Finite Group Databasebeta

← C2×#24737 #6442797

Subgroups — C2×#24737 #6442797

Order 512.

2998 conjugacy classes of subgroups.

The subgroup lattice has 791 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#463C211yesmaximal, characteristic
2C22×#463C211yesmaximal, characteristic
3C22×#461C211yesmaximal, characteristic, complemented
4C22×C4×SD16C211yesmaximal, characteristic, complemented
5C2×#2545C211yesmaximal, characteristic, complemented
6C2×#2349C211yesmaximal, characteristic, complemented
7#24737C2116yesmaximal, direct product factor
8C2×#2066C211yesmaximal, characteristic, complemented
9C2×#2065C211yesmaximal, characteristic, complemented
10C2×#2043C211yesmaximal, characteristic, complemented
11C2×#2042C211yesmaximal, characteristic, complemented
12C2×#1958C211yesmaximal, characteristic, complemented
13C2×#1939C211yesmaximal, characteristic, complemented
14C2×#1879C211yesmaximal, characteristic
15C2×#1877C211yesmaximal, characteristic, complemented
16C2×#1805C211yesmaximal, characteristic, complemented
17C23×SD16C2211yescharacteristic
18C23×SD16C2211yescharacteristic
19C23×D8C2211yescharacteristic
20C22×C4⋊Q8C2211yescharacteristic
21C22×#124C2211yescharacteristic
22C22×#124C2211yescharacteristic
23C22×C4×Q8C2211yescharacteristic
24C22×C4×D4C2211yescharacteristic
25C22×C4×D4C2211yescharacteristic
26C22×C4×D4C2211yescharacteristic
27C2×#463—28no—
28C2×#463—28no—
29C2×#463C2218yes—
30C2×#463C2218yes—
31C2×#461—28no—
32C2×#461C2218yescomplemented
33C2×C4×SD16—28no—
34C2×C4×SD16C2218yescomplemented
35C22×#106C2211yescharacteristic
36C22×C4⋊C8C2211yescharacteristic
37C22×C4⋊C8C2211yescharacteristic
38C22×C4⋊C8C2211yescharacteristic
39C22×#103C2211yescharacteristic
40C22×#103C2211yescharacteristic
41C22×#103C2211yescharacteristic
42C22×#103C2211yescharacteristic
43C22×#103C2211yescharacteristic
44C22×#103C2211yescharacteristic
45C22×#102C2211yescharacteristic
46C22×#102C2211yescharacteristic
47C22×#102C2211yescharacteristic
48C22×#102C2211yescharacteristic
49C22×C4×C8C2211yescharacteristic
50#2545—24no—
51#2545C2218yescomplemented
52C2×#396—21no—
53C2×#396—21no—
54#2349—24no—
55#2349C2218yescomplemented
56C2×#391C2211yescharacteristic
57C2×#390C2211yescharacteristic
58C2×#389C2211yescharacteristic
59C2×#389C2211yescharacteristic
60C2×#388—21no—
61C2×#388—21no—
62C2×#385—21no—
63C2×#385—21no—
64C2×#382C2211yescharacteristic
65C2×#380—21no—
66C2×C4×C4⋊C4C2211yescharacteristic
67C22×#95—21no—
68#2066C2218yescomplemented
69#2065C2218yescomplemented
70#2043C2218yescomplemented
71#2042C2218yescomplemented
72#1958C2218yescomplemented
73#1939C2218yescomplemented
74#1879C2218yes—
75#1877C2218yescomplemented
76#1805C2218yescomplemented
77C2×#340C2211yescharacteristic
78C2×#340C2211yescharacteristic
79C2×#336C2211yescharacteristic
80C2×#336C2211yescharacteristic
81C23×Q8C2311yescharacteristic
82C23×Q8C2311yescharacteristic
83C23×D4C2311yescharacteristic
84C23×D4C2311yescharacteristic
