Finite Group Databasebeta

← C2×#20244839 #26245197

Subgroups — C2×#20244839 #26245197

Order 12032.

906 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689141C211yesmaximal, characteristic
2C2×#15689120C211yesmaximal, characteristic
3C2×#15689105C211yesmaximal, characteristic
4#20244839C218yesmaximal, direct product factor
5C2×#15688895C211yesmaximal, characteristic, complemented
6C2×#15688888C211yesmaximal, characteristic, complemented
7C2×#15688879C211yesmaximal, characteristic, complemented
8C2×C47×#424C211yesmaximal, characteristic, complemented
9C22×#10625350C2211yescharacteristic
10C22×#10625329C2211yescharacteristic
11C22×#10625329C2211yescharacteristic
12C2×#13093983C2211yescharacteristic
13#15689141—22no—
14#15689141C2214yes—
15C2×#13093952—22no—
16#15689120—22no—
17#15689120C2214yes—
18C2×#13093949—21no—
19C2×#13093946—21no—
20#15689105—22no—
21#15689105C2214yes—
22C2×#13093942—21no—
23C2×#13093940—21no—
24#15688895C2214yescomplemented
25#15688888C2214yescomplemented
26#15688879C2214yescomplemented
27C22×M16×C47C2211yescharacteristic
28C23×C8×C47C2211yescharacteristic
29C2×#117×C47C2211yescharacteristic
30C47×#424—22no—
31C47×#424C2214yescomplemented
32C2×C4⋊C8×C47—22no—
33C2×#10625350—21no—
34C2×#10625350—21no—
35C2×#10625350—21no—
36C2×#10625350—21no—
37C2×#10625350—21no—
38C2×#10625350—21no—
39C2×#10625350—21no—
40C2×#10625350—21no—
41C2×#10625350—21no—
42C2×#10625350—21no—
43C2×#10625350D412yes—
44C2×#10625350C2312yes—
45C22×Dic94D411yescharacteristic
46C22×D188D411yescharacteristic
47C22×C22⋊D47—21no—
48C22×C4×D47—21no—
49C2×#10625329—21no—
50C2×#10625329—21no—
51C2×#10625329—21no—
52C2×#10625329—21no—
53C2×#10625329—21no—
54C2×#10625329—21no—
55C2×#10625329—21no—
56C2×#10625329—21no—
57C2×#10625329—21no—
58C2×#10625329—21no—
59C2×#10625329C2312yes—
60C2×#10625329C2312yes—
61C22×C47⋊C8—21no—
62C22×C47⋊C8—21no—
63#13093983—21no—
64#13093983—21no—
65#13093983—21no—
66#13093983C2312yes—
67C2×C4⋊Dic47—21no—
68C2×C22⋊Dic47—21no—
69C2×C4×Dic47—21no—
70#13093952—28no—
71#13093949—24no—
72#13093946—24no—
73#13093942—24no—
74#13093940—24no—
75C23×C4×C47C2311yescharacteristic
76C2×M16×C47—21no—
77C2×M16×C47—21no—
78C2×M16×C47—21no—
79C2×M16×C47—21no—
80C2×M16×C47—21no—
81C2×M16×C47C2312yes—
82C22×C8×C47—21no—
83C22×C8×C47—21no—
84C22×C8×C47—21no—
85C22×C8×C47—21no—
86C22×C8×C47—21no—
87C22×C8×C47—21no—
88C22×C8×C47—21no—
89C22×C8×C47C2312yes—
90#117×C47—21no—
91#117×C47—21no—
92#117×C47D412yes—
93#117×C47C2312yes—
94C2×C4⋊C4×C47—21no—
95C2×C22⋊C4×C47—21no—
96C2×C42×C47D412yes—
97C4⋊C8×C47—28no—
98C24×C47#4111yescharacteristic
99C23×D47—21no—
100C22×C4×C47—22no—
101C22×C4×C47C2×D411yescharacteristic
102C22×C4×C47C2×D411yescharacteristic
103C22×C4×C47C2×D411yescharacteristic
104C22×C4×C47C2×D411yescharacteristic
105C22×C4×C47#4111yescharacteristic
106C22×C4×C47#4111yescharacteristic
107C22×C4×C47#4111yescharacteristic
108C22×C4×C47#4111yescharacteristic
109C22×C4×C47#4111yescharacteristic
