Finite Group Databasebeta

← C47×#22889 #26062587

Subgroups — C47×#22889 #26062587

Order 12032.

1020 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3002C211yesmaximal, characteristic
2C2×C47×#443C211yesmaximal, characteristic, complemented
3C47×#2933C211yesmaximal, characteristic, complemented
4C2×C47×#421C211yesmaximal, characteristic, complemented
5C47×#2880C211yesmaximal, characteristic, complemented
6C47×#1975C211yesmaximal, characteristic, complemented
7C47×#1937C211yesmaximal, characteristic, complemented
8C47×#1929C211yesmaximal, characteristic, complemented
9C47×#1897C211yesmaximal, characteristic, complemented
10C47×#1876C211yesmaximal, characteristic, complemented
11C47×#1876C211yesmaximal, characteristic, complemented
12C47×#1866C211yesmaximal, characteristic, complemented
13C47×#1855C211yesmaximal, characteristic, complemented
14C47×#1765C211yesmaximal, characteristic, complemented
15C47×#1750C211yesmaximal, characteristic, complemented
16C22×#41×C47C2211yescharacteristic
17C2×#135×C47C2211yescharacteristic
18C2×#135×C47C2211yescharacteristic
19C2×#131×C47C2211yescharacteristic
20C2×#131×C47C2211yescharacteristic
21C2×#131×C47C2211yescharacteristic, complemented
22C22×M16×C47C2211yescharacteristic
23C47×#525C2211yescharacteristic
24C2×#117×C47C2211yescharacteristic
25C47×#452C411yescharacteristic, complemented
26C47×#452C411yescharacteristic, complemented
27C47×#451C411yescharacteristic, complemented
28C47×#450C411yescharacteristic, complemented
29C47×#449C411yescharacteristic, complemented
30C47×#449C411yescharacteristic, complemented
31C47×#448C411yescharacteristic, complemented
32C47×#447C411yescharacteristic, complemented
33C47×#443—24no—
34C47×#436—21no—
35C47×#435—21no—
36C47×#435—21no—
37C8×D4×C47—21no—
38C2×#108×C47C2211yescharacteristic, complemented
39C2×#108×C47C2211yescharacteristic, complemented
40C47×#424C2211yescharacteristic, complemented
41C47×#421—24no—
42C2×#104×C47C2211yescharacteristic
43C2×#104×C47C2211yescharacteristic
44C2×#104×C47C2211yescharacteristic
45C2×#104×C47C2211yescharacteristic
46C2×#104×C47C2211yescharacteristic, complemented
47C2×#104×C47C2211yescharacteristic, complemented
48C47×#416C2211yescharacteristic
49C47×#416C2211yescharacteristic
50C47×#408—21no—
51C47×#408—21no—
52C47×#408C2211yescharacteristic
53C47×#408C2211yescharacteristic
54C47×#408C2211yescharacteristic, complemented
55C47×#407—21no—
56C47×#407C2211yescharacteristic
57C2×C22⋊C8×C47—21no—
58C2×C22⋊C8×C47C2211yescharacteristic
59C2×C22⋊C8×C47C2211yescharacteristic
60C47×#405C2211yescharacteristic, complemented
61C2×#97×C47C2211yescharacteristic, complemented
62C2×C4×C8×C47C2211yescharacteristic, complemented
63C47×#341C2211yescharacteristic, complemented
64C47×#341C2211yescharacteristic, complemented
65C47×#339C2211yescharacteristic, complemented
