Finite Group Databasebeta

← C47×#21629 #26061327

Subgroups — C47×#21629 #26061327

Order 12032.

730 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3076C211yesmaximal, characteristic
2C47×#2961C211yesmaximal, characteristic, complemented
3C47×#2875C211yesmaximal, characteristic
4C47×#1986C211yesmaximal, characteristic, complemented
5C47×#1950C211yesmaximal, characteristic, complemented
6C47×#1922C211yesmaximal, characteristic, complemented
7C47×#1922C211yesmaximal, characteristic, complemented
8C47×#1866C211yesmaximal, characteristic
9C47×#1866C211yesmaximal, characteristic
10C47×#1806C211yesmaximal, characteristic
11C47×#1773C211yesmaximal, characteristic, complemented
12C47×#1772C211yesmaximal, characteristic, complemented
13C47×#1771C211yesmaximal, characteristic, complemented
14C47×#1765C211yesmaximal, characteristic
15C47×#1764C211yesmaximal, characteristic
16C2×#131×C47C2211yescharacteristic
17C2×#131×C47C2211yescharacteristic
18C47×#533C2211yescharacteristic
19C4×#41×C47C2211yescharacteristic
20C47×#479C411yescharacteristic, complemented
21C47×#479C411yescharacteristic, complemented
22C47×#478C411yescharacteristic, complemented
23C47×#478C411yescharacteristic, complemented
24C47×#477C411yescharacteristic, complemented
25C47×#476C411yescharacteristic, complemented
26C47×#475C411yescharacteristic, complemented
27C47×#474C411yescharacteristic, complemented
28C47×#446—21no—
29C47×#446—21no—
30C47×#446—21no—
31C47×#446—21no—
32C2×#108×C47C2211yescharacteristic
33C2×#108×C47C2211yescharacteristic
34C47×#427C2211yescharacteristic
35C47×#427C2211yescharacteristic
36C47×#424C2211yescharacteristic
37C47×#424C2211yescharacteristic
38C47×#423C2211yescharacteristic
39C2×C4⋊C8×C47C2211yescharacteristic
40C2×#104×C47C2211yescharacteristic
41C2×#104×C47C2211yescharacteristic
42C47×#416C2211yescharacteristic
43C47×#416C2211yescharacteristic
44C47×#405—21no—
45C47×#405—21no—
46C47×#405C2211yescharacteristic
47C47×#405C2211yescharacteristic
48C47×#405C2211yescharacteristic
49C47×#405C2211yescharacteristic
50C4×M16×C47—21no—
51C4×M16×C47C2211yescharacteristic
52C2×#97×C47—21no—
53C2×#97×C47C2211yescharacteristic
54C2×#97×C47C2211yescharacteristic
55C2×C4×C8×C47C2211yescharacteristic
56C4×C4⋊C4×C47C2211yescharacteristic
57C47×#341C2211yescharacteristic
58C47×#341C2211yescharacteristic
59C47×#339C2211yescharacteristic
60C47×#339C2211yescharacteristic
61C47×#339C2211yescharacteristic
62C47×#339C2211yescharacteristic
63C47×#339C2211yescharacteristic
64C47×#339C2211yescharacteristic
65C47×#336C2211yescharacteristic
66C47×#336C2211yescharacteristic
67C2×#41×C47C2311yescharacteristic
68#131×C47—22no—
69#131×C47—22no—
70#131×C47—22no—
71#131×C47Q814yescomplemented
72C2×M16×C47—21no—
73C2×M16×C47—21no—
74C2×M16×C47C2311yescharacteristic
75C2×M16×C47C2311yescharacteristic
76C2×M16×C47C2311yescharacteristic
77C2×M16×C47C2311yescharacteristic
78C22×C8×C47—21no—
79C22×C8×C47—21no—
80C22×C8×C47C2311yescharacteristic
81C22×C8×C47C2311yescharacteristic
