Finite Group Databasebeta

← C47×#24893 #26064591

Subgroups — C47×#24893 #26064591

Order 12032.

1232 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#447C211yesmaximal, characteristic
2C2×C4×D8×C47C211yesmaximal, characteristic, complemented
3C47×#2422C211yesmaximal, characteristic, complemented
4D4×C22⋊C4×C47C211yesmaximal, characteristic, complemented
5C47×#2093C211yesmaximal, characteristic, complemented
6C47×#2075C211yesmaximal, characteristic, complemented
7C47×#2054C211yesmaximal, characteristic, complemented
8C47×#2033C211yesmaximal, characteristic, complemented
9C47×#1934C211yesmaximal, characteristic, complemented
10C47×#1923C211yesmaximal, characteristic, complemented
11C47×#1879C211yesmaximal, characteristic, complemented
12C47×#1879C211yesmaximal, characteristic, complemented
13C47×#1862C211yesmaximal, characteristic, complemented
14C47×#1802C211yesmaximal, characteristic, complemented
15C47×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C47C2211yescharacteristic
17C22×D8×C47C2211yescharacteristic
18C22×D8×C47C2211yescharacteristic
19C2×#123×C47—21no—
20C2×#121×C47C2211yescharacteristic
21C2×C4×D4×C47C2211yescharacteristic
22C2×C4×D4×C47C2211yescharacteristic
23C2×C4×D4×C47C2211yescharacteristic, complemented
24C22×C22⋊C4×C47—21no—
25C47×#447—24no—
26C4×D8×C47—24no—
27C2×#107×C47C2211yescharacteristic, complemented
28C2×#107×C47C2211yescharacteristic, complemented
29C2×C4⋊C8×C47C2211yescharacteristic, complemented
30C2×#102×C47C2211yescharacteristic
31C2×#102×C47C2211yescharacteristic
32C2×#102×C47C2211yescharacteristic
33C2×#102×C47C2211yescharacteristic
34C2×#102×C47C2211yescharacteristic
35C2×#102×C47C2211yescharacteristic
36C2×#102×C47C2211yescharacteristic, complemented
37C2×#102×C47C2211yescharacteristic, complemented
38C2×C22⋊C8×C47C2211yescharacteristic
39C2×C22⋊C8×C47C2211yescharacteristic
40C2×C4×C8×C47C2211yescharacteristic, complemented
41C47×#397—21no—
42C47×#394—21no—
43C47×#390C2211yescharacteristic
44C47×#390C2211yescharacteristic
45C47×#390C2211yescharacteristic, complemented
46C47×#389C2211yescharacteristic, complemented
47C47×#386—21no—
48C47×#386—21no—
49C47×#385—21no—
50C47×#384C2211yescharacteristic, complemented
51C47×#380C2211yescharacteristic
52C47×#380C2211yescharacteristic
53C47×#379—21no—
54C4×C22⋊C4×C47C2211yescharacteristic
55C47×#340C2211yescharacteristic, complemented
56C47×#340C2211yescharacteristic, complemented
57C47×#340C2211yescharacteristic, complemented
58C47×#340C2211yescharacteristic, complemented
59C47×#336C2211yescharacteristic, complemented
60C47×#336C2211yescharacteristic, complemented
61C25×C47—21no—
62C22×D4×C47—22no—
63C22×D4×C47—22no—
64C22×D4×C47—22no—
65C22×D4×C47—22no—
66C22×D4×C47—21no—
67C22×D4×C47—21no—
68C22×D4×C47—41no—
69C22×D4×C47—41no—
70C22×D4×C47C2311yescharacteristic
71C22×D4×C47C2311yescharacteristic
72C22×D4×C47C2311yescharacteristic
73C23×C4×C47—21no—
74C23×C4×C47—21no—
75C23×C4×C47—21no—
76C23×C4×C47C2311yescharacteristic
77C2×D8×C47—22no—
78C2×D8×C47—22no—
79C2×D8×C47—22no—
80C2×D8×C47—22no—
81C2×D8×C47—41no—
