Finite Group Databasebeta

← #357826

Subgroups — #357826

Order 512.

2946 conjugacy classes of subgroups.

The subgroup lattice has 847 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2911C211yesmaximal, characteristic, complemented
2C22×#413C211yesmaximal, characteristic
3#34044C211yesmaximal, characteristic
4C2×#2297C211yesmaximal, characteristic
5#20347C211yesmaximal, characteristic, complemented
6C22×#339C211yesmaximal, characteristic, complemented
7C22×#339C211yesmaximal, characteristic, complemented
8#11136C214yesmaximal, complemented
9#11135C214yesmaximal, complemented
10C23×#41C2211yescharacteristic
11C23×M16C2211yescharacteristic
12C23×M16C2211yescharacteristic
13C22×#117C2211yescharacteristic
14C22×#117C2211yescharacteristic
15C22×#117C2211yescharacteristic
16C23×C42C2211yescharacteristic
17#2911—24no—
18#2911—24no—
19C2×#428—22no—
20C2×#428C2214yes—
21C2×#427—22no—
22C2×#413—24no—
23C2×#413—24no—
24C2×#413C418yescomplemented
25C22×#101C2212yes—
26C22×#100C2212yes—
27#2311—22no—
28#2311—22no—
29#2310C2212yes—
30#2309C2212yes—
31#2308—22no—
32#2297—24no—
33#2297—24no—
34#2297—22no—
35#2297—22no—
36C2×#391C2212yes—
37C2×#390C2212yes—
38C2×#386—22no—
39#2280—22no—
40C2×C4×C22⋊C4—22no—
41#1736—22no—
42#1736C2214yes—
43#1735—22no—
44C2×#339—24no—
45C2×#339—24no—
46C2×#339C2214yes—
47C2×#339C2214yes—
48C22×#41—21no—
49C22×#41—21no—
50C22×#41—22no—
51C22×#41—22no—
52C22×#41—22no—
53C22×#41—22no—
54C22×#41—21no—
55C22×#41—21no—
56C22×#41—22no—
57C22×#41—22no—
58C22×#41—22no—
59C22×#41—22no—
60C22×#41—22no—
61C22×#41—22no—
62C22×#41C2×C414yes—
63C22×#41Q814yes—
64C23×Q8C2311yescharacteristic
65C23×D4D412yes—
66C23×D4C2311yescharacteristic
67C24×C4—21no—
68C24×C4D412yes—
69C24×C4C2311yescharacteristic
70C22×M16—21no—
71C22×M16—22no—
72C22×M16—22no—
73C22×M16—22no—
74C22×M16—21no—
75C22×M16—22no—
76C22×M16—22no—
77C22×M16—22no—
78C22×M16—22no—
79C22×M16—22no—
80C22×M16C2×C414yes—
81C22×M16C2×C414yes—
82C22×M16D414yes—
83C22×M16D414yes—
84C22×M16C2312yes—
85C22×M16C2312yes—
86C23×C8—21no—
87C23×C8—21no—
88C2×#117—21no—
89C2×#117—21no—
90C2×#117—21no—
91C2×#117—21no—
92C2×#117—22no—
93C2×#117—21no—
94C2×#117—21no—
95C2×#117—22no—
96C2×#117—22no—
97C2×#117—22no—
98C2×#117—22no—
99C2×#117—22no—
100C2×#117—21no—
101C2×#117—21no—
102C2×#117—22no—
103C2×#117—22no—
104C2×#117—22no—
105C2×#117—22no—
106C2×#117—22no—
107C2×#117D412yes—
108C2×#117D414yes—
109C2×#117D412yes—
110C2×#117C2312yes—
111C2×#117C2312yes—
112C22×C4⋊C4D412yes—
113C22×C4⋊C4D412yes—
114C22×C4⋊C4C2312yes—
115C22×C22⋊C4—21no—
116C22×C22⋊C4—21no—
117C22×C22⋊C4—21no—
118C22×C22⋊C4—24no—
119C22×C42—22no—
120C22×C42—22no—
121C22×C42—22no—
