Finite Group Databasebeta

← C47×#22062 #26061760

Subgroups — C47×#22062 #26061760

Order 12032.

900 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
1C47×#3002C211yesmaximal, characteristic
2C47×#2930C211yesmaximal, characteristic, complemented
3C47×#2879C211yesmaximal, characteristic, complemented
4C47×#1975C211yesmaximal, characteristic, complemented
5C47×#1974C211yesmaximal, characteristic, complemented
6C47×#1938C211yesmaximal, characteristic, complemented
7C47×#1937C211yesmaximal, characteristic, complemented
8C47×#1929C211yesmaximal, characteristic, complemented
9C47×#1929C211yesmaximal, characteristic, complemented
10C47×#1876C211yesmaximal, characteristic, complemented
11C47×#1876C211yesmaximal, characteristic, complemented
12C47×#1871C211yesmaximal, characteristic, complemented
13C47×#1855C211yesmaximal, characteristic, complemented
14C47×#1789C211yesmaximal, characteristic, complemented
15C47×#1753C211yesmaximal, characteristic, complemented
16C22×#41×C47C2211yescharacteristic
17C2×#135×C47C2211yescharacteristic
18C2×#135×C47C2211yescharacteristic
19C2×#131×C47C2211yescharacteristic, complemented
20C22×M16×C47C2211yescharacteristic
21C22×M16×C47C2211yescharacteristic
22C47×#525C2211yescharacteristic
23C47×#452C411yescharacteristic, complemented
24C47×#452C411yescharacteristic, complemented
25C47×#451C411yescharacteristic, complemented
26C47×#450C411yescharacteristic, complemented
27C47×#449C411yescharacteristic, complemented
28C47×#449C411yescharacteristic, complemented
29C47×#448C411yescharacteristic, complemented
30C47×#447C411yescharacteristic, complemented
31C47×#436—21no—
32C47×#436—21no—
33C47×#435—21no—
34C47×#435—21no—
35C2×#108×C47C2211yescharacteristic, complemented
36C2×#108×C47C2211yescharacteristic, complemented
37C47×#424C2211yescharacteristic, complemented
38C2×#104×C47C2211yescharacteristic
39C2×#104×C47C2211yescharacteristic
40C2×#104×C47C2211yescharacteristic
41C2×#104×C47C2211yescharacteristic
42C2×#104×C47C2211yescharacteristic, complemented
43C2×#104×C47C2211yescharacteristic, complemented
44C47×#416C2211yescharacteristic
45C47×#416C2211yescharacteristic
46C47×#408—21no—
47C47×#408—21no—
48C47×#408C2211yescharacteristic
49C47×#408C2211yescharacteristic
50C47×#408C2211yescharacteristic
51C47×#408C2211yescharacteristic
52C47×#408C2211yescharacteristic, complemented
53C47×#407—21no—
54C47×#407—21no—
55C47×#407C2211yescharacteristic
56C2×C22⋊C8×C47C2211yescharacteristic
57C47×#405C2211yescharacteristic, complemented
58C2×#97×C47C2211yescharacteristic, complemented
59C2×C4×C8×C47C2211yescharacteristic, complemented
60C4×C22⋊C4×C47C2211yescharacteristic
61C47×#341C2211yescharacteristic, complemented
62C47×#341C2211yescharacteristic, complemented
63C47×#339C2211yescharacteristic, complemented
