Finite Group Databasebeta

← C2×#20244059 #26218861

Subgroups — C2×#20244059 #26218861

Order 12032.

1046 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689172C211yesmaximal, characteristic, complemented
2C2×#15689140C211yesmaximal, characteristic
3C22×#13093951C211yesmaximal, characteristic
4C2×M16×Dic47C211yesmaximal, characteristic, complemented
5#20244059C218yesmaximal, direct product factor
6C2×#15688895C211yesmaximal, characteristic, complemented
7C2×#15688884C211yesmaximal, characteristic, complemented
8C2×C47×#413C211yesmaximal, characteristic
9C22×#10625329C2211yescharacteristic
10C22×#10625329C2211yescharacteristic
11C2×#13093983C2211yescharacteristic
12C22×C4×Dic47C2211yescharacteristic
13#15689172—22no—
14#15689172C2214yescomplemented
15C2×#13093960—22no—
16#15689140—22no—
17#15689140C2214yes—
18C2×#13093951—22no—
19C2×#13093951—21no—
20C2×#13093951—21no—
21C2×#13093951—22no—
22C2×#13093951C2214yes—
23M16×Dic47—22no—
24M16×Dic47C2214yescomplemented
25C2×#13093934—21no—
26C2×C8×Dic47—21no—
27#15688895C2214yescomplemented
28#15688884C2214yescomplemented
29C22×#41×C47C2211yescharacteristic
30C22×M16×C47C2211yescharacteristic
31C22×M16×C47C2211yescharacteristic
32C47×#413C414yescomplemented
33C47×#413C2214yes—
34C2×#101×C47C412yescomplemented
35C2×#100×C47C412yescomplemented
36C23×Dic47—21no—
37C2×#10625329—21no—
38C2×#10625329—21no—
39C2×#10625329—21no—
40C2×#10625329—21no—
41C2×#10625329—21no—
42C2×#10625329—21no—
43C2×#10625329—21no—
44C2×#10625329—21no—
45C2×#10625329D412yes—
46C2×#10625329D412yes—
47C2×#10625329C2312yes—
48C2×#10625329C2312yes—
49C22×C47⋊C8—21no—
50C22×C47⋊C8—21no—
51#13093983—21no—
52#13093983—21no—
53#13093983—21no—
54#13093983C2312yes—
55C2×C4⋊Dic47—21no—
56C2×C22⋊Dic47—21no—
57C2×C4×Dic47—21no—
58C2×C4×Dic47—21no—
59C2×C4×Dic47—21no—
60C2×C4×Dic47—21no—
61C2×C4×Dic47D411yescharacteristic
62C2×C4×Dic47D411yescharacteristic
63C2×C4×Dic47D412yes—
64C2×C4×Dic47C2312yes—
65#13093960—28no—
66#13093951—24no—
67#13093951—24no—
68#13093951—28no—
69#13093934—24no—
70C8×Dic47—24no—
71C2×#41×C47—21no—
72C2×#41×C47—21no—
73C2×#41×C47—21no—
74C2×#41×C47—21no—
75C2×#41×C47—21no—
76C2×#41×C47—21no—
77C2×#41×C47—21no—
78C2×#41×C47—21no—
79C2×#41×C47—21no—
80C2×#41×C47—21no—
81C2×#41×C47C2×C412yes—
82C2×#41×C47C2312yes—
83C22×Q8×C47C2×C411yescharacteristic
84C22×D4×C47—21no—
85C22×D4×C47C2×C411yescharacteristic
86C23×C4×C47—21no—
87C23×C4×C47C2311yescharacteristic
88C2×M16×C47—21no—
89C2×M16×C47—21no—
90C2×M16×C47—21no—
91C2×M16×C47—21no—
92C2×M16×C47—21no—
93C2×M16×C47—21no—
94C2×M16×C47C2×C412yes—
95C2×M16×C47C2×C412yes—
96C2×M16×C47C2×C412yes—
97C2×M16×C47C2×C412yes—
98C2×M16×C47C2312yes—
99C2×M16×C47C2312yes—
100C22×C8×C47—21no—
101C22×C8×C47—21no—
102#101×C47C2×C418yescomplemented
103#100×C47C2×C418yescomplemented
104C24×C47—21no—
105C24×C47#4111yescharacteristic
106#41×C47—22no—
107#41×C47—22no—
108#41×C47—22no—
109#41×C47—22no—
110#41×C47—22no—
111#41×C47—22no—
112#41×C47—22no—
113#41×C47—22no—
114#41×C47—41no—
115#41×C47—41no—
116#41×C47—41no—
117#41×C47—41no—
118#41×C47—41no—
119#41×C47—41no—
