Finite Group Databasebeta

← C2×#26202 #6441817

Subgroups — C2×#26202 #6441817

Order 512.

2808 conjugacy classes of subgroups.

The subgroup lattice has 781 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2416C211yesmaximal, characteristic
2C2×D4×C4⋊C4C211yesmaximal, characteristic, complemented
3#26202C2116yesmaximal, direct product factor
4C2×#2100C211yesmaximal, characteristic, complemented
5C2×#2077C211yesmaximal, characteristic, complemented
6C2×#2071C211yesmaximal, characteristic, complemented
7C2×#2034C211yesmaximal, characteristic, complemented
8C2×#1926C211yesmaximal, characteristic, complemented
9C2×#1919C211yesmaximal, characteristic, complemented
10C2×#1893C211yesmaximal, characteristic, complemented
11C2×#1874C211yesmaximal, characteristic, complemented
12C2×#1874C211yesmaximal, characteristic, complemented
13C2×#1869C211yesmaximal, characteristic, complemented
14C2×#1853C211yesmaximal, characteristic, complemented
15C2×#1824C211yesmaximal, characteristic, complemented
16C22×#340C211yesmaximal, characteristic, complemented
17C24×C8C2211yescharacteristic
18C22×#121—21no—
19C22×#121C2211yescharacteristic
20C22×#121C2211yescharacteristic
21C22×C4×D4—21no—
22C22×C4×D4C2211yescharacteristic
23C23×C4⋊C4C2211yescharacteristic
24C23×C4⋊C4C2211yescharacteristic
25C23×C4⋊C4C2211yescharacteristic
26C22×#106C2211yescharacteristic
27C22×#106C2211yescharacteristic
28C22×#102C2211yescharacteristic
29C22×#102C2211yescharacteristic
30C22×#102C2211yescharacteristic
31C22×#102C2211yescharacteristic
32C22×C22⋊C8C2211yescharacteristic
33C22×C22⋊C8C2211yescharacteristic
34C22×C22⋊C8C2211yescharacteristic
35#2416—24no—
36#2416C2218yes—
37C2×#396—21no—
38C2×#394—21no—
39D4×C4⋊C4—24no—
40D4×C4⋊C4C2218yescomplemented
41C2×#390C2211yescharacteristic
42C2×#389—21no—
43C2×#389C2211yescharacteristic
44C2×#386—21no—
45C2×#385—21no—
46C2×#385—21no—
47C2×#384C2211yescharacteristic
48C2×#380C2211yescharacteristic
49C2×#380C2211yescharacteristic
50C2×#380C2211yescharacteristic
51C2×C4×C4⋊C4C2211yescharacteristic
52#2100C2218yescomplemented
53#2077C2218yescomplemented
54#2071C2218yescomplemented
55#2034C2218yescomplemented
56#1926C2218yescomplemented
57#1919C2218yescomplemented
58#1893C2218yescomplemented
59#1874C2218yescomplemented
60#1874C2218yescomplemented
61#1869C2218yescomplemented
62#1853C2218yescomplemented
63#1824C2218yescomplemented
64C2×#340C2211yescharacteristic
65C2×#340C2211yescharacteristic
66C2×#340C2211yescharacteristic
67C2×#340C2211yescharacteristic
68C2×#340C2211yescharacteristic
69C2×#340C2211yescharacteristic
70C2×#340C2211yescharacteristic
71C2×#340C2211yescharacteristic
72C2×#340C2211yescharacteristic
73C2×#340C2211yescharacteristic
74C2×#340C2218yescomplemented
75C2×#336C2211yescharacteristic
76C2×#336C2211yescharacteristic
77C23×D4—21no—
78C23×D4—21no—
79C23×D4D411yescharacteristic
80C23×D4C2311yescharacteristic
81C24×C4—21no—
82C24×C4—21no—
83C24×C4—21no—
