Finite Group Databasebeta

← C2×#10997 #357549

Subgroups — C2×#10997 #357549

Order 512.

5686 conjugacy classes of subgroups.

The subgroup lattice has 1060 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#535C211yesmaximal, characteristic
2C23×#104C211yesmaximal, characteristic, complemented
3C22×#417C211yesmaximal, characteristic, complemented
4C23×#100C211yesmaximal, characteristic, complemented
5C22×#390C211yesmaximal, characteristic, complemented
6C2×#1736C211yesmaximal, characteristic, complemented
7C22×#339C211yesmaximal, characteristic, complemented
8#10997C218yesmaximal, direct product factor
9C23×#41C2211yescharacteristic
10C24×D4C2211yescharacteristic
11C23×M16C2211yescharacteristic
12C23×M16C2211yescharacteristic
13C2×#535—24no—
14C2×#535—22no—
15C2×#535—24no—
16C2×#535—22no—
17C2×#535—24no—
18C2×#535—22no—
19C2×#535C418yescomplemented
20C2×#535C2214yes—
21C22×#127—21no—
22C22×#124—21no—
23C22×#121—22no—
24C22×#120—22no—
25C22×#117C2211yescharacteristic
26C23×C4⋊C4C2211yescharacteristic
27C23×C22⋊C4—22no—
28C23×C42C2211yescharacteristic
29C22×#104—24no—
30C22×#104—24no—
31C22×#104—24no—
32C22×#104C2214yescomplemented
33C2×#417—22no—
34C2×#417—24no—
35C2×#417—24no—
36C2×#417C2214yescomplemented
37C22×#103—21no—
38C22×#102—21no—
39C22×#100—24no—
40C22×#100—24no—
41C22×#100—24no—
42C22×#100C2214yescomplemented
43C2×#390—24no—
44C2×#390—22no—
45C2×#390—24no—
46C2×#390C2214yescomplemented
47#1736—22no—
48#1736C2214yescomplemented
49C2×#340—22no—
50C2×#339—24no—
51C2×#339C2214yescomplemented
52C26D412yes—
53C22×#41—22no—
54C22×#41—21no—
55C22×#41—22no—
56C22×#41—21no—
57C22×#41—22no—
58C22×#41—22no—
59C22×#41—22no—
60C22×#41—22no—
61C22×#41—22no—
62C22×#41—22no—
63C22×#41—22no—
64C22×#41—22no—
65C22×#41C2×C414yes—
66C22×#41D414yes—
67C22×#41D412yes—
68C22×#41C2312yes—
69C23×Q8D411yescharacteristic
70C23×D4—21no—
71C23×D4—24no—
72C23×D4—22no—
73C23×D4—22no—
74C23×D4—21no—
75C23×D4—21no—
76C23×D4—21no—
77C23×D4—22no—
78C23×D4—21no—
79C23×D4—22no—
80C23×D4—22no—
81C23×D4—22no—
82C23×D4—22no—
83C23×D4—22no—
84C23×D4—22no—
85C23×D4—22no—
86C23×D4C2×C414yes—
87C23×D4D412yes—
88C23×D4D414yes—
89C23×D4D411yescharacteristic
90C23×D4C2312yes—
91C24×C4—21no—
92C24×C4—21no—
93C24×C4—21no—
94C24×C4C2311yescharacteristic
95C22×M16—22no—
96C22×M16—21no—
97C22×M16—21no—
98C22×M16—22no—
99C22×M16—22no—
100C22×M16—22no—
101C22×M16—22no—
102C22×M16—22no—
103C22×M16—22no—
104C22×M16—22no—
105C22×M16—22no—
106C22×M16—22no—
107C22×M16D414yescomplemented
108C22×M16D414yescomplemented
109C22×M16C2312yes—
110C22×M16C2312yes—
111C23×C8—21no—
