Finite Group Databasebeta

← D47×#1863 #26217203

Subgroups — D47×#1863 #26217203

Order 12032.

1542 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Q8×D47C211yesmaximal, characteristic
2C2×#107×D47C211yesmaximal, characteristic
3C2×#103×D47C211yesmaximal, characteristic
4C2×#103×D47C211yesmaximal, characteristic
5#389×D47C211yesmaximal, characteristic
6#20243645C211yesmaximal, characteristic, complemented
7#20243644C211yesmaximal, characteristic, complemented
8#20243643C211yesmaximal, characteristic, complemented
9#20243642C211yesmaximal, characteristic, complemented
10#20243641C211yesmaximal, characteristic, complemented
11#20243640C211yesmaximal, characteristic, complemented
12#20243639C211yesmaximal, characteristic, complemented
13#340×D47C211yesmaximal, characteristic
14#336×D47C211yesmaximal, characteristic
15C47×#1863C211yesmaximal, characteristic, complemented
16C22×Q8×D47C2211yescharacteristic
17C22×C8×D47C2211yescharacteristic
18C22×C8×D47C2211yescharacteristic
19C2×Q8×Dic47C2211yescharacteristic
20C2×C4×Dic94—21no—
21C2×C4×Dic94C2211yescharacteristic
22C2×#13093989—21no—
23C2×#13093989C2211yescharacteristic
24C4×Q8×D47—24no—
25C4×Q8×D47—24no—
26C2×C4⋊C4×D47—21no—
27C2×C4⋊C4×D47—21no—
28C2×C4⋊C4×D47C2211yescharacteristic
29C2×C4⋊C4×D47C2211yescharacteristic
30C2×C4⋊C4×D47C2211yescharacteristic
31C2×C42×D47—21no—
32C2×C42×D47C2211yescharacteristic
33C2×#13093958C2211yescharacteristic
34C2×#13093957C2211yescharacteristic
35C2×#13093957C2211yescharacteristic
36#107×D47—24no—
37C2×#13093949C2211yescharacteristic
38C2×#13093949C2211yescharacteristic
39C2×#13093948C2211yescharacteristic
40C2×#13093948C2211yescharacteristic
41C2×#13093947C2211yescharacteristic
42C2×#13093947C2211yescharacteristic
43#103×D47—24no—
44#103×D47C418yescomplemented
45#15689022C2211yescharacteristic
46#15689021C2211yescharacteristic
47#15689020—21no—
48#15689019C2211yescharacteristic
49#15689018—21no—
50#95×D47—21no—
51#15688886C2211yescharacteristic
52#15688885C2211yescharacteristic
53#15688885C2211yescharacteristic
54#15688878C2211yescharacteristic
55#15688877C2211yescharacteristic
56#15688877C2211yescharacteristic
57C2×C4×Q8×C47C2211yescharacteristic
58C2×#107×C47C2211yescharacteristic
59C2×#103×C47C2211yescharacteristic
60C2×#103×C47C2211yescharacteristic
61C47×#389C2211yescharacteristic
62C47×#340C2211yescharacteristic
63C47×#336C2211yescharacteristic
64C22×Dic94—21no—
65C22×Dic94C2311yescharacteristic
66C2×Q8×D47—22no—
67C2×Q8×D47—22no—
68C2×Q8×D47—22no—
69C2×Q8×D47C2×C414yes—
70C2×Q8×D47D414yes—
71C2×Q8×D47Q814yes—
72C22×C4×D47—21no—
73C22×C4×D47—21no—
74C22×C4×D47—21no—
75C22×C4×D47—21no—
76C22×C4×D47D411yescharacteristic
77C22×C4×D47D411yescharacteristic
78C22×C4×D47C2311yescharacteristic
79C22×C47⋊C8C2311yescharacteristic
80C22×C47⋊C8C2311yescharacteristic
81C2×C8×D47—22no—
82C2×C8×D47—22no—
83C2×C8×D47—22no—
84C2×C8×D47—22no—
