Finite Group Databasebeta

← C47×#22949 #26062647

Subgroups — C47×#22949 #26062647

Order 12032.

730 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3091C211yesmaximal, characteristic
2C47×#2933C211yesmaximal, characteristic
3C47×#2924C211yesmaximal, characteristic, complemented
4C47×#1945C211yesmaximal, characteristic, complemented
5C47×#1938C211yesmaximal, characteristic, complemented
6C47×#1929C211yesmaximal, characteristic, complemented
7C47×#1922C211yesmaximal, characteristic, complemented
8C47×#1922C211yesmaximal, characteristic, complemented
9C47×#1897C211yesmaximal, characteristic
10C47×#1866C211yesmaximal, characteristic, complemented
11C47×#1855C211yesmaximal, characteristic, complemented
12C47×#1773C211yesmaximal, characteristic, complemented
13C47×#1764C211yesmaximal, characteristic, complemented
14C47×#1750C211yesmaximal, characteristic, complemented
15C47×#1733C211yesmaximal, characteristic, complemented
16C2×#131×C47C2211yescharacteristic
17C22×M16×C47C2211yescharacteristic
18C47×#525C2211yescharacteristic
19C2×#117×C47C2211yescharacteristic
20C2×#117×C47C2211yescharacteristic
21C47×#485C411yescharacteristic, complemented
22C47×#485C411yescharacteristic, complemented
23C47×#484C411yescharacteristic, complemented
24C47×#483C411yescharacteristic, complemented
25C47×#482C411yescharacteristic, complemented
26C47×#482C411yescharacteristic, complemented
27C47×#481C411yescharacteristic, complemented
28C47×#480C411yescharacteristic, complemented
29C47×#436—21no—
30C47×#435—21no—
31C47×#435—21no—
32C8×D4×C47—21no—
33C47×#433—21no—
34C47×#433—21no—
35C47×#432—21no—
36C47×#431—21no—
37C2×#108×C47C2211yescharacteristic
38C2×#108×C47C2211yescharacteristic
39C47×#427C2211yescharacteristic
40C47×#427C2211yescharacteristic
41C47×#424C2211yescharacteristic
42C47×#424C2211yescharacteristic
43C47×#424C2211yescharacteristic
44C2×#104×C47C2211yescharacteristic
45C2×#104×C47C2211yescharacteristic
46C47×#416C2211yescharacteristic
47C47×#416C2211yescharacteristic
48C47×#408C2211yescharacteristic
49C47×#407C2211yescharacteristic
50C2×C22⋊C8×C47C2211yescharacteristic
51C2×C22⋊C8×C47C2211yescharacteristic
52C47×#405C2211yescharacteristic
53C47×#405C2211yescharacteristic
54C47×#405C2211yescharacteristic
55C2×#97×C47C2211yescharacteristic
56C2×C4×C8×C47C2211yescharacteristic
57C47×#341C2211yescharacteristic
58C47×#341C2211yescharacteristic
59C47×#339C2211yescharacteristic
60C47×#339C2211yescharacteristic
61C47×#339C2211yescharacteristic
62C47×#339C2211yescharacteristic
63C47×#339C2211yescharacteristic
64C47×#339C2211yescharacteristic
65C47×#336C2211yescharacteristic
66C47×#336C2211yescharacteristic
67C2×#41×C47C2311yescharacteristic
68C23×C4×C47C2311yescharacteristic
69#131×C47—22no—
70#131×C47—41no—
71C2×M16×C47—21no—
72C2×M16×C47—21no—
73C2×M16×C47—22no—
74C2×M16×C47—41no—
75C2×M16×C47C2311yescharacteristic
76C2×M16×C47C2311yescharacteristic
77C2×M16×C47C2311yescharacteristic
78C2×M16×C47C2311yescharacteristic
79C22×C8×C47—21no—
80C22×C8×C47—21no—
81C22×C8×C47C2311yescharacteristic
82C22×C8×C47C2311yescharacteristic
83C22×C8×C47C2311yescharacteristic
84C22×C8×C47C2311yescharacteristic