82C22×C8×C47C2311yescharacteristic
83C22×C8×C47C2311yescharacteristic
84C4⋊Q8×C47C2×C411yescharacteristic
85C4⋊Q8×C47C2×C411yescharacteristic
86#125×C47C2×C411yescharacteristic
87#125×C47C2×C411yescharacteristic
88C22⋊Q8×C47—21no—
89C22⋊Q8×C47—21no—
90C4×Q8×C47—21no—
91C4×Q8×C47—21no—
92C4×Q8×C47C2×C411yescharacteristic
93C4×Q8×C47C2×C411yescharacteristic
94C4×D4×C47—21no—
95C4×D4×C47—21no—
96C4×D4×C47C2×C411yescharacteristic
97C4×D4×C47C2×C411yescharacteristic
98#117×C47—21no—
99#117×C47C2311yescharacteristic
100#117×C47C2311yescharacteristic
101#117×C47C2311yescharacteristic
102C2×C4⋊C4×C47—21no—
103C2×C42×C47—21no—
104C2×C42×C47C2311yescharacteristic
105C2×C42×C47C2311yescharacteristic
106C2×C42×C47C2311yescharacteristic
107#108×C47—22no—
108#108×C47—22no—
109#107×C47C2×C411yescharacteristic
110#107×C47C2×C411yescharacteristic
111#107×C47C2×C411yescharacteristic
112#107×C47C2×C411yescharacteristic
113#106×C47C2×C411yescharacteristic
114#106×C47C2×C411yescharacteristic
115#106×C47C2×C411yescharacteristic
116#106×C47C2×C411yescharacteristic
117C4⋊C8×C47—21no—
118C4⋊C8×C47—21no—
119C4⋊C8×C47—21no—
120C4⋊C8×C47—21no—
121C4⋊C8×C47—21no—
122C4⋊C8×C47—21no—
123C4⋊C8×C47C2×C411yescharacteristic
124C4⋊C8×C47C2×C411yescharacteristic
125C4⋊C8×C47C2×C411yescharacteristic
126C4⋊C8×C47C2×C411yescharacteristic
127#104×C47—22no—
128#104×C47—22no—
129#103×C47C2×C411yescharacteristic
130#103×C47C2×C411yescharacteristic
131#103×C47C2×C411yescharacteristic
132#103×C47C2×C411yescharacteristic
133#102×C47C2×C411yescharacteristic
134#102×C47C2×C411yescharacteristic
135#102×C47C2×C411yescharacteristic
136#102×C47C2×C411yescharacteristic
137#97×C47—21no—
138#97×C47—21no—
139#97×C47—21no—
140#97×C47—21no—
141#97×C47—22no—
142#97×C47—21no—
143#97×C47D411yescharacteristic
144#97×C47D411yescharacteristic
145#97×C47D411yescharacteristic
146#97×C47D411yescharacteristic
147C4×C8×C47—21no—
148C4×C8×C47—21no—
149C4×C8×C47—21no—
150C4×C8×C47—21no—
151C4×C8×C47—22no—
152C4×C8×C47—21no—
153#95×C47—21no—
154#41×C47—21no—
155#41×C47—21no—
156#41×C47C2×Q812yes—
157#41×C47#4112yes—
158C2×Q8×C47—21no—
159C2×Q8×C47—21no—
160C2×Q8×C47C22×C411yescharacteristic
161C2×D4×C47—21no—
162C2×D4×C47C22×C411yescharacteristic
163C22×C4×C47—21no—
164C22×C4×C47—21no—
165C22×C4×C47—21no—
166C22×C4×C47—21no—
167C22×C4×C47—21no—
168C22×C4×C47#4111yescharacteristic
169C22×C4×C47#4111yescharacteristic
170C22×C4×C47C2411yescharacteristic
171M16×C47—24no—
172M16×C47—21no—
173M16×C47—21no—
174M16×C47—24no—
175M16×C47—21no—
176M16×C47—21no—
177M16×C47—21no—
178M16×C47—21no—
179M16×C47C2×Q812yes—
180M16×C47#4112yes—
181C2×C8×C47—24no—
182C2×C8×C47—21no—
183C2×C8×C47—21no—
184C2×C8×C47—21no—
185C2×C8×C47—21no—
186C2×C8×C47—21no—
187C2×C8×C47—21no—
188C2×C8×C47—21no—
189C2×C8×C47—21no—
190C2×C8×C47—24no—
191C2×C8×C47—21no—
192C2×C8×C47—21no—
193C2×C8×C47C22×C411yescharacteristic
194C2×C8×C47C22×C411yescharacteristic
195C2×C8×C47C22×C411yescharacteristic
196C2×C8×C47C22×C411yescharacteristic
