Finite Group Databasebeta

← C47×#24901 #26064599

Subgroups — C47×#24901 #26064599

Order 12032.

1156 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#450C211yesmaximal, characteristic
2C2×C4×SD16×C47C211yesmaximal, characteristic, complemented
3C47×#2423C211yesmaximal, characteristic, complemented
4D4×C22⋊C4×C47C211yesmaximal, characteristic
5C47×#2094C211yesmaximal, characteristic, complemented
6C47×#2077C211yesmaximal, characteristic, complemented
7C47×#2055C211yesmaximal, characteristic, complemented
8C47×#2035C211yesmaximal, characteristic, complemented
9C47×#1934C211yesmaximal, characteristic, complemented
10C47×#1923C211yesmaximal, characteristic, complemented
11C47×#1880C211yesmaximal, characteristic, complemented
12C47×#1877C211yesmaximal, characteristic, complemented
13C47×#1864C211yesmaximal, characteristic, complemented
14C47×#1802C211yesmaximal, characteristic, complemented
15C47×#1786C211yesmaximal, characteristic
16C23×D4×C47C2211yescharacteristic
17C22×SD16×C47C2211yescharacteristic
18C22×SD16×C47C2211yescharacteristic
19C2×C22⋊Q8×C47C2211yescharacteristic
20C2×C4×Q8×C47C2211yescharacteristic, complemented
21C2×C4×D4×C47C2211yescharacteristic
22C2×C4×D4×C47C2211yescharacteristic
23C22×C22⋊C4×C47—21no—
24C47×#450—24no—
25C4×SD16×C47—24no—
26C2×#106×C47C2211yescharacteristic, complemented
27C2×#106×C47C2211yescharacteristic, complemented
28C2×C4⋊C8×C47C2211yescharacteristic, complemented
29C2×#103×C47C2211yescharacteristic, complemented
30C2×#103×C47C2211yescharacteristic, complemented
31C2×#102×C47C2211yescharacteristic
32C2×#102×C47C2211yescharacteristic
33C2×#102×C47C2211yescharacteristic
34C2×#102×C47C2211yescharacteristic
35C2×#102×C47C2211yescharacteristic
36C2×#102×C47C2211yescharacteristic
37C2×C22⋊C8×C47C2211yescharacteristic
38C2×C22⋊C8×C47C2211yescharacteristic
39C2×C4×C8×C47C2211yescharacteristic, complemented
40C47×#399—21no—
41C47×#398—21no—
42C47×#391C2211yescharacteristic, complemented
43C47×#390C2211yescharacteristic
44C47×#390C2211yescharacteristic
45C47×#389C2211yescharacteristic, complemented
46C47×#388—21no—
47C47×#387—21no—
48C47×#386—21no—
49C47×#386—21no—
50C47×#384C2211yescharacteristic, complemented
51C47×#380C2211yescharacteristic
52C47×#380C2211yescharacteristic
53C47×#379—21no—
54C4×C22⋊C4×C47C2211yescharacteristic
55C47×#340C2211yescharacteristic, complemented
56C47×#340C2211yescharacteristic, complemented
57C47×#340C2211yescharacteristic, complemented
58C47×#340C2211yescharacteristic, complemented
59C47×#336C2211yescharacteristic, complemented
60C47×#336C2211yescharacteristic, complemented
61C25×C47—21no—
62C22×Q8×C47C2311yescharacteristic
63C22×D4×C47—22no—
64C22×D4×C47—22no—
