Finite Group Databasebeta

← C47×#25156 #26064854

Subgroups — C47×#25156 #26064854

Order 12032.

1268 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#461C211yesmaximal, characteristic, complemented
2C2×C47×#450C211yesmaximal, characteristic
3C2×C47×#450C211yesmaximal, characteristic
4C2×C4×SD16×C47C211yesmaximal, characteristic, complemented
5C47×#2429C211yesmaximal, characteristic, complemented
6D4×C22⋊C4×C47C211yesmaximal, characteristic
7C47×#2065C211yesmaximal, characteristic, complemented
8C47×#2035C211yesmaximal, characteristic, complemented
9C47×#2035C211yesmaximal, characteristic, complemented
10C47×#2013C211yesmaximal, characteristic, complemented
11C47×#1968C211yesmaximal, characteristic, complemented
12C47×#1923C211yesmaximal, characteristic, complemented
13C47×#1880C211yesmaximal, characteristic, complemented
14C47×#1877C211yesmaximal, characteristic, complemented
15C47×#1864C211yesmaximal, characteristic, complemented
16C23×D4×C47C2211yescharacteristic
17C22×SD16×C47C2211yescharacteristic
18C22×SD16×C47C2211yescharacteristic
19C22×SD16×C47C2211yescharacteristic
20C22×SD16×C47C2211yescharacteristic
21C2×C4⋊Q8×C47C2211yescharacteristic, complemented
22C2×C22⋊Q8×C47C2211yescharacteristic
23C2×C22⋊Q8×C47C2211yescharacteristic
24C2×C4×Q8×C47C2211yescharacteristic, complemented
25C2×C4×D4×C47C2211yescharacteristic
26C2×C4×D4×C47C2211yescharacteristic
27C22×C22⋊C4×C47—21no—
28C47×#461—24no—
29C47×#450—24no—
30C47×#450—24no—
31C4×SD16×C47—24no—
32C2×#106×C47C2211yescharacteristic, complemented
33C2×#106×C47C2211yescharacteristic, complemented
34C2×C4⋊C8×C47C2211yescharacteristic, complemented
35C2×#103×C47C2211yescharacteristic, complemented
36C2×#103×C47C2211yescharacteristic, complemented
37C2×#103×C47C2211yescharacteristic, complemented
38C2×#103×C47C2211yescharacteristic, complemented
39C2×#102×C47C2211yescharacteristic
40C2×#102×C47C2211yescharacteristic
41C2×#102×C47C2211yescharacteristic
42C2×#102×C47C2211yescharacteristic
43C2×C22⋊C8×C47C2211yescharacteristic
44C2×C22⋊C8×C47C2211yescharacteristic
45C2×C4×C8×C47C2211yescharacteristic, complemented
46C47×#398—21no—
47C47×#396—21no—
48C47×#391C2211yescharacteristic, complemented
49C47×#390C2211yescharacteristic
50C47×#390C2211yescharacteristic
51C47×#389—21no—
52C47×#389C2211yescharacteristic, complemented
53C47×#388—21no—
54C47×#386—21no—
55C47×#386—21no—
56C47×#380C2211yescharacteristic
57C47×#379—21no—
58C4×C22⋊C4×C47C2211yescharacteristic
59C47×#340C2211yescharacteristic, complemented
60C47×#340C2211yescharacteristic, complemented
61C47×#336C2211yescharacteristic, complemented
62C47×#336C2211yescharacteristic, complemented
63C25×C47—21no—
64C22×Q8×C47C2311yescharacteristic
65C22×Q8×C47C2311yescharacteristic
