Finite Group Databasebeta

← C2×D4⋊C8×D47 #26182618

Subgroups — C2×D4⋊C8×D47 #26182618

Order 12032.

1886 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D47C211yesmaximal, characteristic
2C2×C4⋊C8×D47C211yesmaximal, characteristic, complemented
3C2×C4×C8×D47C211yesmaximal, characteristic, complemented
4C2×#15688852C211yesmaximal, characteristic, complemented
5C2×D4⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
6C2×#15688850C211yesmaximal, characteristic, complemented
7D4⋊C8×D47C218yesmaximal, direct product factor
8C2×C47×D4⋊C8C211yesmaximal, characteristic, complemented
9C22×D4×D47C411yescharacteristic
10C23×C4×D47—21no—
11C22×C8×D47—21no—
12C22×C8×D47—21no—
13C2×C4×D188C2211yescharacteristic
14C2×D4×Dic47C411yescharacteristic
15C2×#13093986C411yescharacteristic
16C2×C4×C22⋊D47—21no—
17C2×(C22⋊D47)⋊C4—21no—
18C4×D4×D47—22no—
19C4×D4×D47—22no—
20C4×D4×D47C414yes—
21C4×D4×D47C2214yes—
22C2×C4⋊C4×D47C411yescharacteristic
23C2×C22⋊C4×D47—21no—
24C2×C42×D47C2211yescharacteristic
25C2×C4⋊(C47⋊C8)C2211yescharacteristic, complemented
26C2×Dic47⋊C8—21no—
27C4⋊C8×D47—22no—
28C4⋊C8×D47C2214yescomplemented
29C2×C4×C47⋊C8C2211yescharacteristic, complemented
30C2×C8×Dic47—21no—
31C4×C8×D47—22no—
32C4×C8×D47C2214yescomplemented
33#15688852C2214yescomplemented
34D4⋊(C47⋊C8)C2214yescomplemented
35#15688850C2214yescomplemented
36C2×C4×D4×C47C2211yescharacteristic
37C2×C4⋊C8×C47C2211yescharacteristic, complemented
38C2×C4×C8×C47C2211yescharacteristic, complemented
39C47×D4⋊C8C2214yescomplemented
40C24×D47—21no—
41C22×D188C2×C411yescharacteristic
42C22×C22⋊D47—21no—
43C2×D4×D47—22no—
44C2×D4×D47—24no—
45C2×D4×D47C818yescomplemented
46C2×D4×D47C2×C414yes—
47C23×Dic47—21no—
48C22×C4×D47—21no—
49C22×C4×D47—21no—
50C22×C4×D47—21no—
51C22×C4×D47—24no—
52C22×C4×D47—24no—
53C22×C4×D47—44no—
54C22×C4×D47—44no—
55C22×C4×D47C2×C411yescharacteristic
56C22×C4×D47D411yescharacteristic
57C22×C4×D47D411yescharacteristic
58C22×C47⋊C8—21no—
59C22×C47⋊C8—21no—
60C2×C8×D47—28no—
61C2×C8×D47—24no—
62C2×C8×D47—24no—
63C2×C8×D47—44no—
64C4×D188—21no—
65C4×D188—21no—
66C4×D188C2×C412yes—
67C4×D188C2312yes—
68D4×Dic47—22no—
69D4×Dic47C2×C414yes—
70#13093986—22no—
71#13093986C2×C414yes—
72C4×C22⋊D47—24no—
73C4×C22⋊D47—24no—
74(C22⋊D47)⋊C4—24no—
75(C22⋊D47)⋊C4—24no—
76C2×C4⋊Dic47C2×C411yescharacteristic
77C2×Dic47⋊C4—21no—
78C4⋊C4×D47—22no—
79C4⋊C4×D47C2×C414yes—
80C2×C22⋊Dic47—21no—
81C2×(C2×D47)⋊C4—21no—
82C2×(C2×D47)⋊C4—21no—
83C22⋊C4×D47—24no—
84C22⋊C4×D47—24no—
