Finite Group Databasebeta

← C47×#23975 #26063673

Subgroups — C47×#23975 #26063673

Order 12032.

1326 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#553C211yesmaximal, characteristic, complemented
2C2×C47×#449C211yesmaximal, characteristic, complemented
3C2×C47×#417C211yesmaximal, characteristic, complemented
4C47×#2407C211yesmaximal, characteristic, complemented
5C47×#2026C211yesmaximal, characteristic, complemented
6C47×#2025C211yesmaximal, characteristic, complemented
7C47×#2000C211yesmaximal, characteristic, complemented
8C47×#1999C211yesmaximal, characteristic, complemented
9C47×#1895C211yesmaximal, characteristic, complemented
10C47×#1879C211yesmaximal, characteristic, complemented
11C47×#1877C211yesmaximal, characteristic, complemented
12C47×#1875C211yesmaximal, characteristic, complemented
13C47×#1873C211yesmaximal, characteristic, complemented
14C47×#1870C211yesmaximal, characteristic, complemented
15C47×#1823C211yesmaximal, characteristic, complemented
16C22×#41×C47C2211yescharacteristic
17C22×SD16×C47C2211yescharacteristic
18C22×D8×C47C2211yescharacteristic
19C22×M16×C47C2211yescharacteristic
20C47×#553—24no—
21C47×#553—24no—
22C2×#126×C47—21no—
23C2×#125×C47C2211yescharacteristic
24C2×#123×C47—21no—
25C2×C22⋊Q8×C47C2211yescharacteristic
26C2×#121×C47—21no—
27C2×#121×C47C2211yescharacteristic
28C2×#121×C47C2211yescharacteristic
29C2×#121×C47C2211yescharacteristic
30C2×C4×D4×C47—21no—
31C2×C4×D4×C47C2211yescharacteristic
32C2×C4×D4×C47C2211yescharacteristic
33C2×#117×C47C2211yescharacteristic
34C22×C4⋊C4×C47C2211yescharacteristic
35C47×#449—24no—
36C47×#417—24no—
37C2×#103×C47C2211yescharacteristic
38C2×#103×C47C2211yescharacteristic
39C2×#103×C47C2211yescharacteristic
40C2×#102×C47C2211yescharacteristic
41C2×#102×C47C2211yescharacteristic
42C2×#102×C47C2211yescharacteristic
43C2×#102×C47C2211yescharacteristic
44C2×#102×C47C2211yescharacteristic
45C2×C22⋊C8×C47C2211yescharacteristic
46C2×C22⋊C8×C47C2211yescharacteristic
47C2×C22⋊C8×C47C2211yescharacteristic
48C47×#394—21no—
49C47×#392—21no—
50C47×#391C2211yescharacteristic
51C47×#390C2211yescharacteristic
52C47×#386—21no—
53C47×#385—21no—
54C47×#380C2211yescharacteristic
55C47×#340C2211yescharacteristic
56C47×#340C2211yescharacteristic
57C47×#340C2211yescharacteristic
58C47×#340C2211yescharacteristic
59C47×#340C2211yescharacteristic
60C47×#340C2211yescharacteristic
61C47×#336C2211yescharacteristic
62C47×#336C2211yescharacteristic
63C2×#41×C47—22no—
64C2×#41×C47—22no—
65C2×#41×C47—22no—
66C2×#41×C47—22no—
67C2×#41×C47—41no—
68C2×#41×C47—41no—
69C22×Q8×C47C2311yescharacteristic
70C22×D4×C47—21no—
71C22×D4×C47—21no—
72C22×D4×C47—21no—
73C22×D4×C47—21no—
74C22×D4×C47D411yescharacteristic
75C22×D4×C47C2311yescharacteristic
76C22×D4×C47C2311yescharacteristic
77C23×C4×C47—21no—
78C23×C4×C47—21no—
79C23×C4×C47—21no—
80C23×C4×C47C2311yescharacteristic
81C23×C4×C47C2311yescharacteristic
82C2×SD16×C47—22no—
83C2×SD16×C47—22no—
84C2×SD16×C47—41no—
85C2×D8×C47—22no—
86C2×D8×C47—22no—
87C2×D8×C47—41no—
88C2×M16×C47—22no—
89C2×M16×C47—41no—
