Finite Group Databasebeta

← C47×#14722 #26054420

Subgroups — C47×#14722 #26054420

Order 12032.

3246 conjugacy classes of subgroups.

The subgroup lattice has 986 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#121×C47C211yesmaximal, characteristic, complemented
2C22×C4×D4×C47C211yesmaximal, characteristic, complemented
3C2×C47×#394C211yesmaximal, characteristic, complemented
4C2×C47×#392C212yesmaximal, complemented
5C2×C47×#392C211yesmaximal, characteristic, complemented
6C2×C47×#386C212yesmaximal, complemented
7C47×#1441C211yesmaximal, characteristic, complemented
8C47×#1439C211yesmaximal, characteristic, complemented
9C47×#1438C212yesmaximal, complemented
10C47×#1437C212yesmaximal, complemented
11C47×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×D4×C47C2211yescharacteristic
13C23×D4×C47C2212yes—
14C23×D4×C47C2211yescharacteristic
15C23×D4×C47C2212yes—
16C24×C4×C47C2211yescharacteristic
17C24×C4×C47C2211yescharacteristic
18C2×#121×C47—24no—
19C2×#121×C47—28no—
20C2×C4×D4×C47—24no—
21C2×C4×D4×C47—24no—
22C2×C4×D4×C47—24no—
23C22×C4⋊C4×C47C2211yescharacteristic
24C22×C4⋊C4×C47C2211yescharacteristic
25C22×C22⋊C4×C47C2212yes—
26C22×C22⋊C4×C47C2211yescharacteristic
27C22×C22⋊C4×C47C2212yes—
28C22×C22⋊C4×C47C2212yes—
29C22×C22⋊C4×C47C2212yes—
30C22×C22⋊C4×C47C2212yes—
31C22×C22⋊C4×C47C2212yes—
32C22×C22⋊C4×C47C2211yescharacteristic
33C22×C42×C47C2211yescharacteristic
34C47×#394—24no—
35C47×#392—28no—
36C47×#392—24no—
37C47×#386—28no—
38C2×#95×C47C2212yes—
39C2×#95×C47C2212yes—
40C2×#95×C47C2211yescharacteristic
41C2×#95×C47C2212yes—
42C2×#95×C47C2211yescharacteristic
43C2×#95×C47C2212yes—
44C25×C47C2312yes—
45C25×C47C2311yescharacteristic
46C25×C47C2311yescharacteristic
47C22×D4×C47—22no—
48C22×D4×C47—22no—
49C22×D4×C47—22no—
50C22×D4×C47—22no—
51C22×D4×C47—24no—
52C22×D4×C47—24no—
53C22×D4×C47—24no—
54C22×D4×C47—24no—
55C22×D4×C47—24no—
56C22×D4×C47—24no—
57C22×D4×C47—24no—
58C22×D4×C47—24no—
59C22×D4×C47—24no—
60C22×D4×C47—22no—
61C22×D4×C47—24no—
62C22×D4×C47—22no—
63C22×D4×C47—22no—
64C22×D4×C47—22no—
65C22×D4×C47—22no—
66C22×D4×C47—24no—
67C22×D4×C47—42no—
68C22×D4×C47—42no—
69C22×D4×C47—42no—
70C22×D4×C47—42no—
71C22×D4×C47—42no—
72C22×D4×C47D414yescomplemented
73C23×C4×C47—22no—
74C23×C4×C47—22no—
75C23×C4×C47—22no—
76C23×C4×C47—22no—
77C23×C4×C47—22no—
78C23×C4×C47—24no—
79C23×C4×C47—24no—
80C23×C4×C47—42no—
81C23×C4×C47—42no—
82C23×C4×C47D414yescomplemented
83C23×C4×C47C2312yes—
84C23×C4×C47C2311yescharacteristic
85C23×C4×C47C2311yescharacteristic
86C23×C4×C47C2312yes—
87C23×C4×C47C2312yes—
