Finite Group Databasebeta

← C2×#28579 #6459539

Subgroups — C2×#28579 #6459539

Order 512.

3004 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#469C211yesmaximal, characteristic
2C22×#468C211yesmaximal, characteristic, complemented
3C2×#2850C211yesmaximal, characteristic, complemented
4C2×C4×#121C211yesmaximal, characteristic, complemented
5#28579C2116yesmaximal, direct product factor
6C2×#2085C211yesmaximal, characteristic, complemented
7C2×#2073C211yesmaximal, characteristic, complemented
8C2×#2042C211yesmaximal, characteristic, complemented
9C2×#2012C211yesmaximal, characteristic, complemented
10C2×#1927C211yesmaximal, characteristic, complemented
11C2×#1925C211yesmaximal, characteristic, complemented
12C2×#1895C211yesmaximal, characteristic, complemented
13C2×#1894C211yesmaximal, characteristic, complemented
14C2×#1879C211yesmaximal, characteristic, complemented
15C2×#1877C211yesmaximal, characteristic, complemented
16C2×#1728C211yesmaximal, characteristic, complemented
17C23×SD16C2211yescharacteristic
18C23×D8C2211yescharacteristic
19C23×M16C2211yescharacteristic
20C23×M16C2211yescharacteristic
21C22×#124C2211yescharacteristic
22C22×C22⋊Q8C2211yescharacteristic
23C22×#121C2211yescharacteristic
24C22×#121C2211yescharacteristic
25C22×C4×D4—21no—
26C22×C4×D4C2211yescharacteristic
27C23×C42C2211yescharacteristic
28C2×#469—28no—
29C2×#469C2218yes—
30C2×#468—28no—
31C2×#468C2218yescomplemented
32C22×#107C2211yescharacteristic
33C22×#106C2211yescharacteristic
34C22×#103C2211yescharacteristic
35C22×#103C2211yescharacteristic
36C22×#103C2211yescharacteristic
37C22×#102C2211yescharacteristic
38C22×#102C2211yescharacteristic
39C22×#102C2211yescharacteristic
40C22×#102C2211yescharacteristic
41C22×#102C2211yescharacteristic
42#2850—24no—
43#2850C2218yescomplemented
44C4×#121—24no—
45C4×#121C2218yescomplemented
46C2×#391C2211yescharacteristic
47C2×#390C2211yescharacteristic
48C2×#390C2211yescharacteristic
49C2×#389C2211yescharacteristic
50C2×#388—21no—
51C2×#388—21no—
52C2×#388—21no—
53C2×#386—21no—
54C2×#386—21no—
55C2×#386—21no—
56C2×#382C2211yescharacteristic
57C2×#380C2211yescharacteristic
58C2×C4×C4⋊C4C2211yescharacteristic
59C2×C4×C22⋊C4—21no—
60#2085C2218yescomplemented
61#2073C2218yescomplemented
62#2042C2218yescomplemented
63#2012C2218yescomplemented
64#1927C2218yescomplemented
65#1925C2218yescomplemented
66#1895C2218yescomplemented
67#1894C2218yescomplemented
68#1879C2218yescomplemented
69#1877C2218yescomplemented
70C2×#340C2211yescharacteristic
71C2×#340C2211yescharacteristic
72C2×#340C2211yescharacteristic
73C2×#340C2211yescharacteristic
74#1728C2218yescomplemented
75C2×#336C2211yescharacteristic
76C2×#336C2211yescharacteristic
77C2×#336C2211yescharacteristic
78C2×#336C2211yescharacteristic
79C23×Q8C2311yescharacteristic
80C23×D4—21no—
81C23×D4—21no—
82C23×D4C2311yescharacteristic
83C23×D4C2311yescharacteristic
84C24×C4—21no—
85C24×C4D411yescharacteristic
86C24×C4D411yescharacteristic
