Finite Group Databasebeta

← D47×#3228 #27088330

Subgroups — D47×#3228 #27088330

Order 12032.

2058 conjugacy classes of subgroups.

The subgroup lattice has 1044 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#533×D47C211yesmaximal, characteristic, complemented
2#532×D47C211yesmaximal, characteristic
3#20254527C211yesmaximal, characteristic, complemented
4#20254526C211yesmaximal, characteristic, complemented
5#20254525C211yesmaximal, characteristic, complemented
6#20254524C211yesmaximal, characteristic, complemented
7#20254523C214yesmaximal, complemented
8#20254522C214yesmaximal, complemented
9#20254521C211yesmaximal, characteristic, complemented
10#20254520C211yesmaximal, characteristic, complemented
11#20254519C211yesmaximal, characteristic, complemented
12#500×D47C211yesmaximal, characteristic, complemented
13#498×D47C211yesmaximal, characteristic, complemented
14#486×D47C211yesmaximal, characteristic, complemented
15#486×D47C211yesmaximal, characteristic, complemented
16#482×D47C214yesmaximal, complemented
17#478×D47C214yesmaximal, complemented
18#431×D47C211yesmaximal, characteristic, complemented
19C47×#3228C211yesmaximal, characteristic, complemented
20C2×#41×D47—21no—
21#15689680C2211yescharacteristic, complemented
22#15689679C2212yescomplemented
23#15689678C2211yescharacteristic, complemented
24#15689678C2211yescharacteristic, complemented
25#15689677—21no—
26#15689677—21no—
27#15689676C2212yescomplemented
28#15689675—21no—
29#15689675—21no—
30#15689674C2211yescharacteristic
31#15689673C2211yescharacteristic
32#15689672—21no—
33#15689671C2211yescharacteristic
34#15689670—21no—
35#15689670C2212yes—
36#15689669—21no—
37#15689668—21no—
38#15689668C2212yes—
39C4⋊Q8×D47C2211yescharacteristic
40C4⋊Q8×D47C2211yescharacteristic
41C4⋊Q8×D47C2211yescharacteristic
42#127×D47C2211yescharacteristic
43#125×D47C2212yes—
44#124×D47—21no—
45C22⋊Q8×D47—21no—
46C22⋊Q8×D47—21no—
47#121×D47—21no—
48#121×D47C2212yes—
49C4×Q8×D47—21no—
50C4×Q8×D47—21no—
51C4×D4×D47—21no—
52C4×D4×D47C2212yes—
53#117×D47C2212yes—
54C2×C42×D47C2211yescharacteristic
55#15689528C2211yescharacteristic, complemented
56#15689527C2214yescomplemented
57#15689526C2211yescharacteristic, complemented
58#15689526C2211yescharacteristic, complemented
59#15689521C2211yescharacteristic, complemented
60#15689520C2214yescomplemented
61#15689519C2211yescharacteristic, complemented
62#15689519C2211yescharacteristic, complemented
63#15689471C2211yescharacteristic, complemented
64#15689471C2211yescharacteristic, complemented
65#15689470C2211yescharacteristic, complemented
66#15689470C2211yescharacteristic, complemented
67#15689469C2211yescharacteristic, complemented
68#15689469C2211yescharacteristic, complemented
69#15689468C2214yescomplemented
70#15689468C2214yescomplemented
71#15689450C2214yescomplemented
72#15689449C2214yescomplemented
73#15689448C2214yescomplemented
74#15689447C2214yescomplemented
75#15689446C2214yescomplemented
76#15689445C2214yescomplemented
77#15689444C2214yescomplemented
78#15689426C2214yescomplemented
79#15689425C2214yescomplemented
80#15689424C2214yescomplemented
81#15689423C2214yescomplemented