122C22×C42—22no—
123C22×C42—21no—
124C22×C42—22no—
125C22×C42—21no—
126C22×C42—21no—
127C22×C42—21no—
128C22×C42D414yes—
129C22×C42C2312yes—
130#428—216no—
131#428—28no—
132#428—28no—
133#427—216no—
134C2×#107—24no—
135C2×#106—24no—
136#413—232no—
137C2×#101—24no—
138C2×#101—24no—
139C2×#101C2×C418yescomplemented
140C2×#100—24no—
141C2×#100—24no—
142C2×#100C2×C418yescomplemented
143#391—24no—
144#391—24no—
145#391—24no—
146#391—24no—
147#390—24no—
148#390—24no—
149#390—24no—
150#390—24no—
151#386—28no—
152#386—28no—
153#386—216no—
154#381—24no—
155#380—28no—
156#379—24no—
157C4×C22⋊C4—216no—
158C4×C22⋊C4—28no—
159C2×#95—24no—
160#340—28no—
161#339—28no—
162#339—28no—
163C25C2×D412yes—
164C25C2×D411yescharacteristic
165C2×#41—28no—
166C2×#41—28no—
167C2×#41—24no—
168C2×#41—24no—
169C2×#41—28no—
170C2×#41—24no—
171C2×#41—24no—
172C2×#41—28no—
173C2×#41—28no—
174C2×#41—28no—
175C2×#41—24no—
176C2×#41—28no—
177C2×#41—24no—
178C2×#41—24no—
179C2×#41—28no—
180C2×#41—24no—
181C2×#41—42no—
182C2×#41—42no—
183C2×#41—42no—
184C2×#41—42no—
185C2×#41—42no—
186C2×#41—42no—
187C2×#41—42no—
188C2×#41—44no—
189C2×#41—42no—
190C2×#41—44no—
191C2×#41—42no—
192C2×#41—42no—
193C2×#41—44no—
194C2×#41—42no—
195C2×#41—42no—
196C2×#41—44no—
197C2×#41—44no—
198C2×#41—42no—
199C2×#41—42no—
200C2×#41—44no—
201C2×#41—44no—
202C2×#41—44no—
203C2×#41—42no—
204C2×#41—42no—
205C22×Q8—21no—
206C22×Q8—21no—
207C22×Q8—21no—
208C22×Q8—21no—
209C22×Q8—21no—
210C22×Q8—21no—
211C22×Q8—21no—
212C22×Q8—21no—
213C22×Q8—21no—
214C22×Q8—21no—
215C22×Q8—21no—
216C22×Q8—21no—
217C22×Q8C22×C412yes—
218C22×Q8C2×Q812yes—
219C22×D4—22no—
220C22×D4—22no—
221C22×D4—24no—
222C22×D4—24no—
223C22×D4—24no—
224C22×D4—24no—
225C22×D4—24no—
226C22×D4—21no—
227C22×D4—21no—
228C22×D4—21no—
229C22×D4—21no—
230C22×D4—21no—
231C22×D4—21no—
232C22×D4—21no—
233C22×D4—21no—
234C22×D4—21no—
235C22×D4—21no—
236C22×D4—21no—
237C22×D4—21no—
238C22×D4C4⋊C418yes—
239C22×D4C22×C412yes—
240C22×D4C2×Q812yes—
241C23×C4—22no—
242C23×C4—24no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—24no—
246C23×C4—24no—
247C23×C4—24no—
248C23×C4—24no—
249C23×C4—24no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—48no—
254C23×C4—42no—
255C23×C4—42no—
256C23×C4C4⋊C418yes—
257C23×C4C22×C412yes—
258C23×C4C2×D412yes—
259C23×C4C2×D412yes—
260C23×C4C2×D412yes—
261C23×C4C2×D411yescharacteristic
262C23×C4C2×D411yescharacteristic
263C23×C4C2×D412yes—
264C23×C4C2×D411yescharacteristic
265C23×C4C2×D411yescharacteristic
266C23×C4C2×D412yes—
267C23×C4C2×D411yescharacteristic
268C23×C4C2×Q812yes—
269C23×C4#4112yes—
270C23×C4#4112yes—
271C23×C4#4112yes—
272C23×C4#4112yes—
273C23×C4#4112yes—