85#123×C47—21no—
86C22⋊Q8×C47C2×C411yescharacteristic
87C22⋊Q8×C47C2×C411yescharacteristic
88#121×C47C2×C411yescharacteristic
89#121×C47C2×C411yescharacteristic
90#120×C47—21no—
91C4×D4×C47—21no—
92C4×D4×C47—21no—
93#117×C47—21no—
94#117×C47—21no—
95#117×C47—22no—
96#117×C47—41no—
97#117×C47C2×C411yescharacteristic
98#117×C47C2×C411yescharacteristic
99#117×C47C2311yescharacteristic
100#117×C47C2311yescharacteristic
101#117×C47C2311yescharacteristic
102C2×C4⋊C4×C47—21no—
103C2×C4⋊C4×C47C2×C411yescharacteristic
104C2×C4⋊C4×C47C2×C411yescharacteristic
105C2×C22⋊C4×C47—21no—
106C2×C22⋊C4×C47—21no—
107C2×C42×C47—21no—
108C2×C42×C47C2311yescharacteristic
109C2×C42×C47C2311yescharacteristic
110#108×C47—22no—
111#108×C47—41no—
112#107×C47C2×C411yescharacteristic
113#107×C47C2×C411yescharacteristic
114#107×C47C2×C411yescharacteristic
115#107×C47C2×C411yescharacteristic
116#106×C47C2×C411yescharacteristic
117#106×C47C2×C411yescharacteristic
118#106×C47C2×C411yescharacteristic
119#106×C47C2×C411yescharacteristic
120C4⋊C8×C47—21no—
121C4⋊C8×C47—21no—
122C4⋊C8×C47—21no—
123C4⋊C8×C47—21no—
124C4⋊C8×C47—21no—
125C4⋊C8×C47—21no—
126#104×C47—22no—
127#104×C47—41no—
128#103×C47C2×C411yescharacteristic
129#103×C47C2×C411yescharacteristic
130#103×C47C2×C411yescharacteristic
131#103×C47C2×C411yescharacteristic
132#102×C47C2×C411yescharacteristic
133#102×C47C2×C411yescharacteristic
134#102×C47C2×C411yescharacteristic
135#102×C47C2×C411yescharacteristic
136C22⋊C8×C47—21no—
137C22⋊C8×C47—21no—
138C22⋊C8×C47—21no—
139C22⋊C8×C47—21no—
140C22⋊C8×C47C2×C411yescharacteristic
141C22⋊C8×C47C2×C411yescharacteristic
142C22⋊C8×C47C2×C411yescharacteristic
143C22⋊C8×C47C2×C411yescharacteristic
144C22⋊C8×C47D411yescharacteristic
145C22⋊C8×C47D411yescharacteristic
146C22⋊C8×C47D411yescharacteristic
147C22⋊C8×C47D411yescharacteristic
148#97×C47—21no—
149#97×C47—21no—
150#97×C47—21no—
151#97×C47—22no—
152C4×C8×C47—21no—
153C4×C8×C47—21no—
154C4×C8×C47—21no—
155C4×C8×C47—41no—
156C24×C47#4111yescharacteristic
157#41×C47—21no—
158#41×C47—21no—
159#41×C47—21no—
160#41×C47—21no—
161C2×Q8×C47C22×C411yescharacteristic
162C2×D4×C47—21no—
163C2×D4×C47—21no—
164C2×D4×C47—21no—
165C2×D4×C47C22×C411yescharacteristic
166C22×C4×C47—21no—
167C22×C4×C47—21no—
168C22×C4×C47—21no—
169C22×C4×C47—21no—
170C22×C4×C47—21no—
171C22×C4×C47—21no—
172C22×C4×C47—21no—
173C22×C4×C47—21no—
174C22×C4×C47—21no—
175C22×C4×C47C22×C411yescharacteristic
176C22×C4×C47C22×C411yescharacteristic
177C22×C4×C47C2×D411yescharacteristic
178C22×C4×C47C2×D411yescharacteristic
179C22×C4×C47#4111yescharacteristic
180C22×C4×C47C2411yescharacteristic
181M16×C47—21no—
182M16×C47—21no—
183M16×C47—21no—
184M16×C47—21no—
185M16×C47—21no—
186M16×C47—21no—
187M16×C47—21no—
188M16×C47—42no—
189M16×C47—42no—
190M16×C47#4112yes—
191C2×C8×C47—21no—
192C2×C8×C47—21no—
193C2×C8×C47—21no—
194C2×C8×C47—21no—
195C2×C8×C47—21no—
196C2×C8×C47—21no—
197C2×C8×C47—21no—
198C2×C8×C47—21no—
199C2×C8×C47—21no—
200C2×C8×C47—21no—
201C2×C8×C47—21no—
202C2×C8×C47—21no—
203C2×C8×C47—42no—
204C2×C8×C47—42no—
205C2×C8×C47C22×C411yescharacteristic
206C2×C8×C47C22×C411yescharacteristic
