Finite Group Databasebeta

← C47×#25506 #26065204

Subgroups — C47×#25506 #26065204

Order 12032.

1202 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#529C211yesmaximal, characteristic, complemented
2C2×C47×#469C211yesmaximal, characteristic
3C2×C47×#468C211yesmaximal, characteristic, complemented
4C47×#2854C211yesmaximal, characteristic, complemented
5C47×#2059C211yesmaximal, characteristic, complemented
6C47×#2042C211yesmaximal, characteristic, complemented
7C47×#2025C211yesmaximal, characteristic, complemented
8C47×#2012C211yesmaximal, characteristic, complemented
9C47×#1895C211yesmaximal, characteristic, complemented
10C47×#1894C211yesmaximal, characteristic, complemented
11C47×#1880C211yesmaximal, characteristic, complemented
12C47×#1879C211yesmaximal, characteristic, complemented
13C47×#1865C211yesmaximal, characteristic, complemented
14C47×#1862C211yesmaximal, characteristic, complemented
15C47×#1728C211yesmaximal, characteristic, complemented
16C22×SD16×C47C2211yescharacteristic
17C22×D8×C47C2211yescharacteristic
18C22×M16×C47C2211yescharacteristic
19C22×M16×C47C2211yescharacteristic
20C47×#529—24no—
21C47×#529—24no—
22C2×#126×C47—21no—
23C2×#125×C47C2211yescharacteristic
24C2×#124×C47C2211yescharacteristic
25C2×#123×C47—21no—
26C2×#123×C47—21no—
27C2×C22⋊Q8×C47C2211yescharacteristic
28C2×#121×C47C2211yescharacteristic
29C2×#121×C47C2211yescharacteristic
30C2×C4×Q8×C47C2211yescharacteristic
31C2×C4×D4×C47—21no—
32C2×C4×D4×C47C2211yescharacteristic
33C2×#117×C47—21no—
34C22×C42×C47C2211yescharacteristic
35C47×#469—24no—
36C47×#468—24no—
37C2×#107×C47C2211yescharacteristic
38C2×#106×C47C2211yescharacteristic
39C2×#103×C47C2211yescharacteristic
40C2×#103×C47C2211yescharacteristic
41C2×#103×C47C2211yescharacteristic
42C2×#102×C47C2211yescharacteristic
43C2×#102×C47C2211yescharacteristic
44C2×#102×C47C2211yescharacteristic
45C2×#102×C47C2211yescharacteristic
46C2×#102×C47C2211yescharacteristic
47C47×#390C2211yescharacteristic
48C47×#390C2211yescharacteristic
49C47×#389C2211yescharacteristic
50C47×#389C2211yescharacteristic
51C47×#388—21no—
52C47×#388—21no—
53C47×#386—21no—
54C47×#380C2211yescharacteristic
55C47×#340C2211yescharacteristic
56C47×#340C2211yescharacteristic
57C47×#340C2211yescharacteristic
58C47×#340C2211yescharacteristic
59C47×#336C2211yescharacteristic
60C47×#336C2211yescharacteristic
61C47×#336C2211yescharacteristic
62C47×#336C2211yescharacteristic
63C22×Q8×C47C2311yescharacteristic
64C22×D4×C47—21no—
65C22×D4×C47—21no—
66C22×D4×C47C2311yescharacteristic
67C22×D4×C47C2311yescharacteristic
68C23×C4×C47—21no—
69C23×C4×C47D411yescharacteristic
70C23×C4×C47D411yescharacteristic
71C23×C4×C47C2311yescharacteristic
72C2×SD16×C47—22no—
73C2×SD16×C47—22no—
74C2×SD16×C47—41no—
75C2×D8×C47—22no—
76C2×D8×C47—22no—
77C2×D8×C47—41no—
78C2×M16×C47—22no—
79C2×M16×C47—22no—