112C23×C8—21no—
113#535—216no—
114#535—216no—
115#535—216no—
116#535—216no—
117#535—28no—
118#535—216no—
119#535—28no—
120#535—216no—
121#535—28no—
122#535C2×C4116yescomplemented
123C2×#127—28no—
124C2×#127—24no—
125C2×#127—28no—
126C2×#127—24no—
127C2×#124—28no—
128C2×#124—24no—
129C2×#124—28no—
130C2×#124—24no—
131C2×#121—28no—
132C2×#121—216no—
133C2×#121—216no—
134C2×#121—28no—
135C2×#120—28no—
136C2×#120—216no—
137C2×#120—216no—
138C2×#120—28no—
139C2×#117—22no—
140C2×#117—22no—
141C2×#117—21no—
142C2×#117—21no—
143C2×#117C2×C414yes—
144C2×#117D414yes—
145C2×#117D412yes—
146C2×#117C2312yes—
147C22×C4⋊C4—21no—
148C22×C4⋊C4—22no—
149C22×C4⋊C4—21no—
150C22×C4⋊C4—21no—
151C22×C4⋊C4—21no—
152C22×C4⋊C4—22no—
153C22×C4⋊C4—21no—
154C22×C4⋊C4—22no—
155C22×C4⋊C4D412yes—
156C22×C4⋊C4D414yescomplemented
157C22×C4⋊C4C2312yes—
158C22×C22⋊C4—24no—
159C22×C22⋊C4—21no—
160C22×C22⋊C4—216no—
161C22×C22⋊C4—28no—
162C22×C22⋊C4—416no—
163C22×C42—21no—
164C22×C42—22no—
165C22×C42—22no—
166C22×C42—22no—
167C22×C42—22no—
168C22×C42—21no—
169C22×C42—22no—
170C22×C42D414yescomplemented
171C22×C42C2312yes—
172C2×#104—232no—
173C2×#104—28no—
174C2×#104—28no—
175C2×#104—28no—
176#417—216no—
177#417—28no—
178#417—28no—
179C2×#103—28no—
180C2×#103—24no—
181C2×#102—28no—
182C2×#102—24no—
183C2×#100—232no—
184C2×#100—28no—
185C2×#100—28no—
186C2×#100—28no—
187#390—216no—
188#390—28no—
189#390—28no—
190#340—28no—
191#339—28no—
192C25—24no—
193C25—22no—
194C25—21no—
195C25—24no—
196C25—22no—
197C25—24no—
198C25—24no—
199C25—24no—
200C25—48no—
201C25—48no—
202C25C22⋊C418yes—
203C25C2×D411yescharacteristic
204C25C2×D414yes—
205C2×#41—24no—
206C2×#41—24no—
207C2×#41—24no—
208C2×#41—24no—
209C2×#41—24no—
210C2×#41—22no—
211C2×#41—22no—
212C2×#41—28no—
213C2×#41—28no—
214C2×#41—28no—
215C2×#41—28no—
216C2×#41—24no—
217C2×#41—28no—
218C2×#41—28no—
219C2×#41—24no—
220C2×#41—24no—
221C2×#41—28no—
222C2×#41—24no—
223C2×#41—28no—
224C2×#41—22no—
225C2×#41—22no—
226C2×#41—22no—
227C2×#41—22no—
228C2×#41—22no—
229C2×#41—22no—
230C2×#41—22no—
231C2×#41—22no—
232C2×#41—44no—
233C2×#41—42no—
234C2×#41—42no—
235C2×#41—42no—
236C2×#41—44no—
237C2×#41—44no—
238C2×#41—44no—
239C2×#41—42no—
240C2×#41—44no—
241C2×#41—42no—
242C2×#41—44no—
243C2×#41—42no—
244C2×#41—42no—
245C2×#41—44no—
246C2×#41—42no—
247C2×#41—44no—
248C2×#41C22⋊C418yescomplemented
249C2×#41C22×C414yes—
250C2×#41C2×D414yes—
251C22×Q8—21no—
252C22×Q8—22no—
253C22×Q8—22no—
254C22×Q8—22no—
255C22×Q8—22no—
256C22×Q8—22no—
257C22×Q8C22⋊C414yescomplemented
258C22×Q8C2×D412yes—
259C22×D4—24no—
260C22×D4—22no—
