Finite Group Databasebeta

← C47×#25101 #26064799

Subgroups — C47×#25101 #26064799

Order 12032.

1248 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#468C211yesmaximal, characteristic, complemented
2C2×C47×#463C211yesmaximal, characteristic, complemented
3C2×C47×#447C211yesmaximal, characteristic
4C2×C47×#418C211yesmaximal, characteristic, complemented
5C47×#2435C211yesmaximal, characteristic, complemented
6C47×#2363C211yesmaximal, characteristic, complemented
7C47×#2067C211yesmaximal, characteristic, complemented
8C47×#2054C211yesmaximal, characteristic, complemented
9C47×#2042C211yesmaximal, characteristic, complemented
10C47×#2012C211yesmaximal, characteristic, complemented
11C47×#1983C211yesmaximal, characteristic, complemented
12C47×#1925C211yesmaximal, characteristic, complemented
13C47×#1879C211yesmaximal, characteristic, complemented
14C47×#1873C211yesmaximal, characteristic, complemented
15C47×#1851C211yesmaximal, characteristic, complemented
16C23×D4×C47C2211yescharacteristic
17C22×SD16×C47C2211yescharacteristic, complemented
18C22×D8×C47C2211yescharacteristic
19C22×D8×C47C2211yescharacteristic
20C22×M16×C47C2211yescharacteristic
21C2×#124×C47C2211yescharacteristic
22C2×#124×C47C2211yescharacteristic
23C2×C22⋊Q8×C47C2211yescharacteristic
24C2×#121×C47C2211yescharacteristic
25C2×C4×D4×C47C2211yescharacteristic, complemented
26C2×#117×C47C2211yescharacteristic
27C47×#468—24no—
28C47×#463—24no—
29C47×#447—24no—
30C2×#107×C47C2211yescharacteristic, complemented
31C2×C4⋊C8×C47C2211yescharacteristic, complemented
32C2×C4⋊C8×C47C2211yescharacteristic, complemented
33C47×#418—24no—
34C2×#103×C47C2211yescharacteristic, complemented
35C2×#103×C47C2211yescharacteristic, complemented
36C2×#103×C47C2211yescharacteristic, complemented
37C2×#102×C47C2211yescharacteristic
38C2×#102×C47C2211yescharacteristic
39C2×#102×C47C2211yescharacteristic
40C2×#102×C47C2211yescharacteristic
41C2×#102×C47C2211yescharacteristic
42C2×#102×C47C2211yescharacteristic
43C2×#102×C47C2211yescharacteristic, complemented
44C2×C22⋊C8×C47C2211yescharacteristic
45C47×#394—21no—
46C47×#394—21no—
47C47×#390—21no—
48C47×#390C2211yescharacteristic
49C47×#390C2211yescharacteristic
50C47×#390C2211yescharacteristic, complemented
51C47×#389C2211yescharacteristic, complemented
52C47×#388—21no—
53C47×#386—21no—
54C47×#379—21no—
55C47×#379—21no—
56C4×C4⋊C4×C47C2211yescharacteristic, complemented
57C4×C22⋊C4×C47—21no—
58C4×C22⋊C4×C47C2211yescharacteristic
59C47×#340C2211yescharacteristic, complemented
60C47×#340C2211yescharacteristic, complemented
61C47×#336C2211yescharacteristic, complemented
62C47×#336C2211yescharacteristic, complemented
63C25×C47—21no—
64C22×Q8×C47C2311yescharacteristic
65C22×D4×C47—22no—
66C22×D4×C47—22no—
67C22×D4×C47—21no—
68C22×D4×C47—22no—
69C22×D4×C47—21no—