64C47×#339C2211yescharacteristic, complemented
65C47×#336C2211yescharacteristic, complemented
66C47×#336C2211yescharacteristic, complemented
67C2×#41×C47—21no—
68C2×#41×C47—21no—
69C2×#41×C47—41no—
70C2×#41×C47—41no—
71C2×#41×C47—41no—
72C2×#41×C47—41no—
73C2×#41×C47C2×C411yescharacteristic
74C2×#41×C47C2×C411yescharacteristic
75C2×#41×C47C2311yescharacteristic
76C2×#41×C47C2311yescharacteristic
77C2×#41×C47C2311yescharacteristic
78C22×Q8×C47C2×C411yescharacteristic
79C22×D4×C47—21no—
80C22×D4×C47C2×C411yescharacteristic
81C23×C4×C47—21no—
82C23×C4×C47C2311yescharacteristic
83#135×C47—41no—
84#135×C47—41no—
85#135×C47—41no—
86#135×C47—41no—
87C2×Q16×C47C2×C411yescharacteristic
88C2×Q16×C47C2×C411yescharacteristic
89C2×SD16×C47C2×C411yescharacteristic
90C2×SD16×C47C2×C411yescharacteristic
91C2×SD16×C47C2×C411yescharacteristic
92C2×SD16×C47C2×C411yescharacteristic
93C2×D8×C47C2×C411yescharacteristic
94C2×D8×C47C2×C411yescharacteristic
95#131×C47—41no—
96#131×C47—41no—
97C2×M16×C47—21no—
98C2×M16×C47—21no—
99C2×M16×C47—41no—
100C2×M16×C47—41no—
101C2×M16×C47—41no—
102C2×M16×C47—41no—
103C2×M16×C47D411yescharacteristic
104C2×M16×C47D411yescharacteristic
105C2×M16×C47D411yescharacteristic
106C2×M16×C47D411yescharacteristic
107C2×M16×C47C2311yescharacteristic
108C2×M16×C47C2311yescharacteristic
109C2×M16×C47C2311yescharacteristic
110C2×M16×C47C2311yescharacteristic
111C22×C8×C47—21no—
112C22×C8×C47—21no—
113C22×C8×C47C2311yescharacteristic
114C22×C8×C47C2311yescharacteristic
115C22×C8×C47C2311yescharacteristic
116C22×C8×C47C2311yescharacteristic
117#123×C47—21no—
118C22⋊Q8×C47C2×C411yescharacteristic
119C22⋊Q8×C47C2×C411yescharacteristic
120#121×C47C2×C411yescharacteristic
121#121×C47C2×C411yescharacteristic
122#120×C47—21no—
123C4×D4×C47—21no—
124C4×D4×C47—21no—
125#117×C47C2311yescharacteristic
126C2×C22⋊C4×C47—21no—
127C2×C42×C47C2311yescharacteristic
128C2×C42×C47C2311yescharacteristic
129#108×C47—41no—
130#108×C47—41no—
131C4⋊C8×C47—21no—
132C4⋊C8×C47—21no—
133#104×C47—41no—
134#104×C47—41no—
135#104×C47—41no—
136#104×C47—41no—
137#104×C47—41no—
138#104×C47—41no—
139#103×C47C2×C411yescharacteristic
140#103×C47C2×C411yescharacteristic
141#103×C47C2×C411yescharacteristic
142#103×C47C2×C411yescharacteristic
143#102×C47C2×C411yescharacteristic
144#102×C47C2×C411yescharacteristic
145#102×C47C2×C411yescharacteristic
146#102×C47C2×C411yescharacteristic
147C22⋊C8×C47—21no—
148C22⋊C8×C47—21no—
149C22⋊C8×C47—21no—
150C22⋊C8×C47—21no—
151C22⋊C8×C47—21no—
152C22⋊C8×C47—21no—
153C22⋊C8×C47—21no—
154C22⋊C8×C47—21no—
155C22⋊C8×C47—21no—
156C22⋊C8×C47—21no—
157C22⋊C8×C47—21no—
158C22⋊C8×C47—21no—
159C22⋊C8×C47C2×C411yescharacteristic
160C22⋊C8×C47C2×C411yescharacteristic
161C22⋊C8×C47C2×C411yescharacteristic
162C22⋊C8×C47C2×C411yescharacteristic
163#97×C47—21no—
164#97×C47—41no—