82#15689422C2214yescomplemented
83#15689421C2214yescomplemented
84#15689420C2214yescomplemented
85#15689176C2211yescharacteristic, complemented
86#15689175C2212yescomplemented
87#15689174C2211yescharacteristic, complemented
88#15689174C2211yescharacteristic, complemented
89#15689173C2212yescomplemented
90#107×D47C2214yes—
91#106×D47C2214yes—
92C4⋊C8×D47C2212yes—
93#102×D47C2214yes—
94#102×D47C2214yes—
95C22⋊C8×D47C2212yes—
96C4×C8×D47C2211yescharacteristic
97C4×C8×D47C2211yescharacteristic
98C47×#533C2211yescharacteristic, complemented
99C47×#532C2211yescharacteristic
100C47×#500C2211yescharacteristic, complemented
101C47×#498C2211yescharacteristic, complemented
102C47×#486C2211yescharacteristic, complemented
103C47×#486C2211yescharacteristic, complemented
104C47×#482C2214yescomplemented
105C47×#478C2214yescomplemented
106C47×#431C2211yescharacteristic, complemented
107C2×#10625354—21no—
108C2×#10625350—21no—
109C2×#10625350—22no—
110C2×#10625352—22no—
111C2×#10625352—21no—
112#41×D47—48no—
113C2×Q8×D47—21no—
114C2×Q8×D47—21no—
115C2×Q8×D47—21no—
116C2×D4×D47—22no—
117C2×D4×D47—21no—
118C2×D4×D47—21no—
119C2×D4×D47C2312yes—
120C22×C4×D47—22no—
121C22×C4×D47D411yescharacteristic
122C22×C4×D47D411yescharacteristic
123C22×C4×D47C2311yescharacteristic
124C2×C8×D47C2312yes—
125C2×C8×D47C2312yes—
126#13094024C2311yescharacteristic
127#13094024C2311yescharacteristic
128#13094024C2311yescharacteristic
129#13094023—21no—
130#13094023—21no—
131#13094023—21no—
132#13094023C2312yes—
133#13094023C2312yes—
134#13094023C2312yes—
135#13094022—21no—
136#13094022—21no—
137#13094022—21no—
138#13094021C2311yescharacteristic
139#13094020—21no—
140#13094020—21no—
141#13094020C2312yes—
142#13094016C2312yes—
143#13094015C2312yes—
144#13094015C2312yes—
145#13094014—22no—
146#13094014—22no—
147#13094013—21no—
148#13094012—21no—
149#13094011—21no—
150#13094010—22no—
151#13094010—22no—
152#13094004—21no—
153#13094004—21no—
154#13094003—21no—
155#13094003—21no—
156#13094002—22no—
157#13094002—22no—
158#13094001—22no—
159#13094001—22no—
160#13094000—21no—
161#13094000—21no—
162#13093999—21no—
163#13093999C2312yes—
164#13093998—21no—
165#13093998C2312yes—
166#13093997—22no—
167#13093997—22no—
168#13093996—22no—
169#13093996—22no—
170#13093995—21no—
171#13093995C2312yes—
172Q8×Dic47—21no—
173Q8×Dic47—21no—
174C4×Dic94—21no—
175C4×Dic94—21no—
176C4×Dic94—22no—
177C4×Dic94—22no—
178#13093989—21no—
179#13093989—21no—
180#13093989—22no—
181#13093989—22no—
182C4×D188—21no—
183C4×D188C2312yes—
184D4×Dic47—21no—
185D4×Dic47C2312yes—
186#13093986—21no—
187#13093986C2312yes—
188C4×C22⋊D47—22no—
189C4×C22⋊D47—22no—
190(C22⋊D47)⋊C4—22no—
191(C22⋊D47)⋊C4—22no—
192#13093983C2312yes—
193#13093982C2312yes—
194#13093982C2312yes—
195#13093981—22no—
196#13093980—22no—
197C4⋊C4×D47—21no—
198C4⋊C4×D47—22no—
199C4⋊C4×D47—22no—
200C4⋊C4×D47—21no—
201C4⋊C4×D47—21no—
202C4⋊C4×D47C2312yes—
203C4⋊C4×D47C2312yes—
204C4⋊C4×D47C2312yes—
205C22⋊C4×D47—22no—
206C22⋊C4×D47—22no—
207C22⋊C4×D47—22no—
208C2×C4×Dic47D411yescharacteristic
209C2×C4×Dic47D411yescharacteristic
210C2×C4×Dic47C2311yescharacteristic
211C42×D47—22no—