85C2×C8×D47—22no—
86C2×C8×D47C2×C414yes—
87Q8×Dic47—22no—
88Q8×Dic47—22no—
89C4×Dic94—28no—
90C4×Dic94—22no—
91C4×Dic94—22no—
92#13093989—28no—
93#13093989—22no—
94#13093989—22no—
95C2×C4⋊Dic47—21no—
96C2×C4⋊Dic47—21no—
97C2×C4⋊Dic47C2311yescharacteristic
98C2×C4⋊Dic47C2311yescharacteristic
99C2×C4⋊Dic47C2311yescharacteristic
100C2×Dic47⋊C4—21no—
101C2×Dic47⋊C4—21no—
102C2×Dic47⋊C4—21no—
103C2×Dic47⋊C4—21no—
104C2×Dic47⋊C4—21no—
105C2×Dic47⋊C4—21no—
106C2×Dic47⋊C4—21no—
107C4⋊C4×D47—28no—
108C4⋊C4×D47—22no—
109C4⋊C4×D47—22no—
110C4⋊C4×D47—22no—
111C4⋊C4×D47—22no—
112C4⋊C4×D47—44no—
113C4⋊C4×D47C2×C414yes—
114C4⋊C4×D47D414yes—
115C2×C4×Dic47—21no—
116C2×C4×Dic47—21no—
117C2×C4×Dic47—21no—
118C2×C4×Dic47D411yescharacteristic
119C2×C4×Dic47D411yescharacteristic
120C2×C4×Dic47C2311yescharacteristic
121C42×D47—28no—
122C42×D47—22no—
123C42×D47—22no—
124#13093958—22no—
125#13093957—22no—
126#13093957—22no—
127#13093949—22no—
128#13093949C2×C414yescomplemented
129#13093948—22no—
130#13093948C2×C414yescomplemented
131#13093947—22no—
132#13093947C2×C414yescomplemented
133C47⋊#95—21no—
134C47⋊#95—21no—
135C47⋊#95—21no—
136C22×Q8×C47C2311yescharacteristic
137C22×C8×C47C2311yescharacteristic
138C22×C8×C47C2311yescharacteristic
139C4×Q8×C47—22no—
140C4×Q8×C47—22no—
141C2×C4⋊C4×C47—21no—
142C2×C4⋊C4×C47—21no—
143C2×C4⋊C4×C47C2311yescharacteristic
144C2×C4⋊C4×C47C2311yescharacteristic
145C2×C4⋊C4×C47C2311yescharacteristic
146C2×C42×C47—21no—
147C2×C42×C47C2311yescharacteristic
148#107×C47—22no—
149#103×C47—22no—
150#103×C47C2×C414yescomplemented
151#95×C47—21no—
152C23×D47C2×D411yescharacteristic
153C2×Q8×C47—21no—
154C2×Q8×C47—21no—
155C2×Q8×C47—21no—
156C2×Q8×C47C22×C412yes—
157C2×Q8×C47C2×D412yes—
158C2×Q8×C47C2×Q812yes—
159C22×C4×C47—21no—
160C22×C4×C47—21no—
161C22×C4×C47—21no—
162C22×C4×C47—21no—
163C22×C4×C47C2×D411yescharacteristic
164C22×C4×C47C2×D411yescharacteristic
165C22×C4×C47C2411yescharacteristic
166C22×Dic47—21no—
167C22×Dic47—21no—
168C22×Dic47—21no—
169C22×Dic47—21no—
170C22×Dic47C2×D411yescharacteristic
171C22×Dic47C2×D411yescharacteristic
172C22×Dic47C2×D411yescharacteristic
173Q8×D47—28no—
174Q8×D47—28no—
175Q8×D47—28no—
176Q8×D47C4⋊C4116yescomplemented
177C2×C4×D47—24no—
178C2×C4×D47—22no—
179C2×C4×D47—24no—
180C2×C4×D47—24no—
181C2×C4×D47—22no—
182C2×C4×D47—24no—
183C2×C4×D47—22no—
184C2×C4×D47—24no—
185C2×C4×D47—22no—
186C2×C4×D47—22no—
187C2×C4×D47—42no—
188C2×C4×D47—42no—
189C2×C4×D47—42no—
190C2×C4×D47—42no—
191C2×C4×D47—42no—
192C2×C4×D47—42no—
193C2×C4×D47—42no—
194C2×C4×D47Q1614yes—
195C2×C4×D47C22×C412yes—
196C2×C4×D47C2×D412yes—
197C2×C4×D47C2×D412yes—
198C2×C4×D47C2×Q812yes—
199C2×C4×D47#4112yes—
200C2×C4×D47#4112yes—
201C2×Dic94—21no—
202C2×Dic94—21no—
203C2×Dic94—21no—
204C2×Dic94—24no—
205C2×Dic94—24no—
206C2×Dic94—24no—
207C2×Dic94C22×C412yes—
208C2×Dic94C2×D412yes—
209C2×Dic94C2×Q812yes—
