Finite Group Databasebeta

← C2×#462×D47 #27083076

Subgroups — C2×#462×D47 #27083076

Order 12032.

2790 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q16×D47C212yesmaximal
2C2×C4⋊Q8×D47C211yesmaximal, characteristic
3C2×C4×Q8×D47C211yesmaximal, characteristic
4C2×#15689334C211yesmaximal, characteristic, complemented
5C2×#15689333C211yesmaximal, characteristic, complemented
6C2×#15689332C212yesmaximal, complemented
7C2×#15689331C212yesmaximal, complemented
8C2×#15689330C211yesmaximal, characteristic, complemented
9#462×D47C2116yesmaximal, direct product factor
10C2×C4⋊C8×D47C211yesmaximal, characteristic
11C2×#103×D47C212yesmaximal
12C2×C47×#462C211yesmaximal, characteristic, complemented
13C22×Q8×D47C2212yes—
14C22×Q8×D47C2211yescharacteristic
15C22×Dic188C2212yes—
16C22×#10625337C2212yes—
17C22×#10625337C2212yes—
18C2×Q16×D47—216no—
19C2×Q16×D47C22116yes—
20C22×C8×D47C2212yes—
21C2×#13094024C2211yescharacteristic
22C2×#13094023—21no—
23C2×#13094023—21no—
24C2×#13094022C2212yes—
25C4⋊Q8×D47—24no—
26C4⋊Q8×D47C2218yes—
27C2×Q8×Dic47C2211yescharacteristic
28C2×C4×Dic94—21no—
29C2×C4×Dic94C2211yescharacteristic
30C2×#13093989—21no—
31C2×#13093989C2211yescharacteristic
32C4×Q8×D47—24no—
33C4×Q8×D47C2218yes—
34C2×C4⋊C4×D47—21no—
35C2×C4⋊C4×D47—21no—
36C2×C4⋊C4×D47—21no—
37C2×C4⋊C4×D47C2211yescharacteristic
38C2×C42×D47—21no—
39C2×C42×D47C2211yescharacteristic
40#15689334C2218yescomplemented
41#15689333C2218yescomplemented
42#15689332C22116yescomplemented
43#15689331C22116yescomplemented
44#15689330C2218yescomplemented
45C2×C4⋊(C47⋊C8)C2211yescharacteristic
46C2×Dic47⋊C8C2212yes—
47C4⋊C8×D47C2218yes—
48C2×#13093949C2212yes—
49C2×#13093948C2212yes—
50C2×#13093947C2212yes—
51#103×D47C22116yes—
52C22×Q16×C47C2212yes—
53C2×C4⋊Q8×C47C2211yescharacteristic
54C2×C4×Q8×C47C2211yescharacteristic
55C47×#462C2218yescomplemented
56C2×C4⋊C8×C47C2211yescharacteristic
57C2×#103×C47C2212yes—
58C22×Dic94—21no—
59C22×Dic94—22no—
60C22×Dic94C2312yes—
61C22×Dic94C2311yescharacteristic
62C2×Q8×D47—22no—
63C2×Q8×D47—24no—
64C2×Q8×D47—24no—
65C2×Q8×D47—28no—
66C2×Q8×D47—28no—
67C2×Q8×D47D418yes—
68C2×Q8×D47C2318yes—
69C2×Q8×D47C2314yes—
70C22×C4×D47—21no—
71C22×C4×D47—21no—
72C22×C4×D47—22no—
73C22×C4×D47D411yescharacteristic
74C22×C4×D47D411yescharacteristic
75C22×C4×D47C2311yescharacteristic
76C2×Dic188—28no—
77C2×Dic188C2318yes—
78C2×#10625337—28no—
79C2×#10625337—28no—
80C2×#10625337C2318yes—
81C2×#10625337C2318yes—