85C24×C4—21no—
86C24×C4—21no—
87C24×C4—21no—
88C22×SD16—24no—
89C22×SD16—24no—
90C22×SD16—24no—
91C22×SD16—24no—
92C22×SD16—24no—
93C22×SD16D418yes—
94C22×SD16C2314yes—
95C22×SD16C2314yes—
96C22×D8—24no—
97C22×D8—24no—
98C22×D8—24no—
99C22×D8C2314yes—
100C23×C8C2311yescharacteristic
101C23×C8C2311yescharacteristic
102C23×C8C2311yescharacteristic
103C23×C8C2311yescharacteristic
104C2×C4⋊Q8—24no—
105C2×C4⋊Q8—22no—
106C2×C4⋊Q8—42no—
107C2×C4⋊Q8C2314yes—
108C2×#124—24no—
109C2×#124—22no—
110C2×#124—22no—
111C2×#124—24no—
112C2×#124—24no—
113C2×#124—42no—
114C2×#124C2314yes—
115C2×#124C2314yes—
116C2×C4×Q8—22no—
117C2×C4×Q8—24no—
118C2×C4×Q8—24no—
119C2×C4×Q8C2314yes—
120C2×C4×D4—24no—
121C2×C4×D4—24no—
122C2×C4×D4—22no—
123C2×C4×D4—22no—
124C2×C4×D4—22no—
125C2×C4×D4—24no—
126C2×C4×D4—42no—
127C2×C4×D4—42no—
128C2×C4×D4D418yes—
129C2×C4×D4C2314yes—
130C2×C4×D4C2314yes—
131C2×C4×D4C2314yes—
132C22×C4⋊C4—21no—
133C22×C4⋊C4—21no—
134C22×C4⋊C4—21no—
135C22×C4⋊C4—21no—
136C22×C4⋊C4—21no—
137C22×C4⋊C4D411yescharacteristic
138C22×C4⋊C4D411yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2311yescharacteristic
143C22×C22⋊C4—21no—
144C22×C22⋊C4—21no—
145C22×C22⋊C4—21no—
146C22×C22⋊C4—21no—
147C22×C22⋊C4—21no—
148C22×C22⋊C4—21no—
149C22×C22⋊C4—21no—
150C22×C22⋊C4—21no—
151C22×C22⋊C4—21no—
152C22×C42—21no—
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156#463—232no—
157#463—232no—
158#461—232no—
159C4×SD16—232no—
160C2×#106—24no—
161C2×#106C2314yes—
162C2×C4⋊C8—24no—
163C2×C4⋊C8—24no—
164C2×C4⋊C8—24no—
165C2×C4⋊C8C2314yes—
166C2×C4⋊C8C2314yes—
167C2×C4⋊C8C2314yes—
168C2×#103—24no—
169C2×#103—24no—
170C2×#103—24no—
171C2×#103—24no—
172C2×#103—24no—
173C2×#103—42no—
174C2×#103C2314yes—
175C2×#103C2314yes—
176C2×#103C2314yes—
177C2×#103C2314yes—
178C2×#103C2314yes—
179C2×#103C2314yes—
180C2×#102—24no—
181C2×#102—24no—
182C2×#102—24no—
183C2×#102—42no—
184C2×#102C2314yes—
185C2×#102C2314yes—
186C2×#102C2314yes—
187C2×#102C2314yes—
188C2×C4×C8—24no—
189C2×C4×C8C2314yes—
190#396—28no—
191#396—28no—
192#391—22no—
193#391C2314yes—
194#390—22no—
195#390C2314yes—
196#389—22no—
197#389—22no—
198#389C2314yes—
199#389C2314yes—
200#388—28no—
201#388—28no—
202#385—28no—
203#385—28no—
204#382—22no—
205#382C2314yes—
206#380—28no—
207C4×C4⋊C4D414yes—
208C4×C4⋊C4C2314yes—
209C2×#95—21no—
210C2×#95—21no—
211C2×#95—21no—
212C2×#95—21no—
213C2×#95—21no—
214C2×#95—21no—
215C2×#95—28no—
216C2×#95D411yescharacteristic
217C2×#95D411yescharacteristic
218#340C2314yes—
219#340C2314yes—
220#336C2314yes—
221#336C2314yes—
222C25—21no—
223C25—21no—
224C22×Q8—21no—
225C22×Q8—21no—
226C22×Q8—22no—
227C22×Q8—22no—
228C22×Q8—22no—
229C22×Q8—22no—
230C22×Q8—22no—
231C22×Q8—22no—
232C22×Q8—22no—
233C22×Q8—22no—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8C2×D414yes—
238C22×Q8C2412yes—
239C22×Q8C2412yes—
240C22×D4—21no—
241C22×D4—22no—
242C22×D4—22no—
243C22×D4—21no—
244C22×D4—22no—
245C22×D4—22no—
