Finite Group Databasebeta

← C47×#24734 #26064432

Subgroups — C47×#24734 #26064432

Order 12032.

988 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#464C211yesmaximal, characteristic, complemented
2C2×C47×#464C211yesmaximal, characteristic, complemented
3C2×C47×#460C211yesmaximal, characteristic
4C2×C4×SD16×C47C211yesmaximal, characteristic, complemented
5C47×#2544C211yesmaximal, characteristic
6C47×#2351C211yesmaximal, characteristic, complemented
7C47×#2066C211yesmaximal, characteristic, complemented
8C47×#2065C211yesmaximal, characteristic, complemented
9C47×#2042C211yesmaximal, characteristic, complemented
10C47×#2041C211yesmaximal, characteristic
11C47×#1958C211yesmaximal, characteristic, complemented
12C47×#1939C211yesmaximal, characteristic, complemented
13C47×#1880C211yesmaximal, characteristic, complemented
14C47×#1878C211yesmaximal, characteristic, complemented
15C47×#1804C211yesmaximal, characteristic, complemented
16C22×Q16×C47C2211yescharacteristic
17C22×SD16×C47C2211yescharacteristic
18C22×SD16×C47C2211yescharacteristic
19C2×#127×C47C2211yescharacteristic
20C2×#124×C47C2211yescharacteristic
21C2×#124×C47C2211yescharacteristic
22C2×C4×Q8×C47C2211yescharacteristic
23C2×C4×Q8×C47C2211yescharacteristic
24C2×C4×Q8×C47C2211yescharacteristic
25C2×C4×D4×C47C2211yescharacteristic
26C47×#464—24no—
27C47×#464—24no—
28C47×#460—24no—
29C4×SD16×C47—24no—
30C2×#106×C47C2211yescharacteristic
31C2×C4⋊C8×C47C2211yescharacteristic
32C2×C4⋊C8×C47C2211yescharacteristic
33C2×C4⋊C8×C47C2211yescharacteristic
34C2×#103×C47C2211yescharacteristic
35C2×#103×C47C2211yescharacteristic
36C2×#103×C47C2211yescharacteristic
37C2×#103×C47C2211yescharacteristic
38C2×#102×C47C2211yescharacteristic
39C2×#102×C47C2211yescharacteristic
40C2×#102×C47C2211yescharacteristic
41C2×#102×C47C2211yescharacteristic
42C2×#102×C47C2211yescharacteristic
43C2×#102×C47C2211yescharacteristic
44C2×C4×C8×C47C2211yescharacteristic
45C47×#394—21no—
46C47×#394—21no—
47C47×#391C2211yescharacteristic
48C47×#390C2211yescharacteristic
49C47×#389—21no—
50C47×#389—21no—
51C47×#389C2211yescharacteristic
52C47×#389C2211yescharacteristic
53C47×#386—21no—
54C47×#386—21no—
55C47×#382—21no—
56C47×#382C2211yescharacteristic
57C4×C4⋊C4×C47—21no—
58C4×C4⋊C4×C47C2211yescharacteristic
59C47×#340C2211yescharacteristic
60C47×#340C2211yescharacteristic
61C47×#336C2211yescharacteristic
62C47×#336C2211yescharacteristic
63C22×Q8×C47C2311yescharacteristic
64C22×Q8×C47C2311yescharacteristic
65C22×D4×C47—21no—
66C22×D4×C47—21no—
67C22×D4×C47C2311yescharacteristic
68C22×D4×C47C2311yescharacteristic
69C23×C4×C47—21no—
70C2×Q16×C47—22no—
71C2×Q16×C47—22no—
72C2×Q16×C47—22no—
73C2×SD16×C47—22no—
74C2×SD16×C47—22no—
75C2×SD16×C47—22no—
76C2×SD16×C47—22no—