261C22×D4—24no—
262C22×D4—22no—
263C22×D4—216no—
264C22×D4—232no—
265C22×D4—24no—
266C22×D4—24no—
267C22×D4—24no—
268C22×D4—24no—
269C22×D4—28no—
270C22×D4—28no—
271C22×D4—28no—
272C22×D4—28no—
273C22×D4—22no—
274C22×D4—24no—
275C22×D4—22no—
276C22×D4—24no—
277C22×D4—22no—
278C22×D4—22no—
279C22×D4—21no—
280C22×D4—24no—
281C22×D4—24no—
282C22×D4—24no—
283C22×D4—24no—
284C22×D4—28no—
285C22×D4—22no—
286C22×D4—22no—
287C22×D4—28no—
288C22×D4—28no—
289C22×D4—24no—
290C22×D4—24no—
291C22×D4—22no—
292C22×D4—28no—
293C22×D4—24no—
294C22×D4—22no—
295C22×D4—22no—
296C22×D4—22no—
297C22×D4—22no—
298C22×D4—22no—
299C22×D4—22no—
300C22×D4—22no—
301C22×D4—22no—
302C22×D4—22no—
303C22×D4—22no—
304C22×D4—22no—
305C22×D4—22no—
306C22×D4—42no—
307C22×D4—42no—
308C22×D4—42no—
309C22×D4—42no—
310C22×D4—44no—
311C22×D4—42no—
312C22×D4—42no—
313C22×D4—42no—
314C22×D4—42no—
315C22×D4—44no—
316C22×D4—44no—
317C22×D4—42no—
318C22×D4—42no—
319C22×D4—42no—
320C22×D4—42no—
321C22×D4—44no—
322C22×D4—44no—
323C22×D4—42no—
324C22×D4—42no—
325C22×D4—42no—
326C22×D4—42no—
327C22×D4—44no—
328C22×D4—42no—
329C22×D4—42no—
330C22×D4—44no—
331C22×D4—44no—
332C22×D4—42no—
333C22×D4—42no—
334C22×D4—88no—
335C22×D4—88no—
336C22×D4C22⋊C418yes—
337C22×D4C22⋊C414yescomplemented
338C22×D4C22×C414yes—
339C22×D4C2×D414yes—
340C22×D4C2×D412yes—
341C23×C4—28no—
342C23×C4—24no—
343C23×C4—21no—
344C23×C4—22no—
345C23×C4—22no—
346C23×C4—24no—
347C23×C4—22no—
348C23×C4—24no—
349C23×C4—22no—
350C23×C4—24no—
351C23×C4—22no—
352C23×C4—44no—
353C23×C4—42no—
354C23×C4—42no—
355C23×C4—42no—
356C23×C4—42no—
357C23×C4—42no—
358C23×C4—42no—
359C23×C4—48no—
360C23×C4—41no—
361C23×C4—41no—
362C23×C4—42no—
363C23×C4C22×C412yes—
364C23×C4C2×D411yescharacteristic
365C23×C4C2×D411yescharacteristic
366C23×C4C2×D412yes—
367C23×C4C2×D411yescharacteristic
368C23×C4C2×D411yescharacteristic
369C23×C4C2×D412yes—
370C23×C4C2×D411yescharacteristic
371C23×C4C2×D412yes—
372C23×C4C2×D412yes—
373C23×C4C2×D412yes—
374C23×C4C2×D412yes—
375C23×C4C2×D412yes—
376C23×C4#4112yes—
377C23×C4#4112yes—
378C23×C4#4112yes—
379C23×C4#4112yes—
380C23×C4C2411yescharacteristic
381C2×M16—24no—
382C2×M16—24no—
383C2×M16—22no—
384C2×M16—22no—
385C2×M16—28no—
386C2×M16—28no—
387C2×M16—28no—
388C2×M16—28no—
389C2×M16—22no—
390C2×M16—22no—
391C2×M16—22no—
392C2×M16—22no—
393C2×M16—22no—
394C2×M16—22no—
395C2×M16—22no—
396C2×M16—22no—
397C2×M16—42no—
398C2×M16—42no—
399C2×M16—42no—
400C2×M16—44no—
401C2×M16—44no—
402C2×M16—44no—
403C2×M16—42no—
404C2×M16—44no—
405C2×M16C2×D414yescomplemented
406C2×M16C2×D414yescomplemented