246C22×D4—22no—
247C22×D4—22no—
248C22×D4—22no—
249C22×D4—22no—
250C22×D4—22no—
251C22×D4C2×D414yes—
252C22×D4C2×D414yes—
253C22×D4#4114yes—
254C22×D4C2412yes—
255C22×D4C2412yes—
256C23×C4—21no—
257C23×C4—21no—
258C23×C4—28no—
259C23×C4—24no—
260C23×C4—21no—
261C23×C4—21no—
262C23×C4—21no—
263C23×C4—21no—
264C23×C4—24no—
265C23×C4—24no—
266C23×C4—44no—
267C23×C4—44no—
268C23×C4—44no—
269C23×C4—44no—
270C23×C4—82no—
271C23×C4—82no—
272C23×C4—82no—
273C23×C4—82no—
274C23×C4C2×D411yescharacteristic
275C23×C4C2×D411yescharacteristic
276C23×C4C2×D411yescharacteristic
277C23×C4C2×D411yescharacteristic
278C23×C4C2×D411yescharacteristic
279C23×C4C2×D411yescharacteristic
280C23×C4C2411yescharacteristic
281C2×SD16—232no—
282C2×SD16—28no—
283C2×SD16—28no—
284C2×SD16—28no—
285C2×SD16—28no—
286C2×SD16—28no—
287C2×SD16—416no—
288C2×SD16C2×D4116yes—
289C2×D8—28no—
290C2×D8—28no—
291C2×D8—28no—
292C2×D8—416no—
293C22×C8—22no—
294C22×C8—22no—
295C22×C8—22no—
296C22×C8—22no—
297C22×C8—22no—
298C22×C8—22no—
299C22×C8—22no—
300C22×C8—22no—
301C22×C8—22no—
302C22×C8—22no—
303C22×C8—22no—
304C22×C8C2×D414yes—
305C22×C8C2412yes—
306C22×C8C2412yes—
307C22×C8C2412yes—
308C22×C8C2412yes—
309C4⋊Q8—28no—
310C4⋊Q8—44no—
311C4⋊Q8—48no—
312#124—28no—
313#124—28no—
314#124—28no—
315#124—44no—
316#124—48no—
317#124—48no—
318C4×Q8—28no—
319C4×Q8—28no—
320C4×Q8—48no—
321C4×D4—28no—
322C4×D4—28no—
323C4×D4—216no—
324C4×D4—28no—
325C4×D4—44no—
326C4×D4—44no—
327C4×D4—48no—
328C4×D4—48no—
329C4×D4C2×D4116yes—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—21no—
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—24no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—42no—
348C2×C4⋊C4—44no—
349C2×C4⋊C4—44no—
350C2×C4⋊C4—44no—
351C2×C4⋊C4—82no—
352C2×C4⋊C4—82no—
353C2×C4⋊C4C2×D414yes—
354C2×C4⋊C4C2×D414yes—
355C2×C4⋊C4C2×D414yes—
356C2×C4⋊C4C2412yes—
357C2×C4⋊C4C2412yes—
358C2×C4⋊C4C2412yes—
359C2×C4⋊C4C2412yes—
360C2×C22⋊C4—28no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
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×C22⋊C4—44no—
377C2×C22⋊C4—44no—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—24no—
383C2×C42—44no—
384C2×C42C2×D412yes—
385C2×C42C2×D412yes—
386C2×C42C2×D412yes—
387C2×C42C2×D414yes—
388C2×C42#4114yes—
389C2×C42C2412yes—
390C2×C42C2412yes—
391C2×C42C2412yes—
392#106—28no—
393C4⋊C8—28no—
394C4⋊C8—28no—
395C4⋊C8—28no—
396#103—28no—
397#103—28no—
398#103—28no—
399#103—28no—
400#103—28no—
401#103—44no—
402#102—28no—
403#102—28no—
404#102—28no—
405#102—44no—
406C4×C8—28no—
407#95—24no—
408#95—24no—
409#95—24no—
410#95—24no—
411#95—24no—
412#95—24no—
413#95C2×D414yes—
414#95C2×D414yes—
415C24—24no—
416C24—24no—
417C24—24no—
418C24—22no—
419C24—22no—
420C24—42no—
421C24—42no—
422C24—42no—
423C24—42no—
424C24—42no—
425C24—42no—
426C24—42no—
427C24—42no—
428C24—42no—
429C24—42no—
430C24—42no—
431C24C22×D411yescharacteristic
432C2×Q8—24no—
433C2×Q8—22no—
434C2×Q8—28no—
435C2×Q8—28no—
