Finite Group Databasebeta

← C2×#20243891 #26218187

Subgroups — C2×#20243891 #26218187

Order 12032.

1798 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×Dic47C211yesmaximal, characteristic, complemented
2C2×#15689140C211yesmaximal, characteristic, complemented
3C22×#13093951C211yesmaximal, characteristic, complemented
4C2×#15689097C211yesmaximal, characteristic, complemented
5#20243891C218yesmaximal, direct product factor
6C2×#15688895C211yesmaximal, characteristic, complemented
7C2×#15688884C211yesmaximal, characteristic, complemented
8C2×C47×#575C211yesmaximal, characteristic
9C22×#10625329C2211yescharacteristic
10#41×Dic47—22no—
11#41×Dic47—22no—
12#41×Dic47—22no—
13#41×Dic47C2214yescomplemented
14C2×Q8×Dic47—21no—
15C2×D4×Dic47—22no—
16C2×D4×Dic47—21no—
17C2×#13093983—21no—
18C2×#13093983C2211yescharacteristic
19C2×#13093983C2211yescharacteristic
20C22×C4×Dic47—21no—
21C22×C4×Dic47C2211yescharacteristic
22#15689140—22no—
23#15689140C2214yescomplemented
24C2×#13093951—21no—
25C2×#13093951—21no—
26C2×#13093951—22no—
27C2×#13093951—22no—
28C2×#13093951C2214yescomplemented
29#15689097—22no—
30#15689097C2214yescomplemented
31C2×#13093939—22no—
32#15688895C2214yescomplemented
33#15688884C2214yescomplemented
34C22×#41×C47C2211yescharacteristic
35C22×#41×C47C2211yescharacteristic
36C47×#575—22no—
37C47×#575—22no—
38C47×#575C414yescomplemented
39C47×#575C2214yes—
40C2×#137×C47—21no—
41C2×#137×C47C412yescomplemented
42C2×AGL(1,ℤ/8)×C47—21no—
43C2×AGL(1,ℤ/8)×C47C412yescomplemented
44C2×#135×C47—22no—
45C22×M16×C47C2211yescharacteristic
46C23×Dic47—22no—
47C23×Dic47—21no—
48C2×#10625329—21no—
49C2×#10625329—21no—
50C2×#10625329—21no—
51C2×#10625329—21no—
52C2×#10625329—21no—
53C2×#10625329C2312yes—
54C22×C47⋊C8—21no—
55Q8×Dic47—24no—
56Q8×Dic47—24no—
57D4×Dic47—28no—
58D4×Dic47—24no—
59D4×Dic47—24no—
60D4×Dic47—28no—
61#13093983—24no—
62#13093983—21no—
63#13093983—21no—
64#13093983—21no—
65#13093983—24no—
66#13093983—21no—
67#13093983—21no—
68#13093983D412yes—
69#13093983C2312yes—
70#13093983C2312yes—
71C2×C4⋊Dic47—22no—
72C2×C4⋊Dic47—21no—
73C2×C4⋊Dic47—21no—
74C2×C22⋊Dic47—22no—
75C2×C22⋊Dic47—21no—
76C2×C22⋊Dic47D412yes—
77C2×C4×Dic47—22no—
78C2×C4×Dic47—24no—
79C2×C4×Dic47—21no—
80C2×C4×Dic47—21no—
81C2×C4×Dic47—21no—
82C2×C4×Dic47—21no—
83C2×C4×Dic47—24no—
84C2×C4×Dic47—21no—
85C2×C4×Dic47D411yescharacteristic
86C2×C4×Dic47D411yescharacteristic
87C2×C4×Dic47D412yes—
88C2×C4×Dic47C2312yes—
89#13093951—28no—
90#13093951—24no—
91#13093951—24no—
92#13093939—28no—
93C2×#41×C47—21no—
94C2×#41×C47—21no—
95C2×#41×C47—21no—
