Finite Group Databasebeta

← C2×#24490 #6451908

Subgroups — C2×#24490 #6451908

Order 512.

3156 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#480C211yesmaximal, characteristic, complemented
2C22×#417C211yesmaximal, characteristic, complemented
3C2×#2431C211yesmaximal, characteristic
4C2×#2345C211yesmaximal, characteristic, complemented
5#24490C2116yesmaximal, direct product factor
6C2×#2068C211yesmaximal, characteristic, complemented
7C2×#2067C211yesmaximal, characteristic, complemented
8C2×#2042C211yesmaximal, characteristic, complemented
9C2×#2041C211yesmaximal, characteristic, complemented
10C2×#1983C211yesmaximal, characteristic, complemented
11C2×#1982C211yesmaximal, characteristic, complemented
12C2×#1928C211yesmaximal, characteristic, complemented
13C2×#1925C211yesmaximal, characteristic, complemented
14C2×#1895C211yesmaximal, characteristic, complemented
15C2×#1851C211yesmaximal, characteristic, complemented
16C2×#1788C211yesmaximal, characteristic, complemented
17C23×#41C2211yescharacteristic
18C23×M16C2211yescharacteristic
19C22×#127C2211yescharacteristic
20C22×#124C2211yescharacteristic
21C22×#121C2211yescharacteristic
22C23×C4⋊C4C2211yescharacteristic
23C2×#480—28no—
24C2×#480C2218yescomplemented
25C22×#107C2211yescharacteristic
26C22×#107C2211yescharacteristic
27C22×C4⋊C8C2211yescharacteristic
28C22×C4⋊C8C2211yescharacteristic
29C2×#417—28no—
30C2×#417C2218yescomplemented
31C22×#103C2211yescharacteristic
32C22×#103C2211yescharacteristic
33C22×#103C2211yescharacteristic
34C22×#103C2211yescharacteristic
35C22×#102C2211yescharacteristic
36C22×#102C2211yescharacteristic
37C22×#102C2211yescharacteristic
38C22×#102C2211yescharacteristic
39C22×#102C2211yescharacteristic
40C22×#102C2211yescharacteristic
41C22×#102C2211yescharacteristic
42C22×#102C2211yescharacteristic
43C22×C22⋊C8C2211yescharacteristic
44#2431—24no—
45#2431C2218yes—
46C2×#392—21no—
47C2×#392—21no—
48#2345—24no—
49#2345C2218yescomplemented
50C2×#391C2211yescharacteristic
51C2×#390C2211yescharacteristic
52C2×#389C2211yescharacteristic
53C2×#389C2211yescharacteristic
54C2×#387—21no—
55C2×#387—21no—
56C2×#386—21no—
57C2×#386—21no—
58C2×#380—21no—
59C2×#380C2211yescharacteristic
60C2×C4×C4⋊C4C2211yescharacteristic
61C2×C4×C4⋊C4C2211yescharacteristic
62C2×C4×C22⋊C4—21no—
63C2×C4×C22⋊C4C2211yescharacteristic
64#2068C2218yescomplemented
65#2067C2218yescomplemented
66#2042C2218yescomplemented
67#2041C2218yescomplemented
68#1983C2218yescomplemented
69#1982C2218yescomplemented
70#1928C2218yescomplemented
71#1925C2218yescomplemented
72#1895C2218yescomplemented
73#1851C2218yescomplemented
74#1788C2218yescomplemented
75C2×#340C2211yescharacteristic
76C2×#340C2211yescharacteristic
77C2×#336C2211yescharacteristic
78C2×#336C2211yescharacteristic
79C22×#41—22no—
80C22×#41—24no—
81C22×#41—24no—
82C22×#41—24no—
83C22×#41—24no—
84C22×#41—42no—
85C22×#41—42no—
86C22×#41C2314yes—
87C23×Q8C2311yescharacteristic
88C23×D4—21no—
89C23×D4—21no—
90C23×D4—21no—
91C23×D4—21no—
92C23×D4C2311yescharacteristic
