Finite Group Databasebeta

← D47×#1872 #26217468

Subgroups — D47×#1872 #26217468

Order 12032.

2270 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊Q8×D47C211yesmaximal, characteristic
2C22×C4⋊C4×D47C211yesmaximal, characteristic
3C2×#103×D47C212yesmaximal, complemented
4C2×C22⋊C8×D47C211yesmaximal, characteristic
5#20243696C211yesmaximal, characteristic, complemented
6#20243695C211yesmaximal, characteristic, complemented
7#20243694C212yesmaximal, complemented
8#20243693C211yesmaximal, characteristic, complemented
9#20243692C212yesmaximal, complemented
10#340×D47C212yesmaximal, complemented
11C47×#1872C211yesmaximal, characteristic, complemented
12C22×Q8×D47C2211yescharacteristic
13C23×C4×D47—21no—
14C23×C4×D47C2211yescharacteristic
15C22×C8×D47C2212yes—
16C2×#13094004C2211yescharacteristic
17C2×#13094003C2211yescharacteristic
18C2×#13094002—21no—
19C2×#13094001—21no—
20C2×#13094000C2211yescharacteristic
21C22⋊Q8×D47—24no—
22C22⋊Q8×D47C418yescomplemented
23C22×C4⋊Dic47C2211yescharacteristic
24C22×Dic47⋊C4—21no—
25C2×C4⋊C4×D47—21no—
26C2×C4⋊C4×D47—21no—
27C2×C4⋊C4×D47—21no—
28C2×C4⋊C4×D47—28no—
29C2×C4⋊C4×D47C2212yes—
30C2×C4⋊C4×D47C2211yescharacteristic
31C2×C4⋊C4×D47C2212yes—
32C2×C22⋊C4×D47—21no—
33C2×#13093949C2212yescomplemented
34C2×#13093948C2212yescomplemented
35C2×#13093947C2212yescomplemented
36#103×D47—28no—
37C2×C22⋊(C47⋊C8)C2211yescharacteristic
38C2×(C2×D47)⋊C8C2212yes—
39C22⋊C8×D47—24no—
40#15688886C2212yescomplemented
41#15688885C2212yescomplemented
42#15688885C2212yescomplemented
43C2×C22⋊Q8×C47C2211yescharacteristic
44C22×C4⋊C4×C47C2211yescharacteristic
45C2×#103×C47C2212yescomplemented
46C2×C22⋊C8×C47C2211yescharacteristic
47C47×#340C2212yescomplemented
48C24×D47D411yescharacteristic
49C22×Dic94—21no—
50C22×Dic94C2311yescharacteristic
51C2×Q8×D47—22no—
52C2×Q8×D47—24no—
53C2×Q8×D47—24no—
54C2×Q8×D47C2×C414yescomplemented
55C23×Dic47—21no—
56C23×Dic47D411yescharacteristic
57C22×C4×D47—24no—
58C22×C4×D47—24no—
59C22×C4×D47—28no—
60C22×C4×D47—21no—
61C22×C4×D47—21no—
62C22×C4×D47—22no—
63C22×C4×D47—22no—
64C22×C4×D47—44no—
65C22×C4×D47—44no—
66C22×C4×D47C2×C414yes—
67C22×C4×D47D411yescharacteristic
68C22×C4×D47D411yescharacteristic
69C22×C4×D47D414yes—
70C22×C4×D47C2311yescharacteristic
71C22×C4×D47C2311yescharacteristic
72C22×C47⋊C8C2312yes—
73C2×C8×D47—24no—
74C2×C8×D47—24no—
75C2×C8×D47—24no—
76#13094004—22no—
77#13094004C2×C414yescomplemented
78#13094003—22no—
79#13094003C2×C414yescomplemented
80#13094002—28no—
81#13094001—28no—
82#13094000—22no—
83#13094000C2×C414yescomplemented
84C2×C4⋊Dic47—21no—
85C2×C4⋊Dic47—21no—
86C2×C4⋊Dic47—24no—
87C2×C4⋊Dic47C2311yescharacteristic
88C2×C4⋊Dic47C2312yes—
89C2×Dic47⋊C4—28no—
90C2×Dic47⋊C4—21no—
91C2×Dic47⋊C4—22no—
92C2×Dic47⋊C4—22no—
93C2×Dic47⋊C4—21no—
94C2×Dic47⋊C4—21no—
95C4⋊C4×D47—28no—