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—22no—
445C2×Q8—22no—
446C2×Q8—42no—
447C2×Q8—42no—
448C2×Q8—44no—
449C2×Q8—42no—
450C2×Q8—42no—
451C2×Q8—42no—
452C2×Q8—44no—
453C2×Q8—44no—
454C2×Q8—44no—
455C2×Q8—44no—
456C2×Q8—44no—
457C2×Q8C22×D414yes—
458C2×D4—24no—
459C2×D4—28no—
460C2×D4—24no—
461C2×D4—28no—
462C2×D4—24no—
463C2×D4—28no—
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—44no—
474C2×D4—42no—
475C2×D4—44no—
476C2×D4—42no—
477C2×D4—44no—
478C2×D4—42no—
479C2×D4—44no—
480C2×D4#121116yes—
481C2×D4C22×D414yes—
482C2×D4C22×D414yes—
483C2×D4C2×#4114yes—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—24no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—24no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—216no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—48no—
509C22×C4—48no—
510C22×C4—48no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—48no—
528C22×C4—816no—
529C22×C4—84no—
530C22×C4—84no—
531C22×C4—84no—
532C22×C4—84no—
533C22×C4—816no—
534C22×C4—816no—
535C22×C4#12114yes—
536C22×C4#12114yes—
537C22×C4#13514yes—
538C22×C4C22×D412yes—
539C22×C4C22×D412yes—
540C22×C4C22×D412yes—
541C22×C4C22×D412yes—
542C22×C4C22×D412yes—
543C22×C4C22×D412yes—
544C22×C4C22×D412yes—
545C22×C4C22×D411yescharacteristic
546C22×C4C22×D412yes—
547C22×C4C2×#4112yes—
548C22×C4C2×#4112yes—
549C22×C4H(5,𝔽2)12yes—
550C22×C42−1+412yes—
551C22×C4C2511yescharacteristic
552SD16—232no—
553SD16—416no—
554D8—416no—
555C2×C8—28no—
556C2×C8—22no—
557C2×C8—22no—
558C2×C8—22no—
559C2×C8—22no—
560C2×C8—22no—
561C2×C8—22no—
562C2×C8—22no—
563C2×C8—22no—
564C2×C8—22no—
565C2×C8—22no—
566C2×C8—22no—
567C2×C8—44no—
568C2×C8—44no—
569C2×C8—44no—
570C2×C8C22×D414yes—
571C4⋊C4—24no—
572C4⋊C4—28no—
573C4⋊C4—22no—
574C4⋊C4—22no—
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—22no—
579C4⋊C4—22no—
580C4⋊C4—44no—
581C4⋊C4—48no—
582C4⋊C4—48no—
583C4⋊C4—42no—
584C4⋊C4—48no—
585C4⋊C4—42no—
586C4⋊C4—42no—
587C4⋊C4—84no—
588C4⋊C4—84no—
589C4⋊C4C22×D414yes—
590C22⋊C4—216no—
591C22⋊C4—48no—
592C22⋊C4—48no—
593C22⋊C4—48no—
594C22⋊C4—48no—
595C22⋊C4—48no—
596C22⋊C4—48no—
597C22⋊C4—48no—
598C22⋊C4—48no—
599C42—24no—
600C42—24no—
601C42—22no—
602C42—22no—
603C42—22no—
604C42—22no—
605C42—48no—
606C42#12118yes—
607C42C22×D414yes—
608C42C2×#4114yes—
609C23—24no—
610C23—216no—
611C23—24no—
612C23—24no—
613C23—48no—
614C23—48no—
615C23—48no—
616C23—48no—
617C23—48no—
618C23—48no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—84no—
631C23—84no—
632C23—84no—
633C23—84no—
634C23—84no—
635C23—84no—
636C23—84no—
637C23C2×#12112yes—
638C23D4212yes—
639C23#54812yes—
640C23C2×#13512yes—
641C23#57512yes—
642C23#57712yes—
643C23#57712yes—
644C23C23×D411yescharacteristic
645Q8—24no—
646Q8—24no—
647Q8—48no—
648Q8—42no—
649Q8—42no—
650Q8—42no—
651Q8—42no—
652Q8—42no—
653Q8—42no—
654Q8—84no—
655D4—216no—
656D4—24no—
657D4—24no—
658D4—24no—
659D4—42no—
660D4—42no—
661D4—42no—
662D4—42no—
