Finite Group Databasebeta

← C47×#24034 #26063732

Subgroups — C47×#24034 #26063732

Order 12032.

1380 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#550C211yesmaximal, characteristic
2C2×C47×#482C211yesmaximal, characteristic, complemented
3C2×C47×#416C211yesmaximal, characteristic, complemented
4C47×#2485C211yesmaximal, characteristic, complemented
5C47×#2041C211yesmaximal, characteristic, complemented
6C47×#2041C211yesmaximal, characteristic, complemented
7C47×#2034C211yesmaximal, characteristic, complemented
8C47×#2033C211yesmaximal, characteristic, complemented
9C47×#1893C211yesmaximal, characteristic, complemented
10C47×#1869C211yesmaximal, characteristic, complemented
11C47×#1865C211yesmaximal, characteristic, complemented
12C47×#1863C211yesmaximal, characteristic, complemented
13C47×#1788C211yesmaximal, characteristic, complemented
14C47×#1788C211yesmaximal, characteristic, complemented
15C47×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C47C2211yescharacteristic
17C22×#41×C47C2211yescharacteristic
18C23×C8×C47C2211yescharacteristic
19C47×#550—24no—
20C47×#550—24no—
21C2×#127×C47—21no—
22C2×#127×C47C2211yescharacteristic
23C2×#121×C47—21no—
24C2×#121×C47—21no—
25C2×#121×C47C2211yescharacteristic
26C2×#121×C47C2211yescharacteristic
27C2×C4×Q8×C47C2211yescharacteristic
28C2×C4×D4×C47—21no—
29C2×C4×D4×C47C2211yescharacteristic
30C2×#117×C47C2211yescharacteristic
31C47×#482—24no—
32C2×#107×C47C2211yescharacteristic
33C2×#106×C47C2211yescharacteristic
34C47×#416—24no—
35C2×#103×C47C2211yescharacteristic
36C2×#103×C47C2211yescharacteristic
37C2×#103×C47C2211yescharacteristic
38C2×#103×C47C2211yescharacteristic
39C2×#102×C47C2211yescharacteristic
40C2×#102×C47C2211yescharacteristic
41C2×#102×C47C2211yescharacteristic
42C2×#102×C47C2211yescharacteristic
43C2×#102×C47C2211yescharacteristic
44C2×#102×C47C2211yescharacteristic
45C2×#102×C47C2211yescharacteristic
46C2×#102×C47C2211yescharacteristic
47C2×C22⋊C8×C47C2211yescharacteristic
48C2×C22⋊C8×C47C2211yescharacteristic
49C2×C22⋊C8×C47C2211yescharacteristic
50C47×#397—21no—
51C47×#394—21no—
52C47×#389C2211yescharacteristic
53C47×#389C2211yescharacteristic
54C47×#388—21no—
55C47×#387—21no—
56C47×#380C2211yescharacteristic
57C47×#380C2211yescharacteristic
58C47×#380C2211yescharacteristic
59C47×#340C2211yescharacteristic
60C47×#340C2211yescharacteristic
61C47×#336C2211yescharacteristic
62C47×#336C2211yescharacteristic
63C2×#41×C47—22no—
64C2×#41×C47—22no—
65C2×#41×C47—22no—
66C2×#41×C47—22no—
67C2×#41×C47—22no—
68C2×#41×C47—22no—
69C2×#41×C47—22no—
70C2×#41×C47—41no—
71C2×#41×C47—41no—
72C2×#41×C47—41no—
73C2×#41×C47—41no—
74C2×#41×C47D414yes—
75C22×Q8×C47C2311yescharacteristic
76C22×D4×C47—21no—
77C22×D4×C47—21no—
78C22×D4×C47—21no—
79C22×D4×C47—21no—
80C22×D4×C47—21no—
81C22×D4×C47—21no—
82C22×D4×C47D411yescharacteristic
83C22×D4×C47C2311yescharacteristic
84C22×D4×C47C2311yescharacteristic
85C23×C4×C47—21no—
86C23×C4×C47—21no—
87C23×C4×C47C2311yescharacteristic
