Finite Group Databasebeta

← C2×#20253208 #27083815

Subgroups — C2×#20253208 #27083815

Order 12032.

2142 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094015C211yesmaximal, characteristic, complemented
2C2×#41×Dic47C211yesmaximal, characteristic
3#20253208C2116yesmaximal, direct product factor
4C2×#15689432C212yesmaximal, complemented
5C2×#15689428C212yesmaximal, complemented
6C2×#15689425C212yesmaximal, complemented
7C2×#15689421C212yesmaximal, complemented
8C2×#15689165C211yesmaximal, characteristic, complemented
9C2×#15689163C211yesmaximal, characteristic, complemented
10C2×#15689146C211yesmaximal, characteristic, complemented
11C2×#15689124C211yesmaximal, characteristic
12C2×C47×#417C211yesmaximal, characteristic
13C22×#10625329C2211yescharacteristic
14C2×#13094015—21no—
15C2×#13094015—21no—
16C2×#13094015—24no—
17C2×#13094015C2212yes—
18C2×#13094015C2212yes—
19C2×#13094015C2218yescomplemented
20#41×Dic47—24no—
21#41×Dic47C2218yes—
22C2×Q8×Dic47C2211yescharacteristic
23C2×Q8×Dic47C2211yescharacteristic
24C2×D4×Dic47—21no—
25C2×D4×Dic47—21no—
26C2×D4×Dic47C2211yescharacteristic
27C2×D4×Dic47C2211yescharacteristic
28C2×#13093983—21no—
29C2×#13093983C2211yescharacteristic
30C22×C4⋊Dic47—21no—
31C22×C4⋊Dic47C2211yescharacteristic
32C22×Dic47⋊C4—21no—
33C22×C4×Dic47—21no—
34C22×C4×Dic47C2211yescharacteristic
35#15689432C22116yescomplemented
36#15689428C22116yescomplemented
37#15689425C22116yescomplemented
38#15689421C22116yescomplemented
39#15689165C2218yescomplemented
40#15689163C2218yescomplemented
41C2×#13093958C2212yes—
42C2×#13093957C2212yes—
43C2×#13093956C2212yes—
44C2×#13093955C2212yes—
45#15689146C2218yescomplemented
46C2×Dic47⋊C8C2212yes—
47C2×Dic47⋊C8C2212yes—
48#15689124C2218yes—
49C2×#13093948C2212yes—
50C2×#13093945C2212yes—
51C22×#41×C47C2211yescharacteristic
52C22×M16×C47C2211yescharacteristic
53C22×C4⋊C4×C47C2211yescharacteristic
54C47×#417C2218yes—
55C2×#103×C47C2212yes—
56C2×#102×C47C2212yes—
57C23×Dic47—21no—
58C23×Dic47—21no—
59C23×Dic47—21no—
60C23×Dic47D411yescharacteristic
61C23×Dic47D411yescharacteristic
62C2×#10625329—24no—
63C2×#10625329C2314yes—
64C22×C47⋊C8C2312yes—
65#13094015—24no—
66#13094015—24no—
67#13094015—28no—
68#13094015—28no—
69#13094015C2318yes—
70#13094015C2318yes—
71Q8×Dic47—22no—
72Q8×Dic47—22no—
73Q8×Dic47C2314yes—
74Q8×Dic47C2314yes—
75D4×Dic47—28no—
76D4×Dic47—28no—
77D4×Dic47—22no—
78D4×Dic47—22no—
79D4×Dic47C2314yes—
80D4×Dic47C2314yes—
81#13093983—22no—
82#13093983—28no—
83#13093983C2314yes—
84C2×C4⋊Dic47—21no—
85C2×C4⋊Dic47—22no—
86C2×C4⋊Dic47—22no—
87C2×C4⋊Dic47—22no—
88C2×C4⋊Dic47—28no—
89C2×C4⋊Dic47—21no—
90C2×C4⋊Dic47—21no—
91C2×C4⋊Dic47C2312yes—
92C2×C4⋊Dic47C2314yes—
93C2×C4⋊Dic47C2311yescharacteristic
94C2×C4⋊Dic47C2311yescharacteristic