66C47×#339C2211yescharacteristic, complemented
67C47×#336C2211yescharacteristic, complemented
68C47×#336C2211yescharacteristic, complemented
69C2×#41×C47—21no—
70C2×#41×C47—21no—
71C2×#41×C47—22no—
72C2×#41×C47—22no—
73C2×#41×C47—41no—
74C2×#41×C47—41no—
75C2×#41×C47C2×C411yescharacteristic
76C2×#41×C47C2×C411yescharacteristic
77C2×#41×C47C2311yescharacteristic
78C2×#41×C47C2311yescharacteristic
79C2×#41×C47C2311yescharacteristic
80C22×Q8×C47C2×C411yescharacteristic
81C22×D4×C47—21no—
82C22×D4×C47C2×C411yescharacteristic
83C23×C4×C47—21no—
84C23×C4×C47C2311yescharacteristic
85#135×C47—22no—
86#135×C47—22no—
87#135×C47—41no—
88#135×C47—41no—
89C2×Q16×C47C2×C411yescharacteristic
90C2×Q16×C47C2×C411yescharacteristic
91C2×SD16×C47C2×C411yescharacteristic
92C2×SD16×C47C2×C411yescharacteristic
93C2×SD16×C47C2×C411yescharacteristic
94C2×SD16×C47C2×C411yescharacteristic
95C2×D8×C47C2×C411yescharacteristic
96C2×D8×C47C2×C411yescharacteristic
97#131×C47—22no—
98#131×C47—22no—
99#131×C47—22no—
100#131×C47—41no—
101#131×C47—41no—
102#131×C47—41no—
103C2×M16×C47—21no—
104C2×M16×C47—21no—
105C2×M16×C47—21no—
106C2×M16×C47—21no—
107C2×M16×C47—22no—
108C2×M16×C47—41no—
109C2×M16×C47C2311yescharacteristic
110C2×M16×C47C2311yescharacteristic
111C2×M16×C47C2311yescharacteristic
112C2×M16×C47C2311yescharacteristic
113C22×C8×C47—21no—
114C22×C8×C47—21no—
115C22×C8×C47—21no—
116C22×C8×C47—21no—
117C22×C8×C47C2311yescharacteristic
118C22×C8×C47C2311yescharacteristic
119C22×C8×C47C2311yescharacteristic
120C22×C8×C47C2311yescharacteristic
121#123×C47—21no—
122C22⋊Q8×C47C2×C411yescharacteristic
123C22⋊Q8×C47C2×C411yescharacteristic
124#121×C47C2×C411yescharacteristic
125#121×C47C2×C411yescharacteristic
126#120×C47—21no—
127C4×D4×C47—21no—
128C4×D4×C47—21no—
129#117×C47—22no—
130#117×C47—41no—
131#117×C47C2311yescharacteristic
132C2×C4⋊C4×C47—21no—
133C2×C22⋊C4×C47—21no—
134C2×C42×C47C2311yescharacteristic
135C2×C42×C47C2311yescharacteristic
136#108×C47—22no—
137#108×C47—41no—
138C4⋊C8×C47—21no—
139C4⋊C8×C47—21no—
140#104×C47—22no—
141#104×C47—22no—
142#104×C47—22no—
143#104×C47—22no—
144#104×C47—41no—
145#104×C47D414yescomplemented
146#103×C47C2×C411yescharacteristic
147#103×C47C2×C411yescharacteristic
148#103×C47C2×C411yescharacteristic
149#103×C47C2×C411yescharacteristic
150#102×C47C2×C411yescharacteristic
151#102×C47C2×C411yescharacteristic
152#102×C47C2×C411yescharacteristic
153#102×C47C2×C411yescharacteristic
154C22⋊C8×C47—21no—
155C22⋊C8×C47—21no—
156C22⋊C8×C47—21no—
157C22⋊C8×C47—21no—
158C22⋊C8×C47—21no—
159C22⋊C8×C47—21no—
160C22⋊C8×C47—21no—
161C22⋊C8×C47—21no—
162C22⋊C8×C47C2×C411yescharacteristic
163C22⋊C8×C47C2×C411yescharacteristic
164C22⋊C8×C47C2×C411yescharacteristic
165C22⋊C8×C47C2×C411yescharacteristic
166C22⋊C8×C47D411yescharacteristic
167C22⋊C8×C47D411yescharacteristic