96C4⋊C4×D47—28no—
97C4⋊C4×D47—28no—
98C4⋊C4×D47—24no—
99C4⋊C4×D47—22no—
100C4⋊C4×D47—24no—
101C4⋊C4×D47—24no—
102C4⋊C4×D47C2×C414yescomplemented
103C4⋊C4×D47D418yes—
104C2×C22⋊Dic47—21no—
105C2×(C2×D47)⋊C4—21no—
106C2×(C2×D47)⋊C4—21no—
107C22⋊C4×D47—28no—
108#13093949—24no—
109#13093948—24no—
110#13093947—24no—
111C22⋊(C47⋊C8)—22no—
112(C2×D47)⋊C8—24no—
113C22×Q8×C47C2311yescharacteristic
114C23×C4×C47—21no—
115C23×C4×C47C2311yescharacteristic
116C22×C8×C47C2312yes—
117C22⋊Q8×C47—22no—
118C22⋊Q8×C47C2×C414yescomplemented
119C2×C4⋊C4×C47—21no—
120C2×C4⋊C4×C47—21no—
121C2×C4⋊C4×C47—24no—
122C2×C4⋊C4×C47C2311yescharacteristic
123C2×C4⋊C4×C47C2312yes—
124C2×C22⋊C4×C47—21no—
125#103×C47—24no—
126C22⋊C8×C47—22no—
127C24×C47C2×D411yescharacteristic
128C23×D47—22no—
129C23×D47—22no—
130C23×D47—22no—
131C23×D47—22no—
132C23×D47C22⋊C414yes—
133C23×D47SD1614yes—
134C23×D47Q1614yes—
135C23×D47C2×D411yescharacteristic
136C23×D47C2×D411yescharacteristic
137C2×Q8×C47—21no—
138C2×Q8×C47—22no—
139C2×Q8×C47—22no—
140C2×Q8×C47C22×C412yescomplemented
141C22×C4×C47—22no—
142C22×C4×C47—22no—
143C22×C4×C47—24no—
144C22×C4×C47—21no—
145C22×C4×C47—21no—
146C22×C4×C47—22no—
147C22×C4×C47—42no—
148C22×C4×C47—42no—
149C22×C4×C47C22×C412yes—
150C22×C4×C47C2×D411yescharacteristic
151C22×C4×C47C2×D412yes—
152C22×C4×C47C2411yescharacteristic
153C22×Dic47—22no—
154C22×Dic47—22no—
155C22×Dic47—24no—
156C22×Dic47—21no—
157C22×Dic47—21no—
158C22×Dic47—22no—
159C22×Dic47—42no—
160C22×Dic47—42no—
161C22×Dic47C22⋊C414yes—
162C22×Dic47C2×D411yescharacteristic
163C22×Dic47C2×D411yescharacteristic
164Q8×D47—216no—
165Q8×D47—48no—
166C2×C4×D47—22no—
167C2×C4×D47—22no—
168C2×C4×D47—22no—
169C2×C4×D47—22no—
170C2×C4×D47—22no—
171C2×C4×D47—22no—
172C2×C4×D47—216no—
173C2×C4×D47—216no—
174C2×C4×D47—28no—
175C2×C4×D47—24no—
176C2×C4×D47—24no—
177C2×C4×D47—28no—
178C2×C4×D47—44no—
179C2×C4×D47—432no—
180C2×C4×D47—42no—
181C2×C4×D47—42no—
182C2×C4×D47—44no—
183C2×C4×D47—44no—
184C2×C4×D47—42no—
185C2×C4×D47—44no—
186C2×C4×D47—42no—
187C2×C4×D47C22⋊C414yes—
188C2×C4×D47C22⋊C414yes—
189C2×C4×D47C22×C412yes—
190C2×C4×D47C22×C412yes—
191C2×C4×D47C2×D412yes—
192C2×C4×D47C2×D414yes—
193C2×C4×D47C2×D412yes—
194C2×C4×D47#4114yes—
195C2×Dic94—22no—
196C2×Dic94—22no—
197C2×Dic94—21no—
198C2×Dic94—24no—
199C2×Dic94—42no—
200C2×Dic94—42no—
201C2×Dic94C22×C412yescomplemented
202C2×C8×C47—22no—
203C2×C8×C47—22no—
204C2×C8×C47—22no—
205C4⋊C4×C47—24no—
206C4⋊C4×C47—24no—
207C4⋊C4×C47—22no—
208C4⋊C4×C47—21no—
209C4⋊C4×C47C22×C412yescomplemented
210C4⋊C4×C47C2×D414yes—
211C22⋊C4×C47—24no—
212C22⋊Dic47—24no—
213(C2×D47)⋊C4—24no—
214(C2×D47)⋊C4—24no—
215C4⋊Dic47—24no—
216C4⋊Dic47—22no—
217C4⋊Dic47—21no—
218C4⋊Dic47—24no—
219C4⋊Dic47C22×C412yescomplemented
220C4⋊Dic47C2×D414yes—
221Dic47⋊C4—28no—
222Dic47⋊C4—24no—
223Dic47⋊C4—24no—