663D4—84no—
664D4C2×#12118yes—
665C2×C4—22no—
666C2×C4—28no—
667C2×C4—28no—
668C2×C4—28no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—42no—
686C2×C4—48no—
687C2×C4—42no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4—44no—
691C2×C4—48no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—816no—
707C2×C4—816no—
708C2×C4—816no—
709C2×C4—84no—
710C2×C4—84no—
711C2×C4—84no—
712C2×C4—84no—
713C2×C4C2×#12114yes—
714C2×C4C2×#12114yes—
715C2×C4C2×#12114yes—
716C2×C4C2×#12112yes—
717C2×C4#53714yes—
718C2×C4D4212yes—
719C2×C4#54714yes—
720C2×C4#54812yes—
721C2×C4#55314yes—
722C2×C4C2×#13514yes—
723C2×C4C23×D411yescharacteristic
724C2×C4C23×D411yescharacteristic
725C2×C4C22×#4111yescharacteristic
726C2×C4C22×#4111yescharacteristic
727C2×C4C2×H(5,𝔽2)11yescharacteristic
728C2×C4C2×2−1+411yescharacteristic
729C8—24no—
730C8—42no—
731C8—42no—
732C8—42no—
733C22—28no—
734C22—44no—
735C22—44no—
736C22—44no—
737C22—44no—
738C22—44no—
739C22—432no—
740C22—44no—
741C22—82no—
742C22—82no—
743C22—82no—
744C22—82no—
745C22—82no—
746C22—82no—
747C22—82no—
748C22—168no—
749C22#241614yes—
750C22#303514yes—
751C22#304214yes—
752C22#327514yes—
753C22#328214yes—
754C22#336014yes—
755C22#337614yes—
756C22C22×#12111yescharacteristic
757C22C2×D4211yescharacteristic
758C22C2×#54811yescharacteristic
759C22C22×#13511yescharacteristic
760C22C2×#57511yescharacteristic
761C22C2×#57711yescharacteristic
762C22C2×#57711yescharacteristic
763C4—24no—
764C4—24no—
765C4—24no—
766C4—44no—
767C4—42no—
768C4—42no—
769C4—44no—
770C4—42no—
771C4—82no—
772C4—82no—
773C4—82no—
774C4—82no—
775C4#241614yes—
776C4C22×#12111yescharacteristic
777C4C2×#53711yescharacteristic
778C4C2×#54711yescharacteristic
779C4C2×#55311yescharacteristic
780C2—48no—
781C2—162no—
782C2#2473718yesdirect product factor
783C2C2×#241611yescharacteristic
784C2C2×#303511yescharacteristic
785C2C2×#304211yescharacteristic
786C2C2×#327511yescharacteristic
787C2C2×#328211yescharacteristic
788C2C2×#336011yescharacteristic
789C2C2×#337611yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×D8C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C22×#461C2semidirect
4. C22×C4×SD16C2semidirect
5. C2×#2545C2semidirect
6. C2×#2349C2semidirect
7. #24737C2direct (N × H)
8. C2×#2066C2semidirect
9. C2×#2065C2semidirect
10. C2×#2043C2semidirect
11. C2×#2042C2semidirect
12. C2×#1958C2semidirect
13. C2×#1939C2semidirect
15. C2×#1877C2semidirect
16. C2×#1805C2semidirect
32. C2×#461C22semidirect
34. C2×C4×SD16C22semidirect
51. #2545C22semidirect
55. #2349C22semidirect
68. #2066C22semidirect
69. #2065C22semidirect
70. #2043C22semidirect
71. #2042C22semidirect
72. #1958C22semidirect
73. #1939C22semidirect
75. #1877C22semidirect
76. #1805C22semidirect
782. C2#24737direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4632
C22×#4612
C22×C4×SD162
C2×#25452
C2×#23492
#247372
C2×#20662
C2×#20652
C2×#20432
C2×#20422
C2×#19582
C2×#19392
C2×#18792
C2×#18772
C2×#18052