216yescomplemented
64C2×#1892C2216yescomplemented
65#20661C22148yescomplemented
66C2×#1809C22112yescomplemented
67C2×#1808C2216yescomplemented
68C2×#1807C2216yescomplemented
69C2×#1736C2216yescomplemented
70C27D411yescharacteristic
71C23×#41C2311yescharacteristic
72C24×D4—23no—
73C24×D4C2311yescharacteristic
74C25×C4—224no—
75C25×C4—224no—
76C25×C4D418yes—
77C25×C4D411yescharacteristic
78C25×C4D413yes—
79C25×C4D413yes—
80C25×C4C2311yescharacteristic
81C25×C4C2313yes—
82C25×C4C2318yes—
83C25×C4C2313yes—
84C22×AGL(1,ℤ/8)—224no—
85C22×AGL(1,ℤ/8)C2318yescomplemented
86C23×SD16C2312yescomplemented
87C23×D8C2312yescomplemented
88C23×M16—2512no—
89C23×M16—224no—
90C23×M16—248no—
91C23×M16—248no—
92C23×M16—296no—
93C23×M16—2384no—
94C23×M16—248no—
95C23×M16D4148yescomplemented
96C23×M16C2316yes—
97C23×M16C23124yes—
98C23×M16C2313yes—
99C23×M16C2316yes—
100C23×M16C23124yes—
101C23×M16C2311yescharacteristic
102C23×M16C23148yescomplemented
103C24×C8—248no—
104C24×C8C2316yes—
105C24×C8C2316yes—
106C24×C8C23116yescomplemented
107C2×#525—212no—
108C2×#525—224no—
109C2×#525—224no—
110C2×#525C23124yes—
111C22×#123—23no—
112C22×C22⋊Q8C2313yes—
113C22×C22⋊Q8C2313yes—
114C22×#121—23no—
115C22×#121—23no—
116C22×#121—212no—
117C22×#121—224no—
118C22×#121—224no—
119C22×#121C2316yes—
120C22×#121C2316yes—
121C22×#121C2313yes—
122C22×#121C2313yes—
123C22×#121C23124yes—
124C22×#120—23no—
125C22×#120—21no—
126C22×#120—23no—
127C22×#120—26no—
128C22×#120—22no—
129C22×#120—216no—
130C22×#120—416no—
131C22×C4×D4—23no—
132C22×C4×D4—23no—
133C22×#117C2313yes—
134C23×C4⋊C4C2313yes—
135C23×C22⋊C4—23no—
136C23×C22⋊C4—23no—
137#3055—2384no—
138C2×#469—248no—
139C2×#469C23148yescomplemented
140C2×#468—248no—
141C2×#468C23148yescomplemented
142C2×#466—248no—
143C2×#466C23148yescomplemented
144C2×#465—248no—
145C2×#465C23148yescomplemented
146C2×#428—224no—
147C2×#428C23124yescomplemented
148C22×#107C2316yescomplemented
149C22×#106C2316yescomplemented
150C2×#417—224no—
151C2×#417C23124yescomplemented
152C2×#418—224no—
153C2×#418C23124yescomplemented
154C22×#103C2316yescomplemented
155C22×#102C2316yescomplemented
156C22×#102C2316yescomplemented
157C22×#102C2316yescomplemented
158#2849—248no—
159#2848—24no—
160#2848—212no—
161#2848C2318yescomplemented
162#2848C23124yescomplemented
163#2847—28no—
164#2847—224no—
165#2847—248no—
166#2847—216no—
167#2847—24no—
168#2847—212no—
169#2847C23116yes—
170#2847C23148yes—
171#2847C2318yescomplemented
172#2847C23124yescomplemented
173#2846—216no—
174C4×#120—248no—
175C4×#120—216no—
176C2×#386—26no—
177C2×#386—212no—
178C2×#386—26no—
179C2×#386—248no—
180C2×#386—23no—
181C2×#386—26no—
182C2×#386—23no—
183C2×#385—23no—
184C2×#385—26no—
185C2×#385—23no—
186#2280—212no—
187#2280C23124yes—
188C2×#381—23no—
189C2×#380—23no—
190C2×#380—23no—
191C2×#380—212no—
192C2×#380C2316yes—
193C2×#380C2316yes—
194C2×#380C23124yes—
195C2×#380C2313yes—
196C2×#380C2313yes—