87C24×C4C2311yescharacteristic
88C22×SD16—24no—
89C22×SD16—24no—
90C22×SD16—42no—
91C22×SD16C2314yes—
92C22×D8—24no—
93C22×D8—24no—
94C22×D8—42no—
95C22×D8C2314yes—
96C22×M16—24no—
97C22×M16—24no—
98C22×M16—24no—
99C22×M16—24no—
100C22×M16—42no—
101C22×M16—42no—
102C22×M16C2314yes—
103C22×M16C2314yes—
104C23×C8C2311yescharacteristic
105C23×C8C2311yescharacteristic
106C23×C8C2311yescharacteristic
107C23×C8C2311yescharacteristic
108C2×#124—22no—
109C2×#124—42no—
110C2×#124—42no—
111C2×#124C2314yes—
112C2×C22⋊Q8—22no—
113C2×C22⋊Q8—24no—
114C2×C22⋊Q8—24no—
115C2×C22⋊Q8C2314yes—
116C2×#121—22no—
117C2×#121—24no—
118C2×#121—22no—
119C2×#121—24no—
120C2×#121—24no—
121C2×#121D418yes—
122C2×#121C2314yes—
123C2×#121C2314yes—
124C2×C4×D4—28no—
125C2×C4×D4—22no—
126C2×C4×D4—42no—
127C2×C4×D4—42no—
128C2×C4×D4—48no—
129C2×C4×D4C2314yes—
130C22×C4⋊C4—21no—
131C22×C4⋊C4—21no—
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C22⋊C4—21no—
138C22×C22⋊C4—21no—
139C22×C22⋊C4—21no—
140C22×C22⋊C4—21no—
141C22×C22⋊C4—21no—
142C22×C22⋊C4—21no—
143C22×C22⋊C4—21no—
144C22×C22⋊C4—21no—
145C22×C22⋊C4—21no—
146C22×C22⋊C4—21no—
147C22×C22⋊C4—21no—
148C22×C42—21no—
149C22×C42—42no—
150C22×C42—42no—
151C22×C42D414yes—
152C22×C42D411yescharacteristic
153C22×C42D411yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2314yes—
157#469—232no—
158#468—232no—
159C2×#107—24no—
160C2×#107C2314yes—
161C2×#106—24no—
162C2×#106C2314yes—
163C2×#103—24no—
164C2×#103—24no—
165C2×#103—42no—
166C2×#103C2314yes—
167C2×#103C2314yes—
168C2×#103C2314yes—
169C2×#102—24no—
170C2×#102—24no—
171C2×#102—24no—
172C2×#102—24no—
173C2×#102—42no—
174C2×#102C2314yes—
175C2×#102C2314yes—
176C2×#102C2314yes—
177C2×#102C2314yes—
178C2×#102C2314yes—
179#391—22no—
180#391C2314yes—
181#390—22no—
182#390—22no—
183#390C2314yes—
184#390C2314yes—
185#389—22no—
186#389C2314yes—
187#388—28no—
188#388—28no—
189#388—28no—
190#386—28no—
191#386—28no—
192#386—28no—
193#382—22no—
194#382C2314yes—
195#380—22no—
196#380C2314yes—
197C4×C4⋊C4—22no—
198C4×C4⋊C4C2314yes—
199C4×C22⋊C4—28no—
200C2×#95—21no—
201C2×#95—21no—
202C2×#95—21no—
203C2×#95—21no—
204C2×#95—21no—
205C2×#95—21no—
206C2×#95—21no—
207#340C2314yes—
208#340C2314yes—
209#340C2314yes—
210#340C2314yes—
211#336C2314yes—
212#336C2314yes—
213#336C2314yes—
214#336C2314yes—
215C25—21no—
216C25—21no—
217C25C2×D411yescharacteristic
218C22×Q8—21no—
219C22×Q8—22no—
220C22×Q8—22no—
221C22×Q8—22no—
222C22×Q8—22no—
223C22×Q8—22no—
224C22×Q8—22no—
225C22×Q8C2412yes—
226C22×D4—28no—
227C22×D4—24no—
228C22×D4—24no—
229C22×D4—21no—
230C22×D4—22no—
231C22×D4—21no—
232C22×D4—22no—
233C22×D4—22no—
234C22×D4—22no—
235C22×D4—22no—
236C22×D4—22no—
237C22×D4—22no—
238C22×D4—22no—
239C22×D4—22no—
240C22×D4—22no—
241C22×D4—22no—
242C22×D4—44no—
243C22×D4—44no—
244C22×D4—44no—
245C22×D4—44no—
246C22×D4—44no—
247C22×D4C2×D414yes—
248C22×D4C2412yes—
249C22×D4C2412yes—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—21no—
255C23×C4—24no—
256C23×C4—21no—