120#41×C47—41no—
121#41×C47—41no—
122C2×Q8×C47—21no—
123C2×Q8×C47—21no—
124C2×Q8×C47—21no—
125C2×Q8×C47—21no—
126C2×Q8×C47—21no—
127C2×Q8×C47C22×C412yes—
128C2×D4×C47—22no—
129C2×D4×C47—22no—
130C2×D4×C47—21no—
131C2×D4×C47—21no—
132C2×D4×C47—21no—
133C2×D4×C47—21no—
134C2×D4×C47—21no—
135C2×D4×C47—41no—
136C2×D4×C47—41no—
137C2×D4×C47—41no—
138C2×D4×C47—41no—
139C2×D4×C47C22×C412yes—
140C22×C4×C47—21no—
141C22×C4×C47—22no—
142C22×C4×C47—22no—
143C22×C4×C47—41no—
144C22×C4×C47—41no—
145C22×C4×C47—41no—
146C22×C4×C47—41no—
147C22×C4×C47C22×C411yescharacteristic
148C22×C4×C47C22×C411yescharacteristic
149C22×C4×C47C2×D411yescharacteristic
150C22×C4×C47C2×D411yescharacteristic
151C22×C4×C47C2×D411yescharacteristic
152C22×C4×C47C2×D411yescharacteristic
153C22×C4×C47#4111yescharacteristic
154C22×C4×C47#4111yescharacteristic
155C22×C4×C47#4111yescharacteristic
156C22×C4×C47#4111yescharacteristic
157C22×C4×C47#4111yescharacteristic
158C22×C4×C47#4111yescharacteristic
159C22×C4×C47#4111yescharacteristic
160C22×C4×C47C2411yescharacteristic
161C22×Dic47—21no—
162C22×Dic47—22no—
163C22×Dic47—21no—
164C22×Dic47—22no—
165C22×Dic47—44no—
166C22×Dic47—41no—
167M16×C47—22no—
168M16×C47—22no—
169M16×C47—22no—
170M16×C47—22no—
171M16×C47—22no—
172M16×C47—22no—
173M16×C47C22×C414yes—
174M16×C47C22×C414yes—
175C2×C8×C47—22no—
176C2×C8×C47—22no—
177C2×C8×C47—22no—
178C2×C8×C47—22no—
179C2×C8×C47—22no—
180C2×C8×C47—22no—
181C22⋊Dic47—22no—
182C22⋊Dic47—41no—
183C4⋊Dic47—22no—
184C4⋊Dic47—41no—
185C4×Dic47—21no—
186C4×Dic47—22no—
187C4×Dic47—21no—
188C4×Dic47—22no—
189C4×Dic47—22no—
190C4×Dic47—41no—
191C4×Dic47C2×D412yes—
192C4×Dic47C2×D412yes—
193#10625329—22no—
194#10625329—22no—
195#10625329—22no—
196#10625329—22no—
197#10625329—22no—
198#10625329—41no—
199#10625329—41no—
200#10625329C2×D414yes—
201C2×C47⋊C8—22no—
202C2×C47⋊C8—22no—
203C2×C47⋊C8—22no—
204C2×C47⋊C8—22no—
205C2×C47⋊C8—41no—
206C2×C47⋊C8—41no—
207C23×C47—22no—
208C23×C47—42no—
209C23×C47—41no—
210C23×C47—41no—
211C23×C47—82no—
212C23×C47#11711yescharacteristic
213C23×C47#11711yescharacteristic
214C23×C47#12311yescharacteristic
215C23×C47#12311yescharacteristic
216C23×C47#12411yescharacteristic
217C23×C47#12411yescharacteristic
218C23×C47C2×#4111yescharacteristic
219Q8×C47—22no—
220Q8×C47—22no—
221Q8×C47—41no—
222Q8×C47—41no—
223D4×C47—22no—
224D4×C47—22no—
225D4×C47—42no—
226D4×C47—42no—
227D4×C47—42no—
228D4×C47—42no—
229D4×C47—41no—
230D4×C47—41no—
231C2×C4×C47—22no—
232C2×C4×C47—41no—
233C2×C4×C47—41no—
234C2×C4×C47—42no—
235C2×C4×C47—42no—
236C2×C4×C47—42no—
237C2×C4×C47—42no—
238C2×C4×C47#11711yescharacteristic
239C2×C4×C47#11711yescharacteristic
240C2×C4×C47C4×D411yescharacteristic
241C2×C4×C47C4×D411yescharacteristic
242C2×C4×C47C4×D411yescharacteristic
243C2×C4×C47C4×D411yescharacteristic
244C2×C4×C47C4×D411yescharacteristic
245C2×C4×C47C4×D411yescharacteristic
246C2×C4×C47C4×D411yescharacteristic
247C2×C4×C47C4×D411yescharacteristic
248C2×C4×C47#12111yescharacteristic
249C2×C4×C47#12111yescharacteristic
250C2×C4×C47#12111yescharacteristic
251C2×C4×C47#12111yescharacteristic
