Finite Group Databasebeta

← C2×#20243876 #26218161

Subgroups — C2×#20243876 #26218161

Order 12032.

1894 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094052C211yesmaximal, characteristic
2C2×#15689597C211yesmaximal, characteristic, complemented
3C2×#15689141C211yesmaximal, characteristic, complemented
4C2×#15689127C211yesmaximal, characteristic, complemented
5C2×#15689096C211yesmaximal, characteristic, complemented
6#20243876C218yesmaximal, direct product factor
7C2×#15688894C211yesmaximal, characteristic, complemented
8C2×C47×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
9C22×#10625350C2211yescharacteristic
10C23×D188C2211yescharacteristic
11C2×#13094052—22no—
12C2×#13094052—22no—
13C2×#13094052—22no—
14C2×#13094052—22no—
15C2×#13094052C414yescomplemented
16C2×#13094052C2214yes—
17C22×#10625325C412yescomplemented
18C22×D376C412yescomplemented
19C22×#10625329C2211yescharacteristic
20#15689597—22no—
21#15689597—22no—
22#15689597—22no—
23#15689597C2214yescomplemented
24C2×C4×D188—22no—
25C2×#13093986—22no—
26C2×#13093983C2211yescharacteristic
27C2×C22⋊C4×D47—22no—
28#15689141—22no—
29#15689141C2214yescomplemented
30C2×#13093952—22no—
31#15689127—22no—
32#15689127C2214yescomplemented
33C2×#13093944—22no—
34#15689096—22no—
35#15689096C2214yescomplemented
36C2×#13093938—22no—
37#15688894C2214yescomplemented
38C22×M16×C47C2211yescharacteristic
39C2×#117×C47C2211yescharacteristic
40C2×#117×C47C2211yescharacteristic
41C47×H(3,ℤ/4)C2214yescomplemented
42C24×D47—21no—
43C2×#10625350—21no—
44C2×#10625350—21no—
45C2×#10625350—21no—
46C2×#10625350—21no—
47C2×#10625350—21no—
48C2×#10625350—21no—
49C2×#10625350—21no—
50C2×#10625350—21no—
51C2×#10625350—21no—
52C2×#10625350—21no—
53C2×#10625350C2×C412yescomplemented
54C2×#10625350C2312yes—
55C22×Dic94C2×C411yescharacteristic, complemented
56C22×D188—21no—
57C22×D188—21no—
58C22×D188—21no—
59C22×D188—21no—
60C22×D188—21no—
61C22×D188—21no—
62C22×D188—21no—
63C22×D188C2×C412yes—
64C22×D188C2×C412yes—
65C22×D188C2×C411yescharacteristic, complemented
66C22×D188D412yes—
67C22×D188D412yes—
68C22×D188D412yes—
69C22×D188D412yes—
70C22×D188C2312yes—
71C22×C22⋊D47—21no—
72C22×C4×D47—21no—
73C22×C4×D47—24no—
74#13094052—28no—
75#13094052—28no—
76#13094052—28no—
77#13094052—28no—
78C2×#10625325—24no—
79C2×#10625325—24no—
80C2×#10625325C2×C418yescomplemented
81C2×D376—24no—
82C2×D376—24no—
83C2×D376C2×C418yescomplemented
84C2×#10625329—21no—
85C2×#10625329—21no—
86C2×#10625329—21no—
87C2×#10625329—21no—
88C2×#10625329—21no—
89C2×#10625329C2312yes—
90C22×C47⋊C8—21no—
91C4×D188—28no—
92C4×D188—28no—
93#13093986—28no—
94#13093986—28no—
95#13093983—21no—
96#13093983—21no—
97#13093983D412yes—
98#13093983C2312yes—