82Q16×D47—264no—
83C22×C47⋊C8C2312yes—
84C2×C8×D47—28no—
85C2×C8×D47C2318yes—
86#13094024—22no—
87#13094024C2314yes—
88#13094023—28no—
89#13094023—28no—
90#13094022—24no—
91#13094022C2318yes—
92Q8×Dic47—22no—
93Q8×Dic47C2314yes—
94C4×Dic94—22no—
95C4×Dic94—28no—
96C4×Dic94C2314yes—
97#13093989—22no—
98#13093989—28no—
99#13093989C2314yes—
100C2×C4⋊Dic47—21no—
101C2×C4⋊Dic47—21no—
102C2×C4⋊Dic47—21no—
103C2×C4⋊Dic47C2311yescharacteristic
104C2×Dic47⋊C4—21no—
105C2×Dic47⋊C4—21no—
106C2×Dic47⋊C4—22no—
107C2×Dic47⋊C4—22no—
108C2×Dic47⋊C4—21no—
109C4⋊C4×D47—28no—
110C4⋊C4×D47—28no—
111C4⋊C4×D47—28no—
112C4⋊C4×D47—22no—
113C4⋊C4×D47C2314yes—
114C2×C4×Dic47—21no—
115C2×C4×Dic47—21no—
116C2×C4×Dic47—21no—
117C2×C4×Dic47D411yescharacteristic
118C2×C4×Dic47D411yescharacteristic
119C2×C4×Dic47C2311yescharacteristic
120C42×D47—28no—
121C42×D47D414yes—
122C42×D47C2314yes—
123C4⋊(C47⋊C8)C2314yes—
124Dic47⋊C8C2318yes—
125#13093949C2318yes—
126#13093948C2318yes—
127#13093947C2318yes—
128C22×Q8×C47C2312yes—
129C22×Q8×C47C2311yescharacteristic
130C2×Q16×C47—28no—
131C2×Q16×C47C2318yes—
132C22×C8×C47C2312yes—
133C4⋊Q8×C47—22no—
134C4⋊Q8×C47C2314yes—
135C4×Q8×C47—22no—
136C4×Q8×C47C2314yes—
137C2×C4⋊C4×C47—21no—
138C2×C4⋊C4×C47—21no—
139C2×C4⋊C4×C47—21no—
140C2×C4⋊C4×C47C2311yescharacteristic
141C2×C42×C47—21no—
142C2×C42×C47C2311yescharacteristic
143C4⋊C8×C47C2314yes—
144#103×C47C2318yes—
145C23×D47C2×D411yescharacteristic
146C2×Q8×C47—21no—
147C2×Q8×C47—22no—
148C2×Q8×C47—22no—
149C2×Q8×C47—24no—
150C2×Q8×C47—24no—
151C2×Q8×C47C2×D414yes—
152C2×Q8×C47C2414yes—
153C2×Q8×C47C2412yes—
154C22×C4×C47—21no—
155C22×C4×C47—21no—
156C22×C4×C47—22no—
157C22×C4×C47C2×D411yescharacteristic
158C22×C4×C47C2×D411yescharacteristic
159C22×C4×C47C2411yescharacteristic
160C22×Dic47—21no—
161C22×Dic47—21no—
162C22×Dic47—22no—
163C22×Dic47C2×D411yescharacteristic
164C22×Dic47C2×D411yescharacteristic
165C22×Dic47C2×D411yescharacteristic
166Q8×D47—216no—
167Q8×D47—28no—
168Q8×D47—216no—
169Q8×D47—216no—
170Q8×D47—416no—
171Q8×D47C2×D4116yes—
172C2×C4×D47—28no—
173C2×C4×D47—24no—
174C2×C4×D47—24no—
175C2×C4×D47—24no—
176C2×C4×D47—28no—
177C2×C4×D47—48no—
178C2×C4×D47—44no—
179C2×C4×D47Q1618yescomplemented
180C2×C4×D47C2×D414yes—
181C2×C4×D47C2×D412yes—
182C2×C4×D47C2×D414yes—
183C2×C4×D47C2×D414yes—
184C2×C4×D47#4114yes—
185C2×C4×D47C2412yes—
186C2×Dic94—21no—
187C2×Dic94—22no—
188C2×Dic94—28no—
189C2×Dic94—24no—