95C2×Dic47⋊C4—22no—
96C2×Dic47⋊C4—22no—
97C2×Dic47⋊C4—28no—
98C2×C22⋊Dic47—21no—
99C2×C22⋊Dic47—21no—
100C2×C22⋊Dic47—21no—
101C2×C4×Dic47—21no—
102C2×C4×Dic47—21no—
103C2×C4×Dic47—21no—
104C2×C4×Dic47—28no—
105C2×C4×Dic47D411yescharacteristic
106C2×C4×Dic47D411yescharacteristic
107C2×C4×Dic47D414yes—
108C2×C4×Dic47C2311yescharacteristic
109C2×C4×Dic47C2311yescharacteristic
110C2×C4×Dic47C2314yes—
111#13093958C2318yes—
112#13093957C2318yes—
113#13093956C2318yes—
114#13093955C2318yes—
115Dic47⋊C8C2318yes—
116Dic47⋊C8C2318yes—
117#13093948C2318yes—
118#13093945C2318yes—
119C2×#41×C47—22no—
120C2×#41×C47—24no—
121C2×#41×C47Q818yes—
122C2×#41×C47C2314yes—
123C22×Q8×C47C2311yescharacteristic
124C22×D4×C47—21no—
125C22×D4×C47C2311yescharacteristic
126C23×C4×C47—21no—
127C23×C4×C47—21no—
128C23×C4×C47C2311yescharacteristic
129C2×M16×C47—24no—
130C2×M16×C47C2314yes—
131C22×C8×C47C2312yes—
132C2×C4⋊C4×C47—21no—
133C2×C4⋊C4×C47—22no—
134C2×C4⋊C4×C47C2312yes—
135C2×C4⋊C4×C47C2314yes—
136#103×C47C2318yes—
137#102×C47C2318yes—
138C24×C47—21no—
139C24×C47C2×D411yescharacteristic
140#41×C47—216no—
141#41×C47—28no—
142#41×C47C2×Q8116yes—
143C2×Q8×C47—21no—
144C2×Q8×C47—22no—
145C2×Q8×C47C2×Q814yes—
146C2×Q8×C47C2412yes—
147C2×D4×C47—28no—
148C2×D4×C47—24no—
149C2×D4×C47—21no—
150C2×D4×C47—22no—
151C2×D4×C47C2×Q814yes—
152C2×D4×C47C2412yes—
153C22×C4×C47—21no—
154C22×C4×C47—28no—
155C22×C4×C47—24no—
156C22×C4×C47—24no—
157C22×C4×C47—22no—
158C22×C4×C47—44no—
159C22×C4×C47C2×D411yescharacteristic
160C22×C4×C47C2×D412yes—
161C22×C4×C47C2×Q814yes—
162C22×C4×C47#4114yes—
163C22×C4×C47C2411yescharacteristic
164C22×C4×C47C2412yes—
165C22×Dic47—21no—
166C22×Dic47—21no—
167C22×Dic47—24no—
168C22×Dic47—22no—
169C22×Dic47—24no—
170C22×Dic47—24no—
171C22×Dic47—42no—
172C22×Dic47—42no—
173C22×Dic47—44no—
174C22×Dic47—44no—
175C22×Dic47—44no—
176C22×Dic47C2×D411yescharacteristic
177C22×Dic47C2×D411yescharacteristic
178C22×Dic47C2×D411yescharacteristic
179C22×Dic47C2×D411yescharacteristic
180C22×Dic47C2×D414yes—
181C22×Dic47C2×D414yes—
182M16×C47—28no—
183C2×C8×C47—24no—
184C2×C8×C47C2414yes—
185C4⋊C4×C47—24no—
186C4⋊C4×C47—22no—
187C4⋊C4×C47C2414yes—
188C22⋊Dic47—24no—
189C22⋊Dic47—24no—
190C22⋊Dic47—24no—
191C4⋊Dic47—24no—
192C4⋊Dic47—22no—
193C4⋊Dic47—21no—
194C4⋊Dic47—21no—
195C4⋊Dic47—28no—
196C4⋊Dic47—28no—
197C4⋊Dic47—24no—
198C4⋊Dic47—24no—
199C4⋊Dic47C2414yes—
200C4⋊Dic47C2412yes—
201C4⋊Dic47C2412yes—
202Dic47⋊C4—28no—
203Dic47⋊C4—28no—
204C4×Dic47—24no—
205C4×Dic47—24no—
206C4×Dic47—24no—
207C4×Dic47C2×D414yes—
208C4×Dic47C2×D414yes—
209C4×Dic47C2×D412yes—
210C4×Dic47C2×D412yes—
211C4×Dic47C2412yes—
212C4×Dic47C2412yes—
213#10625329—28no—
214C2×C47⋊C8—24no—
215C2×C47⋊C8C2414yes—
216C23×C47—22no—
217C23×C47—22no—
