Finite Group Databasebeta

← C47×#22857 #26062555

Subgroups — C47×#22857 #26062555

Order 12032.

1146 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#449C211yesmaximal, characteristic
2C2×C47×#440C211yesmaximal, characteristic, complemented
3C2×C47×#416C211yesmaximal, characteristic, complemented
4C47×#2363C211yesmaximal, characteristic, complemented
5C47×#2341C211yesmaximal, characteristic, complemented
6C47×#1972C211yesmaximal, characteristic, complemented
7C47×#1936C211yesmaximal, characteristic, complemented
8C47×#1925C211yesmaximal, characteristic, complemented
9C47×#1893C211yesmaximal, characteristic, complemented
10C47×#1880C211yesmaximal, characteristic, complemented
11C47×#1879C211yesmaximal, characteristic, complemented
12C47×#1865C211yesmaximal, characteristic, complemented
13C47×#1854C211yesmaximal, characteristic, complemented
14C47×#1763C211yesmaximal, characteristic, complemented
15C47×#1752C211yesmaximal, characteristic, complemented
16C22×#41×C47C2211yescharacteristic
17C22×SD16×C47C2211yescharacteristic
18C22×D8×C47C2211yescharacteristic
19C23×C8×C47C2211yescharacteristic
20C2×#121×C47C2211yescharacteristic
21C2×C4×Q8×C47C2211yescharacteristic
22C2×C4×Q8×C47C2211yescharacteristic
23C2×C4×D4×C47C2211yescharacteristic
24C2×#117×C47C2211yescharacteristic
25C47×#449C418yescomplemented
26C47×#440—24no—
27C2×#107×C47C2211yescharacteristic
28C2×#106×C47C2211yescharacteristic
29C47×#416—24no—
30C2×#103×C47C2211yescharacteristic
31C2×#103×C47C2211yescharacteristic
32C2×#103×C47C2211yescharacteristic
33C2×#102×C47C2211yescharacteristic
34C2×#102×C47C2211yescharacteristic
35C2×#102×C47C2211yescharacteristic
36C2×#102×C47C2211yescharacteristic
37C2×#102×C47C2211yescharacteristic
38C2×C22⋊C8×C47C2211yescharacteristic
39C2×#97×C47C2211yescharacteristic
40C2×#97×C47C2211yescharacteristic
41C47×#390—21no—
42C47×#390—21no—
43C47×#390—21no—
44C47×#390C2211yescharacteristic
45C47×#390C2211yescharacteristic
46C47×#390C2211yescharacteristic
47C47×#389C2211yescharacteristic
48C47×#388—21no—
49C47×#386—21no—
50C47×#380—21no—
51C47×#380C2211yescharacteristic
52C4×C4⋊C4×C47C2211yescharacteristic
53C4×C22⋊C4×C47—21no—
54C4×C22⋊C4×C47—21no—
55C4×C22⋊C4×C47C2211yescharacteristic
56C47×#340C2211yescharacteristic
57C47×#340C2211yescharacteristic
58C47×#340C2211yescharacteristic
59C47×#340C2211yescharacteristic
60C47×#336C2211yescharacteristic
61C47×#336C2211yescharacteristic
62C2×#41×C47—22no—
63C2×#41×C47—22no—
64C2×#41×C47—22no—
65C2×#41×C47—41no—
66C2×#41×C47—41no—
67C2×#41×C47C2×C414yescomplemented
68C22×Q8×C47C2311yescharacteristic
69C22×D4×C47—21no—
70C22×D4×C47—21no—
71C22×D4×C47C2311yescharacteristic
72C22×D4×C47C2311yescharacteristic
73C23×C4×C47—21no—
74C23×C4×C47—21no—
75C23×C4×C47C2311yescharacteristic
76C2×SD16×C47—22no—
77C2×SD16×C47—22no—
78C2×SD16×C47C2×C414yes—
79C2×D8×C47—41no—
80C2×D8×C47—41no—
81C2×D8×C47C2×C414yes—
82C22×C8×C47—22no—
83C22×C8×C47—22no—
84C22×C8×C47—41no—
85C22×C8×C47C2311yescharacteristic