88C23×C4×C47C2311yescharacteristic
89C22×C8×C47—22no—
90C22×C8×C47—41no—
91C22×C8×C47—41no—
92C22×C8×C47C2311yescharacteristic
93C22×C8×C47C2311yescharacteristic
94C22×C8×C47C2311yescharacteristic
95C22×C8×C47C2311yescharacteristic
96#127×C47—28no—
97#127×C47—22no—
98#127×C47—22no—
99#121×C47—28no—
100#121×C47—28no—
101#121×C47—22no—
102#121×C47—22no—
103#121×C47—22no—
104#121×C47D414yes—
105C4×Q8×C47—22no—
106C4×Q8×C47—22no—
107C4×D4×C47—28no—
108C4×D4×C47—22no—
109C4×D4×C47—22no—
110#117×C47—22no—
111#117×C47—22no—
112C2×C4⋊C4×C47—21no—
113C2×C4⋊C4×C47—21no—
114C2×C4⋊C4×C47—21no—
115C2×C4⋊C4×C47D411yescharacteristic
116C2×C4⋊C4×C47C2311yescharacteristic
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×C47D411yescharacteristic
128C2×C22⋊C4×C47D411yescharacteristic
129C2×C42×C47—21no—
130C2×C42×C47—21no—
131C2×C42×C47C2311yescharacteristic
132#107×C47—22no—
133#106×C47—22no—
134#103×C47—22no—
135#103×C47—22no—
136#103×C47—22no—
137#103×C47—22no—
138#102×C47—22no—
139#102×C47—22no—
140#102×C47—22no—
141#102×C47—22no—
142#102×C47—41no—
143#102×C47—41no—
144#102×C47—41no—
145#102×C47—41no—
146C22⋊C8×C47—22no—
147C22⋊C8×C47—41no—
148C22⋊C8×C47—41no—
149#95×C47—21no—
150#95×C47—21no—
151#95×C47—21no—
152#95×C47—21no—
153#95×C47—21no—
154C24×C47—21no—
155C24×C47—21no—
156C24×C47C2×D411yescharacteristic
157C24×C47C2×D411yescharacteristic
158#41×C47—28no—
159#41×C47—44no—
160#41×C47—44no—
161#41×C47—44no—
162#41×C47—44no—
163#41×C47—44no—
164#41×C47—44no—
165#41×C47—44no—
166C2×Q8×C47—21no—
167C2×Q8×C47—21no—
168C2×Q8×C47—21no—
169C2×Q8×C47C2×D412yes—
170C2×Q8×C47#4112yes—
171C2×Q8×C47#4112yes—
172C2×D4×C47—24no—
173C2×D4×C47—24no—
174C2×D4×C47—22no—
175C2×D4×C47—24no—
176C2×D4×C47—24no—
177C2×D4×C47—24no—
178C2×D4×C47—24no—
179C2×D4×C47—22no—
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—21no—
189C2×D4×C47—21no—
190C2×D4×C47—41no—
191C2×D4×C47—42no—
192C2×D4×C47—42no—
193C2×D4×C47—42no—
194C2×D4×C47—42no—
195C2×D4×C47—42no—
196C2×D4×C47—42no—
197C2×D4×C47—81no—
198C2×D4×C47—81no—
199C2×D4×C47—81no—
200C2×D4×C47—81no—
201C2×D4×C47—81no—
202C2×D4×C47—81no—
203C2×D4×C47C2×D412yes—
204C2×D4×C47C2×D412yes—
205C22×C4×C47—21no—
206C22×C4×C47—21no—
207C22×C4×C47—21no—
208C22×C4×C47—21no—
209C22×C4×C47—21no—
210C22×C4×C47—24no—
211C22×C4×C47—21no—
212C22×C4×C47—24no—
213C22×C4×C47—21no—
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—21no—
223C22×C4×C47—42no—
224C22×C4×C47—42no—
225C22×C4×C47—42no—
226C22×C4×C47—42no—
227C22×C4×C47C2×D411yescharacteristic
228C22×C4×C47C2×D411yescharacteristic
229C22×C4×C47C2×D411yescharacteristic
230C22×C4×C47C2×D412yes—
231C22×C4×C47C2×D412yes—
232C22×C4×C47C2×D411yescharacteristic
233C22×C4×C47C2411yescharacteristic
234C2×C8×C47—21no—
235C2×C8×C47—21no—
236C2×C8×C47—21no—
237C2×C8×C47—21no—
238C2×C8×C47—21no—
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—44no—
247C4⋊C4×C47—24no—
248C4⋊C4×C47—22no—
249C4⋊C4×C47—21no—
250C4⋊C4×C47—21no—
251C4⋊C4×C47—21no—