77C2×SD16×C47—22no—
78C2×SD16×C47D414yes—
79C22×C8×C47C2311yescharacteristic
80C22×C8×C47C2311yescharacteristic
81C22×C8×C47C2311yescharacteristic
82C22×C8×C47C2311yescharacteristic
83#127×C47—22no—
84#127×C47—41no—
85#124×C47—22no—
86#124×C47—22no—
87#124×C47—22no—
88#124×C47—41no—
89C4×Q8×C47—22no—
90C4×Q8×C47—22no—
91C4×Q8×C47—22no—
92C4×Q8×C47—41no—
93C4×Q8×C47—41no—
94C4×Q8×C47D414yescomplemented
95C4×D4×C47—22no—
96C4×D4×C47—22no—
97C2×C4⋊C4×C47—21no—
98C2×C4⋊C4×C47—21no—
99C2×C4⋊C4×C47—21no—
100C2×C4⋊C4×C47—21no—
101C2×C4⋊C4×C47—21no—
102C2×C4⋊C4×C47D411yescharacteristic
103C2×C4⋊C4×C47D411yescharacteristic
104C2×C4⋊C4×C47C2311yescharacteristic
105C2×C4⋊C4×C47C2311yescharacteristic
106C2×C4⋊C4×C47C2311yescharacteristic
107C2×C4⋊C4×C47C2311yescharacteristic
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×C42×C47—21no—
116C2×C42×C47—21no—
117C2×C42×C47—21no—
118C2×C42×C47C2311yescharacteristic
119C2×C42×C47C2311yescharacteristic
120C2×C42×C47C2311yescharacteristic
121#106×C47—22no—
122C4⋊C8×C47—22no—
123C4⋊C8×C47—22no—
124C4⋊C8×C47—22no—
125#103×C47—22no—
126#103×C47—22no—
127#103×C47—22no—
128#103×C47—41no—
129#102×C47—22no—
130#102×C47—22no—
131#102×C47—22no—
132#102×C47—22no—
133#102×C47—22no—
134#102×C47—41no—
135C4×C8×C47—22no—
136#95×C47—21no—
137#95×C47—21no—
138#95×C47—21no—
139#95×C47—21no—
140#95×C47—21no—
141#95×C47—21no—
142#95×C47D411yescharacteristic
143#95×C47D411yescharacteristic
144C24×C47—21no—
145C24×C47—21no—
146C2×Q8×C47—21no—
147C2×Q8×C47—21no—
148C2×Q8×C47—21no—
149C2×Q8×C47—21no—
150C2×Q8×C47—21no—
151C2×Q8×C47—21no—
152C2×Q8×C47—21no—
153C2×Q8×C47—21no—
154C2×Q8×C47—21no—
155C2×Q8×C47C2×D412yes—
156C2×Q8×C47C2×D412yes—
157C2×Q8×C47#4112yes—
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—21no—
169C2×D4×C47—42no—
170C2×D4×C47—42no—
171C2×D4×C47—42no—
172C2×D4×C47—42no—
173C2×D4×C47—81no—
174C2×D4×C47—81no—
175C2×D4×C47C2×D412yes—
176C22×C4×C47—21no—
177C22×C4×C47—21no—
178C22×C4×C47—21no—
179C22×C4×C47—21no—
180C22×C4×C47—21no—
181C22×C4×C47—21no—
182C22×C4×C47—42no—
183C22×C4×C47—81no—
184C22×C4×C47—81no—
185C22×C4×C47C2×D411yescharacteristic
186C22×C4×C47C2×D411yescharacteristic
187C22×C4×C47C2×D411yescharacteristic
188C22×C4×C47C2×D411yescharacteristic
189C22×C4×C47C2×D411yescharacteristic
190C22×C4×C47C2×D411yescharacteristic
191C22×C4×C47C2411yescharacteristic
192Q16×C47—44no—
193SD16×C47—28no—
194SD16×C47—44no—
195C2×C8×C47—21no—
196C2×C8×C47—21no—
197C2×C8×C47—21no—
198C2×C8×C47—21no—
199C2×C8×C47—21no—
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×C47C2×D412yes—
207C4⋊C4×C47—24no—
208C4⋊C4×C47—22no—
209C4⋊C4×C47—21no—
210C4⋊C4×C47—21no—
211C4⋊C4×C47—21no—
212C4⋊C4×C47—21no—
213C4⋊C4×C47—21no—
214C4⋊C4×C47—21no—
215C4⋊C4×C47—21no—
216C4⋊C4×C47—41no—
