Finite Group Databasebeta

← C47×#23482 #26063180

Subgroups — C47×#23482 #26063180

Order 12032.

1650 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#525C211yesmaximal, characteristic
2C2×C47×#428C211yesmaximal, characteristic, complemented
3C2×C47×#417C211yesmaximal, characteristic, complemented
4C2×C47×#417C211yesmaximal, characteristic, complemented
5C2×C47×#407C211yesmaximal, characteristic, complemented
6C2×C47×#380C211yesmaximal, characteristic, complemented
7C47×#2036C212yesmaximal, complemented
8C47×#2035C212yesmaximal, complemented
9C47×#2034C212yesmaximal, complemented
10C47×#2033C212yesmaximal, complemented
11C47×#1736C211yesmaximal, characteristic, complemented
12C22×#41×C47C2211yescharacteristic
13C24×C4×C47C2211yescharacteristic
14C22×M16×C47C2211yescharacteristic
15C22×M16×C47C2211yescharacteristic
16C47×#525—24no—
17C47×#525—24no—
18C2×#123×C47—21no—
19C2×C22⋊Q8×C47C2211yescharacteristic
20C2×C22⋊Q8×C47C2211yescharacteristic
21C2×#121×C47C2211yescharacteristic
22C2×#121×C47C2211yescharacteristic
23C2×#120×C47—21no—
24C2×C4×D4×C47—21no—
25C2×C4×D4×C47—21no—
26C2×#117×C47C2211yescharacteristic
27C22×C4⋊C4×C47C2211yescharacteristic
28C22×C4⋊C4×C47C2211yescharacteristic
29C22×C22⋊C4×C47—21no—
30C47×#428—24no—
31C2×#107×C47C2212yescomplemented
32C2×#106×C47C2212yescomplemented
33C47×#417—24no—
34C47×#417—24no—
35C2×#103×C47C2212yescomplemented
36C2×#103×C47C2212yescomplemented
37C2×#102×C47C2212yescomplemented
38C2×#102×C47C2212yescomplemented
39C47×#407—24no—
40C2×C22⋊C8×C47C2212yes—
41C2×C22⋊C8×C47C2212yes—
42C47×#380—21no—
43C47×#380—21no—
44C47×#380C2212yes—
45C47×#380C2212yes—
46C2×#95×C47—21no—
47C47×#340C2212yescomplemented
48C47×#340C2212yescomplemented
49C25×C47D411yescharacteristic
50C2×#41×C47—22no—
51C2×#41×C47—22no—
52C2×#41×C47—22no—
53C2×#41×C47—22no—
54C2×#41×C47—22no—
55C2×#41×C47D414yes—
56C22×Q8×C47C2311yescharacteristic
57C22×D4×C47—21no—
58C22×D4×C47—21no—
59C22×D4×C47—21no—
60C22×D4×C47C2311yescharacteristic
61C23×C4×C47—21no—
62C23×C4×C47—22no—
63C23×C4×C47—22no—
64C23×C4×C47—22no—
65C23×C4×C47—22no—
66C23×C4×C47—22no—
67C23×C4×C47—22no—
68C23×C4×C47—21no—
69C23×C4×C47—21no—
70C23×C4×C47D411yescharacteristic
71C23×C4×C47D411yescharacteristic
72C23×C4×C47D411yescharacteristic
73C23×C4×C47C2311yescharacteristic
74C23×C4×C47C2311yescharacteristic
75C23×C4×C47C2311yescharacteristic
76C2×M16×C47—22no—
77C2×M16×C47—22no—
78C2×M16×C47—22no—
79C2×M16×C47—22no—
80C2×M16×C47—22no—
81C2×M16×C47D414yescomplemented
82C22×C8×C47C2312yes—
83C22×C8×C47C2312yes—
84#123×C47—28no—
85C22⋊Q8×C47—22no—
86C22⋊Q8×C47—22no—
87C22⋊Q8×C47—22no—
88C22⋊Q8×C47—22no—
89#121×C47—22no—
90#121×C47—22no—
91#121×C47—22no—
92#121×C47—22no—
93#120×C47—28no—
94C4×D4×C47—28no—
95C4×D4×C47—28no—
96#117×C47—22no—
97#117×C47D414yes—
98C2×C4⋊C4×C47—21no—