257C23×C4—21no—
258C23×C4—21no—
259C23×C4—21no—
260C23×C4—21no—
261C23×C4—24no—
262C23×C4—42no—
263C23×C4—42no—
264C23×C4—42no—
265C23×C4—42no—
266C23×C4—42no—
267C23×C4—44no—
268C23×C4—44no—
269C23×C4—44no—
270C23×C4C2×D411yescharacteristic
271C23×C4C2×D411yescharacteristic
272C23×C4C2×D411yescharacteristic
273C23×C4C2×D412yes—
274C23×C4C2×D411yescharacteristic
275C23×C4C2×D414yes—
276C23×C4C2×D411yescharacteristic
277C23×C4C2×D414yes—
278C23×C4C2×D414yes—
279C23×C4#4114yes—
280C23×C4C2412yes—
281C23×C4C2411yescharacteristic
282C2×SD16—28no—
283C2×SD16—28no—
284C2×SD16—44no—
285C2×SD16—416no—
286C2×D8—28no—
287C2×D8—28no—
288C2×D8—44no—
289C2×D8—416no—
290C2×M16—28no—
291C2×M16—28no—
292C2×M16—28no—
293C2×M16—28no—
294C2×M16—44no—
295C2×M16—44no—
296C2×M16—416no—
297C2×M16—416no—
298C22×C8—22no—
299C22×C8—22no—
300C22×C8—22no—
301C22×C8—22no—
302C22×C8—22no—
303C22×C8—22no—
304C22×C8—22no—
305C22×C8—22no—
306C22×C8—22no—
307C22×C8—22no—
308C22×C8#4114yes—
309C22×C8#4114yes—
310C22×C8C2412yes—
311C22×C8C2412yes—
312C22×C8C2412yes—
313C22×C8C2412yes—
314#124—44no—
315#124—44no—
316#124—48no—
317C22⋊Q8—28no—
318C22⋊Q8—28no—
319C22⋊Q8—48no—
320#121—216no—
321#121—28no—
322#121—28no—
323#121—28no—
324#121—48no—
325#121C2×D4116yes—
326C4×D4—44no—
327C4×D4—44no—
328C4×D4—48no—
329C4×D4—432no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—44no—
347C2×C4⋊C4—44no—
348C2×C4⋊C4C2×D414yes—
349C2×C4⋊C4C2412yes—
350C2×C4⋊C4C2412yes—
351C2×C4⋊C4C2412yes—
352C2×C4⋊C4C2412yes—
353C2×C4⋊C4C2412yes—
354C2×C22⋊C4—28no—
355C2×C22⋊C4—24no—
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—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—44no—
367C2×C22⋊C4—44no—
368C2×C22⋊C4—44no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4—44no—
375C2×C22⋊C4—44no—
376C2×C42—22no—
377C2×C42—22no—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—24no—
381C2×C42—48no—
382C2×C42—44no—
383C2×C42—44no—
384C2×C42—42no—
385C2×C42—42no—
386C2×C42—44no—
387C2×C42C2×D412yes—
388C2×C42C2×D412yes—
389C2×C42C2×D414yes—
390C2×C42C2×D414yes—
391C2×C42C2412yes—
392C2×C42C2412yes—
393#107—28no—
394#106—28no—
395#103—28no—
396#103—28no—
397#103—44no—
398#102—28no—
399#102—28no—
400#102—28no—
401#102—28no—
402#102—44no—
403#95—24no—
404#95—24no—
405#95—24no—
406#95—24no—
407#95—24no—
408#95—24no—
409#95—24no—
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
435C2×Q8—22no—
436C2×Q8—22no—
437C2×Q8—22no—
438C2×Q8—22no—
439C2×Q8—22no—
440C2×Q8—22no—
441C2×Q8—42no—
442C2×Q8—42no—
443C2×Q8—42no—
444C2×Q8—44no—
445C2×Q8—44no—
446C2×Q8—44no—
447C2×Q8—44no—
448C2×D4—216no—
449C2×D4—24no—
450C2×D4—28no—
451C2×D4—28no—
452C2×D4—22no—
453C2×D4—22no—
454C2×D4—22no—
455C2×D4—22no—
456C2×D4—22no—
457C2×D4—22no—
458C2×D4—22no—
459C2×D4—22no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—22no—
463C2×D4—48no—
464C2×D4—432no—
465C2×D4—48no—
466C2×D4—48no—
467C2×D4—48no—
468C2×D4—48no—
469C2×D4—42no—
470C2×D4—42no—
471C2×D4—42no—