197C2×#380C2316yes—
198C2×#379—21no—
199C2×#379—23no—
200C2×#379—23no—
201C2×C4×C22⋊C4—23no—
202C2×C4×C22⋊C4—23no—
203C22×#95—23no—
204#1895C23196yescomplemented
205#1895C23148yescomplemented
206#1894C23148yescomplemented
207#1893C23148yescomplemented
208#1893C23148yescomplemented
209#1893C23148yescomplemented
210#1892C23148yescomplemented
211#1809C23196yescomplemented
212#1808C23148yescomplemented
213#1807C23148yescomplemented
214#1736C23148yescomplemented
215C2×#340C23112yescomplemented
216C2×#340C23112yescomplemented
217C26—224no—
218C26—28no—
219C26—21no—
220C26—412no—
221C26C2×D411yescharacteristic
222C26C2×D413yes—
223C26C2×D418yes—
224C26C2×D413yes—
225C22×#41—22no—
226C22×#41—212no—
227C22×#41—212no—
228C22×#41C2414yes—
229C23×Q8C2411yescharacteristic
230C23×D4—224no—
231C23×D4—26no—
232C23×D4—26no—
233C23×D4—21no—
234C23×D4—23no—
235C23×D4—23no—
236C23×D4—212no—
237C23×D4—22no—
238C23×D4—21no—
239C23×D4—212no—
240C23×D4—424no—
241C23×D4—424no—
242C23×D4—424no—
243C23×D4C2412yes—
244C23×D4C2414yes—
245C23×D4C2411yescharacteristic
246C24×C4—2384no—
247C24×C4—2128no—
248C24×C4—224no—
249C24×C4—248no—
250C24×C4—224no—
251C24×C4—248no—
252C24×C4—224no—
253C24×C4—2192no—
254C24×C4—212no—
255C24×C4—224no—
256C24×C4—296no—
257C24×C4—212no—
258C24×C4—224no—
259C24×C4—212no—
260C24×C4—224no—
261C24×C4—212no—
262C24×C4—296no—
263C24×C4—224no—
264C24×C4—23no—
265C24×C4—21no—
266C24×C4C2×D414yes—
267C24×C4C2×D4112yes—
268C24×C4C2×D418yes—
269C24×C4C2×D4124yes—
270C24×C4C2×D4124yes—
271C24×C4C2×D416yes—
272C24×C4C2×D413yes—
273C24×C4C2×D413yes—
274C24×C4C2×D413yes—
275C24×C4C2×D413yes—
276C24×C4C2×D413yes—
277C24×C4C2×D4112yes—
278C24×C4C2×D4124yes—
279C24×C4#41124yes—
280C24×C4C2414yes—
281C24×C4C24112yes—
282C24×C4C2413yes—
283C24×C4C2413yes—
284C24×C4C24112yes—
285C24×C4C2411yescharacteristic
286C2×AGL(1,ℤ/8)—296no—
287C2×AGL(1,ℤ/8)—464no—
288C22×SD16—224no—
289C22×SD16C2418yescomplemented
290C22×D8—224no—
291C22×D8C2418yescomplemented
292C22×M16—2384no—
293C22×M16—22048no—
294C22×M16—2768no—
295C22×M16—224no—
296C22×M16—296no—
297C22×M16—224no—
298C22×M16—2384no—
299C22×M16—2192no—
300C22×M16—2192no—
301C22×M16—2384no—
302C22×M16—248no—
303C22×M16—248no—
304C22×M16—2192no—
305C22×M16C2×D4124yes—
306C22×M16C2×D4124yes—
307C22×M16C2×D4148yescomplemented
308C22×M16C2×D41192yescomplemented
309C22×M16C24124yes—
310C22×M16C24112yes—
311C22×M16C24124yes—
312C22×M16C2414yes—
313C23×C8—2256no—
314C23×C8—224no—
315C23×C8—248no—
316C23×C8—248no—
317C23×C8—2192no—
318C23×C8C2×D4148yescomplemented
319C23×C8C24124yes—
320C23×C8C2416yes—
321C23×C8C24124yes—
322C23×C8C2412yes—
323#525—296no—
324#525—296no—
325#525—496no—
326C2×#123—224no—
327C2×#123—424no—
328C2×C22⋊Q8—26no—
329C2×C22⋊Q8—26no—
330C2×C22⋊Q8—212no—
331C2×C22⋊Q8—212no—
332C2×C22⋊Q8—212no—
333C2×C22⋊Q8—212no—
334C2×C22⋊Q8C24112yes—
335C2×C22⋊Q8C24112yes—
336C2×#121—224no—
337C2×#121—224no—
338C2×#121—212no—
339C2×#121—212no—