70C22×D4×C47—22no—
71C22×D4×C47—41no—
72C22×D4×C47—41no—
73C22×D4×C47C2311yescharacteristic
74C22×D4×C47C2311yescharacteristic
75C22×D4×C47C2311yescharacteristic
76C23×C4×C47—21no—
77C23×C4×C47C2311yescharacteristic
78C2×SD16×C47—22no—
79C2×SD16×C47—22no—
80C2×SD16×C47—41no—
81C2×D8×C47—22no—
82C2×D8×C47—22no—
83C2×D8×C47—22no—
84C2×D8×C47—22no—
85C2×D8×C47—41no—
86C2×D8×C47—41no—
87C2×M16×C47—22no—
88C2×M16×C47—22no—
89C2×M16×C47—41no—
90C22×C8×C47C2311yescharacteristic
91C22×C8×C47C2311yescharacteristic
92C22×C8×C47C2311yescharacteristic
93C22×C8×C47C2311yescharacteristic
94#124×C47—22no—
95#124×C47—22no—
96#124×C47—41no—
97#124×C47—41no—
98C22⋊Q8×C47—22no—
99C22⋊Q8×C47—22no—
100#121×C47—22no—
101#121×C47D414yes—
102C4×D4×C47—22no—
103C4×D4×C47—41no—
104#117×C47—22no—
105#117×C47—41no—
106C2×C4⋊C4×C47—21no—
107C2×C4⋊C4×C47—21no—
108C2×C4⋊C4×C47C2311yescharacteristic
109C2×C4⋊C4×C47C2311yescharacteristic
110C2×C4⋊C4×C47C2311yescharacteristic
111C2×C4⋊C4×C47C2311yescharacteristic
112C2×C22⋊C4×C47—21no—
113C2×C22⋊C4×C47—21no—
114C2×C22⋊C4×C47—21no—
115C2×C22⋊C4×C47—21no—
116C2×C22⋊C4×C47—21no—
117C2×C22⋊C4×C47—21no—
118C2×C22⋊C4×C47—21no—
119C2×C22⋊C4×C47—21no—
120C2×C22⋊C4×C47—21no—
121C2×C22⋊C4×C47—21no—
122C2×C22⋊C4×C47—21no—
123C2×C22⋊C4×C47—21no—
124C2×C22⋊C4×C47—21no—
125C2×C22⋊C4×C47—21no—
126C2×C22⋊C4×C47D411yescharacteristic
127C2×C22⋊C4×C47D411yescharacteristic
128C2×C42×C47—21no—
129C2×C42×C47—21no—
130C2×C42×C47C2311yescharacteristic
131C2×C42×C47C2311yescharacteristic
132#107×C47—22no—
133C4⋊C8×C47—22no—
134C4⋊C8×C47—41no—
135#103×C47—22no—
136#103×C47—22no—
137#103×C47—41no—
138#102×C47—22no—
139#102×C47—22no—
140#102×C47—22no—
141#102×C47—22no—
142#102×C47—22no—
143#102×C47—22no—
144#102×C47D414yescomplemented
145C22⋊C8×C47—22no—
146#95×C47—21no—
147#95×C47—21no—
148#95×C47D411yescharacteristic
149#95×C47D411yescharacteristic
150C24×C47—21no—
151C24×C47—21no—
152C24×C47—21no—
153C24×C47—42no—
154C24×C47—42no—
155C24×C47—42no—
156C24×C47—42no—
157C24×C47—42no—
158C24×C47—81no—
159C24×C47—81no—
160C24×C47C2×D411yescharacteristic
161C2×Q8×C47—21no—
162C2×Q8×C47—21no—
163C2×Q8×C47—21no—
164C2×Q8×C47—21no—
165C2×Q8×C47—21no—
166C2×Q8×C47—21no—
167C2×D4×C47—28no—
168C2×D4×C47—24no—
169C2×D4×C47—21no—
170C2×D4×C47—21no—
171C2×D4×C47—21no—
172C2×D4×C47—21no—
173C2×D4×C47—21no—
174C2×D4×C47—21no—
175C2×D4×C47—21no—
176C2×D4×C47—21no—
177C2×D4×C47—21no—
178C2×D4×C47—21no—
179C2×D4×C47—21no—
180C2×D4×C47—21no—
181C2×D4×C47—21no—
182C2×D4×C47—21no—
183C2×D4×C47—21no—
184C2×D4×C47—44no—
185C2×D4×C47—44no—
186C2×D4×C47—42no—
187C2×D4×C47—42no—
188C2×D4×C47—44no—
189C2×D4×C47—42no—
190C2×D4×C47—81no—
191C2×D4×C47—81no—
192C2×D4×C47C2×D412yes—
193C2×D4×C47C2×D412yes—
194C2×D4×C47#4112yes—
195C22×C4×C47—21no—
196C22×C4×C47—21no—
197C22×C4×C47—21no—