274C23×C4#4112yes—
275C23×C4C2411yescharacteristic
276C2×M16—24no—
277C2×M16—28no—
278C2×M16—24no—
279C2×M16—24no—
280C2×M16—28no—
281C2×M16—28no—
282C2×M16—22no—
283C2×M16—22no—
284C2×M16—22no—
285C2×M16—24no—
286C2×M16—22no—
287C2×M16—28no—
288C2×M16—28no—
289C2×M16—22no—
290C2×M16—22no—
291C2×M16—22no—
292C2×M16—22no—
293C2×M16—42no—
294C2×M16—44no—
295C2×M16—44no—
296C2×M16—42no—
297C2×M16C22⋊C4116yescomplemented
298C2×M16C22×C414yes—
299C2×M16C22×C414yes—
300C2×M16C2×D414yes—
301C2×M16C2×D414yes—
302C22×C8—24no—
303C22×C8—24no—
304C22×C8—24no—
305C22×C8—22no—
306C22×C8—24no—
307C22×C8—22no—
308C22×C8—42no—
309C22×C8—42no—
310#117—24no—
311#117—24no—
312#117—24no—
313#117—24no—
314#117—24no—
315#117—24no—
316#117—24no—
317#117—24no—
318#117—22no—
319#117—22no—
320#117—22no—
321#117—22no—
322#117—22no—
323#117—22no—
324#117—22no—
325#117—22no—
326#117—42no—
327#117—42no—
328#117—42no—
329#117—42no—
330#117—42no—
331#117—42no—
332#117—42no—
333#117—42no—
334#117—42no—
335#117—42no—
336#117—42no—
337#117—42no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4C2×D414yes—
350C2×C4⋊C4C2×D414yes—
351C2×C4⋊C4C2×D414yes—
352C2×C22⋊C4—216no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—216no—
359C2×C22⋊C4—416no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—41no—
362C2×C22⋊C4—41no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—42no—
367C2×C42—28no—
368C2×C42—28no—
369C2×C42—22no—
370C2×C42—22no—
371C2×C42—22no—
372C2×C42—22no—
373C2×C42—24no—
374C2×C42—24no—
375C2×C42—22no—
376C2×C42—22no—
377C2×C42—22no—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—41no—
381C2×C42—41no—
382C2×C42—42no—
383C2×C42—42no—
384C2×C42—42no—
385C2×C42—44no—
386C2×C42—42no—
387C2×C42—42no—
388C2×C42—42no—
389C2×C42—44no—
390C2×C42—42no—
391C2×C42C2×D414yes—
392#107—216no—
393#106—216no—
394#101—216no—
395#100—216no—
396#95—216no—
397#95—216no—
398C24—22no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—44no—
405C24—48no—
406C24C2×C4⋊C414yes—
407C24C2×C4⋊C412yes—
408C24#12011yescharacteristic
409C24#12011yescharacteristic
410C24#12012yes—
411C24#12112yes—
412C24#12112yes—
413C24#12312yes—
414C24#12312yes—
415C24C22×D411yescharacteristic
416#41—48no—
417#41—48no—
418#41—48no—
419#41—48no—
420#41—48no—
421#41—48no—
422#41—48no—
423#41—48no—
424#41—48no—
425#41—48no—
426#41—48no—
427#41—48no—
428#41—48no—
429#41—48no—
430#41—48no—
431#41—48no—
432C2×Q8—22no—
433C2×Q8—22no—
434C2×Q8—22no—
435C2×Q8—22no—
436C2×Q8—22no—
437C2×Q8—22no—
438C2×Q8—22no—
439C2×Q8—22no—
440C2×Q8—22no—
441C2×Q8—22no—
442C2×Q8—22no—
443C2×Q8—22no—
444C2×Q8—41no—
445C2×Q8—41no—
446C2×Q8—41no—
447C2×Q8—41no—
448C2×Q8—41no—