472C2×D4—42no—
473C2×D4—42no—
474C2×D4—44no—
475C2×D4—44no—
476C2×D4—44no—
477C2×D4—44no—
478C2×D4—44no—
479C2×D4—44no—
480C2×D4—816no—
481C2×D4C22×D414yes—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—24no—
487C22×C4—24no—
488C22×C4—28no—
489C22×C4—28no—
490C22×C4—28no—
491C22×C4—28no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—24no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—28no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—44no—
514C22×C4—44no—
515C22×C4—44no—
516C22×C4—44no—
517C22×C4—44no—
518C22×C4—416no—
519C22×C4—48no—
520C22×C4—48no—
521C22×C4—416no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—48no—
540C22×C4—816no—
541C22×C4#12114yes—
542C22×C4#12118yes—
543C22×C4AGL(1,ℤ/8)14yes—
544C22×C4C22×D412yes—
545C22×C4C22×D412yes—
546C22×C4C22×D412yes—
547C22×C4C22×D412yes—
548C22×C4C22×D414yes—
549C22×C4C22×D412yes—
550C22×C4C22×D411yescharacteristic
551C22×C4C22×D412yes—
552C22×C4C2×#4114yes—
553C22×C4C2×#4112yes—
554C22×C4C2×#4112yes—
555C22×C4C2×#4112yes—
556C22×C4H(5,𝔽2)12yes—
557C22×C4H(5,𝔽2)12yes—
558C22×C4C2511yescharacteristic
559SD16—416no—
560D8—416no—
561M16—416no—
562M16—416no—
563C2×C8—28no—
564C2×C8—28no—
565C2×C8—22no—
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8—22no—
570C2×C8—22no—
571C2×C8—22no—
572C2×C8—22no—
573C2×C8—22no—
574C2×C8—22no—
575C2×C8—44no—
576C2×C8—44no—
577C2×C8C2×#4114yes—
578C2×C8C2×#4114yes—
579C4⋊C4—24no—
580C4⋊C4—22no—
581C4⋊C4—22no—
582C4⋊C4—22no—
583C4⋊C4—22no—
584C4⋊C4—22no—
585C4⋊C4—22no—
586C4⋊C4—22no—
587C4⋊C4—22no—
588C4⋊C4—22no—
589C4⋊C4—48no—
590C4⋊C4—42no—
591C4⋊C4—42no—
592C4⋊C4—48no—
593C4⋊C4—42no—
594C4⋊C4—42no—
595C4⋊C4C22×D414yes—
596C22⋊C4—216no—
597C22⋊C4—48no—
598C22⋊C4—48no—
599C22⋊C4—48no—
600C22⋊C4—48no—
601C22⋊C4—48no—
602C22⋊C4—48no—
603C22⋊C4—48no—
604C22⋊C4—48no—
605C22⋊C4—48no—
606C22⋊C4—48no—
607C42—24no—
608C42—24no—
609C42—22no—
610C42—22no—
611C42—22no—
612C42—22no—
613C42—44no—
614C42—44no—
615C42—48no—
616C23—22no—
617C23—22no—
618C23—28no—
619C23—28no—
620C23—28no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—24no—
626C23—44no—
627C23—44no—
628C23—44no—
629C23—44no—
630C23—42no—
631C23—42no—
632C23—48no—
633C23—48no—
634C23—48no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—84no—
647C23—84no—
648C23—84no—
649C23—84no—
650C23—84no—
651C23—84no—
652C23—84no—
653C23—84no—
654C23—84no—
655C23—84no—
656C23—84no—
657C23C2×#12114yes—
658C23C2×#12112yes—
659C23#53212yes—
660C23#53412yes—
661C23C2×AGL(1,ℤ/8)12yes—
662C23#57512yes—
663C23#57512yes—
664C23#57512yes—
665C23C23×D411yescharacteristic
666Q8—42no—
667Q8—42no—
668Q8—42no—
669Q8—42no—
670Q8—84no—
671D4—24no—
672D4—24no—
673D4—432no—
674D4—42no—
675D4—42no—
676D4—42no—
677D4—42no—
678D4—42no—
679D4—42no—
680D4—48no—
681D4—816no—
682D4—84no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—28no—
687C2×C4—28no—
688C2×C4—22no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—216no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—416no—