224Dic47⋊C4—24no—
225Dic47⋊C4—28no—
226C2×C47⋊C8—22no—
227C2×C47⋊C8—22no—
228C2×C47⋊C8—22no—
229C8×D47—48no—
230C23×C47—21no—
231C23×C47—21no—
232C23×C47—21no—
233C23×C47—21no—
234C23×C47C2×C22⋊C412yes—
235C23×C47C2×SD1612yes—
236C23×C47C2×Q1612yes—
237C23×C47C22×D411yescharacteristic
238C22×D47—21no—
239C22×D47—21no—
240C22×D47—21no—
241C22×D47—21no—
242C22×D47—28no—
243C22×D47—28no—
244C22×D47—28no—
245C22×D47—28no—
246C22×D47—28no—
247C22×D47—28no—
248C22×D47#103116yescomplemented
249C22×D47C2×C22⋊C412yes—
250C22×D47C2×C22⋊C412yes—
251C22×D47#12012yes—
252C22×D47#12312yes—
253C22×D47C2×SD1612yes—
254C22×D47C2×SD1612yes—
255C22×D47C2×Q1612yes—
256C22×D47C2×Q1612yes—
257C22×D47AGL(1,ℤ/8)12yes—
258C22×D47#13712yes—
259Q8×C47—24no—
260Q8×C47—42no—
261C2×C4×C47—21no—
262C2×C4×C47—21no—
263C2×C4×C47—24no—
264C2×C4×C47—24no—
265C2×C4×C47—22no—
266C2×C4×C47—22no—
267C2×C4×C47—24no—
268C2×C4×C47—48no—
269C2×C4×C47—41no—
270C2×C4×C47—41no—
271C2×C4×C47—42no—
272C2×C4×C47—42no—
273C2×C4×C47—41no—
274C2×C4×C47—41no—
275C2×C4×C47C2×C22⋊C412yes—
276C2×C4×C47C23×C411yescharacteristic
277C2×C4×C47C22×D412yes—
278C2×C4×C47C22×D411yescharacteristic
279C2×C4×C47C2×#4112yes—
280C2×Dic47—21no—
281C2×Dic47—21no—
282C2×Dic47—28no—
283C2×Dic47—22no—
284C2×Dic47—22no—
285C2×Dic47—24no—
286C2×Dic47—48no—
287C2×Dic47—41no—
288C2×Dic47—41no—
289C2×Dic47—42no—
290C2×Dic47—42no—
291C2×Dic47—41no—
292C2×Dic47—41no—
293C2×Dic47C2×C22⋊C412yes—
294C2×Dic47C2×C22⋊C412yes—
295C2×Dic47#12012yes—
296C2×Dic47#12312yes—
297C4×D47—28no—
298C4×D47—24no—
299C4×D47—24no—
300C4×D47—28no—
301C4×D47—416no—
302C4×D47—48no—
303C4×D47—48no—
304C4×D47—416no—
305C4×D47C4×D418yes—
306C4×D47#12118yes—
307Dic94—24no—
308Dic94—42no—
309Dic94—48no—
310C8×C47—42no—
311C47⋊C8—42no—
312C2×#1872—471nomaximal, Sylow
313C22×C47—22no—
314C22×C47—22no—
315C22×C47—22no—
316C22×C47—22no—
317C22×C47—22no—
318C22×C47—22no—
319C22×C47C2×#10314yescomplemented
320C22×C47C22×C22⋊C411yescharacteristic
321C22×C47C2×#12011yescharacteristic
322C22×C47C2×#12311yescharacteristic
323C22×C47C22×SD1611yescharacteristic
324C22×C47C22×Q1611yescharacteristic
325C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
326C22×C47C2×#13711yescharacteristic
327C2×D47—22no—
328C2×D47—22no—
329C2×D47—22no—
330C2×D47—22no—
331C2×D47—22no—
332C2×D47—22no—
333C2×D47—232no—
334C2×D47#38614yes—
335C2×D47C2×#10314yes—
336C2×D47C2×#10314yescomplemented
337C2×D47#41714yes—
338C2×D47#45014yes—
339C2×D47#45114yes—
340C2×D47#48314yes—
341C2×D47#48414yes—
342C4×C47—22no—
343C4×C47—42no—
344C4×C47—44no—
345C4×C47—42no—
346C4×C47C2×C4×D412yes—
347C4×C47C2×#12112yes—
348Dic47—22no—
349Dic47—42no—
350Dic47—44no—
351Dic47—42no—
352Dic47#38614yes—
353C22×C22⋊Q8—471no—
354C23×C4⋊C4—471no—
355C22×#103—472no—
356C22×C22⋊C8—471no—
357#1872—472no—
358#1872—471no—