165C4×C8×C47—21no—
166C4×C8×C47—41no—
167#95×C47—21no—
168C24×C47—21no—
169C24×C47#4111yescharacteristic
170#41×C47—21no—
171#41×C47—21no—
172#41×C47—21no—
173#41×C47—21no—
174#41×C47—21no—
175#41×C47—21no—
176#41×C47—21no—
177#41×C47—21no—
178#41×C47—21no—
179#41×C47—21no—
180#41×C47—21no—
181#41×C47—21no—
182#41×C47—41no—
183#41×C47—41no—
184#41×C47—41no—
185#41×C47—41no—
186#41×C47—42no—
187#41×C47—42no—
188#41×C47—42no—
189#41×C47—42no—
190C2×Q8×C47—21no—
191C2×Q8×C47—41no—
192C2×Q8×C47—41no—
193C2×Q8×C47C22×C411yescharacteristic
194C2×Q8×C47C22×C411yescharacteristic
195C2×Q8×C47C22×C411yescharacteristic
196C2×D4×C47—21no—
197C2×D4×C47—21no—
198C2×D4×C47—21no—
199C2×D4×C47—21no—
200C2×D4×C47—21no—
201C2×D4×C47—21no—
202C2×D4×C47—21no—
203C2×D4×C47—21no—
204C2×D4×C47—41no—
205C2×D4×C47—41no—
206C2×D4×C47—42no—
207C2×D4×C47—42no—
208C2×D4×C47C22×C411yescharacteristic
209C2×D4×C47C22×C411yescharacteristic
210C2×D4×C47C22×C411yescharacteristic
211C22×C4×C47—21no—
212C22×C4×C47—21no—
213C22×C4×C47—21no—
214C22×C4×C47—21no—
215C22×C4×C47—21no—
216C22×C4×C47—21no—
217C22×C4×C47—21no—
218C22×C4×C47—21no—
219C22×C4×C47—21no—
220C22×C4×C47—21no—
221C22×C4×C47—21no—
222C22×C4×C47—21no—
223C22×C4×C47—42no—
224C22×C4×C47—42no—
225C22×C4×C47C22×C411yescharacteristic
226C22×C4×C47C22×C411yescharacteristic
227C22×C4×C47C2×D411yescharacteristic
228C22×C4×C47C2×D411yescharacteristic
229C22×C4×C47#4111yescharacteristic
230C22×C4×C47C2411yescharacteristic
231Q16×C47—41no—
232Q16×C47—41no—
233SD16×C47—41no—
234SD16×C47—41no—
235SD16×C47—41no—
236SD16×C47—41no—
237D8×C47—41no—
238D8×C47—41no—
239M16×C47—21no—
240M16×C47—21no—
241M16×C47—21no—
242M16×C47—21no—
243M16×C47—21no—
244M16×C47—21no—
245M16×C47—21no—
246M16×C47—21no—
247M16×C47—41no—
248M16×C47—41no—
249M16×C47—41no—
250M16×C47—41no—
251M16×C47—42no—
252M16×C47—42no—
253C2×C8×C47—21no—
254C2×C8×C47—21no—
255C2×C8×C47—21no—
256C2×C8×C47—21no—
257C2×C8×C47—21no—
258C2×C8×C47—21no—
259C2×C8×C47—21no—
260C2×C8×C47—21no—
261C2×C8×C47—21no—
262C2×C8×C47—21no—
263C2×C8×C47—21no—
264C2×C8×C47—21no—
265C2×C8×C47—42no—
266C2×C8×C47—42no—
267C2×C8×C47C22×C411yescharacteristic
268C2×C8×C47C22×C411yescharacteristic
269C2×C8×C47C22×C411yescharacteristic
270C2×C8×C47C22×C411yescharacteristic
271C2×C8×C47C2×D411yescharacteristic
272C2×C8×C47C2×D411yescharacteristic
273C2×C8×C47C2×D411yescharacteristic
274C2×C8×C47C2×D411yescharacteristic
275C4⋊C4×C47—21no—
276C4⋊C4×C47—21no—
277C4⋊C4×C47C22×C411yescharacteristic
278C4⋊C4×C47C22×C411yescharacteristic
279C22⋊C4×C47—21no—
280C22⋊C4×C47—21no—
281C22⋊C4×C47—21no—
282C22⋊C4×C47—21no—
283C22⋊C4×C47—21no—
284C22⋊C4×C47—42no—
285C42×C47—21no—
286C42×C47—21no—
287C42×C47—21no—
288C42×C47—21no—
289C42×C47—21no—
290C23×C47—21no—
291C23×C47—21no—
292C23×C47—21no—
293C23×C47—21no—