217C4⋊C4×C47—42no—
218C4⋊C4×C47—42no—
219C4⋊C4×C47—42no—
220C4⋊C4×C47—42no—
221C4⋊C4×C47C2×D412yes—
222C22⋊C4×C47—42no—
223C22⋊C4×C47—42no—
224C22⋊C4×C47—42no—
225C22⋊C4×C47—42no—
226C22⋊C4×C47—42no—
227C22⋊C4×C47—81no—
228C22⋊C4×C47—81no—
229C42×C47—24no—
230C42×C47—21no—
231C42×C47—21no—
232C42×C47—21no—
233C42×C47—21no—
234C42×C47—42no—
235C42×C47—42no—
236C42×C47C2×D412yes—
237C42×C47#4112yes—
238C23×C47—22no—
239C23×C47—41no—
240C23×C47—41no—
241C23×C47—41no—
242C23×C47—41no—
243C23×C47—41no—
244C23×C47—41no—
245C23×C47—41no—
246C23×C47—41no—
247C23×C47—41no—
248C23×C47—41no—
249C23×C47—41no—
250C23×C47—41no—
251C23×C47—41no—
252C23×C47C22×D411yescharacteristic
253Q8×C47—22no—
254Q8×C47—22no—
255Q8×C47—22no—
256Q8×C47—41no—
257Q8×C47—41no—
258Q8×C47—41no—
259Q8×C47—41no—
260Q8×C47#12114yes—
261D4×C47—22no—
262D4×C47—22no—
263D4×C47—41no—
264D4×C47—41no—
265D4×C47—41no—
266D4×C47—41no—
267D4×C47—41no—
268D4×C47—41no—
269D4×C47—84no—
270D4×C47—84no—
271C2×C4×C47—22no—
272C2×C4×C47—21no—
273C2×C4×C47—22no—
274C2×C4×C47—22no—
275C2×C4×C47—21no—
276C2×C4×C47—21no—
277C2×C4×C47—21no—
278C2×C4×C47—21no—
279C2×C4×C47—21no—
280C2×C4×C47—22no—
281C2×C4×C47—21no—
282C2×C4×C47—21no—
283C2×C4×C47—21no—
284C2×C4×C47—21no—
285C2×C4×C47—21no—
286C2×C4×C47—21no—
287C2×C4×C47—21no—
288C2×C4×C47—21no—
289C2×C4×C47—21no—
290C2×C4×C47—41no—
291C2×C4×C47—41no—
292C2×C4×C47—41no—
293C2×C4×C47—41no—
294C2×C4×C47—41no—
295C2×C4×C47—41no—
296C2×C4×C47—41no—
297C2×C4×C47—41no—
298C2×C4×C47—41no—
299C2×C4×C47—41no—
300C2×C4×C47—41no—
301C2×C4×C47—41no—
302C2×C4×C47—41no—
303C2×C4×C47—41no—
304C2×C4×C47—84no—
305C2×C4×C47#12112yes—
306C2×C4×C47#12112yes—
307C2×C4×C47#13512yes—
308C2×C4×C47C22×D411yescharacteristic
309C2×C4×C47C22×D411yescharacteristic
310C2×C4×C47C2×#4111yescharacteristic
311C2×C4×C47C2×#4111yescharacteristic
312C2×C4×C47H(5,𝔽2)11yescharacteristic
313C2×C4×C472−1+411yescharacteristic
314C8×C47—22no—
315C8×C47—41no—
316C8×C47—41no—
317C8×C47—41no—
318#24734C4711yesmaximal, characteristic, direct product factor, Sylow
319C22×C47—42no—
320C22×C47—42no—
321C22×C47—42no—
322C22×C47—81no—
323C22×C47—81no—
324C22×C47—81no—
325C22×C47—81no—
326C22×C47—81no—
327C22×C47—81no—
328C22×C47—81no—
329C22×C47—81no—
330C22×C47—81no—
331C22×C47—81no—
332C22×C47—81no—
333C22×C47C2×#12111yescharacteristic
334C22×C47D4211yescharacteristic
335C22×C47#54811yescharacteristic
336C22×C47C2×#13511yescharacteristic
337C22×C47#57511yescharacteristic
338C22×C47#57711yescharacteristic
339C22×C47#57711yescharacteristic
340C4×C47—24no—
341C4×C47—22no—
342C4×C47—22no—
343C4×C47—22no—
344C4×C47—41no—
345C4×C47—41no—
346C4×C47—41no—
347C4×C47—42no—
348C4×C47—81no—
349C4×C47—81no—
350C4×C47—81no—
351C4×C47—81no—