84C24×C4C2311yescharacteristic
85C24×C4C2311yescharacteristic
86C23×C8—24no—
87C23×C8—42no—
88C23×C8—42no—
89C23×C8C2311yescharacteristic
90C23×C8C2311yescharacteristic
91C23×C8C2311yescharacteristic
92C23×C8C2311yescharacteristic
93C23×C8C2314yes—
94C2×#121—28no—
95C2×#121—22no—
96C2×#121—22no—
97C2×#121—24no—
98C2×#121—24no—
99C2×#121—24no—
100C2×#121—42no—
101C2×#121—48no—
102C2×#121C2314yes—
103C2×#121C2314yes—
104C2×C4×D4—24no—
105C2×C4×D4—24no—
106C2×C4×D4—28no—
107C2×C4×D4—48no—
108C2×C4×D4D414yes—
109C2×C4×D4C2314yes—
110C22×C4⋊C4—24no—
111C22×C4⋊C4—24no—
112C22×C4⋊C4—24no—
113C22×C4⋊C4—22no—
114C22×C4⋊C4—22no—
115C22×C4⋊C4—21no—
116C22×C4⋊C4—21no—
117C22×C4⋊C4—22no—
118C22×C4⋊C4—21no—
119C22×C4⋊C4—21no—
120C22×C4⋊C4—21no—
121C22×C4⋊C4—21no—
122C22×C4⋊C4—42no—
123C22×C4⋊C4—42no—
124C22×C4⋊C4—42no—
125C22×C4⋊C4D411yescharacteristic
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2314yes—
132C22×C4⋊C4C2314yes—
133C22×C4⋊C4C2314yes—
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2311yescharacteristic
136C22×C22⋊C4—21no—
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⋊C4D411yescharacteristic
144C22×C22⋊C4D411yescharacteristic
145C22×C42—21no—
146C22×C42C2311yescharacteristic
147C2×#106—24no—
148C2×#106—42no—
149C2×#106C2314yes—
150C2×#106C2314yes—
151C2×#102—24no—
152C2×#102—42no—
153C2×#102—42no—
154C2×#102—42no—
155C2×#102C2314yes—
156C2×#102C2314yes—
157C2×#102C2314yes—
158C2×#102C2314yes—
159C2×C22⋊C8—24no—
160C2×C22⋊C8—42no—
161C2×C22⋊C8—42no—
162C2×C22⋊C8C2314yes—
163C2×C22⋊C8C2314yes—
164C2×C22⋊C8C2314yes—
165#396—28no—
166#394—28no—
167#390—22no—
168#390C2314yes—
169#389—28no—
170#389—22no—
171#389C2314yes—
172#386—28no—
173#385—28no—
174#385—28no—
175#384—22no—
176#384C2314yes—
177#380—22no—
178#380—22no—
179#380—22no—
180#380C2314yes—
181#380C2314yes—
182#380C2314yes—
183C4×C4⋊C4—22no—
184C4×C4⋊C4C2314yes—
185C2×#95—21no—
186C2×#95—21no—
187C2×#95—21no—
188C2×#95—21no—
189C2×#95—21no—
190#340C2314yes—
191#340C2314yes—
192#340C2314yes—
193#340C2314yes—
194#340C2314yes—
195#340C2314yes—
196#340C2314yes—
197#340C2314yes—
198#340C2314yes—
199#340C2314yes—
200#336C2314yes—
201#336C2314yes—
202C25—21no—
203C25C2×D411yescharacteristic
204C25C2×D411yescharacteristic
205C22×D4—24no—
206C22×D4—24no—
207C22×D4—24no—
208C22×D4—24no—
209C22×D4—21no—
210C22×D4—22no—
211C22×D4—22no—
212C22×D4—22no—
213C22×D4—22no—
214C22×D4—22no—
215C22×D4—22no—
216C22×D4—44no—
217C22×D4—44no—
218C22×D4—44no—
219C22×D4—44no—
220C22×D4—44no—
221C22×D4—82no—
222C22×D4SD1618yes—
223C22×D4C2×D414yes—
224C22×D4C2412yes—
225C23×C4—22no—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—21no—
230C23×C4—21no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—21no—
238C23×C4—21no—
239C23×C4—21no—
240C23×C4—21no—
241C23×C4—21no—
242C23×C4—24no—
243C23×C4—24no—
244C23×C4—24no—
245C23×C4—44no—
246C23×C4—44no—
247C23×C4—44no—
248C23×C4—44no—
249C23×C4—44no—
250C23×C4—44no—
251C23×C4—82no—