252C2×C4×C47#12311yescharacteristic
253C2×C4×C47#12311yescharacteristic
254C2×C4×C47#12411yescharacteristic
255C2×C4×C47#12411yescharacteristic
256C2×C4×C47#12611yescharacteristic
257C2×C4×C47#12611yescharacteristic
258C2×C4×C47#12611yescharacteristic
259C2×C4×C47#12611yescharacteristic
260C2×C4×C47C23×C411yescharacteristic
261C2×C4×C47C22×D411yescharacteristic
262C2×C4×C47C22×D411yescharacteristic
263C2×C4×C47C2×#4111yescharacteristic
264C2×C4×C47C2×#4111yescharacteristic
265C2×C4×C47C2×#4111yescharacteristic
266C2×Dic47—24no—
267C2×Dic47—22no—
268C2×Dic47—22no—
269C2×Dic47—44no—
270C2×Dic47—44no—
271C2×Dic47—42no—
272C2×Dic47—42no—
273C2×Dic47—82no—
274C8×C47—24no—
275C8×C47—24no—
276C47⋊C8—24no—
277C47⋊C8—42no—
278C2×#1932—471nomaximal, Sylow
279C22×C47—22no—
280C22×C47—22no—
281C22×C47—22no—
282C22×C47—41no—
283C22×C47—41no—
284C22×C47—41no—
285C22×C47—41no—
286C22×C47—42no—
287C22×C47—82no—
288C22×C47—82no—
289C22×C47—82no—
290C22×C47#38811yescharacteristic
291C22×C47#38811yescharacteristic
292C22×C47#38811yescharacteristic
293C22×C47#38811yescharacteristic
294C22×C47C2×#11711yescharacteristic
295C22×C47C2×#12311yescharacteristic
296C22×C47C2×#12411yescharacteristic
297C4×C47—42no—
298C4×C47#38811yescharacteristic
299C4×C47#38811yescharacteristic
300C4×C47#38811yescharacteristic
301C4×C47#38811yescharacteristic
302C4×C47C2×C4×D411yescharacteristic
303C4×C47C2×C4×D411yescharacteristic
304C4×C47C2×#12111yescharacteristic
305C4×C47C2×#12611yescharacteristic
306Dic47—24no—
307Dic47—42no—
308Dic47—82no—
309C2×#430—471no—
310C2×#421—471no—
311C22×#104—471no—
312C2×#413D4711yescharacteristic
313C2×C4×M16—471no—
314#1932—478no—
315C2×#344—471no—
316C2×#339—471no—
317C2×C47—21no—
318C2×C47—21no—
319C2×C47—21no—
320C2×C47—21no—
321C2×C47—21no—
322C2×C47—21no—
323C2×C47—82no—
324C2×C47#193212yescomplemented
325C2×C47C2×#38811yescharacteristic
326C22×#41C2×D4711yescharacteristic
327C22×M16—471no—
328C22×M16—471no—
329C22×M16C2×D4711yescharacteristic
330C22×M16C2×D4711yescharacteristic
331C2×#117—471no—
332C22×C42—471no—
333#430—474no—
334#430—942no—
335C2×#108—942no—
336#421—474no—
337#421—942no—
338C2×#104—474no—
339C2×#104—941no—
340C2×#104—941no—
341C2×#104—942no—
342C2×#104—942no—
343#413Dic4714yescomplemented
344#413C2×D4714yes—
345C2×#101Dic4712yescomplemented
346C2×#100Dic4712yescomplemented
347C4×M16—474no—
348C4×M16—942no—
349C2×#97—941no—
350C2×C4×C8—941no—
351#344—474no—
352#339—474no—
353C47C2×#193211yescharacteristic, complemented, Sylow
354C2×#41—21no—
355C2×#41—21no—
356C2×#41—21no—
357C2×#41—21no—
358C2×#41—21no—
359C2×#41—21no—
360C2×#41—21no—
361C2×#41—21no—
362C2×#41—21no—
363C2×#41—21no—
364C2×#41C2×Dic4712yes—
365C2×#41C22×D4712yes—
366C22×Q8C2×Dic4711yescharacteristic
367C22×D4—21no—
368C22×D4C2×Dic4711yescharacteristic
369C23×C4—21no—
370C23×C4—941no—
371C23×C4C22×D4711yescharacteristic
372C2×M16—21no—
373C2×M16—21no—
374C2×M16—21no—
375C2×M16—21no—
376C2×M16—21no—
377C2×M16—21no—
378C2×M16—472no—
379C2×M16—472no—
380C2×M16—472no—
381C2×M16—472no—
382C2×M16—941no—
383C2×M16—941no—
384C2×M16—941no—
