Finite Group Databasebeta

← C47×#25131 #26064829

Subgroups — C47×#25131 #26064829

Order 12032.

1158 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#468C211yesmaximal, characteristic, complemented
2C2×C47×#449C211yesmaximal, characteristic, complemented
3C2×C47×#435C211yesmaximal, characteristic, complemented
4C2×C47×#416C211yesmaximal, characteristic, complemented
5C47×#2414C211yesmaximal, characteristic, complemented
6C47×#2407C211yesmaximal, characteristic, complemented
7C47×#2067C211yesmaximal, characteristic, complemented
8C47×#2055C211yesmaximal, characteristic, complemented
9C47×#2035C211yesmaximal, characteristic, complemented
10C47×#1999C211yesmaximal, characteristic, complemented
11C47×#1972C211yesmaximal, characteristic, complemented
12C47×#1935C211yesmaximal, characteristic, complemented
13C47×#1895C211yesmaximal, characteristic, complemented
14C47×#1893C211yesmaximal, characteristic, complemented
15C47×#1854C211yesmaximal, characteristic, complemented
16C22×#41×C47C2211yescharacteristic
17C22×SD16×C47C2211yescharacteristic
18C22×D8×C47C2211yescharacteristic
19C22×M16×C47C2211yescharacteristic
20C23×C8×C47C2211yescharacteristic
21C2×C22⋊Q8×C47C2211yescharacteristic
22C2×#121×C47C2211yescharacteristic
23C2×#121×C47C2211yescharacteristic
24C2×#121×C47C2211yescharacteristic
25C2×C4×D4×C47C2211yescharacteristic
26C2×#117×C47C2211yescharacteristic
27C47×#468—24no—
28C47×#449—24no—
29C47×#435—24no—
30C2×#107×C47C2211yescharacteristic
31C2×#106×C47C2211yescharacteristic
32C2×C4⋊C8×C47C2211yescharacteristic
33C47×#416—24no—
34C2×#103×C47C2211yescharacteristic
35C2×#103×C47C2211yescharacteristic
36C2×#103×C47C2211yescharacteristic
37C2×#102×C47C2211yescharacteristic
38C2×#102×C47C2211yescharacteristic
39C2×#102×C47C2211yescharacteristic
40C2×#102×C47C2211yescharacteristic
41C2×#102×C47C2211yescharacteristic
42C2×C22⋊C8×C47C2211yescharacteristic
43C2×C22⋊C8×C47C2211yescharacteristic
44C2×#97×C47C2211yescharacteristic
45C47×#394—21no—
46C47×#394—21no—
47C47×#392—21no—
48C47×#392—21no—
49C47×#391C2211yescharacteristic
50C47×#390—21no—
51C47×#390C2211yescharacteristic
52C47×#390C2211yescharacteristic
53C47×#389C2211yescharacteristic
54C47×#388—21no—
55C47×#386—21no—
56C47×#385—21no—
57C47×#380C2211yescharacteristic
58C47×#380C2211yescharacteristic
59C47×#340C2211yescharacteristic
60C47×#340C2211yescharacteristic
61C47×#340C2211yescharacteristic
62C47×#340C2211yescharacteristic
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×C47C2311yescharacteristic
79C23×C4×C47C2311yescharacteristic
80C2×SD16×C47—22no—
81C2×SD16×C47—22no—
82C2×SD16×C47—41no—
83C2×D8×C47—22no—
84C2×D8×C47—22no—
85C2×D8×C47—41no—
86C2×M16×C47—22no—
87C2×M16×C47—22no—
88C2×M16×C47—41no—
89C22×C8×C47—22no—
90C22×C8×C47—22no—
91C22×C8×C47—41no—
92C22×C8×C47C2311yescharacteristic
93C22×C8×C47C2311yescharacteristic