294C23×C47—21no—
295C23×C47—41no—
296C23×C47—41no—
297C23×C47—42no—
298C23×C47—81no—
299C23×C47—81no—
300C23×C47C4×D411yescharacteristic
301C23×C47C4×D411yescharacteristic
302C23×C47C2×#4111yescharacteristic
303Q8×C47—21no—
304Q8×C47—21no—
305Q8×C47—21no—
306Q8×C47—21no—
307Q8×C47—21no—
308Q8×C47—21no—
309Q8×C47—42no—
310D4×C47—21no—
311D4×C47—21no—
312D4×C47—21no—
313D4×C47—21no—
314D4×C47—21no—
315D4×C47—21no—
316D4×C47—42no—
317D4×C47—42no—
318D4×C47—42no—
319D4×C47—41no—
320D4×C47—41no—
321D4×C47—41no—
322D4×C47—41no—
323D4×C47—41no—
324D4×C47—41no—
325D4×C47—81no—
326D4×C47—81no—
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—22no—
338C2×C4×C47—21no—
339C2×C4×C47—21no—
340C2×C4×C47—21no—
341C2×C4×C47—21no—
342C2×C4×C47—21no—
343C2×C4×C47—42no—
344C2×C4×C47—42no—
345C2×C4×C47—41no—
346C2×C4×C47—42no—
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—41no—
356C2×C4×C47—41no—
357C2×C4×C47C4×D411yescharacteristic
358C2×C4×C47C4×D411yescharacteristic
359C2×C4×C47C23×C411yescharacteristic
360C2×C4×C47C22×D411yescharacteristic
361C2×C4×C47H(5,𝔽2)11yescharacteristic
362C2×C4×C47H(5,𝔽2)11yescharacteristic
363C2×C4×C47H(5,𝔽2)11yescharacteristic
364C2×C4×C47H(5,𝔽2)11yescharacteristic
365C8×C47—21no—
366C8×C47—21no—
367C8×C47—21no—
368C8×C47—21no—
369C8×C47—21no—
370C8×C47—21no—
371C8×C47—21no—
372C8×C47—21no—
373C8×C47—41no—
374C8×C47—41no—
375C8×C47—41no—
376C8×C47—41no—
377#22062C4711yesmaximal, characteristic, direct product factor, Sylow
378C22×C47—21no—
379C22×C47—21no—
380C22×C47—21no—
381C22×C47—21no—
382C22×C47—21no—
383C22×C47—21no—
384C22×C47—21no—
385C22×C47—21no—
386C22×C47—41no—
387C22×C47—41no—
388C22×C47—41no—
389C22×C47—41no—
390C22×C47—41no—
391C22×C47—41no—
392C22×C47—41no—
393C22×C47—41no—
394C22×C47—41no—
395C22×C47—81no—
396C22×C47—81no—
397C22×C47—84no—
398C22×C47C2×C4×D411yescharacteristic
399C22×C47#53811yescharacteristic
400C22×C47#53811yescharacteristic
401C4×C47—21no—
402C4×C47—21no—
403C4×C47—42no—
404C4×C47—41no—
405C4×C47—41no—
406C4×C47—41no—
407C4×C47—41no—
408C4×C47—41no—
409C4×C47—81no—
410C4×C47#51811yescharacteristic
411C4×C47#51811yescharacteristic
412C4×C47#53411yescharacteristic
413C4×C47#53511yescharacteristic
414#3002C2×C4711yescharacteristic
415#2930C2×C4711yescharacteristic, complemented
416#2879C2×C4711yescharacteristic, complemented
417#1975C2×C4711yescharacteristic, complemented
418#1974C2×C4711yescharacteristic, complemented
419#1938C2×C4711yescharacteristic, complemented
420#1937C2×C4711yescharacteristic, complemented
421#1929C2×C4711yescharacteristic, complemented
422#1929C2×C4711yescharacteristic, complemented
423#1876C2×C4711yescharacteristic, complemented
424#1876C2×C4711yescharacteristic, complemented
425#1871C2×C4711yescharacteristic, complemented
426#1855C2×C4711yescharacteristic, complemented