96C2×#41×C47—21no—
97C2×#41×C47—21no—
98C2×#41×C47—21no—
99C2×#41×C47—21no—
100C2×#41×C47—21no—
101C2×#41×C47—21no—
102C2×#41×C47—21no—
103C2×#41×C47—21no—
104C2×#41×C47—21no—
105C2×#41×C47—21no—
106C2×#41×C47—21no—
107C2×#41×C47—21no—
108C2×#41×C47—21no—
109C2×#41×C47C2×C412yes—
110C2×#41×C47C2×C412yes—
111C2×#41×C47C2×C412yescomplemented
112C2×#41×C47D412yes—
113C2×#41×C47D412yes—
114C2×#41×C47D412yes—
115C2×#41×C47C2312yes—
116C2×#41×C47C2312yes—
117C22×Q8×C47C2×C411yescharacteristic, complemented
118C22×Q8×C47D411yescharacteristic
119C22×D4×C47—21no—
120C22×D4×C47—21no—
121C22×D4×C47C2×C411yescharacteristic, complemented
122C22×D4×C47D411yescharacteristic
123C23×C4×C47—21no—
124C23×C4×C47—21no—
125C23×C4×C47C2311yescharacteristic
126#137×C47—24no—
127#137×C47—24no—
128#137×C47—24no—
129#137×C47C2×C418yescomplemented
130AGL(1,ℤ/8)×C47—24no—
131AGL(1,ℤ/8)×C47—24no—
132AGL(1,ℤ/8)×C47—24no—
133AGL(1,ℤ/8)×C47C2×C418yescomplemented
134#135×C47—28no—
135#135×C47—28no—
136C2×Q16×C47—22no—
137C2×SD16×C47—22no—
138C2×SD16×C47—22no—
139C2×D8×C47—22no—
140C2×M16×C47—21no—
141C2×M16×C47—21no—
142C2×M16×C47—21no—
143C2×M16×C47C2×C412yescomplemented
144C2×M16×C47C2×C412yescomplemented
145C2×M16×C47C2312yes—
146C22×C8×C47—21no—
147C24×C47—21no—
148C24×C47—21no—
149C24×C47C2×D411yescharacteristic
150#41×C47—22no—
151#41×C47—22no—
152#41×C47—22no—
153#41×C47—22no—
154#41×C47—22no—
155#41×C47—22no—
156#41×C47—22no—
157#41×C47—22no—
158#41×C47—22no—
159#41×C47—22no—
160#41×C47—22no—
161#41×C47—22no—
162#41×C47—22no—
163#41×C47—22no—
164#41×C47—22no—
165#41×C47—22no—
166#41×C47—22no—
167#41×C47—22no—
168#41×C47—22no—
169#41×C47—22no—
170#41×C47—41no—
171#41×C47—41no—
172#41×C47—41no—
173#41×C47—41no—
174#41×C47—41no—
175#41×C47—41no—
176#41×C47—41no—
177#41×C47—41no—
178#41×C47C22⋊C414yes—
179#41×C47C22⋊C414yes—
180#41×C47C22×C414yes—
181#41×C47C2×D414yes—
182C2×Q8×C47—21no—
183C2×Q8×C47—21no—
184C2×Q8×C47—21no—
185C2×Q8×C47—21no—
186C2×Q8×C47—21no—
187C2×Q8×C47—21no—
188C2×Q8×C47—21no—
189C2×Q8×C47—21no—
190C2×Q8×C47C22⋊C412yes—
191C2×Q8×C47C22⋊C412yes—
192C2×Q8×C47C22×C412yescomplemented
193C2×Q8×C47C2×D412yes—
194C2×D4×C47—22no—
195C2×D4×C47—22no—
196C2×D4×C47—22no—
197C2×D4×C47—22no—
198C2×D4×C47—22no—
199C2×D4×C47—22no—
200C2×D4×C47—22no—
201C2×D4×C47—22no—
202C2×D4×C47—21no—
203C2×D4×C47—21no—
204C2×D4×C47—21no—
205C2×D4×C47—21no—
206C2×D4×C47—21no—
207C2×D4×C47—21no—
208C2×D4×C47—21no—
209C2×D4×C47—21no—
210C2×D4×C47—41no—
211C2×D4×C47—41no—
212C2×D4×C47—41no—
213C2×D4×C47—41no—
214C2×D4×C47C22⋊C412yes—
215C2×D4×C47C22⋊C412yes—
