Finite Group Databasebeta

← C47×#25087 #26064785

Subgroups — C47×#25087 #26064785

Order 12032.

1192 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#466C211yesmaximal, characteristic, complemented
2C2×C47×#463C211yesmaximal, characteristic, complemented
3C2×C47×#449C211yesmaximal, characteristic, complemented
4C2×C47×#416C211yesmaximal, characteristic, complemented
5C47×#2431C211yesmaximal, characteristic, complemented
6C47×#2363C211yesmaximal, characteristic, complemented
7C47×#2067C211yesmaximal, characteristic, complemented
8C47×#2055C211yesmaximal, characteristic, complemented
9C47×#2042C211yesmaximal, characteristic, complemented
10C47×#2011C211yesmaximal, characteristic, complemented
11C47×#1982C211yesmaximal, characteristic, complemented
12C47×#1928C211yesmaximal, characteristic, complemented
13C47×#1879C211yesmaximal, characteristic, complemented
14C47×#1875C211yesmaximal, characteristic, complemented
15C47×#1850C211yesmaximal, characteristic, complemented
16C22×#41×C47C2211yescharacteristic
17C22×SD16×C47C2211yescharacteristic
18C22×D8×C47C2211yescharacteristic
19C22×D8×C47C2211yescharacteristic
20C23×C8×C47C2211yescharacteristic
21C2×#127×C47C2211yescharacteristic
22C2×#124×C47C2211yescharacteristic
23C2×#121×C47C2211yescharacteristic
24C2×#121×C47C2211yescharacteristic
25C2×C4×D4×C47C2211yescharacteristic
26C2×#117×C47C2211yescharacteristic
27C47×#466—24no—
28C47×#463—24no—
29C47×#449—24no—
30C2×#107×C47C2211yescharacteristic
31C2×C4⋊C8×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×#102×C47C2211yescharacteristic
43C2×#102×C47C2211yescharacteristic
44C2×C22⋊C8×C47C2211yescharacteristic
45C47×#392—21no—
46C47×#392—21no—
47C47×#391C2211yescharacteristic
48C47×#390—21no—
49C47×#390C2211yescharacteristic
50C47×#390C2211yescharacteristic
51C47×#389C2211yescharacteristic
52C47×#388—21no—
53C47×#386—21no—
54C47×#386—21no—
55C47×#386—21no—
56C4×C4⋊C4×C47C2211yescharacteristic
57C4×C22⋊C4×C47—21no—
58C4×C22⋊C4×C47C2211yescharacteristic
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×C47—21no—
75C22×D4×C47C2311yescharacteristic
76C22×D4×C47C2311yescharacteristic
77C22×D4×C47C2311yescharacteristic
78C23×C4×C47—21no—
79C23×C4×C47—21no—
80C23×C4×C47C2311yescharacteristic
81C2×SD16×C47—22no—
82C2×SD16×C47—22no—
83C2×SD16×C47—41no—
84C2×D8×C47—22no—
85C2×D8×C47—22no—
86C2×D8×C47—22no—
87C2×D8×C47—22no—
88C2×D8×C47—41no—
89C2×D8×C47—41no—
90C22×C8×C47—22no—
91C22×C8×C47—22no—
92C22×C8×C47—41no—
93C22×C8×C47C2311yescharacteristic
94C22×C8×C47C2311yescharacteristic
95C22×C8×C47C2311yescharacteristic
96C22×C8×C47C2311yescharacteristic
97#127×C47—22no—
98#127×C47—41no—
99#124×C47—22no—
100#124×C47—41no—
101#121×C47—22no—
102#121×C47—22no—
103#121×C47—22no—
104#121×C47D414yescomplemented
105C4×D4×C47—22no—
106C4×D4×C47—41no—
107#117×C47—22no—
108#117×C47—41no—
109C2×C4⋊C4×C47—21no—
110C2×C4⋊C4×C47C2311yescharacteristic
111C2×C4⋊C4×C47C2311yescharacteristic
112C2×C4⋊C4×C47C2311yescharacteristic
113C2×C4⋊C4×C47C2311yescharacteristic
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×C47D411yescharacteristic
125C2×C22⋊C4×C47D411yescharacteristic