218C23×C47—24no—
219C23×C47—22no—
220C23×C47—42no—
221C23×C47—42no—
222C23×C47C22⋊Q814yes—
223C23×C47C22×D412yes—
224C23×C47C22×D411yescharacteristic
225Q8×C47—24no—
226Q8×C47—22no—
227Q8×C47C22×Q814yes—
228D4×C47—216no—
229D4×C47—24no—
230D4×C47—22no—
231D4×C47C22×Q814yes—
232C2×C4×C47—24no—
233C2×C4×C47—22no—
234C2×C4×C47—216no—
235C2×C4×C47—24no—
236C2×C4×C47—48no—
237C2×C4×C47—44no—
238C2×C4×C47C22⋊Q814yes—
239C2×C4×C47C22⋊Q818yes—
240C2×C4×C47C22×D412yes—
241C2×C4×C47C22×D411yescharacteristic
242C2×C4×C47C22×Q812yes—
243C2×C4×C47C22×Q814yes—
244C2×C4×C47C2×#4112yes—
245C2×C4×C47C2×#4114yes—
246C2×C4×C47C2511yescharacteristic
247C2×Dic47—22no—
248C2×Dic47—22no—
249C2×Dic47—22no—
250C2×Dic47—22no—
251C2×Dic47—22no—
252C2×Dic47—22no—
253C2×Dic47—24no—
254C2×Dic47—44no—
255C2×Dic47—44no—
256C2×Dic47—48no—
257C2×Dic47—48no—
258C2×Dic47—48no—
259C2×Dic47—42no—
260C2×Dic47—42no—
261C2×Dic47—44no—
262C2×Dic47C22×D412yes—
263C2×Dic47C22×D412yes—
264C2×Dic47C22×D412yes—
265C2×Dic47C22×D412yes—
266C8×C47—24no—
267C47⋊C8—24no—
268C2×#3080—471nomaximal, Sylow
269C22×C47—28no—
270C22×C47—22no—
271C22×C47—22no—
272C22×C47—24no—
273C22×C47—48no—
274C22×C47—42no—
275C22×C47—42no—
276C22×C47C2×C22⋊Q814yes—
277C22×C47C2×C22⋊Q812yes—
278C22×C47#57512yes—
279C22×C47#57512yes—
280C22×C47C23×D411yescharacteristic
281C4×C47—24no—
282C4×C47—44no—
283C4×C47C2×C22⋊Q814yes—
284C4×C47C2×C22⋊Q812yes—
285C4×C47C23×Q811yescharacteristic
286C4×C47C22×#4111yescharacteristic
287Dic47—22no—
288Dic47—22no—
289Dic47—22no—
290Dic47—22no—
291Dic47—42no—
292Dic47—42no—
293Dic47—44no—
294C22×#125—471no—
295C2×C4×#41—471no—
296#3080—4716no—
297C2×#479—472no—
298C2×#479—472no—
299C2×#478—472no—
300C2×#478—472no—
301C2×#428—471no—
302C2×#428—471no—
303C2×#423—471no—
304C2×#417—471no—
305C2×#417D4711yescharacteristic
306C2×C47—24no—
307C2×C47—44no—
308C2×C47#308014yescomplemented
309C2×C47C22×C22⋊Q811yescharacteristic
310C2×C47C2×#57511yescharacteristic
311C2×C47C2×#57511yescharacteristic
312C22×#41C2×D4711yescharacteristic
313C22×M16—471no—
314C22×M16C2×D4711yescharacteristic
315C2×#125—472no—
316C2×#125—472no—
317C2×#125—478no—
318C2×#125—941no—
319C2×#125—944no—
320C2×#125—941no—
321C4×#41—478no—
322C4×#41—944no—
323C2×C4×Q8—471no—
324C2×C4×Q8—471no—
325C2×C4×D4—471no—
326C2×C4×D4—471no—
327C2×C4×D4—941no—
328C2×C4×D4—941no—
329C2×#117—471no—
330C2×#117—941no—
331C22×C4⋊C4—471no—
332C22×C4⋊C4—941no—
333C22×C4⋊C4—941no—
334C22×C4⋊C4C2×D4711yescharacteristic
335C22×C42—471no—
336C22×C42—941no—
337#479—4716no—
338#479—4716no—
339#478—4716no—
340#478—4716no—
341#428—478no—
342#428—478no—
343C2×#107—472no—
344C2×#107—472no—
345C2×#106—472no—
346C2×#106—472no—
347#423—478no—
348C2×C4⋊C8—472no—
349C2×C4⋊C8—472no—
350#417—478no—
351#417C2×D4718yes—