99C2×C4⋊C4×C47—21no—
100C2×C4⋊C4×C47—22no—
101C2×C4⋊C4×C47—22no—
102C2×C4⋊C4×C47—22no—
103C2×C4⋊C4×C47—22no—
104C2×C4⋊C4×C47—21no—
105C2×C4⋊C4×C47—21no—
106C2×C4⋊C4×C47C2312yes—
107C2×C4⋊C4×C47C2312yes—
108C2×C4⋊C4×C47C2311yescharacteristic
109C2×C4⋊C4×C47C2311yescharacteristic
110C2×C22⋊C4×C47—21no—
111C2×C22⋊C4×C47—21no—
112C2×C22⋊C4×C47—21no—
113C2×C22⋊C4×C47—21no—
114C2×C22⋊C4×C47—21no—
115C2×C22⋊C4×C47—22no—
116C2×C22⋊C4×C47—22no—
117C2×C22⋊C4×C47—44no—
118C2×C42×C47—21no—
119#107×C47—24no—
120#106×C47—24no—
121#103×C47—24no—
122#103×C47—24no—
123#102×C47—24no—
124#102×C47—24no—
125C22⋊C8×C47—24no—
126C22⋊C8×C47—24no—
127#95×C47—22no—
128#95×C47—22no—
129C24×C47—22no—
130C24×C47—22no—
131C24×C47—22no—
132C24×C47—22no—
133C24×C47—22no—
134C24×C47—21no—
135C24×C47—41no—
136C24×C47—41no—
137C24×C47C2×D411yescharacteristic
138C24×C47C2×D411yescharacteristic
139C24×C47C2×D411yescharacteristic
140#41×C47—28no—
141#41×C47—28no—
142#41×C47—44no—
143#41×C47—44no—
144C2×Q8×C47—21no—
145C2×Q8×C47—21no—
146C2×Q8×C47—21no—
147C2×Q8×C47—21no—
148C2×Q8×C47—21no—
149C2×Q8×C47C2×D412yes—
150C2×D4×C47—24no—
151C2×D4×C47—24no—
152C2×D4×C47—24no—
153C2×D4×C47—21no—
154C2×D4×C47—21no—
155C2×D4×C47—21no—
156C2×D4×C47—21no—
157C2×D4×C47—21no—
158C2×D4×C47—42no—
159C2×D4×C47—42no—
160C2×D4×C47—42no—
161C2×D4×C47—42no—
162C2×D4×C47—42no—
163C2×D4×C47—42no—
164C2×D4×C47C2×D412yes—
165C22×C4×C47—22no—
166C22×C4×C47—22no—
167C22×C4×C47—22no—
168C22×C4×C47—21no—
169C22×C4×C47—21no—
170C22×C4×C47—21no—
171C22×C4×C47—22no—
172C22×C4×C47—22no—
173C22×C4×C47—24no—
174C22×C4×C47—22no—
175C22×C4×C47—22no—
176C22×C4×C47—22no—
177C22×C4×C47—22no—
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—21no—
187C22×C4×C47—21no—
188C22×C4×C47—21no—
189C22×C4×C47—21no—
190C22×C4×C47—22no—
191C22×C4×C47—22no—
192C22×C4×C47—44no—
193C22×C4×C47—44no—
194C22×C4×C47—42no—
195C22×C4×C47—44no—
196C22×C4×C47—42no—
197C22×C4×C47—44no—
198C22×C4×C47—42no—
199C22×C4×C47—42no—
200C22×C4×C47—42no—
201C22×C4×C47—42no—
202C22×C4×C47—42no—
203C22×C4×C47—42no—
204C22×C4×C47C2×D411yescharacteristic
205C22×C4×C47C2×D411yescharacteristic
206C22×C4×C47C2×D411yescharacteristic
207C22×C4×C47C2×D412yes—
208C22×C4×C47C2×D412yes—
209C22×C4×C47C2×D412yes—
210C22×C4×C47#4112yes—
211C22×C4×C47#4112yes—
212C22×C4×C47#4112yes—
213C22×C4×C47C2411yescharacteristic
214M16×C47—28no—
215M16×C47—44no—
216C2×C8×C47—22no—
217C2×C8×C47—22no—
218C2×C8×C47—22no—
219C2×C8×C47—22no—
220C2×C8×C47—22no—
221C2×C8×C47C2×D414yes—
222C4⋊C4×C47—24no—
223C4⋊C4×C47—24no—
224C4⋊C4×C47—21no—
225C4⋊C4×C47—21no—
226C4⋊C4×C47—22no—
227C4⋊C4×C47—22no—
228C4⋊C4×C47—22no—
229C4⋊C4×C47—22no—
230C4⋊C4×C47—42no—
231C4⋊C4×C47—42no—
232C4⋊C4×C47C2×D412yes—
233C4⋊C4×C47C2×D412yes—
234C22⋊C4×C47—24no—
235C22⋊C4×C47—24no—
236C22⋊C4×C47—24no—