198C22×C4×C47—21no—
199C22×C4×C47—21no—
200C22×C4×C47—21no—
201C22×C4×C47—21no—
202C22×C4×C47—21no—
203C22×C4×C47—21no—
204C22×C4×C47—42no—
205C22×C4×C47—42no—
206C22×C4×C47—81no—
207C22×C4×C47C2×D411yescharacteristic
208C22×C4×C47C2×D411yescharacteristic
209C22×C4×C47C2×D411yescharacteristic
210C22×C4×C47C2×D411yescharacteristic
211C22×C4×C47C2×D411yescharacteristic
212C22×C4×C47C2×D412yes—
213C22×C4×C47#4112yes—
214C22×C4×C47C2411yescharacteristic
215SD16×C47—44no—
216D8×C47—44no—
217D8×C47—44no—
218M16×C47—44no—
219C2×C8×C47—21no—
220C2×C8×C47—21no—
221C2×C8×C47—21no—
222C2×C8×C47—21no—
223C2×C8×C47—21no—
224C2×C8×C47—21no—
225C2×C8×C47—21no—
226C2×C8×C47—21no—
227C2×C8×C47—21no—
228C2×C8×C47—21no—
229C2×C8×C47—21no—
230C2×C8×C47C2×D412yes—
231C4⋊C4×C47—21no—
232C4⋊C4×C47—21no—
233C4⋊C4×C47—21no—
234C4⋊C4×C47—21no—
235C4⋊C4×C47—21no—
236C4⋊C4×C47—21no—
237C4⋊C4×C47—42no—
238C4⋊C4×C47—81no—
239C4⋊C4×C47C2×D412yes—
240C4⋊C4×C47C2×D412yes—
241C22⋊C4×C47—24no—
242C22⋊C4×C47—41no—
243C22⋊C4×C47—41no—
244C22⋊C4×C47—42no—
245C22⋊C4×C47—42no—
246C22⋊C4×C47—42no—
247C22⋊C4×C47—42no—
248C22⋊C4×C47—42no—
249C22⋊C4×C47—42no—
250C22⋊C4×C47—42no—
251C22⋊C4×C47—42no—
252C22⋊C4×C47—81no—
253C22⋊C4×C47—81no—
254C22⋊C4×C47—81no—
255C22⋊C4×C47—81no—
256C22⋊C4×C47—81no—
257C42×C47—21no—
258C42×C47—21no—
259C42×C47—21no—
260C42×C47—21no—
261C42×C47—42no—
262C42×C47—81no—
263C23×C47—21no—
264C23×C47—21no—
265C23×C47—21no—
266C23×C47—21no—
267C23×C47—21no—
268C23×C47—21no—
269C23×C47—22no—
270C23×C47—22no—
271C23×C47—22no—
272C23×C47—48no—
273C23×C47—41no—
274C23×C47—41no—
275C23×C47—41no—
276C23×C47—41no—
277C23×C47—41no—
278C23×C47—41no—
279C23×C47—41no—
280C23×C47—41no—
281C23×C47—41no—
282C23×C47—41no—
283C23×C47—41no—
284C23×C47—41no—
285C23×C47—41no—
286C23×C47—41no—
287C23×C47—41no—
288C23×C47—41no—
289C23×C47—41no—
290C23×C47—41no—
291C23×C47—84no—
292C23×C47—84no—
293C23×C47—84no—
294C23×C47—84no—
295C23×C47—84no—
296C23×C47—84no—
297C23×C47#12112yes—
298C23×C47C22×D411yescharacteristic
299Q8×C47—41no—
300Q8×C47—41no—
301Q8×C47—41no—
302Q8×C47—41no—
303D4×C47—22no—
304D4×C47—22no—
305D4×C47—22no—
306D4×C47—22no—
307D4×C47—22no—
308D4×C47—22no—
309D4×C47—48no—
310D4×C47—41no—
311D4×C47—41no—
312D4×C47—41no—
313D4×C47—41no—
314D4×C47—41no—
315D4×C47—41no—
316D4×C47—84no—
317C2×C4×C47—21no—
318C2×C4×C47—21no—
319C2×C4×C47—22no—
320C2×C4×C47—22no—
321C2×C4×C47—22no—
322C2×C4×C47—22no—
323C2×C4×C47—22no—
324C2×C4×C47—21no—
325C2×C4×C47—21no—
326C2×C4×C47—22no—
327C2×C4×C47—21no—
328C2×C4×C47—21no—
329C2×C4×C47—21no—
330C2×C4×C47—21no—
331C2×C4×C47—21no—
332C2×C4×C47—21no—
333C2×C4×C47—21no—
334C2×C4×C47—21no—
335C2×C4×C47—21no—
336C2×C4×C47—21no—
337C2×C4×C47—41no—
338C2×C4×C47—41no—
339C2×C4×C47—41no—
340C2×C4×C47—41no—
341C2×C4×C47—41no—
342C2×C4×C47—41no—
343C2×C4×C47—41no—