449C2×Q8—41no—
450C2×Q8—41no—
451C2×Q8—41no—
452C2×Q8—41no—
453C2×Q8—41no—
454C2×Q8—41no—
455C2×Q8—41no—
456C2×Q8—41no—
457C2×Q8—41no—
458C2×Q8—41no—
459C2×Q8—41no—
460C2×D4—216no—
461C2×D4—28no—
462C2×D4—28no—
463C2×D4—216no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—22no—
472C2×D4—22no—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—44no—
477C2×D4—44no—
478C2×D4—44no—
479C2×D4—44no—
480C2×D4—48no—
481C2×D4—48no—
482C2×D4—41no—
483C2×D4—41no—
484C2×D4—41no—
485C2×D4—41no—
486C2×D4—41no—
487C2×D4—41no—
488C2×D4—41no—
489C2×D4—41no—
490C2×D4—41no—
491C2×D4—41no—
492C2×D4—41no—
493C2×D4—41no—
494C2×D4—41no—
495C2×D4—41no—
496C2×D4—41no—
497C2×D4—41no—
498C22×C4—28no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—24no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—216no—
507C22×C4—216no—
508C22×C4—28no—
509C22×C4—28no—
510C22×C4—24no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—416no—
514C22×C4—44no—
515C22×C4—416no—
516C22×C4—416no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—48no—
520C22×C4—44no—
521C22×C4—44no—
522C22×C4—48no—
523C22×C4—44no—
524C22×C4—44no—
525C22×C4—48no—
526C22×C4—48no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—44no—
530C22×C4—44no—
531C22×C4—84no—
532C22×C4—84no—
533C22×C4C2×C22⋊C414yes—
534C22×C4C2×C4⋊C414yes—
535C22×C4C2×C4⋊C412yes—
536C22×C4#11714yes—
537C22×C4C4×D412yes—
538C22×C4C4×D412yes—
539C22×C4C4×D414yes—
540C22×C4C4×D412yes—
541C22×C4C4×D412yes—
542C22×C4C4×D414yes—
543C22×C4#12012yes—
544C22×C4#12012yes—
545C22×C4#12012yes—
546C22×C4#12011yescharacteristic
547C22×C4#12011yescharacteristic
548C22×C4#12112yes—
549C22×C4#12114yes—
550C22×C4#12112yes—
551C22×C4#12112yes—
552C22×C4#12112yes—
553C22×C4#12112yes—
554C22×C4#12112yes—
555C22×C4#12114yes—
556C22×C4#12112yes—
557C22×C4#12112yes—
558C22×C4#12112yes—
559C22×C4#12112yes—
560C22×C4C22⋊Q814yes—
561C22×C4C22⋊Q814yes—
562C22×C4C22⋊Q812yes—
563C22×C4C22⋊Q814yes—
564C22×C4C22⋊Q812yes—
565C22×C4C22⋊Q812yes—
566C22×C4C22⋊Q814yes—
567C22×C4C22⋊Q812yes—
568C22×C4#12314yes—
569C22×C4#12314yes—
570C22×C4#12312yes—
571C22×C4#12312yes—
572C22×C4#12312yes—
573C22×C4#12312yes—
574C22×C4#12414yes—
575C22×C4#12412yes—
576C22×C4#12412yes—
577C22×C4#12414yes—
578C22×C4#12614yes—
579C22×C4#12614yes—
580C22×C4#12712yes—
581C22×C4#12712yes—
582C22×C4C23×C411yescharacteristic
583C22×C4C22×D411yescharacteristic
584C22×C4C22×D411yescharacteristic
585C22×C4C22×D411yescharacteristic
586C22×C4C22×D411yescharacteristic
587C22×C4C22×D411yescharacteristic
588C22×C4C22×D411yescharacteristic
589C22×C4C22×Q811yescharacteristic
590C22×C4C2×#4111yescharacteristic
591C22×C4C2×#4111yescharacteristic