210C2×C8×C47—21no—
211C2×C8×C47—21no—
212C2×C8×C47—21no—
213C2×C8×C47—21no—
214C2×C8×C47—21no—
215C2×C8×C47C22×C412yes—
216C4⋊C4×C47—24no—
217C4⋊C4×C47—21no—
218C4⋊C4×C47—21no—
219C4⋊C4×C47—21no—
220C4⋊C4×C47—21no—
221C4⋊C4×C47—42no—
222C4⋊C4×C47C22×C412yes—
223C4⋊C4×C47C2×D412yes—
224C42×C47—24no—
225C42×C47—21no—
226C42×C47—21no—
227C4⋊Dic47—24no—
228C4⋊Dic47—21no—
229C4⋊Dic47—21no—
230C4⋊Dic47—21no—
231C4⋊Dic47—21no—
232C4⋊Dic47—42no—
233C4⋊Dic47C22×C412yes—
234C4⋊Dic47C2×D412yes—
235Dic47⋊C4—24no—
236Dic47⋊C4—24no—
237Dic47⋊C4—24no—
238Dic47⋊C4—24no—
239Dic47⋊C4—42no—
240Dic47⋊C4—42no—
241Dic47⋊C4—42no—
242C4×Dic47—24no—
243C4×Dic47—24no—
244C4×Dic47—24no—
245C4×Dic47—21no—
246C4×Dic47—21no—
247C4×Dic47—22no—
248C4×Dic47—22no—
249C2×C47⋊C8—21no—
250C2×C47⋊C8—21no—
251C2×C47⋊C8—21no—
252C2×C47⋊C8—21no—
253C2×C47⋊C8—21no—
254C2×C47⋊C8C22×C412yes—
255C8×D47—28no—
256C8×D47—44no—
257C23×C47C22×D411yescharacteristic
258C22×D47C4×D412yes—
259C22×D47#12012yes—
260C22×D47C22⋊Q812yes—
261C22×D47C2×Q1612yes—
262C22×D47#13512yes—
263C22×D47AGL(1,ℤ/8)12yes—
264C22×D47#13712yes—
265Q8×C47—22no—
266Q8×C47—22no—
267Q8×C47—22no—
268Q8×C47C2×C4⋊C414yescomplemented
269C2×C4×C47—22no—
270C2×C4×C47—21no—
271C2×C4×C47—22no—
272C2×C4×C47—22no—
273C2×C4×C47—21no—
274C2×C4×C47—22no—
275C2×C4×C47—21no—
276C2×C4×C47—22no—
277C2×C4×C47—21no—
278C2×C4×C47—21no—
279C2×C4×C47—41no—
280C2×C4×C47—41no—
281C2×C4×C47—41no—
282C2×C4×C47—41no—
283C2×C4×C47—41no—
284C2×C4×C47—41no—
285C2×C4×C47—41no—
286C2×C4×C47C2×Q1612yes—
287C2×C4×C47C23×C411yescharacteristic
288C2×C4×C47C22×D411yescharacteristic
289C2×C4×C47C22×D411yescharacteristic
290C2×C4×C47C22×Q811yescharacteristic
291C2×C4×C47C2×#4111yescharacteristic
292C2×C4×C47C2×#4111yescharacteristic
293C2×Dic47—22no—
294C2×Dic47—21no—
295C2×Dic47—22no—
296C2×Dic47—22no—
297C2×Dic47—21no—
298C2×Dic47—22no—
299C2×Dic47—21no—
300C2×Dic47—22no—
301C2×Dic47—21no—
302C2×Dic47—21no—
303C2×Dic47—41no—
304C2×Dic47—41no—
305C2×Dic47—41no—
306C2×Dic47—41no—
307C2×Dic47—41no—
308C2×Dic47—41no—
309C2×Dic47—41no—
310C2×Dic47C4×D412yes—
311C2×Dic47#12012yes—
312C2×Dic47C22⋊Q812yes—
313C2×Dic47C2×Q1612yes—
314C4×D47—216no—
315C4×D47—28no—
316C4×D47—48no—
317C4×D47—44no—
318C4×D47—48no—
319C4×D47—84no—
320C4×D47C2×C4⋊C414yes—
321C4×D47C4×D414yes—
322C4×D47C22⋊Q814yes—
323C4×D47#12314yes—
324Dic94—22no—
325Dic94—22no—
326Dic94—22no—
327Dic94—216no—
328Dic94C2×C4⋊C414yescomplemented
329C8×C47—22no—
330C8×C47—41no—
331C47⋊C8—22no—
332C47⋊C8—41no—
333C2×#1863—471nomaximal, Sylow
334C22×C47C2×C4×D411yescharacteristic
335C22×C47C2×#12011yescharacteristic
336C22×C47C2×C22⋊Q811yescharacteristic
337C22×C47C22×Q1611yescharacteristic
338C22×C47C2×#13511yescharacteristic
339C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
340C22×C47C2×#13711yescharacteristic
341C2×D47#38514yes—
342C2×D47C4×Q1614yes—
343C2×D47#44014yes—