99C2×C4⋊Dic47—21no—
100C2×C22⋊Dic47D412yes—
101C2×(C2×D47)⋊C4—24no—
102C22⋊C4×D47—28no—
103C22⋊C4×D47—28no—
104C2×C4×Dic47—21no—
105#13093952—28no—
106#13093944—28no—
107#13093938—28no—
108C23×C4×C47C2311yescharacteristic
109C2×M16×C47—21no—
110C2×M16×C47—21no—
111C2×M16×C47—21no—
112C2×M16×C47—21no—
113C2×M16×C47C2×C412yescomplemented
114C2×M16×C47C2312yes—
115C22×C8×C47C2×C412yescomplemented
116#117×C47—21no—
117#117×C47—21no—
118#117×C47—21no—
119#117×C47—21no—
120#117×C47—21no—
121#117×C47D412yes—
122#117×C47C2312yes—
123#117×C47C2312yes—
124C2×C4⋊C4×C47—21no—
125C2×C4⋊C4×C47—21no—
126C2×C22⋊C4×C47—21no—
127C2×C22⋊C4×C47—21no—
128C2×C42×C47—21no—
129C2×C42×C47D412yes—
130C24×C47C2×D411yescharacteristic
131C23×D47—22no—
132C23×D47—22no—
133C23×D47—22no—
134C23×D47—22no—
135C23×D47—22no—
136C23×D47—22no—
137C23×D47—22no—
138C23×D47—21no—
139C23×D47—84no—
140C22×C4×C47—22no—
141C22×C4×C47—41no—
142C22×C4×C47C22×C411yescharacteristic
143C22×C4×C47C22×C411yescharacteristic
144C22×C4×C47C2×D411yescharacteristic
145C22×C4×C47C2×D411yescharacteristic
146C22×C4×C47C2×D411yescharacteristic
147C22×C4×C47C2×D411yescharacteristic
148C22×C4×C47C2×D411yescharacteristic
149C22×C4×C47C2×D411yescharacteristic
150C22×C4×C47C2×D411yescharacteristic
151C22×C4×C47#4111yescharacteristic
152C22×C4×C47#4111yescharacteristic
153C22×C4×C47#4111yescharacteristic
154C22×C4×C47#4111yescharacteristic
155C22×C4×C47C2411yescharacteristic
156C2×C22⋊D47—22no—
157C2×C22⋊D47—22no—
158C2×C22⋊D47—41no—
159C2×C22⋊D47—41no—
160C2×C22⋊D47—41no—
161C2×C22⋊D47—41no—
162C22×Dic47—21no—
163C22×Dic47—22no—
164#10625350—22no—
165#10625350—22no—
166#10625350—22no—
167#10625350—22no—
168#10625350—22no—
169#10625350—22no—
170#10625350—22no—
171#10625350—22no—
172#10625350—41no—
173#10625350—41no—
174#10625350—41no—
175#10625350—41no—
176#10625350—41no—
177#10625350—41no—
178#10625350—41no—
179#10625350—41no—
180C2×D188—22no—
181C2×D188—22no—
182C2×D188—22no—
183C2×D188—22no—
184C2×D188—22no—
185C2×D188—22no—
186C2×D188—22no—
187C2×D188—22no—
188C2×D188—22no—
189C2×D188—22no—
190C2×D188—22no—
191C2×D188—22no—
192C2×D188—22no—
193C2×D188—22no—
194C2×D188—22no—
195C2×D188—22no—
196C2×D188—22no—
197C2×D188—22no—
198C2×D188—22no—
199C2×D188—22no—
200C2×D188—22no—
201C2×D188—21no—
202C2×D188—21no—
203C2×D188—21no—
204C2×D188—21no—
205C2×D188—21no—
206C2×D188C22⋊C414yes—
207C2×D188C22⋊C414yes—
208C2×D188C22⋊C414yes—
209C2×D188C22⋊C414yes—
210C2×D188C22×C414yes—
211C2×D188C22×C412yescomplemented
212C2×D188C2×D414yes—
213C2×D188C2×D414yes—
214C2×C4×D47—22no—
215C2×C4×D47—22no—
216C2×C4×D47—216no—
217C2×C4×D47—41no—
218C2×C4×D47—41no—
219C2×C4×D47—41no—
220C2×C4×D47—41no—
221C2×C4×D47—88no—
222C2×Dic94—21no—