340C2×#121—26no—
341C2×#121—26no—
342C2×#121—224no—
343C2×#121—224no—
344C2×#121—296no—
345C2×#121—212no—
346C2×#121—212no—
347C2×#121—224no—
348C2×#121—224no—
349C2×#121—296no—
350C2×#121—212no—
351C2×#121—212no—
352C2×#121—424no—
353C2×#121—424no—
354C2×#121—496no—
355C2×#121C24124yes—
356C2×#121C24124yes—
357C2×#121C24112yes—
358C2×#121C24112yes—
359C2×#120—224no—
360C2×#120—28no—
361C2×#120—224no—
362C2×#120—248no—
363C2×#120—216no—
364C2×#120—424no—
365C2×#120—4128no—
366C2×#120—448no—
367C2×#120—424no—
368C2×#120—48no—
369C2×#120—416no—
370C2×C4×D4—224no—
371C2×C4×D4—224no—
372C2×C4×D4—424no—
373C2×C4×D4—424no—
374C2×#117—26no—
375C2×#117—212no—
376C2×#117—212no—
377C2×#117C24112yes—
378C22×C4⋊C4—212no—
379C22×C4⋊C4—212no—
380C22×C4⋊C4—26no—
381C22×C4⋊C4—23no—
382C22×C4⋊C4—23no—
383C22×C4⋊C4—23no—
384C22×C4⋊C4C2413yes—
385C22×C4⋊C4C2413yes—
386C22×C4⋊C4C2416yes—
387C22×C4⋊C4C24112yes—
388C22×C22⋊C4—224no—
389C22×C22⋊C4—26no—
390C22×C22⋊C4—26no—
391C22×C22⋊C4—23no—
392C22×C22⋊C4—23no—
393C22×C22⋊C4—23no—
394C22×C22⋊C4—26no—
395C22×C22⋊C4—23no—
396C22×C22⋊C4—23no—
397C22×C22⋊C4—224no—
398C22×C22⋊C4—26no—
399C22×C22⋊C4—26no—
400C22×C22⋊C4—23no—
401C22×C22⋊C4—23no—
402C22×C22⋊C4—424no—
403C22×C22⋊C4—424no—
404C22×C42—23no—
405#469—2192no—
406#468—2192no—
407#466—2192no—
408#465—2192no—
409#428—296no—
410C2×#107—224no—
411C2×#107C24124yescomplemented
412C2×#106—224no—
413C2×#106C24124yescomplemented
414#418—296no—
415#417—296no—
416C2×#103—224no—
417C2×#103C24124yescomplemented
418C2×#102—224no—
419C2×#102—224no—
420C2×#102—224no—
421C2×#102C24124yescomplemented
422C2×#102C24124yescomplemented
423C2×#102C24124yescomplemented
424#386—248no—
425#386—296no—
426#386—248no—
427#386—224no—
428#386—248no—
429#386—224no—
430#385—224no—
431#385—248no—
432#385—224no—
433#381—224no—
434#380—224no—
435#380—224no—
436#380—212no—
437#380—212no—
438#380—26no—
439#380—26no—
440#380—212no—
441#380C24112yes—
442#380C24124yes—
443#380C24112yes—
444#380C24124yes—
445#380C24124yes—
446#379—28no—
447#379—224no—
448#379—224no—
449C4×C22⋊C4—224no—
450C4×C22⋊C4—224no—
451C2×#95—224no—
452C2×#95—26no—
453C2×#95—26no—
454C2×#95—23no—
455C2×#95—23no—
456C2×#95—26no—
457#340C24148yescomplemented
458#340C24148yescomplemented
459C25—212no—
460C25—212no—
461C25—2128no—
462C25—224no—
463C25—296no—
464C25—224no—
465C25—212no—
466C25—212no—
467C25—212no—
468C25—212no—
469C25—232no—
470C25—212no—
471C25—24no—
472C25—21no—
473C25—22no—
474C25—412no—
475C25—412no—
476C25—448no—
477C25—4192no—
478C25—4192no—
479C25—44no—
480C25—412no—
481C25—412no—
482C25#121124yes—
483C25AGL(1,ℤ/8)18yescomplemented
484C25C22×D413yes—
485C25C22×D414yes—
486C25C22×D4112yes—
487C25C22×D4112yes—
488C25C22×D411yescharacteristic
489C25C22×D413yes—
490C2×#41—224no—
491C2×#41—224no—
492C2×#41—424no—
493C2×#41—416no—
494C2×#41—448no—
495C22×Q8—21no—
496C22×Q8—26no—
497C22×Q8—26no—
498C22×Q8C2512yes—
499C22×D4—212no—
