Finite Group Databasebeta

← C47×#25533 #26065231

Subgroups — C47×#25533 #26065231

Order 12032.

1444 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#547C211yesmaximal, characteristic, complemented
2C2×C47×#480C211yesmaximal, characteristic, complemented
3C2×C47×#466C211yesmaximal, characteristic, complemented
4C47×#2416C211yesmaximal, characteristic, complemented
5C47×#2057C211yesmaximal, characteristic, complemented
6C47×#2033C211yesmaximal, characteristic, complemented
7C47×#2023C211yesmaximal, characteristic, complemented
8C47×#1999C211yesmaximal, characteristic, complemented
9C47×#1879C211yesmaximal, characteristic, complemented
10C47×#1874C211yesmaximal, characteristic, complemented
11C47×#1874C211yesmaximal, characteristic, complemented
12C47×#1869C211yesmaximal, characteristic, complemented
13C47×#1862C211yesmaximal, characteristic, complemented
14C47×#1852C211yesmaximal, characteristic, complemented
15C2×C47×#340C211yesmaximal, characteristic, complemented
16C22×#41×C47—21no—
17C22×D8×C47C2211yescharacteristic
18C23×C8×C47C2211yescharacteristic
19C47×#547—24no—
20C47×#547—24no—
21C2×C4⋊Q8×C47C2211yescharacteristic
22C2×#123×C47—21no—
23C2×#123×C47—21no—
24C2×C22⋊Q8×C47—21no—
25C2×#121×C47—21no—
26C2×#121×C47C2211yescharacteristic
27C2×#121×C47C2211yescharacteristic
28C2×#121×C47C2211yescharacteristic
29C2×#121×C47C2211yescharacteristic
30C2×C4×D4×C47C2211yescharacteristic
31C2×C4×D4×C47C2211yescharacteristic
32C22×C4⋊C4×C47C2211yescharacteristic
33C22×C4⋊C4×C47C2211yescharacteristic
34C22×C4⋊C4×C47C2211yescharacteristic
35C47×#480—24no—
36C47×#466—24no—
37C2×#107×C47C2211yescharacteristic
38C2×#107×C47C2211yescharacteristic
39C2×#107×C47C2211yescharacteristic
40C2×#102×C47C2211yescharacteristic
41C2×#102×C47C2211yescharacteristic
42C2×#102×C47C2211yescharacteristic
43C2×#102×C47C2211yescharacteristic
44C2×#102×C47C2211yescharacteristic
45C2×#102×C47C2211yescharacteristic
46C2×C22⋊C8×C47C2211yescharacteristic
47C2×C22⋊C8×C47C2211yescharacteristic
48C2×C22⋊C8×C47C2211yescharacteristic
49C47×#396—21no—
50C47×#394—21no—
51C47×#390C2211yescharacteristic
52C47×#389C2211yescharacteristic
53C47×#386—21no—
54C47×#380C2211yescharacteristic
55C47×#340C2211yescharacteristic
56C47×#340C2211yescharacteristic
57C47×#340C2211yescharacteristic
58C47×#340C2211yescharacteristic
59C47×#340C2211yescharacteristic
60C47×#340C2211yescharacteristic
61C47×#336C2211yescharacteristic
62C47×#336C2211yescharacteristic
63C2×#41×C47—28no—
64C2×#41×C47—44no—
65C2×#41×C47—44no—
66C22×Q8×C47—21no—
67C22×D4×C47—21no—
68C22×D4×C47—21no—
69C22×D4×C47—21no—
70C22×D4×C47—21no—
71C22×D4×C47D411yescharacteristic
72C22×D4×C47C2311yescharacteristic
73C22×D4×C47C2311yescharacteristic
