Finite Group Databasebeta

← C2×#20244056 #26218858

Subgroups — C2×#20244056 #26218858

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×#15689139C211yesmaximal, characteristic
2C22×#13093950C211yesmaximal, characteristic
3C2×#15689105C211yesmaximal, characteristic
4C2×M16×Dic47C211yesmaximal, characteristic, complemented
5#20244056C218yesmaximal, direct product factor
6C2×#15688894C211yesmaximal, characteristic, complemented
7C2×#15688884C211yesmaximal, characteristic, complemented
8C2×C47×#430C211yesmaximal, characteristic, complemented
9C22×#10625350C2211yescharacteristic
10C22×#10625329C2211yescharacteristic
11C2×#13093983C2211yescharacteristic
12C22×C4×Dic47C2211yescharacteristic
13#15689139—22no—
14#15689139C2214yes—
15C2×#13093950—21no—
16C2×#13093950—21no—
17C2×#13093950—22no—
18C2×#13093950—22no—
19C2×#13093950C2214yes—
20#15689105C414yescomplemented
21#15689105C2214yes—
22C2×#13093942C412yescomplemented
23C2×#13093940C412yescomplemented
24M16×Dic47—22no—
25M16×Dic47C2214yescomplemented
26C2×#13093934—21no—
27C2×C8×Dic47—21no—
28#15688894C2214yescomplemented
29#15688884C2214yescomplemented
30C22×M16×C47C2211yescharacteristic
31C22×M16×C47C2211yescharacteristic
32C22×M16×C47C2211yescharacteristic
33C47×#430—22no—
34C47×#430C2214yescomplemented
35C2×#108×C47—22no—
36C2×#10625350—21no—
37C2×#10625350—21no—
38C2×#10625350—21no—
39C2×#10625350—21no—
40C2×#10625350—21no—
41C2×#10625350—21no—
42C2×#10625350—21no—
43C2×#10625350—21no—
44C2×#10625350—21no—
45C2×#10625350—21no—
46C2×#10625350C2×C412yes—
47C2×#10625350C2312yes—
48C22×Dic94C2×C411yescharacteristic
49C22×D188C2×C411yescharacteristic
50C22×C22⋊D47—21no—
51C23×Dic47—21no—
52C22×C4×D47—21no—
53C2×#10625329—21no—
54C2×#10625329—21no—
55C2×#10625329—21no—
56C2×#10625329C2×C412yes—
57C2×#10625329C2×C412yes—
58C2×#10625329C2312yes—
59C22×C47⋊C8—21no—
60#13093983—21no—
61#13093983—21no—
62#13093983—21no—
63#13093983C2312yes—
64C2×C4⋊Dic47—21no—
65C2×C22⋊Dic47—21no—
66C2×C4×Dic47—21no—
67C2×C4×Dic47—21no—
68C2×C4×Dic47—21no—
69C2×C4×Dic47—21no—
70C2×C4×Dic47D411yescharacteristic
71C2×C4×Dic47D411yescharacteristic
72C2×C4×Dic47D412yes—
73C2×C4×Dic47C2312yes—
74#13093950—28no—
75#13093950—24no—
76#13093950—24no—
77#13093942C2×C418yescomplemented
78#13093940C2×C418yescomplemented
79#13093934—24no—
80C8×Dic47—24no—
81C23×C4×C47C2311yescharacteristic
82C2×M16×C47—21no—
83C2×M16×C47—21no—
84C2×M16×C47—21no—
85C2×M16×C47—21no—
86C2×M16×C47—21no—
87C2×M16×C47—21no—
88C2×M16×C47—21no—
89C2×M16×C47—21no—
90C2×M16×C47—21no—
91C2×M16×C47—21no—
92C2×M16×C47—21no—
93C2×M16×C47C2×C412yes—
94C2×M16×C47C2×C412yes—
95C2×M16×C47D412yes—
96C2×M16×C47D412yes—
97C2×M16×C47C2312yes—
98C2×M16×C47C2312yes—
99C2×M16×C47C2312yes—
100C22×C8×C47—21no—
101C22×C8×C47—21no—
102C22×C8×C47—21no—
103#108×C47—28no—
104C24×C47#4111yescharacteristic
105C23×D47—21no—
106C22×C4×C47C22×C411yescharacteristic
107C22×C4×C47C22×C411yescharacteristic