80C2×M16×C47—22no—
81C2×M16×C47—22no—
82C2×M16×C47—41no—
83C2×M16×C47—41no—
84C22×C8×C47C2311yescharacteristic
85C22×C8×C47C2311yescharacteristic
86C22×C8×C47C2311yescharacteristic
87C22×C8×C47C2311yescharacteristic
88#126×C47—28no—
89#125×C47—22no—
90#125×C47—22no—
91#124×C47—22no—
92#124×C47—22no—
93#123×C47—28no—
94#123×C47—44no—
95C22⋊Q8×C47—22no—
96C22⋊Q8×C47D414yes—
97#121×C47—22no—
98#121×C47—22no—
99#121×C47—22no—
100#121×C47D414yes—
101C4×Q8×C47—22no—
102C4×Q8×C47—22no—
103C4×D4×C47—28no—
104C4×D4×C47—22no—
105C4×D4×C47—22no—
106#117×C47—28no—
107C2×C4⋊C4×C47—21no—
108C2×C4⋊C4×C47—21no—
109C2×C4⋊C4×C47—21no—
110C2×C4⋊C4×C47—21no—
111C2×C4⋊C4×C47—21no—
112C2×C4⋊C4×C47—21no—
113C2×C4⋊C4×C47C2311yescharacteristic
114C2×C4⋊C4×C47C2311yescharacteristic
115C2×C4⋊C4×C47C2311yescharacteristic
116C2×C4⋊C4×C47C2311yescharacteristic
117C2×C4⋊C4×C47C2311yescharacteristic
118C2×C22⋊C4×C47—21no—
119C2×C22⋊C4×C47—21no—
120C2×C22⋊C4×C47—21no—
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×C42×C47—22no—
130C2×C42×C47—22no—
131C2×C42×C47—21no—
132C2×C42×C47D411yescharacteristic
133C2×C42×C47D411yescharacteristic
134C2×C42×C47C2311yescharacteristic
135C2×C42×C47C2311yescharacteristic
136#107×C47—22no—
137#106×C47—22no—
138#103×C47—22no—
139#103×C47—22no—
140#103×C47—41no—
141#102×C47—22no—
142#102×C47—22no—
143#102×C47—22no—
144#102×C47—22no—
145#102×C47—41no—
146#95×C47—21no—
147#95×C47—21no—
148#95×C47—21no—
149C24×C47—21no—
150C24×C47—21no—
151C24×C47C2×D411yescharacteristic
152C2×Q8×C47—21no—
153C2×Q8×C47—21no—
154C2×Q8×C47—21no—
155C2×Q8×C47—21no—
156C2×Q8×C47—21no—
157C2×Q8×C47C2×D412yes—
158C2×D4×C47—24no—
159C2×D4×C47—21no—
160C2×D4×C47—21no—
161C2×D4×C47—21no—
162C2×D4×C47—21no—
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—42no—
171C2×D4×C47—42no—
172C2×D4×C47—42no—
173C2×D4×C47—42no—
174C2×D4×C47—42no—
175C2×D4×C47C2×D412yes—
176C22×C4×C47—21no—
177C22×C4×C47—21no—
178C22×C4×C47—21no—
179C22×C4×C47—21no—
180C22×C4×C47—24no—
181C22×C4×C47—22no—
182C22×C4×C47—22no—
183C22×C4×C47—21no—
184C22×C4×C47—21no—
185C22×C4×C47—21no—
186C22×C4×C47—22no—
187C22×C4×C47—21no—
188C22×C4×C47—21no—
189C22×C4×C47—21no—
190C22×C4×C47—41no—
191C22×C4×C47—41no—
192C22×C4×C47—41no—
193C22×C4×C47—42no—
194C22×C4×C47—42no—
195C22×C4×C47C2×D411yescharacteristic
196C22×C4×C47C2×D411yescharacteristic
197C22×C4×C47C2×D411yescharacteristic
198C22×C4×C47C2×D411yescharacteristic
199C22×C4×C47C2×D412yes—
200C22×C4×C47C2×D412yes—
201C22×C4×C47C2×D411yescharacteristic
202C22×C4×C47C2411yescharacteristic
203SD16×C47—44no—
204D8×C47—44no—
205M16×C47—44no—
206M16×C47—44no—
207C2×C8×C47—21no—
208C2×C8×C47—21no—
209C2×C8×C47—21no—
210C2×C8×C47—21no—
211C2×C8×C47—21no—
212C2×C8×C47—21no—
213C2×C8×C47—21no—
214C2×C8×C47—21no—
215C2×C8×C47—21no—
216C2×C8×C47—21no—
217C2×C8×C47#4112yes—
218C2×C8×C47#4112yes—
