Finite Group Databasebeta

← C47×#25076 #26064774

Subgroups — C47×#25076 #26064774

Order 12032.

1440 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#466C211yesmaximal, characteristic, complemented
2C2×C47×#459C211yesmaximal, characteristic, complemented
3C2×C47×#447C211yesmaximal, characteristic, complemented
4C22×#102×C47C211yesmaximal, characteristic, complemented
5C47×#2433C211yesmaximal, characteristic, complemented
6C47×#2361C211yesmaximal, characteristic, complemented
7C47×#2067C211yesmaximal, characteristic, complemented
8C47×#2054C211yesmaximal, characteristic, complemented
9C47×#2041C211yesmaximal, characteristic, complemented
10C47×#2011C211yesmaximal, characteristic, complemented
11C47×#1982C211yesmaximal, characteristic, complemented
12C47×#1925C211yesmaximal, characteristic, complemented
13C47×#1879C211yesmaximal, characteristic, complemented
14C47×#1874C211yesmaximal, characteristic, complemented
15C47×#1850C211yesmaximal, characteristic, complemented
16C23×D4×C47C2211yescharacteristic
17C22×D8×C47C2211yescharacteristic
18C22×D8×C47C2211yescharacteristic
19C22×D8×C47C2211yescharacteristic, complemented
20C23×C8×C47C2211yescharacteristic
21C2×#127×C47C2211yescharacteristic
22C2×#127×C47C2211yescharacteristic
23C2×#121×C47C2211yescharacteristic
24C2×#121×C47C2211yescharacteristic
25C2×#120×C47—21no—
26C2×#120×C47—21no—
27C2×C4×D4×C47—21no—
28C2×C4×D4×C47C2211yescharacteristic, complemented
29C22×C4⋊C4×C47C2211yescharacteristic
30C47×#466—24no—
31C47×#459—24no—
32C47×#447—24no—
33C2×#107×C47C2211yescharacteristic, complemented
34C2×C4⋊C8×C47C2211yescharacteristic, complemented
35C2×C4⋊C8×C47C2211yescharacteristic, complemented
36C2×#102×C47—24no—
37C2×#102×C47C2211yescharacteristic
38C2×#102×C47C2211yescharacteristic
39C2×#102×C47C2211yescharacteristic
40C2×#102×C47C2211yescharacteristic
41C2×#102×C47C2211yescharacteristic
42C2×#102×C47C2211yescharacteristic
43C2×#102×C47C2211yescharacteristic, complemented
44C2×#102×C47C2211yescharacteristic, complemented
45C2×#102×C47C2211yescharacteristic, complemented
46C2×#102×C47C2211yescharacteristic, complemented
47C2×C22⋊C8×C47C2211yescharacteristic
48C47×#392—21no—
49C47×#392—21no—
50C47×#390C2211yescharacteristic
51C47×#390C2211yescharacteristic
52C47×#390C2211yescharacteristic, complemented
53C47×#389C2211yescharacteristic, complemented
54C47×#388—21no—
55C47×#386—21no—
56C47×#385—21no—
57C4×C4⋊C4×C47C2211yescharacteristic, complemented
58C4×C22⋊C4×C47C2211yescharacteristic
59C47×#340C2211yescharacteristic, complemented
60C47×#340C2211yescharacteristic, complemented
61C47×#336C2211yescharacteristic, complemented
62C47×#336C2211yescharacteristic, complemented
63C25×C47—21no—
64C22×D4×C47—22no—
65C22×D4×C47—22no—
66C22×D4×C47—21no—
67C22×D4×C47—21no—
68C22×D4×C47—22no—
69C22×D4×C47—21no—
70C22×D4×C47—21no—
71C22×D4×C47—21no—
72C22×D4×C47—21no—
73C22×D4×C47—21no—
74C22×D4×C47—22no—
75C22×D4×C47—41no—
76C22×D4×C47—41no—
77C22×D4×C47C2311yescharacteristic