168C22⋊C8×C47D411yescharacteristic
169C22⋊C8×C47D411yescharacteristic
170#97×C47—21no—
171#97×C47—41no—
172C4×C8×C47—21no—
173C4×C8×C47—22no—
174C24×C47—21no—
175C24×C47#4111yescharacteristic
176#41×C47—21no—
177#41×C47—21no—
178#41×C47—22no—
179#41×C47—22no—
180#41×C47—21no—
181#41×C47—21no—
182#41×C47—21no—
183#41×C47—21no—
184#41×C47—21no—
185#41×C47—21no—
186#41×C47—21no—
187#41×C47—21no—
188#41×C47—42no—
189#41×C47—42no—
190#41×C47—41no—
191#41×C47—41no—
192#41×C47—42no—
193#41×C47—42no—
194#41×C47C2×D412yes—
195#41×C47#4112yes—
196C2×Q8×C47—21no—
197C2×Q8×C47—22no—
198C2×Q8×C47—41no—
199C2×Q8×C47C22×C411yescharacteristic
200C2×Q8×C47C22×C411yescharacteristic
201C2×Q8×C47C22×C411yescharacteristic
202C2×D4×C47—21no—
203C2×D4×C47—22no—
204C2×D4×C47—21no—
205C2×D4×C47—21no—
206C2×D4×C47—21no—
207C2×D4×C47—21no—
208C2×D4×C47—21no—
209C2×D4×C47—21no—
210C2×D4×C47—21no—
211C2×D4×C47—41no—
212C2×D4×C47—42no—
213C2×D4×C47—42no—
214C2×D4×C47C22×C411yescharacteristic
215C2×D4×C47C22×C411yescharacteristic
216C2×D4×C47C22×C411yescharacteristic
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—21no—
224C22×C4×C47—21no—
225C22×C4×C47—21no—
226C22×C4×C47—21no—
227C22×C4×C47—21no—
228C22×C4×C47—21no—
229C22×C4×C47—42no—
230C22×C4×C47—42no—
231C22×C4×C47C22×C411yescharacteristic
232C22×C4×C47C22×C411yescharacteristic
233C22×C4×C47C2×D411yescharacteristic
234C22×C4×C47C2×D411yescharacteristic
235C22×C4×C47#4111yescharacteristic
236C22×C4×C47C2411yescharacteristic
237Q16×C47—22no—
238Q16×C47—41no—
239SD16×C47—22no—
240SD16×C47—22no—
241SD16×C47—41no—
242SD16×C47—41no—
243D8×C47—22no—
244D8×C47—41no—
245M16×C47—21no—
246M16×C47—21no—
247M16×C47—21no—
248M16×C47—21no—
249M16×C47—21no—
250M16×C47—21no—
251M16×C47—21no—
252M16×C47—42no—
253M16×C47—42no—
254M16×C47—42no—
255M16×C47—42no—
256M16×C47C2×D412yes—
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—21no—
266C2×C8×C47—21no—
267C2×C8×C47—21no—
268C2×C8×C47—21no—
269C2×C8×C47—42no—
270C2×C8×C47—42no—
271C2×C8×C47—42no—
272C2×C8×C47—42no—
273C2×C8×C47C22×C411yescharacteristic
274C2×C8×C47C22×C411yescharacteristic
275C2×C8×C47C22×C411yescharacteristic
276C2×C8×C47C22×C411yescharacteristic
277C2×C8×C47C2×D411yescharacteristic
278C2×C8×C47C2×D411yescharacteristic
279C2×C8×C47C2×D411yescharacteristic
280C2×C8×C47C2×D411yescharacteristic
281C4⋊C4×C47—21no—
282C4⋊C4×C47—21no—
283C4⋊C4×C47—42no—
284C4⋊C4×C47C22×C411yescharacteristic
285C4⋊C4×C47C22×C411yescharacteristic
286C22⋊C4×C47—21no—
287C22⋊C4×C47—21no—
288C22⋊C4×C47—21no—
289C22⋊C4×C47—21no—
290C22⋊C4×C47—21no—
291C22⋊C4×C47—42no—
292C42×C47—21no—
293C42×C47—21no—
294C42×C47—21no—
295C42×C47—21no—
296C42×C47C2×D412yes—
297C23×C47—21no—
298C23×C47—21no—
299C23×C47—21no—
300C23×C47—21no—
301C23×C47—21no—
302C23×C47—41no—
303C23×C47—41no—
304C23×C47—42no—
305C23×C47—42no—
306C23×C47—81no—