592C22×C4C2×#4111yescharacteristic
593C22×C4C2×#4111yescharacteristic
594C22×C4C2×#4111yescharacteristic
595C22×C4C2×#4111yescharacteristic
596M16—24no—
597M16—24no—
598M16—24no—
599M16—216no—
600M16—24no—
601M16—24no—
602M16—42no—
603M16—42no—
604M16—48no—
605M16C2×C22⋊C418yes—
606C2×C8—24no—
607C2×C8—24no—
608C2×C8—24no—
609C2×C8—216no—
610C2×C8—24no—
611C2×C8—42no—
612C2×C8—42no—
613C2×C8—48no—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—24no—
618C4⋊C4—24no—
619C4⋊C4—24no—
620C4⋊C4—42no—
621C4⋊C4—42no—
622C4⋊C4—44no—
623C4⋊C4—44no—
624C22⋊C4—432no—
625C22⋊C4—42no—
626C22⋊C4—42no—
627C22⋊C4—42no—
628C22⋊C4—42no—
629C22⋊C4—44no—
630C22⋊C4—44no—
631C22⋊C4—44no—
632C22⋊C4—44no—
633C22⋊C4—816no—
634C42—24no—
635C42—24no—
636C42—42no—
637C42—42no—
638C42—42no—
639C42—42no—
640C42—42no—
641C42—42no—
642C42—44no—
643C42—44no—
644C42—44no—
645C42—48no—
646C42—44no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—44no—
654C23—44no—
655C23—44no—
656C23—44no—
657C23—44no—
658C23—44no—
659C23—48no—
660C23—48no—
661C23—48no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—48no—
667C23—84no—
668C23—84no—
669C23—84no—
670C23#38014yes—
671C23#38512yes—
672C23#38512yes—
673C23#38514yes—
674C23#39212yes—
675C23#39212yes—
676C23#39412yes—
677C23#39412yes—
678C23#39414yes—
679C23#39714yes—
680C23C22×C4⋊C411yescharacteristic
681C23C2×#12011yescharacteristic
682C23C2×#12011yescharacteristic
683C23C2×#12111yescharacteristic
684C23C2×#12111yescharacteristic
685C23C2×#12311yescharacteristic
686C23C2×#12311yescharacteristic
687Q8—42no—
688Q8—42no—
689Q8—42no—
690Q8—42no—
691Q8—42no—
692Q8—42no—
693Q8—42no—
694Q8—42no—
695D4—416no—
696D4—416no—
697D4—42no—
698D4—42no—
699D4—42no—
700D4—42no—
701D4—42no—
702D4—42no—
703D4—42no—
704D4—42no—
705C2×C4—28no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—44no—
710C2×C4—48no—
711C2×C4—48no—
712C2×C4—432no—
713C2×C4—42no—
714C2×C4—44no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—416no—
719C2×C4—416no—
720C2×C4—48no—
721C2×C4—44no—
722C2×C4—44no—
723C2×C4—44no—
724C2×C4—48no—
725C2×C4—48no—
726C2×C4—84no—
727C2×C4—88no—
728C2×C4—88no—
729C2×C4—84no—
730C2×C4#38014yes—
731C2×C4#38514yes—
732C2×C4#38512yes—
733C2×C4#38512yes—
734C2×C4#38614yes—
735C2×C4#38614yes—
736C2×C4#38814yes—
737C2×C4#38814yes—
738C2×C4#38814yes—
739C2×C4#38814yes—
740C2×C4#39014yes—
741C2×C4#39014yes—
742C2×C4#39212yes—
743C2×C4#39212yes—
744C2×C4#39314yes—
745C2×C4#39314yes—
746C2×C4#39414yes—
747C2×C4#39412yes—
748C2×C4#39412yes—
749C2×C4#39614yes—
750C2×C4#39614yes—
751C2×C4#39614yes—
752C2×C4#39614yes—
753C2×C4#39714yes—
754C2×C4#39914yes—
755C2×C4#39914yes—