500C22×D4—212no—
501C22×D4—24no—
502C22×D4—224no—
503C22×D4—224no—
504C22×D4—26no—
505C22×D4—212no—
506C22×D4—224no—
507C22×D4—24no—
508C22×D4—22no—
509C22×D4—21no—
510C22×D4—212no—
511C22×D4—224no—
512C22×D4—26no—
513C22×D4—496no—
514C22×D4—424no—
515C22×D4—424no—
516C22×D4—496no—
517C22×D4—424no—
518C22×D4—412no—
519C22×D4—412no—
520C22×D4—412no—
521C22×D4—424no—
522C22×D4—496no—
523C22×D4—424no—
524C22×D4—424no—
525C22×D4—412no—
526C22×D4—412no—
527C22×D4—424no—
528C22×D4—416no—
529C22×D4—412no—
530C22×D4—424no—
531C22×D4—448no—
532C22×D4—8192no—
533C22×D4C2512yes—
534C22×D4C2514yes—
535C23×C4—232no—
536C23×C4—2256no—
537C23×C4—296no—
538C23×C4—2384no—
539C23×C4—2128no—
540C23×C4—2384no—
541C23×C4—21024no—
542C23×C4—296no—
543C23×C4—296no—
544C23×C4—2192no—
545C23×C4—2768no—
546C23×C4—224no—
547C23×C4—296no—
548C23×C4—212no—
549C23×C4—212no—
550C23×C4—224no—
551C23×C4—296no—
552C23×C4—224no—
553C23×C4—224no—
554C23×C4—224no—
555C23×C4—224no—
556C23×C4—2192no—
557C23×C4—296no—
558C23×C4—2192no—
559C23×C4—296no—
560C23×C4—248no—
561C23×C4—296no—
562C23×C4—248no—
563C23×C4—224no—
564C23×C4—224no—
565C23×C4—296no—
566C23×C4—296no—
567C23×C4—2192no—
568C23×C4—224no—
569C23×C4—212no—
570C23×C4—248no—
571C23×C4—224no—
572C23×C4—248no—
573C23×C4—212no—
574C23×C4—224no—
575C23×C4—248no—
576C23×C4—224no—
577C23×C4—212no—
578C23×C4—212no—
579C23×C4—248no—
580C23×C4—212no—
581C23×C4—23no—
582C23×C4—23no—
583C23×C4—21no—
584C23×C4—26no—
585C23×C4—24no—
586C23×C4—412no—
587C23×C4—412no—
588C23×C4—412no—
589C23×C4—412no—
590C23×C4#121124yes—
591C23×C4#121124yes—
592C23×C4#121124yes—
593C23×C4#121196yes—
594C23×C4C22×D4124yes—
595C23×C4C22×D4112yes—
596C23×C4C22×D4112yes—
597C23×C4C22×D4112yes—
598C23×C4C22×D4112yes—
599C23×C4C22×D4112yes—
600C23×C4C22×D416yes—
601C23×C4C22×D416yes—
602C23×C4C22×D413yes—
603C23×C4C22×D413yes—
604C23×C4C22×D4112yes—
605C23×C4C22×D4112yes—
606C23×C4C22×D4148yes—
607C23×C4C22×D4112yes—
608C23×C4C22×D412yes—
609C23×C4C22×D411yescharacteristic
610C23×C4C2×#41112yes—
611C23×C4C2×#41112yes—
612C23×C4C2×#41148yes—
613C23×C4C2×#41112yes—
614C23×C4C2516yes—
615C23×C4C2516yes—
616C23×C4C2512yes—
617C23×C4C2511yescharacteristic
618AGL(1,ℤ/8)—4128no—
619C2×SD16—248no—
620C2×SD16—432no—
621C2×D8—248no—
622C2×D8—432no—
623C2×M16—2768no—
624C2×M16—21536no—
625C2×M16—2192no—
626C2×M16—296no—
627C2×M16—248no—
628C2×M16—248no—
629C2×M16—2768no—
630C2×M16—2192no—
631C2×M16—296no—
632C2×M16—296no—
633C2×M16#120164yescomplemented
634C2×M16C22×D4148yes—
635C2×M16C22×D4148yes—
636C2×M16C22×D4196yescomplemented
637C22×C8—2192no—
638C22×C8—2512no—
639C22×C8—248no—
640C22×C8—224no—
641C22×C8—2192no—
642C22×C8—296no—
643C22×C8—296no—
644C22×C8C22×D4124yes—
645C22×C8C22×D4124yes—
646C22×C8C22×D4196yescomplemented
647C22×C8C25112yes—
648C22×C8C2514yes—
649#123—496no—
650C22⋊Q8—224no—
651C22⋊Q8—224no—
652C22⋊Q8—224no—
653C22⋊Q8—224no—
654C22⋊Q8—424no—
655C22⋊Q8—424no—