344C2×C4×C47—41no—
345C2×C4×C47—41no—
346C2×C4×C47—41no—
347C2×C4×C47—41no—
348C2×C4×C47—41no—
349C2×C4×C47—41no—
350C2×C4×C47—84no—
351C2×C4×C47#12112yes—
352C2×C4×C47C22×D411yescharacteristic
353C2×C4×C47C22×D411yescharacteristic
354C2×C4×C47C2×#4111yescharacteristic
355C2×C4×C47C2×#4111yescharacteristic
356C2×C4×C47H(5,𝔽2)11yescharacteristic
357C2×C4×C47H(5,𝔽2)11yescharacteristic
358C8×C47—22no—
359C8×C47—41no—
360C8×C47—41no—
361C8×C47—41no—
362#25101C4711yesmaximal, characteristic, direct product factor, Sylow
363C22×C47—22no—
364C22×C47—22no—
365C22×C47—22no—
366C22×C47—41no—
367C22×C47—41no—
368C22×C47—41no—
369C22×C47—41no—
370C22×C47—42no—
371C22×C47—42no—
372C22×C47—42no—
373C22×C47—42no—
374C22×C47—42no—
375C22×C47—42no—
376C22×C47—42no—
377C22×C47—42no—
378C22×C47—42no—
379C22×C47—816no—
380C22×C47—81no—
381C22×C47—81no—
382C22×C47—81no—
383C22×C47—81no—
384C22×C47—81no—
385C22×C47—81no—
386C22×C47—81no—
387C22×C47—81no—
388C22×C47—81no—
389C22×C47—81no—
390C22×C47—81no—
391C22×C47—81no—
392C22×C47C2×#12111yescharacteristic
393C22×C47D4211yescharacteristic
394C22×C47#54611yescharacteristic
395C22×C47#57511yescharacteristic
396C22×C47#57511yescharacteristic
397C22×C47#57611yescharacteristic
398C22×C47#57611yescharacteristic
399C4×C47—22no—
400C4×C47—41no—
401C4×C47—41no—
402C4×C47—42no—
403C4×C47—42no—
404C4×C47—41no—
405C4×C47—41no—
406C4×C47—81no—
407C4×C47—81no—
408C4×C47—81no—
409C4×C47#52511yescharacteristic
410C4×C47#53811yescharacteristic
411C4×C47D4211yescharacteristic
412C4×C47#54611yescharacteristic
413C2×#468C2×C4711yescharacteristic, complemented
414C2×#463C2×C4711yescharacteristic, complemented
415C2×#447C2×C4711yescharacteristic
416C2×#418C2×C4711yescharacteristic, complemented
417#2435C2×C4711yescharacteristic, complemented
418#2363C2×C4711yescharacteristic, complemented
419#2067C2×C4711yescharacteristic, complemented
420#2054C2×C4711yescharacteristic, complemented
421#2042C2×C4711yescharacteristic, complemented
422#2012C2×C4711yescharacteristic, complemented
423#1983C2×C4711yescharacteristic, complemented
424#1925C2×C4711yescharacteristic, complemented
425#1879C2×C4711yescharacteristic, complemented
426#1873C2×C4711yescharacteristic, complemented
427#1851C2×C4711yescharacteristic, complemented
428C2×C47—42no—
429C2×C47—82no—
430C2×C47—82no—
431C2×C47—82no—
432C2×C47#242411yescharacteristic
433C2×C47#304011yescharacteristic
434C2×C47#304111yescharacteristic
435C2×C47#326811yescharacteristic
436C2×C47#327311yescharacteristic
437C2×C47#331911yescharacteristic
438C2×C47#332211yescharacteristic
439C23×D4C22×C4711yescharacteristic
440C22×SD16C22×C4711yescharacteristic, complemented
441C22×D8C22×C4711yescharacteristic
442C22×D8C22×C4711yescharacteristic
443C22×M16C22×C4711yescharacteristic
444C2×#124C22×C4711yescharacteristic