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—81no—
260C4⋊C4×C47C2×D412yes—
261C22⋊C4×C47—24no—
262C22⋊C4×C47—22no—
263C22⋊C4×C47—24no—
264C22⋊C4×C47—22no—
265C22⋊C4×C47—42no—
266C22⋊C4×C47—42no—
267C22⋊C4×C47—81no—
268C22⋊C4×C47—81no—
269C42×C47—24no—
270C42×C47—21no—
271C42×C47—21no—
272C42×C47—42no—
273C23×C47—21no—
274C23×C47—21no—
275C23×C47—21no—
276C23×C47—21no—
277C23×C47—21no—
278C23×C47—21no—
279C23×C47—21no—
280C23×C47—22no—
281C23×C47—22no—
282C23×C47—21no—
283C23×C47—21no—
284C23×C47—21no—
285C23×C47—21no—
286C23×C47—21no—
287C23×C47—21no—
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#12012yes—
301C23×C47C22×D411yescharacteristic
302Q8×C47—22no—
303Q8×C47—22no—
304Q8×C47—22no—
305Q8×C47#12314yes—
306D4×C47—22no—
307D4×C47—22no—
308D4×C47—22no—
309D4×C47—22no—
310D4×C47—44no—
311D4×C47—48no—
312D4×C47—48no—
313D4×C47—48no—
314D4×C47—41no—
315D4×C47—41no—
316D4×C47—41no—
317D4×C47—41no—
318D4×C47—84no—
319D4×C47—84no—
320D4×C47—84no—
321C2×C4×C47—21no—
322C2×C4×C47—22no—
323C2×C4×C47—21no—
324C2×C4×C47—21no—
325C2×C4×C47—22no—
326C2×C4×C47—22no—
327C2×C4×C47—21no—
328C2×C4×C47—22no—
329C2×C4×C47—22no—
330C2×C4×C47—22no—
331C2×C4×C47—22no—
332C2×C4×C47—21no—
333C2×C4×C47—22no—
334C2×C4×C47—21no—
335C2×C4×C47—21no—
336C2×C4×C47—21no—
337C2×C4×C47—21no—
338C2×C4×C47—21no—
339C2×C4×C47—48no—
340C2×C4×C47—48no—
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—41no—
348C2×C4×C47—41no—
349C2×C4×C47—41no—
350C2×C4×C47—41no—
351C2×C4×C47—41no—
352C2×C4×C47—41no—
353C2×C4×C47—41no—
354C2×C4×C47—41no—
355C2×C4×C47—41no—
356C2×C4×C47—41no—
357C2×C4×C47—41no—
358C2×C4×C47—41no—
359C2×C4×C47#12012yes—
360C2×C4×C47#13512yes—
361C2×C4×C47C22×D411yescharacteristic
362C2×C4×C47C22×D411yescharacteristic
363C2×C4×C47C2×#4111yescharacteristic
364C2×C4×C47C2×#4111yescharacteristic
365C2×C4×C47H(5,𝔽2)11yescharacteristic
366C2×C4×C47H(5,𝔽2)11yescharacteristic
367C8×C47—41no—
368C8×C47—41no—
369C8×C47—41no—
370C8×C47—41no—
371#24034C4711yesmaximal, characteristic, direct product factor, Sylow
372C22×C47—22no—
373C22×C47—22no—
374C22×C47—22no—
375C22×C47—41no—
376C22×C47—41no—
377C22×C47—41no—
378C22×C47—41no—
379C22×C47—42no—
380C22×C47—42no—
381C22×C47—41no—
382C22×C47—41no—
383C22×C47—42no—
384C22×C47—42no—
385C22×C47—41no—
386C22×C47—42no—
387C22×C47—42no—
388C22×C47—41no—
389C22×C47—41no—
390C22×C47—41no—
391C22×C47—41no—
392C22×C47—81no—
393C22×C47—81no—
394C22×C47—81no—
395C22×C47—81no—
396C22×C47—81no—
397C22×C47—81no—
398C22×C47—81no—
399C22×C47—81no—
400C22×C47C2×#12011yescharacteristic
401C22×C47#54611yescharacteristic
402C22×C47#54611yescharacteristic
403C22×C47C2×#13511yescharacteristic
404C22×C47#57511yescharacteristic
405C22×C47#57611yescharacteristic
406C22×C47#57711yescharacteristic
407C4×C47—22no—
408C4×C47—24no—
409C4×C47—22no—
410C4×C47—41no—
411C4×C47—41no—
412C4×C47—42no—
413C4×C47—81no—
414C4×C47—81no—
415C4×C47—81no—
416C4×C47—81no—
417C4×C47C2×#12311yescharacteristic
418C4×C47#53411yescharacteristic