108C22×C4×C47C2×D411yescharacteristic
109C22×C4×C47C2×D411yescharacteristic
110C22×C4×C47C2×D411yescharacteristic
111C22×C4×C47C2×D411yescharacteristic
112C22×C4×C47#4111yescharacteristic
113C22×C4×C47#4111yescharacteristic
114C22×C4×C47#4111yescharacteristic
115C22×C4×C47#4111yescharacteristic
116C22×C4×C47#4111yescharacteristic
117C22×C4×C47#4111yescharacteristic
118C22×C4×C47#4111yescharacteristic
119C22×C4×C47C2411yescharacteristic
120C2×C22⋊D47—22no—
121C2×C22⋊D47—22no—
122C2×C22⋊D47—41no—
123C2×C22⋊D47—41no—
124C2×C22⋊D47—41no—
125C2×C22⋊D47—41no—
126C22×Dic47—21no—
127C22×Dic47—21no—
128C22×Dic47—22no—
129C22×Dic47—21no—
130C22×Dic47—22no—
131C22×Dic47—44no—
132C22×Dic47—41no—
133#10625350—22no—
134#10625350—22no—
135#10625350—22no—
136#10625350—22no—
137#10625350—22no—
138#10625350—22no—
139#10625350—22no—
140#10625350—22no—
141#10625350—41no—
142#10625350—41no—
143#10625350—41no—
144#10625350—41no—
145#10625350—41no—
146#10625350—41no—
147#10625350—41no—
148#10625350—41no—
149C2×D188—21no—
150C2×D188—21no—
151C2×D188—21no—
152C2×D188—21no—
153C2×D188—21no—
154C2×D188C22×C412yes—
155C2×C4×D47—22no—
156C2×C4×D47—22no—
157C2×C4×D47—41no—
158C2×C4×D47—41no—
159C2×C4×D47—41no—
160C2×C4×D47—41no—
161C2×Dic94—21no—
162C2×Dic94—21no—
163C2×Dic94—21no—
164C2×Dic94—21no—
165C2×Dic94—21no—
166C2×Dic94C22×C412yes—
167M16×C47—22no—
168M16×C47—22no—
169M16×C47—22no—
170M16×C47—22no—
171M16×C47—22no—
172M16×C47—22no—
173M16×C47—22no—
174M16×C47—22no—
175M16×C47—41no—
176M16×C47—41no—
177M16×C47C22×C414yes—
178M16×C47C2×D414yes—
179C2×C8×C47—22no—
180C2×C8×C47—22no—
181C2×C8×C47—22no—
182C2×C8×C47—22no—
183C2×C8×C47—22no—
184C2×C8×C47—22no—
185C2×C8×C47—22no—
186C2×C8×C47—41no—
187C2×C8×C47—41no—
188C22⋊Dic47—22no—
189C22⋊Dic47—41no—
190C4⋊Dic47—22no—
191C4⋊Dic47—41no—
192C4×Dic47—21no—
193C4×Dic47—22no—
194C4×Dic47—21no—
195C4×Dic47—22no—
196C4×Dic47—22no—
197C4×Dic47—41no—
198C4×Dic47C2×D412yes—
199C4×Dic47C2×D412yes—
200#10625329—22no—
201#10625329—22no—
202#10625329—22no—
203#10625329C22×C414yes—
204C2×C47⋊C8—22no—
205C2×C47⋊C8—22no—
206C2×C47⋊C8—22no—
207C23×C47—42no—
208C23×C47#11711yescharacteristic
209C23×C47#11711yescharacteristic
210C23×C47#12311yescharacteristic
211C23×C47#12311yescharacteristic
212C23×C47#12411yescharacteristic
213C23×C47#12411yescharacteristic
214C23×C47C2×#4111yescharacteristic
215C22×D47—22no—
216C22×D47—41no—
217C22×D47—41no—
218C22×D47—82no—
219C2×C4×C47#11711yescharacteristic
220C2×C4×C47#11711yescharacteristic
221C2×C4×C47C4×D411yescharacteristic
222C2×C4×C47C4×D411yescharacteristic
223C2×C4×C47C4×D411yescharacteristic
224C2×C4×C47C4×D411yescharacteristic
225C2×C4×C47C4×D411yescharacteristic
226C2×C4×C47C4×D411yescharacteristic
227C2×C4×C47C4×D411yescharacteristic
228C2×C4×C47C4×D411yescharacteristic
229C2×C4×C47#12111yescharacteristic
230C2×C4×C47#12111yescharacteristic
231C2×C4×C47#12111yescharacteristic
232C2×C4×C47#12111yescharacteristic
233C2×C4×C47#12311yescharacteristic