86C22×C8×C47C2311yescharacteristic
87C22×C8×C47C2311yescharacteristic
88C22×C8×C47C2311yescharacteristic
89#121×C47—22no—
90#121×C47C2×C414yes—
91C4×Q8×C47—22no—
92C4×Q8×C47—22no—
93C4×Q8×C47—41no—
94C4×Q8×C47—41no—
95C4×D4×C47—22no—
96C4×D4×C47—41no—
97#117×C47—22no—
98#117×C47—41no—
99C2×C4⋊C4×C47—21no—
100C2×C4⋊C4×C47—21no—
101C2×C4⋊C4×C47—21no—
102C2×C4⋊C4×C47C2311yescharacteristic
103C2×C4⋊C4×C47C2311yescharacteristic
104C2×C4⋊C4×C47C2311yescharacteristic
105C2×C4⋊C4×C47C2311yescharacteristic
106C2×C4⋊C4×C47C2311yescharacteristic
107C2×C22⋊C4×C47—21no—
108C2×C22⋊C4×C47—21no—
109C2×C22⋊C4×C47—21no—
110C2×C22⋊C4×C47—21no—
111C2×C22⋊C4×C47—21no—
112C2×C22⋊C4×C47—21no—
113C2×C22⋊C4×C47—21no—
114C2×C22⋊C4×C47—21no—
115C2×C22⋊C4×C47—21no—
116C2×C22⋊C4×C47—21no—
117C2×C22⋊C4×C47D411yescharacteristic
118C2×C22⋊C4×C47D411yescharacteristic
119C2×C42×C47—21no—
120C2×C42×C47—21no—
121C2×C42×C47—21no—
122C2×C42×C47—21no—
123C2×C42×C47C2311yescharacteristic
124C2×C42×C47C2311yescharacteristic
125#107×C47—22no—
126#106×C47—41no—
127#103×C47—22no—
128#103×C47C2×C414yescomplemented
129#103×C47D414yescomplemented
130#102×C47—22no—
131#102×C47—22no—
132#102×C47—22no—
133#102×C47—41no—
134#102×C47C2×C414yescomplemented
135C22⋊C8×C47C2×C414yescomplemented
136#97×C47—22no—
137#97×C47—41no—
138#95×C47—21no—
139#95×C47—21no—
140#95×C47—21no—
141#95×C47D411yescharacteristic
142#95×C47D411yescharacteristic
143C24×C47—21no—
144C24×C47—21no—
145C24×C47C2×D411yescharacteristic
146#41×C47—28no—
147#41×C47—44no—
148#41×C47—44no—
149#41×C47—44no—
150C2×Q8×C47—21no—
151C2×Q8×C47—21no—
152C2×Q8×C47—21no—
153C2×Q8×C47C22×C412yes—
154C2×Q8×C47C2×D412yes—
155C2×Q8×C47#4112yes—
156C2×D4×C47—24no—
157C2×D4×C47—24no—
158C2×D4×C47—21no—
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—42no—
169C2×D4×C47—42no—
170C2×D4×C47—81no—
171C2×D4×C47—81no—
172C2×D4×C47C22×C412yes—
173C2×D4×C47C22×C412yes—
174C22×C4×C47—21no—
175C22×C4×C47—21no—
176C22×C4×C47—21no—
177C22×C4×C47—21no—
178C22×C4×C47—21no—
179C22×C4×C47—21no—
180C22×C4×C47—21no—
181C22×C4×C47—24no—
182C22×C4×C47—21no—
183C22×C4×C47—21no—
184C22×C4×C47—21no—
185C22×C4×C47—42no—
186C22×C4×C47—42no—
187C22×C4×C47—42no—
188C22×C4×C47—42no—
189C22×C4×C47—81no—
190C22×C4×C47C22×C412yes—
191C22×C4×C47C2×D411yescharacteristic
192C22×C4×C47C2×D411yescharacteristic
193C22×C4×C47C2×D411yescharacteristic
194C22×C4×C47C2×D411yescharacteristic
195C22×C4×C47C2×D411yescharacteristic
196C22×C4×C47#4112yes—
197C22×C4×C47C2411yescharacteristic
198SD16×C47—28no—
199D8×C47—44no—
200C2×C8×C47—21no—
201C2×C8×C47—21no—
202C2×C8×C47—21no—
203C2×C8×C47—21no—
204C2×C8×C47—21no—
205C2×C8×C47—21no—
206C2×C8×C47—21no—
207C2×C8×C47—21no—
208C2×C8×C47—21no—
209C2×C8×C47—44no—
210C2×C8×C47C22×C412yes—
211C2×C8×C47C22×C412yes—
212C2×C8×C47C2×D412yes—
213C4⋊C4×C47—21no—
214C4⋊C4×C47—21no—
215C4⋊C4×C47—21no—
216C4⋊C4×C47—21no—
217C4⋊C4×C47—21no—
218C4⋊C4×C47—21no—
219C4⋊C4×C47—21no—
220C4⋊C4×C47—21no—
221C4⋊C4×C47—42no—
222C4⋊C4×C47—42no—