207C2×C8×C47C22×C411yescharacteristic
208C2×C8×C47C22×C411yescharacteristic
209C2×C8×C47C2×D411yescharacteristic
210C2×C8×C47C2×D411yescharacteristic
211C2×C8×C47C2×D411yescharacteristic
212C2×C8×C47C2×D411yescharacteristic
213C4⋊C4×C47—21no—
214C4⋊C4×C47—21no—
215C4⋊C4×C47—21no—
216C4⋊C4×C47—21no—
217C4⋊C4×C47—42no—
218C4⋊C4×C47C22×C411yescharacteristic
219C4⋊C4×C47C22×C411yescharacteristic
220C4⋊C4×C47C22×C411yescharacteristic
221C4⋊C4×C47C22×C411yescharacteristic
222C4⋊C4×C47C22×C411yescharacteristic
223C4⋊C4×C47C22×C411yescharacteristic
224C22⋊C4×C47—21no—
225C22⋊C4×C47—21no—
226C22⋊C4×C47—21no—
227C22⋊C4×C47—21no—
228C22⋊C4×C47—21no—
229C22⋊C4×C47—21no—
230C22⋊C4×C47—21no—
231C22⋊C4×C47—21no—
232C22⋊C4×C47—21no—
233C22⋊C4×C47—42no—
234C42×C47—21no—
235C42×C47—21no—
236C42×C47—21no—
237C42×C47—21no—
238C42×C47—21no—
239C42×C47—21no—
240C42×C47—21no—
241C42×C47—21no—
242C42×C47#4112yes—
243C23×C47—21no—
244C23×C47—21no—
245C23×C47—21no—
246C23×C47—41no—
247C23×C47—41no—
248C23×C47C4×D411yescharacteristic
249C23×C47C4×D411yescharacteristic
250C23×C47C2×#4111yescharacteristic
251Q8×C47—21no—
252Q8×C47—21no—
253D4×C47—21no—
254D4×C47—21no—
255D4×C47—42no—
256D4×C47—41no—
257D4×C47—41no—
258D4×C47—81no—
259C2×C4×C47—21no—
260C2×C4×C47—21no—
261C2×C4×C47—21no—
262C2×C4×C47—21no—
263C2×C4×C47—21no—
264C2×C4×C47—21no—
265C2×C4×C47—21no—
266C2×C4×C47—21no—
267C2×C4×C47—21no—
268C2×C4×C47—21no—
269C2×C4×C47—21no—
270C2×C4×C47—21no—
271C2×C4×C47—21no—
272C2×C4×C47—21no—
273C2×C4×C47—21no—
274C2×C4×C47—21no—
275C2×C4×C47—21no—
276C2×C4×C47—22no—
277C2×C4×C47—41no—
278C2×C4×C47—41no—
279C2×C4×C47—42no—
280C2×C4×C47—41no—
281C2×C4×C47—41no—
282C2×C4×C47—41no—
283C2×C4×C47—41no—
284C2×C4×C47—41no—
285C2×C4×C47—81no—
286C2×C4×C47C4×D411yescharacteristic
287C2×C4×C47C4×D411yescharacteristic
288C2×C4×C47C23×C411yescharacteristic
289C2×C4×C47C22×D411yescharacteristic
290C2×C4×C47C2×#4111yescharacteristic
291C2×C4×C47C2×#4111yescharacteristic
292C2×C4×C47H(5,𝔽2)11yescharacteristic
293C2×C4×C472−1+411yescharacteristic
294C8×C47—21no—
295C8×C47—21no—
296C8×C47—21no—
297C8×C47—21no—
298C8×C47—21no—
299C8×C47—21no—
300C8×C47—22no—
301C8×C47—21no—
302C8×C47—21no—
303C8×C47—41no—
304C8×C47—41no—
305C8×C47—41no—
306#22949C4711yesmaximal, characteristic, direct product factor, Sylow
307C22×C47—21no—
308C22×C47—21no—
309C22×C47—21no—
310C22×C47—21no—
311C22×C47—21no—
312C22×C47—21no—
313C22×C47—21no—
314C22×C47—21no—
315C22×C47—41no—
316C22×C47—41no—
317C22×C47—41no—
318C22×C47—81no—
319C22×C47—81no—
320C22×C47C2×C4×D411yescharacteristic
321C22×C47#55111yescharacteristic
322C22×C47#55211yescharacteristic
323C4×C47—21no—
324C4×C47—21no—
325C4×C47—42no—
326C4×C47—41no—
327C4×C47—41no—
328C4×C47—41no—
329C4×C47—41no—
330C4×C47—41no—
331C4×C47—41no—
332C4×C47—41no—
333C4×C47—81no—
334C4×C47C4×#4111yescharacteristic
335C4×C47#52011yescharacteristic
336C4×C47#54611yescharacteristic
337C4×C47#54711yescharacteristic
338#3091C2×C4711yescharacteristic
339#2933C2×C4711yescharacteristic
340#2924C2×C4711yescharacteristic, complemented
341#1945C2×C4711yescharacteristic, complemented
342#1938C2×C4711yescharacteristic, complemented