74C23×C4×C47—21no—
75C23×C4×C47—21no—
76C23×C4×C47—21no—
77C23×C4×C47—21no—
78C23×C4×C47C2311yescharacteristic
79C23×C4×C47C2311yescharacteristic
80C2×D8×C47—22no—
81C2×D8×C47—22no—
82C2×D8×C47—41no—
83C22×C8×C47—22no—
84C22×C8×C47—22no—
85C22×C8×C47—41no—
86C22×C8×C47C2311yescharacteristic
87C22×C8×C47C2311yescharacteristic
88C22×C8×C47C2311yescharacteristic
89C22×C8×C47C2311yescharacteristic
90C4⋊Q8×C47—22no—
91C4⋊Q8×C47—22no—
92#123×C47—28no—
93#123×C47—28no—
94C22⋊Q8×C47—28no—
95#121×C47—22no—
96#121×C47—22no—
97#121×C47—22no—
98#121×C47—22no—
99#121×C47—22no—
100#121×C47—22no—
101#121×C47—41no—
102#121×C47—44no—
103#121×C47D414yescomplemented
104C4×D4×C47—22no—
105C4×D4×C47—22no—
106C4×D4×C47—22no—
107C4×D4×C47—22no—
108C2×C4⋊C4×C47—21no—
109C2×C4⋊C4×C47—21no—
110C2×C4⋊C4×C47—22no—
111C2×C4⋊C4×C47—21no—
112C2×C4⋊C4×C47—22no—
113C2×C4⋊C4×C47—22no—
114C2×C4⋊C4×C47—22no—
115C2×C4⋊C4×C47—21no—
116C2×C4⋊C4×C47—21no—
117C2×C4⋊C4×C47—41no—
118C2×C4⋊C4×C47D411yescharacteristic
119C2×C4⋊C4×C47D414yescomplemented
120C2×C4⋊C4×C47C2311yescharacteristic
121C2×C4⋊C4×C47C2311yescharacteristic
122C2×C4⋊C4×C47C2311yescharacteristic
123C2×C4⋊C4×C47C2311yescharacteristic
124C2×C4⋊C4×C47C2311yescharacteristic
125C2×C4⋊C4×C47C2311yescharacteristic
126C2×C22⋊C4×C47—21no—
127C2×C22⋊C4×C47—21no—
128C2×C22⋊C4×C47—21no—
129C2×C22⋊C4×C47—21no—
130C2×C22⋊C4×C47—21no—
131C2×C22⋊C4×C47—21no—
132C2×C22⋊C4×C47—21no—
133C2×C22⋊C4×C47—21no—
134C2×C22⋊C4×C47D411yescharacteristic
135C2×C22⋊C4×C47D411yescharacteristic
136C2×C42×C47C2311yescharacteristic
137#107×C47—22no—
138#107×C47—22no—
139#107×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—41no—
146C22⋊C8×C47—22no—
147C22⋊C8×C47—22no—
148C22⋊C8×C47—41no—
149#95×C47—21no—
150#95×C47—21no—
151C24×C47—21no—
152C24×C47—21no—
153C24×C47C2×D411yescharacteristic
154C24×C47C2×D411yescharacteristic
155#41×C47—432no—
156C2×Q8×C47—24no—
157C2×Q8×C47—42no—
158C2×Q8×C47—42no—
159C2×D4×C47—22no—
160C2×D4×C47—22no—
161C2×D4×C47—24no—
162C2×D4×C47—24no—
163C2×D4×C47—21no—
164C2×D4×C47—21no—
165C2×D4×C47—21no—
166C2×D4×C47—21no—
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—42no—
175C2×D4×C47—42no—
176C2×D4×C47—42no—
177C2×D4×C47—42no—
178C2×D4×C47—42no—
179C2×D4×C47—42no—
180C2×D4×C47—42no—
181C2×D4×C47—42no—
182C2×D4×C47—42no—
183C2×D4×C47—81no—
184C2×D4×C47D814yescomplemented
185C2×D4×C47C2×D412yes—
186C22×C4×C47—21no—
187C22×C4×C47—21no—
188C22×C4×C47—21no—
189C22×C4×C47—21no—
190C22×C4×C47—24no—
191C22×C4×C47—24no—
192C22×C4×C47—24no—
193C22×C4×C47—21no—
194C22×C4×C47—21no—
195C22×C4×C47—21no—
196C22×C4×C47—21no—
197C22×C4×C47—21no—
198C22×C4×C47—21no—
199C22×C4×C47—21no—
200C22×C4×C47—21no—