427#1789C2×C4711yescharacteristic, complemented
428#1753C2×C4711yescharacteristic, complemented
429C2×C47—21no—
430C2×C47—21no—
431C2×C47—41no—
432C2×C47—41no—
433C2×C47—81no—
434C2×C47—81no—
435C2×C47—81no—
436C2×C47#232111yescharacteristic
437C2×C47#295611yescharacteristic
438C2×C47#295711yescharacteristic
439C22×#41C22×C4711yescharacteristic
440C2×#135C22×C4711yescharacteristic
441C2×#135C22×C4711yescharacteristic
442C2×#131C22×C4711yescharacteristic, complemented
443C22×M16C22×C4711yescharacteristic
444C22×M16C22×C4711yescharacteristic
445#525C22×C4711yescharacteristic
446#452C4×C4711yescharacteristic, complemented
447#452C4×C4711yescharacteristic, complemented
448#451C4×C4711yescharacteristic, complemented
449#450C4×C4711yescharacteristic, complemented
450#449C4×C4711yescharacteristic, complemented
451#449C4×C4711yescharacteristic, complemented
452#448C4×C4711yescharacteristic, complemented
453#447C4×C4711yescharacteristic, complemented
454#436—21no—
455#436—21no—
456#435—21no—
457#435—21no—
458C2×#108C22×C4711yescharacteristic, complemented
459C2×#108C22×C4711yescharacteristic, complemented
460#424C22×C4711yescharacteristic, complemented
461C2×#104C22×C4711yescharacteristic
462C2×#104C22×C4711yescharacteristic
463C2×#104C22×C4711yescharacteristic
464C2×#104C22×C4711yescharacteristic
465C2×#104C22×C4711yescharacteristic, complemented
466C2×#104C22×C4711yescharacteristic, complemented
467#416C22×C4711yescharacteristic
468#416C22×C4711yescharacteristic
469#408—21no—
470#408—21no—
471#408C22×C4711yescharacteristic
472#408C22×C4711yescharacteristic
473#408C22×C4711yescharacteristic
474#408C22×C4711yescharacteristic
475#408C22×C4711yescharacteristic, complemented
476#407—21no—
477#407—21no—
478#407C22×C4711yescharacteristic
479C2×C22⋊C8C22×C4711yescharacteristic
480#405C22×C4711yescharacteristic, complemented
481C2×#97C22×C4711yescharacteristic, complemented
482C2×C4×C8C22×C4711yescharacteristic, complemented
483C4×C22⋊C4C22×C4711yescharacteristic
484#341C22×C4711yescharacteristic, complemented
485#341C22×C4711yescharacteristic, complemented
486#339C22×C4711yescharacteristic, complemented
487#339C22×C4711yescharacteristic, complemented
488#336C22×C4711yescharacteristic, complemented
489#336C22×C4711yescharacteristic, complemented
490C47#2206211yescharacteristic, direct product factor, Sylow
491C2×#41—21no—
492C2×#41—21no—
493C2×#41—41no—
494C2×#41—41no—
495C2×#41—41no—
496C2×#41—41no—
497C2×#41C2×C4×C4711yescharacteristic
498C2×#41C2×C4×C4711yescharacteristic
499C2×#41C23×C4711yescharacteristic
500C2×#41C23×C4711yescharacteristic
501C2×#41C23×C4711yescharacteristic
502C22×Q8C2×C4×C4711yescharacteristic
503C22×D4—21no—
504C22×D4C2×C4×C4711yescharacteristic
505C23×C4—21no—
506C23×C4C23×C4711yescharacteristic
507#135—41no—
508#135—41no—