656#121—248no—
657#121—248no—
658#121—224no—
659#121—224no—
660#121—248no—
661#121—248no—
662#121—224no—
663#121—224no—
664#121—496no—
665#121—496no—
666#121—448no—
667#121—448no—
668#121—424no—
669#121—424no—
670#120—496no—
671#120—4192no—
672#120—496no—
673#120—432no—
674#120—464no—
675C4×D4—496no—
676C4×D4—496no—
677#117—224no—
678#117—224no—
679#117—424no—
680C2×C4⋊C4—212no—
681C2×C4⋊C4—224no—
682C2×C4⋊C4—26no—
683C2×C4⋊C4—26no—
684C2×C4⋊C4—212no—
685C2×C4⋊C4—224no—
686C2×C4⋊C4—26no—
687C2×C4⋊C4—26no—
688C2×C4⋊C4—212no—
689C2×C4⋊C4—26no—
690C2×C4⋊C4—212no—
691C2×C4⋊C4—212no—
692C2×C4⋊C4—23no—
693C2×C4⋊C4—23no—
694C2×C4⋊C4—412no—
695C2×C4⋊C4—424no—
696C2×C4⋊C4—412no—
697C2×C4⋊C4—412no—
698C2×C4⋊C4C25112yes—
699C2×C4⋊C4C2516yes—
700C2×C4⋊C4C2516yes—
701C2×C22⋊C4—224no—
702C2×C22⋊C4—224no—
703C2×C22⋊C4—212no—
704C2×C22⋊C4—212no—
705C2×C22⋊C4—212no—
706C2×C22⋊C4—224no—
707C2×C22⋊C4—212no—
708C2×C22⋊C4—212no—
709C2×C22⋊C4—224no—
710C2×C22⋊C4—224no—
711C2×C22⋊C4—212no—
712C2×C22⋊C4—212no—
713C2×C22⋊C4—424no—
714C2×C22⋊C4—496no—
715C2×C22⋊C4—424no—
716C2×C22⋊C4—412no—
717C2×C22⋊C4—412no—
718C2×C22⋊C4—412no—
719C2×C22⋊C4—424no—
720C2×C22⋊C4—412no—
721C2×C22⋊C4—412no—
722C2×C22⋊C4—424no—
723C2×C22⋊C4—424no—
724C2×C22⋊C4—496no—
725C2×C22⋊C4—412no—
726C2×C22⋊C4—412no—
727C2×C42—212no—
728C2×C42—412no—
729#107—248no—
730#106—248no—
731#103—248no—
732#102—248no—
733#102—248no—
734#102—248no—
735#95—224no—
736#95—224no—
737#95—212no—
738#95—212no—
739#95—224no—
740C24—232no—
741C24—296no—
742C24—224no—
743C24—212no—
744C24—296no—
745C24—22no—
746C24—26no—
747C24—224no—
748C24—212no—
749C24—2256no—
750C24—296no—
751C24—296no—
752C24—248no—
753C24—248no—
754C24—224no—
755C24—212no—
756C24—296no—
757C24—224no—
758C24—26no—
759C24—212no—
760C24—224no—
761C24—26no—
762C24—224no—
763C24—224no—
764C24—22no—
765C24—24no—
766C24—448no—
767C24—424no—
768C24—424no—
769C24—496no—
770C24—496no—
771C24—4384no—
772C24—496no—
773C24—496no—
774C24—4384no—
775C24—41024no—
776C24—448no—
777C24—48no—
778C24—424no—
779C24—448no—
780C24—46no—
781C24—424no—
782C24—412no—
783C24—44no—
784C24—42no—
785C24—46no—
786C24—412no—
787C24—848no—
788C24—848no—
789C24—816no—
790C24C2×#121112yes—
791C24C2×#121148yes—
792C24C2×#121112yes—
793C24C2×#121112yes—
794C24C2×AGL(1,ℤ/8)112yes—
795C24C2×AGL(1,ℤ/8)116yescomplemented
796C24#575112yes—
797C24C23×D416yes—
798C24C23×D412yes—
799C24C23×D416yes—
800C24C23×D411yescharacteristic
801#41—416no—
802#41—448no—
803#41—832no—
804C2×Q8—26no—
805C2×Q8—26no—
806C2×Q8—46no—
807C2×Q8—44no—
808C2×Q8—412no—
809C2×D4—26no—
810C2×D4—212no—
811C2×D4—212no—
812C2×D4—26no—
813C2×D4—448no—
814C2×D4—448no—
815C2×D4—448no—
816C2×D4—424no—
817C2×D4—424no—
818C2×D4—424no—
819C2×D4—448no—
820C2×D4—448no—
821C2×D4—448no—
822C2×D4—424no—
823C2×D4—424no—
824C2×D4—448no—
825C2×D4—44no—
826C2×D4—48no—
827C2×D4—416no—
828C2×D4—424no—
829C2×D4—412no—
830C2×D4—46no—
831C2×D4—424no—