93C23×D4C2311yescharacteristic
94C24×C4—21no—
95C24×C4—21no—
96C24×C4C2311yescharacteristic
97C22×M16—24no—
98C22×M16—42no—
99C22×M16—42no—
100C22×M16C2314yes—
101C23×C8C2311yescharacteristic
102C23×C8C2311yescharacteristic
103C23×C8C2311yescharacteristic
104C23×C8C2311yescharacteristic
105C2×#127—24no—
106C2×#127—22no—
107C2×#127—42no—
108C2×#127C2314yes—
109C2×#124—24no—
110C2×#124—22no—
111C2×#124—42no—
112C2×#124C2314yes—
113C2×#121—22no—
114C2×#121—24no—
115C2×#121—24no—
116C2×#121C2314yes—
117C22×C4⋊C4—22no—
118C22×C4⋊C4—21no—
119C22×C4⋊C4—24no—
120C22×C4⋊C4—21no—
121C22×C4⋊C4—21no—
122C22×C4⋊C4D418yescomplemented
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2314yes—
129C22×C22⋊C4—21no—
130C22×C22⋊C4—21no—
131C22×C22⋊C4—21no—
132C22×C22⋊C4—21no—
133C22×C22⋊C4—21no—
134C22×C22⋊C4—21no—
135C22×C22⋊C4D411yescharacteristic
136C22×C22⋊C4D411yescharacteristic
137C22×C42—21no—
138C22×C42—21no—
139C22×C42C2311yescharacteristic
140C22×C42C2311yescharacteristic
141#480—232no—
142C2×#107—24no—
143C2×#107—24no—
144C2×#107C2314yes—
145C2×#107C2314yes—
146C2×C4⋊C8—42no—
147C2×C4⋊C8—42no—
148C2×C4⋊C8C2314yes—
149C2×C4⋊C8C2314yes—
150#417—232no—
151C2×#103—24no—
152C2×#103—24no—
153C2×#103—24no—
154C2×#103—42no—
155C2×#103C2314yes—
156C2×#103C2314yes—
157C2×#103C2314yes—
158C2×#103C2314yes—
159C2×#102—24no—
160C2×#102—24no—
161C2×#102—24no—
162C2×#102—24no—
163C2×#102—24no—
164C2×#102—42no—
165C2×#102—42no—
166C2×#102—42no—
167C2×#102C2314yes—
168C2×#102C2314yes—
169C2×#102C2314yes—
170C2×#102C2314yes—
171C2×#102C2314yes—
172C2×#102C2314yes—
173C2×#102C2314yes—
174C2×#102C2314yes—
175C2×C22⋊C8—24no—
176C2×C22⋊C8C2314yes—
177#392—28no—
178#392—28no—
179#391—22no—
180#391C2314yes—
181#390—22no—
182#390C2314yes—
183#389—22no—
184#389—22no—
185#389C2314yes—
186#389C2314yes—
187#387—28no—
188#387—28no—
189#386—28no—
190#386—28no—
191#380—22no—
192#380—28no—
193#380C2314yes—
194C4×C4⋊C4—22no—
195C4×C4⋊C4—22no—
196C4×C4⋊C4C2314yes—
197C4×C4⋊C4C2314yes—
198C4×C22⋊C4—28no—
199C4×C22⋊C4D414yes—
200C4×C22⋊C4C2314yes—
201C2×#95—21no—
202C2×#95—21no—
203C2×#95—21no—
204C2×#95—21no—
205C2×#95—21no—
206C2×#95—21no—
207C2×#95—21no—
208C2×#95D411yescharacteristic
209C2×#95D411yescharacteristic
210#340C2314yes—
211#340C2314yes—
212#336C2314yes—
213#336C2314yes—
214C25—21no—
215C25—21no—
216C25C2×D411yescharacteristic
217C2×#41—232no—
218C2×#41—28no—
219C2×#41—28no—
220C2×#41—28no—
221C2×#41—28no—
222C2×#41—44no—
223C2×#41—44no—
224C2×#41—48no—
225C2×#41—416no—
226C2×#41—48no—
227C2×#41—416no—
228C2×#41—416no—
229C2×#41—48no—
230C22×Q8—21no—
231C22×Q8—22no—
232C22×Q8—22no—
233C22×Q8—22no—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8#4114yes—
237C22×Q8C2412yes—
238C22×D4—24no—
239C22×D4—24no—
240C22×D4—22no—
241C22×D4—21no—
242C22×D4—22no—
243C22×D4—21no—
244C22×D4—24no—
245C22×D4—24no—
246C22×D4—22no—
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×D4—44no—
261C22×D4—44no—
262C22×D4—44no—
263C22×D4—82no—
264C22×D4—82no—
265C22×D4—82no—
266C22×D4—82no—
267C22×D4#4114yes—
268C22×D4C2412yes—