419C4×C47#54611yescharacteristic
420C4×C47#54611yescharacteristic
421C2×#550C2×C4711yescharacteristic
422C2×#482C2×C4711yescharacteristic, complemented
423C2×#416C2×C4711yescharacteristic, complemented
424#2485C2×C4711yescharacteristic, complemented
425#2041C2×C4711yescharacteristic, complemented
426#2041C2×C4711yescharacteristic, complemented
427#2034C2×C4711yescharacteristic, complemented
428#2033C2×C4711yescharacteristic, complemented
429#1893C2×C4711yescharacteristic, complemented
430#1869C2×C4711yescharacteristic, complemented
431#1865C2×C4711yescharacteristic, complemented
432#1863C2×C4711yescharacteristic, complemented
433#1788C2×C4711yescharacteristic, complemented
434#1788C2×C4711yescharacteristic, complemented
435#1788C2×C4711yescharacteristic, complemented
436C2×C47—42no—
437C2×C47—81no—
438C2×C47—82no—
439C2×C47—82no—
440C2×C47#240511yescharacteristic
441C2×C47#300211yescharacteristic
442C2×C47#301211yescharacteristic
443C2×C47#330411yescharacteristic
444C2×C47#330511yescharacteristic
445C2×C47#330911yescharacteristic
446C2×C47#331711yescharacteristic
447C22×#41C22×C4711yescharacteristic
448C22×#41C22×C4711yescharacteristic
449C23×C8C22×C4711yescharacteristic
450#550—24no—
451#550—24no—
452C2×#127—21no—
453C2×#127C22×C4711yescharacteristic
454C2×#121—21no—
455C2×#121—21no—
456C2×#121C22×C4711yescharacteristic
457C2×#121C22×C4711yescharacteristic
458C2×C4×Q8C22×C4711yescharacteristic
459C2×C4×D4—21no—
460C2×C4×D4C22×C4711yescharacteristic
461C2×#117C22×C4711yescharacteristic
462#482—24no—
463C2×#107C22×C4711yescharacteristic
464C2×#106C22×C4711yescharacteristic
465#416—24no—
466C2×#103C22×C4711yescharacteristic
467C2×#103C22×C4711yescharacteristic
468C2×#103C22×C4711yescharacteristic
469C2×#103C22×C4711yescharacteristic
470C2×#102C22×C4711yescharacteristic
471C2×#102C22×C4711yescharacteristic
472C2×#102C22×C4711yescharacteristic
473C2×#102C22×C4711yescharacteristic
474C2×#102C22×C4711yescharacteristic
475C2×#102C22×C4711yescharacteristic
476C2×#102C22×C4711yescharacteristic
477C2×#102C22×C4711yescharacteristic
478C2×C22⋊C8C22×C4711yescharacteristic
479C2×C22⋊C8C22×C4711yescharacteristic
480C2×C22⋊C8C22×C4711yescharacteristic
481#397—21no—
482#394—21no—
483#389C22×C4711yescharacteristic
484#389C22×C4711yescharacteristic
485#388—21no—
486#387—21no—
487#380C22×C4711yescharacteristic
488#380C22×C4711yescharacteristic
489#380C22×C4711yescharacteristic
490#340C22×C4711yescharacteristic
491#340C22×C4711yescharacteristic
492#336C22×C4711yescharacteristic
493#336C22×C4711yescharacteristic
494C47#2403411yescharacteristic, direct product factor, Sylow
495C2×#41—22no—
496C2×#41—22no—
497C2×#41—22no—
498C2×#41—22no—
499C2×#41—22no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41D4×C4714yes—
507C22×Q8C23×C4711yescharacteristic
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4D4×C4711yescharacteristic
515C22×D4C23×C4711yescharacteristic
516C22×D4C23×C4711yescharacteristic
517C23×C4—21no—
518C23×C4—21no—