359#1872—472no—
360#1872—471no—
361#1872—471no—
362#1872D4711yescharacteristic, direct product factor
363C2×#340—472no—
364C2×C47—24no—
365C2×C47C2×#38611yescharacteristic
366C2×C47C22×#10311yescharacteristic
367C2×C47C2×#41711yescharacteristic
368C2×C47C2×#45011yescharacteristic
369C2×C47C2×#45111yescharacteristic
370C2×C47C2×#48311yescharacteristic
371C2×C47C2×#48411yescharacteristic
372D47—24no—
373D47#187218yesdirect product factor
374C23×Q8—471no—
375C24×C4—471no—
376C24×C4—941no—
377C23×C8—472no—
378C2×C22⋊Q8—471no—
379C2×C22⋊Q8—471no—
380C2×C22⋊Q8—478no—
381C2×C22⋊Q8—471no—
382C2×C22⋊Q8—941no—
383C2×C22⋊Q8—941no—
384C2×C22⋊Q8—944no—
385C2×C22⋊Q8C2×D4711yescharacteristic
386C22×C4⋊C4—472no—
387C22×C4⋊C4—471no—
388C22×C4⋊C4—471no—
389C22×C4⋊C4—472no—
390C22×C4⋊C4—948no—
391C22×C4⋊C4—941no—
392C22×C4⋊C4—941no—
393C22×C4⋊C4—941no—
394C22×C4⋊C4—941no—
395C22×C4⋊C4C2×D4711yescharacteristic
396C22×C22⋊C4—941no—
397C2×#103—472no—
398C2×#103—472no—
399C2×#103—472no—
400C2×#103—948no—
401C2×#103C2×D4712yescomplemented
402C2×C22⋊C8—471no—
403C2×C22⋊C8—472no—
404C2×C22⋊C8—944no—
405C2×C22⋊C8C2×D4711yescharacteristic
406#340—472no—
407#340—472no—
408#340—472no—
409#340C2×D4712yescomplemented
410C47C2×#187211yescharacteristic, complemented, Sylow
411C25—471no—
412C22×Q8—474no—
413C22×Q8—471no—
414C22×Q8—941no—
415C22×Q8—942no—
416C22×Q8—944no—
417C22×Q8—944no—
418C22×Q8C22×D4711yescharacteristic
419C23×C4—21no—
420C23×C4—471no—
421C23×C4—471no—
422C23×C4—474no—
423C23×C4—471no—
424C23×C4—471no—
425C23×C4—474no—
426C23×C4—471no—
427C23×C4—944no—
428C23×C4—944no—
429C23×C4—941no—
430C23×C4—941no—
431C23×C4—942no—
432C23×C4—942no—
433C23×C4—948no—
434C23×C4—941no—
435C23×C4—1884no—
436C23×C4—1884no—
437C23×C4C22×D4711yescharacteristic
438C22×C8—472no—
439C22×C8—944no—
440C22×C8—944no—
441C22×C8—944no—
442C22×C8C22×D4712yes—
443C22⋊Q8—22no—
444C22⋊Q8—474no—
445C22⋊Q8—474no—
446C22⋊Q8—474no—
447C22⋊Q8—948no—
448C22⋊Q8—948no—
449C22⋊Q8—942no—
450C22⋊Q8—942no—
451C22⋊Q8—942no—
452C22⋊Q8C4×D4714yescomplemented
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—24no—
456C2×C4⋊C4—472no—
457C2×C4⋊C4—471no—
458C2×C4⋊C4—474no—
459C2×C4⋊C4—478no—
460C2×C4⋊C4—944no—
461C2×C4⋊C4—944no—
462C2×C4⋊C4—942no—
463C2×C4⋊C4—948no—
464C2×C4⋊C4—948no—
465C2×C4⋊C4—948no—
466C2×C4⋊C4—944no—
467C2×C4⋊C4—942no—
468C2×C4⋊C4—942no—
469C2×C4⋊C4—941no—
470C2×C4⋊C4—941no—
471C2×C4⋊C4—941no—
472C2×C4⋊C4—948no—
473C2×C4⋊C4—941no—
474C2×C4⋊C4—941no—
475C2×C4⋊C4—944no—
476C2×C4⋊C4C22×D4711yescharacteristic
477C2×C4⋊C4C22×D4712yes—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—948no—
480C2×C22⋊C4—941no—
481C2×C22⋊C4—941no—
482C2×C22⋊C4—941no—
483#103—24no—
484#103—944no—
485#103—944no—
486#103—944no—
487C22⋊C8—22no—
488C22⋊C8—944no—
489C22⋊C8—942no—
490C24—471no—
491C24—474no—
492C24—474no—