216C2×D4×C47C22×C412yescomplemented
217C2×D4×C47C2×D412yes—
218C22×C4×C47—21no—
219C22×C4×C47—22no—
220C22×C4×C47—22no—
221C22×C4×C47—22no—
222C22×C4×C47—22no—
223C22×C4×C47—22no—
224C22×C4×C47—22no—
225C22×C4×C47—21no—
226C22×C4×C47—22no—
227C22×C4×C47—22no—
228C22×C4×C47—41no—
229C22×C4×C47—41no—
230C22×C4×C47—41no—
231C22×C4×C47—41no—
232C22×C4×C47C22×C411yescharacteristic
233C22×C4×C47C22×C411yescharacteristic
234C22×C4×C47C2×D411yescharacteristic
235C22×C4×C47C2×D411yescharacteristic
236C22×C4×C47C2×D411yescharacteristic
237C22×C4×C47C2×D411yescharacteristic
238C22×C4×C47C2×D411yescharacteristic
239C22×C4×C47C2×D411yescharacteristic
240C22×C4×C47C2×D411yescharacteristic
241C22×C4×C47#4111yescharacteristic
242C22×C4×C47#4111yescharacteristic
243C22×C4×C47#4111yescharacteristic
244C22×C4×C47#4111yescharacteristic
245C22×C4×C47C2411yescharacteristic
246C22×Dic47—21no—
247C22×Dic47—28no—
248C22×Dic47—22no—
249C22×Dic47—21no—
250C22×Dic47—22no—
251C22×Dic47—22no—
252C22×Dic47—44no—
253C22×Dic47—48no—
254C22×Dic47—41no—
255Q16×C47—28no—
256SD16×C47—28no—
257SD16×C47—28no—
258D8×C47—28no—
259M16×C47—22no—
260M16×C47—22no—
261M16×C47—22no—
262M16×C47C22×C414yescomplemented
263C2×C8×C47—22no—
264C2×C8×C47—22no—
265C2×C8×C47—22no—
266C22⋊Dic47—28no—
267C22⋊Dic47—22no—
268C22⋊Dic47—22no—
269C22⋊Dic47—41no—
270C22⋊Dic47C2×D414yes—
271C4⋊Dic47—28no—
272C4⋊Dic47—22no—
273C4⋊Dic47—22no—
274C4⋊Dic47—22no—
275C4⋊Dic47—41no—
276C4×Dic47—28no—
277C4×Dic47—21no—
278C4×Dic47—22no—
279C4×Dic47—21no—
280C4×Dic47—22no—
281C4×Dic47—22no—
282C4×Dic47—22no—
283C4×Dic47—22no—
284C4×Dic47—41no—
285C4×Dic47C2×D412yes—
286C4×Dic47C2×D412yes—
287#10625329—22no—
288#10625329—22no—
289#10625329—41no—
290#10625329—41no—
291C2×C47⋊C8—22no—
292C2×C47⋊C8—41no—
293C2×C47⋊C8—41no—
294C23×C47—22no—
295C23×C47—22no—
296C23×C47—22no—
297C23×C47—22no—
298C23×C47—42no—
299C23×C47—44no—
300C23×C47—41no—
301C23×C47—41no—
302C23×C47—82no—
303C23×C47C4×D411yescharacteristic
304C23×C47C4×D411yescharacteristic
305C23×C47#12011yescharacteristic
306C23×C47#12011yescharacteristic
307C23×C47#12111yescharacteristic
308C23×C47#12111yescharacteristic
309C23×C47C22×D411yescharacteristic
310Q8×C47—22no—
311Q8×C47—22no—
312Q8×C47—22no—
313Q8×C47—22no—
314Q8×C47—22no—
315Q8×C47—41no—
316Q8×C47—41no—
317Q8×C47C2×C22⋊C414yes—
318D4×C47—24no—
319D4×C47—24no—
320D4×C47—24no—
321D4×C47—24no—
322D4×C47—22no—
323D4×C47—22no—
324D4×C47—22no—
325D4×C47—22no—
326D4×C47—22no—
327D4×C47—42no—
328D4×C47—42no—
329D4×C47—42no—
330D4×C47—42no—
331D4×C47—41no—
332D4×C47—41no—