223C2×Dic94—21no—
224C2×Dic94—21no—
225C2×Dic94—21no—
226C2×Dic94—21no—
227C2×Dic94C22×C412yescomplemented
228M16×C47—22no—
229M16×C47—22no—
230M16×C47—22no—
231M16×C47—22no—
232C2×C8×C47—22no—
233C2×C8×C47—22no—
234C2×C8×C47C22×C414yescomplemented
235C4⋊C4×C47—22no—
236C4⋊C4×C47—22no—
237C4⋊C4×C47—22no—
238C4⋊C4×C47—41no—
239C22⋊C4×C47—22no—
240C22⋊C4×C47—22no—
241C22⋊C4×C47—22no—
242C22⋊C4×C47—41no—
243C42×C47—22no—
244C42×C47—22no—
245C42×C47—41no—
246C42×C47C2×D414yes—
247C22⋊Dic47—22no—
248C22⋊Dic47C2×D414yes—
249(C2×D47)⋊C4—216no—
250C4⋊Dic47—22no—
251C4⋊Dic47—22no—
252C4×Dic47—22no—
253C4×Dic47—22no—
254#10625329—22no—
255#10625329—22no—
256#10625329—41no—
257#10625329—41no—
258C2×C47⋊C8—22no—
259C2×C47⋊C8—41no—
260C2×C47⋊C8—41no—
261D376—216no—
262#10625325—216no—
263C23×C47—42no—
264C23×C47C4×D411yescharacteristic
265C23×C47C4×D411yescharacteristic
266C23×C47#12011yescharacteristic
267C23×C47#12011yescharacteristic
268C23×C47#12111yescharacteristic
269C23×C47#12111yescharacteristic
270C23×C47C22×D411yescharacteristic
271C22×D47—24no—
272C22×D47—24no—
273C22×D47—24no—
274C22×D47—24no—
275C22×D47—24no—
276C22×D47—24no—
277C22×D47—24no—
278C22×D47—22no—
279C22×D47—48no—
280C22×D47—41no—
281C22×D47—41no—
282C22×D47—84no—
283C22×D47—84no—
284C22×D47—84no—
285C22×D47—84no—
286C22×D47—84no—
287C22×D47—84no—
288C22×D47—82no—
289C2×C4×C47—24no—
290C2×C4×C47—44no—
291C2×C4×C47—42no—
292C2×C4×C47—82no—
293C2×C4×C47C2×C22⋊C411yescharacteristic
294C2×C4×C47C2×C22⋊C411yescharacteristic
295C2×C4×C47C2×C22⋊C411yescharacteristic
296C2×C4×C47C2×C22⋊C411yescharacteristic
297C2×C4×C47C4×D411yescharacteristic
298C2×C4×C47C4×D411yescharacteristic
299C2×C4×C47C4×D411yescharacteristic
300C2×C4×C47C4×D411yescharacteristic
301C2×C4×C47C4×D411yescharacteristic
302C2×C4×C47C4×D411yescharacteristic
303C2×C4×C47#12011yescharacteristic
304C2×C4×C47#12011yescharacteristic
305C2×C4×C47#12111yescharacteristic
306C2×C4×C47#12111yescharacteristic
307C2×C4×C47#12111yescharacteristic
308C2×C4×C47#12111yescharacteristic
309C2×C4×C47#12111yescharacteristic
310C2×C4×C47#12111yescharacteristic
311C2×C4×C47#12311yescharacteristic
312C2×C4×C47#12311yescharacteristic
313C2×C4×C47#12311yescharacteristic
314C2×C4×C47#12311yescharacteristic
315C2×C4×C47C23×C411yescharacteristic
316C2×C4×C47C22×D411yescharacteristic
317C2×C4×C47C22×D411yescharacteristic
318C2×C4×C47C22×D411yescharacteristic
319C2×C4×C47C2×#4111yescharacteristic
320C2×C4×C47C2×#4111yescharacteristic
321C22⋊D47—42no—
322C22⋊D47—42no—
323C22⋊D47—42no—
324C22⋊D47—42no—
325C2×Dic47—22no—
326C2×Dic47—24no—
327C2×Dic47—44no—
328C2×Dic47—41no—
329C2×Dic47—41no—
330D188—22no—
331D188—24no—
332D188—22no—
333D188—24no—
