Finite Group Databasebeta

← D47×#1740 #26213707

Subgroups — D47×#1740 #26213707

Order 12032.

2350 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#117×D47C212yesmaximal
2C2×#117×D47C211yesmaximal, characteristic
3#20243121C211yesmaximal, characteristic, complemented
4#20243120C212yesmaximal, complemented
5#20243119C214yesmaximal, complemented
6#342×D47C214yesmaximal
7C47×#1740C211yesmaximal, characteristic, complemented
8C23×C4×D47C2211yescharacteristic
9C2×#13093983C2212yes—
10C2×#13093983C2211yescharacteristic
11C2×#13093982—22no—
12C2×#13093982C412yescomplemented
13C2×#13093981—22no—
14C2×#13093981C412yescomplemented
15C2×#13093980C2214yes—
16C2×#13093980C2212yes—
17#117×D47—28no—
18#117×D47—22no—
19#117×D47—22no—
20#117×D47—22no—
21#117×D47—22no—
22#117×D47C4116yescomplemented
23C2×C4⋊C4×D47—22no—
24C2×C4⋊C4×D47C412yescomplemented
25C2×C22⋊C4×D47C2212yes—
26C2×C22⋊C4×D47C2214yes—
27C2×C42×D47—22no—
28C2×C42×D47C412yescomplemented
29#15688890C2214yes—
30#15688889C2218yes—
31C2×#117×C47C2212yes—
32C2×#117×C47C2211yescharacteristic
33C47×#342C2214yes—
34C24×D47C2311yescharacteristic
35C23×Dic47C2311yescharacteristic
36C22×C4×D47—24no—
37C22×C4×D47C2×C414yes—
38C22×C4×D47C2×C411yescharacteristic
39C22×C4×D47C2×C411yescharacteristic
40C22×C4×D47C2×C418yes—
41C22×C4×D47C2×C411yescharacteristic
42C22×C4×D47C2×C411yescharacteristic
43C22×C4×D47D412yes—
44C22×C4×D47D412yes—
45C22×C4×D47D414yes—
46C22×C4×D47D412yes—
47C22×C4×D47D412yes—
48C22×C4×D47Q814yes—
49#13093983—24no—
50#13093983—22no—
51#13093983—22no—
52#13093983C2×C418yescomplemented
53#13093982—24no—
54#13093982—24no—
55#13093982—216no—
56#13093981—24no—
57#13093981—24no—
58#13093981—216no—
59#13093980—28no—
60#13093980—24no—
61#13093980—24no—
62#13093980C2×C4116yescomplemented
63C2×C4⋊Dic47—22no—
64C2×C4⋊Dic47C2×C412yescomplemented
65C2×Dic47⋊C4—24no—
66C2×Dic47⋊C4C2×C414yescomplemented
67C4⋊C4×D47—216no—
68C4⋊C4×D47—24no—
69C4⋊C4×D47—24no—
70C2×C22⋊Dic47C2312yes—
71C2×C22⋊Dic47C2314yes—
72C2×(C2×D47)⋊C4—24no—
73C2×(C2×D47)⋊C4C2×C414yes—
74C22⋊C4×D47—24no—
75C22⋊C4×D47—24no—
76C22⋊C4×D47—28no—
77C22⋊C4×D47C2×C4116yes—
78C2×C4×Dic47—22no—
79C2×C4×Dic47—24no—
80C2×C4×Dic47C2×C414yescomplemented
81C2×C4×Dic47C2×C412yescomplemented
82C42×D47—216no—
83C42×D47—22no—
84C42×D47—22no—
85C42×D47—22no—
86C42×D47—22no—
87C23×C4×C47C2311yescharacteristic
88#117×C47—24no—
89#117×C47—22no—
90#117×C47—22no—
91#117×C47C2×C418yescomplemented
92C2×C4⋊C4×C47—22no—
93C2×C4⋊C4×C47C2×C412yescomplemented
94C2×C22⋊C4×C47C2312yes—
95C2×C22⋊C4×C47C2314yes—
96C2×C42×C47—22no—
97C2×C42×C47C2×C412yescomplemented
98C24×C47C2411yescharacteristic
99C23×D47—44no—
100C23×D47C22×C411yescharacteristic
101C23×D47C22×C414yes—