90C2×M16×C47—41no—
91C22×C8×C47C2311yescharacteristic
92C22×C8×C47C2311yescharacteristic
93C22×C8×C47C2311yescharacteristic
94C22×C8×C47C2311yescharacteristic
95#126×C47—28no—
96#125×C47—22no—
97#125×C47—22no—
98#123×C47—28no—
99C22⋊Q8×C47—22no—
100C22⋊Q8×C47—41no—
101#121×C47—28no—
102#121×C47—22no—
103#121×C47—22no—
104#121×C47—22no—
105#121×C47—22no—
106#121×C47—41no—
107#121×C47D414yescomplemented
108C4×D4×C47—28no—
109C4×D4×C47—22no—
110C4×D4×C47—22no—
111C4×D4×C47—22no—
112C4×D4×C47—22no—
113#117×C47—22no—
114#117×C47—22no—
115C2×C4⋊C4×C47—21no—
116C2×C4⋊C4×C47—22no—
117C2×C4⋊C4×C47—21no—
118C2×C4⋊C4×C47—21no—
119C2×C4⋊C4×C47—21no—
120C2×C4⋊C4×C47D411yescharacteristic
121C2×C4⋊C4×C47D414yescomplemented
122C2×C4⋊C4×C47C2311yescharacteristic
123C2×C4⋊C4×C47C2311yescharacteristic
124C2×C4⋊C4×C47C2311yescharacteristic
125C2×C4⋊C4×C47C2311yescharacteristic
126C2×C4⋊C4×C47C2311yescharacteristic
127C2×C22⋊C4×C47—21no—
128C2×C22⋊C4×C47—21no—
129C2×C22⋊C4×C47—21no—
130C2×C22⋊C4×C47—21no—
131C2×C22⋊C4×C47—21no—
132C2×C22⋊C4×C47—21no—
133C2×C22⋊C4×C47—21no—
134C2×C22⋊C4×C47—21no—
135C2×C22⋊C4×C47—21no—
136C2×C22⋊C4×C47D411yescharacteristic
137C2×C22⋊C4×C47D411yescharacteristic
138C2×C42×C47—21no—
139C2×C42×C47C2311yescharacteristic
140#103×C47—22no—
141#103×C47—22no—
142#103×C47—22no—
143#102×C47—22no—
144#102×C47—22no—
145#102×C47—22no—
146#102×C47—41no—
147#102×C47—41no—
148C22⋊C8×C47—22no—
149C22⋊C8×C47—41no—
150C22⋊C8×C47—41no—
151#95×C47—21no—
152#95×C47—21no—
153#95×C47—21no—
154C24×C47—21no—
155C24×C47—21no—
156C24×C47C2×D411yescharacteristic
157C24×C47C2×D411yescharacteristic
158#41×C47—28no—
159#41×C47—44no—
160#41×C47—44no—
161#41×C47—44no—
162C2×Q8×C47—21no—
163C2×Q8×C47—21no—
164C2×Q8×C47—21no—
165C2×Q8×C47—21no—
166C2×Q8×C47—21no—
167C2×Q8×C47#4112yes—
168C2×D4×C47—22no—
169C2×D4×C47—24no—
170C2×D4×C47—24no—
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—41no—
182C2×D4×C47—41no—
183C2×D4×C47—42no—
184C2×D4×C47—42no—
185C2×D4×C47—42no—
186C2×D4×C47—42no—
187C2×D4×C47—42no—
188C2×D4×C47—42no—
189C2×D4×C47—42no—
190C2×D4×C47—81no—
191C2×D4×C47—81no—
192C2×D4×C47—81no—
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—24no—
204C22×C4×C47—24no—
205C22×C4×C47—21no—
206C22×C4×C47—21no—
207C22×C4×C47—21no—
208C22×C4×C47—21no—
209C22×C4×C47—21no—
210C22×C4×C47—21no—
211C22×C4×C47—21no—
212C22×C4×C47—21no—
213C22×C4×C47—42no—
214C22×C4×C47—42no—
215C22×C4×C47—42no—
216C22×C4×C47—81no—
217C22×C4×C47—81no—
218C22×C4×C47—81no—
219C22×C4×C47—81no—
220C22×C4×C47C2×D411yescharacteristic
221C22×C4×C47C2×D411yescharacteristic
222C22×C4×C47C2×D411yescharacteristic
223C22×C4×C47C2×D411yescharacteristic
224C22×C4×C47C2×D412yes—
225C22×C4×C47C2×D412yes—
226C22×C4×C47C2411yescharacteristic
227SD16×C47—44no—
228D8×C47—44no—
229M16×C47—44no—
230C2×C8×C47—21no—
231C2×C8×C47—21no—
232C2×C8×C47—21no—
233C2×C8×C47—21no—
234C2×C8×C47—21no—
235C2×C8×C47—21no—
236C2×C8×C47—21no—
237C2×C8×C47—21no—
238C2×C8×C47—21no—
239C2×C8×C47—21no—
240C2×C8×C47—21no—
241C2×C8×C47—21no—
242C4⋊C4×C47—24no—
243C4⋊C4×C47—24no—
244C4⋊C4×C47—24no—