343#1929C2×C4711yescharacteristic, complemented
344#1922C2×C4711yescharacteristic, complemented
345#1922C2×C4711yescharacteristic, complemented
346#1897C2×C4711yescharacteristic
347#1866C2×C4711yescharacteristic, complemented
348#1855C2×C4711yescharacteristic, complemented
349#1773C2×C4711yescharacteristic, complemented
350#1764C2×C4711yescharacteristic, complemented
351#1750C2×C4711yescharacteristic, complemented
352#1733C2×C4711yescharacteristic, complemented
353C2×C47—21no—
354C2×C47—21no—
355C2×C47—41no—
356C2×C47—41no—
357C2×C47—81no—
358C2×C47#235911yescharacteristic
359C2×C47#295511yescharacteristic
360C2×C47#295711yescharacteristic
361C2×#131C22×C4711yescharacteristic
362C22×M16C22×C4711yescharacteristic
363#525C22×C4711yescharacteristic
364C2×#117C22×C4711yescharacteristic
365C2×#117C22×C4711yescharacteristic
366#485C4×C4711yescharacteristic, complemented
367#485C4×C4711yescharacteristic, complemented
368#484C4×C4711yescharacteristic, complemented
369#483C4×C4711yescharacteristic, complemented
370#482C4×C4711yescharacteristic, complemented
371#482C4×C4711yescharacteristic, complemented
372#481C4×C4711yescharacteristic, complemented
373#480C4×C4711yescharacteristic, complemented
374#436—21no—
375#435—21no—
376#435—21no—
377C8×D4—21no—
378#433—21no—
379#433—21no—
380#432—21no—
381#431—21no—
382C2×#108C22×C4711yescharacteristic
383C2×#108C22×C4711yescharacteristic
384#427C22×C4711yescharacteristic
385#427C22×C4711yescharacteristic
386#424C22×C4711yescharacteristic
387#424C22×C4711yescharacteristic
388#424C22×C4711yescharacteristic
389C2×#104C22×C4711yescharacteristic
390C2×#104C22×C4711yescharacteristic
391#416C22×C4711yescharacteristic
392#416C22×C4711yescharacteristic
393#408C22×C4711yescharacteristic
394#407C22×C4711yescharacteristic
395C2×C22⋊C8C22×C4711yescharacteristic
396C2×C22⋊C8C22×C4711yescharacteristic
397#405C22×C4711yescharacteristic
398#405C22×C4711yescharacteristic
399#405C22×C4711yescharacteristic
400C2×#97C22×C4711yescharacteristic
401C2×C4×C8C22×C4711yescharacteristic
402#341C22×C4711yescharacteristic
403#341C22×C4711yescharacteristic
404#339C22×C4711yescharacteristic
405#339C22×C4711yescharacteristic
406#339C22×C4711yescharacteristic
407#339C22×C4711yescharacteristic
408#339C22×C4711yescharacteristic
409#339C22×C4711yescharacteristic
410#336C22×C4711yescharacteristic
411#336C22×C4711yescharacteristic
412C47#2294911yescharacteristic, direct product factor, Sylow
413C2×#41C23×C4711yescharacteristic
414C23×C4C23×C4711yescharacteristic
415#131—22no—
416#131—41no—
417C2×M16—21no—
418C2×M16—21no—
419C2×M16—22no—
420C2×M16—41no—
421C2×M16C23×C4711yescharacteristic
422C2×M16C23×C4711yescharacteristic
423C2×M16C23×C4711yescharacteristic
424C2×M16C23×C4711yescharacteristic
425C22×C8—21no—
426C22×C8—21no—
427C22×C8C23×C4711yescharacteristic
428C22×C8C23×C4711yescharacteristic
429C22×C8C23×C4711yescharacteristic
430C22×C8C23×C4711yescharacteristic
431#123—21no—
432C22⋊Q8C2×C4×C4711yescharacteristic
433C22⋊Q8C2×C4×C4711yescharacteristic
434#121C2×C4×C4711yescharacteristic
435#121C2×C4×C4711yescharacteristic
436#120—21no—
437C4×D4—21no—