88C23×C4×C47C2311yescharacteristic
89C23×C4×C47C2311yescharacteristic
90C23×C4×C47C2311yescharacteristic
91#121×C47—232no—
92C4×D4×C47—232no—
93C2×C4⋊C4×C47—22no—
94C2×C4⋊C4×C47—22no—
95C2×C4⋊C4×C47—24no—
96C2×C4⋊C4×C47—22no—
97C2×C4⋊C4×C47D414yescomplemented
98C2×C22⋊C4×C47—22no—
99C2×C22⋊C4×C47—22no—
100C2×C22⋊C4×C47—22no—
101C2×C22⋊C4×C47—22no—
102C2×C22⋊C4×C47—22no—
103C2×C22⋊C4×C47—24no—
104C2×C22⋊C4×C47—24no—
105C2×C22⋊C4×C47—24no—
106C2×C22⋊C4×C47—24no—
107C2×C22⋊C4×C47—24no—
108C2×C22⋊C4×C47—24no—
109C2×C22⋊C4×C47—24no—
110C2×C22⋊C4×C47—24no—
111C2×C22⋊C4×C47—24no—
112C2×C22⋊C4×C47—24no—
113C2×C22⋊C4×C47—24no—
114C2×C22⋊C4×C47—24no—
115C2×C22⋊C4×C47—24no—
116C2×C22⋊C4×C47—42no—
117C2×C22⋊C4×C47—42no—
118C2×C22⋊C4×C47—42no—
119C2×C22⋊C4×C47—42no—
120C2×C22⋊C4×C47D414yescomplemented
121C2×C22⋊C4×C47D418yescomplemented
122C2×C42×C47—22no—
123C2×C42×C47—22no—
124C2×C42×C47—22no—
125#95×C47—24no—
126#95×C47—24no—
127#95×C47—22no—
128#95×C47—24no—
129#95×C47—22no—
130#95×C47—42no—
131C24×C47—21no—
132C24×C47—21no—
133C24×C47—21no—
134C24×C47—21no—
135C24×C47—22no—
136C24×C47—22no—
137C24×C47—22no—
138C24×C47—21no—
139C24×C47—21no—
140C24×C47—21no—
141C24×C47—21no—
142C24×C47—22no—
143C24×C47—22no—
144C24×C47—22no—
145C24×C47—22no—
146C24×C47—22no—
147C24×C47—22no—
148C24×C47—22no—
149C24×C47—22no—
150C24×C47—22no—
151C24×C47—22no—
152C24×C47—22no—
153C24×C47—22no—
154C24×C47—22no—
155C24×C47—22no—
156C24×C47—22no—
157C24×C47—22no—
158C24×C47—22no—
159C24×C47—22no—
160C24×C47—22no—
161C24×C47C2×D414yes—
162C24×C47C2×D412yes—
163C24×C47C2×D412yes—
164C24×C47C2×D412yes—
165C24×C47C2×D412yes—
166C24×C47#4112yes—
167C24×C47#4112yes—
168C24×C47C2411yescharacteristic
169C2×D4×C47—28no—
170C2×D4×C47—28no—
171C2×D4×C47—28no—
172C2×D4×C47—28no—
173C2×D4×C47—28no—
174C2×D4×C47—28no—
175C2×D4×C47—28no—
176C2×D4×C47—216no—
177C2×D4×C47—216no—
178C2×D4×C47—28no—
179C2×D4×C47—48no—
180C2×D4×C47—48no—
181C2×D4×C47—48no—
182C2×D4×C47—48no—
183C2×D4×C47—48no—
184C2×D4×C47—48no—
185C2×D4×C47—44no—
186C2×D4×C47—48no—
187C2×D4×C47—48no—
188C2×D4×C47—48no—
189C2×D4×C47—48no—
190C2×D4×C47—48no—
191C2×D4×C47—48no—
192C2×D4×C47—48no—
193C2×D4×C47—48no—
194C2×D4×C47—44no—
195C22×C4×C47—21no—
196C22×C4×C47—21no—
197C22×C4×C47—21no—
198C22×C4×C47—21no—
199C22×C4×C47—22no—
200C22×C4×C47—21no—
201C22×C4×C47—21no—
202C22×C4×C47—22no—
203C22×C4×C47—22no—
204C22×C4×C47—28no—
205C22×C4×C47—21no—
206C22×C4×C47—21no—
207C22×C4×C47—21no—
208C22×C4×C47—21no—
209C22×C4×C47—22no—
210C22×C4×C47—22no—
211C22×C4×C47—22no—
212C22×C4×C47—22no—
213C22×C4×C47—22no—
214C22×C4×C47—22no—