493C24—474no—
494C24—471no—
495C24—942no—
496C24—942no—
497C24—942no—
498C24—942no—
499C24D4×D4711yescharacteristic
500C2×Q8—21no—
501C2×Q8—22no—
502C2×Q8—22no—
503C2×Q8—472no—
504C2×Q8—944no—
505C2×Q8—9416no—
506C2×Q8—941no—
507C2×Q8—942no—
508C2×Q8—942no—
509C2×Q8—1882no—
510C2×Q8—1882no—
511C2×Q8—1888no—
512C2×Q8C2×C4×D4712yescomplemented
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—24no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—471no—
522C22×C4—472no—
523C22×C4—474no—
524C22×C4—472no—
525C22×C4—474no—
526C22×C4—474no—
527C22×C4—471no—
528C22×C4—474no—
529C22×C4—474no—
530C22×C4—472no—
531C22×C4—472no—
532C22×C4—942no—
533C22×C4—942no—
534C22×C4—9416no—
535C22×C4—9416no—
536C22×C4—942no—
537C22×C4—942no—
538C22×C4—944no—
539C22×C4—944no—
540C22×C4—948no—
541C22×C4—948no—
542C22×C4—942no—
543C22×C4—942no—
544C22×C4—942no—
545C22×C4—942no—
546C22×C4—944no—
547C22×C4—941no—
548C22×C4—941no—
549C22×C4—942no—
550C22×C4—1882no—
551C22×C4—1882no—
552C22×C4—1884no—
553C22×C4—1884no—
554C22×C4—1884no—
555C22×C4—1882no—
556C22×C4—1882no—
557C22×C4—18832no—
558C22×C4—1884no—
559C22×C4—1882no—
560C22×C4—1882no—
561C22×C4C2×C4×D4712yes—
562C22×C4D4×D4711yescharacteristic
563C22×C4D4×D4712yes—
564C22×C4C23×D4711yescharacteristic
565C2×C8—22no—
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—942no—
569C2×C8—942no—
570C2×C8—942no—
571C2×C8—1888no—
572C4⋊C4—24no—
573C4⋊C4—24no—
574C4⋊C4—22no—
575C4⋊C4—21no—
576C4⋊C4—472no—
577C4⋊C4—474no—
578C4⋊C4—948no—
579C4⋊C4—944no—
580C4⋊C4—944no—
581C4⋊C4—944no—
582C4⋊C4—948no—
583C4⋊C4—944no—
584C4⋊C4—944no—
585C4⋊C4—942no—
586C4⋊C4—941no—
587C4⋊C4C2×C4×D4712yescomplemented
588C4⋊C4D4×D4714yes—
589C22⋊C4—24no—
590C22⋊C4—944no—
591C22⋊C4—944no—
592C22⋊C4—944no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—472no—
598C23—472no—
599C23—472no—
600C23—472no—
601C23—472no—
602C23—472no—
603C23—472no—
604C23—472no—
605C23—4716no—
606C23—472no—
607C23—472no—
608C23—948no—
609C23—948no—
610C23—948no—
611C23—948no—
612C23—948no—
613C23—948no—
614C23—941no—
615C23—941no—
616C23—941no—
617C23—941no—
618C23C22⋊C4×D4712yes—
619C23SD16×D4712yes—
620C23Q16×D4712yes—
621C23C2×D4×D4711yescharacteristic
622Q8—24no—
623Q8—42no—
624Q8—944no—
625Q8—1888no—
626Q8—1882no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—24no—
630C2×C4—24no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—24no—
634C2×C4—48no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—472no—
642C2×C4—472no—
643C2×C4—472no—
644C2×C4—478no—
645C2×C4—478no—
646C2×C4—472no—
647C2×C4—948no—
648C2×C4—948no—
649C2×C4—948no—
650C2×C4—941no—
651C2×C4—941no—
652C2×C4—944no—
653C2×C4—944no—
654C2×C4—942no—
655C2×C4—942no—
656C2×C4—944no—
657C2×C4—1888no—
658C2×C4—18816no—
659C2×C4—1888no—
660C2×C4—18816no—
661C2×C4—1888no—
662C2×C4—1881no—
663C2×C4—1881no—