307C23×C47C4×D411yescharacteristic
308C23×C47C4×D411yescharacteristic
309C23×C47C2×#4111yescharacteristic
310Q8×C47—21no—
311Q8×C47—21no—
312Q8×C47—21no—
313Q8×C47—21no—
314Q8×C47—21no—
315Q8×C47—42no—
316Q8×C47C4×D412yes—
317D4×C47—22no—
318D4×C47—22no—
319D4×C47—21no—
320D4×C47—21no—
321D4×C47—21no—
322D4×C47—21no—
323D4×C47—21no—
324D4×C47—42no—
325D4×C47—42no—
326D4×C47—42no—
327D4×C47—42no—
328D4×C47—41no—
329D4×C47—41no—
330D4×C47—41no—
331D4×C47—41no—
332D4×C47—81no—
333D4×C47C4×D412yes—
334C2×C4×C47—21no—
335C2×C4×C47—21no—
336C2×C4×C47—21no—
337C2×C4×C47—21no—
338C2×C4×C47—21no—
339C2×C4×C47—21no—
340C2×C4×C47—21no—
341C2×C4×C47—21no—
342C2×C4×C47—22no—
343C2×C4×C47—21no—
344C2×C4×C47—22no—
345C2×C4×C47—21no—
346C2×C4×C47—21no—
347C2×C4×C47—21no—
348C2×C4×C47—21no—
349C2×C4×C47—21no—
350C2×C4×C47—21no—
351C2×C4×C47—22no—
352C2×C4×C47—42no—
353C2×C4×C47—42no—
354C2×C4×C47—42no—
355C2×C4×C47—41no—
356C2×C4×C47—41no—
357C2×C4×C47—41no—
358C2×C4×C47—41no—
359C2×C4×C47—41no—
360C2×C4×C47—41no—
361C2×C4×C47—41no—
362C2×C4×C47—41no—
363C2×C4×C47—41no—
364C2×C4×C47C4×D411yescharacteristic
365C2×C4×C47C4×D411yescharacteristic
366C2×C4×C47C23×C411yescharacteristic
367C2×C4×C47C22×D411yescharacteristic
368C2×C4×C47C22×D411yescharacteristic
369C2×C4×C47C2×#4111yescharacteristic
370C2×C4×C47H(5,𝔽2)11yescharacteristic
371C2×C4×C47H(5,𝔽2)11yescharacteristic
372C8×C47—21no—
373C8×C47—21no—
374C8×C47—21no—
375C8×C47—21no—
376C8×C47—21no—
377C8×C47—21no—
378C8×C47—22no—
379C8×C47—21no—
380C8×C47—21no—
381C8×C47—41no—
382C8×C47—41no—
383C8×C47—41no—
384#22889C4711yesmaximal, characteristic, direct product factor, Sylow
385C22×C47—21no—
386C22×C47—21no—
387C22×C47—21no—
388C22×C47—21no—
389C22×C47—22no—
390C22×C47—21no—
391C22×C47—21no—
392C22×C47—21no—
393C22×C47—21no—
394C22×C47—41no—
395C22×C47—41no—
396C22×C47—41no—
397C22×C47—41no—
398C22×C47—41no—
399C22×C47—41no—
400C22×C47—41no—
401C22×C47—41no—
402C22×C47—81no—
403C22×C47—81no—
404C22×C47—84no—
405C22×C47C2×C4×D411yescharacteristic
406C22×C47#54611yescharacteristic
407C22×C47#55111yescharacteristic
408C4×C47—21no—
409C4×C47—21no—
410C4×C47—22no—
411C4×C47—42no—
412C4×C47—41no—
413C4×C47—41no—
414C4×C47—41no—
415C4×C47—41no—
416C4×C47—81no—
417C4×C47C2×C4×D411yescharacteristic
418C4×C47#51811yescharacteristic
419C4×C47D4211yescharacteristic
420C4×C47#54611yescharacteristic
421#3002C2×C4711yescharacteristic
422C2×#443C2×C4711yescharacteristic, complemented
423#2933C2×C4711yescharacteristic, complemented
424C2×#421C2×C4711yescharacteristic, complemented
425#2880C2×C4711yescharacteristic, complemented
426#1975C2×C4711yescharacteristic, complemented
427#1937C2×C4711yescharacteristic, complemented
428#1929C2×C4711yescharacteristic, complemented
429#1897C2×C4711yescharacteristic, complemented
430#1876C2×C4711yescharacteristic, complemented