344C2×D47#44914yes—
345C2×D47#45114yes—
346C2×D47#47714yes—
347C2×D47#47914yes—
348C4×C47—22no—
349C4×C47—24no—
350C4×C47—42no—
351C4×C47—41no—
352C4×C47—42no—
353C4×C47—81no—
354C4×C47C22×C4⋊C411yescharacteristic
355C4×C47C2×C4×D411yescharacteristic
356C4×C47C2×C22⋊Q811yescharacteristic
357C4×C47C2×#12311yescharacteristic
358Dic47—22no—
359Dic47—24no—
360Dic47—42no—
361Dic47—41no—
362Dic47—42no—
363Dic47—81no—
364Dic47#38514yes—
365C22×C4×Q8—471no—
366C22×#107—471no—
367C22×#103—471no—
368C22×#103—471no—
369C2×#389—471no—
370#1863—471no—
371#1863—471no—
372#1863—471no—
373#1863—471no—
374#1863—471no—
375#1863—471no—
376#1863—471no—
377#1863D4711yescharacteristic, direct product factor
378C2×#340—471no—
379C2×#336—471no—
380C2×C47C2×#38511yescharacteristic
381C2×C47C2×C4×Q1611yescharacteristic
382C2×C47C2×#44011yescharacteristic
383C2×C47C2×#45111yescharacteristic
384C2×C47C2×#44911yescharacteristic
385C2×C47C2×#47711yescharacteristic
386C2×C47C2×#47911yescharacteristic
387D47#186318yesdirect product factor
388C23×Q8—471no—
389C23×C8—471no—
390C23×C8—471no—
391C2×C4×Q8—471no—
392C2×C4×Q8—471no—
393C2×C4×Q8—471no—
394C2×C4×Q8—941no—
395C2×C4×Q8—941no—
396C2×C4×Q8—944no—
397C2×C4×Q8—944no—
398C2×C4×Q8C2×D4711yescharacteristic
399C22×C4⋊C4—471no—
400C22×C4⋊C4—471no—
401C22×C4⋊C4—471no—
402C22×C4⋊C4—941no—
403C22×C4⋊C4—941no—
404C22×C42—471no—
405C22×C42—941no—
406C2×#107—471no—
407C2×#107—471no—
408C2×#107—471no—
409C2×#107—944no—
410C2×#107C2×D4711yescharacteristic
411C2×#103—471no—
412C2×#103—471no—
413C2×#103—471no—
414C2×#103—478no—
415C2×#103—471no—
416C2×#103—471no—
417C2×#103—471no—
418C2×#103—944no—
419C2×#103C2×D4711yescharacteristic
420C2×#103C2×D4711yescharacteristic
421#389—471no—
422#389—471no—
423#389—471no—
424#389—941no—
425#389—941no—
426#389C2×D4711yescharacteristic
427C2×#95—941no—
428#340—471no—
429#340—471no—
430#340—471no—
431#340C2×D4711yescharacteristic
432#336—471no—
433#336—471no—
434#336—471no—
435#336C2×D4711yescharacteristic
436C47C2×#186311yescharacteristic, complemented, Sylow
437C22×Q8—474no—
438C22×Q8—474no—
439C22×Q8—474no—
440C22×Q8—471no—
441C22×Q8—941no—
442C22×Q8—942no—
443C22×Q8—942no—
444C22×Q8—942no—
445C22×Q8C22×D4711yescharacteristic
446C23×C4—471no—
447C23×C4—471no—
448C23×C4—471no—
449C23×C4—941no—
450C23×C4—941no—
451C23×C4—941no—
452C23×C4—941no—
453C22×C8—471no—
454C22×C8—474no—
455C22×C8—471no—
456C22×C8—942no—
457C22×C8—942no—
458C22×C8—942no—
459C22×C8—942no—
460C22×C8—942no—
461C22×C8C22×D4711yescharacteristic
462C22×C8C22×D4711yescharacteristic
463C4×Q8—22no—
464C4×Q8—22no—
465C4×Q8—942no—
466C4×Q8—942no—
467C4×Q8—948no—
468C4×Q8—942no—
469C4×Q8—948no—
470C4×Q8—942no—
471C4×Q8—942no—
472C4×Q8—942no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—471no—
476C2×C4⋊C4—471no—
477C2×C4⋊C4—474no—
478C2×C4⋊C4—474no—
479C2×C4⋊C4—471no—
480C2×C4⋊C4—942no—
481C2×C4⋊C4—942no—