82C2×D8×C47D414yes—
83C22×C8×C47C2311yescharacteristic
84C22×C8×C47C2311yescharacteristic
85C22×C8×C47C2311yescharacteristic
86C22×C8×C47C2311yescharacteristic
87#123×C47—44no—
88#121×C47—22no—
89#121×C47—41no—
90C4×D4×C47—22no—
91C4×D4×C47—22no—
92C4×D4×C47—22no—
93C4×D4×C47—41no—
94C4×D4×C47—41no—
95C4×D4×C47—41no—
96C2×C4⋊C4×C47—21no—
97C2×C4⋊C4×C47—21no—
98C2×C4⋊C4×C47—21no—
99C2×C4⋊C4×C47C2311yescharacteristic
100C2×C4⋊C4×C47C2311yescharacteristic
101C2×C4⋊C4×C47C2311yescharacteristic
102C2×C4⋊C4×C47C2311yescharacteristic
103C2×C4⋊C4×C47C2311yescharacteristic
104C2×C22⋊C4×C47—21no—
105C2×C22⋊C4×C47—21no—
106C2×C22⋊C4×C47—21no—
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—44no—
117C2×C22⋊C4×C47D411yescharacteristic
118C2×C22⋊C4×C47D411yescharacteristic
119C2×C42×C47C2311yescharacteristic
120C2×C42×C47C2311yescharacteristic
121#107×C47—22no—
122#107×C47—41no—
123C4⋊C8×C47—41no—
124#102×C47—22no—
125#102×C47—22no—
126#102×C47—22no—
127#102×C47—22no—
128#102×C47—22no—
129#102×C47—22no—
130#102×C47—41no—
131#102×C47—41no—
132C22⋊C8×C47—22no—
133C22⋊C8×C47—41no—
134C4×C8×C47—22no—
135#95×C47—21no—
136#95×C47—21no—
137#95×C47—21no—
138#95×C47D411yescharacteristic
139#95×C47D411yescharacteristic
140C24×C47—21no—
141C24×C47—24no—
142C24×C47—21no—
143C24×C47—21no—
144C24×C47—42no—
145C24×C47—42no—
146C24×C47—42no—
147C24×C47—42no—
148C24×C47—81no—
149C24×C47—81no—
150C24×C47C2×D411yescharacteristic
151C2×D4×C47—24no—
152C2×D4×C47—21no—
153C2×D4×C47—21no—
154C2×D4×C47—21no—
155C2×D4×C47—21no—
156C2×D4×C47—21no—
157C2×D4×C47—21no—
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—42no—
166C2×D4×C47—42no—
167C2×D4×C47—44no—
168C2×D4×C47—44no—
169C2×D4×C47—44no—
170C2×D4×C47—44no—
171C2×D4×C47—42no—
172C2×D4×C47—42no—
173C2×D4×C47—81no—
174C2×D4×C47C2×D412yes—
175C2×D4×C47C2×D412yes—
176C2×D4×C47#4112yes—
177C2×D4×C47#4112yes—
178C2×D4×C47#4112yes—
179C22×C4×C47—21no—
180C22×C4×C47—21no—
181C22×C4×C47—21no—
182C22×C4×C47—21no—
183C22×C4×C47—21no—
184C22×C4×C47—21no—
185C22×C4×C47—21no—
186C22×C4×C47—21no—
187C22×C4×C47—21no—
188C22×C4×C47—21no—
189C22×C4×C47—21no—
190C22×C4×C47—42no—
191C22×C4×C47—42no—
192C22×C4×C47—42no—
193C22×C4×C47—42no—
194C22×C4×C47—42no—
195C22×C4×C47—42no—
196C22×C4×C47—81no—
197C22×C4×C47—81no—
198C22×C4×C47—81no—
199C22×C4×C47C2×D411yescharacteristic
200C22×C4×C47C2×D411yescharacteristic
201C22×C4×C47C2×D411yescharacteristic
202C22×C4×C47C2×D411yescharacteristic
203C22×C4×C47C2×D411yescharacteristic
204C22×C4×C47C2411yescharacteristic
205D8×C47—28no—
206D8×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—21no—
218C2×C8×C47C2×D412yes—
219C4⋊C4×C47—21no—
220C4⋊C4×C47—21no—
221C4⋊C4×C47—21no—
222C4⋊C4×C47—21no—
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—42no—
230C4⋊C4×C47—42no—
231C4⋊C4×C47—81no—
232C22⋊C4×C47—41no—
233C22⋊C4×C47—42no—
234C22⋊C4×C47—42no—
235C22⋊C4×C47—42no—
236C22⋊C4×C47—42no—
237C22⋊C4×C47—42no—
238C22⋊C4×C47—42no—
239C22⋊C4×C47—42no—
240C22⋊C4×C47—42no—
241C22⋊C4×C47—42no—
242C22⋊C4×C47—42no—
243C22⋊C4×C47—81no—
244C22⋊C4×C47—81no—