215C22×C4×C47—22no—
216C22×C4×C47—22no—
217C22×C4×C47—22no—
218C22×C4×C47—22no—
219C22×C4×C47—22no—
220C22×C4×C47—22no—
221C22×C4×C47—22no—
222C22×C4×C47—22no—
223C22×C4×C47—22no—
224C22×C4×C47—22no—
225C22×C4×C47—28no—
226C22×C4×C47—28no—
227C22×C4×C47—22no—
228C22×C4×C47—22no—
229C22×C4×C47—22no—
230C22×C4×C47—22no—
231C22×C4×C47—22no—
232C22×C4×C47—22no—
233C22×C4×C47—22no—
234C22×C4×C47—44no—
235C22×C4×C47—48no—
236C22×C4×C47—48no—
237C22×C4×C47—48no—
238C22×C4×C47—48no—
239C22×C4×C47—44no—
240C22×C4×C47—44no—
241C22×C4×C47C2×D412yes—
242C22×C4×C47C2×D412yes—
243C22×C4×C47C2×D414yes—
244C22×C4×C47C2×D412yes—
245C22×C4×C47C2×D414yes—
246C22×C4×C47C2×D412yes—
247C22×C4×C47C2×D412yes—
248C22×C4×C47C2×D412yes—
249C22×C4×C47C2×D412yes—
250C22×C4×C47C2×D412yes—
251C22×C4×C47#4114yes—
252C22×C4×C47#4112yes—
253C4⋊C4×C47—28no—
254C4⋊C4×C47—28no—
255C22⋊C4×C47—28no—
256C22⋊C4×C47—28no—
257C22⋊C4×C47—216no—
258C22⋊C4×C47—48no—
259C22⋊C4×C47—48no—
260C22⋊C4×C47—48no—
261C22⋊C4×C47—48no—
262C22⋊C4×C47—48no—
263C42×C47—28no—
264C23×C47—22no—
265C23×C47—22no—
266C23×C47—22no—
267C23×C47—22no—
268C23×C47—22no—
269C23×C47—22no—
270C23×C47—22no—
271C23×C47—22no—
272C23×C47—22no—
273C23×C47—22no—
274C23×C47—22no—
275C23×C47—22no—
276C23×C47—22no—
277C23×C47—24no—
278C23×C47—22no—
279C23×C47—22no—
280C23×C47—22no—
281C23×C47—24no—
282C23×C47—24no—
283C23×C47—24no—
284C23×C47—24no—
285C23×C47—24no—
286C23×C47—24no—
287C23×C47—24no—
288C23×C47—24no—
289C23×C47—24no—
290C23×C47—24no—
291C23×C47—24no—
292C23×C47—24no—
293C23×C47—24no—
294C23×C47—24no—
295C23×C47—24no—
296C23×C47—24no—
297C23×C47—41no—
298C23×C47—42no—
299C23×C47—42no—
300C23×C47—42no—
301C23×C47—41no—
302C23×C47—41no—
303C23×C47—41no—
304C23×C47—42no—
305C23×C47—42no—
306C23×C47—42no—
307C23×C47—42no—
308C23×C47—42no—
309C23×C47—42no—
310C23×C47—42no—
311C23×C47—42no—
312C23×C47—42no—
313C23×C47—42no—
314C23×C47—42no—
315C23×C47—42no—
316C23×C47—42no—
317C23×C47—42no—
318C23×C47—42no—
319C23×C47—42no—
320C23×C47—42no—
321C23×C47—42no—
322C23×C47—42no—
323C23×C47—42no—
324C23×C47—42no—
325C23×C47—42no—
326C23×C47—42no—
327C23×C47—42no—
328C23×C47—42no—
329C23×C47—42no—
330C23×C47—42no—
331C23×C47—42no—
332C23×C47—42no—
333C23×C47—42no—
334C23×C47—42no—
335C23×C47—42no—
336C23×C47—42no—
337C23×C47—42no—
338C23×C47—42no—
339C23×C47—42no—
340C23×C47—42no—
341C23×C47—42no—
342C23×C47—42no—
343C23×C47#12114yes—
344C23×C47#12114yescomplemented
345C23×C47C22×D411yescharacteristic
346C23×C47C22×D411yescharacteristic
347C23×C47C22×D411yescharacteristic
348C23×C47C22×D412yes—