219C4⋊C4×C47—24no—
220C4⋊C4×C47—24no—
221C4⋊C4×C47—24no—
222C4⋊C4×C47—24no—
223C4⋊C4×C47—21no—
224C4⋊C4×C47—21no—
225C4⋊C4×C47—21no—
226C4⋊C4×C47—21no—
227C4⋊C4×C47—21no—
228C4⋊C4×C47—21no—
229C4⋊C4×C47—21no—
230C4⋊C4×C47—21no—
231C4⋊C4×C47—42no—
232C4⋊C4×C47—42no—
233C4⋊C4×C47C2×D412yes—
234C4⋊C4×C47C2×D412yes—
235C22⋊C4×C47—24no—
236C22⋊C4×C47—24no—
237C22⋊C4×C47—24no—
238C22⋊C4×C47—24no—
239C22⋊C4×C47—24no—
240C22⋊C4×C47—42no—
241C22⋊C4×C47—42no—
242C22⋊C4×C47—42no—
243C22⋊C4×C47—42no—
244C22⋊C4×C47—42no—
245C22⋊C4×C47—42no—
246C42×C47—24no—
247C42×C47—22no—
248C42×C47—22no—
249C42×C47—21no—
250C42×C47—21no—
251C42×C47—21no—
252C42×C47—21no—
253C23×C47—21no—
254C23×C47—21no—
255C23×C47—21no—
256C23×C47—21no—
257C23×C47—21no—
258C23×C47—21no—
259C23×C47—22no—
260C23×C47—41no—
261C23×C47—41no—
262C23×C47—41no—
263C23×C47—41no—
264C23×C47—41no—
265C23×C47—41no—
266C23×C47—41no—
267C23×C47—41no—
268C23×C47—41no—
269C23×C47—41no—
270C23×C47—41no—
271C23×C47—41no—
272C23×C47—41no—
273C23×C47#12012yes—
274C23×C47C22×D411yescharacteristic
275Q8×C47—22no—
276Q8×C47—22no—
277Q8×C47—41no—
278Q8×C47—41no—
279D4×C47—22no—
280D4×C47—22no—
281D4×C47—48no—
282D4×C47—41no—
283D4×C47—41no—
284D4×C47—41no—
285D4×C47—41no—
286D4×C47—41no—
287D4×C47—41no—
288D4×C47—84no—
289C2×C4×C47—21no—
290C2×C4×C47—21no—
291C2×C4×C47—21no—
292C2×C4×C47—21no—
293C2×C4×C47—22no—
294C2×C4×C47—22no—
295C2×C4×C47—22no—
296C2×C4×C47—22no—
297C2×C4×C47—21no—
298C2×C4×C47—21no—
299C2×C4×C47—21no—
300C2×C4×C47—22no—
301C2×C4×C47—22no—
302C2×C4×C47—22no—
303C2×C4×C47—21no—
304C2×C4×C47—21no—
305C2×C4×C47—21no—
306C2×C4×C47—21no—
307C2×C4×C47—21no—
308C2×C4×C47—21no—
309C2×C4×C47—44no—
310C2×C4×C47—48no—
311C2×C4×C47—44no—
312C2×C4×C47—41no—
313C2×C4×C47—41no—
314C2×C4×C47—41no—
315C2×C4×C47—41no—
316C2×C4×C47—41no—
317C2×C4×C47—41no—
318C2×C4×C47—41no—
319C2×C4×C47—41no—
320C2×C4×C47—41no—
321C2×C4×C47—41no—
322C2×C4×C47—41no—
323C2×C4×C47—41no—
324C2×C4×C47—41no—
325C2×C4×C47—41no—
326C2×C4×C47—41no—
327C2×C4×C47#12012yes—
328C2×C4×C47AGL(1,ℤ/8)12yes—
329C2×C4×C47C22×D411yescharacteristic
330C2×C4×C47C22×D411yescharacteristic
331C2×C4×C47C2×#4111yescharacteristic
332C2×C4×C47C2×#4111yescharacteristic
333C2×C4×C47H(5,𝔽2)11yescharacteristic
334C2×C4×C472−1+411yescharacteristic
335C8×C47—22no—
336C8×C47—22no—
337C8×C47—41no—
338C8×C47—41no—
339#25506C4711yesmaximal, characteristic, direct product factor, Sylow
340C22×C47—22no—
341C22×C47—22no—
342C22×C47—22no—
343C22×C47—41no—
344C22×C47—41no—
345C22×C47—41no—
346C22×C47—41no—
347C22×C47—42no—
348C22×C47—42no—
349C22×C47—42no—
350C22×C47—81no—
351C22×C47—81no—
352C22×C47—81no—
353C22×C47—81no—
354C22×C47—81no—
355C22×C47—81no—
356C22×C47—81no—
357C22×C47—81no—
358C22×C47—81no—
359C22×C47—81no—
360C22×C47—81no—
361C22×C47C2×#12011yescharacteristic
362C22×C47#53211yescharacteristic