333D4×C47C2×C22⋊C414yes—
334C2×C4×C47—22no—
335C2×C4×C47—22no—
336C2×C4×C47—22no—
337C2×C4×C47—24no—
338C2×C4×C47—24no—
339C2×C4×C47—24no—
340C2×C4×C47—24no—
341C2×C4×C47—22no—
342C2×C4×C47—41no—
343C2×C4×C47—41no—
344C2×C4×C47—42no—
345C2×C4×C47—42no—
346C2×C4×C47—42no—
347C2×C4×C47—42no—
348C2×C4×C47C2×C22⋊C411yescharacteristic
349C2×C4×C47C2×C22⋊C411yescharacteristic
350C2×C4×C47C2×C22⋊C411yescharacteristic
351C2×C4×C47C2×C22⋊C411yescharacteristic
352C2×C4×C47C4×D411yescharacteristic
353C2×C4×C47C4×D411yescharacteristic
354C2×C4×C47C4×D411yescharacteristic
355C2×C4×C47C4×D411yescharacteristic
356C2×C4×C47C4×D411yescharacteristic
357C2×C4×C47C4×D411yescharacteristic
358C2×C4×C47#12011yescharacteristic
359C2×C4×C47#12011yescharacteristic
360C2×C4×C47#12111yescharacteristic
361C2×C4×C47#12111yescharacteristic
362C2×C4×C47#12111yescharacteristic
363C2×C4×C47#12111yescharacteristic
364C2×C4×C47#12111yescharacteristic
365C2×C4×C47#12111yescharacteristic
366C2×C4×C47#12311yescharacteristic
367C2×C4×C47#12311yescharacteristic
368C2×C4×C47#12311yescharacteristic
369C2×C4×C47#12311yescharacteristic
370C2×C4×C47C23×C411yescharacteristic
371C2×C4×C47C22×D411yescharacteristic
372C2×C4×C47C22×D411yescharacteristic
373C2×C4×C47C22×D411yescharacteristic
374C2×C4×C47C2×#4111yescharacteristic
375C2×C4×C47C2×#4111yescharacteristic
376C2×Dic47—24no—
377C2×Dic47—22no—
378C2×Dic47—24no—
379C2×Dic47—22no—
380C2×Dic47—44no—
381C2×Dic47—44no—
382C2×Dic47—416no—
383C2×Dic47—44no—
384C2×Dic47—42no—
385C2×Dic47—42no—
386C2×Dic47—82no—
387C8×C47—24no—
388C47⋊C8—42no—
389C2×#1906—471nomaximal, Sylow
390C22×C47—22no—
391C22×C47—22no—
392C22×C47—22no—
393C22×C47—24no—
394C22×C47—41no—
395C22×C47—41no—
396C22×C47—41no—
397C22×C47—41no—
398C22×C47—44no—
399C22×C47—44no—
400C22×C47—44no—
401C22×C47—42no—
402C22×C47—82no—
403C22×C47—82no—
404C22×C47—82no—
405C22×C47#38611yescharacteristic
406C22×C47#38611yescharacteristic
407C22×C47#38611yescharacteristic
408C22×C47#38611yescharacteristic
409C22×C47C2×C4×D411yescharacteristic
410C22×C47C2×#12011yescharacteristic
411C22×C47C2×#12111yescharacteristic
412C4×C47—24no—
413C4×C47—42no—
414C4×C47#38611yescharacteristic
415C4×C47#38611yescharacteristic
416C4×C47#38611yescharacteristic
417C4×C47#38611yescharacteristic
418C4×C47C22×C22⋊C411yescharacteristic
419C4×C47C2×C4×D411yescharacteristic
420C4×C47C2×#12111yescharacteristic
421C4×C47C2×#12311yescharacteristic
422Dic47—24no—
423Dic47—44no—
424Dic47—42no—
425Dic47—82no—
426C2×#575D4711yescharacteristic
427C2×C4×#41—471no—
428C2×#421—471no—
429C22×#104—471no—