110C22×C4×C47#4111yescharacteristic
111C22×C4×C47#4111yescharacteristic
112C22×C4×C47#4111yescharacteristic
113C22×C4×C47#4111yescharacteristic
114C22×C4×C47C2411yescharacteristic
115C2×C22⋊D47—22no—
116C2×C22⋊D47—22no—
117C2×C22⋊D47—41no—
118C2×C22⋊D47—41no—
119C2×C22⋊D47—41no—
120C2×C22⋊D47—41no—
121C22×Dic47—21no—
122C22×Dic47—41no—
123#10625350—22no—
124#10625350—22no—
125#10625350—22no—
126#10625350—22no—
127#10625350—22no—
128#10625350—22no—
129#10625350—22no—
130#10625350—22no—
131#10625350—41no—
132#10625350—41no—
133#10625350—41no—
134#10625350—41no—
135#10625350—41no—
136#10625350—41no—
137#10625350—41no—
138#10625350—41no—
139C2×D188—21no—
140C2×D188—21no—
141C2×D188—21no—
142C2×D188—21no—
143C2×D188—21no—
144C2×D188C2×D412yes—
145C2×C4×D47—22no—
146C2×C4×D47—22no—
147C2×C4×D47—41no—
148C2×C4×D47—41no—
149C2×C4×D47—41no—
150C2×C4×D47—41no—
151C2×Dic94—21no—
152C2×Dic94—21no—
153C2×Dic94—21no—
154C2×Dic94—21no—
155C2×Dic94—21no—
156C2×Dic94C2×D412yes—
157M16×C47—22no—
158M16×C47—22no—
159M16×C47—41no—
160M16×C47—41no—
161C2×C8×C47—22no—
162C2×C8×C47—22no—
163C2×C8×C47—22no—
164C2×C8×C47—22no—
165C2×C8×C47—41no—
166C2×C8×C47—41no—
167C2×C8×C47—41no—
168C2×C8×C47—41no—
169C2×C8×C47—41no—
170C2×C8×C47—41no—
171C4⋊C4×C47—22no—
172C4⋊C4×C47—22no—
173C22⋊C4×C47—22no—
174C22⋊C4×C47—22no—
175C42×C47—22no—
176C42×C47C2×D414yes—
177C22⋊Dic47—22no—
178C22⋊Dic47—41no—
179C4⋊Dic47—22no—
180C4⋊Dic47—41no—
181C4×Dic47—22no—
182C4×Dic47—41no—
183#10625329—22no—
184#10625329—22no—
185#10625329—22no—
186#10625329—22no—
187#10625329—41no—
188#10625329—41no—
189#10625329—41no—
190#10625329—41no—
191C2×C47⋊C8—22no—
192C2×C47⋊C8—22no—
193C2×C47⋊C8—41no—
194C2×C47⋊C8—41no—
195C2×C47⋊C8—41no—
196C2×C47⋊C8—41no—
197C23×C47—42no—
198C23×C47#12311yescharacteristic
199C23×C47#12311yescharacteristic
200C23×C47#12311yescharacteristic
201C23×C47#12311yescharacteristic
202C23×C47#12611yescharacteristic
203C23×C47#12611yescharacteristic
204C23×C47C2×#4111yescharacteristic
205C22×D47—22no—
206C22×D47—41no—
207C22×D47—41no—
208C22×D47—82no—
209C2×C4×C47—24no—
210C2×C4×C47—44no—
211C2×C4×C47#12111yescharacteristic
212C2×C4×C47#12111yescharacteristic
213C2×C4×C47#12111yescharacteristic
214C2×C4×C47#12111yescharacteristic
215C2×C4×C47#12311yescharacteristic
216C2×C4×C47#12311yescharacteristic
217C2×C4×C47#12311yescharacteristic
218C2×C4×C47#12311yescharacteristic
219C2×C4×C47#12311yescharacteristic
220C2×C4×C47#12311yescharacteristic
221C2×C4×C47#12311yescharacteristic
222C2×C4×C47#12311yescharacteristic
223C2×C4×C47#12411yescharacteristic
224C2×C4×C47#12411yescharacteristic
225C2×C4×C47#12411yescharacteristic
226C2×C4×C47#12411yescharacteristic
227C2×C4×C47#12611yescharacteristic
228C2×C4×C47#12611yescharacteristic
229C2×C4×C47#12611yescharacteristic
230C2×C4×C47#12611yescharacteristic
231C2×C4×C47#12611yescharacteristic
232C2×C4×C47#12611yescharacteristic
233C2×C4×C47C22×D411yescharacteristic