65C22×D4×C47—22no—
66C22×D4×C47—22no—
67C22×D4×C47—21no—
68C22×D4×C47—41no—
69C22×D4×C47—41no—
70C22×D4×C47C2311yescharacteristic
71C22×D4×C47C2311yescharacteristic
72C23×C4×C47—21no—
73C23×C4×C47—21no—
74C23×C4×C47C2311yescharacteristic
75C2×SD16×C47—22no—
76C2×SD16×C47—22no—
77C2×SD16×C47—22no—
78C2×SD16×C47—22no—
79C2×SD16×C47—41no—
80C2×SD16×C47D414yes—
81C22×C8×C47C2311yescharacteristic
82C22×C8×C47C2311yescharacteristic
83C22×C8×C47C2311yescharacteristic
84C22×C8×C47C2311yescharacteristic
85C22⋊Q8×C47—22no—
86C22⋊Q8×C47—41no—
87C4×Q8×C47—22no—
88C4×Q8×C47—41no—
89C4×D4×C47—22no—
90C4×D4×C47—22no—
91C4×D4×C47—41no—
92C4×D4×C47—41no—
93C2×C4⋊C4×C47—21no—
94C2×C4⋊C4×C47—21no—
95C2×C4⋊C4×C47—21no—
96C2×C4⋊C4×C47—21no—
97C2×C4⋊C4×C47—21no—
98C2×C4⋊C4×C47C2311yescharacteristic
99C2×C4⋊C4×C47C2311yescharacteristic
100C2×C4⋊C4×C47C2311yescharacteristic
101C2×C4⋊C4×C47C2311yescharacteristic
102C2×C4⋊C4×C47C2311yescharacteristic
103C2×C22⋊C4×C47—21no—
104C2×C22⋊C4×C47—21no—
105C2×C22⋊C4×C47—21no—
106C2×C22⋊C4×C47—21no—
107C2×C22⋊C4×C47—21no—
108C2×C22⋊C4×C47—21no—
109C2×C22⋊C4×C47—21no—
110C2×C22⋊C4×C47—21no—
111C2×C22⋊C4×C47—21no—
112C2×C22⋊C4×C47—44no—
113C2×C22⋊C4×C47D411yescharacteristic
114C2×C22⋊C4×C47D411yescharacteristic
115C2×C42×C47—21no—
116C2×C42×C47C2311yescharacteristic
117C2×C42×C47C2311yescharacteristic
118#106×C47—22no—
119#106×C47—41no—
120C4⋊C8×C47—41no—
121#103×C47—22no—
122#103×C47—41no—
123#102×C47—22no—
124#102×C47—22no—
125#102×C47—22no—
126#102×C47—22no—
127#102×C47—22no—
128#102×C47—41no—
129C22⋊C8×C47—22no—
130C22⋊C8×C47—41no—
131C4×C8×C47—22no—
132#95×C47—21no—
133#95×C47—21no—
134#95×C47—21no—
135#95×C47—21no—
136#95×C47—21no—
137#95×C47D411yescharacteristic
138#95×C47D411yescharacteristic
139C24×C47—21no—
140C24×C47—24no—
141C24×C47—21no—
142C24×C47—42no—
143C24×C47—42no—
144C24×C47—42no—
145C24×C47—42no—
146C24×C47—81no—
147C24×C47—81no—
148C24×C47C2×D411yescharacteristic
149C2×Q8×C47—21no—
150C2×Q8×C47—21no—
151C2×Q8×C47—21no—
152C2×Q8×C47—21no—
153C2×Q8×C47—21no—
154C2×Q8×C47C2×D412yes—
155C2×D4×C47—24no—
156C2×D4×C47—21no—
157C2×D4×C47—21no—
158C2×D4×C47—21no—
159C2×D4×C47—21no—
160C2×D4×C47—21no—
161C2×D4×C47—21no—
162C2×D4×C47—21no—
163C2×D4×C47—21no—
164C2×D4×C47—42no—
165C2×D4×C47—42no—
166C2×D4×C47—44no—
167C2×D4×C47—44no—
168C2×D4×C47—44no—
169C2×D4×C47—44no—
170C2×D4×C47C2×D412yes—
171C2×D4×C47#4112yes—
172C2×D4×C47#4112yes—
173C2×D4×C47#4112yes—
174C22×C4×C47—21no—
175C22×C4×C47—21no—
176C22×C4×C47—21no—
177C22×C4×C47—21no—
178C22×C4×C47—21no—
179C22×C4×C47—21no—
180C22×C4×C47—21no—
181C22×C4×C47—21no—
182C22×C4×C47—21no—
183C22×C4×C47—21no—
184C22×C4×C47—21no—
185C22×C4×C47—21no—
186C22×C4×C47—42no—