407C22×C8—24no—
408C22×C8—24no—
409C22×C8—22no—
410C22×C8—22no—
411C22×C8—42no—
412C22×C8—42no—
413C22×C8—42no—
414C22×C8—42no—
415#127—216no—
416#127—232no—
417#127—216no—
418#124—216no—
419#124—232no—
420#124—216no—
421#121—232no—
422#121—264no—
423#121—232no—
424#120—232no—
425#120—264no—
426#120—232no—
427#117—24no—
428#117—24no—
429#117—24no—
430#117—24no—
431#117—24no—
432#117—22no—
433#117—22no—
434#117C22⋊C418yescomplemented
435#117C22×C414yes—
436#117C2×D414yes—
437C2×C4⋊C4—24no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—24no—
440C2×C4⋊C4—24no—
441C2×C4⋊C4—24no—
442C2×C4⋊C4—24no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—22no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—24no—
448C2×C4⋊C4—22no—
449C2×C4⋊C4—41no—
450C2×C4⋊C4—41no—
451C2×C4⋊C4—42no—
452C2×C4⋊C4—42no—
453C2×C4⋊C4—42no—
454C2×C4⋊C4—42no—
455C2×C4⋊C4—42no—
456C2×C4⋊C4C22⋊C418yescomplemented
457C2×C4⋊C4C2×D414yes—
458C2×C4⋊C4C2×D414yescomplemented
459C2×C22⋊C4—216no—
460C2×C22⋊C4—232no—
461C2×C22⋊C4—24no—
462C2×C22⋊C4—24no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—232no—
466C2×C22⋊C4—432no—
467C2×C22⋊C4—464no—
468C2×C42—24no—
469C2×C42—24no—
470C2×C42—22no—
471C2×C42—22no—
472C2×C42—28no—
473C2×C42—28no—
474C2×C42—22no—
475C2×C42—22no—
476C2×C42—22no—
477C2×C42—22no—
478C2×C42—24no—
479C2×C42—22no—
480C2×C42—42no—
481C2×C42—44no—
482C2×C42—42no—
483C2×C42—44no—
484C2×C42C2×D414yescomplemented
485#104—232no—
486#103—216no—
487#102—216no—
488#100—232no—
489C24—24no—
490C24—24no—
491C24—24no—
492C24—24no—
493C24—22no—
494C24—24no—
495C24—28no—
496C24—24no—
497C24—216no—
498C24—24no—
499C24—24no—
500C24—24no—
501C24—28no—
502C24—216no—
503C24—48no—
504C24—432no—
505C24—48no—
506C24—416no—
507C24—416no—
508C24—432no—
509C24—42no—
510C24—48no—
511C24—44no—
512C24—44no—
513C24—42no—
514C24—48no—
515C24—44no—
516C24—44no—
517C24—44no—
518C24—48no—
519C24—44no—
520C24—48no—
521C24—816no—
522C24—84no—
523C24—84no—
524C24—88no—
525C24—88no—
526C24—816no—
527C24C2×C22⋊C412yes—
528C24C2×C22⋊C418yes—
529C24#12012yes—
530C24#12011yescharacteristic
531C24#12012yes—
532C24#12011yescharacteristic
533C24#12112yes—
534C24#12112yes—
535C24#12312yes—
536C24C22×D411yescharacteristic
537#41—24no—
538#41—24no—
539#41—24no—
540#41—24no—
541#41—24no—
542#41—24no—
543#41—24no—
544#41—24no—
545#41—216no—
546#41—216no—
547#41—42no—
548#41—42no—
549#41—42no—
550#41—42no—
551#41—42no—
552#41—42no—
553#41—42no—
554#41—42no—
555#41—48no—
556#41—48no—
557#41—48no—
558#41—48no—
559#41—48no—
560#41—48no—
561#41—48no—
562#41—48no—
563#41—48no—
564#41—48no—