245C22⋊C4×C47D814yescomplemented
246C42×C47—21no—
247C42×C47—21no—
248C42×C47—21no—
249C42×C47—21no—
250C23×C47—21no—
251C23×C47—22no—
252C23×C47—22no—
253C23×C47—21no—
254C23×C47—22no—
255C23×C47—21no—
256C23×C47—21no—
257C23×C47—21no—
258C23×C47—21no—
259C23×C47—22no—
260C23×C47—22no—
261C23×C47—48no—
262C23×C47—48no—
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—41no—
274C23×C47—41no—
275C23×C47—41no—
276C23×C47—41no—
277C23×C47—41no—
278C23×C47—41no—
279C23×C47—84no—
280C23×C47—84no—
281C23×C47—84no—
282C23×C47—84no—
283C23×C47—84no—
284C23×C47C2×D812yes—
285C23×C47C22×D411yescharacteristic
286D4×C47—22no—
287D4×C47—22no—
288D4×C47—22no—
289D4×C47—22no—
290D4×C47—22no—
291D4×C47—22no—
292D4×C47—22no—
293D4×C47—48no—
294D4×C47—41no—
295D4×C47—41no—
296D4×C47—41no—
297D4×C47—41no—
298D4×C47—84no—
299D4×C47#12314yescomplemented
300C2×C4×C47—21no—
301C2×C4×C47—21no—
302C2×C4×C47—21no—
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—21no—
310C2×C4×C47—21no—
311C2×C4×C47—21no—
312C2×C4×C47—21no—
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—41no—
328C2×C4×C47—41no—
329C2×C4×C47—41no—
330C2×C4×C47—41no—
331C2×C4×C47—41no—
332C2×C4×C47—84no—
333C2×C4×C47—84no—
334C2×C4×C47—84no—
335C2×C4×C47C2×D812yes—
336C2×C4×C47C2×D812yes—
337C2×C4×C47C22×D411yescharacteristic
338C2×C4×C47C2×#4111yescharacteristic
339C2×C4×C47C2×#4111yescharacteristic
340C2×C4×C47C2×#4111yescharacteristic
341C2×C4×C47H(5,𝔽2)11yescharacteristic
342C2×C4×C47H(5,𝔽2)11yescharacteristic
343C8×C47—22no—
344C8×C47—41no—
345C8×C47—41no—
346C8×C47—41no—
347#24893C4711yesmaximal, characteristic, direct product factor, Sylow
348C22×C47—22no—
349C22×C47—24no—
350C22×C47—22no—
351C22×C47—22no—
352C22×C47—42no—
353C22×C47—41no—
354C22×C47—42no—
355C22×C47—41no—
356C22×C47—41no—
357C22×C47—42no—
358C22×C47—42no—
359C22×C47—42no—
360C22×C47—41no—
361C22×C47—42no—
362C22×C47—42no—
363C22×C47—42no—
364C22×C47—42no—
365C22×C47—42no—
366C22×C47—42no—
367C22×C47—42no—
368C22×C47—816no—
369C22×C47—81no—
370C22×C47—81no—
371C22×C47—81no—
372C22×C47—81no—
373C22×C47—81no—
374C22×C47—81no—
375C22×C47—81no—
376C22×C47—81no—
377C22×C47#52511yescharacteristic
378C22×C47D4211yescharacteristic
379C22×C47#54611yescharacteristic
380C22×C47C22×D811yescharacteristic
381C22×C47#57511yescharacteristic
382C22×C47#57611yescharacteristic
383C22×C47#57711yescharacteristic
384C4×C47—22no—
385C4×C47—22no—
386C4×C47—41no—
387C4×C47—41no—
388C4×C47—41no—
389C4×C47—81no—
390C4×C47—81no—
391C4×C47—81no—
392C4×C47—81no—
393C4×C47—81no—
394C4×C47C2×#12311yescharacteristic
395C4×C47#53811yescharacteristic
396C4×C47#54611yescharacteristic
397C4×C47#55111yescharacteristic
398C2×#447C2×C4711yescharacteristic
399C2×C4×D8C2×C4711yescharacteristic, complemented
400#2422C2×C4711yescharacteristic, complemented
401D4×C22⋊C4C2×C4711yescharacteristic, complemented
402#2093C2×C4711yescharacteristic, complemented
403#2075C2×C4711yescharacteristic, complemented
404#2054C2×C4711yescharacteristic, complemented
405#2033C2×C4711yescharacteristic, complemented
406#1934C2×C4711yescharacteristic, complemented