66C22×D4×C47—22no—
67C22×D4×C47—22no—
68C22×D4×C47—22no—
69C22×D4×C47—22no—
70C22×D4×C47—21no—
71C22×D4×C47—41no—
72C22×D4×C47—41no—
73C22×D4×C47C2311yescharacteristic
74C22×D4×C47C2311yescharacteristic
75C23×C4×C47—21no—
76C23×C4×C47—21no—
77C23×C4×C47C2311yescharacteristic
78C2×SD16×C47—22no—
79C2×SD16×C47—22no—
80C2×SD16×C47—22no—
81C2×SD16×C47—22no—
82C2×SD16×C47—22no—
83C2×SD16×C47—22no—
84C2×SD16×C47—22no—
85C2×SD16×C47—22no—
86C2×SD16×C47—22no—
87C2×SD16×C47—41no—
88C2×SD16×C47—41no—
89C2×SD16×C47D414yes—
90C22×C8×C47C2311yescharacteristic
91C22×C8×C47C2311yescharacteristic
92C22×C8×C47C2311yescharacteristic
93C22×C8×C47C2311yescharacteristic
94C4⋊Q8×C47—22no—
95C4⋊Q8×C47—41no—
96C22⋊Q8×C47—22no—
97C22⋊Q8×C47—22no—
98C22⋊Q8×C47—41no—
99C22⋊Q8×C47—41no—
100C4×Q8×C47—22no—
101C4×Q8×C47—41no—
102C4×D4×C47—22no—
103C4×D4×C47—22no—
104C4×D4×C47—41no—
105C4×D4×C47—41no—
106C2×C4⋊C4×C47—21no—
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×C47C2311yescharacteristic
113C2×C4⋊C4×C47C2311yescharacteristic
114C2×C4⋊C4×C47C2311yescharacteristic
115C2×C4⋊C4×C47C2311yescharacteristic
116C2×C22⋊C4×C47—21no—
117C2×C22⋊C4×C47—21no—
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—44no—
126C2×C22⋊C4×C47D411yescharacteristic
127C2×C22⋊C4×C47D411yescharacteristic
128C2×C42×C47—21no—
129C2×C42×C47C2311yescharacteristic
130C2×C42×C47C2311yescharacteristic
131#106×C47—22no—
132#106×C47—41no—
133C4⋊C8×C47—22no—
134#103×C47—22no—
135#103×C47—22no—
136#103×C47—22no—
137#103×C47—41no—
138#102×C47—22no—
139#102×C47—22no—
140#102×C47—22no—
141#102×C47D414yes—
142C22⋊C8×C47—22no—
143C22⋊C8×C47—22no—
144C4×C8×C47—22no—
145#95×C47—21no—
146#95×C47—21no—
147#95×C47—21no—
148#95×C47—21no—
149#95×C47D411yescharacteristic
150#95×C47D411yescharacteristic
151C24×C47—21no—
152C24×C47—24no—
153C24×C47—21no—
154C24×C47—42no—
155C24×C47—42no—
156C24×C47—42no—
157C24×C47—42no—
158C24×C47—81no—
159C24×C47—81no—
160C24×C47C2×D411yescharacteristic
161C2×Q8×C47—21no—
162C2×Q8×C47—21no—
163C2×Q8×C47—21no—
164C2×Q8×C47—21no—
165C2×Q8×C47—21no—
166C2×Q8×C47—21no—
167C2×Q8×C47—21no—
168C2×Q8×C47—21no—
169C2×Q8×C47—21no—
170C2×Q8×C47—21no—
171C2×Q8×C47—21no—
172C2×Q8×C47C2×D412yes—
173C2×D4×C47—24no—
174C2×D4×C47—21no—
175C2×D4×C47—21no—
176C2×D4×C47—21no—
177C2×D4×C47—21no—
178C2×D4×C47—21no—
179C2×D4×C47—21no—
180C2×D4×C47—21no—
181C2×D4×C47—21no—
182C2×D4×C47—42no—
183C2×D4×C47—42no—
184C2×D4×C47—44no—
185C2×D4×C47—44no—
186C2×D4×C47—44no—
187C2×D4×C47—44no—
188C2×D4×C47C2×D412yes—
189C2×D4×C47C2×D412yes—
190C2×D4×C47#4112yes—
191C2×D4×C47#4112yes—
192C22×C4×C47—21no—
193C22×C4×C47—21no—
194C22×C4×C47—21no—
195C22×C4×C47—21no—
196C22×C4×C47—21no—
197C22×C4×C47—21no—
198C22×C4×C47—21no—
199C22×C4×C47—21no—
200C22×C4×C47—21no—