102C23×D47C22×C411yescharacteristic
103C23×D47C2×D412yes—
104C23×D47C2×D412yes—
105C23×D47C2×D412yes—
106C23×D47C2×Q812yes—
107C22×C4×C47—24no—
108C22×C4×C47C22×C414yes—
109C22×C4×C47C22×C411yescharacteristic
110C22×C4×C47C22×C411yescharacteristic
111C22×C4×C47C22×C414yes—
112C22×C4×C47C2×D412yes—
113C22×C4×C47C2×D412yes—
114C22×C4×C47C2×D412yes—
115C22×C4×C47C2×Q812yes—
116C22×Dic47—24no—
117C22×Dic47C22×C414yes—
118C22×Dic47C22×C411yescharacteristic
119C22×Dic47C22×C411yescharacteristic
120C22×Dic47C22×C414yes—
121C22×Dic47C2×D412yes—
122C22×Dic47C2×D412yes—
123C22×Dic47C2×D412yes—
124C22×Dic47C2×Q812yes—
125C2×C4×D47—24no—
126C2×C4×D47—24no—
127C2×C4×D47—216no—
128C2×C4×D47—416no—
129C2×C4×D47—48no—
130C2×C4×D47C4214yes—
131C2×C4×D47C4214yes—
132C2×C4×D47C4214yes—
133C2×C4×D47C4214yes—
134C2×C4×D47C22⋊C418yes—
135C2×C4×D47C22⋊C411yescharacteristic
136C2×C4×D47C22⋊C411yescharacteristic
137C2×C4×D47C22⋊C411yescharacteristic
138C2×C4×D47C22⋊C411yescharacteristic
139C2×C4×D47C22⋊C418yes—
140C2×C4×D47C22⋊C412yes—
141C2×C4×D47C22⋊C412yes—
142C2×C4×D47C22⋊C412yes—
143C2×C4×D47C22⋊C418yes—
144C2×C4×D47C22⋊C412yes—
145C2×C4×D47C22⋊C412yes—
146C2×C4×D47C22⋊C412yes—
147C2×C4×D47C22⋊C418yes—
148C2×C4×D47C4⋊C414yes—
149C2×C4×D47C4⋊C414yes—
150C2×C4×D47C4⋊C418yes—
151C2×C4×D47C4⋊C418yes—
152C2×C4×D47C4⋊C418yes—
153C2×C4×D47C4⋊C418yes—
154C2×C4×D47C4⋊C414yes—
155C2×C4×D47C4⋊C414yes—
156C4⋊C4×C47—28no—
157C4⋊C4×C47—24no—
158C22⋊C4×C47—24no—
159C22⋊C4×C47—24no—
160C22⋊C4×C47C22×C418yes—
161C42×C47—28no—
162C42×C47—22no—
163C42×C47—22no—
164C22⋊Dic47—24no—
165C22⋊Dic47—24no—
166C22⋊Dic47C22×C418yes—
167(C2×D47)⋊C4—28no—
168(C2×D47)⋊C4—216no—
169C4⋊Dic47—28no—
170C4⋊Dic47—24no—
171Dic47⋊C4—216no—
172Dic47⋊C4—28no—
173C4×Dic47—28no—
174C4×Dic47—22no—
175C4×Dic47—22no—
176C4×Dic47—216no—
177C4×Dic47—24no—
178C4×Dic47—24no—
179C23×C47—42no—
180C23×C47C23×C411yescharacteristic
181C23×C47C23×C412yes—
182C23×C47C22×D412yes—
183C23×C47C22×D411yescharacteristic
184C23×C47C22×Q811yescharacteristic
185C22×D47—24no—
186C22×D47—28no—
187C22×D47—48no—
188C22×D47—44no—
189C22×D47—44no—
190C22×D47—42no—
191C22×D47—44no—
192C22×D47C2×C4212yes—
193C22×D47C2×C4212yes—
194C22×D47C2×C22⋊C412yes—
195C22×D47C2×C22⋊C411yescharacteristic
196C22×D47C2×C22⋊C414yes—
197C22×D47C2×C22⋊C414yes—
198C22×D47C2×C22⋊C411yescharacteristic
199C22×D47C2×C4⋊C412yes—
200C22×D47C2×C4⋊C414yes—
201C22×D47C2×C4⋊C414yes—
202C22×D47C2×C4⋊C412yes—
203C2×C4×C47—24no—
204C2×C4×C47—28no—
205C2×C4×C47—48no—
206C2×C4×C47—44no—
207C2×C4×C47C2×C4212yes—
208C2×C4×C47C2×C4212yes—
209C2×C4×C47C2×C22⋊C414yes—
210C2×C4×C47C2×C22⋊C411yescharacteristic
211C2×C4×C47C2×C22⋊C414yes—
212C2×C4×C47C2×C22⋊C412yes—