756C2×C4C22×C22⋊C411yescharacteristic
757C2×C4C2×#11711yescharacteristic
758C2×C4C2×C4×D411yescharacteristic
759C2×C4C2×C4×D411yescharacteristic
760C2×C4C2×C4×D411yescharacteristic
761C2×C4C2×C4×D411yescharacteristic
762C2×C4C2×#12011yescharacteristic
763C2×C4C2×#12111yescharacteristic
764C2×C4C2×#12111yescharacteristic
765C2×C4C2×#12111yescharacteristic
766C2×C4C2×#12111yescharacteristic
767C2×C4C2×#12111yescharacteristic
768C2×C4C2×#12111yescharacteristic
769C2×C4C2×C22⋊Q811yescharacteristic
770C2×C4C2×C22⋊Q811yescharacteristic
771C2×C4C2×C22⋊Q811yescharacteristic
772C2×C4C2×C22⋊Q811yescharacteristic
773C2×C4C2×C22⋊Q811yescharacteristic
774C2×C4C2×C22⋊Q811yescharacteristic
775C2×C4C2×#12311yescharacteristic
776C2×C4C2×#12311yescharacteristic
777C2×C4C2×#12311yescharacteristic
778C2×C4C2×#12411yescharacteristic
779C2×C4C2×#12411yescharacteristic
780C2×C4C2×#12411yescharacteristic
781C2×C4C2×#12611yescharacteristic
782C2×C4C2×#12611yescharacteristic
783C2×C4C2×#12711yescharacteristic
784C8—28no—
785C8—44no—
786C22—22no—
787C22—22no—
788C22—24no—
789C22—24no—
790C22—22no—
791C22—22no—
792C22—24no—
793C22—24no—
794C22—22no—
795C22—24no—
796C22—22no—
797C22—24no—
798C22—44no—
799C22—44no—
800C22—44no—
801C22—44no—
802C22—48no—
803C22—44no—
804C22—48no—
805C22—84no—
806C22—84no—
807C22—84no—
808C22—84no—
809C22—84no—
810C22#143914yes—
811C22#143914yes—
812C22C2×#38011yescharacteristic
813C22C2×#38511yescharacteristic
814C22C2×#38511yescharacteristic
815C22C2×#39211yescharacteristic
816C22C2×#39411yescharacteristic
817C22C2×#39411yescharacteristic
818C22C2×#39711yescharacteristic
819C22#301814yes—
820C4—48no—
821C4—44no—
822C4—84no—
823C4—84no—
824C4—84no—
825C4#143914yes—
826C4#143914yes—
827C4C2×#38611yescharacteristic
828C4C2×#38811yescharacteristic
829C4C2×#38811yescharacteristic
830C4C2×#39011yescharacteristic
831C4C2×#39311yescharacteristic
832C4C2×#39611yescharacteristic
833C4C2×#39611yescharacteristic
834C4C2×#39911yescharacteristic
835C2—21no—
836C2—21no—
837C2—21no—
838C2—21no—
839C2—24no—
840C2—24no—
841C2—84no—
842C2C2×#143911yescharacteristic
843C2#2085512yes—
844C2#2339912yes—
845C2#2349212yes—
subgroupG/H
centerC22×C4#120
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
socleC23C2×#120
prime radicalC23×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2911C2semidirect
5. #20347C2semidirect
6. C22×#339C2semidirect
7. C22×#339C2semidirect
8. #11136C2semidirect
9. #11135C2semidirect
24. C2×#413C4semidirect
139. C2×#101C2×C4semidirect
142. C2×#100C2×C4semidirect
297. C2×M16C22⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#29112
C22×#4132
#340442
C2×#22972
#203472
C22×#3392
#111362
#111352