519C23×C4C23×C4711yescharacteristic
520C23×C4C23×C4711yescharacteristic
521C22×C8—22no—
522C22×C8—41no—
523C22×C8—41no—
524C22×C8C23×C4711yescharacteristic
525C22×C8C23×C4711yescharacteristic
526C22×C8C23×C4711yescharacteristic
527C22×C8C23×C4711yescharacteristic
528#127—28no—
529#127—22no—
530#127—22no—
531#121—28no—
532#121—28no—
533#121—22no—
534#121—22no—
535#121—22no—
536#121D4×C4714yes—
537C4×Q8—22no—
538C4×Q8—22no—
539C4×D4—28no—
540C4×D4—22no—
541C4×D4—22no—
542#117—22no—
543#117—22no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4D4×C4711yescharacteristic
548C2×C4⋊C4C23×C4711yescharacteristic
549C2×C4⋊C4C23×C4711yescharacteristic
550C2×C4⋊C4C23×C4711yescharacteristic
551C2×C4⋊C4C23×C4711yescharacteristic
552C2×C4⋊C4C23×C4711yescharacteristic
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4D4×C4711yescharacteristic
560C2×C22⋊C4D4×C4711yescharacteristic
561C2×C42—21no—
562C2×C42—21no—
563C2×C42C23×C4711yescharacteristic
564#107—22no—
565#106—22no—
566#103—22no—
567#103—22no—
568#103—22no—
569#103—22no—
570#102—22no—
571#102—22no—
572#102—22no—
573#102—22no—
574#102—41no—
575#102—41no—
576#102—41no—
577#102—41no—
578C22⋊C8—22no—
579C22⋊C8—41no—
580C22⋊C8—41no—
581#95—21no—
582#95—21no—
583#95—21no—
584#95—21no—
585#95—21no—
586C24—21no—
587C24—21no—
588C24C2×D4×C4711yescharacteristic
589C24C2×D4×C4711yescharacteristic
590#41—28no—
591#41—44no—
592#41—44no—
593#41—44no—
594#41—44no—
595#41—44no—
596#41—44no—
597#41—44no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8C2×D4×C4712yes—
602C2×Q8#41×C4712yes—
603C2×Q8#41×C4712yes—
604C2×D4—24no—
605C2×D4—24no—
606C2×D4—22no—
607C2×D4—24no—
608C2×D4—24no—
609C2×D4—24no—
610C2×D4—24no—
611C2×D4—22no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—41no—
623C2×D4—42no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—42no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—81no—
630C2×D4—81no—
631C2×D4—81no—
632C2×D4—81no—
633C2×D4—81no—
634C2×D4—81no—
635C2×D4C2×D4×C4712yes—
636C2×D4C2×D4×C4712yes—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—24no—
643C22×C4—21no—
644C22×C4—24no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—42no—
656C22×C4—42no—
657C22×C4—42no—
658C22×C4—42no—
659C22×C4C2×D4×C4711yescharacteristic
660C22×C4C2×D4×C4711yescharacteristic
661C22×C4C2×D4×C4711yescharacteristic
662C22×C4C2×D4×C4712yes—
663C22×C4C2×D4×C4712yes—
664C22×C4C2×D4×C4711yescharacteristic
665C22×C4C24×C4711yescharacteristic
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—44no—
679C4⋊C4—24no—
680C4⋊C4—22no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—42no—
691C4⋊C4—81no—
692C4⋊C4C2×D4×C4712yes—
693C22⋊C4—24no—
694C22⋊C4—22no—
695C22⋊C4—24no—
696C22⋊C4—22no—
697C22⋊C4—42no—
698C22⋊C4—42no—
699C22⋊C4—81no—
700C22⋊C4—81no—
701C42—24no—
702C42—21no—
703C42—21no—
704C42—42no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—22no—
713C23—22no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23#120×C4712yes—
733C23C22×D4×C4711yescharacteristic