482C2×C4⋊C4—948no—
483C2×C4⋊C4—942no—
484C2×C4⋊C4—942no—
485C2×C4⋊C4—941no—
486C2×C4⋊C4—941no—
487C2×C4⋊C4—941no—
488C2×C4⋊C4—941no—
489C2×C4⋊C4—941no—
490C2×C4⋊C4—941no—
491C2×C4⋊C4—941no—
492C2×C4⋊C4—941no—
493C2×C4⋊C4—941no—
494C2×C4⋊C4—1884no—
495C2×C4⋊C4C22×D4711yescharacteristic
496C2×C4⋊C4C22×D4711yescharacteristic
497C2×C4⋊C4C22×D4711yescharacteristic
498C2×C42—21no—
499C2×C42—471no—
500C2×C42—471no—
501C2×C42—471no—
502C2×C42—942no—
503C2×C42—942no—
504C2×C42—948no—
505C2×C42—941no—
506C2×C42—941no—
507C2×C42—941no—
508C2×C42C22×D4711yescharacteristic
509#107—22no—
510#107—942no—
511#107—942no—
512#107—942no—
513#103—22no—
514#103—474no—
515#103—474no—
516#103—474no—
517#103—942no—
518#103—942no—
519#103—942no—
520#103C4×D4714yescomplemented
521#95—21no—
522#95—941no—
523#95—941no—
524#95—941no—
525C24—471no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—4716no—
530C2×Q8—472no—
531C2×Q8—472no—
532C2×Q8—472no—
533C2×Q8—944no—
534C2×Q8—944no—
535C2×Q8—944no—
536C2×Q8—948no—
537C2×Q8—948no—
538C2×Q8—948no—
539C2×Q8—941no—
540C2×Q8—941no—
541C2×Q8—941no—
542C2×Q8C2×C4×D4712yes—
543C2×Q8D4×D4712yes—
544C2×Q8Q8×D4712yes—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—471no—
550C22×C4—472no—
551C22×C4—472no—
552C22×C4—472no—
553C22×C4—472no—
554C22×C4—472no—
555C22×C4—472no—
556C22×C4—471no—
557C22×C4—474no—
558C22×C4—471no—
559C22×C4—942no—
560C22×C4—944no—
561C22×C4—942no—
562C22×C4—944no—
563C22×C4—944no—
564C22×C4—944no—
565C22×C4—942no—
566C22×C4—944no—
567C22×C4—942no—
568C22×C4—942no—
569C22×C4—941no—
570C22×C4—941no—
571C22×C4—941no—
572C22×C4—941no—
573C22×C4—1882no—
574C22×C4—1882no—
575C22×C4—1882no—
576C22×C4—1882no—
577C22×C4—1882no—
578C22×C4—1882no—
579C22×C4—1882no—
580C22×C4D4×D4711yescharacteristic
581C22×C4D4×D4711yescharacteristic
582C22×C4C23×D4711yescharacteristic
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—472no—
589C2×C8—948no—
590C2×C8—941no—
591C2×C8—941no—
592C2×C8—941no—
593C2×C8—941no—
594C2×C8—941no—
595C2×C8—1884no—
596C2×C8C2×C4×D4712yes—
597C4⋊C4—24no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—42no—
603C4⋊C4—472no—
604C4⋊C4—472no—
605C4⋊C4—944no—
606C4⋊C4—944no—
607C4⋊C4—944no—
608C4⋊C4—944no—
609C4⋊C4—944no—
610C4⋊C4—941no—
611C4⋊C4—941no—
612C4⋊C4—941no—
613C4⋊C4—941no—
614C4⋊C4—1882no—
615C4⋊C4—1882no—
616C4⋊C4—1882no—
617C4⋊C4—1882no—
618C4⋊C4C2×C4×D4712yes—
619C4⋊C4D4×D4712yes—
620C42—24no—
621C42—21no—
622C42—21no—
623C42—942no—
624C42—942no—
625C42—944no—
626C42—944no—
627C42—944no—
628C42—941no—
629C42—941no—
630C23—472no—
631C23—472no—
632C23—472no—
633C23—472no—
634C23—472no—
635C23—472no—
636C23—472no—
637C23C2×D4×D4711yescharacteristic
638Q8—22no—
639Q8—22no—
640Q8—22no—
641Q8—474no—
642Q8—9416no—
643Q8—942no—
644Q8—942no—
645Q8—942no—
646Q8C4⋊C4×D4714yescomplemented
647C2×C4—22no—
648C2×C4—21no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—21no—