509#135—41no—
510#135—41no—
511C2×Q16C2×C4×C4711yescharacteristic
512C2×Q16C2×C4×C4711yescharacteristic
513C2×SD16C2×C4×C4711yescharacteristic
514C2×SD16C2×C4×C4711yescharacteristic
515C2×SD16C2×C4×C4711yescharacteristic
516C2×SD16C2×C4×C4711yescharacteristic
517C2×D8C2×C4×C4711yescharacteristic
518C2×D8C2×C4×C4711yescharacteristic
519#131—41no—
520#131—41no—
521C2×M16—21no—
522C2×M16—21no—
523C2×M16—41no—
524C2×M16—41no—
525C2×M16—41no—
526C2×M16—41no—
527C2×M16D4×C4711yescharacteristic
528C2×M16D4×C4711yescharacteristic
529C2×M16D4×C4711yescharacteristic
530C2×M16D4×C4711yescharacteristic
531C2×M16C23×C4711yescharacteristic
532C2×M16C23×C4711yescharacteristic
533C2×M16C23×C4711yescharacteristic
534C2×M16C23×C4711yescharacteristic
535C22×C8—21no—
536C22×C8—21no—
537C22×C8C23×C4711yescharacteristic
538C22×C8C23×C4711yescharacteristic
539C22×C8C23×C4711yescharacteristic
540C22×C8C23×C4711yescharacteristic
541#123—21no—
542C22⋊Q8C2×C4×C4711yescharacteristic
543C22⋊Q8C2×C4×C4711yescharacteristic
544#121C2×C4×C4711yescharacteristic
545#121C2×C4×C4711yescharacteristic
546#120—21no—
547C4×D4—21no—
548C4×D4—21no—
549#117C23×C4711yescharacteristic
550C2×C22⋊C4—21no—
551C2×C42C23×C4711yescharacteristic
552C2×C42C23×C4711yescharacteristic
553#108—41no—
554#108—41no—
555C4⋊C8—21no—
556C4⋊C8—21no—
557#104—41no—
558#104—41no—
559#104—41no—
560#104—41no—
561#104—41no—
562#104—41no—
563#103C2×C4×C4711yescharacteristic
564#103C2×C4×C4711yescharacteristic
565#103C2×C4×C4711yescharacteristic
566#103C2×C4×C4711yescharacteristic
567#102C2×C4×C4711yescharacteristic
568#102C2×C4×C4711yescharacteristic
569#102C2×C4×C4711yescharacteristic
570#102C2×C4×C4711yescharacteristic
571C22⋊C8—21no—
572C22⋊C8—21no—
573C22⋊C8—21no—
574C22⋊C8—21no—
575C22⋊C8—21no—
576C22⋊C8—21no—
577C22⋊C8—21no—
578C22⋊C8—21no—
579C22⋊C8—21no—
580C22⋊C8—21no—
581C22⋊C8—21no—
582C22⋊C8—21no—
583C22⋊C8C2×C4×C4711yescharacteristic
584C22⋊C8C2×C4×C4711yescharacteristic
585C22⋊C8C2×C4×C4711yescharacteristic
586C22⋊C8C2×C4×C4711yescharacteristic
587#97—21no—
588#97—41no—
589C4×C8—21no—
590C4×C8—41no—
591#95—21no—
592C24—21no—
593C24#41×C4711yescharacteristic
594#41—21no—
595#41—21no—
596#41—21no—
597#41—21no—
598#41—21no—
599#41—21no—
600#41—21no—
601#41—21no—
602#41—21no—
603#41—21no—
604#41—21no—
605#41—21no—
606#41—41no—
607#41—41no—
608#41—41no—
609#41—41no—
610#41—42no—
611#41—42no—
612#41—42no—
613#41—42no—
614C2×Q8—21no—
615C2×Q8—41no—
616C2×Q8—41no—
617C2×Q8C22×C4×C4711yescharacteristic
618C2×Q8C22×C4×C4711yescharacteristic
619C2×Q8C22×C4×C4711yescharacteristic
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—41no—
629C2×D4—41no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4C22×C4×C4711yescharacteristic
633C2×D4C22×C4×C4711yescharacteristic
634C2×D4C22×C4×C4711yescharacteristic