245C4⋊C4×C47—22no—
246C4⋊C4×C47—21no—
247C4⋊C4×C47—21no—
248C4⋊C4×C47—21no—
249C4⋊C4×C47—21no—
250C4⋊C4×C47—21no—
251C4⋊C4×C47—21no—
252C4⋊C4×C47—21no—
253C4⋊C4×C47—42no—
254C4⋊C4×C47C2×D412yes—
255C4⋊C4×C47C2×D412yes—
256C4⋊C4×C47C2×D412yes—
257C22⋊C4×C47—24no—
258C22⋊C4×C47—24no—
259C22⋊C4×C47—24no—
260C22⋊C4×C47—22no—
261C22⋊C4×C47—24no—
262C22⋊C4×C47—22no—
263C22⋊C4×C47—42no—
264C22⋊C4×C47—42no—
265C22⋊C4×C47—42no—
266C22⋊C4×C47—81no—
267C22⋊C4×C47—81no—
268C42×C47—24no—
269C42×C47—21no—
270C42×C47—21no—
271C23×C47—21no—
272C23×C47—21no—
273C23×C47—21no—
274C23×C47—21no—
275C23×C47—21no—
276C23×C47—21no—
277C23×C47—21no—
278C23×C47—22no—
279C23×C47—21no—
280C23×C47—22no—
281C23×C47—21no—
282C23×C47—21no—
283C23×C47—21no—
284C23×C47—21no—
285C23×C47—21no—
286C23×C47—41no—
287C23×C47—41no—
288C23×C47—41no—
289C23×C47—41no—
290C23×C47—41no—
291C23×C47—41no—
292C23×C47—41no—
293C23×C47—41no—
294C23×C47—41no—
295C23×C47—41no—
296C23×C47—41no—
297C23×C47—41no—
298C23×C47#12012yes—
299C23×C47C22×D411yescharacteristic
300Q8×C47—22no—
301Q8×C47—22no—
302Q8×C47—41no—
303Q8×C47—41no—
304D4×C47—22no—
305D4×C47—22no—
306D4×C47—22no—
307D4×C47—22no—
308D4×C47—44no—
309D4×C47—48no—
310D4×C47—48no—
311D4×C47—41no—
312D4×C47—41no—
313D4×C47—41no—
314D4×C47—41no—
315D4×C47—84no—
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—21no—
324C2×C4×C47—21no—
325C2×C4×C47—22no—
326C2×C4×C47—21no—
327C2×C4×C47—22no—
328C2×C4×C47—22no—
329C2×C4×C47—21no—
330C2×C4×C47—22no—
331C2×C4×C47—21no—
332C2×C4×C47—21no—
333C2×C4×C47—21no—
334C2×C4×C47—21no—
335C2×C4×C47—21no—
336C2×C4×C47—48no—
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—41no—
351C2×C4×C47—41no—
352C2×C4×C47—41no—
353C2×C4×C47—41no—
354C2×C4×C47—41no—
355C2×C4×C47—84no—
356C2×C4×C47—84no—
357C2×C4×C47#12012yes—
358C2×C4×C47C22×D411yescharacteristic
359C2×C4×C47C22×D411yescharacteristic
360C2×C4×C47C2×#4111yescharacteristic
361C2×C4×C47C2×#4111yescharacteristic
362C2×C4×C47H(5,𝔽2)11yescharacteristic
363C2×C4×C47H(5,𝔽2)11yescharacteristic
364C8×C47—41no—
365C8×C47—41no—
366C8×C47—41no—
367C8×C47—41no—
368#23975C4711yesmaximal, characteristic, direct product factor, Sylow
369C22×C47—22no—
370C22×C47—22no—
371C22×C47—22no—
372C22×C47—41no—
373C22×C47—41no—
374C22×C47—41no—
375C22×C47—41no—
376C22×C47—42no—
377C22×C47—41no—
378C22×C47—42no—
379C22×C47—41no—
380C22×C47—42no—
381C22×C47—42no—
382C22×C47—41no—
383C22×C47—41no—
384C22×C47—42no—
385C22×C47—41no—
386C22×C47—41no—
387C22×C47—42no—
388C22×C47—41no—
389C22×C47—81no—
390C22×C47—81no—
391C22×C47—81no—
392C22×C47—81no—
393C22×C47—81no—
394C22×C47—81no—
395C22×C47—81no—
396C22×C47—81no—
397C22×C47C2×#12011yescharacteristic
398C22×C47#54611yescharacteristic
399C22×C47#54611yescharacteristic
400C22×C47#57511yescharacteristic
401C22×C47#57511yescharacteristic
402C22×C47#57611yescharacteristic
403C22×C47#57711yescharacteristic
404C4×C47—22no—
405C4×C47—41no—
406C4×C47—42no—
407C4×C47—41no—
408C4×C47—42no—
409C4×C47—41no—
410C4×C47—42no—
411C4×C47—42no—
412C4×C47—81no—
413C4×C47—81no—
414C4×C47#52511yescharacteristic