407#1923C2×C4711yescharacteristic, complemented
408#1879C2×C4711yescharacteristic, complemented
409#1879C2×C4711yescharacteristic, complemented
410#1862C2×C4711yescharacteristic, complemented
411#1802C2×C4711yescharacteristic, complemented
412#1786C2×C4711yescharacteristic, complemented
413C2×C47—42no—
414C2×C47—44no—
415C2×C47—82no—
416C2×C47—82no—
417C2×C47#241811yescharacteristic
418C2×C47#310011yescharacteristic
419C2×C47#311811yescharacteristic
420C2×C47#326711yescharacteristic
421C2×C47D4×D811yescharacteristic
422C2×C47#329411yescharacteristic
423C2×C47#332211yescharacteristic
424C23×D4C22×C4711yescharacteristic
425C22×D8C22×C4711yescharacteristic
426C22×D8C22×C4711yescharacteristic
427C2×#123—21no—
428C2×#121C22×C4711yescharacteristic
429C2×C4×D4C22×C4711yescharacteristic
430C2×C4×D4C22×C4711yescharacteristic
431C2×C4×D4C22×C4711yescharacteristic, complemented
432C22×C22⋊C4—21no—
433#447—24no—
434C4×D8—24no—
435C2×#107C22×C4711yescharacteristic, complemented
436C2×#107C22×C4711yescharacteristic, complemented
437C2×C4⋊C8C22×C4711yescharacteristic, complemented
438C2×#102C22×C4711yescharacteristic
439C2×#102C22×C4711yescharacteristic
440C2×#102C22×C4711yescharacteristic
441C2×#102C22×C4711yescharacteristic
442C2×#102C22×C4711yescharacteristic
443C2×#102C22×C4711yescharacteristic
444C2×#102C22×C4711yescharacteristic, complemented
445C2×#102C22×C4711yescharacteristic, complemented
446C2×C22⋊C8C22×C4711yescharacteristic
447C2×C22⋊C8C22×C4711yescharacteristic
448C2×C4×C8C22×C4711yescharacteristic, complemented
449#397—21no—
450#394—21no—
451#390C22×C4711yescharacteristic
452#390C22×C4711yescharacteristic
453#390C22×C4711yescharacteristic, complemented
454#389C22×C4711yescharacteristic, complemented
455#386—21no—
456#386—21no—
457#385—21no—
458#384C22×C4711yescharacteristic, complemented
459#380C22×C4711yescharacteristic
460#380C22×C4711yescharacteristic
461#379—21no—
462C4×C22⋊C4C22×C4711yescharacteristic
463#340C22×C4711yescharacteristic, complemented
464#340C22×C4711yescharacteristic, complemented
465#340C22×C4711yescharacteristic, complemented
466#340C22×C4711yescharacteristic, complemented
467#336C22×C4711yescharacteristic, complemented
468#336C22×C4711yescharacteristic, complemented
469C47#2489311yescharacteristic, direct product factor, Sylow
470C25—21no—
471C22×D4—22no—
472C22×D4—22no—
473C22×D4—22no—
474C22×D4—22no—
475C22×D4—21no—
476C22×D4—21no—
477C22×D4—41no—
478C22×D4—41no—
479C22×D4C23×C4711yescharacteristic
480C22×D4C23×C4711yescharacteristic
481C22×D4C23×C4711yescharacteristic
482C23×C4—21no—
483C23×C4—21no—
484C23×C4—21no—
485C23×C4C23×C4711yescharacteristic
486C2×D8—22no—
487C2×D8—22no—
488C2×D8—22no—
489C2×D8—22no—
490C2×D8—41no—
491C2×D8D4×C4714yes—
492C22×C8C23×C4711yescharacteristic
493C22×C8C23×C4711yescharacteristic
494C22×C8C23×C4711yescharacteristic
495C22×C8C23×C4711yescharacteristic
496#123—44no—
497#121—22no—
498#121—41no—
499C4×D4—22no—
500C4×D4—22no—
501C4×D4—22no—
502C4×D4—41no—
503C4×D4—41no—
504C4×D4—41no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4C23×C4711yescharacteristic