832C2×D4—448no—
833C2×D4—412no—
834C2×D4—848no—
835C2×D4—8384no—
836C2×D4—896no—
837C2×D4—816no—
838C2×D4—848no—
839C2×D4—896no—
840C2×D4—816no—
841C2×D4—832no—
842C22×C4—232no—
843C22×C4—296no—
844C22×C4—296no—
845C22×C4—296no—
846C22×C4—2768no—
847C22×C4—2192no—
848C22×C4—2128no—
849C22×C4—2256no—
850C22×C4—2768no—
851C22×C4—2384no—
852C22×C4—296no—
853C22×C4—296no—
854C22×C4—2192no—
855C22×C4—296no—
856C22×C4—248no—
857C22×C4—224no—
858C22×C4—224no—
859C22×C4—248no—
860C22×C4—212no—
861C22×C4—212no—
862C22×C4—212no—
863C22×C4—212no—
864C22×C4—212no—
865C22×C4—212no—
866C22×C4—296no—
867C22×C4—296no—
868C22×C4—2384no—
869C22×C4—224no—
870C22×C4—296no—
871C22×C4—224no—
872C22×C4—248no—
873C22×C4—248no—
874C22×C4—248no—
875C22×C4—248no—
876C22×C4—248no—
877C22×C4—248no—
878C22×C4—224no—
879C22×C4—224no—
880C22×C4—224no—
881C22×C4—224no—
882C22×C4—296no—
883C22×C4—248no—
884C22×C4—248no—
885C22×C4—2192no—
886C22×C4—26no—
887C22×C4—26no—
888C22×C4—212no—
889C22×C4—22no—
890C22×C4—424no—
891C22×C4—424no—
892C22×C4—46no—
893C22×C4—46no—
894C22×C4—424no—
895C22×C4—412no—
896C22×C4—46no—
897C22×C4—412no—
898C22×C4—46no—
899C22×C4—46no—
900C22×C4—412no—
901C22×C4—412no—
902C22×C4—424no—
903C22×C4—848no—
904C22×C4—816no—
905C22×C4C2×#120116yes—
906C22×C4C2×#121112yes—
907C22×C4C2×#121112yes—
908C22×C4C2×#121148yes—
909C22×C4C2×#121148yes—
910C22×C4C2×#121148yes—
911C22×C4C2×#121124yes—
912C22×C4C2×#121124yes—
913C22×C4C2×#121112yes—
914C22×C4C2×#121124yes—
915C22×C4#525148yes—
916C22×C4C23×D4112yes—
917C22×C4C23×D4112yes—
918C22×C4C23×D416yes—
919C22×C4C23×D416yes—
920C22×C4C23×D416yes—
921C22×C4C23×D4112yes—
922C22×C4C23×D412yes—
923C22×C4C23×D411yescharacteristic
924C22×C4C22×#41112yes—
925C22×C4C22×#41112yes—
926C22×C4C22×#4116yes—
927C22×C4C22×#41112yes—
928C22×C4C2611yescharacteristic
929SD16—432no—
930D8—432no—
931M16—2192no—
932M16—296no—
933M16—2192no—
934M16C2×#120164yescomplemented
935C2×C8—2192no—
936C2×C8—224no—
937C2×C8—248no—
938C2×C8—2192no—
939C2×C8C2×#120132yescomplemented
940C2×C8C23×D4124yes—
941C2×C8C23×D4124yes—
942C4⋊C4—26no—
943C4⋊C4—26no—
944C4⋊C4—212no—
945C4⋊C4—212no—
946C4⋊C4—26no—
947C4⋊C4—26no—
948C4⋊C4—424no—
949C4⋊C4—412no—
950C4⋊C4—46no—
951C4⋊C4—46no—
952C4⋊C4—424no—
953C4⋊C4—424no—
954C22⋊C4—448no—
955C22⋊C4—448no—
956C22⋊C4—424no—
957C22⋊C4—424no—
958C22⋊C4—424no—
959C22⋊C4—448no—
960C22⋊C4—424no—
961C22⋊C4—424no—
962C22⋊C4—448no—
963C22⋊C4—448no—
964C22⋊C4—424no—
965C22⋊C4—424no—
966C42—424no—
967C23—232no—
968C23—296no—
969C23—2256no—
970C23—224no—
971C23—224no—
972C23—248no—
973C23—296no—
974C23—224no—
975C23—248no—
976C23—224no—
977C23—22no—
978C23—26no—
979C23—212no—
980C23—212no—
981C23—296no—
982C23—296no—
983C23—224no—
984C23—224no—
985C23—296no—
986C23—224no—
987C23—26no—
988C23—212no—
989C23—26no—
990C23—212no—
991C23—448no—
992C23—496no—
993C23—496no—
994C23—496no—
995C23—496no—
996C23—4384no—
997C23—41024no—