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—42no—
648C22×C4—42no—
649C22×C4C22×C4×C4711yescharacteristic
650C22×C4C22×C4×C4711yescharacteristic
651C22×C4C2×D4×C4711yescharacteristic
652C22×C4C2×D4×C4711yescharacteristic
653C22×C4#41×C4711yescharacteristic
654C22×C4C24×C4711yescharacteristic
655Q16—41no—
656Q16—41no—
657SD16—41no—
658SD16—41no—
659SD16—41no—
660SD16—41no—
661D8—41no—
662D8—41no—
663M16—21no—
664M16—21no—
665M16—21no—
666M16—21no—
667M16—21no—
668M16—21no—
669M16—21no—
670M16—21no—
671M16—41no—
672M16—41no—
673M16—41no—
674M16—41no—
675M16—42no—
676M16—42no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—42no—
690C2×C8—42no—
691C2×C8C22×C4×C4711yescharacteristic
692C2×C8C22×C4×C4711yescharacteristic
693C2×C8C22×C4×C4711yescharacteristic
694C2×C8C22×C4×C4711yescharacteristic
695C2×C8C2×D4×C4711yescharacteristic
696C2×C8C2×D4×C4711yescharacteristic
697C2×C8C2×D4×C4711yescharacteristic
698C2×C8C2×D4×C4711yescharacteristic
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4C22×C4×C4711yescharacteristic
702C4⋊C4C22×C4×C4711yescharacteristic
703C22⋊C4—21no—
704C22⋊C4—21no—
705C22⋊C4—21no—
706C22⋊C4—21no—
707C22⋊C4—21no—
708C22⋊C4—42no—
709C42—21no—
710C42—21no—
711C42—21no—
712C42—21no—
713C42—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—41no—
720C23—41no—
721C23—42no—
722C23—81no—
723C23—81no—
724C23C4×D4×C4711yescharacteristic
725C23C4×D4×C4711yescharacteristic
726C23C2×#41×C4711yescharacteristic
727Q8—21no—
728Q8—21no—
729Q8—21no—
730Q8—21no—
731Q8—21no—
732Q8—21no—
733Q8—42no—
734D4—21no—
735D4—21no—
736D4—21no—
737D4—21no—
738D4—21no—
739D4—21no—
740D4—42no—
741D4—42no—
742D4—42no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—81no—
750D4—81no—
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—22no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—41no—
770C2×C4—42no—
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×C4C4×D4×C4711yescharacteristic
782C2×C4C4×D4×C4711yescharacteristic
783C2×C4C23×C4×C4711yescharacteristic
784C2×C4C22×D4×C4711yescharacteristic
785C2×C4H(5,𝔽2)×C4711yescharacteristic
786C2×C4H(5,𝔽2)×C4711yescharacteristic
787C2×C4H(5,𝔽2)×C4711yescharacteristic
788C2×C4H(5,𝔽2)×C4711yescharacteristic
789C8—21no—
790C8—21no—
791C8—21no—
792C8—21no—
793C8—21no—
794C8—21no—
795C8—21no—
796C8—21no—
797C8—41no—
798C8—41no—
799C8—41no—
800C8—41no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—21no—
806C22—21no—
807C22—21no—
808C22—21no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—81no—
819C22—81no—
820C22—84no—
821C22C2×C4×D4×C4711yescharacteristic
822C22C47×#53811yescharacteristic
823C22C47×#53811yescharacteristic
824C4—21no—
825C4—21no—
826C4—42no—
827C4—41no—
828C4—41no—
829C4—41no—
830C4—41no—
831C4—41no—
832C4—81no—
833C4C47×#51811yescharacteristic
834C4C47×#51811yescharacteristic