415C4×C47#53511yescharacteristic
416C4×C47#54611yescharacteristic
417C4×C47#54611yescharacteristic
418C2×#553C2×C4711yescharacteristic, complemented
419C2×#449C2×C4711yescharacteristic, complemented
420C2×#417C2×C4711yescharacteristic, complemented
421#2407C2×C4711yescharacteristic, complemented
422#2026C2×C4711yescharacteristic, complemented
423#2025C2×C4711yescharacteristic, complemented
424#2000C2×C4711yescharacteristic, complemented
425#1999C2×C4711yescharacteristic, complemented
426#1895C2×C4711yescharacteristic, complemented
427#1879C2×C4711yescharacteristic, complemented
428#1877C2×C4711yescharacteristic, complemented
429#1875C2×C4711yescharacteristic, complemented
430#1873C2×C4711yescharacteristic, complemented
431#1870C2×C4711yescharacteristic, complemented
432#1823C2×C4711yescharacteristic, complemented
433C2×C47—42no—
434C2×C47—81no—
435C2×C47—82no—
436C2×C47—82no—
437C2×C47#240411yescharacteristic
438C2×C47#300511yescharacteristic
439C2×C47#301211yescharacteristic
440C2×C47#330711yescharacteristic
441C2×C47#330911yescharacteristic
442C2×C47#332211yescharacteristic
443C2×C47#332611yescharacteristic
444C22×#41C22×C4711yescharacteristic
445C22×SD16C22×C4711yescharacteristic
446C22×D8C22×C4711yescharacteristic
447C22×M16C22×C4711yescharacteristic
448#553—24no—
449#553—24no—
450C2×#126—21no—
451C2×#125C22×C4711yescharacteristic
452C2×#123—21no—
453C2×C22⋊Q8C22×C4711yescharacteristic
454C2×#121—21no—
455C2×#121C22×C4711yescharacteristic
456C2×#121C22×C4711yescharacteristic
457C2×#121C22×C4711yescharacteristic
458C2×C4×D4—21no—
459C2×C4×D4C22×C4711yescharacteristic
460C2×C4×D4C22×C4711yescharacteristic
461C2×#117C22×C4711yescharacteristic
462C22×C4⋊C4C22×C4711yescharacteristic
463#449—24no—
464#417—24no—
465C2×#103C22×C4711yescharacteristic
466C2×#103C22×C4711yescharacteristic
467C2×#103C22×C4711yescharacteristic
468C2×#102C22×C4711yescharacteristic
469C2×#102C22×C4711yescharacteristic
470C2×#102C22×C4711yescharacteristic
471C2×#102C22×C4711yescharacteristic
472C2×#102C22×C4711yescharacteristic
473C2×C22⋊C8C22×C4711yescharacteristic
474C2×C22⋊C8C22×C4711yescharacteristic
475C2×C22⋊C8C22×C4711yescharacteristic
476#394—21no—
477#392—21no—
478#391C22×C4711yescharacteristic
479#390C22×C4711yescharacteristic
480#386—21no—
481#385—21no—
482#380C22×C4711yescharacteristic
483#340C22×C4711yescharacteristic
484#340C22×C4711yescharacteristic
485#340C22×C4711yescharacteristic
486#340C22×C4711yescharacteristic
487#340C22×C4711yescharacteristic
488#340C22×C4711yescharacteristic
489#336C22×C4711yescharacteristic
490#336C22×C4711yescharacteristic
491C47#2397511yescharacteristic, direct product factor, Sylow
492C2×#41—22no—
493C2×#41—22no—
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—41no—
497C2×#41—41no—
498C22×Q8C23×C4711yescharacteristic
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4D4×C4711yescharacteristic
504C22×D4C23×C4711yescharacteristic
505C22×D4C23×C4711yescharacteristic
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4C23×C4711yescharacteristic
510C23×C4C23×C4711yescharacteristic