213C2×C4×C47C2×C22⋊C411yescharacteristic
214C2×C4×C47C2×C4⋊C412yes—
215C2×C4×C47C2×C4⋊C412yes—
216C2×C4×C47C2×C4⋊C414yes—
217C2×C4×C47C2×C4⋊C414yes—
218C2×Dic47—24no—
219C2×Dic47—28no—
220C2×Dic47—48no—
221C2×Dic47—44no—
222C2×Dic47C2×C4212yes—
223C2×Dic47C2×C4212yes—
224C2×Dic47C2×C22⋊C414yes—
225C2×Dic47C2×C22⋊C411yescharacteristic
226C2×Dic47C2×C22⋊C411yescharacteristic
227C2×Dic47C2×C22⋊C414yes—
228C2×Dic47C2×C22⋊C412yes—
229C2×Dic47C2×C4⋊C412yes—
230C2×Dic47C2×C4⋊C412yes—
231C2×Dic47C2×C4⋊C414yes—
232C2×Dic47C2×C4⋊C414yes—
233C4×D47—432no—
234C4×D47—48no—
235C4×D47—48no—
236C4×D47#9518yes—
237C4×D47#9514yes—
238C4×D47#9514yes—
239C4×D47#9518yes—
240C4×D47#9518yes—
241C4×D47#9518yes—
242C4×D47#9518yes—
243C4×D47#9514yes—
244C4×D47#9514yes—
245C4×D47#9518yes—
246C2×#1740—471nomaximal, Sylow
247C22×C47—22no—
248C22×C47—24no—
249C22×C47—42no—
250C22×C47—41no—
251C22×C47—41no—
252C22×C47C22×C4211yescharacteristic
253C22×C47C22×C22⋊C412yes—
254C22×C47C22×C22⋊C411yescharacteristic
255C22×C47C22×C4⋊C411yescharacteristic
256C22×C47C22×C4⋊C412yes—
257C2×D47—22no—
258C2×D47—24no—
259C2×D47—28no—
260C2×D47—24no—
261C2×D47—24no—
262C2×D47—28no—
263C2×D47—42no—
264C2×D47—44no—
265C2×D47—44no—
266C2×D47—42no—
267C2×D47C2×#9512yes—
268C2×D47C2×#9514yes—
269C2×D47C2×#9512yes—
270C2×D47#41014yes—
271C4×C47—48no—
272C4×C47—44no—
273C4×C47C2×#9512yes—
274C4×C47C2×#9514yes—
275C4×C47C2×#9512yes—
276Dic47—48no—
277Dic47—44no—
278Dic47C2×#9512yes—
279Dic47C2×#9512yes—
280Dic47C2×#9514yes—
281C22×#117—471no—
282C22×#117—472no—
283#1740—474no—
284#1740—472no—
285#1740—471no—
286#1740D4711yescharacteristic, direct product factor
287C2×#342—474no—
288C2×C47—22no—
289C2×C47—21no—
290C2×C47—22no—
291C2×C47—21no—
292C2×C47C22×#9511yescharacteristic
293C2×C47C2×#41012yes—
294D47—22no—
295D47—24no—
296D47#174014yesdirect product factor
297C24×C4—471no—
298C2×#117—471no—
299C2×#117—472no—
300C2×#117—472no—
301C2×#117—472no—
302C2×#117—472no—
303C2×#117—4716no—
304C2×#117—474no—
305C2×#117—942no—
306C2×#117—942no—
307C2×#117—948no—
308C2×#117—942no—
309C2×#117—942no—
310C2×#117—942no—
311C2×#117—942no—
312C2×#117C2×D4712yes—
313C2×#117C2×D4711yescharacteristic
314C22×C4⋊C4—472no—
315C22×C4⋊C4—942no—
316C22×C22⋊C4—474no—
317C22×C22⋊C4—472no—
318C22×C42—472no—
319C22×C42—942no—
320#342—478no—
321#342—474no—
322#342C2×D4714yes—
323C47C2×#174011yescharacteristic, complemented, Sylow
324C25—471no—
325C23×C4—471no—
326C23×C4—471no—
327C23×C4—471no—
328C23×C4—471no—
329C23×C4—478no—
330C23×C4—471no—
331C23×C4—472no—
332C23×C4—472no—
333C23×C4—472no—
334C23×C4—474no—
335C23×C4—472no—
336C23×C4—474no—
337C23×C4—474no—
338C23×C4—944no—
339C23×C4C22×D4711yescharacteristic
340#117—24no—
