Finite Group Databasebeta

← C2×#20253313 #27084058

Subgroups — C2×#20253313 #27084058

Order 12032.

2650 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689634C211yesmaximal, characteristic
2C23×C4⋊Dic47C211yesmaximal, characteristic, complemented
3#20253313C2116yesmaximal, direct product factor
4C2×#15689459C212yesmaximal, complemented
5C2×#15689442C212yesmaximal, complemented
6C2×#15689454C212yesmaximal, complemented
7C2×#15689437C212yesmaximal, complemented
8C2×#15689165C212yesmaximal, complemented
9C2×#15689125C212yesmaximal, complemented
10C2×C47×#407C211yesmaximal, characteristic, complemented
11C22×#10625350C2211yescharacteristic
12C24×Dic47—21no—
13#15689634—24no—
14#15689634C2218yes—
15C2×#13094007—21no—
16C2×#13094003C2211yescharacteristic
17C2×#13094003C2211yescharacteristic
18C2×#13093998C2211yescharacteristic
19C2×#13093998C2211yescharacteristic
20C2×#13093993—21no—
21C2×C4×C22⋊D47—21no—
22C2×C4×C22⋊D47—21no—
23C2×#13093983C2211yescharacteristic
24C22×C4⋊Dic47—21no—
25C22×C4⋊Dic47—21no—
26C22×C4⋊Dic47—21no—
27C22×C4⋊Dic47—24no—
28C22×C4⋊Dic47C2212yes—
29C22×C4⋊Dic47C2212yes—
30C22×C4⋊Dic47C2212yes—
31C22×C4⋊Dic47C2218yescomplemented
32#15689459C22116yescomplemented
33#15689454C22116yescomplemented
34#15689442C22116yescomplemented
35#15689437C22116yescomplemented
36#15689165C22116yescomplemented
37C2×#13093958C2214yescomplemented
38C2×#13093956C2214yescomplemented
39#15689125C22116yescomplemented
40C2×#13093949C2214yescomplemented
41C2×#13093946C2214yescomplemented
42C24×C4×C47C2211yescharacteristic
43C22×M16×C47C2212yes—
44C47×#407C2218yescomplemented
45C2×C22⋊C8×C47C2212yes—
46C2×C22⋊C8×C47C2212yes—
47C2×#10625350—22no—
48C2×#10625350—28no—
49C2×#10625350C2314yes—
50C22×Dic94C2311yescharacteristic
51C22×D188C2311yescharacteristic
52C22×C22⋊D47—21no—
53C22×C22⋊D47—21no—
54C22×C22⋊D47—21no—
55C23×Dic47—22no—
56C23×Dic47—22no—
57C23×Dic47—22no—
58C23×Dic47—28no—
59C23×Dic47—48no—
60C22×C4×D47—21no—
61#13094007—28no—
62#13094003—22no—
63#13094003—22no—
64#13094003C2314yes—
65#13094003C2314yes—
66#13093998—22no—
67#13093998—22no—
68#13093998C2314yes—
69#13093998C2314yes—
70#13093993—28no—
71C4×C22⋊D47—28no—
72C4×C22⋊D47—28no—
73#13093983—22no—
74#13093983C2314yes—
75C2×C4⋊Dic47—22no—
76C2×C4⋊Dic47—22no—
77C2×C4⋊Dic47—24no—
78C2×C4⋊Dic47—24no—
79C2×C4⋊Dic47—22no—
80C2×C4⋊Dic47—24no—
81C2×C4⋊Dic47—28no—
82C2×C4⋊Dic47—28no—
83C2×C4⋊Dic47—28no—
84C2×C4⋊Dic47C2314yes—
85C2×C4⋊Dic47C2318yes—
86C2×C4⋊Dic47C2318yes—
87C2×C4⋊Dic47C2318yes—
88C2×C4⋊Dic47C2311yescharacteristic
89C2×C4⋊Dic47C2311yescharacteristic
90C2×Dic47⋊C4—21no—
91C2×Dic47⋊C4—21no—
92C2×C22⋊Dic47—21no—
93C2×C22⋊Dic47—21no—
94C2×C22⋊Dic47—21no—
95C2×(C2×D47)⋊C4—21no—
96C2×(C2×D47)⋊C4—21no—
97C2×C4×Dic47—21no—