187C22×C4×C47—42no—
188C22×C4×C47—42no—
189C22×C4×C47—42no—
190C22×C4×C47—81no—
191C22×C4×C47—81no—
192C22×C4×C47C2×D411yescharacteristic
193C22×C4×C47C2×D411yescharacteristic
194C22×C4×C47C2×D411yescharacteristic
195C22×C4×C47C2×D411yescharacteristic
196C22×C4×C47C2×D411yescharacteristic
197C22×C4×C47C2411yescharacteristic
198SD16×C47—28no—
199SD16×C47—44no—
200C2×C8×C47—21no—
201C2×C8×C47—21no—
202C2×C8×C47—21no—
203C2×C8×C47—21no—
204C2×C8×C47—21no—
205C2×C8×C47—21no—
206C2×C8×C47—21no—
207C2×C8×C47—21no—
208C2×C8×C47—21no—
209C2×C8×C47—21no—
210C2×C8×C47—21no—
211C2×C8×C47C2×D412yes—
212C4⋊C4×C47—21no—
213C4⋊C4×C47—21no—
214C4⋊C4×C47—21no—
215C4⋊C4×C47—21no—
216C4⋊C4×C47—21no—
217C4⋊C4×C47—21no—
218C4⋊C4×C47—21no—
219C4⋊C4×C47—21no—
220C4⋊C4×C47—21no—
221C4⋊C4×C47—21no—
222C4⋊C4×C47—42no—
223C4⋊C4×C47—42no—
224C4⋊C4×C47—42no—
225C4⋊C4×C47—81no—
226C4⋊C4×C47—81no—
227C22⋊C4×C47—41no—
228C22⋊C4×C47—42no—
229C22⋊C4×C47—42no—
230C22⋊C4×C47—42no—
231C22⋊C4×C47—42no—
232C22⋊C4×C47—42no—
233C22⋊C4×C47—42no—
234C22⋊C4×C47—81no—
235C22⋊C4×C47—81no—
236C22⋊C4×C47—81no—
237C22⋊C4×C47SD1614yescomplemented
238C42×C47—21no—
239C42×C47—21no—
240C42×C47—21no—
241C42×C47—21no—
242C42×C47—42no—
243C23×C47—21no—
244C23×C47—22no—
245C23×C47—21no—
246C23×C47—22no—
247C23×C47—22no—
248C23×C47—21no—
249C23×C47—21no—
250C23×C47—21no—
251C23×C47—21no—
252C23×C47—22no—
253C23×C47—48no—
254C23×C47—48no—
255C23×C47—41no—
256C23×C47—41no—
257C23×C47—41no—
258C23×C47—41no—
259C23×C47—41no—
260C23×C47—41no—
261C23×C47—41no—
262C23×C47—41no—
263C23×C47—41no—
264C23×C47—41no—
265C23×C47—84no—
266C23×C47—84no—
267C23×C47—84no—
268C23×C47—84no—
269C23×C47—84no—
270C23×C47C2×SD1612yes—
271C23×C47C22×D411yescharacteristic
272Q8×C47—22no—
273Q8×C47—22no—
274Q8×C47—41no—
275Q8×C47—41no—
276D4×C47—22no—
277D4×C47—22no—
278D4×C47—22no—
279D4×C47—22no—
280D4×C47—22no—
281D4×C47—48no—
282D4×C47—41no—
283D4×C47—41no—
284D4×C47#12314yes—
285C2×C4×C47—21no—
286C2×C4×C47—21no—
287C2×C4×C47—21no—
288C2×C4×C47—21no—
289C2×C4×C47—21no—
290C2×C4×C47—21no—
291C2×C4×C47—22no—
292C2×C4×C47—21no—
293C2×C4×C47—21no—
294C2×C4×C47—21no—
295C2×C4×C47—21no—
296C2×C4×C47—21no—
297C2×C4×C47—21no—
298C2×C4×C47—21no—
299C2×C4×C47—41no—
300C2×C4×C47—41no—
301C2×C4×C47—41no—
302C2×C4×C47—41no—
303C2×C4×C47—41no—
304C2×C4×C47—41no—
305C2×C4×C47—41no—
306C2×C4×C47—41no—
307C2×C4×C47—41no—
308C2×C4×C47—41no—
309C2×C4×C47—41no—
310C2×C4×C47—41no—
311C2×C4×C47—41no—
312C2×C4×C47—41no—
313C2×C4×C47—41no—
314C2×C4×C47—41no—
315C2×C4×C47—41no—
316C2×C4×C47—41no—
317C2×C4×C47—41no—
318C2×C4×C47—41no—
319C2×C4×C47—41no—
320C2×C4×C47—84no—
321C2×C4×C47—84no—
322C2×C4×C47C2×SD1612yes—
323C2×C4×C47C2×SD1612yes—