445C2×#124C22×C4711yescharacteristic
446C2×C22⋊Q8C22×C4711yescharacteristic
447C2×#121C22×C4711yescharacteristic
448C2×C4×D4C22×C4711yescharacteristic, complemented
449C2×#117C22×C4711yescharacteristic
450#468—24no—
451#463—24no—
452#447—24no—
453C2×#107C22×C4711yescharacteristic, complemented
454C2×C4⋊C8C22×C4711yescharacteristic, complemented
455C2×C4⋊C8C22×C4711yescharacteristic, complemented
456#418—24no—
457C2×#103C22×C4711yescharacteristic, complemented
458C2×#103C22×C4711yescharacteristic, complemented
459C2×#103C22×C4711yescharacteristic, complemented
460C2×#102C22×C4711yescharacteristic
461C2×#102C22×C4711yescharacteristic
462C2×#102C22×C4711yescharacteristic
463C2×#102C22×C4711yescharacteristic
464C2×#102C22×C4711yescharacteristic
465C2×#102C22×C4711yescharacteristic
466C2×#102C22×C4711yescharacteristic, complemented
467C2×C22⋊C8C22×C4711yescharacteristic
468#394—21no—
469#394—21no—
470#390—21no—
471#390C22×C4711yescharacteristic
472#390C22×C4711yescharacteristic
473#390C22×C4711yescharacteristic, complemented
474#389C22×C4711yescharacteristic, complemented
475#388—21no—
476#386—21no—
477#379—21no—
478#379—21no—
479C4×C4⋊C4C22×C4711yescharacteristic, complemented
480C4×C22⋊C4—21no—
481C4×C22⋊C4C22×C4711yescharacteristic
482#340C22×C4711yescharacteristic, complemented
483#340C22×C4711yescharacteristic, complemented
484#336C22×C4711yescharacteristic, complemented
485#336C22×C4711yescharacteristic, complemented
486C47#2510111yescharacteristic, direct product factor, Sylow
487C25—21no—
488C22×Q8C23×C4711yescharacteristic
489C22×D4—22no—
490C22×D4—22no—
491C22×D4—21no—
492C22×D4—22no—
493C22×D4—21no—
494C22×D4—22no—
495C22×D4—41no—
496C22×D4—41no—
497C22×D4C23×C4711yescharacteristic
498C22×D4C23×C4711yescharacteristic
499C22×D4C23×C4711yescharacteristic
500C23×C4—21no—
501C23×C4C23×C4711yescharacteristic
502C2×SD16—22no—
503C2×SD16—22no—
504C2×SD16—41no—
505C2×D8—22no—
506C2×D8—22no—
507C2×D8—22no—
508C2×D8—22no—
509C2×D8—41no—
510C2×D8—41no—
511C2×M16—22no—
512C2×M16—22no—
513C2×M16—41no—
514C22×C8C23×C4711yescharacteristic
515C22×C8C23×C4711yescharacteristic
516C22×C8C23×C4711yescharacteristic
517C22×C8C23×C4711yescharacteristic
518#124—22no—
519#124—22no—
520#124—41no—
521#124—41no—
522C22⋊Q8—22no—
523C22⋊Q8—22no—
524#121—22no—
525#121D4×C4714yes—
526C4×D4—22no—
527C4×D4—41no—
528#117—22no—
529#117—41no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4C23×C4711yescharacteristic
533C2×C4⋊C4C23×C4711yescharacteristic
534C2×C4⋊C4C23×C4711yescharacteristic
535C2×C4⋊C4C23×C4711yescharacteristic
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4D4×C4711yescharacteristic
551C2×C22⋊C4D4×C4711yescharacteristic
552C2×C42—21no—
553C2×C42—21no—
554C2×C42C23×C4711yescharacteristic
555C2×C42C23×C4711yescharacteristic
556#107—22no—
557C4⋊C8—22no—