85C2×C4×Dic47C2×C411yescharacteristic
86C2×C4×Dic47D411yescharacteristic
87C2×C4×Dic47D411yescharacteristic
88C42×D47C2×C412yes—
89C42×D47D412yes—
90C42×D47D412yes—
91C42×D47C2312yes—
92C4⋊(C47⋊C8)—21no—
93C4⋊(C47⋊C8)C2312yescomplemented
94Dic47⋊C8—24no—
95C4×C47⋊C8—21no—
96C4×C47⋊C8C2312yescomplemented
97C8×Dic47—24no—
98C22×D4×C47C2×C411yescharacteristic
99C23×C4×C47—21no—
100C22×C8×C47—21no—
101C22×C8×C47—21no—
102C4×D4×C47—21no—
103C4×D4×C47—21no—
104C4×D4×C47C2×C412yes—
105C4×D4×C47C2312yes—
106C2×C4⋊C4×C47C2×C411yescharacteristic
107C2×C22⋊C4×C47—21no—
108C2×C42×C47C2311yescharacteristic
109C4⋊C8×C47—21no—
110C4⋊C8×C47C2312yescomplemented
111C4×C8×C47—21no—
112C4×C8×C47C2312yescomplemented
113C24×C47—21no—
114C23×D47—21no—
115C23×D47—28no—
116C23×D47—24no—
117C23×D47—44no—
118C23×D47—44no—
119C23×D47C22⋊C411yescharacteristic
120C2×D4×C47—21no—
121C2×D4×C47—22no—
122C2×D4×C47C2×C814yescomplemented
123C2×D4×C47C22×C412yes—
124C22×C4×C47—21no—
125C22×C4×C47—22no—
126C22×C4×C47—22no—
127C22×C4×C47—42no—
128C22×C4×C47—42no—
129C22×C4×C47C22×C411yescharacteristic
130C22×C4×C47C2×D411yescharacteristic
131C22×C4×C47C2×D411yescharacteristic
132C2×C22⋊D47—28no—
133C2×C22⋊D47—24no—
134C22×Dic47—21no—
135C22×Dic47—24no—
136C22×Dic47—44no—
137C22×Dic47C22⋊C411yescharacteristic
138C22×Dic47C22⋊C411yescharacteristic
139C22×Dic47C22⋊C411yescharacteristic
140D4×D47—216no—
141D4×D47—28no—
142D4×D47C2×C8116yescomplemented
143C2×D188—21no—
144C2×D188—22no—
145C2×D188C2×C814yescomplemented
146C2×D188C22×C412yes—
147C2×C4×D47—24no—
148C2×C4×D47—24no—
149C2×C4×D47—22no—
150C2×C4×D47—22no—
151C2×C4×D47—24no—
152C2×C4×D47—44no—
153C2×C4×D47—42no—
154C2×C4×D47—42no—
155C2×C4×D47—44no—
156C2×C4×D47—416no—
157C2×C4×D47—48no—
158C2×C4×D47—48no—
159C2×C4×D47C22⋊C412yes—
160C2×C4×D47C22⋊C412yes—
161C2×C4×D47C22⋊C412yes—
162C2×C4×D47C2×C814yes—
163C2×C4×D47M1614yes—
164C2×C4×D47D814yes—
165C2×C4×D47SD1614yes—
166C2×C4×D47C22×C412yes—
167C2×C4×D47C2×D412yes—
168C2×C4×D47C2×D412yes—
169C2×C8×C47—24no—
170C2×C8×C47—22no—
171C2×C8×C47—22no—
172C2×C8×C47—42no—
173C4⋊C4×C47—21no—
174C4⋊C4×C47C22×C412yes—
175C22⋊C4×C47—22no—
176C22⋊C4×C47—22no—
177C42×C47C22×C411yescharacteristic
178C42×C47C2×D411yescharacteristic
179C42×C47C2×D411yescharacteristic
180C42×C47C2411yescharacteristic
181C22⋊Dic47—24no—
182(C2×D47)⋊C4—22no—
183(C2×D47)⋊C4—22no—
184(C2×D47)⋊C4—24no—
185C4⋊Dic47—21no—
186C4⋊Dic47C22×C412yes—
187Dic47⋊C4—24no—
188C4×Dic47C22⋊C412yes—
189C4×Dic47C22⋊C412yes—
190C4×Dic47C22⋊C412yes—