78C22×D4×C47C2311yescharacteristic
79C22×D4×C47C2311yescharacteristic
80C22×D4×C47C2311yescharacteristic
81C23×C4×C47—21no—
82C23×C4×C47—21no—
83C23×C4×C47C2311yescharacteristic
84C2×D8×C47—22no—
85C2×D8×C47—22no—
86C2×D8×C47—22no—
87C2×D8×C47—22no—
88C2×D8×C47—22no—
89C2×D8×C47—22no—
90C2×D8×C47—41no—
91C2×D8×C47—41no—
92C2×D8×C47—41no—
93C22×C8×C47—22no—
94C22×C8×C47—22no—
95C22×C8×C47—41no—
96C22×C8×C47C2311yescharacteristic
97C22×C8×C47C2311yescharacteristic
98C22×C8×C47C2311yescharacteristic
99C22×C8×C47C2311yescharacteristic
100#127×C47—22no—
101#127×C47—22no—
102#127×C47—41no—
103#127×C47—41no—
104#121×C47—22no—
105#121×C47—22no—
106#121×C47—22no—
107#121×C47D414yescomplemented
108#120×C47—44no—
109#120×C47—44no—
110C4×D4×C47—22no—
111C4×D4×C47—41no—
112C4×D4×C47—44no—
113C2×C4⋊C4×C47—22no—
114C2×C4⋊C4×C47—21no—
115C2×C4⋊C4×C47—21no—
116C2×C4⋊C4×C47—41no—
117C2×C4⋊C4×C47C2311yescharacteristic
118C2×C4⋊C4×C47C2311yescharacteristic
119C2×C4⋊C4×C47C2311yescharacteristic
120C2×C4⋊C4×C47C2311yescharacteristic
121C2×C22⋊C4×C47—21no—
122C2×C22⋊C4×C47—21no—
123C2×C22⋊C4×C47—21no—
124C2×C22⋊C4×C47—21no—
125C2×C22⋊C4×C47—21no—
126C2×C22⋊C4×C47—21no—
127C2×C22⋊C4×C47—21no—
128C2×C22⋊C4×C47—21no—
129C2×C22⋊C4×C47—21no—
130C2×C22⋊C4×C47D411yescharacteristic
131C2×C22⋊C4×C47D411yescharacteristic
132C2×C42×C47—21no—
133C2×C42×C47C2311yescharacteristic
134C2×C42×C47C2311yescharacteristic
135#107×C47—22no—
136C4⋊C8×C47—22no—
137C4⋊C8×C47—41no—
138#102×C47—22no—
139#102×C47—22no—
140#102×C47—22no—
141#102×C47—22no—
142#102×C47—22no—
143#102×C47—22no—
144#102×C47—22no—
145#102×C47—22no—
146#102×C47—41no—
147#102×C47D414yescomplemented
148C22⋊C8×C47—22no—
149#95×C47—21no—
150#95×C47—21no—
151#95×C47D411yescharacteristic
152#95×C47D411yescharacteristic
153C24×C47—21no—
154C24×C47—21no—
155C24×C47—21no—
156C24×C47—21no—
157C24×C47—42no—
158C24×C47—42no—
159C24×C47—42no—
160C24×C47—42no—
161C24×C47—42no—
162C24×C47—81no—
163C24×C47—81no—
164C24×C47C2×D411yescharacteristic
165C2×D4×C47—28no—
166C2×D4×C47—24no—
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—21no—
182C2×D4×C47—21no—
183C2×D4×C47—21no—
184C2×D4×C47—21no—
185C2×D4×C47—21no—
186C2×D4×C47—21no—
187C2×D4×C47—21no—
188C2×D4×C47—44no—
189C2×D4×C47—44no—
190C2×D4×C47—42no—
191C2×D4×C47—42no—
192C2×D4×C47—44no—
193C2×D4×C47—42no—
194C2×D4×C47—42no—
195C2×D4×C47—42no—
196C2×D4×C47—42no—
197C2×D4×C47—42no—
198C2×D4×C47—42no—
199C2×D4×C47—42no—
200C2×D4×C47—42no—
201C2×D4×C47—42no—
202C2×D4×C47—42no—
203C2×D4×C47—42no—
204C2×D4×C47—42no—
205C2×D4×C47—42no—
206C2×D4×C47—42no—
207C2×D4×C47—81no—
208C2×D4×C47—81no—
209C2×D4×C47—81no—
210C2×D4×C47—81no—
211C2×D4×C47C2×D412yes—
212C2×D4×C47C2×D412yes—
213C2×D4×C47#4112yes—
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—42no—
223C22×C4×C47—42no—
224C22×C4×C47—42no—
225C22×C4×C47—42no—
226C22×C4×C47—81no—
227C22×C4×C47—81no—
228C22×C4×C47C2×D411yescharacteristic
229C22×C4×C47C2×D411yescharacteristic
230C22×C4×C47C2×D411yescharacteristic
231C22×C4×C47C2×D412yes—