349C23×C47C22×D411yescharacteristic
350C23×C47C2×#4111yescharacteristic
351C23×C47C2×#4111yescharacteristic
352C23×C47C2×#4111yescharacteristic
353C23×C47C2×#4112yes—
354C23×C47H(5,𝔽2)12yes—
355C23×C47H(5,𝔽2)12yes—
356D4×C47—232no—
357D4×C47—416no—
358D4×C47—432no—
359D4×C47—432no—
360C2×C4×C47—22no—
361C2×C4×C47—22no—
362C2×C4×C47—22no—
363C2×C4×C47—22no—
364C2×C4×C47—22no—
365C2×C4×C47—22no—
366C2×C4×C47—22no—
367C2×C4×C47—22no—
368C2×C4×C47—22no—
369C2×C4×C47—22no—
370C2×C4×C47—24no—
371C2×C4×C47—24no—
372C2×C4×C47—24no—
373C2×C4×C47—24no—
374C2×C4×C47—22no—
375C2×C4×C47—22no—
376C2×C4×C47—24no—
377C2×C4×C47—24no—
378C2×C4×C47—24no—
379C2×C4×C47—24no—
380C2×C4×C47—24no—
381C2×C4×C47—24no—
382C2×C4×C47—24no—
383C2×C4×C47—24no—
384C2×C4×C47—416no—
385C2×C4×C47—416no—
386C2×C4×C47—41no—
387C2×C4×C47—42no—
388C2×C4×C47—42no—
389C2×C4×C47—41no—
390C2×C4×C47—41no—
391C2×C4×C47—41no—
392C2×C4×C47—42no—
393C2×C4×C47—42no—
394C2×C4×C47—42no—
395C2×C4×C47—42no—
396C2×C4×C47—42no—
397C2×C4×C47—42no—
398C2×C4×C47—42no—
399C2×C4×C47—42no—
400C2×C4×C47—42no—
401C2×C4×C47—42no—
402C2×C4×C47—42no—
403C2×C4×C47—42no—
404C2×C4×C47—42no—
405C2×C4×C47—42no—
406C2×C4×C47—42no—
407C2×C4×C47#12014yes—
408C2×C4×C47#12014yes—
409C2×C4×C47#12114yescomplemented
410#14722C4711yesmaximal, characteristic, direct product factor, Sylow
411C22×C47—24no—
412C22×C47—24no—
413C22×C47—24no—
414C22×C47—28no—
415C22×C47—24no—
416C22×C47—42no—
417C22×C47—42no—
418C22×C47—42no—
419C22×C47—42no—
420C22×C47—42no—
421C22×C47—42no—
422C22×C47—42no—
423C22×C47—44no—
424C22×C47—44no—
425C22×C47—44no—
426C22×C47—42no—
427C22×C47—42no—
428C22×C47—44no—
429C22×C47—44no—
430C22×C47—44no—
431C22×C47—44no—
432C22×C47—42no—
433C22×C47—44no—
434C22×C47—44no—
435C22×C47—44no—
436C22×C47—44no—
437C22×C47—44no—
438C22×C47—44no—
439C22×C47—44no—
440C22×C47—82no—
441C22×C47—82no—
442C22×C47—82no—
443C22×C47—82no—
444C22×C47—82no—
445C22×C47—82no—
446C22×C47—82no—
447C22×C47—82no—
448C22×C47C2×#12011yescharacteristic
449C22×C47C2×#12011yescharacteristic
450C22×C47C2×#12111yescharacteristic
451C22×C47C2×#12111yescharacteristic
452C22×C47C2×#12111yescharacteristic
453C22×C47#52511yescharacteristic
454C22×C47#52511yescharacteristic
455C22×C47#52511yescharacteristic
456C22×C47#52512yes—
457C22×C47#53212yes—
458C22×C47#53211yescharacteristic
459C22×C47#53411yescharacteristic
460C22×C47#53511yescharacteristic
461C22×C47#53812yes—
462C22×C47#54012yes—
463C22×C47D4212yes—
464C22×C47D4212yes—
465C22×C47D4212yes—
466C22×C47#54612yes—
467C22×C47#54612yes—
468C22×C47#54612yes—
469C22×C47#55012yes—