334D188—24no—
335D188—24no—
336D188—24no—
337D188—24no—
338D188—24no—
339D188—41no—
340D188—41no—
341D188C2×C22⋊C418yes—
342C4×D47—42no—
343C4×D47—42no—
344C4×D47—42no—
345C4×D47—42no—
346C4×D47—816no—
347Dic94—22no—
348Dic94—22no—
349Dic94—41no—
350Dic94—41no—
351C8×C47—24no—
352C47⋊C8—42no—
353C2×#1904—471nomaximal, Sylow
354C22×C47—22no—
355C22×C47—22no—
356C22×C47—22no—
357C22×C47—41no—
358C22×C47—41no—
359C22×C47—41no—
360C22×C47—41no—
361C22×C47#38611yescharacteristic
362C22×C47#38611yescharacteristic
363C22×C47#38611yescharacteristic
364C22×C47#38611yescharacteristic
365C22×C47C2×C4×D411yescharacteristic
366C22×C47C2×#12011yescharacteristic
367C22×C47C2×#12111yescharacteristic
368C2×D47—28no—
369C2×D47—48no—
370C2×D47—48no—
371C2×D47—48no—
372C2×D47—42no—
373C2×D47—84no—
374C2×D47—84no—
375C2×D47—84no—
376C2×D47—84no—
377C2×D47—82no—
378C2×D47—82no—
379C2×D47—82no—
380C4×C47—44no—
381C4×C47—82no—
382C4×C47#38611yescharacteristic
383C4×C47#38611yescharacteristic
384C4×C47#38611yescharacteristic
385C4×C47#38611yescharacteristic
386C4×C47C22×C22⋊C411yescharacteristic
387C4×C47C2×C4×D411yescharacteristic
388C4×C47C2×#12111yescharacteristic
389C4×C47C2×#12311yescharacteristic
390Dic47—44no—
391Dic47—42no—
392C22×AGL(1,ℤ/8)—471no—
393C2×#518—471no—
394C2×#421—471no—
395C2×#418—471no—
396C2×#410—471no—
397#1904—478no—
398C2×#344—471no—
399C2×H(3,ℤ/4)D4711yescharacteristic, complemented
400C2×C47—21no—
401C2×C47—21no—
402C2×C47—21no—
403C2×C47—21no—
404C2×C47—21no—
405C2×C47—21no—
406C2×C47#190412yescomplemented
407C2×C47C2×#38611yescharacteristic
408D47—48no—
409D47—82no—
410C22×#41—471no—
411C23×D4—471no—
412C2×AGL(1,ℤ/8)—474no—
413C2×AGL(1,ℤ/8)—474no—
414C2×AGL(1,ℤ/8)—942no—
415C2×AGL(1,ℤ/8)—942no—
416C2×AGL(1,ℤ/8)—942no—
417C2×AGL(1,ℤ/8)—942no—
418C22×SD16—472no—
419C22×D8—472no—
420C22×M16—471no—
421C22×M16C2×D4711yescharacteristic
422#518—474no—
423#518—942no—
424#518—942no—
425#518—942no—
426C2×C4×D4—942no—
427C2×C4×D4—942no—
428C2×#117—471no—
429C2×#117C2×D4711yescharacteristic
430C2×#117C2×D4711yescharacteristic
431C22×C22⋊C4—942no—
432#421—474no—
433#421—942no—
434C2×#104—942no—
435#418—474no—
436#418—942no—
437C2×#102—942no—
438#410—474no—
439#410—942no—
440C2×#99—942no—
441#344—474no—
442H(3,ℤ/4)C2×D4714yescomplemented
443C47C2×#190411yescharacteristic, complemented, Sylow
444C25—941no—
445C2×#41—472no—
446C2×#41—472no—
447C2×#41—941no—
448C2×#41—941no—
449C2×#41—941no—
450C2×#41—941no—
451C2×#41—941no—
452C2×#41—941no—
453C2×#41—941no—
454C2×#41—941no—
455C2×#41—941no—
456C2×#41—941no—
457C22×Q8—471no—
458C22×D4—472no—
459C22×D4—472no—
460C22×D4—471no—
461C22×D4—472no—
462C22×D4—472no—
463C22×D4—472no—
464C22×D4—472no—
465C22×D4—472no—