232C22×C4×C47C2×D411yescharacteristic
233C22×C4×C47C2×D411yescharacteristic
234C22×C4×C47#4112yes—
235C22×C4×C47C2411yescharacteristic
236D8×C47—44no—
237D8×C47—44no—
238D8×C47—44no—
239C2×C8×C47—21no—
240C2×C8×C47—21no—
241C2×C8×C47—21no—
242C2×C8×C47—21no—
243C2×C8×C47—21no—
244C2×C8×C47—21no—
245C2×C8×C47—21no—
246C2×C8×C47—21no—
247C2×C8×C47—21no—
248C2×C8×C47—21no—
249C2×C8×C47—21no—
250C2×C8×C47—44no—
251C2×C8×C47C2×D412yes—
252C4⋊C4×C47—21no—
253C4⋊C4×C47—21no—
254C4⋊C4×C47—21no—
255C4⋊C4×C47—21no—
256C4⋊C4×C47—21no—
257C4⋊C4×C47—21no—
258C4⋊C4×C47—42no—
259C4⋊C4×C47—42no—
260C4⋊C4×C47C2×D412yes—
261C4⋊C4×C47C2×D412yes—
262C22⋊C4×C47—22no—
263C22⋊C4×C47—24no—
264C22⋊C4×C47—42no—
265C22⋊C4×C47—42no—
266C22⋊C4×C47—42no—
267C22⋊C4×C47—42no—
268C22⋊C4×C47—42no—
269C22⋊C4×C47—42no—
270C22⋊C4×C47—42no—
271C22⋊C4×C47—81no—
272C22⋊C4×C47D814yescomplemented
273C42×C47—21no—
274C42×C47—21no—
275C42×C47—21no—
276C42×C47—21no—
277C42×C47—42no—
278C23×C47—21no—
279C23×C47—21no—
280C23×C47—21no—
281C23×C47—21no—
282C23×C47—22no—
283C23×C47—22no—
284C23×C47—22no—
285C23×C47—48no—
286C23×C47—41no—
287C23×C47—41no—
288C23×C47—41no—
289C23×C47—41no—
290C23×C47—41no—
291C23×C47—41no—
292C23×C47—41no—
293C23×C47—41no—
294C23×C47—41no—
295C23×C47—41no—
296C23×C47—41no—
297C23×C47—41no—
298C23×C47—41no—
299C23×C47—41no—
300C23×C47—41no—
301C23×C47—41no—
302C23×C47—41no—
303C23×C47—41no—
304C23×C47—41no—
305C23×C47—41no—
306C23×C47—41no—
307C23×C47—41no—
308C23×C47—41no—
309C23×C47—41no—
310C23×C47—41no—
311C23×C47—84no—
312C23×C47—84no—
313C23×C47—84no—
314C23×C47—84no—
315C23×C47—84no—
316C23×C47—84no—
317C23×C47#12112yes—
318C23×C47C2×D812yes—
319C23×C47AGL(1,ℤ/8)12yes—
320C23×C47C22×D411yescharacteristic
321D4×C47—22no—
322D4×C47—22no—
323D4×C47—22no—
324D4×C47—22no—
325D4×C47—22no—
326D4×C47—22no—
327D4×C47—48no—
328D4×C47—48no—
329D4×C47—41no—
330D4×C47—41no—
331D4×C47—41no—
332D4×C47—41no—
333D4×C47—41no—
334D4×C47—41no—
335D4×C47—41no—
336D4×C47—41no—
337D4×C47—41no—
338D4×C47—41no—
339D4×C47—84no—
340D4×C47—84no—
341D4×C47—84no—
342D4×C47—84no—
343D4×C47—84no—
344C2×C4×C47—21no—
345C2×C4×C47—21no—
346C2×C4×C47—21no—
347C2×C4×C47—21no—
348C2×C4×C47—21no—
349C2×C4×C47—21no—
350C2×C4×C47—22no—
351C2×C4×C47—22no—
352C2×C4×C47—22no—
353C2×C4×C47—22no—
354C2×C4×C47—22no—
355C2×C4×C47—21no—
356C2×C4×C47—22no—
357C2×C4×C47—21no—
358C2×C4×C47—21no—
359C2×C4×C47—21no—
360C2×C4×C47—21no—
361C2×C4×C47—21no—
362C2×C4×C47—41no—
363C2×C4×C47—41no—
364C2×C4×C47—41no—
365C2×C4×C47—41no—
366C2×C4×C47—41no—
367C2×C4×C47—41no—
368C2×C4×C47—41no—
369C2×C4×C47—41no—
370C2×C4×C47—41no—
371C2×C4×C47—41no—
372C2×C4×C47—84no—
373C2×C4×C47—84no—
374C2×C4×C47#12112yes—
375C2×C4×C47C2×D812yes—
376C2×C4×C47C2×D812yes—
377C2×C4×C47C22×D411yescharacteristic
378C2×C4×C47C22×D411yescharacteristic
379C2×C4×C47C2×#4111yescharacteristic
380C2×C4×C47C2×#4111yescharacteristic
381C2×C4×C47H(5,𝔽2)11yescharacteristic
382C2×C4×C47H(5,𝔽2)11yescharacteristic
383C8×C47—22no—