212C42×D47D411yescharacteristic
213C42×D47D411yescharacteristic
214C42×D47D411yescharacteristic
215C42×D47D411yescharacteristic
216C42×D47C2311yescharacteristic
217C42×D47C2311yescharacteristic
218C42×D47C2311yescharacteristic
219C42×D47C2311yescharacteristic
220#13093958C2314yes—
221#13093957C2314yes—
222#13093957C2314yes—
223#13093956C2314yes—
224#13093955C2314yes—
225#13093955C2314yes—
226C4⋊(C47⋊C8)C2312yes—
227Dic47⋊C8C2312yes—
228Dic47⋊C8C2312yes—
229#13093946C2314yes—
230#13093946C2314yes—
231#13093945C2314yes—
232#13093945C2314yes—
233#13093944C2314yes—
234#13093944C2314yes—
235C22⋊(C47⋊C8)C2312yes—
236(C2×D47)⋊C8C2312yes—
237(C2×D47)⋊C8C2312yes—
238C4×C47⋊C8C2311yescharacteristic
239C4×C47⋊C8C2311yescharacteristic
240C8×Dic47C2312yes—
241C8×Dic47C2312yes—
242C2×#41×C47—21no—
243C4⋊Q8×C47C2311yescharacteristic
244C4⋊Q8×C47C2311yescharacteristic
245C4⋊Q8×C47C2311yescharacteristic
246#127×C47C2311yescharacteristic
247#125×C47C2312yes—
248#124×C47—21no—
249C22⋊Q8×C47—21no—
250C22⋊Q8×C47—21no—
251#121×C47—21no—
252#121×C47C2312yes—
253C4×Q8×C47—21no—
254C4×Q8×C47—21no—
255C4×D4×C47—21no—
256C4×D4×C47C2312yes—
257#117×C47C2312yes—
258C2×C42×C47C2311yescharacteristic
259#107×C47C2314yes—
260#106×C47C2314yes—
261C4⋊C8×C47C2312yes—
262#102×C47C2314yes—
263#102×C47C2314yes—
264C22⋊C8×C47C2312yes—
265C4×C8×C47C2311yescharacteristic
266C4×C8×C47C2311yescharacteristic
267C23×D47—22no—
268C23×D47C2×D411yescharacteristic
269#41×C47—44no—
270C2×Q8×C47—21no—
271C2×Q8×C47—21no—
272C2×Q8×C47—21no—
273C2×D4×C47—22no—
274C2×D4×C47—21no—
275C2×D4×C47—21no—
276C2×D4×C47C2412yes—
277C22×C4×C47—22no—
278C22×C4×C47C2×D411yescharacteristic
279C22×C4×C47C2×D411yescharacteristic
280C22×C4×C47C2411yescharacteristic
281C2×C22⋊D47—22no—
282C2×C22⋊D47—22no—
283C2×C22⋊D47—22no—
284C2×C22⋊D47—22no—
285C2×C22⋊D47—22no—
286C22×Dic47—22no—
287C22×Dic47C2×D411yescharacteristic
288C22×Dic47C2×D411yescharacteristic
289C22×Dic47C2×D411yescharacteristic
290#10625354—44no—
291Q8×D47—44no—
292Q8×D47—44no—
293Q8×D47—44no—
294#10625352—44no—
295#10625352—48no—
296D4×D47—28no—
297D4×D47—48no—
298D4×D47—44no—
299D4×D47—44no—
300#10625350—48no—
301#10625350—44no—
302C2×D188—22no—
303C2×D188—21no—
304C2×D188—21no—
305C2×D188C2412yes—
306C2×C4×D47—24no—
307C2×C4×D47—24no—
308C2×C4×D47—24no—
309C2×C4×D47—22no—
310C2×C4×D47—22no—
311C2×C4×D47—22no—
312C2×C4×D47—22no—
313C2×C4×D47—22no—
314C2×C4×D47—48no—
315C2×C4×D47C2×D411yescharacteristic
316C2×C4×D47C2×D411yescharacteristic
317C2×C4×D47C2×D411yescharacteristic
318C2×C4×D47C2×D411yescharacteristic
319C2×C4×D47C2×D411yescharacteristic
320C2×C4×D47C2×D411yescharacteristic
321C2×C4×D47C2×D411yescharacteristic
322C2×C4×D47C2×D411yescharacteristic
323C2×C4×D47C2×D411yescharacteristic
324C2×C4×D47C2×D411yescharacteristic
325C2×C4×D47C2411yescharacteristic
326C2×C4×D47C2411yescharacteristic
327C2×Dic94—21no—
328C2×Dic94—21no—
329C2×Dic94—21no—
330C2×Dic94—22no—
331C2×Dic94—22no—
332C2×Dic94—22no—
333C2×C8×C47C2412yes—
334C2×C8×C47C2412yes—
335C4⋊C4×C47—21no—
336C4⋊C4×C47—22no—
337C4⋊C4×C47—22no—
338C4⋊C4×C47—21no—
339C4⋊C4×C47—21no—
340C4⋊C4×C47C2412yes—
341C4⋊C4×C47C2412yes—