98#13093958C23116yescomplemented
99#13093956C23116yescomplemented
100#13093949C23116yescomplemented
101#13093946C23116yescomplemented
102C25×C47D411yescharacteristic
103C23×C4×C47—28no—
104C23×C4×C47D411yescharacteristic
105C23×C4×C47D411yescharacteristic
106C23×C4×C47D411yescharacteristic
107C23×C4×C47D414yes—
108C23×C4×C47C2311yescharacteristic
109C23×C4×C47C2311yescharacteristic
110C23×C4×C47C2314yes—
111C23×C4×C47C2311yescharacteristic
112C2×M16×C47—28no—
113C2×M16×C47C2318yes—
114C22×C8×C47C2314yes—
115C22⋊C8×C47C2318yes—
116C22⋊C8×C47C2318yes—
117C24×C47—24no—
118C24×C47—24no—
119C24×C47—24no—
120C24×C47C2×D414yes—
121C24×C47C2×D411yescharacteristic
122C24×C47C2×D411yescharacteristic
123C24×C47C2×D411yescharacteristic
124C23×D47—21no—
125C22×C4×C47—24no—
126C22×C4×C47—24no—
127C22×C4×C47—24no—
128C22×C4×C47—216no—
129C22×C4×C47—24no—
130C22×C4×C47—24no—
131C22×C4×C47—216no—
132C22×C4×C47C2×D411yescharacteristic
133C22×C4×C47C2×D411yescharacteristic
134C22×C4×C47C2×D414yes—
135C22×C4×C47C2×D414yes—
136C22×C4×C47C2×D412yes—
137C22×C4×C47C2×D412yes—
138C22×C4×C47C2×D414yes—
139C22×C4×C47C2×D411yescharacteristic
140C22×C4×C47C2×D412yes—
141C22×C4×C47#4118yes—
142C22×C4×C47C2412yes—
143C22×C4×C47C2412yes—
144C22×C4×C47C2411yescharacteristic
145C22×C4×C47C2412yes—
146C2×C22⋊D47—24no—
147C2×C22⋊D47—24no—
148C2×C22⋊D47—24no—
149C2×C22⋊D47—44no—
150C2×C22⋊D47—44no—
151C2×C22⋊D47—44no—
152C22×Dic47—21no—
153C22×Dic47—21no—
154C22×Dic47—21no—
155C22×Dic47—28no—
156C22×Dic47—28no—
157C22×Dic47—28no—
158C22×Dic47—24no—
159C22×Dic47—48no—
160C22×Dic47—48no—
161C22×Dic47—432no—
162C22×Dic47—48no—
163#10625350—216no—
164#10625350—48no—
165C2×D188—24no—
166C2×D188—21no—
167C2×D188C2412yes—
168C2×C4×D47—24no—
169C2×C4×D47—44no—
170C2×Dic94—24no—
171C2×Dic94—21no—
172C2×Dic94C2412yes—
173M16×C47—216no—
174C2×C8×C47—28no—
175C2×C8×C47C2418yes—
176C22⋊Dic47—24no—
177C22⋊Dic47—24no—
178C22⋊Dic47—24no—
179(C2×D47)⋊C4—24no—
180(C2×D47)⋊C4—24no—
181C4⋊Dic47—28no—
182C4⋊Dic47—28no—
183C4⋊Dic47—28no—
184C4⋊Dic47—24no—
185C4⋊Dic47—21no—
186C4⋊Dic47—21no—
187C4⋊Dic47C2418yes—
188C4⋊Dic47C2412yes—
189C4⋊Dic47C2412yes—
190Dic47⋊C4—24no—
191Dic47⋊C4—24no—
192C4×Dic47—24no—
193C23×C47—232no—
194C23×C47—28no—
195C23×C47—22no—
196C23×C47—22no—
197C23×C47—28no—
198C23×C47—22no—
199C23×C47—22no—
200C23×C47—28no—
201C23×C47—22no—
202C23×C47—22no—
203C23×C47#12314yes—
204C23×C47AGL(1,ℤ/8)14yes—
205C23×C47#13714yes—
206C23×C47C22×D412yes—
207C23×C47C22×D412yes—
208C23×C47C22×D412yes—
209C23×C47C22×D411yescharacteristic
210C22×D47—22no—
211C22×D47—42no—
212C22×D47—42no—
213C22×D47—42no—
214C2×C4×C47—28no—
215C2×C4×C47—22no—
216C2×C4×C47—22no—
217C2×C4×C47—24no—
218C2×C4×C47—24no—
219C2×C4×C47—28no—
220C2×C4×C47—28no—
221C2×C4×C47—24no—
222C2×C4×C47—24no—