191C4×Dic47C22×C412yes—
192C4×Dic47C2×D412yes—
193C4×Dic47C2×D412yes—
194C2×C47⋊C8—24no—
195C2×C47⋊C8—22no—
196C2×C47⋊C8—22no—
197C2×C47⋊C8—42no—
198C8×D47—216no—
199C8×D47—48no—
200C23×C47—22no—
201C23×C47—24no—
202C23×C47—42no—
203C23×C47—42no—
204C23×C47C2×C22⋊C411yescharacteristic
205C22×D47—22no—
206C22×D47—24no—
207C22×D47—216no—
208C22×D47—42no—
209C22×D47—42no—
210C22×D47—432no—
211C22×D47—48no—
212C22×D47—48no—
213C22×D47C22⋊C814yes—
214C22×D47#10214yes—
215C22×D47#10414yes—
216C22×D47C2×C22⋊C412yes—
217D4×C47—22no—
218D4×C47—24no—
219D4×C47C22×C814yescomplemented
220C2×C4×C47—22no—
221C2×C4×C47—22no—
222C2×C4×C47—42no—
223C2×C4×C47—42no—
224C2×C4×C47—42no—
225C2×C4×C47—44no—
226C2×C4×C47C2×C22⋊C411yescharacteristic
227C2×C4×C47C2×C22⋊C411yescharacteristic
228C2×C4×C47C2×C22⋊C411yescharacteristic
229C2×C4×C47C22×C812yes—
230C2×C4×C47C2×M1612yes—
231C2×C4×C47C2×D812yes—
232C2×C4×C47C2×SD1612yes—
233C2×C4×C47C23×C411yescharacteristic
234C2×C4×C47C22×D411yescharacteristic
235C2×C4×C47C22×D411yescharacteristic
236C22⋊D47—216no—
237C2×Dic47—22no—
238C2×Dic47—22no—
239C2×Dic47—42no—
240C2×Dic47—48no—
241C2×Dic47C22⋊C814yes—
242C2×Dic47#10214yes—
243C2×Dic47C2×C22⋊C412yes—
244C2×Dic47C2×C22⋊C412yes—
245C2×Dic47C2×C22⋊C412yes—
246D188—22no—
247D188—24no—
248D188C22×C814yescomplemented
249C4×D47—24no—
250C4×D47—24no—
251C4×D47—48no—
252C4×D47—42no—
253C4×D47—42no—
254C4×D47—44no—
255C4×D47—48no—
256C4×D47C22⋊C818yes—
257C4×D47#10218yes—
258C4×D47C22×C814yes—
259C4×D47C2×M1614yes—
260C4×D47C2×D814yes—
261C4×D47C2×SD1614yes—
262C8×C47—24no—
263C8×C47—42no—
264C47⋊C8—24no—
265C47⋊C8—42no—
266C22×D4⋊C8—471nomaximal, Sylow
267C22×C47—24no—
268C22×C47—42no—
269C22×C47—42no—
270C22×C47—48no—
271C22×C47C2×C22⋊C812yes—
272C22×C47C2×#10212yes—
273C22×C47C2×#10412yes—
274C22×C47C22×C22⋊C411yescharacteristic
275C2×D47—24no—
276C2×D47—42no—
277C2×D47—42no—
278C2×D47—48no—
279C2×D47—432no—
280C2×D47D4⋊C8116yesdirect product factor
281C2×D47C2×C22⋊C814yes—
282C2×D47C2×#10214yes—
283C2×D47C2×#10414yes—
284C4×C47—21no—
285C4×C47—21no—
286C4×C47—42no—
287C4×C47C2×C22⋊C812yes—
288C4×C47C2×#10212yes—
289C4×C47C23×C811yescharacteristic
290C4×C47C22×M1611yescharacteristic
291C4×C47C22×D811yescharacteristic
292C4×C47C22×SD1611yescharacteristic
293Dic47—22no—
294Dic47—42no—
295Dic47C2×C22⋊C814yes—
296Dic47C2×#10214yes—
297C22×C4×D4—471no—
298C22×C4⋊C8—471no—
299C22×C4×C8—471no—
300C2×D4⋊C8—471no—
301C2×D4⋊C8—471no—
302C2×D4⋊C8—478no—
303C2×D4⋊C8—471no—