197C2×C8×C47C2×D411yescharacteristic
198C2×C8×C47C2×D411yescharacteristic
199C2×C8×C47C2×D411yescharacteristic
200C2×C8×C47C2×D411yescharacteristic
201C2×C8×C47C2×Q812yes—
202C2×C8×C47#4112yes—
203C4⋊C4×C47—21no—
204C4⋊C4×C47—21no—
205C4⋊C4×C47—21no—
206C4⋊C4×C47—21no—
207C4⋊C4×C47—21no—
208C4⋊C4×C47—21no—
209C4⋊C4×C47—21no—
210C4⋊C4×C47—21no—
211C4⋊C4×C47—42no—
212C4⋊C4×C47C22×C411yescharacteristic
213C4⋊C4×C47C22×C411yescharacteristic
214C4⋊C4×C47C22×C411yescharacteristic
215C4⋊C4×C47C22×C411yescharacteristic
216C4⋊C4×C47C22×C411yescharacteristic
217C4⋊C4×C47C22×C411yescharacteristic
218C22⋊C4×C47—21no—
219C22⋊C4×C47—21no—
220C22⋊C4×C47—21no—
221C22⋊C4×C47—21no—
222C22⋊C4×C47—21no—
223C42×C47—21no—
224C42×C47—21no—
225C42×C47—21no—
226C42×C47—21no—
227C42×C47—21no—
228C42×C47—21no—
229C42×C47—21no—
230C42×C47—21no—
231C42×C47—21no—
232C42×C47C22×C411yescharacteristic
233C42×C47C22×C411yescharacteristic
234C42×C47C2×D411yescharacteristic
235C42×C47C2×D411yescharacteristic
236C23×C47—21no—
237C23×C47C2×#4111yescharacteristic
238Q8×C47—21no—
239Q8×C47—81no—
240Q8×C47—81no—
241Q8×C47C4×Q812yes—
242D4×C47—22no—
243D4×C47—22no—
244D4×C47—21no—
245D4×C47C4×Q812yes—
246C2×C4×C47—21no—
247C2×C4×C47—22no—
248C2×C4×C47—22no—
249C2×C4×C47—22no—
250C2×C4×C47—21no—
251C2×C4×C47—21no—
252C2×C4×C47—21no—
253C2×C4×C47—21no—
254C2×C4×C47—21no—
255C2×C4×C47—21no—
256C2×C4×C47—41no—
257C2×C4×C47—41no—
258C2×C4×C47—41no—
259C2×C4×C47—41no—
260C2×C4×C47—41no—
261C2×C4×C47—41no—
262C2×C4×C47—41no—
263C2×C4×C47—81no—
264C2×C4×C47—81no—
265C2×C4×C47C4×D411yescharacteristic
266C2×C4×C47C4×D411yescharacteristic
267C2×C4×C47C4×D411yescharacteristic
268C2×C4×C47C4×D411yescharacteristic
269C2×C4×C47C23×C411yescharacteristic
270C2×C4×C47C22×D411yescharacteristic
271C2×C4×C47C22×Q811yescharacteristic
272C2×C4×C47C2×#4111yescharacteristic
273C2×C4×C47C2×#4111yescharacteristic
274C2×C4×C47C2×#4111yescharacteristic
275C8×C47—21no—
276C8×C47—21no—
277C8×C47—21no—
278C8×C47—21no—
279C8×C47—22no—
280C8×C47—21no—
281C8×C47—22no—
282C8×C47—21no—
283C8×C47—41no—
284C8×C47—41no—
285C8×C47C22⋊Q812yes—
286C8×C47C22⋊Q812yes—
287#21629C4711yesmaximal, characteristic, direct product factor, Sylow
288C22×C47—21no—
289C22×C47—21no—
290C22×C47—22no—
291C22×C47—41no—
292C22×C47—41no—
293C22×C47C2×C4×D411yescharacteristic
294C22×C47#52911yescharacteristic
295C22×C47#53311yescharacteristic
296C4×C47—21no—
297C4×C47—21no—
298C4×C47—21no—
299C4×C47—21no—
300C4×C47—22no—
301C4×C47—42no—
302C4×C47—41no—
303C4×C47—41no—
304C4×C47—41no—
305C4×C47—41no—
306C4×C47—41no—
307C4×C47—41no—
308C4×C47—81no—
309C4×C47C2×C4×Q811yescharacteristic
310C4×C47C4×#4111yescharacteristic
311C4×C47C2×C22⋊Q811yescharacteristic
312C4×C47#52511yescharacteristic
313#3076C2×C4711yescharacteristic
314#2961C2×C4711yescharacteristic, complemented
315#2875C2×C4711yescharacteristic
316#1986C2×C4711yescharacteristic, complemented
317#1950C2×C4711yescharacteristic, complemented
318#1922C2×C4711yescharacteristic, complemented