363C22×C47#53711yescharacteristic
364C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
365C22×C47#57511yescharacteristic
366C22×C47#57511yescharacteristic
367C22×C47#57511yescharacteristic
368C4×C47—22no—
369C4×C47—22no—
370C4×C47—42no—
371C4×C47—41no—
372C4×C47—41no—
373C4×C47—42no—
374C4×C47—41no—
375C4×C47—42no—
376C4×C47—81no—
377C4×C47—81no—
378C4×C47—81no—
379C4×C47#54611yescharacteristic
380C4×C47#54611yescharacteristic
381C4×C47#54711yescharacteristic
382C4×C47#54711yescharacteristic
383C2×#529C2×C4711yescharacteristic, complemented
384C2×#469C2×C4711yescharacteristic
385C2×#468C2×C4711yescharacteristic, complemented
386#2854C2×C4711yescharacteristic, complemented
387#2059C2×C4711yescharacteristic, complemented
388#2042C2×C4711yescharacteristic, complemented
389#2025C2×C4711yescharacteristic, complemented
390#2012C2×C4711yescharacteristic, complemented
391#1895C2×C4711yescharacteristic, complemented
392#1894C2×C4711yescharacteristic, complemented
393#1880C2×C4711yescharacteristic, complemented
394#1879C2×C4711yescharacteristic, complemented
395#1865C2×C4711yescharacteristic, complemented
396#1862C2×C4711yescharacteristic, complemented
397#1728C2×C4711yescharacteristic, complemented
398C2×C47—42no—
399C2×C47—82no—
400C2×C47—161no—
401C2×C47#243011yescharacteristic
402C2×C47#300511yescharacteristic
403C2×C47#300611yescharacteristic
404C2×C47#317111yescharacteristic
405C2×C47#318311yescharacteristic
406C2×C47#325111yescharacteristic
407C2×C47#325611yescharacteristic
408C22×SD16C22×C4711yescharacteristic
409C22×D8C22×C4711yescharacteristic
410C22×M16C22×C4711yescharacteristic
411C22×M16C22×C4711yescharacteristic
412#529—24no—
413#529—24no—
414C2×#126—21no—
415C2×#125C22×C4711yescharacteristic
416C2×#124C22×C4711yescharacteristic
417C2×#123—21no—
418C2×#123—21no—
419C2×C22⋊Q8C22×C4711yescharacteristic
420C2×#121C22×C4711yescharacteristic
421C2×#121C22×C4711yescharacteristic
422C2×C4×Q8C22×C4711yescharacteristic
423C2×C4×D4—21no—
424C2×C4×D4C22×C4711yescharacteristic
425C2×#117—21no—
426C22×C42C22×C4711yescharacteristic
427#469—24no—
428#468—24no—
429C2×#107C22×C4711yescharacteristic
430C2×#106C22×C4711yescharacteristic
431C2×#103C22×C4711yescharacteristic
432C2×#103C22×C4711yescharacteristic
433C2×#103C22×C4711yescharacteristic
434C2×#102C22×C4711yescharacteristic
435C2×#102C22×C4711yescharacteristic
436C2×#102C22×C4711yescharacteristic
437C2×#102C22×C4711yescharacteristic
438C2×#102C22×C4711yescharacteristic
439#390C22×C4711yescharacteristic
440#390C22×C4711yescharacteristic
441#389C22×C4711yescharacteristic
442#389C22×C4711yescharacteristic
443#388—21no—
444#388—21no—
445#386—21no—
446#380C22×C4711yescharacteristic
447#340C22×C4711yescharacteristic
448#340C22×C4711yescharacteristic
449#340C22×C4711yescharacteristic
450#340C22×C4711yescharacteristic
451#336C22×C4711yescharacteristic