342C4⋊C4×C47C2412yes—
343C22⋊C4×C47—22no—
344C22⋊C4×C47—22no—
345C22⋊C4×C47—22no—
346C42×C47—22no—
347C42×C47C2×D411yescharacteristic
348C42×C47C2×D411yescharacteristic
349C42×C47C2411yescharacteristic
350C42×C47C2411yescharacteristic
351C22⋊Dic47—22no—
352C22⋊Dic47—22no—
353C22⋊Dic47—22no—
354(C2×D47)⋊C4—22no—
355(C2×D47)⋊C4—22no—
356(C2×D47)⋊C4—22no—
357(C2×D47)⋊C4—22no—
358(C2×D47)⋊C4—22no—
359(C2×D47)⋊C4—22no—
360C4⋊Dic47—21no—
361C4⋊Dic47—21no—
362C4⋊Dic47—21no—
363C4⋊Dic47—22no—
364C4⋊Dic47—22no—
365C4⋊Dic47C2412yes—
366C4⋊Dic47C2412yes—
367C4⋊Dic47C2412yes—
368Dic47⋊C4—22no—
369Dic47⋊C4—22no—
370Dic47⋊C4—22no—
371Dic47⋊C4—22no—
372Dic47⋊C4—22no—
373Dic47⋊C4—22no—
374Dic47⋊C4—22no—
375Dic47⋊C4—22no—
376Dic47⋊C4—22no—
377Dic47⋊C4—22no—
378C4×Dic47—22no—
379C4×Dic47—22no—
380C4×Dic47—22no—
381C4×Dic47C2×D411yescharacteristic
382C4×Dic47C2×D411yescharacteristic
383C4×Dic47C2×D411yescharacteristic
384C4×Dic47C2×D411yescharacteristic
385C4×Dic47C2×D411yescharacteristic
386C4×Dic47C2×D411yescharacteristic
387C4×Dic47C2×D411yescharacteristic
388C4×Dic47C2×D411yescharacteristic
389C4×Dic47C2×D411yescharacteristic
390C4×Dic47C2×D411yescharacteristic
391C4×Dic47C2411yescharacteristic
392C4×Dic47C2411yescharacteristic
393C2×C47⋊C8C2412yes—
394C2×C47⋊C8C2412yes—
395C8×D47—24no—
396C8×D47—24no—
397C23×C47—22no—
398C23×C47C22×D411yescharacteristic
399C22×D47—22no—
400C22×D47—22no—
401C22×D47—22no—
402C22×D47—22no—
403C22×D47—44no—
404C22×D47—44no—
405C22×D47—44no—
406C22×D47C22×D411yescharacteristic
407C22×D47C22×D411yescharacteristic
408Q8×C47—42no—
409Q8×C47—42no—
410Q8×C47—42no—
411D4×C47—24no—
412D4×C47—44no—
413D4×C47—42no—
414D4×C47—42no—
415C2×C4×C47—22no—
416C2×C4×C47—22no—
417C2×C4×C47—22no—
418C2×C4×C47—22no—
419C2×C4×C47—22no—
420C2×C4×C47—22no—
421C2×C4×C47—44no—
422C2×C4×C47C22×D411yescharacteristic
423C2×C4×C47C22×D411yescharacteristic
424C2×C4×C47C22×D411yescharacteristic
425C2×C4×C47C22×D411yescharacteristic
426C2×C4×C47C22×D411yescharacteristic
427C2×C4×C47C2511yescharacteristic
428C22⋊D47—44no—
429C22⋊D47—44no—
430C22⋊D47—44no—
431C22⋊D47—44no—
432C22⋊D47—44no—
433C2×Dic47—22no—
434C2×Dic47—22no—
435C2×Dic47—22no—
436C2×Dic47—22no—
437C2×Dic47—22no—
438C2×Dic47—22no—
439C2×Dic47—44no—
440C2×Dic47C22×D411yescharacteristic
441C2×Dic47C22×D411yescharacteristic
442C2×Dic47C22×D411yescharacteristic
443C2×Dic47C22×D411yescharacteristic
444C2×Dic47C22×D411yescharacteristic
445C2×Dic47C22×D411yescharacteristic
446D188—24no—
447D188—44no—
448D188—42no—
449D188—42no—
450C4×D47—22no—
451C4×D47—22no—
452C4×D47—22no—
453C4×D47—22no—
454C4×D47—22no—
455C4×D47—22no—
456C4×D47—22no—
457C4×D47—22no—
458C4×D47—22no—
459C4×D47—44no—
460C4×D47—44no—
461C4×D47—44no—
462C4×D47—44no—
463C4×D47—44no—
464C4×D47#13514yes—
465C4×D47AGL(1,ℤ/8)14yes—
466C4×D472−1+414yes—
467Dic94—42no—
468Dic94—42no—
469Dic94—42no—
470Dic94—44no—
471Dic94—44no—
472Dic94—44no—
473C8×C47—22no—
474C8×C47—22no—
475C47⋊C8—22no—
476C47⋊C8—22no—
477C2×#3228—471nomaximal, Sylow
478C22×C47—21no—
479C22×C47—21no—
480C22×C47—21no—
481C22×C47—42no—
482C22×C47—42no—
483C22×C47—42no—
484C22×C47C23×D411yescharacteristic