223C2×C4×C47#12314yes—
224C2×C4×C47#12318yes—
225C2×C4×C47C22×D412yes—
226C2×C4×C47C22×D412yes—
227C2×C4×C47C22×D412yes—
228C2×C4×C47C22×D411yescharacteristic
229C2×C4×C47C2×#4114yes—
230C2×C4×C47C2×#4118yes—
231C2×C4×C47C2511yescharacteristic
232C22⋊D47—48no—
233C22⋊D47—48no—
234C22⋊D47—48no—
235C2×Dic47—22no—
236C2×Dic47—22no—
237C2×Dic47—22no—
238C2×Dic47—28no—
239C2×Dic47—416no—
240C2×Dic47—416no—
241C2×Dic47—42no—
242C2×Dic47—416no—
243C2×Dic47—48no—
244C2×Dic47—42no—
245C2×Dic47—42no—
246D188—24no—
247D188—42no—
248C4×D47—48no—
249Dic94—24no—
250Dic94—42no—
251C8×C47—28no—
252C2×#3092—471nomaximal, Sylow
253C22×C47—232no—
254C22×C47—28no—
255C22×C47—28no—
256C22×C47—28no—
257C22×C47—22no—
258C22×C47—22no—
259C22×C47—22no—
260C22×C47—22no—
261C22×C47—22no—
262C22×C47—22no—
263C22×C47C2×#12314yes—
264C22×C47C2×#12312yes—
265C22×C47C2×AGL(1,ℤ/8)14yes—
266C22×C47C2×AGL(1,ℤ/8)12yes—
267C22×C47C2×#13714yes—
268C22×C47C2×#13712yes—
269C22×C47C23×D411yescharacteristic
270C2×D47—42no—
271C2×D47—42no—
272C2×D47—42no—
273C2×D47—84no—
274C4×C47—22no—
275C4×C47—22no—
276C4×C47C2×#12312yes—
277C4×C47C2×#12314yes—
278C4×C47C22×#4112yes—
279Dic47—42no—
280Dic47—48no—
281Dic47—42no—
282Dic47—42no—
283C2×#525—471no—
284C23×C4⋊C4—471no—
285#3092—4716no—
286C2×#484—472no—
287C2×#481—472no—
288C2×#483—472no—
289C2×#480—472no—
290C2×#428—472no—
291C2×#417—472no—
292C2×#407D4711yescharacteristic, complemented
293C2×C47—24no—
294C2×C47—24no—
295C2×C47—24no—
296C2×C47#309214yescomplemented
297C2×C47C22×#12311yescharacteristic
298C2×C47C22×AGL(1,ℤ/8)11yescharacteristic
299C2×C47C22×#13711yescharacteristic
300D47—82no—
301C22×#41—471no—
302C24×C4—941no—
303C24×C4C2×D4711yescharacteristic
304C22×M16C2×D4712yes—
305#525—478no—
306#525—944no—
307C2×#123—941no—
308C2×C22⋊Q8—471no—
309C2×C22⋊Q8—471no—
310C2×#121—471no—
311C2×#121—471no—
312C2×#120—941no—
313C2×C4×D4—941no—
314C2×C4×D4—941no—
315C2×#117—471no—
316C22×C4⋊C4—472no—
317C22×C4⋊C4—472no—
318C22×C4⋊C4—478no—
319C22×C4⋊C4—472no—
320C22×C4⋊C4—941no—
321C22×C4⋊C4—941no—
322C22×C4⋊C4—941no—
323C22×C4⋊C4—944no—
324#484—4716no—
325#483—4716no—
326#481—4716no—
327#480—4716no—
328#428—4716no—
329C2×#107—474no—
330C2×#106—474no—
331#417—4716no—
332C2×#103—474no—
333C2×#102—474no—
334#407C2×D4718yescomplemented
335C2×C22⋊C8C2×D4712yes—
336C2×C22⋊C8C2×D4712yes—
337C47C2×#309211yescharacteristic, complemented, Sylow
338C25D18811yescharacteristic
339C2×#41—474no—
340C2×#41—942no—
341C2×#41—948no—
342C22×Q8—471no—
343C22×D4—471no—
344C22×D4—941no—
345C22×D4—941no—
346C22×D4—941no—
347C23×C4—28no—
348C23×C4—948no—
349C23×C4—942no—
350C23×C4—942no—
351C23×C4—942no—
352C23×C4—941no—
353C23×C4—1888no—
354C23×C4D18811yescharacteristic
355C23×C4D18811yescharacteristic