431#1876C2×C4711yescharacteristic, complemented
432#1866C2×C4711yescharacteristic, complemented
433#1855C2×C4711yescharacteristic, complemented
434#1765C2×C4711yescharacteristic, complemented
435#1750C2×C4711yescharacteristic, complemented
436C2×C47—21no—
437C2×C47—21no—
438C2×C47—41no—
439C2×C47—41no—
440C2×C47—42no—
441C2×C47—81no—
442C2×C47—81no—
443C2×C47#235811yescharacteristic
444C2×C47#295511yescharacteristic
445C2×C47#295711yescharacteristic
446C22×#41C22×C4711yescharacteristic
447C2×#135C22×C4711yescharacteristic
448C2×#135C22×C4711yescharacteristic
449C2×#131C22×C4711yescharacteristic
450C2×#131C22×C4711yescharacteristic
451C2×#131C22×C4711yescharacteristic, complemented
452C22×M16C22×C4711yescharacteristic
453#525C22×C4711yescharacteristic
454C2×#117C22×C4711yescharacteristic
455#452C4×C4711yescharacteristic, complemented
456#452C4×C4711yescharacteristic, complemented
457#451C4×C4711yescharacteristic, complemented
458#450C4×C4711yescharacteristic, complemented
459#449C4×C4711yescharacteristic, complemented
460#449C4×C4711yescharacteristic, complemented
461#448C4×C4711yescharacteristic, complemented
462#447C4×C4711yescharacteristic, complemented
463#443—24no—
464#436—21no—
465#435—21no—
466#435—21no—
467C8×D4—21no—
468C2×#108C22×C4711yescharacteristic, complemented
469C2×#108C22×C4711yescharacteristic, complemented
470#424C22×C4711yescharacteristic, complemented
471#421—24no—
472C2×#104C22×C4711yescharacteristic
473C2×#104C22×C4711yescharacteristic
474C2×#104C22×C4711yescharacteristic
475C2×#104C22×C4711yescharacteristic
476C2×#104C22×C4711yescharacteristic, complemented
477C2×#104C22×C4711yescharacteristic, complemented
478#416C22×C4711yescharacteristic
479#416C22×C4711yescharacteristic
480#408—21no—
481#408—21no—
482#408C22×C4711yescharacteristic
483#408C22×C4711yescharacteristic
484#408C22×C4711yescharacteristic, complemented
485#407—21no—
486#407C22×C4711yescharacteristic
487C2×C22⋊C8—21no—
488C2×C22⋊C8C22×C4711yescharacteristic
489C2×C22⋊C8C22×C4711yescharacteristic
490#405C22×C4711yescharacteristic, complemented
491C2×#97C22×C4711yescharacteristic, complemented
492C2×C4×C8C22×C4711yescharacteristic, complemented
493#341C22×C4711yescharacteristic, complemented
494#341C22×C4711yescharacteristic, complemented
495#339C22×C4711yescharacteristic, complemented
496#339C22×C4711yescharacteristic, complemented
497#336C22×C4711yescharacteristic, complemented
498#336C22×C4711yescharacteristic, complemented
499C47#2288911yescharacteristic, direct product factor, Sylow
500C2×#41—21no—
501C2×#41—21no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41C2×C4×C4711yescharacteristic
507C2×#41C2×C4×C4711yescharacteristic
508C2×#41C23×C4711yescharacteristic
509C2×#41C23×C4711yescharacteristic
510C2×#41C23×C4711yescharacteristic
511C22×Q8C2×C4×C4711yescharacteristic
512C22×D4—21no—