385C2×M16—941no—
386C2×M16—941no—
387C2×M16—941no—
388C2×M16—941no—
389C2×M16—941no—
390C2×M16C2×Dic4712yes—
391C2×M16C2×Dic4712yes—
392C2×M16C2×Dic4712yes—
393C2×M16C2×Dic4712yes—
394C2×M16C22×D4712yes—
395C2×M16C22×D4712yes—
396C22×C8—21no—
397C22×C8—21no—
398C22×C8—941no—
399C22×C8—941no—
400#117—472no—
401#117—941no—
402#117—941no—
403#117—941no—
404C2×C4⋊C4—941no—
405C2×C22⋊C4—941no—
406C2×C42—471no—
407C2×C42—471no—
408C2×C42—472no—
409C2×C42—472no—
410C2×C42—941no—
411C2×C42—941no—
412C2×C42—941no—
413C2×C42—941no—
414#108—948no—
415#104—944no—
416#104—944no—
417#104—948no—
418#101C2×Dic4718yescomplemented
419#100C2×Dic4718yescomplemented
420#97—944no—
421C4×C8—944no—
422C24—21no—
423C24#1062535011yescharacteristic
424#41—22no—
425#41—22no—
426#41—22no—
427#41—22no—
428#41—22no—
429#41—22no—
430#41—22no—
431#41—22no—
432#41—41no—
433#41—41no—
434#41—41no—
435#41—41no—
436#41—41no—
437#41—41no—
438#41—41no—
439#41—41no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8C22×Dic4712yes—
446C2×D4—22no—
447C2×D4—22no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—41no—
454C2×D4—41no—
455C2×D4—41no—
456C2×D4—41no—
457C2×D4C22×Dic4712yes—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—941no—
466C22×C4—942no—
467C22×C4—941no—
468C22×C4—942no—
469C22×C4—1884no—
470C22×C4—1881no—
471C22×C4#1062535011yescharacteristic
472C22×C4#1062535011yescharacteristic
473C22×C4#1062535011yescharacteristic
474C22×C4D4×D4711yescharacteristic
475C22×C4D4×D4711yescharacteristic
476C22×C4D4×D4711yescharacteristic
477C22×C4D4×D4711yescharacteristic
478C22×C4#1062535211yescharacteristic
479C22×C4#1062535211yescharacteristic
480C22×C4#1062535211yescharacteristic
481C22×C4#1062535211yescharacteristic
482C22×C4C22×Dic4711yescharacteristic
483C22×C4C22×Dic4711yescharacteristic
484C22×C4C23×D4711yescharacteristic
485M16—22no—
486M16—22no—
487M16—22no—
488M16—22no—
489M16—22no—
490M16—22no—
491M16—474no—
492M16—942no—
493M16—942no—
494M16—942no—
495M16—942no—
496M16—942no—
497M16—1881no—
498M16—1881no—
499M16C22×Dic4714yes—
500M16C22×Dic4714yes—
501C2×C8—22no—
502C2×C8—22no—
503C2×C8—22no—
504C2×C8—22no—
505C2×C8—22no—
506C2×C8—22no—
507C2×C8—942no—
508C2×C8—942no—
509C2×C8—942no—
510C2×C8—942no—
511C2×C8—1881no—
512C2×C8—1881no—
513C4⋊C4—942no—
514C4⋊C4—1881no—
515C22⋊C4—942no—
516C22⋊C4—1881no—
517C42—472no—
518C42—472no—
519C42—941no—
520C42—942no—
521C42—941no—
522C42—942no—
523C42—942no—
524C42—1881no—
525C23—22no—
526C23—42no—
527C23—41no—
528C23—41no—
529C23—82no—
530C23#1309398311yescharacteristic
531C23#1309398311yescharacteristic
532C23#1309400611yescharacteristic
533C23#1309400611yescharacteristic
534C23#1309401011yescharacteristic
535C23#1309401011yescharacteristic
536C23C2×#1062535011yescharacteristic
537Q8—22no—
538Q8—22no—
539Q8—41no—
540Q8—41no—
541D4—22no—
542D4—22no—
543D4—42no—
544D4—42no—
545D4—42no—
546D4—42no—
547D4—41no—
548D4—41no—
549C2×C4—22no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—944no—
557C2×C4—942no—
558C2×C4—942no—
559C2×C4—3762no—
560C2×C4—1884no—
561C2×C4—1884no—
562C2×C4—1882no—
563C2×C4—1882no—