835C4C47×#53411yescharacteristic
836C4C47×#53511yescharacteristic
837C2—21no—
838C2—21no—
839C2—41no—
840C2—41no—
841C2—81no—
842C2—81no—
843C2—81no—
844C2C47×#232111yescharacteristic
845C2C47×#295611yescharacteristic
846C2C47×#295711yescharacteristic
subgroupG/H
centerC2×C4×C47C22×D4
commutatorC2×C4C23×C4×C47
Frattini, cosocleC22×C4C24×C47
socleC22×C47C2×C4×D4
prime radicalC47×#3002C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C47 ◁ C22×M16×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#2930C2semidirect
3. C47×#2879C2semidirect
4. C47×#1975C2semidirect
5. C47×#1974C2semidirect
6. C47×#1938C2semidirect
7. C47×#1937C2semidirect
8. C47×#1929C2semidirect
9. C47×#1929C2semidirect
10. C47×#1876C2semidirect
11. C47×#1876C2semidirect
12. C47×#1871C2semidirect
13. C47×#1855C2semidirect
14. C47×#1789C2semidirect
15. C47×#1753C2semidirect
19. C2×#131×C47C22semidirect
23. C47×#452C4semidirect
24. C47×#452C4semidirect
25. C47×#451C4semidirect
26. C47×#450C4semidirect
27. C47×#449C4semidirect
28. C47×#449C4semidirect
29. C47×#448C4semidirect
30. C47×#447C4semidirect
35. C2×#108×C47C22semidirect
36. C2×#108×C47C22semidirect
37. C47×#424C22semidirect
42. C2×#104×C47C22semidirect
43. C2×#104×C47C22semidirect
52. C47×#408C22semidirect
57. C47×#405C22semidirect
58. C2×#97×C47C22semidirect
59. C2×C4×C8×C47C22semidirect
61. C47×#341C22semidirect
62. C47×#341C22semidirect
63. C47×#339C22semidirect
64. C47×#339C22semidirect
65. C47×#336C22semidirect
66. C47×#336C22semidirect
377. #22062C47direct (N × H)
415. #2930C2×C47semidirect
416. #2879C2×C47semidirect
417. #1975C2×C47semidirect
418. #1974C2×C47semidirect
419. #1938C2×C47semidirect
420. #1937C2×C47semidirect
421. #1929C2×C47semidirect
422. #1929C2×C47semidirect
423. #1876C2×C47semidirect
424. #1876C2×C47semidirect
425. #1871C2×C47semidirect
426. #1855C2×C47semidirect
427. #1789C2×C47semidirect
428. #1753C2×C47semidirect
442. C2×#131C22×C47semidirect
446. #452C4×C47semidirect
447. #452C4×C47semidirect
448. #451C4×C47semidirect
449. #450C4×C47semidirect
450. #449C4×C47semidirect
451. #449C4×C47semidirect
452. #448C4×C47semidirect
453. #447C4×C47semidirect
458. C2×#108C22×C47semidirect
459. C2×#108C22×C47semidirect
460. #424C22×C47semidirect
465. C2×#104C22×C47semidirect
466. C2×#104C22×C47semidirect
475. #408C22×C47semidirect
480. #405C22×C47semidirect
481. C2×#97C22×C47semidirect
482. C2×C4×C8C22×C47semidirect
484. #341C22×C47semidirect
485. #341C22×C47semidirect
486. #339C22×C47semidirect
487. #339C22×C47semidirect
488. #336C22×C47semidirect
489. #336C22×C47semidirect
490. C47#22062direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#30022
C47×#29302
C47×#28792
C47×#19752
C47×#19742
C47×#19382
C47×#19372
C47×#19292
C47×#18762
C47×#18712
C47×#18552
C47×#17892
C47×#17532
#2206247