734Q8—22no—
735Q8—22no—
736Q8—22no—
737Q8#123×C4714yes—
738D4—22no—
739D4—22no—
740D4—22no—
741D4—22no—
742D4—44no—
743D4—48no—
744D4—48no—
745D4—48no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—84no—
751D4—84no—
752D4—84no—
753C2×C4—21no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—21no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—21no—
765C2×C4—22no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—48no—
772C2×C4—48no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4#120×C4712yes—
792C2×C4#135×C4712yes—
793C2×C4C22×D4×C4711yescharacteristic
794C2×C4C22×D4×C4711yescharacteristic
795C2×C4C2×#41×C4711yescharacteristic
796C2×C4C2×#41×C4711yescharacteristic
797C2×C4H(5,𝔽2)×C4711yescharacteristic
798C2×C4H(5,𝔽2)×C4711yescharacteristic
799C8—41no—
800C8—41no—
801C8—41no—
802C8—41no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—42no—
815C22—42no—
816C22—41no—
817C22—41no—
818C22—42no—
819C22—42no—
820C22—41no—
821C22—42no—
822C22—42no—
823C22—81no—
824C22—81no—
825C22—81no—
826C22—81no—
827C22—81no—
828C22—81no—
829C22—81no—
830C22—81no—
831C22C2×#120×C4711yescharacteristic
832C22C47×#54611yescharacteristic
833C22C47×#54611yescharacteristic
834C22C2×#135×C4711yescharacteristic
835C22C47×#57511yescharacteristic
836C22C47×#57611yescharacteristic
837C22C47×#57711yescharacteristic
838C4—22no—
839C4—24no—
840C4—22no—
841C4—41no—
842C4—41no—
843C4—42no—
844C4—81no—
845C4—81no—
846C4—81no—
847C4—81no—
848C4C2×#123×C4711yescharacteristic
849C4C47×#53411yescharacteristic
850C4C47×#54611yescharacteristic
851C4C47×#54611yescharacteristic
852C2—42no—
853C2—81no—
854C2—82no—
855C2—82no—
856C2C47×#240511yescharacteristic
857C2C47×#300211yescharacteristic
858C2C47×#301211yescharacteristic
859C2C47×#330411yescharacteristic
860C2C47×#330511yescharacteristic
861C2C47×#330911yescharacteristic
862C2C47×#331711yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC2×C47×#550C2
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
2. C2×C47×#482C2semidirect
3. C2×C47×#416C2semidirect
4. C47×#2485C2semidirect
5. C47×#2041C2semidirect
6. C47×#2041C2semidirect
7. C47×#2034C2semidirect
8. C47×#2033C2semidirect
9. C47×#1893C2semidirect
10. C47×#1869C2semidirect
11. C47×#1865C2semidirect
12. C47×#1863C2semidirect
13. C47×#1788C2semidirect
14. C47×#1788C2semidirect
15. C47×#1788C2semidirect
371. #24034C47direct (N × H)
422. C2×#482C2×C47semidirect
423. C2×#416C2×C47semidirect
424. #2485C2×C47semidirect
425. #2041C2×C47semidirect
426. #2041C2×C47semidirect
427. #2034C2×C47semidirect
428. #2033C2×C47semidirect
429. #1893C2×C47semidirect
430. #1869C2×C47semidirect
431. #1865C2×C47semidirect
432. #1863C2×C47semidirect
433. #1788C2×C47semidirect
434. #1788C2×C47semidirect
435. #1788C2×C47semidirect
494. C47#24034direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C47×#5502
C2×C47×#4822
C2×C47×#4162
C47×#24852
C47×#20412
C47×#20342
C47×#20332
C47×#18932
C47×#18692
C47×#18652
C47×#18632
C47×#17882
#2403447