252C23×C4—82no—
253C23×C4—82no—
254C23×C4C2×D412yes—
255C23×C4C2×D411yescharacteristic
256C23×C4C2×D411yescharacteristic
257C23×C4C2×D412yes—
258C23×C4C2×D411yescharacteristic
259C23×C4C2×D411yescharacteristic
260C23×C4#4114yes—
261C23×C4#4114yes—
262C23×C4C2412yes—
263C23×C4C2412yes—
264C23×C4C2411yescharacteristic
265C22×C8—28no—
266C22×C8—22no—
267C22×C8—22no—
268C22×C8—22no—
269C22×C8—22no—
270C22×C8—22no—
271C22×C8—22no—
272C22×C8—22no—
273C22×C8—22no—
274C22×C8—22no—
275C22×C8—22no—
276C22×C8—22no—
277C22×C8—22no—
278C22×C8—44no—
279C22×C8—44no—
280C22×C8—416no—
281C22×C8C2412yes—
282C22×C8C2412yes—
283C22×C8C2412yes—
284C22×C8C2412yes—
285#121—28no—
286#121—28no—
287#121—28no—
288#121—44no—
289#121—48no—
290#121—432no—
291#121—48no—
292C4×D4—216no—
293C4×D4—28no—
294C4×D4—28no—
295C4×D4—432no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—28no—
312C2×C4⋊C4—28no—
313C2×C4⋊C4—28no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—44no—
326C2×C4⋊C4—44no—
327C2×C4⋊C4—44no—
328C2×C4⋊C4—48no—
329C2×C4⋊C4—48no—
330C2×C4⋊C4—48no—
331C2×C4⋊C4—44no—
332C2×C4⋊C4—44no—
333C2×C4⋊C4—44no—
334C2×C4⋊C4—44no—
335C2×C4⋊C4—44no—
336C2×C4⋊C4—82no—
337C2×C4⋊C4C2×D414yes—
338C2×C4⋊C4#4114yes—
339C2×C4⋊C4#4114yes—
340C2×C4⋊C4C2412yes—
341C2×C4⋊C4C2412yes—
342C2×C4⋊C4C2412yes—
343C2×C4⋊C4C2412yes—
344C2×C4⋊C4C2412yes—
345C2×C4⋊C4C2412yes—
346C2×C4⋊C4C2412yes—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—44no—
357C2×C22⋊C4—44no—
358C2×C22⋊C4—44no—
359C2×C22⋊C4—44no—
360C2×C22⋊C4—44no—
361C2×C22⋊C4—44no—
362C2×C22⋊C4—82no—
363C2×C22⋊C4C2×D414yes—
364C2×C22⋊C4C2×D414yes—
365C2×C42—22no—
366C2×C42—22no—
367C2×C42—24no—
368C2×C42—44no—
369C2×C42C2×D412yes—
370C2×C42C2412yes—
371#106—28no—
372#106—44no—
373#102—28no—
374#102—44no—
375#102—44no—
376#102—44no—
377C22⋊C8—28no—
378C22⋊C8—44no—
379C22⋊C8—44no—
380#95—24no—
381#95—24no—
382#95—24no—
383#95—24no—
384#95—24no—
385C24—22no—
386C24—22no—
387C24—22no—
388C24—22no—
389C24—22no—
390C24—22no—
391C24—22no—
392C24—22no—
393C24—22no—
394C24—22no—
395C24—22no—
396C24—42no—
397C24—42no—
398C24—42no—
399C24—42no—
400C24—42no—
401C24—42no—
402C24—42no—
403C24#12314yes—
404C24C2×SD1614yes—
405C24C2×SD1614yes—
406C24AGL(1,ℤ/8)14yes—
407C24C22×D412yes—
408C24C22×D412yes—
409C24C22×D411yescharacteristic
410C2×D4—28no—
411C2×D4—28no—
412C2×D4—232no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—48no—
420C2×D4—48no—
421C2×D4—48no—
422C2×D4—48no—
423C2×D4—48no—
424C2×D4—42no—
425C2×D4—44no—
426C2×D4—44no—
427C2×D4—42no—
428C2×D4—42no—
429C2×D4—44no—
430C2×D4—44no—
431C2×D4—84no—
432C2×D4—816no—
433C2×D4—816no—
434C2×D4C2×SD16116yes—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—28no—
440C22×C4—28no—
441C22×C4—24no—
442C22×C4—24no—
443C22×C4—28no—
444C22×C4—28no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—24no—
453C22×C4—24no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—24no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—48no—