384C8×C47—41no—
385C8×C47—41no—
386C8×C47—41no—
387#25076C4711yesmaximal, characteristic, direct product factor, Sylow
388C22×C47—22no—
389C22×C47—22no—
390C22×C47—22no—
391C22×C47—22no—
392C22×C47—22no—
393C22×C47—22no—
394C22×C47—42no—
395C22×C47—42no—
396C22×C47—42no—
397C22×C47—42no—
398C22×C47—42no—
399C22×C47—42no—
400C22×C47—42no—
401C22×C47—42no—
402C22×C47—42no—
403C22×C47—816no—
404C22×C47—81no—
405C22×C47—81no—
406C22×C47—81no—
407C22×C47—81no—
408C22×C47—81no—
409C22×C47—81no—
410C22×C47—81no—
411C22×C47—81no—
412C22×C47—81no—
413C22×C47—81no—
414C22×C47—81no—
415C22×C47—81no—
416C22×C47—81no—
417C22×C47—81no—
418C22×C47—81no—
419C22×C47—81no—
420C22×C47—81no—
421C22×C47—81no—
422C22×C47—81no—
423C22×C47#45914yescomplemented
424C22×C47C2×#12111yescharacteristic
425C22×C47D4211yescharacteristic
426C22×C47#54611yescharacteristic
427C22×C47C22×D811yescharacteristic
428C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
429C22×C47#57611yescharacteristic
430C22×C47#57711yescharacteristic
431C4×C47—22no—
432C4×C47—22no—
433C4×C47—22no—
434C4×C47—41no—
435C4×C47—42no—
436C4×C47—42no—
437C4×C47—41no—
438C4×C47—81no—
439C4×C47—81no—
440C4×C47#52511yescharacteristic
441C4×C47#53811yescharacteristic
442C4×C47D4211yescharacteristic
443C4×C47#54611yescharacteristic
444C2×#466C2×C4711yescharacteristic, complemented
445C2×#459C2×C4711yescharacteristic, complemented
446C2×#447C2×C4711yescharacteristic, complemented
447C22×#102C2×C4711yescharacteristic, complemented
448#2433C2×C4711yescharacteristic, complemented
449#2361C2×C4711yescharacteristic, complemented
450#2067C2×C4711yescharacteristic, complemented
451#2054C2×C4711yescharacteristic, complemented
452#2041C2×C4711yescharacteristic, complemented
453#2011C2×C4711yescharacteristic, complemented
454#1982C2×C4711yescharacteristic, complemented
455#1925C2×C4711yescharacteristic, complemented
456#1879C2×C4711yescharacteristic, complemented
457#1874C2×C4711yescharacteristic, complemented
458#1850C2×C4711yescharacteristic, complemented
459C2×C47—24no—
460C2×C47—82no—
461C2×C47—82no—
462C2×C47—82no—
463C2×C47—161no—
464C2×C47#242411yescharacteristic
465C2×C47C2×#45911yescharacteristic
466C2×C47#304511yescharacteristic
467C2×C47#326511yescharacteristic
468C2×C47D4×D811yescharacteristic
469C2×C47#329411yescharacteristic
470C2×C47#331811yescharacteristic
471C23×D4C22×C4711yescharacteristic
472C22×D8C22×C4711yescharacteristic
473C22×D8C22×C4711yescharacteristic
474C22×D8C22×C4711yescharacteristic, complemented
475C23×C8C22×C4711yescharacteristic
476C2×#127C22×C4711yescharacteristic
477C2×#127C22×C4711yescharacteristic
478C2×#121C22×C4711yescharacteristic
479C2×#121C22×C4711yescharacteristic
480C2×#120—21no—
481C2×#120—21no—
482C2×C4×D4—21no—
483C2×C4×D4C22×C4711yescharacteristic, complemented
484C22×C4⋊C4C22×C4711yescharacteristic
485#466—24no—
486#459—24no—
487#447—24no—
488C2×#107C22×C4711yescharacteristic, complemented
489C2×C4⋊C8C22×C4711yescharacteristic, complemented