237C22⋊C4×C47—24no—
238C22⋊C4×C47—24no—
239C22⋊C4×C47—44no—
240C22⋊C4×C47—44no—
241C42×C47—24no—
242C23×C47—21no—
243C23×C47—21no—
244C23×C47—21no—
245C23×C47—21no—
246C23×C47—28no—
247C23×C47—21no—
248C23×C47—21no—
249C23×C47—21no—
250C23×C47—21no—
251C23×C47—21no—
252C23×C47—21no—
253C23×C47—21no—
254C23×C47—21no—
255C23×C47—21no—
256C23×C47—21no—
257C23×C47—21no—
258C23×C47—21no—
259C23×C47—22no—
260C23×C47—44no—
261C23×C47—44no—
262C23×C47—44no—
263C23×C47—44no—
264C23×C47—44no—
265C23×C47—44no—
266C23×C47—41no—
267C23×C47—41no—
268C23×C47—41no—
269C23×C47—41no—
270C23×C47—41no—
271C23×C47—41no—
272C23×C47#12012yes—
273C23×C47#12112yes—
274C23×C47#12312yes—
275C23×C47AGL(1,ℤ/8)12yes—
276C23×C47#13712yes—
277C23×C47C22×D411yescharacteristic
278Q8×C47—22no—
279Q8×C47—22no—
280Q8×C47—41no—
281Q8×C47—41no—
282D4×C47—22no—
283D4×C47—22no—
284D4×C47—48no—
285D4×C47—48no—
286D4×C47—48no—
287D4×C47—41no—
288D4×C47—41no—
289C2×C4×C47—22no—
290C2×C4×C47—22no—
291C2×C4×C47—21no—
292C2×C4×C47—21no—
293C2×C4×C47—22no—
294C2×C4×C47—21no—
295C2×C4×C47—21no—
296C2×C4×C47—21no—
297C2×C4×C47—21no—
298C2×C4×C47—41no—
299C2×C4×C47—41no—
300C2×C4×C47—41no—
301C2×C4×C47—41no—
302C2×C4×C47—41no—
303C2×C4×C47—41no—
304C2×C4×C47—44no—
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—44no—
314C2×C4×C47—44no—
315C2×C4×C47—48no—
316C2×C4×C47—42no—
317C2×C4×C47—42no—
318C2×C4×C47—42no—
319C2×C4×C47—42no—
320C2×C4×C47—42no—
321C2×C4×C47—42no—
322C2×C4×C47—84no—
323C2×C4×C47—84no—
324C2×C4×C47#12012yes—
325C2×C4×C47#12114yes—
326C2×C4×C47#12114yes—
327C2×C4×C47#12112yes—
328C2×C4×C47#12314yes—
329C2×C4×C47#12312yes—
330C2×C4×C47#12414yes—
331C2×C4×C47C22×D411yescharacteristic
332C2×C4×C47C22×D411yescharacteristic
333C2×C4×C47C22×D411yescharacteristic
334C2×C4×C47C2×#4111yescharacteristic
335C2×C4×C47C2×#4111yescharacteristic
336C2×C4×C47C2×#4111yescharacteristic
337C8×C47—24no—
338C8×C47—42no—
339#23482C4711yesmaximal, characteristic, direct product factor, Sylow
340C22×C47—22no—
341C22×C47—22no—
342C22×C47—22no—
343C22×C47—22no—
344C22×C47—22no—
345C22×C47—22no—
346C22×C47—22no—
347C22×C47—22no—
348C22×C47—22no—
349C22×C47—22no—
350C22×C47—22no—
351C22×C47—22no—
352C22×C47—416no—
353C22×C47—41no—
354C22×C47—41no—
355C22×C47—41no—
356C22×C47—41no—
357C22×C47—41no—
358C22×C47—41no—
359C22×C47—41no—
360C22×C47—41no—
361C22×C47—42no—
362C22×C47—42no—
363C22×C47—42no—
364C22×C47—81no—
365C22×C47—81no—
366C22×C47—81no—
367C22×C47—81no—
368C22×C47#39414yes—
369C22×C47C2×#12011yescharacteristic
370C22×C47C2×#12111yescharacteristic
371C22×C47C2×#12311yescharacteristic
372C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
373C22×C47C2×#13711yescharacteristic
374C22×C47#57511yescharacteristic
375C22×C47#57511yescharacteristic
376C4×C47—41no—
377C4×C47—41no—
378C4×C47—42no—