94C22×C8×C47C2311yescharacteristic
95C22×C8×C47C2311yescharacteristic
96C22⋊Q8×C47—22no—
97C22⋊Q8×C47—41no—
98#121×C47—22no—
99#121×C47—22no—
100#121×C47—22no—
101#121×C47—22no—
102#121×C47—41no—
103#121×C47—41no—
104C4×D4×C47—22no—
105C4×D4×C47—22no—
106#117×C47—22no—
107#117×C47—41no—
108C2×C4⋊C4×C47—21no—
109C2×C4⋊C4×C47—21no—
110C2×C4⋊C4×C47D411yescharacteristic
111C2×C4⋊C4×C47C2311yescharacteristic
112C2×C4⋊C4×C47C2311yescharacteristic
113C2×C4⋊C4×C47C2311yescharacteristic
114C2×C4⋊C4×C47C2311yescharacteristic
115C2×C4⋊C4×C47C2311yescharacteristic
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×C47—21no—
127C2×C22⋊C4×C47D411yescharacteristic
128C2×C22⋊C4×C47D411yescharacteristic
129C2×C42×C47—21no—
130C2×C42×C47C2311yescharacteristic
131#107×C47—22no—
132#106×C47—41no—
133C4⋊C8×C47—22no—
134#103×C47—22no—
135#103×C47—22no—
136#103×C47D414yescomplemented
137#102×C47—22no—
138#102×C47—22no—
139#102×C47—22no—
140#102×C47—22no—
141#102×C47—41no—
142C22⋊C8×C47—22no—
143C22⋊C8×C47D414yescomplemented
144#97×C47—22no—
145#95×C47—21no—
146#95×C47—21no—
147#95×C47—21no—
148#95×C47—21no—
149#95×C47—21no—
150C24×C47—21no—
151C24×C47—21no—
152C24×C47C2×D411yescharacteristic
153C24×C47C2×D411yescharacteristic
154#41×C47—28no—
155#41×C47—44no—
156#41×C47—44no—
157#41×C47—44no—
158C2×Q8×C47—21no—
159C2×Q8×C47—21no—
160C2×Q8×C47—21no—
161C2×Q8×C47—21no—
162C2×Q8×C47—21no—
163C2×Q8×C47C2×D412yes—
164C2×D4×C47—22no—
165C2×D4×C47—21no—
166C2×D4×C47—21no—
167C2×D4×C47—21no—
168C2×D4×C47—21no—
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—41no—
177C2×D4×C47—41no—
178C2×D4×C47—42no—
179C2×D4×C47—42no—
180C2×D4×C47—42no—
181C2×D4×C47—42no—
182C2×D4×C47—42no—
183C2×D4×C47—42no—
184C2×D4×C47—42no—
185C2×D4×C47—42no—
186C2×D4×C47—81no—
187C2×D4×C47—81no—
188C2×D4×C47—81no—
189C2×D4×C47—81no—
190C2×D4×C47#4112yes—
191C22×C4×C47—21no—
192C22×C4×C47—21no—
193C22×C4×C47—21no—
194C22×C4×C47—21no—
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—21no—
205C22×C4×C47—21no—
206C22×C4×C47—21no—
207C22×C4×C47—42no—
208C22×C4×C47—42no—
209C22×C4×C47—42no—
210C22×C4×C47C2×D411yescharacteristic
211C22×C4×C47C2×D411yescharacteristic
212C22×C4×C47C2×D411yescharacteristic
213C22×C4×C47C2×D411yescharacteristic
214C22×C4×C47C2×D412yes—
215C22×C4×C47#4112yes—
216C22×C4×C47C2411yescharacteristic
217SD16×C47—44no—
218D8×C47—44no—
219M16×C47—44no—
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—44no—
230C2×C8×C47C2×D412yes—
231C2×C8×C47C2×D412yes—
232C2×C8×C47C2×D412yes—
233C4⋊C4×C47—22no—
234C4⋊C4×C47—21no—
235C4⋊C4×C47—21no—
236C4⋊C4×C47—21no—
237C4⋊C4×C47—21no—
238C4⋊C4×C47—21no—
239C4⋊C4×C47—21no—
240C4⋊C4×C47—21no—
241C4⋊C4×C47—21no—
242C4⋊C4×C47—21no—
243C4⋊C4×C47—42no—
244C4⋊C4×C47—81no—
245C4⋊C4×C47C2×D412yes—
246C22⋊C4×C47—22no—
247C22⋊C4×C47—22no—
248C22⋊C4×C47—42no—
249C22⋊C4×C47—42no—
250C22⋊C4×C47—42no—
251C22⋊C4×C47—42no—