223C4⋊C4×C47—81no—
224C4⋊C4×C47C22×C412yes—
225C4⋊C4×C47C2×D412yes—
226C22⋊C4×C47—24no—
227C22⋊C4×C47—41no—
228C22⋊C4×C47—41no—
229C22⋊C4×C47—42no—
230C22⋊C4×C47—42no—
231C22⋊C4×C47—42no—
232C22⋊C4×C47—42no—
233C22⋊C4×C47—42no—
234C22⋊C4×C47—81no—
235C22⋊C4×C47—81no—
236C22⋊C4×C47—81no—
237C22⋊C4×C47—81no—
238C42×C47—21no—
239C42×C47—21no—
240C42×C47—21no—
241C42×C47—21no—
242C42×C47—42no—
243C42×C47—42no—
244C42×C47—42no—
245C42×C47—81no—
246C23×C47—21no—
247C23×C47—21no—
248C23×C47—21no—
249C23×C47—21no—
250C23×C47—21no—
251C23×C47—21no—
252C23×C47—22no—
253C23×C47—22no—
254C23×C47—41no—
255C23×C47—41no—
256C23×C47—41no—
257C23×C47—41no—
258C23×C47—41no—
259C23×C47—41no—
260C23×C47—41no—
261C23×C47—41no—
262C23×C47—41no—
263C23×C47—41no—
264C23×C47—41no—
265C23×C47—41no—
266C23×C47C4×D412yes—
267C23×C47C22×D411yescharacteristic
268Q8×C47—22no—
269Q8×C47—22no—
270Q8×C47—22no—
271Q8×C47C4×D414yes—
272D4×C47—22no—
273D4×C47—22no—
274D4×C47—22no—
275D4×C47—22no—
276D4×C47—48no—
277D4×C47—41no—
278D4×C47—41no—
279D4×C47—41no—
280D4×C47—41no—
281D4×C47—84no—
282C2×C4×C47—22no—
283C2×C4×C47—21no—
284C2×C4×C47—22no—
285C2×C4×C47—22no—
286C2×C4×C47—21no—
287C2×C4×C47—22no—
288C2×C4×C47—22no—
289C2×C4×C47—22no—
290C2×C4×C47—22no—
291C2×C4×C47—22no—
292C2×C4×C47—21no—
293C2×C4×C47—21no—
294C2×C4×C47—22no—
295C2×C4×C47—21no—
296C2×C4×C47—21no—
297C2×C4×C47—21no—
298C2×C4×C47—21no—
299C2×C4×C47—21no—
300C2×C4×C47—21no—
301C2×C4×C47—21no—
302C2×C4×C47—21no—
303C2×C4×C47—21no—
304C2×C4×C47—21no—
305C2×C4×C47—48no—
306C2×C4×C47—41no—
307C2×C4×C47—41no—
308C2×C4×C47—41no—
309C2×C4×C47—41no—
310C2×C4×C47—41no—
311C2×C4×C47—41no—
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—84no—
320C2×C4×C47C4×D412yes—
321C2×C4×C47C23×C411yescharacteristic
322C2×C4×C47C22×D411yescharacteristic
323C2×C4×C47C2×#4111yescharacteristic
324C2×C4×C47C2×#4111yescharacteristic
325C2×C4×C47H(5,𝔽2)11yescharacteristic
326C2×C4×C47H(5,𝔽2)11yescharacteristic
327C8×C47—22no—
328C8×C47—22no—
329C8×C47—22no—
330C8×C47—41no—
331#22857C4711yesmaximal, characteristic, direct product factor, Sylow
332C22×C47—22no—
333C22×C47—22no—
334C22×C47—22no—
335C22×C47—41no—
336C22×C47—41no—
337C22×C47—41no—
338C22×C47—41no—
339C22×C47—42no—
340C22×C47—42no—
341C22×C47—42no—
342C22×C47—42no—
343C22×C47—42no—
344C22×C47—42no—
345C22×C47—81no—
346C22×C47—81no—
347C22×C47—81no—
348C22×C47—81no—
349C22×C47—81no—
350C22×C47—81no—
351C22×C47—81no—
352C22×C47—81no—
353C22×C47C2×C4×D411yescharacteristic
354C22×C47D4211yescharacteristic
355C22×C47#54611yescharacteristic
356C22×C47#57511yescharacteristic
357C22×C47#57511yescharacteristic
358C22×C47#57611yescharacteristic
359C22×C47#57711yescharacteristic
360C4×C47—22no—
361C4×C47—24no—
362C4×C47—42no—
363C4×C47—41no—
364C4×C47—42no—
365C4×C47—41no—
366C4×C47—41no—
367C4×C47—41no—
368C4×C47—81no—
369C4×C47—81no—
370C4×C47—81no—
371C4×C47C2×C4×D411yescharacteristic
372C4×C47#51811yescharacteristic
373C4×C47#54611yescharacteristic