652C2×C4—22no—
653C2×C4—21no—
654C2×C4—22no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—472no—
665C2×C4—472no—
666C2×C4—472no—
667C2×C4—474no—
668C2×C4—474no—
669C2×C4—474no—
670C2×C4—474no—
671C2×C4—472no—
672C2×C4—948no—
673C2×C4—9416no—
674C2×C4—942no—
675C2×C4—941no—
676C2×C4—942no—
677C2×C4—942no—
678C2×C4—941no—
679C2×C4—942no—
680C2×C4—942no—
681C2×C4—941no—
682C2×C4—941no—
683C2×C4—941no—
684C2×C4—3764no—
685C2×C4—1884no—
686C2×C4—1888no—
687C2×C4—1888no—
688C2×C4—1881no—
689C2×C4—1881no—
690C2×C4—1881no—
691C2×C4—1881no—
692C2×C4—1881no—
693C2×C4—1881no—
694C2×C4—1881no—
695C2×C4Q16×D4712yes—
696C2×C4C22×C4×D4711yescharacteristic
697C2×C4C2×D4×D4711yescharacteristic
698C2×C4C2×D4×D4711yescharacteristic
699C2×C4C2×Q8×D4711yescharacteristic
700C2×C4#41×D4711yescharacteristic
701C2×C4#41×D4711yescharacteristic
702C8—22no—
703C8—41no—
704C8—942no—
705C8—1881no—
706C22—474no—
707C22—474no—
708C22—474no—
709C22—474no—
710C22—474no—
711C22—474no—
712C22—474no—
713C22C4×D4×D4711yescharacteristic
714C22#120×D4711yescharacteristic
715C22C22⋊Q8×D4711yescharacteristic
716C22C2×Q16×D4711yescharacteristic
717C22#135×D4711yescharacteristic
718C22AGL(1,ℤ/8)×D4711yescharacteristic
719C22#137×D4711yescharacteristic
720C4—24no—
721C4—22no—
722C4—42no—
723C4—41no—
724C4—42no—
725C4—81no—
726C4—474no—
727C4—944no—
728C4—942no—
729C4—3761no—
730C4—1882no—
731C4—1881no—
732C4—1882no—
733C4C2×C4⋊C4×D4711yescharacteristic
734C4C4×D4×D4711yescharacteristic
735C4C22⋊Q8×D4711yescharacteristic
736C4#123×D4711yescharacteristic
737C2—478no—
738C2#385×D4711yescharacteristic
739C2C4×Q16×D4711yescharacteristic
740C2#440×D4711yescharacteristic
741C2#451×D4711yescharacteristic
742C2#449×D4711yescharacteristic
743C2#477×D4711yescharacteristic
744C2#479×D4711yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1863C2
socleC23×C47C22×D4
prime radicalC23×D47C2×D4
cosocleC22×C4×C47C24
hypercenter#1863D47
hypocenterC47C2×#1863
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1863

Complements

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

NH ≅ G/Ntype
6. #20243645C2semidirect
7. #20243644C2semidirect
8. #20243643C2semidirect
9. #20243642C2semidirect
10. #20243641C2semidirect
11. #20243640C2semidirect
12. #20243639C2semidirect
15. C47×#1863C2semidirect
44. #103×D47C4semidirect
128. #13093949C2×C4semidirect
130. #13093948C2×C4semidirect
132. #13093947C2×C4semidirect
150. #103×C47C2×C4semidirect
176. Q8×D47C4⋊C4semidirect
268. Q8×C47C2×C4⋊C4semidirect
328. Dic94C2×C4⋊C4semidirect
377. #1863D47direct (N × H)
387. D47#1863direct (N × H)
436. C47C2×#1863semidirect
520. #103C4×D47semidirect
646. Q8C4⋊C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Q8×D472
C2×#107×D472
C2×#103×D472
#389×D472
#202436452
#202436442
#202436432
#202436422
#202436412
#202436402
#202436392
#340×D472
#336×D472
C47×#18632
C2×#186347