485C2×D47—21no—
486C2×D47—21no—
487C2×D47—21no—
488C2×D47—44no—
489C2×D47—42no—
490C2×D47—42no—
491C2×D47—42no—
492C2×D47—88no—
493C2×D47#53612yes—
494C2×D47C2×#13512yes—
495C2×D47C2×AGL(1,ℤ/8)12yes—
496C4×C47—21no—
497C4×C47—21no—
498C4×C47—21no—
499C4×C47—42no—
500C4×C47—42no—
501C4×C47—42no—
502C4×C47C2×#13512yes—
503C4×C47C2×AGL(1,ℤ/8)12yes—
504C4×C47C2×2−1+412yes—
505Dic47—21no—
506Dic47—21no—
507Dic47—21no—
508Dic47—42no—
509Dic47—42no—
510Dic47—42no—
511Dic47#53612yes—
512Dic47C2×#13512yes—
513Dic47C2×AGL(1,ℤ/8)12yes—
514C2×#533—471no—
515C2×#532—471no—
516#3228—471no—
517#3228—471no—
518#3228—471no—
519#3228—471no—
520#3228—474no—
521#3228—474no—
522#3228—471no—
523#3228—471no—
524#3228—471no—
525#3228D4711yescharacteristic, direct product factor
526C2×#500—471no—
527C2×#498—471no—
528C2×#486—471no—
529C2×#486—471no—
530C2×#482—474no—
531C2×#478—474no—
532C2×#431—471no—
533C2×C47—41no—
534C2×C47—82no—
535C2×C47C2×#53611yescharacteristic
536C2×C47C22×#13511yescharacteristic
537C2×C47C22×AGL(1,ℤ/8)11yescharacteristic
538D47—41no—
539D47—82no—
540D47#322814yesdirect product factor
541C22×#41—941no—
542#533—471no—
543#533—471no—
544#533—472no—
545#533—472no—
546#533—471no—
547#533—941no—
548#533—941no—
549#533—941no—
550#533—941no—
551#533C2×D4711yescharacteristic, complemented
552#532—471no—
553#532—471no—
554#532—472no—
555#532—472no—
556#532—471no—
557#532—941no—
558#532—941no—
559#532—941no—
560#532—941no—
561#532C2×D4711yescharacteristic
562C2×C4⋊Q8—471no—
563C2×C4⋊Q8—471no—
564C2×C4⋊Q8—471no—
565C2×#127—471no—
566C2×#125—472no—
567C2×#124—941no—
568C2×C22⋊Q8—941no—
569C2×C22⋊Q8—941no—
570C2×#121—472no—
571C2×#121—941no—
572C2×C4×Q8—941no—
573C2×C4×Q8—941no—
574C2×C4×D4—472no—
575C2×C4×D4—941no—
576C2×#117—472no—
577C22×C42—471no—
578#500—471no—
579#500—471no—
580#500—474no—
581#500—471no—
582#500C2×D4711yescharacteristic, complemented
583#498—471no—
584#498—471no—
585#498—474no—
586#498—471no—
587#498C2×D4711yescharacteristic, complemented
588#486—471no—
589#486—471no—
590#486—471no—
591#486—471no—
592#486—474no—
593#486—474no—
594#486—471no—
595#486—471no—
596#486C2×D4711yescharacteristic, complemented
597#486C2×D4711yescharacteristic, complemented
598#482—474no—
599#482—474no—
600#482—474no—
601#482—474no—
602#482—474no—
603#482—474no—
604#482—474no—
605#482C2×D4714yescomplemented
606#478—474no—
607#478—474no—
608#478—474no—
609#478—474no—
610#478—474no—
611#478—474no—
612#478—474no—
613#478C2×D4714yescomplemented
614#431—471no—
615#431—472no—
616#431—472no—
617#431—471no—
618#431—471no—
619#431C2×D4711yescharacteristic, complemented
620C2×#107—474no—
621C2×#106—474no—
622C2×C4⋊C8—472no—
623C2×#102—474no—
624C2×#102—474no—
625C2×C22⋊C8—472no—
626C2×C4×C8—471no—
627C2×C4×C8—471no—
628C47C2×#322811yescharacteristic, complemented, Sylow
629C2×#41—21no—
630C2×#41—942no—
631C2×#41—942no—
632C2×#41—941no—
633C2×#41—941no—
634C2×#41—941no—
635C2×#41—1888no—
636C22×Q8—941no—
637C22×Q8—941no—
638C22×Q8—941no—
639C22×D4—472no—
640C22×D4—941no—
641C22×D4—941no—
642C22×D4—942no—
643C23×C4—471no—
644C23×C4—471no—
645C23×C4—471no—
646C23×C4—942no—
647C22×C8—472no—