201C22×C4×C47—21no—
202C22×C4×C47—21no—
203C22×C4×C47—21no—
204C22×C4×C47—42no—
205C22×C4×C47—42no—
206C22×C4×C47—42no—
207C22×C4×C47—42no—
208C22×C4×C47—81no—
209C22×C4×C47—81no—
210C22×C4×C47C2×D411yescharacteristic
211C22×C4×C47C2×D411yescharacteristic
212C22×C4×C47C2×D411yescharacteristic
213C22×C4×C47C2×D411yescharacteristic
214C22×C4×C47C2×D411yescharacteristic
215C22×C4×C47C2411yescharacteristic
216SD16×C47—28no—
217SD16×C47—44no—
218SD16×C47—44no—
219SD16×C47—44no—
220C2×C8×C47—21no—
221C2×C8×C47—21no—
222C2×C8×C47—21no—
223C2×C8×C47—21no—
224C2×C8×C47—21no—
225C2×C8×C47—21no—
226C2×C8×C47—21no—
227C2×C8×C47—21no—
228C2×C8×C47—21no—
229C2×C8×C47—21no—
230C2×C8×C47C2×D412yes—
231C2×C8×C47C2×D412yes—
232C4⋊C4×C47—21no—
233C4⋊C4×C47—21no—
234C4⋊C4×C47—21no—
235C4⋊C4×C47—21no—
236C4⋊C4×C47—21no—
237C4⋊C4×C47—21no—
238C4⋊C4×C47—21no—
239C4⋊C4×C47—42no—
240C4⋊C4×C47—42no—
241C4⋊C4×C47—42no—
242C4⋊C4×C47—42no—
243C4⋊C4×C47—42no—
244C4⋊C4×C47—42no—
245C4⋊C4×C47C2×D412yes—
246C22⋊C4×C47—41no—
247C22⋊C4×C47—42no—
248C22⋊C4×C47—42no—
249C22⋊C4×C47—42no—
250C22⋊C4×C47—42no—
251C22⋊C4×C47—42no—
252C22⋊C4×C47—42no—
253C22⋊C4×C47—42no—
254C22⋊C4×C47—81no—
255C22⋊C4×C47—81no—
256C22⋊C4×C47SD1614yescomplemented
257C42×C47—21no—
258C42×C47—21no—
259C42×C47—21no—
260C42×C47—21no—
261C42×C47—42no—
262C23×C47—21no—
263C23×C47—22no—
264C23×C47—21no—
265C23×C47—21no—
266C23×C47—22no—
267C23×C47—22no—
268C23×C47—21no—
269C23×C47—21no—
270C23×C47—21no—
271C23×C47—22no—
272C23×C47—48no—
273C23×C47—48no—
274C23×C47—41no—
275C23×C47—41no—
276C23×C47—41no—
277C23×C47—41no—
278C23×C47—41no—
279C23×C47—41no—
280C23×C47—41no—
281C23×C47—41no—
282C23×C47—41no—
283C23×C47—41no—
284C23×C47—84no—
285C23×C47—84no—
286C23×C47—84no—
287C23×C47—84no—
288C23×C47—84no—
289C23×C47C2×SD1612yes—
290C23×C47C22×D411yescharacteristic
291Q8×C47—22no—
292Q8×C47—22no—
293Q8×C47—41no—
294Q8×C47—41no—
295Q8×C47—41no—
296Q8×C47—41no—
297Q8×C47—41no—
298Q8×C47—41no—
299D4×C47—22no—
300D4×C47—22no—
301D4×C47—22no—
302D4×C47—22no—
303D4×C47—22no—
304D4×C47—48no—
305D4×C47—41no—
306D4×C47—41no—
307D4×C47#12114yes—
308C2×C4×C47—21no—
309C2×C4×C47—21no—
310C2×C4×C47—21no—
311C2×C4×C47—21no—
312C2×C4×C47—21no—
313C2×C4×C47—21no—
314C2×C4×C47—21no—
315C2×C4×C47—22no—
316C2×C4×C47—22no—
317C2×C4×C47—21no—
318C2×C4×C47—21no—
319C2×C4×C47—21no—
320C2×C4×C47—21no—
321C2×C4×C47—21no—
322C2×C4×C47—21no—
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—41no—
333C2×C4×C47—41no—
334C2×C4×C47—41no—
335C2×C4×C47—41no—
336C2×C4×C47—41no—
337C2×C4×C47—41no—
338C2×C4×C47—41no—
339C2×C4×C47—41no—
340C2×C4×C47—41no—
341C2×C4×C47—41no—
342C2×C4×C47—41no—
343C2×C4×C47—84no—
344C2×C4×C47—84no—
345C2×C4×C47C2×SD1612yes—
346C2×C4×C47C2×SD1612yes—