438C4×D4—21no—
439#117—21no—
440#117—21no—
441#117—22no—
442#117—41no—
443#117C2×C4×C4711yescharacteristic
444#117C2×C4×C4711yescharacteristic
445#117C23×C4711yescharacteristic
446#117C23×C4711yescharacteristic
447#117C23×C4711yescharacteristic
448C2×C4⋊C4—21no—
449C2×C4⋊C4C2×C4×C4711yescharacteristic
450C2×C4⋊C4C2×C4×C4711yescharacteristic
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C42—21no—
454C2×C42C23×C4711yescharacteristic
455C2×C42C23×C4711yescharacteristic
456#108—22no—
457#108—41no—
458#107C2×C4×C4711yescharacteristic
459#107C2×C4×C4711yescharacteristic
460#107C2×C4×C4711yescharacteristic
461#107C2×C4×C4711yescharacteristic
462#106C2×C4×C4711yescharacteristic
463#106C2×C4×C4711yescharacteristic
464#106C2×C4×C4711yescharacteristic
465#106C2×C4×C4711yescharacteristic
466C4⋊C8—21no—
467C4⋊C8—21no—
468C4⋊C8—21no—
469C4⋊C8—21no—
470C4⋊C8—21no—
471C4⋊C8—21no—
472#104—22no—
473#104—41no—
474#103C2×C4×C4711yescharacteristic
475#103C2×C4×C4711yescharacteristic
476#103C2×C4×C4711yescharacteristic
477#103C2×C4×C4711yescharacteristic
478#102C2×C4×C4711yescharacteristic
479#102C2×C4×C4711yescharacteristic
480#102C2×C4×C4711yescharacteristic
481#102C2×C4×C4711yescharacteristic
482C22⋊C8—21no—
483C22⋊C8—21no—
484C22⋊C8—21no—
485C22⋊C8—21no—
486C22⋊C8C2×C4×C4711yescharacteristic
487C22⋊C8C2×C4×C4711yescharacteristic
488C22⋊C8C2×C4×C4711yescharacteristic
489C22⋊C8C2×C4×C4711yescharacteristic
490C22⋊C8D4×C4711yescharacteristic
491C22⋊C8D4×C4711yescharacteristic
492C22⋊C8D4×C4711yescharacteristic
493C22⋊C8D4×C4711yescharacteristic
494#97—21no—
495#97—21no—
496#97—21no—
497#97—22no—
498C4×C8—21no—
499C4×C8—21no—
500C4×C8—21no—
501C4×C8—41no—
502C24#41×C4711yescharacteristic
503#41—21no—
504#41—21no—
505#41—21no—
506#41—21no—
507C2×Q8C22×C4×C4711yescharacteristic
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4C22×C4×C4711yescharacteristic
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4C22×C4×C4711yescharacteristic
522C22×C4C22×C4×C4711yescharacteristic
523C22×C4C2×D4×C4711yescharacteristic
524C22×C4C2×D4×C4711yescharacteristic
525C22×C4#41×C4711yescharacteristic
526C22×C4C24×C4711yescharacteristic
527M16—21no—
528M16—21no—
529M16—21no—
530M16—21no—
531M16—21no—
532M16—21no—
533M16—21no—
534M16—42no—
535M16—42no—
536M16#41×C4712yes—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—42no—
550C2×C8—42no—
551C2×C8C22×C4×C4711yescharacteristic
552C2×C8C22×C4×C4711yescharacteristic
553C2×C8C22×C4×C4711yescharacteristic
554C2×C8C22×C4×C4711yescharacteristic
555C2×C8C2×D4×C4711yescharacteristic
556C2×C8C2×D4×C4711yescharacteristic
557C2×C8C2×D4×C4711yescharacteristic
558C2×C8C2×D4×C4711yescharacteristic
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—42no—
564C4⋊C4C22×C4×C4711yescharacteristic
565C4⋊C4C22×C4×C4711yescharacteristic
566C4⋊C4C22×C4×C4711yescharacteristic
567C4⋊C4C22×C4×C4711yescharacteristic
568C4⋊C4C22×C4×C4711yescharacteristic
569C4⋊C4C22×C4×C4711yescharacteristic
570C22⋊C4—21no—
571C22⋊C4—21no—
572C22⋊C4—21no—
573C22⋊C4—21no—
574C22⋊C4—21no—
575C22⋊C4—21no—
576C22⋊C4—21no—
577C22⋊C4—21no—
578C22⋊C4—21no—
579C22⋊C4—42no—
580C42—21no—
581C42—21no—