190C2×Dic94—24no—
191C2×Dic94—24no—
192C2×Dic94—22no—
193C2×Dic94—28no—
194C2×Dic94—48no—
195C2×Dic94C2×D414yes—
196C2×Dic94C2414yes—
197C2×Dic94C2412yes—
198Q16×C47—216no—
199C2×C8×C47—24no—
200C2×C8×C47C2414yes—
201C4⋊C4×C47—24no—
202C4⋊C4×C47—24no—
203C4⋊C4×C47—24no—
204C4⋊C4×C47—21no—
205C4⋊C4×C47C2412yes—
206C42×C47—24no—
207C42×C47C2×D412yes—
208C42×C47C2412yes—
209#10625337—216no—
210#10625337—216no—
211C4⋊Dic47—24no—
212C4⋊Dic47—24no—
213C4⋊Dic47—21no—
214C4⋊Dic47—24no—
215C4⋊Dic47C2412yes—
216Dic47⋊C4—24no—
217Dic47⋊C4—24no—
218Dic47⋊C4—28no—
219Dic47⋊C4—28no—
220Dic47⋊C4—24no—
221C4×Dic47—24no—
222C4×Dic47—24no—
223C4×Dic47—24no—
224C4×Dic47C2×D412yes—
225C4×Dic47C2×D414yes—
226C4×Dic47C2×D414yes—
227C4×Dic47C2412yes—
228C2×C47⋊C8—24no—
229C2×C47⋊C8C2414yes—
230Dic188—216no—
231C8×D47—216no—
232C23×C47C22×D411yescharacteristic
233C22×D47#12114yes—
234C22×D47C2×Q1614yes—
235C22×D47#13714yes—
236C22×D47C22×D412yes—
237Q8×C47—24no—
238Q8×C47—22no—
239Q8×C47—24no—
240Q8×C47—24no—
241Q8×C47—44no—
242Q8×C47C22×D414yes—
243C2×C4×C47—24no—
244C2×C4×C47—22no—
245C2×C4×C47—22no—
246C2×C4×C47—22no—
247C2×C4×C47—24no—
248C2×C4×C47—44no—
249C2×C4×C47—42no—
250C2×C4×C47C2×Q1614yescomplemented
251C2×C4×C47C22×D412yes—
252C2×C4×C47C22×D411yescharacteristic
253C2×C4×C47C22×D412yes—
254C2×C4×C47C22×D412yes—
255C2×C4×C47C2×#4112yes—
256C2×C4×C47C2511yescharacteristic
257C2×Dic47—24no—
258C2×Dic47—22no—
259C2×Dic47—22no—
260C2×Dic47—22no—
261C2×Dic47—24no—
262C2×Dic47—44no—
263C2×Dic47—42no—
264C2×Dic47#12114yes—
265C2×Dic47C2×Q1614yescomplemented
266C2×Dic47C22×D412yes—
267C2×Dic47C22×D412yes—
268C2×Dic47C22×D412yes—
269C4×D47—216no—
270C4×D47—28no—
271C4×D47—416no—
272C4×D47—48no—
273C4×D47#12118yes—
274C4×D47C2×Q16116yescomplemented
275C4×D47C22×D414yes—
276C4×D47C2×#4114yes—
277Dic94—24no—
278Dic94—22no—
279Dic94—216no—
280Dic94—24no—
281Dic94—24no—
282Dic94—44no—
283Dic94—416no—
284Dic94C22×D414yes—
285C8×C47—24no—
286C47⋊C8—24no—
287C22×#462—471nomaximal, Sylow
288C22×C47C2×#12112yes—
289C22×C47C22×Q1612yes—
290C22×C47C2×#13712yes—
291C22×C47C23×D411yescharacteristic
292C2×D47#462116yesdirect product factor
293C2×D47C2×#12114yes—
294C2×D47C22×Q1614yes—
295C2×D47C2×#13714yes—
296C4×C47—24no—
297C4×C47—22no—
298C4×C47—44no—
299C4×C47—42no—
300C4×C47C2×#12112yes—
301C4×C47C22×Q1614yescomplemented
302C4×C47C23×D411yescharacteristic
303C4×C47C22×#4111yescharacteristic
304Dic47—24no—
305Dic47—22no—