452#336C22×C4711yescharacteristic
453#336C22×C4711yescharacteristic
454#336C22×C4711yescharacteristic
455C47#2550611yescharacteristic, direct product factor, Sylow
456C22×Q8C23×C4711yescharacteristic
457C22×D4—21no—
458C22×D4—21no—
459C22×D4C23×C4711yescharacteristic
460C22×D4C23×C4711yescharacteristic
461C23×C4—21no—
462C23×C4D4×C4711yescharacteristic
463C23×C4D4×C4711yescharacteristic
464C23×C4C23×C4711yescharacteristic
465C2×SD16—22no—
466C2×SD16—22no—
467C2×SD16—41no—
468C2×D8—22no—
469C2×D8—22no—
470C2×D8—41no—
471C2×M16—22no—
472C2×M16—22no—
473C2×M16—22no—
474C2×M16—22no—
475C2×M16—41no—
476C2×M16—41no—
477C22×C8C23×C4711yescharacteristic
478C22×C8C23×C4711yescharacteristic
479C22×C8C23×C4711yescharacteristic
480C22×C8C23×C4711yescharacteristic
481#126—28no—
482#125—22no—
483#125—22no—
484#124—22no—
485#124—22no—
486#123—28no—
487#123—44no—
488C22⋊Q8—22no—
489C22⋊Q8D4×C4714yes—
490#121—22no—
491#121—22no—
492#121—22no—
493#121D4×C4714yes—
494C4×Q8—22no—
495C4×Q8—22no—
496C4×D4—28no—
497C4×D4—22no—
498C4×D4—22no—
499#117—28no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4C23×C4711yescharacteristic
507C2×C4⋊C4C23×C4711yescharacteristic
508C2×C4⋊C4C23×C4711yescharacteristic
509C2×C4⋊C4C23×C4711yescharacteristic
510C2×C4⋊C4C23×C4711yescharacteristic
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C42—21no—
523C2×C42—22no—
524C2×C42—22no—
525C2×C42D4×C4711yescharacteristic
526C2×C42D4×C4711yescharacteristic
527C2×C42C23×C4711yescharacteristic
528C2×C42C23×C4711yescharacteristic
529#107—22no—
530#106—22no—
531#103—22no—
532#103—22no—
533#103—41no—
534#102—22no—
535#102—22no—
536#102—22no—
537#102—22no—
538#102—41no—
539#95—21no—
540#95—21no—
541#95—21no—
542C24—21no—
543C24—21no—
544C24C2×D4×C4711yescharacteristic
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8C2×D4×C4712yes—
551C2×D4—24no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4C2×D4×C4712yes—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—24no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—22no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4C2×D4×C4711yescharacteristic
589C22×C4C2×D4×C4711yescharacteristic
590C22×C4C2×D4×C4711yescharacteristic
591C22×C4C2×D4×C4711yescharacteristic
592C22×C4C2×D4×C4712yes—
593C22×C4C2×D4×C4712yes—
594C22×C4C2×D4×C4711yescharacteristic
595C22×C4C24×C4711yescharacteristic
596SD16—44no—
597D8—44no—
598M16—44no—
599M16—44no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8#41×C4712yes—
611C2×C8#41×C4712yes—
612C4⋊C4—24no—
613C4⋊C4—24no—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—42no—
625C4⋊C4—42no—
626C4⋊C4C2×D4×C4712yes—
627C4⋊C4C2×D4×C4712yes—
628C22⋊C4—24no—
629C22⋊C4—24no—
630C22⋊C4—24no—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C42—24no—
640C42—22no—
641C42—22no—
642C42—21no—
643C42—21no—
644C42—21no—