490C2×C4⋊C8C22×C4711yescharacteristic, complemented
491C2×#102—24no—
492C2×#102C22×C4711yescharacteristic
493C2×#102C22×C4711yescharacteristic
494C2×#102C22×C4711yescharacteristic
495C2×#102C22×C4711yescharacteristic
496C2×#102C22×C4711yescharacteristic
497C2×#102C22×C4711yescharacteristic
498C2×#102C22×C4711yescharacteristic, complemented
499C2×#102C22×C4711yescharacteristic, complemented
500C2×#102C22×C4711yescharacteristic, complemented
501C2×#102C22×C4711yescharacteristic, complemented
502C2×C22⋊C8C22×C4711yescharacteristic
503#392—21no—
504#392—21no—
505#390C22×C4711yescharacteristic
506#390C22×C4711yescharacteristic
507#390C22×C4711yescharacteristic, complemented
508#389C22×C4711yescharacteristic, complemented
509#388—21no—
510#386—21no—
511#385—21no—
512C4×C4⋊C4C22×C4711yescharacteristic, complemented
513C4×C22⋊C4C22×C4711yescharacteristic
514#340C22×C4711yescharacteristic, complemented
515#340C22×C4711yescharacteristic, complemented
516#336C22×C4711yescharacteristic, complemented
517#336C22×C4711yescharacteristic, complemented
518C47#2507611yescharacteristic, direct product factor, Sylow
519C25—21no—
520C22×D4—22no—
521C22×D4—22no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—22no—
525C22×D4—21no—
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—21no—
530C22×D4—22no—
531C22×D4—41no—
532C22×D4—41no—
533C22×D4C23×C4711yescharacteristic
534C22×D4C23×C4711yescharacteristic
535C22×D4C23×C4711yescharacteristic
536C22×D4C23×C4711yescharacteristic
537C23×C4—21no—
538C23×C4—21no—
539C23×C4C23×C4711yescharacteristic
540C2×D8—22no—
541C2×D8—22no—
542C2×D8—22no—
543C2×D8—22no—
544C2×D8—22no—
545C2×D8—22no—
546C2×D8—41no—
547C2×D8—41no—
548C2×D8—41no—
549C22×C8—22no—
550C22×C8—22no—
551C22×C8—41no—
552C22×C8C23×C4711yescharacteristic
553C22×C8C23×C4711yescharacteristic
554C22×C8C23×C4711yescharacteristic
555C22×C8C23×C4711yescharacteristic
556#127—22no—
557#127—22no—
558#127—41no—
559#127—41no—
560#121—22no—
561#121—22no—
562#121—22no—
563#121D4×C4714yescomplemented
564#120—44no—
565#120—44no—
566C4×D4—22no—
567C4×D4—41no—
568C4×D4—44no—
569C2×C4⋊C4—22no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—41no—
573C2×C4⋊C4C23×C4711yescharacteristic
574C2×C4⋊C4C23×C4711yescharacteristic
575C2×C4⋊C4C23×C4711yescharacteristic
576C2×C4⋊C4C23×C4711yescharacteristic
577C2×C22⋊C4—21no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4—21no—
580C2×C22⋊C4—21no—
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4D4×C4711yescharacteristic
587C2×C22⋊C4D4×C4711yescharacteristic
588C2×C42—21no—
589C2×C42C23×C4711yescharacteristic
590C2×C42C23×C4711yescharacteristic
591#107—22no—
592C4⋊C8—22no—
593C4⋊C8—41no—
594#102—22no—
595#102—22no—
596#102—22no—
597#102—22no—
598#102—22no—
599#102—22no—
600#102—22no—
601#102—22no—
602#102—41no—
603#102D4×C4714yescomplemented
604C22⋊C8—22no—
605#95—21no—
606#95—21no—
607#95D4×C4711yescharacteristic
608#95D4×C4711yescharacteristic
609C24—21no—
610C24—21no—
611C24—21no—
612C24—21no—
613C24—42no—
614C24—42no—