306Dic47—44no—
307Dic47—42no—
308Dic47C2×#12114yes—
309Dic47C22×Q1614yescomplemented
310C23×Q16—472no—
311C22×C4⋊Q8—471no—
312C22×C4×Q8—471no—
313C2×#462—4716no—
314C2×#462—471no—
315C2×#462—472no—
316C2×#462—472no—
317C2×#462—471no—
318C2×#462—471no—
319C2×#462D4711yescharacteristic, direct product factor
320C22×C4⋊C8—471no—
321C22×#103—472no—
322C2×C47C2×#46214yescomplemented
323C2×C47C22×#12111yescharacteristic
324C2×C47C23×Q1611yescharacteristic
325C2×C47C22×#13711yescharacteristic
326D47C2×#46218yesdirect product factor
327C23×Q8—471no—
328C23×Q8—472no—
329C22×Q16—472no—
330C22×Q16—472no—
331C22×Q16—4716no—
332C22×Q16—472no—
333C22×Q16—9416no—
334C22×Q16C2×D4712yes—
335C23×C8—472no—
336C2×C4⋊Q8—472no—
337C2×C4⋊Q8—478no—
338C2×C4⋊Q8—471no—
339C2×C4⋊Q8—941no—
340C2×C4⋊Q8—941no—
341C2×C4⋊Q8—944no—
342C2×C4⋊Q8C2×D4711yescharacteristic
343C2×C4×Q8—471no—
344C2×C4×Q8—478no—
345C2×C4×Q8—471no—
346C2×C4×Q8—471no—
347C2×C4×Q8—941no—
348C2×C4×Q8—941no—
349C2×C4×Q8—944no—
350C2×C4×Q8C2×D4711yescharacteristic
351C22×C4⋊C4—471no—
352C22×C4⋊C4—941no—
353C22×C4⋊C4—941no—
354C22×C4⋊C4—941no—
355C22×C42—471no—
356C22×C42—941no—
357#462—4716no—
358#462—478no—
359#462—478no—
360#462—478no—
361#462—4716no—
362#462C2×D4718yesdirect product factor
363C2×C4⋊C8—472no—
364C2×C4⋊C8—471no—
365C2×C4⋊C8—478no—
366C2×C4⋊C8C2×D4711yescharacteristic
367C2×#103—472no—
368C2×#103—472no—
369C2×#103—472no—
370C2×#103—4716no—
371C2×#103C2×D4712yes—
372C47C22×#46211yescharacteristic, complemented, Sylow
373C22×Q8—478no—
374C22×Q8—474no—
375C22×Q8—478no—
376C22×Q8—471no—
377C22×Q8—472no—
378C22×Q8—941no—
379C22×Q8—942no—
380C22×Q8—942no—
381C22×Q8—944no—
382C22×Q8—944no—
383C22×Q8—948no—
384C22×Q8—948no—
385C22×Q8C22×D4712yes—
386C22×Q8C22×D4711yescharacteristic
387C23×C4—471no—
388C23×C4—471no—
389C23×C4—471no—
390C23×C4—941no—
391C23×C4—941no—
392C23×C4—942no—
393C2×Q16—28no—
394C2×Q16—478no—
395C2×Q16—478no—
396C2×Q16—478no—
397C2×Q16—948no—
398C2×Q16—9464no—
399C2×Q16—948no—
400C2×Q16—948no—
401C2×Q16C22×D4718yes—
402C22×C8—472no—
403C22×C8—478no—
404C22×C8—948no—
405C22×C8C22×D4712yes—
406C4⋊Q8—22no—
407C4⋊Q8—478no—
408C4⋊Q8—474no—
409C4⋊Q8—948no—
410C4⋊Q8—948no—
411C4⋊Q8—944no—
412C4⋊Q8—942no—
413C4⋊Q8C22×D4714yes—
414C4×Q8—22no—
415C4×Q8—474no—
416C4×Q8—474no—
417C4×Q8—474no—
418C4×Q8—948no—
419C4×Q8—948no—
420C4×Q8—942no—
421C4×Q8—942no—
422C4×Q8—942no—
423C4×Q8C22×D4714yes—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—471no—