374C4×C47#55111yescharacteristic
375C2×#449C2×C4711yescharacteristic
376C2×#440C2×C4711yescharacteristic, complemented
377C2×#416C2×C4711yescharacteristic, complemented
378#2363C2×C4711yescharacteristic, complemented
379#2341C2×C4711yescharacteristic, complemented
380#1972C2×C4711yescharacteristic, complemented
381#1936C2×C4711yescharacteristic, complemented
382#1925C2×C4711yescharacteristic, complemented
383#1893C2×C4711yescharacteristic, complemented
384#1880C2×C4711yescharacteristic, complemented
385#1879C2×C4711yescharacteristic, complemented
386#1865C2×C4711yescharacteristic, complemented
387#1854C2×C4711yescharacteristic, complemented
388#1763C2×C4711yescharacteristic, complemented
389#1752C2×C4711yescharacteristic, complemented
390C2×C47—42no—
391C2×C47—82no—
392C2×C47—82no—
393C2×C47#235811yescharacteristic
394C2×C47#294311yescharacteristic
395C2×C47#294611yescharacteristic
396C2×C47#326811yescharacteristic
397C2×C47#327111yescharacteristic
398C2×C47#330911yescharacteristic
399C2×C47#332111yescharacteristic
400C22×#41C22×C4711yescharacteristic
401C22×SD16C22×C4711yescharacteristic
402C22×D8C22×C4711yescharacteristic
403C23×C8C22×C4711yescharacteristic
404C2×#121C22×C4711yescharacteristic
405C2×C4×Q8C22×C4711yescharacteristic
406C2×C4×Q8C22×C4711yescharacteristic
407C2×C4×D4C22×C4711yescharacteristic
408C2×#117C22×C4711yescharacteristic
409#449C4×C4718yescomplemented
410#440—24no—
411C2×#107C22×C4711yescharacteristic
412C2×#106C22×C4711yescharacteristic
413#416—24no—
414C2×#103C22×C4711yescharacteristic
415C2×#103C22×C4711yescharacteristic
416C2×#103C22×C4711yescharacteristic
417C2×#102C22×C4711yescharacteristic
418C2×#102C22×C4711yescharacteristic
419C2×#102C22×C4711yescharacteristic
420C2×#102C22×C4711yescharacteristic
421C2×#102C22×C4711yescharacteristic
422C2×C22⋊C8C22×C4711yescharacteristic
423C2×#97C22×C4711yescharacteristic
424C2×#97C22×C4711yescharacteristic
425#390—21no—
426#390—21no—
427#390—21no—
428#390C22×C4711yescharacteristic
429#390C22×C4711yescharacteristic
430#390C22×C4711yescharacteristic
431#389C22×C4711yescharacteristic
432#388—21no—
433#386—21no—
434#380—21no—
435#380C22×C4711yescharacteristic
436C4×C4⋊C4C22×C4711yescharacteristic
437C4×C22⋊C4—21no—
438C4×C22⋊C4—21no—
439C4×C22⋊C4C22×C4711yescharacteristic
440#340C22×C4711yescharacteristic
441#340C22×C4711yescharacteristic
442#340C22×C4711yescharacteristic
443#340C22×C4711yescharacteristic
444#336C22×C4711yescharacteristic
445#336C22×C4711yescharacteristic
446C47#2285711yescharacteristic, direct product factor, Sylow
447C2×#41—22no—
448C2×#41—22no—
449C2×#41—22no—
450C2×#41—41no—
451C2×#41—41no—
452C2×#41C2×C4×C4714yescomplemented
453C22×Q8C23×C4711yescharacteristic
454C22×D4—21no—
455C22×D4—21no—
456C22×D4C23×C4711yescharacteristic
457C22×D4C23×C4711yescharacteristic
458C23×C4—21no—
459C23×C4—21no—
460C23×C4C23×C4711yescharacteristic
461C2×SD16—22no—
462C2×SD16—22no—
463C2×SD16C2×C4×C4714yes—
464C2×D8—41no—
465C2×D8—41no—
466C2×D8C2×C4×C4714yes—
467C22×C8—22no—