126C2×C42×C47—21no—
127C2×C42×C47—21no—
128C2×C42×C47C2311yescharacteristic
129C2×C42×C47C2311yescharacteristic
130#107×C47—22no—
131C4⋊C8×C47—22no—
132C4⋊C8×C47—41no—
133#103×C47—22no—
134#103×C47—22no—
135#103×C47D414yescomplemented
136#102×C47—22no—
137#102×C47—22no—
138#102×C47—22no—
139#102×C47—22no—
140#102×C47—22no—
141#102×C47—22no—
142#102×C47—41no—
143C22⋊C8×C47—22no—
144#95×C47—21no—
145#95×C47—21no—
146#95×C47—21no—
147#95×C47—21no—
148#95×C47D411yescharacteristic
149#95×C47D411yescharacteristic
150C24×C47—21no—
151C24×C47—21no—
152C24×C47—21no—
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—24no—
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—21no—
177C2×D4×C47—21no—
178C2×D4×C47—21no—
179C2×D4×C47—21no—
180C2×D4×C47—21no—
181C2×D4×C47—42no—
182C2×D4×C47—42no—
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—81no—
190C2×D4×C47—81no—
191C2×D4×C47—81no—
192C2×D4×C47—81no—
193C2×D4×C47—81no—
194C2×D4×C47—81no—
195C2×D4×C47C2×D412yes—
196C2×D4×C47#4112yes—
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—42no—
207C22×C4×C47—42no—
208C22×C4×C47—42no—
209C22×C4×C47—42no—
210C22×C4×C47—42no—
211C22×C4×C47—81no—
212C22×C4×C47C2×D411yescharacteristic
213C22×C4×C47C2×D411yescharacteristic
214C22×C4×C47C2×D411yescharacteristic
215C22×C4×C47C2×D411yescharacteristic
216C22×C4×C47C2×D412yes—
217C22×C4×C47C2×D411yescharacteristic
218C22×C4×C47#4112yes—
219C22×C4×C47C2411yescharacteristic
220SD16×C47—44no—
221D8×C47—44no—
222D8×C47—44no—
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×C47—21no—
231C2×C8×C47—21no—
232C2×C8×C47—21no—
233C2×C8×C47—21no—
234C2×C8×C47—44no—
235C2×C8×C47C2×D412yes—
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—81no—
243C4⋊C4×C47C2×D412yes—
244C4⋊C4×C47C2×D412yes—
245C22⋊C4×C47—24no—
246C22⋊C4×C47—22no—
247C22⋊C4×C47—41no—
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—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—41no—
272C23×C47—41no—
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#12112yes—
291C23×C47C22×D411yescharacteristic
292Q8×C47—22no—
293Q8×C47—22no—
294Q8×C47—41no—
295Q8×C47—41no—
296D4×C47—22no—
297D4×C47—22no—
298D4×C47—22no—
299D4×C47—22no—
300D4×C47—48no—
301D4×C47—41no—
302D4×C47—41no—
303D4×C47—41no—
304D4×C47—41no—
305D4×C47—41no—
306D4×C47—41no—
307D4×C47—41no—
308D4×C47—41no—
309D4×C47—84no—
310D4×C47—84no—
311D4×C47—84no—
312D4×C47—84no—
313C2×C4×C47—21no—
314C2×C4×C47—21no—
315C2×C4×C47—21no—
316C2×C4×C47—21no—
317C2×C4×C47—22no—
318C2×C4×C47—22no—
319C2×C4×C47—22no—
320C2×C4×C47—22no—
321C2×C4×C47—22no—
322C2×C4×C47—21no—
323C2×C4×C47—21no—
324C2×C4×C47—22no—
325C2×C4×C47—22no—
326C2×C4×C47—21no—
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—48no—
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—84no—
347C2×C4×C47#12112yes—
348C2×C4×C47#13512yes—
349C2×C4×C47C22×D411yescharacteristic
350C2×C4×C47C22×D411yescharacteristic
351C2×C4×C47C2×#4111yescharacteristic
352C2×C4×C47C2×#4111yescharacteristic
353C2×C4×C47H(5,𝔽2)11yescharacteristic
354C2×C4×C47H(5,𝔽2)11yescharacteristic
355C8×C47—22no—
356C8×C47—41no—
357C8×C47—41no—
358C8×C47—41no—