324C2×C4×C47C22×D411yescharacteristic
325C2×C4×C47C2×#4111yescharacteristic
326C2×C4×C47C2×#4111yescharacteristic
327C2×C4×C47C2×#4111yescharacteristic
328C2×C4×C47H(5,𝔽2)11yescharacteristic
329C2×C4×C47H(5,𝔽2)11yescharacteristic
330C8×C47—22no—
331C8×C47—41no—
332C8×C47—41no—
333C8×C47—41no—
334#24901C4711yesmaximal, characteristic, direct product factor, Sylow
335C22×C47—22no—
336C22×C47—24no—
337C22×C47—22no—
338C22×C47—22no—
339C22×C47—42no—
340C22×C47—41no—
341C22×C47—42no—
342C22×C47—41no—
343C22×C47—41no—
344C22×C47—42no—
345C22×C47—42no—
346C22×C47—42no—
347C22×C47—41no—
348C22×C47—42no—
349C22×C47—42no—
350C22×C47—42no—
351C22×C47—42no—
352C22×C47—816no—
353C22×C47—81no—
354C22×C47—81no—
355C22×C47—81no—
356C22×C47—81no—
357C22×C47#52511yescharacteristic
358C22×C47D4211yescharacteristic
359C22×C47#54611yescharacteristic
360C22×C47C22×SD1611yescharacteristic
361C22×C47#57511yescharacteristic
362C22×C47#57611yescharacteristic
363C22×C47#57711yescharacteristic
364C4×C47—22no—
365C4×C47—22no—
366C4×C47—41no—
367C4×C47—42no—
368C4×C47—41no—
369C4×C47—41no—
370C4×C47—81no—
371C4×C47—81no—
372C4×C47—81no—
373C4×C47—81no—
374C4×C47—81no—
375C4×C47C2×#12311yescharacteristic
376C4×C47#53811yescharacteristic
377C4×C47#54611yescharacteristic
378C4×C47#55111yescharacteristic
379C2×#450C2×C4711yescharacteristic
380C2×C4×SD16C2×C4711yescharacteristic, complemented
381#2423C2×C4711yescharacteristic, complemented
382D4×C22⋊C4C2×C4711yescharacteristic
383#2094C2×C4711yescharacteristic, complemented
384#2077C2×C4711yescharacteristic, complemented
385#2055C2×C4711yescharacteristic, complemented
386#2035C2×C4711yescharacteristic, complemented
387#1934C2×C4711yescharacteristic, complemented
388#1923C2×C4711yescharacteristic, complemented
389#1880C2×C4711yescharacteristic, complemented
390#1877C2×C4711yescharacteristic, complemented
391#1864C2×C4711yescharacteristic, complemented
392#1802C2×C4711yescharacteristic, complemented
393#1786C2×C4711yescharacteristic
394C2×C47—42no—
395C2×C47—44no—
396C2×C47—82no—
397C2×C47#241811yescharacteristic
398C2×C47#310111yescharacteristic
399C2×C47#311811yescharacteristic
400C2×C47#326811yescharacteristic
401C2×C47D4×SD1611yescharacteristic
402C2×C47#329511yescharacteristic
403C2×C47#332311yescharacteristic
404C23×D4C22×C4711yescharacteristic
405C22×SD16C22×C4711yescharacteristic
406C22×SD16C22×C4711yescharacteristic
407C2×C22⋊Q8C22×C4711yescharacteristic
408C2×C4×Q8C22×C4711yescharacteristic, complemented
409C2×C4×D4C22×C4711yescharacteristic
410C2×C4×D4C22×C4711yescharacteristic
411C22×C22⋊C4—21no—
412#450—24no—
413C4×SD16—24no—
414C2×#106C22×C4711yescharacteristic, complemented