304C2×D4⋊C8D4711yescharacteristic, direct product factor
305C2×C47—44no—
306C2×C47C2×D4⋊C814yescomplemented
307C2×C47C22×C22⋊C811yescharacteristic
308C2×C47C22×#10211yescharacteristic
309C2×C47C22×#10411yescharacteristic
310D47—44no—
311D47C2×D4⋊C818yesdirect product factor
312C23×D4—471no—
313C24×C4—941no—
314C23×C8—941no—
315C23×C8—941no—
316C2×C4×D4—471no—
317C2×C4×D4—474no—
318C2×C4×D4—474no—
319C2×C4×D4—471no—
320C2×C4×D4—471no—
321C2×C4×D4—941no—
322C2×C4×D4—942no—
323C2×C4×D4—942no—
324C2×C4×D4—941no—
325C2×C4×D4C2×D4711yescharacteristic
326C22×C4⋊C4—471no—
327C22×C22⋊C4—941no—
328C22×C42—471no—
329C2×C4⋊C8—471no—
330C2×C4⋊C8—474no—
331C2×C4⋊C8—942no—
332C2×C4⋊C8—941no—
333C2×C4⋊C8C2×D4711yescharacteristic, complemented
334C2×C4×C8—471no—
335C2×C4×C8—474no—
336C2×C4×C8—942no—
337C2×C4×C8—941no—
338C2×C4×C8C2×D4711yescharacteristic, complemented
339D4⋊C8—474no—
340D4⋊C8—474no—
341D4⋊C8—474no—
342D4⋊C8C2×D4714yesdirect product factor
343C47C22×D4⋊C811yescharacteristic, complemented, Sylow
344C25—941no—
345C22×D4—478no—
346C22×D4—474no—
347C22×D4—471no—
348C22×D4—942no—
349C22×D4—944no—
350C22×D4—941no—
351C22×D4C4×D4711yescharacteristic
352C23×C4—21no—
353C23×C4—471no—
354C23×C4—471no—
355C23×C4—471no—
356C23×C4—941no—
357C23×C4—944no—
358C23×C4—944no—
359C23×C4—941no—
360C23×C4—941no—
361C23×C4—941no—
362C23×C4—1884no—
363C23×C4—1884no—
364C22×C8—21no—
365C22×C8—21no—
366C22×C8—944no—
367C22×C8—948no—
368C22×C8—944no—
369C22×C8—941no—
370C22×C8—941no—
371C22×C8—1884no—
372C4×D4—21no—
373C4×D4—21no—
374C4×D4—474no—
375C4×D4—474no—
376C4×D4—472no—
377C4×D4—472no—
378C4×D4—944no—
379C4×D4—944no—
380C4×D4—942no—
381C4×D4—944no—
382C4×D4—944no—
383C4×D4—942no—
384C4×D4—941no—
385C4×D4—941no—
386C4×D4C4×D4712yes—
387C4×D4C22×D4712yes—
388C2×C4⋊C4—471no—
389C2×C4⋊C4—474no—
390C2×C4⋊C4—942no—
391C2×C4⋊C4—941no—
392C2×C4⋊C4C4×D4711yescharacteristic
393C2×C22⋊C4—21no—
394C2×C22⋊C4—944no—
395C2×C22⋊C4—944no—
396C2×C22⋊C4—941no—
397C2×C22⋊C4—941no—
398C2×C22⋊C4—941no—
399C2×C42—471no—
400C2×C42—471no—
401C2×C42—471no—
402C2×C42—472no—
403C2×C42—472no—
404C2×C42—472no—
405C2×C42—472no—
406C2×C42C22×D4711yescharacteristic
407C4⋊C8—21no—
408C4⋊C8—472no—
409C4⋊C8—944no—
410C4⋊C8—941no—
411C4⋊C8C22×D4712yescomplemented
412C4×C8—21no—
413C4×C8—472no—
414C4×C8—944no—
415C4×C8—941no—
416C4×C8C22×D4712yescomplemented
417C24—21no—
418C24—471no—
419C24—944no—
420C24—948no—
421C24—941no—
422C24—1884no—
423C24—1884no—
424C2×D4—21no—
425C2×D4—22no—
426C2×D4—4716no—