356C23×C4D18811yescharacteristic
357C23×C4D18814yes—
358C23×C4C22×D4711yescharacteristic
359C23×C4C22×D4711yescharacteristic
360C23×C4C22×D4714yes—
361C23×C4C22×D4711yescharacteristic
362C2×M16—28no—
363C2×M16C22×D4718yes—
364C22×C8C22×D4714yes—
365#123—948no—
366C22⋊Q8—474no—
367C22⋊Q8—474no—
368C22⋊Q8—942no—
369C22⋊Q8—942no—
370#121—474no—
371#121—474no—
372#121—942no—
373#121—942no—
374#120—948no—
375C4×D4—948no—
376C4×D4—948no—
377#117—474no—
378#117—942no—
379C2×C4⋊C4—474no—
380C2×C4⋊C4—478no—
381C2×C4⋊C4—478no—
382C2×C4⋊C4—478no—
383C2×C4⋊C4—471no—
384C2×C4⋊C4—471no—
385C2×C4⋊C4—948no—
386C2×C4⋊C4—948no—
387C2×C4⋊C4—944no—
388C2×C4⋊C4—944no—
389C2×C4⋊C4—948no—
390C2×C4⋊C4—944no—
391C2×C4⋊C4—942no—
392C2×C4⋊C4—942no—
393C2×C4⋊C4—942no—
394C2×C4⋊C4—941no—
395C2×C4⋊C4—941no—
396C2×C22⋊C4—941no—
397C2×C22⋊C4—941no—
398C2×C22⋊C4—941no—
399C2×C22⋊C4—941no—
400C2×C22⋊C4—941no—
401C2×C42—941no—
402#107—4716no—
403#106—4716no—
404#103—4716no—
405#102—4716no—
406C22⋊C8C22×D4718yes—
407C22⋊C8C22×D4718yes—
408C24—24no—
409C24—24no—
410C24—24no—
411C24—941no—
412C24C2×D18814yes—
413C24C2×D18811yescharacteristic
414C24C2×D18811yescharacteristic
415C24C2×D18811yescharacteristic
416#41—9416no—
417#41—1888no—
418C2×Q8—472no—
419C2×Q8—941no—
420C2×Q8—944no—
421C2×D4—472no—
422C2×D4—944no—
423C2×D4—944no—
424C2×D4—944no—
425C2×D4—941no—
426C2×D4—944no—
427C2×D4—1884no—
428C2×D4—1884no—
429C2×D4—1884no—
430C22×C4—24no—
431C22×C4—24no—
432C22×C4—24no—
433C22×C4—216no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—216no—
437C22×C4—948no—
438C22×C4—948no—
439C22×C4—948no—
440C22×C4—941no—
441C22×C4—941no—
442C22×C4—941no—
443C22×C4—944no—
444C22×C4—944no—
445C22×C4—18832no—
446C22×C4—1888no—
447C22×C4—1888no—
448C22×C4—1888no—
449C22×C4—1884no—
450C22×C4C2×D18814yes—
451C22×C4C2×D18814yes—
452C22×C4C2×D18812yes—
453C22×C4C2×D18812yes—
454C22×C4C2×D18814yes—
455C22×C4C2×D18811yescharacteristic
456C22×C4C2×D18811yescharacteristic
457C22×C4C2×D18812yes—
458C22×C4C2×D18811yescharacteristic
459C22×C4#1062535218yes—
460C22×C4C23×D4712yes—
461C22×C4C23×D4712yes—
462C22×C4C23×D4712yes—
463C22×C4C23×D4711yescharacteristic
464M16—216no—
465C2×C8—28no—
466C2×C8C23×D4718yes—
467C4⋊C4—478no—
468C4⋊C4—472no—
469C4⋊C4—472no—
470C4⋊C4—944no—
471C4⋊C4—944no—
472C4⋊C4—948no—
473C4⋊C4—948no—
474C4⋊C4—948no—
475C4⋊C4—944no—
476C4⋊C4—941no—
477C4⋊C4—941no—
478C22⋊C4—944no—
479C22⋊C4—944no—
480C22⋊C4—944no—
481C22⋊C4—944no—
482C22⋊C4—944no—
483C42—944no—
484C23—232no—
485C23—28no—
486C23—22no—
487C23—22no—
488C23—28no—
489C23—22no—
490C23—22no—
491C23—28no—
492C23—22no—
493C23—22no—
494C23—942no—
495C23—1882no—
496C23—1882no—
497C23—1882no—
498C23#1309400814yes—
499C23#1309405214yes—
500C23#1309405714yes—
501C23C22×D18812yes—
502C23C22×D18812yes—