252C22⋊C4×C47—42no—
253C22⋊C4×C47—42no—
254C22⋊C4×C47—42no—
255C22⋊C4×C47—81no—
256C22⋊C4×C47—81no—
257C22⋊C4×C47—81no—
258C22⋊C4×C47—81no—
259C42×C47—21no—
260C42×C47—21no—
261C42×C47—42no—
262C23×C47—21no—
263C23×C47—21no—
264C23×C47—21no—
265C23×C47—21no—
266C23×C47—21no—
267C23×C47—21no—
268C23×C47—21no—
269C23×C47—21no—
270C23×C47—22no—
271C23×C47—21no—
272C23×C47—21no—
273C23×C47—21no—
274C23×C47—21no—
275C23×C47—21no—
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#12112yes—
290C23×C47C22×D411yescharacteristic
291Q8×C47—22no—
292Q8×C47—22no—
293Q8×C47—41no—
294Q8×C47—41no—
295D4×C47—22no—
296D4×C47—22no—
297D4×C47—44no—
298D4×C47—48no—
299D4×C47—41no—
300D4×C47—41no—
301D4×C47—41no—
302D4×C47—41no—
303D4×C47—41no—
304D4×C47—41no—
305D4×C47—84no—
306D4×C47—84no—
307D4×C47—84no—
308C2×C4×C47—21no—
309C2×C4×C47—21no—
310C2×C4×C47—22no—
311C2×C4×C47—22no—
312C2×C4×C47—22no—
313C2×C4×C47—22no—
314C2×C4×C47—21no—
315C2×C4×C47—21no—
316C2×C4×C47—21no—
317C2×C4×C47—22no—
318C2×C4×C47—21no—
319C2×C4×C47—22no—
320C2×C4×C47—21no—
321C2×C4×C47—21no—
322C2×C4×C47—21no—
323C2×C4×C47—21no—
324C2×C4×C47—21no—
325C2×C4×C47—48no—
326C2×C4×C47—41no—
327C2×C4×C47—41no—
328C2×C4×C47—41no—
329C2×C4×C47—41no—
330C2×C4×C47—41no—
331C2×C4×C47—41no—
332C2×C4×C47—41no—
333C2×C4×C47—41no—
334C2×C4×C47—41no—
335C2×C4×C47—41no—
336C2×C4×C47—41no—
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#12112yes—
347C2×C4×C47C22×D411yescharacteristic
348C2×C4×C47C22×D411yescharacteristic
349C2×C4×C47C2×#4111yescharacteristic
350C2×C4×C47C2×#4111yescharacteristic
351C2×C4×C47H(5,𝔽2)11yescharacteristic
352C2×C4×C47H(5,𝔽2)11yescharacteristic
353C8×C47—22no—
354C8×C47—22no—
355C8×C47—22no—
356C8×C47—41no—
357#25131C4711yesmaximal, characteristic, direct product factor, Sylow
358C22×C47—22no—
359C22×C47—22no—
360C22×C47—22no—
361C22×C47—41no—
362C22×C47—41no—
363C22×C47—41no—
364C22×C47—41no—
365C22×C47—42no—
366C22×C47—41no—
367C22×C47—41no—
368C22×C47—41no—
369C22×C47—41no—
370C22×C47—42no—
371C22×C47—41no—
372C22×C47—41no—
373C22×C47—41no—
374C22×C47—42no—
375C22×C47—81no—
376C22×C47—81no—
377C22×C47—81no—
378C22×C47—81no—
379C22×C47—81no—
380C22×C47—81no—
381C22×C47—81no—
382C22×C47—81no—
383C22×C47—81no—
384C22×C47—81no—
385C22×C47—81no—
386C22×C47C2×#12111yescharacteristic
387C22×C47D4211yescharacteristic
388C22×C47#54611yescharacteristic
389C22×C47#57511yescharacteristic
390C22×C47#57511yescharacteristic
391C22×C47#57611yescharacteristic
392C22×C47#57711yescharacteristic
393C4×C47—22no—
394C4×C47—41no—
395C4×C47—42no—
396C4×C47—42no—
397C4×C47—41no—
398C4×C47—41no—
399C4×C47—81no—
400C4×C47—81no—
401C4×C47—81no—
402C4×C47—81no—
403C4×C47#52511yescharacteristic
404C4×C47#53811yescharacteristic
405C4×C47D4211yescharacteristic
406C4×C47#54611yescharacteristic
407C2×#468C2×C4711yescharacteristic, complemented