664C2×C4—1882no—
665C2×C4—1881no—
666C2×C4—1882no—
667C2×C4—1881no—
668C2×C4C22⋊C4×D4712yes—
669C2×C4C22×C4×D4711yescharacteristic
670C2×C4C2×D4×D4712yes—
671C2×C4C2×D4×D4711yescharacteristic
672C2×C4#41×D4712yes—
673C8—42no—
674C8—1882no—
675C22—22no—
676C22—22no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—474no—
682C22—474no—
683C22—474no—
684C22—474no—
685C22—474no—
686C22—474no—
687C22—474no—
688C22—474no—
689C22—9432no—
690C22—942no—
691C22—942no—
692C22—942no—
693C22—942no—
694C22—942no—
695C22—942no—
696C22#103×D4714yescomplemented
697C22C2×C22⋊C4×D4711yescharacteristic
698C22#120×D4711yescharacteristic
699C22#123×D4711yescharacteristic
700C22C2×SD16×D4711yescharacteristic
701C22C2×Q16×D4711yescharacteristic
702C22AGL(1,ℤ/8)×D4711yescharacteristic
703C22#137×D4711yescharacteristic
704C4—22no—
705C4—42no—
706C4—44no—
707C4—42no—
708C4—474no—
709C4—942no—
710C4—1882no—
711C4—1884no—
712C4—1882no—
713C4C4×D4×D4712yes—
714C4#121×D4712yes—
715C2—24no—
716C2—478no—
717C2—944no—
718C2#386×D4711yescharacteristic
719C2C2×#103×D4711yescharacteristic
720C2#417×D4711yescharacteristic
721C2#450×D4711yescharacteristic
722C2#451×D4711yescharacteristic
723C2#483×D4711yescharacteristic
724C2#484×D4711yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1872C2
socleC23×C47C22×D4
prime radicalC24×D47D4
cosocleC22×C4×C47C24
hypercenter#1872D47
hypocenterC47C2×#1872
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1872

Complements

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

NH ≅ G/Ntype
3. C2×#103×D47C2semidirect
5. #20243696C2semidirect
6. #20243695C2semidirect
7. #20243694C2semidirect
8. #20243693C2semidirect
9. #20243692C2semidirect
10. #340×D47C2semidirect
11. C47×#1872C2semidirect
22. C22⋊Q8×D47C4semidirect
33. C2×#13093949C22semidirect
34. C2×#13093948C22semidirect
35. C2×#13093947C22semidirect
40. #15688886C22semidirect
41. #15688885C22semidirect
42. #15688885C22semidirect
45. C2×#103×C47C22semidirect
47. C47×#340C22semidirect
54. C2×Q8×D47C2×C4semidirect
77. #13094004C2×C4semidirect
79. #13094003C2×C4semidirect
83. #13094000C2×C4semidirect
102. C4⋊C4×D47C2×C4semidirect
118. C22⋊Q8×C47C2×C4semidirect
140. C2×Q8×C47C22×C4semidirect
201. C2×Dic94C22×C4semidirect
209. C4⋊C4×C47C22×C4semidirect
219. C4⋊Dic47C22×C4semidirect
248. C22×D47#103semidirect
319. C22×C47C2×#103semidirect
336. C2×D47C2×#103semidirect
362. #1872D47direct (N × H)
373. D47#1872direct (N × H)
401. C2×#103C2×D47semidirect
409. #340C2×D47semidirect
410. C47C2×#1872semidirect
452. C22⋊Q8C4×D47semidirect
512. C2×Q8C2×C4×D47semidirect
587. C4⋊C4C2×C4×D47semidirect
696. C22#103×D47semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊Q8×D472
C22×C4⋊C4×D472
C2×#103×D472
C2×C22⋊C8×D472
#202436962
#202436952
#202436942
#202436932
#202436922
#340×D472
C47×#18722
C2×#187247