645C42—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—22no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23#120×C4712yes—
667C23C22×D4×C4711yescharacteristic
668Q8—22no—
669Q8—22no—
670Q8—41no—
671Q8—41no—
672D4—22no—
673D4—22no—
674D4—48no—
675D4—41no—
676D4—41no—
677D4—41no—
678D4—41no—
679D4—41no—
680D4—41no—
681D4—84no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—44no—
703C2×C4—48no—
704C2×C4—44no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4#120×C4712yes—
721C2×C4AGL(1,ℤ/8)×C4712yes—
722C2×C4C22×D4×C4711yescharacteristic
723C2×C4C22×D4×C4711yescharacteristic
724C2×C4C2×#41×C4711yescharacteristic
725C2×C4C2×#41×C4711yescharacteristic
726C2×C4H(5,𝔽2)×C4711yescharacteristic
727C2×C42−1+4×C4711yescharacteristic
728C8—22no—
729C8—22no—
730C8—41no—
731C8—41no—
732C22—22no—
733C22—22no—
734C22—22no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22C2×#120×C4711yescharacteristic
754C22C47×#53211yescharacteristic
755C22C47×#53711yescharacteristic
756C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
757C22C47×#57511yescharacteristic
758C22C47×#57511yescharacteristic
759C22C47×#57511yescharacteristic
760C4—22no—
761C4—22no—
762C4—42no—
763C4—41no—
764C4—41no—
765C4—42no—
766C4—41no—
767C4—42no—
768C4—81no—
769C4—81no—
770C4—81no—
771C4C47×#54611yescharacteristic
772C4C47×#54611yescharacteristic
773C4C47×#54711yescharacteristic
774C4C47×#54711yescharacteristic
775C2—42no—
776C2—82no—
777C2—161no—
778C2C47×#243011yescharacteristic
779C2C47×#300511yescharacteristic
780C2C47×#300611yescharacteristic
781C2C47×#317111yescharacteristic
782C2C47×#318311yescharacteristic
783C2C47×#325111yescharacteristic
784C2C47×#325611yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC2×C47×#469C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C22×C42×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C47×#529C2semidirect
3. C2×C47×#468C2semidirect
4. C47×#2854C2semidirect
5. C47×#2059C2semidirect
6. C47×#2042C2semidirect
7. C47×#2025C2semidirect
8. C47×#2012C2semidirect
9. C47×#1895C2semidirect
10. C47×#1894C2semidirect
11. C47×#1880C2semidirect
12. C47×#1879C2semidirect
13. C47×#1865C2semidirect
14. C47×#1862C2semidirect
15. C47×#1728C2semidirect
339. #25506C47direct (N × H)
383. C2×#529C2×C47semidirect
385. C2×#468C2×C47semidirect
386. #2854C2×C47semidirect
387. #2059C2×C47semidirect
388. #2042C2×C47semidirect
389. #2025C2×C47semidirect
390. #2012C2×C47semidirect
391. #1895C2×C47semidirect
392. #1894C2×C47semidirect
393. #1880C2×C47semidirect
394. #1879C2×C47semidirect
395. #1865C2×C47semidirect
396. #1862C2×C47semidirect
397. #1728C2×C47semidirect
455. C47#25506direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C47×#5292
C2×C47×#4692
C2×C47×#4682
C47×#28542
C47×#20592
C47×#20422
C47×#20252
C47×#20122
C47×#18952
C47×#18942
C47×#18802
C47×#18792
C47×#18652
C47×#18622
C47×#17282
#2550647