558C4⋊C8—41no—
559#103—22no—
560#103—22no—
561#103—41no—
562#102—22no—
563#102—22no—
564#102—22no—
565#102—22no—
566#102—22no—
567#102—22no—
568#102D4×C4714yescomplemented
569C22⋊C8—22no—
570#95—21no—
571#95—21no—
572#95D4×C4711yescharacteristic
573#95D4×C4711yescharacteristic
574C24—21no—
575C24—21no—
576C24—21no—
577C24—42no—
578C24—42no—
579C24—42no—
580C24—42no—
581C24—42no—
582C24—81no—
583C24—81no—
584C24C2×D4×C4711yescharacteristic
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×D4—28no—
592C2×D4—24no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—44no—
609C2×D4—44no—
610C2×D4—42no—
611C2×D4—42no—
612C2×D4—44no—
613C2×D4—42no—
614C2×D4—81no—
615C2×D4—81no—
616C2×D4C2×D4×C4712yes—
617C2×D4C2×D4×C4712yes—
618C2×D4#41×C4712yes—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—42no—
629C22×C4—42no—
630C22×C4—81no—
631C22×C4C2×D4×C4711yescharacteristic
632C22×C4C2×D4×C4711yescharacteristic
633C22×C4C2×D4×C4711yescharacteristic
634C22×C4C2×D4×C4711yescharacteristic
635C22×C4C2×D4×C4711yescharacteristic
636C22×C4C2×D4×C4712yes—
637C22×C4#41×C4712yes—
638C22×C4C24×C4711yescharacteristic
639SD16—44no—
640D8—44no—
641D8—44no—
642M16—44no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8C2×D4×C4712yes—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—42no—
662C4⋊C4—81no—
663C4⋊C4C2×D4×C4712yes—
664C4⋊C4C2×D4×C4712yes—
665C22⋊C4—24no—
666C22⋊C4—41no—
667C22⋊C4—41no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C22⋊C4—42no—
671C22⋊C4—42no—
672C22⋊C4—42no—
673C22⋊C4—42no—
674C22⋊C4—42no—
675C22⋊C4—42no—
676C22⋊C4—81no—
677C22⋊C4—81no—
678C22⋊C4—81no—
679C22⋊C4—81no—
680C22⋊C4—81no—
681C42—21no—
682C42—21no—
683C42—21no—
684C42—21no—
685C42—42no—
686C42—81no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—22no—
694C23—22no—
695C23—22no—
696C23—48no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—84no—
716C23—84no—
717C23—84no—
718C23—84no—
719C23—84no—
720C23—84no—
721C23#121×C4712yes—
722C23C22×D4×C4711yescharacteristic
723Q8—41no—
724Q8—41no—
725Q8—41no—
726Q8—41no—
727D4—22no—
728D4—22no—
729D4—22no—
730D4—22no—
731D4—22no—
732D4—22no—
733D4—48no—
734D4—41no—
735D4—41no—
736D4—41no—
737D4—41no—
738D4—41no—
739D4—41no—
740D4—84no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—22no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—84no—
775C2×C4#121×C4712yes—
776C2×C4C22×D4×C4711yescharacteristic
777C2×C4C22×D4×C4711yescharacteristic
778C2×C4C2×#41×C4711yescharacteristic
779C2×C4C2×#41×C4711yescharacteristic
780C2×C4H(5,𝔽2)×C4711yescharacteristic
781C2×C4H(5,𝔽2)×C4711yescharacteristic
782C8—22no—
783C8—41no—
784C8—41no—
785C8—41no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—42no—
802C22—816no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22C2×#121×C4711yescharacteristic
816C22D42×C4711yescharacteristic