379C4×C47—42no—
380C4×C47—42no—
381C4×C47—82no—
382C4×C47—82no—
383C4×C47#39414yes—
384C4×C47C2×#12111yescharacteristic
385C4×C47C2×#12111yescharacteristic
386C4×C47C2×#12311yescharacteristic
387C4×C47C2×#12411yescharacteristic
388C2×#525C2×C4711yescharacteristic
389C2×#428C2×C4711yescharacteristic, complemented
390C2×#417C2×C4711yescharacteristic, complemented
391C2×#417C2×C4711yescharacteristic, complemented
392C2×#407C2×C4711yescharacteristic, complemented
393C2×#380C2×C4711yescharacteristic, complemented
394#2036C2×C4712yescomplemented
395#2035C2×C4712yescomplemented
396#2034C2×C4712yescomplemented
397#2033C2×C4712yescomplemented
398#1736C2×C4711yescharacteristic, complemented
399C2×C47—24no—
400C2×C47—42no—
401C2×C47—42no—
402C2×C47—82no—
403C2×C47C2×#39411yescharacteristic
404C2×C47#300611yescharacteristic
405C2×C47#300711yescharacteristic
406C2×C47#305511yescharacteristic
407C2×C47#305611yescharacteristic
408C2×C47#309211yescharacteristic
409C2×C47#309311yescharacteristic
410C22×#41C22×C4711yescharacteristic
411C24×C4C22×C4711yescharacteristic
412C22×M16C22×C4711yescharacteristic
413C22×M16C22×C4711yescharacteristic
414#525—24no—
415#525—24no—
416C2×#123—21no—
417C2×C22⋊Q8C22×C4711yescharacteristic
418C2×C22⋊Q8C22×C4711yescharacteristic
419C2×#121C22×C4711yescharacteristic
420C2×#121C22×C4711yescharacteristic
421C2×#120—21no—
422C2×C4×D4—21no—
423C2×C4×D4—21no—
424C2×#117C22×C4711yescharacteristic
425C22×C4⋊C4C22×C4711yescharacteristic
426C22×C4⋊C4C22×C4711yescharacteristic
427C22×C22⋊C4—21no—
428#428—24no—
429C2×#107C22×C4712yescomplemented
430C2×#106C22×C4712yescomplemented
431#417—24no—
432#417—24no—
433C2×#103C22×C4712yescomplemented
434C2×#103C22×C4712yescomplemented
435C2×#102C22×C4712yescomplemented
436C2×#102C22×C4712yescomplemented
437#407—24no—
438C2×C22⋊C8C22×C4712yes—
439C2×C22⋊C8C22×C4712yes—
440#380—21no—
441#380—21no—
442#380C22×C4712yes—
443#380C22×C4712yes—
444C2×#95—21no—
445#340C22×C4712yescomplemented
446#340C22×C4712yescomplemented
447C47#2348211yescharacteristic, direct product factor, Sylow
448C25D4×C4711yescharacteristic
449C2×#41—22no—
450C2×#41—22no—
451C2×#41—22no—
452C2×#41—22no—
453C2×#41—22no—
454C2×#41D4×C4714yes—
455C22×Q8C23×C4711yescharacteristic
456C22×D4—21no—
457C22×D4—21no—
458C22×D4—21no—
459C22×D4C23×C4711yescharacteristic
460C23×C4—21no—
461C23×C4—22no—
462C23×C4—22no—
463C23×C4—22no—
464C23×C4—22no—
465C23×C4—22no—
466C23×C4—22no—
467C23×C4—21no—
468C23×C4—21no—
469C23×C4D4×C4711yescharacteristic
470C23×C4D4×C4711yescharacteristic
471C23×C4D4×C4711yescharacteristic
472C23×C4C23×C4711yescharacteristic
473C23×C4C23×C4711yescharacteristic
474C23×C4C23×C4711yescharacteristic
475C2×M16—22no—
476C2×M16—22no—
477C2×M16—22no—
478C2×M16—22no—
479C2×M16—22no—
480C2×M16D4×C4714yescomplemented