234C2×C4×C47#12311yescharacteristic
235C2×C4×C47#12411yescharacteristic
236C2×C4×C47#12411yescharacteristic
237C2×C4×C47#12611yescharacteristic
238C2×C4×C47#12611yescharacteristic
239C2×C4×C47#12611yescharacteristic
240C2×C4×C47#12611yescharacteristic
241C2×C4×C47C23×C411yescharacteristic
242C2×C4×C47C22×D411yescharacteristic
243C2×C4×C47C22×D411yescharacteristic
244C2×C4×C47C2×#4111yescharacteristic
245C2×C4×C47C2×#4111yescharacteristic
246C2×C4×C47C2×#4111yescharacteristic
247C22⋊D47—42no—
248C22⋊D47—42no—
249C22⋊D47—42no—
250C22⋊D47—42no—
251C2×Dic47—24no—
252C2×Dic47—22no—
253C2×Dic47—22no—
254C2×Dic47—22no—
255C2×Dic47—44no—
256C2×Dic47—44no—
257C2×Dic47—42no—
258C2×Dic47—41no—
259C2×Dic47—41no—
260C2×Dic47—42no—
261C2×Dic47—82no—
262D188—22no—
263D188—22no—
264D188—41no—
265D188—41no—
266C4×D47—42no—
267C4×D47—42no—
268C4×D47—42no—
269C4×D47—42no—
270Dic94—22no—
271Dic94—22no—
272Dic94—41no—
273Dic94—41no—
274C8×C47—24no—
275C8×C47—24no—
276C8×C47—42no—
277C47⋊C8—24no—
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#38811yescharacteristic
287C22×C47#38811yescharacteristic
288C22×C47#38811yescharacteristic
289C22×C47#38811yescharacteristic
290C22×C47C2×#11711yescharacteristic
291C22×C47C2×#12311yescharacteristic
292C22×C47C2×#12411yescharacteristic
293C2×D47—42no—
294C2×D47—82no—
295C2×D47—82no—
296C2×D47—82no—
297C4×C47#38811yescharacteristic
298C4×C47#38811yescharacteristic
299C4×C47#38811yescharacteristic
300C4×C47#38811yescharacteristic
301C4×C47C2×C4×D411yescharacteristic
302C4×C47C2×C4×D411yescharacteristic
303C4×C47C2×#12111yescharacteristic
304C4×C47C2×#12611yescharacteristic
305Dic47—24no—
306Dic47—42no—
307Dic47—42no—
308Dic47—82no—
309C2×#430D4711yescharacteristic, complemented
310C2×#421—471no—
311C22×#104—471no—
312C2×#413—471no—
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#193212yescomplemented
324C2×C47C2×#38811yescharacteristic
325D47—82no—
326C22×#41—471no—
327C22×M16—471no—
328C22×M16C2×D4711yescharacteristic
329C22×M16C2×D4711yescharacteristic
330C22×M16C2×D4711yescharacteristic
331C2×#117—471no—
332C22×C42—471no—
333#430—22no—
334#430C2×D4714yescomplemented
335C2×#108—22no—
336#421—474no—
337#421—942no—
338C2×#104—474no—
339C2×#104—941no—
340C2×#104—941no—
341C2×#104—942no—
342C2×#104—942no—
343#413—474no—
344#413—474no—
345C2×#101—472no—
346C2×#100—472no—
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—472no—
355C2×#41—472no—
356C2×#41—941no—
357C2×#41—941no—
358C2×#41—941no—
359C2×#41—941no—
360C2×#41—941no—
361C2×#41—941no—
362C2×#41—941no—
363C2×#41—941no—
364C2×#41—941no—
365C2×#41—941no—
366C22×Q8—471no—
367C22×D4—471no—
368C22×D4—941no—
369C23×C4—941no—
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—21no—
379C2×M16—21no—
380C2×M16—21no—
381C2×M16—21no—
382C2×M16—21no—
383C2×M16—472no—
384C2×M16—472no—
385C2×M16—472no—
386C2×M16—941no—
387C2×M16—941no—
388C2×M16—941no—
389C2×M16C4×D4712yes—
390C2×M16C4×D4712yes—