565C2×Q8—22no—
566C2×Q8—24no—
567C2×Q8—22no—
568C2×Q8—22no—
569C2×Q8—22no—
570C2×Q8—22no—
571C2×Q8—28no—
572C2×Q8—28no—
573C2×Q8—42no—
574C2×Q8—44no—
575C2×Q8—42no—
576C2×Q8—44no—
577C2×Q8C2×C22⋊C414yescomplemented
578C2×D4—24no—
579C2×D4—24no—
580C2×D4—28no—
581C2×D4—264no—
582C2×D4—24no—
583C2×D4—24no—
584C2×D4—24no—
585C2×D4—24no—
586C2×D4—24no—
587C2×D4—24no—
588C2×D4—22no—
589C2×D4—24no—
590C2×D4—24no—
591C2×D4—24no—
592C2×D4—22no—
593C2×D4—22no—
594C2×D4—22no—
595C2×D4—24no—
596C2×D4—24no—
597C2×D4—22no—
598C2×D4—24no—
599C2×D4—28no—
600C2×D4—28no—
601C2×D4—24no—
602C2×D4—28no—
603C2×D4—28no—
604C2×D4—216no—
605C2×D4—216no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—42no—
610C2×D4—48no—
611C2×D4—48no—
612C2×D4—44no—
613C2×D4—48no—
614C2×D4—44no—
615C2×D4—48no—
616C2×D4—42no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4—42no—
620C2×D4—42no—
621C2×D4—42no—
622C2×D4—42no—
623C2×D4—42no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—42no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—42no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4—48no—
633C2×D4—48no—
634C2×D4—48no—
635C2×D4—48no—
636C2×D4—48no—
637C2×D4—48no—
638C2×D4—48no—
639C2×D4—48no—
640C2×D4—48no—
641C2×D4—48no—
642C2×D4—48no—
643C2×D4—48no—
644C2×D4—48no—
645C2×D4—44no—
646C2×D4—44no—
647C2×D4—44no—
648C2×D4—42no—
649C2×D4—48no—
650C2×D4—48no—
651C2×D4—48no—
652C2×D4—48no—
653C2×D4—44no—
654C2×D4—44no—
655C2×D4—48no—
656C2×D4—44no—
657C2×D4—42no—
658C2×D4—864no—
659C2×D4—816no—
660C2×D4—816no—
661C2×D4C2×C22⋊C414yescomplemented
662C22×C4—28no—
663C22×C4—216no—
664C22×C4—24no—
665C22×C4—24no—
666C22×C4—22no—
667C22×C4—28no—
668C22×C4—24no—
669C22×C4—24no—
670C22×C4—24no—
671C22×C4—28no—
672C22×C4—24no—
673C22×C4—416no—
674C22×C4—44no—
675C22×C4—48no—
676C22×C4—416no—
677C22×C4—42no—
678C22×C4—42no—
679C22×C4—48no—
680C22×C4—42no—
681C22×C4—42no—
682C22×C4—44no—
683C22×C4—44no—
684C22×C4—42no—
685C22×C4—42no—
686C22×C4—42no—
687C22×C4—42no—
688C22×C4—48no—
689C22×C4—48no—
690C22×C4—44no—
691C22×C4—48no—
692C22×C4—44no—
693C22×C4—48no—
694C22×C4—48no—
695C22×C4—416no—
696C22×C4—42no—
697C22×C4—42no—
698C22×C4—44no—
699C22×C4—44no—
700C22×C4—84no—
701C22×C4—88no—
702C22×C4—84no—
703C22×C4C2×C22⋊C412yes—
704C22×C4C2×C22⋊C412yes—
705C22×C4C2×C22⋊C412yes—
706C22×C4C2×C22⋊C412yes—
707C22×C4C2×C22⋊C412yes—
708C22×C4C4×D414yes—
709C22×C4C4×D414yes—
710C22×C4C4×D414yes—
711C22×C4C4×D414yes—
712C22×C4#12012yes—
713C22×C4#12012yes—
714C22×C4#12012yes—
715C22×C4#12012yes—
716C22×C4#12014yes—
717C22×C4#12012yes—
718C22×C4#12012yes—