481C22×C8C23×C4712yes—
482C22×C8C23×C4712yes—
483#123—28no—
484C22⋊Q8—22no—
485C22⋊Q8—22no—
486C22⋊Q8—22no—
487C22⋊Q8—22no—
488#121—22no—
489#121—22no—
490#121—22no—
491#121—22no—
492#120—28no—
493C4×D4—28no—
494C4×D4—28no—
495#117—22no—
496#117D4×C4714yes—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—22no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4C23×C4712yes—
506C2×C4⋊C4C23×C4712yes—
507C2×C4⋊C4C23×C4711yescharacteristic
508C2×C4⋊C4C23×C4711yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—44no—
517C2×C42—21no—
518#107—24no—
519#106—24no—
520#103—24no—
521#103—24no—
522#102—24no—
523#102—24no—
524C22⋊C8—24no—
525C22⋊C8—24no—
526#95—22no—
527#95—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—21no—
534C24—41no—
535C24—41no—
536C24C2×D4×C4711yescharacteristic
537C24C2×D4×C4711yescharacteristic
538C24C2×D4×C4711yescharacteristic
539#41—28no—
540#41—28no—
541#41—44no—
542#41—44no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8C2×D4×C4712yes—
549C2×D4—24no—
550C2×D4—24no—
551C2×D4—24no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4C2×D4×C4712yes—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—24no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4—42no—
594C22×C4—44no—
595C22×C4—42no—
596C22×C4—44no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4C2×D4×C4711yescharacteristic
604C22×C4C2×D4×C4711yescharacteristic
605C22×C4C2×D4×C4711yescharacteristic
606C22×C4C2×D4×C4712yes—
607C22×C4C2×D4×C4712yes—
608C22×C4C2×D4×C4712yes—
609C22×C4#41×C4712yes—
610C22×C4#41×C4712yes—
611C22×C4#41×C4712yes—
612C22×C4C24×C4711yescharacteristic
613M16—28no—
614M16—44no—
615C2×C8—22no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8C2×D4×C4714yes—
621C4⋊C4—24no—
622C4⋊C4—24no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—22no—
626C4⋊C4—22no—
627C4⋊C4—22no—
628C4⋊C4—22no—
629C4⋊C4—42no—
630C4⋊C4—42no—
631C4⋊C4C2×D4×C4712yes—
632C4⋊C4C2×D4×C4712yes—
633C22⋊C4—24no—
634C22⋊C4—24no—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—24no—
638C22⋊C4—44no—
639C22⋊C4—44no—
640C42—24no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—28no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—22no—
659C23—44no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—44no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23#120×C4712yes—
672C23#121×C4712yes—
673C23#123×C4712yes—
674C23AGL(1,ℤ/8)×C4712yes—
675C23#137×C4712yes—
676C23C22×D4×C4711yescharacteristic
677Q8—22no—
678Q8—22no—
679Q8—41no—
680Q8—41no—
681D4—22no—
682D4—22no—
683D4—48no—
684D4—48no—
685D4—48no—
686D4—41no—
687D4—41no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—22no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—44no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—48no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—84no—