347C2×C4×C47C22×D411yescharacteristic
348C2×C4×C47C22×D411yescharacteristic
349C2×C4×C47C2×#4111yescharacteristic
350C2×C4×C47C2×#4111yescharacteristic
351C2×C4×C47H(5,𝔽2)11yescharacteristic
352C2×C4×C47H(5,𝔽2)11yescharacteristic
353C8×C47—22no—
354C8×C47—22no—
355C8×C47—41no—
356C8×C47—41no—
357#25156C4711yesmaximal, characteristic, direct product factor, Sylow
358C22×C47—22no—
359C22×C47—24no—
360C22×C47—22no—
361C22×C47—22no—
362C22×C47—42no—
363C22×C47—41no—
364C22×C47—42no—
365C22×C47—41no—
366C22×C47—41no—
367C22×C47—42no—
368C22×C47—41no—
369C22×C47—42no—
370C22×C47—42no—
371C22×C47—42no—
372C22×C47—42no—
373C22×C47—42no—
374C22×C47—42no—
375C22×C47—816no—
376C22×C47—81no—
377C22×C47—81no—
378C22×C47—81no—
379C22×C47—81no—
380C22×C47#52511yescharacteristic
381C22×C47D4211yescharacteristic
382C22×C47D4211yescharacteristic
383C22×C47C22×SD1611yescharacteristic
384C22×C47#57511yescharacteristic
385C22×C47#57711yescharacteristic
386C22×C47#57711yescharacteristic
387C4×C47—22no—
388C4×C47—22no—
389C4×C47—41no—
390C4×C47—42no—
391C4×C47—41no—
392C4×C47—42no—
393C4×C47—41no—
394C4×C47—81no—
395C4×C47—81no—
396C4×C47—81no—
397C4×C47—81no—
398C4×C47C2×#12111yescharacteristic
399C4×C47#53811yescharacteristic
400C4×C47#54611yescharacteristic
401C4×C47#54611yescharacteristic
402C2×#461C2×C4711yescharacteristic, complemented
403C2×#450C2×C4711yescharacteristic
404C2×#450C2×C4711yescharacteristic
405C2×C4×SD16C2×C4711yescharacteristic, complemented
406#2429C2×C4711yescharacteristic, complemented
407D4×C22⋊C4C2×C4711yescharacteristic
408#2065C2×C4711yescharacteristic, complemented
409#2035C2×C4711yescharacteristic, complemented
410#2035C2×C4711yescharacteristic, complemented
411#2013C2×C4711yescharacteristic, complemented
412#1968C2×C4711yescharacteristic, complemented
413#1923C2×C4711yescharacteristic, complemented
414#1880C2×C4711yescharacteristic, complemented
415#1877C2×C4711yescharacteristic, complemented
416#1864C2×C4711yescharacteristic, complemented
417C2×C47—42no—
418C2×C47—44no—
419C2×C47—82no—
420C2×C47#242411yescharacteristic
421C2×C47#310111yescharacteristic
422C2×C47#312311yescharacteristic
423C2×C47#326711yescharacteristic
424C2×C47#327511yescharacteristic
425C2×C47D4×SD1611yescharacteristic
426C2×C47D4×SD1611yescharacteristic
427C23×D4C22×C4711yescharacteristic
428C22×SD16C22×C4711yescharacteristic
429C22×SD16C22×C4711yescharacteristic
430C22×SD16C22×C4711yescharacteristic
431C22×SD16C22×C4711yescharacteristic
432C2×C4⋊Q8C22×C4711yescharacteristic, complemented
433C2×C22⋊Q8C22×C4711yescharacteristic
434C2×C22⋊Q8C22×C4711yescharacteristic
435C2×C4×Q8C22×C4711yescharacteristic, complemented
436C2×C4×D4C22×C4711yescharacteristic
437C2×C4×D4C22×C4711yescharacteristic
438C22×C22⋊C4—21no—