509C2×C4⋊C4C23×C4711yescharacteristic
510C2×C4⋊C4C23×C4711yescharacteristic
511C2×C4⋊C4C23×C4711yescharacteristic
512C2×C4⋊C4C23×C4711yescharacteristic
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×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—44no—
526C2×C22⋊C4D4×C4711yescharacteristic
527C2×C22⋊C4D4×C4711yescharacteristic
528C2×C42C23×C4711yescharacteristic
529C2×C42C23×C4711yescharacteristic
530#107—22no—
531#107—41no—
532C4⋊C8—41no—
533#102—22no—
534#102—22no—
535#102—22no—
536#102—22no—
537#102—22no—
538#102—22no—
539#102—41no—
540#102—41no—
541C22⋊C8—22no—
542C22⋊C8—41no—
543C4×C8—22no—
544#95—21no—
545#95—21no—
546#95—21no—
547#95D4×C4711yescharacteristic
548#95D4×C4711yescharacteristic
549C24—21no—
550C24—24no—
551C24—21no—
552C24—21no—
553C24—42no—
554C24—42no—
555C24—42no—
556C24—42no—
557C24—81no—
558C24—81no—
559C24C2×D4×C4711yescharacteristic
560C2×D4—24no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—42no—
575C2×D4—42no—
576C2×D4—44no—
577C2×D4—44no—
578C2×D4—44no—
579C2×D4—44no—
580C2×D4—42no—
581C2×D4—42no—
582C2×D4—81no—
583C2×D4C2×D4×C4712yes—
584C2×D4C2×D4×C4712yes—
585C2×D4#41×C4712yes—
586C2×D4#41×C4712yes—
587C2×D4#41×C4712yes—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—81no—
606C22×C4—81no—
607C22×C4—81no—
608C22×C4C2×D4×C4711yescharacteristic
609C22×C4C2×D4×C4711yescharacteristic
610C22×C4C2×D4×C4711yescharacteristic
611C22×C4C2×D4×C4711yescharacteristic
612C22×C4C2×D4×C4711yescharacteristic
613C22×C4C24×C4711yescharacteristic
614D8—28no—
615D8—44no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8C2×D4×C4712yes—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—42no—
639C4⋊C4—42no—
640C4⋊C4—81no—
641C22⋊C4—41no—
642C22⋊C4—42no—
643C22⋊C4—42no—
644C22⋊C4—42no—
645C22⋊C4—42no—
646C22⋊C4—42no—
647C22⋊C4—42no—
648C22⋊C4—42no—
649C22⋊C4—42no—
650C22⋊C4—42no—
651C22⋊C4—42no—
652C22⋊C4—81no—
653C22⋊C4—81no—
654C22⋊C4D8×C4714yescomplemented
655C42—21no—
656C42—21no—
657C42—21no—
658C42—21no—
659C23—21no—
660C23—22no—
661C23—22no—
662C23—21no—
663C23—22no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—22no—
669C23—22no—
670C23—48no—
671C23—48no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—84no—
689C23—84no—
690C23—84no—
691C23—84no—
692C23—84no—
693C23C2×D8×C4712yes—
694C23C22×D4×C4711yescharacteristic
695D4—22no—
696D4—22no—
697D4—22no—
698D4—22no—
699D4—22no—
700D4—22no—
701D4—22no—
702D4—48no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—84no—
708D4#123×C4714yescomplemented
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—84no—
742C2×C4—84no—
743C2×C4—84no—
744C2×C4C2×D8×C4712yes—
745C2×C4C2×D8×C4712yes—
746C2×C4C22×D4×C4711yescharacteristic
747C2×C4C2×#41×C4711yescharacteristic
748C2×C4C2×#41×C4711yescharacteristic
749C2×C4C2×#41×C4711yescharacteristic
750C2×C4H(5,𝔽2)×C4711yescharacteristic
751C2×C4H(5,𝔽2)×C4711yescharacteristic
752C8—22no—
753C8—41no—
754C8—41no—
755C8—41no—
756C22—22no—
757C22—22no—
758C22—24no—
759C22—22no—
760C22—42no—
761C22—41no—
762C22—42no—
763C22—42no—