201C22×C4×C47—21no—
202C22×C4×C47—21no—
203C22×C4×C47—21no—
204C22×C4×C47—21no—
205C22×C4×C47—42no—
206C22×C4×C47—42no—
207C22×C4×C47—42no—
208C22×C4×C47—42no—
209C22×C4×C47—42no—
210C22×C4×C47—42no—
211C22×C4×C47—42no—
212C22×C4×C47—42no—
213C22×C4×C47—81no—
214C22×C4×C47C2×D411yescharacteristic
215C22×C4×C47C2×D411yescharacteristic
216C22×C4×C47C2×D411yescharacteristic
217C22×C4×C47C2×D412yes—
218C22×C4×C47C2×D412yes—
219C22×C4×C47C2×D411yescharacteristic
220C22×C4×C47C2411yescharacteristic
221D8×C47—44no—
222C2×C8×C47—21no—
223C2×C8×C47—21no—
224C2×C8×C47—21no—
225C2×C8×C47—21no—
226C2×C8×C47—21no—
227C2×C8×C47—21no—
228C2×C8×C47—21no—
229C2×C8×C47—21no—
230C2×C8×C47—21no—
231C2×C8×C47—21no—
232C2×C8×C47—21no—
233C2×C8×C47—44no—
234C2×C8×C47#4112yescomplemented
235C4⋊C4×C47—24no—
236C4⋊C4×C47—24no—
237C4⋊C4×C47—24no—
238C4⋊C4×C47—22no—
239C4⋊C4×C47—21no—
240C4⋊C4×C47—21no—
241C4⋊C4×C47—21no—
242C4⋊C4×C47—21no—
243C4⋊C4×C47—21no—
244C4⋊C4×C47—21no—
245C4⋊C4×C47—21no—
246C4⋊C4×C47—21no—
247C4⋊C4×C47—42no—
248C4⋊C4×C47—42no—
249C4⋊C4×C47C2×D412yes—
250C4⋊C4×C47C2×D412yes—
251C4⋊C4×C47C2×D412yes—
252C4⋊C4×C47#4112yescomplemented
253C22⋊C4×C47—24no—
254C22⋊C4×C47—24no—
255C22⋊C4×C47—22no—
256C22⋊C4×C47—24no—
257C22⋊C4×C47—22no—
258C22⋊C4×C47—42no—
259C22⋊C4×C47—42no—
260C22⋊C4×C47—42no—
261C22⋊C4×C47—42no—
262C22⋊C4×C47—81no—
263C42×C47—21no—
264C42×C47—21no—
265C23×C47—21no—
266C23×C47—21no—
267C23×C47—21no—
268C23×C47—21no—
269C23×C47—21no—
270C23×C47—21no—
271C23×C47—21no—
272C23×C47—21no—
273C23×C47—21no—
274C23×C47—21no—
275C23×C47—22no—
276C23×C47—41no—
277C23×C47—41no—
278C23×C47—41no—
279C23×C47—41no—
280C23×C47—41no—
281C23×C47—41no—
282C23×C47—41no—
283C23×C47—41no—
284C23×C47—41no—
285C23×C47—41no—
286C23×C47—41no—
287C23×C47—41no—
288C23×C47—41no—
289C23×C47#12012yes—
290C23×C47C2×D812yes—
291C23×C47C2×D812yes—
292C23×C47AGL(1,ℤ/8)12yes—
293C23×C47C22×D411yescharacteristic
294Q8×C47—48no—
295D4×C47—28no—
296D4×C47—22no—
297D4×C47—22no—
298D4×C47—48no—
299D4×C47—48no—
300D4×C47—41no—
301D4×C47—41no—
302D4×C47—41no—
303D4×C47—41no—
304D4×C47—41no—
305D4×C47—41no—
306D4×C47—84no—
307D4×C47—84no—
308C2×C4×C47—21no—
309C2×C4×C47—21no—
310C2×C4×C47—21no—
311C2×C4×C47—21no—
312C2×C4×C47—22no—
313C2×C4×C47—22no—
314C2×C4×C47—22no—
315C2×C4×C47—22no—
316C2×C4×C47—21no—
317C2×C4×C47—21no—
318C2×C4×C47—22no—
319C2×C4×C47—22no—
320C2×C4×C47—22no—
321C2×C4×C47—21no—
322C2×C4×C47—22no—
323C2×C4×C47—21no—
324C2×C4×C47—21no—
325C2×C4×C47—21no—
326C2×C4×C47—48no—
327C2×C4×C47—48no—
328C2×C4×C47—41no—
329C2×C4×C47—41no—
330C2×C4×C47—41no—
331C2×C4×C47—41no—
332C2×C4×C47—41no—
333C2×C4×C47—41no—
334C2×C4×C47—41no—
335C2×C4×C47—41no—
336C2×C4×C47—48no—