319#1922C2×C4711yescharacteristic, complemented
320#1866C2×C4711yescharacteristic
321#1866C2×C4711yescharacteristic
322#1806C2×C4711yescharacteristic
323#1773C2×C4711yescharacteristic, complemented
324#1772C2×C4711yescharacteristic, complemented
325#1771C2×C4711yescharacteristic, complemented
326#1765C2×C4711yescharacteristic
327#1764C2×C4711yescharacteristic
328C2×C47—21no—
329C2×C47—21no—
330C2×C47—42no—
331C2×C47C4×C22⋊Q811yescharacteristic
332C2×C47#295611yescharacteristic
333C2×C47#295711yescharacteristic
334C2×#131C22×C4711yescharacteristic
335C2×#131C22×C4711yescharacteristic
336#533C22×C4711yescharacteristic
337C4×#41C22×C4711yescharacteristic
338#479C4×C4711yescharacteristic, complemented
339#479C4×C4711yescharacteristic, complemented
340#478C4×C4711yescharacteristic, complemented
341#478C4×C4711yescharacteristic, complemented
342#477C4×C4711yescharacteristic, complemented
343#476C4×C4711yescharacteristic, complemented
344#475C4×C4711yescharacteristic, complemented
345#474C4×C4711yescharacteristic, complemented
346#446—21no—
347#446—21no—
348#446—21no—
349#446—21no—
350C2×#108C22×C4711yescharacteristic
351C2×#108C22×C4711yescharacteristic
352#427C22×C4711yescharacteristic
353#427C22×C4711yescharacteristic
354#424C22×C4711yescharacteristic
355#424C22×C4711yescharacteristic
356#423C22×C4711yescharacteristic
357C2×C4⋊C8C22×C4711yescharacteristic
358C2×#104C22×C4711yescharacteristic
359C2×#104C22×C4711yescharacteristic
360#416C22×C4711yescharacteristic
361#416C22×C4711yescharacteristic
362#405—21no—
363#405—21no—
364#405C22×C4711yescharacteristic
365#405C22×C4711yescharacteristic
366#405C22×C4711yescharacteristic
367#405C22×C4711yescharacteristic
368C4×M16—21no—
369C4×M16C22×C4711yescharacteristic
370C2×#97—21no—
371C2×#97C22×C4711yescharacteristic
372C2×#97C22×C4711yescharacteristic
373C2×C4×C8C22×C4711yescharacteristic
374C4×C4⋊C4C22×C4711yescharacteristic
375#341C22×C4711yescharacteristic
376#341C22×C4711yescharacteristic
377#339C22×C4711yescharacteristic
378#339C22×C4711yescharacteristic
379#339C22×C4711yescharacteristic
380#339C22×C4711yescharacteristic
381#339C22×C4711yescharacteristic
382#339C22×C4711yescharacteristic
383#336C22×C4711yescharacteristic
384#336C22×C4711yescharacteristic
385C47#2162911yescharacteristic, direct product factor, Sylow
386C2×#41C23×C4711yescharacteristic
387#131—22no—
388#131—22no—
389#131—22no—
390#131Q8×C4714yescomplemented
391C2×M16—21no—
392C2×M16—21no—
393C2×M16C23×C4711yescharacteristic
394C2×M16C23×C4711yescharacteristic
395C2×M16C23×C4711yescharacteristic
396C2×M16C23×C4711yescharacteristic
397C22×C8—21no—
398C22×C8—21no—
399C22×C8C23×C4711yescharacteristic
400C22×C8C23×C4711yescharacteristic
401C22×C8C23×C4711yescharacteristic
402C22×C8C23×C4711yescharacteristic
403C4⋊Q8C2×C4×C4711yescharacteristic
404C4⋊Q8C2×C4×C4711yescharacteristic
405#125C2×C4×C4711yescharacteristic
406#125C2×C4×C4711yescharacteristic
407C22⋊Q8—21no—
408C22⋊Q8—21no—
409C4×Q8—21no—
410C4×Q8—21no—