391C2×M16C22⋊D4712yes—
392C2×M16C22⋊D4712yes—
393C2×M16C22×D4712yes—
394C2×M16C22×D4712yes—
395C2×M16C22×D4712yes—
396C22×C8—21no—
397C22×C8—21no—
398C22×C8—21no—
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—28no—
415#104—944no—
416#104—944no—
417#104—948no—
418#101—478no—
419#100—478no—
420#97—944no—
421C4×C8—944no—
422C24—941no—
423C24#1062535411yescharacteristic
424#41—942no—
425#41—942no—
426#41—942no—
427#41—942no—
428#41—942no—
429#41—942no—
430#41—942no—
431#41—942no—
432#41—1881no—
433#41—1881no—
434#41—1881no—
435#41—1881no—
436#41—1881no—
437#41—1881no—
438#41—1881no—
439#41—1881no—
440C2×Q8—472no—
441C2×Q8—941no—
442C2×Q8—941no—
443C2×Q8—941no—
444C2×Q8—941no—
445C2×Q8—941no—
446C2×D4—472no—
447C2×D4—942no—
448C2×D4—942no—
449C2×D4—941no—
450C2×D4—941no—
451C2×D4—941no—
452C2×D4—941no—
453C2×D4—941no—
454C2×D4—1881no—
455C2×D4—1881no—
456C2×D4—1881no—
457C2×D4—1881no—
458C22×C4—941no—
459C22×C4—941no—
460C22×C4—942no—
461C22×C4—941no—
462C22×C4—942no—
463C22×C4—942no—
464C22×C4—942no—
465C22×C4—1884no—
466C22×C4—1881no—
467C22×C4—1881no—
468C22×C4—1881no—
469C22×C4—1881no—
470C22×C4—1881no—
471C22×C4C2×C4×D4711yescharacteristic
472C22×C4C2×C4×D4711yescharacteristic
473C22×C4#1062535011yescharacteristic
474C22×C4#1062535011yescharacteristic
475C22×C4D4×D4711yescharacteristic
476C22×C4D4×D4711yescharacteristic
477C22×C4#1062535211yescharacteristic
478C22×C4#1062535211yescharacteristic
479C22×C4#1062535411yescharacteristic
480C22×C4#1062535411yescharacteristic
481C22×C4#1062535411yescharacteristic
482C22×C4C2×C22⋊D4711yescharacteristic
483C22×C4C2×C22⋊D4711yescharacteristic
484C22×C4C23×D4711yescharacteristic
485M16—22no—
486M16—22no—
487M16—22no—
488M16—22no—
489M16—22no—
490M16—22no—
491M16—22no—
492M16—22no—
493M16—41no—
494M16—41no—
495M16—474no—
496M16—942no—
497M16—942no—
498M16—942no—
499M16C2×C4×D4714yes—
500M16C2×C22⋊D4714yes—
501C2×C8—22no—
502C2×C8—22no—
503C2×C8—22no—
504C2×C8—22no—
505C2×C8—22no—
506C2×C8—22no—
507C2×C8—22no—
508C2×C8—41no—
509C2×C8—41no—
510C2×C8—942no—
511C2×C8—942no—
512C2×C8—942no—
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—42no—
526C23—942no—
527C23—3762no—
528C23—1881no—
529C23—1881no—
530C23#1309398211yescharacteristic
531C23#1309398211yescharacteristic
532C23#1309400911yescharacteristic
533C23#1309400911yescharacteristic
534C23#1309401311yescharacteristic
535C23#1309401311yescharacteristic
536C23C2×#1062535411yescharacteristic
537Q8—942no—
538Q8—942no—
539Q8—1881no—
540Q8—1881no—
541D4—942no—
542D4—942no—
543D4—1882no—
544D4—1882no—
545D4—1882no—
546D4—1882no—
547D4—1881no—
548D4—1881no—
549C2×C4—944no—
550C2×C4—942no—
551C2×C4—942no—
552C2×C4—942no—
553C2×C4—3762no—
554C2×C4—1884no—
555C2×C4—1884no—
556C2×C4—1882no—
557C2×C4—1882no—
558C2×C4—1881no—
559C2×C4—1881no—
560C2×C4—1882no—
561C2×C4—1882no—
562C2×C4—1882no—
563C2×C4—1882no—
564C2×C4#1309398211yescharacteristic
565C2×C4#1309398211yescharacteristic
566C2×C4C4×C22⋊D4711yescharacteristic