466C22×D4—941no—
467C22×D4—941no—
468C22×D4—941no—
469C22×D4—941no—
470C22×D4—941no—
471C22×D4—941no—
472C22×D4—941no—
473C22×D4—941no—
474C23×C4—944no—
475C23×C4—941no—
476C23×C4C22×D4711yescharacteristic
477AGL(1,ℤ/8)—948no—
478AGL(1,ℤ/8)—948no—
479AGL(1,ℤ/8)—948no—
480AGL(1,ℤ/8)—948no—
481C2×SD16—478no—
482C2×SD16—944no—
483C2×SD16—944no—
484C2×D8—478no—
485C2×D8—944no—
486C2×D8—944no—
487C2×M16—21no—
488C2×M16—21no—
489C2×M16—21no—
490C2×M16—21no—
491C2×M16—472no—
492C2×M16—941no—
493C2×M16—941no—
494C2×M16—941no—
495C2×M16—941no—
496C2×M16—941no—
497C2×M16C4×D4712yescomplemented
498C2×M16C22×D4712yes—
499C22×C8—941no—
500C22×C8C4×D4712yescomplemented
501C4×D4—948no—
502C4×D4—948no—
503C4×D4—948no—
504C4×D4—948no—
505#117—21no—
506#117—21no—
507#117—21no—
508#117—21no—
509#117—21no—
510#117—472no—
511#117—472no—
512#117—941no—
513#117—941no—
514#117D18812yes—
515#117C22×D4712yes—
516#117C22×D4712yes—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—941no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—472no—
523C2×C22⋊C4—948no—
524C2×C22⋊C4—948no—
525C2×C22⋊C4—944no—
526C2×C42—21no—
527C2×C42—941no—
528C2×C42D18812yes—
529#104—948no—
530#102—948no—
531#99—948no—
532C24—942no—
533C24—942no—
534C24—942no—
535C24—942no—
536C24—942no—
537C24—942no—
538C24—942no—
539C24—941no—
540C24—3764no—
541C24D4×D4711yescharacteristic
542#41—942no—
543#41—942no—
544#41—942no—
545#41—942no—
546#41—942no—
547#41—942no—
548#41—942no—
549#41—942no—
550#41—1881no—
551#41—1881no—
552#41—1881no—
553#41—1881no—
554#41—1881no—
555#41—1881no—
556#41—1881no—
557#41—1881no—
558C2×Q8—472no—
559C2×Q8—941no—
560C2×Q8—941no—
561C2×Q8—941no—
562C2×Q8—941no—
563C2×Q8—941no—
564C2×D4—474no—
565C2×D4—474no—
566C2×D4—474no—
567C2×D4—474no—
568C2×D4—474no—
569C2×D4—472no—
570C2×D4—474no—
571C2×D4—474no—
572C2×D4—942no—
573C2×D4—942no—
574C2×D4—941no—
575C2×D4—941no—
576C2×D4—942no—
577C2×D4—942no—
578C2×D4—941no—
579C2×D4—942no—
580C2×D4—942no—
581C2×D4—942no—
582C2×D4—942no—
583C2×D4—941no—
584C2×D4—941no—
585C2×D4—942no—
586C2×D4—942no—
587C2×D4—942no—
588C2×D4—942no—
589C2×D4—942no—
590C2×D4—942no—
591C2×D4—942no—
592C2×D4—942no—
593C2×D4—942no—
594C2×D4—942no—
595C2×D4—942no—
596C2×D4—942no—
597C2×D4—942no—
598C2×D4—942no—
599C2×D4—942no—
600C2×D4—1881no—
601C2×D4—1881no—
602C2×D4—1881no—
603C2×D4—1881no—
604C22×C4—22no—
605C22×C4—41no—
606C22×C4—9416no—
607C22×C4—941no—
608C22×C4—942no—
609C22×C4—942no—
610C22×C4—942no—
611C22×C4—3768no—
612C22×C4—1881no—
613C22×C4—1881no—
614C22×C4—1881no—
615C22×C4—1881no—
616C22×C4C2×C4×D4711yescharacteristic
617C22×C4C2×C4×D4711yescharacteristic
618C22×C4C2×D18811yescharacteristic
619C22×C4C2×D18811yescharacteristic
620C22×C4#1062535011yescharacteristic