411C4×Q8C2×C4×C4711yescharacteristic
412C4×Q8C2×C4×C4711yescharacteristic
413C4×D4—21no—
414C4×D4—21no—
415C4×D4C2×C4×C4711yescharacteristic
416C4×D4C2×C4×C4711yescharacteristic
417#117—21no—
418#117C23×C4711yescharacteristic
419#117C23×C4711yescharacteristic
420#117C23×C4711yescharacteristic
421C2×C4⋊C4—21no—
422C2×C42—21no—
423C2×C42C23×C4711yescharacteristic
424C2×C42C23×C4711yescharacteristic
425C2×C42C23×C4711yescharacteristic
426#108—22no—
427#108—22no—
428#107C2×C4×C4711yescharacteristic
429#107C2×C4×C4711yescharacteristic
430#107C2×C4×C4711yescharacteristic
431#107C2×C4×C4711yescharacteristic
432#106C2×C4×C4711yescharacteristic
433#106C2×C4×C4711yescharacteristic
434#106C2×C4×C4711yescharacteristic
435#106C2×C4×C4711yescharacteristic
436C4⋊C8—21no—
437C4⋊C8—21no—
438C4⋊C8—21no—
439C4⋊C8—21no—
440C4⋊C8—21no—
441C4⋊C8—21no—
442C4⋊C8C2×C4×C4711yescharacteristic
443C4⋊C8C2×C4×C4711yescharacteristic
444C4⋊C8C2×C4×C4711yescharacteristic
445C4⋊C8C2×C4×C4711yescharacteristic
446#104—22no—
447#104—22no—
448#103C2×C4×C4711yescharacteristic
449#103C2×C4×C4711yescharacteristic
450#103C2×C4×C4711yescharacteristic
451#103C2×C4×C4711yescharacteristic
452#102C2×C4×C4711yescharacteristic
453#102C2×C4×C4711yescharacteristic
454#102C2×C4×C4711yescharacteristic
455#102C2×C4×C4711yescharacteristic
456#97—21no—
457#97—21no—
458#97—21no—
459#97—21no—
460#97—22no—
461#97—21no—
462#97D4×C4711yescharacteristic
463#97D4×C4711yescharacteristic
464#97D4×C4711yescharacteristic
465#97D4×C4711yescharacteristic
466C4×C8—21no—
467C4×C8—21no—
468C4×C8—21no—
469C4×C8—21no—
470C4×C8—22no—
471C4×C8—21no—
472#95—21no—
473#41—21no—
474#41—21no—
475#41C2×Q8×C4712yes—
476#41#41×C4712yes—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8C22×C4×C4711yescharacteristic
480C2×D4—21no—
481C2×D4C22×C4×C4711yescharacteristic
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4#41×C4711yescharacteristic
488C22×C4#41×C4711yescharacteristic
489C22×C4C24×C4711yescharacteristic
490M16—24no—
491M16—21no—
492M16—21no—
493M16—24no—
494M16—21no—
495M16—21no—
496M16—21no—
497M16—21no—
498M16C2×Q8×C4712yes—
499M16#41×C4712yes—
500C2×C8—24no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—24no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8C22×C4×C4711yescharacteristic
513C2×C8C22×C4×C4711yescharacteristic
514C2×C8C22×C4×C4711yescharacteristic
515C2×C8C22×C4×C4711yescharacteristic
516C2×C8C2×D4×C4711yescharacteristic
517C2×C8C2×D4×C4711yescharacteristic
518C2×C8C2×D4×C4711yescharacteristic
519C2×C8C2×D4×C4711yescharacteristic
520C2×C8C2×Q8×C4712yes—
521C2×C8#41×C4712yes—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—42no—
531C4⋊C4C22×C4×C4711yescharacteristic
532C4⋊C4C22×C4×C4711yescharacteristic
533C4⋊C4C22×C4×C4711yescharacteristic
534C4⋊C4C22×C4×C4711yescharacteristic
535C4⋊C4C22×C4×C4711yescharacteristic
536C4⋊C4C22×C4×C4711yescharacteristic
537C22⋊C4—21no—
538C22⋊C4—21no—
539C22⋊C4—21no—
540C22⋊C4—21no—
541C22⋊C4—21no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—21no—