430C2×#410—471no—
431#1906—478no—
432C2×#344—471no—
433C2×#339—471no—
434C2×C47—21no—
435C2×C47—21no—
436C2×C47—21no—
437C2×C47—21no—
438C2×C47—21no—
439C2×C47—21no—
440C2×C47—44no—
441C2×C47—82no—
442C2×C47#190612yescomplemented
443C2×C47C2×#38611yescharacteristic
444C22×#41C2×D4711yescharacteristic
445C22×#41C2×D4711yescharacteristic
446#575—22no—
447#575—22no—
448#575Dic4714yescomplemented
449#575C2×D4714yes—
450C2×#137—21no—
451C2×#137Dic4712yescomplemented
452C2×AGL(1,ℤ/8)—21no—
453C2×AGL(1,ℤ/8)Dic4712yescomplemented
454C2×#135—22no—
455C22×M16—471no—
456C22×M16C2×D4711yescharacteristic
457C4×#41—474no—
458C4×#41—942no—
459C4×#41—942no—
460C4×#41—942no—
461C2×C4×Q8—941no—
462C2×C4×D4—942no—
463C2×C4×D4—941no—
464C2×#117—471no—
465C2×#117—471no—
466C2×#117—941no—
467C22×C42—471no—
468C22×C42—941no—
469#421—474no—
470#421—942no—
471C2×#104—474no—
472C2×#104—941no—
473C2×#104—942no—
474C2×#104—941no—
475C2×#104—942no—
476#410—474no—
477#410—942no—
478C2×#99—942no—
479#344—474no—
480#339—474no—
481C47C2×#190611yescharacteristic, complemented, Sylow
482C2×#41—21no—
483C2×#41—21no—
484C2×#41—21no—
485C2×#41—21no—
486C2×#41—21no—
487C2×#41—21no—
488C2×#41—21no—
489C2×#41—21no—
490C2×#41—21no—
491C2×#41—21no—
492C2×#41—21no—
493C2×#41—21no—
494C2×#41—21no—
495C2×#41—21no—
496C2×#41—21no—
497C2×#41—21no—
498C2×#41C2×Dic4712yes—
499C2×#41C2×Dic4712yes—
500C2×#41C2×Dic4712yescomplemented
501C2×#41C22⋊D4712yes—
502C2×#41C22⋊D4712yes—
503C2×#41C22⋊D4712yes—
504C2×#41C22×D4712yes—
505C2×#41C22×D4712yes—
506C22×Q8C2×Dic4711yescharacteristic, complemented
507C22×Q8C22⋊D4711yescharacteristic
508C22×D4—21no—
509C22×D4—21no—
510C22×D4C2×Dic4711yescharacteristic, complemented
511C22×D4C22⋊D4711yescharacteristic
512C23×C4—21no—
513C23×C4—21no—
514C23×C4—942no—
515C23×C4—941no—
516C23×C4C22×D4711yescharacteristic
517#137—24no—
518#137—24no—
519#137—24no—
520#137C2×Dic4718yescomplemented
521AGL(1,ℤ/8)—24no—
522AGL(1,ℤ/8)—24no—
523AGL(1,ℤ/8)—24no—
524AGL(1,ℤ/8)C2×Dic4718yescomplemented
525#135—28no—
526#135—28no—
527C2×Q16—22no—
528C2×SD16—22no—
529C2×SD16—22no—
530C2×D8—22no—
531C2×M16—21no—
532C2×M16—21no—
533C2×M16—21no—
534C2×M16—472no—
535C2×M16—941no—
536C2×M16—941no—
537C2×M16—941no—
538C2×M16—941no—
539C2×M16—941no—
540C2×M16C2×Dic4712yescomplemented
541C2×M16C2×Dic4712yescomplemented
542C2×M16C22×D4712yes—
543C22×C8—21no—
544C22×C8—941no—
545C4×Q8—944no—
546C4×Q8—944no—
547C4×D4—948no—
548C4×D4—948no—
549C4×D4—944no—
550C4×D4—944no—
551#117—472no—
552#117—472no—
553#117—472no—
554#117—944no—
555#117—944no—
556#117—941no—