427C2×D4—474no—
428C2×D4—472no—
429C2×D4—9416no—
430C2×D4—948no—
431C2×D4—944no—
432C2×D4—948no—
433C2×D4—941no—
434C2×D4—942no—
435C2×D4C8×D4714yescomplemented
436C2×D4C2×C4×D4712yes—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—471no—
443C22×C4—471no—
444C22×C4—472no—
445C22×C4—472no—
446C22×C4—474no—
447C22×C4—474no—
448C22×C4—474no—
449C22×C4—474no—
450C22×C4—472no—
451C22×C4—472no—
452C22×C4—471no—
453C22×C4—472no—
454C22×C4—472no—
455C22×C4—944no—
456C22×C4—944no—
457C22×C4—944no—
458C22×C4—944no—
459C22×C4—941no—
460C22×C4—942no—
461C22×C4—942no—
462C22×C4—1884no—
463C22×C4—18816no—
464C22×C4—1888no—
465C22×C4—1888no—
466C22×C4—1884no—
467C22×C4—1884no—
468C22×C4—1882no—
469C22×C4—1882no—
470C22×C4C2×C4×D4711yescharacteristic
471C22×C4D4×D4711yescharacteristic
472C22×C4D4×D4711yescharacteristic
473C2×C8—24no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—42no—
477C2×C8—9416no—
478C2×C8—944no—
479C2×C8—942no—
480C2×C8—942no—
481C2×C8—1888no—
482C2×C8—1882no—
483C4⋊C4—21no—
484C4⋊C4—472no—
485C4⋊C4—944no—
486C4⋊C4—941no—
487C4⋊C4C2×C4×D4712yes—
488C22⋊C4—22no—
489C22⋊C4—22no—
490C22⋊C4—944no—
491C22⋊C4—944no—
492C22⋊C4—942no—
493C22⋊C4—942no—
494C42—472no—
495C42—472no—
496C42—472no—
497C42—472no—
498C42—472no—
499C42—472no—
500C42C2×C4×D4711yescharacteristic
501C42D4×D4711yescharacteristic
502C42D4×D4711yescharacteristic
503C42C23×D4711yescharacteristic
504C23—22no—
505C23—24no—
506C23—42no—
507C23—42no—
508C23—472no—
509C23—474no—
510C23—474no—
511C23—474no—
512C23—9416no—
513C23—942no—
514C23—944no—
515C23—1888no—
516C23—1888no—
517C23—18832no—
518C23—1882no—
519C23—1882no—
520C23C22⋊C4×D4711yescharacteristic
521D4—24no—
522D4—22no—
523D4—474no—
524D4—9416no—
525D4—944no—
526D4—942no—
527D4C2×C8×D4714yescomplemented
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—42no—
531C2×C4—44no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—472no—
535C2×C4—472no—
536C2×C4—474no—
537C2×C4—474no—
538C2×C4—478no—
539C2×C4—478no—
540C2×C4—474no—
541C2×C4—474no—
542C2×C4—474no—
543C2×C4—474no—
544C2×C4—472no—
545C2×C4—944no—
546C2×C4—944no—
547C2×C4—942no—
548C2×C4—942no—
549C2×C4—1888no—
550C2×C4—1888no—
551C2×C4—1888no—
552C2×C4—1882no—
553C2×C4—1884no—
554C2×C4—1882no—
555C2×C4—1882no—
556C2×C4C22⋊C4×D4711yescharacteristic
557C2×C4C22⋊C4×D4711yescharacteristic
558C2×C4C22⋊C4×D4711yescharacteristic
559C2×C4C2×C8×D4712yes—
560C2×C4M16×D4712yes—
561C2×C4D8×D4712yes—
562C2×C4SD16×D4712yes—
563C2×C4C22×C4×D4711yescharacteristic