341#117—22no—
342#117—22no—
343#117—478no—
344#117—4716no—
345#117—9416no—
346#117—944no—
347#117—944no—
348#117—944no—
349#117—944no—
350#117—948no—
351#117—944no—
352#117—944no—
353#117—9416no—
354#117—942no—
355#117—944no—
356#117—942no—
357#117C4×D4718yescomplemented
358C2×C4⋊C4—22no—
359C2×C4⋊C4—474no—
360C2×C4⋊C4—472no—
361C2×C4⋊C4—944no—
362C2×C4⋊C4—944no—
363C2×C4⋊C4—9416no—
364C2×C4⋊C4—944no—
365C2×C4⋊C4—942no—
366C2×C4⋊C4C4×D4712yescomplemented
367C2×C22⋊C4—474no—
368C2×C22⋊C4—4716no—
369C2×C22⋊C4—472no—
370C2×C22⋊C4—474no—
371C2×C22⋊C4—948no—
372C2×C22⋊C4—944no—
373C2×C22⋊C4—944no—
374C2×C22⋊C4—944no—
375C2×C22⋊C4C22×D4712yes—
376C2×C22⋊C4C22×D4714yes—
377C2×C42—22no—
378C2×C42—474no—
379C2×C42—472no—
380C2×C42—9416no—
381C2×C42—942no—
382C2×C42—942no—
383C2×C42—942no—
384C2×C42—942no—
385C2×C42—944no—
386C2×C42—942no—
387C2×C42C4×D4712yescomplemented
388C24—471no—
389C24—472no—
390C24—474no—
391C24—471no—
392C24—472no—
393C24—472no—
394C24—472no—
395C24—1884no—
396C24C23×D4711yescharacteristic
397C22×C4—24no—
398C22×C4—471no—
399C22×C4—471no—
400C22×C4—474no—
401C22×C4—472no—
402C22×C4—472no—
403C22×C4—472no—
404C22×C4—472no—
405C22×C4—474no—
406C22×C4—474no—
407C22×C4—474no—
408C22×C4—474no—
409C22×C4—471no—
410C22×C4—478no—
411C22×C4—471no—
412C22×C4—472no—
413C22×C4—472no—
414C22×C4—478no—
415C22×C4—472no—
416C22×C4—472no—
417C22×C4—478no—
418C22×C4—472no—
419C22×C4—478no—
420C22×C4—471no—
421C22×C4—471no—
422C22×C4—472no—
423C22×C4—474no—
424C22×C4—478no—
425C22×C4—478no—
426C22×C4—474no—
427C22×C4—474no—
428C22×C4—474no—
429C22×C4—478no—
430C22×C4—478no—
431C22×C4—474no—
432C22×C4—9416no—
433C22×C4—944no—
434C22×C4—944no—
435C22×C4—944no—
436C22×C4—18816no—
437C22×C4—1888no—
438C22×C4C2×C4×D4714yes—
439C22×C4C2×C4×D4711yescharacteristic
440C22×C4C2×C4×D4714yes—
441C22×C4C2×C4×D4711yescharacteristic
442C22×C4D4×D4712yes—
443C22×C4D4×D4712yes—
444C22×C4D4×D4712yes—
445C22×C4Q8×D4712yes—
446C4⋊C4—28no—
447C4⋊C4—24no—
448C4⋊C4—948no—
449C4⋊C4—9416no—
450C4⋊C4—944no—
451C4⋊C4—948no—
452C22⋊C4—24no—
453C22⋊C4—24no—
454C22⋊C4—478no—
455C22⋊C4—948no—
456C22⋊C4—9416no—
457C22⋊C4—944no—
458C22⋊C4—944no—
459C22⋊C4C2×C4×D4718yes—
460C42—28no—
461C42—22no—
462C42—22no—
463C42—944no—
464C42—944no—
465C42—9416no—
466C42—942no—
467C42—948no—
468C42—942no—
469C23—42no—
470C23—471no—
471C23—472no—
472C23—472no—
473C23—474no—
474C23—471no—
475C23—472no—
476C23—474no—
477C23—472no—
478C23—474no—
479C23—474no—
480C23—472no—
481C23—944no—
482C23—948no—
483C23—1882no—
484C23—1884no—
485C23—1888no—
486C23—1884no—
487C23—1884no—
488C23C22×C4×D4711yescharacteristic
489C23C22×C4×D4712yes—
490C23C2×D4×D4712yes—
491C23C2×D4×D4711yescharacteristic