415C2×#106C22×C4711yescharacteristic, complemented
416C2×C4⋊C8C22×C4711yescharacteristic, complemented
417C2×#103C22×C4711yescharacteristic, complemented
418C2×#103C22×C4711yescharacteristic, complemented
419C2×#102C22×C4711yescharacteristic
420C2×#102C22×C4711yescharacteristic
421C2×#102C22×C4711yescharacteristic
422C2×#102C22×C4711yescharacteristic
423C2×#102C22×C4711yescharacteristic
424C2×#102C22×C4711yescharacteristic
425C2×C22⋊C8C22×C4711yescharacteristic
426C2×C22⋊C8C22×C4711yescharacteristic
427C2×C4×C8C22×C4711yescharacteristic, complemented
428#399—21no—
429#398—21no—
430#391C22×C4711yescharacteristic, complemented
431#390C22×C4711yescharacteristic
432#390C22×C4711yescharacteristic
433#389C22×C4711yescharacteristic, complemented
434#388—21no—
435#387—21no—
436#386—21no—
437#386—21no—
438#384C22×C4711yescharacteristic, complemented
439#380C22×C4711yescharacteristic
440#380C22×C4711yescharacteristic
441#379—21no—
442C4×C22⋊C4C22×C4711yescharacteristic
443#340C22×C4711yescharacteristic, complemented
444#340C22×C4711yescharacteristic, complemented
445#340C22×C4711yescharacteristic, complemented
446#340C22×C4711yescharacteristic, complemented
447#336C22×C4711yescharacteristic, complemented
448#336C22×C4711yescharacteristic, complemented
449C47#2490111yescharacteristic, direct product factor, Sylow
450C25—21no—
451C22×Q8C23×C4711yescharacteristic
452C22×D4—22no—
453C22×D4—22no—
454C22×D4—22no—
455C22×D4—22no—
456C22×D4—21no—
457C22×D4—41no—
458C22×D4—41no—
459C22×D4C23×C4711yescharacteristic
460C22×D4C23×C4711yescharacteristic
461C23×C4—21no—
462C23×C4—21no—
463C23×C4C23×C4711yescharacteristic
464C2×SD16—22no—
465C2×SD16—22no—
466C2×SD16—22no—
467C2×SD16—22no—
468C2×SD16—41no—
469C2×SD16D4×C4714yes—
470C22×C8C23×C4711yescharacteristic
471C22×C8C23×C4711yescharacteristic
472C22×C8C23×C4711yescharacteristic
473C22×C8C23×C4711yescharacteristic
474C22⋊Q8—22no—
475C22⋊Q8—41no—
476C4×Q8—22no—
477C4×Q8—41no—
478C4×D4—22no—
479C4×D4—22no—
480C4×D4—41no—
481C4×D4—41no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4C23×C4711yescharacteristic
488C2×C4⋊C4C23×C4711yescharacteristic
489C2×C4⋊C4C23×C4711yescharacteristic
490C2×C4⋊C4C23×C4711yescharacteristic
491C2×C4⋊C4C23×C4711yescharacteristic
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—44no—
502C2×C22⋊C4D4×C4711yescharacteristic
503C2×C22⋊C4D4×C4711yescharacteristic
504C2×C42—21no—
505C2×C42C23×C4711yescharacteristic
506C2×C42C23×C4711yescharacteristic
507#106—22no—
508#106—41no—
509C4⋊C8—41no—
510#103—22no—
511#103—41no—
512#102—22no—
513#102—22no—
514#102—22no—
515#102—22no—
516#102—22no—
517#102—41no—
518C22⋊C8—22no—
519C22⋊C8—41no—
520C4×C8—22no—
521#95—21no—
522#95—21no—
523#95—21no—