234C2×C4×C47C22×D411yescharacteristic
235C2×C4×C47C2×#4111yescharacteristic
236C2×C4×C47C2×#4111yescharacteristic
237C2×C4×C47C2×#4111yescharacteristic
238C2×C4×C47C2×#4111yescharacteristic
239C22⋊D47—42no—
240C22⋊D47—42no—
241C22⋊D47—42no—
242C22⋊D47—42no—
243C2×Dic47—22no—
244C2×Dic47—41no—
245C2×Dic47—41no—
246C2×Dic47—42no—
247C2×Dic47—82no—
248D188—22no—
249D188—22no—
250D188—41no—
251D188—41no—
252C4×D47—42no—
253C4×D47—42no—
254C4×D47—42no—
255C4×D47—42no—
256Dic94—22no—
257Dic94—22no—
258Dic94—41no—
259Dic94—41no—
260C8×C47—42no—
261C8×C47—42no—
262C47⋊C8—42no—
263C47⋊C8—42no—
264C2×#2080—471nomaximal, Sylow
265C22×C47—22no—
266C22×C47—22no—
267C22×C47—22no—
268C22×C47—41no—
269C22×C47—41no—
270C22×C47—41no—
271C22×C47—41no—
272C22×C47#39711yescharacteristic
273C22×C47#39711yescharacteristic
274C22×C47#39711yescharacteristic
275C22×C47#39711yescharacteristic
276C22×C47C2×#12311yescharacteristic
277C22×C47C2×#12311yescharacteristic
278C22×C47C2×#12611yescharacteristic
279C2×D47—42no—
280C2×D47—82no—
281C2×D47—82no—
282C2×D47—82no—
283C4×C47—44no—
284C4×C47#39711yescharacteristic
285C4×C47#39711yescharacteristic
286C4×C47#39711yescharacteristic
287C4×C47#39711yescharacteristic
288C4×C47C2×#12111yescharacteristic
289C4×C47C2×#12311yescharacteristic
290C4×C47C2×#12411yescharacteristic
291C4×C47C2×#12611yescharacteristic
292Dic47—42no—
293Dic47—82no—
294C2×#424D4711yescharacteristic, complemented
295C2×#421—471no—
296C2×#416—471no—
297C2×#413—471no—
298#2080—478no—
299C2×#344—471no—
300C2×#341—471no—
301C2×H(3,ℤ/4)—471no—
302C2×C47—21no—
303C2×C47—21no—
304C2×C47—21no—
305C2×C47—21no—
306C2×C47—21no—
307C2×C47—21no—
308C2×C47#208012yescomplemented
309C2×C47C2×#39711yescharacteristic
310D47—82no—
311C22×#41—471no—
312C22×M16—471no—
313C22×M16—471no—
314C22×M16C2×D4711yescharacteristic
315C23×C8C2×D4711yescharacteristic
316C2×#117—471no—
317C2×#117C2×D4711yescharacteristic
318#424—22no—
319#424C2×D4714yescomplemented
320C2×C4⋊C8—22no—
321#421—474no—
322#421—942no—
323C2×#104—942no—
324#416—474no—
325#416—942no—
326C2×#103—941no—
327C2×#102—941no—
328#413—474no—
329#413—942no—
330C2×#101—941no—
331C2×#100—941no—
332#344—474no—
333#341—474no—
334H(3,ℤ/4)—474no—
335C47C2×#208011yescharacteristic, complemented, Sylow
336C2×#41—472no—
337C2×#41—472no—
338C2×#41—941no—
339C2×#41—941no—
340C2×#41—941no—
341C2×#41—941no—
342C2×#41—941no—
343C2×#41—941no—
344C2×#41—941no—
345C2×#41—941no—
346C2×#41—941no—
347C2×#41—941no—
348C22×Q8—471no—
349C22×D4—471no—
350C22×D4—941no—
351C23×C4—941no—
352C23×C4C22×D4711yescharacteristic
353C2×M16—21no—
354C2×M16—21no—
355C2×M16—21no—
356C2×M16—21no—
357C2×M16—21no—
358C2×M16—472no—
359C2×M16—472no—
360C2×M16—941no—
361C2×M16—941no—
362C2×M16—941no—
363C2×M16—941no—
364C2×M16—941no—
365C2×M16—941no—
366C2×M16—941no—
367C2×M16—941no—
368C2×M16—941no—
369C2×M16—941no—
370C2×M16C22×D4712yes—
371C22×C8—21no—
372C22×C8—21no—
373C22×C8—21no—
374C22×C8—21no—
375C22×C8—21no—