719C22×C4#12014yes—
720C22×C4#12011yescharacteristic
721C22×C4#12012yes—
722C22×C4#12011yescharacteristic
723C22×C4#12012yes—
724C22×C4#12112yes—
725C22×C4#12112yes—
726C22×C4#12114yes—
727C22×C4#12114yes—
728C22×C4#12112yes—
729C22×C4#12112yes—
730C22×C4#12114yes—
731C22×C4#12114yes—
732C22×C4#12112yes—
733C22×C4#12112yes—
734C22×C4#12114yes—
735C22×C4#12114yes—
736C22×C4#12112yes—
737C22×C4#12112yes—
738C22×C4#12112yes—
739C22×C4#12112yes—
740C22×C4#12312yes—
741C22×C4#12312yes—
742C22×C4#12314yes—
743C22×C4#12314yes—
744C22×C4#12312yes—
745C22×C4#12412yes—
746C22×C4#12412yes—
747C22×C4#12414yes—
748C22×C4#12714yes—
749C22×C4#12712yes—
750C22×C4#12712yes—
751C22×C4C23×C411yescharacteristic
752C22×C4C22×D411yescharacteristic
753C22×C4C22×D411yescharacteristic
754C22×C4C22×D411yescharacteristic
755C22×C4C22×D411yescharacteristic
756C22×C4C22×D411yescharacteristic
757C22×C4C22×D411yescharacteristic
758C22×C4C22×D411yescharacteristic
759C22×C4C22×D411yescharacteristic
760C22×C4C22×D411yescharacteristic
761C22×C4C2×#4111yescharacteristic
762C22×C4C2×#4111yescharacteristic
763C22×C4C2×#4111yescharacteristic
764C22×C4C2×#4111yescharacteristic
765M16—24no—
766M16—24no—
767M16—24no—
768M16—24no—
769M16—42no—
770M16—42no—
771M16—42no—
772M16—42no—
773M16—48no—
774M16—48no—
775C2×C8—24no—
776C2×C8—24no—
777C2×C8—42no—
778C2×C8—42no—
779C2×C8—42no—
780C2×C8—42no—
781C2×C8—48no—
782C2×C8—48no—
783C4⋊C4—24no—
784C4⋊C4—28no—
785C4⋊C4—24no—
786C4⋊C4—24no—
787C4⋊C4—42no—
788C4⋊C4—42no—
789C4⋊C4—44no—
790C4⋊C4—44no—
791C4⋊C4C2×C22⋊C418yescomplemented
792C22⋊C4—264no—
793C22⋊C4—24no—
794C22⋊C4—24no—
795C22⋊C4—28no—
796C22⋊C4—464no—
797C42—24no—
798C42—24no—
799C42—28no—
800C42—24no—
801C42—24no—
802C42—42no—
803C42—42no—
804C42—48no—
805C23—28no—
806C23—28no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—24no—
812C23—24no—
813C23—24no—
814C23—24no—
815C23—28no—
816C23—28no—
817C23—28no—
818C23—24no—
819C23—28no—
820C23—28no—
821C23—416no—
822C23—48no—
823C23—48no—
824C23—416no—
825C23—464no—
826C23—416no—
827C23—432no—
828C23—42no—
829C23—44no—
830C23—44no—
831C23—42no—
832C23—44no—
833C23—44no—
834C23—48no—
835C23—416no—
836C23—416no—
837C23—44no—
838C23—48no—
839C23—44no—
840C23—48no—
841C23—88no—
842C23—816no—
843C23—84no—
844C23—84no—
845C23—88no—
846C23—832no—
847C23—88no—
848C23—88no—
849C23—816no—
850C23—832no—
851C23—832no—
852C23—84no—
853C23—88no—
854C23—84no—
855C23—88no—
856C23—88no—
857C23—816no—
858C23#37912yes—
859C23#37912yes—
860C23#38614yes—
861C23#38614yes—
862C23#39212yes—
863C23#39214yes—
864C23#39212yes—
865C23#39412yes—