439#461—24no—
440#450—24no—
441#450—24no—
442C4×SD16—24no—
443C2×#106C22×C4711yescharacteristic, complemented
444C2×#106C22×C4711yescharacteristic, complemented
445C2×C4⋊C8C22×C4711yescharacteristic, complemented
446C2×#103C22×C4711yescharacteristic, complemented
447C2×#103C22×C4711yescharacteristic, complemented
448C2×#103C22×C4711yescharacteristic, complemented
449C2×#103C22×C4711yescharacteristic, complemented
450C2×#102C22×C4711yescharacteristic
451C2×#102C22×C4711yescharacteristic
452C2×#102C22×C4711yescharacteristic
453C2×#102C22×C4711yescharacteristic
454C2×C22⋊C8C22×C4711yescharacteristic
455C2×C22⋊C8C22×C4711yescharacteristic
456C2×C4×C8C22×C4711yescharacteristic, complemented
457#398—21no—
458#396—21no—
459#391C22×C4711yescharacteristic, complemented
460#390C22×C4711yescharacteristic
461#390C22×C4711yescharacteristic
462#389—21no—
463#389C22×C4711yescharacteristic, complemented
464#388—21no—
465#386—21no—
466#386—21no—
467#380C22×C4711yescharacteristic
468#379—21no—
469C4×C22⋊C4C22×C4711yescharacteristic
470#340C22×C4711yescharacteristic, complemented
471#340C22×C4711yescharacteristic, complemented
472#336C22×C4711yescharacteristic, complemented
473#336C22×C4711yescharacteristic, complemented
474C47#2515611yescharacteristic, direct product factor, Sylow
475C25—21no—
476C22×Q8C23×C4711yescharacteristic
477C22×Q8C23×C4711yescharacteristic
478C22×D4—22no—
479C22×D4—22no—
480C22×D4—22no—
481C22×D4—22no—
482C22×D4—21no—
483C22×D4—41no—
484C22×D4—41no—
485C22×D4C23×C4711yescharacteristic
486C22×D4C23×C4711yescharacteristic
487C23×C4—21no—
488C23×C4—21no—
489C23×C4C23×C4711yescharacteristic
490C2×SD16—22no—
491C2×SD16—22no—
492C2×SD16—22no—
493C2×SD16—22no—
494C2×SD16—22no—
495C2×SD16—22no—
496C2×SD16—22no—
497C2×SD16—22no—
498C2×SD16—22no—
499C2×SD16—41no—
500C2×SD16—41no—
501C2×SD16D4×C4714yes—
502C22×C8C23×C4711yescharacteristic
503C22×C8C23×C4711yescharacteristic
504C22×C8C23×C4711yescharacteristic
505C22×C8C23×C4711yescharacteristic
506C4⋊Q8—22no—
507C4⋊Q8—41no—
508C22⋊Q8—22no—
509C22⋊Q8—22no—
510C22⋊Q8—41no—
511C22⋊Q8—41no—
512C4×Q8—22no—
513C4×Q8—41no—
514C4×D4—22no—
515C4×D4—22no—
516C4×D4—41no—
517C4×D4—41no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4C23×C4711yescharacteristic
525C2×C4⋊C4C23×C4711yescharacteristic
526C2×C4⋊C4C23×C4711yescharacteristic
527C2×C4⋊C4C23×C4711yescharacteristic
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—44no—
538C2×C22⋊C4D4×C4711yescharacteristic
539C2×C22⋊C4D4×C4711yescharacteristic
540C2×C42—21no—
541C2×C42C23×C4711yescharacteristic
542C2×C42C23×C4711yescharacteristic
543#106—22no—
544#106—41no—
545C4⋊C8—22no—
546#103—22no—
547#103—22no—
548#103—22no—
549#103—41no—
550#102—22no—
551#102—22no—
552#102—22no—
553#102D4×C4714yes—