764C22—41no—
765C22—42no—
766C22—41no—
767C22—41no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—816no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22C47×#52511yescharacteristic
786C22D42×C4711yescharacteristic
787C22C47×#54611yescharacteristic
788C22C22×D8×C4711yescharacteristic
789C22C47×#57511yescharacteristic
790C22C47×#57611yescharacteristic
791C22C47×#57711yescharacteristic
792C4—22no—
793C4—22no—
794C4—41no—
795C4—41no—
796C4—41no—
797C4—81no—
798C4—81no—
799C4—81no—
800C4—81no—
801C4—81no—
802C4C2×#123×C4711yescharacteristic
803C4C47×#53811yescharacteristic
804C4C47×#54611yescharacteristic
805C4C47×#55111yescharacteristic
806C2—42no—
807C2—44no—
808C2—82no—
809C2—82no—
810C2C47×#241811yescharacteristic
811C2C47×#310011yescharacteristic
812C2C47×#311811yescharacteristic
813C2C47×#326711yescharacteristic
814C2D4×D8×C4711yescharacteristic
815C2C47×#329411yescharacteristic
816C2C47×#332211yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC2×C47×#447C2
LCSG ▷ C22×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×C4×D8×C47C2semidirect
3. C47×#2422C2semidirect
4. D4×C22⋊C4×C47C2semidirect
5. C47×#2093C2semidirect
6. C47×#2075C2semidirect
7. C47×#2054C2semidirect
8. C47×#2033C2semidirect
9. C47×#1934C2semidirect
10. C47×#1923C2semidirect
11. C47×#1879C2semidirect
12. C47×#1879C2semidirect
13. C47×#1862C2semidirect
14. C47×#1802C2semidirect
15. C47×#1786C2semidirect
23. C2×C4×D4×C47C22semidirect
27. C2×#107×C47C22semidirect
28. C2×#107×C47C22semidirect
29. C2×C4⋊C8×C47C22semidirect
36. C2×#102×C47C22semidirect
37. C2×#102×C47C22semidirect
40. C2×C4×C8×C47C22semidirect
45. C47×#390C22semidirect
46. C47×#389C22semidirect
50. C47×#384C22semidirect
55. C47×#340C22semidirect
56. C47×#340C22semidirect
57. C47×#340C22semidirect
58. C47×#340C22semidirect
59. C47×#336C22semidirect
60. C47×#336C22semidirect
245. C22⋊C4×C47D8semidirect
299. D4×C47#123semidirect
347. #24893C47direct (N × H)
399. C2×C4×D8C2×C47semidirect
400. #2422C2×C47semidirect
401. D4×C22⋊C4C2×C47semidirect
402. #2093C2×C47semidirect
403. #2075C2×C47semidirect
404. #2054C2×C47semidirect
405. #2033C2×C47semidirect
406. #1934C2×C47semidirect
407. #1923C2×C47semidirect
408. #1879C2×C47semidirect
409. #1879C2×C47semidirect
410. #1862C2×C47semidirect
411. #1802C2×C47semidirect
412. #1786C2×C47semidirect
431. C2×C4×D4C22×C47semidirect
435. C2×#107C22×C47semidirect
436. C2×#107C22×C47semidirect
437. C2×C4⋊C8C22×C47semidirect
444. C2×#102C22×C47semidirect
445. C2×#102C22×C47semidirect
448. C2×C4×C8C22×C47semidirect
453. #390C22×C47semidirect
454. #389C22×C47semidirect
458. #384C22×C47semidirect
463. #340C22×C47semidirect
464. #340C22×C47semidirect
465. #340C22×C47semidirect
466. #340C22×C47semidirect
467. #336C22×C47semidirect
468. #336C22×C47semidirect
469. C47#24893direct (N × H)
654. C22⋊C4D8×C47semidirect
708. D4#123×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#4472
C2×C4×D8×C472
C47×#24222
D4×C22⋊C4×C472
C47×#20932
C47×#20752
C47×#20542
C47×#20332
C47×#19342
C47×#19232
C47×#18792
C47×#18622
C47×#18022
C47×#17862
#2489347