564C2×C4C2×D4×D4711yescharacteristic
565C2×C4C2×D4×D4711yescharacteristic
566C8—24no—
567C8—42no—
568C8—944no—
569C8—1882no—
570C22—24no—
571C22—42no—
572C22—48no—
573C22—42no—
574C22—474no—
575C22—4716no—
576C22—474no—
577C22—474no—
578C22—944no—
579C22—18832no—
580C22—1882no—
581C22—1888no—
582C22—1882no—
583C22C22⋊C8×D4712yes—
584C22#102×D4712yes—
585C22#104×D4712yes—
586C22C2×C22⋊C4×D4711yescharacteristic
587C4—21no—
588C4—21no—
589C4—42no—
590C4—474no—
591C4—474no—
592C4—942no—
593C4—1882no—
594C4C22⋊C8×D4712yes—
595C4#102×D4712yes—
596C4C22×C8×D4711yescharacteristic
597C4C2×M16×D4711yescharacteristic
598C4C2×D8×D4711yescharacteristic
599C4C2×SD16×D4711yescharacteristic
600C2—44no—
601C2—478no—
602C2—1884no—
603C2D4⋊C8×D4714yesdirect product factor
604C2C2×C22⋊C8×D4711yescharacteristic
605C2C2×#102×D4711yescharacteristic
606C2C2×#104×D4711yescharacteristic
subgroupG/H
centerC22×C4D4×D47
commutatorC4×C47C23×C8
FrattiniC42C23×D47
FittingC2×C47×D4⋊C8C2
socleC23×C47C2×C22⋊C4
prime radicalC22×D4×D47C4
cosocleC42×C47C24
hypercenterC2×D4⋊C8D47
hypocenterC47C22×D4⋊C8
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×D4⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C8×D47C2semidirect
3. C2×C4×C8×D47C2semidirect
4. C2×#15688852C2semidirect
5. C2×D4⋊(C47⋊C8)C2semidirect
6. C2×#15688850C2semidirect
7. D4⋊C8×D47C2direct (N × H)
8. C2×C47×D4⋊C8C2semidirect
25. C2×C4⋊(C47⋊C8)C22semidirect
28. C4⋊C8×D47C22semidirect
29. C2×C4×C47⋊C8C22semidirect
32. C4×C8×D47C22semidirect
33. #15688852C22semidirect
34. D4⋊(C47⋊C8)C22semidirect
35. #15688850C22semidirect
37. C2×C4⋊C8×C47C22semidirect
38. C2×C4×C8×C47C22semidirect
39. C47×D4⋊C8C22semidirect
45. C2×D4×D47C8semidirect
93. C4⋊(C47⋊C8)C23semidirect
96. C4×C47⋊C8C23semidirect
110. C4⋊C8×C47C23semidirect
112. C4×C8×C47C23semidirect
122. C2×D4×C47C2×C8semidirect
142. D4×D47C2×C8semidirect
145. C2×D188C2×C8semidirect
219. D4×C47C22×C8semidirect
248. D188C22×C8semidirect
280. C2×D47D4⋊C8direct (N × H)
304. C2×D4⋊C8D47direct (N × H)
306. C2×C47C2×D4⋊C8semidirect
311. D47C2×D4⋊C8direct (N × H)
333. C2×C4⋊C8C2×D47semidirect
338. C2×C4×C8C2×D47semidirect
342. D4⋊C8C2×D47direct (N × H)
343. C47C22×D4⋊C8semidirect
411. C4⋊C8C22×D47semidirect
416. C4×C8C22×D47semidirect
435. C2×D4C8×D47semidirect
527. D4C2×C8×D47semidirect
603. C2D4⋊C8×D47direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×D4×D472
C2×C4⋊C8×D472
C2×C4×C8×D472
C2×#156888522
C2×D4⋊(C47⋊C8)2
C2×#156888502
D4⋊C8×D472
C2×C47×D4⋊C82
C22×D4⋊C847