376C22×C8—21no—
377C22×C8—21no—
378C22×C8—941no—
379C22×C8—941no—
380C22×C8C22×D4712yes—
381#117—21no—
382#117—21no—
383#117—472no—
384#117—941no—
385#117—941no—
386#117—941no—
387#117C22⋊D4712yes—
388#117C22×D4712yes—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—941no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—941no—
393C2×C42—941no—
394C2×C42C22⋊D4712yes—
395C4⋊C8—28no—
396#104—948no—
397#103—944no—
398#102—944no—
399#101—944no—
400#100—944no—
401C24—941no—
402C24#1062535011yescharacteristic
403#41—942no—
404#41—942no—
405#41—942no—
406#41—942no—
407#41—942no—
408#41—942no—
409#41—942no—
410#41—942no—
411#41—1881no—
412#41—1881no—
413#41—1881no—
414#41—1881no—
415#41—1881no—
416#41—1881no—
417#41—1881no—
418#41—1881no—
419C2×Q8—472no—
420C2×Q8—941no—
421C2×Q8—941no—
422C2×Q8—941no—
423C2×Q8—941no—
424C2×Q8—941no—
425C2×D4—472no—
426C2×D4—942no—
427C2×D4—942no—
428C2×D4—941no—
429C2×D4—941no—
430C2×D4—941no—
431C2×D4—941no—
432C2×D4—941no—
433C2×D4—1881no—
434C2×D4—1881no—
435C2×D4—1881no—
436C2×D4—1881no—
437C22×C4—22no—
438C22×C4—941no—
439C22×C4—942no—
440C22×C4—942no—
441C22×C4—1881no—
442C22×C4—1881no—
443C22×C4—1881no—
444C22×C4—1881no—
445C22×C4—1881no—
446C22×C4#1062535011yescharacteristic
447C22×C4#1062535011yescharacteristic
448C22×C4#1062535011yescharacteristic
449C22×C4D4×D4711yescharacteristic
450C22×C4D4×D4711yescharacteristic
451C22×C4#1062535211yescharacteristic
452C22×C4#1062535211yescharacteristic
453C22×C4#1062535411yescharacteristic
454C22×C4#1062535411yescharacteristic
455C22×C4#1062535411yescharacteristic
456C22×C4#1062535411yescharacteristic
457C22×C4C2×C22⋊D4711yescharacteristic
458C22×C4C2×C22⋊D4711yescharacteristic
459C22×C4C23×D4711yescharacteristic
460M16—22no—
461M16—22no—
462M16—41no—
463M16—41no—
464M16—942no—
465M16—942no—
466M16—942no—
467M16—942no—
468M16—1881no—
469M16—1881no—
470M16—1881no—
471M16—1881no—
472C2×C8—22no—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—41no—
477C2×C8—41no—
478C2×C8—41no—
479C2×C8—41no—
480C2×C8—41no—
481C2×C8—41no—
482C2×C8—942no—
483C2×C8—942no—
484C2×C8—1881no—
485C2×C8—1881no—
486C2×C8—1881no—
487C2×C8—1881no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—942no—
491C4⋊C4—1881no—
492C22⋊C4—22no—
493C22⋊C4—22no—
494C22⋊C4—942no—
495C22⋊C4—1881no—
496C42—22no—
497C42—942no—
498C42—1881no—
499C42C2×C22⋊D4714yes—
500C23—42no—
501C23—942no—
502C23—3762no—
503C23—1881no—
504C23—1881no—
505C23#1309400711yescharacteristic
506C23#1309400711yescharacteristic
507C23#1309400911yescharacteristic
508C23#1309400911yescharacteristic
509C23#1309401911yescharacteristic
510C23#1309401911yescharacteristic
511C23C2×#1062535011yescharacteristic
512Q8—942no—
513Q8—942no—
514Q8—1881no—
515Q8—1881no—
516D4—942no—
517D4—942no—
518D4—1882no—
519D4—1882no—
520D4—1882no—
521D4—1882no—
522D4—1881no—
523D4—1881no—
524C2×C4—24no—
525C2×C4—44no—
526C2×C4—942no—
527C2×C4—3762no—
528C2×C4—1882no—
529C2×C4—1881no—