492C23C2×Q8×D4711yescharacteristic
493C2×C4—24no—
494C2×C4—28no—
495C2×C4—48no—
496C2×C4—44no—
497C2×C4—472no—
498C2×C4—472no—
499C2×C4—474no—
500C2×C4—471no—
501C2×C4—471no—
502C2×C4—474no—
503C2×C4—472no—
504C2×C4—472no—
505C2×C4—472no—
506C2×C4—474no—
507C2×C4—474no—
508C2×C4—478no—
509C2×C4—474no—
510C2×C4—474no—
511C2×C4—478no—
512C2×C4—478no—
513C2×C4—478no—
514C2×C4—478no—
515C2×C4—474no—
516C2×C4—478no—
517C2×C4—474no—
518C2×C4—948no—
519C2×C4—944no—
520C2×C4—1888no—
521C2×C4—18832no—
522C2×C4—1888no—
523C2×C4—1888no—
524C2×C4—1884no—
525C2×C4C42×D4712yes—
526C2×C4C42×D4712yes—
527C2×C4C22⋊C4×D4711yescharacteristic
528C2×C4C22⋊C4×D4714yes—
529C2×C4C22⋊C4×D4714yes—
530C2×C4C22⋊C4×D4712yes—
531C2×C4C22⋊C4×D4711yescharacteristic
532C2×C4C4⋊C4×D4712yes—
533C2×C4C4⋊C4×D4714yes—
534C2×C4C4⋊C4×D4714yes—
535C2×C4C4⋊C4×D4712yes—
536C22—22no—
537C22—24no—
538C22—42no—
539C22—41no—
540C22—41no—
541C22—474no—
542C22—472no—
543C22—472no—
544C22—474no—
545C22—948no—
546C22—944no—
547C22—944no—
548C22—948no—
549C22—942no—
550C22—944no—
551C22—1884no—
552C22—1882no—
553C22—1882no—
554C22—1884no—
555C22C2×C42×D4711yescharacteristic
556C22C2×C22⋊C4×D4712yes—
557C22C2×C22⋊C4×D4711yescharacteristic
558C22C2×C4⋊C4×D4711yescharacteristic
559C22C2×C4⋊C4×D4712yes—
560C4—48no—
561C4—44no—
562C4—472no—
563C4—472no—
564C4—474no—
565C4—1888no—
566C4—1884no—
567C4#95×D4714yes—
568C4#95×D4712yes—
569C4#95×D4712yes—
570C2—22no—
571C2—21no—
572C2—21no—
573C2—22no—
574C2—474no—
575C2—944no—
576C2—942no—
577C2C2×#95×D4711yescharacteristic
578C2#410×D4712yes—
subgroupG/H
centerC2×C4C22⋊C4×D47
commutatorC22×C47C22×C42
FrattiniC24C23×D47
FittingC47×#1740C2
socleC22×C47C22×C22⋊C4
prime radicalC24×D47C23
cosocleC24×C47C24
hypercenter#1740D47
hypocenterC47C2×#1740
LCSG ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1740

Complements

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

NH ≅ G/Ntype
3. #20243121C2semidirect
4. #20243120C2semidirect
5. #20243119C2semidirect
7. C47×#1740C2semidirect
12. C2×#13093982C4semidirect
14. C2×#13093981C4semidirect
22. #117×D47C4semidirect
24. C2×C4⋊C4×D47C4semidirect
28. C2×C42×D47C4semidirect
52. #13093983C2×C4semidirect
62. #13093980C2×C4semidirect
64. C2×C4⋊Dic47C2×C4semidirect
66. C2×Dic47⋊C4C2×C4semidirect
80. C2×C4×Dic47C2×C4semidirect
81. C2×C4×Dic47C2×C4semidirect
91. #117×C47C2×C4semidirect
93. C2×C4⋊C4×C47C2×C4semidirect
97. C2×C42×C47C2×C4semidirect
286. #1740D47direct (N × H)
296. D47#1740direct (N × H)
323. C47C2×#1740semidirect
357. #117C4×D47semidirect
366. C2×C4⋊C4C4×D47semidirect
387. C2×C42C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#117×D472
#202431212
#202431202
#202431192
#342×D472
C47×#17402
C2×#174047