554C22⋊C8—22no—
555C22⋊C8—22no—
556C4×C8—22no—
557#95—21no—
558#95—21no—
559#95—21no—
560#95—21no—
561#95D4×C4711yescharacteristic
562#95D4×C4711yescharacteristic
563C24—21no—
564C24—24no—
565C24—21no—
566C24—42no—
567C24—42no—
568C24—42no—
569C24—42no—
570C24—81no—
571C24—81no—
572C24C2×D4×C4711yescharacteristic
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8C2×D4×C4712yes—
585C2×D4—24no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—44no—
597C2×D4—44no—
598C2×D4—44no—
599C2×D4—44no—
600C2×D4C2×D4×C4712yes—
601C2×D4C2×D4×C4712yes—
602C2×D4#41×C4712yes—
603C2×D4#41×C4712yes—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—42no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4—42no—
620C22×C4—81no—
621C22×C4—81no—
622C22×C4C2×D4×C4711yescharacteristic
623C22×C4C2×D4×C4711yescharacteristic
624C22×C4C2×D4×C4711yescharacteristic
625C22×C4C2×D4×C4711yescharacteristic
626C22×C4C2×D4×C4711yescharacteristic
627C22×C4C24×C4711yescharacteristic
628SD16—28no—
629SD16—44no—
630SD16—44no—
631SD16—44no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8C2×D4×C4712yes—
643C2×C8C2×D4×C4712yes—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—42no—
652C4⋊C4—42no—
653C4⋊C4—42no—
654C4⋊C4—42no—
655C4⋊C4—42no—
656C4⋊C4—42no—
657C4⋊C4C2×D4×C4712yes—
658C22⋊C4—41no—
659C22⋊C4—42no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—42no—
665C22⋊C4—42no—
666C22⋊C4—81no—
667C22⋊C4—81no—
668C22⋊C4SD16×C4714yescomplemented
669C42—21no—
670C42—21no—
671C42—21no—
672C42—21no—
673C42—42no—
674C23—21no—
675C23—22no—
676C23—21no—
677C23—21no—
678C23—22no—
679C23—22no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—22no—
684C23—48no—
685C23—48no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—84no—
697C23—84no—
698C23—84no—
699C23—84no—
700C23—84no—
701C23C2×SD16×C4712yes—
702C23C22×D4×C4711yescharacteristic
703Q8—22no—
704Q8—22no—
705Q8—41no—
706Q8—41no—
707Q8—41no—
708Q8—41no—
709Q8—41no—
710Q8—41no—
711D4—22no—
712D4—22no—
713D4—22no—
714D4—22no—
715D4—22no—
716D4—48no—
717D4—41no—
718D4—41no—
719D4#121×C4714yes—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—84no—
756C2×C4—84no—
757C2×C4C2×SD16×C4712yes—
758C2×C4C2×SD16×C4712yes—
759C2×C4C22×D4×C4711yescharacteristic
760C2×C4C22×D4×C4711yescharacteristic
761C2×C4C2×#41×C4711yescharacteristic
762C2×C4C2×#41×C4711yescharacteristic
763C2×C4H(5,𝔽2)×C4711yescharacteristic
764C2×C4H(5,𝔽2)×C4711yescharacteristic
765C8—22no—
766C8—22no—
767C8—41no—
768C8—41no—
769C22—22no—
770C22—24no—
771C22—22no—
772C22—22no—
773C22—42no—
774C22—41no—
775C22—42no—
776C22—41no—
777C22—41no—
778C22—42no—
779C22—41no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—816no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22C47×#52511yescharacteristic