337C2×C4×C47—41no—
338C2×C4×C47—41no—
339C2×C4×C47—41no—
340C2×C4×C47—41no—
341C2×C4×C47—41no—
342C2×C4×C47—41no—
343C2×C4×C47—41no—
344C2×C4×C47—41no—
345C2×C4×C47—41no—
346C2×C4×C47—41no—
347C2×C4×C47—84no—
348C2×C4×C47#12012yes—
349C2×C4×C47C2×D812yes—
350C2×C4×C47C22×D411yescharacteristic
351C2×C4×C47C22×D411yescharacteristic
352C2×C4×C47C2×#4111yescharacteristic
353C2×C4×C47C2×#4111yescharacteristic
354C2×C4×C47H(5,𝔽2)11yescharacteristic
355C2×C4×C472−1+411yescharacteristic
356C8×C47—22no—
357C8×C47—41no—
358C8×C47—41no—
359C8×C47—41no—
360#25533C4711yesmaximal, characteristic, direct product factor, Sylow
361C22×C47—22no—
362C22×C47—22no—
363C22×C47—22no—
364C22×C47—22no—
365C22×C47—22no—
366C22×C47—22no—
367C22×C47—22no—
368C22×C47—22no—
369C22×C47—22no—
370C22×C47—41no—
371C22×C47—41no—
372C22×C47—41no—
373C22×C47—41no—
374C22×C47—42no—
375C22×C47—42no—
376C22×C47—42no—
377C22×C47—81no—
378C22×C47—81no—
379C22×C47—81no—
380C22×C47—81no—
381C22×C47—81no—
382C22×C47—81no—
383C22×C47—81no—
384C22×C47—81no—
385C22×C47—81no—
386C22×C47—81no—
387C22×C47—81no—
388C22×C47#44714yes—
389C22×C47C2×#12011yescharacteristic
390C22×C47#54611yescharacteristic
391C22×C47#54711yescharacteristic
392C22×C47C22×D811yescharacteristic
393C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
394C22×C47#57711yescharacteristic
395C22×C47#57811yescharacteristic
396C4×C47—22no—
397C4×C47—22no—
398C4×C47—41no—
399C4×C47—42no—
400C4×C47—42no—
401C4×C47—42no—
402C4×C47—41no—
403C4×C47—42no—
404C4×C47—81no—
405C4×C47—81no—
406C4×C47#53211yescharacteristic
407C4×C47#53711yescharacteristic
408C4×C47#54611yescharacteristic
409C4×C47#54711yescharacteristic
410C2×#547C2×C4711yescharacteristic, complemented
411C2×#480C2×C4711yescharacteristic, complemented
412C2×#466C2×C4711yescharacteristic, complemented
413#2416C2×C4711yescharacteristic, complemented
414#2057C2×C4711yescharacteristic, complemented
415#2033C2×C4711yescharacteristic, complemented
416#2023C2×C4711yescharacteristic, complemented
417#1999C2×C4711yescharacteristic, complemented
418#1879C2×C4711yescharacteristic, complemented
419#1874C2×C4711yescharacteristic, complemented
420#1874C2×C4711yescharacteristic, complemented
421#1869C2×C4711yescharacteristic, complemented
422#1862C2×C4711yescharacteristic, complemented
423#1852C2×C4711yescharacteristic, complemented
424C2×#340C2×C4711yescharacteristic, complemented
425C2×C47—24no—
426C2×C47—42no—
427C2×C47—82no—
428C2×C47—161no—
429C2×C47#243011yescharacteristic
430C2×C47C2×#44711yescharacteristic
431C2×C47#301311yescharacteristic
432C2×C47#329411yescharacteristic
433C2×C47#330811yescharacteristic
434C2×C47#333411yescharacteristic
435C2×C47#334511yescharacteristic