359#25087C4711yesmaximal, characteristic, direct product factor, Sylow
360C22×C47—22no—
361C22×C47—22no—
362C22×C47—22no—
363C22×C47—41no—
364C22×C47—41no—
365C22×C47—41no—
366C22×C47—41no—
367C22×C47—42no—
368C22×C47—42no—
369C22×C47—42no—
370C22×C47—42no—
371C22×C47—42no—
372C22×C47—42no—
373C22×C47—81no—
374C22×C47—81no—
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×C47—81no—
387C22×C47—81no—
388C22×C47C2×#12111yescharacteristic
389C22×C47D4211yescharacteristic
390C22×C47#54611yescharacteristic
391C22×C47C2×#13511yescharacteristic
392C22×C47#57511yescharacteristic
393C22×C47#57611yescharacteristic
394C22×C47#57611yescharacteristic
395C4×C47—22no—
396C4×C47—22no—
397C4×C47—42no—
398C4×C47—41no—
399C4×C47—42no—
400C4×C47—41no—
401C4×C47—42no—
402C4×C47—41no—
403C4×C47—81no—
404C4×C47—81no—
405C4×C47#52511yescharacteristic
406C4×C47#53811yescharacteristic
407C4×C47D4211yescharacteristic
408C4×C47#54611yescharacteristic
409C2×#466C2×C4711yescharacteristic, complemented
410C2×#463C2×C4711yescharacteristic, complemented
411C2×#449C2×C4711yescharacteristic, complemented
412C2×#416C2×C4711yescharacteristic, complemented
413#2431C2×C4711yescharacteristic, complemented
414#2363C2×C4711yescharacteristic, complemented
415#2067C2×C4711yescharacteristic, complemented
416#2055C2×C4711yescharacteristic, complemented
417#2042C2×C4711yescharacteristic, complemented
418#2011C2×C4711yescharacteristic, complemented
419#1982C2×C4711yescharacteristic, complemented
420#1928C2×C4711yescharacteristic, complemented
421#1879C2×C4711yescharacteristic, complemented
422#1875C2×C4711yescharacteristic, complemented
423#1850C2×C4711yescharacteristic, complemented
424C2×C47—42no—
425C2×C47—82no—
426C2×C47—82no—
427C2×C47—161no—
428C2×C47#242411yescharacteristic
429C2×C47#303511yescharacteristic
430C2×C47#304111yescharacteristic
431C2×C47#326811yescharacteristic
432C2×C47#328711yescharacteristic
433C2×C47#329711yescharacteristic
434C2×C47#331911yescharacteristic
435C22×#41C22×C4711yescharacteristic
436C22×SD16C22×C4711yescharacteristic
437C22×D8C22×C4711yescharacteristic
438C22×D8C22×C4711yescharacteristic
439C23×C8C22×C4711yescharacteristic
440C2×#127C22×C4711yescharacteristic
441C2×#124C22×C4711yescharacteristic
442C2×#121C22×C4711yescharacteristic
443C2×#121C22×C4711yescharacteristic
444C2×C4×D4C22×C4711yescharacteristic
445C2×#117C22×C4711yescharacteristic
446#466—24no—
447#463—24no—
448#449—24no—
449C2×#107C22×C4711yescharacteristic
450C2×C4⋊C8C22×C4711yescharacteristic
451C2×C4⋊C8C22×C4711yescharacteristic
452#416—24no—
453C2×#103C22×C4711yescharacteristic
454C2×#103C22×C4711yescharacteristic
455C2×#103C22×C4711yescharacteristic
456C2×#102C22×C4711yescharacteristic
457C2×#102C22×C4711yescharacteristic
458C2×#102C22×C4711yescharacteristic
459C2×#102C22×C4711yescharacteristic
460C2×#102C22×C4711yescharacteristic
461C2×#102C22×C4711yescharacteristic
462C2×#102C22×C4711yescharacteristic
463C2×C22⋊C8C22×C4711yescharacteristic
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#386—21no—
474#386—21no—
475C4×C4⋊C4C22×C4711yescharacteristic
476C4×C22⋊C4—21no—
477C4×C22⋊C4C22×C4711yescharacteristic