408C2×#449C2×C4711yescharacteristic, complemented
409C2×#435C2×C4711yescharacteristic, complemented
410C2×#416C2×C4711yescharacteristic, complemented
411#2414C2×C4711yescharacteristic, complemented
412#2407C2×C4711yescharacteristic, complemented
413#2067C2×C4711yescharacteristic, complemented
414#2055C2×C4711yescharacteristic, complemented
415#2035C2×C4711yescharacteristic, complemented
416#1999C2×C4711yescharacteristic, complemented
417#1972C2×C4711yescharacteristic, complemented
418#1935C2×C4711yescharacteristic, complemented
419#1895C2×C4711yescharacteristic, complemented
420#1893C2×C4711yescharacteristic, complemented
421#1854C2×C4711yescharacteristic, complemented
422C2×C47—42no—
423C2×C47—81no—
424C2×C47—82no—
425C2×C47—161no—
426C2×C47#242411yescharacteristic
427C2×C47#305411yescharacteristic
428C2×C47#306211yescharacteristic
429C2×C47#326811yescharacteristic
430C2×C47#327111yescharacteristic
431C2×C47#330711yescharacteristic
432C2×C47#331911yescharacteristic
433C22×#41C22×C4711yescharacteristic
434C22×SD16C22×C4711yescharacteristic
435C22×D8C22×C4711yescharacteristic
436C22×M16C22×C4711yescharacteristic
437C23×C8C22×C4711yescharacteristic
438C2×C22⋊Q8C22×C4711yescharacteristic
439C2×#121C22×C4711yescharacteristic
440C2×#121C22×C4711yescharacteristic
441C2×#121C22×C4711yescharacteristic
442C2×C4×D4C22×C4711yescharacteristic
443C2×#117C22×C4711yescharacteristic
444#468—24no—
445#449—24no—
446#435—24no—
447C2×#107C22×C4711yescharacteristic
448C2×#106C22×C4711yescharacteristic
449C2×C4⋊C8C22×C4711yescharacteristic
450#416—24no—
451C2×#103C22×C4711yescharacteristic
452C2×#103C22×C4711yescharacteristic
453C2×#103C22×C4711yescharacteristic
454C2×#102C22×C4711yescharacteristic
455C2×#102C22×C4711yescharacteristic
456C2×#102C22×C4711yescharacteristic
457C2×#102C22×C4711yescharacteristic
458C2×#102C22×C4711yescharacteristic
459C2×C22⋊C8C22×C4711yescharacteristic
460C2×C22⋊C8C22×C4711yescharacteristic
461C2×#97C22×C4711yescharacteristic
462#394—21no—
463#394—21no—
464#392—21no—
465#392—21no—
466#391C22×C4711yescharacteristic
467#390—21no—
468#390C22×C4711yescharacteristic
469#390C22×C4711yescharacteristic
470#389C22×C4711yescharacteristic
471#388—21no—
472#386—21no—
473#385—21no—
474#380C22×C4711yescharacteristic
475#380C22×C4711yescharacteristic
476#340C22×C4711yescharacteristic
477#340C22×C4711yescharacteristic
478#340C22×C4711yescharacteristic
479#340C22×C4711yescharacteristic
480C47#2513111yescharacteristic, direct product factor, Sylow
481C2×#41—22no—
482C2×#41—22no—
483C2×#41—22no—
484C2×#41—22no—
485C2×#41—41no—
486C2×#41—41no—
487C22×Q8C23×C4711yescharacteristic
488C22×D4—21no—
489C22×D4—21no—
490C22×D4—21no—
491C22×D4—21no—
492C22×D4D4×C4711yescharacteristic
493C22×D4C23×C4711yescharacteristic
494C22×D4C23×C4711yescharacteristic
495C23×C4—21no—
496C23×C4C23×C4711yescharacteristic
497C23×C4C23×C4711yescharacteristic