648C22×C8—472no—
649C4⋊Q8—472no—
650C4⋊Q8—472no—
651C4⋊Q8—472no—
652C4⋊Q8—471no—
653C4⋊Q8—471no—
654C4⋊Q8—471no—
655C4⋊Q8—941no—
656C4⋊Q8—941no—
657C4⋊Q8—941no—
658C4⋊Q8—941no—
659C4⋊Q8—941no—
660C4⋊Q8—941no—
661C4⋊Q8C22×D4711yescharacteristic
662C4⋊Q8C22×D4711yescharacteristic
663C4⋊Q8C22×D4711yescharacteristic
664#127—472no—
665#127—471no—
666#127—941no—
667#127—941no—
668#127C22×D4711yescharacteristic
669#125—472no—
670#125—472no—
671#125—472no—
672#125—942no—
673#125—942no—
674#125C22×D4712yes—
675#124—21no—
676#124—942no—
677#124—942no—
678#124—941no—
679#124—941no—
680#124—941no—
681C22⋊Q8—21no—
682C22⋊Q8—21no—
683C22⋊Q8—942no—
684C22⋊Q8—942no—
685C22⋊Q8—942no—
686C22⋊Q8—942no—
687C22⋊Q8—941no—
688C22⋊Q8—941no—
689C22⋊Q8—941no—
690C22⋊Q8—941no—
691C22⋊Q8—941no—
692C22⋊Q8—941no—
693#121—21no—
694#121—472no—
695#121—472no—
696#121—472no—
697#121—942no—
698#121—942no—
699#121—941no—
700#121—942no—
701#121—941no—
702#121—942no—
703#121—941no—
704#121C22×D4712yes—
705C4×Q8—21no—
706C4×Q8—21no—
707C4×Q8—942no—
708C4×Q8—942no—
709C4×Q8—942no—
710C4×Q8—941no—
711C4×Q8—942no—
712C4×Q8—941no—
713C4×Q8—941no—
714C4×Q8—941no—
715C4×Q8—941no—
716C4×Q8—941no—
717C4×D4—21no—
718C4×D4—472no—
719C4×D4—472no—
720C4×D4—472no—
721C4×D4—942no—
722C4×D4—942no—
723C4×D4—941no—
724C4×D4—942no—
725C4×D4—942no—
726C4×D4—941no—
727C4×D4—941no—
728C4×D4C22×D4712yes—
729#117—472no—
730#117—472no—
731#117—472no—
732#117—942no—
733#117—942no—
734#117C22×D4712yes—
735C2×C4⋊C4—472no—
736C2×C4⋊C4—472no—
737C2×C4⋊C4—472no—
738C2×C4⋊C4—941no—
739C2×C4⋊C4—942no—
740C2×C4⋊C4—942no—
741C2×C4⋊C4—941no—
742C2×C4⋊C4—941no—
743C2×C22⋊C4—942no—
744C2×C22⋊C4—942no—
745C2×C22⋊C4—942no—
746C2×C42—471no—
747C2×C42—471no—
748C2×C42—471no—
749C2×C42—471no—
750C2×C42—471no—
751C2×C42—471no—
752C2×C42—471no—
753C2×C42—471no—
754C2×C42—471no—
755C2×C42—471no—
756C2×C42—471no—
757C2×C42—942no—
758C2×C42C22×D4711yescharacteristic
759#107—474no—
760#107—474no—
761#107—474no—
762#107C22×D4714yes—
763#106—474no—
764#106—474no—
765#106—474no—
766#106C22×D4714yes—
767C4⋊C8—472no—
768C4⋊C8—472no—
769C4⋊C8—472no—
770C4⋊C8C22×D4712yes—
771#102—474no—
772#102—474no—
773#102—474no—
774#102—474no—
775#102—474no—
776#102—474no—
777#102C22×D4714yes—
778#102C22×D4714yes—
779C22⋊C8—472no—
780C22⋊C8—472no—
781C22⋊C8—472no—
782C22⋊C8C22×D4712yes—
783C4×C8—472no—
784C4×C8—472no—
785C4×C8—471no—
786C4×C8—471no—
787C4×C8C22×D4711yescharacteristic
788C4×C8C22×D4711yescharacteristic
789C24—471no—
790C24—942no—
791#41—44no—
792#41—1884no—
793#41—1888no—
794#41—1888no—
795#41—1884no—
796#41—1884no—
797C2×Q8—21no—
798C2×Q8—21no—
799C2×Q8—21no—
800C2×Q8—942no—
801C2×Q8—942no—
802C2×Q8—942no—
803C2×Q8—941no—
804C2×Q8—941no—
805C2×Q8—941no—
806C2×Q8—1884no—
807C2×Q8—1884no—
808C2×Q8—1884no—
809C2×D4—22no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—472no—
813C2×D4—942no—
814C2×D4—948no—
815C2×D4—942no—
816C2×D4—942no—
817C2×D4—942no—
818C2×D4—942no—
819C2×D4—942no—
820C2×D4—941no—
821C2×D4—941no—
822C2×D4—1884no—
823C2×D4—1884no—
824C2×D4—1888no—
825C2×D4C23×D4712yes—
826C22×C4—22no—
827C22×C4—471no—
828C22×C4—471no—
829C22×C4—471no—