705C2×C4—416no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—48no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—816no—
728C2×C4—84no—
729C2×C4—84no—
730C2×C4—84no—
731C2×C4—84no—
732C2×C4—84no—
733C2×C4C2×#12114yes—
734C2×C4C2×#12112yes—
735C2×C4#53212yes—
736C2×C4#53412yes—
737C2×C4#54614yes—
738C2×C4#54614yes—
739C2×C4#55314yes—
740C2×C4#55314yes—
741C2×C4C2×AGL(1,ℤ/8)14yes—
742C2×C4C23×D411yescharacteristic
743C2×C4C22×#4111yescharacteristic
744C2×C4C22×#4111yescharacteristic
745C2×C4C22×#4111yescharacteristic
746C2×C4C2×H(5,𝔽2)11yescharacteristic
747C2×C4C2×H(5,𝔽2)11yescharacteristic
748C8—24no—
749C8—24no—
750C8—42no—
751C8—42no—
752C22—24no—
753C22—24no—
754C22—24no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—416no—
760C22—44no—
761C22—44no—
762C22—44no—
763C22—82no—
764C22—82no—
765C22—82no—
766C22—82no—
767C22—816no—
768C22—82no—
769C22—82no—
770C22—82no—
771C22—82no—
772C22—82no—
773C22—82no—
774C22—82no—
775C22—168no—
776C22#254314yes—
777C22#303614yes—
778C22#304014yes—
779C22#317114yes—
780C22#318314yes—
781C22#319414yes—
782C22#319714yes—
783C22C22×#12111yescharacteristic
784C22C2×#53211yescharacteristic
785C22C2×#53411yescharacteristic
786C22C22×AGL(1,ℤ/8)11yescharacteristic
787C22C2×#57511yescharacteristic
788C22C2×#57511yescharacteristic
789C22C2×#57511yescharacteristic
790C4—24no—
791C4—24no—
792C4—42no—
793C4—42no—
794C4—42no—
795C4—44no—
796C4—82no—
797C4—82no—
798C4—82no—
799C4—82no—
800C4—82no—
801C4#254314yes—
802C4C2×#54611yescharacteristic
803C4C2×#54611yescharacteristic
804C4C2×#55311yescharacteristic
805C4C2×#55311yescharacteristic
806C2—44no—
807C2—84no—
808C2—162no—
809C2#2857918yesdirect product factor
810C2C2×#254311yescharacteristic
811C2C2×#303611yescharacteristic
812C2C2×#304011yescharacteristic
813C2C2×#317111yescharacteristic
814C2C2×#318311yescharacteristic
815C2C2×#319411yescharacteristic
816C2C2×#319711yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#469C2
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
2. C22×#468C2semidirect
3. C2×#2850C2semidirect
4. C2×C4×#121C2semidirect
5. #28579C2direct (N × H)
6. C2×#2085C2semidirect
7. C2×#2073C2semidirect
8. C2×#2042C2semidirect
9. C2×#2012C2semidirect
10. C2×#1927C2semidirect
11. C2×#1925C2semidirect
12. C2×#1895C2semidirect
13. C2×#1894C2semidirect
14. C2×#1879C2semidirect
15. C2×#1877C2semidirect
16. C2×#1728C2semidirect
31. C2×#468C22semidirect
43. #2850C22semidirect
45. C4×#121C22semidirect
60. #2085C22semidirect
61. #2073C22semidirect
62. #2042C22semidirect
63. #2012C22semidirect
64. #1927C22semidirect
65. #1925C22semidirect
66. #1895C22semidirect
67. #1894C22semidirect
68. #1879C22semidirect
69. #1877C22semidirect
74. #1728C22semidirect
809. C2#28579direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4692
C22×#4682
C2×#28502
C2×C4×#1212
#285792
C2×#20852
C2×#20732
C2×#20422
C2×#20122
C2×#19272
C2×#19252
C2×#18952
C2×#18942
C2×#18792
C2×#18772
C2×#17282