582C42—21no—
583C42—21no—
584C42—21no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42#41×C4712yes—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—41no—
593C23—41no—
594C23C4×D4×C4711yescharacteristic
595C23C4×D4×C4711yescharacteristic
596C23C2×#41×C4711yescharacteristic
597Q8—21no—
598Q8—21no—
599D4—21no—
600D4—21no—
601D4—42no—
602D4—41no—
603D4—41no—
604D4—81no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—42no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—81no—
632C2×C4C4×D4×C4711yescharacteristic
633C2×C4C4×D4×C4711yescharacteristic
634C2×C4C23×C4×C4711yescharacteristic
635C2×C4C22×D4×C4711yescharacteristic
636C2×C4C2×#41×C4711yescharacteristic
637C2×C4C2×#41×C4711yescharacteristic
638C2×C4H(5,𝔽2)×C4711yescharacteristic
639C2×C42−1+4×C4711yescharacteristic
640C8—21no—
641C8—21no—
642C8—21no—
643C8—21no—
644C8—21no—
645C8—21no—
646C8—22no—
647C8—21no—
648C8—21no—
649C8—41no—
650C8—41no—
651C8—41no—
652C22—21no—
653C22—21no—
654C22—21no—
655C22—21no—
656C22—21no—
657C22—21no—
658C22—21no—
659C22—21no—
660C22—41no—
661C22—41no—
662C22—41no—
663C22—81no—
664C22—81no—
665C22C2×C4×D4×C4711yescharacteristic
666C22C47×#55111yescharacteristic
667C22C47×#55211yescharacteristic
668C4—21no—
669C4—21no—
670C4—42no—
671C4—41no—
672C4—41no—
673C4—41no—
674C4—41no—
675C4—41no—
676C4—41no—
677C4—41no—
678C4—81no—
679C4C4×#41×C4711yescharacteristic
680C4C47×#52011yescharacteristic
681C4C47×#54611yescharacteristic
682C4C47×#54711yescharacteristic
683C2—21no—
684C2—21no—
685C2—41no—
686C2—41no—
687C2—81no—
688C2C47×#235911yescharacteristic
689C2C47×#295511yescharacteristic
690C2C47×#295711yescharacteristic
subgroupG/H
centerC2×C4×C47C22×D4
commutatorC2×C4C23×C4×C47
Frattini, cosocleC22×C4C24×C47
socleC22×C47C2×C4×D4
prime radicalC47×#525C22
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
3. C47×#2924C2semidirect
4. C47×#1945C2semidirect
5. C47×#1938C2semidirect
6. C47×#1929C2semidirect
7. C47×#1922C2semidirect
8. C47×#1922C2semidirect
10. C47×#1866C2semidirect
11. C47×#1855C2semidirect
12. C47×#1773C2semidirect
13. C47×#1764C2semidirect
14. C47×#1750C2semidirect
15. C47×#1733C2semidirect
21. C47×#485C4semidirect
22. C47×#485C4semidirect
23. C47×#484C4semidirect
24. C47×#483C4semidirect
25. C47×#482C4semidirect
26. C47×#482C4semidirect
27. C47×#481C4semidirect
28. C47×#480C4semidirect
306. #22949C47direct (N × H)
340. #2924C2×C47semidirect
341. #1945C2×C47semidirect
342. #1938C2×C47semidirect
343. #1929C2×C47semidirect
344. #1922C2×C47semidirect
345. #1922C2×C47semidirect
347. #1866C2×C47semidirect
348. #1855C2×C47semidirect
349. #1773C2×C47semidirect
350. #1764C2×C47semidirect
351. #1750C2×C47semidirect
352. #1733C2×C47semidirect
366. #485C4×C47semidirect
367. #485C4×C47semidirect
368. #484C4×C47semidirect
369. #483C4×C47semidirect
370. #482C4×C47semidirect
371. #482C4×C47semidirect
372. #481C4×C47semidirect
373. #480C4×C47semidirect
412. C47#22949direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#30912
C47×#29332
C47×#29242
C47×#19452
C47×#19382
C47×#19292
C47×#19222
C47×#18972
C47×#18662
C47×#18552
C47×#17732
C47×#17642
C47×#17502
C47×#17332
#2294947