530C2×C4—1881no—
531C2×C4—1882no—
532C2×C4—1882no—
533C2×C4—1882no—
534C2×C4—1882no—
535C2×C4#1309399511yescharacteristic
536C2×C4#1309399511yescharacteristic
537C2×C4#1309399511yescharacteristic
538C2×C4#1309399511yescharacteristic
539C2×C4#1309400711yescharacteristic
540C2×C4#1309400711yescharacteristic
541C2×C4#1309400911yescharacteristic
542C2×C4#1309400911yescharacteristic
543C2×C4#1309400911yescharacteristic
544C2×C4#1309400911yescharacteristic
545C2×C4#1309400911yescharacteristic
546C2×C4#1309400911yescharacteristic
547C2×C4#1309401311yescharacteristic
548C2×C4#1309401311yescharacteristic
549C2×C4#1309401311yescharacteristic
550C2×C4#1309401311yescharacteristic
551C2×C4#1309401911yescharacteristic
552C2×C4#1309401911yescharacteristic
553C2×C4#1309401911yescharacteristic
554C2×C4#1309401911yescharacteristic
555C2×C4#1309401911yescharacteristic
556C2×C4#1309401911yescharacteristic
557C2×C4C2×D4×D4711yescharacteristic
558C2×C4C22×C22⋊D4711yescharacteristic
559C2×C4C2×#1062535211yescharacteristic
560C2×C4C2×#1062535011yescharacteristic
561C2×C4C2×#1062535411yescharacteristic
562C2×C4C2×#1062535411yescharacteristic
563C8—42no—
564C8—42no—
565C8—1882no—
566C8—1882no—
567C22—22no—
568C22—22no—
569C22—22no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—3762no—
575C22—3762no—
576C22—3762no—
577C22—1882no—
578C22#1568904911yescharacteristic
579C22#1568904911yescharacteristic
580C22#1568904911yescharacteristic
581C22#1568904911yescharacteristic
582C22C2×#1309400711yescharacteristic
583C22C2×#1309400911yescharacteristic
584C22C2×#1309401911yescharacteristic
585C4—44no—
586C4—3762no—
587C4—1882no—
588C4#1568904911yescharacteristic
589C4#1568904911yescharacteristic
590C4#1568904911yescharacteristic
591C4#1568904911yescharacteristic
592C4C2×#1309399511yescharacteristic
593C4C2×#1309400911yescharacteristic
594C4C2×#1309401311yescharacteristic
595C4C2×#1309401911yescharacteristic
596C2—21no—
597C2—21no—
598C2—21no—
599C2—21no—
600C2—21no—
601C2—21no—
602C2—3762no—
603C2#2024483912yesdirect product factor
604C2C2×#1568904911yescharacteristic
subgroupG/H
centerC2×C4#13094013
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC2×C47×#424C2
socleC22×C47#397
prime radicalC22×#10625350C22
hypercenterC2×#424D47
hypocenterC47C2×#2080
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#424

Complements

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

NH ≅ G/Ntype
4. #20244839C2direct (N × H)
5. C2×#15688895C2semidirect
6. C2×#15688888C2semidirect
7. C2×#15688879C2semidirect
8. C2×C47×#424C2semidirect
24. #15688895C22semidirect
25. #15688888C22semidirect
26. #15688879C22semidirect
31. C47×#424C22semidirect
294. C2×#424D47semidirect
308. C2×C47#2080semidirect
319. #424C2×D47semidirect
335. C47C2×#2080semidirect
603. C2#20244839direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156891412
C2×#156891202
C2×#156891052
#202448392
C2×#156888952
C2×#156888882
C2×#156888792
C2×C47×#4242
C2×#208047