470C22×C47#55312yes—
471C4×C47—24no—
472C4×C47—24no—
473C4×C47—24no—
474C4×C47—42no—
475C4×C47—44no—
476C4×C47—44no—
477C4×C47—42no—
478C4×C47—82no—
479C22×#121C2×C4711yescharacteristic, complemented
480C22×C4×D4C2×C4711yescharacteristic, complemented
481C2×#394C2×C4711yescharacteristic, complemented
482C2×#392C2×C4712yescomplemented
483C2×#392C2×C4711yescharacteristic, complemented
484C2×#386C2×C4712yescomplemented
485#1441C2×C4711yescharacteristic, complemented
486#1439C2×C4711yescharacteristic, complemented
487#1438C2×C4712yescomplemented
488#1437C2×C4712yescomplemented
489C22⋊#95C2×C4711yescharacteristic, complemented
490C2×C47—44no—
491C2×C47—44no—
492C2×C47—84no—
493C2×C47#238811yescharacteristic
494C2×C47#240311yescharacteristic
495C2×C47#240811yescharacteristic
496C2×C47#242412yes—
497C2×C47#242812yes—
498C2×C47#243111yescharacteristic
499C2×C47#245612yes—
500C2×C47#246412yes—
501C2×C47#254311yescharacteristic
502C2×C47#263511yescharacteristic
503C2×C47#284711yescharacteristic
504C23×D4C22×C4711yescharacteristic
505C23×D4C22×C4712yes—
506C23×D4C22×C4711yescharacteristic
507C23×D4C22×C4712yes—
508C24×C4C22×C4711yescharacteristic
509C24×C4C22×C4711yescharacteristic
510C2×#121—24no—
511C2×#121—28no—
512C2×C4×D4—24no—
513C2×C4×D4—24no—
514C2×C4×D4—24no—
515C22×C4⋊C4C22×C4711yescharacteristic
516C22×C4⋊C4C22×C4711yescharacteristic
517C22×C22⋊C4C22×C4712yes—
518C22×C22⋊C4C22×C4711yescharacteristic
519C22×C22⋊C4C22×C4712yes—
520C22×C22⋊C4C22×C4712yes—
521C22×C22⋊C4C22×C4712yes—
522C22×C22⋊C4C22×C4712yes—
523C22×C22⋊C4C22×C4711yescharacteristic
524C22×C22⋊C4C22×C4712yes—
525C22×C42C22×C4711yescharacteristic
526#394—24no—
527#392—28no—
528#392—24no—
529#386—28no—
530C2×#95C22×C4711yescharacteristic
531C2×#95C22×C4712yes—
532C2×#95C22×C4711yescharacteristic
533C2×#95C22×C4712yes—
534C2×#95C22×C4712yes—
535C2×#95C22×C4712yes—
536C47#1472211yescharacteristic, direct product factor, Sylow
537C25C23×C4712yes—
538C25C23×C4711yescharacteristic
539C25C23×C4711yescharacteristic
540C22×D4—22no—
541C22×D4—22no—
542C22×D4—22no—
543C22×D4—22no—
544C22×D4—24no—
545C22×D4—24no—
546C22×D4—24no—
547C22×D4—24no—
548C22×D4—24no—
549C22×D4—24no—
550C22×D4—24no—
551C22×D4—24no—
552C22×D4—24no—
553C22×D4—22no—
554C22×D4—24no—
555C22×D4—22no—
556C22×D4—22no—
557C22×D4—22no—
558C22×D4—22no—
559C22×D4—24no—
560C22×D4—42no—
561C22×D4—42no—
562C22×D4—42no—
563C22×D4—42no—
564C22×D4—42no—
565C22×D4D4×C4714yescomplemented
566C23×C4—22no—
567C23×C4—22no—
568C23×C4—22no—
569C23×C4—22no—
570C23×C4—22no—
571C23×C4—24no—
572C23×C4—24no—
573C23×C4—42no—
574C23×C4—42no—