998C23—448no—
999C23—4384no—
1000C23—424no—
1001C23—448no—
1002C23—424no—
1003C23—44no—
1004C23—42no—
1005C23—46no—
1006C23—412no—
1007C23—46no—
1008C23—412no—
1009C23—848no—
1010C23—848no—
1011C23—84no—
1012C23—816no—
1013C23—88no—
1014C23—824no—
1015C23—812no—
1016C23—812no—
1017C23—824no—
1018C23—1664no—
1019C23#2847116yes—
1020C23#3055148yescomplemented
1021C23C22×#121112yes—
1022C23C22×#121112yes—
1023C23C22×#121112yes—
1024C23C22×#12116yes—
1025C23C22×AGL(1,ℤ/8)112yes—
1026C23C22×AGL(1,ℤ/8)12yes—
1027C23C2×#575112yes—
1028C23C2×#57516yes—
1029C23C24×D411yescharacteristic
1030Q8—42no—
1031Q8—46no—
1032Q8—84no—
1033D4—42no—
1034D4—44no—
1035D4—412no—
1036D4—46no—
1037D4—848no—
1038D4—896no—
1039D4—816no—
1040D4—848no—
1041D4—896no—
1042D4—816no—
1043D4—88no—
1044D4—84no—
1045C2×C4—296no—
1046C2×C4—296no—
1047C2×C4—2192no—
1048C2×C4—296no—
1049C2×C4—224no—
1050C2×C4—224no—
1051C2×C4—212no—
1052C2×C4—212no—
1053C2×C4—296no—
1054C2×C4—296no—
1055C2×C4—248no—
1056C2×C4—248no—
1057C2×C4—212no—
1058C2×C4—212no—
1059C2×C4—212no—
1060C2×C4—212no—
1061C2×C4—224no—
1062C2×C4—224no—
1063C2×C4—412no—
1064C2×C4—46no—
1065C2×C4—46no—
1066C2×C4—412no—
1067C2×C4—412no—
1068C2×C4—46no—
1069C2×C4—46no—
1070C2×C4—412no—
1071C2×C4—46no—
1072C2×C4—848no—
1073C2×C4—84no—
1074C2×C4—824no—
1075C2×C4—812no—
1076C2×C4—812no—
1077C2×C4—816no—
1078C2×C4#2847116yes—
1079C2×C4#2847132yes—
1080C2×C4C22×#12014yes—
1081C2×C4C22×#12018yes—
1082C2×C4C22×#121112yes—
1083C2×C4C22×#121112yes—
1084C2×C4C22×#121112yes—
1085C2×C4C22×#12116yes—
1086C2×C4C2×#525112yes—
1087C2×C4C2×#525124yes—
1088C2×C4C24×D413yes—
1089C2×C4C23×#4113yes—
1090C8—224no—
1091C8C22×#120116yescomplemented
1092C22—2128no—
1093C22—212no—
1094C22—224no—
1095C22—212no—
1096C22—224no—
1097C22—212no—
1098C22—296no—
1099C22—232no—
1100C22—212no—
1101C22—212no—
1102C22—212no—
1103C22—212no—
1104C22—4192no—
1105C22—4192no—
1106C22—412no—
1107C22—412no—
1108C22—448no—
1109C22—812no—
1110C22—86no—
1111C22—86no—
1112C22—812no—
1113C22—82no—
1114C22—84no—
1115C22—1632no—
1116C22—168no—
1117C22—1616no—
1118C22C2×#284718yes—
1119C22C2×#284714yes—
1120C22C2×#3055112yes—
1121C22C2×#3055124yescomplemented
1122C22#60444112yes—
1123C22C23×#12113yes—
1124C22C23×AGL(1,ℤ/8)11yescharacteristic
1125C22C22×#57513yes—
1126C4—212no—
1127C4—212no—
1128C4—812no—
1129C4—86no—
1130C4—86no—
1131C4—82no—
1132C4C2×#284718yes—
1133C4C2×#284714yes—
1134C4C23×#12011yescharacteristic
1135C4C22×#52513yes—
1136C2—224no—
1137C2—28no—
1138C2—412no—
1139C2—162no—
1140C2—164no—
1141C2#662900718yesdirect product factor
1142C2C22×#284711yescharacteristic
1143C2C22×#305513yes—
1144C2C2×#6044413yes—
subgroupG/H
center, socleC24C23×D4
commutator, Frattini, cosocleC22×C4C26
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C26×C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C25×M16C2semidirect
2. C22×#3055C2semidirect
3. C2×#36614C2semidirect
4. C22×#2847C2semidirect