615C24—42no—
616C24—42no—
617C24—42no—
618C24—81no—
619C24—81no—
620C24C2×D4×C4711yescharacteristic
621C2×D4—28no—
622C2×D4—24no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—44no—
645C2×D4—44no—
646C2×D4—42no—
647C2×D4—42no—
648C2×D4—44no—
649C2×D4—42no—
650C2×D4—42no—
651C2×D4—42no—
652C2×D4—42no—
653C2×D4—42no—
654C2×D4—42no—
655C2×D4—42no—
656C2×D4—42no—
657C2×D4—42no—
658C2×D4—42no—
659C2×D4—42no—
660C2×D4—42no—
661C2×D4—42no—
662C2×D4—42no—
663C2×D4—81no—
664C2×D4—81no—
665C2×D4—81no—
666C2×D4—81no—
667C2×D4C2×D4×C4712yes—
668C2×D4C2×D4×C4712yes—
669C2×D4#41×C4712yes—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—42no—
679C22×C4—42no—
680C22×C4—42no—
681C22×C4—42no—
682C22×C4—81no—
683C22×C4—81no—
684C22×C4C2×D4×C4711yescharacteristic
685C22×C4C2×D4×C4711yescharacteristic
686C22×C4C2×D4×C4711yescharacteristic
687C22×C4C2×D4×C4712yes—
688C22×C4C2×D4×C4711yescharacteristic
689C22×C4C2×D4×C4711yescharacteristic
690C22×C4#41×C4712yes—
691C22×C4C24×C4711yescharacteristic
692D8—44no—
693D8—44no—
694D8—44no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—21no—
703C2×C8—21no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—44no—
707C2×C8C2×D4×C4712yes—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—42no—
715C4⋊C4—42no—
716C4⋊C4C2×D4×C4712yes—
717C4⋊C4C2×D4×C4712yes—
718C22⋊C4—22no—
719C22⋊C4—24no—
720C22⋊C4—42no—
721C22⋊C4—42no—
722C22⋊C4—42no—
723C22⋊C4—42no—
724C22⋊C4—42no—
725C22⋊C4—42no—
726C22⋊C4—42no—
727C22⋊C4—81no—
728C22⋊C4D8×C4714yescomplemented
729C42—21no—
730C42—21no—
731C42—21no—
732C42—21no—
733C42—42no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—48no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—84no—
768C23—84no—
769C23—84no—
770C23—84no—
771C23—84no—
772C23—84no—
773C23#121×C4712yes—
774C23C2×D8×C4712yes—
775C23AGL(1,ℤ/8)×C4712yes—
776C23C22×D4×C4711yescharacteristic
777D4—22no—
778D4—22no—
779D4—22no—
780D4—22no—
781D4—22no—
782D4—22no—
783D4—48no—
784D4—48no—
785D4—41no—
786D4—41no—
787D4—41no—
788D4—41no—
789D4—41no—
790D4—41no—
791D4—41no—
792D4—41no—
793D4—41no—
794D4—41no—
795D4—84no—
796D4—84no—
797D4—84no—
798D4—84no—
799D4—84no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—21no—
812C2×C4—22no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—84no—
829C2×C4—84no—
830C2×C4#121×C4712yes—
831C2×C4C2×D8×C4712yes—
832C2×C4C2×D8×C4712yes—
833C2×C4C22×D4×C4711yescharacteristic
834C2×C4C22×D4×C4711yescharacteristic
835C2×C4C2×#41×C4711yescharacteristic
836C2×C4C2×#41×C4711yescharacteristic
837C2×C4H(5,𝔽2)×C4711yescharacteristic
838C2×C4H(5,𝔽2)×C4711yescharacteristic
839C8—22no—
840C8—41no—
841C8—41no—
842C8—41no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—816no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—81no—
865C22—81no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22—81no—
871C22—81no—
872C22—81no—
873C22—81no—
874C22—81no—
875C22—81no—
876C22—81no—
877C22—81no—
878C22C47×#45914yescomplemented
879C22C2×#121×C4711yescharacteristic