575C23×C4D4×C4714yescomplemented
576C23×C4C23×C4712yes—
577C23×C4C23×C4711yescharacteristic
578C23×C4C23×C4711yescharacteristic
579C23×C4C23×C4712yes—
580C23×C4C23×C4712yes—
581C23×C4C23×C4711yescharacteristic
582C23×C4C23×C4711yescharacteristic
583C23×C4C23×C4711yescharacteristic
584#121—232no—
585C4×D4—232no—
586C2×C4⋊C4—22no—
587C2×C4⋊C4—22no—
588C2×C4⋊C4—24no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4D4×C4714yescomplemented
591C2×C22⋊C4—22no—
592C2×C22⋊C4—22no—
593C2×C22⋊C4—22no—
594C2×C22⋊C4—22no—
595C2×C22⋊C4—22no—
596C2×C22⋊C4—24no—
597C2×C22⋊C4—24no—
598C2×C22⋊C4—24no—
599C2×C22⋊C4—24no—
600C2×C22⋊C4—24no—
601C2×C22⋊C4—24no—
602C2×C22⋊C4—24no—
603C2×C22⋊C4—24no—
604C2×C22⋊C4—24no—
605C2×C22⋊C4—24no—
606C2×C22⋊C4—24no—
607C2×C22⋊C4—24no—
608C2×C22⋊C4—24no—
609C2×C22⋊C4—42no—
610C2×C22⋊C4—42no—
611C2×C22⋊C4—42no—
612C2×C22⋊C4—42no—
613C2×C22⋊C4D4×C4714yescomplemented
614C2×C22⋊C4D4×C4718yescomplemented
615C2×C42—22no—
616C2×C42—22no—
617C2×C42—22no—
618#95—24no—
619#95—24no—
620#95—22no—
621#95—24no—
622#95—22no—
623#95—42no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—22no—
629C24—22no—
630C24—22no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—22no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24C2×D4×C4714yes—
655C24C2×D4×C4712yes—
656C24C2×D4×C4712yes—
657C24C2×D4×C4712yes—
658C24C2×D4×C4712yes—
659C24#41×C4712yes—
660C24#41×C4712yes—
661C24C24×C4711yescharacteristic
662C2×D4—28no—
663C2×D4—28no—
664C2×D4—28no—
665C2×D4—28no—
666C2×D4—28no—
667C2×D4—28no—
668C2×D4—28no—
669C2×D4—216no—
670C2×D4—216no—
671C2×D4—28no—
672C2×D4—48no—
673C2×D4—48no—
674C2×D4—48no—
675C2×D4—48no—
676C2×D4—48no—
677C2×D4—48no—
678C2×D4—44no—
679C2×D4—48no—
680C2×D4—48no—
681C2×D4—48no—
682C2×D4—48no—
683C2×D4—48no—
684C2×D4—48no—
685C2×D4—48no—
686C2×D4—48no—
687C2×D4—44no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—22no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—28no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—22no—
708C22×C4—22no—
709C22×C4—22no—
710C22×C4—22no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—22no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—28no—
719C22×C4—28no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—44no—
728C22×C4—48no—
729C22×C4—48no—
730C22×C4—48no—
731C22×C4—48no—
732C22×C4—44no—
733C22×C4—44no—
734C22×C4C2×D4×C4714yes—
735C22×C4C2×D4×C4712yes—
736C22×C4C2×D4×C4712yes—
737C22×C4C2×D4×C4714yes—
738C22×C4C2×D4×C4712yes—
739C22×C4C2×D4×C4712yes—
740C22×C4C2×D4×C4712yes—
741C22×C4C2×D4×C4712yes—
742C22×C4C2×D4×C4712yes—
743C22×C4C2×D4×C4712yes—