428C2×C4⋊C4—474no—
429C2×C4⋊C4—942no—
430C2×C4⋊C4—948no—
431C2×C4⋊C4—948no—
432C2×C4⋊C4—948no—
433C2×C4⋊C4—941no—
434C2×C4⋊C4—941no—
435C2×C4⋊C4—941no—
436C2×C4⋊C4—942no—
437C2×C4⋊C4—942no—
438C2×C4⋊C4—941no—
439C2×C4⋊C4—941no—
440C2×C4⋊C4—941no—
441C2×C4⋊C4C22×D4711yescharacteristic
442C2×C42—21no—
443C2×C42—471no—
444C2×C42—471no—
445C2×C42—471no—
446C2×C42—474no—
447C2×C42—474no—
448C2×C42—948no—
449C2×C42—941no—
450C2×C42—941no—
451C2×C42—941no—
452C2×C42C22×D4711yescharacteristic
453C4⋊C8—478no—
454C4⋊C8—474no—
455C4⋊C8C22×D4714yes—
456#103—478no—
457#103—478no—
458#103—478no—
459#103C22×D4718yes—
460C24—471no—
461C2×Q8—21no—
462C2×Q8—22no—
463C2×Q8—22no—
464C2×Q8—24no—
465C2×Q8—24no—
466C2×Q8—4716no—
467C2×Q8—474no—
468C2×Q8—472no—
469C2×Q8—474no—
470C2×Q8—944no—
471C2×Q8—948no—
472C2×Q8—948no—
473C2×Q8—9416no—
474C2×Q8—948no—
475C2×Q8—9416no—
476C2×Q8—9416no—
477C2×Q8—941no—
478C2×Q8—942no—
479C2×Q8—942no—
480C2×Q8—944no—
481C2×Q8—944no—
482C2×Q8—1888no—
483C2×Q8—18816no—
484C2×Q8D4×D4714yes—
485C2×Q8C23×D4714yes—
486C2×Q8C23×D4712yes—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—22no—
490C22×C4—471no—
491C22×C4—471no—
492C22×C4—478no—
493C22×C4—474no—
494C22×C4—472no—
495C22×C4—474no—
496C22×C4—474no—
497C22×C4—472no—
498C22×C4—471no—
499C22×C4—474no—
500C22×C4—944no—
501C22×C4—944no—
502C22×C4—948no—
503C22×C4—944no—
504C22×C4—948no—
505C22×C4—941no—
506C22×C4—941no—
507C22×C4—942no—
508C22×C4—1884no—
509C22×C4—1888no—
510C22×C4D4×D4711yescharacteristic
511C22×C4D4×D4711yescharacteristic
512C22×C4C23×D4711yescharacteristic
513Q16—216no—
514Q16—9416no—
515Q16—9416no—
516Q16—9416no—
517C2×C8—24no—
518C2×C8—474no—
519C2×C8—9416no—
520C2×C8—944no—
521C2×C8C23×D4714yes—
522C4⋊C4—24no—
523C4⋊C4—24no—
524C4⋊C4—24no—
525C4⋊C4—21no—
526C4⋊C4—472no—
527C4⋊C4—944no—
528C4⋊C4—944no—
529C4⋊C4—948no—
530C4⋊C4—948no—
531C4⋊C4—944no—
532C4⋊C4—944no—
533C4⋊C4—941no—
534C4⋊C4—944no—
535C4⋊C4—944no—
536C4⋊C4C23×D4712yes—
537C42—24no—
538C42—474no—
539C42—472no—
540C42—474no—
541C42—472no—
542C42—944no—
543C42—944no—
544C42—944no—
545C42D4×D4712yes—
546C42C23×D4712yes—
547C23—474no—
548C23—474no—
549C23—474no—
550C23—472no—
551C23C2×D4×D4711yescharacteristic
552Q8—24no—
553Q8—22no—
554Q8—24no—
555Q8—24no—
556Q8—44no—
557Q8—474no—
558Q8—9416no—
559Q8—944no—
560Q8—942no—
561Q8—944no—
562Q8—944no—
563Q8—18816no—
564Q8—1884no—
565Q8C2×D4×D4714yes—