352C4×C47C2×#12111yescharacteristic
353C4×C47#53711yescharacteristic
354C4×C47#54711yescharacteristic
355C4×C47#55311yescharacteristic
356C2×#464C2×C4711yescharacteristic, complemented
357C2×#464C2×C4711yescharacteristic, complemented
358C2×#460C2×C4711yescharacteristic
359C2×C4×SD16C2×C4711yescharacteristic, complemented
360#2544C2×C4711yescharacteristic
361#2351C2×C4711yescharacteristic, complemented
362#2066C2×C4711yescharacteristic, complemented
363#2065C2×C4711yescharacteristic, complemented
364#2042C2×C4711yescharacteristic, complemented
365#2041C2×C4711yescharacteristic
366#1958C2×C4711yescharacteristic, complemented
367#1939C2×C4711yescharacteristic, complemented
368#1880C2×C4711yescharacteristic, complemented
369#1878C2×C4711yescharacteristic, complemented
370#1804C2×C4711yescharacteristic, complemented
371C2×C47—82no—
372C2×C47—161no—
373C2×C47#241611yescharacteristic
374C2×C47#303511yescharacteristic
375C2×C47#304311yescharacteristic
376C2×C47#327511yescharacteristic
377C2×C47#328211yescharacteristic
378C2×C47#336511yescharacteristic
379C2×C47#337111yescharacteristic
380C22×Q16C22×C4711yescharacteristic
381C22×SD16C22×C4711yescharacteristic
382C22×SD16C22×C4711yescharacteristic
383C2×#127C22×C4711yescharacteristic
384C2×#124C22×C4711yescharacteristic
385C2×#124C22×C4711yescharacteristic
386C2×C4×Q8C22×C4711yescharacteristic
387C2×C4×Q8C22×C4711yescharacteristic
388C2×C4×Q8C22×C4711yescharacteristic
389C2×C4×D4C22×C4711yescharacteristic
390#464—24no—
391#464—24no—
392#460—24no—
393C4×SD16—24no—
394C2×#106C22×C4711yescharacteristic
395C2×C4⋊C8C22×C4711yescharacteristic
396C2×C4⋊C8C22×C4711yescharacteristic
397C2×C4⋊C8C22×C4711yescharacteristic
398C2×#103C22×C4711yescharacteristic
399C2×#103C22×C4711yescharacteristic
400C2×#103C22×C4711yescharacteristic
401C2×#103C22×C4711yescharacteristic
402C2×#102C22×C4711yescharacteristic
403C2×#102C22×C4711yescharacteristic
404C2×#102C22×C4711yescharacteristic
405C2×#102C22×C4711yescharacteristic
406C2×#102C22×C4711yescharacteristic
407C2×#102C22×C4711yescharacteristic
408C2×C4×C8C22×C4711yescharacteristic
409#394—21no—
410#394—21no—
411#391C22×C4711yescharacteristic
412#390C22×C4711yescharacteristic
413#389—21no—
414#389—21no—
415#389C22×C4711yescharacteristic
416#389C22×C4711yescharacteristic
417#386—21no—
418#386—21no—
419#382—21no—
420#382C22×C4711yescharacteristic
421C4×C4⋊C4—21no—
422C4×C4⋊C4C22×C4711yescharacteristic
423#340C22×C4711yescharacteristic
424#340C22×C4711yescharacteristic
425#336C22×C4711yescharacteristic
426#336C22×C4711yescharacteristic
427C47#2473411yescharacteristic, direct product factor, Sylow
428C22×Q8C23×C4711yescharacteristic
429C22×Q8C23×C4711yescharacteristic
430C22×D4—21no—
431C22×D4—21no—
432C22×D4C23×C4711yescharacteristic