830C22×C4—471no—
831C22×C4—471no—
832C22×C4—471no—
833C22×C4—471no—
834C22×C4—471no—
835C22×C4—471no—
836C22×C4—471no—
837C22×C4—471no—
838C22×C4—471no—
839C22×C4—471no—
840C22×C4—471no—
841C22×C4—471no—
842C22×C4—944no—
843C22×C4—944no—
844C22×C4—944no—
845C22×C4—942no—
846C22×C4—942no—
847C22×C4—942no—
848C22×C4—942no—
849C22×C4—942no—
850C22×C4—942no—
851C22×C4—1888no—
852C22×C4D4×D4711yescharacteristic
853C22×C4D4×D4711yescharacteristic
854C22×C4C23×D4711yescharacteristic
855C2×C8—472no—
856C2×C8—472no—
857C2×C8—944no—
858C2×C8—944no—
859C2×C8C23×D4712yes—
860C2×C8C23×D4712yes—
861C4⋊C4—21no—
862C4⋊C4—22no—
863C4⋊C4—22no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—472no—
867C4⋊C4—472no—
868C4⋊C4—472no—
869C4⋊C4—942no—
870C4⋊C4—942no—
871C4⋊C4—942no—
872C4⋊C4—942no—
873C4⋊C4—942no—
874C4⋊C4—942no—
875C4⋊C4—942no—
876C4⋊C4—942no—
877C4⋊C4—942no—
878C4⋊C4—942no—
879C4⋊C4—942no—
880C4⋊C4—942no—
881C4⋊C4—941no—
882C4⋊C4—941no—
883C4⋊C4—941no—
884C4⋊C4C23×D4712yes—
885C4⋊C4C23×D4712yes—
886C4⋊C4C23×D4712yes—
887C22⋊C4—22no—
888C22⋊C4—22no—
889C22⋊C4—22no—
890C22⋊C4—942no—
891C22⋊C4—942no—
892C22⋊C4—942no—
893C22⋊C4—942no—
894C22⋊C4—942no—
895C22⋊C4—942no—
896C22⋊C4—942no—
897C22⋊C4—942no—
898C22⋊C4—942no—
899C42—22no—
900C42—471no—
901C42—471no—
902C42—471no—
903C42—471no—
904C42—471no—
905C42—471no—
906C42—471no—
907C42—471no—
908C42—471no—
909C42—471no—
910C42—471no—
911C42—471no—
912C42—942no—
913C42—942no—
914C42—942no—
915C42D4×D4711yescharacteristic
916C42D4×D4711yescharacteristic
917C42C23×D4711yescharacteristic
918C42C23×D4711yescharacteristic
919C23—22no—
920C23—471no—
921C23—471no—
922C23—942no—
923C23—942no—
924C23—942no—
925C23—942no—
926C23—1884no—
927C23—1884no—
928C23—1884no—
929C23C2×D4×D4711yescharacteristic
930Q8—42no—
931Q8—42no—
932Q8—42no—
933Q8—1884no—
934Q8—1884no—
935Q8—1884no—
936Q8—1882no—
937Q8—1882no—
938Q8—1882no—
939D4—24no—
940D4—44no—
941D4—42no—
942D4—42no—
943D4—944no—
944D4—1884no—
945D4—1884no—
946D4—1884no—
947D4—1884no—
948D4—1884no—
949D4—1884no—
950D4—1882no—
951D4—1882no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—44no—
959C2×C4—471no—
960C2×C4—471no—
961C2×C4—471no—
962C2×C4—474no—
963C2×C4—474no—
964C2×C4—474no—
965C2×C4—471no—
966C2×C4—471no—
967C2×C4—471no—
968C2×C4—942no—
969C2×C4—942no—
970C2×C4—942no—
971C2×C4—942no—
972C2×C4—942no—
973C2×C4—942no—
974C2×C4—942no—
975C2×C4—942no—
976C2×C4—942no—
977C2×C4—942no—
978C2×C4—942no—
979C2×C4—942no—
980C2×C4—942no—
981C2×C4—942no—
982C2×C4—942no—
983C2×C4—1884no—
984C2×C4—1884no—
985C2×C4—1884no—
986C2×C4—1884no—
987C2×C4—1884no—
988C2×C4—1884no—
989C2×C4C2×D4×D4711yescharacteristic
990C2×C4C2×D4×D4711yescharacteristic
991C2×C4C2×D4×D4711yescharacteristic
992C2×C4C2×D4×D4711yescharacteristic
993C2×C4C2×D4×D4711yescharacteristic
994C2×C4C24×D4711yescharacteristic
995C8—22no—
996C8—22no—
997C8—942no—
998C8—942no—
999C22—21no—
1000C22—21no—
1001C22—21no—
1002C22—42no—
1003C22—42no—
1004C22—42no—
1005C22—472no—
1006C22—472no—
1007C22—472no—
1008C22—941no—
1009C22—941no—
1010C22—941no—
1011C22—3768no—
1012C22—1884no—
1013C22—1882no—
1014C22—1882no—
1015C22—1882no—