436C22×#41—21no—
437C22×D8C22×C4711yescharacteristic
438C23×C8C22×C4711yescharacteristic
439#547—24no—
440#547—24no—
441C2×C4⋊Q8C22×C4711yescharacteristic
442C2×#123—21no—
443C2×#123—21no—
444C2×C22⋊Q8—21no—
445C2×#121—21no—
446C2×#121C22×C4711yescharacteristic
447C2×#121C22×C4711yescharacteristic
448C2×#121C22×C4711yescharacteristic
449C2×#121C22×C4711yescharacteristic
450C2×C4×D4C22×C4711yescharacteristic
451C2×C4×D4C22×C4711yescharacteristic
452C22×C4⋊C4C22×C4711yescharacteristic
453C22×C4⋊C4C22×C4711yescharacteristic
454C22×C4⋊C4C22×C4711yescharacteristic
455#480—24no—
456#466—24no—
457C2×#107C22×C4711yescharacteristic
458C2×#107C22×C4711yescharacteristic
459C2×#107C22×C4711yescharacteristic
460C2×#102C22×C4711yescharacteristic
461C2×#102C22×C4711yescharacteristic
462C2×#102C22×C4711yescharacteristic
463C2×#102C22×C4711yescharacteristic
464C2×#102C22×C4711yescharacteristic
465C2×#102C22×C4711yescharacteristic
466C2×C22⋊C8C22×C4711yescharacteristic
467C2×C22⋊C8C22×C4711yescharacteristic
468C2×C22⋊C8C22×C4711yescharacteristic
469#396—21no—
470#394—21no—
471#390C22×C4711yescharacteristic
472#389C22×C4711yescharacteristic
473#386—21no—
474#380C22×C4711yescharacteristic
475#340C22×C4711yescharacteristic
476#340C22×C4711yescharacteristic
477#340C22×C4711yescharacteristic
478#340C22×C4711yescharacteristic
479#340C22×C4711yescharacteristic
480#340C22×C4711yescharacteristic
481#336C22×C4711yescharacteristic
482#336C22×C4711yescharacteristic
483C47#2553311yescharacteristic, direct product factor, Sylow
484C2×#41—28no—
485C2×#41—44no—
486C2×#41—44no—
487C22×Q8—21no—
488C22×D4—21no—
489C22×D4—21no—
490C22×D4—21no—
491C22×D4—21no—
492C22×D4D4×C4711yescharacteristic
493C22×D4C23×C4711yescharacteristic
494C22×D4C23×C4711yescharacteristic
495C23×C4—21no—
496C23×C4—21no—
497C23×C4—21no—
498C23×C4—21no—
499C23×C4C23×C4711yescharacteristic
500C23×C4C23×C4711yescharacteristic
501C2×D8—22no—
502C2×D8—22no—
503C2×D8—41no—
504C22×C8—22no—
505C22×C8—22no—
506C22×C8—41no—
507C22×C8C23×C4711yescharacteristic
508C22×C8C23×C4711yescharacteristic
509C22×C8C23×C4711yescharacteristic
510C22×C8C23×C4711yescharacteristic
511C4⋊Q8—22no—
512C4⋊Q8—22no—
513#123—28no—
514#123—28no—
515C22⋊Q8—28no—
516#121—22no—
517#121—22no—
518#121—22no—
519#121—22no—
520#121—22no—
521#121—22no—
522#121—41no—
523#121—44no—
524#121D4×C4714yescomplemented
525C4×D4—22no—
526C4×D4—22no—
527C4×D4—22no—
528C4×D4—22no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—22no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—22no—
534C2×C4⋊C4—22no—
535C2×C4⋊C4—22no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—41no—
539C2×C4⋊C4D4×C4711yescharacteristic
540C2×C4⋊C4D4×C4714yescomplemented