474C22×C4—48no—
475C22×C4—48no—
476C22×C4—42no—
477C22×C4—42no—
478C22×C4—42no—
479C22×C4—42no—
480C22×C4—44no—
481C22×C4—44no—
482C22×C4—44no—
483C22×C4—44no—
484C22×C4—48no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—48no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—48no—
497C22×C4—42no—
498C22×C4—42no—
499C22×C4—42no—
500C22×C4—42no—
501C22×C4—42no—
502C22×C4—84no—
503C22×C4—84no—
504C22×C4—84no—
505C22×C4—816no—
506C22×C4—816no—
507C22×C4—816no—
508C22×C4#12314yes—
509C22×C4#12318yes—
510C22×C4C2×SD1614yes—
511C22×C4C22×D412yes—
512C22×C4C22×D412yes—
513C22×C4C22×D412yes—
514C22×C4C22×D412yes—
515C22×C4C22×D411yescharacteristic
516C22×C4C2×#4114yes—
517C22×C4C2×#4114yes—
518C22×C4C2×#4112yes—
519C22×C4C2×#4112yes—
520C22×C4C2×#4112yes—
521C22×C4C2×#4112yes—
522C22×C4H(5,𝔽2)12yes—
523C22×C4H(5,𝔽2)12yes—
524C22×C4C2511yescharacteristic
525C2×C8—22no—
526C2×C8—22no—
527C2×C8—22no—
528C2×C8—22no—
529C2×C8—22no—
530C2×C8—22no—
531C2×C8—22no—
532C2×C8—22no—
533C2×C8—22no—
534C2×C8—22no—
535C2×C8—22no—
536C2×C8—22no—
537C2×C8—416no—
538C2×C8—44no—
539C2×C8—44no—
540C2×C8—44no—
541C2×C8—44no—
542C4⋊C4—28no—
543C4⋊C4—24no—
544C4⋊C4—24no—
545C4⋊C4—22no—
546C4⋊C4—22no—
547C4⋊C4—22no—
548C4⋊C4—22no—
549C4⋊C4—22no—
550C4⋊C4—22no—
551C4⋊C4—22no—
552C4⋊C4—22no—
553C4⋊C4—22no—
554C4⋊C4—22no—
555C4⋊C4—22no—
556C4⋊C4—22no—
557C4⋊C4—48no—
558C4⋊C4—48no—
559C4⋊C4—48no—
560C4⋊C4—48no—
561C4⋊C4—42no—
562C4⋊C4—42no—
563C4⋊C4—42no—
564C4⋊C4—42no—
565C4⋊C4—42no—
566C4⋊C4—48no—
567C4⋊C4—84no—
568C4⋊C4C2×#4114yes—
569C4⋊C4C2×#4114yes—
570C22⋊C4—28no—
571C22⋊C4—28no—
572C22⋊C4—48no—
573C22⋊C4—48no—
574C22⋊C4—48no—
575C22⋊C4—48no—
576C22⋊C4—48no—
577C22⋊C4—48no—
578C22⋊C4—84no—
579C42—24no—
580C42—22no—
581C42—22no—
582C42—48no—
583C23—28no—
584C23—22no—
585C23—22no—
586C23—28no—
587C23—28no—
588C23—28no—
589C23—28no—
590C23—28no—
591C23—22no—
592C23—22no—
593C23—28no—
594C23—22no—
595C23—22no—
596C23—22no—
597C23—28no—
598C23—28no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—44no—
603C23—44no—
604C23—44no—
605C23—44no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—84no—
614C23—84no—
615C23—84no—
616C23—84no—
617C23—84no—
618C23—84no—
619C23—84no—
620C23#481116yes—
621C23C2×#12314yes—
622C23C2×#12312yes—
623C23#54612yes—
624C23#54612yes—
625C23C22×SD1614yes—
626C23C22×SD1614yes—
627C23C22×SD1612yes—
628C23C2×AGL(1,ℤ/8)14yes—
629C23C2×AGL(1,ℤ/8)12yes—
630C23#57612yes—
631C23#57812yes—
632C23C23×D411yescharacteristic
633D4—232no—
634D4—42no—
635D4—42no—
636D4—42no—
637D4—42no—
638D4—816no—
639D4—816no—
640D4—84no—
641C2×C4—28no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—28no—
646C2×C4—22no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—216no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—44no—
661C2×C4—44no—
662C2×C4—48no—
663C2×C4—48no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—48no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—816no—