503C23C22×D18812yes—
504C23C22×D18811yescharacteristic
505Q8—944no—
506Q8—1882no—
507D4—944no—
508D4—1888no—
509D4—1888no—
510D4—1888no—
511D4—1882no—
512C2×C4—28no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—28no—
516C2×C4—28no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—24no—
521C2×C4—942no—
522C2×C4—942no—
523C2×C4—942no—
524C2×C4—948no—
525C2×C4—18816no—
526C2×C4—18816no—
527C2×C4—1882no—
528C2×C4—18816no—
529C2×C4—1888no—
530C2×C4—1882no—
531C2×C4—1882no—
532C2×C4—1888no—
533C2×C4#1309400814yes—
534C2×C4#1309400818yes—
535C2×C4C22×D18812yes—
536C2×C4C22×D18812yes—
537C2×C4C22×D18812yes—
538C2×C4C22×D18811yescharacteristic
539C2×C4C2×#1062535214yes—
540C2×C4C2×#1062535218yes—
541C2×C4C24×D4711yescharacteristic
542C8—28no—
543C22—232no—
544C22—22no—
545C22—22no—
546C22—22no—
547C22—22no—
548C22—22no—
549C22—22no—
550C22—28no—
551C22—28no—
552C22—28no—
553C22—3764no—
554C22—1882no—
555C22—1882no—
556C22—1882no—
557C22C2×#1309400814yes—
558C22C2×#1309400812yes—
559C22C2×#1309405214yes—
560C22C2×#1309405212yes—
561C22C2×#1309405714yes—
562C22C2×#1309405712yes—
563C22C23×D18811yescharacteristic
564C4—22no—
565C4—22no—
566C4—1888no—
567C4—1882no—
568C4—1882no—
569C4—1882no—
570C4C2×#1309400814yes—
571C4C2×#1309400812yes—
572C4C22×#1062535212yes—
573C2—24no—
574C2—24no—
575C2—24no—
576C2—3762no—
577C2#2025331314yesdirect product factor
578C2C22×#1309400811yescharacteristic
579C2C22×#1309405211yescharacteristic
580C2C22×#1309405711yescharacteristic
subgroupG/H
centerC23C22×D188
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#407C2
socleC23×C47C22×D4
prime radicalC2×#15689634C2
hypercenterC2×#407D47
hypocenterC47C2×#3092
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
2. C23×C4⋊Dic47C2semidirect
3. #20253313C2direct (N × H)
4. C2×#15689459C2semidirect
5. C2×#15689442C2semidirect
6. C2×#15689454C2semidirect
7. C2×#15689437C2semidirect
8. C2×#15689165C2semidirect
9. C2×#15689125C2semidirect
10. C2×C47×#407C2semidirect
31. C22×C4⋊Dic47C22semidirect
32. #15689459C22semidirect
33. #15689454C22semidirect
34. #15689442C22semidirect
35. #15689437C22semidirect
36. #15689165C22semidirect
37. C2×#13093958C22semidirect
38. C2×#13093956C22semidirect
39. #15689125C22semidirect
40. C2×#13093949C22semidirect
41. C2×#13093946C22semidirect
44. C47×#407C22semidirect
98. #13093958C23semidirect
99. #13093956C23semidirect
100. #13093949C23semidirect
101. #13093946C23semidirect
292. C2×#407D47semidirect
296. C2×C47#3092semidirect
334. #407C2×D47semidirect
337. C47C2×#3092semidirect
577. C2#20253313direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896342
C23×C4⋊Dic472
#202533132
C2×#156894592
C2×#156894422
C2×#156894542
C2×#156894372
C2×#156891652
C2×#156891252
C2×C47×#4072
C2×#309247