433C22×D4C23×C4711yescharacteristic
434C23×C4—21no—
435C2×Q16—22no—
436C2×Q16—22no—
437C2×Q16—22no—
438C2×SD16—22no—
439C2×SD16—22no—
440C2×SD16—22no—
441C2×SD16—22no—
442C2×SD16—22no—
443C2×SD16D4×C4714yes—
444C22×C8C23×C4711yescharacteristic
445C22×C8C23×C4711yescharacteristic
446C22×C8C23×C4711yescharacteristic
447C22×C8C23×C4711yescharacteristic
448#127—22no—
449#127—41no—
450#124—22no—
451#124—22no—
452#124—22no—
453#124—41no—
454C4×Q8—22no—
455C4×Q8—22no—
456C4×Q8—22no—
457C4×Q8—41no—
458C4×Q8—41no—
459C4×Q8D4×C4714yescomplemented
460C4×D4—22no—
461C4×D4—22no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4D4×C4711yescharacteristic
468C2×C4⋊C4D4×C4711yescharacteristic
469C2×C4⋊C4C23×C4711yescharacteristic
470C2×C4⋊C4C23×C4711yescharacteristic
471C2×C4⋊C4C23×C4711yescharacteristic
472C2×C4⋊C4C23×C4711yescharacteristic
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C42—21no—
481C2×C42—21no—
482C2×C42—21no—
483C2×C42C23×C4711yescharacteristic
484C2×C42C23×C4711yescharacteristic
485C2×C42C23×C4711yescharacteristic
486#106—22no—
487C4⋊C8—22no—
488C4⋊C8—22no—
489C4⋊C8—22no—
490#103—22no—
491#103—22no—
492#103—22no—
493#103—41no—
494#102—22no—
495#102—22no—
496#102—22no—
497#102—22no—
498#102—22no—
499#102—41no—
500C4×C8—22no—
501#95—21no—
502#95—21no—
503#95—21no—
504#95—21no—
505#95—21no—
506#95—21no—
507#95D4×C4711yescharacteristic
508#95D4×C4711yescharacteristic
509C24—21no—
510C24—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8C2×D4×C4712yes—
521C2×Q8C2×D4×C4712yes—
522C2×Q8#41×C4712yes—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—42no—
535C2×D4—42no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4—81no—
539C2×D4—81no—
540C2×D4C2×D4×C4712yes—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—42no—
548C22×C4—81no—
549C22×C4—81no—
550C22×C4C2×D4×C4711yescharacteristic
551C22×C4C2×D4×C4711yescharacteristic
552C22×C4C2×D4×C4711yescharacteristic
553C22×C4C2×D4×C4711yescharacteristic
554C22×C4C2×D4×C4711yescharacteristic
555C22×C4C2×D4×C4711yescharacteristic
556C22×C4C24×C4711yescharacteristic
557Q16—44no—
558SD16—28no—
559SD16—44no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8C2×D4×C4712yes—
572C4⋊C4—24no—
573C4⋊C4—22no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—41no—
582C4⋊C4—42no—
583C4⋊C4—42no—
584C4⋊C4—42no—
585C4⋊C4—42no—
586C4⋊C4C2×D4×C4712yes—
587C22⋊C4—42no—
588C22⋊C4—42no—
589C22⋊C4—42no—
590C22⋊C4—42no—
591C22⋊C4—42no—
592C22⋊C4—81no—
593C22⋊C4—81no—
594C42—24no—
595C42—21no—
596C42—21no—
597C42—21no—
598C42—21no—
599C42—42no—
600C42—42no—
601C42C2×D4×C4712yes—
602C42#41×C4712yes—
603C23—22no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23C22×D4×C4711yescharacteristic
618Q8—22no—
619Q8—22no—
620Q8—22no—
621Q8—41no—
622Q8—41no—