478#340C22×C4711yescharacteristic
479#340C22×C4711yescharacteristic
480#336C22×C4711yescharacteristic
481#336C22×C4711yescharacteristic
482C47#2508711yescharacteristic, direct product factor, Sylow
483C2×#41—22no—
484C2×#41—22no—
485C2×#41—22no—
486C2×#41—22no—
487C2×#41—41no—
488C2×#41—41no—
489C22×Q8C23×C4711yescharacteristic
490C22×D4—21no—
491C22×D4—21no—
492C22×D4—21no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4C23×C4711yescharacteristic
496C22×D4C23×C4711yescharacteristic
497C22×D4C23×C4711yescharacteristic
498C23×C4—21no—
499C23×C4—21no—
500C23×C4C23×C4711yescharacteristic
501C2×SD16—22no—
502C2×SD16—22no—
503C2×SD16—41no—
504C2×D8—22no—
505C2×D8—22no—
506C2×D8—22no—
507C2×D8—22no—
508C2×D8—41no—
509C2×D8—41no—
510C22×C8—22no—
511C22×C8—22no—
512C22×C8—41no—
513C22×C8C23×C4711yescharacteristic
514C22×C8C23×C4711yescharacteristic
515C22×C8C23×C4711yescharacteristic
516C22×C8C23×C4711yescharacteristic
517#127—22no—
518#127—41no—
519#124—22no—
520#124—41no—
521#121—22no—
522#121—22no—
523#121—22no—
524#121D4×C4714yescomplemented
525C4×D4—22no—
526C4×D4—41no—
527#117—22no—
528#117—41no—
529C2×C4⋊C4—21no—
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⋊C4D4×C4711yescharacteristic
545C2×C22⋊C4D4×C4711yescharacteristic
546C2×C42—21no—
547C2×C42—21no—
548C2×C42C23×C4711yescharacteristic
549C2×C42C23×C4711yescharacteristic
550#107—22no—
551C4⋊C8—22no—
552C4⋊C8—41no—
553#103—22no—
554#103—22no—
555#103D4×C4714yescomplemented
556#102—22no—
557#102—22no—
558#102—22no—
559#102—22no—
560#102—22no—
561#102—22no—
562#102—41no—
563C22⋊C8—22no—
564#95—21no—
565#95—21no—
566#95—21no—
567#95—21no—
568#95D4×C4711yescharacteristic
569#95D4×C4711yescharacteristic
570C24—21no—
571C24—21no—
572C24—21no—
573C24C2×D4×C4711yescharacteristic
574#41—28no—
575#41—44no—
576#41—44no—
577#41—44no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8C2×D4×C4712yes—
584C2×D4—24no—
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—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—42no—
602C2×D4—42no—
603C2×D4—42no—
604C2×D4—42no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—81no—
610C2×D4—81no—
611C2×D4—81no—
612C2×D4—81no—
613C2×D4—81no—
614C2×D4—81no—
615C2×D4C2×D4×C4712yes—
616C2×D4#41×C4712yes—
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—21no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4—42no—
629C22×C4—42no—
630C22×C4—42no—
631C22×C4—81no—
632C22×C4C2×D4×C4711yescharacteristic
633C22×C4C2×D4×C4711yescharacteristic
634C22×C4C2×D4×C4711yescharacteristic
635C22×C4C2×D4×C4711yescharacteristic
636C22×C4C2×D4×C4712yes—
637C22×C4C2×D4×C4711yescharacteristic
638C22×C4#41×C4712yes—
639C22×C4C24×C4711yescharacteristic
640SD16—44no—
641D8—44no—
642D8—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×C8—44no—
655C2×C8C2×D4×C4712yes—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—81no—
663C4⋊C4C2×D4×C4712yes—
664C4⋊C4C2×D4×C4712yes—
665C22⋊C4—24no—
666C22⋊C4—22no—
667C22⋊C4—41no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C22⋊C4—42no—
671C22⋊C4—42no—
672C22⋊C4—42no—
673C22⋊C4—42no—
674C22⋊C4—81no—
675C22⋊C4—81no—
676C22⋊C4—81no—
677C42—21no—