564C2×C4#1309398311yescharacteristic
565C2×C4#1309398311yescharacteristic
566C2×C4D4×Dic4711yescharacteristic
567C2×C4D4×Dic4711yescharacteristic
568C2×C4D4×Dic4711yescharacteristic
569C2×C4D4×Dic4711yescharacteristic
570C2×C4D4×Dic4711yescharacteristic
571C2×C4D4×Dic4711yescharacteristic
572C2×C4D4×Dic4711yescharacteristic
573C2×C4D4×Dic4711yescharacteristic
574C2×C4#1309399711yescharacteristic
575C2×C4#1309399711yescharacteristic
576C2×C4#1309399711yescharacteristic
577C2×C4#1309399711yescharacteristic
578C2×C4#1309400611yescharacteristic
579C2×C4#1309400611yescharacteristic
580C2×C4#1309401011yescharacteristic
581C2×C4#1309401011yescharacteristic
582C2×C4#1309401711yescharacteristic
583C2×C4#1309401711yescharacteristic
584C2×C4#1309401711yescharacteristic
585C2×C4#1309401711yescharacteristic
586C2×C4C23×Dic4711yescharacteristic
587C2×C4C2×D4×D4711yescharacteristic
588C2×C4C2×D4×D4711yescharacteristic
589C2×C4C2×#1062535211yescharacteristic
590C2×C4C2×#1062535211yescharacteristic
591C2×C4C2×#1062535011yescharacteristic
592C8—24no—
593C8—24no—
594C8—944no—
595C8—1882no—
596C22—22no—
597C22—22no—
598C22—22no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—42no—
604C22—82no—
605C22—82no—
606C22—82no—
607C22#1568901611yescharacteristic
608C22#1568901611yescharacteristic
609C22#1568901611yescharacteristic
610C22#1568901611yescharacteristic
611C22C2×#1309398311yescharacteristic
612C22C2×#1309400611yescharacteristic
613C22C2×#1309401011yescharacteristic
614C4—42no—
615C4—944no—
616C4—3762no—
617C4—1882no—
618C4#1568901611yescharacteristic
619C4#1568901611yescharacteristic
620C4#1568901611yescharacteristic
621C4#1568901611yescharacteristic
622C4C2×D4×Dic4711yescharacteristic
623C4C2×D4×Dic4711yescharacteristic
624C4C2×#1309399711yescharacteristic
625C4C2×#1309401711yescharacteristic
626C2—21no—
627C2—21no—
628C2—21no—
629C2—21no—
630C2—21no—
631C2—21no—
632C2—82no—
633C2#2024405912yesdirect product factor
634C2C2×#1568901611yescharacteristic
subgroupG/H
centerC2×C4#13093997
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#413C2
socleC22×C47#388
prime radicalC22×#41×C47C22
cosocleC22×C4×C47C24
hypercenterC2×#413D47
hypocenterC47C2×#1932
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#413

Complements

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

NH ≅ G/Ntype
1. C2×#15689172C2semidirect
4. C2×M16×Dic47C2semidirect
5. #20244059C2direct (N × H)
6. C2×#15688895C2semidirect
7. C2×#15688884C2semidirect
14. #15689172C22semidirect
24. M16×Dic47C22semidirect
27. #15688895C22semidirect
28. #15688884C22semidirect
32. C47×#413C4semidirect
34. C2×#101×C47C4semidirect
35. C2×#100×C47C4semidirect
102. #101×C47C2×C4semidirect
103. #100×C47C2×C4semidirect
324. C2×C47#1932semidirect
343. #413Dic47semidirect
345. C2×#101Dic47semidirect
346. C2×#100Dic47semidirect
353. C47C2×#1932semidirect
418. #101C2×Dic47semidirect
419. #100C2×Dic47semidirect
633. C2#20244059direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156891722
C2×#156891402
C22×#130939512
C2×M16×Dic472
#202440592
C2×#156888952
C2×#156888842
C2×C47×#4132
C2×#193247