541C2×C4⋊C4C23×C4711yescharacteristic
542C2×C4⋊C4C23×C4711yescharacteristic
543C2×C4⋊C4C23×C4711yescharacteristic
544C2×C4⋊C4C23×C4711yescharacteristic
545C2×C4⋊C4C23×C4711yescharacteristic
546C2×C4⋊C4C23×C4711yescharacteristic
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4D4×C4711yescharacteristic
556C2×C22⋊C4D4×C4711yescharacteristic
557C2×C42C23×C4711yescharacteristic
558#107—22no—
559#107—22no—
560#107—22no—
561#102—22no—
562#102—22no—
563#102—22no—
564#102—22no—
565#102—22no—
566#102—41no—
567C22⋊C8—22no—
568C22⋊C8—22no—
569C22⋊C8—41no—
570#95—21no—
571#95—21no—
572C24—21no—
573C24—21no—
574C24C2×D4×C4711yescharacteristic
575C24C2×D4×C4711yescharacteristic
576#41—432no—
577C2×Q8—24no—
578C2×Q8—42no—
579C2×Q8—42no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—24no—
583C2×D4—24no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—42no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—42no—
601C2×D4—42no—
602C2×D4—42no—
603C2×D4—42no—
604C2×D4—81no—
605C2×D4D8×C4714yescomplemented
606C2×D4C2×D4×C4712yes—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—24no—
612C22×C4—24no—
613C22×C4—24no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4—42no—
629C22×C4—42no—
630C22×C4—42no—
631C22×C4—42no—
632C22×C4—42no—
633C22×C4—42no—
634C22×C4—81no—
635C22×C4C2×D4×C4711yescharacteristic
636C22×C4C2×D4×C4711yescharacteristic
637C22×C4C2×D4×C4711yescharacteristic
638C22×C4C2×D4×C4712yes—
639C22×C4C2×D4×C4712yes—
640C22×C4C2×D4×C4711yescharacteristic
641C22×C4C24×C4711yescharacteristic
642D8—44no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—44no—
655C2×C8#41×C4712yescomplemented
656C4⋊C4—24no—
657C4⋊C4—24no—
658C4⋊C4—24no—
659C4⋊C4—22no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—42no—
669C4⋊C4—42no—
670C4⋊C4C2×D4×C4712yes—
671C4⋊C4C2×D4×C4712yes—
672C4⋊C4C2×D4×C4712yes—
673C4⋊C4#41×C4712yescomplemented
674C22⋊C4—24no—
675C22⋊C4—24no—
676C22⋊C4—22no—
677C22⋊C4—24no—
678C22⋊C4—22no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—81no—
684C42—21no—
685C42—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—22no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23#120×C4712yes—
711C23C2×D8×C4712yes—
712C23C2×D8×C4712yes—
713C23AGL(1,ℤ/8)×C4712yes—
714C23C22×D4×C4711yescharacteristic
715Q8—48no—
716D4—28no—
717D4—22no—
718D4—22no—
719D4—48no—
720D4—48no—
721D4—41no—
722D4—41no—
723D4—41no—
724D4—41no—
725D4—41no—
726D4—41no—
727D4—84no—
728D4—84no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—21no—
743C2×C4—22no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—48no—
748C2×C4—48no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—48no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—84no—