352C2×#103—472no—
353C2×#103C2×D4712yes—
354C2×#102—472no—
355C2×#102C2×D4712yes—
356C47C2×#308011yescharacteristic, complemented, Sylow
357C2×#41—22no—
358C2×#41—24no—
359C2×#41Dic9418yes—
360C2×#41C22×D4714yes—
361C22×Q8C22×D4711yescharacteristic
362C22×D4—21no—
363C22×D4C22×D4711yescharacteristic
364C23×C4—21no—
365C23×C4—21no—
366C23×C4—471no—
367C23×C4—471no—
368C23×C4—941no—
369C23×C4—941no—
370C23×C4—941no—
371C23×C4C22×D4711yescharacteristic
372C2×M16—24no—
373C2×M16—474no—
374C2×M16—944no—
375C2×M16C22×D4714yes—
376C22×C8—472no—
377C22×C8C22×D4712yes—
378#125—478no—
379#125—478no—
380#125—948no—
381#125—948no—
382#125—944no—
383#125—944no—
384C4×Q8—474no—
385C4×Q8—474no—
386C4×Q8—942no—
387C4×Q8—942no—
388C4×D4—474no—
389C4×D4—474no—
390C4×D4—942no—
391C4×D4—942no—
392C4×D4—948no—
393C4×D4—948no—
394#117—474no—
395#117—948no—
396#117—942no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—472no—
400C2×C4⋊C4—474no—
401C2×C4⋊C4—471no—
402C2×C4⋊C4—471no—
403C2×C4⋊C4—948no—
404C2×C4⋊C4—942no—
405C2×C4⋊C4—942no—
406C2×C4⋊C4—948no—
407C2×C4⋊C4—942no—
408C2×C4⋊C4—942no—
409C2×C4⋊C4—941no—
410C2×C4⋊C4—941no—
411C2×C4⋊C4—942no—
412C2×C4⋊C4—941no—
413C2×C4⋊C4C22×D4712yes—
414C2×C4⋊C4C22×D4714yes—
415C2×C22⋊C4—941no—
416C2×C22⋊C4—941no—
417C2×C22⋊C4—941no—
418C2×C42—471no—
419C2×C42—474no—
420C2×C42—471no—
421C2×C42—471no—
422C2×C42—471no—
423C2×C42—474no—
424C2×C42—948no—
425C2×C42—941no—
426C2×C42—941no—
427C2×C42—941no—
428#107—478no—
429#107—478no—
430#106—478no—
431#106—478no—
432C4⋊C8—478no—
433C4⋊C8—478no—
434#103—478no—
435#103C22×D4718yes—
436#102—478no—
437#102C22×D4718yes—
438C24—21no—
439C24D4×D4711yescharacteristic
440#41—216no—
441#41—28no—
442#41C2×Dic94116yes—
443C2×Q8—21no—
444C2×Q8—22no—
445C2×Q8C2×Dic9414yes—
446C2×Q8C23×D4712yes—
447C2×D4—28no—
448C2×D4—24no—
449C2×D4—21no—
450C2×D4—22no—
451C2×D4C2×Dic9414yes—
452C2×D4C23×D4712yes—
453C22×C4—21no—
454C22×C4—28no—
455C22×C4—24no—
456C22×C4—24no—
457C22×C4—22no—
458C22×C4—44no—
459C22×C4—471no—
460C22×C4—471no—
461C22×C4—471no—
462C22×C4—471no—
463C22×C4—474no—
464C22×C4—474no—
465C22×C4—944no—
466C22×C4—944no—
467C22×C4—944no—
468C22×C4—941no—
469C22×C4—941no—
470C22×C4—942no—
471C22×C4—1882no—
472C22×C4—1882no—
473C22×C4—1884no—
474C22×C4—1884no—
475C22×C4—1884no—
476C22×C4C2×Dic9414yes—
477C22×C4D4×D4712yes—
478C22×C4D4×D4711yescharacteristic
479C22×C4#1062535214yes—
480C22×C4C23×D4712yes—
481C22×C4C23×D4711yescharacteristic
482M16—28no—
483M16—948no—
484C2×C8—24no—
485C2×C8—474no—
486C2×C8—944no—
487C2×C8C23×D4714yes—
488C4⋊C4—24no—
489C4⋊C4—22no—
490C4⋊C4—474no—
491C4⋊C4—472no—
492C4⋊C4—472no—
493C4⋊C4—948no—
494C4⋊C4—948no—
495C4⋊C4—948no—
496C4⋊C4—948no—
497C4⋊C4—944no—
498C4⋊C4—944no—
499C4⋊C4—944no—
500C4⋊C4—942no—