621C22×C4#1062535011yescharacteristic
622C22×C4D4×D4711yescharacteristic
623C22×C4D4×D4711yescharacteristic
624C22×C4D4×D4711yescharacteristic
625C22×C4D4×D4711yescharacteristic
626C22×C4D4×D4711yescharacteristic
627C22×C4#1062535411yescharacteristic
628C22×C4#1062535411yescharacteristic
629C22×C4C23×D4711yescharacteristic
630SD16—9416no—
631D8—9416no—
632M16—22no—
633M16—22no—
634M16—22no—
635M16—22no—
636M16—942no—
637M16—942no—
638M16—1881no—
639M16—1881no—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—942no—
643C2×C8—1881no—
644C2×C8—1881no—
645C2×C8C2×C4×D4714yescomplemented
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—41no—
650C4⋊C4—942no—
651C4⋊C4—942no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—22no—
655C22⋊C4—41no—
656C22⋊C4—474no—
657C22⋊C4—9416no—
658C22⋊C4—942no—
659C42—22no—
660C42—22no—
661C42—41no—
662C42—942no—
663C42—942no—
664C42C2×D18814yes—
665C23—42no—
666C23—944no—
667C23—944no—
668C23—944no—
669C23—944no—
670C23—944no—
671C23—944no—
672C23—944no—
673C23—942no—
674C23—3762no—
675C23—3764no—
676C23—3764no—
677C23—3764no—
678C23—3764no—
679C23—3764no—
680C23—3764no—
681C23—1888no—
682C23—1881no—
683C23—1881no—
684C23#1309398611yescharacteristic
685C23#1309398611yescharacteristic
686C23#1309399411yescharacteristic
687C23#1309399411yescharacteristic
688C23#1309399711yescharacteristic
689C23#1309399711yescharacteristic
690C23C2×D4×D4711yescharacteristic
691Q8—942no—
692Q8—942no—
693Q8—1881no—
694Q8—1881no—
695D4—478no—
696D4—944no—
697D4—944no—
698D4—944no—
699D4—944no—
700D4—942no—
701D4—944no—
702D4—942no—
703D4—944no—
704D4—944no—
705D4—1882no—
706D4—1882no—
707D4—1882no—
708D4—1882no—
709D4—1881no—
710D4—1881no—
711C2×C4—24no—
712C2×C4—44no—
713C2×C4—42no—
714C2×C4—82no—
715C2×C4—942no—
716C2×C4—944no—
717C2×C4—37616no—
718C2×C4—1884no—
719C2×C4—1881no—
720C2×C4—1881no—
721C2×C4—1882no—
722C2×C4—1882no—
723C2×C4—1882no—
724C2×C4—1882no—
725C2×C4C22⋊C4×D4711yescharacteristic
726C2×C4C22⋊C4×D4711yescharacteristic
727C2×C4C22⋊C4×D4711yescharacteristic
728C2×C4C22⋊C4×D4711yescharacteristic
729C2×C4#1309398611yescharacteristic
730C2×C4#1309398611yescharacteristic
731C2×C4C4×D18811yescharacteristic
732C2×C4C4×D18811yescharacteristic
733C2×C4C4×D18811yescharacteristic
734C2×C4C4×D18811yescharacteristic
735C2×C4#1309399411yescharacteristic
736C2×C4#1309399411yescharacteristic
737C2×C4#1309399711yescharacteristic
738C2×C4#1309399711yescharacteristic
739C2×C4#1309399911yescharacteristic
740C2×C4#1309399911yescharacteristic
741C2×C4#1309399911yescharacteristic
742C2×C4#1309399911yescharacteristic
743C2×C4#1309400911yescharacteristic
744C2×C4#1309400911yescharacteristic
745C2×C4#1309400911yescharacteristic