546C42—21no—
547C42—21no—
548C42—21no—
549C42—21no—
550C42—21no—
551C42C22×C4×C4711yescharacteristic
552C42C22×C4×C4711yescharacteristic
553C42C2×D4×C4711yescharacteristic
554C42C2×D4×C4711yescharacteristic
555C23—21no—
556C23C2×#41×C4711yescharacteristic
557Q8—21no—
558Q8—81no—
559Q8—81no—
560Q8C4×Q8×C4712yes—
561D4—22no—
562D4—22no—
563D4—21no—
564D4C4×Q8×C4712yes—
565C2×C4—21no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—81no—
583C2×C4—81no—
584C2×C4C4×D4×C4711yescharacteristic
585C2×C4C4×D4×C4711yescharacteristic
586C2×C4C4×D4×C4711yescharacteristic
587C2×C4C4×D4×C4711yescharacteristic
588C2×C4C23×C4×C4711yescharacteristic
589C2×C4C22×D4×C4711yescharacteristic
590C2×C4C22×Q8×C4711yescharacteristic
591C2×C4C2×#41×C4711yescharacteristic
592C2×C4C2×#41×C4711yescharacteristic
593C2×C4C2×#41×C4711yescharacteristic
594C8—21no—
595C8—21no—
596C8—21no—
597C8—21no—
598C8—22no—
599C8—21no—
600C8—22no—
601C8—21no—
602C8—41no—
603C8—41no—
604C8C22⋊Q8×C4712yes—
605C8C22⋊Q8×C4712yes—
606C22—21no—
607C22—21no—
608C22—22no—
609C22—41no—
610C22—41no—
611C22C2×C4×D4×C4711yescharacteristic
612C22C47×#52911yescharacteristic
613C22C47×#53311yescharacteristic
614C4—22no—
615C4—21no—
616C4—21no—
617C4—21no—
618C4—21no—
619C4—42no—
620C4—41no—
621C4—41no—
622C4—41no—
623C4—41no—
624C4—41no—
625C4—41no—
626C4—81no—
627C4C2×C4×Q8×C4711yescharacteristic
628C4C4×#41×C4711yescharacteristic
629C4C2×C22⋊Q8×C4711yescharacteristic
630C4C47×#52511yescharacteristic
631C2—21no—
632C2—21no—
633C2—42no—
634C2C4×C22⋊Q8×C4711yescharacteristic
635C2C47×#295611yescharacteristic
636C2C47×#295711yescharacteristic
subgroupG/H
centerC2×C4×C47C22×D4
commutatorC2×C4C23×C4×C47
Frattini, cosocleC22×C4C24×C47
socleC22×C47C2×C4×D4
prime radicalC2×#41×C47C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C47 ◁ C2×#97×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#2961C2semidirect
4. C47×#1986C2semidirect
5. C47×#1950C2semidirect
6. C47×#1922C2semidirect
7. C47×#1922C2semidirect
11. C47×#1773C2semidirect
12. C47×#1772C2semidirect
13. C47×#1771C2semidirect
20. C47×#479C4semidirect
21. C47×#479C4semidirect
22. C47×#478C4semidirect
23. C47×#478C4semidirect
24. C47×#477C4semidirect
25. C47×#476C4semidirect
26. C47×#475C4semidirect
27. C47×#474C4semidirect
71. #131×C47Q8semidirect
287. #21629C47direct (N × H)
314. #2961C2×C47semidirect
316. #1986C2×C47semidirect
317. #1950C2×C47semidirect
318. #1922C2×C47semidirect
319. #1922C2×C47semidirect
323. #1773C2×C47semidirect
324. #1772C2×C47semidirect
325. #1771C2×C47semidirect
338. #479C4×C47semidirect
339. #479C4×C47semidirect
340. #478C4×C47semidirect
341. #478C4×C47semidirect
342. #477C4×C47semidirect
343. #476C4×C47semidirect
344. #475C4×C47semidirect
345. #474C4×C47semidirect
385. C47#21629direct (N × H)
390. #131Q8×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#30762
C47×#29612
C47×#28752
C47×#19862
C47×#19502
C47×#19222
C47×#18662
C47×#18062
C47×#17732
C47×#17722
C47×#17712
C47×#17652
C47×#17642
#2162947