557#117—941no—
558#117—941no—
559#117—941no—
560#117—941no—
561C2×C4⋊C4—942no—
562C2×C4⋊C4—941no—
563C2×C4⋊C4—941no—
564C2×C22⋊C4—472no—
565C2×C22⋊C4—942no—
566C2×C22⋊C4—941no—
567C2×C42—471no—
568C2×C42—472no—
569C2×C42—471no—
570C2×C42—472no—
571C2×C42—944no—
572C2×C42—942no—
573C2×C42—944no—
574C2×C42—941no—
575C2×C42—941no—
576C2×C42—941no—
577C2×C42—941no—
578C2×C42—941no—
579#104—944no—
580#104—944no—
581#104—948no—
582#99—948no—
583C24—21no—
584C24—21no—
585C24D4×D4711yescharacteristic
586#41—22no—
587#41—22no—
588#41—22no—
589#41—22no—
590#41—22no—
591#41—22no—
592#41—22no—
593#41—22no—
594#41—22no—
595#41—22no—
596#41—22no—
597#41—22no—
598#41—22no—
599#41—22no—
600#41—22no—
601#41—22no—
602#41—22no—
603#41—22no—
604#41—22no—
605#41—22no—
606#41—41no—
607#41—41no—
608#41—41no—
609#41—41no—
610#41—41no—
611#41—41no—
612#41—41no—
613#41—41no—
614#41C22⋊Dic4714yes—
615#41C22⋊Dic4714yes—
616#41C22×Dic4714yes—
617#41C2×C22⋊D4714yes—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8—21no—
625C2×Q8—21no—
626C2×Q8C22⋊Dic4712yes—
627C2×Q8C22⋊Dic4712yes—
628C2×Q8C22×Dic4712yescomplemented
629C2×Q8C2×C22⋊D4712yes—
630C2×D4—22no—
631C2×D4—22no—
632C2×D4—22no—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—22no—
636C2×D4—22no—
637C2×D4—22no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—41no—
647C2×D4—41no—
648C2×D4—41no—
649C2×D4—41no—
650C2×D4C22⋊Dic4712yes—
651C2×D4C22⋊Dic4712yes—
652C2×D4C22×Dic4712yescomplemented
653C2×D4C2×C22⋊D4712yes—
654C22×C4—21no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—21no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—41no—
665C22×C4—41no—
666C22×C4—41no—
667C22×C4—41no—
668C22×C4—941no—
669C22×C4—948no—
670C22×C4—941no—
671C22×C4—942no—
672C22×C4—942no—
673C22×C4—942no—
674C22×C4—1884no—
675C22×C4—1888no—
676C22×C4—1881no—
677C22×C4D4×D4711yescharacteristic
678C22×C4D4×D4711yescharacteristic
679C22×C4D4×D4711yescharacteristic
680C22×C4#1062535211yescharacteristic
681C22×C4#1062535211yescharacteristic
682C22×C4#1062535211yescharacteristic
683C22×C4#1062535211yescharacteristic
684C22×C4C22×Dic4711yescharacteristic
685C22×C4C22×Dic4711yescharacteristic
686C22×C4C2×C22⋊D4711yescharacteristic
687C22×C4C2×C22⋊D4711yescharacteristic
688C22×C4C2×C22⋊D4711yescharacteristic
689C22×C4C2×C22⋊D4711yescharacteristic
690C22×C4C23×D4711yescharacteristic
691Q16—28no—
692SD16—28no—
693SD16—28no—
694D8—28no—
695M16—22no—
696M16—22no—
697M16—22no—
698M16—942no—
699M16—942no—
700M16—1881no—
701M16—1881no—
702M16C22×Dic4714yescomplemented
703C2×C8—22no—
704C2×C8—22no—
705C2×C8—22no—