769C2×C4#120×C4712yes—
770C2×C4C2×D8×C4712yes—
771C2×C4C22×D4×C4711yescharacteristic
772C2×C4C22×D4×C4711yescharacteristic
773C2×C4C2×#41×C4711yescharacteristic
774C2×C4C2×#41×C4711yescharacteristic
775C2×C4H(5,𝔽2)×C4711yescharacteristic
776C2×C42−1+4×C4711yescharacteristic
777C8—22no—
778C8—41no—
779C8—41no—
780C8—41no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—22no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22C47×#44714yes—
809C22C2×#120×C4711yescharacteristic
810C22C47×#54611yescharacteristic
811C22C47×#54711yescharacteristic
812C22C22×D8×C4711yescharacteristic
813C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
814C22C47×#57711yescharacteristic
815C22C47×#57811yescharacteristic
816C4—22no—
817C4—22no—
818C4—42no—
819C4—41no—
820C4—42no—
821C4—42no—
822C4—42no—
823C4—41no—
824C4—81no—
825C4—81no—
826C4C47×#53211yescharacteristic
827C4C47×#53711yescharacteristic
828C4C47×#54611yescharacteristic
829C4C47×#54711yescharacteristic
830C2—24no—
831C2—42no—
832C2—82no—
833C2—161no—
834C2C47×#243011yescharacteristic
835C2C2×C47×#44711yescharacteristic
836C2C47×#301311yescharacteristic
837C2C47×#329411yescharacteristic
838C2C47×#330811yescharacteristic
839C2C47×#333411yescharacteristic
840C2C47×#334511yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C2×C4×D4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C47×#547C2semidirect
2. C2×C47×#480C2semidirect
3. C2×C47×#466C2semidirect
4. C47×#2416C2semidirect
5. C47×#2057C2semidirect
6. C47×#2033C2semidirect
7. C47×#2023C2semidirect
8. C47×#1999C2semidirect
9. C47×#1879C2semidirect
10. C47×#1874C2semidirect
11. C47×#1874C2semidirect
12. C47×#1869C2semidirect
13. C47×#1862C2semidirect
14. C47×#1852C2semidirect
15. C2×C47×#340C2semidirect
103. #121×C47D4semidirect
119. C2×C4⋊C4×C47D4semidirect
184. C2×D4×C47D8semidirect
234. C2×C8×C47#41semidirect
252. C4⋊C4×C47#41semidirect
360. #25533C47direct (N × H)
410. C2×#547C2×C47semidirect
411. C2×#480C2×C47semidirect
412. C2×#466C2×C47semidirect
413. #2416C2×C47semidirect
414. #2057C2×C47semidirect
415. #2033C2×C47semidirect
416. #2023C2×C47semidirect
417. #1999C2×C47semidirect
418. #1879C2×C47semidirect
419. #1874C2×C47semidirect
420. #1874C2×C47semidirect
421. #1869C2×C47semidirect
422. #1862C2×C47semidirect
423. #1852C2×C47semidirect
424. C2×#340C2×C47semidirect
483. C47#25533direct (N × H)
524. #121D4×C47semidirect
540. C2×C4⋊C4D4×C47semidirect
605. C2×D4D8×C47semidirect
655. C2×C8#41×C47semidirect
673. C4⋊C4#41×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#5472
C2×C47×#4802
C2×C47×#4662
C47×#24162
C47×#20572
C47×#20332
C47×#20232
C47×#19992
C47×#18792
C47×#18742
C47×#18692
C47×#18622
C47×#18522
C2×C47×#3402
#2553347