1016C22C22×D4×D4711yescharacteristic
1017C4—21no—
1018C4—21no—
1019C4—21no—
1020C4—42no—
1021C4—42no—
1022C4—42no—
1023C4—472no—
1024C4—472no—
1025C4—472no—
1026C4—941no—
1027C4—941no—
1028C4—941no—
1029C4—1882no—
1030C4—1882no—
1031C4—1882no—
1032C4#135×D4712yes—
1033C4AGL(1,ℤ/8)×D4712yes—
1034C42−1+4×D4712yes—
1035C2—41no—
1036C2—82no—
1037C2—474no—
1038C2—3762no—
1039C2—1881no—
1040C2#536×D4711yescharacteristic
1041C2C2×#135×D4711yescharacteristic
1042C2C2×AGL(1,ℤ/8)×D4711yescharacteristic
subgroupG/H
centerC22C22×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC47×#3228C2
socleC22×C47C23×D4
prime radical#532×D47C2
hypercenter#3228D47
hypocenterC47C2×#3228
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3228

Complements

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

NH ≅ G/Ntype
1. #533×D47C2semidirect
3. #20254527C2semidirect
4. #20254526C2semidirect
5. #20254525C2semidirect
6. #20254524C2semidirect
7. #20254523C2semidirect
8. #20254522C2semidirect
9. #20254521C2semidirect
10. #20254520C2semidirect
11. #20254519C2semidirect
12. #500×D47C2semidirect
13. #498×D47C2semidirect
14. #486×D47C2semidirect
15. #486×D47C2semidirect
16. #482×D47C2semidirect
17. #478×D47C2semidirect
18. #431×D47C2semidirect
19. C47×#3228C2semidirect
21. #15689680C22semidirect
22. #15689679C22semidirect
23. #15689678C22semidirect
24. #15689678C22semidirect
27. #15689676C22semidirect
55. #15689528C22semidirect
56. #15689527C22semidirect
57. #15689526C22semidirect
58. #15689526C22semidirect
59. #15689521C22semidirect
60. #15689520C22semidirect
61. #15689519C22semidirect
62. #15689519C22semidirect
63. #15689471C22semidirect
64. #15689471C22semidirect
65. #15689470C22semidirect
66. #15689470C22semidirect
67. #15689469C22semidirect
68. #15689469C22semidirect
69. #15689468C22semidirect
70. #15689468C22semidirect
71. #15689450C22semidirect
72. #15689449C22semidirect
73. #15689448C22semidirect
74. #15689447C22semidirect
75. #15689446C22semidirect
76. #15689445C22semidirect
77. #15689444C22semidirect
78. #15689426C22semidirect
79. #15689425C22semidirect
80. #15689424C22semidirect
81. #15689423C22semidirect
82. #15689422C22semidirect
83. #15689421C22semidirect
84. #15689420C22semidirect
85. #15689176C22semidirect
86. #15689175C22semidirect
87. #15689174C22semidirect
88. #15689174C22semidirect
89. #15689173C22semidirect
98. C47×#533C22semidirect
100. C47×#500C22semidirect
101. C47×#498C22semidirect
102. C47×#486C22semidirect
103. C47×#486C22semidirect
104. C47×#482C22semidirect
105. C47×#478C22semidirect
106. C47×#431C22semidirect
525. #3228D47direct (N × H)
540. D47#3228direct (N × H)
551. #533C2×D47semidirect
582. #500C2×D47semidirect
587. #498C2×D47semidirect
596. #486C2×D47semidirect
597. #486C2×D47semidirect
605. #482C2×D47semidirect
613. #478C2×D47semidirect
619. #431C2×D47semidirect
628. C47C2×#3228semidirect

Maximal subgroups

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

subgroupindex
#533×D472
#532×D472
#202545272
#202545262
#202545252
#202545242
#202545232
#202545222
#202545212
#202545202
#202545192
#500×D472
#498×D472
#486×D472
#482×D472
#478×D472
#431×D472
C47×#32282
C2×#322847