866C23#39414yes—
867C23#39412yes—
868C23#45314yes—
869C23#45514yes—
870C23C22×C22⋊C411yescharacteristic
871C23C2×#12011yescharacteristic
872C23C2×#12011yescharacteristic
873C23C2×#12011yescharacteristic
874C23C2×#12111yescharacteristic
875C23C2×#12111yescharacteristic
876C23C2×#12311yescharacteristic
877Q8—24no—
878Q8—24no—
879Q8—42no—
880Q8—42no—
881Q8—48no—
882D4—24no—
883D4—24no—
884D4—44no—
885D4—44no—
886D4—416no—
887D4—44no—
888D4—44no—
889D4—44no—
890D4—44no—
891D4—42no—
892D4—44no—
893D4—44no—
894D4—42no—
895D4—416no—
896D4—416no—
897D4—48no—
898D4—44no—
899D4—44no—
900D4—44no—
901D4—44no—
902D4—864no—
903C2×C4—28no—
904C2×C4—28no—
905C2×C4—24no—
906C2×C4—44no—
907C2×C4—48no—
908C2×C4—48no—
909C2×C4—432no—
910C2×C4—416no—
911C2×C4—44no—
912C2×C4—42no—
913C2×C4—42no—
914C2×C4—48no—
915C2×C4—44no—
916C2×C4—44no—
917C2×C4—44no—
918C2×C4—44no—
919C2×C4—416no—
920C2×C4—44no—
921C2×C4—44no—
922C2×C4—48no—
923C2×C4—44no—
924C2×C4—84no—
925C2×C4—88no—
926C2×C4—84no—
927C2×C4—88no—
928C2×C4#37912yes—
929C2×C4#37912yes—
930C2×C4#38614yes—
931C2×C4#38614yes—
932C2×C4#38614yes—
933C2×C4#38614yes—
934C2×C4#38614yes—
935C2×C4#38614yes—
936C2×C4#39014yes—
937C2×C4#39014yes—
938C2×C4#39014yes—
939C2×C4#39014yes—
940C2×C4#39214yes—
941C2×C4#39214yes—
942C2×C4#39214yes—
943C2×C4#39214yes—
944C2×C4#39214yes—
945C2×C4#39212yes—
946C2×C4#39212yes—
947C2×C4#39414yes—
948C2×C4#39414yes—
949C2×C4#39414yes—
950C2×C4#39414yes—
951C2×C4#39412yes—
952C2×C4#39412yes—
953C2×C4#39414yes—
954C2×C4C22×C22⋊C411yescharacteristic
955C2×C4C22×C22⋊C411yescharacteristic
956C2×C4C2×C4×D411yescharacteristic
957C2×C4C2×C4×D411yescharacteristic
958C2×C4C2×C4×D411yescharacteristic
959C2×C4C2×C4×D411yescharacteristic
960C2×C4C2×#12011yescharacteristic
961C2×C4C2×#12011yescharacteristic
962C2×C4C2×#12011yescharacteristic
963C2×C4C2×#12011yescharacteristic
964C2×C4C2×#12011yescharacteristic
965C2×C4C2×#12111yescharacteristic
966C2×C4C2×#12111yescharacteristic
967C2×C4C2×#12111yescharacteristic
968C2×C4C2×#12111yescharacteristic
969C2×C4C2×#12111yescharacteristic
970C2×C4C2×#12111yescharacteristic
971C2×C4C2×#12111yescharacteristic
972C2×C4C2×#12111yescharacteristic
973C2×C4C2×#12111yescharacteristic
974C2×C4C2×#12111yescharacteristic
975C2×C4C2×#12311yescharacteristic
976C2×C4C2×#12311yescharacteristic
977C2×C4C2×#12311yescharacteristic
978C2×C4C2×#12411yescharacteristic
979C2×C4C2×#12411yescharacteristic
980C2×C4C2×#12711yescharacteristic
981C2×C4C2×#12711yescharacteristic
982C8—44no—
983C8—44no—
984C22—21no—
985C22—21no—
986C22—22no—
987C22—21no—
988C22—21no—