498C2×SD16—22no—
499C2×SD16—22no—
500C2×SD16—41no—
501C2×D8—22no—
502C2×D8—22no—
503C2×D8—41no—
504C2×M16—22no—
505C2×M16—22no—
506C2×M16—41no—
507C22×C8—22no—
508C22×C8—22no—
509C22×C8—41no—
510C22×C8C23×C4711yescharacteristic
511C22×C8C23×C4711yescharacteristic
512C22×C8C23×C4711yescharacteristic
513C22×C8C23×C4711yescharacteristic
514C22⋊Q8—22no—
515C22⋊Q8—41no—
516#121—22no—
517#121—22no—
518#121—22no—
519#121—22no—
520#121—41no—
521#121—41no—
522C4×D4—22no—
523C4×D4—22no—
524#117—22no—
525#117—41no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4D4×C4711yescharacteristic
529C2×C4⋊C4C23×C4711yescharacteristic
530C2×C4⋊C4C23×C4711yescharacteristic
531C2×C4⋊C4C23×C4711yescharacteristic
532C2×C4⋊C4C23×C4711yescharacteristic
533C2×C4⋊C4C23×C4711yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
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⋊C4D4×C4711yescharacteristic
546C2×C22⋊C4D4×C4711yescharacteristic
547C2×C42—21no—
548C2×C42C23×C4711yescharacteristic
549#107—22no—
550#106—41no—
551C4⋊C8—22no—
552#103—22no—
553#103—22no—
554#103D4×C4714yescomplemented
555#102—22no—
556#102—22no—
557#102—22no—
558#102—22no—
559#102—41no—
560C22⋊C8—22no—
561C22⋊C8D4×C4714yescomplemented
562#97—22no—
563#95—21no—
564#95—21no—
565#95—21no—
566#95—21no—
567#95—21no—
568C24—21no—
569C24—21no—
570C24C2×D4×C4711yescharacteristic
571C24C2×D4×C4711yescharacteristic
572#41—28no—
573#41—44no—
574#41—44no—
575#41—44no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8C2×D4×C4712yes—
582C2×D4—22no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—41no—
595C2×D4—41no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—42no—
601C2×D4—42no—
602C2×D4—42no—
603C2×D4—42no—
604C2×D4—81no—
605C2×D4—81no—
606C2×D4—81no—
607C2×D4—81no—
608C2×D4#41×C4712yes—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—42no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4C2×D4×C4711yescharacteristic
629C22×C4C2×D4×C4711yescharacteristic
630C22×C4C2×D4×C4711yescharacteristic
631C22×C4C2×D4×C4711yescharacteristic
632C22×C4C2×D4×C4712yes—
633C22×C4#41×C4712yes—
634C22×C4C24×C4711yescharacteristic
635SD16—44no—
636D8—44no—
637M16—44no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—44no—
648C2×C8C2×D4×C4712yes—
649C2×C8C2×D4×C4712yes—
650C2×C8C2×D4×C4712yes—
651C4⋊C4—22no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
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—
664C22⋊C4—22no—
665C22⋊C4—22no—
666C22⋊C4—42no—
667C22⋊C4—42no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C22⋊C4—42no—
671C22⋊C4—42no—
672C22⋊C4—42no—
673C22⋊C4—81no—
674C22⋊C4—81no—
675C22⋊C4—81no—
676C22⋊C4—81no—
677C42—21no—
678C42—21no—
679C42—42no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—22no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23#121×C4712yes—
708C23C22×D4×C4711yescharacteristic
709Q8—22no—