706C2×C8—942no—
707C2×C8—1881no—
708C2×C8—1881no—
709C4⋊C4—948no—
710C4⋊C4—942no—
711C4⋊C4—942no—
712C4⋊C4—942no—
713C4⋊C4—1881no—
714C22⋊C4—474no—
715C22⋊C4—948no—
716C22⋊C4—942no—
717C22⋊C4—942no—
718C22⋊C4—1881no—
719C42—472no—
720C42—472no—
721C42—948no—
722C42—941no—
723C42—941no—
724C42—942no—
725C42—942no—
726C42—942no—
727C42—942no—
728C42—942no—
729C42—1881no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—42no—
735C23—44no—
736C23—41no—
737C23—41no—
738C23—82no—
739C23D4×Dic4711yescharacteristic
740C23D4×Dic4711yescharacteristic
741C23#1309399211yescharacteristic
742C23#1309399211yescharacteristic
743C23#1309399611yescharacteristic
744C23#1309399611yescharacteristic
745C23C2×D4×D4711yescharacteristic
746Q8—22no—
747Q8—22no—
748Q8—22no—
749Q8—22no—
750Q8—22no—
751Q8—41no—
752Q8—41no—
753Q8C2×C22⋊Dic4714yes—
754D4—24no—
755D4—24no—
756D4—24no—
757D4—24no—
758D4—22no—
759D4—22no—
760D4—22no—
761D4—22no—
762D4—22no—
763D4—42no—
764D4—42no—
765D4—42no—
766D4—42no—
767D4—41no—
768D4—41no—
769D4C2×C22⋊Dic4714yes—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—22no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—944no—
785C2×C4—942no—
786C2×C4—942no—
787C2×C4—944no—
788C2×C4—3762no—
789C2×C4—1884no—
790C2×C4—1884no—
791C2×C4—18816no—
792C2×C4—1882no—
793C2×C4—1882no—
794C2×C4—1884no—
795C2×C4C2×C22⋊Dic4711yescharacteristic
796C2×C4C2×C22⋊Dic4711yescharacteristic
797C2×C4C2×C22⋊Dic4711yescharacteristic
798C2×C4C2×C22⋊Dic4711yescharacteristic
799C2×C4D4×Dic4711yescharacteristic
800C2×C4D4×Dic4711yescharacteristic
801C2×C4D4×Dic4711yescharacteristic
802C2×C4D4×Dic4711yescharacteristic
803C2×C4D4×Dic4711yescharacteristic
804C2×C4D4×Dic4711yescharacteristic
805C2×C4#1309399211yescharacteristic
806C2×C4#1309399211yescharacteristic
807C2×C4#1309399611yescharacteristic
808C2×C4#1309399611yescharacteristic
809C2×C4#1309399611yescharacteristic
810C2×C4#1309399611yescharacteristic
811C2×C4#1309399611yescharacteristic
812C2×C4#1309399611yescharacteristic
813C2×C4#1309400511yescharacteristic
814C2×C4#1309400511yescharacteristic
815C2×C4#1309400511yescharacteristic
816C2×C4#1309400511yescharacteristic
817C2×C4C23×Dic4711yescharacteristic
818C2×C4C2×D4×D4711yescharacteristic
819C2×C4C22×C22⋊D4711yescharacteristic
820C2×C4C22×C22⋊D4711yescharacteristic
821C2×C4C2×#1062535211yescharacteristic
822C2×C4C2×#1062535211yescharacteristic
823C8—24no—
824C8—1882no—
825C22—22no—
826C22—22no—
827C22—22no—
828C22—24no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—44no—
834C22—44no—
835C22—44no—
836C22—42no—