5. #6629007C2direct (N × H)
6. C2×#32936C2semidirect
7. C2×#32935C2semidirect
8. C2×#32930C2semidirect
9. C2×#32929C2semidirect
10. C2×#20973C2semidirect
11. C2×#20971C2semidirect
12. C2×#20661C2semidirect
14. C23×AGL(1,ℤ/8)C22semidirect
18. C24×M16C22semidirect
19. C24×M16C22semidirect
20. C25×C8C22semidirect
25. C2×#3055C22semidirect
26. C22×#469C22semidirect
27. C22×#468C22semidirect
28. C22×#466C22semidirect
29. C22×#465C22semidirect
30. C22×#428C22semidirect
31. C22×#417C22semidirect
32. C22×#418C22semidirect
34. #36614C22semidirect
36. C2×#2848C22semidirect
37. C2×#2848C22semidirect
43. C2×#2847C22semidirect
44. C2×#2847C22semidirect
45. C2×#2847C22semidirect
52. #32936C22semidirect
53. #32935C22semidirect
54. #32930C22semidirect
55. #32929C22semidirect
56. #20973C22semidirect
57. #20971C22semidirect
58. C2×#1895C22semidirect
59. C2×#1895C22semidirect
60. C2×#1894C22semidirect
61. C2×#1893C22semidirect
62. C2×#1893C22semidirect
63. C2×#1893C22semidirect
64. C2×#1892C22semidirect
65. #20661C22semidirect
66. C2×#1809C22semidirect
67. C2×#1808C22semidirect
68. C2×#1807C22semidirect
69. C2×#1736C22semidirect
85. C22×AGL(1,ℤ/8)C23semidirect
86. C23×SD16C23semidirect
87. C23×D8C23semidirect
95. C23×M16D4semidirect
102. C23×M16C23semidirect
106. C24×C8C23semidirect
139. C2×#469C23semidirect
141. C2×#468C23semidirect
143. C2×#466C23semidirect
145. C2×#465C23semidirect
147. C2×#428C23semidirect
148. C22×#107C23semidirect
149. C22×#106C23semidirect
151. C2×#417C23semidirect
153. C2×#418C23semidirect
154. C22×#103C23semidirect
155. C22×#102C23semidirect
156. C22×#102C23semidirect
157. C22×#102C23semidirect
161. #2848C23semidirect
162. #2848C23semidirect
171. #2847C23semidirect
172. #2847C23semidirect
204. #1895C23semidirect
205. #1895C23semidirect
206. #1894C23semidirect
207. #1893C23semidirect
208. #1893C23semidirect
209. #1893C23semidirect
210. #1892C23semidirect
211. #1809C23semidirect
212. #1808C23semidirect
213. #1807C23semidirect
214. #1736C23semidirect
215. C2×#340C23semidirect
216. C2×#340C23semidirect
289. C22×SD16C24semidirect
291. C22×D8C24semidirect
307. C22×M16C2×D4semidirect
308. C22×M16C2×D4semidirect
318. C23×C8C2×D4semidirect
411. C2×#107C24semidirect
413. C2×#106C24semidirect
417. C2×#103C24semidirect
421. C2×#102C24semidirect
422. C2×#102C24semidirect
423. C2×#102C24semidirect
457. #340C24semidirect
458. #340C24semidirect
483. C25AGL(1,ℤ/8)semidirect
633. C2×M16#120semidirect
636. C2×M16C22×D4semidirect
646. C22×C8C22×D4semidirect
795. C24C2×AGL(1,ℤ/8)semidirect
934. M16C2×#120semidirect
939. C2×C8C2×#120semidirect
1020. C23#3055semidirect
1091. C8C22×#120semidirect
1121. C22C2×#3055semidirect
1141. C2#6629007direct (N × H)

Maximal subgroups

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

subgroupindex
C25×M162
C22×#30552
C2×#366142
C22×#28472
#66290072
C2×#329362
C2×#329352
C2×#329302
C2×#329292
C2×#209732
C2×#209712
C2×#206612