468C22×C8—22no—
469C22×C8—41no—
470C22×C8C23×C4711yescharacteristic
471C22×C8C23×C4711yescharacteristic
472C22×C8C23×C4711yescharacteristic
473C22×C8C23×C4711yescharacteristic
474#121—22no—
475#121C2×C4×C4714yes—
476C4×Q8—22no—
477C4×Q8—22no—
478C4×Q8—41no—
479C4×Q8—41no—
480C4×D4—22no—
481C4×D4—41no—
482#117—22no—
483#117—41no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4C23×C4711yescharacteristic
488C2×C4⋊C4C23×C4711yescharacteristic
489C2×C4⋊C4C23×C4711yescharacteristic
490C2×C4⋊C4C23×C4711yescharacteristic
491C2×C4⋊C4C23×C4711yescharacteristic
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4D4×C4711yescharacteristic
503C2×C22⋊C4D4×C4711yescharacteristic
504C2×C42—21no—
505C2×C42—21no—
506C2×C42—21no—
507C2×C42—21no—
508C2×C42C23×C4711yescharacteristic
509C2×C42C23×C4711yescharacteristic
510#107—22no—
511#106—41no—
512#103—22no—
513#103C2×C4×C4714yescomplemented
514#103D4×C4714yescomplemented
515#102—22no—
516#102—22no—
517#102—22no—
518#102—41no—
519#102C2×C4×C4714yescomplemented
520C22⋊C8C2×C4×C4714yescomplemented
521#97—22no—
522#97—41no—
523#95—21no—
524#95—21no—
525#95—21no—
526#95D4×C4711yescharacteristic
527#95D4×C4711yescharacteristic
528C24—21no—
529C24—21no—
530C24C2×D4×C4711yescharacteristic
531#41—28no—
532#41—44no—
533#41—44no—
534#41—44no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8C22×C4×C4712yes—
539C2×Q8C2×D4×C4712yes—
540C2×Q8#41×C4712yes—
541C2×D4—24no—
542C2×D4—24no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—42no—
554C2×D4—42no—
555C2×D4—81no—
556C2×D4—81no—
557C2×D4C22×C4×C4712yes—
558C2×D4C22×C4×C4712yes—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—24no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—81no—
575C22×C4C22×C4×C4712yes—
576C22×C4C2×D4×C4711yescharacteristic
577C22×C4C2×D4×C4711yescharacteristic
578C22×C4C2×D4×C4711yescharacteristic
579C22×C4C2×D4×C4711yescharacteristic
580C22×C4C2×D4×C4711yescharacteristic
581C22×C4#41×C4712yes—
582C22×C4C24×C4711yescharacteristic
583SD16—28no—
584D8—44no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—44no—
595C2×C8C22×C4×C4712yes—
596C2×C8C22×C4×C4712yes—
597C2×C8C2×D4×C4712yes—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—42no—
607C4⋊C4—42no—
608C4⋊C4—81no—
609C4⋊C4C22×C4×C4712yes—
610C4⋊C4C2×D4×C4712yes—
611C22⋊C4—24no—
612C22⋊C4—41no—
613C22⋊C4—41no—
614C22⋊C4—42no—
615C22⋊C4—42no—
616C22⋊C4—42no—
617C22⋊C4—42no—
618C22⋊C4—42no—
619C22⋊C4—81no—
620C22⋊C4—81no—
621C22⋊C4—81no—
622C22⋊C4—81no—
623C42—21no—
624C42—21no—
625C42—21no—
626C42—21no—
627C42—42no—
628C42—42no—
629C42—42no—
630C42—81no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—22no—
638C23—22no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23C4×D4×C4712yes—
652C23C22×D4×C4711yescharacteristic
653Q8—22no—
654Q8—22no—
655Q8—22no—
656Q8C4×D4×C4714yes—
657D4—22no—
658D4—22no—
659D4—22no—
660D4—22no—
661D4—48no—
662D4—41no—
663D4—41no—
664D4—41no—
665D4—41no—
666D4—84no—
667C2×C4—22no—