817C22C47×#54611yescharacteristic
818C22C47×#57511yescharacteristic
819C22C47×#57511yescharacteristic
820C22C47×#57611yescharacteristic
821C22C47×#57611yescharacteristic
822C4—22no—
823C4—42no—
824C4—41no—
825C4—41no—
826C4—41no—
827C4—41no—
828C4—42no—
829C4—81no—
830C4—81no—
831C4—81no—
832C4C47×#52511yescharacteristic
833C4C47×#53811yescharacteristic
834C4D42×C4711yescharacteristic
835C4C47×#54611yescharacteristic
836C2—42no—
837C2—82no—
838C2—82no—
839C2—82no—
840C2C47×#242411yescharacteristic
841C2C47×#304011yescharacteristic
842C2C47×#304111yescharacteristic
843C2C47×#326811yescharacteristic
844C2C47×#327311yescharacteristic
845C2C47×#331911yescharacteristic
846C2C47×#332211yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC2×C47×#447C2
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
1. C2×C47×#468C2semidirect
2. C2×C47×#463C2semidirect
4. C2×C47×#418C2semidirect
5. C47×#2435C2semidirect
6. C47×#2363C2semidirect
7. C47×#2067C2semidirect
8. C47×#2054C2semidirect
9. C47×#2042C2semidirect
10. C47×#2012C2semidirect
11. C47×#1983C2semidirect
12. C47×#1925C2semidirect
13. C47×#1879C2semidirect
14. C47×#1873C2semidirect
15. C47×#1851C2semidirect
17. C22×SD16×C47C22semidirect
25. C2×C4×D4×C47C22semidirect
30. C2×#107×C47C22semidirect
31. C2×C4⋊C8×C47C22semidirect
32. C2×C4⋊C8×C47C22semidirect
34. C2×#103×C47C22semidirect
35. C2×#103×C47C22semidirect
36. C2×#103×C47C22semidirect
43. C2×#102×C47C22semidirect
50. C47×#390C22semidirect
51. C47×#389C22semidirect
56. C4×C4⋊C4×C47C22semidirect
59. C47×#340C22semidirect
60. C47×#340C22semidirect
61. C47×#336C22semidirect
62. C47×#336C22semidirect
144. #102×C47D4semidirect
362. #25101C47direct (N × H)
413. C2×#468C2×C47semidirect
414. C2×#463C2×C47semidirect
416. C2×#418C2×C47semidirect
417. #2435C2×C47semidirect
418. #2363C2×C47semidirect
419. #2067C2×C47semidirect
420. #2054C2×C47semidirect
421. #2042C2×C47semidirect
422. #2012C2×C47semidirect
423. #1983C2×C47semidirect
424. #1925C2×C47semidirect
425. #1879C2×C47semidirect
426. #1873C2×C47semidirect
427. #1851C2×C47semidirect
440. C22×SD16C22×C47semidirect
448. C2×C4×D4C22×C47semidirect
453. C2×#107C22×C47semidirect
454. C2×C4⋊C8C22×C47semidirect
455. C2×C4⋊C8C22×C47semidirect
457. C2×#103C22×C47semidirect
458. C2×#103C22×C47semidirect
459. C2×#103C22×C47semidirect
466. C2×#102C22×C47semidirect
473. #390C22×C47semidirect
474. #389C22×C47semidirect
479. C4×C4⋊C4C22×C47semidirect
482. #340C22×C47semidirect
483. #340C22×C47semidirect
484. #336C22×C47semidirect
485. #336C22×C47semidirect
486. C47#25101direct (N × H)
568. #102D4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#4682
C2×C47×#4632
C2×C47×#4472
C2×C47×#4182
C47×#24352
C47×#23632
C47×#20672
C47×#20542
C47×#20422
C47×#20122
C47×#19832
C47×#19252
C47×#18792
C47×#18732
C47×#18512
#2510147