269C22×D4C2412yes—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—21no—
275C23×C4—21no—
276C23×C4—21no—
277C23×C4—28no—
278C23×C4—24no—
279C23×C4—21no—
280C23×C4—21no—
281C23×C4—21no—
282C23×C4—24no—
283C23×C4—44no—
284C23×C4—44no—
285C23×C4—44no—
286C23×C4—82no—
287C23×C4—82no—
288C23×C4C2×D411yescharacteristic
289C23×C4C2×D411yescharacteristic
290C23×C4C2×D411yescharacteristic
291C23×C4C2×D412yes—
292C23×C4C2×D411yescharacteristic
293C23×C4C2×D414yes—
294C23×C4C2×D411yescharacteristic
295C23×C4#4114yes—
296C23×C4C2412yes—
297C23×C4C2411yescharacteristic
298C2×M16—28no—
299C2×M16—44no—
300C2×M16—44no—
301C2×M16—416no—
302C22×C8—22no—
303C22×C8—22no—
304C22×C8—22no—
305C22×C8—22no—
306C22×C8—22no—
307C22×C8—22no—
308C22×C8—22no—
309C22×C8—22no—
310C22×C8—22no—
311C22×C8—22no—
312C22×C8—22no—
313C22×C8—22no—
314C22×C8C2412yes—
315C22×C8C2412yes—
316C22×C8C2412yes—
317C22×C8C2412yes—
318#127—28no—
319#127—44no—
320#127—48no—
321#124—28no—
322#124—44no—
323#124—48no—
324#121—28no—
325#121—28no—
326#121—48no—
327C2×C4⋊C4—216no—
328C2×C4⋊C4—28no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—28no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—82no—
347C2×C4⋊C4—82no—
348C2×C4⋊C4C2×D414yes—
349C2×C4⋊C4C2×D414yes—
350C2×C4⋊C4C2×D4116yescomplemented
351C2×C4⋊C4C2412yes—
352C2×C4⋊C4C2412yes—
353C2×C4⋊C4C2412yes—
354C2×C4⋊C4C2412yes—
355C2×C4⋊C4C2412yes—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—44no—
365C2×C22⋊C4—44no—
366C2×C22⋊C4—44no—
367C2×C22⋊C4—44no—
368C2×C22⋊C4—82no—
369C2×C22⋊C4—82no—
370C2×C22⋊C4C2×D414yes—
371C2×C22⋊C4C2×D414yes—
372C2×C42—22no—
373C2×C42—22no—
374C2×C42—22no—
375C2×C42—22no—
376C2×C42—24no—
377C2×C42—24no—
378C2×C42—82no—
379C2×C42—82no—
380C2×C42C2×D412yes—
381C2×C42C2×D412yes—
382C2×C42C2412yes—
383C2×C42C2412yes—
384#107—28no—
385#107—28no—
386C4⋊C8—44no—
387C4⋊C8—44no—
388#103—28no—
389#103—28no—
390#103—28no—
391#103—44no—
392#102—28no—
393#102—28no—
394#102—28no—
395#102—28no—
396#102—28no—
397#102—44no—
398#102—44no—
399#102—44no—
400C22⋊C8—28no—
401#95—24no—
402#95—24no—
403#95—24no—
404#95—24no—
405#95—24no—
406#95—24no—
407#95—24no—
408#95C2×D414yes—
409#95C2×D414yes—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—22no—
416C24—24no—
417C24—22no—
418C24—22no—
419C24—42no—
420C24—42no—
421C24—42no—
422C24—42no—
423C24—42no—
424C24—42no—
425C24—42no—
426C24—42no—
427C24—42no—
428C24—42no—
429C24—42no—
430C24—42no—
431C24—42no—
432C24#12114yes—
433C24C22×D412yes—
434C24C22×D411yescharacteristic
435#41—232no—
436#41—416no—
437#41—416no—
438#41—464no—
439#41—416no—
440C2×Q8—24no—
441C2×Q8—22no—
442C2×Q8—28no—
443C2×Q8—28no—
444C2×Q8—22no—
445C2×Q8—22no—
446C2×Q8—22no—
447C2×Q8—22no—
448C2×Q8—42no—
449C2×Q8—44no—
450C2×Q8—42no—
451C2×Q8—44no—
452C2×Q8C2×#4114yes—
453C2×D4—28no—
454C2×D4—24no—
455C2×D4—28no—
456C2×D4—22no—
457C2×D4—22no—
458C2×D4—22no—
459C2×D4—22no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—48no—
468C2×D4—48no—
469C2×D4—48no—
470C2×D4—48no—
471C2×D4—48no—
472C2×D4—432no—
473C2×D4—48no—
474C2×D4—48no—