513C22×D4C2×C4×C4711yescharacteristic
514C23×C4—21no—
515C23×C4C23×C4711yescharacteristic
516#135—22no—
517#135—22no—
518#135—41no—
519#135—41no—
520C2×Q16C2×C4×C4711yescharacteristic
521C2×Q16C2×C4×C4711yescharacteristic
522C2×SD16C2×C4×C4711yescharacteristic
523C2×SD16C2×C4×C4711yescharacteristic
524C2×SD16C2×C4×C4711yescharacteristic
525C2×SD16C2×C4×C4711yescharacteristic
526C2×D8C2×C4×C4711yescharacteristic
527C2×D8C2×C4×C4711yescharacteristic
528#131—22no—
529#131—22no—
530#131—22no—
531#131—41no—
532#131—41no—
533#131—41no—
534C2×M16—21no—
535C2×M16—21no—
536C2×M16—21no—
537C2×M16—21no—
538C2×M16—22no—
539C2×M16—41no—
540C2×M16C23×C4711yescharacteristic
541C2×M16C23×C4711yescharacteristic
542C2×M16C23×C4711yescharacteristic
543C2×M16C23×C4711yescharacteristic
544C22×C8—21no—
545C22×C8—21no—
546C22×C8—21no—
547C22×C8—21no—
548C22×C8C23×C4711yescharacteristic
549C22×C8C23×C4711yescharacteristic
550C22×C8C23×C4711yescharacteristic
551C22×C8C23×C4711yescharacteristic
552#123—21no—
553C22⋊Q8C2×C4×C4711yescharacteristic
554C22⋊Q8C2×C4×C4711yescharacteristic
555#121C2×C4×C4711yescharacteristic
556#121C2×C4×C4711yescharacteristic
557#120—21no—
558C4×D4—21no—
559C4×D4—21no—
560#117—22no—
561#117—41no—
562#117C23×C4711yescharacteristic
563C2×C4⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C42C23×C4711yescharacteristic
566C2×C42C23×C4711yescharacteristic
567#108—22no—
568#108—41no—
569C4⋊C8—21no—
570C4⋊C8—21no—
571#104—22no—
572#104—22no—
573#104—22no—
574#104—22no—
575#104—41no—
576#104D4×C4714yescomplemented
577#103C2×C4×C4711yescharacteristic
578#103C2×C4×C4711yescharacteristic
579#103C2×C4×C4711yescharacteristic
580#103C2×C4×C4711yescharacteristic
581#102C2×C4×C4711yescharacteristic
582#102C2×C4×C4711yescharacteristic
583#102C2×C4×C4711yescharacteristic
584#102C2×C4×C4711yescharacteristic
585C22⋊C8—21no—
586C22⋊C8—21no—
587C22⋊C8—21no—
588C22⋊C8—21no—
589C22⋊C8—21no—
590C22⋊C8—21no—
591C22⋊C8—21no—
592C22⋊C8—21no—
593C22⋊C8C2×C4×C4711yescharacteristic
594C22⋊C8C2×C4×C4711yescharacteristic
595C22⋊C8C2×C4×C4711yescharacteristic
596C22⋊C8C2×C4×C4711yescharacteristic
597C22⋊C8D4×C4711yescharacteristic
598C22⋊C8D4×C4711yescharacteristic
599C22⋊C8D4×C4711yescharacteristic
600C22⋊C8D4×C4711yescharacteristic
601#97—21no—
602#97—41no—
603C4×C8—21no—
604C4×C8—22no—
605C24—21no—
606C24#41×C4711yescharacteristic
607#41—21no—
608#41—21no—
609#41—22no—
610#41—22no—
611#41—21no—
612#41—21no—
613#41—21no—
614#41—21no—
615#41—21no—
616#41—21no—
617#41—21no—
618#41—21no—
619#41—42no—
620#41—42no—
621#41—41no—
622#41—41no—
623#41—42no—
624#41—42no—
625#41C2×D4×C4712yes—
626#41#41×C4712yes—
627C2×Q8—21no—
628C2×Q8—22no—
629C2×Q8—41no—
630C2×Q8C22×C4×C4711yescharacteristic
631C2×Q8C22×C4×C4711yescharacteristic
632C2×Q8C22×C4×C4711yescharacteristic
633C2×D4—21no—