501C4⋊C4—941no—
502C4⋊C4—941no—
503C4⋊C4C23×D4714yes—
504C22⋊C4—944no—
505C22⋊C4—944no—
506C22⋊C4—944no—
507C42—474no—
508C42—474no—
509C42—472no—
510C42—472no—
511C42—472no—
512C42—472no—
513C42—944no—
514C42—944no—
515C42—944no—
516C23—22no—
517C23—22no—
518C23—24no—
519C23—22no—
520C23—42no—
521C23—42no—
522C23#1309400114yes—
523C23C2×D4×D4712yes—
524C23C2×D4×D4711yescharacteristic
525Q8—24no—
526Q8—22no—
527Q8C22×Dic9414yes—
528D4—216no—
529D4—24no—
530D4—22no—
531D4C22×Dic9414yes—
532C2×C4—24no—
533C2×C4—22no—
534C2×C4—216no—
535C2×C4—24no—
536C2×C4—48no—
537C2×C4—44no—
538C2×C4—472no—
539C2×C4—472no—
540C2×C4—472no—
541C2×C4—472no—
542C2×C4—942no—
543C2×C4—942no—
544C2×C4—942no—
545C2×C4—942no—
546C2×C4—942no—
547C2×C4—942no—
548C2×C4—944no—
549C2×C4—1884no—
550C2×C4—1884no—
551C2×C4—1888no—
552C2×C4—1888no—
553C2×C4—1888no—
554C2×C4—1882no—
555C2×C4—1882no—
556C2×C4—1884no—
557C2×C4#1309400114yes—
558C2×C4#1309400118yes—
559C2×C4C2×D4×D4712yes—
560C2×C4C2×D4×D4711yescharacteristic
561C2×C4C22×Dic9412yes—
562C2×C4C22×Dic9414yes—
563C2×C4C2×#1062535212yes—
564C2×C4C2×#1062535214yes—
565C2×C4C24×D4711yescharacteristic
566C8—24no—
567C8—944no—
568C22—28no—
569C22—22no—
570C22—22no—
571C22—24no—
572C22—48no—
573C22—42no—
574C22—42no—
575C22C2×#1309400114yes—
576C22C2×#1309400112yes—
577C22#1568991912yes—
578C22#1568992212yes—
579C22C22×D4×D4711yescharacteristic
580C4—24no—
581C4—44no—
582C4—942no—
583C4—942no—
584C4—942no—
585C4—942no—
586C4—1882no—
587C4—1882no—
588C4—1884no—
589C4C2×#1309400114yes—
590C4C2×#1309400112yes—
591C4C23×Dic9411yescharacteristic
592C4C22×#1062535211yescharacteristic
593C2—24no—
594C2—44no—
595C2#2025320814yesdirect product factor
596C2C22×#1309400111yescharacteristic
597C2C2×#1568991911yescharacteristic
598C2C2×#1568992211yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#417C2
socleC23×C47C22×D4
prime radicalC22×#41×C47C22
hypercenterC2×#417D47
hypocenterC47C2×#3080
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
1. C22×#13094015C2semidirect
3. #20253208C2direct (N × H)
4. C2×#15689432C2semidirect
5. C2×#15689428C2semidirect
6. C2×#15689425C2semidirect
7. C2×#15689421C2semidirect
8. C2×#15689165C2semidirect
9. C2×#15689163C2semidirect
10. C2×#15689146C2semidirect
19. C2×#13094015C22semidirect
35. #15689432C22semidirect
36. #15689428C22semidirect
37. #15689425C22semidirect
38. #15689421C22semidirect
39. #15689165C22semidirect
40. #15689163C22semidirect
45. #15689146C22semidirect
308. C2×C47#3080semidirect
356. C47C2×#3080semidirect
595. C2#20253208direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940152
C2×#41×Dic472
#202532082
C2×#156894322
C2×#156894282
C2×#156894252
C2×#156894212
C2×#156891652
C2×#156891632
C2×#156891462
C2×#156891242
C2×C47×#4172
C2×#308047