475C2×D4—42no—
476C2×D4—42no—
477C2×D4—44no—
478C2×D4—44no—
479C2×D4—44no—
480C2×D4—42no—
481C2×D4—42no—
482C2×D4—42no—
483C2×D4—44no—
484C2×D4—44no—
485C2×D4—44no—
486C2×D4—48no—
487C2×D4—84no—
488C2×D4—84no—
489C2×D4—816no—
490C2×D4—84no—
491C2×D4—84no—
492C2×D4—816no—
493C2×D4—816no—
494C2×D4C2×#4114yes—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—28no—
500C22×C4—28no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—28no—
504C22×C4—28no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—24no—
510C22×C4—24no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—24no—
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—216no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—48no—
529C22×C4—48no—
530C22×C4—432no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—48no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—816no—
548C22×C4—84no—
549C22×C4—84no—
550C22×C4#12114yes—
551C22×C4#12118yes—
552C22×C4#13714yes—
553C22×C4C22×D412yes—
554C22×C4C22×D412yes—
555C22×C4C22×D412yes—
556C22×C4C22×D412yes—
557C22×C4C22×D414yes—
558C22×C4C22×D412yes—
559C22×C4C22×D411yescharacteristic
560C22×C4C22×D412yes—
561C22×C4C2×#4114yes—
562C22×C4C2×#4112yes—
563C22×C4C2×#4112yes—
564C22×C4C2×#4112yes—
565C22×C4H(5,𝔽2)12yes—
566C22×C4H(5,𝔽2)12yes—
567C22×C4C2511yescharacteristic
568M16—416no—
569C2×C8—22no—
570C2×C8—22no—
571C2×C8—22no—
572C2×C8—22no—
573C2×C8—22no—
574C2×C8—22no—
575C2×C8—22no—
576C2×C8—22no—
577C2×C8—22no—
578C2×C8—22no—
579C2×C8—22no—
580C2×C8—22no—
581C2×C8—44no—
582C2×C8—44no—
583C2×C8—44no—
584C2×C8—44no—
585C4⋊C4—24no—
586C4⋊C4—24no—
587C4⋊C4—216no—
588C4⋊C4—22no—
589C4⋊C4—22no—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—42no—
597C4⋊C4—42no—
598C4⋊C4—42no—
599C4⋊C4—84no—
600C4⋊C4—84no—
601C4⋊C4C22×D414yes—
602C4⋊C4C22×D414yes—
603C22⋊C4—28no—
604C22⋊C4—44no—
605C22⋊C4—48no—
606C22⋊C4—48no—
607C22⋊C4—48no—
608C22⋊C4—48no—
609C22⋊C4—84no—
610C22⋊C4—84no—
611C42—24no—
612C42—24no—
613C42—22no—
614C42—22no—
615C42—22no—
616C42—22no—
617C42—84no—
618C42—84no—
619C23—28no—
620C23—22no—
621C23—22no—
622C23—28no—
623C23—28no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—24no—
629C23—44no—
630C23—44no—
631C23—44no—
632C23—44no—
633C23—42no—
634C23—48no—
635C23—42no—
636C23—48no—
637C23—48no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—84no—
650C23—84no—
651C23—84no—
652C23—84no—
653C23—84no—
654C23—84no—
655C23—84no—
656C23—84no—
657C23—84no—
658C23—84no—
659C23—84no—
660C23C2×#12114yes—
661C23C2×#12112yes—
662C23#54612yes—
663C23#54612yes—
664C23C2×#13712yes—
665C23#57512yes—
666C23#57612yes—
667C23#57612yes—
668C23C23×D411yescharacteristic
669Q8—24no—
670Q8—24no—
671Q8—48no—
672Q8—42no—
673Q8—42no—
674D4—24no—
675D4—24no—
676D4—432no—
677D4—48no—
678D4—42no—
679D4—42no—
680D4—42no—
681D4—42no—
682D4—42no—
683D4—42no—
684D4—816no—
685D4—816no—
686D4—816no—
687D4—84no—
688C2×C4—28no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—28no—
693C2×C4—22no—
694C2×C4—216no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—432no—