567C2×C4C4×C22⋊D4711yescharacteristic
568C2×C4C4×C22⋊D4711yescharacteristic
569C2×C4C4×C22⋊D4711yescharacteristic
570C2×C4#1309398611yescharacteristic
571C2×C4#1309398611yescharacteristic
572C2×C4#1309398611yescharacteristic
573C2×C4#1309398611yescharacteristic
574C2×C4#1309399611yescharacteristic
575C2×C4#1309399611yescharacteristic
576C2×C4#1309399611yescharacteristic
577C2×C4#1309399611yescharacteristic
578C2×C4#1309400911yescharacteristic
579C2×C4#1309400911yescharacteristic
580C2×C4#1309401311yescharacteristic
581C2×C4#1309401311yescharacteristic
582C2×C4#1309401911yescharacteristic
583C2×C4#1309401911yescharacteristic
584C2×C4#1309401911yescharacteristic
585C2×C4#1309401911yescharacteristic
586C2×C4C22×C4×D4711yescharacteristic
587C2×C4C2×D4×D4711yescharacteristic
588C2×C4C22×C22⋊D4711yescharacteristic
589C2×C4C2×#1062535211yescharacteristic
590C2×C4C2×#1062535011yescharacteristic
591C2×C4C2×#1062535411yescharacteristic
592C8—24no—
593C8—24no—
594C8—42no—
595C8—944no—
596C22—22no—
597C22—22no—
598C22—22no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—3762no—
604C22—3762no—
605C22—3762no—
606C22—1882no—
607C22#1568901311yescharacteristic
608C22#1568901311yescharacteristic
609C22#1568901311yescharacteristic
610C22#1568901311yescharacteristic
611C22C2×#1309398211yescharacteristic
612C22C2×#1309400911yescharacteristic
613C22C2×#1309401311yescharacteristic
614C4—944no—
615C4—3762no—
616C4—1882no—
617C4—1882no—
618C4#1568901311yescharacteristic
619C4#1568901311yescharacteristic
620C4#1568901311yescharacteristic
621C4#1568901311yescharacteristic
622C4C2×C4×C22⋊D4711yescharacteristic
623C4C2×#1309398611yescharacteristic
624C4C2×#1309399611yescharacteristic
625C4C2×#1309401911yescharacteristic
626C2—21no—
627C2—21no—
628C2—21no—
629C2—21no—
630C2—21no—
631C2—21no—
632C2—3762no—
633C2#2024405612yesdirect product factor
634C2C2×#1568901311yescharacteristic
subgroupG/H
centerC2×C4#13093996
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#430C2
socleC22×C47#388
prime radicalC22×#10625350C22
cosocleC22×C4×C47C24
hypercenterC2×#430D47
hypocenterC47C2×#1932
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#430

Complements

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

NH ≅ G/Ntype
4. C2×M16×Dic47C2semidirect
5. #20244056C2direct (N × H)
6. C2×#15688894C2semidirect
7. C2×#15688884C2semidirect
8. C2×C47×#430C2semidirect
20. #15689105C4semidirect
22. C2×#13093942C4semidirect
23. C2×#13093940C4semidirect
25. M16×Dic47C22semidirect
28. #15688894C22semidirect
29. #15688884C22semidirect
34. C47×#430C22semidirect
77. #13093942C2×C4semidirect
78. #13093940C2×C4semidirect
309. C2×#430D47semidirect
323. C2×C47#1932semidirect
334. #430C2×D47semidirect
353. C47C2×#1932semidirect
633. C2#20244056direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156891392
C22×#130939502
C2×#156891052
C2×M16×Dic472
#202440562
C2×#156888942
C2×#156888842
C2×C47×#4302
C2×#193247