524#95—21no—
525#95—21no—
526#95D4×C4711yescharacteristic
527#95D4×C4711yescharacteristic
528C24—21no—
529C24—24no—
530C24—21no—
531C24—42no—
532C24—42no—
533C24—42no—
534C24—42no—
535C24—81no—
536C24—81no—
537C24C2×D4×C4711yescharacteristic
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8C2×D4×C4712yes—
544C2×D4—24no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—42no—
554C2×D4—42no—
555C2×D4—44no—
556C2×D4—44no—
557C2×D4—44no—
558C2×D4—44no—
559C2×D4C2×D4×C4712yes—
560C2×D4#41×C4712yes—
561C2×D4#41×C4712yes—
562C2×D4#41×C4712yes—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—81no—
580C22×C4—81no—
581C22×C4C2×D4×C4711yescharacteristic
582C22×C4C2×D4×C4711yescharacteristic
583C22×C4C2×D4×C4711yescharacteristic
584C22×C4C2×D4×C4711yescharacteristic
585C22×C4C2×D4×C4711yescharacteristic
586C22×C4C24×C4711yescharacteristic
587SD16—28no—
588SD16—44no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8C2×D4×C4712yes—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—42no—
612C4⋊C4—42no—
613C4⋊C4—42no—
614C4⋊C4—81no—
615C4⋊C4—81no—
616C22⋊C4—41no—
617C22⋊C4—42no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4—42no—
621C22⋊C4—42no—
622C22⋊C4—42no—
623C22⋊C4—81no—
624C22⋊C4—81no—
625C22⋊C4—81no—
626C22⋊C4SD16×C4714yescomplemented
627C42—21no—
628C42—21no—
629C42—21no—
630C42—21no—
631C42—42no—
632C23—21no—
633C23—22no—
634C23—21no—
635C23—22no—
636C23—22no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—22no—
642C23—48no—
643C23—48no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—84no—
655C23—84no—
656C23—84no—
657C23—84no—
658C23—84no—
659C23C2×SD16×C4712yes—
660C23C22×D4×C4711yescharacteristic
661Q8—22no—
662Q8—22no—
663Q8—41no—
664Q8—41no—
665D4—22no—
666D4—22no—
667D4—22no—
668D4—22no—
669D4—22no—
670D4—48no—
671D4—41no—
672D4—41no—
673D4#123×C4714yes—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—22no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—84no—
710C2×C4—84no—
711C2×C4C2×SD16×C4712yes—
712C2×C4C2×SD16×C4712yes—
713C2×C4C22×D4×C4711yescharacteristic
714C2×C4C2×#41×C4711yescharacteristic
715C2×C4C2×#41×C4711yescharacteristic
716C2×C4C2×#41×C4711yescharacteristic
717C2×C4H(5,𝔽2)×C4711yescharacteristic
718C2×C4H(5,𝔽2)×C4711yescharacteristic
719C8—22no—
720C8—41no—
721C8—41no—
722C8—41no—
723C22—22no—
724C22—22no—
725C22—24no—
726C22—22no—
727C22—42no—
728C22—41no—
729C22—42no—
730C22—42no—
731C22—41no—
732C22—42no—
733C22—41no—
734C22—41no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—816no—
741C22—81no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22C47×#52511yescharacteristic
746C22D42×C4711yescharacteristic
747C22C47×#54611yescharacteristic
748C22C22×SD16×C4711yescharacteristic