634C2×D4—22no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—41no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4C22×C4×C4711yescharacteristic
646C2×D4C22×C4×C4711yescharacteristic
647C2×D4C22×C4×C4711yescharacteristic
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4C22×C4×C4711yescharacteristic
663C22×C4C22×C4×C4711yescharacteristic
664C22×C4C2×D4×C4711yescharacteristic
665C22×C4C2×D4×C4711yescharacteristic
666C22×C4#41×C4711yescharacteristic
667C22×C4C24×C4711yescharacteristic
668Q16—22no—
669Q16—41no—
670SD16—22no—
671SD16—22no—
672SD16—41no—
673SD16—41no—
674D8—22no—
675D8—41no—
676M16—21no—
677M16—21no—
678M16—21no—
679M16—21no—
680M16—21no—
681M16—21no—
682M16—21no—
683M16—42no—
684M16—42no—
685M16—42no—
686M16—42no—
687M16C2×D4×C4712yes—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—42no—
701C2×C8—42no—
702C2×C8—42no—
703C2×C8—42no—
704C2×C8C22×C4×C4711yescharacteristic
705C2×C8C22×C4×C4711yescharacteristic
706C2×C8C22×C4×C4711yescharacteristic
707C2×C8C22×C4×C4711yescharacteristic
708C2×C8C2×D4×C4711yescharacteristic
709C2×C8C2×D4×C4711yescharacteristic
710C2×C8C2×D4×C4711yescharacteristic
711C2×C8C2×D4×C4711yescharacteristic
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—42no—
715C4⋊C4C22×C4×C4711yescharacteristic
716C4⋊C4C22×C4×C4711yescharacteristic
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—21no—
721C22⋊C4—21no—
722C22⋊C4—42no—
723C42—21no—
724C42—21no—
725C42—21no—
726C42—21no—
727C42C2×D4×C4712yes—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—41no—
734C23—41no—
735C23—42no—
736C23—42no—
737C23—81no—
738C23C4×D4×C4711yescharacteristic
739C23C4×D4×C4711yescharacteristic
740C23C2×#41×C4711yescharacteristic
741Q8—21no—
742Q8—21no—
743Q8—21no—
744Q8—21no—
745Q8—21no—
746Q8—42no—
747Q8C4×D4×C4712yes—
748D4—22no—
749D4—22no—
750D4—21no—
751D4—21no—
752D4—21no—
753D4—21no—
754D4—21no—
755D4—42no—
756D4—42no—
757D4—42no—
758D4—42no—
759D4—41no—
760D4—41no—
761D4—41no—
762D4—41no—
763D4—81no—
764D4C4×D4×C4712yes—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—22no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4C4×D4×C4711yescharacteristic
796C2×C4C4×D4×C4711yescharacteristic
797C2×C4C23×C4×C4711yescharacteristic
798C2×C4C22×D4×C4711yescharacteristic
799C2×C4C22×D4×C4711yescharacteristic
800C2×C4C2×#41×C4711yescharacteristic
801C2×C4H(5,𝔽2)×C4711yescharacteristic
802C2×C4H(5,𝔽2)×C4711yescharacteristic
803C8—21no—
804C8—21no—
805C8—21no—
806C8—21no—
807C8—21no—
808C8—21no—
809C8—22no—
810C8—21no—
811C8—21no—
812C8—41no—
813C8—41no—
814C8—41no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—22no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—81no—
833C22—81no—
834C22—84no—
835C22C2×C4×D4×C4711yescharacteristic
836C22C47×#54611yescharacteristic
837C22C47×#55111yescharacteristic
838C4—21no—
839C4—21no—
840C4—22no—
841C4—42no—