746C2×C4#1309400911yescharacteristic
747C2×C4C22×C4×D4711yescharacteristic
748C2×C4C2×D4×D4711yescharacteristic
749C2×C4C2×D4×D4711yescharacteristic
750C2×C4C22×D18811yescharacteristic
751C2×C4C2×#1062535011yescharacteristic
752C2×C4C2×#1062535411yescharacteristic
753C8—24no—
754C8—1882no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—948no—
763C22—3762no—
764C22—3762no—
765C22—3764no—
766C22—3764no—
767C22—3764no—
768C22—3764no—
769C22—3762no—
770C22—1888no—
771C22—1888no—
772C22—1882no—
773C22—1888no—
774C22#1568900111yescharacteristic
775C22#1568900111yescharacteristic
776C22#1568900111yescharacteristic
777C22#1568900111yescharacteristic
778C22C2×#1309398611yescharacteristic
779C22C2×#1309399411yescharacteristic
780C22C2×#1309399711yescharacteristic
781C4—44no—
782C4—82no—
783C4—1884no—
784C4—1882no—
785C4#1568900111yescharacteristic
786C4#1568900111yescharacteristic
787C4#1568900111yescharacteristic
788C4#1568900111yescharacteristic
789C4C2×C22⋊C4×D4711yescharacteristic
790C4C2×C4×D18811yescharacteristic
791C4C2×#1309399911yescharacteristic
792C4C2×#1309400911yescharacteristic
793C2—21no—
794C2—21no—
795C2—21no—
796C2—21no—
797C2—21no—
798C2—21no—
799C2—3762no—
800C2—1888no—
801C2#2024387612yesdirect product factor
802C2C2×#1568900111yescharacteristic
subgroupG/H
centerC22#15689001
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×H(3,ℤ/4)C2
socleC22×C47#386
prime radicalC22×#13094052C2
cosocleC22×C4×C47C24
hypercenterC2×H(3,ℤ/4)D47
hypocenterC47C2×#1904
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
2. C2×#15689597C2semidirect
3. C2×#15689141C2semidirect
4. C2×#15689127C2semidirect
5. C2×#15689096C2semidirect
6. #20243876C2direct (N × H)
7. C2×#15688894C2semidirect
8. C2×C47×H(3,ℤ/4)C2semidirect
15. C2×#13094052C4semidirect
17. C22×#10625325C4semidirect
18. C22×D376C4semidirect
23. #15689597C22semidirect
29. #15689141C22semidirect
32. #15689127C22semidirect
35. #15689096C22semidirect
37. #15688894C22semidirect
41. C47×H(3,ℤ/4)C22semidirect
53. C2×#10625350C2×C4semidirect
55. C22×Dic94C2×C4semidirect
65. C22×D188C2×C4semidirect
80. C2×#10625325C2×C4semidirect
83. C2×D376C2×C4semidirect
113. C2×M16×C47C2×C4semidirect
115. C22×C8×C47C2×C4semidirect
211. C2×D188C22×C4semidirect
227. C2×Dic94C22×C4semidirect
234. C2×C8×C47C22×C4semidirect
399. C2×H(3,ℤ/4)D47semidirect
406. C2×C47#1904semidirect
442. H(3,ℤ/4)C2×D47semidirect
443. C47C2×#1904semidirect
497. C2×M16C4×D47semidirect
500. C22×C8C4×D47semidirect
645. C2×C8C2×C4×D47semidirect
801. C2#20243876direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940522
C2×#156895972
C2×#156891412
C2×#156891272
C2×#156890962
#202438762
C2×#156888942
C2×C47×H(3,ℤ/4)2
C2×#190447