712C2×C4—44no—
713C2×C4—42no—
714C2×C4—48no—
715C2×C4—42no—
716C2×C4—48no—
717C2×C4—48no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—42no—
721C2×C4—42no—
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—816no—
734C2×C4—84no—
735C2×C4—84no—
736C2×C4—84no—
737C2×C4C2×#12114yes—
738C2×C4C2×#12112yes—
739C2×C4#52514yes—
740C2×C4#53514yes—
741C2×C4#54612yes—
742C2×C4#54612yes—
743C2×C4#55114yes—
744C2×C4#55114yes—
745C2×C4C2×#13714yes—
746C2×C4C23×D411yescharacteristic
747C2×C4C22×#4111yescharacteristic
748C2×C4C22×#4111yescharacteristic
749C2×C4C22×#4111yescharacteristic
750C2×C4C2×H(5,𝔽2)11yescharacteristic
751C2×C4C2×H(5,𝔽2)11yescharacteristic
752C8—42no—
753C8—42no—
754C8—42no—
755C8—42no—
756C22—24no—
757C22—24no—
758C22—24no—
759C22—416no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—44no—
765C22—44no—
766C22—44no—
767C22—82no—
768C22—816no—
769C22—82no—
770C22—82no—
771C22—82no—
772C22—82no—
773C22—82no—
774C22—82no—
775C22—82no—
776C22—82no—
777C22—82no—
778C22—82no—
779C22—168no—
780C22#241114yes—
781C22#303714yes—
782C22#304114yes—
783C22#330914yes—
784C22#331414yes—
785C22#332214yes—
786C22#333314yes—
787C22C22×#12111yescharacteristic
788C22C2×#54611yescharacteristic
789C22C2×#54611yescharacteristic
790C22C22×#13711yescharacteristic
791C22C2×#57511yescharacteristic
792C22C2×#57611yescharacteristic
793C22C2×#57611yescharacteristic
794C4—24no—
795C4—24no—
796C4—44no—
797C4—44no—
798C4—44no—
799C4—42no—
800C4—42no—
801C4—42no—
802C4—82no—
803C4—82no—
804C4—82no—
805C4#241114yes—
806C4C2×#52511yescharacteristic
807C4C2×#53511yescharacteristic
808C4C2×#55111yescharacteristic
809C4C2×#55111yescharacteristic
810C2—44no—
811C2—84no—
812C2—162no—
813C2#2449018yesdirect product factor
814C2C2×#241111yescharacteristic
815C2C2×#303711yescharacteristic
816C2C2×#304111yescharacteristic
817C2C2×#331411yescharacteristic
818C2C2×#330911yescharacteristic
819C2C2×#332211yescharacteristic
820C2C2×#333311yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#2431C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#480C2semidirect
2. C22×#417C2semidirect
4. C2×#2345C2semidirect
5. #24490C2direct (N × H)
6. C2×#2068C2semidirect
7. C2×#2067C2semidirect
8. C2×#2042C2semidirect
9. C2×#2041C2semidirect
10. C2×#1983C2semidirect
11. C2×#1982C2semidirect
12. C2×#1928C2semidirect
13. C2×#1925C2semidirect
14. C2×#1895C2semidirect
15. C2×#1851C2semidirect
16. C2×#1788C2semidirect
24. C2×#480C22semidirect
30. C2×#417C22semidirect
49. #2345C22semidirect
64. #2068C22semidirect
65. #2067C22semidirect
66. #2042C22semidirect
67. #2041C22semidirect
68. #1983C22semidirect
69. #1982C22semidirect
70. #1928C22semidirect
71. #1925C22semidirect
72. #1895C22semidirect
73. #1851C22semidirect
74. #1788C22semidirect
122. C22×C4⋊C4D4semidirect
350. C2×C4⋊C4C2×D4semidirect
813. C2#24490direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4802
C22×#4172
C2×#24312
C2×#23452
#244902
C2×#20682
C2×#20672
C2×#20422
C2×#20412
C2×#19832
C2×#19822
C2×#19282
C2×#19252
C2×#18952
C2×#18512
C2×#17882