722C2×C4—84no—
723C2×C4#120×C4712yes—
724C2×C4#121×C4714yes—
725C2×C4#121×C4714yes—
726C2×C4#121×C4712yes—
727C2×C4#123×C4714yes—
728C2×C4#123×C4712yes—
729C2×C4#124×C4714yes—
730C2×C4C22×D4×C4711yescharacteristic
731C2×C4C22×D4×C4711yescharacteristic
732C2×C4C22×D4×C4711yescharacteristic
733C2×C4C2×#41×C4711yescharacteristic
734C2×C4C2×#41×C4711yescharacteristic
735C2×C4C2×#41×C4711yescharacteristic
736C8—24no—
737C8—42no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—416no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22C47×#39414yes—
767C22C2×#120×C4711yescharacteristic
768C22C2×#121×C4711yescharacteristic
769C22C2×#123×C4711yescharacteristic
770C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
771C22C2×#137×C4711yescharacteristic
772C22C47×#57511yescharacteristic
773C22C47×#57511yescharacteristic
774C4—41no—
775C4—41no—
776C4—42no—
777C4—42no—
778C4—42no—
779C4—82no—
780C4—82no—
781C4C47×#39414yes—
782C4C2×#121×C4711yescharacteristic
783C4C2×#121×C4711yescharacteristic
784C4C2×#123×C4711yescharacteristic
785C4C2×#124×C4711yescharacteristic
786C2—24no—
787C2—42no—
788C2—42no—
789C2—82no—
790C2C2×C47×#39411yescharacteristic
791C2C47×#300611yescharacteristic
792C2C47×#300711yescharacteristic
793C2C47×#305511yescharacteristic
794C2C47×#305611yescharacteristic
795C2C47×#309211yescharacteristic
796C2C47×#309311yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC2×C47×#525C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C24×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C47×#428C2semidirect
3. C2×C47×#417C2semidirect
4. C2×C47×#417C2semidirect
5. C2×C47×#407C2semidirect
6. C2×C47×#380C2semidirect
7. C47×#2036C2semidirect
8. C47×#2035C2semidirect
9. C47×#2034C2semidirect
10. C47×#2033C2semidirect
11. C47×#1736C2semidirect
31. C2×#107×C47C22semidirect
32. C2×#106×C47C22semidirect
35. C2×#103×C47C22semidirect
36. C2×#103×C47C22semidirect
37. C2×#102×C47C22semidirect
38. C2×#102×C47C22semidirect
47. C47×#340C22semidirect
48. C47×#340C22semidirect
81. C2×M16×C47D4semidirect
339. #23482C47direct (N × H)
389. C2×#428C2×C47semidirect
390. C2×#417C2×C47semidirect
391. C2×#417C2×C47semidirect
392. C2×#407C2×C47semidirect
393. C2×#380C2×C47semidirect
394. #2036C2×C47semidirect
395. #2035C2×C47semidirect
396. #2034C2×C47semidirect
397. #2033C2×C47semidirect
398. #1736C2×C47semidirect
429. C2×#107C22×C47semidirect
430. C2×#106C22×C47semidirect
433. C2×#103C22×C47semidirect
434. C2×#103C22×C47semidirect
435. C2×#102C22×C47semidirect
436. C2×#102C22×C47semidirect
445. #340C22×C47semidirect
446. #340C22×C47semidirect
447. C47#23482direct (N × H)
480. C2×M16D4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#5252
C2×C47×#4282
C2×C47×#4172
C2×C47×#4072
C2×C47×#3802
C47×#20362
C47×#20352
C47×#20342
C47×#20332
C47×#17362
#2348247