689C2×C4—816no—
690C2×C4—816no—
691C2×C4—84no—
692C2×C4—84no—
693C2×C4—84no—
694C2×C4—84no—
695C2×C4—84no—
696C2×C4C2×#12314yes—
697C2×C4C2×#12312yes—
698C2×C4#52914yes—
699C2×C4#53814yes—
700C2×C4#54612yes—
701C2×C4#54612yes—
702C2×C4#55314yes—
703C2×C4#55314yes—
704C2×C4C22×SD1614yes—
705C2×C4C22×#4111yescharacteristic
706C2×C4C22×#4111yescharacteristic
707C2×C4C22×#4111yescharacteristic
708C2×C4C22×#4111yescharacteristic
709C2×C4C2×H(5,𝔽2)11yescharacteristic
710C2×C4C2×H(5,𝔽2)11yescharacteristic
711C8—42no—
712C8—42no—
713C8—42no—
714C8—42no—
715C22—232no—
716C22—24no—
717C22—24no—
718C22—24no—
719C22—24no—
720C22—24no—
721C22—24no—
722C22—24no—
723C22—24no—
724C22—24no—
725C22—416no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—42no—
730C22—82no—
731C22—82no—
732C22—82no—
733C22—82no—
734C22—82no—
735C22—82no—
736C22—82no—
737C22—168no—
738C22#244414yes—
739C22C2×#48118yes—
740C22C2×#48114yes—
741C22#309814yes—
742C22#329514yes—
743C22#329814yes—
744C22#330814yes—
745C22#331814yes—
746C22C22×#12311yescharacteristic
747C22C2×#54611yescharacteristic
748C22C2×#54611yescharacteristic
749C22C23×SD1611yescharacteristic
750C22C22×AGL(1,ℤ/8)11yescharacteristic
751C22C2×#57611yescharacteristic
752C22C2×#57811yescharacteristic
753C4—24no—
754C4—24no—
755C4—42no—
756C4—42no—
757C4—44no—
758C4—44no—
759C4—82no—
760C4—82no—
761C4—82no—
762C4—82no—
763C4—82no—
764C4#244414yes—
765C4C2×#52911yescharacteristic
766C4C2×#53811yescharacteristic
767C4C2×#55311yescharacteristic
768C4C2×#55311yescharacteristic
769C2—28no—
770C2—44no—
771C2—162no—
772C2#2620218yesdirect product factor
773C2C2×#244411yescharacteristic
774C2C22×#48111yescharacteristic
775C2C2×#309811yescharacteristic
776C2C2×#329511yescharacteristic
777C2C2×#329811yescharacteristic
778C2C2×#331811yescharacteristic
779C2C2×#330811yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#2416C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C22×C4×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×D4×C4⋊C4C2semidirect
3. #26202C2direct (N × H)
4. C2×#2100C2semidirect
5. C2×#2077C2semidirect
6. C2×#2071C2semidirect
7. C2×#2034C2semidirect
8. C2×#1926C2semidirect
9. C2×#1919C2semidirect
10. C2×#1893C2semidirect
11. C2×#1874C2semidirect
12. C2×#1874C2semidirect
13. C2×#1869C2semidirect
14. C2×#1853C2semidirect
15. C2×#1824C2semidirect
16. C22×#340C2semidirect
40. D4×C4⋊C4C22semidirect
52. #2100C22semidirect
53. #2077C22semidirect
54. #2071C22semidirect
55. #2034C22semidirect
56. #1926C22semidirect
57. #1919C22semidirect
58. #1893C22semidirect
59. #1874C22semidirect
60. #1874C22semidirect
61. #1869C22semidirect
62. #1853C22semidirect
63. #1824C22semidirect
74. C2×#340C22semidirect
772. C2#26202direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#24162
C2×D4×C4⋊C42
#262022
C2×#21002
C2×#20772
C2×#20712
C2×#20342
C2×#19262
C2×#19192
C2×#18932
C2×#18742
C2×#18692
C2×#18532
C2×#18242
C22×#3402