744C22×C4#41×C4714yes—
745C22×C4#41×C4712yes—
746C4⋊C4—28no—
747C4⋊C4—28no—
748C22⋊C4—28no—
749C22⋊C4—28no—
750C22⋊C4—216no—
751C22⋊C4—48no—
752C22⋊C4—48no—
753C22⋊C4—48no—
754C22⋊C4—48no—
755C22⋊C4—48no—
756C42—28no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—24no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—24no—
775C23—24no—
776C23—24no—
777C23—24no—
778C23—24no—
779C23—24no—
780C23—24no—
781C23—24no—
782C23—24no—
783C23—24no—
784C23—24no—
785C23—24no—
786C23—24no—
787C23—24no—
788C23—24no—
789C23—24no—
790C23—41no—
791C23—42no—
792C23—41no—
793C23—42no—
794C23—42no—
795C23—41no—
796C23—41no—
797C23—42no—
798C23—42no—
799C23—42no—
800C23—42no—
801C23—42no—
802C23—42no—
803C23—42no—
804C23—42no—
805C23—42no—
806C23—42no—
807C23—42no—
808C23—42no—
809C23—42no—
810C23—42no—
811C23—42no—
812C23—42no—
813C23—42no—
814C23—42no—
815C23—42no—
816C23—42no—
817C23—42no—
818C23—42no—
819C23—42no—
820C23—42no—
821C23—42no—
822C23—42no—
823C23—42no—
824C23—42no—
825C23—42no—
826C23—42no—
827C23—42no—
828C23—42no—
829C23—42no—
830C23—42no—
831C23—42no—
832C23—42no—
833C23—42no—
834C23—42no—
835C23—42no—
836C23#121×C4714yes—
837C23#121×C4714yescomplemented
838C23C22×D4×C4711yescharacteristic
839C23C22×D4×C4711yescharacteristic
840C23C22×D4×C4711yescharacteristic
841C23C22×D4×C4712yes—
842C23C22×D4×C4711yescharacteristic
843C23C2×#41×C4711yescharacteristic
844C23C2×#41×C4711yescharacteristic
845C23C2×#41×C4711yescharacteristic
846C23C2×#41×C4712yes—
847C23H(5,𝔽2)×C4712yes—
848C23H(5,𝔽2)×C4712yes—
849D4—232no—
850D4—416no—
851D4—432no—
852D4—432no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—24no—
864C2×C4—24no—
865C2×C4—24no—
866C2×C4—24no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—24no—
870C2×C4—24no—
871C2×C4—24no—
872C2×C4—24no—
873C2×C4—24no—
874C2×C4—24no—
875C2×C4—24no—
876C2×C4—24no—
877C2×C4—416no—
878C2×C4—416no—
879C2×C4—41no—
880C2×C4—42no—
881C2×C4—42no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—42no—
890C2×C4—42no—
891C2×C4—42no—
892C2×C4—42no—
893C2×C4—42no—
894C2×C4—42no—
895C2×C4—42no—
896C2×C4—42no—
897C2×C4—42no—
898C2×C4—42no—
899C2×C4—42no—
900C2×C4#120×C4714yes—
901C2×C4#120×C4714yes—
902C2×C4#121×C4714yescomplemented
903C22—24no—
904C22—24no—
905C22—24no—
906C22—24no—
907C22—28no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—44no—
917C22—44no—
918C22—44no—
919C22—42no—
920C22—42no—
921C22—44no—
922C22—44no—
923C22—44no—
924C22—44no—
925C22—44no—
926C22—44no—
927C22—44no—
928C22—44no—
929C22—44no—
930C22—44no—
931C22—44no—
932C22—82no—
933C22—82no—
934C22—82no—