710Q8—22no—
711Q8—41no—
712Q8—41no—
713D4—22no—
714D4—22no—
715D4—44no—
716D4—48no—
717D4—41no—
718D4—41no—
719D4—41no—
720D4—41no—
721D4—41no—
722D4—41no—
723D4—84no—
724D4—84no—
725D4—84no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—22no—
736C2×C4—21no—
737C2×C4—22no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—48no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4#121×C4712yes—
765C2×C4C22×D4×C4711yescharacteristic
766C2×C4C22×D4×C4711yescharacteristic
767C2×C4C2×#41×C4711yescharacteristic
768C2×C4C2×#41×C4711yescharacteristic
769C2×C4H(5,𝔽2)×C4711yescharacteristic
770C2×C4H(5,𝔽2)×C4711yescharacteristic
771C8—22no—
772C8—22no—
773C8—22no—
774C8—41no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—42no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—42no—
788C22—42no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22C2×#121×C4711yescharacteristic
804C22D42×C4711yescharacteristic
805C22C47×#54611yescharacteristic
806C22C47×#57511yescharacteristic
807C22C47×#57511yescharacteristic
808C22C47×#57611yescharacteristic
809C22C47×#57711yescharacteristic
810C4—22no—
811C4—41no—
812C4—41no—
813C4—41no—
814C4—42no—
815C4—42no—
816C4—81no—
817C4—81no—
818C4—81no—
819C4—81no—
820C4C47×#52511yescharacteristic
821C4C47×#53811yescharacteristic
822C4D42×C4711yescharacteristic
823C4C47×#54611yescharacteristic
824C2—42no—
825C2—81no—
826C2—82no—
827C2—161no—
828C2C47×#242411yescharacteristic
829C2C47×#305411yescharacteristic
830C2C47×#306211yescharacteristic
831C2C47×#326811yescharacteristic
832C2C47×#327111yescharacteristic
833C2C47×#330711yescharacteristic
834C2C47×#331911yescharacteristic
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×#468C2semidirect
2. C2×C47×#449C2semidirect
3. C2×C47×#435C2semidirect
4. C2×C47×#416C2semidirect
5. C47×#2414C2semidirect
6. C47×#2407C2semidirect
7. C47×#2067C2semidirect
8. C47×#2055C2semidirect
9. C47×#2035C2semidirect
10. C47×#1999C2semidirect
11. C47×#1972C2semidirect
12. C47×#1935C2semidirect
13. C47×#1895C2semidirect
14. C47×#1893C2semidirect
15. C47×#1854C2semidirect
136. #103×C47D4semidirect
143. C22⋊C8×C47D4semidirect
357. #25131C47direct (N × H)
407. C2×#468C2×C47semidirect
408. C2×#449C2×C47semidirect
409. C2×#435C2×C47semidirect
410. C2×#416C2×C47semidirect
411. #2414C2×C47semidirect
412. #2407C2×C47semidirect
413. #2067C2×C47semidirect
414. #2055C2×C47semidirect
415. #2035C2×C47semidirect
416. #1999C2×C47semidirect
417. #1972C2×C47semidirect
418. #1935C2×C47semidirect
419. #1895C2×C47semidirect
420. #1893C2×C47semidirect
421. #1854C2×C47semidirect
480. C47#25131direct (N × H)
554. #103D4×C47semidirect
561. C22⋊C8D4×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×#4492
C2×C47×#4352
C2×C47×#4162
C47×#24142
C47×#24072
C47×#20672
C47×#20552
C47×#20352
C47×#19992
C47×#19722
C47×#19352
C47×#18952
C47×#18932
C47×#18542
#2513147