566C2×C4—24no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—24no—
571C2×C4—44no—
572C2×C4—42no—
573C2×C4—474no—
574C2×C4—474no—
575C2×C4—472no—
576C2×C4—472no—
577C2×C4—478no—
578C2×C4—4716no—
579C2×C4—474no—
580C2×C4—474no—
581C2×C4—472no—
582C2×C4—948no—
583C2×C4—9416no—
584C2×C4—944no—
585C2×C4—942no—
586C2×C4—942no—
587C2×C4—942no—
588C2×C4—944no—
589C2×C4—1888no—
590C2×C4—18816no—
591C2×C4—1884no—
592C2×C4—1882no—
593C2×C4Q16×D4714yescomplemented
594C2×C4C2×D4×D4712yes—
595C2×C4C2×D4×D4711yescharacteristic
596C2×C4C2×D4×D4712yes—
597C2×C4C2×D4×D4712yes—
598C2×C4#41×D4712yes—
599C2×C4C24×D4711yescharacteristic
600C8—24no—
601C8—944no—
602C22—474no—
603C22—474no—
604C22—474no—
605C22—4716no—
606C22#121×D4712yes—
607C22C2×Q16×D4712yes—
608C22#137×D4712yes—
609C22C22×D4×D4711yescharacteristic
610C4—22no—
611C4—24no—
612C4—42no—
613C4—44no—
614C4—474no—
615C4—474no—
616C4—942no—
617C4—944no—
618C4—1882no—
619C4—1884no—
620C4#121×D4712yes—
621C4C2×Q16×D4714yescomplemented
622C4C22×D4×D4711yescharacteristic
623C4C2×#41×D4711yescharacteristic
624C2—478no—
625C2#462×D4714yesdirect product factor
626C2C2×#121×D4711yescharacteristic
627C2C22×Q16×D4711yescharacteristic
628C2C2×#137×D4711yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#462C2
socleC23×C47C22×D4
prime radicalC23×D47C2×D4
hypercenterC2×#462D47
hypocenterC47C22×#462
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
4. C2×#15689334C2semidirect
5. C2×#15689333C2semidirect
6. C2×#15689332C2semidirect
7. C2×#15689331C2semidirect
8. C2×#15689330C2semidirect
9. #462×D47C2direct (N × H)
12. C2×C47×#462C2semidirect
40. #15689334C22semidirect
41. #15689333C22semidirect
42. #15689332C22semidirect
43. #15689331C22semidirect
44. #15689330C22semidirect
55. C47×#462C22semidirect
179. C2×C4×D47Q16semidirect
250. C2×C4×C47C2×Q16semidirect
265. C2×Dic47C2×Q16semidirect
274. C4×D47C2×Q16semidirect
292. C2×D47#462direct (N × H)
301. C4×C47C22×Q16semidirect
309. Dic47C22×Q16semidirect
319. C2×#462D47direct (N × H)
322. C2×C47C2×#462semidirect
326. D47C2×#462direct (N × H)
362. #462C2×D47direct (N × H)
372. C47C22×#462semidirect
593. C2×C4Q16×D47semidirect
621. C4C2×Q16×D47semidirect
625. C2#462×D47direct (N × H)

Maximal subgroups

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

subgroupindex
C22×Q16×D472
C2×C4⋊Q8×D472
C2×C4×Q8×D472
C2×#156893342
C2×#156893332
C2×#156893322
C2×#156893312
C2×#156893302
#462×D472
C2×C4⋊C8×D472
C2×#103×D472
C2×C47×#4622
C22×#46247