935C22—82no—
936C22—82no—
937C22—82no—
938C22—82no—
939C22—82no—
940C22C2×#120×C4711yescharacteristic
941C22C2×#120×C4711yescharacteristic
942C22C2×#121×C4711yescharacteristic
943C22C2×#121×C4711yescharacteristic
944C22C2×#121×C4711yescharacteristic
945C22C47×#52511yescharacteristic
946C22C47×#52511yescharacteristic
947C22C47×#52511yescharacteristic
948C22C47×#52512yes—
949C22C47×#53211yescharacteristic
950C22C47×#53212yes—
951C22C47×#53411yescharacteristic
952C22C47×#53511yescharacteristic
953C22C47×#53812yes—
954C22C47×#54012yes—
955C22D42×C4712yes—
956C22D42×C4712yes—
957C22D42×C4712yes—
958C22C47×#54612yes—
959C22C47×#54612yes—
960C22C47×#54612yes—
961C22C47×#55012yes—
962C22C47×#55312yes—
963C4—24no—
964C4—24no—
965C4—24no—
966C4—42no—
967C4—44no—
968C4—44no—
969C4—42no—
970C4—82no—
971C2—44no—
972C2—44no—
973C2—84no—
974C2C47×#238811yescharacteristic
975C2C47×#240311yescharacteristic
976C2C47×#240811yescharacteristic
977C2C47×#242412yes—
978C2C47×#242812yes—
979C2C47×#243111yescharacteristic
980C2C47×#245612yes—
981C2C47×#246412yes—
982C2C47×#254311yescharacteristic
983C2C47×#263511yescharacteristic
984C2C47×#284711yescharacteristic
subgroupG/H
center, socleC24×C47C24
commutator, Frattini, cosocleC24C24×C47
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#121×C47C2semidirect
2. C22×C4×D4×C47C2semidirect
3. C2×C47×#394C2semidirect
4. C2×C47×#392C2semidirect
5. C2×C47×#392C2semidirect
6. C2×C47×#386C2semidirect
7. C47×#1441C2semidirect
8. C47×#1439C2semidirect
9. C47×#1438C2semidirect
10. C47×#1437C2semidirect
11. C47×C22⋊#95C2semidirect
72. C22×D4×C47D4semidirect
82. C23×C4×C47D4semidirect
97. C2×C4⋊C4×C47D4semidirect
120. C2×C22⋊C4×C47D4semidirect
121. C2×C22⋊C4×C47D4semidirect
344. C23×C47#121semidirect
409. C2×C4×C47#121semidirect
410. #14722C47direct (N × H)
479. C22×#121C2×C47semidirect
480. C22×C4×D4C2×C47semidirect
481. C2×#394C2×C47semidirect
482. C2×#392C2×C47semidirect
483. C2×#392C2×C47semidirect
484. C2×#386C2×C47semidirect
485. #1441C2×C47semidirect
486. #1439C2×C47semidirect
487. #1438C2×C47semidirect
488. #1437C2×C47semidirect
489. C22⋊#95C2×C47semidirect
536. C47#14722direct (N × H)
565. C22×D4D4×C47semidirect
575. C23×C4D4×C47semidirect
590. C2×C4⋊C4D4×C47semidirect
613. C2×C22⋊C4D4×C47semidirect
614. C2×C22⋊C4D4×C47semidirect
837. C23#121×C47semidirect
902. C2×C4#121×C47semidirect

Maximal subgroups

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

subgroupindex
C22×#121×C472
C22×C4×D4×C472
C2×C47×#3942
C2×C47×#3922
C2×C47×#3862
C47×#14412
C47×#14392
C47×#14382
C47×#14372
C47×C22⋊#952
#1472247