749C22C47×#57511yescharacteristic
750C22C47×#57611yescharacteristic
751C22C47×#57711yescharacteristic
752C4—22no—
753C4—22no—
754C4—41no—
755C4—41no—
756C4—42no—
757C4—41no—
758C4—81no—
759C4—81no—
760C4—81no—
761C4—81no—
762C4—81no—
763C4C2×#123×C4711yescharacteristic
764C4C47×#53811yescharacteristic
765C4C47×#54611yescharacteristic
766C4C47×#55111yescharacteristic
767C2—42no—
768C2—44no—
769C2—82no—
770C2C47×#241811yescharacteristic
771C2C47×#310111yescharacteristic
772C2C47×#311811yescharacteristic
773C2C47×#326811yescharacteristic
774C2D4×SD16×C4711yescharacteristic
775C2C47×#329511yescharacteristic
776C2C47×#332311yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC23×D4×C47C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C4×C22⋊C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×SD16×C47C2semidirect
3. C47×#2423C2semidirect
5. C47×#2094C2semidirect
6. C47×#2077C2semidirect
7. C47×#2055C2semidirect
8. C47×#2035C2semidirect
9. C47×#1934C2semidirect
10. C47×#1923C2semidirect
11. C47×#1880C2semidirect
12. C47×#1877C2semidirect
13. C47×#1864C2semidirect
14. C47×#1802C2semidirect
20. C2×C4×Q8×C47C22semidirect
26. C2×#106×C47C22semidirect
27. C2×#106×C47C22semidirect
28. C2×C4⋊C8×C47C22semidirect
29. C2×#103×C47C22semidirect
30. C2×#103×C47C22semidirect
39. C2×C4×C8×C47C22semidirect
42. C47×#391C22semidirect
45. C47×#389C22semidirect
50. C47×#384C22semidirect
55. C47×#340C22semidirect
56. C47×#340C22semidirect
57. C47×#340C22semidirect
58. C47×#340C22semidirect
59. C47×#336C22semidirect
60. C47×#336C22semidirect
237. C22⋊C4×C47SD16semidirect
334. #24901C47direct (N × H)
380. C2×C4×SD16C2×C47semidirect
381. #2423C2×C47semidirect
383. #2094C2×C47semidirect
384. #2077C2×C47semidirect
385. #2055C2×C47semidirect
386. #2035C2×C47semidirect
387. #1934C2×C47semidirect
388. #1923C2×C47semidirect
389. #1880C2×C47semidirect
390. #1877C2×C47semidirect
391. #1864C2×C47semidirect
392. #1802C2×C47semidirect
408. C2×C4×Q8C22×C47semidirect
414. C2×#106C22×C47semidirect
415. C2×#106C22×C47semidirect
416. C2×C4⋊C8C22×C47semidirect
417. C2×#103C22×C47semidirect
418. C2×#103C22×C47semidirect
427. C2×C4×C8C22×C47semidirect
430. #391C22×C47semidirect
433. #389C22×C47semidirect
438. #384C22×C47semidirect
443. #340C22×C47semidirect
444. #340C22×C47semidirect
445. #340C22×C47semidirect
446. #340C22×C47semidirect
447. #336C22×C47semidirect
448. #336C22×C47semidirect
449. C47#24901direct (N × H)
626. C22⋊C4SD16×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#4502
C2×C4×SD16×C472
C47×#24232
D4×C22⋊C4×C472
C47×#20942
C47×#20772
C47×#20552
C47×#20352
C47×#19342
C47×#19232
C47×#18802
C47×#18772
C47×#18642
C47×#18022
C47×#17862
#2490147