511C2×SD16—22no—
512C2×SD16—22no—
513C2×SD16—41no—
514C2×D8—22no—
515C2×D8—22no—
516C2×D8—41no—
517C2×M16—22no—
518C2×M16—41no—
519C2×M16—41no—
520C22×C8C23×C4711yescharacteristic
521C22×C8C23×C4711yescharacteristic
522C22×C8C23×C4711yescharacteristic
523C22×C8C23×C4711yescharacteristic
524#126—28no—
525#125—22no—
526#125—22no—
527#123—28no—
528C22⋊Q8—22no—
529C22⋊Q8—41no—
530#121—28no—
531#121—22no—
532#121—22no—
533#121—22no—
534#121—22no—
535#121—41no—
536#121D4×C4714yescomplemented
537C4×D4—28no—
538C4×D4—22no—
539C4×D4—22no—
540C4×D4—22no—
541C4×D4—22no—
542#117—22no—
543#117—22no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—22no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4D4×C4711yescharacteristic
550C2×C4⋊C4D4×C4714yescomplemented
551C2×C4⋊C4C23×C4711yescharacteristic
552C2×C4⋊C4C23×C4711yescharacteristic
553C2×C4⋊C4C23×C4711yescharacteristic
554C2×C4⋊C4C23×C4711yescharacteristic
555C2×C4⋊C4C23×C4711yescharacteristic
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4D4×C4711yescharacteristic
566C2×C22⋊C4D4×C4711yescharacteristic
567C2×C42—21no—
568C2×C42C23×C4711yescharacteristic
569#103—22no—
570#103—22no—
571#103—22no—
572#102—22no—
573#102—22no—
574#102—22no—
575#102—41no—
576#102—41no—
577C22⋊C8—22no—
578C22⋊C8—41no—
579C22⋊C8—41no—
580#95—21no—
581#95—21no—
582#95—21no—
583C24—21no—
584C24—21no—
585C24C2×D4×C4711yescharacteristic
586C24C2×D4×C4711yescharacteristic
587#41—28no—
588#41—44no—
589#41—44no—
590#41—44no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8#41×C4712yes—
597C2×D4—22no—
598C2×D4—24no—
599C2×D4—24no—
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—21no—
609C2×D4—21no—
610C2×D4—41no—
611C2×D4—41no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4—81no—
620C2×D4—81no—
621C2×D4—81no—
622C2×D4C2×D4×C4712yes—
623C2×D4#41×C4712yes—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—24no—
633C22×C4—24no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—42no—
643C22×C4—42no—
644C22×C4—42no—
645C22×C4—81no—
646C22×C4—81no—
647C22×C4—81no—
648C22×C4—81no—
649C22×C4C2×D4×C4711yescharacteristic
650C22×C4C2×D4×C4711yescharacteristic
651C22×C4C2×D4×C4711yescharacteristic
652C22×C4C2×D4×C4711yescharacteristic
653C22×C4C2×D4×C4712yes—
654C22×C4C2×D4×C4712yes—
655C22×C4C24×C4711yescharacteristic
656SD16—44no—
657D8—44no—
658M16—44no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C4⋊C4—24no—
672C4⋊C4—24no—
673C4⋊C4—24no—
674C4⋊C4—22no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—42no—
683C4⋊C4C2×D4×C4712yes—
684C4⋊C4C2×D4×C4712yes—
685C4⋊C4C2×D4×C4712yes—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—24no—
689C22⋊C4—22no—
690C22⋊C4—24no—
691C22⋊C4—22no—
692C22⋊C4—42no—
693C22⋊C4—42no—
694C22⋊C4—42no—
695C22⋊C4—81no—
696C22⋊C4—81no—
697C42—24no—
698C42—21no—
699C42—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—22no—
708C23—21no—
709C23—22no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23#120×C4712yes—
728C23C22×D4×C4711yescharacteristic
729Q8—22no—
730Q8—22no—
731Q8—41no—
732Q8—41no—
733D4—22no—
734D4—22no—