792C22D42×C4711yescharacteristic
793C22D42×C4711yescharacteristic
794C22C22×SD16×C4711yescharacteristic
795C22C47×#57511yescharacteristic
796C22C47×#57711yescharacteristic
797C22C47×#57711yescharacteristic
798C4—22no—
799C4—22no—
800C4—41no—
801C4—42no—
802C4—41no—
803C4—42no—
804C4—41no—
805C4—81no—
806C4—81no—
807C4—81no—
808C4—81no—
809C4C2×#121×C4711yescharacteristic
810C4C47×#53811yescharacteristic
811C4C47×#54611yescharacteristic
812C4C47×#54611yescharacteristic
813C2—42no—
814C2—44no—
815C2—82no—
816C2C47×#242411yescharacteristic
817C2C47×#310111yescharacteristic
818C2C47×#312311yescharacteristic
819C2C47×#326711yescharacteristic
820C2C47×#327511yescharacteristic
821C2D4×SD16×C4711yescharacteristic
822C2D4×SD16×C4711yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC23×D4×C47C22
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
1. C2×C47×#461C2semidirect
4. C2×C4×SD16×C47C2semidirect
5. C47×#2429C2semidirect
7. C47×#2065C2semidirect
8. C47×#2035C2semidirect
9. C47×#2035C2semidirect
10. C47×#2013C2semidirect
11. C47×#1968C2semidirect
12. C47×#1923C2semidirect
13. C47×#1880C2semidirect
14. C47×#1877C2semidirect
15. C47×#1864C2semidirect
21. C2×C4⋊Q8×C47C22semidirect
24. C2×C4×Q8×C47C22semidirect
32. C2×#106×C47C22semidirect
33. C2×#106×C47C22semidirect
34. C2×C4⋊C8×C47C22semidirect
35. C2×#103×C47C22semidirect
36. C2×#103×C47C22semidirect
37. C2×#103×C47C22semidirect
38. C2×#103×C47C22semidirect
45. C2×C4×C8×C47C22semidirect
48. C47×#391C22semidirect
52. C47×#389C22semidirect
59. C47×#340C22semidirect
60. C47×#340C22semidirect
61. C47×#336C22semidirect
62. C47×#336C22semidirect
256. C22⋊C4×C47SD16semidirect
357. #25156C47direct (N × H)
402. C2×#461C2×C47semidirect
405. C2×C4×SD16C2×C47semidirect
406. #2429C2×C47semidirect
408. #2065C2×C47semidirect
409. #2035C2×C47semidirect
410. #2035C2×C47semidirect
411. #2013C2×C47semidirect
412. #1968C2×C47semidirect
413. #1923C2×C47semidirect
414. #1880C2×C47semidirect
415. #1877C2×C47semidirect
416. #1864C2×C47semidirect
432. C2×C4⋊Q8C22×C47semidirect
435. C2×C4×Q8C22×C47semidirect
443. C2×#106C22×C47semidirect
444. C2×#106C22×C47semidirect
445. C2×C4⋊C8C22×C47semidirect
446. C2×#103C22×C47semidirect
447. C2×#103C22×C47semidirect
448. C2×#103C22×C47semidirect
449. C2×#103C22×C47semidirect
456. C2×C4×C8C22×C47semidirect
459. #391C22×C47semidirect
463. #389C22×C47semidirect
470. #340C22×C47semidirect
471. #340C22×C47semidirect
472. #336C22×C47semidirect
473. #336C22×C47semidirect
474. C47#25156direct (N × H)
668. C22⋊C4SD16×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#4612
C2×C47×#4502
C2×C4×SD16×C472
C47×#24292
D4×C22⋊C4×C472
C47×#20652
C47×#20352
C47×#20132
C47×#19682
C47×#19232
C47×#18802
C47×#18772
C47×#18642
#2515647