989C22—22no—
990C22—22no—
991C22—22no—
992C22—24no—
993C22—22no—
994C22—22no—
995C22—24no—
996C22—28no—
997C22—28no—
998C22—28no—
999C22—28no—
1000C22—416no—
1001C22—44no—
1002C22—48no—
1003C22—48no—
1004C22—416no—
1005C22—88no—
1006C22—88no—
1007C22—88no—
1008C22—832no—
1009C22—84no—
1010C22—82no—
1011C22—84no—
1012C22—82no—
1013C22—88no—
1014C22—84no—
1015C22—832no—
1016C22—816no—
1017C22#143814yes—
1018C22#143814yes—
1019C22#179218yes—
1020C22#200214yes—
1021C22#200414yes—
1022C22#203718yes—
1023C22C2×#37911yescharacteristic
1024C22C2×#38611yescharacteristic
1025C22C2×#38611yescharacteristic
1026C22C2×#39211yescharacteristic
1027C22C2×#39211yescharacteristic
1028C22C2×#39411yescharacteristic
1029C22C2×#39411yescharacteristic
1030C22C2×#45312yes—
1031C22C2×#45512yes—
1032C4—48no—
1033C4—44no—
1034C4—48no—
1035C4—84no—
1036C4#143814yes—
1037C4#143814yes—
1038C4C2×#38611yescharacteristic
1039C4C2×#38611yescharacteristic
1040C4C2×#39011yescharacteristic
1041C4C2×#39011yescharacteristic
1042C4C2×#39211yescharacteristic
1043C4C2×#39211yescharacteristic
1044C4C2×#39411yescharacteristic
1045C4C2×#39411yescharacteristic
1046C2—21no—
1047C2—21no—
1048C2—21no—
1049C2—24no—
1050C2—21no—
1051C2—88no—
1052C2—84no—
1053C2#1099718yesdirect product factor
1054C2C2×#143811yescharacteristic
1055C2C2×#179212yes—
1056C2C2×#200211yescharacteristic
1057C2C2×#200411yescharacteristic
1058C2C2×#203712yes—
subgroupG/H
center, socleC24#120
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC22×#535C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C24×C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C23×#104C2semidirect
3. C22×#417C2semidirect
4. C23×#100C2semidirect
5. C22×#390C2semidirect
6. C2×#1736C2semidirect
7. C22×#339C2semidirect
8. #10997C2direct (N × H)
19. C2×#535C4semidirect
32. C22×#104C22semidirect
36. C2×#417C22semidirect
42. C22×#100C22semidirect
46. C2×#390C22semidirect
48. #1736C22semidirect
51. C2×#339C22semidirect
107. C22×M16D4semidirect
108. C22×M16D4semidirect
122. #535C2×C4semidirect
156. C22×C4⋊C4D4semidirect
170. C22×C42D4semidirect
248. C2×#41C22⋊C4semidirect
257. C22×Q8C22⋊C4semidirect
337. C22×D4C22⋊C4semidirect
405. C2×M16C2×D4semidirect
406. C2×M16C2×D4semidirect
434. #117C22⋊C4semidirect
456. C2×C4⋊C4C22⋊C4semidirect
458. C2×C4⋊C4C2×D4semidirect
484. C2×C42C2×D4semidirect
577. C2×Q8C2×C22⋊C4semidirect
661. C2×D4C2×C22⋊C4semidirect
791. C4⋊C4C2×C22⋊C4semidirect
1053. C2#10997direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#5352
C23×#1042
C22×#4172
C23×#1002
C22×#3902
C2×#17362
C22×#3392
#109972