623Q8—41no—
624Q8—41no—
625Q8#121×C4714yes—
626D4—22no—
627D4—22no—
628D4—41no—
629D4—41no—
630D4—41no—
631D4—41no—
632D4—41no—
633D4—41no—
634D4—84no—
635D4—84no—
636C2×C4—22no—
637C2×C4—21no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—22no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—84no—
670C2×C4#121×C4712yes—
671C2×C4#121×C4712yes—
672C2×C4#135×C4712yes—
673C2×C4C22×D4×C4711yescharacteristic
674C2×C4C22×D4×C4711yescharacteristic
675C2×C4C2×#41×C4711yescharacteristic
676C2×C4C2×#41×C4711yescharacteristic
677C2×C4H(5,𝔽2)×C4711yescharacteristic
678C2×C42−1+4×C4711yescharacteristic
679C8—22no—
680C8—41no—
681C8—41no—
682C8—41no—
683C22—42no—
684C22—42no—
685C22—42no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22—81no—
690C22—81no—
691C22—81no—
692C22—81no—
693C22—81no—
694C22—81no—
695C22—81no—
696C22—81no—
697C22C2×#121×C4711yescharacteristic
698C22D42×C4711yescharacteristic
699C22C47×#54811yescharacteristic
700C22C2×#135×C4711yescharacteristic
701C22C47×#57511yescharacteristic
702C22C47×#57711yescharacteristic
703C22C47×#57711yescharacteristic
704C4—22no—
705C4—22no—
706C4—24no—
707C4—22no—
708C4—42no—
709C4—41no—
710C4—41no—
711C4—41no—
712C4—81no—
713C4—81no—
714C4—81no—
715C4—81no—
716C4C2×#121×C4711yescharacteristic
717C4C47×#53711yescharacteristic
718C4C47×#54711yescharacteristic
719C4C47×#55311yescharacteristic
720C2—82no—
721C2—161no—
722C2C47×#241611yescharacteristic
723C2C47×#303511yescharacteristic
724C2C47×#304311yescharacteristic
725C2C47×#327511yescharacteristic
726C2C47×#328211yescharacteristic
727C2C47×#336511yescharacteristic
728C2C47×#337111yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC2×#127×C47C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C4×C4⋊C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C47×#464C2semidirect
2. C2×C47×#464C2semidirect
4. C2×C4×SD16×C47C2semidirect
6. C47×#2351C2semidirect
7. C47×#2066C2semidirect
8. C47×#2065C2semidirect
9. C47×#2042C2semidirect
11. C47×#1958C2semidirect
12. C47×#1939C2semidirect
13. C47×#1880C2semidirect
14. C47×#1878C2semidirect
15. C47×#1804C2semidirect
94. C4×Q8×C47D4semidirect
318. #24734C47direct (N × H)
356. C2×#464C2×C47semidirect
357. C2×#464C2×C47semidirect
359. C2×C4×SD16C2×C47semidirect
361. #2351C2×C47semidirect
362. #2066C2×C47semidirect
363. #2065C2×C47semidirect
364. #2042C2×C47semidirect
366. #1958C2×C47semidirect
367. #1939C2×C47semidirect
368. #1880C2×C47semidirect
369. #1878C2×C47semidirect
370. #1804C2×C47semidirect
427. C47#24734direct (N × H)
459. C4×Q8D4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#4642
C2×C47×#4602
C2×C4×SD16×C472
C47×#25442
C47×#23512
C47×#20662
C47×#20652
C47×#20422
C47×#20412
C47×#19582
C47×#19392
C47×#18802
C47×#18782
C47×#18042
#2473447