880C22D42×C4711yescharacteristic
881C22C47×#54611yescharacteristic
882C22C22×D8×C4711yescharacteristic
883C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
884C22C47×#57611yescharacteristic
885C22C47×#57711yescharacteristic
886C4—22no—
887C4—22no—
888C4—22no—
889C4—41no—
890C4—41no—
891C4—42no—
892C4—42no—
893C4—81no—
894C4—81no—
895C4C47×#52511yescharacteristic
896C4C47×#53811yescharacteristic
897C4D42×C4711yescharacteristic
898C4C47×#54611yescharacteristic
899C2—24no—
900C2—82no—
901C2—82no—
902C2—82no—
903C2—161no—
904C2C47×#242411yescharacteristic
905C2C2×C47×#45911yescharacteristic
906C2C47×#304511yescharacteristic
907C2C47×#326511yescharacteristic
908C2D4×D8×C4711yescharacteristic
909C2C47×#329411yescharacteristic
910C2C47×#331811yescharacteristic
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×#459C2semidirect
3. C2×C47×#447C2semidirect
4. C22×#102×C47C2semidirect
5. C47×#2433C2semidirect
6. C47×#2361C2semidirect
7. C47×#2067C2semidirect
8. C47×#2054C2semidirect
9. C47×#2041C2semidirect
10. C47×#2011C2semidirect
11. C47×#1982C2semidirect
12. C47×#1925C2semidirect
13. C47×#1879C2semidirect
14. C47×#1874C2semidirect
15. C47×#1850C2semidirect
19. C22×D8×C47C22semidirect
28. C2×C4×D4×C47C22semidirect
33. C2×#107×C47C22semidirect
34. C2×C4⋊C8×C47C22semidirect
35. C2×C4⋊C8×C47C22semidirect
43. C2×#102×C47C22semidirect
44. C2×#102×C47C22semidirect
45. C2×#102×C47C22semidirect
46. C2×#102×C47C22semidirect
52. C47×#390C22semidirect
53. C47×#389C22semidirect
57. C4×C4⋊C4×C47C22semidirect
59. C47×#340C22semidirect
60. C47×#340C22semidirect
61. C47×#336C22semidirect
62. C47×#336C22semidirect
107. #121×C47D4semidirect
147. #102×C47D4semidirect
272. C22⋊C4×C47D8semidirect
387. #25076C47direct (N × H)
423. C22×C47#459semidirect
444. C2×#466C2×C47semidirect
445. C2×#459C2×C47semidirect
446. C2×#447C2×C47semidirect
447. C22×#102C2×C47semidirect
448. #2433C2×C47semidirect
449. #2361C2×C47semidirect
450. #2067C2×C47semidirect
451. #2054C2×C47semidirect
452. #2041C2×C47semidirect
453. #2011C2×C47semidirect
454. #1982C2×C47semidirect
455. #1925C2×C47semidirect
456. #1879C2×C47semidirect
457. #1874C2×C47semidirect
458. #1850C2×C47semidirect
474. C22×D8C22×C47semidirect
483. C2×C4×D4C22×C47semidirect
488. C2×#107C22×C47semidirect
489. C2×C4⋊C8C22×C47semidirect
490. C2×C4⋊C8C22×C47semidirect
498. C2×#102C22×C47semidirect
499. C2×#102C22×C47semidirect
500. C2×#102C22×C47semidirect
501. C2×#102C22×C47semidirect
507. #390C22×C47semidirect
508. #389C22×C47semidirect
512. C4×C4⋊C4C22×C47semidirect
514. #340C22×C47semidirect
515. #340C22×C47semidirect
516. #336C22×C47semidirect
517. #336C22×C47semidirect
518. C47#25076direct (N × H)
563. #121D4×C47semidirect
603. #102D4×C47semidirect
728. C22⋊C4D8×C47semidirect
878. C22C47×#459semidirect

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×#4592
C2×C47×#4472
C22×#102×C472
C47×#24332
C47×#23612
C47×#20672
C47×#20542
C47×#20412
C47×#20112
C47×#19822
C47×#19252
C47×#18792
C47×#18742
C47×#18502
#2507647