735D4—22no—
736D4—22no—
737D4—44no—
738D4—48no—
739D4—48no—
740D4—41no—
741D4—41no—
742D4—41no—
743D4—41no—
744D4—84no—
745D4—84no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—21no—
759C2×C4—22no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—48no—
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—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—84no—
785C2×C4—84no—
786C2×C4#120×C4712yes—
787C2×C4C22×D4×C4711yescharacteristic
788C2×C4C22×D4×C4711yescharacteristic
789C2×C4C2×#41×C4711yescharacteristic
790C2×C4C2×#41×C4711yescharacteristic
791C2×C4H(5,𝔽2)×C4711yescharacteristic
792C2×C4H(5,𝔽2)×C4711yescharacteristic
793C8—41no—
794C8—41no—
795C8—41no—
796C8—41no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—42no—
806C22—41no—
807C22—41no—
808C22—42no—
809C22—41no—
810C22—42no—
811C22—41no—
812C22—42no—
813C22—41no—
814C22—42no—
815C22—42no—
816C22—41no—
817C22—81no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22—81no—
822C22—81no—
823C22—81no—
824C22—81no—
825C22C2×#120×C4711yescharacteristic
826C22C47×#54611yescharacteristic
827C22C47×#54611yescharacteristic
828C22C47×#57511yescharacteristic
829C22C47×#57511yescharacteristic
830C22C47×#57611yescharacteristic
831C22C47×#57711yescharacteristic
832C4—22no—
833C4—41no—
834C4—42no—
835C4—41no—
836C4—42no—
837C4—41no—
838C4—42no—
839C4—42no—
840C4—81no—
841C4—81no—
842C4C47×#52511yescharacteristic
843C4C47×#53511yescharacteristic
844C4C47×#54611yescharacteristic
845C4C47×#54611yescharacteristic
846C2—42no—
847C2—81no—
848C2—82no—
849C2—82no—
850C2C47×#240411yescharacteristic
851C2C47×#300511yescharacteristic
852C2C47×#301211yescharacteristic
853C2C47×#330711yescharacteristic
854C2C47×#330911yescharacteristic
855C2C47×#332211yescharacteristic
856C2C47×#332611yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C2×C4×D4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C47×#553C2semidirect
2. C2×C47×#449C2semidirect
3. C2×C47×#417C2semidirect
4. C47×#2407C2semidirect
5. C47×#2026C2semidirect
6. C47×#2025C2semidirect
7. C47×#2000C2semidirect
8. C47×#1999C2semidirect
9. C47×#1895C2semidirect
10. C47×#1879C2semidirect
11. C47×#1877C2semidirect
12. C47×#1875C2semidirect
13. C47×#1873C2semidirect
14. C47×#1870C2semidirect
15. C47×#1823C2semidirect
107. #121×C47D4semidirect
121. C2×C4⋊C4×C47D4semidirect
368. #23975C47direct (N × H)
418. C2×#553C2×C47semidirect
419. C2×#449C2×C47semidirect
420. C2×#417C2×C47semidirect
421. #2407C2×C47semidirect
422. #2026C2×C47semidirect
423. #2025C2×C47semidirect
424. #2000C2×C47semidirect
425. #1999C2×C47semidirect
426. #1895C2×C47semidirect
427. #1879C2×C47semidirect
428. #1877C2×C47semidirect
429. #1875C2×C47semidirect
430. #1873C2×C47semidirect
431. #1870C2×C47semidirect
432. #1823C2×C47semidirect
491. C47#23975direct (N × H)
536. #121D4×C47semidirect
550. C2×C4⋊C4D4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#5532
C2×C47×#4492
C2×C47×#4172
C47×#24072
C47×#20262
C47×#20252
C47×#20002
C47×#19992
C47×#18952
C47×#18792
C47×#18772
C47×#18752
C47×#18732
C47×#18702
C47×#18232
#2397547