837C22—82no—
838C22—82no—
839C22—82no—
840C22#1568900311yescharacteristic
841C22#1568900311yescharacteristic
842C22#1568900311yescharacteristic
843C22#1568900311yescharacteristic
844C22C2×D4×Dic4711yescharacteristic
845C22C2×#1309399211yescharacteristic
846C22C2×#1309399611yescharacteristic
847C4—24no—
848C4—42no—
849C4—944no—
850C4—3762no—
851C4—1882no—
852C4—1884no—
853C4#1568900311yescharacteristic
854C4#1568900311yescharacteristic
855C4#1568900311yescharacteristic
856C4#1568900311yescharacteristic
857C4C22×C22⋊Dic4711yescharacteristic
858C4C2×D4×Dic4711yescharacteristic
859C4C2×#1309399611yescharacteristic
860C4C2×#1309400511yescharacteristic
861C2—21no—
862C2—21no—
863C2—21no—
864C2—21no—
865C2—21no—
866C2—21no—
867C2—44no—
868C2—82no—
869C2#2024389112yesdirect product factor
870C2C2×#1568900311yescharacteristic
subgroupG/H
centerC2×C4#13093996
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
Fitting, prime radicalC2×C47×#575C2
socleC22×C47#386
cosocleC22×C4×C47C24
hypercenterC2×#575D47
hypocenterC47C2×#1906
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#575

Complements

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

NH ≅ G/Ntype
1. C2×#41×Dic47C2semidirect
2. C2×#15689140C2semidirect
3. C22×#13093951C2semidirect
4. C2×#15689097C2semidirect
5. #20243891C2direct (N × H)
6. C2×#15688895C2semidirect
7. C2×#15688884C2semidirect
13. #41×Dic47C22semidirect
23. #15689140C22semidirect
28. C2×#13093951C22semidirect
30. #15689097C22semidirect
32. #15688895C22semidirect
33. #15688884C22semidirect
38. C47×#575C4semidirect
41. C2×#137×C47C4semidirect
43. C2×AGL(1,ℤ/8)×C47C4semidirect
111. C2×#41×C47C2×C4semidirect
117. C22×Q8×C47C2×C4semidirect
121. C22×D4×C47C2×C4semidirect
129. #137×C47C2×C4semidirect
133. AGL(1,ℤ/8)×C47C2×C4semidirect
143. C2×M16×C47C2×C4semidirect
144. C2×M16×C47C2×C4semidirect
192. C2×Q8×C47C22×C4semidirect
216. C2×D4×C47C22×C4semidirect
262. M16×C47C22×C4semidirect
442. C2×C47#1906semidirect
448. #575Dic47semidirect
451. C2×#137Dic47semidirect
453. C2×AGL(1,ℤ/8)Dic47semidirect
481. C47C2×#1906semidirect
500. C2×#41C2×Dic47semidirect
506. C22×Q8C2×Dic47semidirect
510. C22×D4C2×Dic47semidirect
520. #137C2×Dic47semidirect
524. AGL(1,ℤ/8)C2×Dic47semidirect
540. C2×M16C2×Dic47semidirect
541. C2×M16C2×Dic47semidirect
628. C2×Q8C22×Dic47semidirect
652. C2×D4C22×Dic47semidirect
702. M16C22×Dic47semidirect
869. C2#20243891direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#41×Dic472
C2×#156891402
C22×#130939512
C2×#156890972
#202438912
C2×#156888952
C2×#156888842
C2×C47×#5752
C2×#190647