678C42—21no—
679C42—21no—
680C42—21no—
681C42—42no—
682C42—81no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—22no—
690C23—22no—
691C23—41no—
692C23—41no—
693C23—41no—
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—41no—
708C23—41no—
709C23—41no—
710C23#121×C4712yes—
711C23C22×D4×C4711yescharacteristic
712Q8—22no—
713Q8—22no—
714Q8—41no—
715Q8—41no—
716D4—22no—
717D4—22no—
718D4—22no—
719D4—22no—
720D4—48no—
721D4—41no—
722D4—41no—
723D4—41no—
724D4—41no—
725D4—41no—
726D4—41no—
727D4—41no—
728D4—41no—
729D4—84no—
730D4—84no—
731D4—84no—
732D4—84no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—48no—
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—41no—
765C2×C4—41no—
766C2×C4—84no—
767C2×C4#121×C4712yes—
768C2×C4#135×C4712yes—
769C2×C4C22×D4×C4711yescharacteristic
770C2×C4C22×D4×C4711yescharacteristic
771C2×C4C2×#41×C4711yescharacteristic
772C2×C4C2×#41×C4711yescharacteristic
773C2×C4H(5,𝔽2)×C4711yescharacteristic
774C2×C4H(5,𝔽2)×C4711yescharacteristic
775C8—22no—
776C8—41no—
777C8—41no—
778C8—41no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22C2×#121×C4711yescharacteristic
808C22D42×C4711yescharacteristic
809C22C47×#54611yescharacteristic
810C22C2×#135×C4711yescharacteristic
811C22C47×#57511yescharacteristic
812C22C47×#57611yescharacteristic
813C22C47×#57611yescharacteristic
814C4—22no—
815C4—22no—
816C4—41no—
817C4—42no—
818C4—41no—
819C4—42no—
820C4—41no—
821C4—42no—
822C4—81no—
823C4—81no—
824C4C47×#52511yescharacteristic
825C4C47×#53811yescharacteristic
826C4D42×C4711yescharacteristic
827C4C47×#54611yescharacteristic
828C2—42no—
829C2—82no—
830C2—82no—
831C2—161no—
832C2C47×#242411yescharacteristic
833C2C47×#303511yescharacteristic
834C2C47×#304111yescharacteristic
835C2C47×#326811yescharacteristic
836C2C47×#328711yescharacteristic
837C2C47×#329711yescharacteristic
838C2C47×#331911yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
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×#466C2semidirect
2. C2×C47×#463C2semidirect
3. C2×C47×#449C2semidirect
4. C2×C47×#416C2semidirect
5. C47×#2431C2semidirect
6. C47×#2363C2semidirect
7. C47×#2067C2semidirect
8. C47×#2055C2semidirect
9. C47×#2042C2semidirect
10. C47×#2011C2semidirect
11. C47×#1982C2semidirect
12. C47×#1928C2semidirect
13. C47×#1879C2semidirect
14. C47×#1875C2semidirect
15. C47×#1850C2semidirect
104. #121×C47D4semidirect
135. #103×C47D4semidirect
359. #25087C47direct (N × H)
409. C2×#466C2×C47semidirect
410. C2×#463C2×C47semidirect
411. C2×#449C2×C47semidirect
412. C2×#416C2×C47semidirect
413. #2431C2×C47semidirect
414. #2363C2×C47semidirect
415. #2067C2×C47semidirect
416. #2055C2×C47semidirect
417. #2042C2×C47semidirect
418. #2011C2×C47semidirect
419. #1982C2×C47semidirect
420. #1928C2×C47semidirect
421. #1879C2×C47semidirect
422. #1875C2×C47semidirect
423. #1850C2×C47semidirect
482. C47#25087direct (N × H)
524. #121D4×C47semidirect
555. #103D4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#4662
C2×C47×#4632
C2×C47×#4492
C2×C47×#4162
C47×#24312
C47×#23632
C47×#20672
C47×#20552
C47×#20422
C47×#20112
C47×#19822
C47×#19282
C47×#18792
C47×#18752
C47×#18502
#2508747