842C4—41no—
843C4—41no—
844C4—41no—
845C4—41no—
846C4—81no—
847C4C2×C4×D4×C4711yescharacteristic
848C4C47×#51811yescharacteristic
849C4D42×C4711yescharacteristic
850C4C47×#54611yescharacteristic
851C2—21no—
852C2—21no—
853C2—41no—
854C2—41no—
855C2—42no—
856C2—81no—
857C2—81no—
858C2C47×#235811yescharacteristic
859C2C47×#295511yescharacteristic
860C2C47×#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 ◁ C2×C22⋊C8×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C47×#443C2semidirect
3. C47×#2933C2semidirect
4. C2×C47×#421C2semidirect
5. C47×#2880C2semidirect
6. C47×#1975C2semidirect
7. C47×#1937C2semidirect
8. C47×#1929C2semidirect
9. C47×#1897C2semidirect
10. C47×#1876C2semidirect
11. C47×#1876C2semidirect
12. C47×#1866C2semidirect
13. C47×#1855C2semidirect
14. C47×#1765C2semidirect
15. C47×#1750C2semidirect
21. C2×#131×C47C22semidirect
25. C47×#452C4semidirect
26. C47×#452C4semidirect
27. C47×#451C4semidirect
28. C47×#450C4semidirect
29. C47×#449C4semidirect
30. C47×#449C4semidirect
31. C47×#448C4semidirect
32. C47×#447C4semidirect
38. C2×#108×C47C22semidirect
39. C2×#108×C47C22semidirect
40. C47×#424C22semidirect
46. C2×#104×C47C22semidirect
47. C2×#104×C47C22semidirect
54. C47×#408C22semidirect
60. C47×#405C22semidirect
61. C2×#97×C47C22semidirect
62. C2×C4×C8×C47C22semidirect
63. C47×#341C22semidirect
64. C47×#341C22semidirect
65. C47×#339C22semidirect
66. C47×#339C22semidirect
67. C47×#336C22semidirect
68. C47×#336C22semidirect
145. #104×C47D4semidirect
384. #22889C47direct (N × H)
422. C2×#443C2×C47semidirect
423. #2933C2×C47semidirect
424. C2×#421C2×C47semidirect
425. #2880C2×C47semidirect
426. #1975C2×C47semidirect
427. #1937C2×C47semidirect
428. #1929C2×C47semidirect
429. #1897C2×C47semidirect
430. #1876C2×C47semidirect
431. #1876C2×C47semidirect
432. #1866C2×C47semidirect
433. #1855C2×C47semidirect
434. #1765C2×C47semidirect
435. #1750C2×C47semidirect
451. C2×#131C22×C47semidirect
455. #452C4×C47semidirect
456. #452C4×C47semidirect
457. #451C4×C47semidirect
458. #450C4×C47semidirect
459. #449C4×C47semidirect
460. #449C4×C47semidirect
461. #448C4×C47semidirect
462. #447C4×C47semidirect
468. C2×#108C22×C47semidirect
469. C2×#108C22×C47semidirect
470. #424C22×C47semidirect
476. C2×#104C22×C47semidirect
477. C2×#104C22×C47semidirect
484. #408C22×C47semidirect
490. #405C22×C47semidirect
491. C2×#97C22×C47semidirect
492. C2×C4×C8C22×C47semidirect
493. #341C22×C47semidirect
494. #341C22×C47semidirect
495. #339C22×C47semidirect
496. #339C22×C47semidirect
497. #336C22×C47semidirect
498. #336C22×C47semidirect
499. C47#22889direct (N × H)
576. #104D4×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#30022
C2×C47×#4432
C47×#29332
C2×C47×#4212
C47×#28802
C47×#19752
C47×#19372
C47×#19292
C47×#18972
C47×#18762
C47×#18662
C47×#18552
C47×#17652
C47×#17502
#2288947