668C2×C4—21no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—21no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—22no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—48no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—84no—
705C2×C4C4×D4×C4712yes—
706C2×C4C23×C4×C4711yescharacteristic
707C2×C4C22×D4×C4711yescharacteristic
708C2×C4C2×#41×C4711yescharacteristic
709C2×C4C2×#41×C4711yescharacteristic
710C2×C4H(5,𝔽2)×C4711yescharacteristic
711C2×C4H(5,𝔽2)×C4711yescharacteristic
712C8—22no—
713C8—22no—
714C8—22no—
715C8—41no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—81no—
730C22—81no—
731C22—81no—
732C22—81no—
733C22—81no—
734C22—81no—
735C22—81no—
736C22—81no—
737C22C2×C4×D4×C4711yescharacteristic
738C22D42×C4711yescharacteristic
739C22C47×#54611yescharacteristic
740C22C47×#57511yescharacteristic
741C22C47×#57511yescharacteristic
742C22C47×#57611yescharacteristic
743C22C47×#57711yescharacteristic
744C4—22no—
745C4—24no—
746C4—41no—
747C4—41no—
748C4—42no—
749C4—41no—
750C4—42no—
751C4—41no—
752C4—81no—
753C4—81no—
754C4—81no—
755C4C2×C4×D4×C4711yescharacteristic
756C4C47×#51811yescharacteristic
757C4C47×#54611yescharacteristic
758C4C47×#55111yescharacteristic
759C2—42no—
760C2—82no—
761C2—82no—
762C2C47×#235811yescharacteristic
763C2C47×#294311yescharacteristic
764C2C47×#294611yescharacteristic
765C2C47×#326811yescharacteristic
766C2C47×#327111yescharacteristic
767C2C47×#330911yescharacteristic
768C2C47×#332111yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutatorC2×C4C23×C4×C47
Frattini, cosocleC22×C4C24×C47
prime radicalC2×C47×#449C2
LCSG ▷ C2×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
2. C2×C47×#440C2semidirect
3. C2×C47×#416C2semidirect
4. C47×#2363C2semidirect
5. C47×#2341C2semidirect
6. C47×#1972C2semidirect
7. C47×#1936C2semidirect
8. C47×#1925C2semidirect
9. C47×#1893C2semidirect
10. C47×#1880C2semidirect
11. C47×#1879C2semidirect
12. C47×#1865C2semidirect
13. C47×#1854C2semidirect
14. C47×#1763C2semidirect
15. C47×#1752C2semidirect
25. C47×#449C4semidirect
67. C2×#41×C47C2×C4semidirect
128. #103×C47C2×C4semidirect
129. #103×C47D4semidirect
134. #102×C47C2×C4semidirect
135. C22⋊C8×C47C2×C4semidirect
331. #22857C47direct (N × H)
376. C2×#440C2×C47semidirect
377. C2×#416C2×C47semidirect
378. #2363C2×C47semidirect
379. #2341C2×C47semidirect
380. #1972C2×C47semidirect
381. #1936C2×C47semidirect
382. #1925C2×C47semidirect
383. #1893C2×C47semidirect
384. #1880C2×C47semidirect
385. #1879C2×C47semidirect
386. #1865C2×C47semidirect
387. #1854C2×C47semidirect
388. #1763C2×C47semidirect
389. #1752C2×C47semidirect
409. #449C4×C47semidirect
446. C47#22857direct (N × H)
452. C2×#41C2×C4×C47semidirect
513. #103C2×C4×C47semidirect
514. #103D4×C47semidirect
519. #102C2×C4×C47semidirect
520. C22⋊C8C2×C4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#4492
C2×C47×#4402
C2×C47×#4162
C47×#23632
C47×#23412
C47×#19722
C47×#19362
C47×#19252
C47×#18932
C47×#18802
C47×#18792
C47×#18652
C47×#18542
C47×#17632
C47×#17522
#2285747